Update some of the docs.
This commit is contained in:
Simon Forman
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@ -13133,17 +13133,84 @@ joy? </code></pre>
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<div class="prompt input_prompt">In [1]:</div>
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<div class="inner_cell">
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<div class="input_area">
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<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">import</span> <span class="nn">inspect</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">inspect</span>
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<span class="kn">import</span> <span class="nn">joy.utils.stack</span>
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<span class="nb">print</span> <span class="n">inspect</span><span class="o">.</span><span class="n">getdoc</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">utils</span><span class="o">.</span><span class="n">stack</span><span class="p">)</span>
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<span class="nb">print</span><span class="p">(</span><span class="n">inspect</span><span class="o">.</span><span class="n">getdoc</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">utils</span><span class="o">.</span><span class="n">stack</span><span class="p">))</span>
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</pre></div>
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</div>
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</div>
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</div>
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<div class="output_wrapper">
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<div class="output">
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<div class="output_area">
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<div class="prompt"></div>
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<div class="output_subarea output_stream output_stdout output_text">
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<pre>When talking about Joy we use the terms "stack", "quote", "sequence",
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"list", and others to mean the same thing: a simple linear datatype that
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permits certain operations such as iterating and pushing and popping
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values from (at least) one end.
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There is no "Stack" Python class, instead we use the `cons list`_, a
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venerable two-tuple recursive sequence datastructure, where the
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empty tuple ``()`` is the empty stack and ``(head, rest)`` gives the
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recursive form of a stack with one or more items on it::
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stack := () | (item, stack)
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Putting some numbers onto a stack::
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()
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(1, ())
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(2, (1, ()))
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(3, (2, (1, ())))
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...
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Python has very nice "tuple packing and unpacking" in its syntax which
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means we can directly "unpack" the expected arguments to a Joy function.
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For example::
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def dup((head, tail)):
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return head, (head, tail)
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We replace the argument "stack" by the expected structure of the stack,
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in this case "(head, tail)", and Python takes care of unpacking the
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incoming tuple and assigning values to the names. (Note that Python
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syntax doesn't require parentheses around tuples used in expressions
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where they would be redundant.)
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Unfortunately, the Sphinx documentation generator, which is used to generate this
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web page, doesn't handle tuples in the function parameters. And in Python 3, this
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syntax was removed entirely. Instead you would have to write::
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def dup(stack):
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head, tail = stack
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return head, (head, tail)
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We have two very simple functions, one to build up a stack from a Python
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iterable and another to iterate through a stack and yield its items
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one-by-one in order. There are also two functions to generate string representations
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of stacks. They only differ in that one prints the terms in stack from left-to-right while the other prints from right-to-left. In both functions *internal stacks* are
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printed left-to-right. These functions are written to support :doc:`../pretty`.
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.. _cons list: https://en.wikipedia.org/wiki/Cons#Lists
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</pre>
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</div>
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</div>
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</div>
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</div>
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</div>
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<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
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</div><div class="inner_cell">
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@ -13158,26 +13225,66 @@ joy? </code></pre>
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<div class="prompt input_prompt">In [2]:</div>
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<div class="inner_cell">
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<div class="input_area">
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">utils</span><span class="o">.</span><span class="n">stack</span><span class="o">.</span><span class="n">list_to_stack</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">utils</span><span class="o">.</span><span class="n">stack</span><span class="o">.</span><span class="n">list_to_stack</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
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</pre></div>
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</div>
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</div>
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</div>
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<div class="output_wrapper">
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<div class="output">
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<div class="output_area">
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<div class="prompt output_prompt">Out[2]:</div>
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<div class="output_text output_subarea output_execute_result">
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<pre>(1, (2, (3, ())))</pre>
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</div>
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</div>
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</div>
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</div>
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</div>
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<div class="cell border-box-sizing code_cell rendered">
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<div class="input">
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<div class="prompt input_prompt">In [3]:</div>
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<div class="inner_cell">
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<div class="input_area">
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<div class=" highlight hl-ipython2"><pre><span></span><span class="nb">list</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">utils</span><span class="o">.</span><span class="n">stack</span><span class="o">.</span><span class="n">iter_stack</span><span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="p">())))))</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="nb">list</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">utils</span><span class="o">.</span><span class="n">stack</span><span class="o">.</span><span class="n">iter_stack</span><span class="p">((</span><span class="mi">1</span><span class="p">,</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="p">())))))</span>
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</pre></div>
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</div>
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</div>
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</div>
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<div class="output_wrapper">
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<div class="output">
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<div class="output_area">
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<div class="prompt output_prompt">Out[3]:</div>
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<div class="output_text output_subarea output_execute_result">
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<pre>[1, 2, 3]</pre>
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</div>
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</div>
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</div>
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</div>
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</div>
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<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
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</div><div class="inner_cell">
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@ -13192,19 +13299,38 @@ joy? </code></pre>
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<div class="prompt input_prompt">In [4]:</div>
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<div class="inner_cell">
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<div class="input_area">
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">stack</span> <span class="o">=</span> <span class="p">()</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">stack</span> <span class="o">=</span> <span class="p">()</span>
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<span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">]:</span>
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<span class="n">stack</span> <span class="o">=</span> <span class="n">n</span><span class="p">,</span> <span class="n">stack</span>
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<span class="nb">print</span> <span class="n">stack</span>
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<span class="nb">print</span> <span class="nb">list</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">utils</span><span class="o">.</span><span class="n">stack</span><span class="o">.</span><span class="n">iter_stack</span><span class="p">(</span><span class="n">stack</span><span class="p">))</span>
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<span class="nb">print</span><span class="p">(</span><span class="n">stack</span><span class="p">)</span>
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<span class="nb">print</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">utils</span><span class="o">.</span><span class="n">stack</span><span class="o">.</span><span class="n">iter_stack</span><span class="p">(</span><span class="n">stack</span><span class="p">)))</span>
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</pre></div>
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</div>
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</div>
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</div>
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<div class="output_wrapper">
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<div class="output">
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<div class="output_area">
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<div class="prompt"></div>
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<div class="output_subarea output_stream output_stdout output_text">
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<pre>(3, (2, (1, ())))
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[3, 2, 1]
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</pre>
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</div>
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</div>
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</div>
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</div>
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</div>
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<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
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</div><div class="inner_cell">
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@ -13228,15 +13354,64 @@ joy? </code></pre>
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<div class="prompt input_prompt">In [5]:</div>
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<div class="inner_cell">
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<div class="input_area">
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<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">import</span> <span class="nn">joy.joy</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">joy.joy</span>
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<span class="nb">print</span> <span class="n">inspect</span><span class="o">.</span><span class="n">getsource</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">joy</span><span class="o">.</span><span class="n">joy</span><span class="p">)</span>
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<span class="nb">print</span><span class="p">(</span><span class="n">inspect</span><span class="o">.</span><span class="n">getsource</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">joy</span><span class="o">.</span><span class="n">joy</span><span class="p">))</span>
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</pre></div>
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</div>
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</div>
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</div>
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<div class="output_wrapper">
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<div class="output">
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<div class="output_area">
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<div class="prompt"></div>
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<div class="output_subarea output_stream output_stdout output_text">
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<pre>def joy(stack, expression, dictionary, viewer=None):
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'''Evaluate a Joy expression on a stack.
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This function iterates through a sequence of terms which are either
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literals (strings, numbers, sequences of terms) or function symbols.
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Literals are put onto the stack and functions are looked up in the
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disctionary and executed.
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The viewer is a function that is called with the stack and expression
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on every iteration, its return value is ignored.
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:param stack stack: The stack.
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:param stack expression: The expression to evaluate.
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:param dict dictionary: A ``dict`` mapping names to Joy functions.
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:param function viewer: Optional viewer function.
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:rtype: (stack, (), dictionary)
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'''
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while expression:
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if viewer: viewer(stack, expression)
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term, expression = expression
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if isinstance(term, Symbol):
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term = dictionary[term]
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stack, expression, dictionary = term(stack, expression, dictionary)
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else:
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stack = term, stack
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if viewer: viewer(stack, expression)
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return stack, expression, dictionary
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</pre>
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</div>
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</div>
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</div>
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</div>
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</div>
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<div class="cell border-box-sizing text_cell rendered"><div class="prompt input_prompt">
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</div><div class="inner_cell">
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@ -13274,9 +13449,9 @@ joy? </code></pre>
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<div class="prompt input_prompt">In [6]:</div>
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<div class="inner_cell">
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<div class="input_area">
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<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">import</span> <span class="nn">joy.parser</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">joy.parser</span>
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<span class="nb">print</span> <span class="n">inspect</span><span class="o">.</span><span class="n">getdoc</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="p">)</span>
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<span class="nb">print</span><span class="p">(</span><span class="n">inspect</span><span class="o">.</span><span class="n">getdoc</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="p">))</span>
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</pre></div>
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</div>
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@ -13330,7 +13505,7 @@ around square brackets.
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<div class="prompt input_prompt">In [7]:</div>
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<div class="inner_cell">
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<div class="input_area">
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<div class=" highlight hl-ipython2"><pre><span></span><span class="nb">print</span> <span class="n">inspect</span><span class="o">.</span><span class="n">getsource</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">_parse</span><span class="p">)</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="n">inspect</span><span class="o">.</span><span class="n">getsource</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">_parse</span><span class="p">))</span>
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</pre></div>
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</div>
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@ -13391,7 +13566,7 @@ around square brackets.
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<div class="prompt input_prompt">In [8]:</div>
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<div class="inner_cell">
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<div class="input_area">
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">'1 2 3 4 5'</span><span class="p">)</span> <span class="c1"># A simple sequence.</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">'1 2 3 4 5'</span><span class="p">)</span> <span class="c1"># A simple sequence.</span>
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</pre></div>
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</div>
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@ -13424,7 +13599,7 @@ around square brackets.
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<div class="prompt input_prompt">In [9]:</div>
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<div class="inner_cell">
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<div class="input_area">
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">'[1 2 3] 4 5'</span><span class="p">)</span> <span class="c1"># Three items, the first is a list with three items</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">'[1 2 3] 4 5'</span><span class="p">)</span> <span class="c1"># Three items, the first is a list with three items</span>
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</pre></div>
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</div>
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@ -13457,7 +13632,7 @@ around square brackets.
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<div class="prompt input_prompt">In [10]:</div>
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<div class="inner_cell">
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<div class="input_area">
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">'1 23 ["four" [-5.0] cons] 8888'</span><span class="p">)</span> <span class="c1"># A mixed bag. cons is</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">'1 23 ["four" [-5.0] cons] 8888'</span><span class="p">)</span> <span class="c1"># A mixed bag. cons is</span>
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<span class="c1"># a Symbol, no lookup at</span>
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<span class="c1"># parse-time. Haiku docs.</span>
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</pre></div>
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@ -13492,7 +13667,7 @@ around square brackets.
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<div class="prompt input_prompt">In [11]:</div>
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<div class="inner_cell">
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<div class="input_area">
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<div class=" highlight hl-ipython2"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">'[][][][][]'</span><span class="p">)</span> <span class="c1"># Five empty lists.</span>
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<div class=" highlight hl-ipython3"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">'[][][][][]'</span><span class="p">)</span> <span class="c1"># Five empty lists.</span>
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</pre></div>
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</div>
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@ -13525,7 +13700,7 @@ around square brackets.
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<div class="prompt input_prompt">In [12]:</div>
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<div class="inner_cell">
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<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">'[[[[[]]]]]'</span><span class="p">)</span> <span class="c1"># Five nested lists.</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">joy</span><span class="o">.</span><span class="n">parser</span><span class="o">.</span><span class="n">text_to_expression</span><span class="p">(</span><span class="s1">'[[[[[]]]]]'</span><span class="p">)</span> <span class="c1"># Five nested lists.</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13566,9 +13741,9 @@ around square brackets.
|
|||
<div class="prompt input_prompt">In [13]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">import</span> <span class="nn">joy.library</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">import</span> <span class="nn">joy.library</span>
|
||||
|
||||
<span class="nb">print</span> <span class="s1">' '</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">sorted</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">library</span><span class="o">.</span><span class="n">initialize</span><span class="p">()))</span>
|
||||
<span class="nb">print</span><span class="p">(</span><span class="s1">' '</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="nb">sorted</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">library</span><span class="o">.</span><span class="n">initialize</span><span class="p">())))</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13585,7 +13760,7 @@ around square brackets.
|
|||
|
||||
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre>!= % & * *fraction *fraction0 + ++ - -- / // /floor < << <= <> = > >= >> ? ^ _Tree_add_Ee _Tree_delete_R0 _Tree_delete_clear_stuff _Tree_get_E abs add anamorphism and app1 app2 app3 at average b binary bool branch ccons choice clear cleave cmp codireco concat cond cons dinfrirst dip dipd dipdd disenstacken divmod down_to_zero drop dup dupd dupdd dupdip dupdipd enstacken eq first first_two flatten floor floordiv fork fourth gcd ge genrec getitem gt help i id ifte ii infer infra inscribe le least_fraction loop lshift lt make_generator map max min mod modulus mul ne neg not nullary of or over pam parse pick pm pop popd popdd popop popopd popopdd pow pred primrec product quoted range range_to_zero rem remainder remove rest reverse roll< roll> rolldown rollup round rrest rshift run second select sharing shunt size sort sqr sqrt stack step step_zero stuncons stununcons sub succ sum swaack swap swoncat swons take ternary third times truediv truthy tuck unary uncons unique unit unquoted unstack unswons void warranty while words x xor zip •
|
||||
<pre>!= % & * *fraction *fraction0 + ++ - -- / // /floor < << <= <> = > >= >> ? ^ _Tree_add_Ee _Tree_delete_R0 _Tree_delete_clear_stuff _Tree_get_E abs add anamorphism and app1 app2 app3 at average b binary bool branch ccons choice clear cleave cmp codireco concat cond cons dinfrirst dip dipd dipdd disenstacken div divmod down_to_zero drop dup dupd dupdd dupdip dupdipd enstacken eq first first_two flatten floor floordiv fork fourth gcd ge genrec getitem gt help i id ifte ii infra inscribe le least_fraction loop lshift lt make_generator map max min mod modulus mul ne neg not nullary of or over pam parse pick pm pop popd popdd popop popopd popopdd pow pred primrec product quoted range range_to_zero rem remainder remove rest reverse roll< roll> rolldown rollup round rrest rshift run second select sharing shunt size sort sqr sqrt stack step step_zero stuncons stununcons sub succ sum swaack swap swoncat swons tailrec take ternary third times truediv truthy tuck unary uncons unique unit unquoted unstack unswons void warranty while words x xor zip •
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
|
|
@ -13607,7 +13782,7 @@ around square brackets.
|
|||
<div class="prompt input_prompt">In [14]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="nb">print</span> <span class="n">inspect</span><span class="o">.</span><span class="n">getsource</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">library</span><span class="o">.</span><span class="n">dip</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="n">inspect</span><span class="o">.</span><span class="n">getsource</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">library</span><span class="o">.</span><span class="n">dip</span><span class="p">))</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13625,7 +13800,6 @@ around square brackets.
|
|||
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre>@inscribe
|
||||
@combinator_effect(_COMB_NUMS(), a1, s1)
|
||||
@FunctionWrapper
|
||||
def dip(stack, expression, dictionary):
|
||||
'''
|
||||
|
|
@ -13634,9 +13808,9 @@ def dip(stack, expression, dictionary):
|
|||
on the rest of the stack.
|
||||
::
|
||||
|
||||
... x [Q] dip
|
||||
... x [Q] dip
|
||||
-------------------
|
||||
... Q x
|
||||
... Q x
|
||||
|
||||
'''
|
||||
(quote, (x, stack)) = stack
|
||||
|
|
@ -13664,7 +13838,7 @@ def dip(stack, expression, dictionary):
|
|||
<div class="prompt input_prompt">In [15]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="nb">print</span> <span class="n">joy</span><span class="o">.</span><span class="n">library</span><span class="o">.</span><span class="n">definitions</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="n">joy</span><span class="o">.</span><span class="n">library</span><span class="o">.</span><span class="n">definitions</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13681,43 +13855,44 @@ def dip(stack, expression, dictionary):
|
|||
|
||||
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre>? == dup truthy
|
||||
*fraction == [uncons] dip uncons [swap] dip concat [*] infra [*] dip cons
|
||||
*fraction0 == concat [[swap] dip * [*] dip] infra
|
||||
anamorphism == [pop []] swap [dip swons] genrec
|
||||
average == [sum 1.0 *] [size] cleave /
|
||||
binary == nullary [popop] dip
|
||||
cleave == fork [popd] dip
|
||||
codireco == cons dip rest cons
|
||||
dinfrirst == dip infra first
|
||||
unstack == ? [uncons ?] loop pop
|
||||
down_to_zero == [0 >] [dup --] while
|
||||
dupdipd == dup dipd
|
||||
enstacken == stack [clear] dip
|
||||
flatten == [] swap [concat] step
|
||||
fork == [i] app2
|
||||
gcd == 1 [tuck modulus dup 0 >] loop pop
|
||||
ifte == [nullary not] dipd branch
|
||||
ii == [dip] dupdip i
|
||||
least_fraction == dup [gcd] infra [div] concat map
|
||||
make_generator == [codireco] ccons
|
||||
nullary == [stack] dinfrirst
|
||||
of == swap at
|
||||
pam == [i] map
|
||||
primrec == [i] genrec
|
||||
product == 1 swap [*] step
|
||||
quoted == [unit] dip
|
||||
range == [0 <=] [1 - dup] anamorphism
|
||||
range_to_zero == unit [down_to_zero] infra
|
||||
run == [] swap infra
|
||||
size == 0 swap [pop ++] step
|
||||
sqr == dup mul
|
||||
step_zero == 0 roll> step
|
||||
swoncat == swap concat
|
||||
ternary == unary [popop] dip
|
||||
unary == nullary popd
|
||||
unquoted == [i] dip
|
||||
while == swap [nullary] cons dup dipd concat loop
|
||||
<pre>? dup truthy
|
||||
*fraction [uncons] dip uncons [swap] dip concat [*] infra [*] dip cons
|
||||
*fraction0 concat [[swap] dip * [*] dip] infra
|
||||
anamorphism [pop []] swap [dip swons] genrec
|
||||
average [sum 1.0 *] [size] cleave /
|
||||
binary nullary [popop] dip
|
||||
cleave fork [popd] dip
|
||||
codireco cons dip rest cons
|
||||
dinfrirst dip infra first
|
||||
unstack ? [uncons ?] loop pop
|
||||
down_to_zero [0 >] [dup --] while
|
||||
dupdipd dup dipd
|
||||
enstacken stack [clear] dip
|
||||
flatten [] swap [concat] step
|
||||
fork [i] app2
|
||||
gcd 1 [tuck modulus dup 0 >] loop pop
|
||||
ifte [nullary not] dipd branch
|
||||
ii [dip] dupdip i
|
||||
least_fraction dup [gcd] infra [div] concat map
|
||||
make_generator [codireco] ccons
|
||||
nullary [stack] dinfrirst
|
||||
of swap at
|
||||
pam [i] map
|
||||
tailrec [i] genrec
|
||||
product 1 swap [*] step
|
||||
quoted [unit] dip
|
||||
range [0 <=] [1 - dup] anamorphism
|
||||
range_to_zero unit [down_to_zero] infra
|
||||
run [] swap infra
|
||||
size 0 swap [pop ++] step
|
||||
sqr dup mul
|
||||
step_zero 0 roll> step
|
||||
swoncat swap concat
|
||||
tailrec [i] genrec
|
||||
ternary unary [popop] dip
|
||||
unary nullary popd
|
||||
unquoted [i] dip
|
||||
while swap [nullary] cons dup dipd concat loop
|
||||
|
||||
</pre>
|
||||
</div>
|
||||
|
|
@ -13746,7 +13921,7 @@ while == swap [nullary] cons dup dipd concat loop
|
|||
<div class="prompt input_prompt">In [ ]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
|
|||
|
|
@ -549,9 +549,9 @@
|
|||
"\ton the rest of the stack.\n",
|
||||
"\t::\n",
|
||||
"\n",
|
||||
"\t\t\t ... x [Q] dip\n",
|
||||
"\t\t ... x [Q] dip\n",
|
||||
"\t\t-------------------\n",
|
||||
"\t\t\t\t ... Q x\n",
|
||||
"\t\t ... Q x\n",
|
||||
"\n",
|
||||
"\t'''\n",
|
||||
"\t(quote, (x, stack)) = stack\n",
|
||||
|
|
|
|||
|
|
@ -48,9 +48,61 @@ import inspect
|
|||
import joy.utils.stack
|
||||
|
||||
|
||||
print inspect.getdoc(joy.utils.stack)
|
||||
print(inspect.getdoc(joy.utils.stack))
|
||||
```
|
||||
|
||||
When talking about Joy we use the terms "stack", "quote", "sequence",
|
||||
"list", and others to mean the same thing: a simple linear datatype that
|
||||
permits certain operations such as iterating and pushing and popping
|
||||
values from (at least) one end.
|
||||
|
||||
There is no "Stack" Python class, instead we use the `cons list`_, a
|
||||
venerable two-tuple recursive sequence datastructure, where the
|
||||
empty tuple ``()`` is the empty stack and ``(head, rest)`` gives the
|
||||
recursive form of a stack with one or more items on it::
|
||||
|
||||
stack := () | (item, stack)
|
||||
|
||||
Putting some numbers onto a stack::
|
||||
|
||||
()
|
||||
(1, ())
|
||||
(2, (1, ()))
|
||||
(3, (2, (1, ())))
|
||||
...
|
||||
|
||||
Python has very nice "tuple packing and unpacking" in its syntax which
|
||||
means we can directly "unpack" the expected arguments to a Joy function.
|
||||
|
||||
For example::
|
||||
|
||||
def dup((head, tail)):
|
||||
return head, (head, tail)
|
||||
|
||||
We replace the argument "stack" by the expected structure of the stack,
|
||||
in this case "(head, tail)", and Python takes care of unpacking the
|
||||
incoming tuple and assigning values to the names. (Note that Python
|
||||
syntax doesn't require parentheses around tuples used in expressions
|
||||
where they would be redundant.)
|
||||
|
||||
Unfortunately, the Sphinx documentation generator, which is used to generate this
|
||||
web page, doesn't handle tuples in the function parameters. And in Python 3, this
|
||||
syntax was removed entirely. Instead you would have to write::
|
||||
|
||||
def dup(stack):
|
||||
head, tail = stack
|
||||
return head, (head, tail)
|
||||
|
||||
|
||||
We have two very simple functions, one to build up a stack from a Python
|
||||
iterable and another to iterate through a stack and yield its items
|
||||
one-by-one in order. There are also two functions to generate string representations
|
||||
of stacks. They only differ in that one prints the terms in stack from left-to-right while the other prints from right-to-left. In both functions *internal stacks* are
|
||||
printed left-to-right. These functions are written to support :doc:`../pretty`.
|
||||
|
||||
.. _cons list: https://en.wikipedia.org/wiki/Cons#Lists
|
||||
|
||||
|
||||
### The utility functions maintain order.
|
||||
The 0th item in the list will be on the top of the stack and *vise versa*.
|
||||
|
||||
|
|
@ -60,10 +112,24 @@ joy.utils.stack.list_to_stack([1, 2, 3])
|
|||
```
|
||||
|
||||
|
||||
|
||||
|
||||
(1, (2, (3, ())))
|
||||
|
||||
|
||||
|
||||
|
||||
```python
|
||||
list(joy.utils.stack.iter_stack((1, (2, (3, ())))))
|
||||
```
|
||||
|
||||
|
||||
|
||||
|
||||
[1, 2, 3]
|
||||
|
||||
|
||||
|
||||
This requires reversing the sequence (or iterating backwards) otherwise:
|
||||
|
||||
|
||||
|
|
@ -73,10 +139,14 @@ stack = ()
|
|||
for n in [1, 2, 3]:
|
||||
stack = n, stack
|
||||
|
||||
print stack
|
||||
print list(joy.utils.stack.iter_stack(stack))
|
||||
print(stack)
|
||||
print(list(joy.utils.stack.iter_stack(stack)))
|
||||
```
|
||||
|
||||
(3, (2, (1, ())))
|
||||
[3, 2, 1]
|
||||
|
||||
|
||||
### Purely Functional Datastructures.
|
||||
Because Joy lists are made out of Python tuples they are immutable, so all Joy datastructures are *[purely functional](https://en.wikipedia.org/wiki/Purely_functional_data_structure)*.
|
||||
|
||||
|
|
@ -90,9 +160,43 @@ Each function is passed the stack, expression, and dictionary and returns them.
|
|||
```python
|
||||
import joy.joy
|
||||
|
||||
print inspect.getsource(joy.joy.joy)
|
||||
print(inspect.getsource(joy.joy.joy))
|
||||
```
|
||||
|
||||
def joy(stack, expression, dictionary, viewer=None):
|
||||
'''Evaluate a Joy expression on a stack.
|
||||
|
||||
This function iterates through a sequence of terms which are either
|
||||
literals (strings, numbers, sequences of terms) or function symbols.
|
||||
Literals are put onto the stack and functions are looked up in the
|
||||
disctionary and executed.
|
||||
|
||||
The viewer is a function that is called with the stack and expression
|
||||
on every iteration, its return value is ignored.
|
||||
|
||||
:param stack stack: The stack.
|
||||
:param stack expression: The expression to evaluate.
|
||||
:param dict dictionary: A ``dict`` mapping names to Joy functions.
|
||||
:param function viewer: Optional viewer function.
|
||||
:rtype: (stack, (), dictionary)
|
||||
|
||||
'''
|
||||
while expression:
|
||||
|
||||
if viewer: viewer(stack, expression)
|
||||
|
||||
term, expression = expression
|
||||
if isinstance(term, Symbol):
|
||||
term = dictionary[term]
|
||||
stack, expression, dictionary = term(stack, expression, dictionary)
|
||||
else:
|
||||
stack = term, stack
|
||||
|
||||
if viewer: viewer(stack, expression)
|
||||
return stack, expression, dictionary
|
||||
|
||||
|
||||
|
||||
### View function
|
||||
The `joy()` function accepts a "viewer" function which it calls on each iteration passing the current stack and expression just before evaluation. This can be used for tracing, breakpoints, retrying after exceptions, or interrupting an evaluation and saving to disk or sending over the network to resume later. The stack and expression together contain all the state of the computation at each step.
|
||||
|
||||
|
|
@ -109,7 +213,7 @@ One day I thought, What happens if you rewrite Joy to use [CSP](https://en.wikip
|
|||
```python
|
||||
import joy.parser
|
||||
|
||||
print inspect.getdoc(joy.parser)
|
||||
print(inspect.getdoc(joy.parser))
|
||||
```
|
||||
|
||||
This module exports a single function for converting text to a joy
|
||||
|
|
@ -134,7 +238,7 @@ The parser is extremely simple, the undocumented `re.Scanner` class does most of
|
|||
|
||||
|
||||
```python
|
||||
print inspect.getsource(joy.parser._parse)
|
||||
print(inspect.getsource(joy.parser._parse))
|
||||
```
|
||||
|
||||
def _parse(tokens):
|
||||
|
|
@ -233,21 +337,20 @@ The Joy library of functions (aka commands, or "words" after Forth usage) encaps
|
|||
```python
|
||||
import joy.library
|
||||
|
||||
print ' '.join(sorted(joy.library.initialize()))
|
||||
print(' '.join(sorted(joy.library.initialize())))
|
||||
```
|
||||
|
||||
!= % & * *fraction *fraction0 + ++ - -- / // /floor < << <= <> = > >= >> ? ^ _Tree_add_Ee _Tree_delete_R0 _Tree_delete_clear_stuff _Tree_get_E abs add anamorphism and app1 app2 app3 at average b binary bool branch ccons choice clear cleave cmp codireco concat cond cons dinfrirst dip dipd dipdd disenstacken divmod down_to_zero drop dup dupd dupdd dupdip dupdipd enstacken eq first first_two flatten floor floordiv fork fourth gcd ge genrec getitem gt help i id ifte ii infer infra inscribe le least_fraction loop lshift lt make_generator map max min mod modulus mul ne neg not nullary of or over pam parse pick pm pop popd popdd popop popopd popopdd pow pred primrec product quoted range range_to_zero rem remainder remove rest reverse roll< roll> rolldown rollup round rrest rshift run second select sharing shunt size sort sqr sqrt stack step step_zero stuncons stununcons sub succ sum swaack swap swoncat swons take ternary third times truediv truthy tuck unary uncons unique unit unquoted unstack unswons void warranty while words x xor zip •
|
||||
!= % & * *fraction *fraction0 + ++ - -- / // /floor < << <= <> = > >= >> ? ^ _Tree_add_Ee _Tree_delete_R0 _Tree_delete_clear_stuff _Tree_get_E abs add anamorphism and app1 app2 app3 at average b binary bool branch ccons choice clear cleave cmp codireco concat cond cons dinfrirst dip dipd dipdd disenstacken div divmod down_to_zero drop dup dupd dupdd dupdip dupdipd enstacken eq first first_two flatten floor floordiv fork fourth gcd ge genrec getitem gt help i id ifte ii infra inscribe le least_fraction loop lshift lt make_generator map max min mod modulus mul ne neg not nullary of or over pam parse pick pm pop popd popdd popop popopd popopdd pow pred primrec product quoted range range_to_zero rem remainder remove rest reverse roll< roll> rolldown rollup round rrest rshift run second select sharing shunt size sort sqr sqrt stack step step_zero stuncons stununcons sub succ sum swaack swap swoncat swons tailrec take ternary third times truediv truthy tuck unary uncons unique unit unquoted unstack unswons void warranty while words x xor zip •
|
||||
|
||||
|
||||
Many of the functions are defined in Python, like `dip`:
|
||||
|
||||
|
||||
```python
|
||||
print inspect.getsource(joy.library.dip)
|
||||
print(inspect.getsource(joy.library.dip))
|
||||
```
|
||||
|
||||
@inscribe
|
||||
@combinator_effect(_COMB_NUMS(), a1, s1)
|
||||
@FunctionWrapper
|
||||
def dip(stack, expression, dictionary):
|
||||
'''
|
||||
|
|
@ -256,9 +359,9 @@ print inspect.getsource(joy.library.dip)
|
|||
on the rest of the stack.
|
||||
::
|
||||
|
||||
... x [Q] dip
|
||||
... x [Q] dip
|
||||
-------------------
|
||||
... Q x
|
||||
... Q x
|
||||
|
||||
'''
|
||||
(quote, (x, stack)) = stack
|
||||
|
|
@ -271,46 +374,47 @@ Some functions are defined in equations in terms of other functions. When the i
|
|||
|
||||
|
||||
```python
|
||||
print joy.library.definitions
|
||||
print(joy.library.definitions)
|
||||
```
|
||||
|
||||
? == dup truthy
|
||||
*fraction == [uncons] dip uncons [swap] dip concat [*] infra [*] dip cons
|
||||
*fraction0 == concat [[swap] dip * [*] dip] infra
|
||||
anamorphism == [pop []] swap [dip swons] genrec
|
||||
average == [sum 1.0 *] [size] cleave /
|
||||
binary == nullary [popop] dip
|
||||
cleave == fork [popd] dip
|
||||
codireco == cons dip rest cons
|
||||
dinfrirst == dip infra first
|
||||
unstack == ? [uncons ?] loop pop
|
||||
down_to_zero == [0 >] [dup --] while
|
||||
dupdipd == dup dipd
|
||||
enstacken == stack [clear] dip
|
||||
flatten == [] swap [concat] step
|
||||
fork == [i] app2
|
||||
gcd == 1 [tuck modulus dup 0 >] loop pop
|
||||
ifte == [nullary not] dipd branch
|
||||
ii == [dip] dupdip i
|
||||
least_fraction == dup [gcd] infra [div] concat map
|
||||
make_generator == [codireco] ccons
|
||||
nullary == [stack] dinfrirst
|
||||
of == swap at
|
||||
pam == [i] map
|
||||
primrec == [i] genrec
|
||||
product == 1 swap [*] step
|
||||
quoted == [unit] dip
|
||||
range == [0 <=] [1 - dup] anamorphism
|
||||
range_to_zero == unit [down_to_zero] infra
|
||||
run == [] swap infra
|
||||
size == 0 swap [pop ++] step
|
||||
sqr == dup mul
|
||||
step_zero == 0 roll> step
|
||||
swoncat == swap concat
|
||||
ternary == unary [popop] dip
|
||||
unary == nullary popd
|
||||
unquoted == [i] dip
|
||||
while == swap [nullary] cons dup dipd concat loop
|
||||
? dup truthy
|
||||
*fraction [uncons] dip uncons [swap] dip concat [*] infra [*] dip cons
|
||||
*fraction0 concat [[swap] dip * [*] dip] infra
|
||||
anamorphism [pop []] swap [dip swons] genrec
|
||||
average [sum 1.0 *] [size] cleave /
|
||||
binary nullary [popop] dip
|
||||
cleave fork [popd] dip
|
||||
codireco cons dip rest cons
|
||||
dinfrirst dip infra first
|
||||
unstack ? [uncons ?] loop pop
|
||||
down_to_zero [0 >] [dup --] while
|
||||
dupdipd dup dipd
|
||||
enstacken stack [clear] dip
|
||||
flatten [] swap [concat] step
|
||||
fork [i] app2
|
||||
gcd 1 [tuck modulus dup 0 >] loop pop
|
||||
ifte [nullary not] dipd branch
|
||||
ii [dip] dupdip i
|
||||
least_fraction dup [gcd] infra [div] concat map
|
||||
make_generator [codireco] ccons
|
||||
nullary [stack] dinfrirst
|
||||
of swap at
|
||||
pam [i] map
|
||||
tailrec [i] genrec
|
||||
product 1 swap [*] step
|
||||
quoted [unit] dip
|
||||
range [0 <=] [1 - dup] anamorphism
|
||||
range_to_zero unit [down_to_zero] infra
|
||||
run [] swap infra
|
||||
size 0 swap [pop ++] step
|
||||
sqr dup mul
|
||||
step_zero 0 roll> step
|
||||
swoncat swap concat
|
||||
tailrec [i] genrec
|
||||
ternary unary [popop] dip
|
||||
unary nullary popd
|
||||
unquoted [i] dip
|
||||
while swap [nullary] cons dup dipd concat loop
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -22,18 +22,18 @@ that you start by running the package:
|
|||
|
||||
::
|
||||
|
||||
$ python -m joy
|
||||
Joypy - Copyright © 2017 Simon Forman
|
||||
This program comes with ABSOLUTELY NO WARRANTY; for details type "warranty".
|
||||
This is free software, and you are welcome to redistribute it
|
||||
under certain conditions; type "sharing" for details.
|
||||
Type "words" to see a list of all words, and "[<name>] help" to print the
|
||||
docs for a word.
|
||||
$ python -m joy
|
||||
Joypy - Copyright © 2017 Simon Forman
|
||||
This program comes with ABSOLUTELY NO WARRANTY; for details type "warranty".
|
||||
This is free software, and you are welcome to redistribute it
|
||||
under certain conditions; type "sharing" for details.
|
||||
Type "words" to see a list of all words, and "[<name>] help" to print the
|
||||
docs for a word.
|
||||
|
||||
|
||||
<-top
|
||||
<-top
|
||||
|
||||
joy? _
|
||||
joy? _
|
||||
|
||||
The ``<-top`` marker points to the top of the (initially empty) stack.
|
||||
You can enter Joy notation at the prompt and a `trace of
|
||||
|
|
@ -42,18 +42,18 @@ and prompt again:
|
|||
|
||||
::
|
||||
|
||||
joy? 23 sqr 18 +
|
||||
. 23 sqr 18 +
|
||||
23 . sqr 18 +
|
||||
23 . dup mul 18 +
|
||||
23 23 . mul 18 +
|
||||
529 . 18 +
|
||||
529 18 . +
|
||||
547 .
|
||||
joy? 23 sqr 18 +
|
||||
. 23 sqr 18 +
|
||||
23 . sqr 18 +
|
||||
23 . dup mul 18 +
|
||||
23 23 . mul 18 +
|
||||
529 . 18 +
|
||||
529 18 . +
|
||||
547 .
|
||||
|
||||
547 <-top
|
||||
547 <-top
|
||||
|
||||
joy?
|
||||
joy?
|
||||
|
||||
Stacks (aka list, quote, sequence, etc.)
|
||||
========================================
|
||||
|
|
@ -65,13 +65,68 @@ both the stack and the expression. It is a `cons
|
|||
list <https://en.wikipedia.org/wiki/Cons#Lists>`__ made from Python
|
||||
tuples.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
import inspect
|
||||
import joy.utils.stack
|
||||
|
||||
|
||||
print inspect.getdoc(joy.utils.stack)
|
||||
print(inspect.getdoc(joy.utils.stack))
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
When talking about Joy we use the terms "stack", "quote", "sequence",
|
||||
"list", and others to mean the same thing: a simple linear datatype that
|
||||
permits certain operations such as iterating and pushing and popping
|
||||
values from (at least) one end.
|
||||
|
||||
There is no "Stack" Python class, instead we use the `cons list`_, a
|
||||
venerable two-tuple recursive sequence datastructure, where the
|
||||
empty tuple ``()`` is the empty stack and ``(head, rest)`` gives the
|
||||
recursive form of a stack with one or more items on it::
|
||||
|
||||
stack := () | (item, stack)
|
||||
|
||||
Putting some numbers onto a stack::
|
||||
|
||||
()
|
||||
(1, ())
|
||||
(2, (1, ()))
|
||||
(3, (2, (1, ())))
|
||||
...
|
||||
|
||||
Python has very nice "tuple packing and unpacking" in its syntax which
|
||||
means we can directly "unpack" the expected arguments to a Joy function.
|
||||
|
||||
For example::
|
||||
|
||||
def dup((head, tail)):
|
||||
return head, (head, tail)
|
||||
|
||||
We replace the argument "stack" by the expected structure of the stack,
|
||||
in this case "(head, tail)", and Python takes care of unpacking the
|
||||
incoming tuple and assigning values to the names. (Note that Python
|
||||
syntax doesn't require parentheses around tuples used in expressions
|
||||
where they would be redundant.)
|
||||
|
||||
Unfortunately, the Sphinx documentation generator, which is used to generate this
|
||||
web page, doesn't handle tuples in the function parameters. And in Python 3, this
|
||||
syntax was removed entirely. Instead you would have to write::
|
||||
|
||||
def dup(stack):
|
||||
head, tail = stack
|
||||
return head, (head, tail)
|
||||
|
||||
|
||||
We have two very simple functions, one to build up a stack from a Python
|
||||
iterable and another to iterate through a stack and yield its items
|
||||
one-by-one in order. There are also two functions to generate string representations
|
||||
of stacks. They only differ in that one prints the terms in stack from left-to-right while the other prints from right-to-left. In both functions *internal stacks* are
|
||||
printed left-to-right. These functions are written to support :doc:`../pretty`.
|
||||
|
||||
.. _cons list: https://en.wikipedia.org/wiki/Cons#Lists
|
||||
|
||||
|
||||
The utility functions maintain order.
|
||||
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
|
@ -79,32 +134,57 @@ The utility functions maintain order.
|
|||
The 0th item in the list will be on the top of the stack and *vise
|
||||
versa*.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
joy.utils.stack.list_to_stack([1, 2, 3])
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(1, (2, (3, ())))
|
||||
|
||||
|
||||
|
||||
.. code:: ipython3
|
||||
|
||||
list(joy.utils.stack.iter_stack((1, (2, (3, ())))))
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
[1, 2, 3]
|
||||
|
||||
|
||||
|
||||
This requires reversing the sequence (or iterating backwards) otherwise:
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
stack = ()
|
||||
|
||||
for n in [1, 2, 3]:
|
||||
stack = n, stack
|
||||
|
||||
print stack
|
||||
print list(joy.utils.stack.iter_stack(stack))
|
||||
print(stack)
|
||||
print(list(joy.utils.stack.iter_stack(stack)))
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(3, (2, (1, ())))
|
||||
[3, 2, 1]
|
||||
|
||||
|
||||
Purely Functional Datastructures.
|
||||
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
Because Joy lists are made out of Python tuples they are immutable, so
|
||||
all Joy datastructures are `purely
|
||||
functional <https://en.wikipedia.org/wiki/Purely_functional_data_structure>`__.
|
||||
all Joy datastructures are *`purely
|
||||
functional <https://en.wikipedia.org/wiki/Purely_functional_data_structure>`__*.
|
||||
|
||||
The ``joy()`` function.
|
||||
=======================
|
||||
|
|
@ -119,21 +199,58 @@ looks up in the dictionary.
|
|||
|
||||
Each function is passed the stack, expression, and dictionary and
|
||||
returns them. Whatever the function returns becomes the new stack,
|
||||
expression, and dictionary. (The dictionary is passed to enable
|
||||
e.g. writing words that let you enter new words into the dictionary at
|
||||
expression, and dictionary. (The dictionary is passed to enable e.g.
|
||||
writing words that let you enter new words into the dictionary at
|
||||
runtime, which nothing does yet and may be a bad idea, and the ``help``
|
||||
command.)
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
import joy.joy
|
||||
|
||||
print inspect.getsource(joy.joy.joy)
|
||||
print(inspect.getsource(joy.joy.joy))
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
def joy(stack, expression, dictionary, viewer=None):
|
||||
'''Evaluate a Joy expression on a stack.
|
||||
|
||||
This function iterates through a sequence of terms which are either
|
||||
literals (strings, numbers, sequences of terms) or function symbols.
|
||||
Literals are put onto the stack and functions are looked up in the
|
||||
disctionary and executed.
|
||||
|
||||
The viewer is a function that is called with the stack and expression
|
||||
on every iteration, its return value is ignored.
|
||||
|
||||
:param stack stack: The stack.
|
||||
:param stack expression: The expression to evaluate.
|
||||
:param dict dictionary: A ``dict`` mapping names to Joy functions.
|
||||
:param function viewer: Optional viewer function.
|
||||
:rtype: (stack, (), dictionary)
|
||||
|
||||
'''
|
||||
while expression:
|
||||
|
||||
if viewer: viewer(stack, expression)
|
||||
|
||||
term, expression = expression
|
||||
if isinstance(term, Symbol):
|
||||
term = dictionary[term]
|
||||
stack, expression, dictionary = term(stack, expression, dictionary)
|
||||
else:
|
||||
stack = term, stack
|
||||
|
||||
if viewer: viewer(stack, expression)
|
||||
return stack, expression, dictionary
|
||||
|
||||
|
||||
|
||||
View function
|
||||
~~~~~~~~~~~~~
|
||||
|
||||
The ``joy()`` function accepts a “viewer” function which it calls on
|
||||
The ``joy()`` function accepts a "viewer" function which it calls on
|
||||
each iteration passing the current stack and expression just before
|
||||
evaluation. This can be used for tracing, breakpoints, retrying after
|
||||
exceptions, or interrupting an evaluation and saving to disk or sending
|
||||
|
|
@ -147,7 +264,7 @@ A ``viewer`` records each step of the evaluation of a Joy program. The
|
|||
``TracePrinter`` has a facility for printing out a trace of the
|
||||
evaluation, one line per step. Each step is aligned to the current
|
||||
interpreter position, signified by a period separating the stack on the
|
||||
left from the pending expression (“continuation”) on the right.
|
||||
left from the pending expression ("continuation") on the right.
|
||||
|
||||
`Continuation-Passing Style <https://en.wikipedia.org/wiki/Continuation-passing_style>`__
|
||||
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
|
@ -162,11 +279,11 @@ modifying the expression rather than making recursive calls to the
|
|||
Parser
|
||||
======
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
import joy.parser
|
||||
|
||||
print inspect.getdoc(joy.parser)
|
||||
print(inspect.getdoc(joy.parser))
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
|
@ -191,12 +308,12 @@ Parser
|
|||
|
||||
The parser is extremely simple, the undocumented ``re.Scanner`` class
|
||||
does most of the tokenizing work and then you just build the tuple
|
||||
structure out of the tokens. There’s no Abstract Syntax Tree or anything
|
||||
structure out of the tokens. There's no Abstract Syntax Tree or anything
|
||||
like that.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
print inspect.getsource(joy.parser._parse)
|
||||
print(inspect.getsource(joy.parser._parse))
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
|
@ -226,9 +343,9 @@ like that.
|
|||
|
||||
|
||||
|
||||
That’s pretty much all there is to it.
|
||||
That's pretty much all there is to it.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
joy.parser.text_to_expression('1 2 3 4 5') # A simple sequence.
|
||||
|
||||
|
|
@ -241,7 +358,7 @@ That’s pretty much all there is to it.
|
|||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
joy.parser.text_to_expression('[1 2 3] 4 5') # Three items, the first is a list with three items
|
||||
|
||||
|
|
@ -254,7 +371,7 @@ That’s pretty much all there is to it.
|
|||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
joy.parser.text_to_expression('1 23 ["four" [-5.0] cons] 8888') # A mixed bag. cons is
|
||||
# a Symbol, no lookup at
|
||||
|
|
@ -269,7 +386,7 @@ That’s pretty much all there is to it.
|
|||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
joy.parser.text_to_expression('[][][][][]') # Five empty lists.
|
||||
|
||||
|
|
@ -282,7 +399,7 @@ That’s pretty much all there is to it.
|
|||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
joy.parser.text_to_expression('[[[[[]]]]]') # Five nested lists.
|
||||
|
||||
|
|
@ -298,35 +415,34 @@ That’s pretty much all there is to it.
|
|||
Library
|
||||
=======
|
||||
|
||||
The Joy library of functions (aka commands, or “words” after Forth
|
||||
The Joy library of functions (aka commands, or "words" after Forth
|
||||
usage) encapsulates all the actual functionality (no pun intended) of
|
||||
the Joy system. There are simple functions such as addition ``add`` (or
|
||||
``+``, the library module supports aliases), and combinators which
|
||||
provide control-flow and higher-order operations.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
import joy.library
|
||||
|
||||
print ' '.join(sorted(joy.library.initialize()))
|
||||
print(' '.join(sorted(joy.library.initialize())))
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
!= % & * *fraction *fraction0 + ++ - -- / // /floor < << <= <> = > >= >> ? ^ _Tree_add_Ee _Tree_delete_R0 _Tree_delete_clear_stuff _Tree_get_E abs add anamorphism and app1 app2 app3 at average b binary bool branch ccons choice clear cleave cmp codireco concat cond cons dinfrirst dip dipd dipdd disenstacken divmod down_to_zero drop dup dupd dupdd dupdip dupdipd enstacken eq first first_two flatten floor floordiv fork fourth gcd ge genrec getitem gt help i id ifte ii infer infra inscribe le least_fraction loop lshift lt make_generator map max min mod modulus mul ne neg not nullary of or over pam parse pick pm pop popd popdd popop popopd popopdd pow pred primrec product quoted range range_to_zero rem remainder remove rest reverse roll< roll> rolldown rollup round rrest rshift run second select sharing shunt size sort sqr sqrt stack step step_zero stuncons stununcons sub succ sum swaack swap swoncat swons take ternary third times truediv truthy tuck unary uncons unique unit unquoted unstack unswons void warranty while words x xor zip •
|
||||
!= % & * *fraction *fraction0 + ++ - -- / // /floor < << <= <> = > >= >> ? ^ _Tree_add_Ee _Tree_delete_R0 _Tree_delete_clear_stuff _Tree_get_E abs add anamorphism and app1 app2 app3 at average b binary bool branch ccons choice clear cleave cmp codireco concat cond cons dinfrirst dip dipd dipdd disenstacken div divmod down_to_zero drop dup dupd dupdd dupdip dupdipd enstacken eq first first_two flatten floor floordiv fork fourth gcd ge genrec getitem gt help i id ifte ii infra inscribe le least_fraction loop lshift lt make_generator map max min mod modulus mul ne neg not nullary of or over pam parse pick pm pop popd popdd popop popopd popopdd pow pred primrec product quoted range range_to_zero rem remainder remove rest reverse roll< roll> rolldown rollup round rrest rshift run second select sharing shunt size sort sqr sqrt stack step step_zero stuncons stununcons sub succ sum swaack swap swoncat swons tailrec take ternary third times truediv truthy tuck unary uncons unique unit unquoted unstack unswons void warranty while words x xor zip •
|
||||
|
||||
|
||||
Many of the functions are defined in Python, like ``dip``:
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
print inspect.getsource(joy.library.dip)
|
||||
print(inspect.getsource(joy.library.dip))
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
@inscribe
|
||||
@combinator_effect(_COMB_NUMS(), a1, s1)
|
||||
@FunctionWrapper
|
||||
def dip(stack, expression, dictionary):
|
||||
'''
|
||||
|
|
@ -335,9 +451,9 @@ Many of the functions are defined in Python, like ``dip``:
|
|||
on the rest of the stack.
|
||||
::
|
||||
|
||||
... x [Q] dip
|
||||
... x [Q] dip
|
||||
-------------------
|
||||
... Q x
|
||||
... Q x
|
||||
|
||||
'''
|
||||
(quote, (x, stack)) = stack
|
||||
|
|
@ -351,89 +467,90 @@ When the interpreter executes a definition function that function just
|
|||
pushes its body expression onto the pending expression (the
|
||||
continuation) and returns control to the interpreter.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
print joy.library.definitions
|
||||
print(joy.library.definitions)
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
? == dup truthy
|
||||
*fraction == [uncons] dip uncons [swap] dip concat [*] infra [*] dip cons
|
||||
*fraction0 == concat [[swap] dip * [*] dip] infra
|
||||
anamorphism == [pop []] swap [dip swons] genrec
|
||||
average == [sum 1.0 *] [size] cleave /
|
||||
binary == nullary [popop] dip
|
||||
cleave == fork [popd] dip
|
||||
codireco == cons dip rest cons
|
||||
dinfrirst == dip infra first
|
||||
unstack == ? [uncons ?] loop pop
|
||||
down_to_zero == [0 >] [dup --] while
|
||||
dupdipd == dup dipd
|
||||
enstacken == stack [clear] dip
|
||||
flatten == [] swap [concat] step
|
||||
fork == [i] app2
|
||||
gcd == 1 [tuck modulus dup 0 >] loop pop
|
||||
ifte == [nullary not] dipd branch
|
||||
ii == [dip] dupdip i
|
||||
least_fraction == dup [gcd] infra [div] concat map
|
||||
make_generator == [codireco] ccons
|
||||
nullary == [stack] dinfrirst
|
||||
of == swap at
|
||||
pam == [i] map
|
||||
primrec == [i] genrec
|
||||
product == 1 swap [*] step
|
||||
quoted == [unit] dip
|
||||
range == [0 <=] [1 - dup] anamorphism
|
||||
range_to_zero == unit [down_to_zero] infra
|
||||
run == [] swap infra
|
||||
size == 0 swap [pop ++] step
|
||||
sqr == dup mul
|
||||
step_zero == 0 roll> step
|
||||
swoncat == swap concat
|
||||
ternary == unary [popop] dip
|
||||
unary == nullary popd
|
||||
unquoted == [i] dip
|
||||
while == swap [nullary] cons dup dipd concat loop
|
||||
? dup truthy
|
||||
*fraction [uncons] dip uncons [swap] dip concat [*] infra [*] dip cons
|
||||
*fraction0 concat [[swap] dip * [*] dip] infra
|
||||
anamorphism [pop []] swap [dip swons] genrec
|
||||
average [sum 1.0 *] [size] cleave /
|
||||
binary nullary [popop] dip
|
||||
cleave fork [popd] dip
|
||||
codireco cons dip rest cons
|
||||
dinfrirst dip infra first
|
||||
unstack ? [uncons ?] loop pop
|
||||
down_to_zero [0 >] [dup --] while
|
||||
dupdipd dup dipd
|
||||
enstacken stack [clear] dip
|
||||
flatten [] swap [concat] step
|
||||
fork [i] app2
|
||||
gcd 1 [tuck modulus dup 0 >] loop pop
|
||||
ifte [nullary not] dipd branch
|
||||
ii [dip] dupdip i
|
||||
least_fraction dup [gcd] infra [div] concat map
|
||||
make_generator [codireco] ccons
|
||||
nullary [stack] dinfrirst
|
||||
of swap at
|
||||
pam [i] map
|
||||
tailrec [i] genrec
|
||||
product 1 swap [*] step
|
||||
quoted [unit] dip
|
||||
range [0 <=] [1 - dup] anamorphism
|
||||
range_to_zero unit [down_to_zero] infra
|
||||
run [] swap infra
|
||||
size 0 swap [pop ++] step
|
||||
sqr dup mul
|
||||
step_zero 0 roll> step
|
||||
swoncat swap concat
|
||||
tailrec [i] genrec
|
||||
ternary unary [popop] dip
|
||||
unary nullary popd
|
||||
unquoted [i] dip
|
||||
while swap [nullary] cons dup dipd concat loop
|
||||
|
||||
|
||||
|
||||
Currently, there’s no function to add new definitions to the dictionary
|
||||
from “within” Joy code itself. Adding new definitions remains a
|
||||
Currently, there's no function to add new definitions to the dictionary
|
||||
from "within" Joy code itself. Adding new definitions remains a
|
||||
meta-interpreter action. You have to do it yourself, in Python, and wash
|
||||
your hands afterward.
|
||||
|
||||
It would be simple enough to define one, but it would open the door to
|
||||
*name binding* and break the idea that all state is captured in the
|
||||
stack and expression. There’s an implicit *standard dictionary* that
|
||||
stack and expression. There's an implicit *standard dictionary* that
|
||||
defines the actual semantics of the syntactic stack and expression
|
||||
datastructures (which only contain symbols, not the actual functions.
|
||||
Pickle some and see for yourself.)
|
||||
|
||||
“There should be only one.”
|
||||
"There should be only one."
|
||||
^^^^^^^^^^^^^^^^^^^^^^^^^^^
|
||||
|
||||
Which brings me to talking about one of my hopes and dreams for this
|
||||
notation: “There should be only one.” What I mean is that there should
|
||||
notation: "There should be only one." What I mean is that there should
|
||||
be one universal standard dictionary of commands, and all bespoke work
|
||||
done in a UI for purposes takes place by direct interaction and macros.
|
||||
There would be a *Grand Refactoring* biannually (two years, not six
|
||||
months, that’s semi-annually) where any new definitions factored out of
|
||||
months, that's semi-annually) where any new definitions factored out of
|
||||
the usage and macros of the previous time, along with new algorithms and
|
||||
such, were entered into the dictionary and posted to e.g. IPFS.
|
||||
such, were entered into the dictionary and posted to e.g. IPFS.
|
||||
|
||||
Code should not burgeon wildly, as it does today. The variety of code
|
||||
should map more-or-less to the well-factored variety of human
|
||||
computably-solvable problems. There shouldn’t be dozens of chat apps, JS
|
||||
frameworks, programming languages. It’s a waste of time, a `fractal
|
||||
“thundering herd”
|
||||
computably-solvable problems. There shouldn't be dozens of chat apps, JS
|
||||
frameworks, programming languages. It's a waste of time, a `fractal
|
||||
"thundering herd"
|
||||
attack <https://en.wikipedia.org/wiki/Thundering_herd_problem>`__ on
|
||||
human mentality.
|
||||
|
||||
Literary Code Library
|
||||
^^^^^^^^^^^^^^^^^^^^^
|
||||
|
||||
If you read over the other notebooks you’ll see that developing code in
|
||||
If you read over the other notebooks you'll see that developing code in
|
||||
Joy is a lot like doing simple mathematics, and the descriptions of the
|
||||
code resemble math papers. The code also works the first time, no bugs.
|
||||
If you have any experience programming at all, you are probably
|
||||
|
|
|
|||
|
|
@ -13087,7 +13087,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [1]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">from</span> <span class="nn">joy.joy</span> <span class="kn">import</span> <span class="n">run</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">joy.joy</span> <span class="kn">import</span> <span class="n">run</span>
|
||||
<span class="kn">from</span> <span class="nn">joy.library</span> <span class="kn">import</span> <span class="n">initialize</span>
|
||||
<span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="kn">import</span> <span class="n">stack_to_string</span>
|
||||
<span class="kn">from</span> <span class="nn">joy.utils.pretty_print</span> <span class="kn">import</span> <span class="n">TracePrinter</span>
|
||||
|
|
@ -13111,12 +13111,12 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [2]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">D</span> <span class="o">=</span> <span class="n">initialize</span><span class="p">()</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">D</span> <span class="o">=</span> <span class="n">initialize</span><span class="p">()</span>
|
||||
<span class="n">S</span> <span class="o">=</span> <span class="p">()</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">J</span><span class="p">(</span><span class="n">text</span><span class="p">):</span>
|
||||
<span class="nb">print</span> <span class="n">stack_to_string</span><span class="p">(</span><span class="n">run</span><span class="p">(</span><span class="n">text</span><span class="p">,</span> <span class="n">S</span><span class="p">,</span> <span class="n">D</span><span class="p">)[</span><span class="mi">0</span><span class="p">])</span>
|
||||
<span class="nb">print</span><span class="p">(</span><span class="n">stack_to_string</span><span class="p">(</span><span class="n">run</span><span class="p">(</span><span class="n">text</span><span class="p">,</span> <span class="n">S</span><span class="p">,</span> <span class="n">D</span><span class="p">)[</span><span class="mi">0</span><span class="p">]))</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">V</span><span class="p">(</span><span class="n">text</span><span class="p">):</span>
|
||||
|
|
@ -13142,7 +13142,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [3]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 18 +'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 18 +'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13173,7 +13173,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [4]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'45 30 gcd'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'45 30 gcd'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13212,7 +13212,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [5]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'23 18 +'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'23 18 +'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13229,10 +13229,10 @@ div#notebook {
|
|||
|
||||
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre> . 23 18 +
|
||||
23 . 18 +
|
||||
23 18 . +
|
||||
41 .
|
||||
<pre> • 23 18 +
|
||||
23 • 18 +
|
||||
23 18 • +
|
||||
41 •
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
|
|
@ -13246,7 +13246,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [6]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'45 30 gcd'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'45 30 gcd'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13263,28 +13263,28 @@ div#notebook {
|
|||
|
||||
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre> . 45 30 gcd
|
||||
45 . 30 gcd
|
||||
45 30 . gcd
|
||||
45 30 . 1 [tuck modulus dup 0 >] loop pop
|
||||
45 30 1 . [tuck modulus dup 0 >] loop pop
|
||||
45 30 1 [tuck modulus dup 0 >] . loop pop
|
||||
45 30 . tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
30 45 30 . modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
30 15 . dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
30 15 15 . 0 > [tuck modulus dup 0 >] loop pop
|
||||
30 15 15 0 . > [tuck modulus dup 0 >] loop pop
|
||||
30 15 True . [tuck modulus dup 0 >] loop pop
|
||||
30 15 True [tuck modulus dup 0 >] . loop pop
|
||||
30 15 . tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 30 15 . modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 0 . dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 0 0 . 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 0 0 0 . > [tuck modulus dup 0 >] loop pop
|
||||
15 0 False . [tuck modulus dup 0 >] loop pop
|
||||
15 0 False [tuck modulus dup 0 >] . loop pop
|
||||
15 0 . pop
|
||||
15 .
|
||||
<pre> • 45 30 gcd
|
||||
45 • 30 gcd
|
||||
45 30 • gcd
|
||||
45 30 • 1 [tuck modulus dup 0 >] loop pop
|
||||
45 30 1 • [tuck modulus dup 0 >] loop pop
|
||||
45 30 1 [tuck modulus dup 0 >] • loop pop
|
||||
45 30 • tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
30 45 30 • modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
30 15 • dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
30 15 15 • 0 > [tuck modulus dup 0 >] loop pop
|
||||
30 15 15 0 • > [tuck modulus dup 0 >] loop pop
|
||||
30 15 True • [tuck modulus dup 0 >] loop pop
|
||||
30 15 True [tuck modulus dup 0 >] • loop pop
|
||||
30 15 • tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 30 15 • modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 0 • dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 0 0 • 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 0 0 0 • > [tuck modulus dup 0 >] loop pop
|
||||
15 0 False • [tuck modulus dup 0 >] loop pop
|
||||
15 0 False [tuck modulus dup 0 >] • loop pop
|
||||
15 0 • pop
|
||||
15 •
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
|
|
@ -13306,7 +13306,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [7]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'96 27 gcd'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'96 27 gcd'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13323,42 +13323,42 @@ div#notebook {
|
|||
|
||||
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre> . 96 27 gcd
|
||||
96 . 27 gcd
|
||||
96 27 . gcd
|
||||
96 27 . 1 [tuck modulus dup 0 >] loop pop
|
||||
96 27 1 . [tuck modulus dup 0 >] loop pop
|
||||
96 27 1 [tuck modulus dup 0 >] . loop pop
|
||||
96 27 . tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
27 96 27 . modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
27 15 . dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
27 15 15 . 0 > [tuck modulus dup 0 >] loop pop
|
||||
27 15 15 0 . > [tuck modulus dup 0 >] loop pop
|
||||
27 15 True . [tuck modulus dup 0 >] loop pop
|
||||
27 15 True [tuck modulus dup 0 >] . loop pop
|
||||
27 15 . tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 27 15 . modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 12 . dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 12 12 . 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 12 12 0 . > [tuck modulus dup 0 >] loop pop
|
||||
15 12 True . [tuck modulus dup 0 >] loop pop
|
||||
15 12 True [tuck modulus dup 0 >] . loop pop
|
||||
15 12 . tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
12 15 12 . modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
12 3 . dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
12 3 3 . 0 > [tuck modulus dup 0 >] loop pop
|
||||
12 3 3 0 . > [tuck modulus dup 0 >] loop pop
|
||||
12 3 True . [tuck modulus dup 0 >] loop pop
|
||||
12 3 True [tuck modulus dup 0 >] . loop pop
|
||||
12 3 . tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
3 12 3 . modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
3 0 . dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
3 0 0 . 0 > [tuck modulus dup 0 >] loop pop
|
||||
3 0 0 0 . > [tuck modulus dup 0 >] loop pop
|
||||
3 0 False . [tuck modulus dup 0 >] loop pop
|
||||
3 0 False [tuck modulus dup 0 >] . loop pop
|
||||
3 0 . pop
|
||||
3 .
|
||||
<pre> • 96 27 gcd
|
||||
96 • 27 gcd
|
||||
96 27 • gcd
|
||||
96 27 • 1 [tuck modulus dup 0 >] loop pop
|
||||
96 27 1 • [tuck modulus dup 0 >] loop pop
|
||||
96 27 1 [tuck modulus dup 0 >] • loop pop
|
||||
96 27 • tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
27 96 27 • modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
27 15 • dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
27 15 15 • 0 > [tuck modulus dup 0 >] loop pop
|
||||
27 15 15 0 • > [tuck modulus dup 0 >] loop pop
|
||||
27 15 True • [tuck modulus dup 0 >] loop pop
|
||||
27 15 True [tuck modulus dup 0 >] • loop pop
|
||||
27 15 • tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 27 15 • modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 12 • dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 12 12 • 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 12 12 0 • > [tuck modulus dup 0 >] loop pop
|
||||
15 12 True • [tuck modulus dup 0 >] loop pop
|
||||
15 12 True [tuck modulus dup 0 >] • loop pop
|
||||
15 12 • tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
12 15 12 • modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
12 3 • dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
12 3 3 • 0 > [tuck modulus dup 0 >] loop pop
|
||||
12 3 3 0 • > [tuck modulus dup 0 >] loop pop
|
||||
12 3 True • [tuck modulus dup 0 >] loop pop
|
||||
12 3 True [tuck modulus dup 0 >] • loop pop
|
||||
12 3 • tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
3 12 3 • modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
3 0 • dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
3 0 0 • 0 > [tuck modulus dup 0 >] loop pop
|
||||
3 0 0 0 • > [tuck modulus dup 0 >] loop pop
|
||||
3 0 False • [tuck modulus dup 0 >] loop pop
|
||||
3 0 False [tuck modulus dup 0 >] • loop pop
|
||||
3 0 • pop
|
||||
3 •
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
|
|
@ -13366,19 +13366,6 @@ div#notebook {
|
|||
</div>
|
||||
</div>
|
||||
|
||||
</div>
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="prompt input_prompt">In [ ]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
|
|
|||
|
|
@ -39,7 +39,7 @@
|
|||
"\n",
|
||||
"\n",
|
||||
"def J(text):\n",
|
||||
" print stack_to_string(run(text, S, D)[0])\n",
|
||||
" print(stack_to_string(run(text, S, D)[0]))\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"def V(text):\n",
|
||||
|
|
@ -107,10 +107,10 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . 23 18 +\n",
|
||||
" 23 . 18 +\n",
|
||||
"23 18 . +\n",
|
||||
" 41 . \n"
|
||||
" • 23 18 +\n",
|
||||
" 23 • 18 +\n",
|
||||
"23 18 • +\n",
|
||||
" 41 • \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -127,28 +127,28 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . 45 30 gcd\n",
|
||||
" 45 . 30 gcd\n",
|
||||
" 45 30 . gcd\n",
|
||||
" 45 30 . 1 [tuck modulus dup 0 >] loop pop\n",
|
||||
" 45 30 1 . [tuck modulus dup 0 >] loop pop\n",
|
||||
" 45 30 1 [tuck modulus dup 0 >] . loop pop\n",
|
||||
" 45 30 . tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 30 45 30 . modulus dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 30 15 . dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 30 15 15 . 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 30 15 15 0 . > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 30 15 True . [tuck modulus dup 0 >] loop pop\n",
|
||||
"30 15 True [tuck modulus dup 0 >] . loop pop\n",
|
||||
" 30 15 . tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 15 30 15 . modulus dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 15 0 . dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 15 0 0 . 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 15 0 0 0 . > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 15 0 False . [tuck modulus dup 0 >] loop pop\n",
|
||||
"15 0 False [tuck modulus dup 0 >] . loop pop\n",
|
||||
" 15 0 . pop\n",
|
||||
" 15 . \n"
|
||||
" • 45 30 gcd\n",
|
||||
" 45 • 30 gcd\n",
|
||||
" 45 30 • gcd\n",
|
||||
" 45 30 • 1 [tuck modulus dup 0 >] loop pop\n",
|
||||
" 45 30 1 • [tuck modulus dup 0 >] loop pop\n",
|
||||
" 45 30 1 [tuck modulus dup 0 >] • loop pop\n",
|
||||
" 45 30 • tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 30 45 30 • modulus dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 30 15 • dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 30 15 15 • 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 30 15 15 0 • > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 30 15 True • [tuck modulus dup 0 >] loop pop\n",
|
||||
"30 15 True [tuck modulus dup 0 >] • loop pop\n",
|
||||
" 30 15 • tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 15 30 15 • modulus dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 15 0 • dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 15 0 0 • 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 15 0 0 0 • > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 15 0 False • [tuck modulus dup 0 >] loop pop\n",
|
||||
"15 0 False [tuck modulus dup 0 >] • loop pop\n",
|
||||
" 15 0 • pop\n",
|
||||
" 15 • \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -172,55 +172,48 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . 96 27 gcd\n",
|
||||
" 96 . 27 gcd\n",
|
||||
" 96 27 . gcd\n",
|
||||
" 96 27 . 1 [tuck modulus dup 0 >] loop pop\n",
|
||||
" 96 27 1 . [tuck modulus dup 0 >] loop pop\n",
|
||||
" 96 27 1 [tuck modulus dup 0 >] . loop pop\n",
|
||||
" 96 27 . tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 27 96 27 . modulus dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 27 15 . dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 27 15 15 . 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 27 15 15 0 . > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 27 15 True . [tuck modulus dup 0 >] loop pop\n",
|
||||
"27 15 True [tuck modulus dup 0 >] . loop pop\n",
|
||||
" 27 15 . tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 15 27 15 . modulus dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 15 12 . dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 15 12 12 . 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 15 12 12 0 . > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 15 12 True . [tuck modulus dup 0 >] loop pop\n",
|
||||
"15 12 True [tuck modulus dup 0 >] . loop pop\n",
|
||||
" 15 12 . tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 12 15 12 . modulus dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 12 3 . dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 12 3 3 . 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 12 3 3 0 . > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 12 3 True . [tuck modulus dup 0 >] loop pop\n",
|
||||
" 12 3 True [tuck modulus dup 0 >] . loop pop\n",
|
||||
" 12 3 . tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 3 12 3 . modulus dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 3 0 . dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 3 0 0 . 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 3 0 0 0 . > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 3 0 False . [tuck modulus dup 0 >] loop pop\n",
|
||||
" 3 0 False [tuck modulus dup 0 >] . loop pop\n",
|
||||
" 3 0 . pop\n",
|
||||
" 3 . \n"
|
||||
" • 96 27 gcd\n",
|
||||
" 96 • 27 gcd\n",
|
||||
" 96 27 • gcd\n",
|
||||
" 96 27 • 1 [tuck modulus dup 0 >] loop pop\n",
|
||||
" 96 27 1 • [tuck modulus dup 0 >] loop pop\n",
|
||||
" 96 27 1 [tuck modulus dup 0 >] • loop pop\n",
|
||||
" 96 27 • tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 27 96 27 • modulus dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 27 15 • dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 27 15 15 • 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 27 15 15 0 • > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 27 15 True • [tuck modulus dup 0 >] loop pop\n",
|
||||
"27 15 True [tuck modulus dup 0 >] • loop pop\n",
|
||||
" 27 15 • tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 15 27 15 • modulus dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 15 12 • dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 15 12 12 • 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 15 12 12 0 • > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 15 12 True • [tuck modulus dup 0 >] loop pop\n",
|
||||
"15 12 True [tuck modulus dup 0 >] • loop pop\n",
|
||||
" 15 12 • tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 12 15 12 • modulus dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 12 3 • dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 12 3 3 • 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 12 3 3 0 • > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 12 3 True • [tuck modulus dup 0 >] loop pop\n",
|
||||
" 12 3 True [tuck modulus dup 0 >] • loop pop\n",
|
||||
" 12 3 • tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 3 12 3 • modulus dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 3 0 • dup 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 3 0 0 • 0 > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 3 0 0 0 • > [tuck modulus dup 0 >] loop pop\n",
|
||||
" 3 0 False • [tuck modulus dup 0 >] loop pop\n",
|
||||
" 3 0 False [tuck modulus dup 0 >] • loop pop\n",
|
||||
" 3 0 • pop\n",
|
||||
" 3 • \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"V('96 27 gcd')"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
|
|
@ -232,14 +225,14 @@
|
|||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 2
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython2",
|
||||
"version": "2.7.12"
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.8.3"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
|
|
|||
|
|
@ -19,7 +19,7 @@ S = ()
|
|||
|
||||
|
||||
def J(text):
|
||||
print stack_to_string(run(text, S, D)[0])
|
||||
print(stack_to_string(run(text, S, D)[0]))
|
||||
|
||||
|
||||
def V(text):
|
||||
|
|
@ -55,10 +55,10 @@ A `viewer` records each step of the evaluation of a Joy program. The `TracePrin
|
|||
V('23 18 +')
|
||||
```
|
||||
|
||||
. 23 18 +
|
||||
23 . 18 +
|
||||
23 18 . +
|
||||
41 .
|
||||
• 23 18 +
|
||||
23 • 18 +
|
||||
23 18 • +
|
||||
41 •
|
||||
|
||||
|
||||
|
||||
|
|
@ -66,28 +66,28 @@ V('23 18 +')
|
|||
V('45 30 gcd')
|
||||
```
|
||||
|
||||
. 45 30 gcd
|
||||
45 . 30 gcd
|
||||
45 30 . gcd
|
||||
45 30 . 1 [tuck modulus dup 0 >] loop pop
|
||||
45 30 1 . [tuck modulus dup 0 >] loop pop
|
||||
45 30 1 [tuck modulus dup 0 >] . loop pop
|
||||
45 30 . tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
30 45 30 . modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
30 15 . dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
30 15 15 . 0 > [tuck modulus dup 0 >] loop pop
|
||||
30 15 15 0 . > [tuck modulus dup 0 >] loop pop
|
||||
30 15 True . [tuck modulus dup 0 >] loop pop
|
||||
30 15 True [tuck modulus dup 0 >] . loop pop
|
||||
30 15 . tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 30 15 . modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 0 . dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 0 0 . 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 0 0 0 . > [tuck modulus dup 0 >] loop pop
|
||||
15 0 False . [tuck modulus dup 0 >] loop pop
|
||||
15 0 False [tuck modulus dup 0 >] . loop pop
|
||||
15 0 . pop
|
||||
15 .
|
||||
• 45 30 gcd
|
||||
45 • 30 gcd
|
||||
45 30 • gcd
|
||||
45 30 • 1 [tuck modulus dup 0 >] loop pop
|
||||
45 30 1 • [tuck modulus dup 0 >] loop pop
|
||||
45 30 1 [tuck modulus dup 0 >] • loop pop
|
||||
45 30 • tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
30 45 30 • modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
30 15 • dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
30 15 15 • 0 > [tuck modulus dup 0 >] loop pop
|
||||
30 15 15 0 • > [tuck modulus dup 0 >] loop pop
|
||||
30 15 True • [tuck modulus dup 0 >] loop pop
|
||||
30 15 True [tuck modulus dup 0 >] • loop pop
|
||||
30 15 • tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 30 15 • modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 0 • dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 0 0 • 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 0 0 0 • > [tuck modulus dup 0 >] loop pop
|
||||
15 0 False • [tuck modulus dup 0 >] loop pop
|
||||
15 0 False [tuck modulus dup 0 >] • loop pop
|
||||
15 0 • pop
|
||||
15 •
|
||||
|
||||
|
||||
Here's a longer trace.
|
||||
|
|
@ -97,45 +97,40 @@ Here's a longer trace.
|
|||
V('96 27 gcd')
|
||||
```
|
||||
|
||||
. 96 27 gcd
|
||||
96 . 27 gcd
|
||||
96 27 . gcd
|
||||
96 27 . 1 [tuck modulus dup 0 >] loop pop
|
||||
96 27 1 . [tuck modulus dup 0 >] loop pop
|
||||
96 27 1 [tuck modulus dup 0 >] . loop pop
|
||||
96 27 . tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
27 96 27 . modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
27 15 . dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
27 15 15 . 0 > [tuck modulus dup 0 >] loop pop
|
||||
27 15 15 0 . > [tuck modulus dup 0 >] loop pop
|
||||
27 15 True . [tuck modulus dup 0 >] loop pop
|
||||
27 15 True [tuck modulus dup 0 >] . loop pop
|
||||
27 15 . tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 27 15 . modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 12 . dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 12 12 . 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 12 12 0 . > [tuck modulus dup 0 >] loop pop
|
||||
15 12 True . [tuck modulus dup 0 >] loop pop
|
||||
15 12 True [tuck modulus dup 0 >] . loop pop
|
||||
15 12 . tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
12 15 12 . modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
12 3 . dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
12 3 3 . 0 > [tuck modulus dup 0 >] loop pop
|
||||
12 3 3 0 . > [tuck modulus dup 0 >] loop pop
|
||||
12 3 True . [tuck modulus dup 0 >] loop pop
|
||||
12 3 True [tuck modulus dup 0 >] . loop pop
|
||||
12 3 . tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
3 12 3 . modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
3 0 . dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
3 0 0 . 0 > [tuck modulus dup 0 >] loop pop
|
||||
3 0 0 0 . > [tuck modulus dup 0 >] loop pop
|
||||
3 0 False . [tuck modulus dup 0 >] loop pop
|
||||
3 0 False [tuck modulus dup 0 >] . loop pop
|
||||
3 0 . pop
|
||||
3 .
|
||||
• 96 27 gcd
|
||||
96 • 27 gcd
|
||||
96 27 • gcd
|
||||
96 27 • 1 [tuck modulus dup 0 >] loop pop
|
||||
96 27 1 • [tuck modulus dup 0 >] loop pop
|
||||
96 27 1 [tuck modulus dup 0 >] • loop pop
|
||||
96 27 • tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
27 96 27 • modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
27 15 • dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
27 15 15 • 0 > [tuck modulus dup 0 >] loop pop
|
||||
27 15 15 0 • > [tuck modulus dup 0 >] loop pop
|
||||
27 15 True • [tuck modulus dup 0 >] loop pop
|
||||
27 15 True [tuck modulus dup 0 >] • loop pop
|
||||
27 15 • tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 27 15 • modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 12 • dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 12 12 • 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 12 12 0 • > [tuck modulus dup 0 >] loop pop
|
||||
15 12 True • [tuck modulus dup 0 >] loop pop
|
||||
15 12 True [tuck modulus dup 0 >] • loop pop
|
||||
15 12 • tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
12 15 12 • modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
12 3 • dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
12 3 3 • 0 > [tuck modulus dup 0 >] loop pop
|
||||
12 3 3 0 • > [tuck modulus dup 0 >] loop pop
|
||||
12 3 True • [tuck modulus dup 0 >] loop pop
|
||||
12 3 True [tuck modulus dup 0 >] • loop pop
|
||||
12 3 • tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
3 12 3 • modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
3 0 • dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
3 0 0 • 0 > [tuck modulus dup 0 >] loop pop
|
||||
3 0 0 0 • > [tuck modulus dup 0 >] loop pop
|
||||
3 0 False • [tuck modulus dup 0 >] loop pop
|
||||
3 0 False [tuck modulus dup 0 >] • loop pop
|
||||
3 0 • pop
|
||||
3 •
|
||||
|
||||
|
||||
|
||||
```python
|
||||
|
||||
```
|
||||
|
|
|
|||
|
|
@ -3,7 +3,7 @@ Preamble
|
|||
|
||||
First, import what we need.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
from joy.joy import run
|
||||
from joy.library import initialize
|
||||
|
|
@ -13,14 +13,14 @@ First, import what we need.
