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<title>Data/Generics/Uniplate/Zipper.hs</title>
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<pre><a name="line-1"></a><span class='hs-comment'>{-|
<a name="line-2"></a>A zipper is a structure for walking a value and manipulating it in constant time.
<a name="line-3"></a>
<a name="line-4"></a>This module was inspired by the paper:
<a name="line-5"></a>/Michael D. Adams. Scrap Your Zippers: A Generic Zipper for Heterogeneous Types, Workshop on Generic Programming 2010/.
<a name="line-6"></a>-}</span>
<a name="line-7"></a>
<a name="line-8"></a>
<a name="line-9"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Generics</span><span class='hs-varop'>.</span><span class='hs-conid'>Uniplate</span><span class='hs-varop'>.</span><span class='hs-conid'>Zipper</span><span class='hs-layout'>(</span>
<a name="line-10"></a> <span class='hs-comment'>-- * Create a zipper and get back the value</span>
<a name="line-11"></a> <span class='hs-conid'>Zipper</span><span class='hs-layout'>,</span> <span class='hs-varid'>zipper</span><span class='hs-layout'>,</span> <span class='hs-varid'>zipperBi</span><span class='hs-layout'>,</span> <span class='hs-varid'>fromZipper</span><span class='hs-layout'>,</span>
<a name="line-12"></a> <span class='hs-comment'>-- * Navigate within a zipper</span>
<a name="line-13"></a> <span class='hs-varid'>left</span><span class='hs-layout'>,</span> <span class='hs-varid'>right</span><span class='hs-layout'>,</span> <span class='hs-varid'>up</span><span class='hs-layout'>,</span> <span class='hs-varid'>down</span><span class='hs-layout'>,</span>
<a name="line-14"></a> <span class='hs-comment'>-- * Manipulate the zipper hole</span>
<a name="line-15"></a> <span class='hs-varid'>hole</span><span class='hs-layout'>,</span> <span class='hs-varid'>replaceHole</span>
<a name="line-16"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-17"></a>
<a name="line-18"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Generics</span><span class='hs-varop'>.</span><span class='hs-conid'>Uniplate</span><span class='hs-varop'>.</span><span class='hs-conid'>Operations</span>
<a name="line-19"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Generics</span><span class='hs-varop'>.</span><span class='hs-conid'>Str</span>
<a name="line-20"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span>
<a name="line-21"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Maybe</span>
<a name="line-22"></a>
<a name="line-23"></a>
<a name="line-24"></a><a name="zipper"></a><span class='hs-comment'>-- | Create a zipper, focused on the top-left value.</span>
<a name="line-25"></a><span class='hs-definition'>zipper</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Uniplate</span> <span class='hs-varid'>to</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>to</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Zipper</span> <span class='hs-varid'>to</span> <span class='hs-varid'>to</span>
<a name="line-26"></a><span class='hs-definition'>zipper</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fromJust</span> <span class='hs-varop'>.</span> <span class='hs-varid'>toZipper</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>x</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-conid'>One</span> <span class='hs-varid'>x</span><span class='hs-layout'>,</span> <span class='hs-keyglyph'>\</span><span class='hs-layout'>(</span><span class='hs-conid'>One</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-27"></a>
<a name="line-28"></a>
<a name="line-29"></a><a name="zipperBi"></a><span class='hs-comment'>-- | Create a zipper with a different focus type from the outer type. Will return</span>
<a name="line-30"></a><span class='hs-comment'>-- @Nothing@ if there are no instances of the focus type within the original value.</span>
<a name="line-31"></a><span class='hs-definition'>zipperBi</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Biplate</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>from</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Maybe</span> <span class='hs-layout'>(</span><span class='hs-conid'>Zipper</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span><span class='hs-layout'>)</span>
<a name="line-32"></a><span class='hs-definition'>zipperBi</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toZipper</span> <span class='hs-varid'>biplate</span>
<a name="line-33"></a>
<a name="line-34"></a>
<a name="line-35"></a><a name="Zipper"></a><span class='hs-comment'>-- | Zipper structure, whose root type is the first type argument, and whose</span>
<a name="line-36"></a><a name="Zipper"></a><span class='hs-comment'>-- focus type is the second type argument.</span>
<a name="line-37"></a><a name="Zipper"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>Zipper</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Zipper</span>
<a name="line-38"></a> <span class='hs-layout'>{</span><span class='hs-varid'>reform</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Str</span> <span class='hs-varid'>to</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>from</span>
