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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html>
<head>
<!-- Generated by HsColour, http://code.haskell.org/~malcolm/hscolour/ -->
<title>src/Control/Lens/Iso.hs</title>
<link type='text/css' rel='stylesheet' href='hscolour.css' />
</head>
<body>
<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE CPP #-}</span>
<a name="line-2"></a><span class='hs-comment'>{-# LANGUAGE Rank2Types #-}</span>
<a name="line-3"></a><span class='hs-comment'>{-# LANGUAGE MultiParamTypeClasses #-}</span>
<a name="line-4"></a><span class='hs-comment'>{-# LANGUAGE FunctionalDependencies #-}</span>
<a name="line-5"></a><span class='hs-comment'>{-# LANGUAGE ScopedTypeVariables #-}</span>
<a name="line-6"></a>
<a name="line-7"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ &gt;= 710</span>
<a name="line-8"></a><span class='hs-comment'>{-# LANGUAGE PatternSynonyms #-}</span>
<a name="line-9"></a><span class='hs-comment'>{-# LANGUAGE ViewPatterns #-}</span>
<a name="line-10"></a><span class='hs-comment'>{-# LANGUAGE Trustworthy #-}</span>
<a name="line-11"></a><span class='hs-cpp'>#endif</span>
<a name="line-12"></a>
<a name="line-13"></a><span class='hs-cpp'>#ifndef MIN_VERSION_bytestring</span>
<a name="line-14"></a><span class='hs-cpp'>#define MIN_VERSION_bytestring(x,y,z) 1</span>
<a name="line-15"></a><span class='hs-cpp'>#endif</span>
<a name="line-16"></a>
<a name="line-17"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-18"></a><span class='hs-comment'>-- |</span>
<a name="line-19"></a><span class='hs-comment'>-- Module      :  Control.Lens.Iso</span>
<a name="line-20"></a><span class='hs-comment'>-- Copyright   :  (C) 2012-16 Edward Kmett</span>
<a name="line-21"></a><span class='hs-comment'>-- License     :  BSD-style (see the file LICENSE)</span>
<a name="line-22"></a><span class='hs-comment'>-- Maintainer  :  Edward Kmett &lt;ekmett@gmail.com&gt;</span>
<a name="line-23"></a><span class='hs-comment'>-- Stability   :  provisional</span>
<a name="line-24"></a><span class='hs-comment'>-- Portability :  Rank2Types</span>
<a name="line-25"></a><span class='hs-comment'>--</span>
<a name="line-26"></a><span class='hs-comment'>----------------------------------------------------------------------------</span>
<a name="line-27"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Lens</span><span class='hs-varop'>.</span><span class='hs-conid'>Iso</span>
<a name="line-28"></a>  <span class='hs-layout'>(</span>
<a name="line-29"></a>  <span class='hs-comment'>-- * Isomorphism Lenses</span>
<a name="line-30"></a>    <span class='hs-conid'>Iso</span><span class='hs-layout'>,</span> <span class='hs-conid'>Iso'</span>
<a name="line-31"></a>  <span class='hs-layout'>,</span> <span class='hs-conid'>AnIso</span><span class='hs-layout'>,</span> <span class='hs-conid'>AnIso'</span>
<a name="line-32"></a>  <span class='hs-comment'>-- * Isomorphism Construction</span>
<a name="line-33"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>iso</span>
<a name="line-34"></a>  <span class='hs-comment'>-- * Consuming Isomorphisms</span>
<a name="line-35"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>from</span>
<a name="line-36"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>cloneIso</span>
<a name="line-37"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>withIso</span>
<a name="line-38"></a>  <span class='hs-comment'>-- * Working with isomorphisms</span>
<a name="line-39"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>au</span>
<a name="line-40"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>auf</span>
<a name="line-41"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>under</span>
<a name="line-42"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>mapping</span>
<a name="line-43"></a>  <span class='hs-comment'>-- ** Common Isomorphisms</span>
<a name="line-44"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>simple</span>
<a name="line-45"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>non</span><span class='hs-layout'>,</span> <span class='hs-varid'>non'</span>
<a name="line-46"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>anon</span>
<a name="line-47"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>enum</span>
<a name="line-48"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>curried</span><span class='hs-layout'>,</span> <span class='hs-varid'>uncurried</span>
<a name="line-49"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>flipped</span>
<a name="line-50"></a>  <span class='hs-layout'>,</span> <span class='hs-conid'>Swapped</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-51"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ &gt;= 710</span>