|
|||
Define a dictionary, an initial stack, and two helper functions to run
|
||||
Joy code and print results for us.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
D = initialize()
|
||||
S = ()
|
||||
|
||||
|
||||
def J(text):
|
||||
print stack_to_string(run(text, S, D)[0])
|
||||
print(stack_to_string(run(text, S, D)[0]))
|
||||
|
||||
|
||||
def V(text):
|
||||
|
|
@ -31,7 +31,7 @@ Joy code and print results for us.
|
|||
Run some simple programs
|
||||
~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('23 18 +')
|
||||
|
||||
|
|
@ -41,7 +41,7 @@ Run some simple programs
|
|||
41
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('45 30 gcd')
|
||||
|
||||
|
|
@ -58,97 +58,96 @@ A ``viewer`` records each step of the evaluation of a Joy program. The
|
|||
``TracePrinter`` has a facility for printing out a trace of the
|
||||
evaluation, one line per step. Each step is aligned to the current
|
||||
interpreter position, signified by a period separating the stack on the
|
||||
left from the pending expression (“continuation”) on the right. I find
|
||||
left from the pending expression ("continuation") on the right. I find
|
||||
these traces beautiful, like a kind of art.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
V('23 18 +')
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
. 23 18 +
|
||||
23 . 18 +
|
||||
23 18 . +
|
||||
41 .
|
||||
• 23 18 +
|
||||
23 • 18 +
|
||||
23 18 • +
|
||||
41 •
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
V('45 30 gcd')
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
. 45 30 gcd
|
||||
45 . 30 gcd
|
||||
45 30 . gcd
|
||||
45 30 . 1 [tuck modulus dup 0 >] loop pop
|
||||
45 30 1 . [tuck modulus dup 0 >] loop pop
|
||||
45 30 1 [tuck modulus dup 0 >] . loop pop
|
||||
45 30 . tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
30 45 30 . modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
30 15 . dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
30 15 15 . 0 > [tuck modulus dup 0 >] loop pop
|
||||
30 15 15 0 . > [tuck modulus dup 0 >] loop pop
|
||||
30 15 True . [tuck modulus dup 0 >] loop pop
|
||||
30 15 True [tuck modulus dup 0 >] . loop pop
|
||||
30 15 . tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 30 15 . modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 0 . dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 0 0 . 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 0 0 0 . > [tuck modulus dup 0 >] loop pop
|
||||
15 0 False . [tuck modulus dup 0 >] loop pop
|
||||
15 0 False [tuck modulus dup 0 >] . loop pop
|
||||
15 0 . pop
|
||||
15 .
|
||||
• 45 30 gcd
|
||||
45 • 30 gcd
|
||||
45 30 • gcd
|
||||
45 30 • 1 [tuck modulus dup 0 >] loop pop
|
||||
45 30 1 • [tuck modulus dup 0 >] loop pop
|
||||
45 30 1 [tuck modulus dup 0 >] • loop pop
|
||||
45 30 • tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
30 45 30 • modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
30 15 • dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
30 15 15 • 0 > [tuck modulus dup 0 >] loop pop
|
||||
30 15 15 0 • > [tuck modulus dup 0 >] loop pop
|
||||
30 15 True • [tuck modulus dup 0 >] loop pop
|
||||
30 15 True [tuck modulus dup 0 >] • loop pop
|
||||
30 15 • tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 30 15 • modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 0 • dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 0 0 • 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 0 0 0 • > [tuck modulus dup 0 >] loop pop
|
||||
15 0 False • [tuck modulus dup 0 >] loop pop
|
||||
15 0 False [tuck modulus dup 0 >] • loop pop
|
||||
15 0 • pop
|
||||
15 •
|
||||
|
||||
|
||||
Here’s a longer trace.
|
||||
Here's a longer trace.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
V('96 27 gcd')
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
. 96 27 gcd
|
||||
96 . 27 gcd
|
||||
96 27 . gcd
|
||||
96 27 . 1 [tuck modulus dup 0 >] loop pop
|
||||
96 27 1 . [tuck modulus dup 0 >] loop pop
|
||||
96 27 1 [tuck modulus dup 0 >] . loop pop
|
||||
96 27 . tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
27 96 27 . modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
27 15 . dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
27 15 15 . 0 > [tuck modulus dup 0 >] loop pop
|
||||
27 15 15 0 . > [tuck modulus dup 0 >] loop pop
|
||||
27 15 True . [tuck modulus dup 0 >] loop pop
|
||||
27 15 True [tuck modulus dup 0 >] . loop pop
|
||||
27 15 . tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 27 15 . modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 12 . dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 12 12 . 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 12 12 0 . > [tuck modulus dup 0 >] loop pop
|
||||
15 12 True . [tuck modulus dup 0 >] loop pop
|
||||
15 12 True [tuck modulus dup 0 >] . loop pop
|
||||
15 12 . tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
12 15 12 . modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
12 3 . dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
12 3 3 . 0 > [tuck modulus dup 0 >] loop pop
|
||||
12 3 3 0 . > [tuck modulus dup 0 >] loop pop
|
||||
12 3 True . [tuck modulus dup 0 >] loop pop
|
||||
12 3 True [tuck modulus dup 0 >] . loop pop
|
||||
12 3 . tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
3 12 3 . modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
3 0 . dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
3 0 0 . 0 > [tuck modulus dup 0 >] loop pop
|
||||
3 0 0 0 . > [tuck modulus dup 0 >] loop pop
|
||||
3 0 False . [tuck modulus dup 0 >] loop pop
|
||||
3 0 False [tuck modulus dup 0 >] . loop pop
|
||||
3 0 . pop
|
||||
3 .
|
||||
|
||||
• 96 27 gcd
|
||||
96 • 27 gcd
|
||||
96 27 • gcd
|
||||
96 27 • 1 [tuck modulus dup 0 >] loop pop
|
||||
96 27 1 • [tuck modulus dup 0 >] loop pop
|
||||
96 27 1 [tuck modulus dup 0 >] • loop pop
|
||||
96 27 • tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
27 96 27 • modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
27 15 • dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
27 15 15 • 0 > [tuck modulus dup 0 >] loop pop
|
||||
27 15 15 0 • > [tuck modulus dup 0 >] loop pop
|
||||
27 15 True • [tuck modulus dup 0 >] loop pop
|
||||
27 15 True [tuck modulus dup 0 >] • loop pop
|
||||
27 15 • tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 27 15 • modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 12 • dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 12 12 • 0 > [tuck modulus dup 0 >] loop pop
|
||||
15 12 12 0 • > [tuck modulus dup 0 >] loop pop
|
||||
15 12 True • [tuck modulus dup 0 >] loop pop
|
||||
15 12 True [tuck modulus dup 0 >] • loop pop
|
||||
15 12 • tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
12 15 12 • modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
12 3 • dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
12 3 3 • 0 > [tuck modulus dup 0 >] loop pop
|
||||
12 3 3 0 • > [tuck modulus dup 0 >] loop pop
|
||||
12 3 True • [tuck modulus dup 0 >] loop pop
|
||||
12 3 True [tuck modulus dup 0 >] • loop pop
|
||||
12 3 • tuck modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
3 12 3 • modulus dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
3 0 • dup 0 > [tuck modulus dup 0 >] loop pop
|
||||
3 0 0 • 0 > [tuck modulus dup 0 >] loop pop
|
||||
3 0 0 0 • > [tuck modulus dup 0 >] loop pop
|
||||
3 0 False • [tuck modulus dup 0 >] loop pop
|
||||
3 0 False [tuck modulus dup 0 >] • loop pop
|
||||
3 0 • pop
|
||||
3 •
|
||||
|
||||
|
|
|
|||
File diff suppressed because it is too large
Load Diff
|
|
@ -425,16 +425,16 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . 1 [dup] 3 unquoted\n",
|
||||
" 1 . [dup] 3 unquoted\n",
|
||||
" 1 [dup] . 3 unquoted\n",
|
||||
" 1 [dup] 3 . unquoted\n",
|
||||
" 1 [dup] 3 . [i] dip\n",
|
||||
"1 [dup] 3 [i] . dip\n",
|
||||
" 1 [dup] . i 3\n",
|
||||
" 1 . dup 3\n",
|
||||
" 1 1 . 3\n",
|
||||
" 1 1 3 . \n"
|
||||
" • 1 [dup] 3 unquoted\n",
|
||||
" 1 • [dup] 3 unquoted\n",
|
||||
" 1 [dup] • 3 unquoted\n",
|
||||
" 1 [dup] 3 • unquoted\n",
|
||||
" 1 [dup] 3 • [i] dip\n",
|
||||
"1 [dup] 3 [i] • dip\n",
|
||||
" 1 [dup] • i 3\n",
|
||||
" 1 • dup 3\n",
|
||||
" 1 1 • 3\n",
|
||||
" 1 1 3 • \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -1697,11 +1697,11 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . 23 ?\n",
|
||||
" 23 . ?\n",
|
||||
" 23 . dup truthy\n",
|
||||
" 23 23 . truthy\n",
|
||||
"23 True . \n"
|
||||
" • 23 ?\n",
|
||||
" 23 • ?\n",
|
||||
" 23 • dup truthy\n",
|
||||
" 23 23 • truthy\n",
|
||||
"23 True • \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -1992,9 +1992,9 @@
|
|||
"program.\n",
|
||||
"::\n",
|
||||
"\n",
|
||||
" ... x [Q] . app1\n",
|
||||
" -----------------------------------\n",
|
||||
" ... [x ...] [Q] . infra first\n",
|
||||
" ... x [Q] . app1\n",
|
||||
" -----------------------------------\n",
|
||||
" ... [x ...] [Q] . infra first\n",
|
||||
"\n",
|
||||
"---- end (app1)\n",
|
||||
"\n",
|
||||
|
|
@ -2055,10 +2055,10 @@
|
|||
"Like app1 with two items.\n",
|
||||
"::\n",
|
||||
"\n",
|
||||
" ... y x [Q] . app2\n",
|
||||
" -----------------------------------\n",
|
||||
" ... [y ...] [Q] . infra first\n",
|
||||
" [x ...] [Q] infra first\n",
|
||||
" ... y x [Q] . app2\n",
|
||||
" -----------------------------------\n",
|
||||
" ... [y ...] [Q] . infra first\n",
|
||||
" [x ...] [Q] infra first\n",
|
||||
"\n",
|
||||
"---- end (app2)\n",
|
||||
"\n",
|
||||
|
|
@ -2273,13 +2273,13 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . 23 [++] dupdip *\n",
|
||||
" 23 . [++] dupdip *\n",
|
||||
"23 [++] . dupdip *\n",
|
||||
" 23 . ++ 23 *\n",
|
||||
" 24 . 23 *\n",
|
||||
" 24 23 . *\n",
|
||||
" 552 . \n"
|
||||
" • 23 [++] dupdip *\n",
|
||||
" 23 • [++] dupdip *\n",
|
||||
"23 [++] • dupdip *\n",
|
||||
" 23 • ++ 23 *\n",
|
||||
" 24 • 23 *\n",
|
||||
" 24 23 • *\n",
|
||||
" 552 • \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -2309,9 +2309,9 @@
|
|||
"General Recursion Combinator.\n",
|
||||
"::\n",
|
||||
"\n",
|
||||
" [if] [then] [rec1] [rec2] genrec\n",
|
||||
" ---------------------------------------------------------------------\n",
|
||||
" [if] [then] [rec1 [[if] [then] [rec1] [rec2] genrec] rec2] ifte\n",
|
||||
" [if] [then] [rec1] [rec2] genrec\n",
|
||||
" ---------------------------------------------------------------------\n",
|
||||
" [if] [then] [rec1 [[if] [then] [rec1] [rec2] genrec] rec2] ifte\n",
|
||||
"\n",
|
||||
"From \"Recursion Theory and Joy\" (j05cmp.html) by Manfred von Thun:\n",
|
||||
"\"The genrec combinator takes four program parameters in addition to\n",
|
||||
|
|
@ -2332,12 +2332,12 @@
|
|||
"For example, given a (general recursive) function 'F':\n",
|
||||
"::\n",
|
||||
"\n",
|
||||
" F == [I] [T] [R1] [R2] genrec\n",
|
||||
" F == [I] [T] [R1] [R2] genrec\n",
|
||||
"\n",
|
||||
"If the [I] if-part fails you must derive R1 and R2 from:\n",
|
||||
"::\n",
|
||||
"\n",
|
||||
" ... R1 [F] R2\n",
|
||||
" ... R1 [F] R2\n",
|
||||
"\n",
|
||||
"Just set the stack arguments in front, and figure out what R1 and R2\n",
|
||||
"have to do to apply the quoted [F] in the proper way. In effect, the\n",
|
||||
|
|
@ -2345,15 +2345,15 @@
|
|||
"the original definition in the else-part:\n",
|
||||
"::\n",
|
||||
"\n",
|
||||
" F == [I] [T] [R1] [R2] genrec\n",
|
||||
" == [I] [T] [R1 [F] R2] ifte\n",
|
||||
" F == [I] [T] [R1] [R2] genrec\n",
|
||||
" == [I] [T] [R1 [F] R2] ifte\n",
|
||||
"\n",
|
||||
"Primitive recursive functions are those where R2 == i.\n",
|
||||
"::\n",
|
||||
"\n",
|
||||
" P == [I] [T] [R] primrec\n",
|
||||
" == [I] [T] [R [P] i] ifte\n",
|
||||
" == [I] [T] [R P] ifte\n",
|
||||
" P == [I] [T] [R] tailrec\n",
|
||||
" == [I] [T] [R [P] i] ifte\n",
|
||||
" == [I] [T] [R P] ifte\n",
|
||||
"\n",
|
||||
"---- end (genrec)\n",
|
||||
"\n",
|
||||
|
|
@ -2400,14 +2400,14 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . 1 2 3 [+ +] i\n",
|
||||
" 1 . 2 3 [+ +] i\n",
|
||||
" 1 2 . 3 [+ +] i\n",
|
||||
" 1 2 3 . [+ +] i\n",
|
||||
"1 2 3 [+ +] . i\n",
|
||||
" 1 2 3 . + +\n",
|
||||
" 1 5 . +\n",
|
||||
" 6 . \n"
|
||||
" • 1 2 3 [+ +] i\n",
|
||||
" 1 • 2 3 [+ +] i\n",
|
||||
" 1 2 • 3 [+ +] i\n",
|
||||
" 1 2 3 • [+ +] i\n",
|
||||
"1 2 3 [+ +] • i\n",
|
||||
" 1 2 3 • + +\n",
|
||||
" 1 5 • +\n",
|
||||
" 6 • \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -2473,17 +2473,17 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . 1 2 3 [4 5 6] [* +] infra\n",
|
||||
" 1 . 2 3 [4 5 6] [* +] infra\n",
|
||||
" 1 2 . 3 [4 5 6] [* +] infra\n",
|
||||
" 1 2 3 . [4 5 6] [* +] infra\n",
|
||||
" 1 2 3 [4 5 6] . [* +] infra\n",
|
||||
"1 2 3 [4 5 6] [* +] . infra\n",
|
||||
" 6 5 4 . * + [3 2 1] swaack\n",
|
||||
" 6 20 . + [3 2 1] swaack\n",
|
||||
" 26 . [3 2 1] swaack\n",
|
||||
" 26 [3 2 1] . swaack\n",
|
||||
" 1 2 3 [26] . \n"
|
||||
" • 1 2 3 [4 5 6] [* +] infra\n",
|
||||
" 1 • 2 3 [4 5 6] [* +] infra\n",
|
||||
" 1 2 • 3 [4 5 6] [* +] infra\n",
|
||||
" 1 2 3 • [4 5 6] [* +] infra\n",
|
||||
" 1 2 3 [4 5 6] • [* +] infra\n",
|
||||
"1 2 3 [4 5 6] [* +] • infra\n",
|
||||
" 6 5 4 • * + [3 2 1] swaack\n",
|
||||
" 6 20 • + [3 2 1] swaack\n",
|
||||
" 26 • [3 2 1] swaack\n",
|
||||
" 26 [3 2 1] • swaack\n",
|
||||
" 1 2 3 [26] • \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -2513,13 +2513,13 @@
|
|||
"Basic loop combinator.\n",
|
||||
"::\n",
|
||||
"\n",
|
||||
" ... True [Q] loop\n",
|
||||
" ... True [Q] loop\n",
|
||||
" -----------------------\n",
|
||||
" ... Q [Q] loop\n",
|
||||
" ... Q [Q] loop\n",
|
||||
"\n",
|
||||
" ... False [Q] loop\n",
|
||||
" ... False [Q] loop\n",
|
||||
" ------------------------\n",
|
||||
" ...\n",
|
||||
" ...\n",
|
||||
"\n",
|
||||
"---- end (loop)\n",
|
||||
"\n",
|
||||
|
|
@ -2540,26 +2540,26 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . 3 dup [1 - dup] loop\n",
|
||||
" 3 . dup [1 - dup] loop\n",
|
||||
" 3 3 . [1 - dup] loop\n",
|
||||
"3 3 [1 - dup] . loop\n",
|
||||
" 3 . 1 - dup [1 - dup] loop\n",
|
||||
" 3 1 . - dup [1 - dup] loop\n",
|
||||
" 2 . dup [1 - dup] loop\n",
|
||||
" 2 2 . [1 - dup] loop\n",
|
||||
"2 2 [1 - dup] . loop\n",
|
||||
" 2 . 1 - dup [1 - dup] loop\n",
|
||||
" 2 1 . - dup [1 - dup] loop\n",
|
||||
" 1 . dup [1 - dup] loop\n",
|
||||
" 1 1 . [1 - dup] loop\n",
|
||||
"1 1 [1 - dup] . loop\n",
|
||||
" 1 . 1 - dup [1 - dup] loop\n",
|
||||
" 1 1 . - dup [1 - dup] loop\n",
|
||||
" 0 . dup [1 - dup] loop\n",
|
||||
" 0 0 . [1 - dup] loop\n",
|
||||
"0 0 [1 - dup] . loop\n",
|
||||
" 0 . \n"
|
||||
" • 3 dup [1 - dup] loop\n",
|
||||
" 3 • dup [1 - dup] loop\n",
|
||||
" 3 3 • [1 - dup] loop\n",
|
||||
"3 3 [1 - dup] • loop\n",
|
||||
" 3 • 1 - dup [1 - dup] loop\n",
|
||||
" 3 1 • - dup [1 - dup] loop\n",
|
||||
" 2 • dup [1 - dup] loop\n",
|
||||
" 2 2 • [1 - dup] loop\n",
|
||||
"2 2 [1 - dup] • loop\n",
|
||||
" 2 • 1 - dup [1 - dup] loop\n",
|
||||
" 2 1 • - dup [1 - dup] loop\n",
|
||||
" 1 • dup [1 - dup] loop\n",
|
||||
" 1 1 • [1 - dup] loop\n",
|
||||
"1 1 [1 - dup] • loop\n",
|
||||
" 1 • 1 - dup [1 - dup] loop\n",
|
||||
" 1 1 • - dup [1 - dup] loop\n",
|
||||
" 0 • dup [1 - dup] loop\n",
|
||||
" 0 0 • [1 - dup] loop\n",
|
||||
"0 0 [1 - dup] • loop\n",
|
||||
" 0 • \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -2706,19 +2706,19 @@
|
|||
"Run a quoted program on each item in a sequence.\n",
|
||||
"::\n",
|
||||
"\n",
|
||||
" ... [] [Q] . step\n",
|
||||
" -----------------------\n",
|
||||
" ... .\n",
|
||||
" ... [] [Q] . step\n",
|
||||
" -----------------------\n",
|
||||
" ... .\n",
|
||||
"\n",
|
||||
"\n",
|
||||
" ... [a] [Q] . step\n",
|
||||
" ------------------------\n",
|
||||
" ... a . Q\n",
|
||||
" ... [a] [Q] . step\n",
|
||||
" ------------------------\n",
|
||||
" ... a . Q\n",
|
||||
"\n",
|
||||
"\n",
|
||||
" ... [a b c] [Q] . step\n",
|
||||
" ... [a b c] [Q] . step\n",
|
||||
" ----------------------------------------\n",
|
||||
" ... a . Q [b c] [Q] step\n",
|
||||
" ... a . Q [b c] [Q] step\n",
|
||||
"\n",
|
||||
"The step combinator executes the quotation on each member of the list\n",
|
||||
"on top of the stack.\n",
|
||||
|
|
@ -2744,23 +2744,23 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . 0 [1 2 3] [+] step\n",
|
||||
" 0 . [1 2 3] [+] step\n",
|
||||
" 0 [1 2 3] . [+] step\n",
|
||||
"0 [1 2 3] [+] . step\n",
|
||||
" 0 1 [+] . i [2 3] [+] step\n",
|
||||
" 0 1 . + [2 3] [+] step\n",
|
||||
" 1 . [2 3] [+] step\n",
|
||||
" 1 [2 3] . [+] step\n",
|
||||
" 1 [2 3] [+] . step\n",
|
||||
" 1 2 [+] . i [3] [+] step\n",
|
||||
" 1 2 . + [3] [+] step\n",
|
||||
" 3 . [3] [+] step\n",
|
||||
" 3 [3] . [+] step\n",
|
||||
" 3 [3] [+] . step\n",
|
||||
" 3 3 [+] . i\n",
|
||||
" 3 3 . +\n",
|
||||
" 6 . \n"
|
||||
" • 0 [1 2 3] [+] step\n",
|
||||
" 0 • [1 2 3] [+] step\n",
|
||||
" 0 [1 2 3] • [+] step\n",
|
||||
"0 [1 2 3] [+] • step\n",
|
||||
" 0 1 [+] • i [2 3] [+] step\n",
|
||||
" 0 1 • + [2 3] [+] step\n",
|
||||
" 1 • [2 3] [+] step\n",
|
||||
" 1 [2 3] • [+] step\n",
|
||||
" 1 [2 3] [+] • step\n",
|
||||
" 1 2 [+] • i [3] [+] step\n",
|
||||
" 1 2 • + [3] [+] step\n",
|
||||
" 3 • [3] [+] step\n",
|
||||
" 3 [3] • [+] step\n",
|
||||
" 3 [3] [+] • step\n",
|
||||
" 3 3 [+] • i\n",
|
||||
" 3 3 • +\n",
|
||||
" 6 • \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -2784,18 +2784,18 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . 3 2 1 2 [+] times\n",
|
||||
" 3 . 2 1 2 [+] times\n",
|
||||
" 3 2 . 1 2 [+] times\n",
|
||||
" 3 2 1 . 2 [+] times\n",
|
||||
" 3 2 1 2 . [+] times\n",
|
||||
"3 2 1 2 [+] . times\n",
|
||||
" 3 2 1 . + 1 [+] times\n",
|
||||
" 3 3 . 1 [+] times\n",
|
||||
" 3 3 1 . [+] times\n",
|
||||
" 3 3 1 [+] . times\n",
|
||||
" 3 3 . +\n",
|
||||
" 6 . \n"
|
||||
" • 3 2 1 2 [+] times\n",
|
||||
" 3 • 2 1 2 [+] times\n",
|
||||
" 3 2 • 1 2 [+] times\n",
|
||||
" 3 2 1 • 2 [+] times\n",
|
||||
" 3 2 1 2 • [+] times\n",
|
||||
"3 2 1 2 [+] • times\n",
|
||||
" 3 2 1 • + 1 [+] times\n",
|
||||
" 3 3 • 1 [+] times\n",
|
||||
" 3 3 1 • [+] times\n",
|
||||
" 3 3 1 [+] • times\n",
|
||||
" 3 3 • +\n",
|
||||
" 6 • \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -2848,14 +2848,14 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . 1 2 [3] [4] b\n",
|
||||
" 1 . 2 [3] [4] b\n",
|
||||
" 1 2 . [3] [4] b\n",
|
||||
" 1 2 [3] . [4] b\n",
|
||||
"1 2 [3] [4] . b\n",
|
||||
" 1 2 . 3 4\n",
|
||||
" 1 2 3 . 4\n",
|
||||
" 1 2 3 4 . \n"
|
||||
" • 1 2 [3] [4] b\n",
|
||||
" 1 • 2 [3] [4] b\n",
|
||||
" 1 2 • [3] [4] b\n",
|
||||
" 1 2 [3] • [4] b\n",
|
||||
"1 2 [3] [4] • b\n",
|
||||
" 1 2 • 3 4\n",
|
||||
" 1 2 3 • 4\n",
|
||||
" 1 2 3 4 • \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -2934,16 +2934,16 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . 1 [2] [i 3] x\n",
|
||||
" 1 . [2] [i 3] x\n",
|
||||
" 1 [2] . [i 3] x\n",
|
||||
"1 [2] [i 3] . x\n",
|
||||
"1 [2] [i 3] . i 3\n",
|
||||
" 1 [2] . i 3 3\n",
|
||||
" 1 . 2 3 3\n",
|
||||
" 1 2 . 3 3\n",
|
||||
" 1 2 3 . 3\n",
|
||||
" 1 2 3 3 . \n"
|
||||
" • 1 [2] [i 3] x\n",
|
||||
" 1 • [2] [i 3] x\n",
|
||||
" 1 [2] • [i 3] x\n",
|
||||
"1 [2] [i 3] • x\n",
|
||||
"1 [2] [i 3] • i 3\n",
|
||||
" 1 [2] • i 3 3\n",
|
||||
" 1 • 2 3 3\n",
|
||||
" 1 2 • 3 3\n",
|
||||
" 1 2 3 • 3\n",
|
||||
" 1 2 3 3 • \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -3037,14 +3037,14 @@
|
|||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 2
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython2",
|
||||
"version": "2.7.12"
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.8.3"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
|
|
|||
|
|
@ -184,16 +184,16 @@ J('1 [2] 3 unquoted')
|
|||
V('1 [dup] 3 unquoted') # Unquoting evaluates. Be aware.
|
||||
```
|
||||
|
||||
. 1 [dup] 3 unquoted
|
||||
1 . [dup] 3 unquoted
|
||||
1 [dup] . 3 unquoted
|
||||
1 [dup] 3 . unquoted
|
||||
1 [dup] 3 . [i] dip
|
||||
1 [dup] 3 [i] . dip
|
||||
1 [dup] . i 3
|
||||
1 . dup 3
|
||||
1 1 . 3
|
||||
1 1 3 .
|
||||
• 1 [dup] 3 unquoted
|
||||
1 • [dup] 3 unquoted
|
||||
1 [dup] • 3 unquoted
|
||||
1 [dup] 3 • unquoted
|
||||
1 [dup] 3 • [i] dip
|
||||
1 [dup] 3 [i] • dip
|
||||
1 [dup] • i 3
|
||||
1 • dup 3
|
||||
1 1 • 3
|
||||
1 1 3 •
|
||||
|
||||
|
||||
# List words
|
||||
|
|
@ -730,11 +730,11 @@ J('0 truthy')
|
|||
V('23 ?')
|
||||
```
|
||||
|
||||
. 23 ?
|
||||
23 . ?
|
||||
23 . dup truthy
|
||||
23 23 . truthy
|
||||
23 True .
|
||||
• 23 ?
|
||||
23 • ?
|
||||
23 • dup truthy
|
||||
23 23 • truthy
|
||||
23 True •
|
||||
|
||||
|
||||
|
||||
|
|
@ -872,9 +872,9 @@ J('[app1] help')
|
|||
program.
|
||||
::
|
||||
|
||||
... x [Q] . app1
|
||||
-----------------------------------
|
||||
... [x ...] [Q] . infra first
|
||||
... x [Q] . app1
|
||||
-----------------------------------
|
||||
... [x ...] [Q] . infra first
|
||||
|
||||
---- end (app1)
|
||||
|
||||
|
|
@ -908,10 +908,10 @@ J('[app2] help')
|
|||
Like app1 with two items.
|
||||
::
|
||||
|
||||
... y x [Q] . app2
|
||||
-----------------------------------
|
||||
... [y ...] [Q] . infra first
|
||||
[x ...] [Q] infra first
|
||||
... y x [Q] . app2
|
||||
-----------------------------------
|
||||
... [y ...] [Q] . infra first
|
||||
[x ...] [Q] infra first
|
||||
|
||||
---- end (app2)
|
||||
|
||||
|
|
@ -1020,13 +1020,13 @@ Expects a quoted program `[Q]` on the stack and some item under it, `dup` the it
|
|||
V('23 [++] dupdip *') # N(N + 1)
|
||||
```
|
||||
|
||||
. 23 [++] dupdip *
|
||||
23 . [++] dupdip *
|
||||
23 [++] . dupdip *
|
||||
23 . ++ 23 *
|
||||
24 . 23 *
|
||||
24 23 . *
|
||||
552 .
|
||||
• 23 [++] dupdip *
|
||||
23 • [++] dupdip *
|
||||
23 [++] • dupdip *
|
||||
23 • ++ 23 *
|
||||
24 • 23 *
|
||||
24 23 • *
|
||||
552 •
|
||||
|
||||
|
||||
### `genrec` `primrec`
|
||||
|
|
@ -1042,9 +1042,9 @@ J('[genrec] help')
|
|||
General Recursion Combinator.
|
||||
::
|
||||
|
||||
[if] [then] [rec1] [rec2] genrec
|
||||
---------------------------------------------------------------------
|
||||
[if] [then] [rec1 [[if] [then] [rec1] [rec2] genrec] rec2] ifte
|
||||
[if] [then] [rec1] [rec2] genrec
|
||||
---------------------------------------------------------------------
|
||||
[if] [then] [rec1 [[if] [then] [rec1] [rec2] genrec] rec2] ifte
|
||||
|
||||
From "Recursion Theory and Joy" (j05cmp.html) by Manfred von Thun:
|
||||
"The genrec combinator takes four program parameters in addition to
|
||||
|
|
@ -1065,12 +1065,12 @@ J('[genrec] help')
|
|||
For example, given a (general recursive) function 'F':
|
||||
::
|
||||
|
||||
F == [I] [T] [R1] [R2] genrec
|
||||
F == [I] [T] [R1] [R2] genrec
|
||||
|
||||
If the [I] if-part fails you must derive R1 and R2 from:
|
||||
::
|
||||
|
||||
... R1 [F] R2
|
||||
... R1 [F] R2
|
||||
|
||||
Just set the stack arguments in front, and figure out what R1 and R2
|
||||
have to do to apply the quoted [F] in the proper way. In effect, the
|
||||
|
|
@ -1078,15 +1078,15 @@ J('[genrec] help')
|
|||
the original definition in the else-part:
|
||||
::
|
||||
|
||||
F == [I] [T] [R1] [R2] genrec
|
||||
== [I] [T] [R1 [F] R2] ifte
|
||||
F == [I] [T] [R1] [R2] genrec
|
||||
== [I] [T] [R1 [F] R2] ifte
|
||||
|
||||
Primitive recursive functions are those where R2 == i.
|
||||
::
|
||||
|
||||
P == [I] [T] [R] primrec
|
||||
== [I] [T] [R [P] i] ifte
|
||||
== [I] [T] [R P] ifte
|
||||
P == [I] [T] [R] tailrec
|
||||
== [I] [T] [R [P] i] ifte
|
||||
== [I] [T] [R P] ifte
|
||||
|
||||
---- end (genrec)
|
||||
|
||||
|
|
@ -1108,14 +1108,14 @@ J('3 [1 <=] [] [dup --] [i *] genrec')
|
|||
V('1 2 3 [+ +] i')
|
||||
```
|
||||
|
||||
. 1 2 3 [+ +] i
|
||||
1 . 2 3 [+ +] i
|
||||
1 2 . 3 [+ +] i
|
||||
1 2 3 . [+ +] i
|
||||
1 2 3 [+ +] . i
|
||||
1 2 3 . + +
|
||||
1 5 . +
|
||||
6 .
|
||||
• 1 2 3 [+ +] i
|
||||
1 • 2 3 [+ +] i
|
||||
1 2 • 3 [+ +] i
|
||||
1 2 3 • [+ +] i
|
||||
1 2 3 [+ +] • i
|
||||
1 2 3 • + +
|
||||
1 5 • +
|
||||
6 •
|
||||
|
||||
|
||||
### `ifte`
|
||||
|
|
@ -1144,17 +1144,17 @@ J('1 2 [0] [+] [*] ifte')
|
|||
V('1 2 3 [4 5 6] [* +] infra')
|
||||
```
|
||||
|
||||
. 1 2 3 [4 5 6] [* +] infra
|
||||
1 . 2 3 [4 5 6] [* +] infra
|
||||
1 2 . 3 [4 5 6] [* +] infra
|
||||
1 2 3 . [4 5 6] [* +] infra
|
||||
1 2 3 [4 5 6] . [* +] infra
|
||||
1 2 3 [4 5 6] [* +] . infra
|
||||
6 5 4 . * + [3 2 1] swaack
|
||||
6 20 . + [3 2 1] swaack
|
||||
26 . [3 2 1] swaack
|
||||
26 [3 2 1] . swaack
|
||||
1 2 3 [26] .
|
||||
• 1 2 3 [4 5 6] [* +] infra
|
||||
1 • 2 3 [4 5 6] [* +] infra
|
||||
1 2 • 3 [4 5 6] [* +] infra
|
||||
1 2 3 • [4 5 6] [* +] infra
|
||||
1 2 3 [4 5 6] • [* +] infra
|
||||
1 2 3 [4 5 6] [* +] • infra
|
||||
6 5 4 • * + [3 2 1] swaack
|
||||
6 20 • + [3 2 1] swaack
|
||||
26 • [3 2 1] swaack
|
||||
26 [3 2 1] • swaack
|
||||
1 2 3 [26] •
|
||||
|
||||
|
||||
### `loop`
|
||||
|
|
@ -1170,13 +1170,13 @@ J('[loop] help')
|
|||
Basic loop combinator.
|
||||
::
|
||||
|
||||
... True [Q] loop
|
||||
... True [Q] loop
|
||||
-----------------------
|
||||
... Q [Q] loop
|
||||
... Q [Q] loop
|
||||
|
||||
... False [Q] loop
|
||||
... False [Q] loop
|
||||
------------------------
|
||||
...
|
||||
...
|
||||
|
||||
---- end (loop)
|
||||
|
||||
|
|
@ -1188,26 +1188,26 @@ J('[loop] help')
|
|||
V('3 dup [1 - dup] loop')
|
||||
```
|
||||
|
||||
. 3 dup [1 - dup] loop
|
||||
3 . dup [1 - dup] loop
|
||||
3 3 . [1 - dup] loop
|
||||
3 3 [1 - dup] . loop
|
||||
3 . 1 - dup [1 - dup] loop
|
||||
3 1 . - dup [1 - dup] loop
|
||||
2 . dup [1 - dup] loop
|
||||
2 2 . [1 - dup] loop
|
||||
2 2 [1 - dup] . loop
|
||||
2 . 1 - dup [1 - dup] loop
|
||||
2 1 . - dup [1 - dup] loop
|
||||
1 . dup [1 - dup] loop
|
||||
1 1 . [1 - dup] loop
|
||||
1 1 [1 - dup] . loop
|
||||
1 . 1 - dup [1 - dup] loop
|
||||
1 1 . - dup [1 - dup] loop
|
||||
0 . dup [1 - dup] loop
|
||||
0 0 . [1 - dup] loop
|
||||
0 0 [1 - dup] . loop
|
||||
0 .
|
||||
• 3 dup [1 - dup] loop
|
||||
3 • dup [1 - dup] loop
|
||||
3 3 • [1 - dup] loop
|
||||
3 3 [1 - dup] • loop
|
||||
3 • 1 - dup [1 - dup] loop
|
||||
3 1 • - dup [1 - dup] loop
|
||||
2 • dup [1 - dup] loop
|
||||
2 2 • [1 - dup] loop
|
||||
2 2 [1 - dup] • loop
|
||||
2 • 1 - dup [1 - dup] loop
|
||||
2 1 • - dup [1 - dup] loop
|
||||
1 • dup [1 - dup] loop
|
||||
1 1 • [1 - dup] loop
|
||||
1 1 [1 - dup] • loop
|
||||
1 • 1 - dup [1 - dup] loop
|
||||
1 1 • - dup [1 - dup] loop
|
||||
0 • dup [1 - dup] loop
|
||||
0 0 • [1 - dup] loop
|
||||
0 0 [1 - dup] • loop
|
||||
0 •
|
||||
|
||||
|
||||
### `map` `pam`
|
||||
|
|
@ -1276,19 +1276,19 @@ J('[step] help')
|
|||
Run a quoted program on each item in a sequence.
|
||||
::
|
||||
|
||||
... [] [Q] . step
|
||||
-----------------------
|
||||
... .
|
||||
... [] [Q] . step
|
||||
-----------------------
|
||||
... .
|
||||
|
||||
|
||||
... [a] [Q] . step
|
||||
------------------------
|
||||
... a . Q
|
||||
... [a] [Q] . step
|
||||
------------------------
|
||||
... a . Q
|
||||
|
||||
|
||||
... [a b c] [Q] . step
|
||||
... [a b c] [Q] . step
|
||||
----------------------------------------
|
||||
... a . Q [b c] [Q] step
|
||||
... a . Q [b c] [Q] step
|
||||
|
||||
The step combinator executes the quotation on each member of the list
|
||||
on top of the stack.
|
||||
|
|
@ -1303,23 +1303,23 @@ J('[step] help')
|
|||
V('0 [1 2 3] [+] step')
|
||||
```
|
||||
|
||||
. 0 [1 2 3] [+] step
|
||||
0 . [1 2 3] [+] step
|
||||
0 [1 2 3] . [+] step
|
||||
0 [1 2 3] [+] . step
|
||||
0 1 [+] . i [2 3] [+] step
|
||||
0 1 . + [2 3] [+] step
|
||||
1 . [2 3] [+] step
|
||||
1 [2 3] . [+] step
|
||||
1 [2 3] [+] . step
|
||||
1 2 [+] . i [3] [+] step
|
||||
1 2 . + [3] [+] step
|
||||
3 . [3] [+] step
|
||||
3 [3] . [+] step
|
||||
3 [3] [+] . step
|
||||
3 3 [+] . i
|
||||
3 3 . +
|
||||
6 .
|
||||
• 0 [1 2 3] [+] step
|
||||
0 • [1 2 3] [+] step
|
||||
0 [1 2 3] • [+] step
|
||||
0 [1 2 3] [+] • step
|
||||
0 1 [+] • i [2 3] [+] step
|
||||
0 1 • + [2 3] [+] step
|
||||
1 • [2 3] [+] step
|
||||
1 [2 3] • [+] step
|
||||
1 [2 3] [+] • step
|
||||
1 2 [+] • i [3] [+] step
|
||||
1 2 • + [3] [+] step
|
||||
3 • [3] [+] step
|
||||
3 [3] • [+] step
|
||||
3 [3] [+] • step
|
||||
3 3 [+] • i
|
||||
3 3 • +
|
||||
6 •
|
||||
|
||||
|
||||
### `times`
|
||||
|
|
@ -1329,18 +1329,18 @@ V('0 [1 2 3] [+] step')
|
|||
V('3 2 1 2 [+] times')
|
||||
```
|
||||
|
||||
. 3 2 1 2 [+] times
|
||||
3 . 2 1 2 [+] times
|
||||
3 2 . 1 2 [+] times
|
||||
3 2 1 . 2 [+] times
|
||||
3 2 1 2 . [+] times
|
||||
3 2 1 2 [+] . times
|
||||
3 2 1 . + 1 [+] times
|
||||
3 3 . 1 [+] times
|
||||
3 3 1 . [+] times
|
||||
3 3 1 [+] . times
|
||||
3 3 . +
|
||||
6 .
|
||||
• 3 2 1 2 [+] times
|
||||
3 • 2 1 2 [+] times
|
||||
3 2 • 1 2 [+] times
|
||||
3 2 1 • 2 [+] times
|
||||
3 2 1 2 • [+] times
|
||||
3 2 1 2 [+] • times
|
||||
3 2 1 • + 1 [+] times
|
||||
3 3 • 1 [+] times
|
||||
3 3 1 • [+] times
|
||||
3 3 1 [+] • times
|
||||
3 3 • +
|
||||
6 •
|
||||
|
||||
|
||||
### `b`
|
||||
|
|
@ -1370,14 +1370,14 @@ J('[b] help')
|
|||
V('1 2 [3] [4] b')
|
||||
```
|
||||
|
||||
. 1 2 [3] [4] b
|
||||
1 . 2 [3] [4] b
|
||||
1 2 . [3] [4] b
|
||||
1 2 [3] . [4] b
|
||||
1 2 [3] [4] . b
|
||||
1 2 . 3 4
|
||||
1 2 3 . 4
|
||||
1 2 3 4 .
|
||||
• 1 2 [3] [4] b
|
||||
1 • 2 [3] [4] b
|
||||
1 2 • [3] [4] b
|
||||
1 2 [3] • [4] b
|
||||
1 2 [3] [4] • b
|
||||
1 2 • 3 4
|
||||
1 2 3 • 4
|
||||
1 2 3 4 •
|
||||
|
||||
|
||||
### `while`
|
||||
|
|
@ -1419,16 +1419,16 @@ J('[x] help')
|
|||
V('1 [2] [i 3] x') # Kind of a pointless example.
|
||||
```
|
||||
|
||||
. 1 [2] [i 3] x
|
||||
1 . [2] [i 3] x
|
||||
1 [2] . [i 3] x
|
||||
1 [2] [i 3] . x
|
||||
1 [2] [i 3] . i 3
|
||||
1 [2] . i 3 3
|
||||
1 . 2 3 3
|
||||
1 2 . 3 3
|
||||
1 2 3 . 3
|
||||
1 2 3 3 .
|
||||
• 1 [2] [i 3] x
|
||||
1 • [2] [i 3] x
|
||||
1 [2] • [i 3] x
|
||||
1 [2] [i 3] • x
|
||||
1 [2] [i 3] • i 3
|
||||
1 [2] • i 3 3
|
||||
1 • 2 3 3
|
||||
1 2 • 3 3
|
||||
1 2 3 • 3
|
||||
1 2 3 3 •
|
||||
|
||||
|
||||
# `void`
|
||||
|
|
|
|||
File diff suppressed because it is too large
Load Diff
|
|
@ -13090,7 +13090,7 @@ Find the sum of all the multiples of 3 or 5 below 1000.</code></pre>
|
|||
<div class="prompt input_prompt">In [1]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13111,7 +13111,7 @@ Find the sum of all the multiples of 3 or 5 below 1000.</code></pre>
|
|||
<div class="prompt input_prompt">In [2]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'P == [3 % not] dupdip 5 % not or'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'P [3 % not] dupdip 5 % not or'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13124,7 +13124,7 @@ Find the sum of all the multiples of 3 or 5 below 1000.</code></pre>
|
|||
<div class="prompt input_prompt">In [3]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'80 P'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'80 P'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13141,19 +13141,19 @@ Find the sum of all the multiples of 3 or 5 below 1000.</code></pre>
|
|||
|
||||
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre> . 80 P
|
||||
80 . P
|
||||
80 . [3 % not] dupdip 5 % not or
|
||||
80 [3 % not] . dupdip 5 % not or
|
||||
80 . 3 % not 80 5 % not or
|
||||
80 3 . % not 80 5 % not or
|
||||
2 . not 80 5 % not or
|
||||
False . 80 5 % not or
|
||||
False 80 . 5 % not or
|
||||
False 80 5 . % not or
|
||||
False 0 . not or
|
||||
False True . or
|
||||
True .
|
||||
<pre> • 80 P
|
||||
80 • P
|
||||
80 • [3 % not] dupdip 5 % not or
|
||||
80 [3 % not] • dupdip 5 % not or
|
||||
80 • 3 % not 80 5 % not or
|
||||
80 3 • % not 80 5 % not or
|
||||
2 • not 80 5 % not or
|
||||
False • 80 5 % not or
|
||||
False 80 • 5 % not or
|
||||
False 80 5 • % not or
|
||||
False 0 • not or
|
||||
False True • or
|
||||
True •
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
|
|
@ -13219,7 +13219,7 @@ counter to the running sum. This function will do that:</p>
|
|||
<div class="prompt input_prompt">In [4]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'PE1.1 == + [+] dupdip'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'PE1.1 + [+] dupdip'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13232,7 +13232,7 @@ counter to the running sum. This function will do that:</p>
|
|||
<div class="prompt input_prompt">In [5]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'0 0 3 PE1.1'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'0 0 3 PE1.1'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13249,16 +13249,16 @@ counter to the running sum. This function will do that:</p>
|
|||
|
||||
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre> . 0 0 3 PE1.1
|
||||
0 . 0 3 PE1.1
|
||||
0 0 . 3 PE1.1
|
||||
0 0 3 . PE1.1
|
||||
0 0 3 . + [+] dupdip
|
||||
0 3 . [+] dupdip
|
||||
0 3 [+] . dupdip
|
||||
0 3 . + 3
|
||||
3 . 3
|
||||
3 3 .
|
||||
<pre> • 0 0 3 PE1.1
|
||||
0 • 0 3 PE1.1
|
||||
0 0 • 3 PE1.1
|
||||
0 0 3 • PE1.1
|
||||
0 0 3 • + [+] dupdip
|
||||
0 3 • [+] dupdip
|
||||
0 3 [+] • dupdip
|
||||
0 3 • + 3
|
||||
3 • 3
|
||||
3 3 •
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
|
|
@ -13272,7 +13272,7 @@ counter to the running sum. This function will do that:</p>
|
|||
<div class="prompt input_prompt">In [6]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'0 0 [3 2 1 3 1 2 3] [PE1.1] step'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'0 0 [3 2 1 3 1 2 3] [PE1.1] step'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13289,79 +13289,79 @@ counter to the running sum. This function will do that:</p>
|
|||
|
||||
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre> . 0 0 [3 2 1 3 1 2 3] [PE1.1] step
|
||||
0 . 0 [3 2 1 3 1 2 3] [PE1.1] step
|
||||
0 0 . [3 2 1 3 1 2 3] [PE1.1] step
|
||||
0 0 [3 2 1 3 1 2 3] . [PE1.1] step
|
||||
0 0 [3 2 1 3 1 2 3] [PE1.1] . step
|
||||
0 0 3 [PE1.1] . i [2 1 3 1 2 3] [PE1.1] step
|
||||
0 0 3 . PE1.1 [2 1 3 1 2 3] [PE1.1] step
|
||||
0 0 3 . + [+] dupdip [2 1 3 1 2 3] [PE1.1] step
|
||||
0 3 . [+] dupdip [2 1 3 1 2 3] [PE1.1] step
|
||||
0 3 [+] . dupdip [2 1 3 1 2 3] [PE1.1] step
|
||||
0 3 . + 3 [2 1 3 1 2 3] [PE1.1] step
|
||||
3 . 3 [2 1 3 1 2 3] [PE1.1] step
|
||||
3 3 . [2 1 3 1 2 3] [PE1.1] step
|
||||
3 3 [2 1 3 1 2 3] . [PE1.1] step
|
||||
3 3 [2 1 3 1 2 3] [PE1.1] . step
|
||||
3 3 2 [PE1.1] . i [1 3 1 2 3] [PE1.1] step
|
||||
3 3 2 . PE1.1 [1 3 1 2 3] [PE1.1] step
|
||||
3 3 2 . + [+] dupdip [1 3 1 2 3] [PE1.1] step
|
||||
3 5 . [+] dupdip [1 3 1 2 3] [PE1.1] step
|
||||
3 5 [+] . dupdip [1 3 1 2 3] [PE1.1] step
|
||||
3 5 . + 5 [1 3 1 2 3] [PE1.1] step
|
||||
8 . 5 [1 3 1 2 3] [PE1.1] step
|
||||
8 5 . [1 3 1 2 3] [PE1.1] step
|
||||
8 5 [1 3 1 2 3] . [PE1.1] step
|
||||
8 5 [1 3 1 2 3] [PE1.1] . step
|
||||
8 5 1 [PE1.1] . i [3 1 2 3] [PE1.1] step
|
||||
8 5 1 . PE1.1 [3 1 2 3] [PE1.1] step
|
||||
8 5 1 . + [+] dupdip [3 1 2 3] [PE1.1] step
|
||||
8 6 . [+] dupdip [3 1 2 3] [PE1.1] step
|
||||
8 6 [+] . dupdip [3 1 2 3] [PE1.1] step
|
||||
8 6 . + 6 [3 1 2 3] [PE1.1] step
|
||||
14 . 6 [3 1 2 3] [PE1.1] step
|
||||
14 6 . [3 1 2 3] [PE1.1] step
|
||||
14 6 [3 1 2 3] . [PE1.1] step
|
||||
14 6 [3 1 2 3] [PE1.1] . step
|
||||
14 6 3 [PE1.1] . i [1 2 3] [PE1.1] step
|
||||
14 6 3 . PE1.1 [1 2 3] [PE1.1] step
|
||||
14 6 3 . + [+] dupdip [1 2 3] [PE1.1] step
|
||||
14 9 . [+] dupdip [1 2 3] [PE1.1] step
|
||||
14 9 [+] . dupdip [1 2 3] [PE1.1] step
|
||||
14 9 . + 9 [1 2 3] [PE1.1] step
|
||||
23 . 9 [1 2 3] [PE1.1] step
|
||||
23 9 . [1 2 3] [PE1.1] step
|
||||
23 9 [1 2 3] . [PE1.1] step
|
||||
23 9 [1 2 3] [PE1.1] . step
|
||||
23 9 1 [PE1.1] . i [2 3] [PE1.1] step
|
||||
23 9 1 . PE1.1 [2 3] [PE1.1] step
|
||||
23 9 1 . + [+] dupdip [2 3] [PE1.1] step
|
||||
23 10 . [+] dupdip [2 3] [PE1.1] step
|
||||
23 10 [+] . dupdip [2 3] [PE1.1] step
|
||||
23 10 . + 10 [2 3] [PE1.1] step
|
||||
33 . 10 [2 3] [PE1.1] step
|
||||
33 10 . [2 3] [PE1.1] step
|
||||
33 10 [2 3] . [PE1.1] step
|
||||
33 10 [2 3] [PE1.1] . step
|
||||
33 10 2 [PE1.1] . i [3] [PE1.1] step
|
||||
33 10 2 . PE1.1 [3] [PE1.1] step
|
||||
33 10 2 . + [+] dupdip [3] [PE1.1] step
|
||||
33 12 . [+] dupdip [3] [PE1.1] step
|
||||
33 12 [+] . dupdip [3] [PE1.1] step
|
||||
33 12 . + 12 [3] [PE1.1] step
|
||||
45 . 12 [3] [PE1.1] step
|
||||
45 12 . [3] [PE1.1] step
|
||||
45 12 [3] . [PE1.1] step
|
||||
45 12 [3] [PE1.1] . step
|
||||
45 12 3 [PE1.1] . i
|
||||
45 12 3 . PE1.1
|
||||
45 12 3 . + [+] dupdip
|
||||
45 15 . [+] dupdip
|
||||
45 15 [+] . dupdip
|
||||
45 15 . + 15
|
||||
60 . 15
|
||||
60 15 .
|
||||
<pre> • 0 0 [3 2 1 3 1 2 3] [PE1.1] step
|
||||
0 • 0 [3 2 1 3 1 2 3] [PE1.1] step
|
||||
0 0 • [3 2 1 3 1 2 3] [PE1.1] step
|
||||
0 0 [3 2 1 3 1 2 3] • [PE1.1] step
|
||||
0 0 [3 2 1 3 1 2 3] [PE1.1] • step
|
||||
0 0 3 [PE1.1] • i [2 1 3 1 2 3] [PE1.1] step
|
||||
0 0 3 • PE1.1 [2 1 3 1 2 3] [PE1.1] step
|
||||
0 0 3 • + [+] dupdip [2 1 3 1 2 3] [PE1.1] step
|
||||
0 3 • [+] dupdip [2 1 3 1 2 3] [PE1.1] step
|
||||
0 3 [+] • dupdip [2 1 3 1 2 3] [PE1.1] step
|
||||
0 3 • + 3 [2 1 3 1 2 3] [PE1.1] step
|
||||
3 • 3 [2 1 3 1 2 3] [PE1.1] step
|
||||
3 3 • [2 1 3 1 2 3] [PE1.1] step
|
||||
3 3 [2 1 3 1 2 3] • [PE1.1] step
|
||||
3 3 [2 1 3 1 2 3] [PE1.1] • step
|
||||
3 3 2 [PE1.1] • i [1 3 1 2 3] [PE1.1] step
|
||||
3 3 2 • PE1.1 [1 3 1 2 3] [PE1.1] step
|
||||
3 3 2 • + [+] dupdip [1 3 1 2 3] [PE1.1] step
|
||||
3 5 • [+] dupdip [1 3 1 2 3] [PE1.1] step
|
||||
3 5 [+] • dupdip [1 3 1 2 3] [PE1.1] step
|
||||
3 5 • + 5 [1 3 1 2 3] [PE1.1] step
|
||||
8 • 5 [1 3 1 2 3] [PE1.1] step
|
||||
8 5 • [1 3 1 2 3] [PE1.1] step
|
||||
8 5 [1 3 1 2 3] • [PE1.1] step
|
||||
8 5 [1 3 1 2 3] [PE1.1] • step
|
||||
8 5 1 [PE1.1] • i [3 1 2 3] [PE1.1] step
|
||||
8 5 1 • PE1.1 [3 1 2 3] [PE1.1] step
|
||||
8 5 1 • + [+] dupdip [3 1 2 3] [PE1.1] step
|
||||
8 6 • [+] dupdip [3 1 2 3] [PE1.1] step
|
||||
8 6 [+] • dupdip [3 1 2 3] [PE1.1] step
|
||||
8 6 • + 6 [3 1 2 3] [PE1.1] step
|
||||
14 • 6 [3 1 2 3] [PE1.1] step
|
||||
14 6 • [3 1 2 3] [PE1.1] step
|
||||
14 6 [3 1 2 3] • [PE1.1] step
|
||||
14 6 [3 1 2 3] [PE1.1] • step
|
||||
14 6 3 [PE1.1] • i [1 2 3] [PE1.1] step
|
||||
14 6 3 • PE1.1 [1 2 3] [PE1.1] step
|
||||
14 6 3 • + [+] dupdip [1 2 3] [PE1.1] step
|
||||
14 9 • [+] dupdip [1 2 3] [PE1.1] step
|
||||
14 9 [+] • dupdip [1 2 3] [PE1.1] step
|
||||
14 9 • + 9 [1 2 3] [PE1.1] step
|
||||
23 • 9 [1 2 3] [PE1.1] step
|
||||
23 9 • [1 2 3] [PE1.1] step
|
||||
23 9 [1 2 3] • [PE1.1] step
|
||||
23 9 [1 2 3] [PE1.1] • step
|
||||
23 9 1 [PE1.1] • i [2 3] [PE1.1] step
|
||||
23 9 1 • PE1.1 [2 3] [PE1.1] step
|
||||
23 9 1 • + [+] dupdip [2 3] [PE1.1] step
|
||||
23 10 • [+] dupdip [2 3] [PE1.1] step
|
||||
23 10 [+] • dupdip [2 3] [PE1.1] step
|
||||
23 10 • + 10 [2 3] [PE1.1] step
|
||||
33 • 10 [2 3] [PE1.1] step
|
||||
33 10 • [2 3] [PE1.1] step
|
||||
33 10 [2 3] • [PE1.1] step
|
||||
33 10 [2 3] [PE1.1] • step
|
||||
33 10 2 [PE1.1] • i [3] [PE1.1] step
|
||||
33 10 2 • PE1.1 [3] [PE1.1] step
|
||||
33 10 2 • + [+] dupdip [3] [PE1.1] step
|
||||
33 12 • [+] dupdip [3] [PE1.1] step
|
||||
33 12 [+] • dupdip [3] [PE1.1] step
|
||||
33 12 • + 12 [3] [PE1.1] step
|
||||
45 • 12 [3] [PE1.1] step
|
||||
45 12 • [3] [PE1.1] step
|
||||
45 12 [3] • [PE1.1] step
|
||||
45 12 [3] [PE1.1] • step
|
||||
45 12 3 [PE1.1] • i
|
||||
45 12 3 • PE1.1
|
||||
45 12 3 • + [+] dupdip
|
||||
45 15 • [+] dupdip
|
||||
45 15 [+] • dupdip
|
||||
45 15 • + 15
|
||||
60 • 15
|
||||
60 15 •
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
|
|
@ -13383,7 +13383,7 @@ counter to the running sum. This function will do that:</p>
|
|||
<div class="prompt input_prompt">In [7]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="mi">1000</span> <span class="o">/</span> <span class="mi">15</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="mi">1000</span> <span class="o">/</span> <span class="mi">15</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13402,7 +13402,7 @@ counter to the running sum. This function will do that:</p>
|
|||
|
||||
|
||||
<div class="output_text output_subarea output_execute_result">
|
||||
<pre>66</pre>
|
||||
<pre>66.66666666666667</pre>
|
||||
</div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13416,7 +13416,7 @@ counter to the running sum. This function will do that:</p>
|
|||
<div class="prompt input_prompt">In [8]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="mi">66</span> <span class="o">*</span> <span class="mi">15</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="mi">66</span> <span class="o">*</span> <span class="mi">15</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13449,7 +13449,7 @@ counter to the running sum. This function will do that:</p>
|
|||
<div class="prompt input_prompt">In [9]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="mi">1000</span> <span class="o">-</span> <span class="mi">990</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="mi">1000</span> <span class="o">-</span> <span class="mi">990</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13490,7 +13490,7 @@ counter to the running sum. This function will do that:</p>
|
|||
<div class="prompt input_prompt">In [10]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="mi">999</span> <span class="o">-</span> <span class="mi">990</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="mi">999</span> <span class="o">-</span> <span class="mi">990</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13531,7 +13531,7 @@ counter to the running sum. This function will do that:</p>
|
|||
<div class="prompt input_prompt">In [11]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'PE1 == 0 0 66 [[3 2 1 3 1 2 3] [PE1.1] step] times [3 2 1 3] [PE1.1] step pop'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'PE1 0 0 66 [[3 2 1 3 1 2 3] [PE1.1] step] times [3 2 1 3] [PE1.1] step pop'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13544,7 +13544,7 @@ counter to the running sum. This function will do that:</p>
|
|||
<div class="prompt input_prompt">In [12]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'PE1'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'PE1'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13592,7 +13592,7 @@ integer terms from the list.</p>
|
|||
<div class="prompt input_prompt">In [13]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="mb">0b11100111011011</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="mb">0b11100111011011</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13625,7 +13625,7 @@ integer terms from the list.</p>
|
|||
<div class="prompt input_prompt">In [14]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'PE1.2 == [3 & PE1.1] dupdip 2 >>'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'PE1.2 [3 & PE1.1] dupdip 2 >>'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13638,7 +13638,7 @@ integer terms from the list.</p>
|
|||
<div class="prompt input_prompt">In [15]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'0 0 14811 PE1.2'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'0 0 14811 PE1.2'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13655,24 +13655,24 @@ integer terms from the list.</p>
|
|||
|
||||
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre> . 0 0 14811 PE1.2
|
||||
0 . 0 14811 PE1.2
|
||||
0 0 . 14811 PE1.2
|
||||
0 0 14811 . PE1.2
|
||||
0 0 14811 . [3 & PE1.1] dupdip 2 >>
|
||||
0 0 14811 [3 & PE1.1] . dupdip 2 >>
|
||||
0 0 14811 . 3 & PE1.1 14811 2 >>
|
||||
0 0 14811 3 . & PE1.1 14811 2 >>
|
||||
0 0 3 . PE1.1 14811 2 >>
|
||||
0 0 3 . + [+] dupdip 14811 2 >>
|
||||
0 3 . [+] dupdip 14811 2 >>
|
||||
0 3 [+] . dupdip 14811 2 >>
|
||||
0 3 . + 3 14811 2 >>
|
||||
3 . 3 14811 2 >>
|
||||
3 3 . 14811 2 >>
|
||||
3 3 14811 . 2 >>
|
||||
3 3 14811 2 . >>
|
||||
3 3 3702 .
|
||||
<pre> • 0 0 14811 PE1.2
|
||||
0 • 0 14811 PE1.2
|
||||
0 0 • 14811 PE1.2
|
||||
0 0 14811 • PE1.2
|
||||
0 0 14811 • [3 & PE1.1] dupdip 2 >>
|
||||
0 0 14811 [3 & PE1.1] • dupdip 2 >>
|
||||
0 0 14811 • 3 & PE1.1 14811 2 >>
|
||||
0 0 14811 3 • & PE1.1 14811 2 >>
|
||||
0 0 3 • PE1.1 14811 2 >>
|
||||
0 0 3 • + [+] dupdip 14811 2 >>
|
||||
0 3 • [+] dupdip 14811 2 >>
|
||||
0 3 [+] • dupdip 14811 2 >>
|
||||
0 3 • + 3 14811 2 >>
|
||||
3 • 3 14811 2 >>
|
||||
3 3 • 14811 2 >>
|
||||
3 3 14811 • 2 >>
|
||||
3 3 14811 2 • >>
|
||||
3 3 3702 •
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
|
|
@ -13686,7 +13686,7 @@ integer terms from the list.</p>
|
|||
<div class="prompt input_prompt">In [16]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'3 3 3702 PE1.2'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'3 3 3702 PE1.2'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13703,24 +13703,24 @@ integer terms from the list.</p>
|
|||
|
||||
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre> . 3 3 3702 PE1.2
|
||||
3 . 3 3702 PE1.2
|
||||
3 3 . 3702 PE1.2
|
||||
3 3 3702 . PE1.2
|
||||
3 3 3702 . [3 & PE1.1] dupdip 2 >>
|
||||
3 3 3702 [3 & PE1.1] . dupdip 2 >>
|
||||
3 3 3702 . 3 & PE1.1 3702 2 >>
|
||||
3 3 3702 3 . & PE1.1 3702 2 >>
|
||||
3 3 2 . PE1.1 3702 2 >>
|
||||
3 3 2 . + [+] dupdip 3702 2 >>
|
||||
3 5 . [+] dupdip 3702 2 >>
|
||||
3 5 [+] . dupdip 3702 2 >>
|
||||
3 5 . + 5 3702 2 >>
|
||||
8 . 5 3702 2 >>
|
||||
8 5 . 3702 2 >>
|
||||
8 5 3702 . 2 >>
|
||||
8 5 3702 2 . >>
|
||||
8 5 925 .
|
||||
<pre> • 3 3 3702 PE1.2
|
||||
3 • 3 3702 PE1.2
|
||||
3 3 • 3702 PE1.2
|
||||
3 3 3702 • PE1.2
|
||||
3 3 3702 • [3 & PE1.1] dupdip 2 >>
|
||||
3 3 3702 [3 & PE1.1] • dupdip 2 >>
|
||||
3 3 3702 • 3 & PE1.1 3702 2 >>
|
||||
3 3 3702 3 • & PE1.1 3702 2 >>
|
||||
3 3 2 • PE1.1 3702 2 >>
|
||||
3 3 2 • + [+] dupdip 3702 2 >>
|
||||
3 5 • [+] dupdip 3702 2 >>
|
||||
3 5 [+] • dupdip 3702 2 >>
|
||||
3 5 • + 5 3702 2 >>
|
||||
8 • 5 3702 2 >>
|
||||
8 5 • 3702 2 >>
|
||||
8 5 3702 • 2 >>
|
||||
8 5 3702 2 • >>
|
||||
8 5 925 •
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
|
|
@ -13734,7 +13734,7 @@ integer terms from the list.</p>
|
|||
<div class="prompt input_prompt">In [17]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'0 0 14811 7 [PE1.2] times pop'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'0 0 14811 7 [PE1.2] times pop'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13751,137 +13751,130 @@ integer terms from the list.</p>
|
|||
|
||||
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre> . 0 0 14811 7 [PE1.2] times pop
|
||||
0 . 0 14811 7 [PE1.2] times pop
|
||||
0 0 . 14811 7 [PE1.2] times pop
|
||||
0 0 14811 . 7 [PE1.2] times pop
|
||||
0 0 14811 7 . [PE1.2] times pop
|
||||
0 0 14811 7 [PE1.2] . times pop
|
||||
0 0 14811 [PE1.2] . i 6 [PE1.2] times pop
|
||||
0 0 14811 . PE1.2 6 [PE1.2] times pop
|
||||
0 0 14811 . [3 & PE1.1] dupdip 2 >> 6 [PE1.2] times pop
|
||||
0 0 14811 [3 & PE1.1] . dupdip 2 >> 6 [PE1.2] times pop
|
||||
0 0 14811 . 3 & PE1.1 14811 2 >> 6 [PE1.2] times pop
|
||||
0 0 14811 3 . & PE1.1 14811 2 >> 6 [PE1.2] times pop
|
||||
0 0 3 . PE1.1 14811 2 >> 6 [PE1.2] times pop
|
||||
0 0 3 . + [+] dupdip 14811 2 >> 6 [PE1.2] times pop
|
||||
0 3 . [+] dupdip 14811 2 >> 6 [PE1.2] times pop
|
||||
0 3 [+] . dupdip 14811 2 >> 6 [PE1.2] times pop
|
||||
0 3 . + 3 14811 2 >> 6 [PE1.2] times pop
|
||||
3 . 3 14811 2 >> 6 [PE1.2] times pop
|
||||
3 3 . 14811 2 >> 6 [PE1.2] times pop
|
||||
3 3 14811 . 2 >> 6 [PE1.2] times pop
|
||||
3 3 14811 2 . >> 6 [PE1.2] times pop
|
||||
3 3 3702 . 6 [PE1.2] times pop
|
||||
3 3 3702 6 . [PE1.2] times pop
|
||||
3 3 3702 6 [PE1.2] . times pop
|
||||
3 3 3702 [PE1.2] . i 5 [PE1.2] times pop
|
||||
3 3 3702 . PE1.2 5 [PE1.2] times pop
|
||||
3 3 3702 . [3 & PE1.1] dupdip 2 >> 5 [PE1.2] times pop
|
||||
3 3 3702 [3 & PE1.1] . dupdip 2 >> 5 [PE1.2] times pop
|
||||
3 3 3702 . 3 & PE1.1 3702 2 >> 5 [PE1.2] times pop
|
||||
3 3 3702 3 . & PE1.1 3702 2 >> 5 [PE1.2] times pop
|
||||
3 3 2 . PE1.1 3702 2 >> 5 [PE1.2] times pop
|
||||
3 3 2 . + [+] dupdip 3702 2 >> 5 [PE1.2] times pop
|
||||
3 5 . [+] dupdip 3702 2 >> 5 [PE1.2] times pop
|
||||
3 5 [+] . dupdip 3702 2 >> 5 [PE1.2] times pop
|
||||
3 5 . + 5 3702 2 >> 5 [PE1.2] times pop
|
||||
8 . 5 3702 2 >> 5 [PE1.2] times pop
|
||||
8 5 . 3702 2 >> 5 [PE1.2] times pop
|
||||
8 5 3702 . 2 >> 5 [PE1.2] times pop
|
||||
8 5 3702 2 . >> 5 [PE1.2] times pop
|
||||
8 5 925 . 5 [PE1.2] times pop
|
||||
8 5 925 5 . [PE1.2] times pop
|
||||
8 5 925 5 [PE1.2] . times pop
|
||||
8 5 925 [PE1.2] . i 4 [PE1.2] times pop
|
||||
8 5 925 . PE1.2 4 [PE1.2] times pop
|
||||
8 5 925 . [3 & PE1.1] dupdip 2 >> 4 [PE1.2] times pop
|
||||
8 5 925 [3 & PE1.1] . dupdip 2 >> 4 [PE1.2] times pop
|
||||
8 5 925 . 3 & PE1.1 925 2 >> 4 [PE1.2] times pop
|
||||
8 5 925 3 . & PE1.1 925 2 >> 4 [PE1.2] times pop
|
||||
8 5 1 . PE1.1 925 2 >> 4 [PE1.2] times pop
|
||||
8 5 1 . + [+] dupdip 925 2 >> 4 [PE1.2] times pop
|
||||
8 6 . [+] dupdip 925 2 >> 4 [PE1.2] times pop
|
||||
8 6 [+] . dupdip 925 2 >> 4 [PE1.2] times pop
|
||||
8 6 . + 6 925 2 >> 4 [PE1.2] times pop
|
||||
14 . 6 925 2 >> 4 [PE1.2] times pop
|
||||
14 6 . 925 2 >> 4 [PE1.2] times pop
|
||||
14 6 925 . 2 >> 4 [PE1.2] times pop
|
||||
14 6 925 2 . >> 4 [PE1.2] times pop
|
||||
14 6 231 . 4 [PE1.2] times pop
|
||||
14 6 231 4 . [PE1.2] times pop
|
||||
14 6 231 4 [PE1.2] . times pop
|
||||
14 6 231 [PE1.2] . i 3 [PE1.2] times pop
|
||||
14 6 231 . PE1.2 3 [PE1.2] times pop
|
||||
14 6 231 . [3 & PE1.1] dupdip 2 >> 3 [PE1.2] times pop
|
||||
14 6 231 [3 & PE1.1] . dupdip 2 >> 3 [PE1.2] times pop
|
||||
14 6 231 . 3 & PE1.1 231 2 >> 3 [PE1.2] times pop
|
||||
14 6 231 3 . & PE1.1 231 2 >> 3 [PE1.2] times pop
|
||||
14 6 3 . PE1.1 231 2 >> 3 [PE1.2] times pop
|
||||
14 6 3 . + [+] dupdip 231 2 >> 3 [PE1.2] times pop
|
||||
14 9 . [+] dupdip 231 2 >> 3 [PE1.2] times pop
|
||||
14 9 [+] . dupdip 231 2 >> 3 [PE1.2] times pop
|
||||
14 9 . + 9 231 2 >> 3 [PE1.2] times pop
|
||||
23 . 9 231 2 >> 3 [PE1.2] times pop
|
||||
23 9 . 231 2 >> 3 [PE1.2] times pop
|
||||
23 9 231 . 2 >> 3 [PE1.2] times pop
|
||||
23 9 231 2 . >> 3 [PE1.2] times pop
|
||||
23 9 57 . 3 [PE1.2] times pop
|
||||
23 9 57 3 . [PE1.2] times pop
|
||||
23 9 57 3 [PE1.2] . times pop
|
||||
23 9 57 [PE1.2] . i 2 [PE1.2] times pop
|
||||
23 9 57 . PE1.2 2 [PE1.2] times pop
|
||||
23 9 57 . [3 & PE1.1] dupdip 2 >> 2 [PE1.2] times pop
|
||||
23 9 57 [3 & PE1.1] . dupdip 2 >> 2 [PE1.2] times pop
|
||||
23 9 57 . 3 & PE1.1 57 2 >> 2 [PE1.2] times pop
|
||||
23 9 57 3 . & PE1.1 57 2 >> 2 [PE1.2] times pop
|
||||
23 9 1 . PE1.1 57 2 >> 2 [PE1.2] times pop
|
||||
23 9 1 . + [+] dupdip 57 2 >> 2 [PE1.2] times pop
|
||||
23 10 . [+] dupdip 57 2 >> 2 [PE1.2] times pop
|
||||
23 10 [+] . dupdip 57 2 >> 2 [PE1.2] times pop
|
||||
23 10 . + 10 57 2 >> 2 [PE1.2] times pop
|
||||
33 . 10 57 2 >> 2 [PE1.2] times pop
|
||||
33 10 . 57 2 >> 2 [PE1.2] times pop
|
||||
33 10 57 . 2 >> 2 [PE1.2] times pop
|
||||
33 10 57 2 . >> 2 [PE1.2] times pop
|
||||
33 10 14 . 2 [PE1.2] times pop
|
||||
33 10 14 2 . [PE1.2] times pop
|
||||
33 10 14 2 [PE1.2] . times pop
|
||||
33 10 14 [PE1.2] . i 1 [PE1.2] times pop
|
||||
33 10 14 . PE1.2 1 [PE1.2] times pop
|
||||
33 10 14 . [3 & PE1.1] dupdip 2 >> 1 [PE1.2] times pop
|
||||
33 10 14 [3 & PE1.1] . dupdip 2 >> 1 [PE1.2] times pop
|
||||
33 10 14 . 3 & PE1.1 14 2 >> 1 [PE1.2] times pop
|
||||
33 10 14 3 . & PE1.1 14 2 >> 1 [PE1.2] times pop
|
||||
33 10 2 . PE1.1 14 2 >> 1 [PE1.2] times pop
|
||||
33 10 2 . + [+] dupdip 14 2 >> 1 [PE1.2] times pop
|
||||
33 12 . [+] dupdip 14 2 >> 1 [PE1.2] times pop
|
||||
33 12 [+] . dupdip 14 2 >> 1 [PE1.2] times pop
|
||||
33 12 . + 12 14 2 >> 1 [PE1.2] times pop
|
||||
45 . 12 14 2 >> 1 [PE1.2] times pop
|
||||
45 12 . 14 2 >> 1 [PE1.2] times pop
|
||||
45 12 14 . 2 >> 1 [PE1.2] times pop
|
||||
45 12 14 2 . >> 1 [PE1.2] times pop
|
||||
45 12 3 . 1 [PE1.2] times pop
|
||||
45 12 3 1 . [PE1.2] times pop
|
||||
45 12 3 1 [PE1.2] . times pop
|
||||
45 12 3 [PE1.2] . i pop
|
||||
45 12 3 . PE1.2 pop
|
||||
45 12 3 . [3 & PE1.1] dupdip 2 >> pop
|
||||
45 12 3 [3 & PE1.1] . dupdip 2 >> pop
|
||||
45 12 3 . 3 & PE1.1 3 2 >> pop
|
||||
45 12 3 3 . & PE1.1 3 2 >> pop
|
||||
45 12 3 . PE1.1 3 2 >> pop
|
||||
45 12 3 . + [+] dupdip 3 2 >> pop
|
||||
45 15 . [+] dupdip 3 2 >> pop
|
||||
45 15 [+] . dupdip 3 2 >> pop
|
||||
45 15 . + 15 3 2 >> pop
|
||||
60 . 15 3 2 >> pop
|
||||
60 15 . 3 2 >> pop
|
||||
60 15 3 . 2 >> pop
|
||||
60 15 3 2 . >> pop
|
||||
60 15 0 . pop
|
||||
60 15 .
