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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml">
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<head>
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<meta http-equiv="X-UA-Compatible" content="IE=Edge" />
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
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<title>Joypy — Thun 0.1.1 documentation</title>
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<link rel="stylesheet" href="../_static/pygments.css" type="text/css" />
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<link rel="index" title="Index" href="../genindex.html" />
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<link rel="search" title="Search" href="../search.html" />
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<link rel="stylesheet" href="../_static/custom.css" type="text/css" />
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<meta name="viewport" content="width=device-width, initial-scale=0.9, maximum-scale=0.9" />
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</head><body>
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<div class="document">
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<div class="documentwrapper">
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<div class="bodywrapper">
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<div class="body" role="main">
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<div class="section" id="joypy">
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<h1>Joypy<a class="headerlink" href="#joypy" title="Permalink to this headline">¶</a></h1>
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<div class="section" id="joy-in-python">
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<h2>Joy in Python<a class="headerlink" href="#joy-in-python" title="Permalink to this headline">¶</a></h2>
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<p>This implementation is meant as a tool for exploring the programming
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model and method of Joy. Python seems like a great implementation
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language for Joy for several reasons.</p>
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<p>We can lean on the Python immutable types for our basic semantics and
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types: ints, floats, strings, and tuples, which enforces functional
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purity. We get garbage collection for free. Compilation via Cython. Glue
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language with loads of libraries.</p>
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<div class="section" id="read-eval-print-loop-repl">
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<h3><a class="reference external" href="https://en.wikipedia.org/wiki/Read%E2%80%93eval%E2%80%93print_loop">Read-Eval-Print Loop (REPL)</a><a class="headerlink" href="#read-eval-print-loop-repl" title="Permalink to this headline">¶</a></h3>
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<p>The main way to interact with the Joy interpreter is through a simple
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<a class="reference external" href="https://en.wikipedia.org/wiki/Read%E2%80%93eval%E2%80%93print_loop">REPL</a>
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that you start by running the package:</p>
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<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>$ python -m joy
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Joypy - Copyright © 2017 Simon Forman
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This program comes with ABSOLUTELY NO WARRANTY; for details type "warranty".
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This is free software, and you are welcome to redistribute it
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under certain conditions; type "sharing" for details.
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Type "words" to see a list of all words, and "[<name>] help" to print the
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docs for a word.
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<-top
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joy? _
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</pre></div>
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</div>
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<p>The <code class="docutils literal notranslate"><span class="pre"><-top</span></code> marker points to the top of the (initially empty) stack.
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You can enter Joy notation at the prompt and a <a class="reference external" href="#The-TracePrinter.">trace of
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evaluation</a> will be printed followed by the stack
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and prompt again:</p>
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<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>joy? 23 sqr 18 +
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. 23 sqr 18 +
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23 . sqr 18 +
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23 . dup mul 18 +
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23 23 . mul 18 +
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529 . 18 +
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529 18 . +
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547 .
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547 <-top
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joy?
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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>
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<div class="section" id="stacks-aka-list-quote-sequence-etc">
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<h1>Stacks (aka list, quote, sequence, etc.)<a class="headerlink" href="#stacks-aka-list-quote-sequence-etc" title="Permalink to this headline">¶</a></h1>
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<p>In Joy, in addition to the types Boolean, integer, float, and string,
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there is a single sequence type represented by enclosing a sequence of
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terms in brackets <code class="docutils literal notranslate"><span class="pre">[...]</span></code>. This sequence type is used to represent
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both the stack and the expression. It is a <a class="reference external" href="https://en.wikipedia.org/wiki/Cons#Lists">cons
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list</a> made from Python
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tuples.</p>
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<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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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</pre></div>
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</div>
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<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>§ Stack
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When talking about Joy we use the terms "stack", "list", "sequence" and
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"aggregate" to mean the same thing: a simple datatype that permits
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certain operations such as iterating and pushing and popping values from
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(at least) one end.
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We use the venerable two-tuple recursive form of sequences where the
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empty tuple () is the empty stack and (head, rest) gives the recursive
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form of a stack with one or more items on it.
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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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And so on.
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We have two very simple functions to build up a stack from a Python
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iterable and also to iterate through a stack and yield its items
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one-by-one in order, and two functions to generate string representations
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of stacks:
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list_to_stack()
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iter_stack()
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expression_to_string() (prints left-to-right)
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stack_to_string() (prints right-to-left)
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A word about the stack data structure.
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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(stack):
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head, tail = stack
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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 de-structuring the
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incoming argument 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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</pre></div>
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</div>
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<p>The 0th item in the list will be on the top of the stack and <em>vise
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versa</em>.</p>
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<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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 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="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 class="code ipython2 highlight-default notranslate"><div class="highlight"><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 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="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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<p>This requires reversing the sequence (or iterating backwards) otherwise:</p>
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<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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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</pre></div>
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</div>
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<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="mi">3</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">1</span><span class="p">,</span> <span class="p">())))</span>
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<span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
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</pre></div>
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</div>
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<p>Because Joy lists are made out of Python tuples they are immutable, so
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all Joy datastructures are <em>`purely
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functional <https://en.wikipedia.org/wiki/Purely_functional_data_structure>`__</em>.</p>
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</div>
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<div class="section" id="the-joy-function">
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<h1>The <code class="docutils literal notranslate"><span class="pre">joy()</span></code> function.<a class="headerlink" href="#the-joy-function" title="Permalink to this headline">¶</a></h1>
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<div class="section" id="an-interpreter">
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<h2>An Interpreter<a class="headerlink" href="#an-interpreter" title="Permalink to this headline">¶</a></h2>
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<p>The <code class="docutils literal notranslate"><span class="pre">joy()</span></code> function is extrememly simple. It accepts a stack, an
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expression, and a dictionary, and it iterates through the expression
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putting values onto the stack and delegating execution to functions it
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looks up in the dictionary.</p>
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<p>Each function is passed the stack, expression, and dictionary and
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returns them. Whatever the function returns becomes the new stack,
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expression, and dictionary. (The dictionary is passed to enable e.g.
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writing words that let you enter new words into the dictionary at
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runtime, which nothing does yet and may be a bad idea, and the <code class="docutils literal notranslate"><span class="pre">help</span></code>
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command.)</p>
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<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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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</pre></div>
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</div>
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<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">joy</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="n">dictionary</span><span class="p">,</span> <span class="n">viewer</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
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<span class="sd">'''</span>
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<span class="sd"> Evaluate the Joy expression on the stack.</span>
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<span class="sd"> '''</span>
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<span class="k">while</span> <span class="n">expression</span><span class="p">:</span>
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<span class="k">if</span> <span class="n">viewer</span><span class="p">:</span> <span class="n">viewer</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">)</span>
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<span class="n">term</span><span class="p">,</span> <span class="n">expression</span> <span class="o">=</span> <span class="n">expression</span>
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<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">term</span><span class="p">,</span> <span class="n">Symbol</span><span class="p">):</span>
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<span class="n">term</span> <span class="o">=</span> <span class="n">dictionary</span><span class="p">[</span><span class="n">term</span><span class="p">]</span>
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<span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">,</span> <span class="n">dictionary</span> <span class="o">=</span> <span class="n">term</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="n">dictionary</span><span class="p">)</span>
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<span class="k">else</span><span class="p">:</span>
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<span class="n">stack</span> <span class="o">=</span> <span class="n">term</span><span class="p">,</span> <span class="n">stack</span>
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<span class="k">if</span> <span class="n">viewer</span><span class="p">:</span> <span class="n">viewer</span><span class="p">(</span><span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">)</span>
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<span class="k">return</span> <span class="n">stack</span><span class="p">,</span> <span class="n">expression</span><span class="p">,</span> <span class="n">dictionary</span>
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</pre></div>
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</div>
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<div class="section" id="view-function">
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<h3>View function<a class="headerlink" href="#view-function" title="Permalink to this headline">¶</a></h3>
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<p>The <code class="docutils literal notranslate"><span class="pre">joy()</span></code> function accepts a “viewer” function which it calls on
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each iteration passing the current stack and expression just before
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evaluation. This can be used for tracing, breakpoints, retrying after
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exceptions, or interrupting an evaluation and saving to disk or sending
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over the network to resume later. The stack and expression together
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contain all the state of the computation at each step.</p>
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</div>
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<div class="section" id="the-traceprinter">
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<h3>The <code class="docutils literal notranslate"><span class="pre">TracePrinter</span></code>.<a class="headerlink" href="#the-traceprinter" title="Permalink to this headline">¶</a></h3>
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<p>A <code class="docutils literal notranslate"><span class="pre">viewer</span></code> records each step of the evaluation of a Joy program. The
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<code class="docutils literal notranslate"><span class="pre">TracePrinter</span></code> has a facility for printing out a trace of the
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evaluation, one line per step. Each step is aligned to the current
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interpreter position, signified by a period separating the stack on the
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left from the pending expression (“continuation”) on the right.</p>
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</div>
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<div class="section" id="continuation-passing-style">
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<h3><a class="reference external" href="https://en.wikipedia.org/wiki/Continuation-passing_style">Continuation-Passing Style</a><a class="headerlink" href="#continuation-passing-style" title="Permalink to this headline">¶</a></h3>
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<p>One day I thought, What happens if you rewrite Joy to use
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<a class="reference external" href="https://en.wikipedia.org/wiki/Continuation-passing_style">CSP</a>? I
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made all the functions accept and return the expression as well as the
|
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stack and found that all the combinators could be rewritten to work by
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modifying the expression rather than making recursive calls to the
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<code class="docutils literal notranslate"><span class="pre">joy()</span></code> function.</p>
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</div>
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</div>
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</div>
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<div class="section" id="parser">
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<h1>Parser<a class="headerlink" href="#parser" title="Permalink to this headline">¶</a></h1>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">joy.parser</span>
|
||||||
|
|
||||||
|
<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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>§ Converting text to a joy expression.
|
||||||
|
|
||||||
|
This module exports a single function:
|
||||||
|
|
||||||
|
text_to_expression(text)
|
||||||
|
|
||||||
|
As well as a single Symbol class and a single Exception type:
|
||||||
|
|
||||||
|
ParseError
|
||||||
|
|
||||||
|
When supplied with a string this function returns a Python datastructure
|
||||||
|
that represents the Joy datastructure described by the text expression.
|
||||||
|
Any unbalanced square brackets will raise a ParseError.
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>The parser is extremely simple, the undocumented <code class="docutils literal notranslate"><span class="pre">re.Scanner</span></code> 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
|
||||||
|
like that.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">_parse</span><span class="p">(</span><span class="n">tokens</span><span class="p">):</span>
|
||||||
|
<span class="sd">'''</span>
|
||||||
|
<span class="sd"> Return a stack/list expression of the tokens.</span>
|
||||||
|
<span class="sd"> '''</span>
|
||||||
|
<span class="n">frame</span> <span class="o">=</span> <span class="p">[]</span>
|
||||||
|
<span class="n">stack</span> <span class="o">=</span> <span class="p">[]</span>
|
||||||
|
<span class="k">for</span> <span class="n">tok</span> <span class="ow">in</span> <span class="n">tokens</span><span class="p">:</span>
|
||||||
|
<span class="k">if</span> <span class="n">tok</span> <span class="o">==</span> <span class="s1">'['</span><span class="p">:</span>
|
||||||
|
<span class="n">stack</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">frame</span><span class="p">)</span>
|
||||||
|
<span class="n">frame</span> <span class="o">=</span> <span class="p">[]</span>
|
||||||
|
<span class="n">stack</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">frame</span><span class="p">)</span>
|
||||||
|
<span class="k">elif</span> <span class="n">tok</span> <span class="o">==</span> <span class="s1">']'</span><span class="p">:</span>
|
||||||
|
<span class="k">try</span><span class="p">:</span>
|
||||||
|
<span class="n">frame</span> <span class="o">=</span> <span class="n">stack</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
|
||||||
|
<span class="k">except</span> <span class="ne">IndexError</span><span class="p">:</span>
|
||||||
|
<span class="k">raise</span> <span class="n">ParseError</span><span class="p">(</span><span class="s1">'One or more extra closing brackets.'</span><span class="p">)</span>
|
||||||
|
<span class="n">frame</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">list_to_stack</span><span class="p">(</span><span class="n">frame</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
|
||||||
|
<span class="k">else</span><span class="p">:</span>
|
||||||
|
<span class="n">frame</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">tok</span><span class="p">)</span>
|
||||||
|
<span class="k">if</span> <span class="n">stack</span><span class="p">:</span>
|
||||||
|
<span class="k">raise</span> <span class="n">ParseError</span><span class="p">(</span><span class="s1">'One or more unclosed brackets.'</span><span class="p">)</span>
|
||||||
|
<span class="k">return</span> <span class="n">list_to_stack</span><span class="p">(</span><span class="n">frame</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>That’s pretty much all there is to it.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
</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="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><span class="mi">4</span><span class="p">,</span> <span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="p">())))))</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
</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="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> <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="p">())))</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
<span class="c1"># a Symbol, no lookup at</span>
|
||||||
|
<span class="c1"># parse-time. Haiku docs.</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="p">(</span><span class="mi">23</span><span class="p">,</span> <span class="p">((</span><span class="s1">'four'</span><span class="p">,</span> <span class="p">((</span><span class="o">-</span><span class="mf">5.0</span><span class="p">,</span> <span class="p">()),</span> <span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="p">()))),</span> <span class="p">(</span><span class="mi">8888</span><span class="p">,</span> <span class="p">()))))</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((),</span> <span class="p">((),</span> <span class="p">((),</span> <span class="p">((),</span> <span class="p">((),</span> <span class="p">())))))</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((((((),</span> <span class="p">()),</span> <span class="p">()),</span> <span class="p">()),</span> <span class="p">()),</span> <span class="p">())</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="library">
|
||||||
|
<h1>Library<a class="headerlink" href="#library" title="Permalink to this headline">¶</a></h1>
|
||||||
|
<p>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 <code class="docutils literal notranslate"><span class="pre">add</span></code> (or
|
||||||
|
<code class="docutils literal notranslate"><span class="pre">+</span></code>, the library module supports aliases), and combinators which
|
||||||
|
provide control-flow and higher-order operations.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>!= % & * *fraction *fraction0 + ++ - -- / < << <= <> = > >= >> ? ^ add anamorphism and app1 app2 app3 average b binary branch choice clear cleave concat cons dinfrirst dip dipd dipdd disenstacken div down_to_zero dudipd dup dupd dupdip enstacken eq first flatten floordiv gcd ge genrec getitem gt help i id ifte infra le least_fraction loop lshift lt map min mod modulus mul ne neg not nullary or over pam parse pm pop popd popdd popop pow pred primrec product quoted range range_to_zero rem remainder remove rest reverse roll< roll> rolldown rollup rshift run second select sharing shunt size sqr sqrt stack step sub succ sum swaack swap swoncat swons ternary third times truediv truthy tuck unary uncons unit unquoted unstack void warranty while words x xor zip •
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Many of the functions are defined in Python, like <code class="docutils literal notranslate"><span class="pre">dip</span></code>:</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">dip</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="n">dictionary</span><span class="p">):</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>
|
||||||
|
<span class="n">expression</span> <span class="o">=</span> <span class="n">x</span><span class="p">,</span> <span class="n">expression</span>
|
||||||
|
<span class="k">return</span> <span class="n">stack</span><span class="p">,</span> <span class="n">pushback</span><span class="p">(</span><span class="n">quote</span><span class="p">,</span> <span class="n">expression</span><span class="p">),</span> <span class="n">dictionary</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Some functions are defined in equations in terms of other functions.
|
||||||
|
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.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<pre class="literal-block">
|
||||||
|
second == rest first
|
||||||
|
third == rest rest first
|
||||||
|
product == 1 swap [*] step
|
||||||
|
swons == swap cons
|
||||||
|
swoncat == swap concat
|
||||||
|
flatten == [] swap [concat] step
|
||||||
|
unit == [] cons
|
||||||
|
quoted == [unit] dip
|
||||||
|
unquoted == [i] dip
|
||||||
|
enstacken == stack [clear] dip
|
||||||
|
disenstacken == ? [uncons ?] loop pop
|
||||||
|
? == dup truthy
|
||||||
|
dinfrirst == dip infra first
|
||||||
|
nullary == [stack] dinfrirst
|
||||||
|
unary == [stack [pop] dip] dinfrirst
|
||||||
|
binary == [stack [popop] dip] dinfrirst
|
||||||
|
ternary == [stack [popop pop] dip] dinfrirst
|
||||||
|
pam == [i] map
|
||||||
|
run == [] swap infra
|
||||||
|
sqr == dup mul
|
||||||
|
size == 0 swap [pop ++] step
|
||||||
|
cleave == [i] app2 [popd] dip
|
||||||
|
average == [sum 1.0 <em>] [size] cleave /
|
||||||
|
gcd == 1 [tuck modulus dup 0 >] loop pop
|
||||||
|
least_fraction == dup [gcd] infra [div] concat map
|
||||||
|
*fraction == [uncons] dip uncons [swap] dip concat [</em>] infra [*] dip cons
|
||||||
|
<em>fraction0 == concat [[swap] dip * [</em>] dip] infra
|
||||||
|
down_to_zero == [0 >] [dup --] while
|
||||||
|
range_to_zero == unit [down_to_zero] infra
|
||||||
|
anamorphism == [pop []] swap [dip swons] genrec
|
||||||
|
range == [0 <=] [1 - dup] anamorphism
|
||||||
|
while == swap [nullary] cons dup dipd concat loop
|
||||||
|
dudipd == dup dipd
|
||||||
|
primrec == [i] genrec
|
||||||
|
</pre>
|
||||||
|
<p>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.</p>
|
||||||
|
<p>It would be simple enough to define one, but it would open the door to
|
||||||
|
<em>name binding</em> and break the idea that all state is captured in the
|
||||||
|
stack and expression. There’s an implicit <em>standard dictionary</em> 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.)</p>
|
||||||
|
<p>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
|
||||||
|
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 <em>Grand Refactoring</em> biannually (two years, not six
|
||||||
|
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.</p>
|
||||||
|
<p>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 <a class="reference external" href="https://en.wikipedia.org/wiki/Thundering_herd_problem">fractal
|
||||||
|
“thundering herd”
|
||||||
|
attack</a> on
|
||||||
|
human mentality.</p>
|
||||||
|
<p>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
|
||||||
|
skeptical, as I was, but it seems to work: deriving code mathematically
|
||||||
|
seems to lead to fewer errors.</p>
|
||||||
|
<p>But my point now is that this great ratio of textual explanation to wind
|
||||||
|
up with code that consists of a few equations and could fit on an index
|
||||||
|
card is highly desirable. Less code has fewer errors. The structure of
|
||||||
|
Joy engenders a kind of thinking that seems to be very effective for
|
||||||
|
developing structured processes.</p>
|
||||||
|
<p>There seems to be an elegance and power to the notation.</p>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
|
||||||
|
<div class="sphinxsidebarwrapper">
|
||||||
|
<h3><a href="../index.html">Table Of Contents</a></h3>
|
||||||
|
<ul>
|
||||||
|
<li><a class="reference internal" href="#">Joypy</a><ul>
|
||||||
|
<li><a class="reference internal" href="#joy-in-python">Joy in Python</a><ul>
|
||||||
|
<li><a class="reference internal" href="#read-eval-print-loop-repl">Read-Eval-Print Loop (REPL)</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li><a class="reference internal" href="#stacks-aka-list-quote-sequence-etc">Stacks (aka list, quote, sequence, etc.)</a></li>
|
||||||
|
<li><a class="reference internal" href="#the-joy-function">The <code class="docutils literal notranslate"><span class="pre">joy()</span></code> function.</a><ul>
|
||||||
|
<li><a class="reference internal" href="#an-interpreter">An Interpreter</a><ul>
|
||||||
|
<li><a class="reference internal" href="#view-function">View function</a></li>
|
||||||
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.7.3.
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<div class="section" id="preamble">
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<h1>Preamble<a class="headerlink" href="#preamble" title="Permalink to this headline">¶</a></h1>
|
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<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">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span>
|
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<div class="section" id="a-long-trace">
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<h1>A long trace<a class="headerlink" href="#a-long-trace" title="Permalink to this headline">¶</a></h1>
|
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<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'[23 18] average'</span><span class="p">)</span>
|
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</pre></div>
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<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="n">average</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="o">.</span> <span class="n">average</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="p">[</span><span class="n">size</span><span class="p">]</span> <span class="n">cleave</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">size</span><span class="p">]</span> <span class="n">cleave</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="p">[</span><span class="n">size</span><span class="p">]</span> <span class="o">.</span> <span class="n">cleave</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="p">[</span><span class="n">size</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">app2</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="p">[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">.</span> <span class="n">app2</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</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">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="o">.</span> <span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span> <span class="p">[[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="mi">41</span> <span class="o">.</span> <span class="mf">1.0</span> <span class="o">*</span> <span class="p">[[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="mi">41</span> <span class="mf">1.0</span> <span class="o">.</span> <span class="o">*</span> <span class="p">[[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="mf">41.0</span> <span class="o">.</span> <span class="p">[[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="mf">41.0</span> <span class="p">[[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="o">.</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="mf">41.0</span><span class="p">]</span> <span class="o">.</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="o">.</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="o">.</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</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">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="n">size</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="o">.</span> <span class="n">size</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="o">.</span> <span class="mi">0</span> <span class="n">swap</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="n">step</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mi">0</span> <span class="o">.</span> <span class="n">swap</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="n">step</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="mi">0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="n">step</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="mi">0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="mi">0</span> <span class="mi">23</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[</span><span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="n">step</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="mi">0</span> <span class="mi">23</span> <span class="o">.</span> <span class="n">pop</span> <span class="o">++</span> <span class="p">[</span><span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="n">step</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="mi">0</span> <span class="o">.</span> <span class="o">++</span> <span class="p">[</span><span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="n">step</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="mi">1</span> <span class="o">.</span> <span class="p">[</span><span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="n">step</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="mi">1</span> <span class="p">[</span><span class="mi">18</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="n">step</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="mi">1</span> <span class="p">[</span><span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="mi">1</span> <span class="mi">18</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="mi">1</span> <span class="mi">18</span> <span class="o">.</span> <span class="n">pop</span> <span class="o">++</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="mi">1</span> <span class="o">.</span> <span class="o">++</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="mi">2</span> <span class="o">.</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="mi">2</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="o">.</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="mi">2</span> <span class="o">.</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="mi">2</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="o">.</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="o">.</span> <span class="n">popd</span> <span class="mi">2</span> <span class="o">/</span>
|
||||||
|
<span class="mf">41.0</span> <span class="o">.</span> <span class="mi">2</span> <span class="o">/</span>
|
||||||
|
<span class="mf">41.0</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">/</span>
|
||||||
|
<span class="mf">20.5</span> <span class="o">.</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="replacing-sum-and-size-with-compiled-versions">
|
||||||
|
<h1>Replacing <code class="docutils literal notranslate"><span class="pre">sum</span></code> and <code class="docutils literal notranslate"><span class="pre">size</span></code> with “compiled” versions.<a class="headerlink" href="#replacing-sum-and-size-with-compiled-versions" title="Permalink to this headline">¶</a></h1>
|
||||||
|
<p>Both <code class="docutils literal notranslate"><span class="pre">sum</span></code> and <code class="docutils literal notranslate"><span class="pre">size</span></code> are
|
||||||
|
<a class="reference external" href="https://en.wikipedia.org/wiki/Catamorphism">catamorphisms</a>, they
|
||||||
|
each convert a sequence to a single value.</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">'[sum] help'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Given</span> <span class="n">a</span> <span class="n">quoted</span> <span class="n">sequence</span> <span class="n">of</span> <span class="n">numbers</span> <span class="k">return</span> <span class="n">the</span> <span class="nb">sum</span><span class="o">.</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>
|
||||||
|
<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">'[size] help'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">0</span> <span class="n">swap</span> <span class="p">[</span><span class="n">pop</span> <span class="o">++</span><span class="p">]</span> <span class="n">step</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>We can use “compiled” versions (they’re not really compiled in this
|
||||||
|
case, they’re hand-written in Python) to speed up evaluation and make
|
||||||
|
the trace more readable. The <code class="docutils literal notranslate"><span class="pre">sum</span></code> function is already in the library.
|
||||||
|
It gets shadowed by the definition version above during
|
||||||
|
<code class="docutils literal notranslate"><span class="pre">initialize()</span></code>.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.library</span> <span class="k">import</span> <span class="n">SimpleFunctionWrapper</span><span class="p">,</span> <span class="n">primitives</span>
|
||||||
|
<span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="k">import</span> <span class="n">iter_stack</span>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="nd">@SimpleFunctionWrapper</span>
|
||||||
|
<span class="k">def</span> <span class="nf">size</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
|
||||||
|
<span class="sd">'''Return the size of the sequence on the stack.'''</span>
|
||||||
|
<span class="n">sequence</span><span class="p">,</span> <span class="n">stack</span> <span class="o">=</span> <span class="n">stack</span>
|
||||||
|
<span class="n">n</span> <span class="o">=</span> <span class="mi">0</span>
|
||||||
|
<span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="n">iter_stack</span><span class="p">(</span><span class="n">sequence</span><span class="p">):</span>
|
||||||
|
<span class="n">n</span> <span class="o">+=</span> <span class="mi">1</span>
|
||||||
|
<span class="k">return</span> <span class="n">n</span><span class="p">,</span> <span class="n">stack</span>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="n">sum_</span> <span class="o">=</span> <span class="nb">next</span><span class="p">(</span><span class="n">p</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">primitives</span> <span class="k">if</span> <span class="n">p</span><span class="o">.</span><span class="n">name</span> <span class="o">==</span> <span class="s1">'sum'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Now we replace them old versions in the dictionary with the new versions
|
||||||
|
and re-evaluate the expression.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">old_sum</span><span class="p">,</span> <span class="n">D</span><span class="p">[</span><span class="s1">'sum'</span><span class="p">]</span> <span class="o">=</span> <span class="n">D</span><span class="p">[</span><span class="s1">'sum'</span><span class="p">],</span> <span class="n">sum_</span>
|
||||||
|
<span class="n">old_size</span><span class="p">,</span> <span class="n">D</span><span class="p">[</span><span class="s1">'size'</span><span class="p">]</span> <span class="o">=</span> <span class="n">D</span><span class="p">[</span><span class="s1">'size'</span><span class="p">],</span> <span class="n">size</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>You can see that <code class="docutils literal notranslate"><span class="pre">size</span></code> and <code class="docutils literal notranslate"><span class="pre">sum</span></code> now execute in a single step.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'[23 18] average'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="n">average</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="o">.</span> <span class="n">average</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="p">[</span><span class="n">size</span><span class="p">]</span> <span class="n">cleave</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">size</span><span class="p">]</span> <span class="n">cleave</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="p">[</span><span class="n">size</span><span class="p">]</span> <span class="o">.</span> <span class="n">cleave</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="p">[</span><span class="n">size</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">app2</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="p">[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">.</span> <span class="n">app2</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</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">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="o">.</span> <span class="nb">sum</span> <span class="mf">1.0</span> <span class="o">*</span> <span class="p">[[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="mi">41</span> <span class="o">.</span> <span class="mf">1.0</span> <span class="o">*</span> <span class="p">[[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="mi">41</span> <span class="mf">1.0</span> <span class="o">.</span> <span class="o">*</span> <span class="p">[[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="mf">41.0</span> <span class="o">.</span> <span class="p">[[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="mf">41.0</span> <span class="p">[[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="o">.</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="mf">41.0</span><span class="p">]</span> <span class="o">.</span> <span class="n">first</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="o">.</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="o">.</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="p">[[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="p">[</span><span class="n">i</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">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="p">[</span><span class="n">size</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="o">.</span> <span class="n">size</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="mi">2</span> <span class="o">.</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="mi">2</span> <span class="p">[</span><span class="mf">41.0</span> <span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]]</span> <span class="o">.</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="n">first</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="mi">2</span> <span class="o">.</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="mi">2</span> <span class="p">[</span><span class="n">popd</span><span class="p">]</span> <span class="o">.</span> <span class="n">dip</span> <span class="o">/</span>
|
||||||
|
<span class="p">[</span><span class="mi">23</span> <span class="mi">18</span><span class="p">]</span> <span class="mf">41.0</span> <span class="o">.</span> <span class="n">popd</span> <span class="mi">2</span> <span class="o">/</span>
|
||||||
|
<span class="mf">41.0</span> <span class="o">.</span> <span class="mi">2</span> <span class="o">/</span>
|
||||||
|
<span class="mf">41.0</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">/</span>
|
||||||
|
<span class="mf">20.5</span> <span class="o">.</span>
|
||||||
|
</pre></div>
|
||||||
|
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|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
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|
||||||
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|
||||||
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|
||||||
|
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
|
||||||
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|
||||||
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<h3><a href="../index.html">Table Of Contents</a></h3>
|
||||||
|
<ul>
|
||||||
|
<li><a class="reference internal" href="#">Preamble</a></li>
|
||||||
|
<li><a class="reference internal" href="#a-long-trace">A long trace</a></li>
|
||||||
|
<li><a class="reference internal" href="#replacing-sum-and-size-with-compiled-versions">Replacing <code class="docutils literal notranslate"><span class="pre">sum</span></code> and <code class="docutils literal notranslate"><span class="pre">size</span></code> with “compiled” versions.</a></li>
|
||||||
|
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|
||||||
|
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<br />
|
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.7.3.