<a name="line-52"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>pattern</span> <span class='hs-conid'>Swapped</span>
<a name="line-53"></a><span class='hs-cpp'>#endif</span>
<a name="line-54"></a>  <span class='hs-layout'>,</span> <span class='hs-conid'>Strict</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-55"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ &gt;= 710</span>
<a name="line-56"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>pattern</span> <span class='hs-conid'>Strict</span>
<a name="line-57"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>pattern</span> <span class='hs-conid'>Lazy</span>
<a name="line-58"></a><span class='hs-cpp'>#endif</span>
<a name="line-59"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>lazy</span>
<a name="line-60"></a>  <span class='hs-layout'>,</span> <span class='hs-conid'>Reversing</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-61"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>reversed</span>
<a name="line-62"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ &gt;= 710</span>
<a name="line-63"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>pattern</span> <span class='hs-conid'>Reversed</span>
<a name="line-64"></a><span class='hs-cpp'>#endif</span>
<a name="line-65"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>involuted</span>
<a name="line-66"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ &gt;= 710</span>
<a name="line-67"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>pattern</span> <span class='hs-conid'>List</span>
<a name="line-68"></a><span class='hs-cpp'>#endif</span>
<a name="line-69"></a>  <span class='hs-comment'>-- ** Uncommon Isomorphisms</span>
<a name="line-70"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>magma</span>
<a name="line-71"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>imagma</span>
<a name="line-72"></a>  <span class='hs-layout'>,</span> <span class='hs-conid'>Magma</span>
<a name="line-73"></a>  <span class='hs-comment'>-- ** Contravariant functors</span>
<a name="line-74"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>contramapping</span>
<a name="line-75"></a>  <span class='hs-comment'>-- * Profunctors</span>
<a name="line-76"></a>  <span class='hs-layout'>,</span> <span class='hs-conid'>Profunctor</span><span class='hs-layout'>(</span><span class='hs-varid'>dimap</span><span class='hs-layout'>,</span><span class='hs-varid'>rmap</span><span class='hs-layout'>,</span><span class='hs-varid'>lmap</span><span class='hs-layout'>)</span>
<a name="line-77"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>dimapping</span>
<a name="line-78"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>lmapping</span>
<a name="line-79"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>rmapping</span>
<a name="line-80"></a>  <span class='hs-comment'>-- * Bifunctors</span>
<a name="line-81"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>bimapping</span>
<a name="line-82"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>firsting</span>
<a name="line-83"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>seconding</span>
<a name="line-84"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ &gt;= 708</span>
<a name="line-85"></a>  <span class='hs-comment'>-- * Coercions</span>
<a name="line-86"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>coerced</span>
<a name="line-87"></a><span class='hs-cpp'>#endif</span>
<a name="line-88"></a>  <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-89"></a>
<a name="line-90"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Lens</span><span class='hs-varop'>.</span><span class='hs-conid'>Equality</span> <span class='hs-layout'>(</span><span class='hs-varid'>simple</span><span class='hs-layout'>)</span>
<a name="line-91"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Lens</span><span class='hs-varop'>.</span><span class='hs-conid'>Getter</span>
<a name="line-92"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Lens</span><span class='hs-varop'>.</span><span class='hs-conid'>Fold</span>
<a name="line-93"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Lens</span><span class='hs-varop'>.</span><span class='hs-conid'>Internal</span><span class='hs-varop'>.</span><span class='hs-conid'>Context</span>
<a name="line-94"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Lens</span><span class='hs-varop'>.</span><span class='hs-conid'>Internal</span><span class='hs-varop'>.</span><span class='hs-conid'>Coerce</span>
<a name="line-95"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Lens</span><span class='hs-varop'>.</span><span class='hs-conid'>Internal</span><span class='hs-varop'>.</span><span class='hs-conid'>Indexed</span>