|
||||
<pre> • 0 0 14811 7 [PE1.2] times pop
|
||||
0 • 0 14811 7 [PE1.2] times pop
|
||||
0 0 • 14811 7 [PE1.2] times pop
|
||||
0 0 14811 • 7 [PE1.2] times pop
|
||||
0 0 14811 7 • [PE1.2] times pop
|
||||
0 0 14811 7 [PE1.2] • times pop
|
||||
0 0 14811 • PE1.2 6 [PE1.2] times pop
|
||||
0 0 14811 • [3 & PE1.1] dupdip 2 >> 6 [PE1.2] times pop
|
||||
0 0 14811 [3 & PE1.1] • dupdip 2 >> 6 [PE1.2] times pop
|
||||
0 0 14811 • 3 & PE1.1 14811 2 >> 6 [PE1.2] times pop
|
||||
0 0 14811 3 • & PE1.1 14811 2 >> 6 [PE1.2] times pop
|
||||
0 0 3 • PE1.1 14811 2 >> 6 [PE1.2] times pop
|
||||
0 0 3 • + [+] dupdip 14811 2 >> 6 [PE1.2] times pop
|
||||
0 3 • [+] dupdip 14811 2 >> 6 [PE1.2] times pop
|
||||
0 3 [+] • dupdip 14811 2 >> 6 [PE1.2] times pop
|
||||
0 3 • + 3 14811 2 >> 6 [PE1.2] times pop
|
||||
3 • 3 14811 2 >> 6 [PE1.2] times pop
|
||||
3 3 • 14811 2 >> 6 [PE1.2] times pop
|
||||
3 3 14811 • 2 >> 6 [PE1.2] times pop
|
||||
3 3 14811 2 • >> 6 [PE1.2] times pop
|
||||
3 3 3702 • 6 [PE1.2] times pop
|
||||
3 3 3702 6 • [PE1.2] times pop
|
||||
3 3 3702 6 [PE1.2] • times pop
|
||||
3 3 3702 • PE1.2 5 [PE1.2] times pop
|
||||
3 3 3702 • [3 & PE1.1] dupdip 2 >> 5 [PE1.2] times pop
|
||||
3 3 3702 [3 & PE1.1] • dupdip 2 >> 5 [PE1.2] times pop
|
||||
3 3 3702 • 3 & PE1.1 3702 2 >> 5 [PE1.2] times pop
|
||||
3 3 3702 3 • & PE1.1 3702 2 >> 5 [PE1.2] times pop
|
||||
3 3 2 • PE1.1 3702 2 >> 5 [PE1.2] times pop
|
||||
3 3 2 • + [+] dupdip 3702 2 >> 5 [PE1.2] times pop
|
||||
3 5 • [+] dupdip 3702 2 >> 5 [PE1.2] times pop
|
||||
3 5 [+] • dupdip 3702 2 >> 5 [PE1.2] times pop
|
||||
3 5 • + 5 3702 2 >> 5 [PE1.2] times pop
|
||||
8 • 5 3702 2 >> 5 [PE1.2] times pop
|
||||
8 5 • 3702 2 >> 5 [PE1.2] times pop
|
||||
8 5 3702 • 2 >> 5 [PE1.2] times pop
|
||||
8 5 3702 2 • >> 5 [PE1.2] times pop
|
||||
8 5 925 • 5 [PE1.2] times pop
|
||||
8 5 925 5 • [PE1.2] times pop
|
||||
8 5 925 5 [PE1.2] • times pop
|
||||
8 5 925 • PE1.2 4 [PE1.2] times pop
|
||||
8 5 925 • [3 & PE1.1] dupdip 2 >> 4 [PE1.2] times pop
|
||||
8 5 925 [3 & PE1.1] • dupdip 2 >> 4 [PE1.2] times pop
|
||||
8 5 925 • 3 & PE1.1 925 2 >> 4 [PE1.2] times pop
|
||||
8 5 925 3 • & PE1.1 925 2 >> 4 [PE1.2] times pop
|
||||
8 5 1 • PE1.1 925 2 >> 4 [PE1.2] times pop
|
||||
8 5 1 • + [+] dupdip 925 2 >> 4 [PE1.2] times pop
|
||||
8 6 • [+] dupdip 925 2 >> 4 [PE1.2] times pop
|
||||
8 6 [+] • dupdip 925 2 >> 4 [PE1.2] times pop
|
||||
8 6 • + 6 925 2 >> 4 [PE1.2] times pop
|
||||
14 • 6 925 2 >> 4 [PE1.2] times pop
|
||||
14 6 • 925 2 >> 4 [PE1.2] times pop
|
||||
14 6 925 • 2 >> 4 [PE1.2] times pop
|
||||
14 6 925 2 • >> 4 [PE1.2] times pop
|
||||
14 6 231 • 4 [PE1.2] times pop
|
||||
14 6 231 4 • [PE1.2] times pop
|
||||
14 6 231 4 [PE1.2] • times pop
|
||||
14 6 231 • PE1.2 3 [PE1.2] times pop
|
||||
14 6 231 • [3 & PE1.1] dupdip 2 >> 3 [PE1.2] times pop
|
||||
14 6 231 [3 & PE1.1] • dupdip 2 >> 3 [PE1.2] times pop
|
||||
14 6 231 • 3 & PE1.1 231 2 >> 3 [PE1.2] times pop
|
||||
14 6 231 3 • & PE1.1 231 2 >> 3 [PE1.2] times pop
|
||||
14 6 3 • PE1.1 231 2 >> 3 [PE1.2] times pop
|
||||
14 6 3 • + [+] dupdip 231 2 >> 3 [PE1.2] times pop
|
||||
14 9 • [+] dupdip 231 2 >> 3 [PE1.2] times pop
|
||||
14 9 [+] • dupdip 231 2 >> 3 [PE1.2] times pop
|
||||
14 9 • + 9 231 2 >> 3 [PE1.2] times pop
|
||||
23 • 9 231 2 >> 3 [PE1.2] times pop
|
||||
23 9 • 231 2 >> 3 [PE1.2] times pop
|
||||
23 9 231 • 2 >> 3 [PE1.2] times pop
|
||||
23 9 231 2 • >> 3 [PE1.2] times pop
|
||||
23 9 57 • 3 [PE1.2] times pop
|
||||
23 9 57 3 • [PE1.2] times pop
|
||||
23 9 57 3 [PE1.2] • times pop
|
||||
23 9 57 • PE1.2 2 [PE1.2] times pop
|
||||
23 9 57 • [3 & PE1.1] dupdip 2 >> 2 [PE1.2] times pop
|
||||
23 9 57 [3 & PE1.1] • dupdip 2 >> 2 [PE1.2] times pop
|
||||
23 9 57 • 3 & PE1.1 57 2 >> 2 [PE1.2] times pop
|
||||
23 9 57 3 • & PE1.1 57 2 >> 2 [PE1.2] times pop
|
||||
23 9 1 • PE1.1 57 2 >> 2 [PE1.2] times pop
|
||||
23 9 1 • + [+] dupdip 57 2 >> 2 [PE1.2] times pop
|
||||
23 10 • [+] dupdip 57 2 >> 2 [PE1.2] times pop
|
||||
23 10 [+] • dupdip 57 2 >> 2 [PE1.2] times pop
|
||||
23 10 • + 10 57 2 >> 2 [PE1.2] times pop
|
||||
33 • 10 57 2 >> 2 [PE1.2] times pop
|
||||
33 10 • 57 2 >> 2 [PE1.2] times pop
|
||||
33 10 57 • 2 >> 2 [PE1.2] times pop
|
||||
33 10 57 2 • >> 2 [PE1.2] times pop
|
||||
33 10 14 • 2 [PE1.2] times pop
|
||||
33 10 14 2 • [PE1.2] times pop
|
||||
33 10 14 2 [PE1.2] • times pop
|
||||
33 10 14 • PE1.2 1 [PE1.2] times pop
|
||||
33 10 14 • [3 & PE1.1] dupdip 2 >> 1 [PE1.2] times pop
|
||||
33 10 14 [3 & PE1.1] • dupdip 2 >> 1 [PE1.2] times pop
|
||||
33 10 14 • 3 & PE1.1 14 2 >> 1 [PE1.2] times pop
|
||||
33 10 14 3 • & PE1.1 14 2 >> 1 [PE1.2] times pop
|
||||
33 10 2 • PE1.1 14 2 >> 1 [PE1.2] times pop
|
||||
33 10 2 • + [+] dupdip 14 2 >> 1 [PE1.2] times pop
|
||||
33 12 • [+] dupdip 14 2 >> 1 [PE1.2] times pop
|
||||
33 12 [+] • dupdip 14 2 >> 1 [PE1.2] times pop
|
||||
33 12 • + 12 14 2 >> 1 [PE1.2] times pop
|
||||
45 • 12 14 2 >> 1 [PE1.2] times pop
|
||||
45 12 • 14 2 >> 1 [PE1.2] times pop
|
||||
45 12 14 • 2 >> 1 [PE1.2] times pop
|
||||
45 12 14 2 • >> 1 [PE1.2] times pop
|
||||
45 12 3 • 1 [PE1.2] times pop
|
||||
45 12 3 1 • [PE1.2] times pop
|
||||
45 12 3 1 [PE1.2] • times pop
|
||||
45 12 3 • PE1.2 pop
|
||||
45 12 3 • [3 & PE1.1] dupdip 2 >> pop
|
||||
45 12 3 [3 & PE1.1] • dupdip 2 >> pop
|
||||
45 12 3 • 3 & PE1.1 3 2 >> pop
|
||||
45 12 3 3 • & PE1.1 3 2 >> pop
|
||||
45 12 3 • PE1.1 3 2 >> pop
|
||||
45 12 3 • + [+] dupdip 3 2 >> pop
|
||||
45 15 • [+] dupdip 3 2 >> pop
|
||||
45 15 [+] • dupdip 3 2 >> pop
|
||||
45 15 • + 15 3 2 >> pop
|
||||
60 • 15 3 2 >> pop
|
||||
60 15 • 3 2 >> pop
|
||||
60 15 3 • 2 >> pop
|
||||
60 15 3 2 • >> pop
|
||||
60 15 0 • pop
|
||||
60 15 •
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
|
|
@ -13903,7 +13896,7 @@ integer terms from the list.</p>
|
|||
<div class="prompt input_prompt">In [18]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'PE1 == 0 0 66 [14811 7 [PE1.2] times pop] times 14811 4 [PE1.2] times popop'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'PE1 0 0 66 [14811 7 [PE1.2] times pop] times 14811 4 [PE1.2] times popop'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13916,7 +13909,7 @@ integer terms from the list.</p>
|
|||
<div class="prompt input_prompt">In [19]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'PE1'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'PE1'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13960,7 +13953,7 @@ n 14811 swap [PE1.2] times pop</code></pre>
|
|||
<div class="prompt input_prompt">In [20]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'PE1.3 == 14811 swap [PE1.2] times pop'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'PE1.3 14811 swap [PE1.2] times pop'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13981,7 +13974,7 @@ n 14811 swap [PE1.2] times pop</code></pre>
|
|||
<div class="prompt input_prompt">In [21]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'PE1 == 0 0 66 [7 PE1.3] times 4 PE1.3 pop'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'PE1 0 0 66 [7 PE1.3] times 4 PE1.3 pop'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13994,7 +13987,7 @@ n 14811 swap [PE1.2] times pop</code></pre>
|
|||
<div class="prompt input_prompt">In [22]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'PE1'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'PE1'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14046,7 +14039,7 @@ PE1 == 0 0 66 [7 PE1.3] times 4 PE1.3 pop</code></pre>
|
|||
<div class="prompt input_prompt">In [23]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'PE1.terms == [0 swap [dup [pop 14811] [] branch [3 &] dupdip 2 >>] dip rest cons]'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'PE1.terms [0 swap [dup [pop 14811] [] branch [3 &] dupdip 2 >>] dip rest cons]'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14059,7 +14052,7 @@ PE1 == 0 0 66 [7 PE1.3] times 4 PE1.3 pop</code></pre>
|
|||
<div class="prompt input_prompt">In [24]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'PE1.terms 21 [x] times'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'PE1.terms 21 [x] times'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14098,7 +14091,7 @@ PE1 == 0 0 66 [7 PE1.3] times 4 PE1.3 pop</code></pre>
|
|||
<div class="prompt input_prompt">In [25]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'7 66 * 4 +'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'7 66 * 4 +'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14136,7 +14129,7 @@ PE1 == 0 0 66 [7 PE1.3] times 4 PE1.3 pop</code></pre>
|
|||
<div class="prompt input_prompt">In [26]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'PE1.terms 466 [x] times pop'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'PE1.terms 466 [x] times pop'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14174,7 +14167,7 @@ PE1 == 0 0 66 [7 PE1.3] times 4 PE1.3 pop</code></pre>
|
|||
<div class="prompt input_prompt">In [27]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[PE1.terms 466 [x] times pop] run sum'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[PE1.terms 466 [x] times pop] run sum'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14213,7 +14206,7 @@ PE1 == 0 0 66 [7 PE1.3] times 4 PE1.3 pop</code></pre>
|
|||
<div class="prompt input_prompt">In [28]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'0 0 PE1.terms 466 [x [PE1.1] dip] times popop'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'0 0 PE1.terms 466 [x [PE1.1] dip] times popop'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14252,7 +14245,7 @@ PE1 == 0 0 66 [7 PE1.3] times 4 PE1.3 pop</code></pre>
|
|||
<div class="prompt input_prompt">In [29]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[10 9 8 7 6 5 4 3 2 1] sum'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[10 9 8 7 6 5 4 3 2 1] sum'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14306,7 +14299,7 @@ PE1 == 0 0 66 [7 PE1.3] times 4 PE1.3 pop</code></pre>
|
|||
<div class="prompt input_prompt">In [30]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'F == dup ++ * 2 floordiv'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'F dup ++ * 2 floordiv'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14319,7 +14312,7 @@ PE1 == 0 0 66 [7 PE1.3] times 4 PE1.3 pop</code></pre>
|
|||
<div class="prompt input_prompt">In [31]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'10 F'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'10 F'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14336,14 +14329,14 @@ PE1 == 0 0 66 [7 PE1.3] times 4 PE1.3 pop</code></pre>
|
|||
|
||||
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre> . 10 F
|
||||
10 . F
|
||||
10 . dup ++ * 2 floordiv
|
||||
10 10 . ++ * 2 floordiv
|
||||
10 11 . * 2 floordiv
|
||||
110 . 2 floordiv
|
||||
110 2 . floordiv
|
||||
55 .
|
||||
<pre> • 10 F
|
||||
10 • F
|
||||
10 • dup ++ * 2 floordiv
|
||||
10 10 • ++ * 2 floordiv
|
||||
10 11 • * 2 floordiv
|
||||
110 • 2 floordiv
|
||||
110 2 • floordiv
|
||||
55 •
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
|
|
@ -14376,7 +14369,7 @@ PE1 == 0 0 66 [7 PE1.3] times 4 PE1.3 pop</code></pre>
|
|||
<div class="prompt input_prompt">In [32]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[3 5 6 9 10 12 15] reverse [978 980 981 984 985 987 990] zip'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[3 5 6 9 10 12 15] reverse [978 980 981 984 985 987 990] zip'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14407,7 +14400,7 @@ PE1 == 0 0 66 [7 PE1.3] times 4 PE1.3 pop</code></pre>
|
|||
<div class="prompt input_prompt">In [33]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[3 5 6 9 10 12 15] reverse [978 980 981 984 985 987 990] zip [sum] map'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[3 5 6 9 10 12 15] reverse [978 980 981 984 985 987 990] zip [sum] map'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14446,7 +14439,7 @@ PE1 == 0 0 66 [7 PE1.3] times 4 PE1.3 pop</code></pre>
|
|||
<div class="prompt input_prompt">In [34]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[ 3 5 6 9 10 12 15] reverse [978 980 981 984 985 987 990] zip [sum] map sum'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[ 3 5 6 9 10 12 15] reverse [978 980 981 984 985 987 990] zip [sum] map sum'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14490,7 +14483,7 @@ PE1 == 0 0 66 [7 PE1.3] times 4 PE1.3 pop</code></pre>
|
|||
<div class="prompt input_prompt">In [35]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'6945 33 * [993 995 996 999] cons sum'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'6945 33 * [993 995 996 999] cons sum'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
|
|||
|
|
@ -33,7 +33,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('P == [3 % not] dupdip 5 % not or')"
|
||||
"define('P [3 % not] dupdip 5 % not or')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -45,19 +45,19 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . 80 P\n",
|
||||
" 80 . P\n",
|
||||
" 80 . [3 % not] dupdip 5 % not or\n",
|
||||
"80 [3 % not] . dupdip 5 % not or\n",
|
||||
" 80 . 3 % not 80 5 % not or\n",
|
||||
" 80 3 . % not 80 5 % not or\n",
|
||||
" 2 . not 80 5 % not or\n",
|
||||
" False . 80 5 % not or\n",
|
||||
" False 80 . 5 % not or\n",
|
||||
" False 80 5 . % not or\n",
|
||||
" False 0 . not or\n",
|
||||
" False True . or\n",
|
||||
" True . \n"
|
||||
" • 80 P\n",
|
||||
" 80 • P\n",
|
||||
" 80 • [3 % not] dupdip 5 % not or\n",
|
||||
"80 [3 % not] • dupdip 5 % not or\n",
|
||||
" 80 • 3 % not 80 5 % not or\n",
|
||||
" 80 3 • % not 80 5 % not or\n",
|
||||
" 2 • not 80 5 % not or\n",
|
||||
" False • 80 5 % not or\n",
|
||||
" False 80 • 5 % not or\n",
|
||||
" False 80 5 • % not or\n",
|
||||
" False 0 • not or\n",
|
||||
" False True • or\n",
|
||||
" True • \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -124,7 +124,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('PE1.1 == + [+] dupdip')"
|
||||
"define('PE1.1 + [+] dupdip')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -136,16 +136,16 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . 0 0 3 PE1.1\n",
|
||||
" 0 . 0 3 PE1.1\n",
|
||||
" 0 0 . 3 PE1.1\n",
|
||||
" 0 0 3 . PE1.1\n",
|
||||
" 0 0 3 . + [+] dupdip\n",
|
||||
" 0 3 . [+] dupdip\n",
|
||||
"0 3 [+] . dupdip\n",
|
||||
" 0 3 . + 3\n",
|
||||
" 3 . 3\n",
|
||||
" 3 3 . \n"
|
||||
" • 0 0 3 PE1.1\n",
|
||||
" 0 • 0 3 PE1.1\n",
|
||||
" 0 0 • 3 PE1.1\n",
|
||||
" 0 0 3 • PE1.1\n",
|
||||
" 0 0 3 • + [+] dupdip\n",
|
||||
" 0 3 • [+] dupdip\n",
|
||||
"0 3 [+] • dupdip\n",
|
||||
" 0 3 • + 3\n",
|
||||
" 3 • 3\n",
|
||||
" 3 3 • \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -164,79 +164,79 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . 0 0 [3 2 1 3 1 2 3] [PE1.1] step\n",
|
||||
" 0 . 0 [3 2 1 3 1 2 3] [PE1.1] step\n",
|
||||
" 0 0 . [3 2 1 3 1 2 3] [PE1.1] step\n",
|
||||
" 0 0 [3 2 1 3 1 2 3] . [PE1.1] step\n",
|
||||
"0 0 [3 2 1 3 1 2 3] [PE1.1] . step\n",
|
||||
" 0 0 3 [PE1.1] . i [2 1 3 1 2 3] [PE1.1] step\n",
|
||||
" 0 0 3 . PE1.1 [2 1 3 1 2 3] [PE1.1] step\n",
|
||||
" 0 0 3 . + [+] dupdip [2 1 3 1 2 3] [PE1.1] step\n",
|
||||
" 0 3 . [+] dupdip [2 1 3 1 2 3] [PE1.1] step\n",
|
||||
" 0 3 [+] . dupdip [2 1 3 1 2 3] [PE1.1] step\n",
|
||||
" 0 3 . + 3 [2 1 3 1 2 3] [PE1.1] step\n",
|
||||
" 3 . 3 [2 1 3 1 2 3] [PE1.1] step\n",
|
||||
" 3 3 . [2 1 3 1 2 3] [PE1.1] step\n",
|
||||
" 3 3 [2 1 3 1 2 3] . [PE1.1] step\n",
|
||||
" 3 3 [2 1 3 1 2 3] [PE1.1] . step\n",
|
||||
" 3 3 2 [PE1.1] . i [1 3 1 2 3] [PE1.1] step\n",
|
||||
" 3 3 2 . PE1.1 [1 3 1 2 3] [PE1.1] step\n",
|
||||
" 3 3 2 . + [+] dupdip [1 3 1 2 3] [PE1.1] step\n",
|
||||
" 3 5 . [+] dupdip [1 3 1 2 3] [PE1.1] step\n",
|
||||
" 3 5 [+] . dupdip [1 3 1 2 3] [PE1.1] step\n",
|
||||
" 3 5 . + 5 [1 3 1 2 3] [PE1.1] step\n",
|
||||
" 8 . 5 [1 3 1 2 3] [PE1.1] step\n",
|
||||
" 8 5 . [1 3 1 2 3] [PE1.1] step\n",
|
||||
" 8 5 [1 3 1 2 3] . [PE1.1] step\n",
|
||||
" 8 5 [1 3 1 2 3] [PE1.1] . step\n",
|
||||
" 8 5 1 [PE1.1] . i [3 1 2 3] [PE1.1] step\n",
|
||||
" 8 5 1 . PE1.1 [3 1 2 3] [PE1.1] step\n",
|
||||
" 8 5 1 . + [+] dupdip [3 1 2 3] [PE1.1] step\n",
|
||||
" 8 6 . [+] dupdip [3 1 2 3] [PE1.1] step\n",
|
||||
" 8 6 [+] . dupdip [3 1 2 3] [PE1.1] step\n",
|
||||
" 8 6 . + 6 [3 1 2 3] [PE1.1] step\n",
|
||||
" 14 . 6 [3 1 2 3] [PE1.1] step\n",
|
||||
" 14 6 . [3 1 2 3] [PE1.1] step\n",
|
||||
" 14 6 [3 1 2 3] . [PE1.1] step\n",
|
||||
" 14 6 [3 1 2 3] [PE1.1] . step\n",
|
||||
" 14 6 3 [PE1.1] . i [1 2 3] [PE1.1] step\n",
|
||||
" 14 6 3 . PE1.1 [1 2 3] [PE1.1] step\n",
|
||||
" 14 6 3 . + [+] dupdip [1 2 3] [PE1.1] step\n",
|
||||
" 14 9 . [+] dupdip [1 2 3] [PE1.1] step\n",
|
||||
" 14 9 [+] . dupdip [1 2 3] [PE1.1] step\n",
|
||||
" 14 9 . + 9 [1 2 3] [PE1.1] step\n",
|
||||
" 23 . 9 [1 2 3] [PE1.1] step\n",
|
||||
" 23 9 . [1 2 3] [PE1.1] step\n",
|
||||
" 23 9 [1 2 3] . [PE1.1] step\n",
|
||||
" 23 9 [1 2 3] [PE1.1] . step\n",
|
||||
" 23 9 1 [PE1.1] . i [2 3] [PE1.1] step\n",
|
||||
" 23 9 1 . PE1.1 [2 3] [PE1.1] step\n",
|
||||
" 23 9 1 . + [+] dupdip [2 3] [PE1.1] step\n",
|
||||
" 23 10 . [+] dupdip [2 3] [PE1.1] step\n",
|
||||
" 23 10 [+] . dupdip [2 3] [PE1.1] step\n",
|
||||
" 23 10 . + 10 [2 3] [PE1.1] step\n",
|
||||
" 33 . 10 [2 3] [PE1.1] step\n",
|
||||
" 33 10 . [2 3] [PE1.1] step\n",
|
||||
" 33 10 [2 3] . [PE1.1] step\n",
|
||||
" 33 10 [2 3] [PE1.1] . step\n",
|
||||
" 33 10 2 [PE1.1] . i [3] [PE1.1] step\n",
|
||||
" 33 10 2 . PE1.1 [3] [PE1.1] step\n",
|
||||
" 33 10 2 . + [+] dupdip [3] [PE1.1] step\n",
|
||||
" 33 12 . [+] dupdip [3] [PE1.1] step\n",
|
||||
" 33 12 [+] . dupdip [3] [PE1.1] step\n",
|
||||
" 33 12 . + 12 [3] [PE1.1] step\n",
|
||||
" 45 . 12 [3] [PE1.1] step\n",
|
||||
" 45 12 . [3] [PE1.1] step\n",
|
||||
" 45 12 [3] . [PE1.1] step\n",
|
||||
" 45 12 [3] [PE1.1] . step\n",
|
||||
" 45 12 3 [PE1.1] . i\n",
|
||||
" 45 12 3 . PE1.1\n",
|
||||
" 45 12 3 . + [+] dupdip\n",
|
||||
" 45 15 . [+] dupdip\n",
|
||||
" 45 15 [+] . dupdip\n",
|
||||
" 45 15 . + 15\n",
|
||||
" 60 . 15\n",
|
||||
" 60 15 . \n"
|
||||
" • 0 0 [3 2 1 3 1 2 3] [PE1.1] step\n",
|
||||
" 0 • 0 [3 2 1 3 1 2 3] [PE1.1] step\n",
|
||||
" 0 0 • [3 2 1 3 1 2 3] [PE1.1] step\n",
|
||||
" 0 0 [3 2 1 3 1 2 3] • [PE1.1] step\n",
|
||||
"0 0 [3 2 1 3 1 2 3] [PE1.1] • step\n",
|
||||
" 0 0 3 [PE1.1] • i [2 1 3 1 2 3] [PE1.1] step\n",
|
||||
" 0 0 3 • PE1.1 [2 1 3 1 2 3] [PE1.1] step\n",
|
||||
" 0 0 3 • + [+] dupdip [2 1 3 1 2 3] [PE1.1] step\n",
|
||||
" 0 3 • [+] dupdip [2 1 3 1 2 3] [PE1.1] step\n",
|
||||
" 0 3 [+] • dupdip [2 1 3 1 2 3] [PE1.1] step\n",
|
||||
" 0 3 • + 3 [2 1 3 1 2 3] [PE1.1] step\n",
|
||||
" 3 • 3 [2 1 3 1 2 3] [PE1.1] step\n",
|
||||
" 3 3 • [2 1 3 1 2 3] [PE1.1] step\n",
|
||||
" 3 3 [2 1 3 1 2 3] • [PE1.1] step\n",
|
||||
" 3 3 [2 1 3 1 2 3] [PE1.1] • step\n",
|
||||
" 3 3 2 [PE1.1] • i [1 3 1 2 3] [PE1.1] step\n",
|
||||
" 3 3 2 • PE1.1 [1 3 1 2 3] [PE1.1] step\n",
|
||||
" 3 3 2 • + [+] dupdip [1 3 1 2 3] [PE1.1] step\n",
|
||||
" 3 5 • [+] dupdip [1 3 1 2 3] [PE1.1] step\n",
|
||||
" 3 5 [+] • dupdip [1 3 1 2 3] [PE1.1] step\n",
|
||||
" 3 5 • + 5 [1 3 1 2 3] [PE1.1] step\n",
|
||||
" 8 • 5 [1 3 1 2 3] [PE1.1] step\n",
|
||||
" 8 5 • [1 3 1 2 3] [PE1.1] step\n",
|
||||
" 8 5 [1 3 1 2 3] • [PE1.1] step\n",
|
||||
" 8 5 [1 3 1 2 3] [PE1.1] • step\n",
|
||||
" 8 5 1 [PE1.1] • i [3 1 2 3] [PE1.1] step\n",
|
||||
" 8 5 1 • PE1.1 [3 1 2 3] [PE1.1] step\n",
|
||||
" 8 5 1 • + [+] dupdip [3 1 2 3] [PE1.1] step\n",
|
||||
" 8 6 • [+] dupdip [3 1 2 3] [PE1.1] step\n",
|
||||
" 8 6 [+] • dupdip [3 1 2 3] [PE1.1] step\n",
|
||||
" 8 6 • + 6 [3 1 2 3] [PE1.1] step\n",
|
||||
" 14 • 6 [3 1 2 3] [PE1.1] step\n",
|
||||
" 14 6 • [3 1 2 3] [PE1.1] step\n",
|
||||
" 14 6 [3 1 2 3] • [PE1.1] step\n",
|
||||
" 14 6 [3 1 2 3] [PE1.1] • step\n",
|
||||
" 14 6 3 [PE1.1] • i [1 2 3] [PE1.1] step\n",
|
||||
" 14 6 3 • PE1.1 [1 2 3] [PE1.1] step\n",
|
||||
" 14 6 3 • + [+] dupdip [1 2 3] [PE1.1] step\n",
|
||||
" 14 9 • [+] dupdip [1 2 3] [PE1.1] step\n",
|
||||
" 14 9 [+] • dupdip [1 2 3] [PE1.1] step\n",
|
||||
" 14 9 • + 9 [1 2 3] [PE1.1] step\n",
|
||||
" 23 • 9 [1 2 3] [PE1.1] step\n",
|
||||
" 23 9 • [1 2 3] [PE1.1] step\n",
|
||||
" 23 9 [1 2 3] • [PE1.1] step\n",
|
||||
" 23 9 [1 2 3] [PE1.1] • step\n",
|
||||
" 23 9 1 [PE1.1] • i [2 3] [PE1.1] step\n",
|
||||
" 23 9 1 • PE1.1 [2 3] [PE1.1] step\n",
|
||||
" 23 9 1 • + [+] dupdip [2 3] [PE1.1] step\n",
|
||||
" 23 10 • [+] dupdip [2 3] [PE1.1] step\n",
|
||||
" 23 10 [+] • dupdip [2 3] [PE1.1] step\n",
|
||||
" 23 10 • + 10 [2 3] [PE1.1] step\n",
|
||||
" 33 • 10 [2 3] [PE1.1] step\n",
|
||||
" 33 10 • [2 3] [PE1.1] step\n",
|
||||
" 33 10 [2 3] • [PE1.1] step\n",
|
||||
" 33 10 [2 3] [PE1.1] • step\n",
|
||||
" 33 10 2 [PE1.1] • i [3] [PE1.1] step\n",
|
||||
" 33 10 2 • PE1.1 [3] [PE1.1] step\n",
|
||||
" 33 10 2 • + [+] dupdip [3] [PE1.1] step\n",
|
||||
" 33 12 • [+] dupdip [3] [PE1.1] step\n",
|
||||
" 33 12 [+] • dupdip [3] [PE1.1] step\n",
|
||||
" 33 12 • + 12 [3] [PE1.1] step\n",
|
||||
" 45 • 12 [3] [PE1.1] step\n",
|
||||
" 45 12 • [3] [PE1.1] step\n",
|
||||
" 45 12 [3] • [PE1.1] step\n",
|
||||
" 45 12 [3] [PE1.1] • step\n",
|
||||
" 45 12 3 [PE1.1] • i\n",
|
||||
" 45 12 3 • PE1.1\n",
|
||||
" 45 12 3 • + [+] dupdip\n",
|
||||
" 45 15 • [+] dupdip\n",
|
||||
" 45 15 [+] • dupdip\n",
|
||||
" 45 15 • + 15\n",
|
||||
" 60 • 15\n",
|
||||
" 60 15 • \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -259,7 +259,7 @@
|
|||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"66"
|
||||
"66.66666666666667"
|
||||
]
|
||||
},
|
||||
"execution_count": 7,
|
||||
|
|
@ -351,7 +351,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('PE1 == 0 0 66 [[3 2 1 3 1 2 3] [PE1.1] step] times [3 2 1 3] [PE1.1] step pop')"
|
||||
"define('PE1 0 0 66 [[3 2 1 3 1 2 3] [PE1.1] step] times [3 2 1 3] [PE1.1] step pop')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -413,7 +413,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('PE1.2 == [3 & PE1.1] dupdip 2 >>')"
|
||||
"define('PE1.2 [3 & PE1.1] dupdip 2 >>')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -425,24 +425,24 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . 0 0 14811 PE1.2\n",
|
||||
" 0 . 0 14811 PE1.2\n",
|
||||
" 0 0 . 14811 PE1.2\n",
|
||||
" 0 0 14811 . PE1.2\n",
|
||||
" 0 0 14811 . [3 & PE1.1] dupdip 2 >>\n",
|
||||
"0 0 14811 [3 & PE1.1] . dupdip 2 >>\n",
|
||||
" 0 0 14811 . 3 & PE1.1 14811 2 >>\n",
|
||||
" 0 0 14811 3 . & PE1.1 14811 2 >>\n",
|
||||
" 0 0 3 . PE1.1 14811 2 >>\n",
|
||||
" 0 0 3 . + [+] dupdip 14811 2 >>\n",
|
||||
" 0 3 . [+] dupdip 14811 2 >>\n",
|
||||
" 0 3 [+] . dupdip 14811 2 >>\n",
|
||||
" 0 3 . + 3 14811 2 >>\n",
|
||||
" 3 . 3 14811 2 >>\n",
|
||||
" 3 3 . 14811 2 >>\n",
|
||||
" 3 3 14811 . 2 >>\n",
|
||||
" 3 3 14811 2 . >>\n",
|
||||
" 3 3 3702 . \n"
|
||||
" • 0 0 14811 PE1.2\n",
|
||||
" 0 • 0 14811 PE1.2\n",
|
||||
" 0 0 • 14811 PE1.2\n",
|
||||
" 0 0 14811 • PE1.2\n",
|
||||
" 0 0 14811 • [3 & PE1.1] dupdip 2 >>\n",
|
||||
"0 0 14811 [3 & PE1.1] • dupdip 2 >>\n",
|
||||
" 0 0 14811 • 3 & PE1.1 14811 2 >>\n",
|
||||
" 0 0 14811 3 • & PE1.1 14811 2 >>\n",
|
||||
" 0 0 3 • PE1.1 14811 2 >>\n",
|
||||
" 0 0 3 • + [+] dupdip 14811 2 >>\n",
|
||||
" 0 3 • [+] dupdip 14811 2 >>\n",
|
||||
" 0 3 [+] • dupdip 14811 2 >>\n",
|
||||
" 0 3 • + 3 14811 2 >>\n",
|
||||
" 3 • 3 14811 2 >>\n",
|
||||
" 3 3 • 14811 2 >>\n",
|
||||
" 3 3 14811 • 2 >>\n",
|
||||
" 3 3 14811 2 • >>\n",
|
||||
" 3 3 3702 • \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -459,24 +459,24 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . 3 3 3702 PE1.2\n",
|
||||
" 3 . 3 3702 PE1.2\n",
|
||||
" 3 3 . 3702 PE1.2\n",
|
||||
" 3 3 3702 . PE1.2\n",
|
||||
" 3 3 3702 . [3 & PE1.1] dupdip 2 >>\n",
|
||||
"3 3 3702 [3 & PE1.1] . dupdip 2 >>\n",
|
||||
" 3 3 3702 . 3 & PE1.1 3702 2 >>\n",
|
||||
" 3 3 3702 3 . & PE1.1 3702 2 >>\n",
|
||||
" 3 3 2 . PE1.1 3702 2 >>\n",
|
||||
" 3 3 2 . + [+] dupdip 3702 2 >>\n",
|
||||
" 3 5 . [+] dupdip 3702 2 >>\n",
|
||||
" 3 5 [+] . dupdip 3702 2 >>\n",
|
||||
" 3 5 . + 5 3702 2 >>\n",
|
||||
" 8 . 5 3702 2 >>\n",
|
||||
" 8 5 . 3702 2 >>\n",
|
||||
" 8 5 3702 . 2 >>\n",
|
||||
" 8 5 3702 2 . >>\n",
|
||||
" 8 5 925 . \n"
|
||||
" • 3 3 3702 PE1.2\n",
|
||||
" 3 • 3 3702 PE1.2\n",
|
||||
" 3 3 • 3702 PE1.2\n",
|
||||
" 3 3 3702 • PE1.2\n",
|
||||
" 3 3 3702 • [3 & PE1.1] dupdip 2 >>\n",
|
||||
"3 3 3702 [3 & PE1.1] • dupdip 2 >>\n",
|
||||
" 3 3 3702 • 3 & PE1.1 3702 2 >>\n",
|
||||
" 3 3 3702 3 • & PE1.1 3702 2 >>\n",
|
||||
" 3 3 2 • PE1.1 3702 2 >>\n",
|
||||
" 3 3 2 • + [+] dupdip 3702 2 >>\n",
|
||||
" 3 5 • [+] dupdip 3702 2 >>\n",
|
||||
" 3 5 [+] • dupdip 3702 2 >>\n",
|
||||
" 3 5 • + 5 3702 2 >>\n",
|
||||
" 8 • 5 3702 2 >>\n",
|
||||
" 8 5 • 3702 2 >>\n",
|
||||
" 8 5 3702 • 2 >>\n",
|
||||
" 8 5 3702 2 • >>\n",
|
||||
" 8 5 925 • \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -495,137 +495,130 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . 0 0 14811 7 [PE1.2] times pop\n",
|
||||
" 0 . 0 14811 7 [PE1.2] times pop\n",
|
||||
" 0 0 . 14811 7 [PE1.2] times pop\n",
|
||||
" 0 0 14811 . 7 [PE1.2] times pop\n",
|
||||
" 0 0 14811 7 . [PE1.2] times pop\n",
|
||||
" 0 0 14811 7 [PE1.2] . times pop\n",
|
||||
" 0 0 14811 [PE1.2] . i 6 [PE1.2] times pop\n",
|
||||
" 0 0 14811 . PE1.2 6 [PE1.2] times pop\n",
|
||||
" 0 0 14811 . [3 & PE1.1] dupdip 2 >> 6 [PE1.2] times pop\n",
|
||||
"0 0 14811 [3 & PE1.1] . dupdip 2 >> 6 [PE1.2] times pop\n",
|
||||
" 0 0 14811 . 3 & PE1.1 14811 2 >> 6 [PE1.2] times pop\n",
|
||||
" 0 0 14811 3 . & PE1.1 14811 2 >> 6 [PE1.2] times pop\n",
|
||||
" 0 0 3 . PE1.1 14811 2 >> 6 [PE1.2] times pop\n",
|
||||
" 0 0 3 . + [+] dupdip 14811 2 >> 6 [PE1.2] times pop\n",
|
||||
" 0 3 . [+] dupdip 14811 2 >> 6 [PE1.2] times pop\n",
|
||||
" 0 3 [+] . dupdip 14811 2 >> 6 [PE1.2] times pop\n",
|
||||
" 0 3 . + 3 14811 2 >> 6 [PE1.2] times pop\n",
|
||||
" 3 . 3 14811 2 >> 6 [PE1.2] times pop\n",
|
||||
" 3 3 . 14811 2 >> 6 [PE1.2] times pop\n",
|
||||
" 3 3 14811 . 2 >> 6 [PE1.2] times pop\n",
|
||||
" 3 3 14811 2 . >> 6 [PE1.2] times pop\n",
|
||||
" 3 3 3702 . 6 [PE1.2] times pop\n",
|
||||
" 3 3 3702 6 . [PE1.2] times pop\n",
|
||||
" 3 3 3702 6 [PE1.2] . times pop\n",
|
||||
" 3 3 3702 [PE1.2] . i 5 [PE1.2] times pop\n",
|
||||
" 3 3 3702 . PE1.2 5 [PE1.2] times pop\n",
|
||||
" 3 3 3702 . [3 & PE1.1] dupdip 2 >> 5 [PE1.2] times pop\n",
|
||||
" 3 3 3702 [3 & PE1.1] . dupdip 2 >> 5 [PE1.2] times pop\n",
|
||||
" 3 3 3702 . 3 & PE1.1 3702 2 >> 5 [PE1.2] times pop\n",
|
||||
" 3 3 3702 3 . & PE1.1 3702 2 >> 5 [PE1.2] times pop\n",
|
||||
" 3 3 2 . PE1.1 3702 2 >> 5 [PE1.2] times pop\n",
|
||||
" 3 3 2 . + [+] dupdip 3702 2 >> 5 [PE1.2] times pop\n",
|
||||
" 3 5 . [+] dupdip 3702 2 >> 5 [PE1.2] times pop\n",
|
||||
" 3 5 [+] . dupdip 3702 2 >> 5 [PE1.2] times pop\n",
|
||||
" 3 5 . + 5 3702 2 >> 5 [PE1.2] times pop\n",
|
||||
" 8 . 5 3702 2 >> 5 [PE1.2] times pop\n",
|
||||
" 8 5 . 3702 2 >> 5 [PE1.2] times pop\n",
|
||||
" 8 5 3702 . 2 >> 5 [PE1.2] times pop\n",
|
||||
" 8 5 3702 2 . >> 5 [PE1.2] times pop\n",
|
||||
" 8 5 925 . 5 [PE1.2] times pop\n",
|
||||
" 8 5 925 5 . [PE1.2] times pop\n",
|
||||
" 8 5 925 5 [PE1.2] . times pop\n",
|
||||
" 8 5 925 [PE1.2] . i 4 [PE1.2] times pop\n",
|
||||
" 8 5 925 . PE1.2 4 [PE1.2] times pop\n",
|
||||
" 8 5 925 . [3 & PE1.1] dupdip 2 >> 4 [PE1.2] times pop\n",
|
||||
" 8 5 925 [3 & PE1.1] . dupdip 2 >> 4 [PE1.2] times pop\n",
|
||||
" 8 5 925 . 3 & PE1.1 925 2 >> 4 [PE1.2] times pop\n",
|
||||
" 8 5 925 3 . & PE1.1 925 2 >> 4 [PE1.2] times pop\n",
|
||||
" 8 5 1 . PE1.1 925 2 >> 4 [PE1.2] times pop\n",
|
||||
" 8 5 1 . + [+] dupdip 925 2 >> 4 [PE1.2] times pop\n",
|
||||
" 8 6 . [+] dupdip 925 2 >> 4 [PE1.2] times pop\n",
|
||||
" 8 6 [+] . dupdip 925 2 >> 4 [PE1.2] times pop\n",
|
||||
" 8 6 . + 6 925 2 >> 4 [PE1.2] times pop\n",
|
||||
" 14 . 6 925 2 >> 4 [PE1.2] times pop\n",
|
||||
" 14 6 . 925 2 >> 4 [PE1.2] times pop\n",
|
||||
" 14 6 925 . 2 >> 4 [PE1.2] times pop\n",
|
||||
" 14 6 925 2 . >> 4 [PE1.2] times pop\n",
|
||||
" 14 6 231 . 4 [PE1.2] times pop\n",
|
||||
" 14 6 231 4 . [PE1.2] times pop\n",
|
||||
" 14 6 231 4 [PE1.2] . times pop\n",
|
||||
" 14 6 231 [PE1.2] . i 3 [PE1.2] times pop\n",
|
||||
" 14 6 231 . PE1.2 3 [PE1.2] times pop\n",
|
||||
" 14 6 231 . [3 & PE1.1] dupdip 2 >> 3 [PE1.2] times pop\n",
|
||||
" 14 6 231 [3 & PE1.1] . dupdip 2 >> 3 [PE1.2] times pop\n",
|
||||
" 14 6 231 . 3 & PE1.1 231 2 >> 3 [PE1.2] times pop\n",
|
||||
" 14 6 231 3 . & PE1.1 231 2 >> 3 [PE1.2] times pop\n",
|
||||
" 14 6 3 . PE1.1 231 2 >> 3 [PE1.2] times pop\n",
|
||||
" 14 6 3 . + [+] dupdip 231 2 >> 3 [PE1.2] times pop\n",
|
||||
" 14 9 . [+] dupdip 231 2 >> 3 [PE1.2] times pop\n",
|
||||
" 14 9 [+] . dupdip 231 2 >> 3 [PE1.2] times pop\n",
|
||||
" 14 9 . + 9 231 2 >> 3 [PE1.2] times pop\n",
|
||||
" 23 . 9 231 2 >> 3 [PE1.2] times pop\n",
|
||||
" 23 9 . 231 2 >> 3 [PE1.2] times pop\n",
|
||||
" 23 9 231 . 2 >> 3 [PE1.2] times pop\n",
|
||||
" 23 9 231 2 . >> 3 [PE1.2] times pop\n",
|
||||
" 23 9 57 . 3 [PE1.2] times pop\n",
|
||||
" 23 9 57 3 . [PE1.2] times pop\n",
|
||||
" 23 9 57 3 [PE1.2] . times pop\n",
|
||||
" 23 9 57 [PE1.2] . i 2 [PE1.2] times pop\n",
|
||||
" 23 9 57 . PE1.2 2 [PE1.2] times pop\n",
|
||||
" 23 9 57 . [3 & PE1.1] dupdip 2 >> 2 [PE1.2] times pop\n",
|
||||
" 23 9 57 [3 & PE1.1] . dupdip 2 >> 2 [PE1.2] times pop\n",
|
||||
" 23 9 57 . 3 & PE1.1 57 2 >> 2 [PE1.2] times pop\n",
|
||||
" 23 9 57 3 . & PE1.1 57 2 >> 2 [PE1.2] times pop\n",
|
||||
" 23 9 1 . PE1.1 57 2 >> 2 [PE1.2] times pop\n",
|
||||
" 23 9 1 . + [+] dupdip 57 2 >> 2 [PE1.2] times pop\n",
|
||||
" 23 10 . [+] dupdip 57 2 >> 2 [PE1.2] times pop\n",
|
||||
" 23 10 [+] . dupdip 57 2 >> 2 [PE1.2] times pop\n",
|
||||
" 23 10 . + 10 57 2 >> 2 [PE1.2] times pop\n",
|
||||
" 33 . 10 57 2 >> 2 [PE1.2] times pop\n",
|
||||
" 33 10 . 57 2 >> 2 [PE1.2] times pop\n",
|
||||
" 33 10 57 . 2 >> 2 [PE1.2] times pop\n",
|
||||
" 33 10 57 2 . >> 2 [PE1.2] times pop\n",
|
||||
" 33 10 14 . 2 [PE1.2] times pop\n",
|
||||
" 33 10 14 2 . [PE1.2] times pop\n",
|
||||
" 33 10 14 2 [PE1.2] . times pop\n",
|
||||
" 33 10 14 [PE1.2] . i 1 [PE1.2] times pop\n",
|
||||
" 33 10 14 . PE1.2 1 [PE1.2] times pop\n",
|
||||
" 33 10 14 . [3 & PE1.1] dupdip 2 >> 1 [PE1.2] times pop\n",
|
||||
" 33 10 14 [3 & PE1.1] . dupdip 2 >> 1 [PE1.2] times pop\n",
|
||||
" 33 10 14 . 3 & PE1.1 14 2 >> 1 [PE1.2] times pop\n",
|
||||
" 33 10 14 3 . & PE1.1 14 2 >> 1 [PE1.2] times pop\n",
|
||||
" 33 10 2 . PE1.1 14 2 >> 1 [PE1.2] times pop\n",
|
||||
" 33 10 2 . + [+] dupdip 14 2 >> 1 [PE1.2] times pop\n",
|
||||
" 33 12 . [+] dupdip 14 2 >> 1 [PE1.2] times pop\n",
|
||||
" 33 12 [+] . dupdip 14 2 >> 1 [PE1.2] times pop\n",
|
||||
" 33 12 . + 12 14 2 >> 1 [PE1.2] times pop\n",
|
||||
" 45 . 12 14 2 >> 1 [PE1.2] times pop\n",
|
||||
" 45 12 . 14 2 >> 1 [PE1.2] times pop\n",
|
||||
" 45 12 14 . 2 >> 1 [PE1.2] times pop\n",
|
||||
" 45 12 14 2 . >> 1 [PE1.2] times pop\n",
|
||||
" 45 12 3 . 1 [PE1.2] times pop\n",
|
||||
" 45 12 3 1 . [PE1.2] times pop\n",
|
||||
" 45 12 3 1 [PE1.2] . times pop\n",
|
||||
" 45 12 3 [PE1.2] . i pop\n",
|
||||
" 45 12 3 . PE1.2 pop\n",
|
||||
" 45 12 3 . [3 & PE1.1] dupdip 2 >> pop\n",
|
||||
" 45 12 3 [3 & PE1.1] . dupdip 2 >> pop\n",
|
||||
" 45 12 3 . 3 & PE1.1 3 2 >> pop\n",
|
||||
" 45 12 3 3 . & PE1.1 3 2 >> pop\n",
|
||||
" 45 12 3 . PE1.1 3 2 >> pop\n",
|
||||
" 45 12 3 . + [+] dupdip 3 2 >> pop\n",
|
||||
" 45 15 . [+] dupdip 3 2 >> pop\n",
|
||||
" 45 15 [+] . dupdip 3 2 >> pop\n",
|
||||
" 45 15 . + 15 3 2 >> pop\n",
|
||||
" 60 . 15 3 2 >> pop\n",
|
||||
" 60 15 . 3 2 >> pop\n",
|
||||
" 60 15 3 . 2 >> pop\n",
|
||||
" 60 15 3 2 . >> pop\n",
|
||||
" 60 15 0 . pop\n",
|
||||
" 60 15 . \n"
|
||||
" • 0 0 14811 7 [PE1.2] times pop\n",
|
||||
" 0 • 0 14811 7 [PE1.2] times pop\n",
|
||||
" 0 0 • 14811 7 [PE1.2] times pop\n",
|
||||
" 0 0 14811 • 7 [PE1.2] times pop\n",
|
||||
" 0 0 14811 7 • [PE1.2] times pop\n",
|
||||
" 0 0 14811 7 [PE1.2] • times pop\n",
|
||||
" 0 0 14811 • PE1.2 6 [PE1.2] times pop\n",
|
||||
" 0 0 14811 • [3 & PE1.1] dupdip 2 >> 6 [PE1.2] times pop\n",
|
||||
"0 0 14811 [3 & PE1.1] • dupdip 2 >> 6 [PE1.2] times pop\n",
|
||||
" 0 0 14811 • 3 & PE1.1 14811 2 >> 6 [PE1.2] times pop\n",
|
||||
" 0 0 14811 3 • & PE1.1 14811 2 >> 6 [PE1.2] times pop\n",
|
||||
" 0 0 3 • PE1.1 14811 2 >> 6 [PE1.2] times pop\n",
|
||||
" 0 0 3 • + [+] dupdip 14811 2 >> 6 [PE1.2] times pop\n",
|
||||
" 0 3 • [+] dupdip 14811 2 >> 6 [PE1.2] times pop\n",
|
||||
" 0 3 [+] • dupdip 14811 2 >> 6 [PE1.2] times pop\n",
|
||||
" 0 3 • + 3 14811 2 >> 6 [PE1.2] times pop\n",
|
||||
" 3 • 3 14811 2 >> 6 [PE1.2] times pop\n",
|
||||
" 3 3 • 14811 2 >> 6 [PE1.2] times pop\n",
|
||||
" 3 3 14811 • 2 >> 6 [PE1.2] times pop\n",
|
||||
" 3 3 14811 2 • >> 6 [PE1.2] times pop\n",
|
||||
" 3 3 3702 • 6 [PE1.2] times pop\n",
|
||||
" 3 3 3702 6 • [PE1.2] times pop\n",
|
||||
" 3 3 3702 6 [PE1.2] • times pop\n",
|
||||
" 3 3 3702 • PE1.2 5 [PE1.2] times pop\n",
|
||||
" 3 3 3702 • [3 & PE1.1] dupdip 2 >> 5 [PE1.2] times pop\n",
|
||||
" 3 3 3702 [3 & PE1.1] • dupdip 2 >> 5 [PE1.2] times pop\n",
|
||||
" 3 3 3702 • 3 & PE1.1 3702 2 >> 5 [PE1.2] times pop\n",
|
||||
" 3 3 3702 3 • & PE1.1 3702 2 >> 5 [PE1.2] times pop\n",
|
||||
" 3 3 2 • PE1.1 3702 2 >> 5 [PE1.2] times pop\n",
|
||||
" 3 3 2 • + [+] dupdip 3702 2 >> 5 [PE1.2] times pop\n",
|
||||
" 3 5 • [+] dupdip 3702 2 >> 5 [PE1.2] times pop\n",
|
||||
" 3 5 [+] • dupdip 3702 2 >> 5 [PE1.2] times pop\n",
|
||||
" 3 5 • + 5 3702 2 >> 5 [PE1.2] times pop\n",
|
||||
" 8 • 5 3702 2 >> 5 [PE1.2] times pop\n",
|
||||
" 8 5 • 3702 2 >> 5 [PE1.2] times pop\n",
|
||||
" 8 5 3702 • 2 >> 5 [PE1.2] times pop\n",
|
||||
" 8 5 3702 2 • >> 5 [PE1.2] times pop\n",
|
||||
" 8 5 925 • 5 [PE1.2] times pop\n",
|
||||
" 8 5 925 5 • [PE1.2] times pop\n",
|
||||
" 8 5 925 5 [PE1.2] • times pop\n",
|
||||
" 8 5 925 • PE1.2 4 [PE1.2] times pop\n",
|
||||
" 8 5 925 • [3 & PE1.1] dupdip 2 >> 4 [PE1.2] times pop\n",
|
||||
" 8 5 925 [3 & PE1.1] • dupdip 2 >> 4 [PE1.2] times pop\n",
|
||||
" 8 5 925 • 3 & PE1.1 925 2 >> 4 [PE1.2] times pop\n",
|
||||
" 8 5 925 3 • & PE1.1 925 2 >> 4 [PE1.2] times pop\n",
|
||||
" 8 5 1 • PE1.1 925 2 >> 4 [PE1.2] times pop\n",
|
||||
" 8 5 1 • + [+] dupdip 925 2 >> 4 [PE1.2] times pop\n",
|
||||
" 8 6 • [+] dupdip 925 2 >> 4 [PE1.2] times pop\n",
|
||||
" 8 6 [+] • dupdip 925 2 >> 4 [PE1.2] times pop\n",
|
||||
" 8 6 • + 6 925 2 >> 4 [PE1.2] times pop\n",
|
||||
" 14 • 6 925 2 >> 4 [PE1.2] times pop\n",
|
||||
" 14 6 • 925 2 >> 4 [PE1.2] times pop\n",
|
||||
" 14 6 925 • 2 >> 4 [PE1.2] times pop\n",
|
||||
" 14 6 925 2 • >> 4 [PE1.2] times pop\n",
|
||||
" 14 6 231 • 4 [PE1.2] times pop\n",
|
||||
" 14 6 231 4 • [PE1.2] times pop\n",
|
||||
" 14 6 231 4 [PE1.2] • times pop\n",
|
||||
" 14 6 231 • PE1.2 3 [PE1.2] times pop\n",
|
||||
" 14 6 231 • [3 & PE1.1] dupdip 2 >> 3 [PE1.2] times pop\n",
|
||||
" 14 6 231 [3 & PE1.1] • dupdip 2 >> 3 [PE1.2] times pop\n",
|
||||
" 14 6 231 • 3 & PE1.1 231 2 >> 3 [PE1.2] times pop\n",
|
||||
" 14 6 231 3 • & PE1.1 231 2 >> 3 [PE1.2] times pop\n",
|
||||
" 14 6 3 • PE1.1 231 2 >> 3 [PE1.2] times pop\n",
|
||||
" 14 6 3 • + [+] dupdip 231 2 >> 3 [PE1.2] times pop\n",
|
||||
" 14 9 • [+] dupdip 231 2 >> 3 [PE1.2] times pop\n",
|
||||
" 14 9 [+] • dupdip 231 2 >> 3 [PE1.2] times pop\n",
|
||||
" 14 9 • + 9 231 2 >> 3 [PE1.2] times pop\n",
|
||||
" 23 • 9 231 2 >> 3 [PE1.2] times pop\n",
|
||||
" 23 9 • 231 2 >> 3 [PE1.2] times pop\n",
|
||||
" 23 9 231 • 2 >> 3 [PE1.2] times pop\n",
|
||||
" 23 9 231 2 • >> 3 [PE1.2] times pop\n",
|
||||
" 23 9 57 • 3 [PE1.2] times pop\n",
|
||||
" 23 9 57 3 • [PE1.2] times pop\n",
|
||||
" 23 9 57 3 [PE1.2] • times pop\n",
|
||||
" 23 9 57 • PE1.2 2 [PE1.2] times pop\n",
|
||||
" 23 9 57 • [3 & PE1.1] dupdip 2 >> 2 [PE1.2] times pop\n",
|
||||
" 23 9 57 [3 & PE1.1] • dupdip 2 >> 2 [PE1.2] times pop\n",
|
||||
" 23 9 57 • 3 & PE1.1 57 2 >> 2 [PE1.2] times pop\n",
|
||||
" 23 9 57 3 • & PE1.1 57 2 >> 2 [PE1.2] times pop\n",
|
||||
" 23 9 1 • PE1.1 57 2 >> 2 [PE1.2] times pop\n",
|
||||
" 23 9 1 • + [+] dupdip 57 2 >> 2 [PE1.2] times pop\n",
|
||||
" 23 10 • [+] dupdip 57 2 >> 2 [PE1.2] times pop\n",
|
||||
" 23 10 [+] • dupdip 57 2 >> 2 [PE1.2] times pop\n",
|
||||
" 23 10 • + 10 57 2 >> 2 [PE1.2] times pop\n",
|
||||
" 33 • 10 57 2 >> 2 [PE1.2] times pop\n",
|
||||
" 33 10 • 57 2 >> 2 [PE1.2] times pop\n",
|
||||
" 33 10 57 • 2 >> 2 [PE1.2] times pop\n",
|
||||
" 33 10 57 2 • >> 2 [PE1.2] times pop\n",
|
||||
" 33 10 14 • 2 [PE1.2] times pop\n",
|
||||
" 33 10 14 2 • [PE1.2] times pop\n",
|
||||
" 33 10 14 2 [PE1.2] • times pop\n",
|
||||
" 33 10 14 • PE1.2 1 [PE1.2] times pop\n",
|
||||
" 33 10 14 • [3 & PE1.1] dupdip 2 >> 1 [PE1.2] times pop\n",
|
||||
" 33 10 14 [3 & PE1.1] • dupdip 2 >> 1 [PE1.2] times pop\n",
|
||||
" 33 10 14 • 3 & PE1.1 14 2 >> 1 [PE1.2] times pop\n",
|
||||
" 33 10 14 3 • & PE1.1 14 2 >> 1 [PE1.2] times pop\n",
|
||||
" 33 10 2 • PE1.1 14 2 >> 1 [PE1.2] times pop\n",
|
||||
" 33 10 2 • + [+] dupdip 14 2 >> 1 [PE1.2] times pop\n",
|
||||
" 33 12 • [+] dupdip 14 2 >> 1 [PE1.2] times pop\n",
|
||||
" 33 12 [+] • dupdip 14 2 >> 1 [PE1.2] times pop\n",
|
||||
" 33 12 • + 12 14 2 >> 1 [PE1.2] times pop\n",
|
||||
" 45 • 12 14 2 >> 1 [PE1.2] times pop\n",
|
||||
" 45 12 • 14 2 >> 1 [PE1.2] times pop\n",
|
||||
" 45 12 14 • 2 >> 1 [PE1.2] times pop\n",
|
||||
" 45 12 14 2 • >> 1 [PE1.2] times pop\n",
|
||||
" 45 12 3 • 1 [PE1.2] times pop\n",
|
||||
" 45 12 3 1 • [PE1.2] times pop\n",
|
||||
" 45 12 3 1 [PE1.2] • times pop\n",
|
||||
" 45 12 3 • PE1.2 pop\n",
|
||||
" 45 12 3 • [3 & PE1.1] dupdip 2 >> pop\n",
|
||||
" 45 12 3 [3 & PE1.1] • dupdip 2 >> pop\n",
|
||||
" 45 12 3 • 3 & PE1.1 3 2 >> pop\n",
|
||||
" 45 12 3 3 • & PE1.1 3 2 >> pop\n",
|
||||
" 45 12 3 • PE1.1 3 2 >> pop\n",
|
||||
" 45 12 3 • + [+] dupdip 3 2 >> pop\n",
|
||||
" 45 15 • [+] dupdip 3 2 >> pop\n",
|
||||
" 45 15 [+] • dupdip 3 2 >> pop\n",
|
||||
" 45 15 • + 15 3 2 >> pop\n",
|
||||
" 60 • 15 3 2 >> pop\n",
|
||||
" 60 15 • 3 2 >> pop\n",
|
||||
" 60 15 3 • 2 >> pop\n",
|
||||
" 60 15 3 2 • >> pop\n",
|
||||
" 60 15 0 • pop\n",
|
||||
" 60 15 • \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -646,7 +639,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('PE1 == 0 0 66 [14811 7 [PE1.2] times pop] times 14811 4 [PE1.2] times popop')"
|
||||
"define('PE1 0 0 66 [14811 7 [PE1.2] times pop] times 14811 4 [PE1.2] times popop')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -686,7 +679,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('PE1.3 == 14811 swap [PE1.2] times pop')"
|
||||
"define('PE1.3 14811 swap [PE1.2] times pop')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -702,7 +695,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('PE1 == 0 0 66 [7 PE1.3] times 4 PE1.3 pop')"
|
||||
"define('PE1 0 0 66 [7 PE1.3] times 4 PE1.3 pop')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -750,7 +743,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('PE1.terms == [0 swap [dup [pop 14811] [] branch [3 &] dupdip 2 >>] dip rest cons]')"
|
||||
"define('PE1.terms [0 swap [dup [pop 14811] [] branch [3 &] dupdip 2 >>] dip rest cons]')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -925,7 +918,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('F == dup ++ * 2 floordiv')"
|
||||
"define('F dup ++ * 2 floordiv')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -937,14 +930,14 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . 10 F\n",
|
||||
" 10 . F\n",
|
||||
" 10 . dup ++ * 2 floordiv\n",
|
||||
"10 10 . ++ * 2 floordiv\n",
|
||||
"10 11 . * 2 floordiv\n",
|
||||
" 110 . 2 floordiv\n",
|
||||
"110 2 . floordiv\n",
|
||||
" 55 . \n"
|
||||
" • 10 F\n",
|
||||
" 10 • F\n",
|
||||
" 10 • dup ++ * 2 floordiv\n",
|
||||
"10 10 • ++ * 2 floordiv\n",
|
||||
"10 11 • * 2 floordiv\n",
|
||||
" 110 • 2 floordiv\n",
|
||||
"110 2 • floordiv\n",
|
||||
" 55 • \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -1106,14 +1099,14 @@
|
|||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 2
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython2",
|
||||
"version": "2.7.12"
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.8.3"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
|
|
|||
|
|
@ -13,7 +13,7 @@ Let's create a predicate that returns `True` if a number is a multiple of 3 or 5
|
|||
|
||||
|
||||
```python
|
||||
define('P == [3 % not] dupdip 5 % not or')
|
||||
define('P [3 % not] dupdip 5 % not or')
|
||||
```
|
||||
|
||||
|
||||
|
|
@ -21,19 +21,19 @@ define('P == [3 % not] dupdip 5 % not or')
|
|||
V('80 P')
|
||||
```
|
||||
|
||||
. 80 P
|
||||
80 . P
|
||||
80 . [3 % not] dupdip 5 % not or
|
||||
80 [3 % not] . dupdip 5 % not or
|
||||
80 . 3 % not 80 5 % not or
|
||||
80 3 . % not 80 5 % not or
|
||||
2 . not 80 5 % not or
|
||||
False . 80 5 % not or
|
||||
False 80 . 5 % not or
|
||||
False 80 5 . % not or
|
||||
False 0 . not or
|
||||
False True . or
|
||||
True .
|
||||
• 80 P
|
||||
80 • P
|
||||
80 • [3 % not] dupdip 5 % not or
|
||||
80 [3 % not] • dupdip 5 % not or
|
||||
80 • 3 % not 80 5 % not or
|
||||
80 3 • % not 80 5 % not or
|
||||
2 • not 80 5 % not or
|
||||
False • 80 5 % not or
|
||||
False 80 • 5 % not or
|
||||
False 80 5 • % not or
|
||||
False 0 • not or
|
||||
False True • or
|
||||
True •
|
||||
|
||||
|
||||
Given the predicate function `P` a suitable program is:
|
||||
|
|
@ -86,7 +86,7 @@ counter to the running sum. This function will do that:
|
|||
|
||||
|
||||
```python
|
||||
define('PE1.1 == + [+] dupdip')
|
||||
define('PE1.1 + [+] dupdip')
|
||||
```
|
||||
|
||||
|
||||
|
|
@ -94,16 +94,16 @@ define('PE1.1 == + [+] dupdip')
|
|||
V('0 0 3 PE1.1')
|
||||
```
|
||||
|
||||
. 0 0 3 PE1.1
|
||||
0 . 0 3 PE1.1
|
||||
0 0 . 3 PE1.1
|
||||
0 0 3 . PE1.1
|
||||
0 0 3 . + [+] dupdip
|
||||
0 3 . [+] dupdip
|
||||
0 3 [+] . dupdip
|
||||
0 3 . + 3
|
||||
3 . 3
|
||||
3 3 .
|
||||
• 0 0 3 PE1.1
|
||||
0 • 0 3 PE1.1
|
||||
0 0 • 3 PE1.1
|
||||
0 0 3 • PE1.1
|
||||
0 0 3 • + [+] dupdip
|
||||
0 3 • [+] dupdip
|
||||
0 3 [+] • dupdip
|
||||
0 3 • + 3
|
||||
3 • 3
|
||||
3 3 •
|
||||
|
||||
|
||||
|
||||
|
|
@ -111,79 +111,79 @@ V('0 0 3 PE1.1')
|
|||
V('0 0 [3 2 1 3 1 2 3] [PE1.1] step')
|
||||
```
|
||||
|
||||
. 0 0 [3 2 1 3 1 2 3] [PE1.1] step
|
||||
0 . 0 [3 2 1 3 1 2 3] [PE1.1] step
|
||||
0 0 . [3 2 1 3 1 2 3] [PE1.1] step
|
||||
0 0 [3 2 1 3 1 2 3] . [PE1.1] step
|
||||
0 0 [3 2 1 3 1 2 3] [PE1.1] . step
|
||||
0 0 3 [PE1.1] . i [2 1 3 1 2 3] [PE1.1] step
|
||||
0 0 3 . PE1.1 [2 1 3 1 2 3] [PE1.1] step
|
||||
0 0 3 . + [+] dupdip [2 1 3 1 2 3] [PE1.1] step
|
||||
0 3 . [+] dupdip [2 1 3 1 2 3] [PE1.1] step
|
||||
0 3 [+] . dupdip [2 1 3 1 2 3] [PE1.1] step
|
||||
0 3 . + 3 [2 1 3 1 2 3] [PE1.1] step
|
||||
3 . 3 [2 1 3 1 2 3] [PE1.1] step
|
||||
3 3 . [2 1 3 1 2 3] [PE1.1] step
|
||||
3 3 [2 1 3 1 2 3] . [PE1.1] step
|
||||
3 3 [2 1 3 1 2 3] [PE1.1] . step
|
||||
3 3 2 [PE1.1] . i [1 3 1 2 3] [PE1.1] step
|
||||
3 3 2 . PE1.1 [1 3 1 2 3] [PE1.1] step
|
||||
3 3 2 . + [+] dupdip [1 3 1 2 3] [PE1.1] step
|
||||
3 5 . [+] dupdip [1 3 1 2 3] [PE1.1] step
|
||||
3 5 [+] . dupdip [1 3 1 2 3] [PE1.1] step
|
||||
3 5 . + 5 [1 3 1 2 3] [PE1.1] step
|
||||
8 . 5 [1 3 1 2 3] [PE1.1] step
|
||||
8 5 . [1 3 1 2 3] [PE1.1] step
|
||||
8 5 [1 3 1 2 3] . [PE1.1] step
|
||||
8 5 [1 3 1 2 3] [PE1.1] . step
|
||||
8 5 1 [PE1.1] . i [3 1 2 3] [PE1.1] step
|
||||
8 5 1 . PE1.1 [3 1 2 3] [PE1.1] step
|
||||
8 5 1 . + [+] dupdip [3 1 2 3] [PE1.1] step
|
||||
8 6 . [+] dupdip [3 1 2 3] [PE1.1] step
|
||||
8 6 [+] . dupdip [3 1 2 3] [PE1.1] step
|
||||
8 6 . + 6 [3 1 2 3] [PE1.1] step
|
||||
14 . 6 [3 1 2 3] [PE1.1] step
|
||||
14 6 . [3 1 2 3] [PE1.1] step
|
||||
14 6 [3 1 2 3] . [PE1.1] step
|
||||
14 6 [3 1 2 3] [PE1.1] . step
|
||||
14 6 3 [PE1.1] . i [1 2 3] [PE1.1] step
|
||||
14 6 3 . PE1.1 [1 2 3] [PE1.1] step
|
||||
14 6 3 . + [+] dupdip [1 2 3] [PE1.1] step
|
||||
14 9 . [+] dupdip [1 2 3] [PE1.1] step
|
||||
14 9 [+] . dupdip [1 2 3] [PE1.1] step
|
||||
14 9 . + 9 [1 2 3] [PE1.1] step
|
||||
23 . 9 [1 2 3] [PE1.1] step
|
||||
23 9 . [1 2 3] [PE1.1] step
|
||||
23 9 [1 2 3] . [PE1.1] step
|
||||
23 9 [1 2 3] [PE1.1] . step
|
||||
23 9 1 [PE1.1] . i [2 3] [PE1.1] step
|
||||
23 9 1 . PE1.1 [2 3] [PE1.1] step
|
||||
23 9 1 . + [+] dupdip [2 3] [PE1.1] step
|
||||
23 10 . [+] dupdip [2 3] [PE1.1] step
|
||||
23 10 [+] . dupdip [2 3] [PE1.1] step
|
||||
23 10 . + 10 [2 3] [PE1.1] step
|
||||
33 . 10 [2 3] [PE1.1] step
|
||||
33 10 . [2 3] [PE1.1] step
|
||||
33 10 [2 3] . [PE1.1] step
|
||||
33 10 [2 3] [PE1.1] . step
|
||||
33 10 2 [PE1.1] . i [3] [PE1.1] step
|
||||
33 10 2 . PE1.1 [3] [PE1.1] step
|
||||
33 10 2 . + [+] dupdip [3] [PE1.1] step
|
||||
33 12 . [+] dupdip [3] [PE1.1] step
|
||||
33 12 [+] . dupdip [3] [PE1.1] step
|
||||
33 12 . + 12 [3] [PE1.1] step
|
||||
45 . 12 [3] [PE1.1] step
|
||||
45 12 . [3] [PE1.1] step
|
||||
45 12 [3] . [PE1.1] step
|
||||
45 12 [3] [PE1.1] . step
|
||||
45 12 3 [PE1.1] . i
|
||||
45 12 3 . PE1.1
|
||||
45 12 3 . + [+] dupdip
|
||||
45 15 . [+] dupdip
|
||||
45 15 [+] . dupdip
|
||||
45 15 . + 15
|
||||
60 . 15
|
||||
60 15 .
|
||||
• 0 0 [3 2 1 3 1 2 3] [PE1.1] step
|
||||
0 • 0 [3 2 1 3 1 2 3] [PE1.1] step
|
||||
0 0 • [3 2 1 3 1 2 3] [PE1.1] step
|
||||
0 0 [3 2 1 3 1 2 3] • [PE1.1] step
|
||||
0 0 [3 2 1 3 1 2 3] [PE1.1] • step
|
||||
0 0 3 [PE1.1] • i [2 1 3 1 2 3] [PE1.1] step
|
||||
0 0 3 • PE1.1 [2 1 3 1 2 3] [PE1.1] step
|
||||
0 0 3 • + [+] dupdip [2 1 3 1 2 3] [PE1.1] step
|
||||
0 3 • [+] dupdip [2 1 3 1 2 3] [PE1.1] step
|
||||
0 3 [+] • dupdip [2 1 3 1 2 3] [PE1.1] step
|
||||
0 3 • + 3 [2 1 3 1 2 3] [PE1.1] step
|
||||
3 • 3 [2 1 3 1 2 3] [PE1.1] step
|
||||
3 3 • [2 1 3 1 2 3] [PE1.1] step
|
||||
3 3 [2 1 3 1 2 3] • [PE1.1] step
|
||||
3 3 [2 1 3 1 2 3] [PE1.1] • step
|
||||
3 3 2 [PE1.1] • i [1 3 1 2 3] [PE1.1] step
|
||||
3 3 2 • PE1.1 [1 3 1 2 3] [PE1.1] step
|
||||
3 3 2 • + [+] dupdip [1 3 1 2 3] [PE1.1] step
|
||||
3 5 • [+] dupdip [1 3 1 2 3] [PE1.1] step
|
||||
3 5 [+] • dupdip [1 3 1 2 3] [PE1.1] step
|
||||
3 5 • + 5 [1 3 1 2 3] [PE1.1] step
|
||||
8 • 5 [1 3 1 2 3] [PE1.1] step
|
||||
8 5 • [1 3 1 2 3] [PE1.1] step
|
||||
8 5 [1 3 1 2 3] • [PE1.1] step
|
||||
8 5 [1 3 1 2 3] [PE1.1] • step
|
||||
8 5 1 [PE1.1] • i [3 1 2 3] [PE1.1] step
|
||||
8 5 1 • PE1.1 [3 1 2 3] [PE1.1] step
|
||||
8 5 1 • + [+] dupdip [3 1 2 3] [PE1.1] step
|
||||
8 6 • [+] dupdip [3 1 2 3] [PE1.1] step
|
||||
8 6 [+] • dupdip [3 1 2 3] [PE1.1] step
|
||||
8 6 • + 6 [3 1 2 3] [PE1.1] step
|
||||
14 • 6 [3 1 2 3] [PE1.1] step
|
||||
14 6 • [3 1 2 3] [PE1.1] step
|
||||
14 6 [3 1 2 3] • [PE1.1] step
|
||||
14 6 [3 1 2 3] [PE1.1] • step
|
||||
14 6 3 [PE1.1] • i [1 2 3] [PE1.1] step
|
||||
14 6 3 • PE1.1 [1 2 3] [PE1.1] step
|
||||
14 6 3 • + [+] dupdip [1 2 3] [PE1.1] step
|
||||
14 9 • [+] dupdip [1 2 3] [PE1.1] step
|
||||
14 9 [+] • dupdip [1 2 3] [PE1.1] step
|
||||
14 9 • + 9 [1 2 3] [PE1.1] step
|
||||
23 • 9 [1 2 3] [PE1.1] step
|
||||
23 9 • [1 2 3] [PE1.1] step
|
||||
23 9 [1 2 3] • [PE1.1] step
|
||||
23 9 [1 2 3] [PE1.1] • step
|
||||
23 9 1 [PE1.1] • i [2 3] [PE1.1] step
|
||||
23 9 1 • PE1.1 [2 3] [PE1.1] step
|
||||
23 9 1 • + [+] dupdip [2 3] [PE1.1] step
|
||||
23 10 • [+] dupdip [2 3] [PE1.1] step
|
||||
23 10 [+] • dupdip [2 3] [PE1.1] step
|
||||
23 10 • + 10 [2 3] [PE1.1] step
|
||||
33 • 10 [2 3] [PE1.1] step
|
||||
33 10 • [2 3] [PE1.1] step
|
||||
33 10 [2 3] • [PE1.1] step
|
||||
33 10 [2 3] [PE1.1] • step
|
||||
33 10 2 [PE1.1] • i [3] [PE1.1] step
|
||||
33 10 2 • PE1.1 [3] [PE1.1] step
|
||||
33 10 2 • + [+] dupdip [3] [PE1.1] step
|
||||
33 12 • [+] dupdip [3] [PE1.1] step
|
||||
33 12 [+] • dupdip [3] [PE1.1] step
|
||||
33 12 • + 12 [3] [PE1.1] step
|
||||
45 • 12 [3] [PE1.1] step
|
||||
45 12 • [3] [PE1.1] step
|
||||
45 12 [3] • [PE1.1] step
|
||||
45 12 [3] [PE1.1] • step
|
||||
45 12 3 [PE1.1] • i
|
||||
45 12 3 • PE1.1
|
||||
45 12 3 • + [+] dupdip
|
||||
45 15 • [+] dupdip
|
||||
45 15 [+] • dupdip
|
||||
45 15 • + 15
|
||||
60 • 15
|
||||
60 15 •
|
||||
|
||||
|
||||
So one `step` through all seven terms brings the counter to 15 and the total to 60.
|
||||
|
|
@ -196,7 +196,7 @@ So one `step` through all seven terms brings the counter to 15 and the total to
|
|||
|
||||
|
||||
|
||||
66
|
||||
66.66666666666667
|
||||
|
||||
|
||||
|
||||
|
|
@ -242,7 +242,7 @@ That means we want to run the full list of numbers sixty-six times to get to 990
|
|||
|
||||
|
||||
```python
|
||||
define('PE1 == 0 0 66 [[3 2 1 3 1 2 3] [PE1.1] step] times [3 2 1 3] [PE1.1] step pop')
|
||||
define('PE1 0 0 66 [[3 2 1 3 1 2 3] [PE1.1] step] times [3 2 1 3] [PE1.1] step pop')
|
||||
```
|
||||
|
||||
|
||||
|
|
@ -278,7 +278,7 @@ integer terms from the list.
|
|||
|
||||
|
||||
```python
|
||||
define('PE1.2 == [3 & PE1.1] dupdip 2 >>')
|
||||
define('PE1.2 [3 & PE1.1] dupdip 2 >>')
|
||||
```
|
||||
|
||||
|
||||
|
|
@ -286,24 +286,24 @@ define('PE1.2 == [3 & PE1.1] dupdip 2 >>')
|
|||
V('0 0 14811 PE1.2')
|
||||
```
|
||||
|
||||
. 0 0 14811 PE1.2
|
||||
0 . 0 14811 PE1.2
|
||||
0 0 . 14811 PE1.2
|
||||
0 0 14811 . PE1.2
|
||||
0 0 14811 . [3 & PE1.1] dupdip 2 >>
|
||||
0 0 14811 [3 & PE1.1] . dupdip 2 >>
|
||||
0 0 14811 . 3 & PE1.1 14811 2 >>
|
||||
0 0 14811 3 . & PE1.1 14811 2 >>
|
||||
0 0 3 . PE1.1 14811 2 >>
|
||||
0 0 3 . + [+] dupdip 14811 2 >>
|
||||
0 3 . [+] dupdip 14811 2 >>
|
||||
0 3 [+] . dupdip 14811 2 >>
|
||||
0 3 . + 3 14811 2 >>
|
||||
3 . 3 14811 2 >>
|
||||
3 3 . 14811 2 >>
|
||||
3 3 14811 . 2 >>
|
||||
3 3 14811 2 . >>
|
||||
3 3 3702 .
|
||||
• 0 0 14811 PE1.2
|
||||
0 • 0 14811 PE1.2
|
||||
0 0 • 14811 PE1.2
|
||||
0 0 14811 • PE1.2
|
||||
0 0 14811 • [3 & PE1.1] dupdip 2 >>
|
||||
0 0 14811 [3 & PE1.1] • dupdip 2 >>
|
||||
0 0 14811 • 3 & PE1.1 14811 2 >>
|
||||
0 0 14811 3 • & PE1.1 14811 2 >>
|
||||
0 0 3 • PE1.1 14811 2 >>
|
||||
0 0 3 • + [+] dupdip 14811 2 >>
|
||||
0 3 • [+] dupdip 14811 2 >>
|
||||
0 3 [+] • dupdip 14811 2 >>
|
||||
0 3 • + 3 14811 2 >>
|
||||
3 • 3 14811 2 >>
|
||||
3 3 • 14811 2 >>
|
||||
3 3 14811 • 2 >>
|
||||
3 3 14811 2 • >>
|
||||
3 3 3702 •
|
||||
|
||||
|
||||
|
||||
|
|
@ -311,24 +311,24 @@ V('0 0 14811 PE1.2')
|
|||
V('3 3 3702 PE1.2')
|
||||
```
|
||||
|
||||
. 3 3 3702 PE1.2
|
||||
3 . 3 3702 PE1.2
|
||||
3 3 . 3702 PE1.2
|
||||
3 3 3702 . PE1.2
|
||||
3 3 3702 . [3 & PE1.1] dupdip 2 >>
|
||||
3 3 3702 [3 & PE1.1] . dupdip 2 >>
|
||||
3 3 3702 . 3 & PE1.1 3702 2 >>
|
||||
3 3 3702 3 . & PE1.1 3702 2 >>
|
||||
3 3 2 . PE1.1 3702 2 >>
|
||||
3 3 2 . + [+] dupdip 3702 2 >>
|
||||
3 5 . [+] dupdip 3702 2 >>
|
||||
3 5 [+] . dupdip 3702 2 >>
|
||||
3 5 . + 5 3702 2 >>
|
||||
8 . 5 3702 2 >>
|
||||
8 5 . 3702 2 >>
|
||||
8 5 3702 . 2 >>
|
||||
8 5 3702 2 . >>
|
||||
8 5 925 .