<a name="line-39"></a> <span class='hs-layout'>,</span><span class='hs-varid'>zipp</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>ZipN</span> <span class='hs-varid'>to</span>
<a name="line-40"></a> <span class='hs-layout'>}</span>
<a name="line-41"></a>
<a name="line-42"></a><a name="rezipp"></a><span class='hs-definition'>rezipp</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Zipper</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-conid'>Zipper</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span>
<a name="line-43"></a>
<a name="line-44"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Eq</span> <span class='hs-varid'>from</span><span class='hs-layout'>,</span> <span class='hs-conid'>Eq</span> <span class='hs-varid'>to</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Eq</span> <span class='hs-layout'>(</span><span class='hs-conid'>Zipper</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-45"></a> <span class='hs-varid'>a</span> <span class='hs-varop'>==</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fromZipper</span> <span class='hs-varid'>a</span> <span class='hs-varop'>==</span> <span class='hs-varid'>fromZipper</span> <span class='hs-varid'>b</span> <span class='hs-varop'>&&</span> <span class='hs-varid'>zipp</span> <span class='hs-varid'>a</span> <span class='hs-varop'>==</span> <span class='hs-varid'>zipp</span> <span class='hs-varid'>b</span>
<a name="line-46"></a>
<a name="line-47"></a>
<a name="line-48"></a><a name="toZipper"></a><span class='hs-definition'>toZipper</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Uniplate</span> <span class='hs-varid'>to</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-varid'>from</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-conid'>Str</span> <span class='hs-varid'>to</span><span class='hs-layout'>,</span> <span class='hs-conid'>Str</span> <span class='hs-varid'>to</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>from</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>from</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Maybe</span> <span class='hs-layout'>(</span><span class='hs-conid'>Zipper</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span><span class='hs-layout'>)</span>
<a name="line-49"></a><span class='hs-definition'>toZipper</span> <span class='hs-varid'>biplate</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-conid'>Zipper</span> <span class='hs-varid'>gen</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>zipN</span> <span class='hs-varid'>cs</span>
<a name="line-50"></a> <span class='hs-keyword'>where</span> <span class='hs-layout'>(</span><span class='hs-varid'>cs</span><span class='hs-layout'>,</span><span class='hs-varid'>gen</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>biplate</span> <span class='hs-varid'>x</span>
<a name="line-51"></a>
<a name="line-52"></a>
<a name="line-53"></a><a name="fromZipper"></a><span class='hs-comment'>-- | From a zipper take the whole structure, including any modifications.</span>
<a name="line-54"></a><span class='hs-definition'>fromZipper</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Zipper</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>from</span>
<a name="line-55"></a><span class='hs-definition'>fromZipper</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>reform</span> <span class='hs-varid'>x</span> <span class='hs-varop'>$</span> <span class='hs-varid'>top1</span> <span class='hs-varop'>$</span> <span class='hs-varid'>topN</span> <span class='hs-varop'>$</span> <span class='hs-varid'>zipp</span> <span class='hs-varid'>x</span>
<a name="line-56"></a>
<a name="line-57"></a>
<a name="line-58"></a><a name="left"></a><span class='hs-comment'>-- | Move one step left from the current position.</span>
<a name="line-59"></a><span class='hs-definition'>left</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Zipper</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Maybe</span> <span class='hs-layout'>(</span><span class='hs-conid'>Zipper</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span><span class='hs-layout'>)</span>
<a name="line-60"></a><span class='hs-definition'>left</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>rezipp</span> <span class='hs-varid'>leftN</span>
<a name="line-61"></a>
<a name="line-62"></a><a name="right"></a><span class='hs-comment'>-- | Move one step right from the current position.</span>
<a name="line-63"></a><span class='hs-definition'>right</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Zipper</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Maybe</span> <span class='hs-layout'>(</span><span class='hs-conid'>Zipper</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span><span class='hs-layout'>)</span>
<a name="line-64"></a><span class='hs-definition'>right</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>rezipp</span> <span class='hs-varid'>rightN</span>
<a name="line-65"></a>
<a name="line-66"></a><a name="down"></a><span class='hs-comment'>-- | Move one step down from the current position.</span>