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<div class="section" id="advent-of-code-2017">
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<h1>Advent of Code 2017<a class="headerlink" href="#advent-of-code-2017" title="Permalink to this headline">¶</a></h1>
|
||||||
|
<div class="section" id="december-1st">
|
||||||
|
<h2>December 1st<a class="headerlink" href="#december-1st" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>[Given] a sequence of digits (your puzzle input) and find the sum of all
|
||||||
|
digits that match the next digit in the list. The list is circular, so
|
||||||
|
the digit after the last digit is the first digit in the list.</p>
|
||||||
|
<p>For example:</p>
|
||||||
|
<ul class="simple">
|
||||||
|
<li>1122 produces a sum of 3 (1 + 2) because the first digit (1) matches
|
||||||
|
the second digit and the third digit (2) matches the fourth digit.</li>
|
||||||
|
<li>1111 produces 4 because each digit (all 1) matches the next.</li>
|
||||||
|
<li>1234 produces 0 because no digit matches the next.</li>
|
||||||
|
<li>91212129 produces 9 because the only digit that matches the next one
|
||||||
|
is the last digit, 9.</li>
|
||||||
|
</ul>
|
||||||
|
<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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>I’ll assume the input is a Joy sequence of integers (as opposed to a
|
||||||
|
string or something else.)</p>
|
||||||
|
<p>We might proceed by creating a word that makes a copy of the sequence
|
||||||
|
with the first item moved to the last, and zips it with the original to
|
||||||
|
make a list of pairs, and a another word that adds (one of) each pair to
|
||||||
|
a total if the pair matches.</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">AoC2017</span><span class="o">.</span><span class="mi">1</span> <span class="o">==</span> <span class="n">pair_up</span> <span class="n">total_matches</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Let’s derive <code class="docutils literal notranslate"><span class="pre">pair_up</span></code>:</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="n">pair_up</span>
|
||||||
|
<span class="o">-------------------------</span>
|
||||||
|
<span class="p">[[</span><span class="n">a</span> <span class="n">b</span><span class="p">]</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">c</span> <span class="n">a</span><span class="p">]]</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Straightforward (although the order of each pair is reversed, due to the
|
||||||
|
way <code class="docutils literal notranslate"><span class="pre">zip</span></code> works, but it doesn’t matter for this program):</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="n">dup</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">a</span> <span class="n">b</span> <span class="n">c</span><span class="p">]</span> <span class="n">uncons</span> <span class="n">swap</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">b</span> <span class="n">c</span><span class="p">]</span> <span class="n">a</span> <span class="n">unit</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">b</span> <span class="n">c</span> <span class="n">a</span><span class="p">]</span> <span class="nb">zip</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">c</span> <span class="n">b</span><span class="p">]</span> <span class="p">[</span><span class="n">a</span> <span class="n">c</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">'pair_up == dup uncons swap unit concat zip'</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">'[1 2 3] pair_up'</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">2</span> <span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">3</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">'[1 2 2 3] pair_up'</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">2</span> <span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">3</span><span class="p">]]</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Now we need to derive <code class="docutils literal notranslate"><span class="pre">total_matches</span></code>. It will be a <code class="docutils literal notranslate"><span class="pre">step</span></code> function:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">total_matches</span> <span class="o">==</span> <span class="mi">0</span> <span class="n">swap</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="n">step</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Where <code class="docutils literal notranslate"><span class="pre">F</span></code> will have the pair to work with, and it will basically be a
|
||||||
|
<code class="docutils literal notranslate"><span class="pre">branch</span></code> or <code class="docutils literal notranslate"><span class="pre">ifte</span></code>.</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">total</span> <span class="p">[</span><span class="n">n</span> <span class="n">m</span><span class="p">]</span> <span class="n">F</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>It will probably be easier to write if we dequote the pair:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> total [n m] i F′
|
||||||
|
----------------------
|
||||||
|
total n m F′
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Now <code class="docutils literal notranslate"><span class="pre">F′</span></code> becomes just:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">total</span> <span class="n">n</span> <span class="n">m</span> <span class="p">[</span><span class="o">=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="o">+</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</span><span class="p">]</span> <span class="n">ifte</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>So:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">F</span> <span class="o">==</span> <span class="n">i</span> <span class="p">[</span><span class="o">=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="o">+</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</span><span class="p">]</span> <span class="n">ifte</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>And thus:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">total_matches</span> <span class="o">==</span> <span class="mi">0</span> <span class="n">swap</span> <span class="p">[</span><span class="n">i</span> <span class="p">[</span><span class="o">=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="o">+</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</span><span class="p">]</span> <span class="n">ifte</span><span class="p">]</span> <span class="n">step</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">'total_matches == 0 swap [i [=] [pop +] [popop] ifte] step'</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">'[1 2 3] pair_up total_matches'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">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">'[1 2 2 3] pair_up total_matches'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">2</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Now we can define our main program and evaluate it on the examples.</p>
|
||||||
|
<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">'AoC2017.1 == pair_up total_matches'</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">'[1 1 2 2] AoC2017.1'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</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">'[1 1 1 1] AoC2017.1'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">4</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">'[1 2 3 4] AoC2017.1'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">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">'[9 1 2 1 2 1 2 9] AoC2017.1'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">9</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">'[9 1 2 1 2 1 2 9] AoC2017.1'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">9</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">pair_up</span> <span class="o">==</span> <span class="n">dup</span> <span class="n">uncons</span> <span class="n">swap</span> <span class="n">unit</span> <span class="n">concat</span> <span class="nb">zip</span>
|
||||||
|
<span class="n">total_matches</span> <span class="o">==</span> <span class="mi">0</span> <span class="n">swap</span> <span class="p">[</span><span class="n">i</span> <span class="p">[</span><span class="o">=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="o">+</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</span><span class="p">]</span> <span class="n">ifte</span><span class="p">]</span> <span class="n">step</span>
|
||||||
|
|
||||||
|
<span class="n">AoC2017</span><span class="o">.</span><span class="mi">1</span> <span class="o">==</span> <span class="n">pair_up</span> <span class="n">total_matches</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Now the paired digit is “halfway” round.</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="n">dup</span> <span class="n">size</span> <span class="mi">2</span> <span class="o">/</span> <span class="p">[</span><span class="n">drop</span><span class="p">]</span> <span class="p">[</span><span class="n">take</span> <span class="n">reverse</span><span class="p">]</span> <span class="n">cleave</span> <span class="n">concat</span> <span class="nb">zip</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">'[1 2 3 4] dup size 2 / [drop] [take reverse] cleave concat zip'</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">3</span> <span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">4</span><span class="p">]]</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>I realized that each pair is repeated…</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">'[1 2 3 4] dup size 2 / [drop] [take reverse] cleave zip'</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="mi">2</span> <span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="p">[[</span><span class="mi">1</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">4</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">'AoC2017.1.extra == dup size 2 / [drop] [take reverse] cleave zip swap pop total_matches 2 *'</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">'[1 2 1 2] AoC2017.1.extra'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">6</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">'[1 2 2 1] AoC2017.1.extra'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">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">'[1 2 3 4 2 5] AoC2017.1.extra'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">4</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="refactor-ftw">
|
||||||
|
<h1>Refactor FTW<a class="headerlink" href="#refactor-ftw" title="Permalink to this headline">¶</a></h1>
|
||||||
|
<p>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…</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">rotate_seq</span> <span class="o">==</span> <span class="n">uncons</span> <span class="n">swap</span> <span class="n">unit</span> <span class="n">concat</span>
|
||||||
|
<span class="n">pair_up</span> <span class="o">==</span> <span class="n">dup</span> <span class="n">rotate_seq</span> <span class="nb">zip</span>
|
||||||
|
<span class="n">add_if_match</span> <span class="o">==</span> <span class="p">[</span><span class="o">=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="o">+</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</span><span class="p">]</span> <span class="n">ifte</span>
|
||||||
|
<span class="n">total_matches</span> <span class="o">==</span> <span class="p">[</span><span class="n">i</span> <span class="n">add_if_match</span><span class="p">]</span> <span class="n">step_zero</span>
|
||||||
|
|
||||||
|
<span class="n">AoC2017</span><span class="o">.</span><span class="mi">1</span> <span class="o">==</span> <span class="n">pair_up</span> <span class="n">total_matches</span>
|
||||||
|
|
||||||
|
<span class="n">half_of_size</span> <span class="o">==</span> <span class="n">dup</span> <span class="n">size</span> <span class="mi">2</span> <span class="o">/</span>
|
||||||
|
<span class="n">split_at</span> <span class="o">==</span> <span class="p">[</span><span class="n">drop</span><span class="p">]</span> <span class="p">[</span><span class="n">take</span> <span class="n">reverse</span><span class="p">]</span> <span class="n">cleave</span>
|
||||||
|
<span class="n">pair_up</span><span class="o">.</span><span class="n">extra</span> <span class="o">==</span> <span class="n">half_of_size</span> <span class="n">split_at</span> <span class="nb">zip</span> <span class="n">swap</span> <span class="n">pop</span>
|
||||||
|
|
||||||
|
<span class="n">AoC2017</span><span class="o">.</span><span class="mf">1.</span><span class="n">extra</span> <span class="o">==</span> <span class="n">pair_up</span><span class="o">.</span><span class="n">extra</span> <span class="n">total_matches</span> <span class="mi">2</span> <span class="o">*</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
|
||||||
|
<div class="sphinxsidebarwrapper">
|
||||||
|
<h3><a href="../index.html">Table Of Contents</a></h3>
|
||||||
|
<ul>
|
||||||
|
<li><a class="reference internal" href="#">Advent of Code 2017</a><ul>
|
||||||
|
<li><a class="reference internal" href="#december-1st">December 1st</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li><a class="reference internal" href="#refactor-ftw">Refactor FTW</a></li>
|
||||||
|
</ul>
|
||||||
|
<div class="relations">
|
||||||
|
<h3>Related Topics</h3>
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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<div class="section" id="advent-of-code-2017">
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<h1>Advent of Code 2017<a class="headerlink" href="#advent-of-code-2017" title="Permalink to this headline">¶</a></h1>
|
||||||
|
<div class="section" id="december-2nd">
|
||||||
|
<h2>December 2nd<a class="headerlink" href="#december-2nd" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>For each row, determine the difference between the largest value and the
|
||||||
|
smallest value; the checksum is the sum of all of these differences.</p>
|
||||||
|
<p>For example, given the following spreadsheet:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">5</span> <span class="mi">1</span> <span class="mi">9</span> <span class="mi">5</span>
|
||||||
|
<span class="mi">7</span> <span class="mi">5</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">2</span> <span class="mi">4</span> <span class="mi">6</span> <span class="mi">8</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<ul class="simple">
|
||||||
|
<li>The first row’s largest and smallest values are 9 and 1, and their
|
||||||
|
difference is 8.</li>
|
||||||
|
<li>The second row’s largest and smallest values are 7 and 3, and their
|
||||||
|
difference is 4.</li>
|
||||||
|
<li>The third row’s difference is 6.</li>
|
||||||
|
</ul>
|
||||||
|
<p>In this example, the spreadsheet’s checksum would be 8 + 4 + 6 = 18.</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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>I’ll assume the input is a Joy sequence of sequences of integers.</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[[</span><span class="mi">5</span> <span class="mi">1</span> <span class="mi">9</span> <span class="mi">5</span><span class="p">]</span>
|
||||||
|
<span class="p">[</span><span class="mi">7</span> <span class="mi">5</span> <span class="mi">3</span><span class="p">]</span>
|
||||||
|
<span class="p">[</span><span class="mi">2</span> <span class="mi">4</span> <span class="mi">6</span> <span class="mi">8</span><span class="p">]]</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>So, obviously, the initial form will be a <code class="docutils literal notranslate"><span class="pre">step</span></code> function:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">AoC2017</span><span class="o">.</span><span class="mi">2</span> <span class="o">==</span> <span class="mi">0</span> <span class="n">swap</span> <span class="p">[</span><span class="n">F</span> <span class="o">+</span><span class="p">]</span> <span class="n">step</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>This function <code class="docutils literal notranslate"><span class="pre">F</span></code> must get the <code class="docutils literal notranslate"><span class="pre">max</span></code> and <code class="docutils literal notranslate"><span class="pre">min</span></code> of a row of numbers
|
||||||
|
and subtract. We can define a helper function <code class="docutils literal notranslate"><span class="pre">maxmin</span></code> which does
|
||||||
|
this:</p>
|
||||||
|
<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">'maxmin == [max] [min] cleave'</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">'[1 2 3] maxmin'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span> <span class="mi">1</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Then <code class="docutils literal notranslate"><span class="pre">F</span></code> just does that then subtracts the min from the max:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">F</span> <span class="o">==</span> <span class="n">maxmin</span> <span class="o">-</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>So:</p>
|
||||||
|
<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">'AoC2017.2 == [maxmin - +] step_zero'</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">'''</span>
|
||||||
|
|
||||||
|
<span class="s1">[[5 1 9 5]</span>
|
||||||
|
<span class="s1"> [7 5 3]</span>
|
||||||
|
<span class="s1"> [2 4 6 8]] AoC2017.2</span>
|
||||||
|
|
||||||
|
<span class="s1">'''</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">18</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>…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.</p>
|
||||||
|
<p>For example, given the following spreadsheet:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">5</span> <span class="mi">9</span> <span class="mi">2</span> <span class="mi">8</span>
|
||||||
|
<span class="mi">9</span> <span class="mi">4</span> <span class="mi">7</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">3</span> <span class="mi">8</span> <span class="mi">6</span> <span class="mi">5</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<ul class="simple">
|
||||||
|
<li>In the first row, the only two numbers that evenly divide are 8 and
|
||||||
|
2; the result of this division is 4.</li>
|
||||||
|
<li>In the second row, the two numbers are 9 and 3; the result is 3.</li>
|
||||||
|
<li>In the third row, the result is 2.</li>
|
||||||
|
</ul>
|
||||||
|
<p>In this example, the sum of the results would be 4 + 3 + 2 = 9.</p>
|
||||||
|
<p>What is the sum of each row’s result in your puzzle input?</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">'[5 9 2 8] sort reverse'</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">9</span> <span class="mi">8</span> <span class="mi">5</span> <span class="mi">2</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">'[9 8 5 2] uncons [swap [divmod] cons] dupdip'</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">8</span> <span class="mi">5</span> <span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">9</span> <span class="nb">divmod</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span> <span class="mi">5</span> <span class="mi">2</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">9</span> <span class="mi">8</span> <span class="mi">5</span> <span class="mi">2</span><span class="p">]</span> <span class="n">uncons</span> <span class="p">[</span><span class="n">swap</span> <span class="p">[</span><span class="nb">divmod</span><span class="p">]</span> <span class="n">cons</span> <span class="n">F</span><span class="p">]</span> <span class="n">dupdip</span> <span class="n">G</span>
|
||||||
|
<span class="p">[</span><span class="mi">8</span> <span class="mi">5</span> <span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">9</span> <span class="nb">divmod</span><span class="p">]</span> <span class="n">F</span> <span class="p">[</span><span class="mi">8</span> <span class="mi">5</span> <span class="mi">2</span><span class="p">]</span> <span class="n">G</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[</span><span class="mi">8</span> <span class="mi">5</span> <span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">9</span> <span class="nb">divmod</span><span class="p">]</span> <span class="p">[</span><span class="n">uncons</span> <span class="n">swap</span><span class="p">]</span> <span class="n">dip</span> <span class="n">dup</span> <span class="p">[</span><span class="n">i</span> <span class="ow">not</span><span class="p">]</span> <span class="n">dip</span>
|
||||||
|
<span class="p">[</span><span class="mi">8</span> <span class="mi">5</span> <span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="mi">9</span> <span class="nb">divmod</span><span class="p">]</span> <span class="p">[</span><span class="n">uncons</span> <span class="n">swap</span><span class="p">]</span> <span class="n">dip</span> <span class="n">dup</span> <span class="p">[</span><span class="n">i</span> <span class="ow">not</span><span class="p">]</span> <span class="n">dip</span>
|
||||||
|
<span class="p">[</span><span class="mi">8</span> <span class="mi">5</span> <span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">9</span> <span class="nb">divmod</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">uncons</span> <span class="n">swap</span><span class="p">]</span> <span class="n">dip</span> <span class="n">dup</span> <span class="p">[</span><span class="n">i</span> <span class="ow">not</span><span class="p">]</span> <span class="n">dip</span>
|
||||||
|
<span class="p">[</span><span class="mi">8</span> <span class="mi">5</span> <span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">9</span> <span class="nb">divmod</span><span class="p">]</span> <span class="p">[</span><span class="n">uncons</span> <span class="n">swap</span><span class="p">]</span> <span class="o">.</span> <span class="n">dip</span> <span class="n">dup</span> <span class="p">[</span><span class="n">i</span> <span class="ow">not</span><span class="p">]</span> <span class="n">dip</span>
|
||||||
|
<span class="p">[</span><span class="mi">8</span> <span class="mi">5</span> <span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="n">uncons</span> <span class="n">swap</span> <span class="p">[</span><span class="mi">9</span> <span class="nb">divmod</span><span class="p">]</span> <span class="n">dup</span> <span class="p">[</span><span class="n">i</span> <span class="ow">not</span><span class="p">]</span> <span class="n">dip</span>
|
||||||
|
<span class="mi">8</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="n">swap</span> <span class="p">[</span><span class="mi">9</span> <span class="nb">divmod</span><span class="p">]</span> <span class="n">dup</span> <span class="p">[</span><span class="n">i</span> <span class="ow">not</span><span class="p">]</span> <span class="n">dip</span>
|
||||||
|
<span class="p">[</span><span class="mi">5</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">8</span> <span class="o">.</span> <span class="p">[</span><span class="mi">9</span> <span class="nb">divmod</span><span class="p">]</span> <span class="n">dup</span> <span class="p">[</span><span class="n">i</span> <span class="ow">not</span><span class="p">]</span> <span class="n">dip</span>
|
||||||
|
<span class="p">[</span><span class="mi">5</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">8</span> <span class="p">[</span><span class="mi">9</span> <span class="nb">divmod</span><span class="p">]</span> <span class="o">.</span> <span class="n">dup</span> <span class="p">[</span><span class="n">i</span> <span class="ow">not</span><span class="p">]</span> <span class="n">dip</span>
|
||||||
|
<span class="p">[</span><span class="mi">5</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">8</span> <span class="p">[</span><span class="mi">9</span> <span class="nb">divmod</span><span class="p">]</span> <span class="p">[</span><span class="mi">9</span> <span class="nb">divmod</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="n">i</span> <span class="ow">not</span><span class="p">]</span> <span class="n">dip</span>
|
||||||
|
<span class="p">[</span><span class="mi">5</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">8</span> <span class="p">[</span><span class="mi">9</span> <span class="nb">divmod</span><span class="p">]</span> <span class="p">[</span><span class="mi">9</span> <span class="nb">divmod</span><span class="p">]</span> <span class="p">[</span><span class="n">i</span> <span class="ow">not</span><span class="p">]</span> <span class="o">.</span> <span class="n">dip</span>
|
||||||
|
<span class="p">[</span><span class="mi">5</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">8</span> <span class="p">[</span><span class="mi">9</span> <span class="nb">divmod</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="ow">not</span> <span class="p">[</span><span class="mi">9</span> <span class="nb">divmod</span><span class="p">]</span>
|
||||||
|
<span class="p">[</span><span class="mi">5</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">8</span> <span class="o">.</span> <span class="mi">9</span> <span class="nb">divmod</span> <span class="ow">not</span> <span class="p">[</span><span class="mi">9</span> <span class="nb">divmod</span><span class="p">]</span>
|
||||||
|
<span class="p">[</span><span class="mi">5</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">8</span> <span class="mi">9</span> <span class="o">.</span> <span class="nb">divmod</span> <span class="ow">not</span> <span class="p">[</span><span class="mi">9</span> <span class="nb">divmod</span><span class="p">]</span>
|
||||||
|
<span class="p">[</span><span class="mi">5</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">1</span> <span class="mi">1</span> <span class="o">.</span> <span class="ow">not</span> <span class="p">[</span><span class="mi">9</span> <span class="nb">divmod</span><span class="p">]</span>
|
||||||
|
<span class="p">[</span><span class="mi">5</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">1</span> <span class="kc">False</span> <span class="o">.</span> <span class="p">[</span><span class="mi">9</span> <span class="nb">divmod</span><span class="p">]</span>
|
||||||
|
<span class="p">[</span><span class="mi">5</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">1</span> <span class="kc">False</span> <span class="p">[</span><span class="mi">9</span> <span class="nb">divmod</span><span class="p">]</span> <span class="o">.</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="tricky">
|
||||||
|
<h2>Tricky<a class="headerlink" href="#tricky" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>Let’s think.</p>
|
||||||
|
<p>Given a <em>sorted</em> sequence (from highest to lowest) we want to * for
|
||||||
|
head, tail in sequence * for term in tail: * check if the head % term
|
||||||
|
== 0 * if so compute head / term and terminate loop * else continue</p>
|
||||||
|
<div class="section" id="so-we-want-a-loop-i-think">
|
||||||
|
<h3>So we want a <code class="docutils literal notranslate"><span class="pre">loop</span></code> I think<a class="headerlink" href="#so-we-want-a-loop-i-think" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<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="kc">True</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">loop</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="n">Q</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">loop</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p><code class="docutils literal notranslate"><span class="pre">Q</span></code> should either leave the result and False, or the <code class="docutils literal notranslate"><span class="pre">rest</span></code> and
|
||||||
|
True.</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="n">Q</span>
|
||||||
|
<span class="o">-----------------</span>
|
||||||
|
<span class="n">result</span> <span class="mi">0</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="n">Q</span>
|
||||||
|
<span class="o">-----------------</span>
|
||||||
|
<span class="p">[</span><span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="mi">1</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>This suggests that <code class="docutils literal notranslate"><span class="pre">Q</span></code> should start with:</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="n">uncons</span> <span class="n">dup</span> <span class="n">roll</span><span class="o"><</span>
|
||||||
|
<span class="p">[</span><span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="p">[</span><span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="n">a</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Now we just have to <code class="docutils literal notranslate"><span class="pre">pop</span></code> it if we don’t need it.</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="p">[</span><span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="n">a</span> <span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="p">[</span><span class="n">cons</span><span class="p">]</span> <span class="n">app2</span> <span class="n">popdd</span> <span class="p">[</span><span class="n">E</span><span class="p">]</span> <span class="n">primrec</span>
|
||||||
|
<span class="p">[</span><span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="p">[</span><span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="p">[</span><span class="n">a</span> <span class="n">P</span><span class="p">]</span> <span class="p">[</span><span class="n">a</span> <span class="n">T</span><span class="p">]</span> <span class="p">[</span><span class="n">E</span><span class="p">]</span> <span class="n">primrec</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<hr class="docutils" />
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">w</span><span class="o">/</span> <span class="n">Q</span> <span class="o">==</span> <span class="p">[</span><span class="o">%</span> <span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="n">primrec</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="n">uncons</span>
|
||||||
|
<span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="n">tuck</span>
|
||||||
|
<span class="p">[</span><span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="n">uncons</span>
|
||||||
|
<span class="p">[</span><span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="n">a</span> <span class="n">b</span> <span class="p">[</span><span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="n">roll</span><span class="o">></span>
|
||||||
|
<span class="p">[</span><span class="n">b</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> <span class="n">a</span> <span class="n">b</span> <span class="n">Q</span>
|
||||||
|
<span class="p">[</span><span class="n">b</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> <span class="n">a</span> <span class="n">b</span> <span class="p">[</span><span class="o">%</span> <span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="n">primrec</span>
|
||||||
|
|
||||||
|
<span class="p">[</span><span class="n">b</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> <span class="n">a</span> <span class="n">b</span> <span class="n">T</span>
|
||||||
|
<span class="p">[</span><span class="n">b</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> <span class="n">a</span> <span class="n">b</span> <span class="o">/</span> <span class="n">roll</span><span class="o">></span> <span class="n">popop</span> <span class="mi">0</span>
|
||||||
|
|
||||||
|
<span class="p">[</span><span class="n">b</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> <span class="n">a</span> <span class="n">b</span> <span class="n">F</span> <span class="n">Q</span>
|
||||||
|
<span class="p">[</span><span class="n">b</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> <span class="n">a</span> <span class="n">b</span> <span class="n">pop</span> <span class="n">swap</span> <span class="n">uncons</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="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> <span class="n">a</span> <span class="n">swap</span> <span class="n">uncons</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="n">d</span><span class="p">]</span> <span class="n">a</span> <span class="p">[</span><span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="n">uncons</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="n">d</span><span class="p">]</span> <span class="n">a</span> <span class="n">c</span> <span class="p">[</span><span class="n">d</span><span class="p">]</span> <span class="n">roll</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="n">d</span><span class="p">]</span> <span class="p">[</span><span class="n">d</span><span class="p">]</span> <span class="n">a</span> <span class="n">c</span> <span class="n">Q</span>
|
||||||
|
|
||||||
|
<span class="n">Q</span> <span class="o">==</span> <span class="p">[</span><span class="o">%</span> <span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="o">/</span> <span class="n">roll</span><span class="o">></span> <span class="n">popop</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="n">swap</span> <span class="n">uncons</span> <span class="n">roll</span><span class="o">></span><span class="p">]</span> <span class="n">primrec</span>
|
||||||
|
|
||||||
|
<span class="n">uncons</span> <span class="n">tuck</span> <span class="n">uncons</span> <span class="n">roll</span><span class="o">></span> <span class="n">Q</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">'[8 5 3 2] 9 [swap] [% not] [cons] app2 popdd'</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">8</span> <span class="mi">5</span> <span class="mi">3</span> <span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">9</span> <span class="n">swap</span><span class="p">]</span> <span class="p">[</span><span class="mi">9</span> <span class="o">%</span> <span class="ow">not</span><span class="p">]</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<hr class="docutils" />
|
||||||
|
<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="n">uncons</span>
|
||||||
|
<span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="n">tuck</span>
|
||||||
|
<span class="p">[</span><span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</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">ifte</span>
|
||||||
|
|
||||||
|
<span class="p">[</span><span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="n">a</span> <span class="p">[]</span> <span class="n">popop</span> <span class="mi">1</span>
|
||||||
|
<span class="p">[</span><span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="mi">1</span>
|
||||||
|
|
||||||
|
<span class="p">[</span><span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="n">Q</span>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="n">a</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="n">Q</span>
|
||||||
|
<span class="o">---------------</span>
|
||||||
|
<span class="n">result</span> <span class="mi">0</span>
|
||||||
|
|
||||||
|
<span class="n">a</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="n">Q</span>
|
||||||
|
<span class="o">---------------</span>
|
||||||
|
<span class="mi">1</span>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="n">w</span><span class="o">/</span> <span class="n">Q</span> <span class="o">==</span> <span class="p">[</span><span class="n">first</span> <span class="o">%</span> <span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">first</span> <span class="o">/</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[</span><span class="n">rest</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</span> <span class="mi">1</span><span class="p">]]</span> <span class="p">[</span><span class="n">ifte</span><span class="p">]</span>
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
<span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="p">[</span><span class="n">first</span> <span class="o">%</span> <span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">first</span> <span class="o">/</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[</span><span class="n">rest</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</span> <span class="mi">1</span><span class="p">]]</span> <span class="p">[</span><span class="n">ifte</span><span class="p">]</span>
|
||||||
|
<span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="n">first</span> <span class="o">%</span> <span class="ow">not</span>
|
||||||
|
<span class="n">a</span> <span class="n">b</span> <span class="o">%</span> <span class="ow">not</span>
|
||||||
|
<span class="n">a</span><span class="o">%</span><span class="n">b</span> <span class="ow">not</span>
|
||||||
|
<span class="nb">bool</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="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="p">[</span><span class="n">first</span> <span class="o">%</span> <span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">first</span> <span class="o">/</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[</span><span class="n">rest</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</span> <span class="mi">1</span><span class="p">]]</span> <span class="p">[</span><span class="n">ifte</span><span class="p">]</span>
|
||||||
|
<span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="n">first</span> <span class="o">/</span> <span class="mi">0</span>
|
||||||
|
<span class="n">a</span> <span class="n">b</span> <span class="o">/</span> <span class="mi">0</span>
|
||||||
|
<span class="n">a</span><span class="o">/</span><span class="n">b</span> <span class="mi">0</span>
|
||||||
|
|
||||||
|
<span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="p">[</span><span class="n">first</span> <span class="o">%</span> <span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">first</span> <span class="o">/</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[</span><span class="n">rest</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</span> <span class="mi">1</span><span class="p">]]</span> <span class="p">[</span><span class="n">ifte</span><span class="p">]</span>
|
||||||
|
<span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="n">rest</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</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">ifte</span>
|
||||||
|
<span class="n">a</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="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</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">ifte</span>
|
||||||
|
<span class="n">a</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="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</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">ifte</span>
|
||||||
|
|
||||||
|
<span class="n">a</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="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</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">ifte</span>
|
||||||
|
<span class="n">a</span> <span class="p">[</span><span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="ow">not</span>
|
||||||
|
|
||||||
|
<span class="n">a</span> <span class="p">[]</span> <span class="n">popop</span> <span class="mi">1</span>
|
||||||
|
<span class="mi">1</span>
|
||||||
|
|
||||||
|
<span class="n">a</span> <span class="p">[</span><span class="n">c</span> <span class="n">d</span><span class="p">]</span> <span class="n">Q</span>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="n">uncons</span> <span class="n">tuck</span> <span class="p">[</span><span class="n">first</span> <span class="o">%</span> <span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">first</span> <span class="o">/</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[</span><span class="n">rest</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</span> <span class="mi">1</span><span class="p">]]</span> <span class="p">[</span><span class="n">ifte</span><span class="p">]</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="i-finally-sat-down-with-a-piece-of-paper-and-blocked-it-out">
|
||||||
|
<h3>I finally sat down with a piece of paper and blocked it out.<a class="headerlink" href="#i-finally-sat-down-with-a-piece-of-paper-and-blocked-it-out" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>First, I made a function <code class="docutils literal notranslate"><span class="pre">G</span></code> that expects a number and a sequence of
|
||||||
|
candidates and return the result or zero:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">n</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="n">G</span>
|
||||||
|
<span class="o">---------------</span>
|
||||||
|
<span class="n">result</span>
|
||||||
|
|
||||||
|
<span class="n">n</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="n">G</span>
|
||||||
|
<span class="o">---------------</span>
|
||||||
|
<span class="mi">0</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>It’s a recursive function that conditionally executes the recursive part
|
||||||
|
of its recursive branch</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">Pg</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">R1</span> <span class="p">[</span><span class="n">Pi</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]]</span> <span class="p">[</span><span class="n">ifte</span><span class="p">]</span> <span class="n">genrec</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>The recursive branch is the else-part of the inner <code class="docutils literal notranslate"><span class="pre">ifte</span></code>:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">G</span> <span class="o">==</span> <span class="p">[</span><span class="n">Pg</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">R1</span> <span class="p">[</span><span class="n">Pi</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]]</span> <span class="p">[</span><span class="n">ifte</span><span class="p">]</span> <span class="n">genrec</span>
|
||||||
|
<span class="o">==</span> <span class="p">[</span><span class="n">Pg</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">R1</span> <span class="p">[</span><span class="n">Pi</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="n">ifte</span><span class="p">]</span> <span class="n">ifte</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>But this is in hindsight. Going forward I derived:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">G</span> <span class="o">==</span> <span class="p">[</span><span class="n">first</span> <span class="o">%</span> <span class="ow">not</span><span class="p">]</span>
|
||||||
|
<span class="p">[</span><span class="n">first</span> <span class="o">/</span><span class="p">]</span>
|
||||||
|
<span class="p">[</span><span class="n">rest</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</span> <span class="mi">0</span><span class="p">]]</span>
|
||||||
|
<span class="p">[</span><span class="n">ifte</span><span class="p">]</span> <span class="n">genrec</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>The predicate detects if the <code class="docutils literal notranslate"><span class="pre">n</span></code> can be evenly divided by the
|
||||||
|
<code class="docutils literal notranslate"><span class="pre">first</span></code> item in the list. If so, the then-part returns the result.