|
||||
• 3 3 3702 PE1.2
|
||||
3 • 3 3702 PE1.2
|
||||
3 3 • 3702 PE1.2
|
||||
3 3 3702 • PE1.2
|
||||
3 3 3702 • [3 & PE1.1] dupdip 2 >>
|
||||
3 3 3702 [3 & PE1.1] • dupdip 2 >>
|
||||
3 3 3702 • 3 & PE1.1 3702 2 >>
|
||||
3 3 3702 3 • & PE1.1 3702 2 >>
|
||||
3 3 2 • PE1.1 3702 2 >>
|
||||
3 3 2 • + [+] dupdip 3702 2 >>
|
||||
3 5 • [+] dupdip 3702 2 >>
|
||||
3 5 [+] • dupdip 3702 2 >>
|
||||
3 5 • + 5 3702 2 >>
|
||||
8 • 5 3702 2 >>
|
||||
8 5 • 3702 2 >>
|
||||
8 5 3702 • 2 >>
|
||||
8 5 3702 2 • >>
|
||||
8 5 925 •
|
||||
|
||||
|
||||
|
||||
|
|
@ -336,144 +336,137 @@ V('3 3 3702 PE1.2')
|
|||
V('0 0 14811 7 [PE1.2] times pop')
|
||||
```
|
||||
|
||||
. 0 0 14811 7 [PE1.2] times pop
|
||||
0 . 0 14811 7 [PE1.2] times pop
|
||||
0 0 . 14811 7 [PE1.2] times pop
|
||||
0 0 14811 . 7 [PE1.2] times pop
|
||||
0 0 14811 7 . [PE1.2] times pop
|
||||
0 0 14811 7 [PE1.2] . times pop
|
||||
0 0 14811 [PE1.2] . i 6 [PE1.2] times pop
|
||||
0 0 14811 . PE1.2 6 [PE1.2] times pop
|
||||
0 0 14811 . [3 & PE1.1] dupdip 2 >> 6 [PE1.2] times pop
|
||||
0 0 14811 [3 & PE1.1] . dupdip 2 >> 6 [PE1.2] times pop
|
||||
0 0 14811 . 3 & PE1.1 14811 2 >> 6 [PE1.2] times pop
|
||||
0 0 14811 3 . & PE1.1 14811 2 >> 6 [PE1.2] times pop
|
||||
0 0 3 . PE1.1 14811 2 >> 6 [PE1.2] times pop
|
||||
0 0 3 . + [+] dupdip 14811 2 >> 6 [PE1.2] times pop
|
||||
0 3 . [+] dupdip 14811 2 >> 6 [PE1.2] times pop
|
||||
0 3 [+] . dupdip 14811 2 >> 6 [PE1.2] times pop
|
||||
0 3 . + 3 14811 2 >> 6 [PE1.2] times pop
|
||||
3 . 3 14811 2 >> 6 [PE1.2] times pop
|
||||
3 3 . 14811 2 >> 6 [PE1.2] times pop
|
||||
3 3 14811 . 2 >> 6 [PE1.2] times pop
|
||||
3 3 14811 2 . >> 6 [PE1.2] times pop
|
||||
3 3 3702 . 6 [PE1.2] times pop
|
||||
3 3 3702 6 . [PE1.2] times pop
|
||||
3 3 3702 6 [PE1.2] . times pop
|
||||
3 3 3702 [PE1.2] . i 5 [PE1.2] times pop
|
||||
3 3 3702 . PE1.2 5 [PE1.2] times pop
|
||||
3 3 3702 . [3 & PE1.1] dupdip 2 >> 5 [PE1.2] times pop
|
||||
3 3 3702 [3 & PE1.1] . dupdip 2 >> 5 [PE1.2] times pop
|
||||
3 3 3702 . 3 & PE1.1 3702 2 >> 5 [PE1.2] times pop
|
||||
3 3 3702 3 . & PE1.1 3702 2 >> 5 [PE1.2] times pop
|
||||
3 3 2 . PE1.1 3702 2 >> 5 [PE1.2] times pop
|
||||
3 3 2 . + [+] dupdip 3702 2 >> 5 [PE1.2] times pop
|
||||
3 5 . [+] dupdip 3702 2 >> 5 [PE1.2] times pop
|
||||
3 5 [+] . dupdip 3702 2 >> 5 [PE1.2] times pop
|
||||
3 5 . + 5 3702 2 >> 5 [PE1.2] times pop
|
||||
8 . 5 3702 2 >> 5 [PE1.2] times pop
|
||||
8 5 . 3702 2 >> 5 [PE1.2] times pop
|
||||
8 5 3702 . 2 >> 5 [PE1.2] times pop
|
||||
8 5 3702 2 . >> 5 [PE1.2] times pop
|
||||
8 5 925 . 5 [PE1.2] times pop
|
||||
8 5 925 5 . [PE1.2] times pop
|
||||
8 5 925 5 [PE1.2] . times pop
|
||||
8 5 925 [PE1.2] . i 4 [PE1.2] times pop
|
||||
8 5 925 . PE1.2 4 [PE1.2] times pop
|
||||
8 5 925 . [3 & PE1.1] dupdip 2 >> 4 [PE1.2] times pop
|
||||
8 5 925 [3 & PE1.1] . dupdip 2 >> 4 [PE1.2] times pop
|
||||
8 5 925 . 3 & PE1.1 925 2 >> 4 [PE1.2] times pop
|
||||
8 5 925 3 . & PE1.1 925 2 >> 4 [PE1.2] times pop
|
||||
8 5 1 . PE1.1 925 2 >> 4 [PE1.2] times pop
|
||||
8 5 1 . + [+] dupdip 925 2 >> 4 [PE1.2] times pop
|
||||
8 6 . [+] dupdip 925 2 >> 4 [PE1.2] times pop
|
||||
8 6 [+] . dupdip 925 2 >> 4 [PE1.2] times pop
|
||||
8 6 . + 6 925 2 >> 4 [PE1.2] times pop
|
||||
14 . 6 925 2 >> 4 [PE1.2] times pop
|
||||
14 6 . 925 2 >> 4 [PE1.2] times pop
|
||||
14 6 925 . 2 >> 4 [PE1.2] times pop
|
||||
14 6 925 2 . >> 4 [PE1.2] times pop
|
||||
14 6 231 . 4 [PE1.2] times pop
|
||||
14 6 231 4 . [PE1.2] times pop
|
||||
14 6 231 4 [PE1.2] . times pop
|
||||
14 6 231 [PE1.2] . i 3 [PE1.2] times pop
|
||||
14 6 231 . PE1.2 3 [PE1.2] times pop
|
||||
14 6 231 . [3 & PE1.1] dupdip 2 >> 3 [PE1.2] times pop
|
||||
14 6 231 [3 & PE1.1] . dupdip 2 >> 3 [PE1.2] times pop
|
||||
14 6 231 . 3 & PE1.1 231 2 >> 3 [PE1.2] times pop
|
||||
14 6 231 3 . & PE1.1 231 2 >> 3 [PE1.2] times pop
|
||||
14 6 3 . PE1.1 231 2 >> 3 [PE1.2] times pop
|
||||
14 6 3 . + [+] dupdip 231 2 >> 3 [PE1.2] times pop
|
||||
14 9 . [+] dupdip 231 2 >> 3 [PE1.2] times pop
|
||||
14 9 [+] . dupdip 231 2 >> 3 [PE1.2] times pop
|
||||
14 9 . + 9 231 2 >> 3 [PE1.2] times pop
|
||||
23 . 9 231 2 >> 3 [PE1.2] times pop
|
||||
23 9 . 231 2 >> 3 [PE1.2] times pop
|
||||
23 9 231 . 2 >> 3 [PE1.2] times pop
|
||||
23 9 231 2 . >> 3 [PE1.2] times pop
|
||||
23 9 57 . 3 [PE1.2] times pop
|
||||
23 9 57 3 . [PE1.2] times pop
|
||||
23 9 57 3 [PE1.2] . times pop
|
||||
23 9 57 [PE1.2] . i 2 [PE1.2] times pop
|
||||
23 9 57 . PE1.2 2 [PE1.2] times pop
|
||||
23 9 57 . [3 & PE1.1] dupdip 2 >> 2 [PE1.2] times pop
|
||||
23 9 57 [3 & PE1.1] . dupdip 2 >> 2 [PE1.2] times pop
|
||||
23 9 57 . 3 & PE1.1 57 2 >> 2 [PE1.2] times pop
|
||||
23 9 57 3 . & PE1.1 57 2 >> 2 [PE1.2] times pop
|
||||
23 9 1 . PE1.1 57 2 >> 2 [PE1.2] times pop
|
||||
23 9 1 . + [+] dupdip 57 2 >> 2 [PE1.2] times pop
|
||||
23 10 . [+] dupdip 57 2 >> 2 [PE1.2] times pop
|
||||
23 10 [+] . dupdip 57 2 >> 2 [PE1.2] times pop
|
||||
23 10 . + 10 57 2 >> 2 [PE1.2] times pop
|
||||
33 . 10 57 2 >> 2 [PE1.2] times pop
|
||||
33 10 . 57 2 >> 2 [PE1.2] times pop
|
||||
33 10 57 . 2 >> 2 [PE1.2] times pop
|
||||
33 10 57 2 . >> 2 [PE1.2] times pop
|
||||
33 10 14 . 2 [PE1.2] times pop
|
||||
33 10 14 2 . [PE1.2] times pop
|
||||
33 10 14 2 [PE1.2] . times pop
|
||||
33 10 14 [PE1.2] . i 1 [PE1.2] times pop
|
||||
33 10 14 . PE1.2 1 [PE1.2] times pop
|
||||
33 10 14 . [3 & PE1.1] dupdip 2 >> 1 [PE1.2] times pop
|
||||
33 10 14 [3 & PE1.1] . dupdip 2 >> 1 [PE1.2] times pop
|
||||
33 10 14 . 3 & PE1.1 14 2 >> 1 [PE1.2] times pop
|
||||
33 10 14 3 . & PE1.1 14 2 >> 1 [PE1.2] times pop
|
||||
33 10 2 . PE1.1 14 2 >> 1 [PE1.2] times pop
|
||||
33 10 2 . + [+] dupdip 14 2 >> 1 [PE1.2] times pop
|
||||
33 12 . [+] dupdip 14 2 >> 1 [PE1.2] times pop
|
||||
33 12 [+] . dupdip 14 2 >> 1 [PE1.2] times pop
|
||||
33 12 . + 12 14 2 >> 1 [PE1.2] times pop
|
||||
45 . 12 14 2 >> 1 [PE1.2] times pop
|
||||
45 12 . 14 2 >> 1 [PE1.2] times pop
|
||||
45 12 14 . 2 >> 1 [PE1.2] times pop
|
||||
45 12 14 2 . >> 1 [PE1.2] times pop
|
||||
45 12 3 . 1 [PE1.2] times pop
|
||||
45 12 3 1 . [PE1.2] times pop
|
||||
45 12 3 1 [PE1.2] . times pop
|
||||
45 12 3 [PE1.2] . i pop
|
||||
45 12 3 . PE1.2 pop
|
||||
45 12 3 . [3 & PE1.1] dupdip 2 >> pop
|
||||
45 12 3 [3 & PE1.1] . dupdip 2 >> pop
|
||||
45 12 3 . 3 & PE1.1 3 2 >> pop
|
||||
45 12 3 3 . & PE1.1 3 2 >> pop
|
||||
45 12 3 . PE1.1 3 2 >> pop
|
||||
45 12 3 . + [+] dupdip 3 2 >> pop
|
||||
45 15 . [+] dupdip 3 2 >> pop
|
||||
45 15 [+] . dupdip 3 2 >> pop
|
||||
45 15 . + 15 3 2 >> pop
|
||||
60 . 15 3 2 >> pop
|
||||
60 15 . 3 2 >> pop
|
||||
60 15 3 . 2 >> pop
|
||||
60 15 3 2 . >> pop
|
||||
60 15 0 . pop
|
||||
60 15 .
|
||||
• 0 0 14811 7 [PE1.2] times pop
|
||||
0 • 0 14811 7 [PE1.2] times pop
|
||||
0 0 • 14811 7 [PE1.2] times pop
|
||||
0 0 14811 • 7 [PE1.2] times pop
|
||||
0 0 14811 7 • [PE1.2] times pop
|
||||
0 0 14811 7 [PE1.2] • times pop
|
||||
0 0 14811 • PE1.2 6 [PE1.2] times pop
|
||||
0 0 14811 • [3 & PE1.1] dupdip 2 >> 6 [PE1.2] times pop
|
||||
0 0 14811 [3 & PE1.1] • dupdip 2 >> 6 [PE1.2] times pop
|
||||
0 0 14811 • 3 & PE1.1 14811 2 >> 6 [PE1.2] times pop
|
||||
0 0 14811 3 • & PE1.1 14811 2 >> 6 [PE1.2] times pop
|
||||
0 0 3 • PE1.1 14811 2 >> 6 [PE1.2] times pop
|
||||
0 0 3 • + [+] dupdip 14811 2 >> 6 [PE1.2] times pop
|
||||
0 3 • [+] dupdip 14811 2 >> 6 [PE1.2] times pop
|
||||
0 3 [+] • dupdip 14811 2 >> 6 [PE1.2] times pop
|
||||
0 3 • + 3 14811 2 >> 6 [PE1.2] times pop
|
||||
3 • 3 14811 2 >> 6 [PE1.2] times pop
|
||||
3 3 • 14811 2 >> 6 [PE1.2] times pop
|
||||
3 3 14811 • 2 >> 6 [PE1.2] times pop
|
||||
3 3 14811 2 • >> 6 [PE1.2] times pop
|
||||
3 3 3702 • 6 [PE1.2] times pop
|
||||
3 3 3702 6 • [PE1.2] times pop
|
||||
3 3 3702 6 [PE1.2] • times pop
|
||||
3 3 3702 • PE1.2 5 [PE1.2] times pop
|
||||
3 3 3702 • [3 & PE1.1] dupdip 2 >> 5 [PE1.2] times pop
|
||||
3 3 3702 [3 & PE1.1] • dupdip 2 >> 5 [PE1.2] times pop
|
||||
3 3 3702 • 3 & PE1.1 3702 2 >> 5 [PE1.2] times pop
|
||||
3 3 3702 3 • & PE1.1 3702 2 >> 5 [PE1.2] times pop
|
||||
3 3 2 • PE1.1 3702 2 >> 5 [PE1.2] times pop
|
||||
3 3 2 • + [+] dupdip 3702 2 >> 5 [PE1.2] times pop
|
||||
3 5 • [+] dupdip 3702 2 >> 5 [PE1.2] times pop
|
||||
3 5 [+] • dupdip 3702 2 >> 5 [PE1.2] times pop
|
||||
3 5 • + 5 3702 2 >> 5 [PE1.2] times pop
|
||||
8 • 5 3702 2 >> 5 [PE1.2] times pop
|
||||
8 5 • 3702 2 >> 5 [PE1.2] times pop
|
||||
8 5 3702 • 2 >> 5 [PE1.2] times pop
|
||||
8 5 3702 2 • >> 5 [PE1.2] times pop
|
||||
8 5 925 • 5 [PE1.2] times pop
|
||||
8 5 925 5 • [PE1.2] times pop
|
||||
8 5 925 5 [PE1.2] • times pop
|
||||
8 5 925 • PE1.2 4 [PE1.2] times pop
|
||||
8 5 925 • [3 & PE1.1] dupdip 2 >> 4 [PE1.2] times pop
|
||||
8 5 925 [3 & PE1.1] • dupdip 2 >> 4 [PE1.2] times pop
|
||||
8 5 925 • 3 & PE1.1 925 2 >> 4 [PE1.2] times pop
|
||||
8 5 925 3 • & PE1.1 925 2 >> 4 [PE1.2] times pop
|
||||
8 5 1 • PE1.1 925 2 >> 4 [PE1.2] times pop
|
||||
8 5 1 • + [+] dupdip 925 2 >> 4 [PE1.2] times pop
|
||||
8 6 • [+] dupdip 925 2 >> 4 [PE1.2] times pop
|
||||
8 6 [+] • dupdip 925 2 >> 4 [PE1.2] times pop
|
||||
8 6 • + 6 925 2 >> 4 [PE1.2] times pop
|
||||
14 • 6 925 2 >> 4 [PE1.2] times pop
|
||||
14 6 • 925 2 >> 4 [PE1.2] times pop
|
||||
14 6 925 • 2 >> 4 [PE1.2] times pop
|
||||
14 6 925 2 • >> 4 [PE1.2] times pop
|
||||
14 6 231 • 4 [PE1.2] times pop
|
||||
14 6 231 4 • [PE1.2] times pop
|
||||
14 6 231 4 [PE1.2] • times pop
|
||||
14 6 231 • PE1.2 3 [PE1.2] times pop
|
||||
14 6 231 • [3 & PE1.1] dupdip 2 >> 3 [PE1.2] times pop
|
||||
14 6 231 [3 & PE1.1] • dupdip 2 >> 3 [PE1.2] times pop
|
||||
14 6 231 • 3 & PE1.1 231 2 >> 3 [PE1.2] times pop
|
||||
14 6 231 3 • & PE1.1 231 2 >> 3 [PE1.2] times pop
|
||||
14 6 3 • PE1.1 231 2 >> 3 [PE1.2] times pop
|
||||
14 6 3 • + [+] dupdip 231 2 >> 3 [PE1.2] times pop
|
||||
14 9 • [+] dupdip 231 2 >> 3 [PE1.2] times pop
|
||||
14 9 [+] • dupdip 231 2 >> 3 [PE1.2] times pop
|
||||
14 9 • + 9 231 2 >> 3 [PE1.2] times pop
|
||||
23 • 9 231 2 >> 3 [PE1.2] times pop
|
||||
23 9 • 231 2 >> 3 [PE1.2] times pop
|
||||
23 9 231 • 2 >> 3 [PE1.2] times pop
|
||||
23 9 231 2 • >> 3 [PE1.2] times pop
|
||||
23 9 57 • 3 [PE1.2] times pop
|
||||
23 9 57 3 • [PE1.2] times pop
|
||||
23 9 57 3 [PE1.2] • times pop
|
||||
23 9 57 • PE1.2 2 [PE1.2] times pop
|
||||
23 9 57 • [3 & PE1.1] dupdip 2 >> 2 [PE1.2] times pop
|
||||
23 9 57 [3 & PE1.1] • dupdip 2 >> 2 [PE1.2] times pop
|
||||
23 9 57 • 3 & PE1.1 57 2 >> 2 [PE1.2] times pop
|
||||
23 9 57 3 • & PE1.1 57 2 >> 2 [PE1.2] times pop
|
||||
23 9 1 • PE1.1 57 2 >> 2 [PE1.2] times pop
|
||||
23 9 1 • + [+] dupdip 57 2 >> 2 [PE1.2] times pop
|
||||
23 10 • [+] dupdip 57 2 >> 2 [PE1.2] times pop
|
||||
23 10 [+] • dupdip 57 2 >> 2 [PE1.2] times pop
|
||||
23 10 • + 10 57 2 >> 2 [PE1.2] times pop
|
||||
33 • 10 57 2 >> 2 [PE1.2] times pop
|
||||
33 10 • 57 2 >> 2 [PE1.2] times pop
|
||||
33 10 57 • 2 >> 2 [PE1.2] times pop
|
||||
33 10 57 2 • >> 2 [PE1.2] times pop
|
||||
33 10 14 • 2 [PE1.2] times pop
|
||||
33 10 14 2 • [PE1.2] times pop
|
||||
33 10 14 2 [PE1.2] • times pop
|
||||
33 10 14 • PE1.2 1 [PE1.2] times pop
|
||||
33 10 14 • [3 & PE1.1] dupdip 2 >> 1 [PE1.2] times pop
|
||||
33 10 14 [3 & PE1.1] • dupdip 2 >> 1 [PE1.2] times pop
|
||||
33 10 14 • 3 & PE1.1 14 2 >> 1 [PE1.2] times pop
|
||||
33 10 14 3 • & PE1.1 14 2 >> 1 [PE1.2] times pop
|
||||
33 10 2 • PE1.1 14 2 >> 1 [PE1.2] times pop
|
||||
33 10 2 • + [+] dupdip 14 2 >> 1 [PE1.2] times pop
|
||||
33 12 • [+] dupdip 14 2 >> 1 [PE1.2] times pop
|
||||
33 12 [+] • dupdip 14 2 >> 1 [PE1.2] times pop
|
||||
33 12 • + 12 14 2 >> 1 [PE1.2] times pop
|
||||
45 • 12 14 2 >> 1 [PE1.2] times pop
|
||||
45 12 • 14 2 >> 1 [PE1.2] times pop
|
||||
45 12 14 • 2 >> 1 [PE1.2] times pop
|
||||
45 12 14 2 • >> 1 [PE1.2] times pop
|
||||
45 12 3 • 1 [PE1.2] times pop
|
||||
45 12 3 1 • [PE1.2] times pop
|
||||
45 12 3 1 [PE1.2] • times pop
|
||||
45 12 3 • PE1.2 pop
|
||||
45 12 3 • [3 & PE1.1] dupdip 2 >> pop
|
||||
45 12 3 [3 & PE1.1] • dupdip 2 >> pop
|
||||
45 12 3 • 3 & PE1.1 3 2 >> pop
|
||||
45 12 3 3 • & PE1.1 3 2 >> pop
|
||||
45 12 3 • PE1.1 3 2 >> pop
|
||||
45 12 3 • + [+] dupdip 3 2 >> pop
|
||||
45 15 • [+] dupdip 3 2 >> pop
|
||||
45 15 [+] • dupdip 3 2 >> pop
|
||||
45 15 • + 15 3 2 >> pop
|
||||
60 • 15 3 2 >> pop
|
||||
60 15 • 3 2 >> pop
|
||||
60 15 3 • 2 >> pop
|
||||
60 15 3 2 • >> pop
|
||||
60 15 0 • pop
|
||||
60 15 •
|
||||
|
||||
|
||||
And so we have at last:
|
||||
|
||||
|
||||
```python
|
||||
define('PE1 == 0 0 66 [14811 7 [PE1.2] times pop] times 14811 4 [PE1.2] times popop')
|
||||
define('PE1 0 0 66 [14811 7 [PE1.2] times pop] times 14811 4 [PE1.2] times popop')
|
||||
```
|
||||
|
||||
|
||||
|
|
@ -493,14 +486,14 @@ Let's refactor.
|
|||
|
||||
|
||||
```python
|
||||
define('PE1.3 == 14811 swap [PE1.2] times pop')
|
||||
define('PE1.3 14811 swap [PE1.2] times pop')
|
||||
```
|
||||
|
||||
Now we can simplify the definition above:
|
||||
|
||||
|
||||
```python
|
||||
define('PE1 == 0 0 66 [7 PE1.3] times 4 PE1.3 pop')
|
||||
define('PE1 0 0 66 [7 PE1.3] times 4 PE1.3 pop')
|
||||
```
|
||||
|
||||
|
||||
|
|
@ -523,7 +516,7 @@ It's a little clunky iterating sixty-six times though the seven numbers then fou
|
|||
|
||||
|
||||
```python
|
||||
define('PE1.terms == [0 swap [dup [pop 14811] [] branch [3 &] dupdip 2 >>] dip rest cons]')
|
||||
define('PE1.terms [0 swap [dup [pop 14811] [] branch [3 &] dupdip 2 >>] dip rest cons]')
|
||||
```
|
||||
|
||||
|
||||
|
|
@ -602,7 +595,7 @@ From the above example we can deduce that the sum of the first N positive intege
|
|||
|
||||
|
||||
```python
|
||||
define('F == dup ++ * 2 floordiv')
|
||||
define('F dup ++ * 2 floordiv')
|
||||
```
|
||||
|
||||
|
||||
|
|
@ -610,14 +603,14 @@ define('F == dup ++ * 2 floordiv')
|
|||
V('10 F')
|
||||
```
|
||||
|
||||
. 10 F
|
||||
10 . F
|
||||
10 . dup ++ * 2 floordiv
|
||||
10 10 . ++ * 2 floordiv
|
||||
10 11 . * 2 floordiv
|
||||
110 . 2 floordiv
|
||||
110 2 . floordiv
|
||||
55 .
|
||||
• 10 F
|
||||
10 • F
|
||||
10 • dup ++ * 2 floordiv
|
||||
10 10 • ++ * 2 floordiv
|
||||
10 11 • * 2 floordiv
|
||||
110 • 2 floordiv
|
||||
110 2 • floordiv
|
||||
55 •
|
||||
|
||||
|
||||
## Generalizing to Blocks of Terms
|
||||
|
|
|
|||
File diff suppressed because it is too large
Load Diff
|
|
@ -13094,7 +13094,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [1]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13139,7 +13139,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [2]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'pair_up == dup uncons swap unit concat zip'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'pair_up dup uncons swap unit concat zip'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13152,7 +13152,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [3]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3] pair_up'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3] pair_up'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13183,7 +13183,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [4]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 2 3] pair_up'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 2 3] pair_up'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13251,7 +13251,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [5]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'total_matches == 0 swap [i [=] [pop +] [popop] ifte] step'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'total_matches 0 swap [i [=] [pop +] [popop] ifte] step'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13264,7 +13264,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [6]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3] pair_up total_matches'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3] pair_up total_matches'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13295,7 +13295,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [7]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 2 3] pair_up total_matches'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 2 3] pair_up total_matches'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13334,7 +13334,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [8]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'AoC2017.1 == pair_up total_matches'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'AoC2017.1 pair_up total_matches'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13347,7 +13347,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [9]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 1 2 2] AoC2017.1'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 1 2 2] AoC2017.1'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13378,7 +13378,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [10]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 1 1 1] AoC2017.1'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 1 1 1] AoC2017.1'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13409,7 +13409,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [11]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3 4] AoC2017.1'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3 4] AoC2017.1'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13440,7 +13440,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [12]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[9 1 2 1 2 1 2 9] AoC2017.1'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[9 1 2 1 2 1 2 9] AoC2017.1'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13471,7 +13471,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [13]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[9 1 2 1 2 1 2 9] AoC2017.1'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[9 1 2 1 2 1 2 9] AoC2017.1'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13514,7 +13514,7 @@ total_matches == 0 swap [i [=] [pop +] [popop] ifte] step
|
|||
<div class="prompt input_prompt">In [ ]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13537,7 +13537,7 @@ total_matches == 0 swap [i [=] [pop +] [popop] ifte] step
|
|||
<div class="prompt input_prompt">In [14]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3 4] dup size 2 / [drop] [take reverse] cleave concat zip'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3 4] dup size 2 / [drop] [take reverse] cleave concat zip'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13576,7 +13576,7 @@ total_matches == 0 swap [i [=] [pop +] [popop] ifte] step
|
|||
<div class="prompt input_prompt">In [15]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3 4] dup size 2 / [drop] [take reverse] cleave zip'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3 4] dup size 2 / [drop] [take reverse] cleave zip'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13607,7 +13607,7 @@ total_matches == 0 swap [i [=] [pop +] [popop] ifte] step
|
|||
<div class="prompt input_prompt">In [16]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'AoC2017.1.extra == dup size 2 / [drop] [take reverse] cleave zip swap pop total_matches 2 *'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'AoC2017.1.extra dup size 2 / [drop] [take reverse] cleave zip swap pop total_matches 2 *'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13620,7 +13620,7 @@ total_matches == 0 swap [i [=] [pop +] [popop] ifte] step
|
|||
<div class="prompt input_prompt">In [17]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 1 2] AoC2017.1.extra'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 1 2] AoC2017.1.extra'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13651,7 +13651,7 @@ total_matches == 0 swap [i [=] [pop +] [popop] ifte] step
|
|||
<div class="prompt input_prompt">In [18]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 2 1] AoC2017.1.extra'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 2 1] AoC2017.1.extra'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13682,7 +13682,7 @@ total_matches == 0 swap [i [=] [pop +] [popop] ifte] step
|
|||
<div class="prompt input_prompt">In [19]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3 4 2 5] AoC2017.1.extra'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3 4 2 5] AoC2017.1.extra'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
|
|||
|
|
@ -63,7 +63,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('pair_up == dup uncons swap unit concat zip')"
|
||||
"define('pair_up dup uncons swap unit concat zip')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -139,7 +139,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('total_matches == 0 swap [i [=] [pop +] [popop] ifte] step')"
|
||||
"define('total_matches 0 swap [i [=] [pop +] [popop] ifte] step')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -189,7 +189,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('AoC2017.1 == pair_up total_matches')"
|
||||
"define('AoC2017.1 pair_up total_matches')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -354,7 +354,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('AoC2017.1.extra == dup size 2 / [drop] [take reverse] cleave zip swap pop total_matches 2 *')"
|
||||
"define('AoC2017.1.extra dup size 2 / [drop] [take reverse] cleave zip swap pop total_matches 2 *')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -440,14 +440,14 @@
|
|||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 2
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython2",
|
||||
"version": "2.7.13"
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.8.3"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
|
|
|||
|
|
@ -39,7 +39,7 @@ Straightforward (although the order of each pair is reversed, due to the way `zi
|
|||
|
||||
|
||||
```python
|
||||
define('pair_up == dup uncons swap unit concat zip')
|
||||
define('pair_up dup uncons swap unit concat zip')
|
||||
```
|
||||
|
||||
|
||||
|
|
@ -86,7 +86,7 @@ And thus:
|
|||
|
||||
|
||||
```python
|
||||
define('total_matches == 0 swap [i [=] [pop +] [popop] ifte] step')
|
||||
define('total_matches 0 swap [i [=] [pop +] [popop] ifte] step')
|
||||
```
|
||||
|
||||
|
||||
|
|
@ -109,7 +109,7 @@ Now we can define our main program and evaluate it on the examples.
|
|||
|
||||
|
||||
```python
|
||||
define('AoC2017.1 == pair_up total_matches')
|
||||
define('AoC2017.1 pair_up total_matches')
|
||||
```
|
||||
|
||||
|
||||
|
|
@ -186,7 +186,7 @@ J('[1 2 3 4] dup size 2 / [drop] [take reverse] cleave zip')
|
|||
|
||||
|
||||
```python
|
||||
define('AoC2017.1.extra == dup size 2 / [drop] [take reverse] cleave zip swap pop total_matches 2 *')
|
||||
define('AoC2017.1.extra dup size 2 / [drop] [take reverse] cleave zip swap pop total_matches 2 *')
|
||||
```
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -17,11 +17,11 @@ For example:
|
|||
- 91212129 produces 9 because the only digit that matches the next one
|
||||
is the last digit, 9.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
from notebook_preamble import J, V, define
|
||||
|
||||
I’ll assume the input is a Joy sequence of integers (as opposed to a
|
||||
I'll assume the input is a Joy sequence of integers (as opposed to a
|
||||
string or something else.)
|
||||
|
||||
We might proceed by creating a word that makes a copy of the sequence
|
||||
|
|
@ -31,32 +31,32 @@ a total if the pair matches.
|
|||
|
||||
::
|
||||
|
||||
AoC2017.1 == pair_up total_matches
|
||||
AoC2017.1 == pair_up total_matches
|
||||
|
||||
Let’s derive ``pair_up``:
|
||||
Let's derive ``pair_up``:
|
||||
|
||||
::
|
||||
|
||||
[a b c] pair_up
|
||||
-------------------------
|
||||
[[a b] [b c] [c a]]
|
||||
[a b c] pair_up
|
||||
-------------------------
|
||||
[[a b] [b c] [c a]]
|
||||
|
||||
Straightforward (although the order of each pair is reversed, due to the
|
||||
way ``zip`` works, but it doesn’t matter for this program):
|
||||
way ``zip`` works, but it doesn't matter for this program):
|
||||
|
||||
::
|
||||
|
||||
[a b c] dup
|
||||
[a b c] [a b c] uncons swap
|
||||
[a b c] [b c] a unit concat
|
||||
[a b c] [b c a] zip
|
||||
[[b a] [c b] [a c]]
|
||||
[a b c] dup
|
||||
[a b c] [a b c] uncons swap
|
||||
[a b c] [b c] a unit concat
|
||||
[a b c] [b c a] zip
|
||||
[[b a] [c b] [a c]]
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('pair_up == dup uncons swap unit concat zip')
|
||||
define('pair_up dup uncons swap unit concat zip')
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[1 2 3] pair_up')
|
||||
|
||||
|
|
@ -66,7 +66,7 @@ way ``zip`` works, but it doesn’t matter for this program):
|
|||
[[2 1] [3 2] [1 3]]
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[1 2 2 3] pair_up')
|
||||
|
||||
|
|
@ -80,46 +80,46 @@ Now we need to derive ``total_matches``. It will be a ``step`` function:
|
|||
|
||||
::
|
||||
|
||||
total_matches == 0 swap [F] step
|
||||
total_matches == 0 swap [F] step
|
||||
|
||||
Where ``F`` will have the pair to work with, and it will basically be a
|
||||
``branch`` or ``ifte``.
|
||||
|
||||
::
|
||||
|
||||
total [n m] F
|
||||
total [n m] F
|
||||
|
||||
It will probably be easier to write if we dequote the pair:
|
||||
|
||||
::
|
||||
|
||||
total [n m] i F′
|
||||
----------------------
|
||||
total n m F′
|
||||
total [n m] i F′
|
||||
----------------------
|
||||
total n m F′
|
||||
|
||||
Now ``F′`` becomes just:
|
||||
|
||||
::
|
||||
|
||||
total n m [=] [pop +] [popop] ifte
|
||||
total n m [=] [pop +] [popop] ifte
|
||||
|
||||
So:
|
||||
|
||||
::
|
||||
|
||||
F == i [=] [pop +] [popop] ifte
|
||||
F == i [=] [pop +] [popop] ifte
|
||||
|
||||
And thus:
|
||||
|
||||
::
|
||||
|
||||
total_matches == 0 swap [i [=] [pop +] [popop] ifte] step
|
||||
total_matches == 0 swap [i [=] [pop +] [popop] ifte] step
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('total_matches == 0 swap [i [=] [pop +] [popop] ifte] step')
|
||||
define('total_matches 0 swap [i [=] [pop +] [popop] ifte] step')
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[1 2 3] pair_up total_matches')
|
||||
|
||||
|
|
@ -129,7 +129,7 @@ And thus:
|
|||
0
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[1 2 2 3] pair_up total_matches')
|
||||
|
||||
|
|
@ -141,11 +141,11 @@ And thus:
|
|||
|
||||
Now we can define our main program and evaluate it on the examples.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('AoC2017.1 == pair_up total_matches')
|
||||
define('AoC2017.1 pair_up total_matches')
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[1 1 2 2] AoC2017.1')
|
||||
|
||||
|
|
@ -155,7 +155,7 @@ Now we can define our main program and evaluate it on the examples.
|
|||
3
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[1 1 1 1] AoC2017.1')
|
||||
|
||||
|
|
@ -165,7 +165,7 @@ Now we can define our main program and evaluate it on the examples.
|
|||
4
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[1 2 3 4] AoC2017.1')
|
||||
|
||||
|
|
@ -175,7 +175,7 @@ Now we can define our main program and evaluate it on the examples.
|
|||
0
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[9 1 2 1 2 1 2 9] AoC2017.1')
|
||||
|
||||
|
|
@ -185,7 +185,7 @@ Now we can define our main program and evaluate it on the examples.
|
|||
9
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[9 1 2 1 2 1 2 9] AoC2017.1')
|
||||
|
||||
|
|
@ -197,19 +197,19 @@ Now we can define our main program and evaluate it on the examples.
|
|||
|
||||
::
|
||||
|
||||
pair_up == dup uncons swap unit concat zip
|
||||
total_matches == 0 swap [i [=] [pop +] [popop] ifte] step
|
||||
pair_up == dup uncons swap unit concat zip
|
||||
total_matches == 0 swap [i [=] [pop +] [popop] ifte] step
|
||||
|
||||
AoC2017.1 == pair_up total_matches
|
||||
AoC2017.1 == pair_up total_matches
|
||||
|
||||
|
||||
Now the paired digit is “halfway” round.
|
||||
Now the paired digit is "halfway" round.
|
||||
|
||||
::
|
||||
|
||||
[a b c d] dup size 2 / [drop] [take reverse] cleave concat zip
|
||||
[a b c d] dup size 2 / [drop] [take reverse] cleave concat zip
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[1 2 3 4] dup size 2 / [drop] [take reverse] cleave concat zip')
|
||||
|
||||
|
|
@ -219,9 +219,9 @@ Now the paired digit is “halfway” round.
|
|||
[[3 1] [4 2] [1 3] [2 4]]
|
||||
|
||||
|
||||
I realized that each pair is repeated…
|
||||
I realized that each pair is repeated...
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[1 2 3 4] dup size 2 / [drop] [take reverse] cleave zip')
|
||||
|
||||
|
|
@ -231,11 +231,11 @@ I realized that each pair is repeated…
|
|||
[1 2 3 4] [[1 3] [2 4]]
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('AoC2017.1.extra == dup size 2 / [drop] [take reverse] cleave zip swap pop total_matches 2 *')
|
||||
define('AoC2017.1.extra dup size 2 / [drop] [take reverse] cleave zip swap pop total_matches 2 *')
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[1 2 1 2] AoC2017.1.extra')
|
||||
|
||||
|
|
@ -245,7 +245,7 @@ I realized that each pair is repeated…
|
|||
6
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[1 2 2 1] AoC2017.1.extra')
|
||||
|
||||
|
|
@ -255,7 +255,7 @@ I realized that each pair is repeated…
|
|||
0
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[1 2 3 4 2 5] AoC2017.1.extra')
|
||||
|
||||
|
|
@ -270,19 +270,19 @@ Refactor FTW
|
|||
|
||||
With Joy a great deal of the heuristics from Forth programming carry
|
||||
over nicely. For example, refactoring into small, well-scoped commands
|
||||
with mnemonic names…
|
||||
with mnemonic names...
|
||||
|
||||
::
|
||||
|
||||
rotate_seq == uncons swap unit concat
|
||||
pair_up == dup rotate_seq zip
|
||||
add_if_match == [=] [pop +] [popop] ifte
|
||||
total_matches == [i add_if_match] step_zero
|
||||
rotate_seq == uncons swap unit concat
|
||||
pair_up == dup rotate_seq zip
|
||||
add_if_match == [=] [pop +] [popop] ifte
|
||||
total_matches == [i add_if_match] step_zero
|
||||
|
||||
AoC2017.1 == pair_up total_matches
|
||||
AoC2017.1 == pair_up total_matches
|
||||
|
||||
half_of_size == dup size 2 /
|
||||
split_at == [drop] [take reverse] cleave
|
||||
pair_up.extra == half_of_size split_at zip swap pop
|
||||
half_of_size == dup size 2 /
|
||||
split_at == [drop] [take reverse] cleave
|
||||
pair_up.extra == half_of_size split_at zip swap pop
|
||||
|
||||
AoC2017.1.extra == pair_up.extra total_matches 2 *
|
||||
AoC2017.1.extra == pair_up.extra total_matches 2 *
|
||||
|
|
|
|||
|
|
@ -13100,7 +13100,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [1]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13138,7 +13138,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [2]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'maxmin == [max] [min] cleave'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'maxmin [max] [min] cleave'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13151,7 +13151,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [3]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3] maxmin'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3] maxmin'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13195,7 +13195,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [4]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'AoC2017.2 == [maxmin - +] step_zero'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'AoC2017.2 [maxmin - +] step_zero'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13208,7 +13208,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [5]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'''</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'''</span>
|
||||
|
||||
<span class="s1">[[5 1 9 5]</span>
|
||||
<span class="s1"> [7 5 3]</span>
|
||||
|
|
@ -13267,7 +13267,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [6]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[5 9 2 8] sort reverse'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[5 9 2 8] sort reverse'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13298,7 +13298,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [7]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[9 8 5 2] uncons [swap [divmod] cons] dupdip'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[9 8 5 2] uncons [swap [divmod] cons] dupdip'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13339,7 +13339,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [8]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'[8 5 2] [9 divmod] [uncons swap] dip dup [i not] dip'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'[8 5 2] [9 divmod] [uncons swap] dip dup [i not] dip'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13356,22 +13356,22 @@ div#notebook {
|
|||
|
||||
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre> . [8 5 2] [9 divmod] [uncons swap] dip dup [i not] dip
|
||||
[8 5 2] . [9 divmod] [uncons swap] dip dup [i not] dip
|
||||
[8 5 2] [9 divmod] . [uncons swap] dip dup [i not] dip
|
||||
[8 5 2] [9 divmod] [uncons swap] . dip dup [i not] dip
|
||||
[8 5 2] . uncons swap [9 divmod] dup [i not] dip
|
||||
8 [5 2] . swap [9 divmod] dup [i not] dip
|
||||
[5 2] 8 . [9 divmod] dup [i not] dip
|
||||
[5 2] 8 [9 divmod] . dup [i not] dip
|
||||
[5 2] 8 [9 divmod] [9 divmod] . [i not] dip
|
||||
[5 2] 8 [9 divmod] [9 divmod] [i not] . dip
|
||||
[5 2] 8 [9 divmod] . i not [9 divmod]
|
||||
[5 2] 8 . 9 divmod not [9 divmod]
|
||||
[5 2] 8 9 . divmod not [9 divmod]
|
||||
[5 2] 1 1 . not [9 divmod]
|
||||
[5 2] 1 False . [9 divmod]
|
||||
[5 2] 1 False [9 divmod] .
|
||||
<pre> • [8 5 2] [9 divmod] [uncons swap] dip dup [i not] dip
|
||||
[8 5 2] • [9 divmod] [uncons swap] dip dup [i not] dip
|
||||
[8 5 2] [9 divmod] • [uncons swap] dip dup [i not] dip
|
||||
[8 5 2] [9 divmod] [uncons swap] • dip dup [i not] dip
|
||||
[8 5 2] • uncons swap [9 divmod] dup [i not] dip
|
||||
8 [5 2] • swap [9 divmod] dup [i not] dip
|
||||
[5 2] 8 • [9 divmod] dup [i not] dip
|
||||
[5 2] 8 [9 divmod] • dup [i not] dip
|
||||
[5 2] 8 [9 divmod] [9 divmod] • [i not] dip
|
||||
[5 2] 8 [9 divmod] [9 divmod] [i not] • dip
|
||||
[5 2] 8 [9 divmod] • i not [9 divmod]
|
||||
[5 2] 8 • 9 divmod not [9 divmod]
|
||||
[5 2] 8 9 • divmod not [9 divmod]
|
||||
[5 2] 1 1 • not [9 divmod]
|
||||
[5 2] 1 False • [9 divmod]
|
||||
[5 2] 1 False [9 divmod] •
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
|
|
@ -13471,7 +13471,7 @@ uncons tuck uncons roll> Q</code></pre>
|
|||
<div class="prompt input_prompt">In [9]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[8 5 3 2] 9 [swap] [% not] [cons] app2 popdd'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[8 5 3 2] 9 [swap] [% not] [cons] app2 popdd'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13604,7 +13604,7 @@ n [...] [not] [popop 0] [G] ifte
|
|||
<div class="prompt input_prompt">In [10]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'G == [first % not] [first /] [rest [not] [popop 0]] [ifte] genrec'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'G [first % not] [first /] [rest [not] [popop 0]] [ifte] genrec'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13624,9 +13624,9 @@ n [...] [not] [popop 0] [G] ifte
|
|||
</code></pre>
|
||||
<p>It applies <code>G</code> using <code>nullary</code> because if it fails with one candidate it needs the list to get the next one (the list is otherwise consumed by <code>G</code>.)</p>
|
||||
|
||||
<pre><code>find-result == [0 >] [roll> popop] [roll< popop uncons [G] nullary] primrec
|
||||
<pre><code>find-result == [0 >] [roll> popop] [roll< popop uncons [G] nullary] tailrec
|
||||
|
||||
n [...] p [0 >] [roll> popop] [roll< popop uncons [G] nullary] primrec
|
||||
n [...] p [0 >] [roll> popop] [roll< popop uncons [G] nullary] tailrec
|
||||
|
||||
</code></pre>
|
||||
<p>The base-case is trivial, return the (non-zero) result. The recursive branch...</p>
|
||||
|
|
@ -13648,7 +13648,7 @@ m [..] p find-result
|
|||
<div class="prompt input_prompt">In [11]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'find-result == [0 >] [roll> popop] [roll< popop uncons [G] nullary] primrec'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'find-result [0 >] [roll> popop] [roll< popop uncons [G] nullary] tailrec'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13658,10 +13658,10 @@ m [..] p find-result
|
|||
</div>
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="prompt input_prompt">In [14]:</div>
|
||||
<div class="prompt input_prompt">In [12]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[11 9 8 7 3 2] 0 tuck find-result'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[11 9 8 7 3 2] 0 tuck find-result'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13697,10 +13697,10 @@ m [..] p find-result
|
|||
</div>
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="prompt input_prompt">In [12]:</div>
|
||||
<div class="prompt input_prompt">In [13]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'prep-row == sort reverse 0 tuck'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'prep-row sort reverse 0 tuck'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13718,10 +13718,10 @@ m [..] p find-result
|
|||
</div>
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="prompt input_prompt">In [13]:</div>
|
||||
<div class="prompt input_prompt">In [14]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'AoC20017.2.extra == [prep-row find-result +] step_zero'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'AoC20017.2.extra [prep-row find-result +] step_zero'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13734,7 +13734,7 @@ m [..] p find-result
|
|||
<div class="prompt input_prompt">In [15]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'''</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'''</span>
|
||||
|
||||
<span class="s1">[[5 9 2 8]</span>
|
||||
<span class="s1"> [9 4 7 3]</span>
|
||||
|
|
|
|||
|
|
@ -60,7 +60,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('maxmin == [max] [min] cleave')"
|
||||
"define('maxmin [max] [min] cleave')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -97,7 +97,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('AoC2017.2 == [maxmin - +] step_zero')"
|
||||
"define('AoC2017.2 [maxmin - +] step_zero')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -197,22 +197,22 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . [8 5 2] [9 divmod] [uncons swap] dip dup [i not] dip\n",
|
||||
" [8 5 2] . [9 divmod] [uncons swap] dip dup [i not] dip\n",
|
||||
" [8 5 2] [9 divmod] . [uncons swap] dip dup [i not] dip\n",
|
||||
" [8 5 2] [9 divmod] [uncons swap] . dip dup [i not] dip\n",
|
||||
" [8 5 2] . uncons swap [9 divmod] dup [i not] dip\n",
|
||||
" 8 [5 2] . swap [9 divmod] dup [i not] dip\n",
|
||||
" [5 2] 8 . [9 divmod] dup [i not] dip\n",
|
||||
" [5 2] 8 [9 divmod] . dup [i not] dip\n",
|
||||
" [5 2] 8 [9 divmod] [9 divmod] . [i not] dip\n",
|
||||
"[5 2] 8 [9 divmod] [9 divmod] [i not] . dip\n",
|
||||
" [5 2] 8 [9 divmod] . i not [9 divmod]\n",
|
||||
" [5 2] 8 . 9 divmod not [9 divmod]\n",
|
||||
" [5 2] 8 9 . divmod not [9 divmod]\n",
|
||||
" [5 2] 1 1 . not [9 divmod]\n",
|
||||
" [5 2] 1 False . [9 divmod]\n",
|
||||
" [5 2] 1 False [9 divmod] . \n"
|
||||
" • [8 5 2] [9 divmod] [uncons swap] dip dup [i not] dip\n",
|
||||
" [8 5 2] • [9 divmod] [uncons swap] dip dup [i not] dip\n",
|
||||
" [8 5 2] [9 divmod] • [uncons swap] dip dup [i not] dip\n",
|
||||
" [8 5 2] [9 divmod] [uncons swap] • dip dup [i not] dip\n",
|
||||
" [8 5 2] • uncons swap [9 divmod] dup [i not] dip\n",
|
||||
" 8 [5 2] • swap [9 divmod] dup [i not] dip\n",
|
||||
" [5 2] 8 • [9 divmod] dup [i not] dip\n",
|
||||
" [5 2] 8 [9 divmod] • dup [i not] dip\n",
|
||||
" [5 2] 8 [9 divmod] [9 divmod] • [i not] dip\n",
|
||||
"[5 2] 8 [9 divmod] [9 divmod] [i not] • dip\n",
|
||||
" [5 2] 8 [9 divmod] • i not [9 divmod]\n",
|
||||
" [5 2] 8 • 9 divmod not [9 divmod]\n",
|
||||
" [5 2] 8 9 • divmod not [9 divmod]\n",
|
||||
" [5 2] 1 1 • not [9 divmod]\n",
|
||||
" [5 2] 1 False • [9 divmod]\n",
|
||||
" [5 2] 1 False [9 divmod] • \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -418,7 +418,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('G == [first % not] [first /] [rest [not] [popop 0]] [ifte] genrec')"
|
||||
"define('G [first % not] [first /] [rest [not] [popop 0]] [ifte] genrec')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -433,9 +433,9 @@
|
|||
"\n",
|
||||
"It applies `G` using `nullary` because if it fails with one candidate it needs the list to get the next one (the list is otherwise consumed by `G`.)\n",
|
||||
"\n",
|
||||
" find-result == [0 >] [roll> popop] [roll< popop uncons [G] nullary] primrec\n",
|
||||
" find-result == [0 >] [roll> popop] [roll< popop uncons [G] nullary] tailrec\n",
|
||||
"\n",
|
||||
" n [...] p [0 >] [roll> popop] [roll< popop uncons [G] nullary] primrec\n",
|
||||
" n [...] p [0 >] [roll> popop] [roll< popop uncons [G] nullary] tailrec\n",
|
||||
"\n",
|
||||
"The base-case is trivial, return the (non-zero) result. The recursive branch...\n",
|
||||
"\n",
|
||||
|
|
@ -454,12 +454,12 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('find-result == [0 >] [roll> popop] [roll< popop uncons [G] nullary] primrec')"
|
||||
"define('find-result [0 >] [roll> popop] [roll< popop uncons [G] nullary] tailrec')"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 14,
|
||||
"execution_count": 12,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
|
|
@ -483,11 +483,11 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 12,
|
||||
"execution_count": 13,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('prep-row == sort reverse 0 tuck')"
|
||||
"define('prep-row sort reverse 0 tuck')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -499,11 +499,11 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 13,
|
||||
"execution_count": 14,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('AoC20017.2.extra == [prep-row find-result +] step_zero')"
|
||||
"define('AoC20017.2.extra [prep-row find-result +] step_zero')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -539,14 +539,14 @@
|
|||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 2
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython2",
|
||||
"version": "2.7.13"
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.8.3"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
|
|
|||
|
|
@ -35,7 +35,7 @@ This function `F` must get the `max` and `min` of a row of numbers and subtract.
|
|||
|
||||
|
||||
```python
|
||||
define('maxmin == [max] [min] cleave')
|
||||
define('maxmin [max] [min] cleave')
|
||||
```
|
||||
|
||||
|
||||
|
|
@ -54,7 +54,7 @@ So:
|
|||
|
||||
|
||||
```python
|
||||
define('AoC2017.2 == [maxmin - +] step_zero')
|
||||
define('AoC2017.2 [maxmin - +] step_zero')
|
||||
```
|
||||
|
||||
|
||||
|
|
@ -114,22 +114,22 @@ J('[9 8 5 2] uncons [swap [divmod] cons] dupdip')
|
|||
V('[8 5 2] [9 divmod] [uncons swap] dip dup [i not] dip')
|
||||
```
|
||||
|
||||
. [8 5 2] [9 divmod] [uncons swap] dip dup [i not] dip
|
||||
[8 5 2] . [9 divmod] [uncons swap] dip dup [i not] dip
|
||||
[8 5 2] [9 divmod] . [uncons swap] dip dup [i not] dip
|
||||
[8 5 2] [9 divmod] [uncons swap] . dip dup [i not] dip
|
||||
[8 5 2] . uncons swap [9 divmod] dup [i not] dip
|
||||
8 [5 2] . swap [9 divmod] dup [i not] dip
|
||||
[5 2] 8 . [9 divmod] dup [i not] dip
|
||||
[5 2] 8 [9 divmod] . dup [i not] dip
|
||||
[5 2] 8 [9 divmod] [9 divmod] . [i not] dip
|
||||
[5 2] 8 [9 divmod] [9 divmod] [i not] . dip
|
||||
[5 2] 8 [9 divmod] . i not [9 divmod]
|
||||
[5 2] 8 . 9 divmod not [9 divmod]
|
||||
[5 2] 8 9 . divmod not [9 divmod]
|
||||
[5 2] 1 1 . not [9 divmod]
|
||||
[5 2] 1 False . [9 divmod]
|
||||
[5 2] 1 False [9 divmod] .
|
||||
• [8 5 2] [9 divmod] [uncons swap] dip dup [i not] dip
|
||||
[8 5 2] • [9 divmod] [uncons swap] dip dup [i not] dip
|
||||
[8 5 2] [9 divmod] • [uncons swap] dip dup [i not] dip
|
||||
[8 5 2] [9 divmod] [uncons swap] • dip dup [i not] dip
|
||||
[8 5 2] • uncons swap [9 divmod] dup [i not] dip
|
||||
8 [5 2] • swap [9 divmod] dup [i not] dip
|
||||
[5 2] 8 • [9 divmod] dup [i not] dip
|
||||
[5 2] 8 [9 divmod] • dup [i not] dip
|
||||
[5 2] 8 [9 divmod] [9 divmod] • [i not] dip
|
||||
[5 2] 8 [9 divmod] [9 divmod] [i not] • dip
|
||||
[5 2] 8 [9 divmod] • i not [9 divmod]
|
||||
[5 2] 8 • 9 divmod not [9 divmod]
|
||||
[5 2] 8 9 • divmod not [9 divmod]
|
||||
[5 2] 1 1 • not [9 divmod]
|
||||
[5 2] 1 False • [9 divmod]
|
||||
[5 2] 1 False [9 divmod] •
|
||||
|
||||
|
||||
## Tricky
|
||||
|
|
@ -293,7 +293,7 @@ This `ifte` guards against empty sequences and returns zero in that case, otherw
|
|||
|
||||
|
||||
```python
|
||||
define('G == [first % not] [first /] [rest [not] [popop 0]] [ifte] genrec')
|
||||
define('G [first % not] [first /] [rest [not] [popop 0]] [ifte] genrec')
|
||||
```
|
||||
|
||||
Now we need a word that uses `G` on each (head, tail) pair of a sequence until it finds a (non-zero) result. It's going to be designed to work on a stack that has some candidate `n`, a sequence of possible divisors, and a result that is zero to signal to continue (a non-zero value implies that it is the discovered result):
|
||||
|
|
@ -304,9 +304,9 @@ Now we need a word that uses `G` on each (head, tail) pair of a sequence until i
|
|||
|
||||
It applies `G` using `nullary` because if it fails with one candidate it needs the list to get the next one (the list is otherwise consumed by `G`.)
|
||||
|
||||
find-result == [0 >] [roll> popop] [roll< popop uncons [G] nullary] primrec
|
||||
find-result == [0 >] [roll> popop] [roll< popop uncons [G] nullary] tailrec
|
||||
|
||||
n [...] p [0 >] [roll> popop] [roll< popop uncons [G] nullary] primrec
|
||||
n [...] p [0 >] [roll> popop] [roll< popop uncons [G] nullary] tailrec
|
||||
|
||||
The base-case is trivial, return the (non-zero) result. The recursive branch...
|
||||
|
||||
|
|
@ -320,7 +320,7 @@ The puzzle states that the input is well-formed, meaning that we can expect a re
|
|||
|
||||
|
||||
```python
|
||||
define('find-result == [0 >] [roll> popop] [roll< popop uncons [G] nullary] primrec')
|
||||
define('find-result [0 >] [roll> popop] [roll< popop uncons [G] nullary] tailrec')
|
||||
```
|
||||
|
||||
|
||||
|
|
@ -335,14 +335,14 @@ In order to get the thing started, we need to `sort` the list in descending orde
|
|||
|
||||
|
||||
```python
|
||||
define('prep-row == sort reverse 0 tuck')
|
||||
define('prep-row sort reverse 0 tuck')
|
||||
```
|
||||
|
||||
Now we can define our program.
|
||||
|
||||
|
||||
```python
|
||||
define('AoC20017.2.extra == [prep-row find-result +] step_zero')
|
||||
define('AoC20017.2.extra [prep-row find-result +] step_zero')
|
||||
```
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -11,45 +11,45 @@ For example, given the following spreadsheet:
|
|||
|
||||
::
|
||||
|
||||
5 1 9 5
|
||||
7 5 3
|
||||
2 4 6 8
|
||||
5 1 9 5
|
||||
7 5 3
|
||||
2 4 6 8
|
||||
|
||||
- The first row’s largest and smallest values are 9 and 1, and their
|
||||
- The first row's largest and smallest values are 9 and 1, and their
|
||||
difference is 8.
|
||||
- The second row’s largest and smallest values are 7 and 3, and their
|
||||
- The second row's largest and smallest values are 7 and 3, and their
|
||||
difference is 4.
|
||||
- The third row’s difference is 6.
|
||||
- The third row's difference is 6.
|
||||
|
||||
In this example, the spreadsheet’s checksum would be 8 + 4 + 6 = 18.
|
||||
In this example, the spreadsheet's checksum would be 8 + 4 + 6 = 18.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
from notebook_preamble import J, V, define
|
||||
|
||||
I’ll assume the input is a Joy sequence of sequences of integers.
|
||||
I'll assume the input is a Joy sequence of sequences of integers.
|
||||
|
||||
::
|
||||
|
||||
[[5 1 9 5]
|
||||
[7 5 3]
|
||||
[2 4 6 8]]
|
||||
[[5 1 9 5]
|
||||
[7 5 3]
|
||||
[2 4 6 8]]
|
||||
|
||||
So, obviously, the initial form will be a ``step`` function:
|
||||
|
||||
::
|
||||
|
||||
AoC2017.2 == 0 swap [F +] step
|
||||
AoC2017.2 == 0 swap [F +] step
|
||||
|
||||
This function ``F`` must get the ``max`` and ``min`` of a row of numbers
|
||||
and subtract. We can define a helper function ``maxmin`` which does
|
||||
this:
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('maxmin == [max] [min] cleave')
|
||||
define('maxmin [max] [min] cleave')
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[1 2 3] maxmin')
|
||||
|
||||
|
|
@ -63,15 +63,15 @@ Then ``F`` just does that then subtracts the min from the max:
|
|||
|
||||
::
|
||||
|
||||
F == maxmin -
|
||||
F == maxmin -
|
||||
|
||||
So:
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('AoC2017.2 == [maxmin - +] step_zero')
|
||||
define('AoC2017.2 [maxmin - +] step_zero')
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('''
|
||||
|
||||
|
|
@ -87,18 +87,18 @@ So:
|
|||
18
|
||||
|
||||
|
||||
…find the only two numbers in each row where one evenly divides the
|
||||
...find the only two numbers in each row where one evenly divides the
|
||||
other - that is, where the result of the division operation is a whole
|
||||
number. They would like you to find those numbers on each line, divide
|
||||
them, and add up each line’s result.
|
||||
them, and add up each line's result.
|
||||
|
||||
For example, given the following spreadsheet:
|
||||
|
||||
::
|
||||
|
||||
5 9 2 8
|
||||
9 4 7 3
|
||||
3 8 6 5
|
||||
5 9 2 8
|
||||
9 4 7 3
|
||||
3 8 6 5
|
||||
|
||||
- In the first row, the only two numbers that evenly divide are 8 and
|
||||
2; the result of this division is 4.
|
||||
|
|
@ -107,9 +107,9 @@ For example, given the following spreadsheet:
|
|||
|
||||
In this example, the sum of the results would be 4 + 3 + 2 = 9.
|
||||
|
||||
What is the sum of each row’s result in your puzzle input?
|
||||
What is the sum of each row's result in your puzzle input?
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[5 9 2 8] sort reverse')
|
||||
|
||||
|
|
@ -119,7 +119,7 @@ What is the sum of each row’s result in your puzzle input?
|
|||
[9 8 5 2]
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[9 8 5 2] uncons [swap [divmod] cons] dupdip')
|
||||
|
||||
|
|
@ -131,38 +131,38 @@ What is the sum of each row’s result in your puzzle input?
|
|||
|
||||
::
|
||||
|
||||
[9 8 5 2] uncons [swap [divmod] cons F] dupdip G
|
||||
[8 5 2] [9 divmod] F [8 5 2] G
|
||||
[9 8 5 2] uncons [swap [divmod] cons F] dupdip G
|
||||
[8 5 2] [9 divmod] F [8 5 2] G
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
V('[8 5 2] [9 divmod] [uncons swap] dip dup [i not] dip')
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
. [8 5 2] [9 divmod] [uncons swap] dip dup [i not] dip
|
||||
[8 5 2] . [9 divmod] [uncons swap] dip dup [i not] dip
|
||||
[8 5 2] [9 divmod] . [uncons swap] dip dup [i not] dip
|
||||
[8 5 2] [9 divmod] [uncons swap] . dip dup [i not] dip
|
||||
[8 5 2] . uncons swap [9 divmod] dup [i not] dip
|
||||
8 [5 2] . swap [9 divmod] dup [i not] dip
|
||||
[5 2] 8 . [9 divmod] dup [i not] dip
|
||||
[5 2] 8 [9 divmod] . dup [i not] dip
|
||||
[5 2] 8 [9 divmod] [9 divmod] . [i not] dip
|
||||
[5 2] 8 [9 divmod] [9 divmod] [i not] . dip
|
||||
[5 2] 8 [9 divmod] . i not [9 divmod]
|
||||
[5 2] 8 . 9 divmod not [9 divmod]
|
||||
[5 2] 8 9 . divmod not [9 divmod]
|
||||
[5 2] 1 1 . not [9 divmod]
|
||||
[5 2] 1 False . [9 divmod]
|
||||
[5 2] 1 False [9 divmod] .
|
||||
• [8 5 2] [9 divmod] [uncons swap] dip dup [i not] dip
|
||||
[8 5 2] • [9 divmod] [uncons swap] dip dup [i not] dip
|
||||
[8 5 2] [9 divmod] • [uncons swap] dip dup [i not] dip
|
||||
[8 5 2] [9 divmod] [uncons swap] • dip dup [i not] dip
|
||||
[8 5 2] • uncons swap [9 divmod] dup [i not] dip
|
||||
8 [5 2] • swap [9 divmod] dup [i not] dip
|
||||
[5 2] 8 • [9 divmod] dup [i not] dip
|
||||
[5 2] 8 [9 divmod] • dup [i not] dip
|
||||
[5 2] 8 [9 divmod] [9 divmod] • [i not] dip
|
||||
[5 2] 8 [9 divmod] [9 divmod] [i not] • dip
|
||||
[5 2] 8 [9 divmod] • i not [9 divmod]
|
||||
[5 2] 8 • 9 divmod not [9 divmod]
|
||||
[5 2] 8 9 • divmod not [9 divmod]
|
||||
[5 2] 1 1 • not [9 divmod]
|
||||
[5 2] 1 False • [9 divmod]
|
||||
[5 2] 1 False [9 divmod] •
|
||||
|
||||
|
||||
Tricky
|
||||
------
|
||||
|
||||
Let’s think.
|
||||
Let's think.
|
||||
|
||||
Given a *sorted* sequence (from highest to lowest) we want to \* for
|
||||
head, tail in sequence \* for term in tail: \* check if the head % term
|
||||
|
|
@ -173,64 +173,64 @@ So we want a ``loop`` I think
|
|||
|
||||
::
|
||||
|
||||
[a b c d] True [Q] loop
|
||||
[a b c d] Q [Q] loop
|
||||
[a b c d] True [Q] loop
|
||||
[a b c d] Q [Q] loop
|
||||
|
||||
``Q`` should either leave the result and False, or the ``rest`` and
|
||||
True.
|
||||
|
||||
::
|
||||
|
||||
[a b c d] Q
|
||||
-----------------
|
||||
result 0
|
||||
[a b c d] Q
|
||||
-----------------
|
||||
result 0
|
||||
|
||||
[a b c d] Q
|
||||
-----------------
|
||||
[b c d] 1
|
||||
[a b c d] Q
|
||||
-----------------
|
||||
[b c d] 1
|
||||
|
||||
This suggests that ``Q`` should start with:
|
||||
|
||||
::
|
||||
|
||||
[a b c d] uncons dup roll<
|
||||
[b c d] [b c d] a
|
||||
[a b c d] uncons dup roll<
|
||||
[b c d] [b c d] a
|
||||
|
||||
Now we just have to ``pop`` it if we don’t need it.
|
||||
Now we just have to ``pop`` it if we don't need it.
|
||||
|
||||
::
|
||||
|
||||
[b c d] [b c d] a [P] [T] [cons] app2 popdd [E] primrec
|
||||
[b c d] [b c d] [a P] [a T] [E] primrec
|
||||
[b c d] [b c d] a [P] [T] [cons] app2 popdd [E] primrec
|
||||
[b c d] [b c d] [a P] [a T] [E] primrec
|
||||
|
||||
--------------
|
||||
|
||||
::
|
||||
|
||||
w/ Q == [% not] [T] [F] primrec
|
||||
w/ Q == [% not] [T] [F] primrec
|
||||
|
||||
[a b c d] uncons
|
||||
a [b c d] tuck
|
||||
[b c d] a [b c d] uncons
|
||||
[b c d] a b [c d] roll>
|
||||
[b c d] [c d] a b Q
|
||||
[b c d] [c d] a b [% not] [T] [F] primrec
|
||||
[a b c d] uncons
|
||||
a [b c d] tuck
|
||||
[b c d] a [b c d] uncons
|
||||
[b c d] a b [c d] roll>
|
||||
[b c d] [c d] a b Q
|
||||
[b c d] [c d] a b [% not] [T] [F] primrec
|
||||
|
||||
[b c d] [c d] a b T
|
||||
[b c d] [c d] a b / roll> popop 0
|
||||
[b c d] [c d] a b T
|
||||
[b c d] [c d] a b / roll> popop 0
|
||||
|
||||
[b c d] [c d] a b F Q
|
||||
[b c d] [c d] a b pop swap uncons ... Q
|
||||
[b c d] [c d] a swap uncons ... Q
|
||||
[b c d] a [c d] uncons ... Q
|
||||
[b c d] a c [d] roll> Q
|
||||
[b c d] [d] a c Q
|
||||
[b c d] [c d] a b F Q
|
||||
[b c d] [c d] a b pop swap uncons ... Q
|
||||
[b c d] [c d] a swap uncons ... Q
|
||||
[b c d] a [c d] uncons ... Q
|
||||
[b c d] a c [d] roll> Q
|
||||
[b c d] [d] a c Q
|
||||
|
||||
Q == [% not] [/ roll> popop 0] [pop swap uncons roll>] primrec
|
||||
Q == [% not] [/ roll> popop 0] [pop swap uncons roll>] primrec
|
||||
|
||||
uncons tuck uncons roll> Q
|
||||
uncons tuck uncons roll> Q
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[8 5 3 2] 9 [swap] [% not] [cons] app2 popdd')
|
||||
|
||||
|
|
@ -244,55 +244,55 @@ Now we just have to ``pop`` it if we don’t need it.
|
|||
|
||||
::
|
||||
|
||||
[a b c d] uncons
|
||||
a [b c d] tuck
|
||||
[b c d] a [b c d] [not] [popop 1] [Q] ifte
|
||||
[a b c d] uncons
|
||||
a [b c d] tuck
|
||||
[b c d] a [b c d] [not] [popop 1] [Q] ifte
|
||||
|
||||
[b c d] a [] popop 1
|
||||
[b c d] 1
|
||||
[b c d] a [] popop 1
|
||||
[b c d] 1
|
||||
|
||||
[b c d] a [b c d] Q
|
||||
[b c d] a [b c d] Q
|
||||
|
||||
|
||||
a [...] Q
|
||||
---------------
|
||||
result 0
|
||||
a [...] Q
|
||||
---------------
|
||||
result 0
|
||||
|
||||
a [...] Q
|
||||
---------------
|
||||
1
|
||||
a [...] Q
|
||||
---------------
|
||||
1
|
||||
|
||||
|
||||
w/ Q == [first % not] [first / 0] [rest [not] [popop 1]] [ifte]
|
||||
w/ Q == [first % not] [first / 0] [rest [not] [popop 1]] [ifte]
|
||||
|
||||
|
||||
|
||||
a [b c d] [first % not] [first / 0] [rest [not] [popop 1]] [ifte]
|
||||
a [b c d] first % not
|
||||
a b % not
|
||||
a%b not
|
||||
bool(a%b)
|
||||
a [b c d] [first % not] [first / 0] [rest [not] [popop 1]] [ifte]
|
||||
a [b c d] first % not
|
||||
a b % not
|
||||
a%b not
|
||||
bool(a%b)
|
||||
|
||||
a [b c d] [first % not] [first / 0] [rest [not] [popop 1]] [ifte]
|
||||
a [b c d] first / 0
|
||||
a b / 0
|
||||
a/b 0
|
||||
a [b c d] [first % not] [first / 0] [rest [not] [popop 1]] [ifte]
|
||||
a [b c d] first / 0
|
||||
a b / 0
|
||||
a/b 0
|
||||
|
||||
a [b c d] [first % not] [first / 0] [rest [not] [popop 1]] [ifte]
|
||||
a [b c d] rest [not] [popop 1] [Q] ifte
|
||||
a [c d] [not] [popop 1] [Q] ifte
|
||||
a [c d] [not] [popop 1] [Q] ifte
|
||||
a [b c d] [first % not] [first / 0] [rest [not] [popop 1]] [ifte]
|
||||
a [b c d] rest [not] [popop 1] [Q] ifte
|
||||
a [c d] [not] [popop 1] [Q] ifte
|
||||
a [c d] [not] [popop 1] [Q] ifte
|
||||
|
||||
a [c d] [not] [popop 1] [Q] ifte
|
||||
a [c d] not
|
||||
a [c d] [not] [popop 1] [Q] ifte
|
||||
a [c d] not
|
||||
|
||||
a [] popop 1
|
||||
1
|
||||
a [] popop 1
|
||||
1
|
||||
|
||||
a [c d] Q
|
||||
a [c d] Q
|
||||
|
||||
|
||||
uncons tuck [first % not] [first / 0] [rest [not] [popop 1]] [ifte]
|
||||
uncons tuck [first % not] [first / 0] [rest [not] [popop 1]] [ifte]
|
||||
|
||||
I finally sat down with a piece of paper and blocked it out.
|
||||
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
|
@ -302,36 +302,36 @@ candidates and return the result or zero:
|
|||
|
||||
::
|
||||
|
||||
n [...] G
|
||||
---------------
|
||||
result
|
||||
n [...] G
|
||||
---------------
|
||||
result
|
||||
|
||||
n [...] G
|
||||
---------------
|
||||
0
|
||||
n [...] G
|
||||
---------------
|
||||
0
|
||||
|
||||
It’s a recursive function that conditionally executes the recursive part
|
||||
It's a recursive function that conditionally executes the recursive part
|
||||
of its recursive branch
|
||||
|
||||
::
|
||||
|
||||
[Pg] [E] [R1 [Pi] [T]] [ifte] genrec
|
||||
[Pg] [E] [R1 [Pi] [T]] [ifte] genrec
|
||||
|
||||
The recursive branch is the else-part of the inner ``ifte``:
|
||||
|
||||
::
|
||||
|
||||
G == [Pg] [E] [R1 [Pi] [T]] [ifte] genrec
|
||||
== [Pg] [E] [R1 [Pi] [T] [G] ifte] ifte
|
||||
G == [Pg] [E] [R1 [Pi] [T]] [ifte] genrec
|
||||
== [Pg] [E] [R1 [Pi] [T] [G] ifte] ifte
|
||||
|
||||
But this is in hindsight. Going forward I derived:
|
||||
|
||||
::
|
||||
|
||||
G == [first % not]
|
||||
[first /]
|
||||
[rest [not] [popop 0]]
|
||||
[ifte] genrec
|
||||
G == [first % not]
|
||||
[first /]
|
||||
[rest [not] [popop 0]]
|
||||
[ifte] genrec
|
||||
|
||||
The predicate detects if the ``n`` can be evenly divided by the
|
||||
``first`` item in the list. If so, the then-part returns the result.
|
||||
|
|
@ -339,27 +339,27 @@ Otherwise, we have:
|
|||
|
||||
::
|
||||
|
||||
n [m ...] rest [not] [popop 0] [G] ifte
|
||||
n [...] [not] [popop 0] [G] ifte
|
||||
n [m ...] rest [not] [popop 0] [G] ifte
|
||||
n [...] [not] [popop 0] [G] ifte
|
||||
|
||||
This ``ifte`` guards against empty sequences and returns zero in that
|
||||
case, otherwise it executes ``G``.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('G == [first % not] [first /] [rest [not] [popop 0]] [ifte] genrec')
|
||||
define('G [first % not] [first /] [rest [not] [popop 0]] [ifte] genrec')
|
||||
|
||||
Now we need a word that uses ``G`` on each (head, tail) pair of a
|
||||
sequence until it finds a (non-zero) result. It’s going to be designed
|
||||
sequence until it finds a (non-zero) result. It's going to be designed
|
||||
to work on a stack that has some candidate ``n``, a sequence of possible
|
||||
divisors, and a result that is zero to signal to continue (a non-zero
|
||||
value implies that it is the discovered result):
|
||||
|
||||
::
|
||||
|
||||
n [...] p find-result
|
||||
---------------------------
|
||||
result
|
||||
n [...] p find-result
|
||||
---------------------------
|
||||
result
|
||||
|
||||
It applies ``G`` using ``nullary`` because if it fails with one
|
||||
candidate it needs the list to get the next one (the list is otherwise
|
||||
|
|
@ -367,30 +367,30 @@ consumed by ``G``.)
|
|||
|
||||
::
|
||||
|
||||
find-result == [0 >] [roll> popop] [roll< popop uncons [G] nullary] primrec
|
||||
find-result == [0 >] [roll> popop] [roll< popop uncons [G] nullary] tailrec
|
||||
|
||||
n [...] p [0 >] [roll> popop] [roll< popop uncons [G] nullary] primrec
|
||||
n [...] p [0 >] [roll> popop] [roll< popop uncons [G] nullary] tailrec
|
||||
|
||||
The base-case is trivial, return the (non-zero) result. The recursive
|
||||
branch…
|
||||
branch...
|
||||
|
||||
::
|
||||
|
||||
n [...] p roll< popop uncons [G] nullary find-result
|
||||
[...] p n popop uncons [G] nullary find-result
|
||||
[...] uncons [G] nullary find-result
|
||||
m [..] [G] nullary find-result
|
||||
m [..] p find-result
|
||||
n [...] p roll< popop uncons [G] nullary find-result
|
||||
[...] p n popop uncons [G] nullary find-result
|
||||
[...] uncons [G] nullary find-result
|
||||
m [..] [G] nullary find-result
|
||||
m [..] p find-result
|
||||
|
||||
The puzzle states that the input is well-formed, meaning that we can
|
||||
expect a result before the row sequence empties and so do not need to
|
||||
guard the ``uncons``.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('find-result == [0 >] [roll> popop] [roll< popop uncons [G] nullary] primrec')
|
||||
define('find-result [0 >] [roll> popop] [roll< popop uncons [G] nullary] tailrec')
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[11 9 8 7 3 2] 0 tuck find-result')
|
||||
|
||||
|
|
@ -402,19 +402,19 @@ guard the ``uncons``.
|
|||
|
||||
In order to get the thing started, we need to ``sort`` the list in
|
||||
descending order, then prime the ``find-result`` function with a dummy
|
||||
candidate value and zero (“continue”) flag.
|
||||
candidate value and zero ("continue") flag.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('prep-row == sort reverse 0 tuck')
|
||||
define('prep-row sort reverse 0 tuck')
|
||||
|
||||
Now we can define our program.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('AoC20017.2.extra == [prep-row find-result +] step_zero')
|
||||
define('AoC20017.2.extra [prep-row find-result +] step_zero')
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('''
|
||||
|
||||
|
|
|
|||
|
|
@ -13194,7 +13194,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [1]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">k</span> <span class="o">=</span> <span class="mi">4</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">k</span> <span class="o">=</span> <span class="mi">4</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13215,8 +13215,8 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [2]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">k</span><span class="p">):</span>
|
||||
<span class="nb">print</span> <span class="nb">abs</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="n">k</span><span class="p">),</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">k</span><span class="p">):</span>
|
||||
<span class="nb">print</span><span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="n">k</span><span class="p">),)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13233,7 +13233,14 @@ div#notebook {
|
|||
|
||||
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre>4 3 2 1 0 1 2 3
|
||||
<pre>4
|
||||
3
|
||||
2
|
||||
1
|
||||
0
|
||||
1
|
||||
2
|
||||
3
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
|
|
@ -13255,8 +13262,8 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [3]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">k</span><span class="p">):</span>
|
||||
<span class="nb">print</span> <span class="nb">abs</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="p">(</span><span class="n">k</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)),</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">k</span><span class="p">):</span>
|
||||
<span class="nb">print</span><span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="p">(</span><span class="n">k</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)),</span> <span class="n">end</span><span class="o">=</span><span class="s1">' '</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13273,8 +13280,7 @@ div#notebook {
|
|||
|
||||
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre>3 2 1 0 1 2 3 4
|
||||
</pre>
|
||||
<pre>3 2 1 0 1 2 3 4 </pre>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
|
|
@ -13295,8 +13301,8 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [4]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">k</span><span class="p">):</span>
|
||||
<span class="nb">print</span> <span class="nb">abs</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="p">(</span><span class="n">k</span> <span class="o">-</span> <span class="mi">1</span><span class="p">))</span> <span class="o">+</span> <span class="n">k</span><span class="p">,</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">k</span><span class="p">):</span>
|
||||
<span class="nb">print</span><span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="p">(</span><span class="n">k</span> <span class="o">-</span> <span class="mi">1</span><span class="p">))</span> <span class="o">+</span> <span class="n">k</span><span class="p">,</span> <span class="n">end</span><span class="o">=</span><span class="s1">' '</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13313,8 +13319,7 @@ div#notebook {
|
|||
|
||||
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre>7 6 5 4 5 6 7 8
|
||||
</pre>
|
||||
<pre>7 6 5 4 5 6 7 8 </pre>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
|
|
@ -13335,7 +13340,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [5]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">row_value</span><span class="p">(</span><span class="n">k</span><span class="p">,</span> <span class="n">i</span><span class="p">):</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">row_value</span><span class="p">(</span><span class="n">k</span><span class="p">,</span> <span class="n">i</span><span class="p">):</span>
|
||||
<span class="n">i</span> <span class="o">%=</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">k</span><span class="p">)</span> <span class="c1"># wrap the index at the row boundary.</span>
|
||||
<span class="k">return</span> <span class="nb">abs</span><span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="p">(</span><span class="n">k</span> <span class="o">-</span> <span class="mi">1</span><span class="p">))</span> <span class="o">+</span> <span class="n">k</span>
|
||||
</pre></div>
|
||||
|
|
@ -13350,9 +13355,9 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [6]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">k</span> <span class="o">=</span> <span class="mi">5</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">k</span> <span class="o">=</span> <span class="mi">5</span>
|
||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">k</span><span class="p">):</span>
|
||||
<span class="nb">print</span> <span class="n">row_value</span><span class="p">(</span><span class="n">k</span><span class="p">,</span> <span class="n">i</span><span class="p">),</span>
|
||||
<span class="nb">print</span><span class="p">(</span><span class="n">row_value</span><span class="p">(</span><span class="n">k</span><span class="p">,</span> <span class="n">i</span><span class="p">),</span> <span class="n">end</span><span class="o">=</span><span class="s1">' '</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13369,8 +13374,7 @@ div#notebook {
|
|||
|
||||
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre>9 8 7 6 5 6 7 8 9 10
|
||||
</pre>
|
||||
<pre>9 8 7 6 5 6 7 8 9 10 </pre>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
|
|
@ -13402,7 +13406,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [7]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">rank_and_offset</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">rank_and_offset</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||||
<span class="k">assert</span> <span class="n">n</span> <span class="o">>=</span> <span class="mi">2</span> <span class="c1"># Guard the domain.</span>
|
||||
<span class="n">n</span> <span class="o">-=</span> <span class="mi">2</span> <span class="c1"># Subtract two,</span>
|
||||
<span class="c1"># one for the initial square,</span>
|
||||
|
|
@ -13426,8 +13430,8 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [8]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">51</span><span class="p">):</span>
|
||||
<span class="nb">print</span> <span class="n">n</span><span class="p">,</span> <span class="n">rank_and_offset</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">51</span><span class="p">):</span>
|
||||
<span class="nb">print</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">rank_and_offset</span><span class="p">(</span><span class="n">n</span><span class="p">))</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13506,9 +13510,9 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [9]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">51</span><span class="p">):</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">51</span><span class="p">):</span>
|
||||
<span class="n">k</span><span class="p">,</span> <span class="n">i</span> <span class="o">=</span> <span class="n">rank_and_offset</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||||
<span class="nb">print</span> <span class="n">n</span><span class="p">,</span> <span class="n">row_value</span><span class="p">(</span><span class="n">k</span><span class="p">,</span> <span class="n">i</span><span class="p">)</span>
|
||||
<span class="nb">print</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">row_value</span><span class="p">(</span><span class="n">k</span><span class="p">,</span> <span class="n">i</span><span class="p">))</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13594,7 +13598,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [10]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">row_value</span><span class="p">(</span><span class="n">k</span><span class="p">,</span> <span class="n">i</span><span class="p">):</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">row_value</span><span class="p">(</span><span class="n">k</span><span class="p">,</span> <span class="n">i</span><span class="p">):</span>
|
||||
<span class="k">return</span> <span class="nb">abs</span><span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="p">(</span><span class="n">k</span> <span class="o">-</span> <span class="mi">1</span><span class="p">))</span> <span class="o">+</span> <span class="n">k</span>
|
||||
|
||||
|
||||
|
|
@ -13628,7 +13632,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [11]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">aoc20173</span><span class="p">(</span><span class="mi">23</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">aoc20173</span><span class="p">(</span><span class="mi">23</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13661,7 +13665,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [12]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">aoc20173</span><span class="p">(</span><span class="mi">23000</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">aoc20173</span><span class="p">(</span><span class="mi">23000</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13694,7 +13698,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [13]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">aoc20173</span><span class="p">(</span><span class="mi">23000000000000</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">aoc20173</span><span class="p">(</span><span class="mi">23000000000000</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13735,7 +13739,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [14]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">floor</span><span class="p">,</span> <span class="n">lambdify</span><span class="p">,</span> <span class="n">solve</span><span class="p">,</span> <span class="n">symbols</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">floor</span><span class="p">,</span> <span class="n">lambdify</span><span class="p">,</span> <span class="n">solve</span><span class="p">,</span> <span class="n">symbols</span>
|
||||
<span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">init_printing</span>
|
||||
<span class="n">init_printing</span><span class="p">()</span>
|
||||
</pre></div>
|
||||
|
|
@ -13750,7 +13754,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [15]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">k</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">'k'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">k</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">'k'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13775,7 +13779,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [16]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">E</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">+</span> <span class="mi">8</span> <span class="o">*</span> <span class="n">k</span> <span class="o">*</span> <span class="p">(</span><span class="n">k</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span> <span class="c1"># For the reason for adding 2 see above.</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">E</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">+</span> <span class="mi">8</span> <span class="o">*</span> <span class="n">k</span> <span class="o">*</span> <span class="p">(</span><span class="n">k</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span> <span class="c1"># For the reason for adding 2 see above.</span>
|
||||
|
||||
<span class="n">E</span>
|
||||
</pre></div>
|
||||
|
|
@ -13796,7 +13800,7 @@ div#notebook {
|
|||
|
||||
|
||||
<div class="output_latex output_subarea output_execute_result">
|
||||
$$4 k \left(k + 1\right) + 2$$
|
||||
$\displaystyle 4 k \left(k + 1\right) + 2$
|
||||
</div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13818,7 +13822,7 @@ $$4 k \left(k + 1\right) + 2$$
|
|||
<div class="prompt input_prompt">In [17]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">rank_of</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">rank_of</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||||
<span class="k">return</span> <span class="n">floor</span><span class="p">(</span><span class="nb">max</span><span class="p">(</span><span class="n">solve</span><span class="p">(</span><span class="n">E</span> <span class="o">-</span> <span class="n">n</span><span class="p">,</span> <span class="n">k</span><span class="p">)))</span> <span class="o">+</span> <span class="mi">1</span>
|
||||
</pre></div>
|
||||
|
||||
|
|
@ -13841,8 +13845,8 @@ $$4 k \left(k + 1\right) + 2$$
|
|||
<div class="prompt input_prompt">In [18]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="p">(</span><span class="mi">9</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">25</span><span class="p">,</span> <span class="mi">26</span><span class="p">,</span> <span class="mi">49</span><span class="p">,</span> <span class="mi">50</span><span class="p">):</span>
|
||||
<span class="nb">print</span> <span class="n">n</span><span class="p">,</span> <span class="n">rank_of</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="p">(</span><span class="mi">9</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">25</span><span class="p">,</span> <span class="mi">26</span><span class="p">,</span> <span class="mi">49</span><span class="p">,</span> <span class="mi">50</span><span class="p">):</span>
|
||||
<span class="nb">print</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">rank_of</span><span class="p">(</span><span class="n">n</span><span class="p">))</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13886,7 +13890,7 @@ $$4 k \left(k + 1\right) + 2$$
|
|||
<div class="prompt input_prompt">In [19]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="o">%</span><span class="k">time</span> rank_of(23000000000000) # Compare runtime with rank_and_offset()!
