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<div class="section" id="categorical-programming">
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<section id="categorical-programming">
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<h1>Categorical Programming<a class="headerlink" href="#categorical-programming" title="Permalink to this headline">¶</a></h1>
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<p>DRAFT</p>
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<p><a class="reference external" href="https://en.wikipedia.org/wiki/Category_theory">Categorical</a></p>
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<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>
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<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>
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<blockquote>
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<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>
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<div><p>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.</p>
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</div></blockquote>
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<p>What he’s doing is translating lambda 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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<li class="toctree-l2"><a class="reference internal" href="Ordered_Binary_Trees.html">Treating Trees I: Ordered Binary Trees</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Types.html">The Blissful Elegance of Typing Joy</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="thun-joy-in-python">
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<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>
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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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<ul class="simple">
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<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>
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<li>We get garbage collection for free.</li>
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<li>Compilation via Cython.</li>
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<li>Python is a “glue language” with loads of libraries which we can wrap in Joy functions.</li>
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<li><p>We can lean on the Python immutable types for our basic semantics and types: ints, floats, strings, and tuples, which enforces functional purity.</p></li>
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<li><p>We get garbage collection for free.</p></li>
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<li><p>Compilation via Cython.</p></li>
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<li><p>Python is a “glue language” with loads of libraries which we can wrap in Joy functions.</p></li>
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</ul>
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<div class="section" id="read-eval-print-loop-repl">
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<section id="read-eval-print-loop-repl">
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<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>
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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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joy?
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</pre></div>
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<div class="section" id="the-stack">
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<section id="the-stack">
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<h2>The Stack<a class="headerlink" href="#the-stack" title="Permalink to this headline">¶</a></h2>
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<p>In Joy, in addition to the types Boolean, integer, float, and string,
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there is a <a class="reference internal" href="../stack.html"><span class="doc">single sequence type</span></a> represented by enclosing a sequence of
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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>
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<div class="section" id="purely-functional-datastructures">
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</section>
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<section id="purely-functional-datastructures">
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<h2>Purely Functional Datastructures<a class="headerlink" href="#purely-functional-datastructures" title="Permalink to this headline">¶</a></h2>
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<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>
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</div>
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<div class="section" id="the-joy-function">
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</section>
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<section id="the-joy-function">
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<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>
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<div class="section" id="an-interpreter">
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<section id="an-interpreter">
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<h3>An Interpreter<a class="headerlink" href="#an-interpreter" title="Permalink to this headline">¶</a></h3>
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<p>The <code class="docutils literal notranslate"><span class="pre">joy()</span></code> interpreter 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 which it
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looks up in the dictionary.</p>
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</div>
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<div class="section" id="continuation-passing-style">
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</section>
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<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">CPS</a>? I
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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 class="section" id="view-function">
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</section>
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<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 an optional <code class="docutils literal notranslate"><span class="pre">viewer</span></code> argument that
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is a function which it calls on
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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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</section>
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<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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<section id="parser">
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<h2>Parser<a class="headerlink" href="#parser" title="Permalink to this headline">¶</a></h2>
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<p>The parser is extremely simple. The undocumented <code class="docutils literal notranslate"><span class="pre">re.Scanner</span></code> class
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does the tokenizing and then the parser builds the tuple
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structure out of the tokens. There’s no Abstract Syntax Tree or anything
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like that.</p>
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<div class="section" id="symbols">
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<section id="symbols">
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<h3>Symbols<a class="headerlink" href="#symbols" title="Permalink to this headline">¶</a></h3>
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<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">foo</span> <span class="pre">...</span></code> but don’t do that.</p>
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</div>
|
||||
<div class="section" id="token-regular-expressions">
|
||||
</section>
|
||||
<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">
|
||||
</section>
|
||||
<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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>joy.parser.text_to_expression('1 2 3 4 5') # A simple sequence.
|
||||
</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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>joy.parser.text_to_expression('[1 2 3] 4 5') # Three items, the first is a list with three items
|
||||
</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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>joy.parser.text_to_expression('1 23 ["four" [-5.0] cons] 8888') # A mixed bag. cons is
|
||||
# a Symbol, no lookup at
|
||||
# parse-time. Haiku docs.
|
||||
</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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>joy.parser.text_to_expression('[][][][][]') # Five empty lists.
|
||||
</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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>joy.parser.text_to_expression('[[[[[]]]]]') # Five nested lists.
|
||||
</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">
|
||||
</section>
|
||||
</section>
|
||||
<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
|
||||
@@ -198,7 +199,7 @@ the Joy system. There are simple functions such as addition <code class="docutil
|
||||
<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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>print inspect.getsource(joy.library.dip)
|
||||
</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>
|
||||
@@ -211,11 +212,10 @@ provide control-flow and higher-order operations.</p>
|
||||
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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>print joy.library.definitions
|
||||
</pre></div>
|
||||
</div>
|
||||
<pre class="literal-block">
|
||||
second == rest first
|
||||
<pre class="literal-block">second == rest first
|
||||
third == rest rest first
|
||||
product == 1 swap [*] step
|
||||
swons == swap cons
|
||||
@@ -248,8 +248,7 @@ 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>
|
||||
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
|
||||
@@ -260,7 +259,7 @@ 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">
|
||||
<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
|
||||
@@ -277,8 +276,8 @@ frameworks, programming languages. It’s a waste of time, a <a class="reference
|
||||
“thundering herd”
|
||||
attack</a> on
|
||||
human mentality.</p>
|
||||
</div>
|
||||
<div class="section" id="literary-code-library">
|
||||
</section>
|
||||
<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
|
||||
@@ -292,43 +291,47 @@ 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>
|
||||
</section>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
|
||||
</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>
|
||||
<h1 class="logo"><a href="../index.html">Thun</a></h1>
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
<h3>Navigation</h3>
|
||||
<ul class="current">
|
||||
<li class="toctree-l1 current"><a class="current reference internal" href="#">Thun: Joy in Python</a><ul>
|
||||
<li class="toctree-l2"><a class="reference internal" href="#read-eval-print-loop-repl">Read-Eval-Print Loop (REPL)</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="#the-stack">The Stack</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="#purely-functional-datastructures">Purely Functional Datastructures</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="#the-joy-function">The <code class="docutils literal notranslate"><span class="pre">joy()</span></code> function</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="#parser">Parser</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="#library">Library</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../joy.html">Joy Interpreter</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../stack.html">Stack or Quote or Sequence or List…</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../parser.html">Parsing Text into Joy Expressions</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../pretty.html">Tracing Joy Execution</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../library.html">Function Reference</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../lib.html">Functions Grouped by, er, Function with Examples</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../types.html">Type Inference of Joy Expressions</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="index.html">Essays about Programming in Joy</a></li>
|
||||
</ul>
|
||||
|
||||
<div class="relations">
|
||||
<h3>Related Topics</h3>
|
||||
<ul>
|
||||
@@ -338,25 +341,24 @@ developing structured processes.</p>
|
||||
</ul></li>
|
||||
</ul>
|
||||
</div>
|
||||
<div role="note" aria-label="source link">
|
||||
<h3>This Page</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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<div class="clearer"></div>
|
||||
@@ -367,7 +369,7 @@ developing structured processes.</p>
|
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</a>
|
||||
<br />
|
||||
<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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@@ -1,19 +1,19 @@
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<div class="section" id="newton-s-method">
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||||
<section id="newton-s-method">
|
||||
<h1><a class="reference external" href="https://en.wikipedia.org/wiki/Newton%27s_method">Newton’s method</a><a class="headerlink" href="#newton-s-method" title="Permalink to this headline">¶</a></h1>
|
||||
<p>Let’s use the Newton-Raphson method for finding the root of an equation
|
||||
to write a function that can compute the square root of a number.</p>
|
||||
<p>Cf. <a class="reference external" href="https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf">“Why Functional Programming Matters” by John
|
||||
Hughes</a></p>
|
||||
<div class="code ipython3 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="k">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>from notebook_preamble import J, V, define
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="section" id="a-generator-for-approximations">
|
||||
<section id="a-generator-for-approximations">
|
||||
<h2>A Generator for Approximations<a class="headerlink" href="#a-generator-for-approximations" title="Permalink to this headline">¶</a></h2>
|
||||
<p>To make a generator that generates successive approximations let’s start
|
||||
by assuming an initial approximation and then derive the function that
|
||||
@@ -51,7 +53,7 @@ computes the next approximation:</p>
|
||||
<span class="n">a</span><span class="s1">'</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="section" id="a-function-to-compute-the-next-approximation">
|
||||
<section id="a-function-to-compute-the-next-approximation">
|
||||
<h3>A Function to Compute the Next Approximation<a class="headerlink" href="#a-function-to-compute-the-next-approximation" title="Permalink to this headline">¶</a></h3>
|
||||
<p>This is the equation for computing the next approximate value of the
|
||||
square root:</p>
|
||||
@@ -67,8 +69,8 @@ square root:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">F</span> <span class="o">==</span> <span class="n">n</span> <span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="make-it-into-a-generator">
|
||||
</section>
|
||||
<section id="make-it-into-a-generator">
|
||||
<h3>Make it into a Generator<a class="headerlink" href="#make-it-into-a-generator" title="Permalink to this headline">¶</a></h3>
|
||||
<p>Our generator would be created by:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="p">[</span><span class="n">dup</span> <span class="n">F</span><span class="p">]</span> <span class="n">make_generator</span>
|
||||
@@ -90,10 +92,10 @@ function we’re writing. If we let 1 be the initial approximation:</p>
|
||||
<span class="mi">1</span> <span class="p">[</span><span class="n">dup</span> <span class="mi">23</span> <span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span> <span class="n">make_generator</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython3 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>define('gsra 1 swap [over / + 2 /] cons [dup] swoncat make_generator')
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython3 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 gsra'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>J('23 gsra')
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">1</span> <span class="p">[</span><span class="n">dup</span> <span class="mi">23</span> <span class="n">over</span> <span class="o">/</span> <span class="o">+</span> <span class="mi">2</span> <span class="o">/</span><span class="p">]</span> <span class="n">codireco</span><span class="p">]</span>
|
||||
@@ -101,23 +103,24 @@ function we’re writing. If we let 1 be the initial approximation:</p>
|
||||
</div>
|
||||
<p>Let’s drive the generator a few time (with the <code class="docutils literal notranslate"><span class="pre">x</span></code> combinator) and
|
||||
square the approximation to see how well it works…</p>
|
||||
<div class="code ipython3 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 gsra 6 [x popd] times first sqr'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>J('23 gsra 6 [x popd] times first sqr')
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">23.0000000001585</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="finding-consecutive-approximations-within-a-tolerance">
|
||||
</section>
|
||||
</section>
|
||||
<section id="finding-consecutive-approximations-within-a-tolerance">
|
||||
<h2>Finding Consecutive Approximations within a Tolerance<a class="headerlink" href="#finding-consecutive-approximations-within-a-tolerance" title="Permalink to this headline">¶</a></h2>
|
||||
<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>
|
||||
<blockquote>
|
||||
<div>The remainder of a square root finder is a function <em>within</em>, which
|
||||
<div><p>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>
|
||||
the given tolerance.</p>
|
||||
</div></blockquote>
|
||||
<p>(And note that by “list” he means a lazily-evaluated list.)</p>
|
||||
<p>Using the <em>output</em> <code class="docutils literal notranslate"><span class="pre">[a</span> <span class="pre">G]</span></code> of the above generator for square root
|
||||
approximations, and further assuming that the first term a has been
|
||||
@@ -132,7 +135,7 @@ generated already and epsilon ε is handy on the stack…</p>
|
||||
<span class="n">b</span> <span class="p">[</span><span class="n">c</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="n">within</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="section" id="predicate">
|
||||
<section id="predicate">
|
||||
<h3>Predicate<a class="headerlink" href="#predicate" title="Permalink to this headline">¶</a></h3>
|
||||
<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>
|
||||
@@ -142,11 +145,11 @@ generated already and epsilon ε is handy on the stack…</p>
|
||||
<span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">a</span><span class="o">-</span><span class="n">b</span><span class="p">)</span><span class="o"><=</span><span class="n">ε</span><span class="p">)</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython3 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_P [first - abs] dip <='</span><span class="p">)</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>define('_within_P [first - abs] dip <=')
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="base-case">
|
||||
</section>
|
||||
<section id="base-case">
|
||||
<h3>Base-Case<a class="headerlink" href="#base-case" title="Permalink to this headline">¶</a></h3>
|
||||
<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>
|
||||
@@ -154,19 +157,19 @@ generated already and epsilon ε is handy on the stack…</p>
|
||||
<span class="n">b</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython3 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_B roll< popop first'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>define('_within_B roll< popop first')
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="recur">
|
||||
</section>
|
||||
<section id="recur">
|
||||
<h3>Recur<a class="headerlink" href="#recur" title="Permalink to this headline">¶</a></h3>
|
||||
<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 a.</li>
|
||||
<li>Use <code class="docutils literal notranslate"><span class="pre">x</span></code> combinator to generate next term from <code class="docutils literal notranslate"><span class="pre">G</span></code>.</li>
|
||||
<li>Run <code class="docutils literal notranslate"><span class="pre">within</span></code> with <code class="docutils literal notranslate"><span class="pre">i</span></code> (it is a “tail-recursive” function.)</li>
|
||||
<li><p>Discard a.</p></li>
|
||||
<li><p>Use <code class="docutils literal notranslate"><span class="pre">x</span></code> combinator to generate next term from <code class="docutils literal notranslate"><span class="pre">G</span></code>.</p></li>
|
||||
<li><p>Run <code class="docutils literal notranslate"><span class="pre">within</span></code> with <code class="docutils literal notranslate"><span class="pre">i</span></code> (it is a “tail-recursive” function.)</p></li>
|
||||
</ol>
|
||||
<p>Pretty straightforward:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="n">R0</span> <span class="p">[</span><span class="n">within</span><span class="p">]</span> <span class="n">R1</span>
|
||||
@@ -179,11 +182,11 @@ generated already and epsilon ε is handy on the stack…</p>
|
||||
<span class="n">b</span> <span class="p">[</span><span class="n">c</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="n">within</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython3 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'_within_R [popd x] dip'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>define('_within_R [popd x] dip')
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="setting-up">
|
||||
</section>
|
||||
<section id="setting-up">
|
||||
<h3>Setting up<a class="headerlink" href="#setting-up" title="Permalink to this headline">¶</a></h3>
|
||||
<p>The recursive function we have defined so far needs a slight preamble:
|
||||
<code class="docutils literal notranslate"><span class="pre">x</span></code> to prime the generator and the epsilon value to use:</p>
|
||||
@@ -191,66 +194,88 @@ generated already and epsilon ε is handy on the stack…</p>
|
||||
<span class="n">a</span> <span class="p">[</span><span class="n">b</span> <span class="n">G</span><span class="p">]</span> <span class="n">ε</span> <span class="o">...</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython3 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">define</span><span class="p">(</span><span class="s1">'within x 0.000000001 [_within_P] [_within_B] [_within_R] tailrec'</span><span class="p">)</span>
|
||||
<span class="n">define</span><span class="p">(</span><span class="s1">'sqrt gsra within'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>define('within x 0.000000001 [_within_P] [_within_B] [_within_R] tailrec')
|
||||
define('sqrt gsra within')
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Try it out…</p>
|
||||
<div class="code ipython3 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'36 sqrt'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>J('36 sqrt')
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">6.0</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython3 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'23 sqrt'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>J('23 sqrt')
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Check it.</p>
|
||||
<div class="code ipython3 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span><span class="o">**</span><span class="mi">2</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>4.795831523312719**2
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">22.999999999999996</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython3 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">math</span> <span class="k">import</span> <span class="n">sqrt</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span>from math import sqrt
|
||||
|
||||
<span class="n">sqrt</span><span class="p">(</span><span class="mi">23</span><span class="p">)</span>
|
||||
sqrt(23)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">4.795831523312719</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</section>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
|
||||
</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="#">Newton’s method</a><ul>
|
||||
<li><a class="reference internal" href="#a-generator-for-approximations">A Generator for Approximations</a><ul>
|
||||
<li><a class="reference internal" href="#a-function-to-compute-the-next-approximation">A Function to Compute the Next Approximation</a></li>
|
||||
<li><a class="reference internal" href="#make-it-into-a-generator">Make it into a Generator</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a class="reference internal" href="#finding-consecutive-approximations-within-a-tolerance">Finding Consecutive Approximations within a Tolerance</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>
|
||||
</ul>
|
||||
</li>
|
||||
<h1 class="logo"><a href="../index.html">Thun</a></h1>
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
<h3>Navigation</h3>
|
||||
<ul class="current">
|
||||
<li class="toctree-l1"><a class="reference internal" href="Intro.html">Thun: Joy in Python</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../joy.html">Joy Interpreter</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../stack.html">Stack or Quote or Sequence or List…</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../parser.html">Parsing Text into Joy Expressions</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../pretty.html">Tracing Joy Execution</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../library.html">Function Reference</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../lib.html">Functions Grouped by, er, Function with Examples</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../types.html">Type Inference of Joy Expressions</a></li>
|
||||
<li class="toctree-l1 current"><a class="reference internal" href="index.html">Essays about Programming in Joy</a><ul class="current">
|
||||
<li class="toctree-l2"><a class="reference internal" href="Developing.html">Developing a Program in Joy</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Quadratic.html">Quadratic formula</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Replacing.html">Replacing Functions in the Dictionary</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Recursion_Combinators.html">Recursion Combinators</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Ordered_Binary_Trees.html">Treating Trees I: Ordered Binary Trees</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Treestep.html">Treating Trees II: <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a></li>
|
||||
<li class="toctree-l2 current"><a class="current reference internal" href="#">Newton’s method</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Zipper.html">Traversing Datastructures with Zippers</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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<h1>No Updates<a class="headerlink" href="#no-updates" title="Permalink to this headline">¶</a></h1>
|
||||
<p>DRAFT</p>
|
||||
<ol class="arabic simple">
|
||||
<li>Joy doesn’t need to change.</li>
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||||
<li><p>Joy doesn’t need to change.</p></li>
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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>The language evolves by adding new definitions and refactoring, always choosing new names for new functions.</li>
|
||||
<li><p>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.</p></li>
|
||||
<li><p>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.</p></li>
|
||||
<li><p>The language evolves by adding new definitions and refactoring, always choosing new names for new functions.</p></li>
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|
||||
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||||
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||||
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@@ -102,7 +143,7 @@
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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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File diff suppressed because it is too large
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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">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from notebook_preamble import J, V, define
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="section" id="quadratic-formula">
|
||||
<section id="quadratic-formula">
|
||||
<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>
|
||||
<p>Cf.
