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<pre><a name="line-1"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-2"></a><span class='hs-comment'>-- |</span>
<a name="line-3"></a><span class='hs-comment'>-- Module : Data.Semigroup</span>
<a name="line-4"></a><span class='hs-comment'>-- Copyright : (C) 2011 Edward Kmett,</span>
<a name="line-5"></a><span class='hs-comment'>-- License : BSD-style (see the file LICENSE)</span>
<a name="line-6"></a><span class='hs-comment'>--</span>
<a name="line-7"></a><span class='hs-comment'>-- Maintainer : Edward Kmett <ekmett@gmail.com></span>
<a name="line-8"></a><span class='hs-comment'>-- Stability : provisional</span>
<a name="line-9"></a><span class='hs-comment'>-- Portability : portable</span>
<a name="line-10"></a><span class='hs-comment'>--</span>
<a name="line-11"></a><span class='hs-comment'>-- In mathematics, a semigroup is an algebraic structure consisting of a </span>
<a name="line-12"></a><span class='hs-comment'>-- set together with an associative binary operation. A semigroup </span>
<a name="line-13"></a><span class='hs-comment'>-- generalizes a monoid in that there might not exist an identity </span>
<a name="line-14"></a><span class='hs-comment'>-- element. It also (originally) generalized a group (a monoid with all </span>
<a name="line-15"></a><span class='hs-comment'>-- inverses) to a type where every element did not have to have an inverse, </span>
<a name="line-16"></a><span class='hs-comment'>-- thus the name semigroup.</span>
<a name="line-17"></a><span class='hs-comment'>--</span>
<a name="line-18"></a><span class='hs-comment'>-- The use of (<>) in this module conflicts with an operator with the same</span>
<a name="line-19"></a><span class='hs-comment'>-- name that is being exported by Data.Monoid. However, this package </span>
<a name="line-20"></a><span class='hs-comment'>-- re-exports (most of) the contents of Data.Monoid, so to use semigroups</span>
<a name="line-21"></a><span class='hs-comment'>-- and monoids in the same package just</span>
<a name="line-22"></a><span class='hs-comment'>--</span>
<a name="line-23"></a><span class='hs-comment'>-- > import Data.Semigroup</span>
<a name="line-24"></a><span class='hs-comment'>--</span>
<a name="line-25"></a><span class='hs-comment'>----------------------------------------------------------------------------</span>
<a name="line-26"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span>
<a name="line-27"></a> <span class='hs-conid'>Semigroup</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-28"></a> <span class='hs-comment'>-- * Semigroups</span>
<a name="line-29"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Min</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-30"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Max</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-31"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>First</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-32"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Last</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-33"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>WrappedMonoid</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-34"></a> <span class='hs-comment'>-- * Re-exported monoids from Data.Monoid </span>
<a name="line-35"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Monoid</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-36"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Dual</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-37"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Endo</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-38"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>All</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-39"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Any</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-40"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Sum</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-41"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Product</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-42"></a> <span class='hs-comment'>-- * A better monoid for Maybe</span>
<a name="line-43"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Option</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-44"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>option</span>
<a name="line-45"></a> <span class='hs-comment'>-- * Difference lists of a semigroup</span>
<a name="line-46"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>diff</span>
<a name="line-47"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>cycle1</span>
<a name="line-48"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-49"></a>
<a name="line-50"></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-varid'>foldr1</span><span class='hs-layout'>)</span>
<a name="line-51"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Monoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>Monoid</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span><span class='hs-conid'>Dual</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span><span class='hs-conid'>Endo</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span><span class='hs-conid'>All</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span><span class='hs-conid'>Any</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span><span class='hs-conid'>Sum</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span><span class='hs-conid'>Product</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span><span class='hs-conid'>Endo</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-52"></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-53"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span>
<a name="line-54"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span><span class='hs-varop'>.</span><span class='hs-conid'>Fix</span>
<a name="line-55"></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'>Monoid</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>Monoid</span>
<a name="line-56"></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-57"></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-58"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>List</span><span class='hs-varop'>.</span><span class='hs-conid'>NonEmpty</span>
<a name="line-59"></a>