|
||||||
|
Otherwise, we have:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">n</span> <span class="p">[</span><span class="n">m</span> <span class="o">...</span><span class="p">]</span> <span class="n">rest</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="n">ifte</span>
|
||||||
|
<span class="n">n</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="n">ifte</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>This <code class="docutils literal notranslate"><span class="pre">ifte</span></code> guards against empty sequences and returns zero in that
|
||||||
|
case, otherwise it executes <code class="docutils literal notranslate"><span class="pre">G</span></code>.</p>
|
||||||
|
<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">'G == [first % not] [first /] [rest [not] [popop 0]] [ifte] genrec'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Now we need a word that uses <code class="docutils literal notranslate"><span class="pre">G</span></code> 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 <code class="docutils literal notranslate"><span class="pre">n</span></code>, 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):</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">n</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="n">p</span> <span class="n">find</span><span class="o">-</span><span class="n">result</span>
|
||||||
|
<span class="o">---------------------------</span>
|
||||||
|
<span class="n">result</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>It applies <code class="docutils literal notranslate"><span class="pre">G</span></code> using <code class="docutils literal notranslate"><span class="pre">nullary</span></code> because if it fails with one
|
||||||
|
candidate it needs the list to get the next one (the list is otherwise
|
||||||
|
consumed by <code class="docutils literal notranslate"><span class="pre">G</span></code>.)</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">find</span><span class="o">-</span><span class="n">result</span> <span class="o">==</span> <span class="p">[</span><span class="mi">0</span> <span class="o">></span><span class="p">]</span> <span class="p">[</span><span class="n">roll</span><span class="o">></span> <span class="n">popop</span><span class="p">]</span> <span class="p">[</span><span class="n">roll</span><span class="o"><</span> <span class="n">popop</span> <span class="n">uncons</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="n">nullary</span><span class="p">]</span> <span class="n">primrec</span>
|
||||||
|
|
||||||
|
<span class="n">n</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="n">p</span> <span class="p">[</span><span class="mi">0</span> <span class="o">></span><span class="p">]</span> <span class="p">[</span><span class="n">roll</span><span class="o">></span> <span class="n">popop</span><span class="p">]</span> <span class="p">[</span><span class="n">roll</span><span class="o"><</span> <span class="n">popop</span> <span class="n">uncons</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="n">nullary</span><span class="p">]</span> <span class="n">primrec</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>The base-case is trivial, return the (non-zero) result. The recursive
|
||||||
|
branch…</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">n</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="n">p</span> <span class="n">roll</span><span class="o"><</span> <span class="n">popop</span> <span class="n">uncons</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="n">nullary</span> <span class="n">find</span><span class="o">-</span><span class="n">result</span>
|
||||||
|
<span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="n">p</span> <span class="n">n</span> <span class="n">popop</span> <span class="n">uncons</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="n">nullary</span> <span class="n">find</span><span class="o">-</span><span class="n">result</span>
|
||||||
|
<span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="n">uncons</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="n">nullary</span> <span class="n">find</span><span class="o">-</span><span class="n">result</span>
|
||||||
|
<span class="n">m</span> <span class="p">[</span><span class="o">..</span><span class="p">]</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="n">nullary</span> <span class="n">find</span><span class="o">-</span><span class="n">result</span>
|
||||||
|
<span class="n">m</span> <span class="p">[</span><span class="o">..</span><span class="p">]</span> <span class="n">p</span> <span class="n">find</span><span class="o">-</span><span class="n">result</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>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 <code class="docutils literal notranslate"><span class="pre">uncons</span></code>.</p>
|
||||||
|
<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">'find-result == [0 >] [roll> popop] [roll< popop uncons [G] nullary] primrec'</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">'[11 9 8 7 3 2] 0 tuck find-result'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">3.0</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>In order to get the thing started, we need to <code class="docutils literal notranslate"><span class="pre">sort</span></code> the list in
|
||||||
|
descending order, then prime the <code class="docutils literal notranslate"><span class="pre">find-result</span></code> function with a dummy
|
||||||
|
candidate value and zero (“continue”) flag.</p>
|
||||||
|
<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">'prep-row == sort reverse 0 tuck'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Now we can define our program.</p>
|
||||||
|
<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">'AoC20017.2.extra == [prep-row find-result +] step_zero'</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">'''</span>
|
||||||
|
|
||||||
|
<span class="s1">[[5 9 2 8]</span>
|
||||||
|
<span class="s1"> [9 4 7 3]</span>
|
||||||
|
<span class="s1"> [3 8 6 5]] AoC20017.2.extra</span>
|
||||||
|
|
||||||
|
<span class="s1">'''</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">9.0</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
|
||||||
|
<div class="sphinxsidebarwrapper">
|
||||||
|
<h3><a href="../index.html">Table Of Contents</a></h3>
|
||||||
|
<ul>
|
||||||
|
<li><a class="reference internal" href="#">Advent of Code 2017</a><ul>
|
||||||
|
<li><a class="reference internal" href="#december-2nd">December 2nd</a></li>
|
||||||
|
<li><a class="reference internal" href="#tricky">Tricky</a><ul>
|
||||||
|
<li><a class="reference internal" href="#so-we-want-a-loop-i-think">So we want a <code class="docutils literal notranslate"><span class="pre">loop</span></code> I think</a></li>
|
||||||
|
<li><a class="reference internal" href="#i-finally-sat-down-with-a-piece-of-paper-and-blocked-it-out">I finally sat down with a piece of paper and blocked it out.</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
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|
||||||
|
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|
||||||
|
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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<meta name="viewport" content="width=device-width, initial-scale=0.9, maximum-scale=0.9" />
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</head><body>
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<div class="document">
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<div class="documentwrapper">
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<div class="bodywrapper">
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<div class="body" role="main">
|
||||||
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|
||||||
|
<div class="section" id="advent-of-code-2017">
|
||||||
|
<h1>Advent of Code 2017<a class="headerlink" href="#advent-of-code-2017" title="Permalink to this headline">¶</a></h1>
|
||||||
|
<div class="section" id="december-3rd">
|
||||||
|
<h2>December 3rd<a class="headerlink" href="#december-3rd" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>You come across an experimental new kind of memory stored on an infinite
|
||||||
|
two-dimensional grid.</p>
|
||||||
|
<p>Each square on the grid is allocated in a spiral pattern starting at a
|
||||||
|
location marked 1 and then counting up while spiraling outward. For
|
||||||
|
example, the first few squares are allocated like this:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">17</span> <span class="mi">16</span> <span class="mi">15</span> <span class="mi">14</span> <span class="mi">13</span>
|
||||||
|
<span class="mi">18</span> <span class="mi">5</span> <span class="mi">4</span> <span class="mi">3</span> <span class="mi">12</span>
|
||||||
|
<span class="mi">19</span> <span class="mi">6</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">11</span>
|
||||||
|
<span class="mi">20</span> <span class="mi">7</span> <span class="mi">8</span> <span class="mi">9</span> <span class="mi">10</span>
|
||||||
|
<span class="mi">21</span> <span class="mi">22</span> <span class="mi">23</span><span class="o">---></span> <span class="o">...</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>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
|
||||||
|
port for this memory system) by programs that can only move up, down,
|
||||||
|
left, or right. They always take the shortest path: the Manhattan
|
||||||
|
Distance between the location of the data and square 1.</p>
|
||||||
|
<p>For example:</p>
|
||||||
|
<ul class="simple">
|
||||||
|
<li>Data from square 1 is carried 0 steps, since it’s at the access port.</li>
|
||||||
|
<li>Data from square 12 is carried 3 steps, such as: down, left, left.</li>
|
||||||
|
<li>Data from square 23 is carried only 2 steps: up twice.</li>
|
||||||
|
<li>Data from square 1024 must be carried 31 steps.</li>
|
||||||
|
</ul>
|
||||||
|
<p>How many steps are required to carry the data from the square identified
|
||||||
|
in your puzzle input all the way to the access port?</p>
|
||||||
|
<div class="section" id="analysis">
|
||||||
|
<h3>Analysis<a class="headerlink" href="#analysis" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>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.</p>
|
||||||
|
<p>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
|
||||||
|
patterns directly:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">1</span> <span class="mi">0</span>
|
||||||
|
<span class="mi">2</span> <span class="mi">1</span>
|
||||||
|
<span class="mi">3</span> <span class="mi">2</span>
|
||||||
|
<span class="mi">4</span> <span class="mi">1</span>
|
||||||
|
<span class="mi">5</span> <span class="mi">2</span>
|
||||||
|
<span class="mi">6</span> <span class="mi">1</span>
|
||||||
|
<span class="mi">7</span> <span class="mi">2</span>
|
||||||
|
<span class="mi">8</span> <span class="mi">1</span>
|
||||||
|
<span class="mi">9</span> <span class="mi">2</span>
|
||||||
|
<span class="mi">10</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">11</span> <span class="mi">2</span>
|
||||||
|
<span class="mi">12</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">13</span> <span class="mi">4</span>
|
||||||
|
<span class="mi">14</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">15</span> <span class="mi">2</span>
|
||||||
|
<span class="mi">16</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">17</span> <span class="mi">4</span>
|
||||||
|
<span class="mi">18</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">19</span> <span class="mi">2</span>
|
||||||
|
<span class="mi">20</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">21</span> <span class="mi">4</span>
|
||||||
|
<span class="mi">22</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">23</span> <span class="mi">2</span>
|
||||||
|
<span class="mi">24</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">25</span> <span class="mi">4</span>
|
||||||
|
<span class="mi">26</span> <span class="mi">5</span>
|
||||||
|
<span class="mi">27</span> <span class="mi">4</span>
|
||||||
|
<span class="mi">28</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">29</span> <span class="mi">4</span>
|
||||||
|
<span class="mi">30</span> <span class="mi">5</span>
|
||||||
|
<span class="mi">31</span> <span class="mi">6</span>
|
||||||
|
<span class="mi">32</span> <span class="mi">5</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>There are four groups repeating for a given “rank”, then the pattern
|
||||||
|
enlarges and four groups repeat again, etc.</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="mi">1</span> <span class="mi">2</span>
|
||||||
|
<span class="mi">3</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span>
|
||||||
|
<span class="mi">5</span> <span class="mi">4</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">5</span> <span class="mi">6</span>
|
||||||
|
<span class="mi">7</span> <span class="mi">6</span> <span class="mi">5</span> <span class="mi">4</span> <span class="mi">5</span> <span class="mi">6</span> <span class="mi">7</span> <span class="mi">8</span>
|
||||||
|
<span class="mi">9</span> <span class="mi">8</span> <span class="mi">7</span> <span class="mi">6</span> <span class="mi">5</span> <span class="mi">6</span> <span class="mi">7</span> <span class="mi">8</span> <span class="mi">9</span> <span class="mi">10</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Four of this pyramid interlock to tile the plane extending from the
|
||||||
|
initial “1” square.</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="mi">2</span> <span class="mi">3</span> <span class="o">|</span> <span class="mi">4</span> <span class="mi">5</span> <span class="o">|</span> <span class="mi">6</span> <span class="mi">7</span> <span class="o">|</span> <span class="mi">8</span> <span class="mi">9</span>
|
||||||
|
<span class="mi">10</span> <span class="mi">11</span> <span class="mi">12</span> <span class="mi">13</span><span class="o">|</span><span class="mi">14</span> <span class="mi">15</span> <span class="mi">16</span> <span class="mi">17</span><span class="o">|</span><span class="mi">18</span> <span class="mi">19</span> <span class="mi">20</span> <span class="mi">21</span><span class="o">|</span><span class="mi">22</span> <span class="mi">23</span> <span class="mi">24</span> <span class="mi">25</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>And so on.</p>
|
||||||
|
<p>We can figure out the pattern for a row of the pyramid at a given “rank”
|
||||||
|
<span class="math notranslate nohighlight">\(k\)</span>:</p>
|
||||||
|
<p><span class="math notranslate nohighlight">\(2k - 1, 2k - 2, ..., k, k + 1, k + 2, ..., 2k\)</span></p>
|
||||||
|
<p>or</p>
|
||||||
|
<p><span class="math notranslate nohighlight">\(k + (k - 1), k + (k - 2), ..., k, k + 1, k + 2, ..., k + k\)</span></p>
|
||||||
|
<p>This shows that the series consists at each place of <span class="math notranslate nohighlight">\(k\)</span> plus some
|
||||||
|
number that begins at <span class="math notranslate nohighlight">\(k - 1\)</span>, decreases to zero, then increases
|
||||||
|
to <span class="math notranslate nohighlight">\(k\)</span>. Each row has <span class="math notranslate nohighlight">\(2k\)</span> members.</p>
|
||||||
|
<p>Let’s figure out how, given an index into a row, we can calculate the
|
||||||
|
value there. The index will be from 0 to <span class="math notranslate nohighlight">\(k - 1\)</span>.</p>
|
||||||
|
<p>Let’s look at an example, with <span class="math notranslate nohighlight">\(k = 4\)</span>:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">5</span> <span class="mi">6</span> <span class="mi">7</span>
|
||||||
|
<span class="mi">7</span> <span class="mi">6</span> <span class="mi">5</span> <span class="mi">4</span> <span class="mi">5</span> <span class="mi">6</span> <span class="mi">7</span> <span class="mi">8</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">k</span> <span class="o">=</span> <span class="mi">4</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Subtract <span class="math notranslate nohighlight">\(k\)</span> from the index and take the absolute value:</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">4</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Not quite. Subtract <span class="math notranslate nohighlight">\(k - 1\)</span> from the index and take the absolute
|
||||||
|
value:</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Great, now add <span class="math notranslate nohighlight">\(k\)</span>…</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">7</span> <span class="mi">6</span> <span class="mi">5</span> <span class="mi">4</span> <span class="mi">5</span> <span class="mi">6</span> <span class="mi">7</span> <span class="mi">8</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>So to write a function that can give us the value of a row at a given
|
||||||
|
index:</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">9</span> <span class="mi">8</span> <span class="mi">7</span> <span class="mi">6</span> <span class="mi">5</span> <span class="mi">6</span> <span class="mi">7</span> <span class="mi">8</span> <span class="mi">9</span> <span class="mi">10</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>(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.)</p>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="finding-the-rank-and-offset-of-a-number">
|
||||||
|
<h3>Finding the rank and offset of a number.<a class="headerlink" href="#finding-the-rank-and-offset-of-a-number" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>Now that we can compute the desired output value for a given rank and
|
||||||
|
the offset (index) into that rank, we need to determine how to find the
|
||||||
|
rank and offset of a number.</p>
|
||||||
|
<p>The rank is easy to find by iteratively stripping off the amount already
|
||||||
|
covered by previous ranks until you find the one that brackets the
|
||||||
|
target number. Because each row is <span class="math notranslate nohighlight">\(2k\)</span> places and there are
|
||||||
|
<span class="math notranslate nohighlight">\(4\)</span> per rank each rank contains <span class="math notranslate nohighlight">\(8k\)</span> places. Counting the
|
||||||
|
initial square we have:</p>
|
||||||
|
<p><span class="math notranslate nohighlight">\(corner_k = 1 + \sum_{n=1}^k 8n\)</span></p>
|
||||||
|
<p>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:</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
<span class="c1"># and one because we are counting from 1 instead of 0.</span>
|
||||||
|
<span class="n">k</span> <span class="o">=</span> <span class="mi">1</span>
|
||||||
|
<span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
|
||||||
|
<span class="n">m</span> <span class="o">=</span> <span class="mi">8</span> <span class="o">*</span> <span class="n">k</span> <span class="c1"># The number of places total in this rank, 4(2k).</span>
|
||||||
|
<span class="k">if</span> <span class="n">n</span> <span class="o"><</span> <span class="n">m</span><span class="p">:</span>
|
||||||
|
<span class="k">return</span> <span class="n">k</span><span class="p">,</span> <span class="n">n</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="n">n</span> <span class="o">-=</span> <span class="n">m</span> <span class="c1"># Remove this rank's worth.</span>
|
||||||
|
<span class="n">k</span> <span class="o">+=</span> <span class="mi">1</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">2</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
|
||||||
|
<span class="mi">3</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||||||
|
<span class="mi">4</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
|
||||||
|
<span class="mi">5</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||||||
|
<span class="mi">6</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
|
||||||
|
<span class="mi">7</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||||||
|
<span class="mi">8</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
|
||||||
|
<span class="mi">9</span> <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||||||
|
<span class="mi">10</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
|
||||||
|
<span class="mi">11</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||||||
|
<span class="mi">12</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
|
||||||
|
<span class="mi">13</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
|
||||||
|
<span class="mi">14</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
|
||||||
|
<span class="mi">15</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||||||
|
<span class="mi">16</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
|
||||||
|
<span class="mi">17</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
|
||||||
|
<span class="mi">18</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
|
||||||
|
<span class="mi">19</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||||||
|
<span class="mi">20</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
|
||||||
|
<span class="mi">21</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
|
||||||
|
<span class="mi">22</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
|
||||||
|
<span class="mi">23</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||||||
|
<span class="mi">24</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
|
||||||
|
<span class="mi">25</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
|
||||||
|
<span class="mi">26</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
|
||||||
|
<span class="mi">27</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||||||
|
<span class="mi">28</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
|
||||||
|
<span class="mi">29</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
|
||||||
|
<span class="mi">30</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
|
||||||
|
<span class="mi">31</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
|
||||||
|
<span class="mi">32</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
|
||||||
|
<span class="mi">33</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||||||
|
<span class="mi">34</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
|
||||||
|
<span class="mi">35</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
|
||||||
|
<span class="mi">36</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
|
||||||
|
<span class="mi">37</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
|
||||||
|
<span class="mi">38</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
|
||||||
|
<span class="mi">39</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||||||
|
<span class="mi">40</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
|
||||||
|
<span class="mi">41</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
|
||||||
|
<span class="mi">42</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
|
||||||
|
<span class="mi">43</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
|
||||||
|
<span class="mi">44</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
|
||||||
|
<span class="mi">45</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
|
||||||
|
<span class="mi">46</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
|
||||||
|
<span class="mi">47</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
|
||||||
|
<span class="mi">48</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
|
||||||
|
<span class="mi">49</span> <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
|
||||||
|
<span class="mi">50</span> <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">2</span> <span class="mi">1</span>
|
||||||
|
<span class="mi">3</span> <span class="mi">2</span>
|
||||||
|
<span class="mi">4</span> <span class="mi">1</span>
|
||||||
|
<span class="mi">5</span> <span class="mi">2</span>
|
||||||
|
<span class="mi">6</span> <span class="mi">1</span>
|
||||||
|
<span class="mi">7</span> <span class="mi">2</span>
|
||||||
|
<span class="mi">8</span> <span class="mi">1</span>
|
||||||
|
<span class="mi">9</span> <span class="mi">2</span>
|
||||||
|
<span class="mi">10</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">11</span> <span class="mi">2</span>
|
||||||
|
<span class="mi">12</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">13</span> <span class="mi">4</span>
|
||||||
|
<span class="mi">14</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">15</span> <span class="mi">2</span>
|
||||||
|
<span class="mi">16</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">17</span> <span class="mi">4</span>
|
||||||
|
<span class="mi">18</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">19</span> <span class="mi">2</span>
|
||||||
|
<span class="mi">20</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">21</span> <span class="mi">4</span>
|
||||||
|
<span class="mi">22</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">23</span> <span class="mi">2</span>
|
||||||
|
<span class="mi">24</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">25</span> <span class="mi">4</span>
|
||||||
|
<span class="mi">26</span> <span class="mi">5</span>
|
||||||
|
<span class="mi">27</span> <span class="mi">4</span>
|
||||||
|
<span class="mi">28</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">29</span> <span class="mi">4</span>
|
||||||
|
<span class="mi">30</span> <span class="mi">5</span>
|
||||||
|
<span class="mi">31</span> <span class="mi">6</span>
|
||||||
|
<span class="mi">32</span> <span class="mi">5</span>
|
||||||
|
<span class="mi">33</span> <span class="mi">4</span>
|
||||||
|
<span class="mi">34</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">35</span> <span class="mi">4</span>
|
||||||
|
<span class="mi">36</span> <span class="mi">5</span>
|
||||||
|
<span class="mi">37</span> <span class="mi">6</span>
|
||||||
|
<span class="mi">38</span> <span class="mi">5</span>
|
||||||
|
<span class="mi">39</span> <span class="mi">4</span>
|
||||||
|
<span class="mi">40</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">41</span> <span class="mi">4</span>
|
||||||
|
<span class="mi">42</span> <span class="mi">5</span>
|
||||||
|
<span class="mi">43</span> <span class="mi">6</span>
|
||||||
|
<span class="mi">44</span> <span class="mi">5</span>
|
||||||
|
<span class="mi">45</span> <span class="mi">4</span>
|
||||||
|
<span class="mi">46</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">47</span> <span class="mi">4</span>
|
||||||
|
<span class="mi">48</span> <span class="mi">5</span>
|
||||||
|
<span class="mi">49</span> <span class="mi">6</span>
|
||||||
|
<span class="mi">50</span> <span class="mi">7</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="putting-it-all-together">
|
||||||
|
<h3>Putting it all together<a class="headerlink" href="#putting-it-all-together" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
|
||||||
|
|
||||||
|
<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="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>
|
||||||
|
<span class="c1"># and one because we are counting from 1 instead of 0.</span>
|
||||||
|
<span class="n">k</span> <span class="o">=</span> <span class="mi">1</span>
|
||||||
|
<span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
|
||||||
|
<span class="n">m</span> <span class="o">=</span> <span class="mi">8</span> <span class="o">*</span> <span class="n">k</span> <span class="c1"># The number of places total in this rank, 4(2k).</span>
|
||||||
|
<span class="k">if</span> <span class="n">n</span> <span class="o"><</span> <span class="n">m</span><span class="p">:</span>
|
||||||
|
<span class="k">return</span> <span class="n">k</span><span class="p">,</span> <span class="n">n</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="n">n</span> <span class="o">-=</span> <span class="n">m</span> <span class="c1"># Remove this rank's worth.</span>
|
||||||
|
<span class="n">k</span> <span class="o">+=</span> <span class="mi">1</span>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="k">def</span> <span class="nf">aoc20173</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||||||
|
<span class="k">if</span> <span class="n">n</span> <span class="o"><=</span> <span class="mi">1</span><span class="p">:</span>
|
||||||
|
<span class="k">return</span> <span class="mi">0</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="k">return</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>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">aoc20173</span><span class="p">(</span><span class="mi">23</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">2</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">aoc20173</span><span class="p">(</span><span class="mi">23000</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">105</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">aoc20173</span><span class="p">(</span><span class="mi">23000000000000</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">4572225</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="sympy-to-the-rescue">
|
||||||
|
<h1>Sympy to the Rescue<a class="headerlink" href="#sympy-to-the-rescue" title="Permalink to this headline">¶</a></h1>
|
||||||
|
<p>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 <code class="docutils literal notranslate"><span class="pre">rank_and_offset()</span></code> does.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sympy</span> <span class="k">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="k">import</span> <span class="n">init_printing</span>
|
||||||
|
<span class="n">init_printing</span><span class="p">()</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
<p>Since</p>
|
||||||
|
<p><span class="math notranslate nohighlight">\(1 + 2 + 3 + ... + N = \frac{N(N + 1)}{2}\)</span></p>
|
||||||
|
<p>and</p>
|
||||||
|
<p><span class="math notranslate nohighlight">\(\sum_{n=1}^k 8n = 8(\sum_{n=1}^k n) = 8\frac{k(k + 1)}{2}\)</span></p>
|
||||||
|
<p>We want:</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
</div>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[4 k \left(k + 1\right) + 2\]</div>
|
||||||
|
<p>We can write a function to solve for <span class="math notranslate nohighlight">\(k\)</span> given some <span class="math notranslate nohighlight">\(n\)</span>…</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
</div>
|
||||||
|
<p>First <code class="docutils literal notranslate"><span class="pre">solve()</span></code> for <span class="math notranslate nohighlight">\(E - n = 0\)</span> which has two solutions (because
|
||||||
|
the equation is quadratic so it has two roots) and since we only care
|
||||||
|
about the larger one we use <code class="docutils literal notranslate"><span class="pre">max()</span></code> to select it. It will generally
|
||||||
|
not be a nice integer (unless <span class="math notranslate nohighlight">\(n\)</span> is the number of an end-corner
|
||||||
|
of a rank) so we take the <code class="docutils literal notranslate"><span class="pre">floor()</span></code> and add 1 to get the integer rank
|
||||||
|
of <span class="math notranslate nohighlight">\(n\)</span>. (Taking the <code class="docutils literal notranslate"><span class="pre">ceiling()</span></code> gives off-by-one errors on the
|
||||||
|
rank boundaries. I don’t know why. I’m basically like a monkey doing
|
||||||
|
math here.) =-D</p>
|
||||||
|
<p>It gives correct answers:</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">9</span> <span class="mi">1</span>
|
||||||
|
<span class="mi">10</span> <span class="mi">2</span>
|
||||||
|
<span class="mi">25</span> <span class="mi">2</span>
|
||||||
|
<span class="mi">26</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">49</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">50</span> <span class="mi">4</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>And it runs much faster (at least for large numbers):</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">%</span><span class="n">time</span> <span class="n">rank_of</span><span class="p">(</span><span class="mi">23000000000000</span><span class="p">)</span> <span class="c1"># Compare runtime with rank_and_offset()!</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">CPU</span> <span class="n">times</span><span class="p">:</span> <span class="n">user</span> <span class="mi">68</span> <span class="n">ms</span><span class="p">,</span> <span class="n">sys</span><span class="p">:</span> <span class="mi">8</span> <span class="n">ms</span><span class="p">,</span> <span class="n">total</span><span class="p">:</span> <span class="mi">76</span> <span class="n">ms</span>
|
||||||
|
<span class="n">Wall</span> <span class="n">time</span><span class="p">:</span> <span class="mf">73.8</span> <span class="n">ms</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[2397916\]</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">%</span><span class="n">time</span> <span class="n">rank_and_offset</span><span class="p">(</span><span class="mi">23000000000000</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">CPU</span> <span class="n">times</span><span class="p">:</span> <span class="n">user</span> <span class="mi">308</span> <span class="n">ms</span><span class="p">,</span> <span class="n">sys</span><span class="p">:</span> <span class="mi">0</span> <span class="n">ns</span><span class="p">,</span> <span class="n">total</span><span class="p">:</span> <span class="mi">308</span> <span class="n">ms</span>
|
||||||
|
<span class="n">Wall</span> <span class="n">time</span><span class="p">:</span> <span class="mi">306</span> <span class="n">ms</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[\left ( 2397916, \quad 223606\right )\]</div>