|
||||
<a class="reference external" href="http://www.kevinalbrecht.com/code/joy-mirror/jp-quadratic.html">jp-quadratic.html</a></p>
|
||||
@@ -45,47 +47,47 @@
|
||||
</pre></div>
|
||||
</div>
|
||||
<p><span class="math notranslate nohighlight">\(\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)</span></p>
|
||||
<div class="section" id="write-a-straightforward-program-with-variable-names">
|
||||
<section id="write-a-straightforward-program-with-variable-names">
|
||||
<h2>Write a straightforward program with variable names.<a class="headerlink" href="#write-a-straightforward-program-with-variable-names" title="Permalink to this headline">¶</a></h2>
|
||||
<p>This math translates to Joy code in a straightforward manner. We are
|
||||
going to use named variables to keep track of the arguments, then write
|
||||
a definition without them.</p>
|
||||
<div class="section" id="b">
|
||||
<section id="b">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">-b</span></code><a class="headerlink" href="#b" title="Permalink to this headline">¶</a></h3>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">b</span> <span class="n">neg</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="sqrt-b-2-4-a-c">
|
||||
</section>
|
||||
<section id="sqrt-b-2-4-a-c">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">sqrt(b^2</span> <span class="pre">-</span> <span class="pre">4</span> <span class="pre">*</span> <span class="pre">a</span> <span class="pre">*</span> <span class="pre">c)</span></code><a class="headerlink" href="#sqrt-b-2-4-a-c" title="Permalink to this headline">¶</a></h3>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></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>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="a">
|
||||
</section>
|
||||
<section id="a">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">/2a</span></code><a class="headerlink" href="#a" title="Permalink to this headline">¶</a></h3>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="mi">2</span> <span class="o">*</span> <span class="o">/</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="id1">
|
||||
</section>
|
||||
<section id="id1">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">±</span></code><a class="headerlink" href="#id1" title="Permalink to this headline">¶</a></h3>
|
||||
<p>There is a function <code class="docutils literal notranslate"><span class="pre">pm</span></code> that accepts two values on the stack and
|
||||
replaces them with their sum and difference.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">pm</span> <span class="o">==</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">popdd</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="putting-them-together">
|
||||
</section>
|
||||
<section id="putting-them-together">
|
||||
<h3>Putting Them Together<a class="headerlink" href="#putting-them-together" title="Permalink to this headline">¶</a></h3>
|
||||
<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="n">pm</span> <span class="n">a</span> <span class="mi">2</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">app2</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>We use <code class="docutils literal notranslate"><span class="pre">app2</span></code> to compute both roots by using a quoted program
|
||||
<code class="docutils literal notranslate"><span class="pre">[2a</span> <span class="pre">/]</span></code> built with <code class="docutils literal notranslate"><span class="pre">cons</span></code>.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="derive-a-definition">
|
||||
</section>
|
||||
</section>
|
||||
<section id="derive-a-definition">
|
||||
<h2>Derive a definition.<a class="headerlink" href="#derive-a-definition" title="Permalink to this headline">¶</a></h2>
|
||||
<p>Working backwards we use <code class="docutils literal notranslate"><span class="pre">dip</span></code> and <code class="docutils literal notranslate"><span class="pre">dipd</span></code> to extract the code from
|
||||
the variables:</p>
|
||||
@@ -98,11 +100,11 @@ the variables:</p>
|
||||
</div>
|
||||
<p>The three arguments are to the left, so we can “chop off” everything to
|
||||
the right and say it’s the definition of the <code class="docutils literal notranslate"><span class="pre">quadratic</span></code> 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">'quadratic == over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define('quadratic == over [[[neg] dupdip sqr 4] dipd * * - sqrt pm] dip 2 * [/] cons app2')
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Let’s try it out:</p>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">J</span><span class="p">(</span><span class="s1">'3 1 1 quadratic'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('3 1 1 quadratic')
|
||||
</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>
|
||||
@@ -112,7 +114,7 @@ the right and say it’s the definition of the <code class="docutils literal not
|
||||
lines are the <code class="docutils literal notranslate"><span class="pre">dip</span></code> and <code class="docutils literal notranslate"><span class="pre">dipd</span></code> combinators building the main program
|
||||
by incorporating the values on the stack. Then that program runs and you
|
||||
get the results. This is pretty typical of Joy code.</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">'-5 1 4 quadratic'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V('-5 1 4 quadratic')
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">.</span> <span class="o">-</span><span class="mi">5</span> <span class="mi">1</span> <span class="mi">4</span> <span class="n">quadratic</span>
|
||||
@@ -162,30 +164,55 @@ get the results. This is pretty typical of Joy code.</p>
|
||||
<span class="mf">4.0</span> <span class="mf">1.0</span> <span class="o">.</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
|
||||
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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="#">Quadratic formula</a><ul>
|
||||
<li><a class="reference internal" href="#write-a-straightforward-program-with-variable-names">Write a straightforward program with variable names.</a><ul>
|
||||
<li><a class="reference internal" href="#b"><code class="docutils literal notranslate"><span class="pre">-b</span></code></a></li>
|
||||
<li><a class="reference internal" href="#sqrt-b-2-4-a-c"><code class="docutils literal notranslate"><span class="pre">sqrt(b^2</span> <span class="pre">-</span> <span class="pre">4</span> <span class="pre">*</span> <span class="pre">a</span> <span class="pre">*</span> <span class="pre">c)</span></code></a></li>
|
||||
<li><a class="reference internal" href="#a"><code class="docutils literal notranslate"><span class="pre">/2a</span></code></a></li>
|
||||
<li><a class="reference internal" href="#id1"><code class="docutils literal notranslate"><span class="pre">±</span></code></a></li>
|
||||
<li><a class="reference internal" href="#putting-them-together">Putting Them Together</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a class="reference internal" href="#derive-a-definition">Derive a definition.</a></li>
|
||||
<h1 class="logo"><a href="../index.html">Thun</a></h1>
|
||||
|
||||
|
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|
||||
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|
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|
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|
||||
|
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<h3>Navigation</h3>
|
||||
<ul class="current">
|
||||
<li class="toctree-l1"><a class="reference internal" href="Intro.html">Thun: Joy in Python</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../joy.html">Joy Interpreter</a></li>
|
||||
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|
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|
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<li class="toctree-l1 current"><a class="reference internal" href="index.html">Essays about Programming in Joy</a><ul class="current">
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|
||||
<li class="toctree-l2 current"><a class="current reference internal" href="#">Quadratic formula</a></li>
|
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<li class="toctree-l2"><a class="reference internal" href="Replacing.html">Replacing Functions in the Dictionary</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Recursion_Combinators.html">Recursion Combinators</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Ordered_Binary_Trees.html">Treating Trees I: Ordered Binary Trees</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Treestep.html">Treating Trees II: <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a></li>
|
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<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a></li>
|
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<li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html">Newton’s method</a></li>
|
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<li class="toctree-l2"><a class="reference internal" href="Zipper.html">Traversing Datastructures with Zippers</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Types.html">The Blissful Elegance of Typing Joy</a></li>
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<li class="toctree-l2"><a class="reference internal" href="NoUpdates.html">No Updates</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Categorical.html">Categorical Programming</a></li>
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<li class="toctree-l2"><a class="reference internal" href="The_Four_Operations.html">The Four Fundamental Operations of Definite Action</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html">∂RE</a></li>
|
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|
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<h3>Related Topics</h3>
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|
||||
@@ -197,25 +224,24 @@ get the results. This is pretty typical of Joy code.</p>
|
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@@ -226,7 +252,7 @@ get the results. This is pretty typical of Joy 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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<div class="document">
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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">DefinitionWrapper</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from notebook_preamble import D, DefinitionWrapper, J, V, define
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="section" id="recursion-combinators">
|
||||
<section id="recursion-combinators">
|
||||
<h1>Recursion Combinators<a class="headerlink" href="#recursion-combinators" title="Permalink to this headline">¶</a></h1>
|
||||
<p>This article describes the <code class="docutils literal notranslate"><span class="pre">genrec</span></code> combinator, how to use it, and
|
||||
several generic specializations.</p>
|
||||
@@ -46,7 +47,7 @@ several generic specializations.</p>
|
||||
</div>
|
||||
<p>From “Recursion Theory and Joy” (j05cmp.html) by Manfred von Thun:</p>
|
||||
<blockquote>
|
||||
<div>“The genrec combinator takes four program parameters in addition to
|
||||
<div><p>“The genrec combinator takes four program parameters in addition to
|
||||
whatever data parameters it needs. Fourth from the top is an if-part,
|
||||
followed by a then-part. If the if-part yields true, then the
|
||||
then-part is executed and the combinator terminates. The other two
|
||||
@@ -55,8 +56,9 @@ false, the rec1-part is executed. Following that the four program
|
||||
parameters and the combinator are again pushed onto the stack bundled
|
||||
up in a quoted form. Then the rec2-part is executed, where it will
|
||||
find the bundled form. Typically it will then execute the bundled
|
||||
form, either with i or with app2, or some other combinator.”</div></blockquote>
|
||||
<div class="section" id="designing-recursive-functions">
|
||||
form, either with i or with app2, or some other combinator.”</p>
|
||||
</div></blockquote>
|
||||
<section id="designing-recursive-functions">
|
||||
<h2>Designing Recursive Functions<a class="headerlink" href="#designing-recursive-functions" title="Permalink to this headline">¶</a></h2>
|
||||
<p>The way to design one of these is to fix your base case and test and
|
||||
then treat <code class="docutils literal notranslate"><span class="pre">R1</span></code> and <code class="docutils literal notranslate"><span class="pre">R2</span></code> as an else-part “sandwiching” a quotation
|
||||
@@ -73,8 +75,8 @@ from:</p>
|
||||
</div>
|
||||
<p>Set the stack arguments in front and figure out what <code class="docutils literal notranslate"><span class="pre">R1</span></code> and <code class="docutils literal notranslate"><span class="pre">R2</span></code>
|
||||
have to do to apply the quoted <code class="docutils literal notranslate"><span class="pre">[F]</span></code> in the proper way.</p>
|
||||
</div>
|
||||
<div class="section" id="primitive-recursive-functions">
|
||||
</section>
|
||||
<section id="primitive-recursive-functions">
|
||||
<h2>Primitive Recursive Functions<a class="headerlink" href="#primitive-recursive-functions" title="Permalink to this headline">¶</a></h2>
|
||||
<p>Primitive recursive functions are those where <code class="docutils literal notranslate"><span class="pre">R2</span> <span class="pre">==</span> <span class="pre">i</span></code>.</p>
|
||||
<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">I</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">R</span><span class="p">]</span> <span class="n">primrec</span>
|
||||
@@ -82,35 +84,35 @@ have to do to apply the quoted <code class="docutils literal notranslate"><span
|
||||
<span class="o">==</span> <span class="p">[</span><span class="n">I</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">R</span> <span class="n">P</span><span class="p">]</span> <span class="n">ifte</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="hylomorphism">
|
||||
</section>
|
||||
<section id="hylomorphism">
|
||||
<h2><a class="reference external" href="https://en.wikipedia.org/wiki/Hylomorphism_%28computer_science%29">Hylomorphism</a><a class="headerlink" href="#hylomorphism" title="Permalink to this headline">¶</a></h2>
|
||||
<p>A
|
||||
<a class="reference external" href="https://en.wikipedia.org/wiki/Hylomorphism_%28computer_science%29">hylomorphism</a>
|
||||
is a recursive function <code class="docutils literal notranslate"><span class="pre">H</span> <span class="pre">::</span> <span class="pre">A</span> <span class="pre">-></span> <span class="pre">C</span></code> that converts a value of type
|
||||
<code class="docutils literal notranslate"><span class="pre">A</span></code> into a value of type <code class="docutils literal notranslate"><span class="pre">C</span></code> by means of:</p>
|
||||
<ul class="simple">
|
||||
<li>A generator <code class="docutils literal notranslate"><span class="pre">G</span> <span class="pre">::</span> <span class="pre">A</span> <span class="pre">-></span> <span class="pre">(B,</span> <span class="pre">A)</span></code></li>
|
||||
<li>A combiner <code class="docutils literal notranslate"><span class="pre">F</span> <span class="pre">::</span> <span class="pre">(B,</span> <span class="pre">C)</span> <span class="pre">-></span> <span class="pre">C</span></code></li>
|
||||
<li>A predicate <code class="docutils literal notranslate"><span class="pre">P</span> <span class="pre">::</span> <span class="pre">A</span> <span class="pre">-></span> <span class="pre">Bool</span></code> to detect the base case</li>
|
||||
<li>A base case value <code class="docutils literal notranslate"><span class="pre">c</span> <span class="pre">::</span> <span class="pre">C</span></code></li>
|
||||
<li>Recursive calls (zero or more); it has a “call stack in the form of a
|
||||
cons list”.</li>
|
||||
<li><p>A generator <code class="docutils literal notranslate"><span class="pre">G</span> <span class="pre">::</span> <span class="pre">A</span> <span class="pre">-></span> <span class="pre">(B,</span> <span class="pre">A)</span></code></p></li>
|
||||
<li><p>A combiner <code class="docutils literal notranslate"><span class="pre">F</span> <span class="pre">::</span> <span class="pre">(B,</span> <span class="pre">C)</span> <span class="pre">-></span> <span class="pre">C</span></code></p></li>
|
||||
<li><p>A predicate <code class="docutils literal notranslate"><span class="pre">P</span> <span class="pre">::</span> <span class="pre">A</span> <span class="pre">-></span> <span class="pre">Bool</span></code> to detect the base case</p></li>
|
||||
<li><p>A base case value <code class="docutils literal notranslate"><span class="pre">c</span> <span class="pre">::</span> <span class="pre">C</span></code></p></li>
|
||||
<li><p>Recursive calls (zero or more); it has a “call stack in the form of a
|
||||
cons list”.</p></li>
|
||||
</ul>
|
||||
<p>It may be helpful to see this function implemented in imperative Python
|
||||
code.</p>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">hylomorphism</span><span class="p">(</span><span class="n">c</span><span class="p">,</span> <span class="n">F</span><span class="p">,</span> <span class="n">P</span><span class="p">,</span> <span class="n">G</span><span class="p">):</span>
|
||||
<span class="sd">'''Return a hylomorphism function H.'''</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>def hylomorphism(c, F, P, G):
|
||||
'''Return a hylomorphism function H.'''