<a name="line-60"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Numeric</span><span class='hs-varop'>.</span><span class='hs-conid'>Natural</span><span class='hs-varop'>.</span><span class='hs-conid'>Internal</span>
<a name="line-61"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Sequence</span> <span class='hs-layout'>(</span><span class='hs-conid'>Seq</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>
<a name="line-62"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Set</span> <span class='hs-layout'>(</span><span class='hs-conid'>Set</span><span class='hs-layout'>)</span>
<a name="line-63"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>IntSet</span> <span class='hs-layout'>(</span><span class='hs-conid'>IntSet</span><span class='hs-layout'>)</span>
<a name="line-64"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Map</span> <span class='hs-layout'>(</span><span class='hs-conid'>Map</span><span class='hs-layout'>)</span>
<a name="line-65"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>IntMap</span> <span class='hs-layout'>(</span><span class='hs-conid'>IntMap</span><span class='hs-layout'>)</span>
<a name="line-66"></a>
<a name="line-67"></a><span class='hs-cpp'>#ifdef LANGUAGE_DeriveDataTypeable</span>
<a name="line-68"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Data</span>
<a name="line-69"></a><span class='hs-cpp'>#endif</span>
<a name="line-70"></a>
<a name="line-71"></a><span class='hs-keyword'>infixr</span> <span class='hs-num'>6</span> <span class='hs-varop'><></span>
<a name="line-72"></a>
<a name="line-73"></a><a name="Semigroup"></a><span class='hs-keyword'>class</span> <span class='hs-conid'>Semigroup</span> <span class='hs-varid'>a</span> <span class='hs-keyword'>where</span>
<a name="line-74"></a> <span class='hs-comment'>-- | An associative operation. </span>
<a name="line-75"></a> <span class='hs-comment'>-- </span>
<a name="line-76"></a> <span class='hs-comment'>-- > (a <> b) <> c = a <> (b <> c)</span>
<a name="line-77"></a> <span class='hs-layout'>(</span><span class='hs-varop'><></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-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-78"></a>
<a name="line-79"></a> <span class='hs-comment'>-- | Reduce a non-empty list with @\<\>@</span>
<a name="line-80"></a> <span class='hs-comment'>--</span>
<a name="line-81"></a> <span class='hs-comment'>-- The default definition should be sufficient, but this can be overridden for efficiency.</span>
<a name="line-82"></a> <span class='hs-comment'>-- </span>
<a name="line-83"></a> <span class='hs-varid'>sconcat</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>NonEmpty</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-84"></a> <span class='hs-varid'>sconcat</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-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>go</span> <span class='hs-varid'>a</span> <span class='hs-keyword'>as</span> <span class='hs-keyword'>where</span>
<a name="line-85"></a> <span class='hs-varid'>go</span> <span class='hs-varid'>b</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> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>b</span> <span class='hs-varop'><></span> <span class='hs-varid'>go</span> <span class='hs-varid'>c</span> <span class='hs-varid'>cs</span>
<a name="line-86"></a> <span class='hs-varid'>go</span> <span class='hs-varid'>b</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>b</span>
<a name="line-87"></a>
<a name="line-88"></a> <span class='hs-comment'>-- | Repeat a value (n + 1) times.</span>
<a name="line-89"></a> <span class='hs-comment'>--</span>
<a name="line-90"></a> <span class='hs-comment'>-- > times1p n a = a <> a <> ... <> a -- using <> n times</span>
<a name="line-91"></a> <span class='hs-comment'>-- </span>
<a name="line-92"></a> <span class='hs-comment'>-- The default definition uses peasant multiplication, exploiting associativity to only</span>
<a name="line-93"></a> <span class='hs-comment'>-- require /O(log n)/ uses of @\<\>@.</span>
<a name="line-94"></a>
<a name="line-95"></a> <span class='hs-varid'>times1p</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Whole</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-96"></a> <span class='hs-varid'>times1p</span> <span class='hs-varid'>y0</span> <span class='hs-varid'>x0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x0</span> <span class='hs-layout'>(</span><span class='hs-num'>1</span> <span class='hs-conid'>Prelude</span><span class='hs-varop'>.+</span> <span class='hs-varid'>y0</span><span class='hs-layout'>)</span>
<a name="line-97"></a> <span class='hs-keyword'>where</span>
<a name="line-98"></a> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span>
<a name="line-99"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>even</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'><></span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>y</span> <span class='hs-varop'>`quot`</span> <span class='hs-num'>2</span><span class='hs-layout'>)</span>
<a name="line-100"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>y</span> <span class='hs-varop'>==</span> <span class='hs-num'>1</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span>
<a name="line-101"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>g</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'><></span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>unsafePred</span> <span class='hs-varid'>y</span> <span class='hs-varop'>`quot`</span> <span class='hs-num'>2</span><span class='hs-layout'>)</span> <span class='hs-varid'>x</span>
<a name="line-102"></a> <span class='hs-varid'>g</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-varid'>z</span>
<a name="line-103"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>even</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>g</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'><></span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>y</span> <span class='hs-varop'>`quot`</span> <span class='hs-num'>2</span><span class='hs-layout'>)</span> <span class='hs-varid'>z</span>
<a name="line-104"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>y</span> <span class='hs-varop'>==</span> <span class='hs-num'>1</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span> <span class='hs-varop'><></span> <span class='hs-varid'>z</span>