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="o">%</span><span class="k">time</span> rank_of(23000000000000) # Compare runtime with rank_and_offset()!
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13903,8 +13907,8 @@ $$4 k \left(k + 1\right) + 2$$
|
|||
|
||||
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre>CPU times: user 68 ms, sys: 8 ms, total: 76 ms
|
||||
Wall time: 73.8 ms
|
||||
<pre>CPU times: user 27.8 ms, sys: 5 µs, total: 27.8 ms
|
||||
Wall time: 27.3 ms
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
|
|
@ -13917,7 +13921,7 @@ Wall time: 73.8 ms
|
|||
|
||||
|
||||
<div class="output_latex output_subarea output_execute_result">
|
||||
$$2397916$$
|
||||
$\displaystyle 2397916$
|
||||
</div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13931,7 +13935,7 @@ $$2397916$$
|
|||
<div class="prompt input_prompt">In [20]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="o">%</span><span class="k">time</span> rank_and_offset(23000000000000)
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="o">%</span><span class="k">time</span> rank_and_offset(23000000000000)
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13948,8 +13952,8 @@ $$2397916$$
|
|||
|
||||
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre>CPU times: user 308 ms, sys: 0 ns, total: 308 ms
|
||||
Wall time: 306 ms
|
||||
<pre>CPU times: user 216 ms, sys: 89 µs, total: 216 ms
|
||||
Wall time: 215 ms
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
|
|
@ -13962,7 +13966,7 @@ Wall time: 306 ms
|
|||
|
||||
|
||||
<div class="output_latex output_subarea output_execute_result">
|
||||
$$\left ( 2397916, \quad 223606\right )$$
|
||||
$\displaystyle \left( 2397916, \ 223606\right)$
|
||||
</div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13993,7 +13997,7 @@ $$\left ( 2397916, \quad 223606\right )$$
|
|||
<div class="prompt input_prompt">In [21]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">y</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">'y'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">y</span> <span class="o">=</span> <span class="n">symbols</span><span class="p">(</span><span class="s1">'y'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14006,7 +14010,7 @@ $$\left ( 2397916, \quad 223606\right )$$
|
|||
<div class="prompt input_prompt">In [22]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">g</span><span class="p">,</span> <span class="n">f</span> <span class="o">=</span> <span class="n">solve</span><span class="p">(</span><span class="n">E</span> <span class="o">-</span> <span class="n">y</span><span class="p">,</span> <span class="n">k</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">g</span><span class="p">,</span> <span class="n">f</span> <span class="o">=</span> <span class="n">solve</span><span class="p">(</span><span class="n">E</span> <span class="o">-</span> <span class="n">y</span><span class="p">,</span> <span class="n">k</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14027,7 +14031,7 @@ $$\left ( 2397916, \quad 223606\right )$$
|
|||
<div class="prompt input_prompt">In [23]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">g</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">g</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14046,7 +14050,7 @@ $$\left ( 2397916, \quad 223606\right )$$
|
|||
|
||||
|
||||
<div class="output_latex output_subarea output_execute_result">
|
||||
$$- \frac{1}{2} \sqrt{y - 1} - \frac{1}{2}$$
|
||||
$\displaystyle - \frac{\sqrt{y - 1}}{2} - \frac{1}{2}$
|
||||
</div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14060,7 +14064,7 @@ $$- \frac{1}{2} \sqrt{y - 1} - \frac{1}{2}$$
|
|||
<div class="prompt input_prompt">In [24]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">f</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">f</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14079,7 +14083,7 @@ $$- \frac{1}{2} \sqrt{y - 1} - \frac{1}{2}$$
|
|||
|
||||
|
||||
<div class="output_latex output_subarea output_execute_result">
|
||||
$$\frac{1}{2} \sqrt{y - 1} - \frac{1}{2}$$
|
||||
$\displaystyle \frac{\sqrt{y - 1}}{2} - \frac{1}{2}$
|
||||
</div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14101,7 +14105,7 @@ $$\frac{1}{2} \sqrt{y - 1} - \frac{1}{2}$$
|
|||
<div class="prompt input_prompt">In [25]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">floor</span><span class="p">(</span><span class="n">f</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">floor</span><span class="p">(</span><span class="n">f</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14120,7 +14124,7 @@ $$\frac{1}{2} \sqrt{y - 1} - \frac{1}{2}$$
|
|||
|
||||
|
||||
<div class="output_latex output_subarea output_execute_result">
|
||||
$$\lfloor{\frac{1}{2} \sqrt{y - 1} - \frac{1}{2}}\rfloor + 1$$
|
||||
$\displaystyle \left\lfloor{\frac{\sqrt{y - 1}}{2} - \frac{1}{2}}\right\rfloor + 1$
|
||||
</div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14134,7 +14138,7 @@ $$\lfloor{\frac{1}{2} \sqrt{y - 1} - \frac{1}{2}}\rfloor + 1$$
|
|||
<div class="prompt input_prompt">In [26]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">F</span> <span class="o">=</span> <span class="n">lambdify</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">floor</span><span class="p">(</span><span class="n">f</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">F</span> <span class="o">=</span> <span class="n">lambdify</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">floor</span><span class="p">(</span><span class="n">f</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14147,8 +14151,8 @@ $$\lfloor{\frac{1}{2} \sqrt{y - 1} - \frac{1}{2}}\rfloor + 1$$
|
|||
<div class="prompt input_prompt">In [27]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="p">(</span><span class="mi">9</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">25</span><span class="p">,</span> <span class="mi">26</span><span class="p">,</span> <span class="mi">49</span><span class="p">,</span> <span class="mi">50</span><span class="p">):</span>
|
||||
<span class="nb">print</span> <span class="n">n</span><span class="p">,</span> <span class="nb">int</span><span class="p">(</span><span class="n">F</span><span class="p">(</span><span class="n">n</span><span class="p">))</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="p">(</span><span class="mi">9</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">25</span><span class="p">,</span> <span class="mi">26</span><span class="p">,</span> <span class="mi">49</span><span class="p">,</span> <span class="mi">50</span><span class="p">):</span>
|
||||
<span class="nb">print</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="nb">int</span><span class="p">(</span><span class="n">F</span><span class="p">(</span><span class="n">n</span><span class="p">)))</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14192,7 +14196,7 @@ $$\lfloor{\frac{1}{2} \sqrt{y - 1} - \frac{1}{2}}\rfloor + 1$$
|
|||
<div class="prompt input_prompt">In [28]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="o">%</span><span class="k">time</span> int(F(23000000000000)) # The clear winner.
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="o">%</span><span class="k">time</span> int(F(23000000000000)) # The clear winner.
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14209,8 +14213,8 @@ $$\lfloor{\frac{1}{2} \sqrt{y - 1} - \frac{1}{2}}\rfloor + 1$$
|
|||
|
||||
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre>CPU times: user 0 ns, sys: 0 ns, total: 0 ns
|
||||
Wall time: 11.9 µs
|
||||
<pre>CPU times: user 60 µs, sys: 4 µs, total: 64 µs
|
||||
Wall time: 67 µs
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
|
|
@ -14223,7 +14227,7 @@ Wall time: 11.9 µs
|
|||
|
||||
|
||||
<div class="output_latex output_subarea output_execute_result">
|
||||
$$2397916$$
|
||||
$\displaystyle 2397916$
|
||||
</div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14245,10 +14249,10 @@ $$2397916$$
|
|||
<div class="prompt input_prompt">In [29]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">floor</span> <span class="k">as</span> <span class="n">mfloor</span><span class="p">,</span> <span class="n">sqrt</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">floor</span> <span class="k">as</span> <span class="n">mfloor</span><span class="p">,</span> <span class="n">sqrt</span>
|
||||
|
||||
<span class="k">def</span> <span class="nf">mrank_of</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||||
<span class="k">return</span> <span class="nb">int</span><span class="p">(</span><span class="n">mfloor</span><span class="p">(</span><span class="n">sqrt</span><span class="p">(</span><span class="mi">23000000000000</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span> <span class="o">-</span> <span class="mf">0.5</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<span class="k">return</span> <span class="nb">int</span><span class="p">(</span><span class="n">mfloor</span><span class="p">(</span><span class="n">sqrt</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span> <span class="o">-</span> <span class="mf">0.5</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14261,7 +14265,7 @@ $$2397916$$
|
|||
<div class="prompt input_prompt">In [30]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="o">%</span><span class="k">time</span> mrank_of(23000000000000)
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="o">%</span><span class="k">time</span> mrank_of(23000000000000)
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14278,8 +14282,8 @@ $$2397916$$
|
|||
|
||||
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre>CPU times: user 0 ns, sys: 0 ns, total: 0 ns
|
||||
Wall time: 12.9 µs
|
||||
<pre>CPU times: user 7 µs, sys: 1 µs, total: 8 µs
|
||||
Wall time: 10 µs
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
|
|
@ -14292,7 +14296,7 @@ Wall time: 12.9 µs
|
|||
|
||||
|
||||
<div class="output_latex output_subarea output_execute_result">
|
||||
$$2397916$$
|
||||
$\displaystyle 2397916$
|
||||
</div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14314,7 +14318,7 @@ $$2397916$$
|
|||
<div class="prompt input_prompt">In [31]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">offset_of</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">k</span><span class="p">):</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">offset_of</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">k</span><span class="p">):</span>
|
||||
<span class="k">return</span> <span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">2</span> <span class="o">+</span> <span class="mi">4</span> <span class="o">*</span> <span class="n">k</span> <span class="o">*</span> <span class="p">(</span><span class="n">k</span> <span class="o">-</span> <span class="mi">1</span><span class="p">))</span> <span class="o">%</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">k</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
|
|
@ -14336,7 +14340,7 @@ $$2397916$$
|
|||
<div class="prompt input_prompt">In [32]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">offset_of</span><span class="p">(</span><span class="mi">23000000000000</span><span class="p">,</span> <span class="mi">2397916</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">offset_of</span><span class="p">(</span><span class="mi">23000000000000</span><span class="p">,</span> <span class="mi">2397916</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14355,7 +14359,7 @@ $$2397916$$
|
|||
|
||||
|
||||
<div class="output_latex output_subarea output_execute_result">
|
||||
$$223606$$
|
||||
$\displaystyle 223606$
|
||||
</div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14377,7 +14381,7 @@ $$223606$$
|
|||
<div class="prompt input_prompt">In [33]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">rank_of</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="k">def</span> <span class="nf">rank_of</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||||
<span class="k">return</span> <span class="nb">int</span><span class="p">(</span><span class="n">mfloor</span><span class="p">(</span><span class="n">sqrt</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span> <span class="o">-</span> <span class="mf">0.5</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
|
||||
|
||||
|
||||
|
|
@ -14405,7 +14409,7 @@ $$223606$$
|
|||
<div class="prompt input_prompt">In [34]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">aoc20173</span><span class="p">(</span><span class="mi">23</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">aoc20173</span><span class="p">(</span><span class="mi">23</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14424,7 +14428,7 @@ $$223606$$
|
|||
|
||||
|
||||
<div class="output_latex output_subarea output_execute_result">
|
||||
$$2$$
|
||||
$\displaystyle 2$
|
||||
</div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14438,7 +14442,7 @@ $$2$$
|
|||
<div class="prompt input_prompt">In [35]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">aoc20173</span><span class="p">(</span><span class="mi">23000</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">aoc20173</span><span class="p">(</span><span class="mi">23000</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14457,7 +14461,7 @@ $$2$$
|
|||
|
||||
|
||||
<div class="output_latex output_subarea output_execute_result">
|
||||
$$105$$
|
||||
$\displaystyle 105$
|
||||
</div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14471,7 +14475,7 @@ $$105$$
|
|||
<div class="prompt input_prompt">In [36]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">aoc20173</span><span class="p">(</span><span class="mi">23000000000000</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">aoc20173</span><span class="p">(</span><span class="mi">23000000000000</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14490,7 +14494,7 @@ $$105$$
|
|||
|
||||
|
||||
<div class="output_latex output_subarea output_execute_result">
|
||||
$$4572225$$
|
||||
$\displaystyle 4572225$
|
||||
</div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14504,7 +14508,7 @@ $$4572225$$
|
|||
<div class="prompt input_prompt">In [37]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="o">%</span><span class="k">time</span> aoc20173(23000000000000000000000000) # Fast for large values.
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="o">%</span><span class="k">time</span> aoc20173(23000000000000000000000000) # Fast for large values.
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14521,8 +14525,8 @@ $$4572225$$
|
|||
|
||||
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre>CPU times: user 0 ns, sys: 0 ns, total: 0 ns
|
||||
Wall time: 20 µs
|
||||
<pre>CPU times: user 22 µs, sys: 2 µs, total: 24 µs
|
||||
Wall time: 26.7 µs
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
|
|
@ -14535,7 +14539,7 @@ Wall time: 20 µs
|
|||
|
||||
|
||||
<div class="output_latex output_subarea output_execute_result">
|
||||
$$2690062495969$$
|
||||
$\displaystyle 2690062495969$
|
||||
</div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14557,7 +14561,7 @@ $$2690062495969$$
|
|||
<div class="prompt input_prompt">In [38]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14588,7 +14592,7 @@ rank_of == -- sqrt 2 / 0.5 - floor ++</code></pre>
|
|||
<div class="prompt input_prompt">In [39]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'rank_of == -- sqrt 2 / 0.5 - floor ++'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'rank_of -- sqrt 2 / 0.5 - floor ++'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14637,7 +14641,7 @@ n-k*k-1*4+2%k*2
|
|||
<div class="prompt input_prompt">In [40]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'offset_of == dup 2 * [dup -- 4 * * 2 + -] dip %'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'offset_of dup 2 * [dup -- 4 * * 2 + -] dip %'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14670,7 +14674,7 @@ k+|i-k-1|</code></pre>
|
|||
<div class="prompt input_prompt">In [41]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'row_value == over -- - abs +'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'row_value over -- - abs +'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14701,7 +14705,7 @@ m</code></pre>
|
|||
<div class="prompt input_prompt">In [42]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'aoc2017.3 == dup rank_of [offset_of] dupdip swap row_value'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'aoc2017.3 dup rank_of [offset_of] dupdip swap row_value'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14714,7 +14718,7 @@ m</code></pre>
|
|||
<div class="prompt input_prompt">In [43]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 aoc2017.3'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 aoc2017.3'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14745,7 +14749,7 @@ m</code></pre>
|
|||
<div class="prompt input_prompt">In [44]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23000 aoc2017.3'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23000 aoc2017.3'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14776,7 +14780,7 @@ m</code></pre>
|
|||
<div class="prompt input_prompt">In [45]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'23000000000000 aoc2017.3'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'23000000000000 aoc2017.3'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -14793,45 +14797,45 @@ m</code></pre>
|
|||
|
||||
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre> . 23000000000000 aoc2017.3
|
||||
23000000000000 . aoc2017.3
|
||||
23000000000000 . dup rank_of [offset_of] dupdip swap row_value
|
||||
23000000000000 23000000000000 . rank_of [offset_of] dupdip swap row_value
|
||||
23000000000000 23000000000000 . -- sqrt 2 / 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 22999999999999 . sqrt 2 / 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 4795831.523312615 . 2 / 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 4795831.523312615 2 . / 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397915.7616563076 . 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397915.7616563076 0.5 . - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397915.2616563076 . floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397915 . ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397916 . [offset_of] dupdip swap row_value
|
||||
23000000000000 2397916 [offset_of] . dupdip swap row_value
|
||||
23000000000000 2397916 . offset_of 2397916 swap row_value
|
||||
23000000000000 2397916 . dup 2 * [dup -- 4 * * 2 + -] dip % 2397916 swap row_value
|
||||
23000000000000 2397916 2397916 . 2 * [dup -- 4 * * 2 + -] dip % 2397916 swap row_value
|
||||
23000000000000 2397916 2397916 2 . * [dup -- 4 * * 2 + -] dip % 2397916 swap row_value
|
||||
23000000000000 2397916 4795832 . [dup -- 4 * * 2 + -] dip % 2397916 swap row_value
|
||||
23000000000000 2397916 4795832 [dup -- 4 * * 2 + -] . dip % 2397916 swap row_value
|
||||
23000000000000 2397916 . dup -- 4 * * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 2397916 2397916 . -- 4 * * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 2397916 2397915 . 4 * * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 2397916 2397915 4 . * * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 2397916 9591660 . * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 22999994980560 . 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 22999994980560 2 . + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 22999994980562 . - 4795832 % 2397916 swap row_value
|
||||
5019438 . 4795832 % 2397916 swap row_value
|
||||
5019438 4795832 . % 2397916 swap row_value
|
||||
223606 . 2397916 swap row_value
|
||||
223606 2397916 . swap row_value
|
||||
2397916 223606 . row_value
|
||||
2397916 223606 . over -- - abs +
|
||||
2397916 223606 2397916 . -- - abs +
|
||||
2397916 223606 2397915 . - abs +
|
||||
2397916 -2174309 . abs +
|
||||
2397916 2174309 . +
|
||||
4572225 .
|
||||
<pre> • 23000000000000 aoc2017.3
|
||||
23000000000000 • aoc2017.3
|
||||
23000000000000 • dup rank_of [offset_of] dupdip swap row_value
|
||||
23000000000000 23000000000000 • rank_of [offset_of] dupdip swap row_value
|
||||
23000000000000 23000000000000 • -- sqrt 2 / 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 22999999999999 • sqrt 2 / 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 4795831.523312615 • 2 / 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 4795831.523312615 2 • / 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397915.7616563076 • 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397915.7616563076 0.5 • - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397915.2616563076 • floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397915 • ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397916 • [offset_of] dupdip swap row_value
|
||||
23000000000000 2397916 [offset_of] • dupdip swap row_value
|
||||
23000000000000 2397916 • offset_of 2397916 swap row_value
|
||||
23000000000000 2397916 • dup 2 * [dup -- 4 * * 2 + -] dip % 2397916 swap row_value
|
||||
23000000000000 2397916 2397916 • 2 * [dup -- 4 * * 2 + -] dip % 2397916 swap row_value
|
||||
23000000000000 2397916 2397916 2 • * [dup -- 4 * * 2 + -] dip % 2397916 swap row_value
|
||||
23000000000000 2397916 4795832 • [dup -- 4 * * 2 + -] dip % 2397916 swap row_value
|
||||
23000000000000 2397916 4795832 [dup -- 4 * * 2 + -] • dip % 2397916 swap row_value
|
||||
23000000000000 2397916 • dup -- 4 * * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 2397916 2397916 • -- 4 * * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 2397916 2397915 • 4 * * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 2397916 2397915 4 • * * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 2397916 9591660 • * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 22999994980560 • 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 22999994980560 2 • + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 22999994980562 • - 4795832 % 2397916 swap row_value
|
||||
5019438 • 4795832 % 2397916 swap row_value
|
||||
5019438 4795832 • % 2397916 swap row_value
|
||||
223606 • 2397916 swap row_value
|
||||
223606 2397916 • swap row_value
|
||||
2397916 223606 • row_value
|
||||
2397916 223606 • over -- - abs +
|
||||
2397916 223606 2397916 • -- - abs +
|
||||
2397916 223606 2397915 • - abs +
|
||||
2397916 -2174309 • abs +
|
||||
2397916 2174309 • +
|
||||
4572225 •
|
||||
</pre>
|
||||
</div>
|
||||
</div>
|
||||
|
|
|
|||
|
|
@ -147,13 +147,20 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"4 3 2 1 0 1 2 3\n"
|
||||
"4\n",
|
||||
"3\n",
|
||||
"2\n",
|
||||
"1\n",
|
||||
"0\n",
|
||||
"1\n",
|
||||
"2\n",
|
||||
"3\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"for n in range(2 * k):\n",
|
||||
" print abs(n - k),"
|
||||
" print(abs(n - k),)"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -172,13 +179,13 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"3 2 1 0 1 2 3 4\n"
|
||||
"3 2 1 0 1 2 3 4 "
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"for n in range(2 * k):\n",
|
||||
" print abs(n - (k - 1)),"
|
||||
" print(abs(n - (k - 1)), end=' ')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -197,13 +204,13 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"7 6 5 4 5 6 7 8\n"
|
||||
"7 6 5 4 5 6 7 8 "
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"for n in range(2 * k):\n",
|
||||
" print abs(n - (k - 1)) + k,"
|
||||
" print(abs(n - (k - 1)) + k, end=' ')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -233,14 +240,14 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"9 8 7 6 5 6 7 8 9 10\n"
|
||||
"9 8 7 6 5 6 7 8 9 10 "
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"k = 5\n",
|
||||
"for i in range(2 * k):\n",
|
||||
" print row_value(k, i),"
|
||||
" print(row_value(k, i), end=' ')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -349,7 +356,7 @@
|
|||
],
|
||||
"source": [
|
||||
"for n in range(2, 51):\n",
|
||||
" print n, rank_and_offset(n)"
|
||||
" print(n, rank_and_offset(n))"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -418,7 +425,7 @@
|
|||
"source": [
|
||||
"for n in range(2, 51):\n",
|
||||
" k, i = rank_and_offset(n)\n",
|
||||
" print n, row_value(k, i)"
|
||||
" print(n, row_value(k, i))"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -575,9 +582,8 @@
|
|||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAHwAAAAUBAMAAAC9l0S6AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
|
||||
"text/latex": [
|
||||
"$$4 k \\left(k + 1\\right) + 2$$"
|
||||
"$\\displaystyle 4 k \\left(k + 1\\right) + 2$"
|
||||
],
|
||||
"text/plain": [
|
||||
"4⋅k⋅(k + 1) + 2"
|
||||
|
|
@ -640,7 +646,7 @@
|
|||
],
|
||||
"source": [
|
||||
"for n in (9, 10, 25, 26, 49, 50):\n",
|
||||
" print n, rank_of(n)"
|
||||
" print(n, rank_of(n))"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -659,15 +665,14 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"CPU times: user 68 ms, sys: 8 ms, total: 76 ms\n",
|
||||
"Wall time: 73.8 ms\n"
|
||||
"CPU times: user 27.8 ms, sys: 5 µs, total: 27.8 ms\n",
|
||||
"Wall time: 27.3 ms\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAEcAAAAPBAMAAABElc8tAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
|
||||
"text/latex": [
|
||||
"$$2397916$$"
|
||||
"$\\displaystyle 2397916$"
|
||||
],
|
||||
"text/plain": [
|
||||
"2397916"
|
||||
|
|
@ -691,15 +696,14 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"CPU times: user 308 ms, sys: 0 ns, total: 308 ms\n",
|
||||
"Wall time: 306 ms\n"
|
||||
"CPU times: user 216 ms, sys: 89 µs, total: 216 ms\n",
|
||||
"Wall time: 215 ms\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAALAAAAAUBAMAAADfFKqVAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nSUVORK5CYII=\n",
|
||||
"text/latex": [
|
||||
"$$\\left ( 2397916, \\quad 223606\\right )$$"
|
||||
"$\\displaystyle \\left( 2397916, \\ 223606\\right)$"
|
||||
],
|
||||
"text/plain": [
|
||||
"(2397916, 223606)"
|
||||
|
|
@ -763,9 +767,8 @@
|
|||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAIkAAAAqBAMAAAB1gmW6AAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\njL/8wqcY1Dcp15UsZrvPlwAAAABJRU5ErkJggg==\n",
|
||||
"text/latex": [
|
||||
"$$- \\frac{1}{2} \\sqrt{y - 1} - \\frac{1}{2}$$"
|
||||
"$\\displaystyle - \\frac{\\sqrt{y - 1}}{2} - \\frac{1}{2}$"
|
||||
],
|
||||
"text/plain": [
|
||||
" _______ \n",
|
||||
|
|
@ -790,9 +793,8 @@
|
|||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAHgAAAAqBAMAAACKDIIdAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAVO8Qq5l2zWYiuzKJ\nRN0MreaOAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAB9ElEQVRIDe2Vu0vDUBTGvzRNSrSNILgX3TVD\nwU2LD3DRVqgIOthF0akdXETQbi4OVXDQoTg46aCLexedCvY/aEHBRVQQfOCj3nOrmCa3ubGuHmjP\nyXe+3z1tb24K/C06rVZ4pYdR6miiFTiWeuAjM63A0P/h322Y8AfTauK4d6wthPccpmaXQni8mduh\ni2Aj6zA1u6zDqb7l3I9DK//UXpU29DTm6ve7lF8Ik0Kvv4OnVgWw34MXzglgwN/BGxCyPuFF9nSY\nT2PbalzE3+QqEFaiyDSy8sk0TE8DW1oWhz5hfgzugUKRASZ7WYE0HllW125ZXJ+w8mtyPwm3qyR0\ncIwqishGlL1vUlnJt79StoXsOyvPzHxJwDT0KGVbyGD0AkqRgAO0xSnbQgpnygjxHZpBJWcDqZTC\ng/vo4kzsfC7fCDcePHtvZ+aIX2ovWPnSp+19cW1MHbJ9UOO4KJPBeIvEKQez6jtl74ghzFxBC4Eo\nNx6H+Kc1c21pb5C6w0A3EKgiWN/WyghnIguzcpb2JnGC0MM3bDpvDa811i2CWZj1Pzx938vt7t1Z\npFWK7o5cibxxz5XcKXCYcRK1pKAll6a4ZV5uFDh0PlJJYlfQlEldMPLAKbAkc7r77UnoeRg3pVTV\n3ZQphdLZBBBiD5QW4PVa7QOfZ0qXehvwRMIAAAAASUVORK5CYII=\n",
|
||||
"text/latex": [
|
||||
"$$\\frac{1}{2} \\sqrt{y - 1} - \\frac{1}{2}$$"
|
||||
"$\\displaystyle \\frac{\\sqrt{y - 1}}{2} - \\frac{1}{2}$"
|
||||
],
|
||||
"text/plain": [
|
||||
" _______ \n",
|
||||
|
|
@ -824,9 +826,8 @@
|
|||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAK0AAAAqBAMAAAAzNMYQAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n5n/E50UAAAAASUVORK5CYII=\n",
|
||||
"text/latex": [
|
||||
"$$\\lfloor{\\frac{1}{2} \\sqrt{y - 1} - \\frac{1}{2}}\\rfloor + 1$$"
|
||||
"$\\displaystyle \\left\\lfloor{\\frac{\\sqrt{y - 1}}{2} - \\frac{1}{2}}\\right\\rfloor + 1$"
|
||||
],
|
||||
"text/plain": [
|
||||
"⎢ _______ ⎥ \n",
|
||||
|
|
@ -873,7 +874,7 @@
|
|||
],
|
||||
"source": [
|
||||
"for n in (9, 10, 25, 26, 49, 50):\n",
|
||||
" print n, int(F(n))"
|
||||
" print(n, int(F(n)))"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -894,15 +895,14 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n",
|
||||
"Wall time: 11.9 µs\n"
|
||||
"CPU times: user 60 µs, sys: 4 µs, total: 64 µs\n",
|
||||
"Wall time: 67 µs\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAEcAAAAPBAMAAABElc8tAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
|
||||
"text/latex": [
|
||||
"$$2397916$$"
|
||||
"$\\displaystyle 2397916$"
|
||||
],
|
||||
"text/plain": [
|
||||
"2397916"
|
||||
|
|
@ -933,7 +933,7 @@
|
|||
"from math import floor as mfloor, sqrt\n",
|
||||
"\n",
|
||||
"def mrank_of(n):\n",
|
||||
" return int(mfloor(sqrt(23000000000000 - 1) / 2 - 0.5) + 1)"
|
||||
" return int(mfloor(sqrt(n - 1) / 2 - 0.5) + 1)"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -947,15 +947,14 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n",
|
||||
"Wall time: 12.9 µs\n"
|
||||
"CPU times: user 7 µs, sys: 1 µs, total: 8 µs\n",
|
||||
"Wall time: 10 µs\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAEcAAAAPBAMAAABElc8tAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
|
||||
"text/latex": [
|
||||
"$$2397916$$"
|
||||
"$\\displaystyle 2397916$"
|
||||
],
|
||||
"text/plain": [
|
||||
"2397916"
|
||||
|
|
@ -1003,9 +1002,8 @@
|
|||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAADsAAAAOBAMAAABjvHmeAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIpm7MhCriUTv3c12\nVGZoascqAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABIElEQVQYGTWQoU8DMRSHvwuULWNLDgwJ6jIS\nCJlcQoLaOeSKQaAwCDAsg2WCiTMI1AQIRjIBFoHFjSCwNPwDmyMYSBBAdoTjtR2iX76+X/r6WoJy\nNcajfWgg1zlCrbzE3tgi9+0xT+kXdUeFWaOuvLELPY8nw5ipiCqvcOyNSziIHU4TldINgTUYamcM\ntMQO2ObrkvIJXePM7m71BNsN0o2HRH1IfG/NpvmvCRautUpH9AMp1FvWbFzY+UfuQmWa1U05XW9Z\ns23Lsjzo6TG8n7jm1hIoRpJazEHN3EhxJKMNvcEzQegg3Wpmz56pCrQzpiOKocOZvCGsy432Wyo4\nY7Hd3Pd4o/TDTEP1KRh17o1Blo098uUlGaW5HKM6j7G3P7xTb/ft54xWAAAAAElFTkSuQmCC\n",
|
||||
"text/latex": [
|
||||
"$$223606$$"
|
||||
"$\\displaystyle 223606$"
|
||||
],
|
||||
"text/plain": [
|
||||
"223606"
|
||||
|
|
@ -1060,9 +1058,8 @@
|
|||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAAkAAAAOBAMAAAAPuiubAAAALVBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAADAOrOgAAAADnRSTlMAIpm7MhCriUTv3c12VLge\nopIAAAAJcEhZcwAADsQAAA7EAZUrDhsAAABOSURBVAgdY2BUMnZgYAhjYH/BwJDKwDCTgWEWA0Oe\nA8O+ABAJBOsCgATHcxCTKwFEKoEIHgUQeYmBUYCBRYGBR4BBqrwoi4Fh37t3rxgAK5QOlzv7snYA\nAAAASUVORK5CYII=\n",
|
||||
"text/latex": [
|
||||
"$$2$$"
|
||||
"$\\displaystyle 2$"
|
||||
],
|
||||
"text/plain": [
|
||||
"2"
|
||||
|
|
@ -1086,9 +1083,8 @@
|
|||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAB0AAAAPBAMAAADqo9msAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAVO8Qq5l2zWaJMt0i\nu0SCRuA9AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAArElEQVQIHWNgAAHmyM4FDOzJXIFANqMyAwO7\nAPMeBqb//ycwMJiEfGZgaGJgmM7APiUHpJYNyL/CwCBvwALiQfhfGBjeCyD4zF+B/ASWjtQFEHme\nnwwM6yfwGvD8g/KB8uuBZjPchvAh6oHs+ANw8+QF3BkY5j+A8O8yMPQbqAPlDSB8oHvCGQIYGLZD\n9DNwCzBrMRxl4NBhYGB1+u7BwDwtZQEDT6QrUDkaAADf+TCFzC1FdQAAAABJRU5ErkJggg==\n",
|
||||
"text/latex": [
|
||||
"$$105$$"
|
||||
"$\\displaystyle 105$"
|
||||
],
|
||||
"text/plain": [
|
||||
"105"
|
||||
|
|
@ -1110,9 +1106,8 @@
|
|||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAEgAAAAPBAMAAAC1npSgAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAMpndu3bvImbNiRBU\nq0Qb3U6NAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABGklEQVQoFYWQsUrDUBRAT6I1pVYJ/YLYURcH\nV9HBzS9wtjgJPnRx00XnDLq4tIhTQOjiIojiLghSKEjRxR9QUajU5715hfc2Qzi83HMgjwvQgNNu\n4y5ani8KkuZaGqA00rAEO3ZI1Vo74obab4DSSFNpwVnPEBt45Bm2ApRGov0TlVCTN2UTXlKP0ojs\njCM5vkG7K5HHOKoaifpHc9KwqmClG8CZKyRa5+BV/nYoltlhCGc6GsHkItzqgQm9oIeaeuqi+Bs2\nyqip9EDMNRLN5LodXZhsJAvhzMNg8NWbyol/mB5pdE9iPJyRcYtYLpETvctHlFExHs7I/JMk49hQ\n12ivOH8K4Axc2D67lwuQbEvUtvYjgDMy//f5A0ICeXTNG40LAAAAAElFTkSuQmCC\n",
|
||||
"text/latex": [
|
||||
"$$4572225$$"
|
||||
"$\\displaystyle 4572225$"
|
||||
],
|
||||
"text/plain": [
|
||||
"4572225"
|
||||
|
|
@ -1136,15 +1131,14 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n",
|
||||
"Wall time: 20 µs\n"
|
||||
"CPU times: user 22 µs, sys: 2 µs, total: 24 µs\n",
|
||||
"Wall time: 26.7 µs\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAIUAAAAPBAMAAAA43xGxAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n8tBsnlivhsyu4f2yOhc0WRflcP/7+QN1gvGXxRfSRAAAAABJRU5ErkJggg==\n",
|
||||
"text/latex": [
|
||||
"$$2690062495969$$"
|
||||
"$\\displaystyle 2690062495969$"
|
||||
],
|
||||
"text/plain": [
|
||||
"2690062495969"
|
||||
|
|
@ -1199,7 +1193,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('rank_of == -- sqrt 2 / 0.5 - floor ++')"
|
||||
"define('rank_of -- sqrt 2 / 0.5 - floor ++')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -1242,7 +1236,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('offset_of == dup 2 * [dup -- 4 * * 2 + -] dip %')"
|
||||
"define('offset_of dup 2 * [dup -- 4 * * 2 + -] dip %')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -1271,7 +1265,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('row_value == over -- - abs +')"
|
||||
"define('row_value over -- - abs +')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -1298,7 +1292,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('aoc2017.3 == dup rank_of [offset_of] dupdip swap row_value')"
|
||||
"define('aoc2017.3 dup rank_of [offset_of] dupdip swap row_value')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -1344,45 +1338,45 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . 23000000000000 aoc2017.3\n",
|
||||
" 23000000000000 . aoc2017.3\n",
|
||||
" 23000000000000 . dup rank_of [offset_of] dupdip swap row_value\n",
|
||||
" 23000000000000 23000000000000 . rank_of [offset_of] dupdip swap row_value\n",
|
||||
" 23000000000000 23000000000000 . -- sqrt 2 / 0.5 - floor ++ [offset_of] dupdip swap row_value\n",
|
||||
" 23000000000000 22999999999999 . sqrt 2 / 0.5 - floor ++ [offset_of] dupdip swap row_value\n",
|
||||
" 23000000000000 4795831.523312615 . 2 / 0.5 - floor ++ [offset_of] dupdip swap row_value\n",
|
||||
" 23000000000000 4795831.523312615 2 . / 0.5 - floor ++ [offset_of] dupdip swap row_value\n",
|
||||
" 23000000000000 2397915.7616563076 . 0.5 - floor ++ [offset_of] dupdip swap row_value\n",
|
||||
" 23000000000000 2397915.7616563076 0.5 . - floor ++ [offset_of] dupdip swap row_value\n",
|
||||
" 23000000000000 2397915.2616563076 . floor ++ [offset_of] dupdip swap row_value\n",
|
||||
" 23000000000000 2397915 . ++ [offset_of] dupdip swap row_value\n",
|
||||
" 23000000000000 2397916 . [offset_of] dupdip swap row_value\n",
|
||||
" 23000000000000 2397916 [offset_of] . dupdip swap row_value\n",
|
||||
" 23000000000000 2397916 . offset_of 2397916 swap row_value\n",
|
||||
" 23000000000000 2397916 . dup 2 * [dup -- 4 * * 2 + -] dip % 2397916 swap row_value\n",
|
||||
" 23000000000000 2397916 2397916 . 2 * [dup -- 4 * * 2 + -] dip % 2397916 swap row_value\n",
|
||||
" 23000000000000 2397916 2397916 2 . * [dup -- 4 * * 2 + -] dip % 2397916 swap row_value\n",
|
||||
" 23000000000000 2397916 4795832 . [dup -- 4 * * 2 + -] dip % 2397916 swap row_value\n",
|
||||
"23000000000000 2397916 4795832 [dup -- 4 * * 2 + -] . dip % 2397916 swap row_value\n",
|
||||
" 23000000000000 2397916 . dup -- 4 * * 2 + - 4795832 % 2397916 swap row_value\n",
|
||||
" 23000000000000 2397916 2397916 . -- 4 * * 2 + - 4795832 % 2397916 swap row_value\n",
|
||||
" 23000000000000 2397916 2397915 . 4 * * 2 + - 4795832 % 2397916 swap row_value\n",
|
||||
" 23000000000000 2397916 2397915 4 . * * 2 + - 4795832 % 2397916 swap row_value\n",
|
||||
" 23000000000000 2397916 9591660 . * 2 + - 4795832 % 2397916 swap row_value\n",
|
||||
" 23000000000000 22999994980560 . 2 + - 4795832 % 2397916 swap row_value\n",
|
||||
" 23000000000000 22999994980560 2 . + - 4795832 % 2397916 swap row_value\n",
|
||||
" 23000000000000 22999994980562 . - 4795832 % 2397916 swap row_value\n",
|
||||
" 5019438 . 4795832 % 2397916 swap row_value\n",
|
||||
" 5019438 4795832 . % 2397916 swap row_value\n",
|
||||
" 223606 . 2397916 swap row_value\n",
|
||||
" 223606 2397916 . swap row_value\n",
|
||||
" 2397916 223606 . row_value\n",
|
||||
" 2397916 223606 . over -- - abs +\n",
|
||||
" 2397916 223606 2397916 . -- - abs +\n",
|
||||
" 2397916 223606 2397915 . - abs +\n",
|
||||
" 2397916 -2174309 . abs +\n",
|
||||
" 2397916 2174309 . +\n",
|
||||
" 4572225 . \n"
|
||||
" • 23000000000000 aoc2017.3\n",
|
||||
" 23000000000000 • aoc2017.3\n",
|
||||
" 23000000000000 • dup rank_of [offset_of] dupdip swap row_value\n",
|
||||
" 23000000000000 23000000000000 • rank_of [offset_of] dupdip swap row_value\n",
|
||||
" 23000000000000 23000000000000 • -- sqrt 2 / 0.5 - floor ++ [offset_of] dupdip swap row_value\n",
|
||||
" 23000000000000 22999999999999 • sqrt 2 / 0.5 - floor ++ [offset_of] dupdip swap row_value\n",
|
||||
" 23000000000000 4795831.523312615 • 2 / 0.5 - floor ++ [offset_of] dupdip swap row_value\n",
|
||||
" 23000000000000 4795831.523312615 2 • / 0.5 - floor ++ [offset_of] dupdip swap row_value\n",
|
||||
" 23000000000000 2397915.7616563076 • 0.5 - floor ++ [offset_of] dupdip swap row_value\n",
|
||||
" 23000000000000 2397915.7616563076 0.5 • - floor ++ [offset_of] dupdip swap row_value\n",
|
||||
" 23000000000000 2397915.2616563076 • floor ++ [offset_of] dupdip swap row_value\n",
|
||||
" 23000000000000 2397915 • ++ [offset_of] dupdip swap row_value\n",
|
||||
" 23000000000000 2397916 • [offset_of] dupdip swap row_value\n",
|
||||
" 23000000000000 2397916 [offset_of] • dupdip swap row_value\n",
|
||||
" 23000000000000 2397916 • offset_of 2397916 swap row_value\n",
|
||||
" 23000000000000 2397916 • dup 2 * [dup -- 4 * * 2 + -] dip % 2397916 swap row_value\n",
|
||||
" 23000000000000 2397916 2397916 • 2 * [dup -- 4 * * 2 + -] dip % 2397916 swap row_value\n",
|
||||
" 23000000000000 2397916 2397916 2 • * [dup -- 4 * * 2 + -] dip % 2397916 swap row_value\n",
|
||||
" 23000000000000 2397916 4795832 • [dup -- 4 * * 2 + -] dip % 2397916 swap row_value\n",
|
||||
"23000000000000 2397916 4795832 [dup -- 4 * * 2 + -] • dip % 2397916 swap row_value\n",
|
||||
" 23000000000000 2397916 • dup -- 4 * * 2 + - 4795832 % 2397916 swap row_value\n",
|
||||
" 23000000000000 2397916 2397916 • -- 4 * * 2 + - 4795832 % 2397916 swap row_value\n",
|
||||
" 23000000000000 2397916 2397915 • 4 * * 2 + - 4795832 % 2397916 swap row_value\n",
|
||||
" 23000000000000 2397916 2397915 4 • * * 2 + - 4795832 % 2397916 swap row_value\n",
|
||||
" 23000000000000 2397916 9591660 • * 2 + - 4795832 % 2397916 swap row_value\n",
|
||||
" 23000000000000 22999994980560 • 2 + - 4795832 % 2397916 swap row_value\n",
|
||||
" 23000000000000 22999994980560 2 • + - 4795832 % 2397916 swap row_value\n",
|
||||
" 23000000000000 22999994980562 • - 4795832 % 2397916 swap row_value\n",
|
||||
" 5019438 • 4795832 % 2397916 swap row_value\n",
|
||||
" 5019438 4795832 • % 2397916 swap row_value\n",
|
||||
" 223606 • 2397916 swap row_value\n",
|
||||
" 223606 2397916 • swap row_value\n",
|
||||
" 2397916 223606 • row_value\n",
|
||||
" 2397916 223606 • over -- - abs +\n",
|
||||
" 2397916 223606 2397916 • -- - abs +\n",
|
||||
" 2397916 223606 2397915 • - abs +\n",
|
||||
" 2397916 -2174309 • abs +\n",
|
||||
" 2397916 2174309 • +\n",
|
||||
" 4572225 • \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -1411,14 +1405,14 @@
|
|||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 2
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython2",
|
||||
"version": "2.7.13"
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.8.3"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
|
|
|||
|
|
@ -105,10 +105,17 @@ Subtract $k$ from the index and take the absolute value:
|
|||
|
||||
```python
|
||||
for n in range(2 * k):
|
||||
print abs(n - k),
|
||||
print(abs(n - k),)
|
||||
```
|
||||
|
||||
4 3 2 1 0 1 2 3
|
||||
4
|
||||
3
|
||||
2
|
||||
1
|
||||
0
|
||||
1
|
||||
2
|
||||
3
|
||||
|
||||
|
||||
Not quite. Subtract $k - 1$ from the index and take the absolute value:
|
||||
|
|
@ -116,22 +123,20 @@ Not quite. Subtract $k - 1$ from the index and take the absolute value:
|
|||
|
||||
```python
|
||||
for n in range(2 * k):
|
||||
print abs(n - (k - 1)),
|
||||
print(abs(n - (k - 1)), end=' ')
|
||||
```
|
||||
|
||||
3 2 1 0 1 2 3 4
|
||||
|
||||
3 2 1 0 1 2 3 4
|
||||
|
||||
Great, now add $k$...
|
||||
|
||||
|
||||
```python
|
||||
for n in range(2 * k):
|
||||
print abs(n - (k - 1)) + k,
|
||||
print(abs(n - (k - 1)) + k, end=' ')
|
||||
```
|
||||
|
||||
7 6 5 4 5 6 7 8
|
||||
|
||||
7 6 5 4 5 6 7 8
|
||||
|
||||
So to write a function that can give us the value of a row at a given index:
|
||||
|
||||
|
|
@ -146,11 +151,10 @@ def row_value(k, i):
|
|||
```python
|
||||
k = 5
|
||||
for i in range(2 * k):
|
||||
print row_value(k, i),
|
||||
print(row_value(k, i), end=' ')
|
||||
```
|
||||
|
||||
9 8 7 6 5 6 7 8 9 10
|
||||
|
||||
9 8 7 6 5 6 7 8 9 10
|
||||
|
||||
(I'm leaving out details of how I figured this all out and just giving the relevent bits. It took a little while to zero in of the aspects of the pattern that were important for the task.)
|
||||
|
||||
|
|
@ -182,7 +186,7 @@ def rank_and_offset(n):
|
|||
|
||||
```python
|
||||
for n in range(2, 51):
|
||||
print n, rank_and_offset(n)
|
||||
print(n, rank_and_offset(n))
|
||||
```
|
||||
|
||||
2 (1, 0)
|
||||
|
|
@ -240,7 +244,7 @@ for n in range(2, 51):
|
|||
```python
|
||||
for n in range(2, 51):
|
||||
k, i = rank_and_offset(n)
|
||||
print n, row_value(k, i)
|
||||
print(n, row_value(k, i))
|
||||
```
|
||||
|
||||
2 1
|
||||
|
|
@ -394,7 +398,7 @@ E
|
|||
|
||||
|
||||
|
||||
$$4 k \left(k + 1\right) + 2$$
|
||||
$\displaystyle 4 k \left(k + 1\right) + 2$
|
||||
|
||||
|
||||
|
||||
|
|
@ -413,7 +417,7 @@ It gives correct answers:
|
|||
|
||||
```python
|
||||
for n in (9, 10, 25, 26, 49, 50):
|
||||
print n, rank_of(n)
|
||||
print(n, rank_of(n))
|
||||
```
|
||||
|
||||
9 1
|
||||
|
|
@ -431,14 +435,14 @@ And it runs much faster (at least for large numbers):
|
|||
%time rank_of(23000000000000) # Compare runtime with rank_and_offset()!
|
||||
```
|
||||
|
||||
CPU times: user 68 ms, sys: 8 ms, total: 76 ms
|
||||
Wall time: 73.8 ms
|
||||
CPU times: user 27.8 ms, sys: 5 µs, total: 27.8 ms
|
||||
Wall time: 27.3 ms
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
$$2397916$$
|
||||
$\displaystyle 2397916$
|
||||
|
||||
|
||||
|
||||
|
|
@ -447,14 +451,14 @@ $$2397916$$
|
|||
%time rank_and_offset(23000000000000)
|
||||
```
|
||||
|
||||
CPU times: user 308 ms, sys: 0 ns, total: 308 ms
|
||||
Wall time: 306 ms
|
||||
CPU times: user 216 ms, sys: 89 µs, total: 216 ms
|
||||
Wall time: 215 ms
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
$$\left ( 2397916, \quad 223606\right )$$
|
||||
$\displaystyle \left( 2397916, \ 223606\right)$
|
||||
|
||||
|
||||
|
||||
|
|
@ -485,7 +489,7 @@ g
|
|||
|
||||
|
||||
|
||||
$$- \frac{1}{2} \sqrt{y - 1} - \frac{1}{2}$$
|
||||
$\displaystyle - \frac{\sqrt{y - 1}}{2} - \frac{1}{2}$
|
||||
|
||||
|
||||
|
||||
|
|
@ -497,7 +501,7 @@ f
|
|||
|
||||
|
||||
|
||||
$$\frac{1}{2} \sqrt{y - 1} - \frac{1}{2}$$
|
||||
$\displaystyle \frac{\sqrt{y - 1}}{2} - \frac{1}{2}$
|
||||
|
||||
|
||||
|
||||
|
|
@ -511,7 +515,7 @@ floor(f) + 1
|
|||
|
||||
|
||||
|
||||
$$\lfloor{\frac{1}{2} \sqrt{y - 1} - \frac{1}{2}}\rfloor + 1$$
|
||||
$\displaystyle \left\lfloor{\frac{\sqrt{y - 1}}{2} - \frac{1}{2}}\right\rfloor + 1$
|
||||
|
||||
|
||||
|
||||
|
|
@ -523,7 +527,7 @@ F = lambdify(y, floor(f) + 1)
|
|||
|
||||
```python
|
||||
for n in (9, 10, 25, 26, 49, 50):
|
||||
print n, int(F(n))
|
||||
print(n, int(F(n)))
|
||||
```
|
||||
|
||||
9 1
|
||||
|
|
@ -541,14 +545,14 @@ It's pretty fast.
|
|||
%time int(F(23000000000000)) # The clear winner.
|
||||
```
|
||||
|
||||
CPU times: user 0 ns, sys: 0 ns, total: 0 ns
|
||||
Wall time: 11.9 µs
|
||||
CPU times: user 60 µs, sys: 4 µs, total: 64 µs
|
||||
Wall time: 67 µs
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
$$2397916$$
|
||||
$\displaystyle 2397916$
|
||||
|
||||
|
||||
|
||||
|
|
@ -559,7 +563,7 @@ Knowing the equation we could write our own function manually, but the speed is
|
|||
from math import floor as mfloor, sqrt
|
||||
|
||||
def mrank_of(n):
|
||||
return int(mfloor(sqrt(23000000000000 - 1) / 2 - 0.5) + 1)
|
||||
return int(mfloor(sqrt(n - 1) / 2 - 0.5) + 1)
|
||||
```
|
||||
|
||||
|
||||
|
|
@ -567,14 +571,14 @@ def mrank_of(n):
|
|||
%time mrank_of(23000000000000)
|
||||
```
|
||||
|
||||
CPU times: user 0 ns, sys: 0 ns, total: 0 ns
|
||||
Wall time: 12.9 µs
|
||||
CPU times: user 7 µs, sys: 1 µs, total: 8 µs
|
||||
Wall time: 10 µs
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
$$2397916$$
|
||||
$\displaystyle 2397916$
|
||||
|
||||
|
||||
|
||||
|
|
@ -598,7 +602,7 @@ offset_of(23000000000000, 2397916)
|
|||
|
||||
|
||||
|
||||
$$223606$$
|
||||
$\displaystyle 223606$
|
||||
|
||||
|
||||
|
||||
|
|
@ -632,7 +636,7 @@ aoc20173(23)
|
|||
|
||||
|
||||
|
||||
$$2$$
|
||||
$\displaystyle 2$
|
||||
|
||||
|
||||
|
||||
|
|
@ -644,7 +648,7 @@ aoc20173(23000)
|
|||
|
||||
|
||||
|
||||
$$105$$
|
||||
$\displaystyle 105$
|
||||
|
||||
|
||||
|
||||
|
|
@ -656,7 +660,7 @@ aoc20173(23000000000000)
|
|||
|
||||
|
||||
|
||||
$$4572225$$
|
||||
$\displaystyle 4572225$
|
||||
|
||||
|
||||
|
||||
|
|
@ -665,14 +669,14 @@ $$4572225$$
|
|||
%time aoc20173(23000000000000000000000000) # Fast for large values.
|
||||
```
|
||||
|
||||
CPU times: user 0 ns, sys: 0 ns, total: 0 ns
|
||||
Wall time: 20 µs
|
||||
CPU times: user 22 µs, sys: 2 µs, total: 24 µs
|
||||
Wall time: 26.7 µs
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
$$2690062495969$$
|
||||
$\displaystyle 2690062495969$
|
||||
|
||||
|
||||
|
||||
|
|
@ -698,7 +702,7 @@ The translation is straightforward.
|
|||
|
||||
|
||||
```python
|
||||
define('rank_of == -- sqrt 2 / 0.5 - floor ++')
|
||||
define('rank_of -- sqrt 2 / 0.5 - floor ++')
|
||||
```
|
||||
|
||||
### `offset_of`
|
||||
|
|
@ -732,7 +736,7 @@ Ergo:
|
|||
|
||||
|
||||
```python
|
||||
define('offset_of == dup 2 * [dup -- 4 * * 2 + -] dip %')
|
||||
define('offset_of dup 2 * [dup -- 4 * * 2 + -] dip %')
|
||||
```
|
||||
|
||||
### `row_value`
|
||||
|
|
@ -752,7 +756,7 @@ define('offset_of == dup 2 * [dup -- 4 * * 2 + -] dip %')
|
|||
|
||||
|
||||
```python
|
||||
define('row_value == over -- - abs +')
|
||||
define('row_value over -- - abs +')
|
||||
```
|
||||
|
||||
### `aoc2017.3`
|
||||
|
|
@ -770,7 +774,7 @@ define('row_value == over -- - abs +')
|
|||
|
||||
|
||||
```python
|
||||
define('aoc2017.3 == dup rank_of [offset_of] dupdip swap row_value')
|
||||
define('aoc2017.3 dup rank_of [offset_of] dupdip swap row_value')
|
||||
```
|
||||
|
||||
|
||||
|
|
@ -794,45 +798,45 @@ J('23000 aoc2017.3')
|
|||
V('23000000000000 aoc2017.3')
|
||||
```
|
||||
|
||||
. 23000000000000 aoc2017.3
|
||||
23000000000000 . aoc2017.3
|
||||
23000000000000 . dup rank_of [offset_of] dupdip swap row_value
|
||||
23000000000000 23000000000000 . rank_of [offset_of] dupdip swap row_value
|
||||
23000000000000 23000000000000 . -- sqrt 2 / 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 22999999999999 . sqrt 2 / 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 4795831.523312615 . 2 / 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 4795831.523312615 2 . / 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397915.7616563076 . 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397915.7616563076 0.5 . - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397915.2616563076 . floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397915 . ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397916 . [offset_of] dupdip swap row_value
|
||||
23000000000000 2397916 [offset_of] . dupdip swap row_value
|
||||
23000000000000 2397916 . offset_of 2397916 swap row_value
|
||||
23000000000000 2397916 . dup 2 * [dup -- 4 * * 2 + -] dip % 2397916 swap row_value
|
||||
23000000000000 2397916 2397916 . 2 * [dup -- 4 * * 2 + -] dip % 2397916 swap row_value
|
||||
23000000000000 2397916 2397916 2 . * [dup -- 4 * * 2 + -] dip % 2397916 swap row_value
|
||||
23000000000000 2397916 4795832 . [dup -- 4 * * 2 + -] dip % 2397916 swap row_value
|
||||
23000000000000 2397916 4795832 [dup -- 4 * * 2 + -] . dip % 2397916 swap row_value
|
||||
23000000000000 2397916 . dup -- 4 * * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 2397916 2397916 . -- 4 * * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 2397916 2397915 . 4 * * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 2397916 2397915 4 . * * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 2397916 9591660 . * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 22999994980560 . 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 22999994980560 2 . + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 22999994980562 . - 4795832 % 2397916 swap row_value
|
||||
5019438 . 4795832 % 2397916 swap row_value
|
||||
5019438 4795832 . % 2397916 swap row_value
|
||||
223606 . 2397916 swap row_value
|
||||
223606 2397916 . swap row_value
|
||||
2397916 223606 . row_value
|
||||
2397916 223606 . over -- - abs +
|
||||
2397916 223606 2397916 . -- - abs +
|
||||
2397916 223606 2397915 . - abs +
|
||||
2397916 -2174309 . abs +
|
||||
2397916 2174309 . +
|
||||
4572225 .
|
||||
• 23000000000000 aoc2017.3
|
||||
23000000000000 • aoc2017.3
|
||||
23000000000000 • dup rank_of [offset_of] dupdip swap row_value
|
||||
23000000000000 23000000000000 • rank_of [offset_of] dupdip swap row_value
|
||||
23000000000000 23000000000000 • -- sqrt 2 / 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 22999999999999 • sqrt 2 / 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 4795831.523312615 • 2 / 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 4795831.523312615 2 • / 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397915.7616563076 • 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397915.7616563076 0.5 • - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397915.2616563076 • floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397915 • ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397916 • [offset_of] dupdip swap row_value
|
||||
23000000000000 2397916 [offset_of] • dupdip swap row_value
|
||||
23000000000000 2397916 • offset_of 2397916 swap row_value
|
||||
23000000000000 2397916 • dup 2 * [dup -- 4 * * 2 + -] dip % 2397916 swap row_value
|
||||
23000000000000 2397916 2397916 • 2 * [dup -- 4 * * 2 + -] dip % 2397916 swap row_value
|
||||
23000000000000 2397916 2397916 2 • * [dup -- 4 * * 2 + -] dip % 2397916 swap row_value
|
||||
23000000000000 2397916 4795832 • [dup -- 4 * * 2 + -] dip % 2397916 swap row_value
|
||||
23000000000000 2397916 4795832 [dup -- 4 * * 2 + -] • dip % 2397916 swap row_value
|
||||
23000000000000 2397916 • dup -- 4 * * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 2397916 2397916 • -- 4 * * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 2397916 2397915 • 4 * * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 2397916 2397915 4 • * * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 2397916 9591660 • * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 22999994980560 • 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 22999994980560 2 • + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 22999994980562 • - 4795832 % 2397916 swap row_value
|
||||
5019438 • 4795832 % 2397916 swap row_value
|
||||
5019438 4795832 • % 2397916 swap row_value
|
||||
223606 • 2397916 swap row_value
|
||||
223606 2397916 • swap row_value
|
||||
2397916 223606 • row_value
|
||||
2397916 223606 • over -- - abs +
|
||||
2397916 223606 2397916 • -- - abs +
|
||||
2397916 223606 2397915 • - abs +
|
||||
2397916 -2174309 • abs +
|
||||
2397916 2174309 • +
|
||||
4572225 •
|
||||
|
||||
|
||||
rank_of == -- sqrt 2 / 0.5 - floor ++
|
||||
|
|
|
|||
|
|
@ -13,11 +13,11 @@ example, the first few squares are allocated like this:
|
|||
|
||||
::
|
||||
|
||||
17 16 15 14 13
|
||||
18 5 4 3 12
|
||||
19 6 1 2 11
|
||||
20 7 8 9 10
|
||||
21 22 23---> ...
|
||||
17 16 15 14 13
|
||||
18 5 4 3 12
|
||||
19 6 1 2 11
|
||||
20 7 8 9 10
|
||||
21 22 23---> ...
|
||||
|
||||
While this is very space-efficient (no squares are skipped), requested
|
||||
data must be carried back to square 1 (the location of the only access
|
||||
|
|
@ -27,7 +27,7 @@ Distance between the location of the data and square 1.
|
|||
|
||||
For example:
|
||||
|
||||
- Data from square 1 is carried 0 steps, since it’s at the access port.
|
||||
- Data from square 1 is carried 0 steps, since it's at the access port.
|
||||
- Data from square 12 is carried 3 steps, such as: down, left, left.
|
||||
- Data from square 23 is carried only 2 steps: up twice.
|
||||
- Data from square 1024 must be carried 31 steps.
|
||||
|
|
@ -39,8 +39,8 @@ Analysis
|
|||
~~~~~~~~
|
||||
|
||||
I freely admit that I worked out the program I wanted to write using
|
||||
graph paper and some Python doodles. There’s no point in trying to write
|
||||
a Joy program until I’m sure I understand the problem well enough.
|
||||
graph paper and some Python doodles. There's no point in trying to write
|
||||
a Joy program until I'm sure I understand the problem well enough.
|
||||
|
||||
The first thing I did was to write a column of numbers from 1 to n (32
|
||||
as it happens) and next to them the desired output number, to look for
|
||||
|
|
@ -48,61 +48,61 @@ patterns directly:
|
|||
|
||||
::
|
||||
|
||||
1 0
|
||||
2 1
|
||||
3 2
|
||||
4 1
|
||||
5 2
|
||||
6 1
|
||||
7 2
|
||||
8 1
|
||||
9 2
|
||||
10 3
|
||||
11 2
|
||||
12 3
|
||||
13 4
|
||||
14 3
|
||||
15 2
|
||||
16 3
|
||||
17 4
|
||||
18 3
|
||||
19 2
|
||||
20 3
|
||||
21 4
|
||||
22 3
|
||||
23 2
|
||||
24 3
|
||||
25 4
|
||||
26 5
|
||||
27 4
|
||||
28 3
|
||||
29 4
|
||||
30 5
|
||||
31 6
|
||||
32 5
|
||||
1 0
|
||||
2 1
|
||||
3 2
|
||||
4 1
|
||||
5 2
|
||||
6 1
|
||||
7 2
|
||||
8 1
|
||||
9 2
|
||||
10 3
|
||||
11 2
|
||||
12 3
|
||||
13 4
|
||||
14 3
|
||||
15 2
|
||||
16 3
|
||||
17 4
|
||||
18 3
|
||||
19 2
|
||||
20 3
|
||||
21 4
|
||||
22 3
|
||||
23 2
|
||||
24 3
|
||||
25 4
|
||||
26 5
|
||||
27 4
|
||||
28 3
|
||||
29 4
|
||||
30 5
|
||||
31 6
|
||||
32 5
|
||||
|
||||
There are four groups repeating for a given “rank”, then the pattern
|
||||
There are four groups repeating for a given "rank", then the pattern
|
||||
enlarges and four groups repeat again, etc.
|
||||
|
||||
::
|
||||
|
||||
1 2
|
||||
3 2 3 4
|
||||
5 4 3 4 5 6
|
||||
7 6 5 4 5 6 7 8
|
||||
9 8 7 6 5 6 7 8 9 10
|
||||
1 2
|
||||
3 2 3 4
|
||||
5 4 3 4 5 6
|
||||
7 6 5 4 5 6 7 8
|
||||
9 8 7 6 5 6 7 8 9 10
|
||||
|
||||
Four of this pyramid interlock to tile the plane extending from the
|
||||
initial “1” square.
|
||||
initial "1" square.
|
||||
|
||||
::
|
||||
|
||||
2 3 | 4 5 | 6 7 | 8 9
|
||||
10 11 12 13|14 15 16 17|18 19 20 21|22 23 24 25
|
||||
2 3 | 4 5 | 6 7 | 8 9
|
||||
10 11 12 13|14 15 16 17|18 19 20 21|22 23 24 25
|
||||
|
||||
And so on.
|
||||
|
||||
We can figure out the pattern for a row of the pyramid at a given “rank”
|
||||
We can figure out the pattern for a row of the pyramid at a given "rank"
|
||||
:math:`k`:
|
||||
|
||||
:math:`2k - 1, 2k - 2, ..., k, k + 1, k + 2, ..., 2k`
|
||||
|
|
@ -115,82 +115,86 @@ This shows that the series consists at each place of :math:`k` plus some
|
|||
number that begins at :math:`k - 1`, decreases to zero, then increases
|
||||
to :math:`k`. Each row has :math:`2k` members.
|
||||
|
||||
Let’s figure out how, given an index into a row, we can calculate the
|
||||
Let's figure out how, given an index into a row, we can calculate the
|
||||
value there. The index will be from 0 to :math:`k - 1`.
|
||||
|
||||
Let’s look at an example, with :math:`k = 4`:
|
||||
Let's look at an example, with :math:`k = 4`:
|
||||
|
||||
::
|
||||
|
||||
0 1 2 3 4 5 6 7
|
||||
7 6 5 4 5 6 7 8
|
||||
0 1 2 3 4 5 6 7
|
||||
7 6 5 4 5 6 7 8
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
k = 4
|
||||
|
||||
Subtract :math:`k` from the index and take the absolute value:
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
for n in range(2 * k):
|
||||
print abs(n - k),
|
||||
print(abs(n - k),)
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
4 3 2 1 0 1 2 3
|
||||
4
|
||||
3
|
||||
2
|
||||
1
|
||||
0
|
||||
1
|
||||
2
|
||||
3
|
||||
|
||||
|
||||
Not quite. Subtract :math:`k - 1` from the index and take the absolute
|
||||
value:
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
for n in range(2 * k):
|
||||
print abs(n - (k - 1)),
|
||||
print(abs(n - (k - 1)), end=' ')
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
3 2 1 0 1 2 3 4
|
||||
3 2 1 0 1 2 3 4
|
||||
|
||||
Great, now add :math:`k`...
|
||||
|
||||
Great, now add :math:`k`\ …
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
for n in range(2 * k):
|
||||
print abs(n - (k - 1)) + k,
|
||||
print(abs(n - (k - 1)) + k, end=' ')
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
7 6 5 4 5 6 7 8
|
||||
|
||||
7 6 5 4 5 6 7 8
|
||||
|
||||
So to write a function that can give us the value of a row at a given
|
||||
index:
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
def row_value(k, i):
|
||||
i %= (2 * k) # wrap the index at the row boundary.
|
||||
return abs(i - (k - 1)) + k
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
k = 5
|
||||
for i in range(2 * k):
|
||||
print row_value(k, i),
|
||||
print(row_value(k, i), end=' ')
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
9 8 7 6 5 6 7 8 9 10
|
||||
9 8 7 6 5 6 7 8 9 10
|
||||
|
||||
|
||||
(I’m leaving out details of how I figured this all out and just giving
|
||||
(I'm leaving out details of how I figured this all out and just giving
|
||||
the relevent bits. It took a little while to zero in of the aspects of
|
||||
the pattern that were important for the task.)
|
||||
|
||||
|
|
@ -209,11 +213,11 @@ initial square we have:
|
|||
|
||||
:math:`corner_k = 1 + \sum_{n=1}^k 8n`
|
||||
|
||||
I’m not mathematically sophisticated enough to turn this directly into a
|
||||
formula (but Sympy is, see below.) I’m going to write a simple Python
|
||||
I'm not mathematically sophisticated enough to turn this directly into a
|
||||
formula (but Sympy is, see below.) I'm going to write a simple Python
|
||||
function to iterate and search:
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
def rank_and_offset(n):
|
||||
assert n >= 2 # Guard the domain.
|
||||
|
|
@ -228,10 +232,10 @@ function to iterate and search:
|
|||
n -= m # Remove this rank's worth.
|
||||
k += 1
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
for n in range(2, 51):
|
||||
print n, rank_and_offset(n)
|
||||
print(n, rank_and_offset(n))
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
|
@ -287,11 +291,11 @@ function to iterate and search:
|
|||
50 (4, 0)
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
for n in range(2, 51):
|
||||
k, i = rank_and_offset(n)
|
||||
print n, row_value(k, i)
|
||||
print(n, row_value(k, i))
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
|
@ -350,7 +354,7 @@ function to iterate and search:
|
|||
Putting it all together
|
||||
~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
def row_value(k, i):
|
||||
return abs(i - (k - 1)) + k
|
||||
|
|
@ -375,7 +379,7 @@ Putting it all together
|
|||
k, i = rank_and_offset(n)
|
||||
return row_value(k, i)
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
aoc20173(23)
|
||||
|
||||
|
|
@ -388,7 +392,7 @@ Putting it all together
|
|||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
aoc20173(23000)
|
||||
|
||||
|
|
@ -401,7 +405,7 @@ Putting it all together
|
|||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
aoc20173(23000000000000)
|
||||
|
||||
|
|
@ -420,17 +424,17 @@ Sympy to the Rescue
|
|||
Find the rank for large numbers
|
||||
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
Using e.g. Sympy we can find the rank directly by solving for the roots
|
||||
Using e.g. Sympy we can find the rank directly by solving for the roots
|
||||
of an equation. For large numbers this will (eventually) be faster than
|
||||
iterating as ``rank_and_offset()`` does.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
from sympy import floor, lambdify, solve, symbols
|
||||
from sympy import init_printing
|
||||
init_printing()
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
k = symbols('k')
|
||||
|
||||
|
|
@ -444,7 +448,7 @@ and
|
|||
|
||||
We want:
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
E = 2 + 8 * k * (k + 1) / 2 # For the reason for adding 2 see above.
|
||||
|
||||
|
|
@ -455,13 +459,13 @@ We want:
|
|||
|
||||
.. math::
|
||||
|
||||
4 k \left(k + 1\right) + 2
|
||||
\displaystyle 4 k \left(k + 1\right) + 2
|
||||
|
||||
|
||||
|
||||
We can write a function to solve for :math:`k` given some :math:`n`\ …
|
||||
We can write a function to solve for :math:`k` given some :math:`n`...
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
def rank_of(n):
|
||||
return floor(max(solve(E - n, k))) + 1
|
||||
|
|
@ -472,15 +476,15 @@ about the larger one we use ``max()`` to select it. It will generally
|
|||
not be a nice integer (unless :math:`n` is the number of an end-corner
|
||||
of a rank) so we take the ``floor()`` and add 1 to get the integer rank
|
||||
of :math:`n`. (Taking the ``ceiling()`` gives off-by-one errors on the
|
||||
rank boundaries. I don’t know why. I’m basically like a monkey doing
|
||||
rank boundaries. I don't know why. I'm basically like a monkey doing
|
||||
math here.) =-D
|
||||
|
||||
It gives correct answers:
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
for n in (9, 10, 25, 26, 49, 50):
|
||||
print n, rank_of(n)
|
||||
print(n, rank_of(n))
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
|
@ -495,46 +499,46 @@ It gives correct answers:
|
|||
|
||||
And it runs much faster (at least for large numbers):
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
%time rank_of(23000000000000) # Compare runtime with rank_and_offset()!