|
||||
|
||||
<span class="k">def</span> <span class="nf">H</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
|
||||
<span class="k">if</span> <span class="n">P</span><span class="p">(</span><span class="n">a</span><span class="p">):</span>
|
||||
<span class="n">result</span> <span class="o">=</span> <span class="n">c</span>
|
||||
<span class="k">else</span><span class="p">:</span>
|
||||
<span class="n">b</span><span class="p">,</span> <span class="n">aa</span> <span class="o">=</span> <span class="n">G</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
|
||||
<span class="n">result</span> <span class="o">=</span> <span class="n">F</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">H</span><span class="p">(</span><span class="n">aa</span><span class="p">))</span> <span class="c1"># b is stored in the stack frame during recursive call to H().</span>
|
||||
<span class="k">return</span> <span class="n">result</span>
|
||||
def H(a):
|
||||
if P(a):
|
||||
result = c
|
||||
else:
|
||||
b, aa = G(a)
|
||||
result = F(b, H(aa)) # b is stored in the stack frame during recursive call to H().
|
||||
return result
|
||||
|
||||
<span class="k">return</span> <span class="n">H</span>
|
||||
return H
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Cf. <a class="reference external" href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.125">“Bananas, Lenses, & Barbed
|
||||
@@ -118,8 +120,8 @@ Wire”</a></p>
|
||||
<p>Note that during evaluation of <code class="docutils literal notranslate"><span class="pre">H()</span></code> the intermediate <code class="docutils literal notranslate"><span class="pre">b</span></code> values are
|
||||
stored in the Python call stack. This is what is meant by “call stack in
|
||||
the form of a cons list”.</p>
|
||||
</div>
|
||||
<div class="section" id="hylomorphism-in-joy">
|
||||
</section>
|
||||
<section id="hylomorphism-in-joy">
|
||||
<h2>Hylomorphism in Joy<a class="headerlink" href="#hylomorphism-in-joy" title="Permalink to this headline">¶</a></h2>
|
||||
<p>We can define a combinator <code class="docutils literal notranslate"><span class="pre">hylomorphism</span></code> that will make a
|
||||
hylomorphism combinator <code class="docutils literal notranslate"><span class="pre">H</span></code> from constituent parts.</p>
|
||||
@@ -155,8 +157,8 @@ it is a simple specialization of the general recursion combinator.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">H</span> <span class="o">==</span> <span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="n">c</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="n">hylomorphism</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">pop</span> <span class="n">c</span><span class="p">]</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="p">[</span><span class="n">dip</span> <span class="n">F</span><span class="p">]</span> <span class="n">genrec</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="derivation-of-hylomorphism-combinator">
|
||||
</section>
|
||||
<section id="derivation-of-hylomorphism-combinator">
|
||||
<h2>Derivation of <code class="docutils literal notranslate"><span class="pre">hylomorphism</span></code> combinator<a class="headerlink" href="#derivation-of-hylomorphism-combinator" title="Permalink to this headline">¶</a></h2>
|
||||
<p>Now we just need to derive a definition that builds the <code class="docutils literal notranslate"><span class="pre">genrec</span></code>
|
||||
arguments out of the pieces given to the <code class="docutils literal notranslate"><span class="pre">hylomorphism</span></code> combinator.</p>
|
||||
@@ -167,9 +169,9 @@ arguments out of the pieces given to the <code class="docutils literal notransla
|
||||
</div>
|
||||
<p>Working in reverse:</p>
|
||||
<ul class="simple">
|
||||
<li>Use <code class="docutils literal notranslate"><span class="pre">swoncat</span></code> twice to decouple <code class="docutils literal notranslate"><span class="pre">[c]</span></code> and <code class="docutils literal notranslate"><span class="pre">[F]</span></code>.</li>
|
||||
<li>Use <code class="docutils literal notranslate"><span class="pre">unit</span></code> to dequote <code class="docutils literal notranslate"><span class="pre">c</span></code>.</li>
|
||||
<li>Use <code class="docutils literal notranslate"><span class="pre">dipd</span></code> to untangle <code class="docutils literal notranslate"><span class="pre">[unit</span> <span class="pre">[pop]</span> <span class="pre">swoncat]</span></code> from the givens.</li>
|
||||
<li><p>Use <code class="docutils literal notranslate"><span class="pre">swoncat</span></code> twice to decouple <code class="docutils literal notranslate"><span class="pre">[c]</span></code> and <code class="docutils literal notranslate"><span class="pre">[F]</span></code>.</p></li>
|
||||
<li><p>Use <code class="docutils literal notranslate"><span class="pre">unit</span></code> to dequote <code class="docutils literal notranslate"><span class="pre">c</span></code>.</p></li>
|
||||
<li><p>Use <code class="docutils literal notranslate"><span class="pre">dipd</span></code> to untangle <code class="docutils literal notranslate"><span class="pre">[unit</span> <span class="pre">[pop]</span> <span class="pre">swoncat]</span></code> from the givens.</p></li>
|
||||
</ul>
|
||||
<p>So:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">H</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">pop</span> <span class="n">c</span><span class="p">]</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="p">[</span><span class="n">dip</span> <span class="n">F</span><span class="p">]</span> <span class="n">genrec</span>
|
||||
@@ -183,40 +185,40 @@ the left so we have a definition for <code class="docutils literal notranslate">
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">hylomorphism</span> <span class="o">==</span> <span class="p">[</span><span class="n">unit</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="n">swoncat</span><span class="p">]</span> <span class="n">dipd</span> <span class="p">[</span><span class="n">dip</span><span class="p">]</span> <span class="n">swoncat</span> <span class="n">genrec</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">'hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define('hylomorphism == [unit [pop] swoncat] dipd [dip] swoncat genrec')
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="section" id="example-finding-triangular-numbers">
|
||||
<section id="example-finding-triangular-numbers">
|
||||
<h3>Example: Finding <a class="reference external" href="https://en.wikipedia.org/wiki/Triangular_number">Triangular Numbers</a><a class="headerlink" href="#example-finding-triangular-numbers" title="Permalink to this headline">¶</a></h3>
|
||||
<p>Let’s write a function that, given a positive integer, returns the sum
|
||||
of all positive integers less than that one. (In this case the types
|
||||
<code class="docutils literal notranslate"><span class="pre">A</span></code>, <code class="docutils literal notranslate"><span class="pre">B</span></code> and <code class="docutils literal notranslate"><span class="pre">C</span></code> are all <code class="docutils literal notranslate"><span class="pre">int</span></code>.)</p>
|
||||
<p>To sum a range of integers from 0 to <em>n</em> - 1:</p>
|
||||
<ul class="simple">
|
||||
<li><code class="docutils literal notranslate"><span class="pre">[P]</span></code> is <code class="docutils literal notranslate"><span class="pre">[1</span> <span class="pre"><=]</span></code></li>
|
||||
<li><code class="docutils literal notranslate"><span class="pre">c</span></code> is <code class="docutils literal notranslate"><span class="pre">0</span></code></li>
|
||||
<li><code class="docutils literal notranslate"><span class="pre">[G]</span></code> is <code class="docutils literal notranslate"><span class="pre">[--</span> <span class="pre">dup]</span></code></li>
|
||||
<li><code class="docutils literal notranslate"><span class="pre">[F]</span></code> is <code class="docutils literal notranslate"><span class="pre">[+]</span></code></li>
|
||||
<li><p><code class="docutils literal notranslate"><span class="pre">[P]</span></code> is <code class="docutils literal notranslate"><span class="pre">[1</span> <span class="pre"><=]</span></code></p></li>
|
||||
<li><p><code class="docutils literal notranslate"><span class="pre">c</span></code> is <code class="docutils literal notranslate"><span class="pre">0</span></code></p></li>
|
||||
<li><p><code class="docutils literal notranslate"><span class="pre">[G]</span></code> is <code class="docutils literal notranslate"><span class="pre">[--</span> <span class="pre">dup]</span></code></p></li>
|
||||
<li><p><code class="docutils literal notranslate"><span class="pre">[F]</span></code> is <code class="docutils literal notranslate"><span class="pre">[+]</span></code></p></li>
|
||||
</ul>
|
||||
<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">'triangular_number == [1 <=] 0 [-- dup] [+] hylomorphism'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define('triangular_number == [1 <=] 0 [-- dup] [+] hylomorphism')
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Let’s try it:</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 triangular_number'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('5 triangular_number')
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">10</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 1 2 3 4 5 6] [triangular_number] map'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[0 1 2 3 4 5 6] [triangular_number] map')
|
||||
</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">0</span> <span class="mi">1</span> <span class="mi">3</span> <span class="mi">6</span> <span class="mi">10</span> <span class="mi">15</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="four-specializations">
|
||||
</section>
|
||||
</section>
|
||||
<section id="four-specializations">
|
||||
<h2>Four Specializations<a class="headerlink" href="#four-specializations" title="Permalink to this headline">¶</a></h2>
|
||||
<p>There are at least four kinds of recursive combinator, depending on two
|
||||
choices. The first choice is whether the combiner function <code class="docutils literal notranslate"><span class="pre">F</span></code> should
|
||||
@@ -244,7 +246,7 @@ Consider the recursive branches:</p>
|
||||
</div>
|
||||
<p>The following four sections illustrate how these work, omitting the
|
||||
predicate evaluation.</p>
|
||||
<div class="section" id="h1">
|
||||
<section id="h1">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">H1</span></code><a class="headerlink" href="#h1" title="Permalink to this headline">¶</a></h3>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">H1</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">pop</span> <span class="n">c</span><span class="p">]</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="p">[</span><span class="n">dip</span> <span class="n">F</span><span class="p">]</span> <span class="n">genrec</span>
|
||||
</pre></div>
|
||||
@@ -271,8 +273,8 @@ the intermediate results along with the pending combiner functions. When
|
||||
the base case is reached the last term is replaced by the identity value
|
||||
<code class="docutils literal notranslate"><span class="pre">c</span></code> and the continuation “collapses” into the final result using the
|
||||
combiner <code class="docutils literal notranslate"><span class="pre">F</span></code>.</p>
|
||||
</div>
|
||||
<div class="section" id="h2">
|
||||
</section>
|
||||
<section id="h2">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">H2</span></code><a class="headerlink" href="#h2" title="Permalink to this headline">¶</a></h3>
|
||||
<p>When you can start with the identity value <code class="docutils literal notranslate"><span class="pre">c</span></code> on the stack and the
|
||||
combiner <code class="docutils literal notranslate"><span class="pre">F</span></code> can operate as you go using the intermediate results
|
||||
@@ -297,8 +299,8 @@ reverse order.</p>
|
||||
... d″
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="h3">
|
||||
</section>
|
||||
<section id="h3">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">H3</span></code><a class="headerlink" href="#h3" title="Permalink to this headline">¶</a></h3>
|
||||
<p>If you examine the traces above you’ll see that the combiner <code class="docutils literal notranslate"><span class="pre">F</span></code> only
|
||||
gets to operate on the results of <code class="docutils literal notranslate"><span class="pre">G</span></code>, it never “sees” the first value
|
||||
@@ -326,8 +328,8 @@ one item instead of two (the b is instead the duplicate of a.)</p>
|
||||
... d″
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="h4">
|
||||
</section>
|
||||
<section id="h4">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">H4</span></code><a class="headerlink" href="#h4" title="Permalink to this headline">¶</a></h3>
|
||||
<p>And, last but not least, if you can combine as you go, starting with
|
||||
<code class="docutils literal notranslate"><span class="pre">c</span></code>, and the combiner <code class="docutils literal notranslate"><span class="pre">F</span></code> needs to work on the current item, this is
|
||||
@@ -350,9 +352,9 @@ the form:</p>
|
||||
... d″
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="anamorphism">
|
||||
</section>
|
||||
</section>
|
||||
<section id="anamorphism">
|
||||
<h2>Anamorphism<a class="headerlink" href="#anamorphism" title="Permalink to this headline">¶</a></h2>
|
||||
<p>An anamorphism can be defined as a hylomorphism that uses <code class="docutils literal notranslate"><span class="pre">[]</span></code> for
|
||||
<code class="docutils literal notranslate"><span class="pre">c</span></code> and <code class="docutils literal notranslate"><span class="pre">swons</span></code> for <code class="docutils literal notranslate"><span class="pre">F</span></code>. An anamorphic function builds a list of
|
||||
@@ -360,68 +362,68 @@ values.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">A</span> <span class="o">==</span> <span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="p">[</span><span class="n">swons</span><span class="p">]</span> <span class="n">hylomorphism</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="section" id="range-et-al-an-example-of-an-anamorphism-is-the-range-function-which-generates-the-list-of-integers-from-0-to-n-1-given-n">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">range</span></code> et. al. An example of an anamorphism is the <code class="docutils literal notranslate"><span class="pre">range</span></code> function which generates the list of integers from 0 to <em>n</em> - 1 given <em>n</em>.<a class="headerlink" href="#range-et-al-an-example-of-an-anamorphism-is-the-range-function-which-generates-the-list-of-integers-from-0-to-n-1-given-n" title="Permalink to this headline">¶</a></h3>
|
||||
<section id="range-et-al-an-example-of-an-anamorphism-is-the-range-function-which-generates-the-list-of-integers-from-0-to-n-1-given-n">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">range</span></code> et. al. An example of an anamorphism is the <code class="docutils literal notranslate"><span class="pre">range</span></code> function which generates the list of integers from 0 to <em>n</em> - 1 given <em>n</em>.<a class="headerlink" href="#range-et-al-an-example-of-an-anamorphism-is-the-range-function-which-generates-the-list-of-integers-from-0-to-n-1-given-n" title="Permalink to this headline">¶</a></h3>
|
||||
<p>Each of the above variations can be used to make four slightly different
|
||||
<code class="docutils literal notranslate"><span class="pre">range</span></code> functions.</p>
|
||||
<div class="section" id="range-with-h1">
|
||||
<section id="range-with-h1">
|
||||
<h4><code class="docutils literal notranslate"><span class="pre">range</span></code> with <code class="docutils literal notranslate"><span class="pre">H1</span></code><a class="headerlink" href="#range-with-h1" title="Permalink to this headline">¶</a></h4>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">H1</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">pop</span> <span class="n">c</span><span class="p">]</span> <span class="p">[</span><span class="n">G</span><span class="p">]</span> <span class="p">[</span><span class="n">dip</span> <span class="n">F</span><span class="p">]</span> <span class="n">genrec</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">pop</span> <span class="p">[]]</span> <span class="p">[</span><span class="o">--</span> <span class="n">dup</span><span class="p">]</span> <span class="p">[</span><span class="n">dip</span> <span class="n">swons</span><span class="p">]</span> <span class="n">genrec</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">'range == [0 <=] [] [-- dup] [swons] hylomorphism'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define('range == [0 <=] [] [-- dup] [swons] hylomorphism')
|
||||
</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">'5 range'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('5 range')
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</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="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="range-with-h2">
|
||||
</section>
|
||||
<section id="range-with-h2">
|
||||
<h4><code class="docutils literal notranslate"><span class="pre">range</span></code> with <code class="docutils literal notranslate"><span class="pre">H2</span></code><a class="headerlink" href="#range-with-h2" title="Permalink to this headline">¶</a></h4>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">H2</span> <span class="o">==</span> <span class="n">c</span> <span class="n">swap</span> <span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="p">[</span><span class="n">G</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="n">primrec</span>
|
||||
<span class="o">==</span> <span class="p">[]</span> <span class="n">swap</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">pop</span><span class="p">]</span> <span class="p">[</span><span class="o">--</span> <span class="n">dup</span> <span class="p">[</span><span class="n">swons</span><span class="p">]</span> <span class="n">dip</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">'range_reverse == [] swap [0 <=] [pop] [-- dup [swons] dip] primrec'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define('range_reverse == [] swap [0 <=] [pop] [-- dup [swons] dip] primrec')
|
||||
</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">'5 range_reverse'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('5 range_reverse')
|
||||
</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">3</span> <span class="mi">4</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="range-with-h3">
|
||||
</section>
|
||||
<section id="range-with-h3">
|
||||