<a name="line-105"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>g</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'><></span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>unsafePred</span> <span class='hs-varid'>y</span> <span class='hs-varop'>`quot`</span> <span class='hs-num'>2</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'><></span> <span class='hs-varid'>z</span><span class='hs-layout'>)</span>
<a name="line-106"></a> <span class='hs-comment'>{-# INLINE times1p #-}</span>
<a name="line-107"></a>
<a name="line-108"></a><a name="cycle1"></a><span class='hs-comment'>-- | A generalization of 'Data.List.cycle' to an arbitrary 'Semigroup'.</span>
<a name="line-109"></a><span class='hs-comment'>-- May fail to terminate for some values in some semigroups.</span>
<a name="line-110"></a><span class='hs-definition'>cycle1</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Semigroup</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span>
<a name="line-111"></a><span class='hs-definition'>cycle1</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>xs'</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>xs'</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>xs</span> <span class='hs-varop'><></span> <span class='hs-varid'>xs'</span>
<a name="line-112"></a>
<a name="line-113"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-conid'>()</span> <span class='hs-keyword'>where</span>
<a name="line-114"></a> <span class='hs-keyword'>_</span> <span class='hs-varop'><></span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>()</span>
<a name="line-115"></a> <span class='hs-varid'>sconcat</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>()</span>
<a name="line-116"></a> <span class='hs-varid'>times1p</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>()</span>
<a name="line-117"></a>
<a name="line-118"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Semigroup</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-keyword'>where</span>
<a name="line-119"></a> <span class='hs-varid'>f</span> <span class='hs-varop'><></span> <span class='hs-varid'>g</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-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-varop'><></span> <span class='hs-varid'>g</span> <span class='hs-varid'>a</span>
<a name="line-120"></a> <span class='hs-varid'>times1p</span> <span class='hs-varid'>n</span> <span class='hs-varid'>f</span> <span class='hs-varid'>e</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>times1p</span> <span class='hs-varid'>n</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span>
<a name="line-121"></a>
<a name="line-122"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>a</span><span class='hs-keyglyph'>]</span> <span class='hs-keyword'>where</span>
<a name="line-123"></a> <span class='hs-layout'>(</span><span class='hs-varop'><></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varop'>++</span><span class='hs-layout'>)</span>
<a name="line-124"></a>
<a name="line-125"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>Maybe</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-126"></a> <span class='hs-conid'>Nothing</span> <span class='hs-varop'><></span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>b</span>
<a name="line-127"></a> <span class='hs-varid'>a</span> <span class='hs-varop'><></span> <span class='hs-conid'>Nothing</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>a</span>
<a name="line-128"></a> <span class='hs-conid'>Just</span> <span class='hs-varid'>a</span> <span class='hs-varop'><></span> <span class='hs-conid'>Just</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Just</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-129"></a>
<a name="line-130"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>Either</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-131"></a> <span class='hs-conid'>Left</span> <span class='hs-keyword'>_</span> <span class='hs-varop'><></span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>b</span>
<a name="line-132"></a> <span class='hs-varid'>a</span> <span class='hs-varop'><></span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>a</span>
<a name="line-133"></a>
<a name="line-134"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Semigroup</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Semigroup</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-135"></a> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span><span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-varop'><></span> <span class='hs-layout'>(</span><span class='hs-varid'>a'</span><span class='hs-layout'>,</span><span class='hs-varid'>b'</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-varop'><></span><span class='hs-varid'>a'</span><span class='hs-layout'>,</span><span class='hs-varid'>b</span><span class='hs-varop'><></span><span class='hs-varid'>b'</span><span class='hs-layout'>)</span>
<a name="line-136"></a> <span class='hs-varid'>times1p</span> <span class='hs-varid'>n</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span><span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>times1p</span> <span class='hs-varid'>n</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>times1p</span> <span class='hs-varid'>n</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-137"></a>
<a name="line-138"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Semigroup</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Semigroup</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-conid'>Semigroup</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-139"></a> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span><span class='hs-varid'>b</span><span class='hs-layout'>,</span><span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-varop'><></span> <span class='hs-layout'>(</span><span class='hs-varid'>a'</span><span class='hs-layout'>,</span><span class='hs-varid'>b'</span><span class='hs-layout'>,</span><span class='hs-varid'>c'</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-varop'><></span><span class='hs-varid'>a'</span><span class='hs-layout'>,</span><span class='hs-varid'>b</span><span class='hs-varop'><></span><span class='hs-varid'>b'</span><span class='hs-layout'>,</span><span class='hs-varid'>c</span><span class='hs-varop'><></span><span class='hs-varid'>c'</span><span class='hs-layout'>)</span>
