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<title>src/Control/Lens/Internal/Level.hs</title>
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<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE CPP #-}</span>
<a name="line-2"></a><span class='hs-comment'>{-# LANGUAGE GADTs #-}</span>
<a name="line-3"></a><span class='hs-comment'>{-# LANGUAGE Rank2Types #-}</span>
<a name="line-4"></a><span class='hs-comment'>{-# LANGUAGE FlexibleInstances #-}</span>
<a name="line-5"></a><span class='hs-comment'>{-# LANGUAGE ScopedTypeVariables #-}</span>
<a name="line-6"></a><span class='hs-comment'>{-# LANGUAGE UndecidableInstances #-}</span>
<a name="line-7"></a><span class='hs-comment'>{-# LANGUAGE MultiParamTypeClasses #-}</span>
<a name="line-8"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-9"></a><span class='hs-comment'>-- |</span>
<a name="line-10"></a><span class='hs-comment'>-- Module : Control.Lens.Internal.Level</span>
<a name="line-11"></a><span class='hs-comment'>-- Copyright : (C) 2012-2015 Edward Kmett</span>
<a name="line-12"></a><span class='hs-comment'>-- License : BSD-style (see the file LICENSE)</span>
<a name="line-13"></a><span class='hs-comment'>-- Maintainer : Edward Kmett <ekmett@gmail.com></span>
<a name="line-14"></a><span class='hs-comment'>-- Stability : experimental</span>
<a name="line-15"></a><span class='hs-comment'>-- Portability : non-portable</span>
<a name="line-16"></a><span class='hs-comment'>--</span>
<a name="line-17"></a><span class='hs-comment'>-- This module provides implementation details of the combinators in</span>
<a name="line-18"></a><span class='hs-comment'>-- "Control.Lens.Level", which provides for the breadth-first 'Control.Lens.Traversal.Traversal' of</span>
<a name="line-19"></a><span class='hs-comment'>-- an arbitrary 'Control.Lens.Traversal.Traversal'.</span>
<a name="line-20"></a><span class='hs-comment'>----------------------------------------------------------------------------</span>
<a name="line-21"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Lens</span><span class='hs-varop'>.</span><span class='hs-conid'>Internal</span><span class='hs-varop'>.</span><span class='hs-conid'>Level</span>
<a name="line-22"></a> <span class='hs-layout'>(</span>
<a name="line-23"></a> <span class='hs-comment'>-- * Levels</span>
<a name="line-24"></a> <span class='hs-conid'>Level</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-25"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Deepening</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-varid'>deepening</span>
<a name="line-26"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Flows</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-27"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-28"></a>
<a name="line-29"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Applicative</span>
<a name="line-30"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Category</span>
<a name="line-31"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Comonad</span>
<a name="line-32"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Foldable</span>
<a name="line-33"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Functor</span><span class='hs-varop'>.</span><span class='hs-conid'>Apply</span>
<a name="line-34"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Int</span>
<a name="line-35"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Semigroup</span>
<a name="line-36"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Traversable</span>
<a name="line-37"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Word</span>
<a name="line-38"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Prelude</span> <span class='hs-varid'>hiding</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varop'>.</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span><span class='hs-varid'>id</span><span class='hs-layout'>)</span>
<a name="line-39"></a>
<a name="line-40"></a><span class='hs-comment'>------------------------------------------------------------------------------</span>
<a name="line-41"></a><span class='hs-comment'>-- Levels</span>
<a name="line-42"></a><span class='hs-comment'>------------------------------------------------------------------------------</span>
<a name="line-43"></a>
<a name="line-44"></a><a name="Level"></a><span class='hs-comment'>-- | This data type represents a path-compressed copy of one level of a source</span>
<a name="line-45"></a><a name="Level"></a><span class='hs-comment'>-- data structure. We can safely use path-compression because we know the depth</span>
<a name="line-46"></a><a name="Level"></a><span class='hs-comment'>-- of the tree.</span>
<a name="line-47"></a><a name="Level"></a><span class='hs-comment'>--</span>