<h4><code class="docutils literal notranslate"><span class="pre">range</span></code> with <code class="docutils literal notranslate"><span class="pre">H3</span></code><a class="headerlink" href="#range-with-h3" title="Permalink to this headline">¶</a></h4>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">H3</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">pop</span> <span class="n">c</span><span class="p">]</span> <span class="p">[[</span><span class="n">G</span><span class="p">]</span> <span class="n">dupdip</span><span class="p">]</span> <span class="p">[</span><span class="n">dip</span> <span class="n">F</span><span class="p">]</span> <span class="n">genrec</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">pop</span> <span class="p">[]]</span> <span class="p">[[</span><span class="o">--</span><span class="p">]</span> <span class="n">dupdip</span><span class="p">]</span> <span class="p">[</span><span class="n">dip</span> <span class="n">swons</span><span class="p">]</span> <span class="n">genrec</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">'ranger == [0 <=] [pop []] [[--] dupdip] [dip swons] genrec'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define('ranger == [0 <=] [pop []] [[--] dupdip] [dip swons] genrec')
|
||||
</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">'5 ranger'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('5 ranger')
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">5</span> <span class="mi">4</span> <span class="mi">3</span> <span class="mi">2</span> <span class="mi">1</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="range-with-h4">
|
||||
</section>
|
||||
<section id="range-with-h4">
|
||||
<h4><code class="docutils literal notranslate"><span class="pre">range</span></code> with <code class="docutils literal notranslate"><span class="pre">H4</span></code><a class="headerlink" href="#range-with-h4" title="Permalink to this headline">¶</a></h4>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">H4</span> <span class="o">==</span> <span class="n">c</span> <span class="n">swap</span> <span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="p">[[</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="n">primrec</span>
|
||||
<span class="o">==</span> <span class="p">[]</span> <span class="n">swap</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">pop</span><span class="p">]</span> <span class="p">[[</span><span class="n">swons</span><span class="p">]</span> <span class="n">dupdip</span> <span class="o">--</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">'ranger_reverse == [] swap [0 <=] [pop] [[swons] dupdip --] primrec'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define('ranger_reverse == [] swap [0 <=] [pop] [[swons] dupdip --] primrec')
|
||||
</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">'5 ranger_reverse'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('5 ranger_reverse')
|
||||
</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="mi">5</span><span class="p">]</span>
|
||||
@@ -430,10 +432,10 @@ values.</p>
|
||||
<p>Hopefully this illustrates the workings of the variations. For more
|
||||
insight you can run the cells using the <code class="docutils literal notranslate"><span class="pre">V()</span></code> function instead of the
|
||||
<code class="docutils literal notranslate"><span class="pre">J()</span></code> function to get a trace of the Joy evaluation.</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="catamorphism">
|
||||
</section>
|
||||
</section>
|
||||
</section>
|
||||
<section id="catamorphism">
|
||||
<h2>Catamorphism<a class="headerlink" href="#catamorphism" title="Permalink to this headline">¶</a></h2>
|
||||
<p>A catamorphism can be defined as a hylomorphism that uses
|
||||
<code class="docutils literal notranslate"><span class="pre">[uncons</span> <span class="pre">swap]</span></code> for <code class="docutils literal notranslate"><span class="pre">[G]</span></code> and <code class="docutils literal notranslate"><span class="pre">[[]</span> <span class="pre">=]</span></code> (or just <code class="docutils literal notranslate"><span class="pre">[not]</span></code>) for the
|
||||
@@ -442,27 +444,27 @@ and makes some new value.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">C</span> <span class="o">==</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</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="p">[</span><span class="n">F</span><span class="p">]</span> <span class="n">hylomorphism</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">'swuncons == uncons swap'</span><span class="p">)</span> <span class="c1"># Awkward name.</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define('swuncons == uncons swap') # Awkward name.
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>An example of a catamorphism is the sum function.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">sum</span> <span class="o">==</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="mi">0</span> <span class="p">[</span><span class="n">swuncons</span><span class="p">]</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">hylomorphism</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">'sum == [not] 0 [swuncons] [+] hylomorphism'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define('sum == [not] 0 [swuncons] [+] hylomorphism')
|
||||
</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">'[5 4 3 2 1] sum'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[5 4 3 2 1] sum')
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">15</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="section" id="the-step-combinator">
|
||||
<section id="the-step-combinator">
|
||||
<h3>The <code class="docutils literal notranslate"><span class="pre">step</span></code> combinator<a class="headerlink" href="#the-step-combinator" title="Permalink to this headline">¶</a></h3>
|
||||
<p>The <code class="docutils literal notranslate"><span class="pre">step</span></code> combinator will usually be better to use than
|
||||
<code class="docutils literal notranslate"><span class="pre">catamorphism</span></code>.</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] help'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[step] help')
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Run</span> <span class="n">a</span> <span class="n">quoted</span> <span class="n">program</span> <span class="n">on</span> <span class="n">each</span> <span class="n">item</span> <span class="ow">in</span> <span class="n">a</span> <span class="n">sequence</span><span class="o">.</span>
|
||||
@@ -486,18 +488,18 @@ and makes some new value.</p>
|
||||
<span class="n">on</span> <span class="n">top</span> <span class="n">of</span> <span class="n">the</span> <span class="n">stack</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">'sum == 0 swap [+] step'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define('sum == 0 swap [+] step')
|
||||
</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">'[5 4 3 2 1] sum'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[5 4 3 2 1] sum')
|
||||
</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 class="section" id="example-factorial-function">
|
||||
</section>
|
||||
</section>
|
||||
<section id="example-factorial-function">
|
||||
<h2>Example: Factorial Function<a class="headerlink" href="#example-factorial-function" title="Permalink to this headline">¶</a></h2>
|
||||
<p>For the Factorial function:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">H4</span> <span class="o">==</span> <span class="n">c</span> <span class="n">swap</span> <span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span><span class="p">]</span> <span class="p">[[</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="n">primrec</span>
|
||||
@@ -510,17 +512,17 @@ and makes some new value.</p>
|
||||
<span class="n">P</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">'factorial == 1 swap [1 <=] [pop] [[*] dupdip --] primrec'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define('factorial == 1 swap [1 <=] [pop] [[*] dupdip --] primrec')
|
||||
</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">'5 factorial'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('5 factorial')
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">120</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="example-tails">
|
||||
</section>
|
||||
<section id="example-tails">
|
||||
<h2>Example: <code class="docutils literal notranslate"><span class="pre">tails</span></code><a class="headerlink" href="#example-tails" title="Permalink to this headline">¶</a></h2>
|
||||
<p>An example of a paramorphism for lists given in the <a class="reference external" href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.125">“Bananas…”
|
||||
paper</a>
|
||||
@@ -542,37 +544,37 @@ pattern <code class="docutils literal notranslate"><span class="pre">H2</span></
|
||||
<span class="n">P</span> <span class="o">==</span> <span class="ow">not</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">'tails == [] swap [not] [pop] [rest dup [swons] dip] primrec'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define('tails == [] swap [not] [pop] [rest dup [swons] dip] primrec')
|
||||
</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] tails'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[1 2 3] tails')
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></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">2</span> <span class="mi">3</span><span class="p">]]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="conclusion-patterns-of-recursion">
|
||||
</section>
|
||||
<section id="conclusion-patterns-of-recursion">
|
||||
<h2>Conclusion: Patterns of Recursion<a class="headerlink" href="#conclusion-patterns-of-recursion" title="Permalink to this headline">¶</a></h2>
|
||||
<p>Our story so far…</p>
|
||||
<div class="section" id="hylo-ana-cata">
|
||||
<section id="hylo-ana-cata">
|
||||
<h3>Hylo-, Ana-, Cata-<a class="headerlink" href="#hylo-ana-cata" title="Permalink to this headline">¶</a></h3>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">H</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">pop</span> <span class="n">c</span> <span class="p">]</span> <span class="p">[</span><span class="n">G</span> <span class="p">]</span> <span class="p">[</span><span class="n">dip</span> <span class="n">F</span> <span class="p">]</span> <span class="n">genrec</span>
|
||||
<span class="n">A</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">pop</span> <span class="p">[]]</span> <span class="p">[</span><span class="n">G</span> <span class="p">]</span> <span class="p">[</span><span class="n">dip</span> <span class="n">swap</span> <span class="n">cons</span><span class="p">]</span> <span class="n">genrec</span>
|
||||
<span class="n">C</span> <span class="o">==</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">pop</span> <span class="n">c</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="p">[</span><span class="n">dip</span> <span class="n">F</span> <span class="p">]</span> <span class="n">genrec</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="para">
|
||||
</section>
|
||||
<section id="para">
|
||||
<h3>Para-, ?-, ?-<a class="headerlink" href="#para" title="Permalink to this headline">¶</a></h3>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>P == c swap [P ] [pop] [[F ] dupdip G ] primrec
|
||||
? == [] swap [P ] [pop] [[swap cons] dupdip G ] primrec
|
||||
? == c swap [not] [pop] [[F ] dupdip uncons swap] primrec
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="appendix-fun-with-symbols">
|
||||
</section>
|
||||
</section>
|
||||
<section id="appendix-fun-with-symbols">
|
||||
<h2>Appendix: Fun with Symbols<a class="headerlink" href="#appendix-fun-with-symbols" title="Permalink to this headline">¶</a></h2>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>|[ (c, F), (G, P) ]| == (|c, F|) • [(G, P)]
|
||||
</pre></div>
|
||||
@@ -584,58 +586,55 @@ Wire”</a></p>
|
||||
</div>
|
||||
<p>I think they are having slightly too much fun with the symbols. However,
|
||||
“Too much is always better than not enough.”</p>
|
||||
</div>
|
||||
</div>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
|
||||
</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="#">Recursion Combinators</a><ul>
|
||||
<li><a class="reference internal" href="#designing-recursive-functions">Designing Recursive Functions</a></li>
|
||||
<li><a class="reference internal" href="#primitive-recursive-functions">Primitive Recursive Functions</a></li>
|
||||
<li><a class="reference internal" href="#hylomorphism">Hylomorphism</a></li>
|
||||
<li><a class="reference internal" href="#hylomorphism-in-joy">Hylomorphism in Joy</a></li>
|
||||
<li><a class="reference internal" href="#derivation-of-hylomorphism-combinator">Derivation of <code class="docutils literal notranslate"><span class="pre">hylomorphism</span></code> combinator</a><ul>
|
||||
<li><a class="reference internal" href="#example-finding-triangular-numbers">Example: Finding Triangular Numbers</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a class="reference internal" href="#four-specializations">Four Specializations</a><ul>
|
||||
<li><a class="reference internal" href="#h1"><code class="docutils literal notranslate"><span class="pre">H1</span></code></a></li>
|
||||
<li><a class="reference internal" href="#h2"><code class="docutils literal notranslate"><span class="pre">H2</span></code></a></li>
|
||||
<li><a class="reference internal" href="#h3"><code class="docutils literal notranslate"><span class="pre">H3</span></code></a></li>
|
||||
<li><a class="reference internal" href="#h4"><code class="docutils literal notranslate"><span class="pre">H4</span></code></a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a class="reference internal" href="#anamorphism">Anamorphism</a><ul>
|
||||
<li><a class="reference internal" href="#range-et-al-an-example-of-an-anamorphism-is-the-range-function-which-generates-the-list-of-integers-from-0-to-n-1-given-n"><code class="docutils literal notranslate"><span class="pre">range</span></code> et. al. An example of an anamorphism is the <code class="docutils literal notranslate"><span class="pre">range</span></code> function which generates the list of integers from 0 to <em>n</em> - 1 given <em>n</em>.</a><ul>
|
||||
<li><a class="reference internal" href="#range-with-h1"><code class="docutils literal notranslate"><span class="pre">range</span></code> with <code class="docutils literal notranslate"><span class="pre">H1</span></code></a></li>
|
||||
<li><a class="reference internal" href="#range-with-h2"><code class="docutils literal notranslate"><span class="pre">range</span></code> with <code class="docutils literal notranslate"><span class="pre">H2</span></code></a></li>
|
||||
<li><a class="reference internal" href="#range-with-h3"><code class="docutils literal notranslate"><span class="pre">range</span></code> with <code class="docutils literal notranslate"><span class="pre">H3</span></code></a></li>
|
||||
<li><a class="reference internal" href="#range-with-h4"><code class="docutils literal notranslate"><span class="pre">range</span></code> with <code class="docutils literal notranslate"><span class="pre">H4</span></code></a></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a class="reference internal" href="#catamorphism">Catamorphism</a><ul>
|
||||
<li><a class="reference internal" href="#the-step-combinator">The <code class="docutils literal notranslate"><span class="pre">step</span></code> combinator</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a class="reference internal" href="#example-factorial-function">Example: Factorial Function</a></li>
|
||||
<li><a class="reference internal" href="#example-tails">Example: <code class="docutils literal notranslate"><span class="pre">tails</span></code></a></li>
|
||||
<li><a class="reference internal" href="#conclusion-patterns-of-recursion">Conclusion: Patterns of Recursion</a><ul>
|
||||
<li><a class="reference internal" href="#hylo-ana-cata">Hylo-, Ana-, Cata-</a></li>
|
||||
<li><a class="reference internal" href="#para">Para-, ?-, ?-</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a class="reference internal" href="#appendix-fun-with-symbols">Appendix: Fun with Symbols</a></li>
|
||||
<h1 class="logo"><a href="../index.html">Thun</a></h1>
|
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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="document">
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<div class="bodywrapper">
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<div class="body" role="main">
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<div class="section" id="replacing-functions-in-the-dictionary">
|
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<section id="replacing-functions-in-the-dictionary">
|
||||
<h1>Replacing Functions in the Dictionary<a class="headerlink" href="#replacing-functions-in-the-dictionary" title="Permalink to this headline">¶</a></h1>
|
||||
<p>For now, there is no way to define new functions from within the Joy
|
||||
language. All functions (and the interpreter) all accept and return a
|
||||
dictionary parameter (in addition to the stack and expression) so that
|
||||
we can implement e.g. a function that adds new functions to the
|
||||
we can implement e.g. a function that adds new functions to the
|
||||
dictionary. However, there’s no function that does that. Adding a new
|
||||
function to the dictionary is a meta-interpreter action, you have to do
|
||||
it in Python, not 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">D</span><span class="p">,</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from notebook_preamble import D, J, V
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="section" id="a-long-trace">
|
||||
<section id="a-long-trace">
|
||||
<h2>A long trace<a class="headerlink" href="#a-long-trace" title="Permalink to this headline">¶</a></h2>
|
||||
<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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V('[23 18] average')
|
||||
</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>
|
||||
@@ -93,8 +94,8 @@ it in Python, not Joy.</p>
|
||||
<span class="mf">20.5</span> <span class="o">.</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="replacing-size-with-a-python-version">
|
||||
</section>
|
||||
<section id="replacing-size-with-a-python-version">
|
||||
<h2>Replacing <code class="docutils literal notranslate"><span class="pre">size</span></code> with a Python version<a class="headerlink" href="#replacing-size-with-a-python-version" title="Permalink to this headline">¶</a></h2>
|
||||
<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> each convert a sequence to a single value.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="nb">sum</span> <span class="o">==</span> <span class="mi">0</span> <span class="n">swap</span> <span class="p">[</span><span class="o">+</span><span class="p">]</span> <span class="n">step</span>
|
||||
@@ -104,30 +105,30 @@ it in Python, not Joy.</p>
|
||||
<p>An efficient <code class="docutils literal notranslate"><span class="pre">sum</span></code> function is already in the library. But for
|
||||
<code class="docutils literal notranslate"><span class="pre">size</span></code> we can use a “compiled” version hand-written in Python to speed
|
||||
up evaluation and make the trace more readable.</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">joy.utils.stack</span> <span class="k">import</span> <span class="n">iter_stack</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from joy.library import SimpleFunctionWrapper
|
||||
from joy.utils.stack import iter_stack
|
||||
|
||||
|
||||
<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>
|
||||
@SimpleFunctionWrapper
|
||||
def size(stack):
|
||||
'''Return the size of the sequence on the stack.'''