<a name="line-140"></a> <span class='hs-varid'>times1p</span> <span class='hs-varid'>n</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span><span class='hs-varid'>b</span><span class='hs-layout'>,</span><span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>times1p</span> <span class='hs-varid'>n</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>times1p</span> <span class='hs-varid'>n</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-varid'>times1p</span> <span class='hs-varid'>n</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span>
<a name="line-141"></a>
<a name="line-142"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Semigroup</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Semigroup</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-conid'>Semigroup</span> <span class='hs-varid'>c</span><span class='hs-layout'>,</span> <span class='hs-conid'>Semigroup</span> <span class='hs-varid'>d</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-varid'>c</span><span class='hs-layout'>,</span> <span class='hs-varid'>d</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-143"></a> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span><span class='hs-varid'>b</span><span class='hs-layout'>,</span><span class='hs-varid'>c</span><span class='hs-layout'>,</span><span class='hs-varid'>d</span><span class='hs-layout'>)</span> <span class='hs-varop'><></span> <span class='hs-layout'>(</span><span class='hs-varid'>a'</span><span class='hs-layout'>,</span><span class='hs-varid'>b'</span><span class='hs-layout'>,</span><span class='hs-varid'>c'</span><span class='hs-layout'>,</span><span class='hs-varid'>d'</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-varop'><></span><span class='hs-varid'>a'</span><span class='hs-layout'>,</span><span class='hs-varid'>b</span><span class='hs-varop'><></span><span class='hs-varid'>b'</span><span class='hs-layout'>,</span><span class='hs-varid'>c</span><span class='hs-varop'><></span><span class='hs-varid'>c'</span><span class='hs-layout'>,</span><span class='hs-varid'>d</span><span class='hs-varop'><></span><span class='hs-varid'>d'</span><span class='hs-layout'>)</span>
<a name="line-144"></a> <span class='hs-varid'>times1p</span> <span class='hs-varid'>n</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span><span class='hs-varid'>b</span><span class='hs-layout'>,</span><span class='hs-varid'>c</span><span class='hs-layout'>,</span><span class='hs-varid'>d</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>times1p</span> <span class='hs-varid'>n</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>times1p</span> <span class='hs-varid'>n</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-varid'>times1p</span> <span class='hs-varid'>n</span> <span class='hs-varid'>c</span><span class='hs-layout'>,</span> <span class='hs-varid'>times1p</span> <span class='hs-varid'>n</span> <span class='hs-varid'>d</span><span class='hs-layout'>)</span>
<a name="line-145"></a>
<a name="line-146"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Semigroup</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Semigroup</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-conid'>Semigroup</span> <span class='hs-varid'>c</span><span class='hs-layout'>,</span> <span class='hs-conid'>Semigroup</span> <span class='hs-varid'>d</span><span class='hs-layout'>,</span> <span class='hs-conid'>Semigroup</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-varid'>c</span><span class='hs-layout'>,</span> <span class='hs-varid'>d</span><span class='hs-layout'>,</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-147"></a> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span><span class='hs-varid'>b</span><span class='hs-layout'>,</span><span class='hs-varid'>c</span><span class='hs-layout'>,</span><span class='hs-varid'>d</span><span class='hs-layout'>,</span><span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-varop'><></span> <span class='hs-layout'>(</span><span class='hs-varid'>a'</span><span class='hs-layout'>,</span><span class='hs-varid'>b'</span><span class='hs-layout'>,</span><span class='hs-varid'>c'</span><span class='hs-layout'>,</span><span class='hs-varid'>d'</span><span class='hs-layout'>,</span><span class='hs-varid'>e'</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-varop'><></span><span class='hs-varid'>a'</span><span class='hs-layout'>,</span><span class='hs-varid'>b</span><span class='hs-varop'><></span><span class='hs-varid'>b'</span><span class='hs-layout'>,</span><span class='hs-varid'>c</span><span class='hs-varop'><></span><span class='hs-varid'>c'</span><span class='hs-layout'>,</span><span class='hs-varid'>d</span><span class='hs-varop'><></span><span class='hs-varid'>d'</span><span class='hs-layout'>,</span><span class='hs-varid'>e</span><span class='hs-varop'><></span><span class='hs-varid'>e'</span><span class='hs-layout'>)</span>
<a name="line-148"></a> <span class='hs-varid'>times1p</span> <span class='hs-varid'>n</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span><span class='hs-varid'>b</span><span class='hs-layout'>,</span><span class='hs-varid'>c</span><span class='hs-layout'>,</span><span class='hs-varid'>d</span><span class='hs-layout'>,</span><span class='hs-varid'>e</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>times1p</span> <span class='hs-varid'>n</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>times1p</span> <span class='hs-varid'>n</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-varid'>times1p</span> <span class='hs-varid'>n</span> <span class='hs-varid'>c</span><span class='hs-layout'>,</span> <span class='hs-varid'>times1p</span> <span class='hs-varid'>n</span> <span class='hs-varid'>d</span><span class='hs-layout'>,</span> <span class='hs-varid'>times1p</span> <span class='hs-varid'>n</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span>
<a name="line-149"></a>
<a name="line-150"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dual</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-151"></a> <span class='hs-conid'>Dual</span> <span class='hs-varid'>a</span> <span class='hs-varop'><></span> <span class='hs-conid'>Dual</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Dual</span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span> <span class='hs-varop'><></span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-152"></a> <span class='hs-varid'>times1p</span> <span class='hs-varid'>n</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dual</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Dual</span> <span class='hs-layout'>(</span><span class='hs-varid'>times1p</span> <span class='hs-varid'>n</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-153"></a>
<a name="line-154"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>Endo</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-155"></a> <span class='hs-conid'>Endo</span> <span class='hs-varid'>f</span> <span class='hs-varop'><></span> <span class='hs-conid'>Endo</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Endo</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-156"></a>
<a name="line-157"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-conid'>All</span> <span class='hs-keyword'>where</span>
<a name="line-158"></a> <span class='hs-conid'>All</span> <span class='hs-varid'>a</span> <span class='hs-varop'><></span> <span class='hs-conid'>All</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>All</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-159"></a> <span class='hs-varid'>times1p</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>a</span>
<a name="line-160"></a>
<a name="line-161"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-conid'>Any</span> <span class='hs-keyword'>where</span>
<a name="line-162"></a> <span class='hs-conid'>Any</span> <span class='hs-varid'>a</span> <span class='hs-varop'><></span> <span class='hs-conid'>Any</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Any</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-163"></a> <span class='hs-varid'>times1p</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>a</span>
<a name="line-164"></a>
<a name="line-165"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Num</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sum</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-166"></a> <span class='hs-conid'>Sum</span> <span class='hs-varid'>a</span> <span class='hs-varop'><></span> <span class='hs-conid'>Sum</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Sum</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-167"></a>
<a name="line-168"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Num</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>Product</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-169"></a> <span class='hs-conid'>Product</span> <span class='hs-varid'>a</span> <span class='hs-varop'><></span> <span class='hs-conid'>Product</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Product</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-170"></a>
<a name="line-171"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>Monoid</span><span class='hs-varop'>.</span><span class='hs-conid'>First</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-172"></a> <span class='hs-conid'>Monoid</span><span class='hs-varop'>.</span><span class='hs-conid'>First</span> <span class='hs-conid'>Nothing</span> <span class='hs-varop'><></span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>b</span>
<a name="line-173"></a> <span class='hs-varid'>a</span> <span class='hs-varop'><></span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>a</span>
<a name="line-174"></a> <span class='hs-varid'>times1p</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>a</span>
<a name="line-175"></a>
<a name="line-176"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>Monoid</span><span class='hs-varop'>.</span><span class='hs-conid'>Last</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-177"></a> <span class='hs-varid'>a</span> <span class='hs-varop'><></span> <span class='hs-conid'>Monoid</span><span class='hs-varop'>.</span><span class='hs-conid'>Last</span> <span class='hs-conid'>Nothing</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>a</span>
<a name="line-178"></a> <span class='hs-keyword'>_</span> <span class='hs-varop'><></span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>b</span>
<a name="line-179"></a> <span class='hs-varid'>times1p</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>a</span>
<a name="line-180"></a>
<a name="line-181"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>NonEmpty</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-182"></a> <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-layout'>)</span> <span class='hs-varop'><></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-keyglyph'>=</span> <span class='hs-varid'>a</span> <span class='hs-conop'>:|</span> <span class='hs-layout'>(</span><span class='hs-keyword'>as</span> <span class='hs-varop'>++</span> <span class='hs-varid'>b</span> <span class='hs-conop'>:</span> <span class='hs-varid'>bs</span><span class='hs-layout'>)</span>
<a name="line-183"></a>
<a name="line-184"></a><a name="Min"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>Min</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Min</span> <span class='hs-layout'>{</span> <span class='hs-varid'>getMin</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-layout'>}</span> <span class='hs-keyword'>deriving</span>
<a name="line-185"></a> <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'>Bounded</span><span class='hs-layout'>,</span> <span class='hs-conid'>Show</span><span class='hs-layout'>,</span> <span class='hs-conid'>Read</span>
<a name="line-186"></a><span class='hs-cpp'>#ifdef LANGUAGE_DeriveDataTypeable</span>
<a name="line-187"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Data</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span>
<a name="line-188"></a><span class='hs-cpp'>#endif</span>
<a name="line-189"></a> <span class='hs-layout'>)</span>
<a name="line-190"></a>
<a name="line-191"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Ord</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>Min</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-192"></a> <span class='hs-conid'>Min</span> <span class='hs-varid'>a</span> <span class='hs-varop'><></span> <span class='hs-conid'>Min</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Min</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-varop'>`min`</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-193"></a> <span class='hs-varid'>times1p</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>a</span>
<a name="line-194"></a>
<a name="line-195"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Ord</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Bounded</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Monoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>Min</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-196"></a> <span class='hs-varid'>mempty</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>maxBound</span>
<a name="line-197"></a> <span class='hs-varid'>mappend</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varop'><></span><span class='hs-layout'>)</span>
<a name="line-198"></a>
<a name="line-199"></a><a name="Max"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>Max</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Max</span> <span class='hs-layout'>{</span> <span class='hs-varid'>getMax</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-layout'>}</span> <span class='hs-keyword'>deriving</span>
<a name="line-200"></a> <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'>Bounded</span><span class='hs-layout'>,</span> <span class='hs-conid'>Show</span><span class='hs-layout'>,</span> <span class='hs-conid'>Read</span>
<a name="line-201"></a><span class='hs-cpp'>#ifdef LANGUAGE_DeriveDataTypeable</span>
<a name="line-202"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Data</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span>
<a name="line-203"></a><span class='hs-cpp'>#endif</span>
<a name="line-204"></a> <span class='hs-layout'>)</span>
<a name="line-205"></a>
<a name="line-206"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Ord</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>Max</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-207"></a> <span class='hs-conid'>Max</span> <span class='hs-varid'>a</span> <span class='hs-varop'><></span> <span class='hs-conid'>Max</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Max</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-varop'>`max`</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-208"></a> <span class='hs-varid'>times1p</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>a</span>
<a name="line-209"></a>
<a name="line-210"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Ord</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Bounded</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Monoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>Max</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-211"></a> <span class='hs-varid'>mempty</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>minBound</span>
<a name="line-212"></a> <span class='hs-varid'>mappend</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varop'><></span><span class='hs-layout'>)</span>
<a name="line-213"></a>
<a name="line-214"></a><a name="First"></a><span class='hs-comment'>-- | Use @'Option' ('First' a)@ -- to get the behavior of 'Data.Monoid.First'</span>
<a name="line-215"></a><a name="First"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>First</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>First</span> <span class='hs-layout'>{</span> <span class='hs-varid'>getFirst</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-layout'>}</span> <span class='hs-keyword'>deriving</span>
<a name="line-216"></a> <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'>Bounded</span><span class='hs-layout'>,</span> <span class='hs-conid'>Show</span><span class='hs-layout'>,</span> <span class='hs-conid'>Read</span>
<a name="line-217"></a><span class='hs-cpp'>#ifdef LANGUAGE_DeriveDataTypeable</span>
<a name="line-218"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Data</span>
<a name="line-219"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span>
<a name="line-220"></a><span class='hs-cpp'>#endif</span>
<a name="line-221"></a> <span class='hs-layout'>)</span>
<a name="line-222"></a>
<a name="line-223"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>First</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-224"></a> <span class='hs-varid'>a</span> <span class='hs-varop'><></span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>a</span>
<a name="line-225"></a> <span class='hs-varid'>times1p</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>a</span>
<a name="line-226"></a>
<a name="line-227"></a><a name="Last"></a><span class='hs-comment'>-- | Use @'Option' ('Last' a)@ -- to get the behavior of 'Data.Monoid.Last'</span>
<a name="line-228"></a><a name="Last"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>Last</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Last</span> <span class='hs-layout'>{</span> <span class='hs-varid'>getLast</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-layout'>}</span> <span class='hs-keyword'>deriving</span>
<a name="line-229"></a> <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'>Bounded</span><span class='hs-layout'>,</span> <span class='hs-conid'>Show</span><span class='hs-layout'>,</span> <span class='hs-conid'>Read</span>
<a name="line-230"></a><span class='hs-cpp'>#ifdef LANGUAGE_DeriveDataTypeable</span>
<a name="line-231"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Data</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span>
<a name="line-232"></a><span class='hs-cpp'>#endif</span>
<a name="line-233"></a> <span class='hs-layout'>)</span>
<a name="line-234"></a>
<a name="line-235"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>Last</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-236"></a> <span class='hs-keyword'>_</span> <span class='hs-varop'><></span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>b</span>
<a name="line-237"></a> <span class='hs-varid'>times1p</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>a</span>
<a name="line-238"></a>
<a name="line-239"></a><span class='hs-comment'>-- (==)/XNOR on Bool forms a 'Semigroup', but has no good name</span>
<a name="line-240"></a>
<a name="line-241"></a>
<a name="line-242"></a><a name="WrappedMonoid"></a><span class='hs-comment'>-- | Provide a Semigroup for an arbitrary Monoid.</span>
<a name="line-243"></a><a name="WrappedMonoid"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>WrappedMonoid</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>WrapMonoid</span>
<a name="line-244"></a> <span class='hs-layout'>{</span> <span class='hs-varid'>unwrapMonoid</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>m</span> <span class='hs-layout'>}</span> <span class='hs-keyword'>deriving</span>
<a name="line-245"></a> <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'>Bounded</span><span class='hs-layout'>,</span> <span class='hs-conid'>Show</span><span class='hs-layout'>,</span> <span class='hs-conid'>Read</span>
<a name="line-246"></a><span class='hs-cpp'>#ifdef LANGUAGE_DeriveDataTypeable</span>
<a name="line-247"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Data</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span>
<a name="line-248"></a><span class='hs-cpp'>#endif</span>
<a name="line-249"></a> <span class='hs-layout'>)</span>
<a name="line-250"></a>
<a name="line-251"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Monoid</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>WrappedMonoid</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-252"></a> <span class='hs-conid'>WrapMonoid</span> <span class='hs-varid'>a</span> <span class='hs-varop'><></span> <span class='hs-conid'>WrapMonoid</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>WrapMonoid</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-varop'>`mappend`</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-253"></a>
<a name="line-254"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Monoid</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Monoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>WrappedMonoid</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-255"></a> <span class='hs-varid'>mempty</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>WrapMonoid</span> <span class='hs-varid'>mempty</span>
<a name="line-256"></a> <span class='hs-conid'>WrapMonoid</span> <span class='hs-varid'>a</span> <span class='hs-varop'>`mappend`</span> <span class='hs-conid'>WrapMonoid</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>WrapMonoid</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-varop'>`mappend`</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-257"></a>
<a name="line-258"></a>
<a name="line-259"></a><a name="Option"></a><span class='hs-comment'>-- | Option is effectively 'Maybe' with a better instance of 'Monoid', built off of an underlying 'Semigroup'</span>
<a name="line-260"></a><a name="Option"></a><span class='hs-comment'>-- instead of an underlying 'Monoid'. Ideally, this type would not exist at all and we would just fix the 'Monoid' intance of 'Maybe'</span>
<a name="line-261"></a><a name="Option"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>Option</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Option</span>
<a name="line-262"></a> <span class='hs-layout'>{</span> <span class='hs-varid'>getOption</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Maybe</span> <span class='hs-varid'>a</span> <span class='hs-layout'>}</span> <span class='hs-keyword'>deriving</span>
<a name="line-263"></a> <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>
<a name="line-264"></a><span class='hs-cpp'>#ifdef LANGUAGE_DeriveDataTypeable</span>
<a name="line-265"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Data</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span>
<a name="line-266"></a><span class='hs-cpp'>#endif</span>
<a name="line-267"></a> <span class='hs-layout'>)</span>
<a name="line-268"></a>
<a name="line-269"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Functor</span> <span class='hs-conid'>Option</span> <span class='hs-keyword'>where</span>
<a name="line-270"></a> <span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Option</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Option</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-271"></a>
<a name="line-272"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Applicative</span> <span class='hs-conid'>Option</span> <span class='hs-keyword'>where</span>
<a name="line-273"></a> <span class='hs-varid'>pure</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Option</span> <span class='hs-layout'>(</span><span class='hs-conid'>Just</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-274"></a> <span class='hs-conid'>Option</span> <span class='hs-varid'>a</span> <span class='hs-varop'><*></span> <span class='hs-conid'>Option</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Option</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-275"></a>
<a name="line-276"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Monad</span> <span class='hs-conid'>Option</span> <span class='hs-keyword'>where</span>
<a name="line-277"></a> <span class='hs-varid'>return</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pure</span>
<a name="line-278"></a>
<a name="line-279"></a> <span class='hs-conid'>Option</span> <span class='hs-layout'>(</span><span class='hs-conid'>Just</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-varop'>>>=</span> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>k</span> <span class='hs-varid'>a</span>
<a name="line-280"></a> <span class='hs-keyword'>_</span> <span class='hs-varop'>>>=</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Option</span> <span class='hs-conid'>Nothing</span>
<a name="line-281"></a>
<a name="line-282"></a> <span class='hs-conid'>Option</span> <span class='hs-conid'>Nothing</span> <span class='hs-varop'>>></span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Option</span> <span class='hs-conid'>Nothing</span>
<a name="line-283"></a> <span class='hs-keyword'>_</span> <span class='hs-varop'>>></span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>b</span>
<a name="line-284"></a>
<a name="line-285"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Alternative</span> <span class='hs-conid'>Option</span> <span class='hs-keyword'>where</span>
<a name="line-286"></a> <span class='hs-varid'>empty</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Option</span> <span class='hs-conid'>Nothing</span>
<a name="line-287"></a> <span class='hs-conid'>Option</span> <span class='hs-conid'>Nothing</span> <span class='hs-varop'><|></span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>b</span>
<a name="line-288"></a> <span class='hs-varid'>a</span> <span class='hs-varop'><|></span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>a</span>
<a name="line-289"></a>
<a name="line-290"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>MonadPlus</span> <span class='hs-conid'>Option</span> <span class='hs-keyword'>where</span>
<a name="line-291"></a> <span class='hs-varid'>mzero</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>empty</span>
<a name="line-292"></a> <span class='hs-varid'>mplus</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varop'><|></span><span class='hs-layout'>)</span>
<a name="line-293"></a>
<a name="line-294"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>MonadFix</span> <span class='hs-conid'>Option</span> <span class='hs-keyword'>where</span>
<a name="line-295"></a> <span class='hs-varid'>mfix</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Option</span> <span class='hs-layout'>(</span><span class='hs-varid'>mfix</span> <span class='hs-layout'>(</span><span class='hs-varid'>getOption</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-296"></a>
<a name="line-297"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Foldable</span> <span class='hs-conid'>Option</span> <span class='hs-keyword'>where</span>
<a name="line-298"></a> <span class='hs-varid'>foldMap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Option</span> <span class='hs-layout'>(</span><span class='hs-conid'>Just</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span>
<a name="line-299"></a> <span class='hs-varid'>foldMap</span> <span class='hs-keyword'>_</span> <span class='hs-layout'>(</span><span class='hs-conid'>Option</span> <span class='hs-conid'>Nothing</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mempty</span>
<a name="line-300"></a>
<a name="line-301"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Traversable</span> <span class='hs-conid'>Option</span> <span class='hs-keyword'>where</span>
<a name="line-302"></a> <span class='hs-varid'>traverse</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Option</span> <span class='hs-layout'>(</span><span class='hs-conid'>Just</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Option</span> <span class='hs-varop'>.</span> <span class='hs-conid'>Just</span> <span class='hs-varop'><$></span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span>
<a name="line-303"></a> <span class='hs-varid'>traverse</span> <span class='hs-keyword'>_</span> <span class='hs-layout'>(</span><span class='hs-conid'>Option</span> <span class='hs-conid'>Nothing</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pure</span> <span class='hs-layout'>(</span><span class='hs-conid'>Option</span> <span class='hs-conid'>Nothing</span><span class='hs-layout'>)</span>
<a name="line-304"></a>
<a name="line-305"></a><a name="option"></a><span class='hs-definition'>option</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-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-conid'>Option</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span>
<a name="line-306"></a><span class='hs-definition'>option</span> <span class='hs-varid'>n</span> <span class='hs-varid'>j</span> <span class='hs-layout'>(</span><span class='hs-conid'>Option</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>maybe</span> <span class='hs-varid'>n</span> <span class='hs-varid'>j</span> <span class='hs-varid'>m</span>
<a name="line-307"></a>
<a name="line-308"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>Option</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-309"></a> <span class='hs-conid'>Option</span> <span class='hs-varid'>a</span> <span class='hs-varop'><></span> <span class='hs-conid'>Option</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Option</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-310"></a>
<a name="line-311"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Monoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>Option</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-312"></a> <span class='hs-varid'>mempty</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>empty</span>
<a name="line-313"></a> <span class='hs-conid'>Option</span> <span class='hs-varid'>a</span> <span class='hs-varop'>`mappend`</span> <span class='hs-conid'>Option</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Option</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-314"></a>
<a name="line-315"></a><a name="diff"></a><span class='hs-comment'>-- | This lets you use a difference list of a Semigroup as a Monoid.</span>
<a name="line-316"></a><span class='hs-definition'>diff</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Semigroup</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Endo</span> <span class='hs-varid'>m</span>
<a name="line-317"></a><span class='hs-definition'>diff</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Endo</span> <span class='hs-varop'>.</span> <span class='hs-layout'>(</span><span class='hs-varop'><></span><span class='hs-layout'>)</span>
<a name="line-318"></a>
<a name="line-319"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>Seq</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-320"></a> <span class='hs-layout'>(</span><span class='hs-varop'><></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varop'>><</span><span class='hs-layout'>)</span>
<a name="line-321"></a>
<a name="line-322"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-conid'>IntSet</span> <span class='hs-keyword'>where</span>
<a name="line-323"></a> <span class='hs-layout'>(</span><span class='hs-varop'><></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mappend</span>
<a name="line-324"></a> <span class='hs-varid'>times1p</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>a</span>
<a name="line-325"></a>
<a name="line-326"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Ord</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>Set</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-327"></a> <span class='hs-layout'>(</span><span class='hs-varop'><></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mappend</span>
<a name="line-328"></a> <span class='hs-varid'>times1p</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>a</span>
<a name="line-329"></a>
<a name="line-330"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>IntMap</span> <span class='hs-varid'>v</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-331"></a> <span class='hs-layout'>(</span><span class='hs-varop'><></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mappend</span>
<a name="line-332"></a> <span class='hs-varid'>times1p</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>a</span>
<a name="line-333"></a>
<a name="line-334"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Ord</span> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Semigroup</span> <span class='hs-layout'>(</span><span class='hs-conid'>Map</span> <span class='hs-varid'>k</span> <span class='hs-varid'>v</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-335"></a> <span class='hs-layout'>(</span><span class='hs-varop'><></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mappend</span>
<a name="line-336"></a> <span class='hs-varid'>times1p</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>a</span>
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