<a name="line-67"></a><span class='hs-definition'>down</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Uniplate</span> <span class='hs-varid'>to</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Zipper</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Maybe</span> <span class='hs-layout'>(</span><span class='hs-conid'>Zipper</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span><span class='hs-layout'>)</span>
<a name="line-68"></a><span class='hs-definition'>down</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>rezipp</span> <span class='hs-varid'>downN</span>
<a name="line-69"></a>
<a name="line-70"></a><a name="up"></a><span class='hs-comment'>-- | Move one step up from the current position.</span>
<a name="line-71"></a><span class='hs-definition'>up</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Zipper</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Maybe</span> <span class='hs-layout'>(</span><span class='hs-conid'>Zipper</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span><span class='hs-layout'>)</span>
<a name="line-72"></a><span class='hs-definition'>up</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>rezipp</span> <span class='hs-varid'>upN</span>
<a name="line-73"></a>
<a name="line-74"></a>
<a name="line-75"></a><a name="hole"></a><span class='hs-comment'>-- | Retrieve the current focus of the zipper..</span>
<a name="line-76"></a><span class='hs-definition'>hole</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Zipper</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>to</span>
<a name="line-77"></a><span class='hs-definition'>hole</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>holeN</span> <span class='hs-varop'>.</span> <span class='hs-varid'>zipp</span>
<a name="line-78"></a>
<a name="line-79"></a>
<a name="line-80"></a><a name="replaceHole"></a><span class='hs-comment'>-- | Replace the value currently at the focus of the zipper.</span>
<a name="line-81"></a><span class='hs-definition'>replaceHole</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>to</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Zipper</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Zipper</span> <span class='hs-varid'>from</span> <span class='hs-varid'>to</span>
<a name="line-82"></a><span class='hs-definition'>replaceHole</span> <span class='hs-varid'>x</span> <span class='hs-varid'>z</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>z</span><span class='hs-layout'>{</span><span class='hs-varid'>zipp</span><span class='hs-keyglyph'>=</span><span class='hs-varid'>replaceN</span> <span class='hs-varid'>x</span> <span class='hs-layout'>(</span><span class='hs-varid'>zipp</span> <span class='hs-varid'>z</span><span class='hs-layout'>)</span><span class='hs-layout'>}</span>
<a name="line-83"></a>
<a name="line-84"></a>
<a name="line-85"></a><span class='hs-comment'>---------------------------------------------------------------------</span>
<a name="line-86"></a><span class='hs-comment'>-- N LEVEL ZIPPER ON Str</span>
<a name="line-87"></a>
<a name="line-88"></a><a name="ZipN"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>ZipN</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ZipN</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Str</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Zip1</span> <span class='hs-varid'>x</span><span class='hs-keyglyph'>]</span> <span class='hs-layout'>(</span><span class='hs-conid'>Zip1</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span>
<a name="line-89"></a>
<a name="line-90"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Eq</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Eq</span> <span class='hs-layout'>(</span><span class='hs-conid'>ZipN</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-91"></a> <span class='hs-varid'>x</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-conid'>ZipN</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>xx</span><span class='hs-layout'>)</span> <span class='hs-varop'>==</span> <span class='hs-varid'>y</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-conid'>ZipN</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>yy</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>xx</span> <span class='hs-varop'>==</span> <span class='hs-varid'>yy</span> <span class='hs-varop'>&&</span> <span class='hs-varid'>upN</span> <span class='hs-varid'>x</span> <span class='hs-varop'>==</span> <span class='hs-varid'>upN</span> <span class='hs-varid'>y</span>
<a name="line-92"></a>
<a name="line-93"></a><a name="zipN"></a><span class='hs-definition'>zipN</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Str</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Maybe</span> <span class='hs-layout'>(</span><span class='hs-conid'>ZipN</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span>
<a name="line-94"></a><span class='hs-definition'>zipN</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-conid'>ZipN</span> <span class='hs-conid'>[]</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>zip1</span> <span class='hs-varid'>x</span>
<a name="line-95"></a>