<a name="line-48"></a><a name="Level"></a><span class='hs-comment'>-- Path compression is performed by viewing a 'Level' as a PATRICIA trie of the</span>
<a name="line-49"></a><a name="Level"></a><span class='hs-comment'>-- paths into the structure to leaves at a given depth, similar in many ways</span>
<a name="line-50"></a><a name="Level"></a><span class='hs-comment'>-- to a 'Data.IntMap.IntMap', but unlike a regular PATRICIA trie we do not need</span>
<a name="line-51"></a><a name="Level"></a><span class='hs-comment'>-- to store the mask bits merely the depth of the fork.</span>
<a name="line-52"></a><a name="Level"></a><span class='hs-comment'>--</span>
<a name="line-53"></a><a name="Level"></a><span class='hs-comment'>-- One invariant of this structure is that underneath a 'Two' node you will not</span>
<a name="line-54"></a><a name="Level"></a><span class='hs-comment'>-- find any 'Zero' nodes, so 'Zero' can only occur at the root.</span>
<a name="line-55"></a><a name="Level"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>Level</span> <span class='hs-varid'>i</span> <span class='hs-varid'>a</span>
<a name="line-56"></a> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Two</span> <span class='hs-comment'>{-# UNPACK #-}</span> <span class='hs-varop'>!</span><span class='hs-conid'>Word</span> <span class='hs-varop'>!</span><span class='hs-layout'>(</span><span class='hs-conid'>Level</span> <span class='hs-varid'>i</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-varop'>!</span><span class='hs-layout'>(</span><span class='hs-conid'>Level</span> <span class='hs-varid'>i</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-57"></a> <span class='hs-keyglyph'>|</span> <span class='hs-conid'>One</span> <span class='hs-varid'>i</span> <span class='hs-varid'>a</span>
<a name="line-58"></a> <span class='hs-keyglyph'>|</span> <span class='hs-conid'>Zero</span>
<a name="line-59"></a> <span class='hs-keyword'>deriving</span> <span class='hs-layout'>(</span><span class='hs-conid'>Eq</span><span class='hs-layout'>,</span><span class='hs-conid'>Ord</span><span class='hs-layout'>,</span><span class='hs-conid'>Show</span><span class='hs-layout'>,</span><span class='hs-conid'>Read</span><span class='hs-layout'>)</span>
<a name="line-60"></a>
<a name="line-61"></a><a name="lappend"></a><span class='hs-comment'>-- | Append a pair of 'Level' values to get a new 'Level' with path compression.</span>
<a name="line-62"></a><span class='hs-comment'>--</span>
<a name="line-63"></a><span class='hs-comment'>-- As the 'Level' type is user-visible, we do not expose this as an illegal</span>
<a name="line-64"></a><span class='hs-comment'>-- 'Semigroup' instance, and just use it directly in 'Deepening' as needed.</span>
<a name="line-65"></a><span class='hs-definition'>lappend</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Level</span> <span class='hs-varid'>i</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Level</span> <span class='hs-varid'>i</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Level</span> <span class='hs-varid'>i</span> <span class='hs-varid'>a</span>
<a name="line-66"></a><span class='hs-definition'>lappend</span> <span class='hs-conid'>Zero</span> <span class='hs-conid'>Zero</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Zero</span>
<a name="line-67"></a><span class='hs-definition'>lappend</span> <span class='hs-conid'>Zero</span> <span class='hs-varid'>r</span><span class='hs-keyglyph'>@</span><span class='hs-conid'>One</span><span class='hs-layout'>{</span><span class='hs-layout'>}</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>r</span>
<a name="line-68"></a><span class='hs-definition'>lappend</span> <span class='hs-varid'>l</span><span class='hs-keyglyph'>@</span><span class='hs-conid'>One</span><span class='hs-layout'>{</span><span class='hs-layout'>}</span> <span class='hs-conid'>Zero</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>l</span>
<a name="line-69"></a><span class='hs-definition'>lappend</span> <span class='hs-conid'>Zero</span> <span class='hs-layout'>(</span><span class='hs-conid'>Two</span> <span class='hs-varid'>n</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-conid'>Two</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span> <span class='hs-varop'>+</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varid'>l</span> <span class='hs-varid'>r</span>
<a name="line-70"></a><span class='hs-definition'>lappend</span> <span class='hs-layout'>(</span><span class='hs-conid'>Two</span> <span class='hs-varid'>n</span> <span class='hs-varid'>l</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-conid'>Zero</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Two</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span> <span class='hs-varop'>+</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varid'>l</span> <span class='hs-varid'>r</span>