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
CPU times: user 68 ms, sys: 8 ms, total: 76 ms
|
||||
Wall time: 73.8 ms
|
||||
CPU times: user 27.8 ms, sys: 5 µs, total: 27.8 ms
|
||||
Wall time: 27.3 ms
|
||||
|
||||
|
||||
|
||||
|
||||
.. math::
|
||||
|
||||
2397916
|
||||
\displaystyle 2397916
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
%time rank_and_offset(23000000000000)
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
CPU times: user 308 ms, sys: 0 ns, total: 308 ms
|
||||
Wall time: 306 ms
|
||||
CPU times: user 216 ms, sys: 89 µs, total: 216 ms
|
||||
Wall time: 215 ms
|
||||
|
||||
|
||||
|
||||
|
||||
.. math::
|
||||
|
||||
\left ( 2397916, \quad 223606\right )
|
||||
\displaystyle \left( 2397916, \ 223606\right)
|
||||
|
||||
|
||||
|
||||
After finding the rank you would still have to find the actual value of
|
||||
the rank’s first corner and subtract it (plus 2) from the number and
|
||||
the rank's first corner and subtract it (plus 2) from the number and
|
||||
compute the offset as above and then the final output, but this overhead
|
||||
is partially shared by the other method, and overshadowed by the time it
|
||||
(the other iterative method) would take for really big inputs.
|
||||
|
|
@ -542,25 +546,25 @@ is partially shared by the other method, and overshadowed by the time it
|
|||
The fun thing to do here would be to graph the actual runtime of both
|
||||
methods against each other to find the trade-off point.
|
||||
|
||||
It took me a second to realize I could do this…
|
||||
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
It took me a second to realize I could do this...
|
||||
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
Sympy is a *symbolic* math library, and it supports symbolic
|
||||
manipulation of equations. I can put in :math:`y` (instead of a value)
|
||||
and ask it to solve for :math:`k`.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
y = symbols('y')
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
g, f = solve(E - y, k)
|
||||
|
||||
The equation is quadratic so there are two roots, we are interested in
|
||||
the greater one…
|
||||
the greater one...
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
g
|
||||
|
||||
|
|
@ -569,11 +573,11 @@ the greater one…
|
|||
|
||||
.. math::
|
||||
|
||||
- \frac{1}{2} \sqrt{y - 1} - \frac{1}{2}
|
||||
\displaystyle - \frac{\sqrt{y - 1}}{2} - \frac{1}{2}
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
f
|
||||
|
||||
|
|
@ -582,14 +586,14 @@ the greater one…
|
|||
|
||||
.. math::
|
||||
|
||||
\frac{1}{2} \sqrt{y - 1} - \frac{1}{2}
|
||||
\displaystyle \frac{\sqrt{y - 1}}{2} - \frac{1}{2}
|
||||
|
||||
|
||||
|
||||
Now we can take the ``floor()``, add 1, and ``lambdify()`` the equation
|
||||
to get a Python function that calculates the rank directly.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
floor(f) + 1
|
||||
|
||||
|
|
@ -598,18 +602,18 @@ to get a Python function that calculates the rank directly.
|
|||
|
||||
.. math::
|
||||
|
||||
\lfloor{\frac{1}{2} \sqrt{y - 1} - \frac{1}{2}}\rfloor + 1
|
||||
\displaystyle \left\lfloor{\frac{\sqrt{y - 1}}{2} - \frac{1}{2}}\right\rfloor + 1
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
F = lambdify(y, floor(f) + 1)
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
for n in (9, 10, 25, 26, 49, 50):
|
||||
print n, int(F(n))
|
||||
print(n, int(F(n)))
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
|
@ -622,53 +626,53 @@ to get a Python function that calculates the rank directly.
|
|||
50 4
|
||||
|
||||
|
||||
It’s pretty fast.
|
||||
It's pretty fast.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
%time int(F(23000000000000)) # The clear winner.
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
CPU times: user 0 ns, sys: 0 ns, total: 0 ns
|
||||
Wall time: 11.9 µs
|
||||
CPU times: user 60 µs, sys: 4 µs, total: 64 µs
|
||||
Wall time: 67 µs
|
||||
|
||||
|
||||
|
||||
|
||||
.. math::
|
||||
|
||||
2397916
|
||||
\displaystyle 2397916
|
||||
|
||||
|
||||
|
||||
Knowing the equation we could write our own function manually, but the
|
||||
speed is no better.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
from math import floor as mfloor, sqrt
|
||||
|
||||
def mrank_of(n):
|
||||
return int(mfloor(sqrt(23000000000000 - 1) / 2 - 0.5) + 1)
|
||||
return int(mfloor(sqrt(n - 1) / 2 - 0.5) + 1)
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
%time mrank_of(23000000000000)
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
CPU times: user 0 ns, sys: 0 ns, total: 0 ns
|
||||
Wall time: 12.9 µs
|
||||
CPU times: user 7 µs, sys: 1 µs, total: 8 µs
|
||||
Wall time: 10 µs
|
||||
|
||||
|
||||
|
||||
|
||||
.. math::
|
||||
|
||||
2397916
|
||||
\displaystyle 2397916
|
||||
|
||||
|
||||
|
||||
|
|
@ -678,19 +682,19 @@ Given :math:`n` and a rank, compute the offset.
|
|||
Now that we have a fast way to get the rank, we still need to use it to
|
||||
compute the offset into a pyramid row.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
def offset_of(n, k):
|
||||
return (n - 2 + 4 * k * (k - 1)) % (2 * k)
|
||||
|
||||
(Note the sneaky way the sign changes from :math:`k(k + 1)` to
|
||||
:math:`k(k - 1)`. This is because we want to subract the
|
||||
:math:`(k - 1)`\ th rank’s total places (its own and those of lesser
|
||||
:math:`(k - 1)`\ th rank's total places (its own and those of lesser
|
||||
rank) from our :math:`n` of rank :math:`k`. Substituting :math:`k - 1`
|
||||
for :math:`k` in :math:`k(k + 1)` gives :math:`(k - 1)(k - 1 + 1)`,
|
||||
which of course simplifies to :math:`k(k - 1)`.)
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
offset_of(23000000000000, 2397916)
|
||||
|
||||
|
|
@ -699,13 +703,13 @@ which of course simplifies to :math:`k(k - 1)`.)
|
|||
|
||||
.. math::
|
||||
|
||||
223606
|
||||
\displaystyle 223606
|
||||
|
||||
|
||||
|
||||
So, we can compute the rank, then the offset, then the row value.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
def rank_of(n):
|
||||
return int(mfloor(sqrt(n - 1) / 2 - 0.5) + 1)
|
||||
|
|
@ -724,7 +728,7 @@ So, we can compute the rank, then the offset, then the row value.
|
|||
i = offset_of(n, k)
|
||||
return row_value(k, i)
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
aoc20173(23)
|
||||
|
||||
|
|
@ -733,11 +737,11 @@ So, we can compute the rank, then the offset, then the row value.
|
|||
|
||||
.. math::
|
||||
|
||||
2
|
||||
\displaystyle 2
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
aoc20173(23000)
|
||||
|
||||
|
|
@ -746,11 +750,11 @@ So, we can compute the rank, then the offset, then the row value.
|
|||
|
||||
.. math::
|
||||
|
||||
105
|
||||
\displaystyle 105
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
aoc20173(23000000000000)
|
||||
|
||||
|
|
@ -759,26 +763,26 @@ So, we can compute the rank, then the offset, then the row value.
|
|||
|
||||
.. math::
|
||||
|
||||
4572225
|
||||
\displaystyle 4572225
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
%time aoc20173(23000000000000000000000000) # Fast for large values.
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
CPU times: user 0 ns, sys: 0 ns, total: 0 ns
|
||||
Wall time: 20 µs
|
||||
CPU times: user 22 µs, sys: 2 µs, total: 24 µs
|
||||
Wall time: 26.7 µs
|
||||
|
||||
|
||||
|
||||
|
||||
.. math::
|
||||
|
||||
2690062495969
|
||||
\displaystyle 2690062495969
|
||||
|
||||
|
||||
|
||||
|
|
@ -788,7 +792,7 @@ A Joy Version
|
|||
At this point I feel confident that I can implement a concise version of
|
||||
this code in Joy. ;-)
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
from notebook_preamble import J, V, define
|
||||
|
||||
|
|
@ -797,105 +801,105 @@ this code in Joy. ;-)
|
|||
|
||||
::
|
||||
|
||||
n rank_of
|
||||
---------------
|
||||
k
|
||||
n rank_of
|
||||
---------------
|
||||
k
|
||||
|
||||
The translation is straightforward.
|
||||
|
||||
::
|
||||
|
||||
int(floor(sqrt(n - 1) / 2 - 0.5) + 1)
|
||||
int(floor(sqrt(n - 1) / 2 - 0.5) + 1)
|
||||
|
||||
rank_of == -- sqrt 2 / 0.5 - floor ++
|
||||
rank_of == -- sqrt 2 / 0.5 - floor ++
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('rank_of == -- sqrt 2 / 0.5 - floor ++')
|
||||
define('rank_of -- sqrt 2 / 0.5 - floor ++')
|
||||
|
||||
``offset_of``
|
||||
~~~~~~~~~~~~~
|
||||
|
||||
::
|
||||
|
||||
n k offset_of
|
||||
-------------------
|
||||
i
|
||||
n k offset_of
|
||||
-------------------
|
||||
i
|
||||
|
||||
(n - 2 + 4 * k * (k - 1)) % (2 * k)
|
||||
(n - 2 + 4 * k * (k - 1)) % (2 * k)
|
||||
|
||||
A little tricky…
|
||||
A little tricky...
|
||||
|
||||
::
|
||||
|
||||
n k dup 2 *
|
||||
n k k 2 *
|
||||
n k k*2 [Q] dip %
|
||||
n k Q k*2 %
|
||||
n k dup 2 *
|
||||
n k k 2 *
|
||||
n k k*2 [Q] dip %
|
||||
n k Q k*2 %
|
||||
|
||||
n k dup --
|
||||
n k k --
|
||||
n k k-1 4 * * 2 + -
|
||||
n k*k-1*4 2 + -
|
||||
n k*k-1*4+2 -
|
||||
n-k*k-1*4+2
|
||||
n k dup --
|
||||
n k k --
|
||||
n k k-1 4 * * 2 + -
|
||||
n k*k-1*4 2 + -
|
||||
n k*k-1*4+2 -
|
||||
n-k*k-1*4+2
|
||||
|
||||
n-k*k-1*4+2 k*2 %
|
||||
n-k*k-1*4+2%k*2
|
||||
n-k*k-1*4+2 k*2 %
|
||||
n-k*k-1*4+2%k*2
|
||||
|
||||
Ergo:
|
||||
|
||||
::
|
||||
|
||||
offset_of == dup 2 * [dup -- 4 * * 2 + -] dip %
|
||||
offset_of == dup 2 * [dup -- 4 * * 2 + -] dip %
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('offset_of == dup 2 * [dup -- 4 * * 2 + -] dip %')
|
||||
define('offset_of dup 2 * [dup -- 4 * * 2 + -] dip %')
|
||||
|
||||
``row_value``
|
||||
~~~~~~~~~~~~~
|
||||
|
||||
::
|
||||
|
||||
k i row_value
|
||||
-------------------
|
||||
n
|
||||
k i row_value
|
||||
-------------------
|
||||
n
|
||||
|
||||
abs(i - (k - 1)) + k
|
||||
abs(i - (k - 1)) + k
|
||||
|
||||
k i over -- - abs +
|
||||
k i k -- - abs +
|
||||
k i k-1 - abs +
|
||||
k i-k-1 abs +
|
||||
k |i-k-1| +
|
||||
k+|i-k-1|
|
||||
k i over -- - abs +
|
||||
k i k -- - abs +
|
||||
k i k-1 - abs +
|
||||
k i-k-1 abs +
|
||||
k |i-k-1| +
|
||||
k+|i-k-1|
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('row_value == over -- - abs +')
|
||||
define('row_value over -- - abs +')
|
||||
|
||||
``aoc2017.3``
|
||||
~~~~~~~~~~~~~
|
||||
|
||||
::
|
||||
|
||||
n aoc2017.3
|
||||
-----------------
|
||||
m
|
||||
n aoc2017.3
|
||||
-----------------
|
||||
m
|
||||
|
||||
n dup rank_of
|
||||
n k [offset_of] dupdip
|
||||
n k offset_of k
|
||||
i k swap row_value
|
||||
k i row_value
|
||||
m
|
||||
n dup rank_of
|
||||
n k [offset_of] dupdip
|
||||
n k offset_of k
|
||||
i k swap row_value
|
||||
k i row_value
|
||||
m
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('aoc2017.3 == dup rank_of [offset_of] dupdip swap row_value')
|
||||
define('aoc2017.3 dup rank_of [offset_of] dupdip swap row_value')
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('23 aoc2017.3')
|
||||
|
||||
|
|
@ -905,7 +909,7 @@ Ergo:
|
|||
2
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('23000 aoc2017.3')
|
||||
|
||||
|
|
@ -915,58 +919,58 @@ Ergo:
|
|||
105
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
V('23000000000000 aoc2017.3')
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
. 23000000000000 aoc2017.3
|
||||
23000000000000 . aoc2017.3
|
||||
23000000000000 . dup rank_of [offset_of] dupdip swap row_value
|
||||
23000000000000 23000000000000 . rank_of [offset_of] dupdip swap row_value
|
||||
23000000000000 23000000000000 . -- sqrt 2 / 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 22999999999999 . sqrt 2 / 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 4795831.523312615 . 2 / 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 4795831.523312615 2 . / 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397915.7616563076 . 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397915.7616563076 0.5 . - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397915.2616563076 . floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397915 . ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397916 . [offset_of] dupdip swap row_value
|
||||
23000000000000 2397916 [offset_of] . dupdip swap row_value
|
||||
23000000000000 2397916 . offset_of 2397916 swap row_value
|
||||
23000000000000 2397916 . dup 2 * [dup -- 4 * * 2 + -] dip % 2397916 swap row_value
|
||||
23000000000000 2397916 2397916 . 2 * [dup -- 4 * * 2 + -] dip % 2397916 swap row_value
|
||||
23000000000000 2397916 2397916 2 . * [dup -- 4 * * 2 + -] dip % 2397916 swap row_value
|
||||
23000000000000 2397916 4795832 . [dup -- 4 * * 2 + -] dip % 2397916 swap row_value
|
||||
23000000000000 2397916 4795832 [dup -- 4 * * 2 + -] . dip % 2397916 swap row_value
|
||||
23000000000000 2397916 . dup -- 4 * * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 2397916 2397916 . -- 4 * * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 2397916 2397915 . 4 * * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 2397916 2397915 4 . * * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 2397916 9591660 . * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 22999994980560 . 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 22999994980560 2 . + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 22999994980562 . - 4795832 % 2397916 swap row_value
|
||||
5019438 . 4795832 % 2397916 swap row_value
|
||||
5019438 4795832 . % 2397916 swap row_value
|
||||
223606 . 2397916 swap row_value
|
||||
223606 2397916 . swap row_value
|
||||
2397916 223606 . row_value
|
||||
2397916 223606 . over -- - abs +
|
||||
2397916 223606 2397916 . -- - abs +
|
||||
2397916 223606 2397915 . - abs +
|
||||
2397916 -2174309 . abs +
|
||||
2397916 2174309 . +
|
||||
4572225 .
|
||||
• 23000000000000 aoc2017.3
|
||||
23000000000000 • aoc2017.3
|
||||
23000000000000 • dup rank_of [offset_of] dupdip swap row_value
|
||||
23000000000000 23000000000000 • rank_of [offset_of] dupdip swap row_value
|
||||
23000000000000 23000000000000 • -- sqrt 2 / 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 22999999999999 • sqrt 2 / 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 4795831.523312615 • 2 / 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 4795831.523312615 2 • / 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397915.7616563076 • 0.5 - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397915.7616563076 0.5 • - floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397915.2616563076 • floor ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397915 • ++ [offset_of] dupdip swap row_value
|
||||
23000000000000 2397916 • [offset_of] dupdip swap row_value
|
||||
23000000000000 2397916 [offset_of] • dupdip swap row_value
|
||||
23000000000000 2397916 • offset_of 2397916 swap row_value
|
||||
23000000000000 2397916 • dup 2 * [dup -- 4 * * 2 + -] dip % 2397916 swap row_value
|
||||
23000000000000 2397916 2397916 • 2 * [dup -- 4 * * 2 + -] dip % 2397916 swap row_value
|
||||
23000000000000 2397916 2397916 2 • * [dup -- 4 * * 2 + -] dip % 2397916 swap row_value
|
||||
23000000000000 2397916 4795832 • [dup -- 4 * * 2 + -] dip % 2397916 swap row_value
|
||||
23000000000000 2397916 4795832 [dup -- 4 * * 2 + -] • dip % 2397916 swap row_value
|
||||
23000000000000 2397916 • dup -- 4 * * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 2397916 2397916 • -- 4 * * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 2397916 2397915 • 4 * * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 2397916 2397915 4 • * * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 2397916 9591660 • * 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 22999994980560 • 2 + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 22999994980560 2 • + - 4795832 % 2397916 swap row_value
|
||||
23000000000000 22999994980562 • - 4795832 % 2397916 swap row_value
|
||||
5019438 • 4795832 % 2397916 swap row_value
|
||||
5019438 4795832 • % 2397916 swap row_value
|
||||
223606 • 2397916 swap row_value
|
||||
223606 2397916 • swap row_value
|
||||
2397916 223606 • row_value
|
||||
2397916 223606 • over -- - abs +
|
||||
2397916 223606 2397916 • -- - abs +
|
||||
2397916 223606 2397915 • - abs +
|
||||
2397916 -2174309 • abs +
|
||||
2397916 2174309 • +
|
||||
4572225 •
|
||||
|
||||
|
||||
::
|
||||
|
||||
rank_of == -- sqrt 2 / 0.5 - floor ++
|
||||
offset_of == dup 2 * [dup -- 4 * * 2 + -] dip %
|
||||
row_value == over -- - abs +
|
||||
rank_of == -- sqrt 2 / 0.5 - floor ++
|
||||
offset_of == dup 2 * [dup -- 4 * * 2 + -] dip %
|
||||
row_value == over -- - abs +
|
||||
|
||||
aoc2017.3 == dup rank_of [offset_of] dupdip swap row_value
|
||||
aoc2017.3 == dup rank_of [offset_of] dupdip swap row_value
|
||||
|
|
|
|||
|
|
@ -13094,7 +13094,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [1]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13141,7 +13141,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [2]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[step_zero] help'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[step_zero] help'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13158,7 +13158,13 @@ div#notebook {
|
|||
|
||||
|
||||
<div class="output_subarea output_stream output_stdout output_text">
|
||||
<pre>0 roll> step
|
||||
<pre>
|
||||
==== Help on step_zero ====
|
||||
|
||||
0 roll> step
|
||||
|
||||
---- end (step_zero)
|
||||
|
||||
|
||||
</pre>
|
||||
</div>
|
||||
|
|
@ -13182,7 +13188,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [3]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'AoC2017.4 == [[size] [unique size] cleave = +] step_zero'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'AoC2017.4 [[size] [unique size] cleave = +] step_zero'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13195,7 +13201,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [4]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'''</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'''</span>
|
||||
|
||||
<span class="s1">[[5 1 9 5]</span>
|
||||
<span class="s1"> [7 5 4 3]</span>
|
||||
|
|
|
|||
|
|
@ -66,7 +66,13 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"\n",
|
||||
"==== Help on step_zero ====\n",
|
||||
"\n",
|
||||
"0 roll> step\n",
|
||||
"\n",
|
||||
"---- end (step_zero)\n",
|
||||
"\n",
|
||||
"\n"
|
||||
]
|
||||
}
|
||||
|
|
@ -88,7 +94,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('AoC2017.4 == [[size] [unique size] cleave = +] step_zero')"
|
||||
"define('AoC2017.4 [[size] [unique size] cleave = +] step_zero')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -124,14 +130,14 @@
|
|||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 2
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython2",
|
||||
"version": "2.7.13"
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.8.3"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
|
|
|||
|
|
@ -37,15 +37,21 @@ The `step_zero` combinator includes the `0 swap` that would normally open one of
|
|||
J('[step_zero] help')
|
||||
```
|
||||
|
||||
|
||||
==== Help on step_zero ====
|
||||
|
||||
0 roll> step
|
||||
|
||||
---- end (step_zero)
|
||||
|
||||
|
||||
|
||||
|
||||
AoC2017.4 == [F +] step_zero
|
||||
|
||||
|
||||
```python
|
||||
define('AoC2017.4 == [[size] [unique size] cleave = +] step_zero')
|
||||
define('AoC2017.4 [[size] [unique size] cleave = +] step_zero')
|
||||
```
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -12,54 +12,60 @@ For example:
|
|||
- aa bb cc dd aa is not valid - the word aa appears more than once.
|
||||
- aa bb cc dd aaa is valid - aa and aaa count as different words.
|
||||
|
||||
The system’s full passphrase list is available as your puzzle input. How
|
||||
The system's full passphrase list is available as your puzzle input. How
|
||||
many passphrases are valid?
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
from notebook_preamble import J, V, define
|
||||
|
||||
I’ll assume the input is a Joy sequence of sequences of integers.
|
||||
I'll assume the input is a Joy sequence of sequences of integers.
|
||||
|
||||
::
|
||||
|
||||
[[5 1 9 5]
|
||||
[7 5 4 3]
|
||||
[2 4 6 8]]
|
||||
[[5 1 9 5]
|
||||
[7 5 4 3]
|
||||
[2 4 6 8]]
|
||||
|
||||
So, obviously, the initial form will be a ``step`` function:
|
||||
|
||||
::
|
||||
|
||||
AoC2017.4 == 0 swap [F +] step
|
||||
AoC2017.4 == 0 swap [F +] step
|
||||
|
||||
::
|
||||
|
||||
F == [size] [unique size] cleave =
|
||||
F == [size] [unique size] cleave =
|
||||
|
||||
The ``step_zero`` combinator includes the ``0 swap`` that would normally
|
||||
open one of these definitions:
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[step_zero] help')
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
|
||||
==== Help on step_zero ====
|
||||
|
||||
0 roll> step
|
||||
|
||||
---- end (step_zero)
|
||||
|
||||
|
||||
|
||||
|
||||
::
|
||||
|
||||
AoC2017.4 == [F +] step_zero
|
||||
AoC2017.4 == [F +] step_zero
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('AoC2017.4 == [[size] [unique size] cleave = +] step_zero')
|
||||
define('AoC2017.4 [[size] [unique size] cleave = +] step_zero')
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('''
|
||||
|
||||
|
|
|
|||
|
|
@ -13178,7 +13178,7 @@ E == roll< popop</code></pre>
|
|||
<div class="prompt input_prompt">In [1]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
<span class="kn">from</span> <span class="nn">joy.library</span> <span class="kn">import</span> <span class="n">SimpleFunctionWrapper</span>
|
||||
<span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="kn">import</span> <span class="n">list_to_stack</span>
|
||||
|
||||
|
|
@ -13217,7 +13217,7 @@ E == roll< popop</code></pre>
|
|||
<div class="prompt input_prompt">In [2]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'3 [0 1 2 3 4 5] incr_at'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'3 [0 1 2 3 4 5] incr_at'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13300,7 +13300,7 @@ R1 == get_value incr_value add_value incr_step_count
|
|||
|
||||
F == [P] [T] [R1] primrec
|
||||
|
||||
F == [popop !size! >=] [roll< pop] [get_value incr_value add_value incr_step_count] primrec</code></pre>
|
||||
F == [popop !size! >=] [roll< pop] [get_value incr_value add_value incr_step_count] tailrec</code></pre>
|
||||
|
||||
</div>
|
||||
</div>
|
||||
|
|
@ -13310,17 +13310,17 @@ F == [popop !size! >=] [roll< pop] [get_value incr_value add_value incr_st
|
|||
<div class="prompt input_prompt">In [3]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">from</span> <span class="nn">joy.library</span> <span class="kn">import</span> <span class="n">DefinitionWrapper</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">joy.library</span> <span class="kn">import</span> <span class="n">DefinitionWrapper</span>
|
||||
|
||||
|
||||
<span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">'''</span>
|
||||
|
||||
<span class="s1"> get_value == [roll< at] nullary</span>
|
||||
<span class="s1"> incr_value == [[popd incr_at] unary] dip</span>
|
||||
<span class="s1"> add_value == [+] cons dipd</span>
|
||||
<span class="s1">incr_step_count == [++] dip</span>
|
||||
<span class="s1"> get_value [roll< at] nullary</span>
|
||||
<span class="s1"> incr_value [[popd incr_at] unary] dip</span>
|
||||
<span class="s1"> add_value [+] cons dipd</span>
|
||||
<span class="s1">incr_step_count [++] dip</span>
|
||||
|
||||
<span class="s1"> AoC2017.5.0 == get_value incr_value add_value incr_step_count</span>
|
||||
<span class="s1"> AoC2017.5.0 get_value incr_value add_value incr_step_count</span>
|
||||
|
||||
<span class="s1">'''</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
|
@ -13335,7 +13335,19 @@ F == [popop !size! >=] [roll< pop] [get_value incr_value add_value incr_st
|
|||
<div class="prompt input_prompt">In [4]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'F == [popop 5 >=] [roll< popop] [AoC2017.5.0] primrec'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">joy.library</span> <span class="kn">import</span> <span class="n">DefinitionWrapper</span>
|
||||
|
||||
|
||||
<span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">'''</span>
|
||||
|
||||
<span class="s1"> get_value [roll< at] nullary</span>
|
||||
<span class="s1"> incr_value [[popd incr_at] unary] dip</span>
|
||||
<span class="s1"> add_value [+] cons dipd</span>
|
||||
<span class="s1">incr_step_count [++] dip</span>
|
||||
|
||||
<span class="s1"> AoC2017.5.0 get_value incr_value add_value incr_step_count</span>
|
||||
|
||||
<span class="s1">'''</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13348,7 +13360,20 @@ F == [popop !size! >=] [roll< pop] [get_value incr_value add_value incr_st
|
|||
<div class="prompt input_prompt">In [5]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'0 0 [0 3 0 1 -3] F'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'F [popop 5 >=] [roll< popop] [AoC2017.5.0] tailrec'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
</div>
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="prompt input_prompt">In [6]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'0 0 [0 3 0 1 -3] F'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13408,17 +13433,17 @@ AoC2017.5.preamble == init-index-and-step-count prepare-predicate</code></pre>
|
|||
</div>
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="prompt input_prompt">In [6]:</div>
|
||||
<div class="prompt input_prompt">In [7]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">'''</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">DefinitionWrapper</span><span class="o">.</span><span class="n">add_definitions</span><span class="p">(</span><span class="s1">'''</span>
|
||||
|
||||
<span class="s1">init-index-and-step-count == 0 0 roll<</span>
|
||||
<span class="s1"> prepare-predicate == dup size [>=] cons [popop] swoncat</span>
|
||||
<span class="s1">init-index-and-step-count 0 0 roll<</span>
|
||||
<span class="s1">prepare-predicate dup size [>=] cons [popop] swoncat</span>
|
||||
|
||||
<span class="s1"> AoC2017.5.preamble == init-index-and-step-count prepare-predicate</span>
|
||||
<span class="s1">AoC2017.5.preamble init-index-and-step-count prepare-predicate</span>
|
||||
|
||||
<span class="s1"> AoC2017.5 == AoC2017.5.preamble [roll< popop] [AoC2017.5.0] primrec</span>
|
||||
<span class="s1">AoC2017.5 AoC2017.5.preamble [roll< popop] [AoC2017.5.0] tailrec</span>
|
||||
|
||||
<span class="s1">'''</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
|
@ -13430,10 +13455,10 @@ AoC2017.5.preamble == init-index-and-step-count prepare-predicate</code></pre>
|
|||
</div>
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="prompt input_prompt">In [7]:</div>
|
||||
<div class="prompt input_prompt">In [8]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[0 3 0 1 -3] AoC2017.5'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[0 3 0 1 -3] AoC2017.5'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
|
|||
|
|
@ -209,7 +209,7 @@
|
|||
"\n",
|
||||
" F == [P] [T] [R1] primrec\n",
|
||||
" \n",
|
||||
" F == [popop !size! >=] [roll< pop] [get_value incr_value add_value incr_step_count] primrec"
|
||||
" F == [popop !size! >=] [roll< pop] [get_value incr_value add_value incr_step_count] tailrec"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -223,12 +223,12 @@
|
|||
"\n",
|
||||
"DefinitionWrapper.add_definitions('''\n",
|
||||
"\n",
|
||||
" get_value == [roll< at] nullary\n",
|
||||
" incr_value == [[popd incr_at] unary] dip\n",
|
||||
" add_value == [+] cons dipd\n",
|
||||
"incr_step_count == [++] dip\n",
|
||||
" get_value [roll< at] nullary\n",
|
||||
" incr_value [[popd incr_at] unary] dip\n",
|
||||
" add_value [+] cons dipd\n",
|
||||
"incr_step_count [++] dip\n",
|
||||
"\n",
|
||||
" AoC2017.5.0 == get_value incr_value add_value incr_step_count\n",
|
||||
" AoC2017.5.0 get_value incr_value add_value incr_step_count\n",
|
||||
"\n",
|
||||
"''', D)"
|
||||
]
|
||||
|
|
@ -239,12 +239,33 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('F == [popop 5 >=] [roll< popop] [AoC2017.5.0] primrec')"
|
||||
"from joy.library import DefinitionWrapper\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"DefinitionWrapper.add_definitions('''\n",
|
||||
"\n",
|
||||
" get_value [roll< at] nullary\n",
|
||||
" incr_value [[popd incr_at] unary] dip\n",
|
||||
" add_value [+] cons dipd\n",
|
||||
"incr_step_count [++] dip\n",
|
||||
"\n",
|
||||
" AoC2017.5.0 get_value incr_value add_value incr_step_count\n",
|
||||
"\n",
|
||||
"''', D)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 5,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('F [popop 5 >=] [roll< popop] [AoC2017.5.0] tailrec')"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 6,
|
||||
"metadata": {
|
||||
"scrolled": true
|
||||
},
|
||||
|
|
@ -294,25 +315,25 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 6,
|
||||
"execution_count": 7,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"DefinitionWrapper.add_definitions('''\n",
|
||||
"\n",
|
||||
"init-index-and-step-count == 0 0 roll<\n",
|
||||
" prepare-predicate == dup size [>=] cons [popop] swoncat\n",
|
||||
"init-index-and-step-count 0 0 roll<\n",
|
||||
"prepare-predicate dup size [>=] cons [popop] swoncat\n",
|
||||
"\n",
|
||||
" AoC2017.5.preamble == init-index-and-step-count prepare-predicate\n",
|
||||
"AoC2017.5.preamble init-index-and-step-count prepare-predicate\n",
|
||||
"\n",
|
||||
" AoC2017.5 == AoC2017.5.preamble [roll< popop] [AoC2017.5.0] primrec\n",
|
||||
"AoC2017.5 AoC2017.5.preamble [roll< popop] [AoC2017.5.0] tailrec\n",
|
||||
"\n",
|
||||
"''', D)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 7,
|
||||
"execution_count": 8,
|
||||
"metadata": {
|
||||
"scrolled": false
|
||||
},
|
||||
|
|
@ -365,14 +386,14 @@
|
|||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 2
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython2",
|
||||
"version": "2.7.13"
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.8.3"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
|
|
|||
|
|
@ -145,7 +145,7 @@ J('3 [0 1 2 3 4 5] incr_at')
|
|||
|
||||
F == [P] [T] [R1] primrec
|
||||
|
||||
F == [popop !size! >=] [roll< pop] [get_value incr_value add_value incr_step_count] primrec
|
||||
F == [popop !size! >=] [roll< pop] [get_value incr_value add_value incr_step_count] tailrec
|
||||
|
||||
|
||||
```python
|
||||
|
|
@ -154,19 +154,36 @@ from joy.library import DefinitionWrapper
|
|||
|
||||
DefinitionWrapper.add_definitions('''
|
||||
|
||||
get_value == [roll< at] nullary
|
||||
incr_value == [[popd incr_at] unary] dip
|
||||
add_value == [+] cons dipd
|
||||
incr_step_count == [++] dip
|
||||
get_value [roll< at] nullary
|
||||
incr_value [[popd incr_at] unary] dip
|
||||
add_value [+] cons dipd
|
||||
incr_step_count [++] dip
|
||||
|
||||
AoC2017.5.0 == get_value incr_value add_value incr_step_count
|
||||
AoC2017.5.0 get_value incr_value add_value incr_step_count
|
||||
|
||||
''', D)
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
define('F == [popop 5 >=] [roll< popop] [AoC2017.5.0] primrec')
|
||||
from joy.library import DefinitionWrapper
|
||||
|
||||
|
||||
DefinitionWrapper.add_definitions('''
|
||||
|
||||
get_value [roll< at] nullary
|
||||
incr_value [[popd incr_at] unary] dip
|
||||
add_value [+] cons dipd
|
||||
incr_step_count [++] dip
|
||||
|
||||
AoC2017.5.0 get_value incr_value add_value incr_step_count
|
||||
|
||||
''', D)
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
define('F [popop 5 >=] [roll< popop] [AoC2017.5.0] tailrec')
|
||||
```
|
||||
|
||||
|
||||
|
|
@ -207,12 +224,12 @@ So:
|
|||
```python
|
||||
DefinitionWrapper.add_definitions('''
|
||||
|
||||
init-index-and-step-count == 0 0 roll<
|
||||
prepare-predicate == dup size [>=] cons [popop] swoncat
|
||||
init-index-and-step-count 0 0 roll<
|
||||
prepare-predicate dup size [>=] cons [popop] swoncat
|
||||
|
||||
AoC2017.5.preamble == init-index-and-step-count prepare-predicate
|
||||
AoC2017.5.preamble init-index-and-step-count prepare-predicate
|
||||
|
||||
AoC2017.5 == AoC2017.5.preamble [roll< popop] [AoC2017.5.0] primrec
|
||||
AoC2017.5 AoC2017.5.preamble [roll< popop] [AoC2017.5.0] tailrec
|
||||
|
||||
''', D)
|
||||
```
|
||||
|
|
|
|||
|
|
@ -4,7 +4,7 @@ Advent of Code 2017
|
|||
December 5th
|
||||
------------
|
||||
|
||||
…a list of the offsets for each jump. Jumps are relative: -1 moves to
|
||||
...a list of the offsets for each jump. Jumps are relative: -1 moves to
|
||||
the previous instruction, and 2 skips the next one. Start at the first
|
||||
instruction in the list. The goal is to follow the jumps until one leads
|
||||
outside the list.
|
||||
|
|
@ -18,13 +18,13 @@ For example, consider the following list of jump offsets:
|
|||
|
||||
::
|
||||
|
||||
0
|
||||
3
|
||||
0
|
||||
1
|
||||
-3
|
||||
0
|
||||
3
|
||||
0
|
||||
1
|
||||
-3
|
||||
|
||||
Positive jumps (“forward”) move downward; negative jumps move upward.
|
||||
Positive jumps ("forward") move downward; negative jumps move upward.
|
||||
For legibility in this example, these offset values will be written all
|
||||
on one line, with the current instruction marked in parentheses. The
|
||||
following steps would be taken before an exit is found:
|
||||
|
|
@ -35,24 +35,14 @@ following steps would be taken before an exit is found:
|
|||
|
||||
-
|
||||
|
||||
(1) 3 0 1 -3 - jump with offset 0 (that is, don’t jump at all).
|
||||
(1) 3 0 1 -3 - jump with offset 0 (that is, don't jump at all).
|
||||
Fortunately, the instruction is then incremented to 1.
|
||||
|
||||
- ::
|
||||
|
||||
2 (3) 0 1 -3 - step forward because of the instruction we just modified. The first instruction is incremented again, now to 2.
|
||||
|
||||
- ::
|
||||
|
||||
2 4 0 1 (-3) - jump all the way to the end; leave a 4 behind.
|
||||
|
||||
- ::
|
||||
|
||||
2 (4) 0 1 -2 - go back to where we just were; increment -3 to -2.
|
||||
|
||||
- ::
|
||||
|
||||
2 5 0 1 -2 - jump 4 steps forward, escaping the maze.
|
||||
- 2 (3) 0 1 -3 - step forward because of the instruction we just
|
||||
modified. The first instruction is incremented again, now to 2.
|
||||
- 2 4 0 1 (-3) - jump all the way to the end; leave a 4 behind.
|
||||
- 2 (4) 0 1 -2 - go back to where we just were; increment -3 to -2.
|
||||
- 2 5 0 1 -2 - jump 4 steps forward, escaping the maze.
|
||||
|
||||
In this example, the exit is reached in 5 steps.
|
||||
|
||||
|
|
@ -61,7 +51,7 @@ How many steps does it take to reach the exit?
|
|||
Breakdown
|
||||
---------
|
||||
|
||||
For now, I’m going to assume a starting state with the size of the
|
||||
For now, I'm going to assume a starting state with the size of the
|
||||
sequence pre-computed. We need it to define the exit condition and it is
|
||||
a trivial preamble to generate it. We then need and ``index`` and a
|
||||
``step-count``, which are both initially zero. Then we have the sequence
|
||||
|
|
@ -69,69 +59,69 @@ itself, and some recursive function ``F`` that does the work.
|
|||
|
||||
::
|
||||
|
||||
size index step-count [...] F
|
||||
-----------------------------------
|
||||
step-count
|
||||
size index step-count [...] F
|
||||
-----------------------------------
|
||||
step-count
|
||||
|
||||
F == [P] [T] [R1] [R2] genrec
|
||||
F == [P] [T] [R1] [R2] genrec
|
||||
|
||||
Later on I was thinking about it and the Forth heuristic came to mind,
|
||||
to wit: four things on the stack are kind of much. Immediately I
|
||||
realized that the size properly belongs in the predicate of ``F``! D’oh!
|
||||
realized that the size properly belongs in the predicate of ``F``! D'oh!
|
||||
|
||||
::
|
||||
|
||||
index step-count [...] F
|
||||
------------------------------
|
||||
step-count
|
||||
index step-count [...] F
|
||||
------------------------------
|
||||
step-count
|
||||
|
||||
So, let’s start by nailing down the predicate:
|
||||
So, let's start by nailing down the predicate:
|
||||
|
||||
::
|
||||
|
||||
F == [P] [T] [R1] [R2] genrec
|
||||
== [P] [T] [R1 [F] R2] ifte
|
||||
F == [P] [T] [R1] [R2] genrec
|
||||
== [P] [T] [R1 [F] R2] ifte
|
||||
|
||||
0 0 [0 3 0 1 -3] popop 5 >=
|
||||
0 0 [0 3 0 1 -3] popop 5 >=
|
||||
|
||||
P == popop 5 >=
|
||||
P == popop 5 >=
|
||||
|
||||
Now we need the else-part:
|
||||
|
||||
::
|
||||
|
||||
index step-count [0 3 0 1 -3] roll< popop
|
||||
index step-count [0 3 0 1 -3] roll< popop
|
||||
|
||||
E == roll< popop
|
||||
E == roll< popop
|
||||
|
||||
Last but not least, the recursive branch
|
||||
|
||||
::
|
||||
|
||||
0 0 [0 3 0 1 -3] R1 [F] R2
|
||||
0 0 [0 3 0 1 -3] R1 [F] R2
|
||||
|
||||
The ``R1`` function has a big job:
|
||||
|
||||
::
|
||||
|
||||
R1 == get the value at index
|
||||
increment the value at the index
|
||||
add the value gotten to the index
|
||||
increment the step count
|
||||
R1 == get the value at index
|
||||
increment the value at the index
|
||||
add the value gotten to the index
|
||||
increment the step count
|
||||
|
||||
The only tricky thing there is incrementing an integer in the sequence.
|
||||
Joy sequences are not particularly good for random access. We could
|
||||
encode the list of jump offsets in a big integer and use math to do the
|
||||
processing for a good speed-up, but it still wouldn’t beat the
|
||||
performance of e.g. a mutable array. This is just one of those places
|
||||
where “plain vanilla” Joypy doesn’t shine (in default performance. The
|
||||
processing for a good speed-up, but it still wouldn't beat the
|
||||
performance of e.g. a mutable array. This is just one of those places
|
||||
where "plain vanilla" Joypy doesn't shine (in default performance. The
|
||||
legendary *Sufficiently-Smart Compiler* would of course rewrite this
|
||||
function to use an array “under the hood”.)
|
||||
function to use an array "under the hood".)
|
||||
|
||||
In the meantime, I’m going to write a primitive function that just does
|
||||
In the meantime, I'm going to write a primitive function that just does
|
||||
what we need.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
from notebook_preamble import D, J, V, define
|
||||
from joy.library import SimpleFunctionWrapper
|
||||
|
|
@ -161,7 +151,7 @@ what we need.
|
|||
|
||||
D['incr_at'] = incr_at
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('3 [0 1 2 3 4 5] incr_at')
|
||||
|
||||
|
|
@ -176,74 +166,90 @@ get the value at index
|
|||
|
||||
::
|
||||
|
||||
3 0 [0 1 2 3 4] [roll< at] nullary
|
||||
3 0 [0 1 2 n 4] n
|
||||
3 0 [0 1 2 3 4] [roll< at] nullary
|
||||
3 0 [0 1 2 n 4] n
|
||||
|
||||
increment the value at the index
|
||||
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
::
|
||||
|
||||
3 0 [0 1 2 n 4] n [Q] dip
|
||||
3 0 [0 1 2 n 4] Q n
|
||||
3 0 [0 1 2 n 4] [popd incr_at] unary n
|
||||
3 0 [0 1 2 n+1 4] n
|
||||
3 0 [0 1 2 n 4] n [Q] dip
|
||||
3 0 [0 1 2 n 4] Q n
|
||||
3 0 [0 1 2 n 4] [popd incr_at] unary n
|
||||
3 0 [0 1 2 n+1 4] n
|
||||
|
||||
add the value gotten to the index
|
||||
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
::
|
||||
|
||||
3 0 [0 1 2 n+1 4] n [+] cons dipd
|
||||
3 0 [0 1 2 n+1 4] [n +] dipd
|
||||
3 n + 0 [0 1 2 n+1 4]
|
||||
3+n 0 [0 1 2 n+1 4]
|
||||
3 0 [0 1 2 n+1 4] n [+] cons dipd
|
||||
3 0 [0 1 2 n+1 4] [n +] dipd
|
||||
3 n + 0 [0 1 2 n+1 4]
|
||||
3+n 0 [0 1 2 n+1 4]
|
||||
|
||||
increment the step count
|
||||
~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
::
|
||||
|
||||
3+n 0 [0 1 2 n+1 4] [++] dip
|
||||
3+n 1 [0 1 2 n+1 4]
|
||||
3+n 0 [0 1 2 n+1 4] [++] dip
|
||||
3+n 1 [0 1 2 n+1 4]
|
||||
|
||||
All together now…
|
||||
~~~~~~~~~~~~~~~~~
|
||||
All together now...
|
||||
~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
::
|
||||
|
||||
get_value == [roll< at] nullary
|
||||
incr_value == [[popd incr_at] unary] dip
|
||||
add_value == [+] cons dipd
|
||||
incr_step_count == [++] dip
|
||||
get_value == [roll< at] nullary
|
||||
incr_value == [[popd incr_at] unary] dip
|
||||
add_value == [+] cons dipd
|
||||
incr_step_count == [++] dip
|
||||
|
||||
R1 == get_value incr_value add_value incr_step_count
|
||||
R1 == get_value incr_value add_value incr_step_count
|
||||
|
||||
F == [P] [T] [R1] primrec
|
||||
F == [P] [T] [R1] primrec
|
||||
|
||||
F == [popop !size! >=] [roll< pop] [get_value incr_value add_value incr_step_count] primrec
|
||||
F == [popop !size! >=] [roll< pop] [get_value incr_value add_value incr_step_count] tailrec
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
from joy.library import DefinitionWrapper
|
||||
|
||||
|
||||
DefinitionWrapper.add_definitions('''
|
||||
|
||||
get_value == [roll< at] nullary
|
||||
incr_value == [[popd incr_at] unary] dip
|
||||
add_value == [+] cons dipd
|
||||
incr_step_count == [++] dip
|
||||
get_value [roll< at] nullary
|
||||
incr_value [[popd incr_at] unary] dip
|
||||
add_value [+] cons dipd
|
||||
incr_step_count [++] dip
|
||||
|
||||
AoC2017.5.0 == get_value incr_value add_value incr_step_count
|
||||
AoC2017.5.0 get_value incr_value add_value incr_step_count
|
||||
|
||||
''', D)
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('F == [popop 5 >=] [roll< popop] [AoC2017.5.0] primrec')
|
||||
from joy.library import DefinitionWrapper
|
||||
|
||||
|
||||
DefinitionWrapper.add_definitions('''
|
||||
|
||||
get_value [roll< at] nullary
|
||||
incr_value [[popd incr_at] unary] dip
|
||||
add_value [+] cons dipd
|
||||
incr_step_count [++] dip
|
||||
|
||||
AoC2017.5.0 get_value incr_value add_value incr_step_count
|
||||
|
||||
''', D)
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('F [popop 5 >=] [roll< popop] [AoC2017.5.0] tailrec')
|
||||
|
||||
.. code:: ipython3
|
||||
|
||||
J('0 0 [0 3 0 1 -3] F')
|
||||
|
||||
|
|
@ -260,9 +266,9 @@ We want to go from this to this:
|
|||
|
||||
::
|
||||
|
||||
[...] AoC2017.5.preamble
|
||||
------------------------------
|
||||
0 0 [...] [popop n >=]
|
||||
[...] AoC2017.5.preamble
|
||||
------------------------------
|
||||
0 0 [...] [popop n >=]
|
||||
|
||||
Where ``n`` is the size of the sequence.
|
||||
|
||||
|
|
@ -270,38 +276,38 @@ The first part is obviously ``0 0 roll<``, then ``dup size``:
|
|||
|
||||
::
|
||||
|
||||
[...] 0 0 roll< dup size
|
||||
0 0 [...] n
|
||||
[...] 0 0 roll< dup size
|
||||
0 0 [...] n
|
||||
|
||||
Then:
|
||||
|
||||
::
|
||||
|
||||
0 0 [...] n [>=] cons [popop] swoncat
|
||||
0 0 [...] n [>=] cons [popop] swoncat
|
||||
|
||||
So:
|
||||
|
||||
::
|
||||
|
||||
init-index-and-step-count == 0 0 roll<
|
||||
prepare-predicate == dup size [>=] cons [popop] swoncat
|
||||
init-index-and-step-count == 0 0 roll<
|
||||
prepare-predicate == dup size [>=] cons [popop] swoncat
|
||||
|
||||
AoC2017.5.preamble == init-index-and-step-count prepare-predicate
|
||||
AoC2017.5.preamble == init-index-and-step-count prepare-predicate
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
DefinitionWrapper.add_definitions('''
|
||||
|
||||
init-index-and-step-count == 0 0 roll<
|
||||
prepare-predicate == dup size [>=] cons [popop] swoncat
|
||||
init-index-and-step-count 0 0 roll<
|
||||
prepare-predicate dup size [>=] cons [popop] swoncat
|
||||
|
||||
AoC2017.5.preamble == init-index-and-step-count prepare-predicate
|
||||
AoC2017.5.preamble init-index-and-step-count prepare-predicate
|
||||
|
||||
AoC2017.5 == AoC2017.5.preamble [roll< popop] [AoC2017.5.0] primrec
|
||||
AoC2017.5 AoC2017.5.preamble [roll< popop] [AoC2017.5.0] tailrec
|
||||
|
||||
''', D)
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[0 3 0 1 -3] AoC2017.5')
|
||||
|
||||
|
|
@ -313,21 +319,21 @@ So:
|
|||
|
||||
::
|
||||
|
||||
AoC2017.5 == AoC2017.5.preamble [roll< popop] [AoC2017.5.0] primrec
|
||||
AoC2017.5 == AoC2017.5.preamble [roll< popop] [AoC2017.5.0] primrec
|
||||
|
||||
AoC2017.5.0 == get_value incr_value add_value incr_step_count
|
||||
AoC2017.5.preamble == init-index-and-step-count prepare-predicate
|
||||
AoC2017.5.0 == get_value incr_value add_value incr_step_count
|
||||
AoC2017.5.preamble == init-index-and-step-count prepare-predicate
|
||||
|
||||
get_value == [roll< at] nullary
|
||||
incr_value == [[popd incr_at] unary] dip
|
||||
add_value == [+] cons dipd
|
||||
incr_step_count == [++] dip
|
||||
get_value == [roll< at] nullary
|
||||
incr_value == [[popd incr_at] unary] dip
|
||||
add_value == [+] cons dipd
|
||||
incr_step_count == [++] dip
|
||||
|
||||
init-index-and-step-count == 0 0 roll<
|
||||
prepare-predicate == dup size [>=] cons [popop] swoncat
|
||||
init-index-and-step-count == 0 0 roll<
|
||||
prepare-predicate == dup size [>=] cons [popop] swoncat
|
||||
|
||||
This is by far the largest program I have yet written in Joy. Even with
|
||||
the ``incr_at`` function it is still a bear. There may be an arrangement
|
||||
of the parameters that would permit more elegant definitions, but it
|
||||
still wouldn’t be as efficient as something written in assembly, C, or
|
||||
still wouldn't be as efficient as something written in assembly, C, or
|
||||
even Python.
|
||||
|
|
|
|||
|
|
@ -13088,7 +13088,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [1]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13101,7 +13101,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [2]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[0 2 7 0] dup max'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[0 2 7 0] dup max'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13132,7 +13132,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [3]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">from</span> <span class="nn">joy.library</span> <span class="kn">import</span> <span class="n">SimpleFunctionWrapper</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">joy.library</span> <span class="kn">import</span> <span class="n">SimpleFunctionWrapper</span>
|
||||
<span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="kn">import</span> <span class="n">list_to_stack</span>
|
||||
|
||||
|
||||
|
|
@ -13176,7 +13176,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [4]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[0 2 7 0] 7 index_of'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[0 2 7 0] 7 index_of'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13207,7 +13207,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [5]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[0 2 7 0] 23 index_of'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[0 2 7 0] 23 index_of'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13253,7 +13253,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [6]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="kn">import</span> <span class="n">iter_stack</span><span class="p">,</span> <span class="n">list_to_stack</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="kn">import</span> <span class="n">iter_stack</span><span class="p">,</span> <span class="n">list_to_stack</span>
|
||||
|
||||
|
||||
<span class="nd">@SimpleFunctionWrapper</span>
|
||||
|
|
@ -13292,7 +13292,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [7]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[0 2 7 0] dup max [index_of] nullary distribute'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[0 2 7 0] dup max [index_of] nullary distribute'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13323,7 +13323,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [8]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[2 4 1 2] dup max [index_of] nullary distribute'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[2 4 1 2] dup max [index_of] nullary distribute'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13354,7 +13354,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [9]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[3 1 2 3] dup max [index_of] nullary distribute'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[3 1 2 3] dup max [index_of] nullary distribute'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13385,7 +13385,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [10]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[0 2 3 4] dup max [index_of] nullary distribute'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[0 2 3 4] dup max [index_of] nullary distribute'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13416,7 +13416,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [11]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 3 4 1] dup max [index_of] nullary distribute'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 3 4 1] dup max [index_of] nullary distribute'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13469,7 +13469,7 @@ w/ G == dup max [index_of] nullary distribute</code></pre>
|
|||
<div class="prompt input_prompt">In [12]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'direco == dip rest cons'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'direco dip rest cons'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13482,7 +13482,7 @@ w/ G == dup max [index_of] nullary distribute</code></pre>
|
|||
<div class="prompt input_prompt">In [13]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'G == [direco] cons [swap] swoncat cons'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'G [direco] cons [swap] swoncat cons'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13495,7 +13495,7 @@ w/ G == dup max [index_of] nullary distribute</code></pre>
|
|||
<div class="prompt input_prompt">In [14]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'make_distributor == [dup dup max [index_of] nullary distribute] G'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'make_distributor [dup dup max [index_of] nullary distribute] G'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13508,7 +13508,7 @@ w/ G == dup max [index_of] nullary distribute</code></pre>
|
|||
<div class="prompt input_prompt">In [15]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[0 2 7 0] make_distributor 6 [x] times pop'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[0 2 7 0] make_distributor 6 [x] times pop'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13539,13 +13539,13 @@ w/ G == dup max [index_of] nullary distribute</code></pre>
|
|||
<div class="text_cell_render border-box-sizing rendered_html">
|
||||
<h3 id="A-function-to-drive-a-generator-and-count-how-many-states-before-a-repeat.">A function to drive a generator and count how many states before a repeat.<a class="anchor-link" href="#A-function-to-drive-a-generator-and-count-how-many-states-before-a-repeat.">¶</a></h3><p>First draft:</p>
|
||||
|
||||
<pre><code>[] [GEN] x [pop index_of 0 >=] [pop size --] [[swons] dip x] primrec
|
||||
<pre><code>[] [GEN] x [pop index_of 0 >=] [pop size --] [[swons] dip x] tailrec
|
||||
|
||||
</code></pre>
|
||||
<p>(?)</p>
|
||||
|
||||
<pre><code>[] [GEN] x [pop index_of 0 >=] [pop size --] [[swons] dip x] primrec
|
||||
[] [...] [GEN] [pop index_of 0 >=] [pop size --] [[swons] dip x] primrec
|
||||
<pre><code>[] [GEN] x [pop index_of 0 >=] [pop size --] [[swons] dip x] tailrec
|
||||
[] [...] [GEN] [pop index_of 0 >=] [pop size --] [[swons] dip x] tailrec
|
||||
[] [...] [GEN] pop index_of 0 >=
|
||||
[] [...] index_of 0 >=
|
||||
-1 0 >=
|
||||
|
|
@ -13554,7 +13554,7 @@ w/ G == dup max [index_of] nullary distribute</code></pre>
|
|||
</code></pre>
|
||||
<p>Base case</p>
|
||||
|
||||
<pre><code>[] [...] [GEN] [pop index_of 0 >=] [pop size --] [[swons] dip x] primrec
|
||||
<pre><code>[] [...] [GEN] [pop index_of 0 >=] [pop size --] [[swons] dip x] tailrec
|
||||
[] [...] [GEN] pop size --
|
||||
[] [...] size --
|
||||
[] [...] size --
|
||||
|
|
@ -13569,7 +13569,7 @@ n
|
|||
</code></pre>
|
||||
<p>Recursive case</p>
|
||||
|
||||
<pre><code>[] [...] [GEN] [pop index_of 0 >=] [popop size] [[swons] dip x] primrec
|
||||
<pre><code>[] [...] [GEN] [pop index_of 0 >=] [popop size] [[swons] dip x] tailrec
|
||||
[] [...] [GEN] [swons] dip x F
|
||||
[] [...] swons [GEN] x F
|
||||
[[...]] [GEN] x F
|
||||
|
|
@ -13580,7 +13580,7 @@ n
|
|||
</code></pre>
|
||||
<p>What have we learned?</p>
|
||||
|
||||
<pre><code>F == [pop index_of 0 >=] [popop size] [[swons] dip x] primrec</code></pre>
|
||||
<pre><code>F == [pop index_of 0 >=] [popop size] [[swons] dip x] tailrec</code></pre>
|
||||
|
||||
</div>
|
||||
</div>
|
||||
|
|
@ -13590,7 +13590,7 @@ n
|
|||
<div class="prompt input_prompt">In [16]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'count_states == [] swap x [pop index_of 0 >=] [popop size] [[swons] dip x] primrec'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'count_states [] swap x [pop index_of 0 >=] [popop size] [[swons] dip x] tailrec'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13603,7 +13603,7 @@ n
|
|||
<div class="prompt input_prompt">In [17]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'AoC2017.6 == make_distributor count_states'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'AoC2017.6 make_distributor count_states'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13616,7 +13616,7 @@ n
|
|||
<div class="prompt input_prompt">In [18]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[0 2 7 0] AoC2017.6'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[0 2 7 0] AoC2017.6'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13647,7 +13647,7 @@ n
|
|||
<div class="prompt input_prompt">In [19]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 1 1] AoC2017.6'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 1 1] AoC2017.6'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13678,7 +13678,7 @@ n
|
|||
<div class="prompt input_prompt">In [20]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[8 0 0 0 0 0] AoC2017.6'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[8 0 0 0 0 0] AoC2017.6'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
|
|||
|
|
@ -275,7 +275,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('direco == dip rest cons')"
|
||||
"define('direco dip rest cons')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -284,7 +284,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('G == [direco] cons [swap] swoncat cons')"
|
||||
"define('G [direco] cons [swap] swoncat cons')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -293,7 +293,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('make_distributor == [dup dup max [index_of] nullary distribute] G')"
|
||||
"define('make_distributor [dup dup max [index_of] nullary distribute] G')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -320,12 +320,12 @@
|
|||
"### A function to drive a generator and count how many states before a repeat.\n",
|
||||
"First draft:\n",
|
||||
"\n",
|
||||
" [] [GEN] x [pop index_of 0 >=] [pop size --] [[swons] dip x] primrec\n",
|
||||
" [] [GEN] x [pop index_of 0 >=] [pop size --] [[swons] dip x] tailrec\n",
|
||||
"\n",
|
||||
"(?)\n",
|
||||
"\n",
|
||||
" [] [GEN] x [pop index_of 0 >=] [pop size --] [[swons] dip x] primrec\n",
|
||||
" [] [...] [GEN] [pop index_of 0 >=] [pop size --] [[swons] dip x] primrec\n",
|
||||
" [] [GEN] x [pop index_of 0 >=] [pop size --] [[swons] dip x] tailrec\n",
|
||||
" [] [...] [GEN] [pop index_of 0 >=] [pop size --] [[swons] dip x] tailrec\n",
|
||||
" [] [...] [GEN] pop index_of 0 >=\n",
|
||||
" [] [...] index_of 0 >=\n",
|
||||
" -1 0 >=\n",
|
||||
|
|
@ -333,7 +333,7 @@
|
|||
"\n",
|
||||
"Base case\n",
|
||||
"\n",
|
||||
" [] [...] [GEN] [pop index_of 0 >=] [pop size --] [[swons] dip x] primrec\n",
|
||||
" [] [...] [GEN] [pop index_of 0 >=] [pop size --] [[swons] dip x] tailrec\n",
|
||||
" [] [...] [GEN] pop size --\n",
|
||||
" [] [...] size --\n",
|
||||
" [] [...] size --\n",
|
||||
|
|
@ -346,7 +346,7 @@
|
|||
"\n",
|
||||
"Recursive case\n",
|
||||
"\n",
|
||||
" [] [...] [GEN] [pop index_of 0 >=] [popop size] [[swons] dip x] primrec\n",
|
||||
" [] [...] [GEN] [pop index_of 0 >=] [popop size] [[swons] dip x] tailrec\n",
|
||||
" [] [...] [GEN] [swons] dip x F\n",
|
||||
" [] [...] swons [GEN] x F\n",
|
||||
" [[...]] [GEN] x F\n",
|
||||
|
|
@ -356,7 +356,7 @@
|
|||
"\n",
|
||||
"What have we learned?\n",
|
||||
"\n",
|
||||
" F == [pop index_of 0 >=] [popop size] [[swons] dip x] primrec"
|
||||
" F == [pop index_of 0 >=] [popop size] [[swons] dip x] tailrec"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -365,7 +365,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('count_states == [] swap x [pop index_of 0 >=] [popop size] [[swons] dip x] primrec')"
|
||||
"define('count_states [] swap x [pop index_of 0 >=] [popop size] [[swons] dip x] tailrec')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -374,7 +374,7 @@
|
|||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('AoC2017.6 == make_distributor count_states')"
|
||||
"define('AoC2017.6 make_distributor count_states')"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -442,14 +442,14 @@
|
|||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 2
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython2",
|
||||
"version": "2.7.13"
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.8.3"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
|
|
|||
|
|
@ -169,17 +169,17 @@ J('[1 3 4 1] dup max [index_of] nullary distribute')
|
|||
|
||||
|
||||
```python
|
||||
define('direco == dip rest cons')
|
||||
define('direco dip rest cons')
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
define('G == [direco] cons [swap] swoncat cons')
|
||||
define('G [direco] cons [swap] swoncat cons')
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
define('make_distributor == [dup dup max [index_of] nullary distribute] G')
|
||||
define('make_distributor [dup dup max [index_of] nullary distribute] G')
|
||||
```
|
||||
|
||||
|
||||
|
|
@ -193,12 +193,12 @@ J('[0 2 7 0] make_distributor 6 [x] times pop')
|
|||
### A function to drive a generator and count how many states before a repeat.
|
||||
First draft:
|
||||
|
||||
[] [GEN] x [pop index_of 0 >=] [pop size --] [[swons] dip x] primrec
|
||||
[] [GEN] x [pop index_of 0 >=] [pop size --] [[swons] dip x] tailrec
|
||||
|
||||
(?)
|
||||
|
||||
[] [GEN] x [pop index_of 0 >=] [pop size --] [[swons] dip x] primrec
|
||||
[] [...] [GEN] [pop index_of 0 >=] [pop size --] [[swons] dip x] primrec
|
||||
[] [GEN] x [pop index_of 0 >=] [pop size --] [[swons] dip x] tailrec
|
||||
[] [...] [GEN] [pop index_of 0 >=] [pop size --] [[swons] dip x] tailrec
|
||||
[] [...] [GEN] pop index_of 0 >=
|
||||
[] [...] index_of 0 >=
|
||||
-1 0 >=
|
||||
|
|
@ -206,7 +206,7 @@ First draft:
|
|||
|
||||
Base case
|
||||
|
||||
[] [...] [GEN] [pop index_of 0 >=] [pop size --] [[swons] dip x] primrec
|
||||
[] [...] [GEN] [pop index_of 0 >=] [pop size --] [[swons] dip x] tailrec
|
||||
[] [...] [GEN] pop size --
|
||||
[] [...] size --
|
||||
[] [...] size --
|
||||
|
|
@ -219,7 +219,7 @@ A mistake, `popop` and no need for `--`
|
|||
|
||||
Recursive case
|
||||
|
||||
[] [...] [GEN] [pop index_of 0 >=] [popop size] [[swons] dip x] primrec
|
||||
[] [...] [GEN] [pop index_of 0 >=] [popop size] [[swons] dip x] tailrec
|
||||
[] [...] [GEN] [swons] dip x F
|
||||
[] [...] swons [GEN] x F
|
||||
[[...]] [GEN] x F
|
||||
|
|
@ -229,16 +229,16 @@ Recursive case
|
|||
|
||||
What have we learned?
|
||||
|
||||
F == [pop index_of 0 >=] [popop size] [[swons] dip x] primrec
|
||||
F == [pop index_of 0 >=] [popop size] [[swons] dip x] tailrec
|
||||
|
||||
|
||||
```python
|
||||
define('count_states == [] swap x [pop index_of 0 >=] [popop size] [[swons] dip x] primrec')
|
||||
define('count_states [] swap x [pop index_of 0 >=] [popop size] [[swons] dip x] tailrec')
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
define('AoC2017.6 == make_distributor count_states')
|
||||
define('AoC2017.6 make_distributor count_states')
|
||||
```
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -6,13 +6,13 @@ December 6th
|
|||
|
||||
::
|
||||
|
||||
[0 2 7 0] dup max
|
||||
[0 2 7 0] dup max
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
from notebook_preamble import D, J, V, define
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[0 2 7 0] dup max')
|
||||
|
||||
|
|
@ -22,7 +22,7 @@ December 6th
|
|||
[0 2 7 0] 7
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
from joy.library import SimpleFunctionWrapper
|
||||
from joy.utils.stack import list_to_stack
|
||||
|
|
@ -57,7 +57,7 @@ December 6th
|
|||
|
||||
D['index_of'] = index_of
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[0 2 7 0] 7 index_of')
|
||||
|
||||
|
|
@ -67,7 +67,7 @@ December 6th
|
|||
2
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[0 2 7 0] 23 index_of')
|
||||
|
||||
|
|
@ -77,18 +77,18 @@ December 6th
|
|||
-1
|
||||
|
||||
|
||||
Starting at ``index`` distribute ``count`` “blocks” to the “banks” in
|
||||
Starting at ``index`` distribute ``count`` "blocks" to the "banks" in
|
||||
the sequence.
|
||||
|
||||
::
|
||||
|
||||
[...] count index distribute
|
||||
----------------------------
|
||||
[...]
|
||||
[...] count index distribute
|
||||
----------------------------
|
||||
[...]
|
||||
|
||||
This seems like it would be a PITA to implement in Joypy…
|
||||
This seems like it would be a PITA to implement in Joypy...
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
from joy.utils.stack import iter_stack, list_to_stack
|
||||
|
||||
|
|
@ -118,7 +118,7 @@ This seems like it would be a PITA to implement in Joypy…
|
|||
|
||||
D['distribute'] = distribute
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[0 2 7 0] dup max [index_of] nullary distribute')
|
||||
|
||||
|
|
@ -128,7 +128,7 @@ This seems like it would be a PITA to implement in Joypy…
|
|||
[2 4 1 2]
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[2 4 1 2] dup max [index_of] nullary distribute')
|
||||
|
||||
|
|
@ -138,7 +138,7 @@ This seems like it would be a PITA to implement in Joypy…
|
|||
[3 1 2 3]
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[3 1 2 3] dup max [index_of] nullary distribute')
|
||||
|
||||
|
|
@ -148,7 +148,7 @@ This seems like it would be a PITA to implement in Joypy…
|
|||
[0 2 3 4]
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[0 2 3 4] dup max [index_of] nullary distribute')
|
||||
|
||||
|
|
@ -158,7 +158,7 @@ This seems like it would be a PITA to implement in Joypy…
|
|||
[1 3 4 1]
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[1 3 4 1] dup max [index_of] nullary distribute')
|
||||
|
||||
|
|
@ -168,39 +168,39 @@ This seems like it would be a PITA to implement in Joypy…
|
|||
[2 4 1 2]
|
||||
|
||||
|
||||
Recalling “Generator Programs”
|
||||
Recalling "Generator Programs"
|
||||
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
::
|
||||
|
||||
[a F] x
|
||||
[a F] a F
|
||||
[a F] x
|
||||
[a F] a F
|
||||
|
||||
[a F] a swap [C] dip rest cons
|
||||
a [a F] [C] dip rest cons
|
||||
a C [a F] rest cons
|
||||
a C [F] cons
|
||||
[a F] a swap [C] dip rest cons
|
||||
a [a F] [C] dip rest cons
|
||||
a C [a F] rest cons
|
||||
a C [F] cons
|
||||
|
||||
w/ C == dup G
|
||||
w/ C == dup G
|
||||
|
||||
a dup G [F] cons
|
||||
a a G [F] cons
|
||||
a dup G [F] cons
|
||||
a a G [F] cons
|
||||
|
||||
w/ G == dup max [index_of] nullary distribute
|
||||
w/ G == dup max [index_of] nullary distribute
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('direco == dip rest cons')
|
||||
define('direco dip rest cons')
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('G == [direco] cons [swap] swoncat cons')
|
||||
define('G [direco] cons [swap] swoncat cons')
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('make_distributor == [dup dup max [index_of] nullary distribute] G')
|
||||
define('make_distributor [dup dup max [index_of] nullary distribute] G')
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[0 2 7 0] make_distributor 6 [x] times pop')
|
||||
|
||||
|
|
@ -217,63 +217,63 @@ First draft:
|
|||
|
||||
::
|
||||
|
||||
[] [GEN] x [pop index_of 0 >=] [pop size --] [[swons] dip x] primrec
|
||||
[] [GEN] x [pop index_of 0 >=] [pop size --] [[swons] dip x] tailrec
|
||||
|
||||
(?)
|
||||
|
||||
::
|
||||
|
||||
[] [GEN] x [pop index_of 0 >=] [pop size --] [[swons] dip x] primrec
|
||||
[] [...] [GEN] [pop index_of 0 >=] [pop size --] [[swons] dip x] primrec
|
||||
[] [...] [GEN] pop index_of 0 >=
|
||||
[] [...] index_of 0 >=
|
||||
-1 0 >=
|
||||
False
|
||||
[] [GEN] x [pop index_of 0 >=] [pop size --] [[swons] dip x] tailrec
|
||||
[] [...] [GEN] [pop index_of 0 >=] [pop size --] [[swons] dip x] tailrec
|
||||
[] [...] [GEN] pop index_of 0 >=
|
||||
[] [...] index_of 0 >=
|
||||
-1 0 >=
|
||||
False
|
||||
|
||||
Base case
|
||||
|
||||
::
|
||||
|
||||
[] [...] [GEN] [pop index_of 0 >=] [pop size --] [[swons] dip x] primrec
|
||||
[] [...] [GEN] pop size --
|
||||
[] [...] size --
|
||||
[] [...] size --
|
||||
[] [...] [GEN] [pop index_of 0 >=] [pop size --] [[swons] dip x] tailrec
|
||||
[] [...] [GEN] pop size --
|
||||
[] [...] size --
|
||||
[] [...] size --
|
||||
|
||||
A mistake, ``popop`` and no need for ``--``
|
||||
|
||||
::
|
||||
|
||||
[] [...] [GEN] popop size
|
||||
[] size
|
||||
n
|
||||
[] [...] [GEN] popop size
|
||||
[] size
|
||||
n
|
||||
|
||||
Recursive case
|
||||
|
||||
::
|
||||
|
||||
[] [...] [GEN] [pop index_of 0 >=] [popop size] [[swons] dip x] primrec
|
||||
[] [...] [GEN] [swons] dip x F
|
||||
[] [...] swons [GEN] x F
|
||||
[[...]] [GEN] x F
|
||||
[[...]] [...] [GEN] F
|
||||
[] [...] [GEN] [pop index_of 0 >=] [popop size] [[swons] dip x] tailrec
|
||||
[] [...] [GEN] [swons] dip x F
|
||||
[] [...] swons [GEN] x F
|
||||
[[...]] [GEN] x F
|
||||
[[...]] [...] [GEN] F
|
||||
|
||||
[[...]] [...] [GEN] F
|
||||
[[...]] [...] [GEN] F
|
||||
|
||||
What have we learned?
|
||||
|
||||
::
|
||||
|
||||
F == [pop index_of 0 >=] [popop size] [[swons] dip x] primrec
|
||||
F == [pop index_of 0 >=] [popop size] [[swons] dip x] tailrec
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('count_states == [] swap x [pop index_of 0 >=] [popop size] [[swons] dip x] primrec')
|
||||
define('count_states [] swap x [pop index_of 0 >=] [popop size] [[swons] dip x] tailrec')
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('AoC2017.6 == make_distributor count_states')
|
||||
define('AoC2017.6 make_distributor count_states')
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[0 2 7 0] AoC2017.6')
|
||||
|
||||
|
|
@ -283,7 +283,7 @@ What have we learned?
|
|||
5
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[1 1 1] AoC2017.6')
|
||||
|
||||
|
|
@ -293,7 +293,7 @@ What have we learned?
|
|||
4
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[8 0 0 0 0 0] AoC2017.6')
|
||||
|
||||
|
|
|
|||
File diff suppressed because it is too large
Load Diff
|
|
@ -29,11 +29,11 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . 23 sqr\n",
|
||||
" 23 . sqr\n",
|
||||
" 23 . dup mul\n",
|
||||
"23 23 . mul\n",
|
||||
" 529 . \n"
|
||||
" • 23 sqr\n",
|
||||
" 23 • sqr\n",
|
||||
" 23 • dup mul\n",
|
||||
"23 23 • mul\n",
|
||||
" 529 • \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -89,9 +89,9 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . 23 sqr\n",
|
||||
" 23 . sqr\n",
|
||||
"529 . \n"
|
||||
" • 23 sqr\n",
|
||||
" 23 • sqr\n",
|
||||
"529 • \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -131,7 +131,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 8,
|
||||
"execution_count": 10,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
|
|
@ -145,7 +145,7 @@
|
|||
}
|
||||
],
|
||||
"source": [
|
||||
"print compile_joy_definition(old_sqr)"
|
||||
"print(compile_joy_definition(old_sqr))"
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -159,7 +159,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 9,
|
||||
"execution_count": 11,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -168,7 +168,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 10,
|
||||
"execution_count": 12,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -186,7 +186,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 11,
|
||||
"execution_count": 13,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -214,9 +214,21 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 12,
|
||||
"execution_count": 14,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"outputs": [
|
||||
{
|
||||
"ename": "ModuleNotFoundError",
|
||||
"evalue": "No module named 'joy.utils.types'",
|
||||
"output_type": "error",
|
||||
"traceback": [
|
||||
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
||||
"\u001b[0;31mModuleNotFoundError\u001b[0m Traceback (most recent call last)",
|
||||
"\u001b[0;32m<ipython-input-14-d5ef3c7560be>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mfrom\u001b[0m \u001b[0mjoy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mutils\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtypes\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mcompile_\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdoc_from_stack_effect\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minfer_string\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 2\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mjoy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlibrary\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mSimpleFunctionWrapper\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'joy.utils.types'"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"from joy.utils.types import compile_, doc_from_stack_effect, infer_string\n",
|
||||
"from joy.library import SimpleFunctionWrapper"
|
||||
|
|
@ -224,7 +236,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 13,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -240,17 +252,9 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 14,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"(a2 a1 -- a1 a2 a1 a2 a2)\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"for fi, fo in stack_effects:\n",
|
||||
" print doc_from_stack_effect(fi, fo)"
|
||||
|
|
@ -258,7 +262,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 15,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -274,34 +278,27 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 16,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"def foo(stack):\n",
|
||||
" \"\"\"\n",
|
||||
" ::\n",
|
||||
"\n",
|
||||
" (a2 a1 -- a1 a2 a1 a2 a2)\n",
|
||||
"\n",
|
||||
" \"\"\"\n",
|
||||
" (a1, (a2, s1)) = stack\n",
|
||||
" return (a2, (a2, (a1, (a2, (a1, s1)))))\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"print source"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 17,
|
||||
"execution_count": 9,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"outputs": [
|
||||
{
|
||||
"ename": "SyntaxError",
|
||||
"evalue": "invalid syntax (<ipython-input-9-1a7e90bf2d7b>, line 1)",
|
||||
"output_type": "error",
|
||||
"traceback": [
|
||||
"\u001b[0;36m File \u001b[0;32m\"<ipython-input-9-1a7e90bf2d7b>\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m exec compile(source, '__main__', 'single')\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"exec compile(source, '__main__', 'single')\n",
|
||||
"\n",
|
||||
|
|
@ -310,20 +307,9 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 18,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . 23 18 foo\n",
|
||||
" 23 . 18 foo\n",
|
||||
" 23 18 . foo\n",
|
||||
"18 23 18 23 23 . \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"V('23 18 foo')"
|
||||
]
|
||||
|
|
@ -351,7 +337,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 19,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -360,17 +346,9 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 20,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"[[a b c d] e a [f]] [[a e c d]]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"Ein = '[a b c d] e a [f]' # The terms should be reversed here but I don't realize that until later.\n",
|
||||
"Eout = '[a e c d]'\n",
|
||||
|
|
@ -381,7 +359,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 21,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -390,38 +368,18 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 22,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(((a, (b, (c, (d, ())))), (e, (a, ((f, ()), ())))),\n",
|
||||
" ((a, (e, (c, (d, ())))), ()))"
|
||||
]
|
||||
},
|
||||
"execution_count": 22,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"fi, fo"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 23,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"[[a1 a2 a3 a4] a5 a6 a7] [[a1 a5 a3 a4]]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"Ein = '[a1 a2 a3 a4] a5 a6 a7'\n",
|
||||
"Eout = '[a1 a5 a3 a4]'\n",
|
||||
|
|
@ -432,7 +390,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 24,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -441,49 +399,18 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 25,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"(((a1, (a2, (a3, (a4, ())))), (a5, (a6, (a7, ())))),\n",
|
||||
" ((a1, (a5, (a3, (a4, ())))), ()))"
|
||||
]
|
||||
},
|
||||
"execution_count": 25,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"fi, fo"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 26,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"{'a1': a1,\n",
|
||||
" 'a2': a2,\n",
|
||||
" 'a3': a3,\n",
|
||||
" 'a4': a4,\n",
|
||||
" 'a5': a5,\n",
|
||||
" 'a6': a6,\n",
|
||||
" 'a7': a7,\n",
|
||||
" 's0': s0,\n",
|
||||
" 's1': s1}"
|
||||
]
|
||||
},
|
||||
"execution_count": 26,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def type_vars():\n",
|
||||
" from joy.library import a1, a2, a3, a4, a5, a6, a7, s0, s1\n",
|
||||
|
|
@ -495,7 +422,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 27,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -504,17 +431,9 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 28,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"(... a7 a6 a5 [a1 a2 a3 a4 ] -- ... [a1 a5 a3 a4 ])\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"stack_effect = reify(tv, (fi, fo))\n",
|
||||
"print doc_from_stack_effect(*stack_effect)"
|
||||
|
|
@ -522,17 +441,9 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 29,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"(((a1, (a2, (a3, (a4, ())))), (a5, (a6, (a7, ())))), ((a1, (a5, (a3, (a4, ())))), ()))\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"print stack_effect"
|
||||
]
|
||||
|
|
@ -546,7 +457,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 30,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -562,17 +473,9 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 31,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"(a7 a6 a5 [a1 a2 a3 a4 ...1] -- [a1 a5 a3 a4 ...1])\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"print doc_from_stack_effect(*stack_effect)"
|
||||
]
|
||||
|
|
@ -586,7 +489,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 32,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -602,42 +505,18 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 33,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"(a7 a6 a5 [a1 a2 ...1] -- [a1 a5 ...1])\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"print doc_from_stack_effect(*stack_effect)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 34,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"def Ee(stack):\n",
|
||||
" \"\"\"\n",
|
||||
" ::\n",
|
||||
"\n",
|
||||
" (a7 a6 a5 [a1 a2 ...1] -- [a1 a5 ...1])\n",
|
||||
"\n",
|
||||
" \"\"\"\n",
|
||||
" ((a1, (a2, s1)), (a5, (a6, (a7, s0)))) = stack\n",
|
||||
" return ((a1, (a5, s1)), s0)\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"source = compile_('Ee', stack_effect)\n",
|
||||
"print source"
|
||||
|
|
@ -652,7 +531,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 35,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -661,42 +540,18 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 36,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"([a1 a2 ...1] a5 a6 a7 -- [a1 a5 ...1])\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"print doc_from_stack_effect(*stack_effect)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 37,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"def Ee(stack):\n",
|
||||
" \"\"\"\n",
|
||||
" ::\n",
|
||||
"\n",
|
||||
" ([a1 a2 ...1] a5 a6 a7 -- [a1 a5 ...1])\n",
|
||||
"\n",
|
||||
" \"\"\"\n",
|
||||
" (a7, (a6, (a5, ((a1, (a2, s1)), s0)))) = stack\n",
|
||||
" return ((a1, (a5, s1)), s0)\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"source = compile_('Ee', stack_effect)\n",
|
||||
"print source"
|
||||
|
|
@ -715,7 +570,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 38,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -725,24 +580,11 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 39,
|
||||
"execution_count": null,
|
||||
"metadata": {
|
||||
"scrolled": true
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
" . [a b c d] 1 2 [f] Ee\n",
|
||||
" [a b c d] . 1 2 [f] Ee\n",
|
||||
" [a b c d] 1 . 2 [f] Ee\n",
|
||||
" [a b c d] 1 2 . [f] Ee\n",
|
||||
"[a b c d] 1 2 [f] . Ee\n",
|
||||
" [a 1 c d] . \n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"V('[a b c d] 1 2 [f] Ee')"
|
||||
]
|
||||
|
|
@ -765,7 +607,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 40,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -785,17 +627,9 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 41,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"(n1 -- n2)\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"stack_effects = infer_string('dup mul')\n",
|
||||
"for fi, fo in stack_effects:\n",
|
||||
|
|
@ -811,7 +645,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 42,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -846,17 +680,9 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 43,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"(n4 n3 n2 n1 -- n5)\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"stack_effects = infer_string('mul mul sub')\n",
|
||||
"for fi, fo in stack_effects:\n",
|
||||
|
|
@ -865,7 +691,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 44,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -896,17 +722,9 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 45,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"(a2 a1 -- a1 a2 a1)\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"stack_effects = infer_string('tuck')\n",
|
||||
"for fi, fo in stack_effects:\n",
|
||||
|
|
@ -936,7 +754,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 46,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -945,7 +763,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 47,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -967,7 +785,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 80,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -992,7 +810,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 64,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1023,7 +841,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 50,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1092,7 +910,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 69,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -1102,18 +920,9 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 74,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stderr",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"<ipython-input-74-a6ea700b09d9>:1: SyntaxWarning: import * only allowed at module level\n",
|
||||
" def import_yin():\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"def import_yin():\n",
|
||||
" from joy.utils.generated_library import *\n",
|
||||
|
|
@ -1139,44 +948,18 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 75,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"def mul_(stack):\n",
|
||||
" (a31, (a32, stack)) = stack\n",
|
||||
" a33 = mul(a32, a31)\n",
|
||||
" stack = (a33, stack)\n",
|
||||
" return stack\n",
|
||||
"\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"print compile_yinyang('mul_', (names(), (names(), (mul, ()))))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 76,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"def sqr(stack):\n",
|
||||
" (a34, stack) = stack\n",
|
||||
" a35 = mul(a34, a34)\n",
|
||||
" stack = (a35, stack)\n",
|
||||
" return stack\n",
|
||||
"\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"e = (names(), (dup, (mul, ())))\n",
|
||||
"print compile_yinyang('sqr', e)"
|
||||
|
|
@ -1184,25 +967,11 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 77,
|
||||
"execution_count": null,
|
||||
"metadata": {
|
||||
"scrolled": true
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"def foo(stack):\n",
|
||||
" (a36, (a37, stack)) = stack\n",
|
||||
" a38 = sub(a37, a36)\n",
|
||||
" a39 = mul(a38, a36)\n",
|
||||
" stack = (a39, stack)\n",
|
||||
" return stack\n",
|
||||
"\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"e = (names(), (dup, (names(), (sub, (mul, ())))))\n",
|
||||
"print compile_yinyang('foo', e)"
|
||||
|
|
@ -1210,23 +979,9 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 78,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"def bar(stack):\n",
|
||||
" (a40, (a41, stack)) = stack\n",
|
||||
" a42 = mul(a41, a40)\n",
|
||||
" a43 = sub(a42, a42)\n",
|
||||
" stack = (a43, (a43, stack))\n",
|
||||
" return stack\n",
|
||||
"\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"e = (names(), (names(), (mul, (dup, (sub, (dup, ()))))))\n",
|
||||
"print compile_yinyang('bar', e)"
|
||||
|
|
@ -1234,24 +989,9 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 79,
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"def to_the_fifth_power(stack):\n",
|
||||
" (a44, stack) = stack\n",
|
||||
" a45 = mul(a44, a44)\n",
|
||||
" a46 = mul(a45, a45)\n",
|
||||
" a47 = mul(a46, a44)\n",
|
||||
" stack = (a47, stack)\n",
|
||||
" return stack\n",
|
||||
"\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"e = (names(), (dup, (dup, (mul, (dup, (mul, (mul, ())))))))\n",
|
||||
"print compile_yinyang('to_the_fifth_power', e)"
|
||||
|
|
@ -1295,14 +1035,14 @@
|
|||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 2
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython2",
|
||||
"version": "2.7.15"
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.8.3"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
|
|
|||
|
|
@ -13,11 +13,11 @@ Given a Joy program like:
|
|||
V('23 sqr')
|
||||
```
|
||||
|
||||
. 23 sqr
|
||||
23 . sqr
|
||||
23 . dup mul
|
||||
23 23 . mul
|
||||
529 .