|
||||
sequence, stack = stack
|
||||
n = 0
|
||||
for _ in iter_stack(sequence):
|
||||
n += 1
|
||||
return n, stack
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Now we replace the old version in the dictionary with the new version,
|
||||
and re-evaluate the expression.</p>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></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">size</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>D['size'] = size
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="a-shorter-trace">
|
||||
</section>
|
||||
<section id="a-shorter-trace">
|
||||
<h2>A shorter trace<a class="headerlink" href="#a-shorter-trace" title="Permalink to this headline">¶</a></h2>
|
||||
<p>You can see that <code class="docutils literal notranslate"><span class="pre">size</span></code> now executes 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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V('[23 18] average')
|
||||
</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>
|
||||
@@ -161,24 +162,55 @@ and re-evaluate the expression.</p>
|
||||
<span class="mf">20.5</span> <span class="o">.</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</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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<ul>
|
||||
<li><a class="reference internal" href="#">Replacing Functions in the Dictionary</a><ul>
|
||||
<li><a class="reference internal" href="#a-long-trace">A long trace</a></li>
|
||||
<li><a class="reference internal" href="#replacing-size-with-a-python-version">Replacing <code class="docutils literal notranslate"><span class="pre">size</span></code> with a Python version</a></li>
|
||||
<li><a class="reference internal" href="#a-shorter-trace">A shorter trace</a></li>
|
||||
<h1 class="logo"><a href="../index.html">Thun</a></h1>
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<li class="toctree-l2"><a class="reference internal" href="The_Four_Operations.html">The Four Fundamental Operations of Definite Action</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html">∂RE</a></li>
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<h3>Related Topics</h3>
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<ul>
|
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@@ -190,25 +222,24 @@ and re-evaluate the expression.</p>
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</ul>
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@@ -219,7 +250,7 @@ and re-evaluate the expression.</p>
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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="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="the-four-fundamental-operations-of-definite-action">
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||||
<section id="the-four-fundamental-operations-of-definite-action">
|
||||
<h1>The Four Fundamental Operations of Definite Action<a class="headerlink" href="#the-four-fundamental-operations-of-definite-action" title="Permalink to this headline">¶</a></h1>
|
||||
<p>All definite actions (computer program) can be defined by four
|
||||
fundamental patterns of combination:</p>
|
||||
<ol class="arabic simple">
|
||||
<li>Sequence</li>
|
||||
<li>Branch</li>
|
||||
<li>Loop</li>
|
||||
<li>Parallel</li>
|
||||
<li><p>Sequence</p></li>
|
||||
<li><p>Branch</p></li>
|
||||
<li><p>Loop</p></li>
|
||||
<li><p>Parallel</p></li>
|
||||
</ol>
|
||||
<div class="section" id="sequence">
|
||||
<section id="sequence">
|
||||
<h2>Sequence<a class="headerlink" href="#sequence" title="Permalink to this headline">¶</a></h2>
|
||||
<p>Do one thing after another. In joy this is represented by putting two
|
||||
symbols together, juxtaposition:</p>
|
||||
@@ -51,8 +52,8 @@ symbols together, juxtaposition:</p>
|
||||
</div>
|
||||
<p>Operations have inputs and outputs. The outputs of <code class="docutils literal notranslate"><span class="pre">foo</span></code> must be
|
||||
compatible in “arity”, type, and shape with the inputs of <code class="docutils literal notranslate"><span class="pre">bar</span></code>.</p>
|
||||
</div>
|
||||
<div class="section" id="branch">
|
||||
</section>
|
||||
<section id="branch">
|
||||
<h2>Branch<a class="headerlink" href="#branch" title="Permalink to this headline">¶</a></h2>
|
||||
<p>Do one thing or another.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">boolean</span> <span class="p">[</span><span class="n">F</span><span class="p">]</span> <span class="p">[</span><span class="n">T</span><span class="p">]</span> <span class="n">branch</span>
|
||||
@@ -93,7 +94,7 @@ outputs for <code class="docutils literal notranslate"><span class="pre">foo</sp
|
||||
<span class="n">foo</span> <span class="n">T</span> <span class="n">bar</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="section" id="ifte">
|
||||
<section id="ifte">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">ifte</span></code><a class="headerlink" href="#ifte" title="Permalink to this headline">¶</a></h3>
|
||||
<p>Often it will be easier on the programmer to write branching code with
|
||||
the predicate specified in a quote. The <code class="docutils literal notranslate"><span class="pre">ifte</span></code> combinator provides
|
||||
@@ -115,9 +116,9 @@ evaluate it. I reflect this in the structure of the stack effect comment
|
||||
of <code class="docutils literal notranslate"><span class="pre">branch</span></code>, it will only accept Boolean values, and in the definition
|
||||
of <code class="docutils literal notranslate"><span class="pre">ifte</span></code> above by including <code class="docutils literal notranslate"><span class="pre">not</span></code> in the quote, which also has the
|
||||
effect that the subject quotes are in the proper order for <code class="docutils literal notranslate"><span class="pre">branch</span></code>.)</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="loop">
|
||||
</section>
|
||||
</section>
|
||||
<section id="loop">
|
||||
<h2>Loop<a class="headerlink" href="#loop" title="Permalink to this headline">¶</a></h2>
|
||||
<p>Do one thing zero or more times.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">boolean</span> <span class="p">[</span><span class="n">Q</span><span class="p">]</span> <span class="n">loop</span>
|
||||
@@ -168,7 +169,7 @@ boolean flag for the next iteration:</p>
|
||||
<span class="n">G</span> <span class="n">G</span> <span class="n">G</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="section" id="while">
|
||||
<section id="while">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">while</span></code><a class="headerlink" href="#while" title="Permalink to this headline">¶</a></h3>
|
||||
<p>Keep doing <code class="docutils literal notranslate"><span class="pre">B</span></code> <em>while</em> some predicate <code class="docutils literal notranslate"><span class="pre">P</span></code> is true. This is
|
||||
convenient as the predicate function is made nullary automatically and
|
||||
@@ -191,9 +192,9 @@ flag for the next iteration:</p>
|
||||
<span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="n">nullary</span> <span class="p">[</span><span class="n">B</span> <span class="p">[</span><span class="n">P</span><span class="p">]</span> <span class="n">nullary</span><span class="p">]</span> <span class="n">loop</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="parallel">
|
||||
</section>
|
||||
</section>
|
||||
<section id="parallel">
|
||||
<h2>Parallel<a class="headerlink" href="#parallel" title="Permalink to this headline">¶</a></h2>
|
||||
<p>The <em>parallel</em> operation indicates that two (or more) functions <em>do not
|
||||
interfere</em> with each other and so can run in parallel. The main
|
||||
@@ -201,10 +202,10 @@ difficulty in this sort of thing is orchestrating the recombining
|
||||
(“join” or “wait”) of the results of the functions after they finish.</p>
|
||||
<p>The current implementaions and the following definitions <em>are not
|
||||
actually parallel</em> (yet), but there is no reason they couldn’t be
|
||||
reimplemented in terms of e.g. Python threads. I am not concerned with
|
||||
reimplemented in terms of e.g. Python threads. I am not concerned with
|
||||
performance of the system just yet, only the elegance of the code it
|
||||
allows us to write.</p>
|
||||
<div class="section" id="cleave">
|
||||
<section id="cleave">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">cleave</span></code><a class="headerlink" href="#cleave" title="Permalink to this headline">¶</a></h3>
|
||||
<p>Joy has a few parallel combinators, the main one being <code class="docutils literal notranslate"><span class="pre">cleave</span></code>:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> <span class="o">...</span> <span class="n">x</span> <span class="p">[</span><span class="n">A</span><span class="p">]</span> <span class="p">[</span><span class="n">B</span><span class="p">]</span> <span class="n">cleave</span>
|
||||
@@ -225,8 +226,8 @@ Elliott’s “Compiling to Categories” paper, et. al.)</p>
|
||||
<p>Just a thought, if you <code class="docutils literal notranslate"><span class="pre">cleave</span></code> two jobs and one requires more time to
|
||||
finish than the other you’d like to be able to assign resources
|
||||
accordingly so that they both finish at the same time.</p>
|
||||
</div>
|
||||
<div class="section" id="apply-functions">
|
||||
</section>
|
||||
<section id="apply-functions">
|
||||
<h3>“Apply” Functions<a class="headerlink" href="#apply-functions" title="Permalink to this headline">¶</a></h3>
|
||||
<p>There are also <code class="docutils literal notranslate"><span class="pre">app2</span></code> and <code class="docutils literal notranslate"><span class="pre">app3</span></code> which run a single quote on more
|
||||
than one value:</p>
|
||||
@@ -257,8 +258,8 @@ value.)</p>
|
||||
<span class="n">a</span> <span class="n">b</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="map">
|
||||
</section>
|
||||
<section id="map">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">map</span></code><a class="headerlink" href="#map" title="Permalink to this headline">¶</a></h3>
|
||||
<p>The common <code class="docutils literal notranslate"><span class="pre">map</span></code> function in Joy should also be though of as a
|
||||
<em>parallel</em> operator:</p>
|
||||
@@ -266,9 +267,9 @@ value.)</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>There is no reason why the implementation of <code class="docutils literal notranslate"><span class="pre">map</span></code> couldn’t distribute
|
||||
the <code class="docutils literal notranslate"><span class="pre">Q</span></code> function over e.g. a pool of worker CPUs.</p>
|
||||
</div>
|
||||
<div class="section" id="pam">
|
||||
the <code class="docutils literal notranslate"><span class="pre">Q</span></code> function over e.g. a pool of worker CPUs.</p>
|
||||
</section>
|
||||
<section id="pam">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">pam</span></code><a class="headerlink" href="#pam" title="Permalink to this headline">¶</a></h3>
|
||||
<p>One of my favorite combinators, the <code class="docutils literal notranslate"><span class="pre">pam</span></code> combinator is just:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">pam</span> <span class="o">==</span> <span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="nb">map</span>
|
||||
@@ -281,21 +282,21 @@ stack and combine their (first) outputs in a result list.</p>
|
||||
<span class="p">[</span> <span class="n">a</span> <span class="n">b</span> <span class="n">c</span> <span class="o">...</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="handling-other-kinds-of-join">
|
||||
</section>
|
||||
<section id="handling-other-kinds-of-join">
|
||||
<h3>Handling Other Kinds of Join<a class="headerlink" href="#handling-other-kinds-of-join" title="Permalink to this headline">¶</a></h3>
|
||||
<p>The <code class="docutils literal notranslate"><span class="pre">cleave</span></code> operators and others all have pretty brutal join
|
||||
semantics: everything works and we always wait for every
|
||||
sub-computation. We can imagine a few different potentially useful
|
||||
patterns of “joining” results from parallel combinators.</p>
|
||||
<div class="section" id="first-to-finish">
|
||||
<section id="first-to-finish">
|
||||
<h4>first-to-finish<a class="headerlink" href="#first-to-finish" title="Permalink to this headline">¶</a></h4>
|
||||
<p>Thinking about variations of <code class="docutils literal notranslate"><span class="pre">pam</span></code> there could be one that only
|
||||
returns the first result of the first-to-finish sub-program, or the
|
||||
stack could be replaced by its output stack.</p>
|
||||
<p>The other sub-programs would be cancelled.</p>
|
||||
</div>
|
||||
<div class="section" id="fulminators">
|
||||
</section>
|
||||
<section id="fulminators">
|
||||
<h4>“Fulminators”<a class="headerlink" href="#fulminators" title="Permalink to this headline">¶</a></h4>
|
||||
<p>Also known as “Futures” or “Promises” (by <em>everybody</em> else. “Fulinators”
|
||||
is what I was going to call them when I was thinking about implementing
|
||||
@@ -312,44 +313,57 @@ with “asyncronous” … events?</p>
|
||||
sort of thing works perfectly in Joy code I’m not going to worry about
|
||||
it. (And I think the Categories can deal with it anyhow? Incremental
|
||||
evaluation, yeah?)</p>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</section>
|
||||
</section>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
|
||||
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|
||||
|
||||
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|
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|
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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="#">The Four Fundamental Operations of Definite Action</a><ul>
|
||||
<li><a class="reference internal" href="#sequence">Sequence</a></li>
|
||||
<li><a class="reference internal" href="#branch">Branch</a><ul>
|
||||
<li><a class="reference internal" href="#ifte"><code class="docutils literal notranslate"><span class="pre">ifte</span></code></a></li>
|
||||
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|
||||
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|
||||
<li><a class="reference internal" href="#loop">Loop</a><ul>
|
||||
<li><a class="reference internal" href="#while"><code class="docutils literal notranslate"><span class="pre">while</span></code></a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a class="reference internal" href="#parallel">Parallel</a><ul>
|
||||
<li><a class="reference internal" href="#cleave"><code class="docutils literal notranslate"><span class="pre">cleave</span></code></a></li>
|
||||
<li><a class="reference internal" href="#apply-functions">“Apply” Functions</a></li>
|
||||
<li><a class="reference internal" href="#map"><code class="docutils literal notranslate"><span class="pre">map</span></code></a></li>
|
||||
<li><a class="reference internal" href="#pam"><code class="docutils literal notranslate"><span class="pre">pam</span></code></a></li>
|
||||
<li><a class="reference internal" href="#handling-other-kinds-of-join">Handling Other Kinds of Join</a><ul>
|
||||
<li><a class="reference internal" href="#first-to-finish">first-to-finish</a></li>
|
||||
<li><a class="reference internal" href="#fulminators">“Fulminators”</a></li>
|
||||
</ul>
|
||||
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|
||||
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|
||||
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|
||||
<h1 class="logo"><a href="../index.html">Thun</a></h1>
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||||
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||||
|
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<h3>Navigation</h3>
|
||||
<ul class="current">
|
||||
<li class="toctree-l1"><a class="reference internal" href="Intro.html">Thun: Joy in Python</a></li>
|
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<li class="toctree-l2"><a class="reference internal" href="Ordered_Binary_Trees.html">Treating Trees I: Ordered Binary Trees</a></li>
|
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|
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<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a></li>
|
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<li class="toctree-l2"><a class="reference internal" href="NoUpdates.html">No Updates</a></li>
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<li class="toctree-l2"><a class="reference internal" href="Categorical.html">Categorical Programming</a></li>
|
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<li class="toctree-l2 current"><a class="current reference internal" href="#">The Four Fundamental Operations of Definite Action</a></li>
|
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<li class="toctree-l2"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html">∂RE</a></li>
|
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@@ -361,25 +375,24 @@ evaluation, yeah?)</p>
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@@ -390,7 +403,7 @@ evaluation, yeah?)</p>
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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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@@ -1,19 +1,18 @@
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<div class="body" role="main">
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<div class="section" id="treating-trees-ii-treestep">
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<section id="treating-trees-ii-treestep">
|
||||
<h1>Treating Trees II: <code class="docutils literal notranslate"><span class="pre">treestep</span></code><a class="headerlink" href="#treating-trees-ii-treestep" title="Permalink to this headline">¶</a></h1>
|
||||
<p>Let’s consider a tree structure, similar to one described <a class="reference external" href="https://www.cs.kent.ac.uk/people/staff/dat/miranda/whyfp90.pdf">“Why
|
||||
functional programming matters” by John
|
||||
