1214 lines
68 KiB
HTML
1214 lines
68 KiB
HTML
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<meta property="og:title" content="*-Morpisms – Nicole Dresselhaus">
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<meta property="og:description" content="This weekend I spend some time on Morphisms.
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Knowing that this might sound daunting to many dabbling Haskellers (like I am), I decided to write a real short MergeSort hylomorphism quickstarter.">
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<span class="navbar-title">Nicole Dresselhaus</span>
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<span class="menu-text">Anforderungskatalog für die Dokumentation von Forschungssoftware (Digital Humanities)</span></a>
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<span class="menu-text">RAG für eine Obsidian-Wissensdatenbank: Technische Ansätze</span></a>
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<div class="block-title">Abstract</div>
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<p>This weekend I spend some time on Morphisms.</p>
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<p>Knowing that this might sound daunting to many dabbling Haskellers (like I am), I decided to write a real short MergeSort hylomorphism quickstarter.</p>
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Note
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<p>Backup eines Blogposts eines Kommilitonen</p>
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</div>
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<p>This weekend I spend some time on Morphisms.</p>
|
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<p>Knowing that this might sound daunting to many dabbling Haskellers (like I am), I decided to write a real short MergeSort hylomorphism quickstarter.</p>
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<hr>
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<p>For those who need a refresher: MergeSort works by creating a balanced binary tree from the input list and directly collapsing it back into itself while treating the children as sorted lists and merging these with an O(n) algorithm.</p>
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<hr>
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||
<p>First the usual prelude:</p>
|
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<div class="sourceCode" id="cb1"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="ot">{-# LANGUAGE DeriveFunctor #-}</span></span>
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<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="ot">{-# LANGUAGE TypeFamilies #-}</span></span>
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<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a></span>
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||
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a><span class="kw">import</span> <span class="dt">Data.Functor.Foldable</span></span>
|
||
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a><span class="kw">import</span> <span class="dt">Data.List</span> (splitAt, unfoldr)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<hr>
|
||
<p>We will use a binary tree like this. Note that there is no explicit recursion used, but <code>NodeF</code> has two <em>holes</em>. These will eventually filled later.</p>
|
||
<div class="sourceCode" id="cb2"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="kw">data</span> <span class="dt">TreeF</span> c f <span class="ot">=</span> <span class="dt">EmptyF</span> <span class="op">|</span> <span class="dt">LeafF</span> c <span class="op">|</span> <span class="dt">NodeF</span> f f</span>
|
||