|
||||
• 23 sqr
|
||||
23 • sqr
|
||||
23 • dup mul
|
||||
23 23 • mul
|
||||
529 •
|
||||
|
||||
|
||||
How would we go about compiling this code (to Python for now)?
|
||||
|
|
@ -47,9 +47,9 @@ D['sqr'] = sqr
|
|||
V('23 sqr')
|
||||
```
|
||||
|
||||
. 23 sqr
|
||||
23 . sqr
|
||||
529 .
|
||||
• 23 sqr
|
||||
23 • sqr
|
||||
529 •
|
||||
|
||||
|
||||
It's simple to write a function to emit this kind of crude "compiled" code.
|
||||
|
|
@ -76,7 +76,7 @@ def compile_joy_definition(defi):
|
|||
|
||||
|
||||
```python
|
||||
print compile_joy_definition(old_sqr)
|
||||
print(compile_joy_definition(old_sqr))
|
||||
```
|
||||
|
||||
def sqr(stack, expression, dictionary):
|
||||
|
|
@ -123,6 +123,19 @@ from joy.library import SimpleFunctionWrapper
|
|||
```
|
||||
|
||||
|
||||
---------------------------------------------------------------------------
|
||||
|
||||
ModuleNotFoundError Traceback (most recent call last)
|
||||
|
||||
<ipython-input-14-d5ef3c7560be> in <module>
|
||||
----> 1 from joy.utils.types import compile_, doc_from_stack_effect, infer_string
|
||||
2 from joy.library import SimpleFunctionWrapper
|
||||
|
||||
|
||||
ModuleNotFoundError: No module named 'joy.utils.types'
|
||||
|
||||
|
||||
|
||||
```python
|
||||
stack_effects = infer_string('tuck over dup')
|
||||
```
|
||||
|
|
@ -135,9 +148,6 @@ for fi, fo in stack_effects:
|
|||
print doc_from_stack_effect(fi, fo)
|
||||
```
|
||||
|
||||
(a2 a1 -- a1 a2 a1 a2 a2)
|
||||
|
||||
|
||||
|
||||
```python
|
||||
source = compile_('foo', stack_effects[0])
|
||||
|
|
@ -150,17 +160,6 @@ All Yin functions can be described in Python as a tuple-unpacking (or "-destruct
|
|||
print source
|
||||
```
|
||||
|
||||
def foo(stack):
|
||||
"""
|
||||
::
|
||||
|
||||
(a2 a1 -- a1 a2 a1 a2 a2)
|
||||
|
||||
"""
|
||||
(a1, (a2, s1)) = stack
|
||||
return (a2, (a2, (a1, (a2, (a1, s1)))))
|
||||
|
||||
|
||||
|
||||
```python
|
||||
exec compile(source, '__main__', 'single')
|
||||
|
|
@ -169,16 +168,18 @@ D['foo'] = SimpleFunctionWrapper(foo)
|
|||
```
|
||||
|
||||
|
||||
File "<ipython-input-9-1a7e90bf2d7b>", line 1
|
||||
exec compile(source, '__main__', 'single')
|
||||
^
|
||||
SyntaxError: invalid syntax
|
||||
|
||||
|
||||
|
||||
|
||||
```python
|
||||
V('23 18 foo')
|
||||
```
|
||||
|
||||
. 23 18 foo
|
||||
23 . 18 foo
|
||||
23 18 . foo
|
||||
18 23 18 23 23 .
|
||||
|
||||
|
||||
## Compiling from Stack Effects
|
||||
|
||||
There are times when you're deriving a Joy program when you have a stack effect for a Yin function and you need to define it. For example, in the Ordered Binary Trees notebook there is a point where we must derive a function `Ee`:
|
||||
|
|
@ -209,9 +210,6 @@ E = '[%s] [%s]' % (Ein, Eout)
|
|||
print E
|
||||
```
|
||||
|
||||
[[a b c d] e a [f]] [[a e c d]]
|
||||
|
||||
|
||||
|
||||
```python
|
||||
(fi, (fo, _)) = text_to_expression(E)
|
||||
|
|
@ -223,14 +221,6 @@ fi, fo
|
|||
```
|
||||
|
||||
|
||||
|
||||
|
||||
(((a, (b, (c, (d, ())))), (e, (a, ((f, ()), ())))),
|
||||
((a, (e, (c, (d, ())))), ()))
|
||||
|
||||
|
||||
|
||||
|
||||
```python
|
||||
Ein = '[a1 a2 a3 a4] a5 a6 a7'
|
||||
Eout = '[a1 a5 a3 a4]'
|
||||
|
|
@ -239,9 +229,6 @@ E = '[%s] [%s]' % (Ein, Eout)
|
|||
print E
|
||||
```
|
||||
|
||||
[[a1 a2 a3 a4] a5 a6 a7] [[a1 a5 a3 a4]]
|
||||
|
||||
|
||||
|
||||
```python
|
||||
(fi, (fo, _)) = text_to_expression(E)
|
||||
|
|
@ -253,14 +240,6 @@ fi, fo
|
|||
```
|
||||
|
||||
|
||||
|
||||
|
||||
(((a1, (a2, (a3, (a4, ())))), (a5, (a6, (a7, ())))),
|
||||
((a1, (a5, (a3, (a4, ())))), ()))
|
||||
|
||||
|
||||
|
||||
|
||||
```python
|
||||
def type_vars():
|
||||
from joy.library import a1, a2, a3, a4, a5, a6, a7, s0, s1
|
||||
|
|
@ -271,21 +250,6 @@ tv
|
|||
```
|
||||
|
||||
|
||||
|
||||
|
||||
{'a1': a1,
|
||||
'a2': a2,
|
||||
'a3': a3,
|
||||
'a4': a4,
|
||||
'a5': a5,
|
||||
'a6': a6,
|
||||
'a7': a7,
|
||||
's0': s0,
|
||||
's1': s1}
|
||||
|
||||
|
||||
|
||||
|
||||
```python
|
||||
from joy.utils.types import reify
|
||||
```
|
||||
|
|
@ -296,17 +260,11 @@ stack_effect = reify(tv, (fi, fo))
|
|||
print doc_from_stack_effect(*stack_effect)
|
||||
```
|
||||
|
||||
(... a7 a6 a5 [a1 a2 a3 a4 ] -- ... [a1 a5 a3 a4 ])
|
||||
|
||||
|
||||
|
||||
```python
|
||||
print stack_effect
|
||||
```
|
||||
|
||||
(((a1, (a2, (a3, (a4, ())))), (a5, (a6, (a7, ())))), ((a1, (a5, (a3, (a4, ())))), ()))
|
||||
|
||||
|
||||
Almost, but what we really want is something like this:
|
||||
|
||||
|
||||
|
|
@ -321,9 +279,6 @@ Note the change of `()` to `JoyStackType` type variables.
|
|||
print doc_from_stack_effect(*stack_effect)
|
||||
```
|
||||
|
||||
(a7 a6 a5 [a1 a2 a3 a4 ...1] -- [a1 a5 a3 a4 ...1])
|
||||
|
||||
|
||||
Now we can omit `a3` and `a4` if we like:
|
||||
|
||||
|
||||
|
|
@ -338,26 +293,12 @@ The `right` and `left` parts of the ordered binary tree node are subsumed in the
|
|||
print doc_from_stack_effect(*stack_effect)
|
||||
```
|
||||
|
||||
(a7 a6 a5 [a1 a2 ...1] -- [a1 a5 ...1])
|
||||
|
||||
|
||||
|
||||
```python
|
||||
source = compile_('Ee', stack_effect)
|
||||
print source
|
||||
```
|
||||
|
||||
def Ee(stack):
|
||||
"""
|
||||
::
|
||||
|
||||
(a7 a6 a5 [a1 a2 ...1] -- [a1 a5 ...1])
|
||||
|
||||
"""
|
||||
((a1, (a2, s1)), (a5, (a6, (a7, s0)))) = stack
|
||||
return ((a1, (a5, s1)), s0)
|
||||
|
||||
|
||||
Oops! The input stack is backwards...
|
||||
|
||||
|
||||
|
|
@ -370,26 +311,12 @@ stack_effect = eval('((a7, (a6, (a5, ((a1, (a2, s1)), s0)))), ((a1, (a5, s1)), s
|
|||
print doc_from_stack_effect(*stack_effect)
|
||||
```
|
||||
|
||||
([a1 a2 ...1] a5 a6 a7 -- [a1 a5 ...1])
|
||||
|
||||
|
||||
|
||||
```python
|
||||
source = compile_('Ee', stack_effect)
|
||||
print source
|
||||
```
|
||||
|
||||
def Ee(stack):
|
||||
"""
|
||||
::
|
||||
|
||||
([a1 a2 ...1] a5 a6 a7 -- [a1 a5 ...1])
|
||||
|
||||
"""
|
||||
(a7, (a6, (a5, ((a1, (a2, s1)), s0)))) = stack
|
||||
return ((a1, (a5, s1)), s0)
|
||||
|
||||
|
||||
Compare:
|
||||
|
||||
[key old_value left right] new_value key [Tree-add] Ee
|
||||
|
|
@ -408,14 +335,6 @@ D['Ee'] = SimpleFunctionWrapper(Ee)
|
|||
V('[a b c d] 1 2 [f] Ee')
|
||||
```
|
||||
|
||||
. [a b c d] 1 2 [f] Ee
|
||||
[a b c d] . 1 2 [f] Ee
|
||||
[a b c d] 1 . 2 [f] Ee
|
||||
[a b c d] 1 2 . [f] Ee
|
||||
[a b c d] 1 2 [f] . Ee
|
||||
[a 1 c d] .
|
||||
|
||||
|
||||
|
||||
```python
|
||||
|
||||
|
|
@ -444,9 +363,6 @@ for fi, fo in stack_effects:
|
|||
print doc_from_stack_effect(fi, fo)
|
||||
```
|
||||
|
||||
(n1 -- n2)
|
||||
|
||||
|
||||
Then we would want something like this:
|
||||
|
||||
|
||||
|
|
@ -479,9 +395,6 @@ for fi, fo in stack_effects:
|
|||
print doc_from_stack_effect(fi, fo)
|
||||
```
|
||||
|
||||
(n4 n3 n2 n1 -- n5)
|
||||
|
||||
|
||||
|
||||
```python
|
||||
|
||||
|
|
@ -515,9 +428,6 @@ for fi, fo in stack_effects:
|
|||
print doc_from_stack_effect(fi, fo)
|
||||
```
|
||||
|
||||
(a2 a1 -- a1 a2 a1)
|
||||
|
||||
|
||||
|
||||
```python
|
||||
|
||||
|
|
@ -667,10 +577,6 @@ dup = yin_dict['dup']
|
|||
# return (n, (n, stack)), expression
|
||||
```
|
||||
|
||||
<ipython-input-74-a6ea700b09d9>:1: SyntaxWarning: import * only allowed at module level
|
||||
def import_yin():
|
||||
|
||||
|
||||
... and there we are.
|
||||
|
||||
|
||||
|
|
@ -678,74 +584,30 @@ dup = yin_dict['dup']
|
|||
print compile_yinyang('mul_', (names(), (names(), (mul, ()))))
|
||||
```
|
||||
|
||||
def mul_(stack):
|
||||
(a31, (a32, stack)) = stack
|
||||
a33 = mul(a32, a31)
|
||||
stack = (a33, stack)
|
||||
return stack
|
||||
|
||||
|
||||
|
||||
|
||||
```python
|
||||
e = (names(), (dup, (mul, ())))
|
||||
print compile_yinyang('sqr', e)
|
||||
```
|
||||
|
||||
def sqr(stack):
|
||||
(a34, stack) = stack
|
||||
a35 = mul(a34, a34)
|
||||
stack = (a35, stack)
|
||||
return stack
|
||||
|
||||
|
||||
|
||||
|
||||
```python
|
||||
e = (names(), (dup, (names(), (sub, (mul, ())))))
|
||||
print compile_yinyang('foo', e)
|
||||
```
|
||||
|
||||
def foo(stack):
|
||||
(a36, (a37, stack)) = stack
|
||||
a38 = sub(a37, a36)
|
||||
a39 = mul(a38, a36)
|
||||
stack = (a39, stack)
|
||||
return stack
|
||||
|
||||
|
||||
|
||||
|
||||
```python
|
||||
e = (names(), (names(), (mul, (dup, (sub, (dup, ()))))))
|
||||
print compile_yinyang('bar', e)
|
||||
```
|
||||
|
||||
def bar(stack):
|
||||
(a40, (a41, stack)) = stack
|
||||
a42 = mul(a41, a40)
|
||||
a43 = sub(a42, a42)
|
||||
stack = (a43, (a43, stack))
|
||||
return stack
|
||||
|
||||
|
||||
|
||||
|
||||
```python
|
||||
e = (names(), (dup, (dup, (mul, (dup, (mul, (mul, ())))))))
|
||||
print compile_yinyang('to_the_fifth_power', e)
|
||||
```
|
||||
|
||||
def to_the_fifth_power(stack):
|
||||
(a44, stack) = stack
|
||||
a45 = mul(a44, a44)
|
||||
a46 = mul(a45, a45)
|
||||
a47 = mul(a46, a44)
|
||||
stack = (a47, stack)
|
||||
return stack
|
||||
|
||||
|
||||
|
||||
|
||||
```python
|
||||
|
||||
|
|
|
|||
|
|
@ -1,4 +1,4 @@
|
|||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
from notebook_preamble import D, J, V, define
|
||||
|
||||
|
|
@ -9,20 +9,20 @@ Given a Joy program like:
|
|||
|
||||
::
|
||||
|
||||
sqr == dup mul
|
||||
sqr == dup mul
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
V('23 sqr')
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
. 23 sqr
|
||||
23 . sqr
|
||||
23 . dup mul
|
||||
23 23 . mul
|
||||
529 .
|
||||
• 23 sqr
|
||||
23 • sqr
|
||||
23 • dup mul
|
||||
23 23 • mul
|
||||
529 •
|
||||
|
||||
|
||||
How would we go about compiling this code (to Python for now)?
|
||||
|
|
@ -32,36 +32,36 @@ Naive Call Chaining
|
|||
|
||||
The simplest thing would be to compose the functions from the library:
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
dup, mul = D['dup'], D['mul']
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
def sqr(stack, expression, dictionary):
|
||||
return mul(*dup(stack, expression, dictionary))
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
old_sqr = D['sqr']
|
||||
D['sqr'] = sqr
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
V('23 sqr')
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
. 23 sqr
|
||||
23 . sqr
|
||||
529 .
|
||||
• 23 sqr
|
||||
23 • sqr
|
||||
529 •
|
||||
|
||||
|
||||
It’s simple to write a function to emit this kind of crude “compiled”
|
||||
It's simple to write a function to emit this kind of crude "compiled"
|
||||
code.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
def compile_joy(name, expression):
|
||||
term, expression = expression
|
||||
|
|
@ -80,9 +80,9 @@ code.
|
|||
return compile_joy(defi.name, defi.body)
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
print compile_joy_definition(old_sqr)
|
||||
print(compile_joy_definition(old_sqr))
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
|
@ -96,13 +96,13 @@ But what about literals?
|
|||
|
||||
::
|
||||
|
||||
quoted == [unit] dip
|
||||
quoted == [unit] dip
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
unit, dip = D['unit'], D['dip']
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
# print compile_joy_definition(D['quoted'])
|
||||
# raises
|
||||
|
|
@ -111,7 +111,7 @@ But what about literals?
|
|||
For a program like ``foo == bar baz 23 99 baq lerp barp`` we would want
|
||||
something like:
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
def foo(stack, expression, dictionary):
|
||||
stack, expression, dictionary = baz(*bar(stack, expression, dictionary))
|
||||
|
|
@ -126,95 +126,93 @@ Compiling Yin Functions
|
|||
|
||||
Call-chaining results in code that does too much work. For functions
|
||||
that operate on stacks and only rearrange values, what I like to call
|
||||
“Yin Functions”, we can do better.
|
||||
"Yin Functions", we can do better.
|
||||
|
||||
We can infer the stack effects of these functions (or “expressions” or
|
||||
“programs”) automatically, and the stack effects completely define the
|
||||
We can infer the stack effects of these functions (or "expressions" or
|
||||
"programs") automatically, and the stack effects completely define the
|
||||
semantics of the functions, so we can directly write out a two-line
|
||||
Python function for them. This is already implemented in the
|
||||
``joy.utils.types.compile_()`` function.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
from joy.utils.types import compile_, doc_from_stack_effect, infer_string
|
||||
from joy.library import SimpleFunctionWrapper
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
::
|
||||
|
||||
|
||||
---------------------------------------------------------------------------
|
||||
|
||||
ModuleNotFoundError Traceback (most recent call last)
|
||||
|
||||
<ipython-input-14-d5ef3c7560be> in <module>
|
||||
----> 1 from joy.utils.types import compile_, doc_from_stack_effect, infer_string
|
||||
2 from joy.library import SimpleFunctionWrapper
|
||||
|
||||
|
||||
ModuleNotFoundError: No module named 'joy.utils.types'
|
||||
|
||||
|
||||
.. code:: ipython3
|
||||
|
||||
stack_effects = infer_string('tuck over dup')
|
||||
|
||||
Yin functions have only a single stack effect, they do not branch or
|
||||
loop.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
for fi, fo in stack_effects:
|
||||
print doc_from_stack_effect(fi, fo)
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(a2 a1 -- a1 a2 a1 a2 a2)
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
source = compile_('foo', stack_effects[0])
|
||||
|
||||
All Yin functions can be described in Python as a tuple-unpacking (or
|
||||
“-destructuring”) of the stack datastructure followed by building up the
|
||||
"-destructuring") of the stack datastructure followed by building up the
|
||||
new stack structure.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
print source
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
def foo(stack):
|
||||
"""
|
||||
::
|
||||
|
||||
(a2 a1 -- a1 a2 a1 a2 a2)
|
||||
|
||||
"""
|
||||
(a1, (a2, s1)) = stack
|
||||
return (a2, (a2, (a1, (a2, (a1, s1)))))
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
exec compile(source, '__main__', 'single')
|
||||
|
||||
D['foo'] = SimpleFunctionWrapper(foo)
|
||||
|
||||
.. code:: ipython2
|
||||
|
||||
::
|
||||
|
||||
|
||||
File "<ipython-input-9-1a7e90bf2d7b>", line 1
|
||||
exec compile(source, '__main__', 'single')
|
||||
^
|
||||
SyntaxError: invalid syntax
|
||||
|
||||
|
||||
|
||||
.. code:: ipython3
|
||||
|
||||
V('23 18 foo')
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
. 23 18 foo
|
||||
23 . 18 foo
|
||||
23 18 . foo
|
||||
18 23 18 23 23 .
|
||||
|
||||
|
||||
Compiling from Stack Effects
|
||||
----------------------------
|
||||
|
||||
There are times when you’re deriving a Joy program when you have a stack
|
||||
There are times when you're deriving a Joy program when you have a stack
|
||||
effect for a Yin function and you need to define it. For example, in the
|
||||
Ordered Binary Trees notebook there is a point where we must derive a
|
||||
function ``Ee``:
|
||||
|
||||
::
|
||||
|
||||
[key old_value left right] new_value key [Tree-add] Ee
|
||||
------------------------------------------------------------
|
||||
[key new_value left right]
|
||||
[key old_value left right] new_value key [Tree-add] Ee
|
||||
------------------------------------------------------------
|
||||
[key new_value left right]
|
||||
|
||||
While it is not hard to come up with this function manually, there is no
|
||||
necessity. This function can be defined (in Python) directly from its
|
||||
|
|
@ -222,18 +220,18 @@ stack effect:
|
|||
|
||||
::
|
||||
|
||||
[a b c d] e a [f] Ee
|
||||
--------------------------
|
||||
[a e c d]
|
||||
[a b c d] e a [f] Ee
|
||||
--------------------------
|
||||
[a e c d]
|
||||
|
||||
(I haven’t yet implemented a simple interface for this yet. What follow
|
||||
(I haven't yet implemented a simple interface for this yet. What follow
|
||||
is an exploration of how to do it.)
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
from joy.parser import text_to_expression
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
Ein = '[a b c d] e a [f]' # The terms should be reversed here but I don't realize that until later.
|
||||
Eout = '[a e c d]'
|
||||
|
|
@ -241,31 +239,15 @@ is an exploration of how to do it.)
|
|||
|
||||
print E
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
[[a b c d] e a [f]] [[a e c d]]
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
(fi, (fo, _)) = text_to_expression(E)
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
fi, fo
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(((a, (b, (c, (d, ())))), (e, (a, ((f, ()), ())))),
|
||||
((a, (e, (c, (d, ())))), ()))
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
Ein = '[a1 a2 a3 a4] a5 a6 a7'
|
||||
Eout = '[a1 a5 a3 a4]'
|
||||
|
|
@ -273,31 +255,15 @@ is an exploration of how to do it.)
|
|||
|
||||
print E
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
[[a1 a2 a3 a4] a5 a6 a7] [[a1 a5 a3 a4]]
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
(fi, (fo, _)) = text_to_expression(E)
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
fi, fo
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(((a1, (a2, (a3, (a4, ())))), (a5, (a6, (a7, ())))),
|
||||
((a1, (a5, (a3, (a4, ())))), ()))
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
def type_vars():
|
||||
from joy.library import a1, a2, a3, a4, a5, a6, a7, s0, s1
|
||||
|
|
@ -306,174 +272,88 @@ is an exploration of how to do it.)
|
|||
tv = type_vars()
|
||||
tv
|
||||
|
||||
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
{'a1': a1,
|
||||
'a2': a2,
|
||||
'a3': a3,
|
||||
'a4': a4,
|
||||
'a5': a5,
|
||||
'a6': a6,
|
||||
'a7': a7,
|
||||
's0': s0,
|
||||
's1': s1}
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
from joy.utils.types import reify
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
stack_effect = reify(tv, (fi, fo))
|
||||
print doc_from_stack_effect(*stack_effect)
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(... a7 a6 a5 [a1 a2 a3 a4 ] -- ... [a1 a5 a3 a4 ])
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
print stack_effect
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(((a1, (a2, (a3, (a4, ())))), (a5, (a6, (a7, ())))), ((a1, (a5, (a3, (a4, ())))), ()))
|
||||
|
||||
|
||||
Almost, but what we really want is something like this:
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
stack_effect = eval('(((a1, (a2, (a3, (a4, s1)))), (a5, (a6, (a7, s0)))), ((a1, (a5, (a3, (a4, s1)))), s0))', tv)
|
||||
|
||||
Note the change of ``()`` to ``JoyStackType`` type variables.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
print doc_from_stack_effect(*stack_effect)
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(a7 a6 a5 [a1 a2 a3 a4 ...1] -- [a1 a5 a3 a4 ...1])
|
||||
|
||||
|
||||
Now we can omit ``a3`` and ``a4`` if we like:
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
stack_effect = eval('(((a1, (a2, s1)), (a5, (a6, (a7, s0)))), ((a1, (a5, s1)), s0))', tv)
|
||||
|
||||
The ``right`` and ``left`` parts of the ordered binary tree node are
|
||||
subsumed in the tail of the node’s stack/list.
|
||||
subsumed in the tail of the node's stack/list.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
print doc_from_stack_effect(*stack_effect)
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(a7 a6 a5 [a1 a2 ...1] -- [a1 a5 ...1])
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
source = compile_('Ee', stack_effect)
|
||||
print source
|
||||
|
||||
Oops! The input stack is backwards...
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
def Ee(stack):
|
||||
"""
|
||||
::
|
||||
|
||||
(a7 a6 a5 [a1 a2 ...1] -- [a1 a5 ...1])
|
||||
|
||||
"""
|
||||
((a1, (a2, s1)), (a5, (a6, (a7, s0)))) = stack
|
||||
return ((a1, (a5, s1)), s0)
|
||||
|
||||
|
||||
Oops! The input stack is backwards…
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
stack_effect = eval('((a7, (a6, (a5, ((a1, (a2, s1)), s0)))), ((a1, (a5, s1)), s0))', tv)
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
print doc_from_stack_effect(*stack_effect)
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
([a1 a2 ...1] a5 a6 a7 -- [a1 a5 ...1])
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
source = compile_('Ee', stack_effect)
|
||||
print source
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
def Ee(stack):
|
||||
"""
|
||||
::
|
||||
|
||||
([a1 a2 ...1] a5 a6 a7 -- [a1 a5 ...1])
|
||||
|
||||
"""
|
||||
(a7, (a6, (a5, ((a1, (a2, s1)), s0)))) = stack
|
||||
return ((a1, (a5, s1)), s0)
|
||||
|
||||
|
||||
Compare:
|
||||
|
||||
::
|
||||
|
||||
[key old_value left right] new_value key [Tree-add] Ee
|
||||
------------------------------------------------------------
|
||||
[key new_value left right]
|
||||
[key old_value left right] new_value key [Tree-add] Ee
|
||||
------------------------------------------------------------
|
||||
[key new_value left right]
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
eval(compile(source, '__main__', 'single'))
|
||||
D['Ee'] = SimpleFunctionWrapper(Ee)
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
V('[a b c d] 1 2 [f] Ee')
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
. [a b c d] 1 2 [f] Ee
|
||||
[a b c d] . 1 2 [f] Ee
|
||||
[a b c d] 1 . 2 [f] Ee
|
||||
[a b c d] 1 2 . [f] Ee
|
||||
[a b c d] 1 2 [f] . Ee
|
||||
[a 1 c d] .
|
||||
|
||||
|
||||
|
||||
Working with Yang Functions
|
||||
---------------------------
|
||||
|
||||
Consider the compiled code of ``dup``:
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
|
||||
def dup(stack):
|
||||
|
|
@ -484,21 +364,15 @@ Consider the compiled code of ``dup``:
|
|||
|
||||
To compile ``sqr == dup mul`` we can compute the stack effect:
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
stack_effects = infer_string('dup mul')
|
||||
for fi, fo in stack_effects:
|
||||
print doc_from_stack_effect(fi, fo)
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(n1 -- n2)
|
||||
|
||||
|
||||
Then we would want something like this:
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
|
||||
def sqr(stack):
|
||||
|
|
@ -510,21 +384,15 @@ Then we would want something like this:
|
|||
|
||||
|
||||
|
||||
How about…
|
||||
How about...
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
stack_effects = infer_string('mul mul sub')
|
||||
for fi, fo in stack_effects:
|
||||
print doc_from_stack_effect(fi, fo)
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(n4 n3 n2 n1 -- n5)
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
|
||||
def foo(stack):
|
||||
|
|
@ -545,30 +413,24 @@ How about…
|
|||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
stack_effects = infer_string('tuck')
|
||||
for fi, fo in stack_effects:
|
||||
print doc_from_stack_effect(fi, fo)
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
(a2 a1 -- a1 a2 a1)
|
||||
|
||||
|
||||
|
||||
Compiling Yin~Yang Functions
|
||||
----------------------------
|
||||
|
||||
First, we need a source of Python identifiers. I’m going to reuse
|
||||
First, we need a source of Python identifiers. I'm going to reuse
|
||||
``Symbol`` class for this.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
from joy.parser import Symbol
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
def _names():
|
||||
n = 0
|
||||
|
|
@ -579,9 +441,9 @@ First, we need a source of Python identifiers. I’m going to reuse
|
|||
names = _names().next
|
||||
|
||||
Now we need an object that represents a Yang function that accepts two
|
||||
args and return one result (we’ll implement other kinds a little later.)
|
||||
args and return one result (we'll implement other kinds a little later.)
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
class Foo(object):
|
||||
|
||||
|
|
@ -594,10 +456,10 @@ args and return one result (we’ll implement other kinds a little later.)
|
|||
code.append(('call', out, self.name, (in0, in1)))
|
||||
return (out, stack), expression, code
|
||||
|
||||
A crude “interpreter” that translates expressions of args and Yin and
|
||||
A crude "interpreter" that translates expressions of args and Yin and
|
||||
Yang functions into a kind of simple dataflow graph.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
def I(stack, expression, code):
|
||||
while expression:
|
||||
|
|
@ -618,7 +480,7 @@ Yang functions into a kind of simple dataflow graph.
|
|||
|
||||
Something to convert the graph into Python code.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
strtup = lambda a, b: '(%s, %s)' % (b, a)
|
||||
strstk = lambda rest: reduce(strtup, rest, 'stack')
|
||||
|
|
@ -676,14 +538,14 @@ Something to convert the graph into Python code.
|
|||
''' % (name, code_gen(I((), expression, [])))
|
||||
|
||||
|
||||
A few functions to try it with…
|
||||
A few functions to try it with...
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
mul = Foo('mul')
|
||||
sub = Foo('sub')
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
def import_yin():
|
||||
from joy.utils.generated_library import *
|
||||
|
|
@ -699,98 +561,32 @@ A few functions to try it with…
|
|||
# n, stack = stack
|
||||
# return (n, (n, stack)), expression
|
||||
|
||||
... and there we are.
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
<ipython-input-74-a6ea700b09d9>:1: SyntaxWarning: import * only allowed at module level
|
||||
def import_yin():
|
||||
|
||||
|
||||
… and there we are.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
print compile_yinyang('mul_', (names(), (names(), (mul, ()))))
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
def mul_(stack):
|
||||
(a31, (a32, stack)) = stack
|
||||
a33 = mul(a32, a31)
|
||||
stack = (a33, stack)
|
||||
return stack
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
e = (names(), (dup, (mul, ())))
|
||||
print compile_yinyang('sqr', e)
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
def sqr(stack):
|
||||
(a34, stack) = stack
|
||||
a35 = mul(a34, a34)
|
||||
stack = (a35, stack)
|
||||
return stack
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
e = (names(), (dup, (names(), (sub, (mul, ())))))
|
||||
print compile_yinyang('foo', e)
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
def foo(stack):
|
||||
(a36, (a37, stack)) = stack
|
||||
a38 = sub(a37, a36)
|
||||
a39 = mul(a38, a36)
|
||||
stack = (a39, stack)
|
||||
return stack
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
e = (names(), (names(), (mul, (dup, (sub, (dup, ()))))))
|
||||
print compile_yinyang('bar', e)
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
def bar(stack):
|
||||
(a40, (a41, stack)) = stack
|
||||
a42 = mul(a41, a40)
|
||||
a43 = sub(a42, a42)
|
||||
stack = (a43, (a43, stack))
|
||||
return stack
|
||||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
e = (names(), (dup, (dup, (mul, (dup, (mul, (mul, ())))))))
|
||||
print compile_yinyang('to_the_fifth_power', e)
|
||||
|
||||
|
||||
.. parsed-literal::
|
||||
|
||||
def to_the_fifth_power(stack):
|
||||
(a44, stack) = stack
|
||||
a45 = mul(a44, a44)
|
||||
a46 = mul(a45, a45)
|
||||
a47 = mul(a46, a44)
|
||||
stack = (a47, stack)
|
||||
return stack
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -13088,7 +13088,7 @@ div#notebook {
|
|||
<div class="prompt input_prompt">In [1]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13167,7 +13167,7 @@ n+1 2 /
|
|||
<div class="prompt input_prompt">In [2]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'gsra == 1 swap [over / + 2 /] cons [dup] swoncat make_generator'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13180,7 +13180,7 @@ n+1 2 /
|
|||
<div class="prompt input_prompt">In [3]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 gsra'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 gsra'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13219,7 +13219,7 @@ n+1 2 /
|
|||
<div class="prompt input_prompt">In [4]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 gsra 6 [x popd] times first sqr'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 gsra 6 [x popd] times first sqr'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13285,7 +13285,7 @@ abs(a-b) ε <=
|
|||
<div class="prompt input_prompt">In [5]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_P == [first - abs] dip <='</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_P [first - abs] dip <='</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13310,7 +13310,7 @@ abs(a-b) ε <=
|
|||
<div class="prompt input_prompt">In [6]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_B == roll< popop first'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_B roll< popop first'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13328,7 +13328,7 @@ abs(a-b) ε <=
|
|||
<ol>
|
||||
<li>Discard a.</li>
|
||||
<li>Use <code>x</code> combinator to generate next term from <code>G</code>.</li>
|
||||
<li>Run <code>within</code> with <code>i</code> (it is a <code>primrec</code> function.)</li>
|
||||
<li>Run <code>within</code> with <code>i</code> (it is a "tail-recursive" function.)</li>
|
||||
</ol>
|
||||
<p>Pretty straightforward:</p>
|
||||
|
||||
|
|
@ -13349,7 +13349,7 @@ b [c G] ε within</code></pre>
|
|||
<div class="prompt input_prompt">In [7]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_R == [popd x] dip'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_R [popd x] dip'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13373,8 +13373,8 @@ a [b G] ε ...</code></pre>
|
|||
<div class="prompt input_prompt">In [8]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'within == x 0.000000001 [_within_P] [_within_B] [_within_R] primrec'</span><span class="p">)</span>
|
||||
<span class="n">define</span><span class="p">(</span><span class="s1">'sqrt == gsra within'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'within x 0.000000001 [_within_P] [_within_B] [_within_R] tailrec'</span><span class="p">)</span>
|
||||
<span class="n">define</span><span class="p">(</span><span class="s1">'sqrt gsra within'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13395,7 +13395,7 @@ a [b G] ε ...</code></pre>
|
|||
<div class="prompt input_prompt">In [9]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'36 sqrt'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'36 sqrt'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13426,7 +13426,7 @@ a [b G] ε ...</code></pre>
|
|||
<div class="prompt input_prompt">In [10]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 sqrt'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 sqrt'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13465,7 +13465,7 @@ a [b G] ε ...</code></pre>
|
|||
<div class="prompt input_prompt">In [11]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="mf">4.795831523312719</span><span class="o">**</span><span class="mi">2</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="mf">4.795831523312719</span><span class="o">**</span><span class="mi">2</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13498,7 +13498,7 @@ a [b G] ε ...</code></pre>
|
|||
<div class="prompt input_prompt">In [12]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">sqrt</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">sqrt</span>
|
||||
|
||||
<span class="n">sqrt</span><span class="p">(</span><span class="mi">23</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
|
|
|||
|
|
@ -55,7 +55,7 @@ The generator can be written as:
|
|||
|
||||
|
||||
```python
|
||||
define('gsra == 1 swap [over / + 2 /] cons [dup] swoncat make_generator')
|
||||
define('gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator')
|
||||
```
|
||||
|
||||
|
||||
|
|
@ -109,7 +109,7 @@ Using the _output_ `[a G]` of the above generator for square root approximations
|
|||
|
||||
|
||||
```python
|
||||
define('_within_P == [first - abs] dip <=')
|
||||
define('_within_P [first - abs] dip <=')
|
||||
```
|
||||
|
||||
### Base-Case
|
||||
|
|
@ -121,7 +121,7 @@ define('_within_P == [first - abs] dip <=')
|
|||
|
||||
|
||||
```python
|
||||
define('_within_B == roll< popop first')
|
||||
define('_within_B roll< popop first')
|
||||
```
|
||||
|
||||
### Recur
|
||||
|
|
@ -130,7 +130,7 @@ define('_within_B == roll< popop first')
|
|||
|
||||
1. Discard a.
|
||||
2. Use `x` combinator to generate next term from `G`.
|
||||
3. Run `within` with `i` (it is a `primrec` function.)
|
||||
3. Run `within` with `i` (it is a "tail-recursive" function.)
|
||||
|
||||
Pretty straightforward:
|
||||
|
||||
|
|
@ -145,7 +145,7 @@ Pretty straightforward:
|
|||
|
||||
|
||||
```python
|
||||
define('_within_R == [popd x] dip')
|
||||
define('_within_R [popd x] dip')
|
||||
```
|
||||
|
||||
### Setting up
|
||||
|
|
@ -157,8 +157,8 @@ The recursive function we have defined so far needs a slight preamble: `x` to pr
|
|||
|
||||
|
||||
```python
|
||||
define('within == x 0.000000001 [_within_P] [_within_B] [_within_R] primrec')
|
||||
define('sqrt == gsra within')
|
||||
define('within x 0.000000001 [_within_P] [_within_B] [_within_R] tailrec')
|
||||
define('sqrt gsra within')
|
||||
```
|
||||
|
||||
Try it out...
|
||||
|
|
|
|||
|
|
@ -1,13 +1,13 @@
|
|||
`Newton’s method <https://en.wikipedia.org/wiki/Newton%27s_method>`__
|
||||
`Newton's method <https://en.wikipedia.org/wiki/Newton%27s_method>`__
|
||||
=====================================================================
|
||||
|
||||
Let’s use the Newton-Raphson method for finding the root of an equation
|
||||
Let's use the Newton-Raphson method for finding the root of an equation
|
||||
to write a function that can compute the square root of a number.
|
||||
|
||||
Cf. `“Why Functional Programming Matters” by John
|
||||
Cf. `"Why Functional Programming Matters" by John
|
||||
Hughes <https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf>`__
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
from notebook_preamble import J, V, define
|
||||
|
||||
|
|
@ -20,9 +20,9 @@ computes the next approximation:
|
|||
|
||||
::
|
||||
|
||||
a F
|
||||
---------
|
||||
a'
|
||||
a F
|
||||
---------
|
||||
a'
|
||||
|
||||
A Function to Compute the Next Approximation
|
||||
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
|
@ -34,17 +34,17 @@ square root:
|
|||
|
||||
::
|
||||
|
||||
a n over / + 2 /
|
||||
a n a / + 2 /
|
||||
a n/a + 2 /
|
||||
a+n/a 2 /
|
||||
(a+n/a)/2
|
||||
a n over / + 2 /
|
||||
a n a / + 2 /
|
||||
a n/a + 2 /
|
||||
a+n/a 2 /
|
||||
(a+n/a)/2
|
||||
|
||||
The function we want has the argument ``n`` in it:
|
||||
|
||||
::
|
||||
|
||||
F == n over / + 2 /
|
||||
F == n over / + 2 /
|
||||
|
||||
Make it into a Generator
|
||||
~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
|
@ -53,33 +53,33 @@ Our generator would be created by:
|
|||
|
||||
::
|
||||
|
||||
a [dup F] make_generator
|
||||
a [dup F] make_generator
|
||||
|
||||
With n as part of the function F, but n is the input to the sqrt
|
||||
function we’re writing. If we let 1 be the initial approximation:
|
||||
|
||||
::
|
||||
|
||||
1 n 1 / + 2 /
|
||||
1 n/1 + 2 /
|
||||
1 n + 2 /
|
||||
n+1 2 /
|
||||
(n+1)/2
|
||||
1 n 1 / + 2 /
|
||||
1 n/1 + 2 /
|
||||
1 n + 2 /
|
||||
n+1 2 /
|
||||
(n+1)/2
|
||||
|
||||
The generator can be written as:
|
||||
|
||||
::
|
||||
|
||||
23 1 swap [over / + 2 /] cons [dup] swoncat make_generator
|
||||
1 23 [over / + 2 /] cons [dup] swoncat make_generator
|
||||
1 [23 over / + 2 /] [dup] swoncat make_generator
|
||||
1 [dup 23 over / + 2 /] make_generator
|
||||
23 1 swap [over / + 2 /] cons [dup] swoncat make_generator
|
||||
1 23 [over / + 2 /] cons [dup] swoncat make_generator
|
||||
1 [23 over / + 2 /] [dup] swoncat make_generator
|
||||
1 [dup 23 over / + 2 /] make_generator
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('gsra == 1 swap [over / + 2 /] cons [dup] swoncat make_generator')
|
||||
define('gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator')
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('23 gsra')
|
||||
|
||||
|
|
@ -89,10 +89,10 @@ The generator can be written as:
|
|||
[1 [dup 23 over / + 2 /] codireco]
|
||||
|
||||
|
||||
Let’s drive the generator a few time (with the ``x`` combinator) and
|
||||
square the approximation to see how well it works…
|
||||
Let's drive the generator a few time (with the ``x`` combinator) and
|
||||
square the approximation to see how well it works...
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('23 gsra 6 [x popd] times first sqr')
|
||||
|
||||
|
|
@ -105,88 +105,88 @@ square the approximation to see how well it works…
|
|||
Finding Consecutive Approximations within a Tolerance
|
||||
-----------------------------------------------------
|
||||
|
||||
From `“Why Functional Programming Matters” by John
|
||||
From `"Why Functional Programming Matters" by John
|
||||
Hughes <https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf>`__:
|
||||
|
||||
The remainder of a square root finder is a function *within*, which
|
||||
takes a tolerance and a list of approximations and looks down the
|
||||
list for two successive approximations that differ by no more than
|
||||
the given tolerance.
|
||||
The remainder of a square root finder is a function *within*, which
|
||||
takes a tolerance and a list of approximations and looks down the
|
||||
list for two successive approximations that differ by no more than
|
||||
the given tolerance.
|
||||
|
||||
(And note that by “list” he means a lazily-evaluated list.)
|
||||
|
||||
Using the *output* ``[a G]`` of the above generator for square root
|
||||
approximations, and further assuming that the first term a has been
|
||||
generated already and epsilon ε is handy on the stack…
|
||||
generated already and epsilon ε is handy on the stack...
|
||||
|
||||
::
|
||||
|
||||
a [b G] ε within
|
||||
---------------------- a b - abs ε <=
|
||||
b
|
||||
a [b G] ε within
|
||||
---------------------- a b - abs ε <=
|
||||
b
|
||||
|
||||
|
||||
a [b G] ε within
|
||||
---------------------- a b - abs ε >
|
||||
b [c G] ε within
|
||||
a [b G] ε within
|
||||
---------------------- a b - abs ε >
|
||||
b [c G] ε within
|
||||
|
||||
Predicate
|
||||
~~~~~~~~~
|
||||
|
||||
::
|
||||
|
||||
a [b G] ε [first - abs] dip <=
|
||||
a [b G] first - abs ε <=
|
||||
a b - abs ε <=
|
||||
a-b abs ε <=
|
||||
abs(a-b) ε <=
|
||||
(abs(a-b)<=ε)
|
||||
a [b G] ε [first - abs] dip <=
|
||||
a [b G] first - abs ε <=
|
||||
a b - abs ε <=
|
||||
a-b abs ε <=
|
||||
abs(a-b) ε <=
|
||||
(abs(a-b)<=ε)
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('_within_P == [first - abs] dip <=')
|
||||
define('_within_P [first - abs] dip <=')
|
||||
|
||||
Base-Case
|
||||
~~~~~~~~~
|
||||
|
||||
::
|
||||
|
||||
a [b G] ε roll< popop first
|
||||
[b G] ε a popop first
|
||||
[b G] first
|
||||
b
|
||||
a [b G] ε roll< popop first
|
||||
[b G] ε a popop first
|
||||
[b G] first
|
||||
b
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('_within_B == roll< popop first')
|
||||
define('_within_B roll< popop first')
|
||||
|
||||
Recur
|
||||
~~~~~
|
||||
|
||||
::
|
||||
|
||||
a [b G] ε R0 [within] R1
|
||||
a [b G] ε R0 [within] R1
|
||||
|
||||
1. Discard a.
|
||||
2. Use ``x`` combinator to generate next term from ``G``.
|
||||
3. Run ``within`` with ``i`` (it is a ``primrec`` function.)
|
||||
3. Run ``within`` with ``i`` (it is a "tail-recursive" function.)
|
||||
|
||||
Pretty straightforward:
|
||||
|
||||
::
|
||||
|
||||
a [b G] ε R0 [within] R1
|
||||
a [b G] ε [popd x] dip [within] i
|
||||
a [b G] popd x ε [within] i
|
||||
[b G] x ε [within] i
|
||||
b [c G] ε [within] i
|
||||
b [c G] ε within
|
||||
a [b G] ε R0 [within] R1
|
||||
a [b G] ε [popd x] dip [within] i
|
||||
a [b G] popd x ε [within] i
|
||||
[b G] x ε [within] i
|
||||
b [c G] ε [within] i
|
||||
b [c G] ε within
|
||||
|
||||
b [c G] ε within
|
||||
b [c G] ε within
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('_within_R == [popd x] dip')
|
||||
define('_within_R [popd x] dip')
|
||||
|
||||
Setting up
|
||||
~~~~~~~~~~
|
||||
|
|
@ -196,17 +196,17 @@ The recursive function we have defined so far needs a slight preamble:
|
|||
|
||||
::
|
||||
|
||||
[a G] x ε ...
|
||||
a [b G] ε ...
|
||||
[a G] x ε ...
|
||||
a [b G] ε ...
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('within == x 0.000000001 [_within_P] [_within_B] [_within_R] primrec')
|
||||
define('sqrt == gsra within')
|
||||
define('within x 0.000000001 [_within_P] [_within_B] [_within_R] tailrec')
|
||||
define('sqrt gsra within')
|
||||
|
||||
Try it out…
|
||||
Try it out...
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('36 sqrt')
|
||||
|
||||
|
|
@ -216,7 +216,7 @@ Try it out…
|
|||
6.0
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('23 sqrt')
|
||||
|
||||
|
|
@ -228,7 +228,7 @@ Try it out…
|
|||
|
||||
Check it.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
4.795831523312719**2
|
||||
|
||||
|
|
@ -241,7 +241,7 @@ Check it.
|
|||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
from math import sqrt
|
||||
|
||||
|
|
|
|||
|
|
@ -13076,10 +13076,10 @@ div#notebook {
|
|||
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="prompt input_prompt">In [2]:</div>
|
||||
<div class="prompt input_prompt">In [1]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">DefinitionWrapper</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="kn">import</span> <span class="n">D</span><span class="p">,</span> <span class="n">DefinitionWrapper</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13234,10 +13234,10 @@ scan == [size 1 <=] [pop []] [[[F] infra] dupdip first] [dip swons] genrec</c
|
|||
</div>
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="prompt input_prompt">In [3]:</div>
|
||||
<div class="prompt input_prompt">In [2]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3] [size 1 <=] [pop []] [[[+] infra] dupdip first] [dip swons] genrec'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3] [size 1 <=] [pop []] [[[+] infra] dupdip first] [dip swons] genrec'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13273,10 +13273,10 @@ scan == [size 1 <=] [pop []] [[[F] infra] dupdip first] [dip swons] genrec</c
|
|||
</div>
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="prompt input_prompt">In [4]:</div>
|
||||
<div class="prompt input_prompt">In [3]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3] [size 1 <=] [[]] [[[+] infra] dupdip first] [dip swons] genrec'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3] [size 1 <=] [[]] [[[+] infra] dupdip first] [dip swons] genrec'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13312,10 +13312,10 @@ scan == [size 1 <=] [pop []] [[[F] infra] dupdip first] [dip swons] genrec</c
|
|||
</div>
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="prompt input_prompt">In [5]:</div>
|
||||
<div class="prompt input_prompt">In [4]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3] [size 1 <=] [] [[[+] infra] dupdip first] [dip swons] genrec'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3] [size 1 <=] [] [[[+] infra] dupdip first] [dip swons] genrec'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13366,10 +13366,10 @@ scan == [size 1 <=] [pop []] [[[F] infra] dupdip first] [dip swons] genrec</c
|
|||
</div>
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="prompt input_prompt">In [6]:</div>
|
||||
<div class="prompt input_prompt">In [5]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'scan == [infra] cons [dupdip first] cons [size 1 <=] [] roll< [dip swons] genrec'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'scan [infra] cons [dupdip first] cons [size 1 <=] [] roll< [dip swons] genrec'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13379,10 +13379,10 @@ scan == [size 1 <=] [pop []] [[[F] infra] dupdip first] [dip swons] genrec</c
|
|||
</div>
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="prompt input_prompt">In [7]:</div>
|
||||
<div class="prompt input_prompt">In [6]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3 4] [+] scan'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3 4] [+] scan'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13410,10 +13410,10 @@ scan == [size 1 <=] [pop []] [[[F] infra] dupdip first] [dip swons] genrec</c
|
|||
</div>
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="prompt input_prompt">In [8]:</div>
|
||||
<div class="prompt input_prompt">In [7]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3 4] [*] scan'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3 4] [*] scan'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13441,10 +13441,10 @@ scan == [size 1 <=] [pop []] [[[F] infra] dupdip first] [dip swons] genrec</c
|
|||
</div>
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="prompt input_prompt">In [9]:</div>
|
||||
<div class="prompt input_prompt">In [8]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3 4 5 6 7] [neg +] scan'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'[1 2 3 4 5 6 7] [neg +] scan'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13485,10 +13485,10 @@ scan == [size 1 <=] [pop []] [[[F] infra] dupdip first] [dip swons] genrec</c
|
|||
</div>
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="prompt input_prompt">In [10]:</div>
|
||||
<div class="prompt input_prompt">In [9]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'["hello" "world"] uncons ["</span><span class="se">\n</span><span class="s1">" swap + +] step'</span><span class="p">)</span>
|
||||
<div class=" highlight hl-ipython3"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'["hello" "world"] uncons ["</span><span class="se">\n</span><span class="s1">" swap + +] step'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
|
|
@ -13592,19 +13592,6 @@ Lines == ["\n" in] [unit] [split-at-newline swap] [dip swons] genrec</code></pre
|
|||
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell border-box-sizing code_cell rendered">
|
||||
<div class="input">
|
||||
<div class="prompt input_prompt">In [ ]:</div>
|
||||
<div class="inner_cell">
|
||||
<div class="input_area">
|
||||
<div class=" highlight hl-ipython2"><pre><span></span>
|
||||
</pre></div>
|
||||
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
|
|
|||
|
|
@ -2,7 +2,7 @@
|
|||
"cells": [
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"execution_count": 1,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
|
|
@ -155,7 +155,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 3,
|
||||
"execution_count": 2,
|
||||
"metadata": {
|
||||
"scrolled": false
|
||||
},
|
||||
|
|
@ -181,7 +181,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 4,
|
||||
"execution_count": 3,
|
||||
"metadata": {
|
||||
"scrolled": false
|
||||
},
|
||||
|
|
@ -207,7 +207,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 5,
|
||||
"execution_count": 4,
|
||||
"metadata": {
|
||||
"scrolled": false
|
||||
},
|
||||
|
|
@ -247,16 +247,16 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 6,
|
||||
"execution_count": 5,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"define('scan == [infra] cons [dupdip first] cons [size 1 <=] [] roll< [dip swons] genrec')"
|
||||
"define('scan [infra] cons [dupdip first] cons [size 1 <=] [] roll< [dip swons] genrec')"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 7,
|
||||
"execution_count": 6,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
|
|
@ -273,7 +273,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 8,
|
||||
"execution_count": 7,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
|
|
@ -290,7 +290,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 9,
|
||||
"execution_count": 8,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
|
|
@ -322,7 +322,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 10,
|
||||
"execution_count": 9,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
|
|
@ -410,13 +410,6 @@
|
|||
"To limit `F` to working on pairs of terms from its domain.\n",
|
||||
"\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
|
|
@ -428,14 +421,14 @@
|
|||
"language_info": {
|
||||
"codemirror_mode": {
|
||||
"name": "ipython",
|
||||
"version": 2
|
||||
"version": 3
|
||||
},
|
||||
"file_extension": ".py",
|
||||
"mimetype": "text/x-python",
|
||||
"name": "python",
|
||||
"nbconvert_exporter": "python",
|
||||
"pygments_lexer": "ipython2",
|
||||
"version": "2.7.12"
|
||||
"pygments_lexer": "ipython3",
|
||||
"version": "3.8.3"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
|
|
|||
|
|
@ -137,7 +137,7 @@ And so:
|
|||
|
||||
|
||||
```python
|
||||
define('scan == [infra] cons [dupdip first] cons [size 1 <=] [] roll< [dip swons] genrec')
|
||||
define('scan [infra] cons [dupdip first] cons [size 1 <=] [] roll< [dip swons] genrec')
|
||||
```
|
||||
|
||||
|
||||
|
|
@ -232,8 +232,3 @@ Or:
|
|||
To limit `F` to working on pairs of terms from its domain.
|
||||
|
||||
|
||||
|
||||
|
||||
```python
|
||||
|
||||
```
|
||||
|
|
|
|||
|
|
@ -1,8 +1,8 @@
|
|||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
from notebook_preamble import D, DefinitionWrapper, J, V, define
|
||||
|
||||
On “Two Exercises Found in a Book on Algorithmics”
|
||||
On "Two Exercises Found in a Book on Algorithmics"
|
||||
==================================================
|
||||
|
||||
Bird & Meertens
|
||||
|
|
@ -13,27 +13,25 @@ here <https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.694.2614>`__
|
|||
Define ``scan`` in terms of a reduction.
|
||||
----------------------------------------
|
||||
|
||||
Problem I. The reduction operator ``/`` of APL takes some binary
|
||||
operator ``⨁`` on its left and a vector ``x`` of values on its right.
|
||||
The meaning of ``⨁/x`` for ``x = [a b ... z]`` is the value
|
||||
``a⨁b⨁...⨁z``. For this to be well-defined in the absence of
|
||||
brackets, the operation ``⨁`` has to be associative. Now there is
|
||||
another operator ``\`` of APL called ``scan``. Its effect is closely
|
||||
related to reduction in that we have:
|
||||
Problem I. The reduction operator ``/`` of APL takes some binary
|
||||
operator ``⨁`` on its left and a vector ``x`` of values on its
|
||||
right. The meaning of ``⨁/x`` for ``x = [a b ... z]`` is the value
|
||||
``a⨁b⨁...⨁z``. For this to be well-defined in the absence of
|
||||
brackets, the operation ``⨁`` has to be associative. Now there is
|
||||
another operator ``\`` of APL called ``scan``. Its effect is closely
|
||||
related to reduction in that we have:
|
||||
|
||||
::
|
||||
|
||||
⨁\x = [a a⨁b a⨁b⨁c ... a⨁b⨁...⨁z]
|
||||
⨁\x = [a a⨁b a⨁b⨁c ... a⨁b⨁...⨁z]
|
||||
|
||||
..
|
||||
|
||||
The problem is to find some definition of ``scan`` as a reduction. In
|
||||
other words, we have to find some function ``f`` and an operator
|
||||
``⨂`` so that
|
||||
The problem is to find some definition of ``scan`` as a reduction.
|
||||
In other words, we have to find some function ``f`` and an operator
|
||||
``⨂`` so that
|
||||
|
||||
::
|
||||
|
||||
⨁\x = f(a)⨂f(b)⨂...⨂f(z)
|
||||
⨁\x = f(a)⨂f(b)⨂...⨂f(z)
|
||||
|
||||
Designing the Recursive Function
|
||||
--------------------------------
|
||||
|
|
@ -52,48 +50,48 @@ instead of two (the b is instead the duplicate of a.)
|
|||
|
||||
::
|
||||
|
||||
H3 == [P] [pop c] [[G] dupdip] [dip F] genrec
|
||||
H3 == [P] [pop c] [[G] dupdip] [dip F] genrec
|
||||
|
||||
... a [G] dupdip [H3] dip F
|
||||
... a G a [H3] dip F
|
||||
... a′ a [H3] dip F
|
||||
... a′ H3 a F
|
||||
... a′ [G] dupdip [H3] dip F a F
|
||||
... a′ G a′ [H3] dip F a F
|
||||
... a″ a′ [H3] dip F a F
|
||||
... a″ H3 a′ F a F
|
||||
... a″ [G] dupdip [H3] dip F a′ F a F
|
||||
... a″ G a″ [H3] dip F a′ F a F
|
||||
... a‴ a″ [H3] dip F a′ F a F
|
||||
... a‴ H3 a″ F a′ F a F
|
||||
... a‴ pop c a″ F a′ F a F
|
||||
... c a″ F a′ F a F
|
||||
... d a′ F a F
|
||||
... d′ a F
|
||||
... d″
|
||||
... a [G] dupdip [H3] dip F
|
||||
... a G a [H3] dip F
|
||||
... a′ a [H3] dip F
|
||||
... a′ H3 a F
|
||||
... a′ [G] dupdip [H3] dip F a F
|
||||
... a′ G a′ [H3] dip F a F
|
||||
... a″ a′ [H3] dip F a F
|
||||
... a″ H3 a′ F a F
|
||||
... a″ [G] dupdip [H3] dip F a′ F a F
|
||||
... a″ G a″ [H3] dip F a′ F a F
|
||||
... a‴ a″ [H3] dip F a′ F a F
|
||||
... a‴ H3 a″ F a′ F a F
|
||||
... a‴ pop c a″ F a′ F a F
|
||||
... c a″ F a′ F a F
|
||||
... d a′ F a F
|
||||
... d′ a F
|
||||
... d″
|
||||
|
||||
Initial Definition
|
||||
~~~~~~~~~~~~~~~~~~
|
||||
|
||||
We’re building a list of values so this is an “anamorphism”. (An
|
||||
We're building a list of values so this is an "anamorphism". (An
|
||||
anamorphism uses ``[]`` for ``c`` and ``swons`` for ``F``.)
|
||||
|
||||
::
|
||||
|
||||
scan == [P] [pop []] [[G] dupdip] [dip swons] genrec
|
||||
scan == [P] [pop []] [[G] dupdip] [dip swons] genrec
|
||||
|
||||
Convert to ``ifte``:
|
||||
|
||||
::
|
||||
|
||||
scan == [P] [pop []] [[G] dupdip [scan] dip swons] ifte
|
||||
scan == [P] [pop []] [[G] dupdip [scan] dip swons] ifte
|
||||
|
||||
On the recursive branch ``[G] dupdip`` doesn’t cut it:
|
||||
On the recursive branch ``[G] dupdip`` doesn't cut it:
|
||||
|
||||
::
|
||||
|
||||
[1 2 3] [G] dupdip [scan] dip swons
|
||||
[1 2 3] G [1 2 3] [scan] dip swons
|
||||
[1 2 3] [G] dupdip [scan] dip swons
|
||||
[1 2 3] G [1 2 3] [scan] dip swons
|
||||
|
||||
Use ``first``
|
||||
~~~~~~~~~~~~~
|
||||
|
|
@ -103,11 +101,11 @@ use ``first``.
|
|||
|
||||
::
|
||||
|
||||
scan == [P] [pop []] [[G] dupdip first] [dip swons] genrec
|
||||
scan == [P] [pop []] [[G] dupdip first] [dip swons] genrec
|
||||
|
||||
[1 2 3] [G] dupdip first [scan] dip swons
|
||||
[1 2 3] G [1 2 3] first [scan] dip swons
|
||||
[1 2 3] G 1 [scan] dip swons
|
||||
[1 2 3] [G] dupdip first [scan] dip swons
|
||||
[1 2 3] G [1 2 3] first [scan] dip swons
|
||||
[1 2 3] G 1 [scan] dip swons
|
||||
|
||||
``G`` applies ``⨁``
|
||||
~~~~~~~~~~~~~~~~~~~
|
||||
|
|
@ -117,10 +115,10 @@ in the list.
|
|||
|
||||
::
|
||||
|
||||
[1 2 3] G
|
||||
[1 2 3] [⨁] infra
|
||||
[1 2 3] [+] infra
|
||||
[3 3]
|
||||
[1 2 3] G
|
||||
[1 2 3] [⨁] infra
|
||||
[1 2 3] [+] infra
|
||||
[3 3]
|
||||
|
||||
Predicate ``P``
|
||||
~~~~~~~~~~~~~~~
|
||||
|
|
@ -130,21 +128,21 @@ less that two items in them:
|
|||
|
||||
::
|
||||
|
||||
P == size 1 <=
|
||||
P == size 1 <=
|
||||
|
||||
Let’s see what we’ve got so far:
|
||||
Let's see what we've got so far:
|
||||
|
||||
::
|
||||
|
||||
scan == [P ] [pop []] [[G] dupdip first] [dip swons] genrec
|
||||
scan == [size 1 <=] [pop []] [[[F] infra] dupdip first] [dip swons] genrec
|
||||
scan == [P ] [pop []] [[G] dupdip first] [dip swons] genrec
|
||||
scan == [size 1 <=] [pop []] [[[F] infra] dupdip first] [dip swons] genrec
|
||||
|
||||
Handling the Last Term
|
||||
~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
This works to a point, but it throws away the last term:
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[1 2 3] [size 1 <=] [pop []] [[[+] infra] dupdip first] [dip swons] genrec')
|
||||
|
||||
|
|
@ -154,9 +152,9 @@ This works to a point, but it throws away the last term:
|
|||
[1 3]
|
||||
|
||||
|
||||
Hmm… Let’s take out the ``pop`` for a sec…
|
||||
Hmm... Let's take out the ``pop`` for a sec...
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[1 2 3] [size 1 <=] [[]] [[[+] infra] dupdip first] [dip swons] genrec')
|
||||
|
||||
|
|
@ -167,11 +165,11 @@ Hmm… Let’s take out the ``pop`` for a sec…
|
|||
|
||||
|
||||
That leaves the last item in our list, then it puts an empty list on the
|
||||
stack and ``swons``\ ’s the new terms onto that. If we leave out that
|
||||
empty list, they will be ``swons``\ ’d onto that list that already has
|
||||
the last item.
|
||||
stack and ``swons``'s the new terms onto that. If we leave out that
|
||||
empty list, they will be ``swons``'d onto that list that already has the
|
||||
last item.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[1 2 3] [size 1 <=] [] [[[+] infra] dupdip first] [dip swons] genrec')
|
||||
|
||||
|
|
@ -188,28 +186,28 @@ So we have:
|
|||
|
||||
::
|
||||
|
||||
[⨁] scan == [size 1 <=] [] [[[⨁] infra] dupdip first] [dip swons] genrec
|
||||
[⨁] scan == [size 1 <=] [] [[[⨁] infra] dupdip first] [dip swons] genrec
|
||||
|
||||
Trivially:
|
||||
|
||||
::
|
||||
|
||||
== [size 1 <=] [] [[[⨁] infra] dupdip first] [dip swons] genrec
|
||||
== [[[⨁] infra] dupdip first] [size 1 <=] [] roll< [dip swons] genrec
|
||||
== [[⨁] infra] [dupdip first] cons [size 1 <=] [] roll< [dip swons] genrec
|
||||
== [⨁] [infra] cons [dupdip first] cons [size 1 <=] [] roll< [dip swons] genrec
|
||||
== [size 1 <=] [] [[[⨁] infra] dupdip first] [dip swons] genrec
|
||||
== [[[⨁] infra] dupdip first] [size 1 <=] [] roll< [dip swons] genrec
|
||||
== [[⨁] infra] [dupdip first] cons [size 1 <=] [] roll< [dip swons] genrec
|
||||
== [⨁] [infra] cons [dupdip first] cons [size 1 <=] [] roll< [dip swons] genrec
|
||||
|
||||
And so:
|
||||
|
||||
::
|
||||
|
||||
scan == [infra] cons [dupdip first] cons [size 1 <=] [] roll< [dip swons] genrec
|
||||
scan == [infra] cons [dupdip first] cons [size 1 <=] [] roll< [dip swons] genrec
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('scan == [infra] cons [dupdip first] cons [size 1 <=] [] roll< [dip swons] genrec')
|
||||
define('scan [infra] cons [dupdip first] cons [size 1 <=] [] roll< [dip swons] genrec')
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[1 2 3 4] [+] scan')
|
||||
|
||||
|
|
@ -219,7 +217,7 @@ And so:
|
|||
[1 3 6 10]
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[1 2 3 4] [*] scan')
|
||||
|
||||
|
|
@ -229,7 +227,7 @@ And so:
|
|||
[1 2 6 24]
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('[1 2 3 4 5 6 7] [neg +] scan')
|
||||
|
||||
|
|
@ -242,24 +240,24 @@ And so:
|
|||
Problem 2.
|
||||
----------
|
||||
|
||||
Define a line to be a sequence of characters not containing the
|
||||
newline character. It is easy to define a function ``Unlines`` that
|
||||
converts a non-empty sequence of lines into a sequence of characters
|
||||
by inserting newline characters between every two lines.
|
||||
Define a line to be a sequence of characters not containing the
|
||||
newline character. It is easy to define a function ``Unlines`` that
|
||||
converts a non-empty sequence of lines into a sequence of characters
|
||||
by inserting newline characters between every two lines.
|
||||
|
||||
Since ``Unlines`` is injective, the function ``Lines``, which
|
||||
converts a sequence of characters into a sequence of lines by
|
||||
splitting on newline characters, can be specified as the inverse of
|
||||
``Unlines``.
|
||||
Since ``Unlines`` is injective, the function ``Lines``, which
|
||||
converts a sequence of characters into a sequence of lines by
|
||||
splitting on newline characters, can be specified as the inverse of
|
||||
``Unlines``.
|
||||
|
||||
The problem, just as in Problem 1. is to find a definition by
|
||||
reduction of the function ``Lines``.
|
||||
The problem, just as in Problem 1. is to find a definition by
|
||||
reduction of the function ``Lines``.
|
||||
|
||||
::
|
||||
|
||||
Unlines = uncons ['\n' swap + +] step
|
||||
Unlines = uncons ['\n' swap + +] step
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('["hello" "world"] uncons ["\n" swap + +] step')
|
||||
|
||||
|
|
@ -269,41 +267,41 @@ Problem 2.
|
|||
'hello\nworld'
|
||||
|
||||
|
||||
Again ignoring the actual task let’s just derive ``Lines``:
|
||||
Again ignoring the actual task let's just derive ``Lines``:
|
||||
|
||||
::
|
||||
|
||||
"abc\nefg\nhij" Lines
|
||||
---------------------------
|
||||
["abc" "efg" "hij"]
|
||||
"abc\nefg\nhij" Lines
|
||||
---------------------------
|
||||
["abc" "efg" "hij"]
|
||||
|
||||
Instead of ``P == [size 1 <=]`` we want ``["\n" in]``, and for the
|
||||
base-case of a string with no newlines in it we want to use ``unit``:
|
||||
|
||||
::
|
||||
|
||||
Lines == ["\n" in] [unit] [R0] [dip swons] genrec
|
||||
Lines == ["\n" in] [unit] [R0 [Lines] dip swons] ifte
|
||||
Lines == ["\n" in] [unit] [R0] [dip swons] genrec
|
||||
Lines == ["\n" in] [unit] [R0 [Lines] dip swons] ifte
|
||||
|
||||
Derive ``R0``:
|
||||
|
||||
::
|
||||
|
||||
"a \n b" R0 [Lines] dip swons
|
||||
"a \n b" split-at-newline swap [Lines] dip swons
|
||||
"a " " b" swap [Lines] dip swons
|
||||
" b" "a " [Lines] dip swons
|
||||
" b" Lines "a " swons
|
||||
[" b"] "a " swons
|
||||
["a " " b"]
|
||||
"a \n b" R0 [Lines] dip swons
|
||||
"a \n b" split-at-newline swap [Lines] dip swons
|
||||
"a " " b" swap [Lines] dip swons
|
||||
" b" "a " [Lines] dip swons
|
||||
" b" Lines "a " swons
|
||||
[" b"] "a " swons
|
||||
["a " " b"]
|
||||
|
||||
So:
|
||||
|
||||
::
|
||||
|
||||
R0 == split-at-newline swap
|
||||
R0 == split-at-newline swap
|
||||
|
||||
Lines == ["\n" in] [unit] [split-at-newline swap] [dip swons] genrec
|
||||
Lines == ["\n" in] [unit] [split-at-newline swap] [dip swons] genrec
|
||||
|
||||
Missing the Point?
|
||||
------------------
|
||||
|
|
@ -313,27 +311,26 @@ properties are discussed. Am I missing the point?
|
|||
|
||||
::
|
||||
|
||||
0 [a b c d] [F] step == 0 [a b] [F] step 0 [c d] [F] step concat
|
||||
0 [a b c d] [F] step == 0 [a b] [F] step 0 [c d] [F] step concat
|
||||
|
||||
For associative function ``F`` and a “unit” element for that function,
|
||||
For associative function ``F`` and a "unit" element for that function,
|
||||
here represented by ``0``.
|
||||
|
||||
For functions that don’t have a “unit” we can fake it (the example is
|
||||
For functions that don't have a "unit" we can fake it (the example is
|
||||
given of infinity for the ``min(a, b)`` function.) We can also use:
|
||||
|
||||
::
|
||||
|
||||
safe_step == [size 1 <=] [] [uncons [F] step] ifte
|
||||
safe_step == [size 1 <=] [] [uncons [F] step] ifte
|
||||
|
||||
Or:
|
||||
|
||||
::
|
||||
|
||||
safe_step == [pop size 1 <=] [pop] [[uncons] dip step] ifte
|
||||
safe_step == [pop size 1 <=] [pop] [[uncons] dip step] ifte
|
||||
|
||||
[a b c] [F] safe_step
|
||||
---------------------------
|
||||
a [b c] [F] step
|
||||
[a b c] [F] safe_step
|
||||
---------------------------
|
||||
a [b c] [F] step
|
||||
|
||||
To limit ``F`` to working on pairs of terms from its domain.