<a name="line-96"></a><a name="leftN"></a><span class='hs-definition'>leftN</span> <span class='hs-layout'>(</span><span class='hs-conid'>ZipN</span> <span class='hs-varid'>p</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-conid'>ZipN</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>left1</span> <span class='hs-varid'>x</span>
<a name="line-97"></a><a name="rightN"></a><span class='hs-definition'>rightN</span> <span class='hs-layout'>(</span><span class='hs-conid'>ZipN</span> <span class='hs-varid'>p</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-conid'>ZipN</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>right1</span> <span class='hs-varid'>x</span>
<a name="line-98"></a><a name="holeN"></a><span class='hs-definition'>holeN</span> <span class='hs-layout'>(</span><span class='hs-conid'>ZipN</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>hole1</span> <span class='hs-varid'>x</span>
<a name="line-99"></a><a name="replaceN"></a><span class='hs-definition'>replaceN</span> <span class='hs-varid'>v</span> <span class='hs-layout'>(</span><span class='hs-conid'>ZipN</span> <span class='hs-varid'>p</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ZipN</span> <span class='hs-varid'>p</span> <span class='hs-varop'>$</span> <span class='hs-varid'>replace1</span> <span class='hs-varid'>x</span> <span class='hs-varid'>v</span>
<a name="line-100"></a>
<a name="line-101"></a><a name="upN"></a><span class='hs-definition'>upN</span> <span class='hs-layout'>(</span><span class='hs-conid'>ZipN</span> <span class='hs-conid'>[]</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Nothing</span>
<a name="line-102"></a><span class='hs-definition'>upN</span> <span class='hs-layout'>(</span><span class='hs-conid'>ZipN</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span><span class='hs-conop'>:</span><span class='hs-varid'>ps</span><span class='hs-layout'>)</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Just</span> <span class='hs-varop'>$</span> <span class='hs-conid'>ZipN</span> <span class='hs-varid'>ps</span> <span class='hs-varop'>$</span> <span class='hs-varid'>p</span> <span class='hs-varop'>$</span> <span class='hs-varid'>top1</span> <span class='hs-varid'>x</span>
<a name="line-103"></a>
<a name="line-104"></a><a name="topN"></a><span class='hs-definition'>topN</span> <span class='hs-layout'>(</span><span class='hs-conid'>ZipN</span> <span class='hs-conid'>[]</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span>
<a name="line-105"></a><span class='hs-definition'>topN</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>topN</span> <span class='hs-varop'>$</span> <span class='hs-varid'>fromJust</span> <span class='hs-varop'>$</span> <span class='hs-varid'>upN</span> <span class='hs-varid'>x</span>
<a name="line-106"></a>
<a name="line-107"></a><a name="downN"></a><span class='hs-definition'>downN</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Uniplate</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>ZipN</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Maybe</span> <span class='hs-layout'>(</span><span class='hs-conid'>ZipN</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span>
<a name="line-108"></a><span class='hs-definition'>downN</span> <span class='hs-layout'>(</span><span class='hs-conid'>ZipN</span> <span class='hs-varid'>ps</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-conid'>ZipN</span> <span class='hs-varop'>$</span> <span class='hs-varid'>replace1</span> <span class='hs-varid'>x</span> <span class='hs-varop'>.</span> <span class='hs-varid'>gen</span> <span class='hs-conop'>:</span> <span class='hs-varid'>ps</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>zip1</span> <span class='hs-varid'>cs</span>
<a name="line-109"></a> <span class='hs-keyword'>where</span> <span class='hs-layout'>(</span><span class='hs-varid'>cs</span><span class='hs-layout'>,</span><span class='hs-varid'>gen</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>uniplate</span> <span class='hs-varop'>$</span> <span class='hs-varid'>hole1</span> <span class='hs-varid'>x</span>
<a name="line-110"></a>
<a name="line-111"></a>
<a name="line-112"></a><span class='hs-comment'>---------------------------------------------------------------------</span>
<a name="line-113"></a><span class='hs-comment'>-- 1 LEVEL ZIPPER ON Str</span>
<a name="line-114"></a>
<a name="line-115"></a><a name="Diff1"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>Diff1</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>TwoLeft</span> <span class='hs-layout'>(</span><span class='hs-conid'>Str</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>|</span> <span class='hs-conid'>TwoRight</span> <span class='hs-layout'>(</span><span class='hs-conid'>Str</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Eq</span>
<a name="line-116"></a>
<a name="line-117"></a><a name="undiff1"></a><span class='hs-definition'>undiff1</span> <span class='hs-varid'>r</span> <span class='hs-layout'>(</span><span class='hs-conid'>TwoLeft</span> <span class='hs-varid'>l</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Two</span> <span class='hs-varid'>l</span> <span class='hs-varid'>r</span>