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a> <span class="kw">deriving</span> (<span class="dt">Eq</span>, <span class="dt">Show</span>, <span class="dt">Functor</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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<hr>
|
||
<p>Aside: We could use this as a <em>normal</em> binary tree by wrapping it in <code>Fix</code>: <code>type Tree a = Fix (TreeF a)</code> But this would require us to write our tree like <code>Fix (NodeF (Fix (LeafF 'l')) (Fix (LeafF 'r')))</code> which would get tedious fast. Luckily Edward build a much better way to do this into <em>recursion-schemes</em>. I will touch on this later.</p>
|
||
<hr>
|
||
<p>Without further ado we start to write a Coalgebra, which in my book is just a scary name for “function that is used to construct datastructures”.</p>
|
||
<div class="sourceCode" id="cb3"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="ot">unflatten ::</span> [a] <span class="ot">-></span> <span class="dt">TreeF</span> a [a]</span>
|
||
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a>unflatten ( []) <span class="ot">=</span> <span class="dt">EmptyF</span></span>
|
||
<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a>unflatten (x<span class="op">:</span>[]) <span class="ot">=</span> <span class="dt">LeafF</span> x</span>
|
||
<span id="cb3-4"><a href="#cb3-4" aria-hidden="true" tabindex="-1"></a>unflatten ( xs) <span class="ot">=</span> <span class="dt">NodeF</span> l r <span class="kw">where</span> (l,r) <span class="ot">=</span> <span class="fu">splitAt</span> (<span class="fu">length</span> xs <span class="ot">`div`</span> <span class="dv">2</span>) xs</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<p>From the type signature it’s immediately obvious, that we take a list of ’a’s and use it to create a part of our tree.</p>
|
||
<p>The nice thing is that due to the fact that we haven’t commited to a type in our tree nodes we can just put lists in there.</p>
|
||
<hr>
|
||
<p>Aside: At this point we could use this Coalgebra to construct (unsorted) binary trees from lists:</p>
|
||
<div class="sourceCode" id="cb4"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>example1 <span class="ot">=</span> ana unflatten [<span class="dv">1</span>,<span class="dv">3</span>] <span class="op">==</span> <span class="dt">Fix</span> (<span class="dt">NodeF</span> (<span class="dt">Fix</span> (<span class="dt">LeafF</span> <span class="dv">1</span>)) (<span class="dt">Fix</span> (<span class="dt">LeafF</span> <span class="dv">3</span>)))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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||
<hr>
|
||
<p>On to our sorting, tree-collapsing Algebra. Which again is just a creepy word for “function that is used to deconstruct datastructures”.</p>
|
||
<p>The function <code>mergeList</code> is defined below and just merges two sorted lists into one sorted list in O(n), I would probably take this from the <code>ordlist</code> package if I were to implement this <em>for real</em>.</p>
|
||
<p>Again we see that we can just construct our sorted output list from a <code>TreeF</code> that apparently contains just lists.</p>
|
||
<div class="sourceCode" id="cb5"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="ot">flatten ::</span> <span class="dt">Ord</span> a <span class="ot">=></span> <span class="dt">TreeF</span> a [a] <span class="ot">-></span> [a]</span>
|
||
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a>flatten <span class="dt">EmptyF</span> <span class="ot">=</span> []</span>
|
||
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a>flatten (<span class="dt">LeafF</span> c) <span class="ot">=</span> [c]</span>
|
||
<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a>flatten (<span class="dt">NodeF</span> l r) <span class="ot">=</span> mergeLists l r</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<hr>
|
||
<p>Aside: We could use a Coalgebra to deconstruct trees:</p>
|
||
<div class="sourceCode" id="cb6"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a>example2 <span class="ot">=</span> cata flatten (<span class="dt">Fix</span> (<span class="dt">NodeF</span> (<span class="dt">Fix</span> (<span class="dt">LeafF</span> <span class="dv">3</span>)) (<span class="dt">Fix</span> (<span class="dt">LeafF</span> <span class="dv">1</span>)))) <span class="op">==</span> [<span class="dv">1</span>,<span class="dv">3</span>]</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<hr>
|
||
<p>Now we just combine the Coalgebra and the Algebra with one from the functions from Edwards <code>recursion-schemes</code> library:</p>
|
||
<div class="sourceCode" id="cb7"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="ot">mergeSort ::</span> <span class="dt">Ord</span> a <span class="ot">=></span> [a] <span class="ot">-></span> [a]</span>
|
||
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a>mergeSort <span class="ot">=</span> hylo flatten unflatten</span>
|
||
<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a></span>
|
||
<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a>example3 <span class="ot">=</span> mergeSort [<span class="dv">5</span>,<span class="dv">2</span>,<span class="dv">7</span>,<span class="dv">9</span>,<span class="dv">1</span>,<span class="dv">4</span>] <span class="op">==</span> [<span class="dv">1</span>,<span class="dv">2</span>,<span class="dv">4</span>,<span class="dv">5</span>,<span class="dv">7</span>,<span class="dv">9</span>]</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<hr>
|
||
<p>What have we gained?</p>
|
||
<p>We have implemented a MergeSort variant in 9 lines of code, not counting the <code>mergeLists</code> function below. Not bad, but <a href="http://en.literateprograms.org/Merge_sort_(Haskell)">this implementation</a> is not much longer.</p>
|
||
<p>On the other hand the morphism based implementation cleanly describes what happens during construction and deconstruction of our intermediate structure.</p>
|
||
<p>My guess is that, as soon as the algortihms get more complex, this will really make a difference.</p>
|
||
<hr>
|
||
<p>At this point I wasn’t sure if this was useful or remotely applicable. Telling someone “I spend a whole weekend learning about Hylomorphism” isn’t something the cool developer kids do.</p>
|
||
<p>It appeared to me that maybe I should have a look at the Core to see what the compiler finally comes up with (edited for brevity):</p>
|
||
<div class="sourceCode" id="cb8"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a><span class="ot"> mergeSort ::</span> [<span class="dt">Integer</span>] <span class="ot">-></span> [<span class="dt">Integer</span>]</span>
|
||
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a> mergeSort <span class="ot">=</span></span>
|
||
<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a> \ (<span class="ot">x ::</span> [<span class="dt">Integer</span>]) <span class="ot">-></span></span>
|
||
<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a> <span class="kw">case</span> x <span class="kw">of</span> wild {</span>
|
||
<span id="cb8-5"><a href="#cb8-5" aria-hidden="true" tabindex="-1"></a> [] <span class="ot">-></span> [];</span>
|
||
<span id="cb8-6"><a href="#cb8-6" aria-hidden="true" tabindex="-1"></a> <span class="op">:</span> x1 ds <span class="ot">-></span></span>
|
||
<span id="cb8-7"><a href="#cb8-7" aria-hidden="true" tabindex="-1"></a> <span class="kw">case</span> ds <span class="kw">of</span> _ {</span>
|
||
<span id="cb8-8"><a href="#cb8-8" aria-hidden="true" tabindex="-1"></a> [] <span class="ot">-></span> <span class="op">:</span> x1 ([]);</span>
|
||
<span id="cb8-9"><a href="#cb8-9" aria-hidden="true" tabindex="-1"></a> <span class="op">:</span> ipv ipv1 <span class="ot">-></span></span>
|
||
<span id="cb8-10"><a href="#cb8-10" aria-hidden="true" tabindex="-1"></a> unfoldr</span>
|
||
<span id="cb8-11"><a href="#cb8-11" aria-hidden="true" tabindex="-1"></a> lvl9</span>
|
||
<span id="cb8-12"><a href="#cb8-12" aria-hidden="true" tabindex="-1"></a> (<span class="kw">let</span> {</span>
|
||
<span id="cb8-13"><a href="#cb8-13" aria-hidden="true" tabindex="-1"></a><span class="ot"> p ::</span> ([<span class="dt">Integer</span>], [<span class="dt">Integer</span>])</span>
|
||
<span id="cb8-14"><a href="#cb8-14" aria-hidden="true" tabindex="-1"></a> p <span class="ot">=</span></span>
|
||
<span id="cb8-15"><a href="#cb8-15" aria-hidden="true" tabindex="-1"></a> <span class="kw">case</span> <span class="op">$</span>wlenAcc wild <span class="dv">0</span> <span class="kw">of</span> ww { __DEFAULT <span class="ot">-></span></span>
|
||
<span id="cb8-16"><a href="#cb8-16" aria-hidden="true" tabindex="-1"></a> <span class="kw">case</span> divInt<span class="op">#</span> ww <span class="dv">2</span> <span class="kw">of</span> ww4 { __DEFAULT <span class="ot">-></span></span>
|
||
<span id="cb8-17"><a href="#cb8-17" aria-hidden="true" tabindex="-1"></a> <span class="kw">case</span> tagToEnum<span class="op">#</span> (<span class="op"><#</span> ww4 <span class="dv">0</span>) <span class="kw">of</span> _ {</span>
|
||
<span id="cb8-18"><a href="#cb8-18" aria-hidden="true" tabindex="-1"></a> <span class="dt">False</span> <span class="ot">-></span></span>
|
||
<span id="cb8-19"><a href="#cb8-19" aria-hidden="true" tabindex="-1"></a> <span class="kw">case</span> <span class="op">$</span>wsplitAt<span class="op">#</span> ww4 wild <span class="kw">of</span> _ { (<span class="op">#</span> ww2, ww3 <span class="op">#</span>) <span class="ot">-></span> (ww2, ww3) };</span>
|
||
<span id="cb8-20"><a href="#cb8-20" aria-hidden="true" tabindex="-1"></a> <span class="dt">True</span> <span class="ot">-></span> ([], wild)</span>
|
||
<span id="cb8-21"><a href="#cb8-21" aria-hidden="true" tabindex="-1"></a> }</span>
|
||
<span id="cb8-22"><a href="#cb8-22" aria-hidden="true" tabindex="-1"></a> }</span>
|
||
<span id="cb8-23"><a href="#cb8-23" aria-hidden="true" tabindex="-1"></a> } } <span class="kw">in</span></span>
|
||
<span id="cb8-24"><a href="#cb8-24" aria-hidden="true" tabindex="-1"></a> (<span class="kw">case</span> p <span class="kw">of</span> _ { (x2, ds1) <span class="ot">-></span> mergeSort x2 },</span>
|
||
<span id="cb8-25"><a href="#cb8-25" aria-hidden="true" tabindex="-1"></a> <span class="kw">case</span> p <span class="kw">of</span> _ { (ds1, y) <span class="ot">-></span> mergeSort y }))</span>
|
||
<span id="cb8-26"><a href="#cb8-26" aria-hidden="true" tabindex="-1"></a> }</span>
|
||
<span id="cb8-27"><a href="#cb8-27" aria-hidden="true" tabindex="-1"></a> }</span>
|
||
<span id="cb8-28"><a href="#cb8-28" aria-hidden="true" tabindex="-1"></a> end <span class="dt">Rec</span> }</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<p>While I am not really competent in reading Core and this is actually the first time I bothered to try, it is immediately obvious that there is no trace of any intermediate tree structure.</p>
|
||
<p>This is when it struck me. I was dazzled and amazed. And am still. Although we are writing our algorithm as if we are working on a real tree structure the library and the compiler are able to just remove the whole intermediate step.</p>
|
||
<hr>
|
||
<p>Aftermath:</p>
|
||
<p>In the beginning I promised a way to work on non-functor data structures. Actually that was how I began to work with the <code>recursion-schemes</code> library.</p>
|
||
<p>We are able to create a ‘normal’ version of our tree from above:</p>
|
||
<div class="sourceCode" id="cb9"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a><span class="kw">data</span> <span class="dt">Tree</span> c <span class="ot">=</span> <span class="dt">Empty</span> <span class="op">|</span> <span class="dt">Leaf</span> c <span class="op">|</span> <span class="dt">Node</span> (<span class="dt">Tree</span> c) (<span class="dt">Tree</span> c)</span>
|
||
<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a> <span class="kw">deriving</span> (<span class="dt">Eq</span>, <span class="dt">Show</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<p>But we can not use this directly with our (Co-)Algebras. Luckily Edward build a little bit of type magic into the library:</p>
|
||
<div class="sourceCode" id="cb10"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a><span class="kw">type</span> <span class="kw">instance</span> <span class="dt">Base</span> (<span class="dt">Tree</span> c) <span class="ot">=</span> (<span class="dt">TreeF</span> c)</span>
|
||
<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a></span>
|
||
<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a><span class="kw">instance</span> <span class="dt">Unfoldable</span> (<span class="dt">Tree</span> c) <span class="kw">where</span></span>
|
||
<span id="cb10-4"><a href="#cb10-4" aria-hidden="true" tabindex="-1"></a> embed <span class="dt">EmptyF</span> <span class="ot">=</span> <span class="dt">Empty</span></span>
|
||
<span id="cb10-5"><a href="#cb10-5" aria-hidden="true" tabindex="-1"></a> embed (<span class="dt">LeafF</span> c) <span class="ot">=</span> <span class="dt">Leaf</span> c</span>
|
||
<span id="cb10-6"><a href="#cb10-6" aria-hidden="true" tabindex="-1"></a> embed (<span class="dt">NodeF</span> l r) <span class="ot">=</span> <span class="dt">Node</span> l r</span>
|
||
<span id="cb10-7"><a href="#cb10-7" aria-hidden="true" tabindex="-1"></a></span>
|
||
<span id="cb10-8"><a href="#cb10-8" aria-hidden="true" tabindex="-1"></a><span class="kw">instance</span> <span class="dt">Foldable</span> (<span class="dt">Tree</span> c) <span class="kw">where</span></span>
|
||
<span id="cb10-9"><a href="#cb10-9" aria-hidden="true" tabindex="-1"></a> project <span class="dt">Empty</span> <span class="ot">=</span> <span class="dt">EmptyF</span></span>
|
||
<span id="cb10-10"><a href="#cb10-10" aria-hidden="true" tabindex="-1"></a> project (<span class="dt">Leaf</span> c) <span class="ot">=</span> <span class="dt">LeafF</span> c</span>
|
||
<span id="cb10-11"><a href="#cb10-11" aria-hidden="true" tabindex="-1"></a> project (<span class="dt">Node</span> l r) <span class="ot">=</span> <span class="dt">NodeF</span> l r</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<p>Without going into detail by doing this we establish a relationship between <code>Tree</code> and <code>TreeF</code> and teach the compiler how to translate between these types.</p>
|
||
<p>Now we can use our Alebra on our non functor type:</p>
|
||
<div class="sourceCode" id="cb11"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a>example4 <span class="ot">=</span> cata flatten (<span class="dt">Node</span> (<span class="dt">Leaf</span> <span class="ch">'l'</span>) (<span class="dt">Leaf</span> <span class="ch">'r'</span>)) <span class="op">==</span> <span class="st">"lr"</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<p>The great thing about this is that, looking at the Core output again, there is no traces of the <code>TreeF</code> structure to be found. As far as I can tell, the algorithm is working directly on our <code>Tree</code> type.</p>
|
||
<hr>
|
||
<p>Literature:</p>
|
||
<ul>
|
||
<li><a href="https://www.fpcomplete.com/user/bartosz/understanding-algebras">Understanding F-Algebras</a></li>
|
||
<li><a href="http://www.timphilipwilliams.com/slides.html">Recursion Schemes by Example</a></li>
|
||
<li><a href="http://comonad.com/reader/2009/recursion-schemes/">Recursion Schemes: A Field Guide</a></li>
|
||
<li><a href="http://stackoverflow.com/questions/6941904/recursion-schemes-for-dummies">This StackOverflow question</a></li>
|
||
</ul>
|
||
<hr>
|
||
<p>Appendix:</p>
|
||
<div class="sourceCode" id="cb12"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a><span class="ot">mergeLists ::</span> <span class="dt">Ord</span> a <span class="ot">=></span> [a] <span class="ot">-></span> [a] <span class="ot">-></span> [a]</span>
|
||
<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a>mergeLists <span class="ot">=</span> <span class="fu">curry</span> <span class="op">$</span> unfoldr c <span class="kw">where</span></span>
|
||
<span id="cb12-3"><a href="#cb12-3" aria-hidden="true" tabindex="-1"></a> c ([], []) <span class="ot">=</span> <span class="dt">Nothing</span></span>
|
||
<span id="cb12-4"><a href="#cb12-4" aria-hidden="true" tabindex="-1"></a> c ([], y<span class="op">:</span>ys) <span class="ot">=</span> <span class="dt">Just</span> (y, ([], ys))</span>
|
||
<span id="cb12-5"><a href="#cb12-5" aria-hidden="true" tabindex="-1"></a> c (x<span class="op">:</span>xs, []) <span class="ot">=</span> <span class="dt">Just</span> (x, (xs, []))</span>
|
||
<span id="cb12-6"><a href="#cb12-6" aria-hidden="true" tabindex="-1"></a> c (x<span class="op">:</span>xs, y<span class="op">:</span>ys) <span class="op">|</span> x <span class="op"><=</span> y <span class="ot">=</span> <span class="dt">Just</span> (x, (xs, y<span class="op">:</span>ys))</span>
|
||
<span id="cb12-7"><a href="#cb12-7" aria-hidden="true" tabindex="-1"></a> <span class="op">|</span> x <span class="op">></span> y <span class="ot">=</span> <span class="dt">Just</span> (y, (x<span class="op">:</span>xs, ys))</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
|
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interactive: true,
|
||
interactiveBorder: 10,
|
||
theme: 'quarto',
|
||
placement: 'bottom-start',
|
||
};
|
||
if (contentFn) {
|
||
config.content = contentFn;
|
||
}
|
||
if (onTriggerFn) {
|
||
config.onTrigger = onTriggerFn;
|
||
}
|
||
if (onUntriggerFn) {
|
||
config.onUntrigger = onUntriggerFn;
|
||
}
|
||
window.tippy(el, config);
|
||
}
|
||
const noterefs = window.document.querySelectorAll('a[role="doc-noteref"]');
|
||
for (var i=0; i<noterefs.length; i++) {
|
||
const ref = noterefs[i];
|
||
tippyHover(ref, function() {
|
||
// use id or data attribute instead here
|
||
let href = ref.getAttribute('data-footnote-href') || ref.getAttribute('href');
|
||
try { href = new URL(href).hash; } catch {}
|
||
const id = href.replace(/^#\/?/, "");
|
||
const note = window.document.getElementById(id);
|
||
if (note) {
|
||
return note.innerHTML;
|
||
} else {
|
||
return "";
|
||
}
|
||
});
|
||
}
|
||
const xrefs = window.document.querySelectorAll('a.quarto-xref');
|
||
const processXRef = (id, note) => {
|
||
// Strip column container classes
|
||
const stripColumnClz = (el) => {
|
||
el.classList.remove("page-full", "page-columns");
|
||
if (el.children) {
|
||
for (const child of el.children) {
|
||
stripColumnClz(child);
|
||
}
|
||
}
|
||
}
|
||
stripColumnClz(note)
|
||
if (id === null || id.startsWith('sec-')) {
|
||
// Special case sections, only their first couple elements
|
||
const container = document.createElement("div");
|
||
if (note.children && note.children.length > 2) {
|
||
container.appendChild(note.children[0].cloneNode(true));
|
||
for (let i = 1; i < note.children.length; i++) {
|
||
const child = note.children[i];
|
||
if (child.tagName === "P" && child.innerText === "") {
|
||
continue;
|
||
} else {
|
||
container.appendChild(child.cloneNode(true));
|
||
break;
|
||
}
|
||
}
|
||
if (window.Quarto?.typesetMath) {
|
||
window.Quarto.typesetMath(container);
|
||
}
|
||
return container.innerHTML
|
||
} else {
|
||
if (window.Quarto?.typesetMath) {
|
||
window.Quarto.typesetMath(note);
|
||
}
|
||
return note.innerHTML;
|
||
}
|
||
} else {
|
||
// Remove any anchor links if they are present
|
||
const anchorLink = note.querySelector('a.anchorjs-link');
|
||
if (anchorLink) {
|
||
anchorLink.remove();
|
||
}
|
||
if (window.Quarto?.typesetMath) {
|
||
window.Quarto.typesetMath(note);
|
||
}
|
||
if (note.classList.contains("callout")) {
|
||
return note.outerHTML;
|
||
} else {
|
||
return note.innerHTML;
|
||
}
|
||
}
|
||
}
|
||
for (var i=0; i<xrefs.length; i++) {
|
||
const xref = xrefs[i];
|
||
tippyHover(xref, undefined, function(instance) {
|
||
instance.disable();
|
||
let url = xref.getAttribute('href');
|
||
let hash = undefined;
|
||
if (url.startsWith('#')) {
|
||
hash = url;
|
||
} else {
|
||
try { hash = new URL(url).hash; } catch {}
|
||
}
|
||
if (hash) {
|
||
const id = hash.replace(/^#\/?/, "");
|
||
const note = window.document.getElementById(id);
|
||
if (note !== null) {
|
||
try {
|
||
const html = processXRef(id, note.cloneNode(true));
|
||
instance.setContent(html);
|
||
} finally {
|
||
instance.enable();
|
||
instance.show();
|
||
}
|
||
} else {
|
||
// See if we can fetch this
|
||
fetch(url.split('#')[0])
|
||
.then(res => res.text())
|
||
.then(html => {
|
||
const parser = new DOMParser();
|
||
const htmlDoc = parser.parseFromString(html, "text/html");
|
||
const note = htmlDoc.getElementById(id);
|
||
if (note !== null) {
|
||
const html = processXRef(id, note);
|
||
instance.setContent(html);
|
||
}
|
||
}).finally(() => {
|
||
instance.enable();
|
||
instance.show();
|
||
});
|
||
}
|
||
} else {
|
||
// See if we can fetch a full url (with no hash to target)
|
||
// This is a special case and we should probably do some content thinning / targeting
|
||
fetch(url)
|
||
.then(res => res.text())
|
||
.then(html => {
|
||
const parser = new DOMParser();
|
||
const htmlDoc = parser.parseFromString(html, "text/html");
|
||
const note = htmlDoc.querySelector('main.content');
|
||
if (note !== null) {
|
||
// This should only happen for chapter cross references
|
||
// (since there is no id in the URL)
|
||
// remove the first header
|
||
if (note.children.length > 0 && note.children[0].tagName === "HEADER") {
|
||
note.children[0].remove();
|
||
}
|
||
const html = processXRef(null, note);
|
||
instance.setContent(html);
|
||
}
|
||
}).finally(() => {
|
||
instance.enable();
|
||
instance.show();
|
||
});
|
||
}
|
||
}, function(instance) {
|
||
});
|
||
}
|
||
let selectedAnnoteEl;
|
||
const selectorForAnnotation = ( cell, annotation) => {
|
||
let cellAttr = 'data-code-cell="' + cell + '"';
|
||
let lineAttr = 'data-code-annotation="' + annotation + '"';
|
||
const selector = 'span[' + cellAttr + '][' + lineAttr + ']';
|
||
return selector;
|
||
}
|
||
const selectCodeLines = (annoteEl) => {
|
||
const doc = window.document;
|
||
const targetCell = annoteEl.getAttribute("data-target-cell");
|
||
const targetAnnotation = annoteEl.getAttribute("data-target-annotation");
|
||
const annoteSpan = window.document.querySelector(selectorForAnnotation(targetCell, targetAnnotation));
|
||
const lines = annoteSpan.getAttribute("data-code-lines").split(",");
|
||
const lineIds = lines.map((line) => {
|
||
return targetCell + "-" + line;
|
||
})
|
||
let top = null;
|
||
let height = null;
|
||
let parent = null;
|
||
if (lineIds.length > 0) {
|
||
//compute the position of the single el (top and bottom and make a div)
|
||
const el = window.document.getElementById(lineIds[0]);
|
||
top = el.offsetTop;
|
||
height = el.offsetHeight;
|
||
parent = el.parentElement.parentElement;
|
||
if (lineIds.length > 1) {
|
||
const lastEl = window.document.getElementById(lineIds[lineIds.length - 1]);
|
||
const bottom = lastEl.offsetTop + lastEl.offsetHeight;
|
||
height = bottom - top;
|
||
}
|
||
if (top !== null && height !== null && parent !== null) {
|
||
// cook up a div (if necessary) and position it
|
||
let div = window.document.getElementById("code-annotation-line-highlight");