|
||||
|
||||
|
|
|
|||
|
|
@ -58,7 +58,7 @@
|
|||
<span class="sd">'''</span>
|
||||
<span class="kn">from</span> <span class="nn">__future__</span> <span class="k">import</span> <span class="n">print_function</span>
|
||||
<span class="kn">from</span> <span class="nn">builtins</span> <span class="k">import</span> <span class="nb">input</span>
|
||||
<span class="kn">from</span> <span class="nn">traceback</span> <span class="k">import</span> <span class="n">print_exc</span><span class="p">,</span> <span class="n">format_exc</span>
|
||||
<span class="kn">from</span> <span class="nn">traceback</span> <span class="k">import</span> <span class="n">print_exc</span>
|
||||
<span class="kn">from</span> <span class="nn">.parser</span> <span class="k">import</span> <span class="n">text_to_expression</span><span class="p">,</span> <span class="n">ParseError</span><span class="p">,</span> <span class="n">Symbol</span>
|
||||
<span class="kn">from</span> <span class="nn">.utils.stack</span> <span class="k">import</span> <span class="n">stack_to_string</span>
|
||||
|
||||
|
|
@ -136,8 +136,7 @@
|
|||
<span class="k">try</span><span class="p">:</span>
|
||||
<span class="n">stack</span><span class="p">,</span> <span class="n">_</span><span class="p">,</span> <span class="n">dictionary</span> <span class="o">=</span> <span class="n">run</span><span class="p">(</span><span class="n">text</span><span class="p">,</span> <span class="n">stack</span><span class="p">,</span> <span class="n">dictionary</span><span class="p">)</span>
|
||||
<span class="k">except</span><span class="p">:</span>
|
||||
<span class="n">exc</span> <span class="o">=</span> <span class="n">format_exc</span><span class="p">()</span> <span class="c1"># Capture the exception.</span>
|
||||
<span class="nb">print</span><span class="p">(</span><span class="n">exc</span><span class="p">)</span> <span class="c1"># Print the original exception.</span>
|
||||
<span class="n">print_exc</span><span class="p">()</span>
|
||||
<span class="k">except</span><span class="p">:</span>
|
||||
<span class="n">print_exc</span><span class="p">()</span>
|
||||
<span class="nb">print</span><span class="p">()</span>
|
||||
|
|
|
|||
|
|
@ -56,12 +56,9 @@
|
|||
<span class="sd">returns a dictionary of Joy functions suitable for use with the joy()</span>
|
||||
<span class="sd">function.</span>
|
||||
<span class="sd">'''</span>
|
||||
<span class="kn">from</span> <span class="nn">builtins</span> <span class="k">import</span> <span class="nb">map</span><span class="p">,</span> <span class="nb">object</span><span class="p">,</span> <span class="nb">range</span><span class="p">,</span> <span class="nb">zip</span>
|
||||
|
||||
<span class="kn">from</span> <span class="nn">inspect</span> <span class="k">import</span> <span class="n">getdoc</span>
|
||||
<span class="kn">from</span> <span class="nn">inspect</span> <span class="k">import</span> <span class="n">getdoc</span><span class="p">,</span> <span class="n">getmembers</span><span class="p">,</span> <span class="n">isfunction</span>
|
||||
<span class="kn">from</span> <span class="nn">functools</span> <span class="k">import</span> <span class="n">wraps</span>
|
||||
<span class="kn">from</span> <span class="nn">itertools</span> <span class="k">import</span> <span class="n">count</span>
|
||||
<span class="kn">from</span> <span class="nn">inspect</span> <span class="k">import</span> <span class="n">getmembers</span><span class="p">,</span> <span class="n">isfunction</span>
|
||||
<span class="kn">import</span> <span class="nn">operator</span><span class="o">,</span> <span class="nn">math</span>
|
||||
|
||||
<span class="kn">from</span> <span class="nn">.parser</span> <span class="k">import</span> <span class="n">text_to_expression</span><span class="p">,</span> <span class="n">Symbol</span>
|
||||
|
|
@ -325,7 +322,7 @@
|
|||
<span class="k">return</span> <span class="p">(</span>
|
||||
<span class="n">line</span><span class="o">.</span><span class="n">strip</span><span class="p">()</span>
|
||||
<span class="k">for</span> <span class="n">line</span> <span class="ow">in</span> <span class="n">text</span><span class="o">.</span><span class="n">splitlines</span><span class="p">()</span>
|
||||
<span class="k">if</span> <span class="ow">not</span> <span class="n">line</span><span class="o">.</span><span class="n">startswith</span><span class="p">(</span><span class="s1">'#'</span><span class="p">)</span>
|
||||
<span class="k">if</span> <span class="n">line</span> <span class="ow">and</span> <span class="ow">not</span> <span class="n">line</span><span class="o">.</span><span class="n">startswith</span><span class="p">(</span><span class="s1">'#'</span><span class="p">)</span>
|
||||
<span class="p">)</span>
|
||||
|
||||
|
||||
|
|
@ -342,7 +339,7 @@
|
|||
<span class="sd"> definition is given as a string with a name followed by a double</span>
|
||||
<span class="sd"> equal sign then one or more Joy functions, the body. for example:</span>
|
||||
|
||||
<span class="sd"> sqr == dup mul</span>
|
||||
<span class="sd"> sqr == dup mul</span>
|
||||
|
||||
<span class="sd"> If you want the definition to persist over restarts, enter it into</span>
|
||||
<span class="sd"> the definitions.txt resource.</span>
|
||||
|
|
@ -383,9 +380,9 @@
|
|||
<span class="sd"> nth position in the quote counting from 0.</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> [a b c d] 0 getitem</span>
|
||||
<span class="sd"> [a b c d] 0 getitem</span>
|
||||
<span class="sd"> -------------------------</span>
|
||||
<span class="sd"> a</span>
|
||||
<span class="sd"> a</span>
|
||||
|
||||
<span class="sd"> '''</span>
|
||||
<span class="n">n</span><span class="p">,</span> <span class="p">(</span><span class="n">Q</span><span class="p">,</span> <span class="n">stack</span><span class="p">)</span> <span class="o">=</span> <span class="n">stack</span>
|
||||
|
|
@ -404,9 +401,9 @@
|
|||
<span class="sd"> n items removed off the top.</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> [a b c d] 2 drop</span>
|
||||
<span class="sd"> [a b c d] 2 drop</span>
|
||||
<span class="sd"> ----------------------</span>
|
||||
<span class="sd"> [c d]</span>
|
||||
<span class="sd"> [c d]</span>
|
||||
|
||||
<span class="sd"> '''</span>
|
||||
<span class="n">n</span><span class="p">,</span> <span class="p">(</span><span class="n">Q</span><span class="p">,</span> <span class="n">stack</span><span class="p">)</span> <span class="o">=</span> <span class="n">stack</span>
|
||||
|
|
@ -428,9 +425,9 @@
|
|||
<span class="sd"> use reverse if needed.)</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> [a b c d] 2 take</span>
|
||||
<span class="sd"> [a b c d] 2 take</span>
|
||||
<span class="sd"> ----------------------</span>
|
||||
<span class="sd"> [b a]</span>
|
||||
<span class="sd"> [b a]</span>
|
||||
|
||||
<span class="sd"> '''</span>
|
||||
<span class="n">n</span><span class="p">,</span> <span class="p">(</span><span class="n">Q</span><span class="p">,</span> <span class="n">stack</span><span class="p">)</span> <span class="o">=</span> <span class="n">stack</span>
|
||||
|
|
@ -452,14 +449,14 @@
|
|||
<span class="sd"> Use a Boolean value to select one of two items.</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> A B False choice</span>
|
||||
<span class="sd"> ----------------------</span>
|
||||
<span class="sd"> A</span>
|
||||
<span class="sd"> A B False choice</span>
|
||||
<span class="sd"> ----------------------</span>
|
||||
<span class="sd"> A</span>
|
||||
|
||||
|
||||
<span class="sd"> A B True choice</span>
|
||||
<span class="sd"> ---------------------</span>
|
||||
<span class="sd"> B</span>
|
||||
<span class="sd"> A B True choice</span>
|
||||
<span class="sd"> ---------------------</span>
|
||||
<span class="sd"> B</span>
|
||||
|
||||
<span class="sd"> Currently Python semantics are used to evaluate the "truthiness" of the</span>
|
||||
<span class="sd"> Boolean value (so empty string, zero, etc. are counted as false, etc.)</span>
|
||||
|
|
@ -475,14 +472,14 @@
|
|||
<span class="sd"> Use a Boolean value to select one of two items from a sequence.</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> [A B] False select</span>
|
||||
<span class="sd"> ------------------------</span>
|
||||
<span class="sd"> A</span>
|
||||
<span class="sd"> [A B] False select</span>
|
||||
<span class="sd"> ------------------------</span>
|
||||
<span class="sd"> A</span>
|
||||
|
||||
|
||||
<span class="sd"> [A B] True select</span>
|
||||
<span class="sd"> -----------------------</span>
|
||||
<span class="sd"> B</span>
|
||||
<span class="sd"> [A B] True select</span>
|
||||
<span class="sd"> -----------------------</span>
|
||||
<span class="sd"> B</span>
|
||||
|
||||
<span class="sd"> The sequence can contain more than two items but not fewer.</span>
|
||||
<span class="sd"> Currently Python semantics are used to evaluate the "truthiness" of the</span>
|
||||
|
|
@ -512,9 +509,12 @@
|
|||
<div class="viewcode-block" id="sum_"><a class="viewcode-back" href="../../library.html#joy.library.sum_">[docs]</a><span class="nd">@inscribe</span>
|
||||
<span class="nd">@SimpleFunctionWrapper</span>
|
||||
<span class="k">def</span> <span class="nf">sum_</span><span class="p">(</span><span class="n">S</span><span class="p">):</span>
|
||||
<span class="sd">'''Given a quoted sequence of numbers return the sum.</span>
|
||||
<span class="sd">'''</span>
|
||||
<span class="sd"> Given a quoted sequence of numbers return the sum.</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> sum == 0 swap [+] step</span>
|
||||
|
||||
<span class="sd"> sum == 0 swap [+] step</span>
|
||||
<span class="sd"> '''</span>
|
||||
<span class="n">tos</span><span class="p">,</span> <span class="n">stack</span> <span class="o">=</span> <span class="n">S</span>
|
||||
<span class="k">return</span> <span class="nb">sum</span><span class="p">(</span><span class="n">iter_stack</span><span class="p">(</span><span class="n">tos</span><span class="p">)),</span> <span class="n">stack</span></div>
|
||||
|
|
@ -528,9 +528,9 @@
|
|||
<span class="sd"> from the the quote. The item is only removed once.</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> [1 2 3 1] 1 remove</span>
|
||||
<span class="sd"> [1 2 3 1] 1 remove</span>
|
||||
<span class="sd"> ------------------------</span>
|
||||
<span class="sd"> [2 3 1]</span>
|
||||
<span class="sd"> [2 3 1]</span>
|
||||
|
||||
<span class="sd"> '''</span>
|
||||
<span class="p">(</span><span class="n">tos</span><span class="p">,</span> <span class="p">(</span><span class="n">second</span><span class="p">,</span> <span class="n">stack</span><span class="p">))</span> <span class="o">=</span> <span class="n">S</span>
|
||||
|
|
@ -564,7 +564,7 @@
|
|||
|
||||
<span class="sd"> clear == stack [pop stack] loop</span>
|
||||
|
||||
<span class="sd"> ... clear</span>
|
||||
<span class="sd"> ... clear</span>
|
||||
<span class="sd"> ---------------</span>
|
||||
|
||||
<span class="sd"> '''</span>
|
||||
|
|
@ -584,7 +584,8 @@
|
|||
<div class="viewcode-block" id="reverse"><a class="viewcode-back" href="../../library.html#joy.library.reverse">[docs]</a><span class="nd">@inscribe</span>
|
||||
<span class="nd">@SimpleFunctionWrapper</span>
|
||||
<span class="k">def</span> <span class="nf">reverse</span><span class="p">(</span><span class="n">S</span><span class="p">):</span>
|
||||
<span class="sd">'''Reverse the list on the top of the stack.</span>
|
||||
<span class="sd">'''</span>
|
||||
<span class="sd"> Reverse the list on the top of the stack.</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> reverse == [] swap shunt</span>
|
||||
|
|
@ -599,12 +600,13 @@
|
|||
<div class="viewcode-block" id="concat_"><a class="viewcode-back" href="../../library.html#joy.library.concat_">[docs]</a><span class="nd">@inscribe</span>
|
||||
<span class="nd">@SimpleFunctionWrapper</span>
|
||||
<span class="k">def</span> <span class="nf">concat_</span><span class="p">(</span><span class="n">S</span><span class="p">):</span>
|
||||
<span class="sd">'''Concatinate the two lists on the top of the stack.</span>
|
||||
<span class="sd">'''</span>
|
||||
<span class="sd"> Concatinate the two lists on the top of the stack.</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> [a b c] [d e f] concat</span>
|
||||
<span class="sd"> [a b c] [d e f] concat</span>
|
||||
<span class="sd"> ----------------------------</span>
|
||||
<span class="sd"> [a b c d e f]</span>
|
||||
<span class="sd"> [a b c d e f]</span>
|
||||
|
||||
<span class="sd"> '''</span>
|
||||
<span class="p">(</span><span class="n">tos</span><span class="p">,</span> <span class="p">(</span><span class="n">second</span><span class="p">,</span> <span class="n">stack</span><span class="p">))</span> <span class="o">=</span> <span class="n">S</span>
|
||||
|
|
@ -614,14 +616,15 @@
|
|||
<div class="viewcode-block" id="shunt"><a class="viewcode-back" href="../../library.html#joy.library.shunt">[docs]</a><span class="nd">@inscribe</span>
|
||||
<span class="nd">@SimpleFunctionWrapper</span>
|
||||
<span class="k">def</span> <span class="nf">shunt</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
|
||||
<span class="sd">'''Like concat but reverses the top list into the second.</span>
|
||||
<span class="sd">'''</span>
|
||||
<span class="sd"> Like concat but reverses the top list into the second.</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> shunt == [swons] step == reverse swap concat</span>
|
||||
|
||||
<span class="sd"> [a b c] [d e f] shunt</span>
|
||||
<span class="sd"> [a b c] [d e f] shunt</span>
|
||||
<span class="sd"> ---------------------------</span>
|
||||
<span class="sd"> [f e d a b c] </span>
|
||||
<span class="sd"> [f e d a b c] </span>
|
||||
|
||||
<span class="sd"> '''</span>
|
||||
<span class="p">(</span><span class="n">tos</span><span class="p">,</span> <span class="p">(</span><span class="n">second</span><span class="p">,</span> <span class="n">stack</span><span class="p">))</span> <span class="o">=</span> <span class="n">stack</span>
|
||||
|
|
@ -669,9 +672,9 @@
|
|||
<span class="sd"> Plus or minus</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> a b pm</span>
|
||||
<span class="sd"> a b pm</span>
|
||||
<span class="sd"> -------------</span>
|
||||
<span class="sd"> a+b a-b</span>
|
||||
<span class="sd"> a+b a-b</span>
|
||||
|
||||
<span class="sd"> '''</span>
|
||||
<span class="n">a</span><span class="p">,</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">stack</span><span class="p">)</span> <span class="o">=</span> <span class="n">stack</span>
|
||||
|
|
@ -844,9 +847,9 @@
|
|||
<span class="sd"> onto the pending expression for evaluation.</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> [Q] i</span>
|
||||
<span class="sd"> [Q] i</span>
|
||||
<span class="sd"> -----------</span>
|
||||
<span class="sd"> Q</span>
|
||||
<span class="sd"> Q</span>
|
||||
|
||||
<span class="sd"> '''</span>
|
||||
<span class="n">quote</span><span class="p">,</span> <span class="n">stack</span> <span class="o">=</span> <span class="n">stack</span>
|
||||
|
|
@ -913,9 +916,9 @@
|
|||
<span class="sd"> with the list as its stack. Does not affect the rest of the stack.</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> ... [a b c] [Q] . infra</span>
|
||||
<span class="sd"> ... [a b c] [Q] . infra</span>
|
||||
<span class="sd"> -----------------------------</span>
|
||||
<span class="sd"> c b a . Q [...] swaack</span>
|
||||
<span class="sd"> c b a . Q [...] swaack</span>
|
||||
|
||||
<span class="sd"> '''</span>
|
||||
<span class="p">(</span><span class="n">quote</span><span class="p">,</span> <span class="p">(</span><span class="n">aggregate</span><span class="p">,</span> <span class="n">stack</span><span class="p">))</span> <span class="o">=</span> <span class="n">stack</span>
|
||||
|
|
@ -952,12 +955,12 @@
|
|||
<span class="sd"> For example, given a (general recursive) function 'F':</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> F == [I] [T] [R1] [R2] genrec</span>
|
||||
<span class="sd"> F == [I] [T] [R1] [R2] genrec</span>
|
||||
|
||||
<span class="sd"> If the [I] if-part fails you must derive R1 and R2 from:</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> ... R1 [F] R2</span>
|
||||
<span class="sd"> ... R1 [F] R2</span>
|
||||
|
||||
<span class="sd"> Just set the stack arguments in front, and figure out what R1 and R2</span>
|
||||
<span class="sd"> have to do to apply the quoted [F] in the proper way. In effect, the</span>
|
||||
|
|
@ -965,15 +968,15 @@
|
|||
<span class="sd"> the original definition in the else-part:</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> F == [I] [T] [R1] [R2] genrec</span>
|
||||
<span class="sd"> == [I] [T] [R1 [F] R2] ifte</span>
|
||||
<span class="sd"> F == [I] [T] [R1] [R2] genrec</span>
|
||||
<span class="sd"> == [I] [T] [R1 [F] R2] ifte</span>
|
||||
|
||||
<span class="sd"> Primitive recursive functions are those where R2 == i.</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> P == [I] [T] [R] tailrec</span>
|
||||
<span class="sd"> == [I] [T] [R [P] i] ifte</span>
|
||||
<span class="sd"> == [I] [T] [R P] ifte</span>
|
||||
<span class="sd"> P == [I] [T] [R] tailrec</span>
|
||||
<span class="sd"> == [I] [T] [R [P] i] ifte</span>
|
||||
<span class="sd"> == [I] [T] [R P] ifte</span>
|
||||
|
||||
<span class="sd"> '''</span>
|
||||
<span class="p">(</span><span class="n">rec2</span><span class="p">,</span> <span class="p">(</span><span class="n">rec1</span><span class="p">,</span> <span class="n">stack</span><span class="p">))</span> <span class="o">=</span> <span class="n">stack</span>
|
||||
|
|
@ -1018,9 +1021,9 @@
|
|||
<span class="sd"> the data parameter is zero, then the first quotation has to produce</span>
|
||||
<span class="sd"> the value to be returned. If the data parameter is positive then the</span>
|
||||
<span class="sd"> second has to combine the data parameter with the result of applying</span>
|
||||
<span class="sd"> the function to its predecessor.</span>
|
||||
<span class="sd"> the function to its predecessor.::</span>
|
||||
|
||||
<span class="sd"> 5 [1] [*] primrec</span>
|
||||
<span class="sd"> 5 [1] [*] primrec</span>
|
||||
|
||||
<span class="sd"> > Then primrec tests whether the top element on the stack (initially</span>
|
||||
<span class="sd"> the 5) is equal to zero. If it is, it pops it off and executes one of</span>
|
||||
|
|
@ -1028,17 +1031,17 @@
|
|||
<span class="sd"> Otherwise it pushes a decremented copy of the top element and</span>
|
||||
<span class="sd"> recurses. On the way back from the recursion it uses the other</span>
|
||||
<span class="sd"> quotation, [*], to multiply what is now a factorial on top of the</span>
|
||||
<span class="sd"> stack by the second element on the stack.</span>
|
||||
<span class="sd"> stack by the second element on the stack.::</span>
|
||||
|
||||
<span class="sd"> n [Base] [Recur] primrec</span>
|
||||
|
||||
<span class="sd"> 0 [Base] [Recur] primrec</span>
|
||||
<span class="sd"> ------------------------------</span>
|
||||
<span class="sd"> Base</span>
|
||||
<span class="sd"> 0 [Base] [Recur] primrec</span>
|
||||
<span class="sd"> ------------------------------</span>
|
||||
<span class="sd"> Base</span>
|
||||
|
||||
<span class="sd"> n [Base] [Recur] primrec</span>
|
||||
<span class="sd"> ------------------------------------------ n > 0</span>
|
||||
<span class="sd"> n (n-1) [Base] [Recur] primrec Recur</span>
|
||||
<span class="sd"> n [Base] [Recur] primrec</span>
|
||||
<span class="sd"> ------------------------------------------ n > 0</span>
|
||||
<span class="sd"> n (n-1) [Base] [Recur] primrec Recur</span>
|
||||
|
||||
<span class="sd"> '''</span>
|
||||
<span class="n">recur</span><span class="p">,</span> <span class="p">(</span><span class="n">base</span><span class="p">,</span> <span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">stack</span><span class="p">))</span> <span class="o">=</span> <span class="n">stack</span>
|
||||
|
|
@ -1072,17 +1075,17 @@
|
|||
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> branch == roll< choice i</span>
|
||||
<span class="sd"> branch == roll< choice i</span>
|
||||
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> False [F] [T] branch</span>
|
||||
<span class="sd"> --------------------------</span>
|
||||
<span class="sd"> F</span>
|
||||
<span class="sd"> False [F] [T] branch</span>
|
||||
<span class="sd"> --------------------------</span>
|
||||
<span class="sd"> F</span>
|
||||
|
||||
<span class="sd"> True [F] [T] branch</span>
|
||||
<span class="sd"> -------------------------</span>
|
||||
<span class="sd"> T</span>
|
||||
<span class="sd"> True [F] [T] branch</span>
|
||||
<span class="sd"> -------------------------</span>
|
||||
<span class="sd"> T</span>
|
||||
|
||||
<span class="sd"> '''</span>
|
||||
<span class="p">(</span><span class="n">then</span><span class="p">,</span> <span class="p">(</span><span class="n">else_</span><span class="p">,</span> <span class="p">(</span><span class="n">flag</span><span class="p">,</span> <span class="n">stack</span><span class="p">)))</span> <span class="o">=</span> <span class="n">stack</span>
|
||||
|
|
@ -1129,9 +1132,9 @@
|
|||
|
||||
<span class="sd"> It works by rewriting into a chain of nested `ifte` expressions, e.g.::</span>
|
||||
|
||||
<span class="sd"> [[[B0] T0] [[B1] T1] [D]] cond</span>
|
||||
<span class="sd"> -----------------------------------------</span>
|
||||
<span class="sd"> [B0] [T0] [[B1] [T1] [D] ifte] ifte</span>
|
||||
<span class="sd"> [[[B0] T0] [[B1] T1] [D]] cond</span>
|
||||
<span class="sd"> -----------------------------------------</span>
|
||||
<span class="sd"> [B0] [T0] [[B1] [T1] [D] ifte] ifte</span>
|
||||
|
||||
<span class="sd"> '''</span>
|
||||
<span class="n">conditions</span><span class="p">,</span> <span class="n">stack</span> <span class="o">=</span> <span class="n">stack</span>
|
||||
|
|
@ -1166,9 +1169,9 @@
|
|||
<span class="sd"> on the rest of the stack.</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> ... x [Q] dip</span>
|
||||
<span class="sd"> ... x [Q] dip</span>
|
||||
<span class="sd"> -------------------</span>
|
||||
<span class="sd"> ... Q x</span>
|
||||
<span class="sd"> ... Q x</span>
|
||||
|
||||
<span class="sd"> '''</span>
|
||||
<span class="p">(</span><span class="n">quote</span><span class="p">,</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">stack</span><span class="p">))</span> <span class="o">=</span> <span class="n">stack</span>
|
||||
|
|
@ -1183,9 +1186,9 @@
|
|||
<span class="sd"> Like dip but expects two items.</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> ... y x [Q] dip</span>
|
||||
<span class="sd"> ... y x [Q] dip</span>
|
||||
<span class="sd"> ---------------------</span>
|
||||
<span class="sd"> ... Q y x</span>
|
||||
<span class="sd"> ... Q y x</span>
|
||||
|
||||
<span class="sd"> '''</span>
|
||||
<span class="p">(</span><span class="n">quote</span><span class="p">,</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">stack</span><span class="p">)))</span> <span class="o">=</span> <span class="n">S</span>
|
||||
|
|
@ -1200,9 +1203,9 @@
|
|||
<span class="sd"> Like dip but expects three items.</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> ... z y x [Q] dip</span>
|
||||
<span class="sd"> ... z y x [Q] dip</span>
|
||||
<span class="sd"> -----------------------</span>
|
||||
<span class="sd"> ... Q z y x</span>
|
||||
<span class="sd"> ... Q z y x</span>
|
||||
|
||||
<span class="sd"> '''</span>
|
||||
<span class="p">(</span><span class="n">quote</span><span class="p">,</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="p">(</span><span class="n">z</span><span class="p">,</span> <span class="n">stack</span><span class="p">))))</span> <span class="o">=</span> <span class="n">S</span>
|
||||
|
|
@ -1219,9 +1222,10 @@
|
|||
<span class="sd"> program.</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> ... x [Q] . app1</span>
|
||||
<span class="sd"> -----------------------------------</span>
|
||||
<span class="sd"> ... [x ...] [Q] . infra first</span>
|
||||
<span class="sd"> ... x [Q] . app1</span>
|
||||
<span class="sd"> -----------------------------------</span>
|
||||
<span class="sd"> ... [x ...] [Q] . infra first</span>
|
||||
|
||||
<span class="sd"> '''</span>
|
||||
<span class="p">(</span><span class="n">quote</span><span class="p">,</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">stack</span><span class="p">))</span> <span class="o">=</span> <span class="n">S</span>
|
||||
<span class="n">stack</span> <span class="o">=</span> <span class="p">(</span><span class="n">quote</span><span class="p">,</span> <span class="p">((</span><span class="n">x</span><span class="p">,</span> <span class="n">stack</span><span class="p">),</span> <span class="n">stack</span><span class="p">))</span>
|
||||
|
|
@ -1235,10 +1239,10 @@
|
|||
<span class="sd">'''Like app1 with two items.</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> ... y x [Q] . app2</span>
|
||||
<span class="sd"> -----------------------------------</span>
|
||||
<span class="sd"> ... [y ...] [Q] . infra first</span>
|
||||
<span class="sd"> [x ...] [Q] infra first</span>
|
||||
<span class="sd"> ... y x [Q] . app2</span>
|
||||
<span class="sd"> -----------------------------------</span>
|
||||
<span class="sd"> ... [y ...] [Q] . infra first</span>
|
||||
<span class="sd"> [x ...] [Q] infra first</span>
|
||||
|
||||
<span class="sd"> '''</span>
|
||||
<span class="p">(</span><span class="n">quote</span><span class="p">,</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">stack</span><span class="p">)))</span> <span class="o">=</span> <span class="n">S</span>
|
||||
|
|
@ -1255,11 +1259,11 @@
|
|||
<span class="sd">'''Like app1 with three items.</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> ... z y x [Q] . app3</span>
|
||||
<span class="sd"> -----------------------------------</span>
|
||||
<span class="sd"> ... [z ...] [Q] . infra first</span>
|
||||
<span class="sd"> [y ...] [Q] infra first</span>
|
||||
<span class="sd"> [x ...] [Q] infra first</span>
|
||||
<span class="sd"> ... z y x [Q] . app3</span>
|
||||
<span class="sd"> -----------------------------------</span>
|
||||
<span class="sd"> ... [z ...] [Q] . infra first</span>
|
||||
<span class="sd"> [y ...] [Q] infra first</span>
|
||||
<span class="sd"> [x ...] [Q] infra first</span>
|
||||
|
||||
<span class="sd"> '''</span>
|
||||
<span class="p">(</span><span class="n">quote</span><span class="p">,</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="p">(</span><span class="n">z</span><span class="p">,</span> <span class="n">stack</span><span class="p">))))</span> <span class="o">=</span> <span class="n">S</span>
|
||||
|
|
@ -1278,19 +1282,19 @@
|
|||
<span class="sd"> Run a quoted program on each item in a sequence.</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> ... [] [Q] . step</span>
|
||||
<span class="sd"> -----------------------</span>
|
||||
<span class="sd"> ... .</span>
|
||||
<span class="sd"> ... [] [Q] . step</span>
|
||||
<span class="sd"> -----------------------</span>
|
||||
<span class="sd"> ... .</span>
|
||||
|
||||
|
||||
<span class="sd"> ... [a] [Q] . step</span>
|
||||
<span class="sd"> ------------------------</span>
|
||||
<span class="sd"> ... a . Q</span>
|
||||
<span class="sd"> ... [a] [Q] . step</span>
|
||||
<span class="sd"> ------------------------</span>
|
||||
<span class="sd"> ... a . Q</span>
|
||||
|
||||
|
||||
<span class="sd"> ... [a b c] [Q] . step</span>
|
||||
<span class="sd"> ... [a b c] [Q] . step</span>
|
||||
<span class="sd"> ----------------------------------------</span>
|
||||
<span class="sd"> ... a . Q [b c] [Q] step</span>
|
||||
<span class="sd"> ... a . Q [b c] [Q] step</span>
|
||||
|
||||
<span class="sd"> The step combinator executes the quotation on each member of the list</span>
|
||||
<span class="sd"> on top of the stack.</span>
|
||||
|
|
@ -1313,19 +1317,19 @@
|
|||
<span class="sd"> times == [-- dip] cons [swap] infra [0 >] swap while pop</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> ... n [Q] . times</span>
|
||||
<span class="sd"> ... n [Q] . times</span>
|
||||
<span class="sd"> --------------------- w/ n <= 0</span>
|
||||
<span class="sd"> ... .</span>
|
||||
<span class="sd"> ... .</span>
|
||||
|
||||
|
||||
<span class="sd"> ... 1 [Q] . times</span>
|
||||
<span class="sd"> ---------------------------------</span>
|
||||
<span class="sd"> ... . Q</span>
|
||||
<span class="sd"> ... 1 [Q] . times</span>
|
||||
<span class="sd"> -----------------------</span>
|
||||
<span class="sd"> ... . Q</span>
|
||||
|
||||
|
||||
<span class="sd"> ... n [Q] . times</span>
|
||||
<span class="sd"> --------------------------------- w/ n > 1</span>
|
||||
<span class="sd"> ... . Q (n - 1) [Q] times</span>
|
||||
<span class="sd"> ... n [Q] . times</span>
|
||||
<span class="sd"> ------------------------------------- w/ n > 1</span>
|
||||
<span class="sd"> ... . Q (n - 1) [Q] times</span>
|
||||
|
||||
<span class="sd"> '''</span>
|
||||
<span class="c1"># times == [-- dip] cons [swap] infra [0 >] swap while pop</span>
|
||||
|
|
@ -1362,13 +1366,13 @@
|
|||
<span class="sd"> Basic loop combinator.</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> ... True [Q] loop</span>
|
||||
<span class="sd"> ... True [Q] loop</span>
|
||||
<span class="sd"> -----------------------</span>
|
||||
<span class="sd"> ... Q [Q] loop</span>
|
||||
<span class="sd"> ... Q [Q] loop</span>
|
||||
|
||||
<span class="sd"> ... False [Q] loop</span>
|
||||
<span class="sd"> ... False [Q] loop</span>
|
||||
<span class="sd"> ------------------------</span>
|
||||
<span class="sd"> ...</span>
|
||||
<span class="sd"> ...</span>
|
||||
|
||||
<span class="sd"> '''</span>
|
||||
<span class="n">quote</span><span class="p">,</span> <span class="p">(</span><span class="n">flag</span><span class="p">,</span> <span class="n">stack</span><span class="p">)</span> <span class="o">=</span> <span class="n">stack</span>
|
||||
|
|
@ -1385,17 +1389,17 @@
|
|||
<span class="sd"> one of the three depending on the results of comparing the two values:</span>
|
||||
<span class="sd"> ::</span>
|
||||
|
||||
<span class="sd"> a b [G] [E] [L] cmp</span>
|
||||
<span class="sd"> ------------------------- a > b</span>
|
||||
<span class="sd"> G</span>
|
||||
<span class="sd"> a b [G] [E] [L] cmp</span>
|
||||
<span class="sd"> ------------------------- a > b</span>
|
||||
<span class="sd"> G</span>
|
||||
|
||||
<span class="sd"> a b [G] [E] [L] cmp</span>
|
||||
<span class="sd"> ------------------------- a = b</span>
|
||||
<span class="sd"> E</span>
|
||||
<span class="sd"> a b [G] [E] [L] cmp</span>
|
||||
<span class="sd"> ------------------------- a = b</span>
|
||||
<span class="sd"> E</span>
|
||||
|
||||
<span class="sd"> a b [G] [E] [L] cmp</span>
|
||||
<span class="sd"> ------------------------- a < b</span>
|
||||
<span class="sd"> L</span>
|
||||
<span class="sd"> a b [G] [E] [L] cmp</span>
|
||||
<span class="sd"> ------------------------- a < b</span>
|
||||
<span class="sd"> L</span>
|
||||
<span class="sd"> '''</span>
|
||||
<span class="n">L</span><span class="p">,</span> <span class="p">(</span><span class="n">E</span><span class="p">,</span> <span class="p">(</span><span class="n">G</span><span class="p">,</span> <span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">stack</span><span class="p">))))</span> <span class="o">=</span> <span class="n">stack</span>
|
||||
<span class="n">expression</span> <span class="o">=</span> <span class="n">concat</span><span class="p">(</span><span class="n">G</span> <span class="k">if</span> <span class="n">a</span> <span class="o">></span> <span class="n">b</span> <span class="k">else</span> <span class="n">L</span> <span class="k">if</span> <span class="n">a</span> <span class="o"><</span> <span class="n">b</span> <span class="k">else</span> <span class="n">E</span><span class="p">,</span> <span class="n">expression</span><span class="p">)</span>
|
||||
|
|
|
|||
|
|
@ -53,22 +53,21 @@
|
|||
<span class="sd">'''</span>
|
||||
<span class="sd">Pretty printing support, e.g.::</span>
|
||||
|
||||
<span class="sd"> Joy? 23 18 * 99 +</span>
|
||||
<span class="sd"> . 23 18 mul 99 add</span>
|
||||
<span class="sd"> 23 . 18 mul 99 add</span>
|
||||
<span class="sd"> 23 18 . mul 99 add</span>
|
||||
<span class="sd"> 414 . 99 add</span>
|
||||
<span class="sd"> 414 99 . add</span>
|
||||
<span class="sd"> 513 . </span>
|
||||
<span class="sd"> Joy? [23 18 * 99 +] trace</span>
|
||||
<span class="sd"> • 23 18 mul 99 add</span>
|
||||
<span class="sd"> 23 • 18 mul 99 add</span>
|
||||
<span class="sd"> 23 18 • mul 99 add</span>
|
||||
<span class="sd"> 414 • 99 add</span>
|
||||
<span class="sd"> 414 99 • add</span>
|
||||
<span class="sd"> 513 • </span>
|
||||
|
||||
<span class="sd"> 513 <-top</span>
|
||||
|
||||
<span class="sd"> joy? </span>
|
||||
|
||||
<span class="sd">On each line the stack is printed with the top to the right, then a ``.`` to</span>
|
||||
<span class="sd">represent the current locus of processing, then the pending expression to the</span>
|
||||
<span class="sd">left.</span>
|
||||
|
||||
<span class="sd">On each line the stack is printed with the top to the left, then a</span>
|
||||
<span class="sd">bullet symbol,``•``, to represent the current locus of processing, then</span>
|
||||
<span class="sd">the pending expression to the right.</span>
|
||||
<span class="sd">'''</span>
|
||||
<span class="c1"># (Kinda clunky and hacky. This should be swapped out in favor of much</span>
|
||||
<span class="c1"># smarter stuff.)</span>
|
||||
|
|
@ -147,8 +146,8 @@
|
|||
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">stack</span><span class="p">)</span>
|
||||
<span class="k">if</span> <span class="n">n</span> <span class="o">></span> <span class="n">max_stack_length</span><span class="p">:</span>
|
||||
<span class="n">max_stack_length</span> <span class="o">=</span> <span class="n">n</span>
|
||||
<span class="n">lines</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">n</span><span class="p">,</span> <span class="s1">'</span><span class="si">%s</span><span class="s1"> . </span><span class="si">%s</span><span class="s1">'</span> <span class="o">%</span> <span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">)))</span>
|
||||
<span class="k">return</span> <span class="p">[</span> <span class="c1"># Prefix spaces to line up '.'s.</span>
|
||||
<span class="n">lines</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">n</span><span class="p">,</span> <span class="s1">'</span><span class="si">%s</span><span class="s1"> • </span><span class="si">%s</span><span class="s1">'</span> <span class="o">%</span> <span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">)))</span>
|
||||
<span class="k">return</span> <span class="p">[</span> <span class="c1"># Prefix spaces to line up '•'s.</span>
|
||||
<span class="p">(</span><span class="s1">' '</span> <span class="o">*</span> <span class="p">(</span><span class="n">max_stack_length</span> <span class="o">-</span> <span class="n">length</span><span class="p">)</span> <span class="o">+</span> <span class="n">line</span><span class="p">)</span>
|
||||
<span class="k">for</span> <span class="n">length</span><span class="p">,</span> <span class="n">line</span> <span class="ow">in</span> <span class="n">lines</span>
|
||||
<span class="p">]</span></div>
|
||||
|
|
|
|||
|
|
@ -104,9 +104,9 @@ if it’s in the dict. Aliases for functions not in the dict are ignored.</p>
|
|||
<dd><p>Given a quoted program on TOS and anything as the second stack item run
|
||||
the program and replace the two args with the first result of the
|
||||
program.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">x</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">app1</span>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">x</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">app1</span>
|
||||
<span class="o">-----------------------------------</span>
|
||||
<span class="o">...</span> <span class="p">[</span><span class="n">x</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">infra</span> <span class="n">first</span>
|
||||
<span class="o">...</span> <span class="p">[</span><span class="n">x</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">infra</span> <span class="n">first</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
|
@ -115,10 +115,10 @@ program.</p>
|
|||
<dt id="joy.library.app2">
|
||||
<code class="descclassname">joy.library.</code><code class="descname">app2</code><span class="sig-paren">(</span><em>S</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#app2"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.app2" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><p>Like app1 with two items.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">y</span> <span class="n">x</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">app2</span>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">y</span> <span class="n">x</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">app2</span>
|
||||
<span class="o">-----------------------------------</span>
|
||||
<span class="o">...</span> <span class="p">[</span><span class="n">y</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">infra</span> <span class="n">first</span>
|
||||
<span class="p">[</span><span class="n">x</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span>
|
||||
<span class="o">...</span> <span class="p">[</span><span class="n">y</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">infra</span> <span class="n">first</span>
|
||||
<span class="p">[</span><span class="n">x</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
|
@ -127,11 +127,11 @@ program.</p>
|
|||
<dt id="joy.library.app3">
|
||||
<code class="descclassname">joy.library.</code><code class="descname">app3</code><span class="sig-paren">(</span><em>S</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#app3"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.app3" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><p>Like app1 with three items.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">z</span> <span class="n">y</span> <span class="n">x</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">app3</span>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">z</span> <span class="n">y</span> <span class="n">x</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">app3</span>
|
||||
<span class="o">-----------------------------------</span>
|
||||
<span class="o">...</span> <span class="p">[</span><span class="n">z</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">infra</span> <span class="n">first</span>
|
||||
<span class="p">[</span><span class="n">y</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span>
|
||||
<span class="p">[</span><span class="n">x</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span>
|
||||
<span class="o">...</span> <span class="p">[</span><span class="n">z</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">infra</span> <span class="n">first</span>
|
||||
<span class="p">[</span><span class="n">y</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span>
|
||||
<span class="p">[</span><span class="n">x</span> <span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
|
@ -154,13 +154,13 @@ program.</p>
|
|||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">branch</span> <span class="o">==</span> <span class="n">roll</span><span class="o"><</span> <span class="n">choice</span> <span class="n">i</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="kc">False</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="n">branch</span>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="kc">False</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="n">branch</span>
|
||||
<span class="o">--------------------------</span>
|
||||
<span class="n">F</span>
|
||||
<span class="n">F</span>
|
||||
|
||||
<span class="kc">True</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="n">branch</span>
|
||||
<span class="kc">True</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="n">branch</span>
|
||||
<span class="o">-------------------------</span>
|
||||
<span class="n">T</span>
|
||||
<span class="n">T</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
|
@ -169,14 +169,14 @@ program.</p>
|
|||
<dt id="joy.library.choice">
|
||||
<code class="descclassname">joy.library.</code><code class="descname">choice</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#choice"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.choice" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><p>Use a Boolean value to select one of two items.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">A</span> <span class="n">B</span> <span class="kc">False</span> <span class="n">choice</span>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">A</span> <span class="n">B</span> <span class="kc">False</span> <span class="n">choice</span>
|
||||
<span class="o">----------------------</span>
|
||||
<span class="n">A</span>
|
||||
<span class="n">A</span>
|
||||
|
||||
|
||||
<span class="n">A</span> <span class="n">B</span> <span class="kc">True</span> <span class="n">choice</span>
|
||||
<span class="n">A</span> <span class="n">B</span> <span class="kc">True</span> <span class="n">choice</span>
|
||||
<span class="o">---------------------</span>
|
||||
<span class="n">B</span>
|
||||
<span class="n">B</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Currently Python semantics are used to evaluate the “truthiness” of the
|
||||
|
|
@ -189,7 +189,7 @@ Boolean value (so empty string, zero, etc. are counted as false, etc.)</p>
|
|||
<dd><p>Clear everything from the stack.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">clear</span> <span class="o">==</span> <span class="n">stack</span> <span class="p">[</span><span class="n">pop</span> <span class="n">stack</span><span class="p">]</span> <span class="n">loop</span>
|
||||
|
||||
<span class="o">...</span> <span class="n">clear</span>
|
||||
<span class="o">...</span> <span class="n">clear</span>
|
||||
<span class="o">---------------</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
|
|
@ -200,17 +200,17 @@ Boolean value (so empty string, zero, etc. are counted as false, etc.)</p>
|
|||
<code class="descclassname">joy.library.</code><code class="descname">cmp_</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#cmp_"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.cmp_" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><p>cmp takes two values and three quoted programs on the stack and runs
|
||||
one of the three depending on the results of comparing the two values:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">a</span> <span class="n">b</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="p">[</span><span class="n">E</span><span class="p">]</span> <span class="p">[</span><span class="n">L</span><span class="p">]</span> <span class="nb">cmp</span>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">a</span> <span class="n">b</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="p">[</span><span class="n">E</span><span class="p">]</span> <span class="p">[</span><span class="n">L</span><span class="p">]</span> <span class="nb">cmp</span>
|
||||
<span class="o">-------------------------</span> <span class="n">a</span> <span class="o">></span> <span class="n">b</span>
|
||||
<span class="n">G</span>
|
||||
<span class="n">G</span>
|
||||
|
||||
<span class="n">a</span> <span class="n">b</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="p">[</span><span class="n">E</span><span class="p">]</span> <span class="p">[</span><span class="n">L</span><span class="p">]</span> <span class="nb">cmp</span>
|
||||
<span class="n">a</span> <span class="n">b</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="p">[</span><span class="n">E</span><span class="p">]</span> <span class="p">[</span><span class="n">L</span><span class="p">]</span> <span class="nb">cmp</span>
|
||||
<span class="o">-------------------------</span> <span class="n">a</span> <span class="o">=</span> <span class="n">b</span>
|
||||
<span class="n">E</span>
|
||||
<span class="n">E</span>
|
||||
|
||||
<span class="n">a</span> <span class="n">b</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="p">[</span><span class="n">E</span><span class="p">]</span> <span class="p">[</span><span class="n">L</span><span class="p">]</span> <span class="nb">cmp</span>
|
||||
<span class="n">a</span> <span class="n">b</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="p">[</span><span class="n">E</span><span class="p">]</span> <span class="p">[</span><span class="n">L</span><span class="p">]</span> <span class="nb">cmp</span>
|
||||
<span class="o">-------------------------</span> <span class="n">a</span> <span class="o"><</span> <span class="n">b</span>
|
||||
<span class="n">L</span>
|
||||
<span class="n">L</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
|
@ -219,9 +219,9 @@ one of the three depending on the results of comparing the two values:</p>
|
|||
<dt id="joy.library.concat_">
|
||||
<code class="descclassname">joy.library.</code><code class="descname">concat_</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#concat_"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.concat_" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><p>Concatinate the two lists on the top of the stack.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span><span class="p">]</span> <span class="p">[</span><span class="n">d</span> <span class="n">e</span> <span class="n">f</span><span class="p">]</span> <span class="n">concat</span>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span><span class="p">]</span> <span class="p">[</span><span class="n">d</span> <span class="n">e</span> <span class="n">f</span><span class="p">]</span> <span class="n">concat</span>
|
||||
<span class="o">----------------------------</span>
|
||||
<span class="p">[</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span> <span class="n">d</span> <span class="n">e</span> <span class="n">f</span><span class="p">]</span>
|
||||
<span class="p">[</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span> <span class="n">d</span> <span class="n">e</span> <span class="n">f</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
|
@ -235,9 +235,9 @@ default quote. Each condition clause should contain a quoted predicate
|
|||
followed by the function expression to run if that predicate returns
|
||||
true. If no predicates return true the default function runs.</p>
|
||||
<p>It works by rewriting into a chain of nested <cite>ifte</cite> expressions, e.g.:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[[[</span><span class="n">B0</span><span class="p">]</span> <span class="n">T0</span><span class="p">]</span> <span class="p">[[</span><span class="n">B1</span><span class="p">]</span> <span class="n">T1</span><span class="p">]</span> <span class="p">[</span><span class="n">D</span><span class="p">]]</span> <span class="n">cond</span>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[[[</span><span class="n">B0</span><span class="p">]</span> <span class="n">T0</span><span class="p">]</span> <span class="p">[[</span><span class="n">B1</span><span class="p">]</span> <span class="n">T1</span><span class="p">]</span> <span class="p">[</span><span class="n">D</span><span class="p">]]</span> <span class="n">cond</span>
|
||||
<span class="o">-----------------------------------------</span>
|
||||
<span class="p">[</span><span class="n">B0</span><span class="p">]</span> <span class="p">[</span><span class="n">T0</span><span class="p">]</span> <span class="p">[[</span><span class="n">B1</span><span class="p">]</span> <span class="p">[</span><span class="n">T1</span><span class="p">]</span> <span class="p">[</span><span class="n">D</span><span class="p">]</span> <span class="n">ifte</span><span class="p">]</span> <span class="n">ifte</span>
|
||||
<span class="p">[</span><span class="n">B0</span><span class="p">]</span> <span class="p">[</span><span class="n">T0</span><span class="p">]</span> <span class="p">[[</span><span class="n">B1</span><span class="p">]</span> <span class="p">[</span><span class="n">T1</span><span class="p">]</span> <span class="p">[</span><span class="n">D</span><span class="p">]</span> <span class="n">ifte</span><span class="p">]</span> <span class="n">ifte</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
|
@ -248,9 +248,9 @@ true. If no predicates return true the default function runs.</p>
|
|||
<dd><p>The dip combinator expects a quoted program on the stack and below it
|
||||
some item, it hoists the item into the expression and runs the program
|
||||
on the rest of the stack.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">x</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">dip</span>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">x</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">dip</span>
|
||||
<span class="o">-------------------</span>
|
||||
<span class="o">...</span> <span class="n">Q</span> <span class="n">x</span>
|
||||
<span class="o">...</span> <span class="n">Q</span> <span class="n">x</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
|
@ -259,9 +259,9 @@ on the rest of the stack.</p>
|
|||
<dt id="joy.library.dipd">
|
||||
<code class="descclassname">joy.library.</code><code class="descname">dipd</code><span class="sig-paren">(</span><em>S</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#dipd"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.dipd" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><p>Like dip but expects two items.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">y</span> <span class="n">x</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">dip</span>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">y</span> <span class="n">x</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">dip</span>
|
||||
<span class="o">---------------------</span>
|
||||
<span class="o">...</span> <span class="n">Q</span> <span class="n">y</span> <span class="n">x</span>
|
||||
<span class="o">...</span> <span class="n">Q</span> <span class="n">y</span> <span class="n">x</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
|
@ -270,9 +270,9 @@ on the rest of the stack.</p>
|
|||
<dt id="joy.library.dipdd">
|
||||
<code class="descclassname">joy.library.</code><code class="descname">dipdd</code><span class="sig-paren">(</span><em>S</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#dipdd"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.dipdd" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><p>Like dip but expects three items.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">z</span> <span class="n">y</span> <span class="n">x</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">dip</span>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">z</span> <span class="n">y</span> <span class="n">x</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">dip</span>
|
||||
<span class="o">-----------------------</span>
|
||||
<span class="o">...</span> <span class="n">Q</span> <span class="n">z</span> <span class="n">y</span> <span class="n">x</span>
|
||||
<span class="o">...</span> <span class="n">Q</span> <span class="n">z</span> <span class="n">y</span> <span class="n">x</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
|
@ -299,9 +299,9 @@ the stack discarding the rest of the stack.</p>
|
|||
</div>
|
||||
<p>Expects an integer and a quote on the stack and returns the quote with
|
||||
n items removed off the top.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="mi">2</span> <span class="n">drop</span>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="mi">2</span> <span class="n">drop</span>
|
||||
<span class="o">----------------------</span>
|
||||
<span class="p">[</span><span class="n">c</span> <span class="n">d</span><span class="p">]</span>
|
||||
<span class="p">[</span><span class="n">c</span> <span class="n">d</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
|
@ -381,9 +381,9 @@ the original definition in the else-part:</p>
|
|||
</div>
|
||||
<p>Expects an integer and a quote on the stack and returns the item at the
|
||||
nth position in the quote counting from 0.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="mi">0</span> <span class="n">getitem</span>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="mi">0</span> <span class="n">getitem</span>
|
||||
<span class="o">-------------------------</span>
|
||||
<span class="n">a</span>
|
||||
<span class="n">a</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
|
@ -399,9 +399,9 @@ nth position in the quote counting from 0.</p>
|
|||
<code class="descclassname">joy.library.</code><code class="descname">i</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#i"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.i" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><p>The i combinator expects a quoted program on the stack and unpacks it
|
||||
onto the pending expression for evaluation.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">i</span>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">i</span>
|
||||
<span class="o">-----------</span>
|
||||
<span class="n">Q</span>
|
||||
<span class="n">Q</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
|
@ -417,9 +417,9 @@ onto the pending expression for evaluation.</p>
|
|||
<code class="descclassname">joy.library.</code><code class="descname">infra</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#infra"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.infra" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><p>Accept a quoted program and a list on the stack and run the program
|
||||
with the list as its stack. Does not affect the rest of the stack.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="p">[</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">infra</span>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="p">[</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">infra</span>
|
||||
<span class="o">-----------------------------</span>
|
||||
<span class="n">c</span> <span class="n">b</span> <span class="n">a</span> <span class="o">.</span> <span class="n">Q</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="n">swaack</span>
|
||||
<span class="n">c</span> <span class="n">b</span> <span class="n">a</span> <span class="o">.</span> <span class="n">Q</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="n">swaack</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
|
@ -452,13 +452,13 @@ the definitions.txt resource.</p>
|
|||
<dt id="joy.library.loop">
|
||||
<code class="descclassname">joy.library.</code><code class="descname">loop</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#loop"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.loop" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><p>Basic loop combinator.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="kc">True</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">loop</span>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="kc">True</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">loop</span>
|
||||
<span class="o">-----------------------</span>
|
||||
<span class="o">...</span> <span class="n">Q</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">loop</span>
|
||||
<span class="o">...</span> <span class="n">Q</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">loop</span>
|
||||
|
||||
<span class="o">...</span> <span class="kc">False</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">loop</span>
|
||||
<span class="o">...</span> <span class="kc">False</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">loop</span>
|
||||
<span class="o">------------------------</span>
|
||||
<span class="o">...</span>
|
||||
<span class="o">...</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
|
@ -492,9 +492,9 @@ new list with the results in place of the program and original list.</p>
|
|||
<dt id="joy.library.pm">
|
||||
<code class="descclassname">joy.library.</code><code class="descname">pm</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#pm"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.pm" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><p>Plus or minus</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">a</span> <span class="n">b</span> <span class="n">pm</span>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">a</span> <span class="n">b</span> <span class="n">pm</span>
|
||||
<span class="o">-------------</span>
|
||||
<span class="n">a</span><span class="o">+</span><span class="n">b</span> <span class="n">a</span><span class="o">-</span><span class="n">b</span>
|
||||
<span class="n">a</span><span class="o">+</span><span class="n">b</span> <span class="n">a</span><span class="o">-</span><span class="n">b</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
|
@ -514,29 +514,28 @@ data parameter. For an integer data parameter it works like this: If
|
|||
the data parameter is zero, then the first quotation has to produce
|
||||
the value to be returned. If the data parameter is positive then the
|
||||
second has to combine the data parameter with the result of applying
|
||||
the function to its predecessor.</p>
|
||||
<p>5 [1] [*] primrec</p>
|
||||
the function to its predecessor.:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">5</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="o">*</span><span class="p">]</span> <span class="n">primrec</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>> Then primrec tests whether the top element on the stack (initially
|
||||
the 5) is equal to zero. If it is, it pops it off and executes one of
|
||||
the quotations, the [1] which leaves 1 on the stack as the result.
|
||||
Otherwise it pushes a decremented copy of the top element and
|
||||
recurses. On the way back from the recursion it uses the other
|
||||
quotation, [*], to multiply what is now a factorial on top of the
|
||||
stack by the second element on the stack.</p>
|
||||
<blockquote>
|
||||
<div><blockquote>
|
||||
<div>n [Base] [Recur] primrec</div></blockquote>
|
||||
<p>0 [Base] [Recur] primrec</p>
|
||||
</div></blockquote>
|
||||
<blockquote>
|
||||
<div><blockquote>
|
||||
<div>Base</div></blockquote>
|
||||
<p>n [Base] [Recur] primrec</p>
|
||||
</div></blockquote>
|
||||
<dl class="docutils">
|
||||
<dt>—————————————— n > 0</dt>
|
||||
<dd>n (n-1) [Base] [Recur] primrec Recur</dd>
|
||||
</dl>
|
||||
stack by the second element on the stack.:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">n</span> <span class="p">[</span><span class="n">Base</span><span class="p">]</span> <span class="p">[</span><span class="n">Recur</span><span class="p">]</span> <span class="n">primrec</span>
|
||||
|
||||
<span class="mi">0</span> <span class="p">[</span><span class="n">Base</span><span class="p">]</span> <span class="p">[</span><span class="n">Recur</span><span class="p">]</span> <span class="n">primrec</span>
|
||||
<span class="o">------------------------------</span>
|
||||
<span class="n">Base</span>
|
||||
|
||||
<span class="n">n</span> <span class="p">[</span><span class="n">Base</span><span class="p">]</span> <span class="p">[</span><span class="n">Recur</span><span class="p">]</span> <span class="n">primrec</span>
|
||||
<span class="o">------------------------------------------</span> <span class="n">n</span> <span class="o">></span> <span class="mi">0</span>
|
||||
<span class="n">n</span> <span class="p">(</span><span class="n">n</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="p">[</span><span class="n">Base</span><span class="p">]</span> <span class="p">[</span><span class="n">Recur</span><span class="p">]</span> <span class="n">primrec</span> <span class="n">Recur</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
||||
<dl class="function">
|
||||
|
|
@ -544,9 +543,9 @@ stack by the second element on the stack.</p>
|
|||
<code class="descclassname">joy.library.</code><code class="descname">remove</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#remove"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.remove" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><p>Expects an item on the stack and a quote under it and removes that item
|
||||
from the the quote. The item is only removed once.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">1</span><span class="p">]</span> <span class="mi">1</span> <span class="n">remove</span>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">1</span><span class="p">]</span> <span class="mi">1</span> <span class="n">remove</span>
|
||||
<span class="o">------------------------</span>
|
||||
<span class="p">[</span><span class="mi">2</span> <span class="mi">3</span> <span class="mi">1</span><span class="p">]</span>
|
||||
<span class="p">[</span><span class="mi">2</span> <span class="mi">3</span> <span class="mi">1</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
|
@ -564,14 +563,14 @@ from the the quote. The item is only removed once.</p>
|
|||
<dt id="joy.library.select">
|
||||
<code class="descclassname">joy.library.</code><code class="descname">select</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#select"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.select" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><p>Use a Boolean value to select one of two items from a sequence.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="n">A</span> <span class="n">B</span><span class="p">]</span> <span class="kc">False</span> <span class="n">select</span>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="n">A</span> <span class="n">B</span><span class="p">]</span> <span class="kc">False</span> <span class="n">select</span>
|
||||
<span class="o">------------------------</span>
|
||||
<span class="n">A</span>
|
||||
<span class="n">A</span>
|
||||
|
||||
|
||||
<span class="p">[</span><span class="n">A</span> <span class="n">B</span><span class="p">]</span> <span class="kc">True</span> <span class="n">select</span>
|
||||
<span class="p">[</span><span class="n">A</span> <span class="n">B</span><span class="p">]</span> <span class="kc">True</span> <span class="n">select</span>
|
||||
<span class="o">-----------------------</span>
|
||||
<span class="n">B</span>
|
||||
<span class="n">B</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>The sequence can contain more than two items but not fewer.
|
||||
|
|
@ -591,9 +590,9 @@ Boolean value (so empty string, zero, etc. are counted as false, etc.)</p>
|
|||
<dd><p>Like concat but reverses the top list into the second.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">shunt</span> <span class="o">==</span> <span class="p">[</span><span class="n">swons</span><span class="p">]</span> <span class="n">step</span> <span class="o">==</span> <span class="n">reverse</span> <span class="n">swap</span> <span class="n">concat</span>
|
||||
|
||||
<span class="p">[</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span><span class="p">]</span> <span class="p">[</span><span class="n">d</span> <span class="n">e</span> <span class="n">f</span><span class="p">]</span> <span class="n">shunt</span>
|
||||
<span class="p">[</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span><span class="p">]</span> <span class="p">[</span><span class="n">d</span> <span class="n">e</span> <span class="n">f</span><span class="p">]</span> <span class="n">shunt</span>
|
||||
<span class="o">---------------------------</span>
|
||||
<span class="p">[</span><span class="n">f</span> <span class="n">e</span> <span class="n">d</span> <span class="n">a</span> <span class="n">b</span> <span class="n">c</span><span class="p">]</span>
|
||||
<span class="p">[</span><span class="n">f</span> <span class="n">e</span> <span class="n">d</span> <span class="n">a</span> <span class="n">b</span> <span class="n">c</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
|
@ -615,19 +614,19 @@ Negative numbers return complex roots.</p>
|
|||
<dt id="joy.library.step">
|
||||
<code class="descclassname">joy.library.</code><code class="descname">step</code><span class="sig-paren">(</span><em>S</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#step"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.step" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><p>Run a quoted program on each item in a sequence.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="p">[]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span>
|
||||
<span class="o">-----------------------</span>
|
||||
<span class="o">...</span> <span class="o">.</span>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="p">[]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span>
|
||||
<span class="o">-----------------------</span>
|
||||
<span class="o">...</span> <span class="o">.</span>
|
||||
|
||||
|
||||
<span class="o">...</span> <span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span>
|
||||
<span class="o">------------------------</span>
|
||||
<span class="o">...</span> <span class="n">a</span> <span class="o">.</span> <span class="n">Q</span>
|
||||
<span class="o">...</span> <span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span>
|
||||
<span class="o">------------------------</span>
|
||||
<span class="o">...</span> <span class="n">a</span> <span class="o">.</span> <span class="n">Q</span>
|
||||
|
||||
|
||||
<span class="o">...</span> <span class="p">[</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span>
|
||||
<span class="o">...</span> <span class="p">[</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span>
|
||||
<span class="o">----------------------------------------</span>
|
||||
<span class="o">...</span> <span class="n">a</span> <span class="o">.</span> <span class="n">Q</span> <span class="p">[</span><span class="n">b</span> <span class="n">c</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">step</span>
|
||||
<span class="o">...</span> <span class="n">a</span> <span class="o">.</span> <span class="n">Q</span> <span class="p">[</span><span class="n">b</span> <span class="n">c</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">step</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>The step combinator executes the quotation on each member of the list
|
||||
|
|
@ -644,7 +643,9 @@ on top of the stack.</p>
|
|||
<dt id="joy.library.sum_">
|
||||
<code class="descclassname">joy.library.</code><code class="descname">sum_</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#sum_"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.sum_" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><p>Given a quoted sequence of numbers return the sum.</p>
|
||||
<p>sum == 0 swap [+] step</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">sum</span> <span class="o">==</span> <span class="mi">0</span> <span class="n">swap</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">step</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
||||
<dl class="function">
|
||||
|
|
@ -653,9 +654,9 @@ on top of the stack.</p>
|
|||
<dd><p>Expects an integer and a quote on the stack and returns the quote with
|
||||
just the top n items in reverse order (because that’s easier and you can
|
||||
use reverse if needed.)</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="mi">2</span> <span class="n">take</span>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="n">a</span> <span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="mi">2</span> <span class="n">take</span>
|
||||
<span class="o">----------------------</span>
|
||||
<span class="p">[</span><span class="n">b</span> <span class="n">a</span><span class="p">]</span>
|
||||
<span class="p">[</span><span class="n">b</span> <span class="n">a</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
|
@ -664,19 +665,19 @@ use reverse if needed.)</p>
|
|||
<dt id="joy.library.times">
|
||||
<code class="descclassname">joy.library.</code><code class="descname">times</code><span class="sig-paren">(</span><em>stack</em>, <em>expression</em>, <em>dictionary</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/joy/library.html#times"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.library.times" title="Permalink to this definition">¶</a></dt>
|
||||
<dd><p>times == [– dip] cons [swap] infra [0 >] swap while pop</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">n</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">times</span>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">n</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">times</span>
|
||||
<span class="o">---------------------</span> <span class="n">w</span><span class="o">/</span> <span class="n">n</span> <span class="o"><=</span> <span class="mi">0</span>
|
||||
<span class="o">...</span> <span class="o">.</span>
|
||||
<span class="o">...</span> <span class="o">.</span>
|
||||
|
||||
|
||||
<span class="o">...</span> <span class="mi">1</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">times</span>
|
||||
<span class="o">---------------------------------</span>
|
||||
<span class="o">...</span> <span class="o">.</span> <span class="n">Q</span>
|
||||
<span class="o">...</span> <span class="mi">1</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">times</span>
|
||||
<span class="o">-----------------------</span>
|
||||
<span class="o">...</span> <span class="o">.</span> <span class="n">Q</span>
|
||||
|
||||
|
||||
<span class="o">...</span> <span class="n">n</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">times</span>
|
||||
<span class="o">---------------------------------</span> <span class="n">w</span><span class="o">/</span> <span class="n">n</span> <span class="o">></span> <span class="mi">1</span>
|
||||
<span class="o">...</span> <span class="o">.</span> <span class="n">Q</span> <span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">times</span>
|
||||
<span class="o">...</span> <span class="n">n</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="o">.</span> <span class="n">times</span>
|
||||
<span class="o">-------------------------------------</span> <span class="n">w</span><span class="o">/</span> <span class="n">n</span> <span class="o">></span> <span class="mi">1</span>
|
||||
<span class="o">...</span> <span class="o">.</span> <span class="n">Q</span> <span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">times</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</dd></dl>
|
||||
|
|
|
|||
|
|
@ -32,13 +32,13 @@
|
|||
<div class="bodywrapper">
|
||||
<div class="body" role="main">
|
||||
|
||||
<div class="section" id="newtons-method">
|
||||
<h1><a class="reference external" href="https://en.wikipedia.org/wiki/Newton%27s_method">Newton’s method</a><a class="headerlink" href="#newtons-method" title="Permalink to this headline">¶</a></h1>
|
||||
<div class="section" id="newton-s-method">
|
||||
<h1><a class="reference external" href="https://en.wikipedia.org/wiki/Newton%27s_method">Newton’s method</a><a class="headerlink" href="#newton-s-method" title="Permalink to this headline">¶</a></h1>
|
||||
<p>Let’s use the Newton-Raphson method for finding the root of an equation
|
||||
to write a function that can compute the square root of a number.</p>
|
||||
<p>Cf. <a class="reference external" href="https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf">“Why Functional Programming Matters” by John
|
||||
Hughes</a></p>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="k">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
<div class="code ipython3 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="k">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="section" id="a-generator-for-approximations">
|
||||
|
|
@ -90,10 +90,10 @@ function we’re writing. If we let 1 be the initial approximation:</p>
|
|||
<span class="mi">1</span> <span class="p">[</span><span class="n">dup</span> <span class="mi">23</span> <span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span> <span class="n">make_generator</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'gsra == 1 swap [over / + 2 /] cons [dup] swoncat make_generator'</span><span class="p">)</span>
|
||||
<div class="code ipython3 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 gsra'</span><span class="p">)</span>
|
||||
<div class="code ipython3 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 gsra'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="n">dup</span> <span class="mi">23</span> <span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span>
|
||||
|
|
@ -101,7 +101,7 @@ function we’re writing. If we let 1 be the initial approximation:</p>
|
|||
</div>
|
||||
<p>Let’s drive the generator a few time (with the <code class="docutils literal notranslate"><span class="pre">x</span></code> combinator) and
|
||||
square the approximation to see how well it works…</p>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 gsra 6 [x popd] times first sqr'</span><span class="p">)</span>
|
||||
<div class="code ipython3 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 gsra 6 [x popd] times first sqr'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">23.0000000001585</span>
|
||||
|
|
@ -142,7 +142,7 @@ generated already and epsilon ε is handy on the stack…</p>
|
|||
<span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">a</span><span class="o">-</span><span class="n">b</span><span class="p">)</span><span class="o"><=</span><span class="n">ε</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_P == [first - abs] dip <='</span><span class="p">)</span>
|
||||
<div class="code ipython3 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_P [first - abs] dip <='</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
|
|
@ -154,7 +154,7 @@ generated already and epsilon ε is handy on the stack…</p>
|
|||
<span class="n">b</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_B == roll< popop first'</span><span class="p">)</span>
|
||||
<div class="code ipython3 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_B roll< popop first'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
|
|
@ -166,7 +166,7 @@ generated already and epsilon ε is handy on the stack…</p>
|
|||
<ol class="arabic simple">
|
||||
<li>Discard a.</li>
|
||||
<li>Use <code class="docutils literal notranslate"><span class="pre">x</span></code> combinator to generate next term from <code class="docutils literal notranslate"><span class="pre">G</span></code>.</li>
|
||||
<li>Run <code class="docutils literal notranslate"><span class="pre">within</span></code> with <code class="docutils literal notranslate"><span class="pre">i</span></code> (it is a <code class="docutils literal notranslate"><span class="pre">primrec</span></code> function.)</li>
|
||||
<li>Run <code class="docutils literal notranslate"><span class="pre">within</span></code> with <code class="docutils literal notranslate"><span class="pre">i</span></code> (it is a “tail-recursive” function.)</li>
|
||||
</ol>
|
||||
<p>Pretty straightforward:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="n">R0</span> <span class="p">[</span><span class="n">within</span><span class="p">]</span> <span class="n">R1</span>
|
||||
|
|
@ -179,7 +179,7 @@ generated already and epsilon ε is handy on the stack…</p>
|
|||
<span class="n">b</span> <span class="p">[</span><span class="n">c</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="n">within</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_R == [popd x] dip'</span><span class="p">)</span>
|
||||
<div class="code ipython3 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_R [popd x] dip'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
|
|
@ -191,31 +191,31 @@ generated already and epsilon ε is handy on the stack…</p>
|
|||
<span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="o">...</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'within == x 0.000000001 [_within_P] [_within_B] [_within_R] primrec'</span><span class="p">)</span>
|
||||
<span class="n">define</span><span class="p">(</span><span class="s1">'sqrt == gsra within'</span><span class="p">)</span>
|
||||
<div class="code ipython3 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'within x 0.000000001 [_within_P] [_within_B] [_within_R] tailrec'</span><span class="p">)</span>
|
||||
<span class="n">define</span><span class="p">(</span><span class="s1">'sqrt gsra within'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Try it out…</p>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'36 sqrt'</span><span class="p">)</span>
|
||||
<div class="code ipython3 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'36 sqrt'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">6.0</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 sqrt'</span><span class="p">)</span>
|
||||
<div class="code ipython3 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 sqrt'</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Check it.</p>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span><span class="o">**</span><span class="mi">2</span>
|
||||
<div class="code ipython3 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span><span class="o">**</span><span class="mi">2</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">22.999999999999996</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">math</span> <span class="k">import</span> <span class="n">sqrt</span>
|
||||
<div class="code ipython3 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">math</span> <span class="k">import</span> <span class="n">sqrt</span>
|
||||
|
||||
<span class="n">sqrt</span><span class="p">(</span><span class="mi">23</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
|
|
|
|||
|
|
@ -37,22 +37,22 @@
|
|||
<div class="section" id="module-joy.utils.pretty_print">
|
||||
<span id="joy-utils-pretty-print"></span><h2><code class="docutils literal notranslate"><span class="pre">joy.utils.pretty_print</span></code><a class="headerlink" href="#module-joy.utils.pretty_print" title="Permalink to this headline">¶</a></h2>
|
||||
<p>Pretty printing support, e.g.:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>Joy? 23 18 * 99 +
|
||||
. 23 18 mul 99 add
|
||||
23 . 18 mul 99 add
|
||||
23 18 . mul 99 add
|
||||
414 . 99 add
|
||||
414 99 . add
|
||||
513 .
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>Joy? [23 18 * 99 +] trace
|
||||
• 23 18 mul 99 add
|
||||
23 • 18 mul 99 add
|
||||
23 18 • mul 99 add
|
||||
414 • 99 add
|
||||
414 99 • add
|
||||
513 •
|
||||
|
||||
513 <-top
|
||||
|
||||
joy?
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>On each line the stack is printed with the top to the right, then a <code class="docutils literal notranslate"><span class="pre">.</span></code> to
|
||||
represent the current locus of processing, then the pending expression to the
|
||||
left.</p>
|
||||
<p>On each line the stack is printed with the top to the left, then a
|
||||
bullet symbol,``•<a href="#id1"><span class="problematic" id="id2">``</span></a>, to represent the current locus of processing, then
|
||||
the pending expression to the right.</p>
|
||||
<dl class="class">
|
||||
<dt id="joy.utils.pretty_print.TracePrinter">
|
||||
<em class="property">class </em><code class="descclassname">joy.utils.pretty_print.</code><code class="descname">TracePrinter</code><a class="reference internal" href="_modules/joy/utils/pretty_print.html#TracePrinter"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#joy.utils.pretty_print.TracePrinter" title="Permalink to this definition">¶</a></dt>
|
||||
|
|
|
|||
File diff suppressed because one or more lines are too long
|
|
@ -1,13 +1,13 @@
|
|||
`Newton’s method <https://en.wikipedia.org/wiki/Newton%27s_method>`__
|
||||
`Newton's method <https://en.wikipedia.org/wiki/Newton%27s_method>`__
|
||||
=====================================================================
|
||||
|
||||
Let’s use the Newton-Raphson method for finding the root of an equation
|
||||
Let's use the Newton-Raphson method for finding the root of an equation
|
||||
to write a function that can compute the square root of a number.
|
||||
|
||||
Cf. `“Why Functional Programming Matters” by John
|
||||
Cf. `"Why Functional Programming Matters" by John
|
||||
Hughes <https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf>`__
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
from notebook_preamble import J, V, define
|
||||
|
||||
|
|
@ -20,9 +20,9 @@ computes the next approximation:
|
|||
|
||||
::
|
||||
|
||||
a F
|
||||
---------
|
||||
a'
|
||||
a F
|
||||
---------
|
||||
a'
|
||||
|
||||
A Function to Compute the Next Approximation
|
||||
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
|
@ -34,17 +34,17 @@ square root:
|
|||
|
||||
::
|
||||
|
||||
a n over / + 2 /
|
||||
a n a / + 2 /
|
||||
a n/a + 2 /
|
||||
a+n/a 2 /
|
||||
(a+n/a)/2
|
||||
a n over / + 2 /
|
||||
a n a / + 2 /
|
||||
a n/a + 2 /
|
||||
a+n/a 2 /
|
||||
(a+n/a)/2
|
||||
|
||||
The function we want has the argument ``n`` in it:
|
||||
|
||||
::
|
||||
|
||||
F == n over / + 2 /
|
||||
F == n over / + 2 /
|
||||
|
||||
Make it into a Generator
|
||||
~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
|
@ -53,33 +53,33 @@ Our generator would be created by:
|
|||
|
||||
::
|
||||
|
||||
a [dup F] make_generator
|
||||
a [dup F] make_generator
|
||||
|
||||
With n as part of the function F, but n is the input to the sqrt
|
||||
function we’re writing. If we let 1 be the initial approximation:
|
||||
|
||||
::
|
||||
|
||||
1 n 1 / + 2 /
|
||||
1 n/1 + 2 /
|
||||
1 n + 2 /
|
||||
n+1 2 /
|
||||
(n+1)/2
|
||||
1 n 1 / + 2 /
|
||||
1 n/1 + 2 /
|
||||
1 n + 2 /
|
||||
n+1 2 /
|
||||
(n+1)/2
|
||||
|
||||
The generator can be written as:
|
||||
|
||||
::
|
||||
|
||||
23 1 swap [over / + 2 /] cons [dup] swoncat make_generator
|
||||
1 23 [over / + 2 /] cons [dup] swoncat make_generator
|
||||
1 [23 over / + 2 /] [dup] swoncat make_generator
|
||||
1 [dup 23 over / + 2 /] make_generator
|
||||
23 1 swap [over / + 2 /] cons [dup] swoncat make_generator
|
||||
1 23 [over / + 2 /] cons [dup] swoncat make_generator
|
||||
1 [23 over / + 2 /] [dup] swoncat make_generator
|
||||
1 [dup 23 over / + 2 /] make_generator
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('gsra == 1 swap [over / + 2 /] cons [dup] swoncat make_generator')
|
||||
define('gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator')
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('23 gsra')
|
||||
|
||||
|
|
@ -89,10 +89,10 @@ The generator can be written as:
|
|||
[1 [dup 23 over / + 2 /] codireco]
|
||||
|
||||
|
||||
Let’s drive the generator a few time (with the ``x`` combinator) and
|
||||
square the approximation to see how well it works…
|
||||
Let's drive the generator a few time (with the ``x`` combinator) and
|
||||
square the approximation to see how well it works...
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('23 gsra 6 [x popd] times first sqr')
|
||||
|
||||
|
|
@ -105,88 +105,88 @@ square the approximation to see how well it works…
|
|||
Finding Consecutive Approximations within a Tolerance
|
||||
-----------------------------------------------------
|
||||
|
||||
From `“Why Functional Programming Matters” by John
|
||||
From `"Why Functional Programming Matters" by John
|
||||
Hughes <https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf>`__:
|
||||
|
||||
The remainder of a square root finder is a function *within*, which
|
||||
takes a tolerance and a list of approximations and looks down the
|
||||
list for two successive approximations that differ by no more than
|
||||
the given tolerance.
|
||||
The remainder of a square root finder is a function *within*, which
|
||||
takes a tolerance and a list of approximations and looks down the
|
||||
list for two successive approximations that differ by no more than
|
||||
the given tolerance.
|
||||
|
||||
(And note that by “list” he means a lazily-evaluated list.)
|
||||
|
||||
Using the *output* ``[a G]`` of the above generator for square root
|
||||
approximations, and further assuming that the first term a has been
|
||||
generated already and epsilon ε is handy on the stack…
|
||||
generated already and epsilon ε is handy on the stack...
|
||||
|
||||
::
|
||||
|
||||
a [b G] ε within
|
||||
---------------------- a b - abs ε <=
|
||||
b
|
||||
a [b G] ε within
|
||||
---------------------- a b - abs ε <=
|
||||
b
|
||||
|
||||
|
||||
a [b G] ε within
|
||||
---------------------- a b - abs ε >
|
||||
b [c G] ε within
|
||||
a [b G] ε within
|
||||
---------------------- a b - abs ε >
|
||||
b [c G] ε within
|
||||
|
||||
Predicate
|
||||
~~~~~~~~~
|
||||
|
||||
::
|
||||
|
||||
a [b G] ε [first - abs] dip <=
|
||||
a [b G] first - abs ε <=
|
||||
a b - abs ε <=
|
||||
a-b abs ε <=
|
||||
abs(a-b) ε <=
|
||||
(abs(a-b)<=ε)
|
||||
a [b G] ε [first - abs] dip <=
|
||||
a [b G] first - abs ε <=
|
||||
a b - abs ε <=
|
||||
a-b abs ε <=
|
||||
abs(a-b) ε <=
|
||||
(abs(a-b)<=ε)
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('_within_P == [first - abs] dip <=')
|
||||
define('_within_P [first - abs] dip <=')
|
||||
|
||||
Base-Case
|
||||
~~~~~~~~~
|
||||
|
||||
::
|
||||
|
||||
a [b G] ε roll< popop first
|
||||
[b G] ε a popop first
|
||||
[b G] first
|
||||
b
|
||||
a [b G] ε roll< popop first
|
||||
[b G] ε a popop first
|
||||
[b G] first
|
||||
b
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('_within_B == roll< popop first')
|
||||
define('_within_B roll< popop first')
|
||||
|
||||
Recur
|
||||
~~~~~
|
||||
|
||||
::
|
||||
|
||||
a [b G] ε R0 [within] R1
|
||||
a [b G] ε R0 [within] R1
|
||||
|
||||
1. Discard a.
|
||||
2. Use ``x`` combinator to generate next term from ``G``.
|
||||
3. Run ``within`` with ``i`` (it is a ``primrec`` function.)
|
||||
3. Run ``within`` with ``i`` (it is a "tail-recursive" function.)
|
||||
|
||||
Pretty straightforward:
|
||||
|
||||
::
|
||||
|
||||
a [b G] ε R0 [within] R1
|
||||
a [b G] ε [popd x] dip [within] i
|
||||
a [b G] popd x ε [within] i
|
||||
[b G] x ε [within] i
|
||||
b [c G] ε [within] i
|
||||
b [c G] ε within
|
||||
a [b G] ε R0 [within] R1
|
||||
a [b G] ε [popd x] dip [within] i
|
||||
a [b G] popd x ε [within] i
|
||||
[b G] x ε [within] i
|
||||
b [c G] ε [within] i
|
||||
b [c G] ε within
|
||||
|
||||
b [c G] ε within
|
||||
b [c G] ε within
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('_within_R == [popd x] dip')
|
||||
define('_within_R [popd x] dip')
|
||||
|
||||
Setting up
|
||||
~~~~~~~~~~
|
||||
|
|
@ -196,17 +196,17 @@ The recursive function we have defined so far needs a slight preamble:
|
|||
|
||||
::
|
||||
|
||||
[a G] x ε ...
|
||||
a [b G] ε ...
|
||||
[a G] x ε ...
|
||||
a [b G] ε ...
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
define('within == x 0.000000001 [_within_P] [_within_B] [_within_R] primrec')
|
||||
define('sqrt == gsra within')
|
||||
define('within x 0.000000001 [_within_P] [_within_B] [_within_R] tailrec')
|
||||
define('sqrt gsra within')
|
||||
|
||||
Try it out…
|
||||
Try it out...
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('36 sqrt')
|
||||
|
||||
|
|
@ -216,7 +216,7 @@ Try it out…
|
|||
6.0
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
J('23 sqrt')
|
||||
|
||||
|
|
@ -228,7 +228,7 @@ Try it out…
|
|||
|
||||
Check it.
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
4.795831523312719**2
|
||||
|
||||
|
|
@ -241,7 +241,7 @@ Check it.
|
|||
|
||||
|
||||
|
||||
.. code:: ipython2
|
||||
.. code:: ipython3
|
||||
|
||||
from math import sqrt
|
||||
|
||||
|
|
|
|||
|
|
@ -23,12 +23,9 @@ functions. Its main export is a Python function initialize() that
|
|||
returns a dictionary of Joy functions suitable for use with the joy()
|
||||
function.
|
||||
'''
|
||||
from builtins import map, object, range, zip
|
||||
|
||||
from inspect import getdoc
|
||||
from inspect import getdoc, getmembers, isfunction
|
||||
from functools import wraps
|
||||
from itertools import count
|
||||
from inspect import getmembers, isfunction
|
||||
import operator, math
|
||||
|
||||
from .parser import text_to_expression, Symbol
|
||||
|
|
@ -292,7 +289,7 @@ def _text_to_defs(text):
|
|||
return (
|
||||
line.strip()
|
||||
for line in text.splitlines()
|
||||
if not line.startswith('#')
|
||||
if line and not line.startswith('#')
|
||||
)
|
||||
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue