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<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE CPP #-}</span>
<a name="line-2"></a>
<a name="line-3"></a><span class='hs-comment'>{-| Utitlity functions on lists.
<a name="line-4"></a>-}</span>
<a name="line-5"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Utils</span><span class='hs-varop'>.</span><span class='hs-conid'>List</span> <span class='hs-keyword'>where</span>
<a name="line-6"></a>
<a name="line-7"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Utils</span><span class='hs-varop'>.</span><span class='hs-conid'>TestHelpers</span>
<a name="line-8"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Utils</span><span class='hs-varop'>.</span><span class='hs-conid'>QuickCheck</span>
<a name="line-9"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Utils</span><span class='hs-varop'>.</span><span class='hs-conid'>Tuple</span>
<a name="line-10"></a>
<a name="line-11"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Text</span><span class='hs-varop'>.</span><span class='hs-conid'>Show</span><span class='hs-varop'>.</span><span class='hs-conid'>Functions</span>
<a name="line-12"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Function</span>
<a name="line-13"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>List</span>
<a name="line-14"></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-15"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Set</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>Set</span>
<a name="line-16"></a>
<a name="line-17"></a><span class='hs-cpp'>#include "../undefined.h"</span>
<a name="line-18"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Utils</span><span class='hs-varop'>.</span><span class='hs-conid'>Impossible</span>
<a name="line-19"></a>
<a name="line-20"></a><a name="mhead"></a><span class='hs-comment'>-- | Head function (safe).</span>
<a name="line-21"></a><span class='hs-definition'>mhead</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Maybe</span> <span class='hs-varid'>a</span>
<a name="line-22"></a><span class='hs-definition'>mhead</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Nothing</span>
<a name="line-23"></a><span class='hs-definition'>mhead</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-conop'>:</span><span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Just</span> <span class='hs-varid'>x</span>
<a name="line-24"></a>
<a name="line-25"></a><a name="uncons"></a><span class='hs-comment'>-- | Opposite of cons @(:)@, safe.</span>
<a name="line-26"></a><span class='hs-definition'>uncons</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Maybe</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span>
<a name="line-27"></a><span class='hs-definition'>uncons</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Nothing</span>
<a name="line-28"></a><span class='hs-definition'>uncons</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</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-conid'>Just</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span><span class='hs-varid'>xs</span><span class='hs-layout'>)</span>
<a name="line-29"></a>
<a name="line-30"></a><a name="downFrom"></a><span class='hs-comment'>-- | downFrom n = [n-1,..1,0]</span>
<a name="line-31"></a><span class='hs-definition'>downFrom</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Integral</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-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span>
<a name="line-32"></a><span class='hs-definition'>downFrom</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>n</span> <span class='hs-varop'><=</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>[]</span>
<a name="line-33"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</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'>n'</span> <span class='hs-conop'>:</span> <span class='hs-varid'>downFrom</span> <span class='hs-varid'>n'</span>
<a name="line-34"></a>
<a name="line-35"></a><a name="updateLast"></a><span class='hs-comment'>-- | Update the last element of a list, if it exists</span>
<a name="line-36"></a><span class='hs-definition'>updateLast</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span>
<a name="line-37"></a><span class='hs-definition'>updateLast</span> <span class='hs-varid'>f</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>[]</span>
<a name="line-38"></a><span class='hs-definition'>updateLast</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span>
<a name="line-39"></a><span class='hs-definition'>updateLast</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-conop'>:</span> <span class='hs-keyword'>as</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-keyword'>_</span> <span class='hs-conop'>:</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>a</span> <span class='hs-conop'>:</span> <span class='hs-varid'>updateLast</span> <span class='hs-varid'>f</span> <span class='hs-keyword'>as</span>
<a name="line-40"></a>
<a name="line-41"></a><a name="mapEither"></a><span class='hs-comment'>-- | A generalized version of @partition@.</span>