<a name="line-118"></a><span class='hs-definition'>undiff1</span> <span class='hs-varid'>l</span> <span class='hs-layout'>(</span><span class='hs-conid'>TwoRight</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Two</span> <span class='hs-varid'>l</span> <span class='hs-varid'>r</span>
<a name="line-119"></a>
<a name="line-120"></a><a name="Zip1"></a><span class='hs-comment'>-- Warning: this definition of Eq may look too strong (Str Left/Right is not relevant)</span>
<a name="line-121"></a><a name="Zip1"></a><span class='hs-comment'>-- but you don't know what the uniplate.gen function will do</span>
<a name="line-122"></a><a name="Zip1"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>Zip1</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Zip1</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Diff1</span> <span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-varid'>a</span> <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Eq</span>
<a name="line-123"></a>
<a name="line-124"></a><a name="zip1"></a><span class='hs-definition'>zip1</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Str</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Maybe</span> <span class='hs-layout'>(</span><span class='hs-conid'>Zip1</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span>
<a name="line-125"></a><span class='hs-definition'>zip1</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>insert1</span> <span class='hs-conid'>True</span> <span class='hs-conid'>[]</span>
<a name="line-126"></a>
<a name="line-127"></a><a name="insert1"></a><span class='hs-definition'>insert1</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Bool</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Diff1</span> <span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Str</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Maybe</span> <span class='hs-layout'>(</span><span class='hs-conid'>Zip1</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-128"></a><span class='hs-definition'>insert1</span> <span class='hs-varid'>leftmost</span> <span class='hs-varid'>c</span> <span class='hs-conid'>Zero</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Nothing</span>
<a name="line-129"></a><span class='hs-definition'>insert1</span> <span class='hs-varid'>leftmost</span> <span class='hs-varid'>c</span> <span class='hs-layout'>(</span><span class='hs-conid'>One</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Just</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Zip1</span> <span class='hs-varid'>c</span> <span class='hs-varid'>x</span>
<a name="line-130"></a><span class='hs-definition'>insert1</span> <span class='hs-varid'>leftmost</span> <span class='hs-varid'>c</span> <span class='hs-layout'>(</span><span class='hs-conid'>Two</span> <span class='hs-varid'>l</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>if</span> <span class='hs-varid'>leftmost</span> <span class='hs-keyword'>then</span> <span class='hs-varid'>ll</span> <span class='hs-varop'>`mplus`</span> <span class='hs-varid'>rr</span> <span class='hs-keyword'>else</span> <span class='hs-varid'>rr</span> <span class='hs-varop'>`mplus`</span> <span class='hs-varid'>ll</span>
<a name="line-131"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>ll</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>insert1</span> <span class='hs-varid'>leftmost</span> <span class='hs-layout'>(</span><span class='hs-conid'>TwoRight</span> <span class='hs-varid'>r</span><span class='hs-conop'>:</span><span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-varid'>l</span>
<a name="line-132"></a> <span class='hs-varid'>rr</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>insert1</span> <span class='hs-varid'>leftmost</span> <span class='hs-layout'>(</span><span class='hs-conid'>TwoLeft</span> <span class='hs-varid'>l</span><span class='hs-conop'>:</span><span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-varid'>r</span>
<a name="line-133"></a>
<a name="line-134"></a><a name="left1"></a><span class='hs-definition'>left1</span><span class='hs-layout'>,</span> <span class='hs-varid'>right1</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Zip1</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Maybe</span> <span class='hs-layout'>(</span><span class='hs-conid'>Zip1</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-135"></a><span class='hs-definition'>left1</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>move1</span> <span class='hs-conid'>True</span>
<a name="line-136"></a><a name="right1"></a><span class='hs-definition'>right1</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>move1</span> <span class='hs-conid'>False</span>
<a name="line-137"></a>