|
||||||
|
<p>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
|
||||||
|
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.</p>
|
||||||
|
<p>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.</p>
|
||||||
|
<p>Sympy is a <em>symbolic</em> math library, and it supports symbolic
|
||||||
|
manipulation of equations. I can put in <span class="math notranslate nohighlight">\(y\)</span> (instead of a value)
|
||||||
|
and ask it to solve for <span class="math notranslate nohighlight">\(k\)</span>.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
<p>The equation is quadratic so there are two roots, we are interested in
|
||||||
|
the greater one…</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">g</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[- \frac{1}{2} \sqrt{y - 1} - \frac{1}{2}\]</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">f</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[\frac{1}{2} \sqrt{y - 1} - \frac{1}{2}\]</div>
|
||||||
|
<p>Now we can take the <code class="docutils literal notranslate"><span class="pre">floor()</span></code>, add 1, and <code class="docutils literal notranslate"><span class="pre">lambdify()</span></code> the equation
|
||||||
|
to get a Python function that calculates the rank directly.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[\lfloor{\frac{1}{2} \sqrt{y - 1} - \frac{1}{2}}\rfloor + 1\]</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">9</span> <span class="mi">1</span>
|
||||||
|
<span class="mi">10</span> <span class="mi">2</span>
|
||||||
|
<span class="mi">25</span> <span class="mi">2</span>
|
||||||
|
<span class="mi">26</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">49</span> <span class="mi">3</span>
|
||||||
|
<span class="mi">50</span> <span class="mi">4</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>It’s pretty fast.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">%</span><span class="n">time</span> <span class="nb">int</span><span class="p">(</span><span class="n">F</span><span class="p">(</span><span class="mi">23000000000000</span><span class="p">))</span> <span class="c1"># The clear winner.</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">CPU</span> <span class="n">times</span><span class="p">:</span> <span class="n">user</span> <span class="mi">0</span> <span class="n">ns</span><span class="p">,</span> <span class="n">sys</span><span class="p">:</span> <span class="mi">0</span> <span class="n">ns</span><span class="p">,</span> <span class="n">total</span><span class="p">:</span> <span class="mi">0</span> <span class="n">ns</span>
|
||||||
|
<span class="n">Wall</span> <span class="n">time</span><span class="p">:</span> <span class="mf">11.9</span> <span class="n">µs</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[2397916\]</div>
|
||||||
|
<p>Knowing the equation we could write our own function manually, but the
|
||||||
|
speed is no better.</p>
|
||||||
|
<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">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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">%</span><span class="n">time</span> <span class="n">mrank_of</span><span class="p">(</span><span class="mi">23000000000000</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">CPU</span> <span class="n">times</span><span class="p">:</span> <span class="n">user</span> <span class="mi">0</span> <span class="n">ns</span><span class="p">,</span> <span class="n">sys</span><span class="p">:</span> <span class="mi">0</span> <span class="n">ns</span><span class="p">,</span> <span class="n">total</span><span class="p">:</span> <span class="mi">0</span> <span class="n">ns</span>
|
||||||
|
<span class="n">Wall</span> <span class="n">time</span><span class="p">:</span> <span class="mf">12.9</span> <span class="n">µs</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[2397916\]</div>
|
||||||
|
<p>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.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
</div>
|
||||||
|
<p>(Note the sneaky way the sign changes from <span class="math notranslate nohighlight">\(k(k + 1)\)</span> to
|
||||||
|
<span class="math notranslate nohighlight">\(k(k - 1)\)</span>. This is because we want to subract the
|
||||||
|
<span class="math notranslate nohighlight">\((k - 1)\)</span>th rank’s total places (its own and those of lesser
|
||||||
|
rank) from our <span class="math notranslate nohighlight">\(n\)</span> of rank <span class="math notranslate nohighlight">\(k\)</span>. Substituting <span class="math notranslate nohighlight">\(k - 1\)</span>
|
||||||
|
for <span class="math notranslate nohighlight">\(k\)</span> in <span class="math notranslate nohighlight">\(k(k + 1)\)</span> gives <span class="math notranslate nohighlight">\((k - 1)(k - 1 + 1)\)</span>,
|
||||||
|
which of course simplifies to <span class="math notranslate nohighlight">\(k(k - 1)\)</span>.)</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[223606\]</div>
|
||||||
|
<p>So, we can compute the rank, then the offset, then the row value.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
|
||||||
|
|
||||||
|
<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>
|
||||||
|
|
||||||
|
|
||||||
|
<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>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="k">def</span> <span class="nf">aoc20173</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||||||
|
<span class="n">k</span> <span class="o">=</span> <span class="n">rank_of</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
|
||||||
|
<span class="n">i</span> <span class="o">=</span> <span class="n">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="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>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">aoc20173</span><span class="p">(</span><span class="mi">23</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[2\]</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">aoc20173</span><span class="p">(</span><span class="mi">23000</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[105\]</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">aoc20173</span><span class="p">(</span><span class="mi">23000000000000</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[4572225\]</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">%</span><span class="n">time</span> <span class="n">aoc20173</span><span class="p">(</span><span class="mi">23000000000000000000000000</span><span class="p">)</span> <span class="c1"># Fast for large values.</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">CPU</span> <span class="n">times</span><span class="p">:</span> <span class="n">user</span> <span class="mi">0</span> <span class="n">ns</span><span class="p">,</span> <span class="n">sys</span><span class="p">:</span> <span class="mi">0</span> <span class="n">ns</span><span class="p">,</span> <span class="n">total</span><span class="p">:</span> <span class="mi">0</span> <span class="n">ns</span>
|
||||||
|
<span class="n">Wall</span> <span class="n">time</span><span class="p">:</span> <span class="mi">20</span> <span class="n">µs</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="math notranslate nohighlight">
|
||||||
|
\[2690062495969\]</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="a-joy-version">
|
||||||
|
<h1>A Joy Version<a class="headerlink" href="#a-joy-version" title="Permalink to this headline">¶</a></h1>
|
||||||
|
<p>At this point I feel confident that I can implement a concise version of
|
||||||
|
this code in Joy. ;-)</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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">n</span> <span class="n">rank_of</span>
|
||||||
|
<span class="o">---------------</span>
|
||||||
|
<span class="n">k</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>The translation is straightforward.</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">int</span><span class="p">(</span><span class="n">floor</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>
|
||||||
|
|
||||||
|
<span class="n">rank_of</span> <span class="o">==</span> <span class="o">--</span> <span class="n">sqrt</span> <span class="mi">2</span> <span class="o">/</span> <span class="mf">0.5</span> <span class="o">-</span> <span class="n">floor</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">'rank_of == -- sqrt 2 / 0.5 - floor ++'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">n</span> <span class="n">k</span> <span class="n">offset_of</span>
|
||||||
|
<span class="o">-------------------</span>
|
||||||
|
<span class="n">i</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>
|
||||||
|
</div>
|
||||||
|
<p>A little tricky…</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">n</span> <span class="n">k</span> <span class="n">dup</span> <span class="mi">2</span> <span class="o">*</span>
|
||||||
|
<span class="n">n</span> <span class="n">k</span> <span class="n">k</span> <span class="mi">2</span> <span class="o">*</span>
|
||||||
|
<span class="n">n</span> <span class="n">k</span> <span class="n">k</span><span class="o">*</span><span class="mi">2</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="n">n</span> <span class="n">k</span> <span class="n">Q</span> <span class="n">k</span><span class="o">*</span><span class="mi">2</span> <span class="o">%</span>
|
||||||
|
|
||||||
|
<span class="n">n</span> <span class="n">k</span> <span class="n">dup</span> <span class="o">--</span>
|
||||||
|
<span class="n">n</span> <span class="n">k</span> <span class="n">k</span> <span class="o">--</span>
|
||||||
|
<span class="n">n</span> <span class="n">k</span> <span class="n">k</span><span class="o">-</span><span class="mi">1</span> <span class="mi">4</span> <span class="o">*</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">+</span> <span class="o">-</span>
|
||||||
|
<span class="n">n</span> <span class="n">k</span><span class="o">*</span><span class="n">k</span><span class="o">-</span><span class="mi">1</span><span class="o">*</span><span class="mi">4</span> <span class="mi">2</span> <span class="o">+</span> <span class="o">-</span>
|
||||||
|
<span class="n">n</span> <span class="n">k</span><span class="o">*</span><span class="n">k</span><span class="o">-</span><span class="mi">1</span><span class="o">*</span><span class="mi">4</span><span class="o">+</span><span class="mi">2</span> <span class="o">-</span>
|
||||||
|
<span class="n">n</span><span class="o">-</span><span class="n">k</span><span class="o">*</span><span class="n">k</span><span class="o">-</span><span class="mi">1</span><span class="o">*</span><span class="mi">4</span><span class="o">+</span><span class="mi">2</span>
|
||||||
|
|
||||||
|
<span class="n">n</span><span class="o">-</span><span class="n">k</span><span class="o">*</span><span class="n">k</span><span class="o">-</span><span class="mi">1</span><span class="o">*</span><span class="mi">4</span><span class="o">+</span><span class="mi">2</span> <span class="n">k</span><span class="o">*</span><span class="mi">2</span> <span class="o">%</span>
|
||||||
|
<span class="n">n</span><span class="o">-</span><span class="n">k</span><span class="o">*</span><span class="n">k</span><span class="o">-</span><span class="mi">1</span><span class="o">*</span><span class="mi">4</span><span class="o">+</span><span class="mi">2</span><span class="o">%</span><span class="n">k</span><span class="o">*</span><span class="mi">2</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Ergo:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">offset_of</span> <span class="o">==</span> <span class="n">dup</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">dup</span> <span class="o">--</span> <span class="mi">4</span> <span class="o">*</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">+</span> <span class="o">-</span><span class="p">]</span> <span class="n">dip</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">'offset_of == dup 2 * [dup -- 4 * * 2 + -] dip %'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">k</span> <span class="n">i</span> <span class="n">row_value</span>
|
||||||
|
<span class="o">-------------------</span>
|
||||||
|
<span class="n">n</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>
|
||||||
|
|
||||||
|
<span class="n">k</span> <span class="n">i</span> <span class="n">over</span> <span class="o">--</span> <span class="o">-</span> <span class="nb">abs</span> <span class="o">+</span>
|
||||||
|
<span class="n">k</span> <span class="n">i</span> <span class="n">k</span> <span class="o">--</span> <span class="o">-</span> <span class="nb">abs</span> <span class="o">+</span>
|
||||||
|
<span class="n">k</span> <span class="n">i</span> <span class="n">k</span><span class="o">-</span><span class="mi">1</span> <span class="o">-</span> <span class="nb">abs</span> <span class="o">+</span>
|
||||||
|
<span class="n">k</span> <span class="n">i</span><span class="o">-</span><span class="n">k</span><span class="o">-</span><span class="mi">1</span> <span class="nb">abs</span> <span class="o">+</span>
|
||||||
|
<span class="n">k</span> <span class="o">|</span><span class="n">i</span><span class="o">-</span><span class="n">k</span><span class="o">-</span><span class="mi">1</span><span class="o">|</span> <span class="o">+</span>
|
||||||
|
<span class="n">k</span><span class="o">+|</span><span class="n">i</span><span class="o">-</span><span class="n">k</span><span class="o">-</span><span class="mi">1</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">'row_value == over -- - abs +'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">n</span> <span class="n">aoc2017</span><span class="o">.</span><span class="mi">3</span>
|
||||||
|
<span class="o">-----------------</span>
|
||||||
|
<span class="n">m</span>
|
||||||
|
|
||||||
|
<span class="n">n</span> <span class="n">dup</span> <span class="n">rank_of</span>
|
||||||
|
<span class="n">n</span> <span class="n">k</span> <span class="p">[</span><span class="n">offset_of</span><span class="p">]</span> <span class="n">dupdip</span>
|
||||||
|
<span class="n">n</span> <span class="n">k</span> <span class="n">offset_of</span> <span class="n">k</span>
|
||||||
|
<span class="n">i</span> <span class="n">k</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="n">k</span> <span class="n">i</span> <span class="n">row_value</span>
|
||||||
|
<span class="n">m</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">'aoc2017.3 == dup rank_of [offset_of] dupdip swap row_value'</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 aoc2017.3'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">2</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">'23000 aoc2017.3'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">105</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="mi">23000000000000</span> <span class="n">aoc2017</span><span class="o">.</span><span class="mi">3</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="o">.</span> <span class="n">aoc2017</span><span class="o">.</span><span class="mi">3</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="o">.</span> <span class="n">dup</span> <span class="n">rank_of</span> <span class="p">[</span><span class="n">offset_of</span><span class="p">]</span> <span class="n">dupdip</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="mi">23000000000000</span> <span class="o">.</span> <span class="n">rank_of</span> <span class="p">[</span><span class="n">offset_of</span><span class="p">]</span> <span class="n">dupdip</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="mi">23000000000000</span> <span class="o">.</span> <span class="o">--</span> <span class="n">sqrt</span> <span class="mi">2</span> <span class="o">/</span> <span class="mf">0.5</span> <span class="o">-</span> <span class="n">floor</span> <span class="o">++</span> <span class="p">[</span><span class="n">offset_of</span><span class="p">]</span> <span class="n">dupdip</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="mi">22999999999999</span> <span class="o">.</span> <span class="n">sqrt</span> <span class="mi">2</span> <span class="o">/</span> <span class="mf">0.5</span> <span class="o">-</span> <span class="n">floor</span> <span class="o">++</span> <span class="p">[</span><span class="n">offset_of</span><span class="p">]</span> <span class="n">dupdip</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="mf">4795831.523312615</span> <span class="o">.</span> <span class="mi">2</span> <span class="o">/</span> <span class="mf">0.5</span> <span class="o">-</span> <span class="n">floor</span> <span class="o">++</span> <span class="p">[</span><span class="n">offset_of</span><span class="p">]</span> <span class="n">dupdip</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="mf">4795831.523312615</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">/</span> <span class="mf">0.5</span> <span class="o">-</span> <span class="n">floor</span> <span class="o">++</span> <span class="p">[</span><span class="n">offset_of</span><span class="p">]</span> <span class="n">dupdip</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="mf">2397915.7616563076</span> <span class="o">.</span> <span class="mf">0.5</span> <span class="o">-</span> <span class="n">floor</span> <span class="o">++</span> <span class="p">[</span><span class="n">offset_of</span><span class="p">]</span> <span class="n">dupdip</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="mf">2397915.7616563076</span> <span class="mf">0.5</span> <span class="o">.</span> <span class="o">-</span> <span class="n">floor</span> <span class="o">++</span> <span class="p">[</span><span class="n">offset_of</span><span class="p">]</span> <span class="n">dupdip</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="mf">2397915.2616563076</span> <span class="o">.</span> <span class="n">floor</span> <span class="o">++</span> <span class="p">[</span><span class="n">offset_of</span><span class="p">]</span> <span class="n">dupdip</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="mi">2397915</span> <span class="o">.</span> <span class="o">++</span> <span class="p">[</span><span class="n">offset_of</span><span class="p">]</span> <span class="n">dupdip</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="mi">2397916</span> <span class="o">.</span> <span class="p">[</span><span class="n">offset_of</span><span class="p">]</span> <span class="n">dupdip</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="mi">2397916</span> <span class="p">[</span><span class="n">offset_of</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="mi">2397916</span> <span class="o">.</span> <span class="n">offset_of</span> <span class="mi">2397916</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="mi">2397916</span> <span class="o">.</span> <span class="n">dup</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">dup</span> <span class="o">--</span> <span class="mi">4</span> <span class="o">*</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">+</span> <span class="o">-</span><span class="p">]</span> <span class="n">dip</span> <span class="o">%</span> <span class="mi">2397916</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="mi">2397916</span> <span class="mi">2397916</span> <span class="o">.</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">dup</span> <span class="o">--</span> <span class="mi">4</span> <span class="o">*</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">+</span> <span class="o">-</span><span class="p">]</span> <span class="n">dip</span> <span class="o">%</span> <span class="mi">2397916</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="mi">2397916</span> <span class="mi">2397916</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">*</span> <span class="p">[</span><span class="n">dup</span> <span class="o">--</span> <span class="mi">4</span> <span class="o">*</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">+</span> <span class="o">-</span><span class="p">]</span> <span class="n">dip</span> <span class="o">%</span> <span class="mi">2397916</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="mi">2397916</span> <span class="mi">4795832</span> <span class="o">.</span> <span class="p">[</span><span class="n">dup</span> <span class="o">--</span> <span class="mi">4</span> <span class="o">*</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">+</span> <span class="o">-</span><span class="p">]</span> <span class="n">dip</span> <span class="o">%</span> <span class="mi">2397916</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="mi">2397916</span> <span class="mi">4795832</span> <span class="p">[</span><span class="n">dup</span> <span class="o">--</span> <span class="mi">4</span> <span class="o">*</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">+</span> <span class="o">-</span><span class="p">]</span> <span class="o">.</span> <span class="n">dip</span> <span class="o">%</span> <span class="mi">2397916</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="mi">2397916</span> <span class="o">.</span> <span class="n">dup</span> <span class="o">--</span> <span class="mi">4</span> <span class="o">*</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">+</span> <span class="o">-</span> <span class="mi">4795832</span> <span class="o">%</span> <span class="mi">2397916</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="mi">2397916</span> <span class="mi">2397916</span> <span class="o">.</span> <span class="o">--</span> <span class="mi">4</span> <span class="o">*</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">+</span> <span class="o">-</span> <span class="mi">4795832</span> <span class="o">%</span> <span class="mi">2397916</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="mi">2397916</span> <span class="mi">2397915</span> <span class="o">.</span> <span class="mi">4</span> <span class="o">*</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">+</span> <span class="o">-</span> <span class="mi">4795832</span> <span class="o">%</span> <span class="mi">2397916</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="mi">2397916</span> <span class="mi">2397915</span> <span class="mi">4</span> <span class="o">.</span> <span class="o">*</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">+</span> <span class="o">-</span> <span class="mi">4795832</span> <span class="o">%</span> <span class="mi">2397916</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="mi">2397916</span> <span class="mi">9591660</span> <span class="o">.</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">+</span> <span class="o">-</span> <span class="mi">4795832</span> <span class="o">%</span> <span class="mi">2397916</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="mi">22999994980560</span> <span class="o">.</span> <span class="mi">2</span> <span class="o">+</span> <span class="o">-</span> <span class="mi">4795832</span> <span class="o">%</span> <span class="mi">2397916</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="mi">22999994980560</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">+</span> <span class="o">-</span> <span class="mi">4795832</span> <span class="o">%</span> <span class="mi">2397916</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">23000000000000</span> <span class="mi">22999994980562</span> <span class="o">.</span> <span class="o">-</span> <span class="mi">4795832</span> <span class="o">%</span> <span class="mi">2397916</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">5019438</span> <span class="o">.</span> <span class="mi">4795832</span> <span class="o">%</span> <span class="mi">2397916</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">5019438</span> <span class="mi">4795832</span> <span class="o">.</span> <span class="o">%</span> <span class="mi">2397916</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">223606</span> <span class="o">.</span> <span class="mi">2397916</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">223606</span> <span class="mi">2397916</span> <span class="o">.</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">2397916</span> <span class="mi">223606</span> <span class="o">.</span> <span class="n">row_value</span>
|
||||||
|
<span class="mi">2397916</span> <span class="mi">223606</span> <span class="o">.</span> <span class="n">over</span> <span class="o">--</span> <span class="o">-</span> <span class="nb">abs</span> <span class="o">+</span>
|
||||||
|
<span class="mi">2397916</span> <span class="mi">223606</span> <span class="mi">2397916</span> <span class="o">.</span> <span class="o">--</span> <span class="o">-</span> <span class="nb">abs</span> <span class="o">+</span>
|
||||||
|
<span class="mi">2397916</span> <span class="mi">223606</span> <span class="mi">2397915</span> <span class="o">.</span> <span class="o">-</span> <span class="nb">abs</span> <span class="o">+</span>
|
||||||
|
<span class="mi">2397916</span> <span class="o">-</span><span class="mi">2174309</span> <span class="o">.</span> <span class="nb">abs</span> <span class="o">+</span>
|
||||||
|
<span class="mi">2397916</span> <span class="mi">2174309</span> <span class="o">.</span> <span class="o">+</span>
|
||||||
|
<span class="mi">4572225</span> <span class="o">.</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">rank_of</span> <span class="o">==</span> <span class="o">--</span> <span class="n">sqrt</span> <span class="mi">2</span> <span class="o">/</span> <span class="mf">0.5</span> <span class="o">-</span> <span class="n">floor</span> <span class="o">++</span>
|
||||||
|
<span class="n">offset_of</span> <span class="o">==</span> <span class="n">dup</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">dup</span> <span class="o">--</span> <span class="mi">4</span> <span class="o">*</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">+</span> <span class="o">-</span><span class="p">]</span> <span class="n">dip</span> <span class="o">%</span>
|
||||||
|
<span class="n">row_value</span> <span class="o">==</span> <span class="n">over</span> <span class="o">--</span> <span class="o">-</span> <span class="nb">abs</span> <span class="o">+</span>
|
||||||
|
|
||||||
|
<span class="n">aoc2017</span><span class="o">.</span><span class="mi">3</span> <span class="o">==</span> <span class="n">dup</span> <span class="n">rank_of</span> <span class="p">[</span><span class="n">offset_of</span><span class="p">]</span> <span class="n">dupdip</span> <span class="n">swap</span> <span class="n">row_value</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
|
||||||
|
<div class="sphinxsidebarwrapper">
|
||||||
|
<h3><a href="../index.html">Table Of Contents</a></h3>
|
||||||
|
<ul>
|
||||||
|
<li><a class="reference internal" href="#">Advent of Code 2017</a><ul>
|
||||||
|
<li><a class="reference internal" href="#december-3rd">December 3rd</a><ul>
|
||||||
|
<li><a class="reference internal" href="#analysis">Analysis</a></li>
|
||||||
|
<li><a class="reference internal" href="#finding-the-rank-and-offset-of-a-number">Finding the rank and offset of a number.</a></li>
|
||||||
|
<li><a class="reference internal" href="#putting-it-all-together">Putting it all together</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li><a class="reference internal" href="#sympy-to-the-rescue">Sympy to the Rescue</a></li>
|
||||||
|
<li><a class="reference internal" href="#a-joy-version">A Joy Version</a></li>
|
||||||
|
</ul>
|
||||||
|
<div class="relations">
|
||||||
|
<h3>Related Topics</h3>
|
||||||
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|
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|
||||||
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|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
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<h3>This Page</h3>
|
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<br />
|
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.7.3.
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<div class="section" id="advent-of-code-2017">
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<h1>Advent of Code 2017<a class="headerlink" href="#advent-of-code-2017" title="Permalink to this headline">¶</a></h1>
|
||||||
|
<div class="section" id="december-4th">
|
||||||
|
<h2>December 4th<a class="headerlink" href="#december-4th" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>To ensure security, a valid passphrase must contain no duplicate words.</p>
|
||||||
|
<p>For example:</p>
|
||||||
|
<ul class="simple">
|
||||||
|
<li>aa bb cc dd ee is valid.</li>
|
||||||
|
<li>aa bb cc dd aa is not valid - the word aa appears more than once.</li>
|
||||||
|
<li>aa bb cc dd aaa is valid - aa and aaa count as different words.</li>
|
||||||
|
</ul>
|
||||||
|
<p>The system’s full passphrase list is available as your puzzle input. How
|
||||||
|
many passphrases are valid?</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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>I’ll assume the input is a Joy sequence of sequences of integers.</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[[</span><span class="mi">5</span> <span class="mi">1</span> <span class="mi">9</span> <span class="mi">5</span><span class="p">]</span>
|
||||||
|
<span class="p">[</span><span class="mi">7</span> <span class="mi">5</span> <span class="mi">4</span> <span class="mi">3</span><span class="p">]</span>
|
||||||
|
<span class="p">[</span><span class="mi">2</span> <span class="mi">4</span> <span class="mi">6</span> <span class="mi">8</span><span class="p">]]</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>So, obviously, the initial form will be a <code class="docutils literal notranslate"><span class="pre">step</span></code> function:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">AoC2017</span><span class="o">.</span><span class="mi">4</span> <span class="o">==</span> <span class="mi">0</span> <span class="n">swap</span> <span class="p">[</span><span class="n">F</span> <span class="o">+</span><span class="p">]</span> <span class="n">step</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">F</span> <span class="o">==</span> <span class="p">[</span><span class="n">size</span><span class="p">]</span> <span class="p">[</span><span class="n">unique</span> <span class="n">size</span><span class="p">]</span> <span class="n">cleave</span> <span class="o">=</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>The <code class="docutils literal notranslate"><span class="pre">step_zero</span></code> combinator includes the <code class="docutils literal notranslate"><span class="pre">0</span> <span class="pre">swap</span></code> that would normally
|
||||||
|
open one of these definitions:</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">'[step_zero] help'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">0</span> <span class="n">roll</span><span class="o">></span> <span class="n">step</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">AoC2017</span><span class="o">.</span><span class="mi">4</span> <span class="o">==</span> <span class="p">[</span><span class="n">F</span> <span class="o">+</span><span class="p">]</span> <span class="n">step_zero</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">'AoC2017.4 == [[size] [unique size] cleave = +] step_zero'</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">'''</span>
|
||||||
|
|
||||||
|
<span class="s1">[[5 1 9 5]</span>
|
||||||
|
<span class="s1"> [7 5 4 3]</span>
|
||||||
|
<span class="s1"> [2 4 6 8]] AoC2017.4</span>
|
||||||
|
|
||||||
|
<span class="s1">'''</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">2</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
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|
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<h3><a href="../index.html">Table Of Contents</a></h3>
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|
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<li><a class="reference internal" href="#">Advent of Code 2017</a><ul>
|
||||||
|
<li><a class="reference internal" href="#december-4th">December 4th</a></li>
|
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<br />
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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<div class="section" id="advent-of-code-2017">
|
||||||
|
<h1>Advent of Code 2017<a class="headerlink" href="#advent-of-code-2017" title="Permalink to this headline">¶</a></h1>
|
||||||
|
<div class="section" id="december-5th">
|
||||||
|
<h2>December 5th<a class="headerlink" href="#december-5th" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>…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.</p>
|
||||||
|
<p>In addition, these instructions are a little strange; after each jump,
|
||||||
|
the offset of that instruction increases by 1. So, if you come across an
|
||||||
|
offset of 3, you would move three instructions forward, but change it to
|
||||||
|
a 4 for the next time it is encountered.</p>
|
||||||
|
<p>For example, consider the following list of jump offsets:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">0</span>
|
||||||
|
<span class="mi">3</span>
|
||||||
|
<span class="mi">0</span>
|
||||||
|
<span class="mi">1</span>
|
||||||
|
<span class="o">-</span><span class="mi">3</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>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:</p>
|
||||||
|
<ul class="simple">
|
||||||
|
<li><ol class="first arabic" start="0">
|
||||||
|
<li>3 0 1 -3 - before we have taken any steps.</li>
|
||||||
|
</ol>
|
||||||
|
</li>
|
||||||
|
<li><ol class="first arabic">
|
||||||
|
<li>3 0 1 -3 - jump with offset 0 (that is, don’t jump at all).