<a name="line-42"></a><span class='hs-comment'>-- (Cf. @mapMaybe@ vs. @filter@).</span>
<a name="line-43"></a><span class='hs-definition'>mapEither</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Either</span> <span class='hs-varid'>b</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>[</span><span class='hs-varid'>b</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>,</span><span class='hs-keyglyph'>[</span><span class='hs-varid'>c</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span>
<a name="line-44"></a><span class='hs-comment'>{-# INLINE mapEither #-}</span>
<a name="line-45"></a><span class='hs-definition'>mapEither</span> <span class='hs-varid'>f</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>foldr</span> <span class='hs-layout'>(</span><span class='hs-varid'>deal</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>[]</span><span class='hs-layout'>,</span><span class='hs-conid'>[]</span><span class='hs-layout'>)</span> <span class='hs-varid'>xs</span>
<a name="line-46"></a>
<a name="line-47"></a><a name="deal"></a><span class='hs-definition'>deal</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Either</span> <span class='hs-varid'>b</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>[</span><span class='hs-varid'>b</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>,</span><span class='hs-keyglyph'>[</span><span class='hs-varid'>c</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>[</span><span class='hs-varid'>b</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>,</span><span class='hs-keyglyph'>[</span><span class='hs-varid'>c</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span>
<a name="line-48"></a><span class='hs-definition'>deal</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-varid'>bs</span><span class='hs-layout'>,</span><span class='hs-varid'>cs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyword'>of</span>
<a name="line-49"></a> <span class='hs-conid'>Left</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span><span class='hs-conop'>:</span><span class='hs-varid'>bs</span><span class='hs-layout'>,</span> <span class='hs-varid'>cs</span><span class='hs-layout'>)</span>
<a name="line-50"></a> <span class='hs-conid'>Right</span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-varid'>bs</span><span class='hs-layout'>,</span> <span class='hs-varid'>c</span><span class='hs-conop'>:</span><span class='hs-varid'>cs</span><span class='hs-layout'>)</span>
<a name="line-51"></a>
<a name="line-52"></a><a name="isSublistOf"></a><span class='hs-comment'>-- | Sublist relation.</span>
<a name="line-53"></a><span class='hs-definition'>isSublistOf</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Eq</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-54"></a><span class='hs-definition'>isSublistOf</span> <span class='hs-conid'>[]</span> <span class='hs-varid'>ys</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>True</span>
<a name="line-55"></a><span class='hs-definition'>isSublistOf</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-conop'>:</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-varid'>ys</span> <span class='hs-keyglyph'>=</span>
<a name="line-56"></a> <span class='hs-keyword'>case</span> <span class='hs-varid'>dropWhile</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'>/=</span><span class='hs-layout'>)</span> <span class='hs-varid'>ys</span> <span class='hs-keyword'>of</span>
<a name="line-57"></a> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>False</span>
<a name="line-58"></a> <span class='hs-layout'>(</span><span class='hs-keyword'>_</span><span class='hs-conop'>:</span><span class='hs-varid'>ys</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>isSublistOf</span> <span class='hs-varid'>xs</span> <span class='hs-varid'>ys</span>
<a name="line-59"></a>
<a name="line-60"></a><a name="Prefix"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>Prefix</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span>
<a name="line-61"></a><a name="Suffix"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>Suffix</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span>
<a name="line-62"></a>
<a name="line-63"></a><a name="maybePrefixMatch"></a><span class='hs-comment'>-- | Check if a list has a given prefix. If so, return the list</span>
<a name="line-64"></a><span class='hs-comment'>-- minus the prefix.</span>
<a name="line-65"></a><span class='hs-definition'>maybePrefixMatch</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Eq</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Prefix</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Maybe</span> <span class='hs-layout'>(</span><span class='hs-conid'>Suffix</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-66"></a><span class='hs-definition'>maybePrefixMatch</span> <span class='hs-conid'>[]</span> <span class='hs-varid'>rest</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Just</span> <span class='hs-varid'>rest</span>
<a name="line-67"></a><span class='hs-definition'>maybePrefixMatch</span> <span class='hs-layout'>(</span><span class='hs-keyword'>_</span><span class='hs-conop'>:</span><span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Nothing</span>
<a name="line-68"></a><span class='hs-definition'>maybePrefixMatch</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span><span class='hs-conop'>:</span><span class='hs-varid'>pat</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>r</span><span class='hs-conop'>:</span><span class='hs-varid'>rest</span><span class='hs-layout'>)</span>
<a name="line-69"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>p</span> <span class='hs-varop'>==</span> <span class='hs-varid'>r</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>maybePrefixMatch</span> <span class='hs-varid'>pat</span> <span class='hs-varid'>rest</span>
<a name="line-70"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Nothing</span>
<a name="line-71"></a>
<a name="line-72"></a><a name="wordsBy"></a><span class='hs-comment'>-- | Split a list into sublists. Generalisation of the prelude function</span>
<a name="line-73"></a><span class='hs-comment'>-- @words@.</span>
<a name="line-74"></a><span class='hs-comment'>--</span>
<a name="line-75"></a><span class='hs-comment'>-- > words xs == wordsBy isSpace xs</span>
<a name="line-76"></a><span class='hs-definition'>wordsBy</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span><span class='hs-keyglyph'>]</span>
<a name="line-77"></a><span class='hs-definition'>wordsBy</span> <span class='hs-varid'>p</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>yesP</span> <span class='hs-varid'>xs</span>
<a name="line-78"></a> <span class='hs-keyword'>where</span>
<a name="line-79"></a> <span class='hs-varid'>yesP</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>noP</span> <span class='hs-layout'>(</span><span class='hs-varid'>dropWhile</span> <span class='hs-varid'>p</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span>
<a name="line-80"></a>
<a name="line-81"></a> <span class='hs-varid'>noP</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>[]</span>
<a name="line-82"></a> <span class='hs-varid'>noP</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>ys</span> <span class='hs-conop'>:</span> <span class='hs-varid'>yesP</span> <span class='hs-varid'>zs</span>
<a name="line-83"></a> <span class='hs-keyword'>where</span>
<a name="line-84"></a> <span class='hs-layout'>(</span><span class='hs-varid'>ys</span><span class='hs-layout'>,</span><span class='hs-varid'>zs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>break</span> <span class='hs-varid'>p</span> <span class='hs-varid'>xs</span>
<a name="line-85"></a>
<a name="line-86"></a><a name="chop"></a><span class='hs-comment'>-- | Chop up a list in chunks of a given length.</span>
<a name="line-87"></a><span class='hs-definition'>chop</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Int</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span><span class='hs-keyglyph'>]</span>
<a name="line-88"></a><span class='hs-definition'>chop</span> <span class='hs-keyword'>_</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>[]</span>
<a name="line-89"></a><span class='hs-definition'>chop</span> <span class='hs-varid'>n</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>ys</span> <span class='hs-conop'>:</span> <span class='hs-varid'>chop</span> <span class='hs-varid'>n</span> <span class='hs-varid'>zs</span>
<a name="line-90"></a> <span class='hs-keyword'>where</span> <span class='hs-layout'>(</span><span class='hs-varid'>ys</span><span class='hs-layout'>,</span><span class='hs-varid'>zs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>splitAt</span> <span class='hs-varid'>n</span> <span class='hs-varid'>xs</span>
<a name="line-91"></a>
<a name="line-92"></a><a name="holes"></a><span class='hs-comment'>-- | All ways of removing one element from a list.</span>
<a name="line-93"></a><span class='hs-definition'>holes</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>]</span>
<a name="line-94"></a><span class='hs-definition'>holes</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>[]</span>
<a name="line-95"></a><span class='hs-definition'>holes</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</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-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-conop'>:</span> <span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-varid'>id</span> <span class='hs-varop'>-*-</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-conop'>:</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>holes</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span>
<a name="line-96"></a>
<a name="line-97"></a><span class='hs-comment'>-- | Check whether a list is sorted.</span>
<a name="line-98"></a><span class='hs-comment'>--</span>
<a name="line-99"></a><span class='hs-comment'>-- Assumes that the 'Ord' instance implements a partial order.</span>
<a name="line-100"></a>
<a name="line-101"></a><a name="sorted"></a><span class='hs-definition'>sorted</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Ord</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-102"></a><span class='hs-definition'>sorted</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>True</span>
<a name="line-103"></a><span class='hs-definition'>sorted</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>and</span> <span class='hs-varop'>$</span> <span class='hs-varid'>zipWith</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'>init</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>tail</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span>
<a name="line-104"></a>
<a name="line-105"></a><a name="distinct"></a><span class='hs-comment'>-- | Check whether all elements in a list are distinct from each</span>
<a name="line-106"></a><span class='hs-comment'>-- other. Assumes that the 'Eq' instance stands for an equivalence</span>
<a name="line-107"></a><span class='hs-comment'>-- relation.</span>
<a name="line-108"></a><span class='hs-definition'>distinct</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Eq</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-109"></a><span class='hs-definition'>distinct</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>True</span>
<a name="line-110"></a><span class='hs-definition'>distinct</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</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'>x</span> <span class='hs-varop'>`notElem`</span> <span class='hs-varid'>xs</span> <span class='hs-varop'>&&</span> <span class='hs-varid'>distinct</span> <span class='hs-varid'>xs</span>
<a name="line-111"></a>
<a name="line-112"></a><span class='hs-comment'>-- | An optimised version of 'distinct'.</span>
<a name="line-113"></a><span class='hs-comment'>--</span>
<a name="line-114"></a><span class='hs-comment'>-- Precondition: The list's length must fit in an 'Int'.</span>
<a name="line-115"></a>
<a name="line-116"></a><a name="fastDistinct"></a><span class='hs-definition'>fastDistinct</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Ord</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-117"></a><span class='hs-definition'>fastDistinct</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Set</span><span class='hs-varop'>.</span><span class='hs-varid'>size</span> <span class='hs-layout'>(</span><span class='hs-conid'>Set</span><span class='hs-varop'>.</span><span class='hs-varid'>fromList</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-varop'>==</span> <span class='hs-varid'>length</span> <span class='hs-varid'>xs</span>
<a name="line-118"></a>
<a name="line-119"></a><a name="prop_distinct_fastDistinct"></a><span class='hs-definition'>prop_distinct_fastDistinct</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Integer</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-120"></a><span class='hs-definition'>prop_distinct_fastDistinct</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>distinct</span> <span class='hs-varid'>xs</span> <span class='hs-varop'>==</span> <span class='hs-varid'>fastDistinct</span> <span class='hs-varid'>xs</span>
<a name="line-121"></a>
<a name="line-122"></a><a name="allEqual"></a><span class='hs-comment'>-- | Checks if all the elements in the list are equal. Assumes that</span>
<a name="line-123"></a><span class='hs-comment'>-- the 'Eq' instance stands for an equivalence relation.</span>
<a name="line-124"></a><span class='hs-definition'>allEqual</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Eq</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-125"></a><span class='hs-definition'>allEqual</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>True</span>
<a name="line-126"></a><span class='hs-definition'>allEqual</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</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'>all</span> <span class='hs-layout'>(</span><span class='hs-varop'>==</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-varid'>xs</span>
<a name="line-127"></a>
<a name="line-128"></a><span class='hs-comment'>-- | A variant of 'groupBy' which applies the predicate to consecutive</span>
<a name="line-129"></a><span class='hs-comment'>-- pairs.</span>
<a name="line-130"></a>
<a name="line-131"></a><a name="groupBy'"></a><span class='hs-definition'>groupBy'</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</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'>Bool</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span><span class='hs-keyglyph'>]</span>
<a name="line-132"></a><span class='hs-definition'>groupBy'</span> <span class='hs-keyword'>_</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>[]</span>
<a name="line-133"></a><span class='hs-definition'>groupBy'</span> <span class='hs-varid'>p</span> <span class='hs-varid'>xxs</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-varid'>x</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'>grp</span> <span class='hs-varid'>x</span> <span class='hs-varop'>$</span> <span class='hs-varid'>zipWith</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>,</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-varid'>xxs</span> <span class='hs-varid'>xs</span>
<a name="line-134"></a> <span class='hs-keyword'>where</span>
<a name="line-135"></a> <span class='hs-varid'>grp</span> <span class='hs-varid'>x</span> <span class='hs-varid'>ys</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-conop'>:</span> <span class='hs-varid'>map</span> <span class='hs-varid'>snd</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-conop'>:</span> <span class='hs-varid'>tail</span>
<a name="line-136"></a> <span class='hs-keyword'>where</span> <span class='hs-layout'>(</span><span class='hs-varid'>xs</span><span class='hs-layout'>,</span> <span class='hs-varid'>rest</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>span</span> <span class='hs-varid'>fst</span> <span class='hs-varid'>ys</span>
<a name="line-137"></a> <span class='hs-varid'>tail</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>rest</span> <span class='hs-keyword'>of</span>
<a name="line-138"></a> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>[]</span>
<a name="line-139"></a> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-keyword'>_</span><span class='hs-layout'>,</span> <span class='hs-varid'>z</span><span class='hs-layout'>)</span> <span class='hs-conop'>:</span> <span class='hs-varid'>zs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>grp</span> <span class='hs-varid'>z</span> <span class='hs-varid'>zs</span>
<a name="line-140"></a>
<a name="line-141"></a><a name="prop_groupBy'"></a><span class='hs-definition'>prop_groupBy'</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Bool</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></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'>Property</span>
<a name="line-142"></a><span class='hs-definition'>prop_groupBy'</span> <span class='hs-varid'>p</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span>
<a name="line-143"></a> <span class='hs-varid'>classify</span> <span class='hs-layout'>(</span><span class='hs-varid'>length</span> <span class='hs-varid'>xs</span> <span class='hs-comment'>-</span> <span class='hs-varid'>length</span> <span class='hs-varid'>gs</span> <span class='hs-varop'>>=</span> <span class='hs-num'>3</span><span class='hs-layout'>)</span> <span class='hs-str'>"interesting"</span> <span class='hs-varop'>$</span>
<a name="line-144"></a> <span class='hs-varid'>concat</span> <span class='hs-varid'>gs</span> <span class='hs-varop'>==</span> <span class='hs-varid'>xs</span>
<a name="line-145"></a> <span class='hs-varop'>&&</span>
<a name="line-146"></a> <span class='hs-varid'>and</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>not</span> <span class='hs-layout'>(</span><span class='hs-varid'>null</span> <span class='hs-varid'>zs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>zs</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>gs</span><span class='hs-keyglyph'>]</span>
<a name="line-147"></a> <span class='hs-varop'>&&</span>
<a name="line-148"></a> <span class='hs-varid'>and</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>and</span> <span class='hs-layout'>(</span><span class='hs-varid'>pairInitTail</span> <span class='hs-varid'>zs</span> <span class='hs-varid'>zs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>zs</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>gs</span><span class='hs-keyglyph'>]</span>
<a name="line-149"></a> <span class='hs-varop'>&&</span>
<a name="line-150"></a> <span class='hs-layout'>(</span><span class='hs-varid'>null</span> <span class='hs-varid'>gs</span> <span class='hs-varop'>||</span> <span class='hs-varid'>not</span> <span class='hs-layout'>(</span><span class='hs-varid'>or</span> <span class='hs-layout'>(</span><span class='hs-varid'>pairInitTail</span> <span class='hs-layout'>(</span><span class='hs-varid'>map</span> <span class='hs-varid'>last</span> <span class='hs-varid'>gs</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>map</span> <span class='hs-varid'>head</span> <span class='hs-varid'>gs</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-151"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>gs</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>groupBy'</span> <span class='hs-varid'>p</span> <span class='hs-varid'>xs</span>
<a name="line-152"></a> <span class='hs-varid'>pairInitTail</span> <span class='hs-varid'>xs</span> <span class='hs-varid'>ys</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>zipWith</span> <span class='hs-varid'>p</span> <span class='hs-layout'>(</span><span class='hs-varid'>init</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>tail</span> <span class='hs-varid'>ys</span><span class='hs-layout'>)</span>
<a name="line-153"></a>
<a name="line-154"></a><span class='hs-comment'>-- | @'groupOn' f = 'groupBy' (('==') \`on\` f) '.' 'sortBy' ('compare' \`on\` f)@.</span>
<a name="line-155"></a>
<a name="line-156"></a><a name="groupOn"></a><span class='hs-definition'>groupOn</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Ord</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span><span class='hs-keyglyph'>]</span>
<a name="line-157"></a><span class='hs-definition'>groupOn</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>groupBy</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varop'>==</span><span class='hs-layout'>)</span> <span class='hs-varop'>`on`</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span> <span class='hs-varid'>sortBy</span> <span class='hs-layout'>(</span><span class='hs-varid'>compare</span> <span class='hs-varop'>`on`</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span>
<a name="line-158"></a>
<a name="line-159"></a><span class='hs-comment'>-- | @'extractNthElement' n xs@ gives the @n@-th element in @xs@</span>
<a name="line-160"></a><span class='hs-comment'>-- (counting from 0), plus the remaining elements (preserving order).</span>
<a name="line-161"></a>
<a name="line-162"></a><a name="extractNthElement'"></a><span class='hs-definition'>extractNthElement'</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Integral</span> <span class='hs-varid'>i</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>i</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>,</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span>
<a name="line-163"></a><span class='hs-definition'>extractNthElement'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>left</span><span class='hs-layout'>,</span> <span class='hs-varid'>el</span><span class='hs-layout'>,</span> <span class='hs-varid'>right</span><span class='hs-layout'>)</span>
<a name="line-164"></a> <span class='hs-keyword'>where</span>
<a name="line-165"></a> <span class='hs-layout'>(</span><span class='hs-varid'>left</span><span class='hs-layout'>,</span> <span class='hs-varid'>el</span> <span class='hs-conop'>:</span> <span class='hs-varid'>right</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>genericSplitAt</span> <span class='hs-varid'>n</span> <span class='hs-varid'>xs</span>
<a name="line-166"></a>
<a name="line-167"></a><a name="extractNthElement"></a><span class='hs-definition'>extractNthElement</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Integral</span> <span class='hs-varid'>i</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>i</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span>
<a name="line-168"></a><span class='hs-definition'>extractNthElement</span> <span class='hs-varid'>n</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>el</span><span class='hs-layout'>,</span> <span class='hs-varid'>left</span> <span class='hs-varop'>++</span> <span class='hs-varid'>right</span><span class='hs-layout'>)</span>
<a name="line-169"></a> <span class='hs-keyword'>where</span>
<a name="line-170"></a> <span class='hs-layout'>(</span><span class='hs-varid'>left</span><span class='hs-layout'>,</span> <span class='hs-varid'>el</span><span class='hs-layout'>,</span> <span class='hs-varid'>right</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>extractNthElement'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>xs</span>
<a name="line-171"></a>
<a name="line-172"></a><a name="prop_extractNthElement"></a><span class='hs-definition'>prop_extractNthElement</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Integer</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Integer</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Property</span>
<a name="line-173"></a><span class='hs-definition'>prop_extractNthElement</span> <span class='hs-varid'>n</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span>
<a name="line-174"></a> <span class='hs-num'>0</span> <span class='hs-varop'><=</span> <span class='hs-varid'>n</span> <span class='hs-varop'>&&</span> <span class='hs-varid'>n</span> <span class='hs-varop'><</span> <span class='hs-varid'>genericLength</span> <span class='hs-varid'>xs</span> <span class='hs-varop'>==></span>
<a name="line-175"></a> <span class='hs-varid'>genericTake</span> <span class='hs-varid'>n</span> <span class='hs-varid'>rest</span> <span class='hs-varop'>++</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>elem</span><span class='hs-keyglyph'>]</span> <span class='hs-varop'>++</span> <span class='hs-varid'>genericDrop</span> <span class='hs-varid'>n</span> <span class='hs-varid'>rest</span> <span class='hs-varop'>==</span> <span class='hs-varid'>xs</span>
<a name="line-176"></a> <span class='hs-keyword'>where</span> <span class='hs-layout'>(</span><span class='hs-varid'>elem</span><span class='hs-layout'>,</span> <span class='hs-varid'>rest</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>extractNthElement</span> <span class='hs-varid'>n</span> <span class='hs-varid'>xs</span>
<a name="line-177"></a>
<a name="line-178"></a><span class='hs-comment'>-- A generalised variant of 'elemIndex'.</span>
<a name="line-179"></a>
<a name="line-180"></a><a name="genericElemIndex"></a><span class='hs-definition'>genericElemIndex</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Eq</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Integral</span> <span class='hs-varid'>i</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Maybe</span> <span class='hs-varid'>i</span>
<a name="line-181"></a><span class='hs-definition'>genericElemIndex</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span>
<a name="line-182"></a> <span class='hs-varid'>listToMaybe</span> <span class='hs-varop'>$</span>
<a name="line-183"></a> <span class='hs-varid'>map</span> <span class='hs-varid'>fst</span> <span class='hs-varop'>$</span>
<a name="line-184"></a> <span class='hs-varid'>filter</span> <span class='hs-varid'>snd</span> <span class='hs-varop'>$</span>
<a name="line-185"></a> <span class='hs-varid'>zip</span> <span class='hs-keyglyph'>[</span><span class='hs-num'>0</span><span class='hs-keyglyph'>..</span><span class='hs-keyglyph'>]</span> <span class='hs-varop'>$</span>
<a name="line-186"></a> <span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-varop'>==</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-varid'>xs</span>
<a name="line-187"></a>
<a name="line-188"></a><a name="prop_genericElemIndex"></a><span class='hs-definition'>prop_genericElemIndex</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Integer</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Integer</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Property</span>
<a name="line-189"></a><span class='hs-definition'>prop_genericElemIndex</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span>
<a name="line-190"></a> <span class='hs-varid'>classify</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'>`elem`</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-str'>"members"</span> <span class='hs-varop'>$</span>
<a name="line-191"></a> <span class='hs-varid'>genericElemIndex</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span> <span class='hs-varop'>==</span> <span class='hs-varid'>elemIndex</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xs</span>
<a name="line-192"></a>
<a name="line-193"></a><span class='hs-comment'>-- | Requires both lists to have the same length.</span>
<a name="line-194"></a>
<a name="line-195"></a><a name="zipWith'"></a><span class='hs-definition'>zipWith'</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>b</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>c</span><span class='hs-keyglyph'>]</span>
<a name="line-196"></a><span class='hs-definition'>zipWith'</span> <span class='hs-varid'>f</span> <span class='hs-conid'>[]</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>[]</span>
<a name="line-197"></a><span class='hs-definition'>zipWith'</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-conop'>:</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>y</span> <span class='hs-conop'>:</span> <span class='hs-varid'>ys</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-conop'>:</span> <span class='hs-varid'>zipWith'</span> <span class='hs-varid'>f</span> <span class='hs-varid'>xs</span> <span class='hs-varid'>ys</span>
<a name="line-198"></a><span class='hs-definition'>zipWith'</span> <span class='hs-varid'>f</span> <span class='hs-conid'>[]</span> <span class='hs-layout'>(</span><span class='hs-keyword'>_</span> <span class='hs-conop'>:</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>{- ' -}</span> <span class='hs-sel'>__IMPOSSIBLE__</span>
<a name="line-199"></a><span class='hs-definition'>zipWith'</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-keyword'>_</span> <span class='hs-conop'>:</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>{- ' -}</span> <span class='hs-sel'>__IMPOSSIBLE__</span>
<a name="line-200"></a>
<a name="line-201"></a><a name="prop_zipWith'"></a><span class='hs-definition'>prop_zipWith'</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Integer</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Integer</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Integer</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Property</span>
<a name="line-202"></a><span class='hs-definition'>prop_zipWith'</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span>
<a name="line-203"></a> <span class='hs-varid'>forAll</span> <span class='hs-varid'>natural</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>n</span> <span class='hs-keyglyph'>-></span>
<a name="line-204"></a> <span class='hs-varid'>forAll</span> <span class='hs-layout'>(</span><span class='hs-varid'>two</span> <span class='hs-varop'>$</span> <span class='hs-varid'>vector</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-layout'>(</span><span class='hs-varid'>xs</span><span class='hs-layout'>,</span> <span class='hs-varid'>ys</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span>
<a name="line-205"></a> <span class='hs-varid'>zipWith'</span> <span class='hs-varid'>f</span> <span class='hs-varid'>xs</span> <span class='hs-varid'>ys</span> <span class='hs-varop'>==</span> <span class='hs-varid'>zipWith</span> <span class='hs-varid'>f</span> <span class='hs-varid'>xs</span> <span class='hs-varid'>ys</span>
<a name="line-206"></a>
<a name="line-207"></a><a name="zipWithTails"></a><span class='hs-comment'>-- | Like zipWith, but returns the leftover elements of the input lists.</span>
<a name="line-208"></a><span class='hs-definition'>zipWithTails</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>b</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>[</span><span class='hs-varid'>c</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>,</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-layout'>,</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>b</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span>
<a name="line-209"></a><span class='hs-definition'>zipWithTails</span> <span class='hs-varid'>f</span> <span class='hs-varid'>xs</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>[]</span><span class='hs-layout'>,</span> <span class='hs-varid'>xs</span><span class='hs-layout'>,</span> <span class='hs-conid'>[]</span><span class='hs-layout'>)</span>
<a name="line-210"></a><span class='hs-definition'>zipWithTails</span> <span class='hs-varid'>f</span> <span class='hs-conid'>[]</span> <span class='hs-varid'>ys</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>[]</span><span class='hs-layout'>,</span> <span class='hs-conid'>[]</span> <span class='hs-layout'>,</span> <span class='hs-varid'>ys</span><span class='hs-layout'>)</span>
<a name="line-211"></a><span class='hs-definition'>zipWithTails</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-conop'>:</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>y</span> <span class='hs-conop'>:</span> <span class='hs-varid'>ys</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-conop'>:</span> <span class='hs-varid'>zs</span> <span class='hs-layout'>,</span> <span class='hs-keyword'>as</span> <span class='hs-layout'>,</span> <span class='hs-varid'>bs</span><span class='hs-layout'>)</span>
<a name="line-212"></a> <span class='hs-keyword'>where</span> <span class='hs-layout'>(</span><span class='hs-varid'>zs</span> <span class='hs-layout'>,</span> <span class='hs-keyword'>as</span> <span class='hs-layout'>,</span> <span class='hs-varid'>bs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>zipWithTails</span> <span class='hs-varid'>f</span> <span class='hs-varid'>xs</span> <span class='hs-varid'>ys</span>
<a name="line-213"></a>
<a name="line-214"></a><a name="uniqBy"></a><span class='hs-comment'>-- | Efficient version of nub that sorts the list first. The tag function is</span>
<a name="line-215"></a><span class='hs-comment'>-- assumed to be cheap. If it isn't pair up the elements with their tags and</span>
<a name="line-216"></a><span class='hs-comment'>-- call uniqBy fst (or snd).</span>
<a name="line-217"></a><span class='hs-definition'>uniqBy</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Ord</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span>
<a name="line-218"></a><span class='hs-definition'>uniqBy</span> <span class='hs-varid'>tag</span> <span class='hs-keyglyph'>=</span>
<a name="line-219"></a> <span class='hs-varid'>map</span> <span class='hs-varid'>head</span>
<a name="line-220"></a> <span class='hs-varop'>.</span> <span class='hs-varid'>groupBy</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varop'>==</span><span class='hs-layout'>)</span> <span class='hs-varop'>`on`</span> <span class='hs-varid'>tag</span><span class='hs-layout'>)</span>
<a name="line-221"></a> <span class='hs-varop'>.</span> <span class='hs-varid'>sortBy</span> <span class='hs-layout'>(</span><span class='hs-varid'>compare</span> <span class='hs-varop'>`on`</span> <span class='hs-varid'>tag</span><span class='hs-layout'>)</span>
<a name="line-222"></a>
<a name="line-223"></a><a name="prop_uniqBy"></a><span class='hs-definition'>prop_uniqBy</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Integer</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-224"></a><span class='hs-definition'>prop_uniqBy</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>sort</span> <span class='hs-layout'>(</span><span class='hs-varid'>nub</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-varop'>==</span> <span class='hs-varid'>uniqBy</span> <span class='hs-varid'>id</span> <span class='hs-varid'>xs</span>
<a name="line-225"></a>
<a name="line-226"></a><span class='hs-comment'>------------------------------------------------------------------------</span>
<a name="line-227"></a><span class='hs-comment'>-- All tests</span>
<a name="line-228"></a>
<a name="line-229"></a><a name="tests"></a><span class='hs-definition'>tests</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>IO</span> <span class='hs-conid'>Bool</span>
<a name="line-230"></a><span class='hs-definition'>tests</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>runTests</span> <span class='hs-str'>"Agda.Utils.List"</span>
<a name="line-231"></a> <span class='hs-keyglyph'>[</span> <span class='hs-varid'>quickCheck'</span> <span class='hs-varid'>prop_distinct_fastDistinct</span>
<a name="line-232"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>quickCheck'</span> <span class='hs-varid'>prop_groupBy'</span>
<a name="line-233"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>quickCheck'</span> <span class='hs-varid'>prop_extractNthElement</span>
<a name="line-234"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>quickCheck'</span> <span class='hs-varid'>prop_genericElemIndex</span>
<a name="line-235"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>quickCheck'</span> <span class='hs-varid'>prop_zipWith'</span>
<a name="line-236"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>quickCheck'</span> <span class='hs-varid'>prop_uniqBy</span>
<a name="line-237"></a> <span class='hs-keyglyph'>]</span>
</pre></body>
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