@@ -65,7 +66,7 @@ combine the result with <code class="docutils literal notranslate"><span class="
|
||||
</div>
|
||||
<p>(Later on we’ll experiment with making <code class="docutils literal notranslate"><span class="pre">map</span></code> part of <code class="docutils literal notranslate"><span class="pre">C</span></code> so you can
|
||||
use other combinators.)</p>
|
||||
<div class="section" id="derive-the-recursive-function">
|
||||
<section id="derive-the-recursive-function">
|
||||
<h2>Derive the recursive function.<a class="headerlink" href="#derive-the-recursive-function" title="Permalink to this headline">¶</a></h2>
|
||||
<p>We can begin to derive it by finding the <code class="docutils literal notranslate"><span class="pre">ifte</span></code> stage that <code class="docutils literal notranslate"><span class="pre">genrec</span></code>
|
||||
will produce.</p>
|
||||
@@ -110,8 +111,8 @@ the desired outcome.</p>
|
||||
<span class="o">==</span> <span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">B</span><span class="p">]</span> <span class="p">[</span><span class="n">uncons</span> <span class="p">[</span><span class="n">N</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="p">[</span><span class="nb">map</span> <span class="n">C</span><span class="p">]</span> <span class="n">genrec</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="extract-the-givens-to-parameterize-the-program">
|
||||
</section>
|
||||
<section id="extract-the-givens-to-parameterize-the-program">
|
||||
<h2>Extract the givens to parameterize the program.<a class="headerlink" href="#extract-the-givens-to-parameterize-the-program" title="Permalink to this headline">¶</a></h2>
|
||||
<p>Working backwards:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">B</span><span class="p">]</span> <span class="p">[</span><span class="n">uncons</span> <span class="p">[</span><span class="n">N</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="p">[</span><span class="nb">map</span> <span class="n">C</span><span class="p">]</span> <span class="n">genrec</span>
|
||||
@@ -134,7 +135,7 @@ the desired outcome.</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>The givens are all to the left so we have our definition.</p>
|
||||
<div class="section" id="alternate-extract-the-givens-to-parameterize-the-program">
|
||||
<section id="alternate-extract-the-givens-to-parameterize-the-program">
|
||||
<h3>(alternate) Extract the givens to parameterize the program.<a class="headerlink" href="#alternate-extract-the-givens-to-parameterize-the-program" title="Permalink to this headline">¶</a></h3>
|
||||
<p>Working backwards:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="n">B</span><span class="p">]</span> <span class="p">[</span><span class="n">uncons</span> <span class="p">[</span><span class="n">N</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="p">[</span><span class="nb">map</span> <span class="n">C</span><span class="p">]</span> <span class="n">genrec</span>
|
||||
@@ -143,32 +144,32 @@ the desired outcome.</p>
|
||||
<span class="o">^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="define-treestep">
|
||||
</section>
|
||||
</section>
|
||||
<section id="define-treestep">
|
||||
<h2>Define <code class="docutils literal notranslate"><span class="pre">treestep</span></code><a class="headerlink" href="#define-treestep" title="Permalink to this headline">¶</a></h2>
|
||||
<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="p">,</span> <span class="n">DefinitionWrapper</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from notebook_preamble import D, J, V, define, DefinitionWrapper
|
||||
</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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>DefinitionWrapper.add_definitions('''
|
||||
|
||||
<span class="s1"> _treestep_0 == [[not] swap] dip</span>
|
||||
<span class="s1"> _treestep_1 == [dip] cons [uncons] swoncat</span>
|
||||
<span class="s1"> treegrind == [_treestep_1 _treestep_0] dip genrec</span>
|
||||
<span class="s1"> treestep == [map] swoncat treegrind</span>
|
||||
_treestep_0 == [[not] swap] dip
|
||||
_treestep_1 == [dip] cons [uncons] swoncat
|
||||
treegrind == [_treestep_1 _treestep_0] dip genrec
|
||||
treestep == [map] swoncat treegrind
|
||||
|
||||
<span class="s1">'''</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
|
||||
''', D)
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="examples">
|
||||
</section>
|
||||
<section id="examples">
|
||||
<h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
|
||||
<p>Consider trees, the nodes of which are integers. We can find the sum of
|
||||
all nodes in a tree with this function:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">sumtree</span> <span class="o">==</span> <span class="p">[</span><span class="n">pop</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[</span><span class="nb">sum</span> <span class="o">+</span><span class="p">]</span> <span class="n">treestep</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">'sumtree == [pop 0] [] [sum +] treestep'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define('sumtree == [pop 0] [] [sum +] treestep')
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Running this function on an empty tree value gives zero:</p>
|
||||
@@ -177,7 +178,7 @@ all nodes in a tree with this function:</p>
|
||||
<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">'[] sumtree'</span><span class="p">)</span> <span class="c1"># Empty tree.</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[] sumtree') # Empty tree.
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">0</span>
|
||||
@@ -191,68 +192,68 @@ all nodes in a tree with this function:</p>
|
||||
<span class="n">n</span><span class="o">+</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">J</span><span class="p">(</span><span class="s1">'[23] sumtree'</span><span class="p">)</span> <span class="c1"># No child trees.</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[23] sumtree') # No child trees.
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">23</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 []] sumtree'</span><span class="p">)</span> <span class="c1"># Child tree, empty.</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[23 []] sumtree') # Child tree, empty.
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">23</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 [2 [4]] [3]] sumtree'</span><span class="p">)</span> <span class="c1"># Non-empty child trees.</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[23 [2 [4]] [3]] sumtree') # Non-empty child trees.
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">32</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 [2 [8] [9]] [3] [4 []]] sumtree'</span><span class="p">)</span> <span class="c1"># Etc...</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[23 [2 [8] [9]] [3] [4 []]] sumtree') # Etc...
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">49</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 [2 [8] [9]] [3] [4 []]] [pop 0] [] [cons sum] treestep'</span><span class="p">)</span> <span class="c1"># Alternate "spelling".</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[23 [2 [8] [9]] [3] [4 []]] [pop 0] [] [cons sum] treestep') # Alternate "spelling".
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">49</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 [2 [8] [9]] [3] [4 []]] [] [pop 23] [cons] treestep'</span><span class="p">)</span> <span class="c1"># Replace each node.</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[23 [2 [8] [9]] [3] [4 []]] [] [pop 23] [cons] treestep') # Replace each node.
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="mi">23</span> <span class="p">[</span><span class="mi">23</span> <span class="p">[</span><span class="mi">23</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</span><span class="p">]]</span> <span class="p">[</span><span class="mi">23</span><span class="p">]</span> <span class="p">[</span><span class="mi">23</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 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep')
|
||||
</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">1</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</span><span class="mi">1</span><span class="p">]]</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="p">[</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">'[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep sumtree'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[23 [2 [8] [9]] [3] [4 []]] [] [pop 1] [cons] treestep sumtree')
|
||||
</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">'[23 [2 [8] [9]] [3] [4 []]] [pop 0] [pop 1] [sum +] treestep'</span><span class="p">)</span> <span class="c1"># Combine replace and sum into one function.</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[23 [2 [8] [9]] [3] [4 []]] [pop 0] [pop 1] [sum +] treestep') # Combine replace and sum into one function.
|
||||
</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">'[4 [3 [] [7]]] [pop 0] [pop 1] [sum +] treestep'</span><span class="p">)</span> <span class="c1"># Combine replace and sum into one function.</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[4 [3 [] [7]]] [pop 0] [pop 1] [sum +] treestep') # Combine replace and sum into one function.
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="redefining-the-ordered-binary-tree-in-terms-of-treestep">
|
||||
</section>
|
||||
<section id="redefining-the-ordered-binary-tree-in-terms-of-treestep">
|
||||
<h2>Redefining the Ordered Binary Tree in terms of <code class="docutils literal notranslate"><span class="pre">treestep</span></code>.<a class="headerlink" href="#redefining-the-ordered-binary-tree-in-terms-of-treestep" title="Permalink to this headline">¶</a></h2>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Tree</span> <span class="o">=</span> <span class="p">[]</span> <span class="o">|</span> <span class="p">[[</span><span class="n">key</span> <span class="n">value</span><span class="p">]</span> <span class="n">left</span> <span class="n">right</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
@@ -266,7 +267,7 @@ all nodes in a tree with this function:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">key</span> <span class="n">value</span><span class="p">]</span> <span class="n">N</span> <span class="p">[</span><span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">K</span><span class="p">]</span> <span class="nb">map</span> <span class="n">C</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="section" id="traversal">
|
||||
<section id="traversal">
|
||||
<h3>Traversal<a class="headerlink" href="#traversal" 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">key</span> <span class="n">value</span><span class="p">]</span> <span class="n">first</span> <span class="p">[</span><span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">K</span><span class="p">]</span> <span class="nb">map</span> <span class="n">i</span>
|
||||
<span class="n">key</span> <span class="p">[</span><span class="n">value</span><span class="p">]</span> <span class="p">[</span><span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">K</span><span class="p">]</span> <span class="nb">map</span> <span class="n">i</span>
|
||||
@@ -276,7 +277,7 @@ all nodes in a tree with this function:</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>This doesn’t quite work:</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">'[[3 0] [[2 0] [][]] [[9 0] [[5 0] [[4 0] [][]] [[8 0] [[6 0] [] [[7 0] [][]]][]]][]]] ["B"] [first] [i] treestep'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[[3 0] [[2 0] [][]] [[9 0] [[5 0] [[4 0] [][]] [[8 0] [[6 0] [] [[7 0] [][]]][]]][]]] ["B"] [first] [i] treestep')
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">3</span> <span class="s1">'B'</span> <span class="s1">'B'</span>
|
||||
@@ -298,15 +299,15 @@ depositing our results directly on the stack.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[]</span> <span class="p">[</span><span class="n">first</span><span class="p">]</span> <span class="p">[</span><span class="n">flatten</span> <span class="n">cons</span><span class="p">]</span> <span class="n">treestep</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] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [first] [flatten cons] treestep'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [first] [flatten cons] treestep')
|
||||
</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">2</span> <span class="mi">9</span> <span class="mi">5</span> <span class="mi">4</span> <span class="mi">8</span> <span class="mi">6</span> <span class="mi">7</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>There we go.</p>
|
||||
</div>
|
||||
<div class="section" id="in-order-traversal">
|
||||
</section>
|
||||
<section id="in-order-traversal">
|
||||
<h3>In-order traversal<a class="headerlink" href="#in-order-traversal" title="Permalink to this headline">¶</a></h3>
|
||||
<p>From here:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">key</span> <span class="p">[[</span><span class="n">lk</span><span class="p">]</span> <span class="p">[</span><span class="n">rk</span><span class="p">]]</span> <span class="n">C</span>
|
||||
@@ -321,15 +322,15 @@ depositing our results directly on the stack.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[]</span> <span class="p">[</span><span class="n">i</span> <span class="n">roll</span><span class="o"><</span> <span class="n">swons</span> <span class="n">concat</span><span class="p">]</span> <span class="p">[</span><span class="n">first</span><span class="p">]</span> <span class="n">treestep</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] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [uncons pop] [i roll< swons concat] treestep'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [uncons pop] [i roll< swons concat] treestep')
|
||||
</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">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">8</span> <span class="mi">9</span><span class="p">]</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="with-treegrind">
|
||||
</section>
|
||||
</section>
|
||||
<section id="with-treegrind">
|
||||
<h2>With <code class="docutils literal notranslate"><span class="pre">treegrind</span></code>?<a class="headerlink" href="#with-treegrind" title="Permalink to this headline">¶</a></h2>
|
||||
<p>The <code class="docutils literal notranslate"><span class="pre">treegrind</span></code> function doesn’t include the <code class="docutils literal notranslate"><span class="pre">map</span></code> combinator, so
|
||||
the <code class="docutils literal notranslate"><span class="pre">[C]</span></code> function must arrange to use some combinator on the quoted
|
||||
@@ -342,38 +343,38 @@ non-empty node is:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">key</span> <span class="n">value</span><span class="p">]</span> <span class="n">N</span> <span class="p">[</span><span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">K</span><span class="p">]</span> <span class="n">C</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">'[["key" "value"] ["left"] ["right"] ] ["B"] ["N"] ["C"] treegrind'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[["key" "value"] ["left"] ["right"] ] ["B"] ["N"] ["C"] treegrind')
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="s1">'key'</span> <span class="s1">'value'</span><span class="p">]</span> <span class="s1">'N'</span> <span class="p">[[</span><span class="s1">'left'</span><span class="p">]</span> <span class="p">[</span><span class="s1">'right'</span><span class="p">]]</span> <span class="p">[[</span><span class="ow">not</span><span class="p">]</span> <span class="p">[</span><span class="s1">'B'</span><span class="p">]</span> <span class="p">[</span><span class="n">uncons</span> <span class="p">[</span><span class="s1">'N'</span><span class="p">]</span> <span class="n">dip</span><span class="p">]</span> <span class="p">[</span><span class="s1">'C'</span><span class="p">]</span> <span class="n">genrec</span><span class="p">]</span> <span class="s1">'C'</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="treegrind-with-step">
|
||||
</section>
|
||||
<section id="treegrind-with-step">
|
||||
<h2><code class="docutils literal notranslate"><span class="pre">treegrind</span></code> with <code class="docutils literal notranslate"><span class="pre">step</span></code><a class="headerlink" href="#treegrind-with-step" title="Permalink to this headline">¶</a></h2>
|
||||
<p>Iteration through the nodes</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">'[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] ["N"] [step] treegrind'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] ["N"] [step] treegrind')
|
||||
</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">0</span><span class="p">]</span> <span class="s1">'N'</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">'N'</span> <span class="p">[</span><span class="mi">9</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">'N'</span> <span class="p">[</span><span class="mi">5</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">'N'</span> <span class="p">[</span><span class="mi">4</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">'N'</span> <span class="p">[</span><span class="mi">8</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">'N'</span> <span class="p">[</span><span class="mi">6</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">'N'</span> <span class="p">[</span><span class="mi">7</span> <span class="mi">0</span><span class="p">]</span> <span class="s1">'N'</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Sum the nodes’ keys.</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">'0 [[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] [first +] [step] treegrind'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('0 [[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [pop] [first +] [step] treegrind')