|
||||||
|
Fortunately, the instruction is then incremented to 1.</li>
|
||||||
|
</ol>
|
||||||
|
</li>
|
||||||
|
<li>2 (3) 0 1 -3 - step forward because of the instruction we just
|
||||||
|
modified. The first instruction is incremented again, now to 2.</li>
|
||||||
|
<li>2 4 0 1 (-3) - jump all the way to the end; leave a 4 behind.</li>
|
||||||
|
<li>2 (4) 0 1 -2 - go back to where we just were; increment -3 to -2.</li>
|
||||||
|
<li>2 5 0 1 -2 - jump 4 steps forward, escaping the maze.</li>
|
||||||
|
</ul>
|
||||||
|
<p>In this example, the exit is reached in 5 steps.</p>
|
||||||
|
<p>How many steps does it take to reach the exit?</p>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="breakdown">
|
||||||
|
<h2>Breakdown<a class="headerlink" href="#breakdown" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>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 <code class="docutils literal notranslate"><span class="pre">index</span></code> and a
|
||||||
|
<code class="docutils literal notranslate"><span class="pre">step-count</span></code>, which are both initially zero. Then we have the sequence
|
||||||
|
itself, and some recursive function <code class="docutils literal notranslate"><span class="pre">F</span></code> that does the work.</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">size</span> <span class="n">index</span> <span class="n">step</span><span class="o">-</span><span class="n">count</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="n">F</span>
|
||||||
|
<span class="o">-----------------------------------</span>
|
||||||
|
<span class="n">step</span><span class="o">-</span><span class="n">count</span>
|
||||||
|
|
||||||
|
<span class="n">F</span> <span class="o">==</span> <span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="p">[</span><span class="n">R1</span><span class="p">]</span> <span class="p">[</span><span class="n">R2</span><span class="p">]</span> <span class="n">genrec</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>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 <code class="docutils literal notranslate"><span class="pre">F</span></code>! D’oh!</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">index</span> <span class="n">step</span><span class="o">-</span><span class="n">count</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="n">F</span>
|
||||||
|
<span class="o">------------------------------</span>
|
||||||
|
<span class="n">step</span><span class="o">-</span><span class="n">count</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>So, let’s start by nailing down the predicate:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">F</span> <span class="o">==</span> <span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="p">[</span><span class="n">R1</span><span class="p">]</span> <span class="p">[</span><span class="n">R2</span><span class="p">]</span> <span class="n">genrec</span>
|
||||||
|
<span class="o">==</span> <span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="p">[</span><span class="n">R1</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="n">R2</span><span class="p">]</span> <span class="n">ifte</span>
|
||||||
|
|
||||||
|
<span class="mi">0</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">0</span> <span class="mi">3</span> <span class="mi">0</span> <span class="mi">1</span> <span class="o">-</span><span class="mi">3</span><span class="p">]</span> <span class="n">popop</span> <span class="mi">5</span> <span class="o">>=</span>
|
||||||
|
|
||||||
|
<span class="n">P</span> <span class="o">==</span> <span class="n">popop</span> <span class="mi">5</span> <span class="o">>=</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Now we need the else-part:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">index</span> <span class="n">step</span><span class="o">-</span><span class="n">count</span> <span class="p">[</span><span class="mi">0</span> <span class="mi">3</span> <span class="mi">0</span> <span class="mi">1</span> <span class="o">-</span><span class="mi">3</span><span class="p">]</span> <span class="n">roll</span><span class="o"><</span> <span class="n">popop</span>
|
||||||
|
|
||||||
|
<span class="n">E</span> <span class="o">==</span> <span class="n">roll</span><span class="o"><</span> <span class="n">popop</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Last but not least, the recursive branch</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">0</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">0</span> <span class="mi">3</span> <span class="mi">0</span> <span class="mi">1</span> <span class="o">-</span><span class="mi">3</span><span class="p">]</span> <span class="n">R1</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="n">R2</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>The <code class="docutils literal notranslate"><span class="pre">R1</span></code> function has a big job:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">R1</span> <span class="o">==</span> <span class="n">get</span> <span class="n">the</span> <span class="n">value</span> <span class="n">at</span> <span class="n">index</span>
|
||||||
|
<span class="n">increment</span> <span class="n">the</span> <span class="n">value</span> <span class="n">at</span> <span class="n">the</span> <span class="n">index</span>
|
||||||
|
<span class="n">add</span> <span class="n">the</span> <span class="n">value</span> <span class="n">gotten</span> <span class="n">to</span> <span class="n">the</span> <span class="n">index</span>
|
||||||
|
<span class="n">increment</span> <span class="n">the</span> <span class="n">step</span> <span class="n">count</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>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
|
||||||
|
legendary <em>Sufficiently-Smart Compiler</em> would of course rewrite this
|
||||||
|
function to use an array “under the hood”.)</p>
|
||||||
|
<p>In the meantime, I’m going to write a primitive function that just does
|
||||||
|
what we need.</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">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="k">import</span> <span class="n">SimpleFunctionWrapper</span>
|
||||||
|
<span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="k">import</span> <span class="n">list_to_stack</span>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="nd">@SimpleFunctionWrapper</span>
|
||||||
|
<span class="k">def</span> <span class="nf">incr_at</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
|
||||||
|
<span class="sd">'''Given a index and a sequence of integers, increment the integer at the index.</span>
|
||||||
|
|
||||||
|
<span class="sd"> E.g.:</span>
|
||||||
|
|
||||||
|
<span class="sd"> 3 [0 1 2 3 4 5] incr_at</span>
|
||||||
|
<span class="sd"> -----------------------------</span>
|
||||||
|
<span class="sd"> [0 1 2 4 4 5]</span>
|
||||||
|
|
||||||
|
<span class="sd"> '''</span>
|
||||||
|
<span class="n">sequence</span><span class="p">,</span> <span class="p">(</span><span class="n">i</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">mem</span> <span class="o">=</span> <span class="p">[]</span>
|
||||||
|
<span class="k">while</span> <span class="n">i</span> <span class="o">>=</span> <span class="mi">0</span><span class="p">:</span>
|
||||||
|
<span class="n">term</span><span class="p">,</span> <span class="n">sequence</span> <span class="o">=</span> <span class="n">sequence</span>
|
||||||
|
<span class="n">mem</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">term</span><span class="p">)</span>
|
||||||
|
<span class="n">i</span> <span class="o">-=</span> <span class="mi">1</span>
|
||||||
|
<span class="n">mem</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
|
||||||
|
<span class="k">return</span> <span class="n">list_to_stack</span><span class="p">(</span><span class="n">mem</span><span class="p">,</span> <span class="n">sequence</span><span class="p">),</span> <span class="n">stack</span>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="n">D</span><span class="p">[</span><span class="s1">'incr_at'</span><span class="p">]</span> <span class="o">=</span> <span class="n">incr_at</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">'3 [0 1 2 3 4 5] incr_at'</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">0</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">4</span> <span class="mi">4</span> <span class="mi">5</span><span class="p">]</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="get-the-value-at-index">
|
||||||
|
<h3>get the value at index<a class="headerlink" href="#get-the-value-at-index" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="p">[</span><span class="n">roll</span><span class="o"><</span> <span class="n">at</span><span class="p">]</span> <span class="n">nullary</span>
|
||||||
|
<span class="mi">3</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span> <span class="n">n</span> <span class="mi">4</span><span class="p">]</span> <span class="n">n</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="increment-the-value-at-the-index">
|
||||||
|
<h3>increment the value at the index<a class="headerlink" href="#increment-the-value-at-the-index" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span> <span class="n">n</span> <span class="mi">4</span><span class="p">]</span> <span class="n">n</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">dip</span>
|
||||||
|
<span class="mi">3</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span> <span class="n">n</span> <span class="mi">4</span><span class="p">]</span> <span class="n">Q</span> <span class="n">n</span>
|
||||||
|
<span class="mi">3</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span> <span class="n">n</span> <span class="mi">4</span><span class="p">]</span> <span class="p">[</span><span class="n">popd</span> <span class="n">incr_at</span><span class="p">]</span> <span class="n">unary</span> <span class="n">n</span>
|
||||||
|
<span class="mi">3</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span> <span class="n">n</span><span class="o">+</span><span class="mi">1</span> <span class="mi">4</span><span class="p">]</span> <span class="n">n</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="add-the-value-gotten-to-the-index">
|
||||||
|
<h3>add the value gotten to the index<a class="headerlink" href="#add-the-value-gotten-to-the-index" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span> <span class="n">n</span><span class="o">+</span><span class="mi">1</span> <span class="mi">4</span><span class="p">]</span> <span class="n">n</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">cons</span> <span class="n">dipd</span>
|
||||||
|
<span class="mi">3</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span> <span class="n">n</span><span class="o">+</span><span class="mi">1</span> <span class="mi">4</span><span class="p">]</span> <span class="p">[</span><span class="n">n</span> <span class="o">+</span><span class="p">]</span> <span class="n">dipd</span>
|
||||||
|
<span class="mi">3</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span> <span class="n">n</span><span class="o">+</span><span class="mi">1</span> <span class="mi">4</span><span class="p">]</span>
|
||||||
|
<span class="mi">3</span><span class="o">+</span><span class="n">n</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span> <span class="n">n</span><span class="o">+</span><span class="mi">1</span> <span class="mi">4</span><span class="p">]</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="increment-the-step-count">
|
||||||
|
<h3>increment the step count<a class="headerlink" href="#increment-the-step-count" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span><span class="o">+</span><span class="n">n</span> <span class="mi">0</span> <span class="p">[</span><span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span> <span class="n">n</span><span class="o">+</span><span class="mi">1</span> <span class="mi">4</span><span class="p">]</span> <span class="p">[</span><span class="o">++</span><span class="p">]</span> <span class="n">dip</span>
|
||||||
|
<span class="mi">3</span><span class="o">+</span><span class="n">n</span> <span class="mi">1</span> <span class="p">[</span><span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span> <span class="n">n</span><span class="o">+</span><span class="mi">1</span> <span class="mi">4</span><span class="p">]</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="all-together-now">
|
||||||
|
<h3>All together now…<a class="headerlink" href="#all-together-now" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>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
|
||||||
|
|
||||||
|
F == [P] [T] [R1] primrec
|
||||||
|
|
||||||
|
F == [popop !size! >=] [roll< pop] [get_value incr_value add_value incr_step_count] primrec
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.library</span> <span class="k">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>
|
||||||
|
<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">'F == [popop 5 >=] [roll< popop] [AoC2017.5.0] primrec'</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">'0 0 [0 3 0 1 -3] F'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">5</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="preamble-for-setting-up-predicate-index-and-step-count">
|
||||||
|
<h3>Preamble for setting up predicate, <code class="docutils literal notranslate"><span class="pre">index</span></code>, and <code class="docutils literal notranslate"><span class="pre">step-count</span></code><a class="headerlink" href="#preamble-for-setting-up-predicate-index-and-step-count" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>We want to go from this to this:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="n">AoC2017</span><span class="o">.</span><span class="mf">5.</span><span class="n">preamble</span>
|
||||||
|
<span class="o">------------------------------</span>
|
||||||
|
<span class="mi">0</span> <span class="mi">0</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</span> <span class="n">n</span> <span class="o">>=</span><span class="p">]</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Where <code class="docutils literal notranslate"><span class="pre">n</span></code> is the size of the sequence.</p>
|
||||||
|
<p>The first part is obviously <code class="docutils literal notranslate"><span class="pre">0</span> <span class="pre">0</span> <span class="pre">roll<</span></code>, then <code class="docutils literal notranslate"><span class="pre">dup</span> <span class="pre">size</span></code>:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="mi">0</span> <span class="mi">0</span> <span class="n">roll</span><span class="o"><</span> <span class="n">dup</span> <span class="n">size</span>
|
||||||
|
<span class="mi">0</span> <span class="mi">0</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="n">n</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Then:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">0</span> <span class="mi">0</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="n">n</span> <span class="p">[</span><span class="o">>=</span><span class="p">]</span> <span class="n">cons</span> <span class="p">[</span><span class="n">popop</span><span class="p">]</span> <span class="n">swoncat</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>So:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">init</span><span class="o">-</span><span class="n">index</span><span class="o">-</span><span class="ow">and</span><span class="o">-</span><span class="n">step</span><span class="o">-</span><span class="n">count</span> <span class="o">==</span> <span class="mi">0</span> <span class="mi">0</span> <span class="n">roll</span><span class="o"><</span>
|
||||||
|
<span class="n">prepare</span><span class="o">-</span><span class="n">predicate</span> <span class="o">==</span> <span class="n">dup</span> <span class="n">size</span> <span class="p">[</span><span class="o">>=</span><span class="p">]</span> <span class="n">cons</span> <span class="p">[</span><span class="n">popop</span><span class="p">]</span> <span class="n">swoncat</span>
|
||||||
|
|
||||||
|
<span class="n">AoC2017</span><span class="o">.</span><span class="mf">5.</span><span class="n">preamble</span> <span class="o">==</span> <span class="n">init</span><span class="o">-</span><span class="n">index</span><span class="o">-</span><span class="ow">and</span><span class="o">-</span><span class="n">step</span><span class="o">-</span><span class="n">count</span> <span class="n">prepare</span><span class="o">-</span><span class="n">predicate</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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"> 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">'''</span><span class="p">,</span> <span class="n">D</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">'[0 3 0 1 -3] AoC2017.5'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">5</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">AoC2017</span><span class="o">.</span><span class="mi">5</span> <span class="o">==</span> <span class="n">AoC2017</span><span class="o">.</span><span class="mf">5.</span><span class="n">preamble</span> <span class="p">[</span><span class="n">roll</span><span class="o"><</span> <span class="n">popop</span><span class="p">]</span> <span class="p">[</span><span class="n">AoC2017</span><span class="o">.</span><span class="mf">5.0</span><span class="p">]</span> <span class="n">primrec</span>
|
||||||
|
|
||||||
|
<span class="n">AoC2017</span><span class="o">.</span><span class="mf">5.0</span> <span class="o">==</span> <span class="n">get_value</span> <span class="n">incr_value</span> <span class="n">add_value</span> <span class="n">incr_step_count</span>
|
||||||
|
<span class="n">AoC2017</span><span class="o">.</span><span class="mf">5.</span><span class="n">preamble</span> <span class="o">==</span> <span class="n">init</span><span class="o">-</span><span class="n">index</span><span class="o">-</span><span class="ow">and</span><span class="o">-</span><span class="n">step</span><span class="o">-</span><span class="n">count</span> <span class="n">prepare</span><span class="o">-</span><span class="n">predicate</span>
|
||||||
|
|
||||||
|
<span class="n">get_value</span> <span class="o">==</span> <span class="p">[</span><span class="n">roll</span><span class="o"><</span> <span class="n">at</span><span class="p">]</span> <span class="n">nullary</span>
|
||||||
|
<span class="n">incr_value</span> <span class="o">==</span> <span class="p">[[</span><span class="n">popd</span> <span class="n">incr_at</span><span class="p">]</span> <span class="n">unary</span><span class="p">]</span> <span class="n">dip</span>
|
||||||
|
<span class="n">add_value</span> <span class="o">==</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">cons</span> <span class="n">dipd</span>
|
||||||
|
<span class="n">incr_step_count</span> <span class="o">==</span> <span class="p">[</span><span class="o">++</span><span class="p">]</span> <span class="n">dip</span>
|
||||||
|
|
||||||
|
<span class="n">init</span><span class="o">-</span><span class="n">index</span><span class="o">-</span><span class="ow">and</span><span class="o">-</span><span class="n">step</span><span class="o">-</span><span class="n">count</span> <span class="o">==</span> <span class="mi">0</span> <span class="mi">0</span> <span class="n">roll</span><span class="o"><</span>
|
||||||
|
<span class="n">prepare</span><span class="o">-</span><span class="n">predicate</span> <span class="o">==</span> <span class="n">dup</span> <span class="n">size</span> <span class="p">[</span><span class="o">>=</span><span class="p">]</span> <span class="n">cons</span> <span class="p">[</span><span class="n">popop</span><span class="p">]</span> <span class="n">swoncat</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>This is by far the largest program I have yet written in Joy. Even with
|
||||||
|
the <code class="docutils literal notranslate"><span class="pre">incr_at</span></code> 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
|
||||||
|
even Python.</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
|
||||||
|
<div class="sphinxsidebarwrapper">
|
||||||
|
<h3><a href="../index.html">Table Of Contents</a></h3>
|
||||||
|
<ul>
|
||||||
|
<li><a class="reference internal" href="#">Advent of Code 2017</a><ul>
|
||||||
|
<li><a class="reference internal" href="#december-5th">December 5th</a></li>
|
||||||
|
<li><a class="reference internal" href="#breakdown">Breakdown</a><ul>
|
||||||
|
<li><a class="reference internal" href="#get-the-value-at-index">get the value at index</a></li>
|
||||||
|
<li><a class="reference internal" href="#increment-the-value-at-the-index">increment the value at the index</a></li>
|
||||||
|
<li><a class="reference internal" href="#add-the-value-gotten-to-the-index">add the value gotten to the index</a></li>
|
||||||
|
<li><a class="reference internal" href="#increment-the-step-count">increment the step count</a></li>
|
||||||
|
<li><a class="reference internal" href="#all-together-now">All together now…</a></li>
|
||||||
|
<li><a class="reference internal" href="#preamble-for-setting-up-predicate-index-and-step-count">Preamble for setting up predicate, <code class="docutils literal notranslate"><span class="pre">index</span></code>, and <code class="docutils literal notranslate"><span class="pre">step-count</span></code></a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
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</li>
|
||||||
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</ul>
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||||||
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<h3>Related Topics</h3>
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<br />
|
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.7.3.
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<div class="section" id="advent-of-code-2017">
|
||||||
|
<h1>Advent of Code 2017<a class="headerlink" href="#advent-of-code-2017" title="Permalink to this headline">¶</a></h1>
|
||||||
|
<div class="section" id="december-6th">
|
||||||
|
<h2>December 6th<a class="headerlink" href="#december-6th" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">0</span> <span class="mi">2</span> <span class="mi">7</span> <span class="mi">0</span><span class="p">]</span> <span class="n">dup</span> <span class="nb">max</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">notebook_preamble</span> <span class="k">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>
|
||||||
|
<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">'[0 2 7 0] dup max'</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">0</span> <span class="mi">2</span> <span class="mi">7</span> <span class="mi">0</span><span class="p">]</span> <span class="mi">7</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">joy.library</span> <span class="k">import</span> <span class="n">SimpleFunctionWrapper</span>
|
||||||
|
<span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="k">import</span> <span class="n">list_to_stack</span>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="nd">@SimpleFunctionWrapper</span>
|
||||||
|
<span class="k">def</span> <span class="nf">index_of</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
|
||||||
|
<span class="sd">'''Given a sequence and a item, return the index of the item, or -1 if not found.</span>
|
||||||
|
|
||||||
|
<span class="sd"> E.g.:</span>
|
||||||
|
|
||||||
|
<span class="sd"> [a b c] a index_of</span>
|
||||||
|
<span class="sd"> ------------------------</span>
|
||||||
|
<span class="sd"> 0</span>
|
||||||
|
|
||||||
|
<span class="sd"> [a b c] d index_of</span>
|
||||||
|
<span class="sd"> ------------------------</span>
|
||||||
|
<span class="sd"> -1</span>
|
||||||
|
|
||||||
|
<span class="sd"> '''</span>
|
||||||
|
<span class="n">item</span><span class="p">,</span> <span class="p">(</span><span class="n">sequence</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">i</span> <span class="o">=</span> <span class="mi">0</span>
|
||||||
|
<span class="k">while</span> <span class="n">sequence</span><span class="p">:</span>
|
||||||
|
<span class="n">term</span><span class="p">,</span> <span class="n">sequence</span> <span class="o">=</span> <span class="n">sequence</span>
|
||||||
|
<span class="k">if</span> <span class="n">term</span> <span class="o">==</span> <span class="n">item</span><span class="p">:</span>
|
||||||
|
<span class="k">break</span>
|
||||||
|
<span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
|
||||||
|
<span class="k">else</span><span class="p">:</span>
|
||||||
|
<span class="n">i</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span>
|
||||||
|
<span class="k">return</span> <span class="n">i</span><span class="p">,</span> <span class="n">stack</span>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="n">D</span><span class="p">[</span><span class="s1">'index_of'</span><span class="p">]</span> <span class="o">=</span> <span class="n">index_of</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">'[0 2 7 0] 7 index_of'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">2</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">'[0 2 7 0] 23 index_of'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">-</span><span class="mi">1</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Starting at <code class="docutils literal notranslate"><span class="pre">index</span></code> distribute <code class="docutils literal notranslate"><span class="pre">count</span></code> “blocks” to the “banks” in
|
||||||
|
the sequence.</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="n">count</span> <span class="n">index</span> <span class="n">distribute</span>
|
||||||
|
<span class="o">----------------------------</span>
|
||||||
|
<span class="p">[</span><span class="o">...</span><span class="p">]</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>This seems like it would be a PITA to implement in Joypy…</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="k">import</span> <span class="n">iter_stack</span><span class="p">,</span> <span class="n">list_to_stack</span>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="nd">@SimpleFunctionWrapper</span>
|
||||||
|
<span class="k">def</span> <span class="nf">distribute</span><span class="p">(</span><span class="n">stack</span><span class="p">):</span>
|
||||||
|
<span class="sd">'''Starting at index+1 distribute count "blocks" to the "banks" in the sequence.</span>
|
||||||
|
|
||||||
|
<span class="sd"> [...] count index distribute</span>
|
||||||
|
<span class="sd"> ----------------------------</span>
|
||||||
|
<span class="sd"> [...]</span>
|
||||||
|
|
||||||
|
<span class="sd"> '''</span>
|
||||||
|
<span class="n">index</span><span class="p">,</span> <span class="p">(</span><span class="n">count</span><span class="p">,</span> <span class="p">(</span><span class="n">sequence</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="k">assert</span> <span class="n">count</span> <span class="o">>=</span> <span class="mi">0</span>
|
||||||
|
<span class="n">cheat</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">iter_stack</span><span class="p">(</span><span class="n">sequence</span><span class="p">))</span>
|
||||||
|
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">cheat</span><span class="p">)</span>
|
||||||
|
<span class="k">assert</span> <span class="n">index</span> <span class="o"><</span> <span class="n">n</span>
|
||||||
|
<span class="n">cheat</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
|
||||||
|
<span class="k">while</span> <span class="n">count</span><span class="p">:</span>
|
||||||
|
<span class="n">index</span> <span class="o">+=</span> <span class="mi">1</span>
|
||||||
|
<span class="n">index</span> <span class="o">%=</span> <span class="n">n</span>
|
||||||
|
<span class="n">cheat</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
|
||||||
|
<span class="n">count</span> <span class="o">-=</span> <span class="mi">1</span>
|
||||||
|
<span class="k">return</span> <span class="n">list_to_stack</span><span class="p">(</span><span class="n">cheat</span><span class="p">),</span> <span class="n">stack</span>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="n">D</span><span class="p">[</span><span class="s1">'distribute'</span><span class="p">]</span> <span class="o">=</span> <span class="n">distribute</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">'[0 2 7 0] dup max [index_of] nullary distribute'</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">2</span> <span class="mi">4</span> <span class="mi">1</span> <span class="mi">2</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">'[2 4 1 2] dup max [index_of] nullary distribute'</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">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</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">'[3 1 2 3] dup max [index_of] nullary distribute'</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">0</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</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">'[0 2 3 4] dup max [index_of] nullary distribute'</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="mi">3</span> <span class="mi">4</span> <span class="mi">1</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">'[1 3 4 1] dup max [index_of] nullary distribute'</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">2</span> <span class="mi">4</span> <span class="mi">1</span> <span class="mi">2</span><span class="p">]</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="recalling-generator-programs">
|
||||||
|
<h3>Recalling “Generator Programs”<a class="headerlink" href="#recalling-generator-programs" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">a</span> <span class="n">F</span><span class="p">]</span> <span class="n">x</span>
|
||||||
|
<span class="p">[</span><span class="n">a</span> <span class="n">F</span><span class="p">]</span> <span class="n">a</span> <span class="n">F</span>
|
||||||
|
|
||||||
|
<span class="p">[</span><span class="n">a</span> <span class="n">F</span><span class="p">]</span> <span class="n">a</span> <span class="n">swap</span> <span class="p">[</span><span class="n">C</span><span class="p">]</span> <span class="n">dip</span> <span class="n">rest</span> <span class="n">cons</span>
|
||||||
|
<span class="n">a</span> <span class="p">[</span><span class="n">a</span> <span class="n">F</span><span class="p">]</span> <span class="p">[</span><span class="n">C</span><span class="p">]</span> <span class="n">dip</span> <span class="n">rest</span> <span class="n">cons</span>
|
||||||
|
<span class="n">a</span> <span class="n">C</span> <span class="p">[</span><span class="n">a</span> <span class="n">F</span><span class="p">]</span> <span class="n">rest</span> <span class="n">cons</span>
|
||||||
|
<span class="n">a</span> <span class="n">C</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="n">cons</span>
|
||||||
|
|
||||||
|
<span class="n">w</span><span class="o">/</span> <span class="n">C</span> <span class="o">==</span> <span class="n">dup</span> <span class="n">G</span>
|
||||||
|
|
||||||
|