<a name="line-71"></a><span class='hs-definition'>lappend</span> <span class='hs-varid'>l</span> <span class='hs-varid'>r</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Two</span> <span class='hs-num'>0</span> <span class='hs-varid'>l</span> <span class='hs-varid'>r</span>
<a name="line-72"></a><span class='hs-comment'>{-# INLINE lappend #-}</span>
<a name="line-73"></a>
<a name="line-74"></a><a name="instance%20Functor%20(Level%20i)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Functor</span> <span class='hs-layout'>(</span><span class='hs-conid'>Level</span> <span class='hs-varid'>i</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-75"></a> <span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>go</span> <span class='hs-keyword'>where</span>
<a name="line-76"></a> <span class='hs-varid'>go</span> <span class='hs-layout'>(</span><span class='hs-conid'>Two</span> <span class='hs-varid'>n</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-conid'>Two</span> <span class='hs-varid'>n</span> <span class='hs-layout'>(</span><span class='hs-varid'>go</span> <span class='hs-varid'>l</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>go</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span>
<a name="line-77"></a> <span class='hs-varid'>go</span> <span class='hs-layout'>(</span><span class='hs-conid'>One</span> <span class='hs-varid'>i</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>One</span> <span class='hs-varid'>i</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-78"></a> <span class='hs-varid'>go</span> <span class='hs-conid'>Zero</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Zero</span>
<a name="line-79"></a> <span class='hs-comment'>{-# INLINE fmap #-}</span>
<a name="line-80"></a>
<a name="line-81"></a><a name="instance%20Foldable%20(Level%20i)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Foldable</span> <span class='hs-layout'>(</span><span class='hs-conid'>Level</span> <span class='hs-varid'>i</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-82"></a> <span class='hs-varid'>foldMap</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>go</span> <span class='hs-keyword'>where</span>
<a name="line-83"></a> <span class='hs-varid'>go</span> <span class='hs-layout'>(</span><span class='hs-conid'>Two</span> <span class='hs-keyword'>_</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-varid'>go</span> <span class='hs-varid'>l</span> <span class='hs-varop'>`mappend`</span> <span class='hs-varid'>go</span> <span class='hs-varid'>r</span>
<a name="line-84"></a> <span class='hs-varid'>go</span> <span class='hs-layout'>(</span><span class='hs-conid'>One</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span>
<a name="line-85"></a> <span class='hs-varid'>go</span> <span class='hs-conid'>Zero</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mempty</span>
<a name="line-86"></a> <span class='hs-comment'>{-# INLINE foldMap #-}</span>
<a name="line-87"></a>
<a name="line-88"></a><a name="instance%20Traversable%20(Level%20i)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Traversable</span> <span class='hs-layout'>(</span><span class='hs-conid'>Level</span> <span class='hs-varid'>i</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-89"></a> <span class='hs-varid'>traverse</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>go</span> <span class='hs-keyword'>where</span>
<a name="line-90"></a> <span class='hs-varid'>go</span> <span class='hs-layout'>(</span><span class='hs-conid'>Two</span> <span class='hs-varid'>n</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-conid'>Two</span> <span class='hs-varid'>n</span> <span class='hs-varop'><$></span> <span class='hs-varid'>go</span> <span class='hs-varid'>l</span> <span class='hs-varop'><*></span> <span class='hs-varid'>go</span> <span class='hs-varid'>r</span>
<a name="line-91"></a> <span class='hs-varid'>go</span> <span class='hs-layout'>(</span><span class='hs-conid'>One</span> <span class='hs-varid'>i</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>One</span> <span class='hs-varid'>i</span> <span class='hs-varop'><$></span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span>
<a name="line-92"></a> <span class='hs-varid'>go</span> <span class='hs-conid'>Zero</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pure</span> <span class='hs-conid'>Zero</span>
<a name="line-93"></a> <span class='hs-comment'>{-# INLINE traverse #-}</span>
<a name="line-94"></a>
<a name="line-95"></a><span class='hs-comment'>------------------------------------------------------------------------------</span>
<a name="line-96"></a><span class='hs-comment'>-- Generating Levels</span>
<a name="line-97"></a><span class='hs-comment'>------------------------------------------------------------------------------</span>
<a name="line-98"></a>
<a name="line-99"></a><a name="Deepening"></a><span class='hs-comment'>-- | This is an illegal 'Monoid' used to construct a single 'Level'.</span>
<a name="line-100"></a><a name="Deepening"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>Deepening</span> <span class='hs-varid'>i</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Deepening</span> <span class='hs-layout'>{</span> <span class='hs-varid'>runDeepening</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyword'>forall</span> <span class='hs-varid'>r</span><span class='hs-varop'>.</span> <span class='hs-conid'>Int</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-conid'>Level</span> <span class='hs-varid'>i</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span> <span class='hs-layout'>}</span>
<a name="line-101"></a>
<a name="line-102"></a><a name="instance%20Semigroup%20(Deepening%20i%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>Deepening</span> <span class='hs-varid'>i</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-103"></a> <span class='hs-conid'>Deepening</span> <span class='hs-varid'>l</span> <span class='hs-varop'><></span> <span class='hs-conid'>Deepening</span> <span class='hs-varid'>r</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Deepening</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span> <span class='hs-varid'>n</span> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-varid'>n</span> <span class='hs-keyword'>of</span>
<a name="line-104"></a> <span class='hs-num'>0</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>k</span> <span class='hs-conid'>Zero</span> <span class='hs-conid'>True</span>
<a name="line-105"></a> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>let</span> <span class='hs-varid'>n'</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>n</span> <span class='hs-comment'>-</span> <span class='hs-num'>1</span> <span class='hs-keyword'>in</span> <span class='hs-varid'>l</span> <span class='hs-varid'>n'</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>x</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span> <span class='hs-varid'>n'</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>y</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>k</span> <span class='hs-layout'>(</span><span class='hs-varid'>lappend</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-varop'>||</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-106"></a> <span class='hs-comment'>{-# INLINE (<>) #-}</span>
<a name="line-107"></a>
<a name="line-108"></a><a name="instance%20Monoid%20(Deepening%20i%20a)"></a><span class='hs-comment'>-- | This is an illegal 'Monoid'.</span>
<a name="line-109"></a><a name="instance%20Monoid%20(Deepening%20i%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Monoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>Deepening</span> <span class='hs-varid'>i</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-110"></a> <span class='hs-varid'>mempty</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Deepening</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>k</span> <span class='hs-conid'>Zero</span> <span class='hs-conid'>False</span>
<a name="line-111"></a> <span class='hs-comment'>{-# INLINE mempty #-}</span>
<a name="line-112"></a> <span class='hs-varid'>mappend</span> <span class='hs-layout'>(</span><span class='hs-conid'>Deepening</span> <span class='hs-varid'>l</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Deepening</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Deepening</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span> <span class='hs-varid'>n</span> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-varid'>n</span> <span class='hs-keyword'>of</span>
<a name="line-113"></a> <span class='hs-num'>0</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>k</span> <span class='hs-conid'>Zero</span> <span class='hs-conid'>True</span>
<a name="line-114"></a> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>let</span> <span class='hs-varid'>n'</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>n</span> <span class='hs-comment'>-</span> <span class='hs-num'>1</span> <span class='hs-keyword'>in</span> <span class='hs-varid'>l</span> <span class='hs-varid'>n'</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>x</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span> <span class='hs-varid'>n'</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>y</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>k</span> <span class='hs-layout'>(</span><span class='hs-varid'>lappend</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-varop'>||</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-115"></a> <span class='hs-comment'>{-# INLINE mappend #-}</span>
<a name="line-116"></a>
<a name="line-117"></a><a name="deepening"></a><span class='hs-comment'>-- | Generate the leaf of a given 'Deepening' based on whether or not we're at the correct depth.</span>
<a name="line-118"></a><span class='hs-definition'>deepening</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>i</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Deepening</span> <span class='hs-varid'>i</span> <span class='hs-varid'>a</span>
<a name="line-119"></a><span class='hs-definition'>deepening</span> <span class='hs-varid'>i</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Deepening</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>n</span> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>k</span> <span class='hs-layout'>(</span><span class='hs-keyword'>if</span> <span class='hs-varid'>n</span> <span class='hs-varop'>==</span> <span class='hs-num'>0</span> <span class='hs-keyword'>then</span> <span class='hs-conid'>One</span> <span class='hs-varid'>i</span> <span class='hs-varid'>a</span> <span class='hs-keyword'>else</span> <span class='hs-conid'>Zero</span><span class='hs-layout'>)</span> <span class='hs-conid'>False</span>
<a name="line-120"></a><span class='hs-comment'>{-# INLINE deepening #-}</span>
<a name="line-121"></a>
<a name="line-122"></a><span class='hs-comment'>------------------------------------------------------------------------------</span>
<a name="line-123"></a><span class='hs-comment'>-- Reassembling Levels</span>
<a name="line-124"></a><span class='hs-comment'>------------------------------------------------------------------------------</span>
<a name="line-125"></a>
<a name="line-126"></a><a name="Flows"></a><span class='hs-comment'>-- | This is an illegal 'Applicative' used to replace the contents of a list of consecutive 'Level' values</span>
<a name="line-127"></a><a name="Flows"></a><span class='hs-comment'>-- representing each layer of a structure into the original shape that they were derived from.</span>
<a name="line-128"></a><a name="Flows"></a><span class='hs-comment'>--</span>
<a name="line-129"></a><a name="Flows"></a><span class='hs-comment'>-- Attempting to 'Flow' something back into a shape other than the one it was taken from will fail.</span>
<a name="line-130"></a><a name="Flows"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>Flows</span> <span class='hs-varid'>i</span> <span class='hs-varid'>b</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Flows</span> <span class='hs-layout'>{</span> <span class='hs-varid'>runFlows</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Level</span> <span class='hs-varid'>i</span> <span class='hs-varid'>b</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-layout'>}</span>
<a name="line-131"></a>
<a name="line-132"></a><a name="instance%20Functor%20(Flows%20i%20b)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Functor</span> <span class='hs-layout'>(</span><span class='hs-conid'>Flows</span> <span class='hs-varid'>i</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-133"></a> <span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Flows</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Flows</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span>
<a name="line-134"></a> <span class='hs-comment'>{-# INLINE fmap #-}</span>
<a name="line-135"></a>
<a name="line-136"></a><a name="triml"></a><span class='hs-comment'>-- | Walk down one constructor in a 'Level', veering left.</span>
<a name="line-137"></a><span class='hs-definition'>triml</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Level</span> <span class='hs-varid'>i</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Level</span> <span class='hs-varid'>i</span> <span class='hs-varid'>b</span>
<a name="line-138"></a><span class='hs-definition'>triml</span> <span class='hs-layout'>(</span><span class='hs-conid'>Two</span> <span class='hs-num'>0</span> <span class='hs-varid'>l</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>l</span>
<a name="line-139"></a><span class='hs-definition'>triml</span> <span class='hs-layout'>(</span><span class='hs-conid'>Two</span> <span class='hs-varid'>n</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-conid'>Two</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span> <span class='hs-comment'>-</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varid'>l</span> <span class='hs-varid'>r</span>
<a name="line-140"></a><span class='hs-definition'>triml</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span>
<a name="line-141"></a><span class='hs-comment'>{-# INLINE triml #-}</span>
<a name="line-142"></a>
<a name="line-143"></a><a name="trimr"></a><span class='hs-comment'>-- | Walk down one constructor in a 'Level', veering right.</span>
