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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>
<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>
<div class="toctree-wrapper compound">
<ul>
<li class="toctree-l1"><a class="reference internal" href="Developing.html">Developing a Program in Joy</a><ul>
<li class="toctree-l2"><a class="reference internal" href="Developing.html#project-euler-first-problem-multiples-of-3-and-5">Project Euler, first problem: “Multiples of 3 and 5”</a></li>
<li class="toctree-l2"><a class="reference internal" href="Developing.html#generator-version">Generator Version</a></li>
<li class="toctree-l2"><a class="reference internal" href="Developing.html#a-little-further-analysis-renders-iteration-unnecessary">A little further analysis renders iteration unnecessary.</a></li>
<li class="toctree-l2"><a class="reference internal" href="Developing.html#the-simplest-program">The Simplest Program</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="Quadratic.html">Quadratic formula</a><ul>
<li class="toctree-l2"><a class="reference internal" href="Quadratic.html#write-a-straightforward-program-with-variable-names">Write a straightforward program with variable names.</a></li>
<li class="toctree-l2"><a class="reference internal" href="Quadratic.html#derive-a-definition">Derive a definition.</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="Replacing.html">Replacing Functions in the Dictionary</a><ul>
<li class="toctree-l2"><a class="reference internal" href="Replacing.html#a-long-trace">A long trace</a></li>
<li class="toctree-l2"><a class="reference internal" href="Replacing.html#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 class="toctree-l2"><a class="reference internal" href="Replacing.html#a-shorter-trace">A shorter trace</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="Recursion_Combinators.html">Recursion Combinators</a><ul>
<li class="toctree-l2"><a class="reference internal" href="Recursion_Combinators.html#designing-recursive-functions">Designing Recursive Functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="Recursion_Combinators.html#primitive-recursive-functions">Primitive Recursive Functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="Recursion_Combinators.html#hylomorphism">Hylomorphism</a></li>
<li class="toctree-l2"><a class="reference internal" href="Recursion_Combinators.html#hylomorphism-in-joy">Hylomorphism in Joy</a></li>
<li class="toctree-l2"><a class="reference internal" href="Recursion_Combinators.html#derivation-of-hylomorphism-combinator">Derivation of <code class="docutils literal notranslate"><span class="pre">hylomorphism</span></code> combinator</a></li>
<li class="toctree-l2"><a class="reference internal" href="Recursion_Combinators.html#four-specializations">Four Specializations</a></li>
<li class="toctree-l2"><a class="reference internal" href="Recursion_Combinators.html#anamorphism">Anamorphism</a></li>
<li class="toctree-l2"><a class="reference internal" href="Recursion_Combinators.html#catamorphism">Catamorphism</a></li>
<li class="toctree-l2"><a class="reference internal" href="Recursion_Combinators.html#example-factorial-function">Example: Factorial Function</a></li>
<li class="toctree-l2"><a class="reference internal" href="Recursion_Combinators.html#example-tails">Example: <code class="docutils literal notranslate"><span class="pre">tails</span></code></a></li>
<li class="toctree-l2"><a class="reference internal" href="Recursion_Combinators.html#conclusion-patterns-of-recursion">Conclusion: Patterns of Recursion</a></li>
<li class="toctree-l2"><a class="reference internal" href="Recursion_Combinators.html#appendix-fun-with-symbols">Appendix: Fun with Symbols</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="Ordered_Binary_Trees.html">Treating Trees I: Ordered Binary Trees</a><ul>
<li class="toctree-l2"><a class="reference internal" href="Ordered_Binary_Trees.html#adding-nodes-to-the-tree">Adding Nodes to the Tree</a></li>
<li class="toctree-l2"><a class="reference internal" href="Ordered_Binary_Trees.html#interlude-cmp-combinator">Interlude: <code class="docutils literal notranslate"><span class="pre">cmp</span></code> combinator</a></li>
<li class="toctree-l2"><a class="reference internal" href="Ordered_Binary_Trees.html#a-function-to-traverse-this-structure">A Function to Traverse this Structure</a></li>
<li class="toctree-l2"><a class="reference internal" href="Ordered_Binary_Trees.html#interlude-a-set-like-datastructure">Interlude: A Set-like Datastructure</a></li>
<li class="toctree-l2"><a class="reference internal" href="Ordered_Binary_Trees.html#a-version-of-tree-iter-that-does-in-order-traversal">A Version of <code class="docutils literal notranslate"><span class="pre">Tree-iter</span></code> that does In-Order Traversal</a></li>
<li class="toctree-l2"><a class="reference internal" href="Ordered_Binary_Trees.html#getting-values-by-key">Getting values by key</a></li>
<li class="toctree-l2"><a class="reference internal" href="Ordered_Binary_Trees.html#tree-delete">Tree-delete</a></li>
<li class="toctree-l2"><a class="reference internal" href="Ordered_Binary_Trees.html#appendix-the-source-code">Appendix: The source code.</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="Treestep.html">Treating Trees II: <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a><ul>
<li class="toctree-l2"><a class="reference internal" href="Treestep.html#derive-the-recursive-function">Derive the recursive function.</a></li>
<li class="toctree-l2"><a class="reference internal" href="Treestep.html#extract-the-givens-to-parameterize-the-program">Extract the givens to parameterize the program.</a></li>
<li class="toctree-l2"><a class="reference internal" href="Treestep.html#define-treestep">Define <code class="docutils literal notranslate"><span class="pre">treestep</span></code></a></li>
<li class="toctree-l2"><a class="reference internal" href="Treestep.html#examples">Examples</a></li>
<li class="toctree-l2"><a class="reference internal" href="Treestep.html#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></li>
<li class="toctree-l2"><a class="reference internal" href="Treestep.html#with-treegrind">With <code class="docutils literal notranslate"><span class="pre">treegrind</span></code>?</a></li>