<span class="n">a</span> <span class="n">dup</span> <span class="n">G</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="n">cons</span>
|
||||||
|
<span class="n">a</span> <span class="n">a</span> <span class="n">G</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="n">cons</span>
|
||||||
|
|
||||||
|
<span class="n">w</span><span class="o">/</span> <span class="n">G</span> <span class="o">==</span> <span class="n">dup</span> <span class="nb">max</span> <span class="p">[</span><span class="n">index_of</span><span class="p">]</span> <span class="n">nullary</span> <span class="n">distribute</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">'direco == dip rest cons'</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">'G == [direco] cons [swap] swoncat cons'</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">'make_distributor == [dup dup max [index_of] nullary distribute] G'</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">'[0 2 7 0] make_distributor 6 [x] times pop'</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">0</span> <span class="mi">2</span> <span class="mi">7</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">4</span> <span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">0</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">3</span> <span class="mi">4</span> <span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">4</span> <span class="mi">1</span> <span class="mi">2</span><span class="p">]</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="a-function-to-drive-a-generator-and-count-how-many-states-before-a-repeat">
|
||||||
|
<h3>A function to drive a generator and count how many states before a repeat.<a class="headerlink" href="#a-function-to-drive-a-generator-and-count-how-many-states-before-a-repeat" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>First draft:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[]</span> <span class="p">[</span><span class="n">GEN</span><span class="p">]</span> <span class="n">x</span> <span class="p">[</span><span class="n">pop</span> <span class="n">index_of</span> <span class="mi">0</span> <span class="o">>=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="n">size</span> <span class="o">--</span><span class="p">]</span> <span class="p">[[</span><span class="n">swons</span><span class="p">]</span> <span class="n">dip</span> <span class="n">x</span><span class="p">]</span> <span class="n">primrec</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>(?)</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[]</span> <span class="p">[</span><span class="n">GEN</span><span class="p">]</span> <span class="n">x</span> <span class="p">[</span><span class="n">pop</span> <span class="n">index_of</span> <span class="mi">0</span> <span class="o">>=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="n">size</span> <span class="o">--</span><span class="p">]</span> <span class="p">[[</span><span class="n">swons</span><span class="p">]</span> <span class="n">dip</span> <span class="n">x</span><span class="p">]</span> <span class="n">primrec</span>
|
||||||
|
<span class="p">[]</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">GEN</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="n">index_of</span> <span class="mi">0</span> <span class="o">>=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="n">size</span> <span class="o">--</span><span class="p">]</span> <span class="p">[[</span><span class="n">swons</span><span class="p">]</span> <span class="n">dip</span> <span class="n">x</span><span class="p">]</span> <span class="n">primrec</span>
|
||||||
|
<span class="p">[]</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">GEN</span><span class="p">]</span> <span class="n">pop</span> <span class="n">index_of</span> <span class="mi">0</span> <span class="o">>=</span>
|
||||||
|
<span class="p">[]</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="n">index_of</span> <span class="mi">0</span> <span class="o">>=</span>
|
||||||
|
<span class="o">-</span><span class="mi">1</span> <span class="mi">0</span> <span class="o">>=</span>
|
||||||
|
<span class="kc">False</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Base case</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[]</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">GEN</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="n">index_of</span> <span class="mi">0</span> <span class="o">>=</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="n">size</span> <span class="o">--</span><span class="p">]</span> <span class="p">[[</span><span class="n">swons</span><span class="p">]</span> <span class="n">dip</span> <span class="n">x</span><span class="p">]</span> <span class="n">primrec</span>
|
||||||
|
<span class="p">[]</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">GEN</span><span class="p">]</span> <span class="n">pop</span> <span class="n">size</span> <span class="o">--</span>
|
||||||
|
<span class="p">[]</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="n">size</span> <span class="o">--</span>
|
||||||
|
<span class="p">[]</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="n">size</span> <span class="o">--</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>A mistake, <code class="docutils literal notranslate"><span class="pre">popop</span></code> and no need for <code class="docutils literal notranslate"><span class="pre">--</span></code></p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[]</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">GEN</span><span class="p">]</span> <span class="n">popop</span> <span class="n">size</span>
|
||||||
|
<span class="p">[]</span> <span class="n">size</span>
|
||||||
|
<span class="n">n</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Recursive case</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[]</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">GEN</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="n">index_of</span> <span class="mi">0</span> <span class="o">>=</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</span> <span class="n">size</span><span class="p">]</span> <span class="p">[[</span><span class="n">swons</span><span class="p">]</span> <span class="n">dip</span> <span class="n">x</span><span class="p">]</span> <span class="n">primrec</span>
|
||||||
|
<span class="p">[]</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">GEN</span><span class="p">]</span> <span class="p">[</span><span class="n">swons</span><span class="p">]</span> <span class="n">dip</span> <span class="n">x</span> <span class="n">F</span>
|
||||||
|
<span class="p">[]</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="n">swons</span> <span class="p">[</span><span class="n">GEN</span><span class="p">]</span> <span class="n">x</span> <span class="n">F</span>
|
||||||
|
<span class="p">[[</span><span class="o">...</span><span class="p">]]</span> <span class="p">[</span><span class="n">GEN</span><span class="p">]</span> <span class="n">x</span> <span class="n">F</span>
|
||||||
|
<span class="p">[[</span><span class="o">...</span><span class="p">]]</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">GEN</span><span class="p">]</span> <span class="n">F</span>
|
||||||
|
|
||||||
|
<span class="p">[[</span><span class="o">...</span><span class="p">]]</span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">GEN</span><span class="p">]</span> <span class="n">F</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>What have we learned?</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">F</span> <span class="o">==</span> <span class="p">[</span><span class="n">pop</span> <span class="n">index_of</span> <span class="mi">0</span> <span class="o">>=</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</span> <span class="n">size</span><span class="p">]</span> <span class="p">[[</span><span class="n">swons</span><span class="p">]</span> <span class="n">dip</span> <span class="n">x</span><span class="p">]</span> <span class="n">primrec</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">'count_states == [] swap x [pop index_of 0 >=] [popop size] [[swons] dip x] primrec'</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">'AoC2017.6 == make_distributor count_states'</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">'[0 2 7 0] AoC2017.6'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">5</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">'[1 1 1] AoC2017.6'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">4</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">'[8 0 0 0 0 0] AoC2017.6'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">15</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
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|
||||||
|
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|
||||||
|
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|
||||||
|
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
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||||||
|
<div class="sphinxsidebarwrapper">
|
||||||
|
<h3><a href="../index.html">Table Of Contents</a></h3>
|
||||||
|
<ul>
|
||||||
|
<li><a class="reference internal" href="#">Advent of Code 2017</a><ul>
|
||||||
|
<li><a class="reference internal" href="#december-6th">December 6th</a><ul>
|
||||||
|
<li><a class="reference internal" href="#recalling-generator-programs">Recalling “Generator Programs”</a></li>
|
||||||
|
<li><a class="reference internal" href="#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></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
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|
||||||
|
</ul>
|
||||||
|
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||||||
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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<h1><code class="docutils literal notranslate"><span class="pre">within</span></code><a class="headerlink" href="#within" title="Permalink to this headline">¶</a></h1>
|
||||||
|
<blockquote>
|
||||||
|
<div>The remainder of a square root finder is a function <em>within</em>, 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.</div></blockquote>
|
||||||
|
<p>From <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>
|
||||||
|
<p>(And note that by “list” he means a lazily-evaluated list.)</p>
|
||||||
|
<p>Using a <a class="reference internal" href="Generator Programs.html"><span class="doc">generator</span></a> driven by <code class="docutils literal notranslate"><span class="pre">x</span></code> and assuming such for square root approximations (or whatever) <code class="docutils literal notranslate"><span class="pre">G</span></code>, and further assuming that the first term <code class="docutils literal notranslate"><span class="pre">a</span></code> has been generated already and epsilon <code class="docutils literal notranslate"><span class="pre">ε</span></code> is handy on the stack…</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">within</span>
|
||||||
|
<span class="o">--------------------</span> <span class="n">a</span> <span class="n">b</span> <span class="o">-</span> <span class="nb">abs</span> <span class="n">ε</span> <span class="o"><=</span>
|
||||||
|
<span class="n">b</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">within</span>
|
||||||
|
<span class="o">--------------------</span> <span class="n">a</span> <span class="n">b</span> <span class="o">-</span> <span class="nb">abs</span> <span class="n">ε</span> <span class="o">></span>
|
||||||
|
<span class="o">.</span>
|
||||||
|
<span class="p">[</span><span class="n">b</span> <span class="n">G</span><span class="p">]</span> <span class="n">x</span> <span class="n">ε</span> <span class="o">...</span>
|
||||||
|
<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="o">...</span>
|
||||||
|
<span class="o">.</span>
|
||||||
|
<span class="o">--------------------</span>
|
||||||
|
<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="section" id="predicate">
|
||||||
|
<h2>Predicate<a class="headerlink" href="#predicate" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<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="p">[</span><span class="n">first</span> <span class="o">-</span> <span class="nb">abs</span><span class="p">]</span> <span class="n">dip</span> <span class="o"><=</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">first</span> <span class="o">-</span> <span class="nb">abs</span> <span class="n">ε</span> <span class="o"><=</span>
|
||||||
|
<span class="n">a</span> <span class="n">b</span> <span class="o">-</span> <span class="nb">abs</span> <span class="n">ε</span> <span class="o"><=</span>
|
||||||
|
<span class="n">a</span><span class="o">-</span><span class="n">b</span> <span class="nb">abs</span> <span class="n">ε</span> <span class="o"><=</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="n">ε</span> <span class="o"><=</span>
|
||||||
|
<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="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">P</span> <span class="o">==</span> <span class="p">[</span><span class="n">first</span> <span class="o">-</span> <span class="nb">abs</span><span class="p">]</span> <span class="n">dip</span> <span class="o"><=</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="base-case">
|
||||||
|
<h2>Base-Case<a class="headerlink" href="#base-case" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<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">roll</span><span class="o"><</span> <span class="n">popop</span> <span class="n">first</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">a</span> <span class="n">popop</span> <span class="n">first</span>
|
||||||
|
<span class="p">[</span><span class="n">b</span> <span class="n">G</span><span class="p">]</span> <span class="n">first</span>
|
||||||
|
<span class="n">b</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">B</span> <span class="o">==</span> <span class="n">roll</span><span class="o"><</span> <span class="n">popop</span> <span class="n">first</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="recur">
|
||||||
|
<h2>Recur<a class="headerlink" href="#recur" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<ol class="arabic simple">
|
||||||
|
<li>Discard <code class="docutils literal notranslate"><span class="pre">a</span></code>.</li>
|
||||||
|
<li>Use <code class="docutils literal notranslate"><span class="pre">x</span></code> combinator to generate next term from G.</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>
|
||||||
|
</ol>
|
||||||
|
<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>
|
||||||
|
<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="p">[</span><span class="n">popd</span> <span class="n">x</span><span class="p">]</span> <span class="n">dip</span> <span class="p">[</span><span class="n">within</span><span class="p">]</span> <span class="n">i</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">popd</span> <span class="n">x</span> <span class="n">ε</span> <span class="p">[</span><span class="n">within</span><span class="p">]</span> <span class="n">i</span>
|
||||||
|
<span class="p">[</span><span class="n">b</span> <span class="n">G</span><span class="p">]</span> <span class="n">x</span> <span class="n">ε</span> <span class="p">[</span><span class="n">within</span><span class="p">]</span> <span class="n">i</span>
|
||||||
|
<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="p">[</span><span class="n">within</span><span class="p">]</span> <span class="n">i</span>
|
||||||
|
<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>
|
||||||
|
|
||||||
|
<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="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">R0</span> <span class="o">==</span> <span class="p">[</span><span class="n">popd</span> <span class="n">x</span><span class="p">]</span> <span class="n">dip</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="setting-up">
|
||||||
|
<h2>Setting up<a class="headerlink" href="#setting-up" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">a</span> <span class="n">G</span><span class="p">]</span> <span class="n">x</span> <span class="n">ε</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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">within</span> <span class="o">==</span> <span class="n">x</span> <span class="n">ε</span> <span class="p">[[</span><span class="n">first</span> <span class="o">-</span> <span class="nb">abs</span><span class="p">]</span> <span class="n">dip</span> <span class="o"><=</span><span class="p">]</span> <span class="p">[</span><span class="n">roll</span><span class="o"><</span> <span class="n">popop</span> <span class="n">first</span><span class="p">]</span> <span class="p">[[</span><span class="n">popd</span> <span class="n">x</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">primrec</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
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<li><a class="reference internal" href="#"><code class="docutils literal notranslate"><span class="pre">within</span></code></a><ul>
|
||||||
|
<li><a class="reference internal" href="#predicate">Predicate</a></li>
|
||||||
|
<li><a class="reference internal" href="#base-case">Base-Case</a></li>
|
||||||
|
<li><a class="reference internal" href="#recur">Recur</a></li>
|
||||||
|
<li><a class="reference internal" href="#setting-up">Setting up</a></li>
|
||||||
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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<div class="section" id="categorical-programming">
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<h1>Categorical Programming<a class="headerlink" href="#categorical-programming" title="Permalink to this headline">¶</a></h1>
|
||||||
|
<p>DRAFT</p>
|
||||||
|
<p><a class="reference external" href="https://en.wikipedia.org/wiki/Category_theory">Categorical</a></p>
|
||||||
|
<p>In Manfred von Thun’s article <a class="reference external" href="http://www.kevinalbrecht.com/code/joy-mirror/j08cnt.html">Joy compared with other functional languages</a> he asks, “Could the language of categories be used for writing programs? Any lambda expression can be translated into a categorical expression, so the language of categories is expressively complete. But this does not make it a suitable language for writing programs. As it stands it is a very low-level language.”</p>
|
||||||
|
<p>In <a class="reference external" href="http://conal.net/papers/compiling-to-categories/">Compiling to categories</a> Conal Elliott give a taste of what this might mean.</p>
|
||||||
|
<blockquote>
|
||||||
|
<div>It is well-known that the simply typed lambda-calculus is modeled by any cartesian closed category (CCC). This correspondence suggests giving typed functional programs a variety of interpretations, each corresponding to a different category. A convenient way to realize this idea is as a collection of meaning-preserving transformations added to an existing compiler, such as GHC for Haskell. This paper describes such an implementation and demonstrates its use for a variety of interpretations including hardware circuits, automatic differentiation, incremental computation, and interval analysis. Each such interpretation is a category easily defined in Haskell (outside of the compiler). The general technique appears to provide a compelling alternative to deeply embedded domain-specific languages.</div></blockquote>
|
||||||
|
<p>What he’s doing is translating labda forms into a kind of “point-free” style that is very close to Joy code (although more verbose) and then showing how to instantiate that code over different categories to get several different kinds of program out of the same code.</p>
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<br />
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.7.3.
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<div class="section" id="thun-joy-in-python">
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<h1>Thun: Joy in Python<a class="headerlink" href="#thun-joy-in-python" title="Permalink to this headline">¶</a></h1>
|
||||||
|
<p>This implementation is meant as a tool for exploring the programming
|
||||||
|
model and method of Joy. Python seems like a great implementation
|
||||||
|
language for Joy for several reasons.</p>
|
||||||
|
<ul class="simple">
|
||||||
|
<li>We can lean on the Python immutable types for our basic semantics and types: ints, floats, strings, and tuples, which enforces functional purity.</li>
|
||||||
|
<li>We get garbage collection for free.</li>
|
||||||
|
<li>Compilation via Cython.</li>
|
||||||
|
<li>Python is a “glue language” with loads of libraries which we can wrap in Joy functions.</li>
|
||||||
|
</ul>
|
||||||
|
<div class="section" id="read-eval-print-loop-repl">
|
||||||
|
<h2><a class="reference external" href="https://en.wikipedia.org/wiki/Read%E2%80%93eval%E2%80%93print_loop">Read-Eval-Print Loop (REPL)</a><a class="headerlink" href="#read-eval-print-loop-repl" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>The main way to interact with the Joy interpreter is through a simple
|
||||||
|
<a class="reference external" href="https://en.wikipedia.org/wiki/Read%E2%80%93eval%E2%80%93print_loop">REPL</a>
|
||||||
|
that you start by running the package:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>$ 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
|
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docs for a word.
|
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|
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<-top
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joy? _
|
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|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>The <code class="docutils literal notranslate"><span class="pre"><-top</span></code> marker points to the top of the (initially empty) stack.
|
||||||
|
You can enter Joy notation at the prompt and a <a class="reference internal" href="../pretty.html"><span class="doc">trace of evaluation</span></a> will
|
||||||
|
be printed followed by the stack and prompt again:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>joy? 23 sqr 18 +
|
||||||
|
. 23 sqr 18 +
|
||||||
|
23 . sqr 18 +
|
||||||
|
23 . dup mul 18 +
|
||||||
|
23 23 . mul 18 +
|
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|
529 . 18 +
|
||||||
|
529 18 . +
|
||||||
|
547 .
|
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|
|
||||||
|
547 <-top
|
||||||
|
|
||||||
|
joy?
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="the-stack">
|
||||||
|
<h2>The Stack<a class="headerlink" href="#the-stack" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>In Joy, in addition to the types Boolean, integer, float, and string,
|
||||||
|
there is a <a class="reference internal" href="../stack.html"><span class="doc">single sequence type</span></a> represented by enclosing a sequence of
|
||||||
|
terms in brackets <code class="docutils literal notranslate"><span class="pre">[...]</span></code>. This sequence type is used to represent
|
||||||
|
both the stack and the expression. It is a <a class="reference external" href="https://en.wikipedia.org/wiki/Cons#Lists">cons
|
||||||
|
list</a> made from Python
|
||||||
|
tuples.</p>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="purely-functional-datastructures">
|
||||||
|
<h2>Purely Functional Datastructures.<a class="headerlink" href="#purely-functional-datastructures" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>Because Joy stacks are made out of Python tuples they are immutable, as are the other Python types we “borrow” for Joy, so all Joy datastructures are <a class="reference external" href="https://en.wikipedia.org/wiki/Purely_functional_data_structure">purely functional</a>.</p>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="the-joy-function">
|
||||||
|
<h2>The <code class="docutils literal notranslate"><span class="pre">joy()</span></code> function<a class="headerlink" href="#the-joy-function" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<div class="section" id="an-interpreter">
|
||||||
|
<h3>An Interpreter<a class="headerlink" href="#an-interpreter" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>The <code class="docutils literal notranslate"><span class="pre">joy()</span></code> interpreter function is extrememly simple. It accepts a stack, an
|
||||||
|
expression, and a dictionary, and it iterates through the expression
|
||||||
|
putting values onto the stack and delegating execution to functions which it
|
||||||
|
looks up in the dictionary.</p>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="continuation-passing-style">
|
||||||
|
<h3><a class="reference external" href="https://en.wikipedia.org/wiki/Continuation-passing_style">Continuation-Passing Style</a><a class="headerlink" href="#continuation-passing-style" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>One day I thought, What happens if you rewrite Joy to use
|
||||||
|
<a class="reference external" href="https://en.wikipedia.org/wiki/Continuation-passing_style">CPS</a>? I
|
||||||
|
made all the functions accept and return the expression as well as the
|
||||||
|
stack and found that all the combinators could be rewritten to work by
|
||||||
|
modifying the expression rather than making recursive calls to the
|
||||||
|
<code class="docutils literal notranslate"><span class="pre">joy()</span></code> function.</p>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="view-function">
|
||||||
|
<h3>View function<a class="headerlink" href="#view-function" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>The <code class="docutils literal notranslate"><span class="pre">joy()</span></code> function accepts an optional <code class="docutils literal notranslate"><span class="pre">viewer</span></code> argument that
|
||||||
|
is a 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.</p>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="the-traceprinter">
|
||||||
|
<h3>The <code class="docutils literal notranslate"><span class="pre">TracePrinter</span></code>.<a class="headerlink" href="#the-traceprinter" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>A <code class="docutils literal notranslate"><span class="pre">viewer</span></code> records each step of the evaluation of a Joy program. The
|
||||||
|
<code class="docutils literal notranslate"><span class="pre">TracePrinter</span></code> 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.</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="parser">
|
||||||
|
<h2>Parser<a class="headerlink" href="#parser" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>The parser is extremely simple. The undocumented <code class="docutils literal notranslate"><span class="pre">re.Scanner</span></code> class
|
||||||
|
does the tokenizing and then the parser builds the tuple
|
||||||
|
structure out of the tokens. There’s no Abstract Syntax Tree or anything
|
||||||
|
like that.</p>
|
||||||
|
<div class="section" id="symbols">
|
||||||
|
<h3>Symbols<a class="headerlink" href="#symbols" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>TODO: Symbols are just a string subclass; used by the parser to represent function names and by the interpreter to look up functions in the dictionary. N.B.: Symbols are not looked up at parse-time. You <em>could</em> define recursive functions, er, recusively, without <code class="docutils literal notranslate"><span class="pre">genrec</span></code> or other recursion combinators <code class="docutils literal notranslate"><span class="pre">foo</span> <span class="pre">==</span> <span class="pre">...</span> <span class="pre">fooo</span> <span class="pre">...</span></code> but don’t do that.</p>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="token-regular-expressions">
|
||||||
|
<h3>Token Regular Expressions<a class="headerlink" href="#token-regular-expressions" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">123</span> <span class="mf">1.2</span> <span class="s1">'single quotes'</span> <span class="s2">"double quotes"</span> <span class="n">function</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>TBD (look in the :module: joy.parser module.)</p>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="examples">
|
||||||
|
<h3>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
</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="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><span class="mi">4</span><span class="p">,</span> <span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="p">())))))</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
</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="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> <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="p">())))</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
<span class="c1"># a Symbol, no lookup at</span>
|
||||||
|
<span class="c1"># parse-time. Haiku docs.</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="p">(</span><span class="mi">23</span><span class="p">,</span> <span class="p">((</span><span class="s1">'four'</span><span class="p">,</span> <span class="p">((</span><span class="o">-</span><span class="mf">5.0</span><span class="p">,</span> <span class="p">()),</span> <span class="p">(</span><span class="n">cons</span><span class="p">,</span> <span class="p">()))),</span> <span class="p">(</span><span class="mi">8888</span><span class="p">,</span> <span class="p">()))))</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((),</span> <span class="p">((),</span> <span class="p">((),</span> <span class="p">((),</span> <span class="p">((),</span> <span class="p">())))))</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">((((((),</span> <span class="p">()),</span> <span class="p">()),</span> <span class="p">()),</span> <span class="p">()),</span> <span class="p">())</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="library">
|
||||||
|
<h2>Library<a class="headerlink" href="#library" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>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 <code class="docutils literal notranslate"><span class="pre">add</span></code> (or
|
||||||
|
<code class="docutils literal notranslate"><span class="pre">+</span></code>, the library module supports aliases), and combinators which
|
||||||
|
provide control-flow and higher-order operations.</p>
|
||||||
|
<p>Many of the functions are defined in Python, like <code class="docutils literal notranslate"><span class="pre">dip</span></code>:</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">dip</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="n">dictionary</span><span class="p">):</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>
|
||||||
|
<span class="n">expression</span> <span class="o">=</span> <span class="n">x</span><span class="p">,</span> <span class="n">expression</span>
|
||||||
|
<span class="k">return</span> <span class="n">stack</span><span class="p">,</span> <span class="n">pushback</span><span class="p">(</span><span class="n">quote</span><span class="p">,</span> <span class="n">expression</span><span class="p">),</span> <span class="n">dictionary</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Some functions are defined in equations in terms of other functions.