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mi">44</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Rebuild the tree using <code class="docutils literal notranslate"><span class="pre">map</span></code> (imitating <code class="docutils literal notranslate"><span class="pre">treestep</span></code>.)</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">'[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [[100 +] infra] [map cons] treegrind'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[[3 0] [[2 0] [] []] [[9 0] [[5 0] [[4 0] [] []] [[8 0] [[6 0] [] [[7 0] [] []]] []]] []]] [] [[100 +] infra] [map cons] treegrind')
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[[</span><span class="mi">103</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[[</span><span class="mi">102</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[[</span><span class="mi">109</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[[</span><span class="mi">105</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[[</span><span class="mi">104</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[]]</span> <span class="p">[[</span><span class="mi">108</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[[</span><span class="mi">106</span> <span class="mi">0</span><span class="p">]</span> <span class="p">[]</span> <span class="p">[[</span><span class="mi">107</span> <span class="mi">0</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="do-we-have-the-flexibility-to-reimplement-tree-get">
|
||||
</section>
|
||||
<section id="do-we-have-the-flexibility-to-reimplement-tree-get">
|
||||
<h2>Do we have the flexibility to reimplement <code class="docutils literal notranslate"><span class="pre">Tree-get</span></code>?<a class="headerlink" href="#do-we-have-the-flexibility-to-reimplement-tree-get" title="Permalink to this headline">¶</a></h2>
|
||||
<p>I think we do:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">B</span><span class="p">]</span> <span class="p">[</span><span class="n">N</span><span class="p">]</span> <span class="p">[</span><span class="n">C</span><span class="p">]</span> <span class="n">treegrind</span>
|
||||
@@ -389,12 +390,12 @@ user defined, and the per-node function is just the query key literal:</p>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Let’s try <code class="docutils literal notranslate"><span class="pre">cmp</span></code>:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">C</span> <span class="o">==</span> <span class="n">P</span> <span class="p">[</span><span class="n">T</span><span class="o">></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">T</span><span class="o"><</span><span class="p">]</span> <span class="nb">cmp</span>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">C</span> <span class="o">==</span> <span class="n">P</span> <span class="p">[</span><span class="n">T</span><span class="o">></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">T</span><span class="o"><</span><span class="p">]</span> <span class="n">cmp</span>
|
||||
|
||||
<span class="p">[</span><span class="n">key</span> <span class="n">value</span><span class="p">]</span> <span class="n">query_key</span> <span class="p">[</span><span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">K</span><span class="p">]</span> <span class="n">P</span> <span class="p">[</span><span class="n">T</span><span class="o">></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">T</span><span class="o"><</span><span class="p">]</span> <span class="nb">cmp</span>
|
||||
<span class="p">[</span><span class="n">key</span> <span class="n">value</span><span class="p">]</span> <span class="n">query_key</span> <span class="p">[</span><span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">K</span><span class="p">]</span> <span class="n">P</span> <span class="p">[</span><span class="n">T</span><span class="o">></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">T</span><span class="o"><</span><span class="p">]</span> <span class="n">cmp</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="section" id="the-predicate-p">
|
||||
<section id="the-predicate-p">
|
||||
<h3>The predicate <code class="docutils literal notranslate"><span class="pre">P</span></code><a class="headerlink" href="#the-predicate-p" title="Permalink to this headline">¶</a></h3>
|
||||
<p>Seems pretty easy (we must preserve the value in case the keys are
|
||||
equal):</p>
|
||||
@@ -412,7 +413,7 @@ equal):</p>
|
||||
</div>
|
||||
<p>(Possibly with a swap at the end? Or just swap <code class="docutils literal notranslate"><span class="pre">T<</span></code> and <code class="docutils literal notranslate"><span class="pre">T></span></code>.)</p>
|
||||
<p>So now:</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">K</span><span class="p">]</span> <span class="p">[</span><span class="n">value</span><span class="p">]</span> <span class="n">key</span> <span class="n">query_key</span> <span class="p">[</span><span class="n">T</span><span class="o">></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">T</span><span class="o"><</span><span class="p">]</span> <span class="nb">cmp</span>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[</span><span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">K</span><span class="p">]</span> <span class="p">[</span><span class="n">value</span><span class="p">]</span> <span class="n">key</span> <span class="n">query_key</span> <span class="p">[</span><span class="n">T</span><span class="o">></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">T</span><span class="o"><</span><span class="p">]</span> <span class="n">cmp</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Becomes one of these three:</p>
|
||||
@@ -421,105 +422,118 @@ equal):</p>
|
||||
<span class="p">[</span><span class="n">left</span> <span class="n">right</span><span class="p">]</span> <span class="p">[</span><span class="n">K</span><span class="p">]</span> <span class="p">[</span><span class="n">value</span><span class="p">]</span> <span class="n">T</span><span class="o"><</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="e">
|
||||
</section>
|
||||
<section id="e">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">E</span></code><a class="headerlink" href="#e" title="Permalink to this headline">¶</a></h3>
|
||||
<p>Easy.</p>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">E</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="t-and-t">
|
||||
</section>
|
||||
<section id="t-and-t">
|
||||
<h3><code class="docutils literal notranslate"><span class="pre">T<</span></code> and <code class="docutils literal notranslate"><span class="pre">T></span></code><a class="headerlink" href="#t-and-t" title="Permalink to this headline">¶</a></h3>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">T</span><span class="o"><</span> <span class="o">==</span> <span class="n">pop</span> <span class="p">[</span><span class="n">first</span><span class="p">]</span> <span class="n">dip</span> <span class="n">i</span>
|
||||
<span class="n">T</span><span class="o">></span> <span class="o">==</span> <span class="n">pop</span> <span class="p">[</span><span class="n">second</span><span class="p">]</span> <span class="n">dip</span> <span class="n">i</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="putting-it-together">
|
||||
</section>
|
||||
</section>
|
||||
<section id="putting-it-together">
|
||||
<h2>Putting it together<a class="headerlink" href="#putting-it-together" title="Permalink to this headline">¶</a></h2>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">T</span><span class="o">></span> <span class="o">==</span> <span class="n">pop</span> <span class="p">[</span><span class="n">first</span><span class="p">]</span> <span class="n">dip</span> <span class="n">i</span>
|
||||
<span class="n">T</span><span class="o"><</span> <span class="o">==</span> <span class="n">pop</span> <span class="p">[</span><span class="n">second</span><span class="p">]</span> <span class="n">dip</span> <span class="n">i</span>
|
||||
<span class="n">E</span> <span class="o">==</span> <span class="n">roll</span><span class="o">></span> <span class="n">popop</span> <span class="n">first</span>
|
||||
<span class="n">P</span> <span class="o">==</span> <span class="n">roll</span><span class="o"><</span> <span class="p">[</span><span class="n">roll</span><span class="o"><</span> <span class="n">uncons</span> <span class="n">swap</span><span class="p">]</span> <span class="n">dip</span>
|
||||
|
||||
<span class="n">Tree</span><span class="o">-</span><span class="n">get</span> <span class="o">==</span> <span class="p">[</span><span class="n">P</span> <span class="p">[</span><span class="n">T</span><span class="o">></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">T</span><span class="o"><</span><span class="p">]</span> <span class="nb">cmp</span><span class="p">]</span> <span class="n">treegrind</span>
|
||||
<span class="n">Tree</span><span class="o">-</span><span class="n">get</span> <span class="o">==</span> <span class="p">[</span><span class="n">P</span> <span class="p">[</span><span class="n">T</span><span class="o">></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">T</span><span class="o"><</span><span class="p">]</span> <span class="n">cmp</span><span class="p">]</span> <span class="n">treegrind</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>To me, that seems simpler than the <code class="docutils literal notranslate"><span class="pre">genrec</span></code> version.</p>
|
||||
<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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>DefinitionWrapper.add_definitions('''
|
||||
|
||||
<span class="s1"> T> == pop [first] dip i</span>
|
||||
<span class="s1"> T< == pop [second] dip i</span>
|
||||
<span class="s1"> E == roll> popop first</span>
|
||||
<span class="s1"> P == roll< [roll< uncons swap] dip</span>
|
||||
T> == pop [first] dip i
|
||||
T< == pop [second] dip i
|
||||
E == roll> popop first
|
||||
P == roll< [roll< uncons swap] dip
|
||||
|
||||
<span class="s1"> Tree-get == [P [T>] [E] [T<] cmp] treegrind</span>
|
||||
Tree-get == [P [T>] [E] [T<] cmp] treegrind
|
||||
|
||||
<span class="s1">'''</span><span class="p">,</span> <span class="n">D</span><span class="p">)</span>
|
||||
''', D)
|
||||
</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="se">\</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('''\
|
||||
|
||||
<span class="s1">[[3 13] [[2 12] [] []] [[9 19] [[5 15] [[4 14] [] []] [[8 18] [[6 16] [] [[7 17] [] []]] []]] []]]</span>
|
||||
[[3 13] [[2 12] [] []] [[9 19] [[5 15] [[4 14] [] []] [[8 18] [[6 16] [] [[7 17] [] []]] []]] []]]
|
||||
|
||||
<span class="s1">[] [5] Tree-get</span>
|
||||
[] [5] Tree-get
|
||||
|
||||
<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">15</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="se">\</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('''\
|
||||
|
||||
<span class="s1">[[3 13] [[2 12] [] []] [[9 19] [[5 15] [[4 14] [] []] [[8 18] [[6 16] [] [[7 17] [] []]] []]] []]]</span>
|
||||
[[3 13] [[2 12] [] []] [[9 19] [[5 15] [[4 14] [] []] [[8 18] [[6 16] [] [[7 17] [] []]] []]] []]]
|
||||
|
||||
<span class="s1">[pop "nope"] [25] Tree-get</span>
|
||||
[pop "nope"] [25] Tree-get
|
||||
|
||||
<span class="s1">'''</span><span class="p">)</span>
|
||||
''')
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">'nope'</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
|
||||
</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="#">Treating Trees II: <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a><ul>
|
||||
<li><a class="reference internal" href="#derive-the-recursive-function">Derive the recursive function.</a></li>
|
||||
<li><a class="reference internal" href="#extract-the-givens-to-parameterize-the-program">Extract the givens to parameterize the program.</a><ul>
|
||||
<li><a class="reference internal" href="#alternate-extract-the-givens-to-parameterize-the-program">(alternate) Extract the givens to parameterize the program.</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a class="reference internal" href="#define-treestep">Define <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a></li>
|
||||
<li><a class="reference internal" href="#examples">Examples</a></li>
|
||||
<li><a class="reference internal" href="#redefining-the-ordered-binary-tree-in-terms-of-treestep">Redefining the Ordered Binary Tree in terms of <code class="docutils literal notranslate"><span class="pre">treestep</span></code>.</a><ul>
|
||||
<li><a class="reference internal" href="#traversal">Traversal</a></li>
|
||||
<li><a class="reference internal" href="#in-order-traversal">In-order traversal</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a class="reference internal" href="#with-treegrind">With <code class="docutils literal notranslate"><span class="pre">treegrind</span></code>?</a></li>
|
||||
<li><a class="reference internal" href="#treegrind-with-step"><code class="docutils literal notranslate"><span class="pre">treegrind</span></code> with <code class="docutils literal notranslate"><span class="pre">step</span></code></a></li>
|
||||
<li><a class="reference internal" href="#do-we-have-the-flexibility-to-reimplement-tree-get">Do we have the flexibility to reimplement <code class="docutils literal notranslate"><span class="pre">Tree-get</span></code>?</a><ul>
|
||||
<li><a class="reference internal" href="#the-predicate-p">The predicate <code class="docutils literal notranslate"><span class="pre">P</span></code></a></li>
|
||||
<li><a class="reference internal" href="#e"><code class="docutils literal notranslate"><span class="pre">E</span></code></a></li>
|
||||
<li><a class="reference internal" href="#t-and-t"><code class="docutils literal notranslate"><span class="pre">T<</span></code> and <code class="docutils literal notranslate"><span class="pre">T></span></code></a></li>
|
||||
</ul>
|
||||
</li>
|
||||
<li><a class="reference internal" href="#putting-it-together">Putting it together</a></li>
|
||||
<h1 class="logo"><a href="../index.html">Thun</a></h1>
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
<h3>Navigation</h3>
|
||||
<ul class="current">
|
||||
<li class="toctree-l1"><a class="reference internal" href="Intro.html">Thun: Joy in Python</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../joy.html">Joy Interpreter</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../stack.html">Stack or Quote or Sequence or List…</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../parser.html">Parsing Text into Joy Expressions</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../pretty.html">Tracing Joy Execution</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../library.html">Function Reference</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../lib.html">Functions Grouped by, er, Function with Examples</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../types.html">Type Inference of Joy Expressions</a></li>
|
||||
<li class="toctree-l1 current"><a class="reference internal" href="index.html">Essays about Programming in Joy</a><ul class="current">
|
||||
<li class="toctree-l2"><a class="reference internal" href="Developing.html">Developing a Program in Joy</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Quadratic.html">Quadratic formula</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Replacing.html">Replacing Functions in the Dictionary</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Recursion_Combinators.html">Recursion Combinators</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Ordered_Binary_Trees.html">Treating Trees I: Ordered Binary Trees</a></li>
|
||||
<li class="toctree-l2 current"><a class="current reference internal" href="#">Treating Trees II: <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html">Newton’s method</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Zipper.html">Traversing Datastructures with Zippers</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Types.html">The Blissful Elegance of Typing Joy</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="TypeChecking.html">Type Checking</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="NoUpdates.html">No Updates</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Categorical.html">Categorical Programming</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="The_Four_Operations.html">The Four Fundamental Operations of Definite Action</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html">∂RE</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
|
||||
<div class="relations">
|
||||
<h3>Related Topics</h3>
|
||||
<ul>
|
||||
@@ -531,25 +545,24 @@ equal):</p>
|
||||
</ul></li>
|
||||
</ul>
|
||||
</div>
|
||||
<div role="note" aria-label="source link">
|
||||
<h3>This Page</h3>
|
||||
<ul class="this-page-menu">
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<li><a href="../_sources/notebooks/Treestep.rst.txt"
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rel="nofollow">Show Source</a></li>
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</ul>
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</div>
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<div id="searchbox" style="display: none" role="search">
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<h3>Quick search</h3>
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<h3 id="searchlabel">Quick search</h3>
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<div class="searchformwrapper">
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<form class="search" action="../search.html" method="get">
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<input type="text" name="q" aria-labelledby="searchlabel" autocomplete="off" autocorrect="off" autocapitalize="off" spellcheck="false"/>
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||||
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|
||||
</div>
|
||||
<div class="clearer"></div>
|
||||
@@ -560,7 +573,7 @@ equal):</p>
|
||||
</a>
|
||||
<br />
|
||||
<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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Created using <a href="http://sphinx-doc.org/">Sphinx</a> 4.3.0.