|
||
if (div === null) {
|
||
div = window.document.createElement("div");
|
||
div.setAttribute("id", "code-annotation-line-highlight");
|
||
div.style.position = 'absolute';
|
||
parent.appendChild(div);
|
||
}
|
||
div.style.top = top - 2 + "px";
|
||
div.style.height = height + 4 + "px";
|
||
div.style.left = 0;
|
||
let gutterDiv = window.document.getElementById("code-annotation-line-highlight-gutter");
|
||
if (gutterDiv === null) {
|
||
gutterDiv = window.document.createElement("div");
|
||
gutterDiv.setAttribute("id", "code-annotation-line-highlight-gutter");
|
||
gutterDiv.style.position = 'absolute';
|
||
const codeCell = window.document.getElementById(targetCell);
|
||
const gutter = codeCell.querySelector('.code-annotation-gutter');
|
||
gutter.appendChild(gutterDiv);
|
||
}
|
||
gutterDiv.style.top = top - 2 + "px";
|
||
gutterDiv.style.height = height + 4 + "px";
|
||
}
|
||
selectedAnnoteEl = annoteEl;
|
||
}
|
||
};
|
||
const unselectCodeLines = () => {
|
||
const elementsIds = ["code-annotation-line-highlight", "code-annotation-line-highlight-gutter"];
|
||
elementsIds.forEach((elId) => {
|
||
const div = window.document.getElementById(elId);
|
||
if (div) {
|
||
div.remove();
|
||
}
|
||
});
|
||
selectedAnnoteEl = undefined;
|
||
};
|
||
// Handle positioning of the toggle
|
||
window.addEventListener(
|
||
"resize",
|
||
throttle(() => {
|
||
elRect = undefined;
|
||
if (selectedAnnoteEl) {
|
||
selectCodeLines(selectedAnnoteEl);
|
||
}
|
||
}, 10)
|
||
);
|
||
function throttle(fn, ms) {
|
||
let throttle = false;
|
||
let timer;
|
||
return (...args) => {
|
||
if(!throttle) { // first call gets through
|
||
fn.apply(this, args);
|
||
throttle = true;
|
||
} else { // all the others get throttled
|
||
if(timer) clearTimeout(timer); // cancel #2
|
||
timer = setTimeout(() => {
|
||
fn.apply(this, args);
|
||
timer = throttle = false;
|
||
}, ms);
|
||
}
|
||
};
|
||
}
|
||
// Attach click handler to the DT
|
||
const annoteDls = window.document.querySelectorAll('dt[data-target-cell]');
|
||
for (const annoteDlNode of annoteDls) {
|
||
annoteDlNode.addEventListener('click', (event) => {
|
||
const clickedEl = event.target;
|
||
if (clickedEl !== selectedAnnoteEl) {
|
||
unselectCodeLines();
|
||
const activeEl = window.document.querySelector('dt[data-target-cell].code-annotation-active');
|
||
if (activeEl) {
|
||
activeEl.classList.remove('code-annotation-active');
|
||
}
|
||
selectCodeLines(clickedEl);
|
||
clickedEl.classList.add('code-annotation-active');
|
||
} else {
|
||
// Unselect the line
|
||
unselectCodeLines();
|
||
clickedEl.classList.remove('code-annotation-active');
|
||
}
|
||
});
|
||
}
|
||
const findCites = (el) => {
|
||
const parentEl = el.parentElement;
|
||
if (parentEl) {
|
||
const cites = parentEl.dataset.cites;
|
||
if (cites) {
|
||
return {
|
||
el,
|
||
cites: cites.split(' ')
|
||
};
|
||
} else {
|
||
return findCites(el.parentElement)
|
||
}
|
||
} else {
|
||
return undefined;
|
||
}
|
||
};
|
||
var bibliorefs = window.document.querySelectorAll('a[role="doc-biblioref"]');
|
||
for (var i=0; i<bibliorefs.length; i++) {
|
||
const ref = bibliorefs[i];
|
||
const citeInfo = findCites(ref);
|
||
if (citeInfo) {
|
||
tippyHover(citeInfo.el, function() {
|
||
var popup = window.document.createElement('div');
|
||
citeInfo.cites.forEach(function(cite) {
|
||
var citeDiv = window.document.createElement('div');
|
||
citeDiv.classList.add('hanging-indent');
|
||
citeDiv.classList.add('csl-entry');
|
||
var biblioDiv = window.document.getElementById('ref-' + cite);
|
||
if (biblioDiv) {
|
||
citeDiv.innerHTML = biblioDiv.innerHTML;
|
||
}
|
||
popup.appendChild(citeDiv);
|
||
});
|
||
return popup.innerHTML;
|
||
});
|
||
}
|
||
}
|
||
});
|
||
</script>
|
||
</div> <!-- /content -->
|
||
|
||
|
||
|
||
|
||
</body></html> |