|
||||||
|
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.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<pre class="literal-block">
|
||||||
|
second == rest first
|
||||||
|
third == rest rest first
|
||||||
|
product == 1 swap [*] step
|
||||||
|
swons == swap cons
|
||||||
|
swoncat == swap concat
|
||||||
|
flatten == [] swap [concat] step
|
||||||
|
unit == [] cons
|
||||||
|
quoted == [unit] dip
|
||||||
|
unquoted == [i] dip
|
||||||
|
enstacken == stack [clear] dip
|
||||||
|
disenstacken == ? [uncons ?] loop pop
|
||||||
|
? == dup truthy
|
||||||
|
dinfrirst == dip infra first
|
||||||
|
nullary == [stack] dinfrirst
|
||||||
|
unary == [stack [pop] dip] dinfrirst
|
||||||
|
binary == [stack [popop] dip] dinfrirst
|
||||||
|
ternary == [stack [popop pop] dip] dinfrirst
|
||||||
|
pam == [i] map
|
||||||
|
run == [] swap infra
|
||||||
|
sqr == dup mul
|
||||||
|
size == 0 swap [pop ++] step
|
||||||
|
cleave == [i] app2 [popd] dip
|
||||||
|
average == [sum 1.0 <em>] [size] cleave /
|
||||||
|
gcd == 1 [tuck modulus dup 0 >] loop pop
|
||||||
|
least_fraction == dup [gcd] infra [div] concat map
|
||||||
|
*fraction == [uncons] dip uncons [swap] dip concat [</em>] infra [*] dip cons
|
||||||
|
<em>fraction0 == concat [[swap] dip * [</em>] dip] infra
|
||||||
|
down_to_zero == [0 >] [dup --] while
|
||||||
|
range_to_zero == unit [down_to_zero] infra
|
||||||
|
anamorphism == [pop []] swap [dip swons] genrec
|
||||||
|
range == [0 <=] [1 - dup] anamorphism
|
||||||
|
while == swap [nullary] cons dup dipd concat loop
|
||||||
|
dudipd == dup dipd
|
||||||
|
primrec == [i] genrec
|
||||||
|
</pre>
|
||||||
|
<p>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.</p>
|
||||||
|
<p>It would be simple enough to define one, but it would open the door to
|
||||||
|
<em>name binding</em> and break the idea that all state is captured in the
|
||||||
|
stack and expression. There’s an implicit <em>standard dictionary</em> 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.)</p>
|
||||||
|
<div class="section" id="there-should-be-only-one">
|
||||||
|
<h3>“There should be only one.”<a class="headerlink" href="#there-should-be-only-one" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>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
|
||||||
|
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 <em>Grand Refactoring</em> biannually (two years, not six
|
||||||
|
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.</p>
|
||||||
|
<p>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 <a class="reference external" href="https://en.wikipedia.org/wiki/Thundering_herd_problem">fractal
|
||||||
|
“thundering herd”
|
||||||
|
attack</a> on
|
||||||
|
human mentality.</p>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="literary-code-library">
|
||||||
|
<h3>Literary Code Library<a class="headerlink" href="#literary-code-library" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>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
|
||||||
|
skeptical, as I was, but it seems to work: deriving code mathematically
|
||||||
|
seems to lead to fewer errors.</p>
|
||||||
|
<p>But my point now is that this great ratio of textual explanation to wind
|
||||||
|
up with code that consists of a few equations and could fit on an index
|
||||||
|
card is highly desirable. Less code has fewer errors. The structure of
|
||||||
|
Joy engenders a kind of thinking that seems to be very effective for
|
||||||
|
developing structured processes.</p>
|
||||||
|
<p>There seems to be an elegance and power to the notation.</p>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
|
||||||
|
<div class="sphinxsidebarwrapper">
|
||||||
|
<h3><a href="../index.html">Table Of Contents</a></h3>
|
||||||
|
<ul>
|
||||||
|
<li><a class="reference internal" href="#">Thun: Joy in Python</a><ul>
|
||||||
|
<li><a class="reference internal" href="#read-eval-print-loop-repl">Read-Eval-Print Loop (REPL)</a></li>
|
||||||
|
<li><a class="reference internal" href="#the-stack">The Stack</a></li>
|
||||||
|
<li><a class="reference internal" href="#purely-functional-datastructures">Purely Functional Datastructures.</a></li>
|
||||||
|
<li><a class="reference internal" href="#the-joy-function">The <code class="docutils literal notranslate"><span class="pre">joy()</span></code> function</a><ul>
|
||||||
|
<li><a class="reference internal" href="#an-interpreter">An Interpreter</a></li>
|
||||||
|
<li><a class="reference internal" href="#continuation-passing-style">Continuation-Passing Style</a></li>
|
||||||
|
<li><a class="reference internal" href="#view-function">View function</a></li>
|
||||||
|
<li><a class="reference internal" href="#the-traceprinter">The <code class="docutils literal notranslate"><span class="pre">TracePrinter</span></code>.</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li><a class="reference internal" href="#parser">Parser</a><ul>
|
||||||
|
<li><a class="reference internal" href="#symbols">Symbols</a></li>
|
||||||
|
<li><a class="reference internal" href="#token-regular-expressions">Token Regular Expressions</a></li>
|
||||||
|
<li><a class="reference internal" href="#examples">Examples</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li><a class="reference internal" href="#library">Library</a><ul>
|
||||||
|
<li><a class="reference internal" href="#there-should-be-only-one">“There should be only one.”</a></li>
|
||||||
|
<li><a class="reference internal" href="#literary-code-library">Literary Code Library</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
</ul>
|
||||||
|
<div class="relations">
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||||||
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<h3>Related Topics</h3>
|
||||||
|
<ul>
|
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|
<li><a href="../index.html">Documentation overview</a><ul>
|
||||||
|
<li>Previous: <a href="../index.html" title="previous chapter">Thun 0.1.1 Documentation</a></li>
|
||||||
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<li>Next: <a href="../joy.html" title="next chapter">Joy Interpreter</a></li>
|
||||||
|
</ul></li>
|
||||||
|
</ul>
|
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|
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|
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<br />
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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<div class="bodywrapper">
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<div class="body" role="main">
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|
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<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>Newton-Raphson for finding the root of an equation.</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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<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="section" id="finding-the-square-root-of-a-number">
|
||||||
|
<h2>Finding the Square-Root of a Number<a class="headerlink" href="#finding-the-square-root-of-a-number" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>Let’s define a function that computes this equation:</p>
|
||||||
|
<p><span class="math notranslate nohighlight">\(a_{i+1} = \frac{(a_i+\frac{n}{a_i})}{2}\)</span></p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">n</span> <span class="n">a</span> <span class="n">Q</span>
|
||||||
|
<span class="o">---------------</span>
|
||||||
|
<span class="p">(</span><span class="n">a</span><span class="o">+</span><span class="n">n</span><span class="o">/</span><span class="n">a</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span>
|
||||||
|
|
||||||
|
<span class="n">n</span> <span class="n">a</span> <span class="n">tuck</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span>
|
||||||
|
<span class="n">a</span> <span class="n">n</span> <span class="n">a</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span>
|
||||||
|
<span class="n">a</span> <span class="n">n</span><span class="o">/</span><span class="n">a</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span>
|
||||||
|
<span class="n">a</span><span class="o">+</span><span class="n">n</span><span class="o">/</span><span class="n">a</span> <span class="mi">2</span> <span class="o">/</span>
|
||||||
|
<span class="p">(</span><span class="n">a</span><span class="o">+</span><span class="n">n</span><span class="o">/</span><span class="n">a</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>We want it to leave n but replace a, so we execute it with <code class="docutils literal notranslate"><span class="pre">unary</span></code>:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Q</span> <span class="o">==</span> <span class="p">[</span><span class="n">tuck</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">unary</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">'Q == [tuck / + 2 /] unary'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="compute-the-error">
|
||||||
|
<h2>Compute the Error<a class="headerlink" href="#compute-the-error" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>And a function to compute the error:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">n</span> <span class="n">a</span> <span class="n">sqr</span> <span class="o">-</span> <span class="nb">abs</span>
|
||||||
|
<span class="o">|</span><span class="n">n</span><span class="o">-</span><span class="n">a</span><span class="o">**</span><span class="mi">2</span><span class="o">|</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>This should be <code class="docutils literal notranslate"><span class="pre">nullary</span></code> so as to leave both n and a on the stack
|
||||||
|
below the error.</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">err</span> <span class="o">==</span> <span class="p">[</span><span class="n">sqr</span> <span class="o">-</span> <span class="nb">abs</span><span class="p">]</span> <span class="n">nullary</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">'err == [sqr - abs] nullary'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="square-root">
|
||||||
|
<h2><code class="docutils literal notranslate"><span class="pre">square-root</span></code><a class="headerlink" href="#square-root" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>Now we can define a recursive program that expects a number <code class="docutils literal notranslate"><span class="pre">n</span></code>, an
|
||||||
|
initial estimate <code class="docutils literal notranslate"><span class="pre">a</span></code>, and an epsilon value <code class="docutils literal notranslate"><span class="pre">ε</span></code>, and that leaves on
|
||||||
|
the stack the square root of <code class="docutils literal notranslate"><span class="pre">n</span></code> to within the precision of the
|
||||||
|
epsilon value. (Later on we’ll refine it to generate the initial
|
||||||
|
estimate and hard-code an epsilon value.)</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>n a ε square-root
|
||||||
|
-----------------
|
||||||
|
√n
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>If we apply the two functions <code class="docutils literal notranslate"><span class="pre">Q</span></code> and <code class="docutils literal notranslate"><span class="pre">err</span></code> defined above we get the
|
||||||
|
next approximation and the error on the stack below the epsilon.</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">n</span> <span class="n">a</span> <span class="n">ε</span> <span class="p">[</span><span class="n">Q</span> <span class="n">err</span><span class="p">]</span> <span class="n">dip</span>
|
||||||
|
<span class="n">n</span> <span class="n">a</span> <span class="n">Q</span> <span class="n">err</span> <span class="n">ε</span>
|
||||||
|
<span class="n">n</span> <span class="n">a</span><span class="s1">' err ε</span>
|
||||||
|
<span class="n">n</span> <span class="n">a</span><span class="s1">' e ε</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Let’s define a recursive function <code class="docutils literal notranslate"><span class="pre">K</span></code> from here.</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">n</span> <span class="n">a</span><span class="s1">' e ε K</span>
|
||||||
|
|
||||||
|
<span class="n">K</span> <span class="o">==</span> <span class="p">[</span><span class="n">P</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">R0</span><span class="p">]</span> <span class="p">[</span><span class="n">R1</span><span class="p">]</span> <span class="n">genrec</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="base-case">
|
||||||
|
<h3>Base-case<a class="headerlink" href="#base-case" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>The predicate and the base case are obvious:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">K</span> <span class="o">==</span> <span class="p">[</span><span class="o"><</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</span> <span class="n">popd</span><span class="p">]</span> <span class="p">[</span><span class="n">R0</span><span class="p">]</span> <span class="p">[</span><span class="n">R1</span><span class="p">]</span> <span class="n">genrec</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">n</span> <span class="n">a</span><span class="s1">' e ε popop popd</span>
|
||||||
|
<span class="n">n</span> <span class="n">a</span><span class="s1">' popd</span>
|
||||||
|
<span class="n">a</span><span class="s1">'</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="recur">
|
||||||
|
<h3>Recur<a class="headerlink" href="#recur" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>The recursive branch is pretty easy. Discard the error and recur.</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">K</span> <span class="o">==</span> <span class="p">[</span><span class="o"><</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</span> <span class="n">popd</span><span class="p">]</span> <span class="p">[</span><span class="n">R0</span><span class="p">]</span> <span class="p">[</span><span class="n">R1</span><span class="p">]</span> <span class="n">genrec</span>
|
||||||
|
<span class="n">K</span> <span class="o">==</span> <span class="p">[</span><span class="o"><</span><span class="p">]</span> <span class="p">[</span><span class="n">popop</span> <span class="n">popd</span><span class="p">]</span> <span class="p">[</span><span class="n">R0</span> <span class="p">[</span><span class="n">K</span><span class="p">]</span> <span class="n">R1</span><span class="p">]</span> <span class="n">ifte</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">n</span> <span class="n">a</span><span class="s1">' e ε R0 [K] R1</span>
|
||||||
|
<span class="n">n</span> <span class="n">a</span><span class="s1">' e ε popd [Q err] dip [K] i</span>
|
||||||
|
<span class="n">n</span> <span class="n">a</span><span class="s1">' ε [Q err] dip [K] i</span>
|
||||||
|
<span class="n">n</span> <span class="n">a</span><span class="s1">' Q err ε [K] i</span>
|
||||||
|
<span class="n">n</span> <span class="n">a</span><span class="s1">''</span> <span class="n">e</span> <span class="n">ε</span> <span class="n">K</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>This fragment alone is pretty useful. (<code class="docutils literal notranslate"><span class="pre">R1</span></code> is <code class="docutils literal notranslate"><span class="pre">i</span></code> so this is a <code class="docutils literal notranslate"><span class="pre">primrec</span></code> “primitive recursive” function.)</p>
|
||||||
|
<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">'K == [<] [popop popd] [popd [Q err] dip] primrec'</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">'25 10 0.001 dup K'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">5.000000232305737</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">'25 10 0.000001 dup K'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">5.000000000000005</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="initial-approximation-and-epsilon">
|
||||||
|
<h3>Initial Approximation and Epsilon<a class="headerlink" href="#initial-approximation-and-epsilon" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>So now all we need is a way to generate an initial approximation and an
|
||||||
|
epsilon value:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">square</span><span class="o">-</span><span class="n">root</span> <span class="o">==</span> <span class="n">dup</span> <span class="mi">3</span> <span class="o">/</span> <span class="mf">0.000001</span> <span class="n">dup</span> <span class="n">K</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">'square-root == dup 3 / 0.000001 dup K'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="examples">
|
||||||
|
<h3>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<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 square-root'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">6.000000000000007</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">'4895048365636 square-root'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">2212475.6192184356</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">2212475.6192184356</span> <span class="o">*</span> <span class="mf">2212475.6192184356</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">4895048365636.0</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
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<h3><a href="../index.html">Table Of Contents</a></h3>
|
||||||
|
<ul>
|
||||||
|
<li><a class="reference internal" href="#">Newton’s method</a><ul>
|
||||||
|
<li><a class="reference internal" href="#finding-the-square-root-of-a-number">Finding the Square-Root of a Number</a></li>
|
||||||
|
<li><a class="reference internal" href="#compute-the-error">Compute the Error</a></li>
|
||||||
|
<li><a class="reference internal" href="#square-root"><code class="docutils literal notranslate"><span class="pre">square-root</span></code></a><ul>
|
||||||
|
<li><a class="reference internal" href="#base-case">Base-case</a></li>
|
||||||
|
<li><a class="reference internal" href="#recur">Recur</a></li>
|
||||||
|
<li><a class="reference internal" href="#initial-approximation-and-epsilon">Initial Approximation and Epsilon</a></li>
|
||||||
|
<li><a class="reference internal" href="#examples">Examples</a></li>
|
||||||
|
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|
||||||
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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<h1>No Updates<a class="headerlink" href="#no-updates" title="Permalink to this headline">¶</a></h1>
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<p>DRAFT</p>
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<li>The interpreter doesn’t need to change, <code class="docutils literal notranslate"><span class="pre">viewer</span></code> function can customize mainloop. Or use a sub-interpreter (Joy in Joy.) The base interpreter remains static.</li>
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<li>Once a function has been named and defined <em>never change that name</em>. It’s just not allowed. If you need to change a function <code class="docutils literal notranslate"><span class="pre">foo</span></code> you have to call it <code class="docutils literal notranslate"><span class="pre">foo_II</span></code> or something. Once a function (name mapped to behavior) is released to the public <em>that’s it</em>, it’s done.</li>
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<li>We never implement any backwards incompatible changes, so…</li>
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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<div class="section" id="quadratic-formula">
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<h1><a class="reference external" href="https://en.wikipedia.org/wiki/Quadratic_formula">Quadratic formula</a><a class="headerlink" href="#quadratic-formula" title="Permalink to this headline">¶</a></h1>
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<p><a class="reference external" href="https://en.wikipedia.org/wiki/Quadratic_formula">The Quadratic formula</a></p>
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<p><span class="math notranslate nohighlight">\(\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)</span></p>
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<p>In
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<a class="reference external" href="http://www.kevinalbrecht.com/code/joy-mirror/jp-quadratic.html">jp-quadratic.html</a>
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a Joy function for the Quadratic formula is derived (along with one of my favorite combinators <code class="docutils literal notranslate"><span class="pre">[i]</span> <span class="pre">map</span></code>,
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which I like to call <code class="docutils literal notranslate"><span class="pre">pam</span></code>) starting with a version written in Scheme. Here we investigate a different approach.</p>
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<div class="section" id="write-a-program-with-variable-names">
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<h2>Write a program with variable names.<a class="headerlink" href="#write-a-program-with-variable-names" title="Permalink to this headline">¶</a></h2>
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<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">b</span> <span class="n">neg</span> <span class="n">b</span> <span class="n">sqr</span> <span class="mi">4</span> <span class="n">a</span> <span class="n">c</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="p">[</span><span class="o">-</span><span class="p">]</span> <span class="n">cleave</span> <span class="n">a</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
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</pre></div>
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<p>We use <code class="docutils literal notranslate"><span class="pre">cleave</span></code> to compute the sum and difference (“plus-or-minus”) and then <code class="docutils literal notranslate"><span class="pre">app2</span></code> to finish computing both roots using a quoted program <code class="docutils literal notranslate"><span class="pre">[2a</span> <span class="pre">truediv]</span></code> built with <code class="docutils literal notranslate"><span class="pre">cons</span></code>.</p>
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<div class="section" id="check-it">
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<h3>Check it.<a class="headerlink" href="#check-it" title="Permalink to this headline">¶</a></h3>
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<p>Evaluating by hand:</p>
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<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="n">b</span> <span class="n">neg</span> <span class="n">b</span> <span class="n">sqr</span> <span class="mi">4</span> <span class="n">a</span> <span class="n">c</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="p">[</span><span class="o">-</span><span class="p">]</span> <span class="n">cleave</span> <span class="n">a</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
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<span class="o">-</span><span class="n">b</span> <span class="n">b</span> <span class="n">sqr</span> <span class="mi">4</span> <span class="n">a</span> <span class="n">c</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="p">[</span><span class="o">-</span><span class="p">]</span> <span class="n">cleave</span> <span class="n">a</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="o">-</span><span class="n">b</span> <span class="n">b</span><span class="o">^</span><span class="mi">2</span> <span class="mi">4</span> <span class="n">a</span> <span class="n">c</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="p">[</span><span class="o">-</span><span class="p">]</span> <span class="n">cleave</span> <span class="n">a</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="o">-</span><span class="n">b</span> <span class="n">b</span><span class="o">^</span><span class="mi">2</span> <span class="mi">4</span><span class="n">ac</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="p">[</span><span class="o">-</span><span class="p">]</span> <span class="n">cleave</span> <span class="n">a</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
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<span class="o">-</span><span class="n">b</span> <span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span> <span class="n">sqrt</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="p">[</span><span class="o">-</span><span class="p">]</span> <span class="n">cleave</span> <span class="n">a</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
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<span class="o">-</span><span class="n">b</span> <span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="p">[</span><span class="o">-</span><span class="p">]</span> <span class="n">cleave</span> <span class="n">a</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
|
||||||
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<span class="o">-</span><span class="n">b</span> <span class="o">-</span><span class="n">b</span><span class="o">+</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span> <span class="o">-</span><span class="n">b</span><span class="o">-</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span> <span class="n">a</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="o">-</span><span class="n">b</span> <span class="o">-</span><span class="n">b</span><span class="o">+</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span> <span class="o">-</span><span class="n">b</span><span class="o">-</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span> <span class="mi">2</span><span class="n">a</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="o">-</span><span class="n">b</span> <span class="o">-</span><span class="n">b</span><span class="o">+</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span> <span class="o">-</span><span class="n">b</span><span class="o">-</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span> <span class="p">[</span><span class="mi">2</span><span class="n">a</span> <span class="n">truediv</span><span class="p">]</span> <span class="n">app2</span>
|
||||||
|
<span class="o">-</span><span class="n">b</span> <span class="o">-</span><span class="n">b</span><span class="o">+</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="n">a</span> <span class="o">-</span><span class="n">b</span><span class="o">-</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="n">a</span>
|
||||||
|
</pre></div>
|
||||||
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</div>
|
||||||
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<p>(Eventually we’ll be able to use e.g. Sympy versions of the Joy commands to do this sort of thing symbolically. This is part of what is meant by a “categorical” language.)</p>
|
||||||
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</div>
|
||||||
|
<div class="section" id="cleanup">
|
||||||
|
<h3>Cleanup<a class="headerlink" href="#cleanup" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">-</span><span class="n">b</span> <span class="o">-</span><span class="n">b</span><span class="o">+</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="n">a</span> <span class="o">-</span><span class="n">b</span><span class="o">-</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="n">a</span> <span class="n">roll</span><span class="o"><</span> <span class="n">pop</span>
|
||||||
|
<span class="o">-</span><span class="n">b</span><span class="o">+</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="n">a</span> <span class="o">-</span><span class="n">b</span><span class="o">-</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="n">a</span> <span class="o">-</span><span class="n">b</span> <span class="n">pop</span>
|
||||||
|
<span class="o">-</span><span class="n">b</span><span class="o">+</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="n">a</span> <span class="o">-</span><span class="n">b</span><span class="o">-</span><span class="n">sqrt</span><span class="p">(</span><span class="n">b</span><span class="o">^</span><span class="mi">2</span><span class="o">-</span><span class="mi">4</span><span class="n">ac</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="n">a</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="derive-a-definition">
|
||||||
|
<h2>Derive a definition.<a class="headerlink" href="#derive-a-definition" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">b</span> <span class="n">neg</span> <span class="n">b</span> <span class="n">sqr</span> <span class="mi">4</span> <span class="n">a</span> <span class="n">c</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="p">[</span><span class="o">-</span><span class="p">]</span> <span class="n">cleave</span> <span class="n">a</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span> <span class="n">roll</span><span class="o"><</span> <span class="n">pop</span>
|
||||||
|
<span class="n">b</span> <span class="p">[</span><span class="n">neg</span><span class="p">]</span> <span class="n">dupdip</span> <span class="n">sqr</span> <span class="mi">4</span> <span class="n">a</span> <span class="n">c</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="p">[</span><span class="o">-</span><span class="p">]</span> <span class="n">cleave</span> <span class="n">a</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span> <span class="n">roll</span><span class="o"><</span> <span class="n">pop</span>
|
||||||
|
<span class="n">b</span> <span class="n">a</span> <span class="n">c</span> <span class="p">[[</span><span class="n">neg</span><span class="p">]</span> <span class="n">dupdip</span> <span class="n">sqr</span> <span class="mi">4</span><span class="p">]</span> <span class="n">dipd</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="p">[</span><span class="o">-</span><span class="p">]</span> <span class="n">cleave</span> <span class="n">a</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span> <span class="n">roll</span><span class="o"><</span> <span class="n">pop</span>
|
||||||
|
<span class="n">b</span> <span class="n">a</span> <span class="n">c</span> <span class="n">a</span> <span class="p">[[[</span><span class="n">neg</span><span class="p">]</span> <span class="n">dupdip</span> <span class="n">sqr</span> <span class="mi">4</span><span class="p">]</span> <span class="n">dipd</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="p">[</span><span class="o">-</span><span class="p">]</span> <span class="n">cleave</span><span class="p">]</span> <span class="n">dip</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span> <span class="n">roll</span><span class="o"><</span> <span class="n">pop</span>
|
||||||
|
<span class="n">b</span> <span class="n">a</span> <span class="n">c</span> <span class="n">over</span> <span class="p">[[[</span><span class="n">neg</span><span class="p">]</span> <span class="n">dupdip</span> <span class="n">sqr</span> <span class="mi">4</span><span class="p">]</span> <span class="n">dipd</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="p">[</span><span class="o">-</span><span class="p">]</span> <span class="n">cleave</span><span class="p">]</span> <span class="n">dip</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span> <span class="n">roll</span><span class="o"><</span> <span class="n">pop</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">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="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'quadratic == over [[[neg] dupdip sqr 4] dipd * * - sqrt [+] [-] cleave] dip 2 * [truediv] cons app2 roll< pop'</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">'3 1 1 quadratic'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">-</span><span class="mf">0.3819660112501051</span> <span class="o">-</span><span class="mf">2.618033988749895</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="simplify">
|
||||||
|
<h3>Simplify<a class="headerlink" href="#simplify" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>We can define a <code class="docutils literal notranslate"><span class="pre">pm</span></code> plus-or-minus function:</p>
|
||||||
|
<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">'pm == [+] [-] cleave popdd'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Then <code class="docutils literal notranslate"><span class="pre">quadratic</span></code> becomes:</p>
|
||||||
|
<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">'quadratic == over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [truediv] cons app2'</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">'3 1 1 quadratic'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">-</span><span class="mf">0.3819660112501051</span> <span class="o">-</span><span class="mf">2.618033988749895</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="define-a-native-pm-function">
|
||||||
|
<h3>Define a “native” <code class="docutils literal notranslate"><span class="pre">pm</span></code> function.<a class="headerlink" href="#define-a-native-pm-function" title="Permalink to this headline">¶</a></h3>
|
||||||
|
<p>The definition of <code class="docutils literal notranslate"><span class="pre">pm</span></code> above is pretty elegant, but the implementation
|
||||||
|
takes a lot of steps relative to what it’s accomplishing. Since we are
|
||||||
|
likely to use <code class="docutils literal notranslate"><span class="pre">pm</span></code> more than once in the future, let’s write a
|
||||||
|
primitive in Python and add it to the dictionary.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">joy.library</span> <span class="k">import</span> <span class="n">SimpleFunctionWrapper</span>
|
||||||
|
<span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="k">import</span> <span class="n">D</span>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="nd">@SimpleFunctionWrapper</span>
|
||||||
|
<span class="k">def</span> <span class="nf">pm</span><span class="p">(</span><span class="n">stack</span><span class="p">):</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>
|
||||||
|
<span class="n">p</span><span class="p">,</span> <span class="n">m</span><span class="p">,</span> <span class="o">=</span> <span class="n">b</span> <span class="o">+</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="o">-</span> <span class="n">a</span>
|
||||||
|
<span class="k">return</span> <span class="n">m</span><span class="p">,</span> <span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">stack</span><span class="p">)</span>
|
||||||
|
|
||||||
|
|
||||||
|
<span class="n">D</span><span class="p">[</span><span class="s1">'pm'</span><span class="p">]</span> <span class="o">=</span> <span class="n">pm</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>The resulting trace is short enough to fit on a page.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'3 1 1 quadratic'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="mi">3</span> <span class="mi">1</span> <span class="mi">1</span> <span class="n">quadratic</span>
|
||||||
|
<span class="mi">3</span> <span class="o">.</span> <span class="mi">1</span> <span class="mi">1</span> <span class="n">quadratic</span>
|
||||||
|
<span class="mi">3</span> <span class="mi">1</span> <span class="o">.</span> <span class="mi">1</span> <span class="n">quadratic</span>
|
||||||
|
<span class="mi">3</span> <span class="mi">1</span> <span class="mi">1</span> <span class="o">.</span> <span class="n">quadratic</span>
|
||||||
|
<span class="mi">3</span> <span class="mi">1</span> <span class="mi">1</span> <span class="o">.</span> <span class="n">over</span> <span class="p">[[[</span><span class="n">neg</span><span class="p">]</span> <span class="n">dupdip</span> <span class="n">sqr</span> <span class="mi">4</span><span class="p">]</span> <span class="n">dipd</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="n">pm</span><span class="p">]</span> <span class="n">dip</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="mi">3</span> <span class="mi">1</span> <span class="mi">1</span> <span class="mi">1</span> <span class="o">.</span> <span class="p">[[[</span><span class="n">neg</span><span class="p">]</span> <span class="n">dupdip</span> <span class="n">sqr</span> <span class="mi">4</span><span class="p">]</span> <span class="n">dipd</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="n">pm</span><span class="p">]</span> <span class="n">dip</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="mi">3</span> <span class="mi">1</span> <span class="mi">1</span> <span class="mi">1</span> <span class="p">[[[</span><span class="n">neg</span><span class="p">]</span> <span class="n">dupdip</span> <span class="n">sqr</span> <span class="mi">4</span><span class="p">]</span> <span class="n">dipd</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="n">pm</span><span class="p">]</span> <span class="o">.</span> <span class="n">dip</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="mi">3</span> <span class="mi">1</span> <span class="mi">1</span> <span class="o">.</span> <span class="p">[[</span><span class="n">neg</span><span class="p">]</span> <span class="n">dupdip</span> <span class="n">sqr</span> <span class="mi">4</span><span class="p">]</span> <span class="n">dipd</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="n">pm</span> <span class="mi">1</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="mi">3</span> <span class="mi">1</span> <span class="mi">1</span> <span class="p">[[</span><span class="n">neg</span><span class="p">]</span> <span class="n">dupdip</span> <span class="n">sqr</span> <span class="mi">4</span><span class="p">]</span> <span class="o">.</span> <span class="n">dipd</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="n">pm</span> <span class="mi">1</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="mi">3</span> <span class="o">.</span> <span class="p">[</span><span class="n">neg</span><span class="p">]</span> <span class="n">dupdip</span> <span class="n">sqr</span> <span class="mi">4</span> <span class="mi">1</span> <span class="mi">1</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="n">pm</span> <span class="mi">1</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="mi">3</span> <span class="p">[</span><span class="n">neg</span><span class="p">]</span> <span class="o">.</span> <span class="n">dupdip</span> <span class="n">sqr</span> <span class="mi">4</span> <span class="mi">1</span> <span class="mi">1</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="n">pm</span> <span class="mi">1</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="mi">3</span> <span class="o">.</span> <span class="n">neg</span> <span class="mi">3</span> <span class="n">sqr</span> <span class="mi">4</span> <span class="mi">1</span> <span class="mi">1</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="n">pm</span> <span class="mi">1</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="o">-</span><span class="mi">3</span> <span class="o">.</span> <span class="mi">3</span> <span class="n">sqr</span> <span class="mi">4</span> <span class="mi">1</span> <span class="mi">1</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="n">pm</span> <span class="mi">1</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="o">-</span><span class="mi">3</span> <span class="mi">3</span> <span class="o">.</span> <span class="n">sqr</span> <span class="mi">4</span> <span class="mi">1</span> <span class="mi">1</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="n">pm</span> <span class="mi">1</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="o">-</span><span class="mi">3</span> <span class="mi">3</span> <span class="o">.</span> <span class="n">dup</span> <span class="n">mul</span> <span class="mi">4</span> <span class="mi">1</span> <span class="mi">1</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="n">pm</span> <span class="mi">1</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="o">-</span><span class="mi">3</span> <span class="mi">3</span> <span class="mi">3</span> <span class="o">.</span> <span class="n">mul</span> <span class="mi">4</span> <span class="mi">1</span> <span class="mi">1</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="n">pm</span> <span class="mi">1</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="o">-</span><span class="mi">3</span> <span class="mi">9</span> <span class="o">.</span> <span class="mi">4</span> <span class="mi">1</span> <span class="mi">1</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="n">pm</span> <span class="mi">1</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="o">-</span><span class="mi">3</span> <span class="mi">9</span> <span class="mi">4</span> <span class="o">.</span> <span class="mi">1</span> <span class="mi">1</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="n">pm</span> <span class="mi">1</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="o">-</span><span class="mi">3</span> <span class="mi">9</span> <span class="mi">4</span> <span class="mi">1</span> <span class="o">.</span> <span class="mi">1</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="n">pm</span> <span class="mi">1</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="o">-</span><span class="mi">3</span> <span class="mi">9</span> <span class="mi">4</span> <span class="mi">1</span> <span class="mi">1</span> <span class="o">.</span> <span class="o">*</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="n">pm</span> <span class="mi">1</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="o">-</span><span class="mi">3</span> <span class="mi">9</span> <span class="mi">4</span> <span class="mi">1</span> <span class="o">.</span> <span class="o">*</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="n">pm</span> <span class="mi">1</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="o">-</span><span class="mi">3</span> <span class="mi">9</span> <span class="mi">4</span> <span class="o">.</span> <span class="o">-</span> <span class="n">sqrt</span> <span class="n">pm</span> <span class="mi">1</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="o">-</span><span class="mi">3</span> <span class="mi">5</span> <span class="o">.</span> <span class="n">sqrt</span> <span class="n">pm</span> <span class="mi">1</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="o">-</span><span class="mi">3</span> <span class="mf">2.23606797749979</span> <span class="o">.</span> <span class="n">pm</span> <span class="mi">1</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="o">-</span><span class="mf">0.7639320225002102</span> <span class="o">-</span><span class="mf">5.23606797749979</span> <span class="o">.</span> <span class="mi">1</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="o">-</span><span class="mf">0.7639320225002102</span> <span class="o">-</span><span class="mf">5.23606797749979</span> <span class="mi">1</span> <span class="o">.</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="o">-</span><span class="mf">0.7639320225002102</span> <span class="o">-</span><span class="mf">5.23606797749979</span> <span class="mi">1</span> <span class="mi">2</span> <span class="o">.</span> <span class="o">*</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="o">-</span><span class="mf">0.7639320225002102</span> <span class="o">-</span><span class="mf">5.23606797749979</span> <span class="mi">2</span> <span class="o">.</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="o">-</span><span class="mf">0.7639320225002102</span> <span class="o">-</span><span class="mf">5.23606797749979</span> <span class="mi">2</span> <span class="p">[</span><span class="n">truediv</span><span class="p">]</span> <span class="o">.</span> <span class="n">cons</span> <span class="n">app2</span>
|
||||||
|
<span class="o">-</span><span class="mf">0.7639320225002102</span> <span class="o">-</span><span class="mf">5.23606797749979</span> <span class="p">[</span><span class="mi">2</span> <span class="n">truediv</span><span class="p">]</span> <span class="o">.</span> <span class="n">app2</span>
|
||||||
|
<span class="p">[</span><span class="o">-</span><span class="mf">0.7639320225002102</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="n">truediv</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="o">-</span><span class="mf">5.23606797749979</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="n">truediv</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span>
|
||||||
|
<span class="o">-</span><span class="mf">0.7639320225002102</span> <span class="o">.</span> <span class="mi">2</span> <span class="n">truediv</span> <span class="p">[]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="o">-</span><span class="mf">5.23606797749979</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="n">truediv</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span>
|
||||||
|
<span class="o">-</span><span class="mf">0.7639320225002102</span> <span class="mi">2</span> <span class="o">.</span> <span class="n">truediv</span> <span class="p">[]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="o">-</span><span class="mf">5.23606797749979</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="n">truediv</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span>
|
||||||
|
<span class="o">-</span><span class="mf">0.3819660112501051</span> <span class="o">.</span> <span class="p">[]</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="o">-</span><span class="mf">5.23606797749979</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="n">truediv</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span>
|
||||||
|
<span class="o">-</span><span class="mf">0.3819660112501051</span> <span class="p">[]</span> <span class="o">.</span> <span class="n">swaack</span> <span class="n">first</span> <span class="p">[</span><span class="o">-</span><span class="mf">5.23606797749979</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="n">truediv</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span>
|
||||||
|
<span class="p">[</span><span class="o">-</span><span class="mf">0.3819660112501051</span><span class="p">]</span> <span class="o">.</span> <span class="n">first</span> <span class="p">[</span><span class="o">-</span><span class="mf">5.23606797749979</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="n">truediv</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span>
|
||||||
|
<span class="o">-</span><span class="mf">0.3819660112501051</span> <span class="o">.</span> <span class="p">[</span><span class="o">-</span><span class="mf">5.23606797749979</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="n">truediv</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span>
|
||||||
|
<span class="o">-</span><span class="mf">0.3819660112501051</span> <span class="p">[</span><span class="o">-</span><span class="mf">5.23606797749979</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="mi">2</span> <span class="n">truediv</span><span class="p">]</span> <span class="n">infra</span> <span class="n">first</span>
|
||||||
|
<span class="o">-</span><span class="mf">0.3819660112501051</span> <span class="p">[</span><span class="o">-</span><span class="mf">5.23606797749979</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="n">truediv</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="mf">5.23606797749979</span> <span class="o">.</span> <span class="mi">2</span> <span class="n">truediv</span> <span class="p">[</span><span class="o">-</span><span class="mf">0.3819660112501051</span><span class="p">]</span> <span class="n">swaack</span> <span class="n">first</span>
|
||||||
|
<span class="o">-</span><span class="mf">5.23606797749979</span> <span class="mi">2</span> <span class="o">.</span> <span class="n">truediv</span> <span class="p">[</span><span class="o">-</span><span class="mf">0.3819660112501051</span><span class="p">]</span> <span class="n">swaack</span> <span class="n">first</span>
|
||||||
|
<span class="o">-</span><span class="mf">2.618033988749895</span> <span class="o">.</span> <span class="p">[</span><span class="o">-</span><span class="mf">0.3819660112501051</span><span class="p">]</span> <span class="n">swaack</span> <span class="n">first</span>
|
||||||
|
<span class="o">-</span><span class="mf">2.618033988749895</span> <span class="p">[</span><span class="o">-</span><span class="mf">0.3819660112501051</span><span class="p">]</span> <span class="o">.</span> <span class="n">swaack</span> <span class="n">first</span>
|
||||||
|
<span class="o">-</span><span class="mf">0.3819660112501051</span> <span class="p">[</span><span class="o">-</span><span class="mf">2.618033988749895</span><span class="p">]</span> <span class="o">.</span> <span class="n">first</span>
|
||||||
|
<span class="o">-</span><span class="mf">0.3819660112501051</span> <span class="o">-</span><span class="mf">2.618033988749895</span> <span class="o">.</span>
|
||||||
|
</pre></div>
|
||||||
|
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|
||||||
|
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|
||||||
|
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|
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|
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|
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|
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|
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<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
|
||||||
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|
||||||
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<h3><a href="../index.html">Table Of Contents</a></h3>
|
||||||
|
<ul>
|
||||||
|
<li><a class="reference internal" href="#">Quadratic formula</a><ul>
|
||||||
|
<li><a class="reference internal" href="#write-a-program-with-variable-names">Write a program with variable names.</a><ul>
|
||||||
|
<li><a class="reference internal" href="#check-it">Check it.</a></li>
|
||||||
|
<li><a class="reference internal" href="#cleanup">Cleanup</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
<li><a class="reference internal" href="#derive-a-definition">Derive a definition.</a><ul>
|
||||||
|
<li><a class="reference internal" href="#simplify">Simplify</a></li>
|
||||||
|
<li><a class="reference internal" href="#define-a-native-pm-function">Define a “native” <code class="docutils literal notranslate"><span class="pre">pm</span></code> function.</a></li>
|
||||||
|
</ul>
|
||||||
|
</li>
|
||||||
|
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|
||||||
|
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|
||||||
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|
||||||
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.7.3.