<li class="toctree-l2"><a class="reference internal" href="Treestep.html#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 class="toctree-l2"><a class="reference internal" href="Treestep.html#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></li>
<li class="toctree-l2"><a class="reference internal" href="Treestep.html#putting-it-together">Putting it together</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="Generator_Programs.html">Using <code class="docutils literal notranslate"><span class="pre">x</span></code> to Generate Values</a><ul>
<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html#direco"><code class="docutils literal notranslate"><span class="pre">direco</span></code></a></li>
<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html#making-generators">Making Generators</a></li>
<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html#generating-multiples-of-three-and-five">Generating Multiples of Three and Five</a></li>
<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html#project-euler-problem-one">Project Euler Problem One</a></li>
<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html#a-generator-for-the-fibonacci-sequence">A generator for the Fibonacci Sequence.</a></li>
<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html#project-euler-problem-two">Project Euler Problem Two</a></li>
<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html#how-to-compile-these">How to compile these?</a></li>
<li class="toctree-l2"><a class="reference internal" href="Generator_Programs.html#an-interesting-variation">An Interesting Variation</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="Newton-Raphson.html">Newton’s method</a><ul>
<li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html#a-generator-for-approximations">A Generator for Approximations</a></li>
<li class="toctree-l2"><a class="reference internal" href="Newton-Raphson.html#finding-consecutive-approximations-within-a-tolerance">Finding Consecutive Approximations within a Tolerance</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="Zipper.html">Traversing Datastructures with Zippers</a><ul>
<li class="toctree-l2"><a class="reference internal" href="Zipper.html#trees">Trees</a></li>
<li class="toctree-l2"><a class="reference internal" href="Zipper.html#zipper-in-joy">Zipper in Joy</a></li>
<li class="toctree-l2"><a class="reference internal" href="Zipper.html#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 class="toctree-l2"><a class="reference internal" href="Zipper.html#z"><code class="docutils literal notranslate"><span class="pre">Z</span></code></a></li>
<li class="toctree-l2"><a class="reference internal" href="Zipper.html#addressing">Addressing</a></li>
<li class="toctree-l2"><a class="reference internal" href="Zipper.html#determining-the-right-path-for-an-item-in-a-tree">Determining the right “path” for an item in a tree.</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="Types.html">The Blissful Elegance of Typing Joy</a><ul>
<li class="toctree-l2"><a class="reference internal" href="Types.html#part-i-poials-rules">Part I: Pöial’s Rules</a></li>
<li class="toctree-l2"><a class="reference internal" href="Types.html#part-ii-implementation">Part II: Implementation</a></li>
<li class="toctree-l2"><a class="reference internal" href="Types.html#part-iii-compiling-yin-functions">Part III: Compiling Yin Functions</a></li>
<li class="toctree-l2"><a class="reference internal" href="Types.html#part-iv-types-and-subtypes-of-arguments">Part IV: Types and Subtypes of Arguments</a></li>
<li class="toctree-l2"><a class="reference internal" href="Types.html#part-v-functions-that-use-the-stack">Part V: Functions that use the Stack</a></li>
<li class="toctree-l2"><a class="reference internal" href="Types.html#part-vi-multiple-stack-effects">Part VI: Multiple Stack Effects</a></li>
<li class="toctree-l2"><a class="reference internal" href="Types.html#part-vii-typing-combinators">Part VII: Typing Combinators</a></li>
<li class="toctree-l2"><a class="reference internal" href="Types.html#conclusion">Conclusion</a></li>
<li class="toctree-l2"><a class="reference internal" href="Types.html#appendix-joy-in-the-logical-paradigm">Appendix: Joy in the Logical Paradigm</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="TypeChecking.html">Type Checking</a><ul>
<li class="toctree-l2"><a class="reference internal" href="TypeChecking.html#an-example">An Example</a></li>
<li class="toctree-l2"><a class="reference internal" href="TypeChecking.html#unification-works-in-reverse">Unification Works “in Reverse”</a></li>
<li class="toctree-l2"><a class="reference internal" href="TypeChecking.html#failing-a-check">Failing a Check</a></li>
</ul>
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<li class="toctree-l1"><a class="reference internal" href="NoUpdates.html">No Updates</a></li>
<li class="toctree-l1"><a class="reference internal" href="Categorical.html">Categorical Programming</a></li>
<li class="toctree-l1"><a class="reference internal" href="The_Four_Operations.html">The Four Fundamental Operations of Definite Action</a><ul>
<li class="toctree-l2"><a class="reference internal" href="The_Four_Operations.html#sequence">Sequence</a></li>
<li class="toctree-l2"><a class="reference internal" href="The_Four_Operations.html#branch">Branch</a></li>
<li class="toctree-l2"><a class="reference internal" href="The_Four_Operations.html#loop">Loop</a></li>
<li class="toctree-l2"><a class="reference internal" href="The_Four_Operations.html#parallel">Parallel</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html">∂RE</a><ul>
<li class="toctree-l2"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html#brzozowskis-derivatives-of-regular-expressions">Brzozowski’s Derivatives of Regular Expressions</a></li>
<li class="toctree-l2"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html#implementation">Implementation</a></li>
<li class="toctree-l2"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html#lets-try-it-out">Let’s try it out…</a></li>
<li class="toctree-l2"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html#larger-alphabets">Larger Alphabets</a></li>
<li class="toctree-l2"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html#state-machine">State Machine</a></li>
<li class="toctree-l2"><a class="reference internal" href="Derivatives_of_Regular_Expressions.html#reversing-the-derivatives-to-generate-matching-strings">Reversing the Derivatives to Generate Matching Strings</a></li>
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