<a name="line-144"></a><span class='hs-definition'>trimr</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Level</span> <span class='hs-varid'>i</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Level</span> <span class='hs-varid'>i</span> <span class='hs-varid'>b</span>
<a name="line-145"></a><span class='hs-definition'>trimr</span> <span class='hs-layout'>(</span><span class='hs-conid'>Two</span> <span class='hs-num'>0</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>r</span>
<a name="line-146"></a><span class='hs-definition'>trimr</span> <span class='hs-layout'>(</span><span class='hs-conid'>Two</span> <span class='hs-varid'>n</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-conid'>Two</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span> <span class='hs-comment'>-</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varid'>l</span> <span class='hs-varid'>r</span>
<a name="line-147"></a><span class='hs-definition'>trimr</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span>
<a name="line-148"></a><span class='hs-comment'>{-# INLINE trimr #-}</span>
<a name="line-149"></a>
<a name="line-150"></a><a name="instance%20Apply%20(Flows%20i%20b)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Apply</span> <span class='hs-layout'>(</span><span class='hs-conid'>Flows</span> <span class='hs-varid'>i</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-151"></a> <span class='hs-conid'>Flows</span> <span class='hs-varid'>mf</span> <span class='hs-varop'><.></span> <span class='hs-conid'>Flows</span> <span class='hs-varid'>ma</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Flows</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span> <span class='hs-varid'>xss</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-varid'>xss</span> <span class='hs-keyword'>of</span>
<a name="line-152"></a> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>mf</span> <span class='hs-conid'>[]</span> <span class='hs-layout'>(</span><span class='hs-varid'>ma</span> <span class='hs-conid'>[]</span><span class='hs-layout'>)</span>
<a name="line-153"></a> <span class='hs-layout'>(</span><span class='hs-keyword'>_</span><span class='hs-conop'>:</span><span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>mf</span> <span class='hs-layout'>(</span><span class='hs-varid'>triml</span> <span class='hs-varop'><$></span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>ma</span> <span class='hs-layout'>(</span><span class='hs-varid'>trimr</span> <span class='hs-varop'><$></span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span>
<a name="line-154"></a> <span class='hs-comment'>{-# INLINE (<.>) #-}</span>
<a name="line-155"></a>
<a name="line-156"></a><a name="instance%20Applicative%20(Flows%20i%20b)"></a><span class='hs-comment'>-- | This is an illegal 'Applicative'.</span>
<a name="line-157"></a><a name="instance%20Applicative%20(Flows%20i%20b)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Applicative</span> <span class='hs-layout'>(</span><span class='hs-conid'>Flows</span> <span class='hs-varid'>i</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-158"></a> <span class='hs-varid'>pure</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Flows</span> <span class='hs-layout'>(</span><span class='hs-varid'>const</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-159"></a> <span class='hs-comment'>{-# INLINE pure #-}</span>
<a name="line-160"></a> <span class='hs-conid'>Flows</span> <span class='hs-varid'>mf</span> <span class='hs-varop'><*></span> <span class='hs-conid'>Flows</span> <span class='hs-varid'>ma</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Flows</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span> <span class='hs-varid'>xss</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-varid'>xss</span> <span class='hs-keyword'>of</span>
<a name="line-161"></a> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>mf</span> <span class='hs-conid'>[]</span> <span class='hs-layout'>(</span><span class='hs-varid'>ma</span> <span class='hs-conid'>[]</span><span class='hs-layout'>)</span>
<a name="line-162"></a> <span class='hs-layout'>(</span><span class='hs-keyword'>_</span><span class='hs-conop'>:</span><span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>mf</span> <span class='hs-layout'>(</span><span class='hs-varid'>triml</span> <span class='hs-varop'><$></span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>ma</span> <span class='hs-layout'>(</span><span class='hs-varid'>trimr</span> <span class='hs-varop'><$></span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span>
<a name="line-163"></a> <span class='hs-comment'>{-# INLINE (<*>) #-}</span>
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