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<div class="body" role="main">
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||||||
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|
||||||
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<p>This notebook is about using the “zipper” with joy datastructures. See
|
||||||
|
the <a class="reference external" href="https://en.wikipedia.org/wiki/Zipper_%28data_structure%29">Zipper wikipedia
|
||||||
|
entry</a> or
|
||||||
|
the original paper: <a class="reference external" href="https://www.st.cs.uni-saarland.de/edu/seminare/2005/advanced-fp/docs/huet-zipper.pdf">“FUNCTIONAL PEARL The Zipper” by Gérard
|
||||||
|
Huet</a></p>
|
||||||
|
<p>Given a datastructure on the stack we can navigate through it, modify
|
||||||
|
it, and rebuild it using the “zipper” technique.</p>
|
||||||
|
<div class="section" id="preamble">
|
||||||
|
<h1>Preamble<a class="headerlink" href="#preamble" title="Permalink to this headline">¶</a></h1>
|
||||||
|
<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>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="trees">
|
||||||
|
<h2>Trees<a class="headerlink" href="#trees" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>In Joypy there aren’t any complex datastructures, just ints, floats,
|
||||||
|
strings, Symbols (strings that are names of functions) and sequences
|
||||||
|
(aka lists, aka quoted literals, aka aggregates, etc…), but we can
|
||||||
|
build
|
||||||
|
<a class="reference external" href="https://en.wikipedia.org/wiki/Tree_%28data_structure%29">trees</a> out
|
||||||
|
of sequences.</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">'[1 [2 [3 4 25 6] 7] 8]'</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="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="zipper-in-joy">
|
||||||
|
<h2>Zipper in Joy<a class="headerlink" href="#zipper-in-joy" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>Zippers work by keeping track of the current item, the already-seen
|
||||||
|
items, and the yet-to-be seen items as you traverse a datastructure (the
|
||||||
|
datastructure used to keep track of these items is the zipper.)</p>
|
||||||
|
<p>In Joy we can do this with the following words:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">z</span><span class="o">-</span><span class="n">down</span> <span class="o">==</span> <span class="p">[]</span> <span class="n">swap</span> <span class="n">uncons</span> <span class="n">swap</span>
|
||||||
|
<span class="n">z</span><span class="o">-</span><span class="n">up</span> <span class="o">==</span> <span class="n">swons</span> <span class="n">swap</span> <span class="n">shunt</span>
|
||||||
|
<span class="n">z</span><span class="o">-</span><span class="n">right</span> <span class="o">==</span> <span class="p">[</span><span class="n">swons</span><span class="p">]</span> <span class="n">cons</span> <span class="n">dip</span> <span class="n">uncons</span> <span class="n">swap</span>
|
||||||
|
<span class="n">z</span><span class="o">-</span><span class="n">left</span> <span class="o">==</span> <span class="n">swons</span> <span class="p">[</span><span class="n">uncons</span> <span class="n">swap</span><span class="p">]</span> <span class="n">dip</span> <span class="n">swap</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Let’s use them to change 25 into 625. The first time a word is used I
|
||||||
|
show the trace so you can see how it works. If we were going to use
|
||||||
|
these a lot it would make sense to write Python versions for efficiency,
|
||||||
|
but see below.</p>
|
||||||
|
<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">'z-down == [] swap uncons swap'</span><span class="p">)</span>
|
||||||
|
<span class="n">define</span><span class="p">(</span><span class="s1">'z-up == swons swap shunt'</span><span class="p">)</span>
|
||||||
|
<span class="n">define</span><span class="p">(</span><span class="s1">'z-right == [swons] cons dip uncons swap'</span><span class="p">)</span>
|
||||||
|
<span class="n">define</span><span class="p">(</span><span class="s1">'z-left == swons [uncons swap] dip swap'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'[1 [2 [3 4 25 6] 7] 8] z-down'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</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="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="n">z</span><span class="o">-</span><span class="n">down</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="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="o">.</span> <span class="n">z</span><span class="o">-</span><span class="n">down</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="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="o">.</span> <span class="p">[]</span> <span class="n">swap</span> <span class="n">uncons</span> <span class="n">swap</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="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="p">[]</span> <span class="o">.</span> <span class="n">swap</span> <span class="n">uncons</span> <span class="n">swap</span>
|
||||||
|
<span class="p">[]</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="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="o">.</span> <span class="n">uncons</span> <span class="n">swap</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="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="o">.</span> <span class="n">swap</span>
|
||||||
|
<span class="p">[]</span> <span class="p">[[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="mi">1</span> <span class="o">.</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'[] [[2 [3 4 25 6] 7] 8] 1 z-right'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<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="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="mi">1</span> <span class="n">z</span><span class="o">-</span><span class="n">right</span>
|
||||||
|
<span class="p">[]</span> <span class="o">.</span> <span class="p">[[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="mi">1</span> <span class="n">z</span><span class="o">-</span><span class="n">right</span>
|
||||||
|
<span class="p">[]</span> <span class="p">[[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="o">.</span> <span class="mi">1</span> <span class="n">z</span><span class="o">-</span><span class="n">right</span>
|
||||||
|
<span class="p">[]</span> <span class="p">[[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="mi">1</span> <span class="o">.</span> <span class="n">z</span><span class="o">-</span><span class="n">right</span>
|
||||||
|
<span class="p">[]</span> <span class="p">[[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="mi">1</span> <span class="o">.</span> <span class="p">[</span><span class="n">swons</span><span class="p">]</span> <span class="n">cons</span> <span class="n">dip</span> <span class="n">uncons</span> <span class="n">swap</span>
|
||||||
|
<span class="p">[]</span> <span class="p">[[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="mi">1</span> <span class="p">[</span><span class="n">swons</span><span class="p">]</span> <span class="o">.</span> <span class="n">cons</span> <span class="n">dip</span> <span class="n">uncons</span> <span class="n">swap</span>
|
||||||
|
<span class="p">[]</span> <span class="p">[[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">1</span> <span class="n">swons</span><span class="p">]</span> <span class="o">.</span> <span class="n">dip</span> <span class="n">uncons</span> <span class="n">swap</span>
|
||||||
|
<span class="p">[]</span> <span class="o">.</span> <span class="mi">1</span> <span class="n">swons</span> <span class="p">[[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="n">uncons</span> <span class="n">swap</span>
|
||||||
|
<span class="p">[]</span> <span class="mi">1</span> <span class="o">.</span> <span class="n">swons</span> <span class="p">[[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="n">uncons</span> <span class="n">swap</span>
|
||||||
|
<span class="p">[]</span> <span class="mi">1</span> <span class="o">.</span> <span class="n">swap</span> <span class="n">cons</span> <span class="p">[[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="n">uncons</span> <span class="n">swap</span>
|
||||||
|
<span class="mi">1</span> <span class="p">[]</span> <span class="o">.</span> <span class="n">cons</span> <span class="p">[[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="n">uncons</span> <span class="n">swap</span>
|
||||||
|
<span class="p">[</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="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="n">uncons</span> <span class="n">swap</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="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="o">.</span> <span class="n">uncons</span> <span class="n">swap</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="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="o">.</span> <span class="n">swap</span>
|
||||||
|
<span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="o">.</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">'[1] [8] [2 [3 4 25 6] 7] z-down'</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="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">2</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">'[1] [8] [] [[3 4 25 6] 7] 2 z-right'</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="p">[</span><span class="mi">8</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">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</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">'[1] [8] [2] [7] [3 4 25 6] z-down'</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="p">[</span><span class="mi">8</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">7</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">3</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">'[1] [8] [2] [7] [] [4 25 6] 3 z-right'</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="p">[</span><span class="mi">8</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">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">4</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">'[1] [8] [2] [7] [3] [25 6] 4 z-right'</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="p">[</span><span class="mi">8</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">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">25</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">'[1] [8] [2] [7] [4 3] [6] 25 sqr'</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="p">[</span><span class="mi">8</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">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">625</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'[1] [8] [2] [7] [4 3] [6] 625 z-up'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</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">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">625</span> <span class="n">z</span><span class="o">-</span><span class="n">up</span>
|
||||||
|
<span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="mi">8</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">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">625</span> <span class="n">z</span><span class="o">-</span><span class="n">up</span>
|
||||||
|
<span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">625</span> <span class="n">z</span><span class="o">-</span><span class="n">up</span>
|
||||||
|
<span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">625</span> <span class="n">z</span><span class="o">-</span><span class="n">up</span>
|
||||||
|
<span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</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">7</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">625</span> <span class="n">z</span><span class="o">-</span><span class="n">up</span>
|
||||||
|
<span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</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">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">625</span> <span class="n">z</span><span class="o">-</span><span class="n">up</span>
|
||||||
|
<span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</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">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="o">.</span> <span class="mi">625</span> <span class="n">z</span><span class="o">-</span><span class="n">up</span>
|
||||||
|
<span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</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">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">625</span> <span class="o">.</span> <span class="n">z</span><span class="o">-</span><span class="n">up</span>
|
||||||
|
<span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</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">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">625</span> <span class="o">.</span> <span class="n">swons</span> <span class="n">swap</span> <span class="n">shunt</span>
|
||||||
|
<span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</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">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="mi">625</span> <span class="o">.</span> <span class="n">swap</span> <span class="n">cons</span> <span class="n">swap</span> <span class="n">shunt</span>
|
||||||
|
<span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</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">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="mi">625</span> <span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="o">.</span> <span class="n">cons</span> <span class="n">swap</span> <span class="n">shunt</span>
|
||||||
|
<span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</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">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="o">.</span> <span class="n">swap</span> <span class="n">shunt</span>
|
||||||
|
<span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</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">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">3</span><span class="p">]</span> <span class="o">.</span> <span class="n">shunt</span>
|
||||||
|
<span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">8</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">7</span><span class="p">]</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="o">.</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">'[1] [8] [2] [7] [3 4 625 6] z-up'</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="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</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">'[1] [8] [2 [3 4 625 6] 7] z-up'</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="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="dip-and-infra">
|
||||||
|
<h2><code class="docutils literal notranslate"><span class="pre">dip</span></code> and <code class="docutils literal notranslate"><span class="pre">infra</span></code><a class="headerlink" href="#dip-and-infra" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>In Joy we have the <code class="docutils literal notranslate"><span class="pre">dip</span></code> and <code class="docutils literal notranslate"><span class="pre">infra</span></code> combinators which can “target”
|
||||||
|
or “address” any particular item in a Joy tree structure.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'[1 [2 [3 4 25 6] 7] 8] [[[[[[sqr] dipd] infra] dip] infra] dip] infra'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</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="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="p">[[[[[[</span><span class="n">sqr</span><span class="p">]</span> <span class="n">dipd</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</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="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="o">.</span> <span class="p">[[[[[[</span><span class="n">sqr</span><span class="p">]</span> <span class="n">dipd</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</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="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="p">[[[[[[</span><span class="n">sqr</span><span class="p">]</span> <span class="n">dipd</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="o">.</span> <span class="n">infra</span>
|
||||||
|
<span class="mi">8</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">1</span> <span class="o">.</span> <span class="p">[[[[[</span><span class="n">sqr</span><span class="p">]</span> <span class="n">dipd</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span> <span class="p">[]</span> <span class="n">swaack</span>
|
||||||
|
<span class="mi">8</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">1</span> <span class="p">[[[[[</span><span class="n">sqr</span><span class="p">]</span> <span class="n">dipd</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="o">.</span> <span class="n">dip</span> <span class="p">[]</span> <span class="n">swaack</span>
|
||||||
|
<span class="mi">8</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="o">.</span> <span class="p">[[[[</span><span class="n">sqr</span><span class="p">]</span> <span class="n">dipd</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
|
||||||
|
<span class="mi">8</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="p">[[[[</span><span class="n">sqr</span><span class="p">]</span> <span class="n">dipd</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="o">.</span> <span class="n">infra</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
|
||||||
|
<span class="mi">7</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">2</span> <span class="o">.</span> <span class="p">[[[</span><span class="n">sqr</span><span class="p">]</span> <span class="n">dipd</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
|
||||||
|
<span class="mi">7</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">2</span> <span class="p">[[[</span><span class="n">sqr</span><span class="p">]</span> <span class="n">dipd</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="o">.</span> <span class="n">dip</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
|
||||||
|
<span class="mi">7</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="o">.</span> <span class="p">[[</span><span class="n">sqr</span><span class="p">]</span> <span class="n">dipd</span><span class="p">]</span> <span class="n">infra</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
|
||||||
|
<span class="mi">7</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">25</span> <span class="mi">6</span><span class="p">]</span> <span class="p">[[</span><span class="n">sqr</span><span class="p">]</span> <span class="n">dipd</span><span class="p">]</span> <span class="o">.</span> <span class="n">infra</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
|
||||||
|
<span class="mi">6</span> <span class="mi">25</span> <span class="mi">4</span> <span class="mi">3</span> <span class="o">.</span> <span class="p">[</span><span class="n">sqr</span><span class="p">]</span> <span class="n">dipd</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
|
||||||
|
<span class="mi">6</span> <span class="mi">25</span> <span class="mi">4</span> <span class="mi">3</span> <span class="p">[</span><span class="n">sqr</span><span class="p">]</span> <span class="o">.</span> <span class="n">dipd</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
|
||||||
|
<span class="mi">6</span> <span class="mi">25</span> <span class="o">.</span> <span class="n">sqr</span> <span class="mi">4</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
|
||||||
|
<span class="mi">6</span> <span class="mi">25</span> <span class="o">.</span> <span class="n">dup</span> <span class="n">mul</span> <span class="mi">4</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
|
||||||
|
<span class="mi">6</span> <span class="mi">25</span> <span class="mi">25</span> <span class="o">.</span> <span class="n">mul</span> <span class="mi">4</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
|
||||||
|
<span class="mi">6</span> <span class="mi">625</span> <span class="o">.</span> <span class="mi">4</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
|
||||||
|
<span class="mi">6</span> <span class="mi">625</span> <span class="mi">4</span> <span class="o">.</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
|
||||||
|
<span class="mi">6</span> <span class="mi">625</span> <span class="mi">4</span> <span class="mi">3</span> <span class="o">.</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
|
||||||
|
<span class="mi">6</span> <span class="mi">625</span> <span class="mi">4</span> <span class="mi">3</span> <span class="p">[</span><span class="mi">7</span><span class="p">]</span> <span class="o">.</span> <span class="n">swaack</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
|
||||||
|
<span class="mi">7</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="o">.</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
|
||||||
|
<span class="mi">7</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">2</span> <span class="o">.</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
|
||||||
|
<span class="mi">7</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">2</span> <span class="p">[</span><span class="mi">8</span><span class="p">]</span> <span class="o">.</span> <span class="n">swaack</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
|
||||||
|
<span class="mi">8</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="o">.</span> <span class="mi">1</span> <span class="p">[]</span> <span class="n">swaack</span>
|
||||||
|
<span class="mi">8</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">1</span> <span class="o">.</span> <span class="p">[]</span> <span class="n">swaack</span>
|
||||||
|
<span class="mi">8</span> <span class="p">[</span><span class="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">1</span> <span class="p">[]</span> <span class="o">.</span> <span class="n">swaack</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="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span> <span class="o">.</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>If you read the trace carefully you’ll see that about half of it is the
|
||||||
|
<code class="docutils literal notranslate"><span class="pre">dip</span></code> and <code class="docutils literal notranslate"><span class="pre">infra</span></code> combinators de-quoting programs and “digging” into
|
||||||
|
the subject datastructure. Instead of maintaining temporary results on
|
||||||
|
the stack they are pushed into the pending expression (continuation).
|
||||||
|
When <code class="docutils literal notranslate"><span class="pre">sqr</span></code> has run the rest of the pending expression rebuilds the
|
||||||
|
datastructure.</p>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="z">
|
||||||
|
<h2><code class="docutils literal notranslate"><span class="pre">Z</span></code><a class="headerlink" href="#z" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>Imagine a function <code class="docutils literal notranslate"><span class="pre">Z</span></code> that accepts a sequence of <code class="docutils literal notranslate"><span class="pre">dip</span></code> and
|
||||||
|
<code class="docutils literal notranslate"><span class="pre">infra</span></code> combinators, a quoted program <code class="docutils literal notranslate"><span class="pre">[Q]</span></code>, and a datastructure to
|
||||||
|
work on. It would effectively execute the quoted program as if it had
|
||||||
|
been embedded in a nested series of quoted programs, e.g.:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="p">[</span><span class="n">dip</span> <span class="n">dip</span> <span class="n">infra</span> <span class="n">dip</span> <span class="n">infra</span> <span class="n">dip</span> <span class="n">infra</span><span class="p">]</span> <span class="n">Z</span>
|
||||||
|
<span class="o">-------------------------------------------------------------</span>
|
||||||
|
<span class="p">[</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">dip</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>The <code class="docutils literal notranslate"><span class="pre">Z</span></code> function isn’t hard to make.</p>
|
||||||
|
<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">'Z == [[] cons cons] step i'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>Here it is in action in a simplified scenario.</p>
|
||||||
|
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">V</span><span class="p">(</span><span class="s1">'1 [2 3 4] Z'</span><span class="p">)</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="n">Z</span>
|
||||||
|
<span class="mi">1</span> <span class="o">.</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="n">Z</span>
|
||||||
|
<span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="o">.</span> <span class="n">Z</span>
|
||||||
|
<span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="o">.</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</span>
|
||||||
|
<span class="mi">1</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span> <span class="n">i</span>
|
||||||
|
<span class="mi">1</span> <span class="mi">2</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</span>
|
||||||
|
<span class="mi">1</span> <span class="mi">2</span> <span class="o">.</span> <span class="p">[]</span> <span class="n">cons</span> <span class="n">cons</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</span>
|
||||||
|
<span class="mi">1</span> <span class="mi">2</span> <span class="p">[]</span> <span class="o">.</span> <span class="n">cons</span> <span class="n">cons</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</span>
|
||||||
|
<span class="mi">1</span> <span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="n">cons</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</span>
|
||||||
|
<span class="p">[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</span>
|
||||||
|
<span class="p">[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="o">.</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</span>
|
||||||
|
<span class="p">[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span><span class="p">]</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span> <span class="n">i</span>
|
||||||
|
<span class="p">[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">3</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="p">[</span><span class="mi">4</span><span class="p">]</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</span>
|
||||||
|
<span class="p">[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">3</span> <span class="o">.</span> <span class="p">[]</span> <span class="n">cons</span> <span class="n">cons</span> <span class="p">[</span><span class="mi">4</span><span class="p">]</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</span>
|
||||||
|
<span class="p">[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">3</span> <span class="p">[]</span> <span class="o">.</span> <span class="n">cons</span> <span class="n">cons</span> <span class="p">[</span><span class="mi">4</span><span class="p">]</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</span>
|
||||||
|
<span class="p">[</span><span class="mi">1</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="o">.</span> <span class="n">cons</span> <span class="p">[</span><span class="mi">4</span><span class="p">]</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</span>
|
||||||
|
<span class="p">[[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">3</span><span class="p">]</span> <span class="o">.</span> <span class="p">[</span><span class="mi">4</span><span class="p">]</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</span>
|
||||||
|
<span class="p">[[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span><span class="p">]</span> <span class="o">.</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="n">step</span> <span class="n">i</span>
|
||||||
|
<span class="p">[[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span><span class="p">]</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="o">.</span> <span class="n">step</span> <span class="n">i</span>
|
||||||
|
<span class="p">[[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">3</span><span class="p">]</span> <span class="mi">4</span> <span class="p">[[]</span> <span class="n">cons</span> <span class="n">cons</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span> <span class="n">i</span>
|
||||||
|
<span class="p">[[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">3</span><span class="p">]</span> <span class="mi">4</span> <span class="o">.</span> <span class="p">[]</span> <span class="n">cons</span> <span class="n">cons</span> <span class="n">i</span>
|
||||||
|
<span class="p">[[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">3</span><span class="p">]</span> <span class="mi">4</span> <span class="p">[]</span> <span class="o">.</span> <span class="n">cons</span> <span class="n">cons</span> <span class="n">i</span>
|
||||||
|
<span class="p">[[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">3</span><span class="p">]</span> <span class="p">[</span><span class="mi">4</span><span class="p">]</span> <span class="o">.</span> <span class="n">cons</span> <span class="n">i</span>
|
||||||
|
<span class="p">[[[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">3</span><span class="p">]</span> <span class="mi">4</span><span class="p">]</span> <span class="o">.</span> <span class="n">i</span>
|
||||||
|
<span class="o">.</span> <span class="p">[[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">3</span><span class="p">]</span> <span class="mi">4</span>
|
||||||
|
<span class="p">[[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">3</span><span class="p">]</span> <span class="o">.</span> <span class="mi">4</span>
|
||||||
|
<span class="p">[[</span><span class="mi">1</span> <span class="mi">2</span><span class="p">]</span> <span class="mi">3</span><span class="p">]</span> <span class="mi">4</span> <span class="o">.</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>And here it is doing the main thing.</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">'[1 [2 [3 4 25 6] 7] 8] [sqr] [dip dip infra dip infra dip infra] Z'</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="mi">2</span> <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">625</span> <span class="mi">6</span><span class="p">]</span> <span class="mi">7</span><span class="p">]</span> <span class="mi">8</span><span class="p">]</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="addressing">
|
||||||
|
<h2>Addressing<a class="headerlink" href="#addressing" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>Because we are only using two combinators we could replace the list with
|
||||||
|
a string made from only two characters.</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="s1">'ddididi'</span> <span class="n">Zstr</span>
|
||||||
|
<span class="o">-------------------------------------------------------------</span>
|
||||||
|
<span class="p">[</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">dip</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">infra</span>
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
<p>The string can be considered a name or address for an item in the
|
||||||
|
subject datastructure.</p>
|
||||||
|
</div>
|
||||||
|
<div class="section" id="determining-the-right-path-for-an-item-in-a-tree">
|
||||||
|
<h2>Determining the right “path” for an item in a tree.<a class="headerlink" href="#determining-the-right-path-for-an-item-in-a-tree" title="Permalink to this headline">¶</a></h2>
|
||||||
|
<p>It’s easy to read off (in reverse) the right sequence of “d” and “i”
|
||||||
|
from the subject datastructure:</p>
|
||||||
|
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>[ n [ n [ n n x ...
|
||||||
|
i d i d i d d Bingo!
|
||||||
|
</pre></div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
|
||||||
|
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
</div>
|
||||||
|
<div class="sphinxsidebar" role="navigation" aria-label="main navigation">
|
||||||
|
<div class="sphinxsidebarwrapper">
|
||||||
|
<h3><a href="../index.html">Table Of Contents</a></h3>
|
||||||
|
<ul>
|
||||||
|
<li><a class="reference internal" href="#">Preamble</a><ul>
|
||||||
|
<li><a class="reference internal" href="#trees">Trees</a></li>
|
||||||
|
<li><a class="reference internal" href="#zipper-in-joy">Zipper in Joy</a></li>
|
||||||
|
<li><a class="reference internal" href="#dip-and-infra"><code class="docutils literal notranslate"><span class="pre">dip</span></code> and <code class="docutils literal notranslate"><span class="pre">infra</span></code></a></li>
|
||||||
|
<li><a class="reference internal" href="#z"><code class="docutils literal notranslate"><span class="pre">Z</span></code></a></li>
|
||||||
|
<li><a class="reference internal" href="#addressing">Addressing</a></li>
|
||||||
|
<li><a class="reference internal" href="#determining-the-right-path-for-an-item-in-a-tree">Determining the right “path” for an item in a tree.</a></li>
|
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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<div class="section" id="essays-about-programming-in-joy">
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<h1>Essays about Programming in Joy<a class="headerlink" href="#essays-about-programming-in-joy" title="Permalink to this headline">¶</a></h1>
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<p>These essays are adapted from Jupyter notebooks. I hope to have those hosted somewhere where people can view them “live” and interact with them, possibly on MS Azure. For now, Sphinx does such a great job rendering the HTML that I am copying over some notebooks in ReST format and hand-editing them into these documents.</p>
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<li class="toctree-l1"><a class="reference internal" href="Developing.html">Developing a Program in Joy</a><ul>
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<li class="toctree-l2"><a class="reference internal" href="Developing.html#project-euler-first-problem-multiples-of-3-and-5">Project Euler, first problem: “Multiples of 3 and 5”</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Developing.html#generator-version">Generator Version</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Trees.html">Treating Trees</a><ul>
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<li class="toctree-l2"><a class="reference internal" href="Trees.html#a-function-to-traverse-a-btree">A Function to Traverse a BTree</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Trees.html#adding-nodes-to-the-btree">Adding Nodes to the BTree</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Trees.html#interlude-the-cmp-combinator">Interlude: The <code class="docutils literal notranslate"><span class="pre">cmp</span></code> combinator</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Trees.html#interlude-factoring-and-naming">Interlude: Factoring and Naming</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Trees.html#a-version-of-btree-iter-that-does-in-order-traversal">A Version of <code class="docutils literal notranslate"><span class="pre">BTree-iter</span></code> that does In-Order Traversal</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Trees.html#getting-values-by-key">Getting values by key</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Trees.html#todo-btree-delete">TODO: BTree-delete</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Trees.html#tree-with-node-and-list-of-trees">Tree with node and list of trees.</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Trees.html#miscellaneous-crap">Miscellaneous Crap</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Trees.html#a-general-form-for-trees">A General Form for Trees</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Trees.html#automatically-deriving-the-recursion-combinator-for-a-data-type">Automatically deriving the recursion combinator for a data type?</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Newton-Raphson.html">Newton’s method</a><ul>
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<li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html#finding-the-square-root-of-a-number">Finding the Square-Root of a Number</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html#compute-the-error">Compute the Error</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html#square-root"><code class="docutils literal notranslate"><span class="pre">square-root</span></code></a></li>
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<li class="toctree-l1"><a class="reference internal" href="Quadratic.html">Quadratic formula</a><ul>
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<li class="toctree-l2"><a class="reference internal" href="Quadratic.html#write-a-program-with-variable-names">Write a program with variable names.</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Quadratic.html#derive-a-definition">Derive a definition.</a></li>
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<li class="toctree-l1"><a class="reference internal" href="NoUpdates.html">No Updates</a></li>
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<li class="toctree-l1"><a class="reference internal" href="Categorical.html">Categorical Programming</a></li>
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<span xmlns:dct="http://purl.org/dc/terms/" property="dct:title">Thun Documentation</span> by <a xmlns:cc="http://creativecommons.org/ns#" href="https://joypy.osdn.io/" property="cc:attributionName" rel="cc:attributionURL">Simon Forman</a> is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License</a>.<br />Based on a work at <a xmlns:dct="http://purl.org/dc/terms/" href="https://osdn.net/projects/joypy/" rel="dct:source">https://osdn.net/projects/joypy/</a>.
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Created using <a href="http://sphinx-doc.org/">Sphinx</a> 1.7.3.
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