<a name="line-138"></a><a name="move1"></a><span class='hs-definition'>move1</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Bool</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Zip1</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Maybe</span> <span class='hs-layout'>(</span><span class='hs-conid'>Zip1</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-139"></a><span class='hs-definition'>move1</span> <span class='hs-varid'>leftward</span> <span class='hs-layout'>(</span><span class='hs-conid'>Zip1</span> <span class='hs-varid'>p</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varid'>p</span> <span class='hs-varop'>$</span> <span class='hs-conid'>One</span> <span class='hs-varid'>x</span>
<a name="line-140"></a> <span class='hs-keyword'>where</span>
<a name="line-141"></a> <span class='hs-varid'>f</span> <span class='hs-varid'>p</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>msum</span> <span class='hs-varop'>$</span>
<a name="line-142"></a> <span class='hs-keyglyph'>[</span><span class='hs-varid'>insert1</span> <span class='hs-conid'>False</span> <span class='hs-layout'>(</span><span class='hs-conid'>TwoRight</span> <span class='hs-varid'>x</span><span class='hs-conop'>:</span><span class='hs-varid'>ps</span><span class='hs-layout'>)</span> <span class='hs-varid'>l</span> <span class='hs-keyglyph'>|</span> <span class='hs-conid'>TwoLeft</span> <span class='hs-varid'>l</span><span class='hs-conop'>:</span><span class='hs-varid'>ps</span> <span class='hs-keyglyph'><-</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>p</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>,</span> <span class='hs-varid'>leftward</span><span class='hs-keyglyph'>]</span> <span class='hs-varop'>++</span>
<a name="line-143"></a> <span class='hs-keyglyph'>[</span><span class='hs-varid'>insert1</span> <span class='hs-conid'>True</span> <span class='hs-layout'>(</span><span class='hs-conid'>TwoLeft</span> <span class='hs-varid'>x</span><span class='hs-conop'>:</span><span class='hs-varid'>ps</span><span class='hs-layout'>)</span> <span class='hs-varid'>r</span> <span class='hs-keyglyph'>|</span> <span class='hs-conid'>TwoRight</span> <span class='hs-varid'>r</span><span class='hs-conop'>:</span><span class='hs-varid'>ps</span> <span class='hs-keyglyph'><-</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>p</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>,</span> <span class='hs-varid'>not</span> <span class='hs-varid'>leftward</span><span class='hs-keyglyph'>]</span> <span class='hs-varop'>++</span>
<a name="line-144"></a> <span class='hs-keyglyph'>[</span><span class='hs-varid'>f</span> <span class='hs-varid'>ps</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'>`undiff1`</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>p</span><span class='hs-conop'>:</span><span class='hs-varid'>ps</span> <span class='hs-keyglyph'><-</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>p</span><span class='hs-keyglyph'>]</span><span class='hs-keyglyph'>]</span>
<a name="line-145"></a>
<a name="line-146"></a><a name="top1"></a><span class='hs-definition'>top1</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Zip1</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Str</span> <span class='hs-varid'>a</span>
<a name="line-147"></a><span class='hs-definition'>top1</span> <span class='hs-layout'>(</span><span class='hs-conid'>Zip1</span> <span class='hs-varid'>p</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varid'>p</span> <span class='hs-layout'>(</span><span class='hs-conid'>One</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span>
<a name="line-148"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Diff1</span> <span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Str</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Str</span> <span class='hs-varid'>a</span>
<a name="line-149"></a> <span class='hs-varid'>f</span> <span class='hs-conid'>[]</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span>
<a name="line-150"></a> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span><span class='hs-conop'>:</span><span class='hs-varid'>ps</span><span class='hs-layout'>)</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varid'>ps</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'>`undiff1`</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span>
<a name="line-151"></a>
<a name="line-152"></a><a name="hole1"></a><span class='hs-definition'>hole1</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Zip1</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-153"></a><span class='hs-definition'>hole1</span> <span class='hs-layout'>(</span><span class='hs-conid'>Zip1</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span>
<a name="line-154"></a>
<a name="line-155"></a><a name="replace1"></a><span class='hs-comment'>-- this way round so the a can be disguarded quickly</span>
<a name="line-156"></a><span class='hs-definition'>replace1</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Zip1</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Zip1</span> <span class='hs-varid'>a</span>
<a name="line-157"></a><span class='hs-definition'>replace1</span> <span class='hs-layout'>(</span><span class='hs-conid'>Zip1</span> <span class='hs-varid'>p</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Zip1</span> <span class='hs-varid'>p</span>
</pre></body>
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