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</body>
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@@ -1,19 +1,18 @@
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
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<meta charset="utf-8" />
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<meta name="viewport" content="width=device-width, initial-scale=1.0" /><meta name="generator" content="Docutils 0.17.1: http://docutils.sourceforge.net/" />
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<title>Type Checking — Thun 0.4.1 documentation</title>
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<link rel="stylesheet" href="../_static/alabaster.css" type="text/css" />
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<link rel="search" title="Search" href="../search.html" />
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<link rel="next" title="No Updates" href="NoUpdates.html" />
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@@ -30,37 +29,39 @@
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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="type-checking">
|
||||
<section id="type-checking">
|
||||
<h1>Type Checking<a class="headerlink" href="#type-checking" 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">logging</span><span class="o">,</span> <span class="nn">sys</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>import logging, sys
|
||||
|
||||
<span class="n">logging</span><span class="o">.</span><span class="n">basicConfig</span><span class="p">(</span>
|
||||
<span class="nb">format</span><span class="o">=</span><span class="s1">'</span><span class="si">%(message)s</span><span class="s1">'</span><span class="p">,</span>
|
||||
<span class="n">stream</span><span class="o">=</span><span class="n">sys</span><span class="o">.</span><span class="n">stdout</span><span class="p">,</span>
|
||||
<span class="n">level</span><span class="o">=</span><span class="n">logging</span><span class="o">.</span><span class="n">INFO</span><span class="p">,</span>
|
||||
<span class="p">)</span>
|
||||
logging.basicConfig(
|
||||
format='%(message)s',
|
||||
stream=sys.stdout,
|
||||
level=logging.INFO,
|
||||
)
|
||||
</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.utils.types</span> <span class="k">import</span> <span class="p">(</span>
|
||||
<span class="n">doc_from_stack_effect</span><span class="p">,</span>
|
||||
<span class="n">infer</span><span class="p">,</span>
|
||||
<span class="n">reify</span><span class="p">,</span>
|
||||
<span class="n">unify</span><span class="p">,</span>
|
||||
<span class="n">FUNCTIONS</span><span class="p">,</span>
|
||||
<span class="n">JoyTypeError</span><span class="p">,</span>
|
||||
<span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from joy.utils.types import (
|
||||
doc_from_stack_effect,
|
||||
infer,
|
||||
reify,
|
||||
unify,
|
||||
FUNCTIONS,
|
||||
JoyTypeError,
|
||||
)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">D</span> <span class="o">=</span> <span class="n">FUNCTIONS</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
|
||||
<span class="k">del</span> <span class="n">D</span><span class="p">[</span><span class="s1">'product'</span><span class="p">]</span>
|
||||
<span class="nb">globals</span><span class="p">()</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">D</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>D = FUNCTIONS.copy()
|
||||
del D['product']
|
||||
globals().update(D)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="section" id="an-example">
|
||||
<section id="an-example">
|
||||
<h2>An Example<a class="headerlink" href="#an-example" title="Permalink to this headline">¶</a></h2>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span> <span class="o">=</span> <span class="n">infer</span><span class="p">(</span><span class="n">pop</span><span class="p">,</span> <span class="n">swap</span><span class="p">,</span> <span class="n">rolldown</span><span class="p">,</span> <span class="n">rrest</span><span class="p">,</span> <span class="n">ccons</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>fi, fo = infer(pop, swap, rolldown, rrest, ccons)[0]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>25 (--) ∘ pop swap rolldown rrest ccons
|
||||
@@ -71,61 +72,61 @@
|
||||
40 ([a4 a5 ...1] a3 a2 a1 -- [a2 a3 ...1]) ∘
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>print doc_from_stack_effect(fi, fo)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">([</span><span class="n">a4</span> <span class="n">a5</span> <span class="o">...</span><span class="mi">1</span><span class="p">]</span> <span class="n">a3</span> <span class="n">a2</span> <span class="n">a1</span> <span class="o">--</span> <span class="p">[</span><span class="n">a2</span> <span class="n">a3</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="kn">from</span> <span class="nn">joy.parser</span> <span class="k">import</span> <span class="n">text_to_expression</span>
|
||||
<span class="kn">from</span> <span class="nn">joy.utils.stack</span> <span class="k">import</span> <span class="n">stack_to_string</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from joy.parser import text_to_expression
|
||||
from joy.utils.stack import stack_to_string
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">'0 1 2 [3 4]'</span><span class="p">)</span> <span class="c1"># reverse order</span>
|
||||
<span class="nb">print</span> <span class="n">stack_to_string</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>e = text_to_expression('0 1 2 [3 4]') # reverse order
|
||||
print stack_to_string(e)
|
||||
</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">4</span><span class="p">]</span> <span class="mi">2</span> <span class="mi">1</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">u</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">fi</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
|
||||
<span class="n">u</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>u = unify(e, fi)[0]
|
||||
u
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="n">a1</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">a2</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">a3</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="n">a4</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span> <span class="n">a5</span><span class="p">:</span> <span class="mi">4</span><span class="p">,</span> <span class="n">s2</span><span class="p">:</span> <span class="p">(),</span> <span class="n">s1</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">g</span> <span class="o">=</span> <span class="n">reify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">))</span>
|
||||
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">g</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>g = reify(u, (fi, fo))
|
||||
print doc_from_stack_effect(*g)
|
||||
</pre></div>
|
||||
</div>
|
||||
<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">3</span> <span class="mi">4</span> <span class="p">]</span> <span class="mi">2</span> <span class="mi">1</span> <span class="mi">0</span> <span class="o">--</span> <span class="o">...</span> <span class="p">[</span><span class="mi">1</span> <span class="mi">2</span> <span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="unification-works-in-reverse">
|
||||
</section>
|
||||
<section id="unification-works-in-reverse">
|
||||
<h2>Unification Works “in Reverse”<a class="headerlink" href="#unification-works-in-reverse" title="Permalink to this headline">¶</a></h2>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">'[2 3]'</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>e = text_to_expression('[2 3]')
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">u</span> <span class="o">=</span> <span class="n">unify</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">fo</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span> <span class="c1"># output side, not input side</span>
|
||||
<span class="n">u</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>u = unify(e, fo)[0] # output side, not input side
|
||||
u
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">{</span><span class="n">a2</span><span class="p">:</span> <span class="mi">2</span><span class="p">,</span> <span class="n">a3</span><span class="p">:</span> <span class="mi">3</span><span class="p">,</span> <span class="n">s2</span><span class="p">:</span> <span class="p">(),</span> <span class="n">s1</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">g</span> <span class="o">=</span> <span class="n">reify</span><span class="p">(</span><span class="n">u</span><span class="p">,</span> <span class="p">(</span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span><span class="p">))</span>
|
||||
<span class="nb">print</span> <span class="n">doc_from_stack_effect</span><span class="p">(</span><span class="o">*</span><span class="n">g</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>g = reify(u, (fi, fo))
|
||||
print doc_from_stack_effect(*g)
|
||||
</pre></div>
|
||||
</div>
|
||||
<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">a4</span> <span class="n">a5</span> <span class="p">]</span> <span class="mi">3</span> <span class="mi">2</span> <span class="n">a1</span> <span class="o">--</span> <span class="o">...</span> <span class="p">[</span><span class="mi">2</span> <span class="mi">3</span> <span class="p">])</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
<div class="section" id="failing-a-check">
|
||||
</section>
|
||||
<section id="failing-a-check">
|
||||
<h2>Failing a Check<a class="headerlink" href="#failing-a-check" title="Permalink to this headline">¶</a></h2>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">fi</span><span class="p">,</span> <span class="n">fo</span> <span class="o">=</span> <span class="n">infer</span><span class="p">(</span><span class="n">dup</span><span class="p">,</span> <span class="n">mul</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>fi, fo = infer(dup, mul)[0]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>25 (--) ∘ dup mul
|
||||
@@ -134,40 +135,71 @@
|
||||
31 (i1 -- i2) ∘
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">e</span> <span class="o">=</span> <span class="n">text_to_expression</span><span class="p">(</span><span class="s1">'"two"'</span><span class="p">)</span>
|
||||
<span class="nb">print</span> <span class="n">stack_to_string</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>e = text_to_expression('"two"')
|
||||
print stack_to_string(e)
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="s1">'two'</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="k">try</span><span class="p">:</span>
|
||||
<span class="n">unify</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">fi</span><span class="p">)</span>
|
||||
<span class="k">except</span> <span class="n">JoyTypeError</span><span class="p">,</span> <span class="n">err</span><span class="p">:</span>
|
||||
<span class="nb">print</span> <span class="n">err</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>try:
|
||||
unify(e, fi)
|
||||
except JoyTypeError, err:
|
||||
print err
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Cannot</span> <span class="n">unify</span> <span class="s1">'two'</span> <span class="ow">and</span> <span class="n">f1</span><span class="o">.</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
|
||||
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|
||||
|
||||
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|
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|
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|
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|
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<ul>
|
||||
<li><a class="reference internal" href="#">Type Checking</a><ul>
|
||||
<li><a class="reference internal" href="#an-example">An Example</a></li>
|
||||
<li><a class="reference internal" href="#unification-works-in-reverse">Unification Works “in Reverse”</a></li>
|
||||
<li><a class="reference internal" href="#failing-a-check">Failing a Check</a></li>
|
||||
<h1 class="logo"><a href="../index.html">Thun</a></h1>
|
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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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|
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|
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|
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|
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<li class="toctree-l2"><a class="reference internal" href="Quadratic.html">Quadratic formula</a></li>
|
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<li class="toctree-l2"><a class="reference internal" href="Replacing.html">Replacing Functions in the Dictionary</a></li>
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|
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<li class="toctree-l2"><a class="reference internal" href="Ordered_Binary_Trees.html">Treating Trees I: Ordered Binary Trees</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Treestep.html">Treating Trees II: <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html">Newton’s method</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Zipper.html">Traversing Datastructures with Zippers</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Types.html">The Blissful Elegance of Typing Joy</a></li>
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|
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<li class="toctree-l2"><a class="reference internal" href="NoUpdates.html">No Updates</a></li>
|
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<li class="toctree-l2"><a class="reference internal" href="Categorical.html">Categorical Programming</a></li>
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<li class="toctree-l2"><a class="reference internal" href="The_Four_Operations.html">The Four Fundamental Operations of Definite Action</a></li>
|
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<li class="toctree-l2"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html">∂RE</a></li>
|
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|
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|
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|
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<div class="clearer"></div>
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@@ -208,7 +239,7 @@
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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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File diff suppressed because it is too large
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@@ -30,9 +29,11 @@
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<div class="document">
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<div class="documentwrapper">
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<div class="body" role="main">
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<div class="section" id="traversing-datastructures-with-zippers">
|
||||
<section id="traversing-datastructures-with-zippers">
|
||||
<h1>Traversing Datastructures with Zippers<a class="headerlink" href="#traversing-datastructures-with-zippers" title="Permalink to this headline">¶</a></h1>
|
||||
<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
|
||||
@@ -41,24 +42,24 @@ the original paper: <a class="reference external" href="https://www.st.cs.uni-sa
|
||||
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="code ipython2 highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">notebook_preamble</span> <span class="k">import</span> <span class="n">J</span><span class="p">,</span> <span class="n">V</span><span class="p">,</span> <span class="n">define</span>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>from notebook_preamble import J, V, define
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="section" id="trees">
|
||||
<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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[1 [2 [3 4 25 6] 7] 8]')
|
||||
</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">
|
||||
</section>
|
||||
<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
|
||||
@@ -74,13 +75,13 @@ datastructure used to keep track of these items is the zipper.)</p>
|
||||
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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define('z-down == [] swap uncons swap')
|
||||
define('z-up == swons swap shunt')
|
||||
define('z-right == [swons] cons dip uncons swap')
|
||||
define('z-left == swons [uncons swap] dip swap')
|
||||
</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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V('[1 [2 [3 4 25 6] 7] 8] z-down')
|
||||
</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>
|
||||
@@ -92,7 +93,7 @@ but see below.</p>
|
||||
<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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V('[] [[2 [3 4 25 6] 7] 8] 1 z-right')
|
||||
</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>
|
||||
@@ -112,43 +113,43 @@ but see below.</p>
|
||||
<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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[1] [8] [2 [3 4 25 6] 7] z-down')
|
||||
</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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[1] [8] [] [[3 4 25 6] 7] 2 z-right')
|
||||
</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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[1] [8] [2] [7] [3 4 25 6] z-down')
|
||||
</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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[1] [8] [2] [7] [] [4 25 6] 3 z-right')
|
||||
</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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[1] [8] [2] [7] [3] [25 6] 4 z-right')
|
||||
</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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[1] [8] [2] [7] [4 3] [6] 25 sqr')
|
||||
</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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V('[1] [8] [2] [7] [4 3] [6] 625 z-up')
|
||||
</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>
|
||||
@@ -167,24 +168,24 @@ but see below.</p>
|
||||
<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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[1] [8] [2] [7] [3 4 625 6] z-up')
|
||||
</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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[1] [8] [2 [3 4 625 6] 7] z-up')
|
||||
</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">
|
||||
</section>
|
||||
<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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V('[1 [2 [3 4 25 6] 7] 8] [[[[[[sqr] dipd] infra] dip] infra] dip] infra')
|
||||
</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>
|
||||
@@ -222,8 +223,8 @@ 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">
|
||||
</section>
|
||||
<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
|
||||
@@ -235,11 +236,11 @@ been embedded in a nested series of quoted programs, e.g.:</p>
|
||||
</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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>define('Z == [[] cons cons] step i')
|
||||
</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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>V('1 [2 3 4] Z')
|
||||
</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>
|
||||
@@ -272,14 +273,14 @@ been embedded in a nested series of quoted programs, e.g.:</p>
|
||||
</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>
|
||||
<div class="highlight-ipython2 notranslate"><div class="highlight"><pre><span></span>J('[1 [2 [3 4 25 6] 7] 8] [sqr] [dip dip infra dip infra dip infra] Z')
|
||||
</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">
|
||||
</section>
|
||||
<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>
|
||||
@@ -290,8 +291,8 @@ a string made from only two characters.</p>
|
||||
</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">
|
||||
</section>
|
||||
<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>
|
||||
@@ -299,27 +300,55 @@ from the subject datastructure:</p>
|
||||
i d i d i d d Bingo!
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
|
||||
</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="#">Traversing Datastructures with Zippers</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>
|
||||
<h1 class="logo"><a href="../index.html">Thun</a></h1>
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
<h3>Navigation</h3>
|
||||
<ul class="current">
|
||||
<li class="toctree-l1"><a class="reference internal" href="Intro.html">Thun: Joy in Python</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../joy.html">Joy Interpreter</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../stack.html">Stack or Quote or Sequence or List…</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../parser.html">Parsing Text into Joy Expressions</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../pretty.html">Tracing Joy Execution</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../library.html">Function Reference</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../lib.html">Functions Grouped by, er, Function with Examples</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="../types.html">Type Inference of Joy Expressions</a></li>
|
||||
<li class="toctree-l1 current"><a class="reference internal" href="index.html">Essays about Programming in Joy</a><ul class="current">
|
||||
<li class="toctree-l2"><a class="reference internal" href="Developing.html">Developing a Program in Joy</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Quadratic.html">Quadratic formula</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Replacing.html">Replacing Functions in the Dictionary</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Recursion_Combinators.html">Recursion Combinators</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Ordered_Binary_Trees.html">Treating Trees I: Ordered Binary Trees</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Treestep.html">Treating Trees II: <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html">Newton’s method</a></li>
|
||||
<li class="toctree-l2 current"><a class="current reference internal" href="#">Traversing Datastructures with Zippers</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Types.html">The Blissful Elegance of Typing Joy</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="TypeChecking.html">Type Checking</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="NoUpdates.html">No Updates</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Categorical.html">Categorical Programming</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="The_Four_Operations.html">The Four Fundamental Operations of Definite Action</a></li>
|
||||
<li class="toctree-l2"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html">∂RE</a></li>
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
|
||||
<div class="relations">
|
||||
<h3>Related Topics</h3>
|
||||
<ul>
|
||||
@@ -331,25 +360,24 @@ i d i d i d d Bingo!
|
||||
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|
||||
</ul>
|
||||
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|
||||
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||||
<h3>This Page</h3>
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@@ -360,7 +388,7 @@ i d i d i d d Bingo!
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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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