<a name="line-96"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Lens</span><span class='hs-varop'>.</span><span class='hs-conid'>Internal</span><span class='hs-varop'>.</span><span class='hs-conid'>Iso</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>Iso</span>
<a name="line-97"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Lens</span><span class='hs-varop'>.</span><span class='hs-conid'>Internal</span><span class='hs-varop'>.</span><span class='hs-conid'>Magma</span>
<a name="line-98"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Lens</span><span class='hs-varop'>.</span><span class='hs-conid'>Prism</span>
<a name="line-99"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Lens</span><span class='hs-varop'>.</span><span class='hs-conid'>Review</span>
<a name="line-100"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Lens</span><span class='hs-varop'>.</span><span class='hs-conid'>Type</span>
<a name="line-101"></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'>State</span><span class='hs-varop'>.</span><span class='hs-conid'>Lazy</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>Lazy</span>
<a name="line-102"></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'>State</span><span class='hs-varop'>.</span><span class='hs-conid'>Strict</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>Strict</span>
<a name="line-103"></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'>Writer</span><span class='hs-varop'>.</span><span class='hs-conid'>Lazy</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>Lazy</span>
<a name="line-104"></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'>Writer</span><span class='hs-varop'>.</span><span class='hs-conid'>Strict</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>Strict</span>
<a name="line-105"></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'>RWS</span><span class='hs-varop'>.</span><span class='hs-conid'>Lazy</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>Lazy</span>
<a name="line-106"></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'>RWS</span><span class='hs-varop'>.</span><span class='hs-conid'>Strict</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>Strict</span>
<a name="line-107"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Bifunctor</span>
<a name="line-108"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>ByteString</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>StrictB</span> <span class='hs-varid'>hiding</span> <span class='hs-layout'>(</span><span class='hs-varid'>reverse</span><span class='hs-layout'>)</span>
<a name="line-109"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>ByteString</span><span class='hs-varop'>.</span><span class='hs-conid'>Lazy</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>LazyB</span> <span class='hs-varid'>hiding</span> <span class='hs-layout'>(</span><span class='hs-varid'>reverse</span><span class='hs-layout'>)</span>
<a name="line-110"></a>
<a name="line-111"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Functor</span><span class='hs-varop'>.</span><span class='hs-conid'>Identity</span>
<a name="line-112"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Text</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>StrictT</span> <span class='hs-varid'>hiding</span> <span class='hs-layout'>(</span><span class='hs-varid'>reverse</span><span class='hs-layout'>)</span>
<a name="line-113"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Text</span><span class='hs-varop'>.</span><span class='hs-conid'>Lazy</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>LazyT</span> <span class='hs-varid'>hiding</span> <span class='hs-layout'>(</span><span class='hs-varid'>reverse</span><span class='hs-layout'>)</span>
<a name="line-114"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Tuple</span> <span class='hs-layout'>(</span><span class='hs-varid'>swap</span><span class='hs-layout'>)</span>
<a name="line-115"></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-116"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Profunctor</span>
<a name="line-117"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Profunctor</span><span class='hs-varop'>.</span><span class='hs-conid'>Unsafe</span>
<a name="line-118"></a>
<a name="line-119"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ &gt;= 708</span>
<a name="line-120"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Coerce</span> <span class='hs-layout'>(</span><span class='hs-conid'>Coercible</span><span class='hs-layout'>)</span>
<a name="line-121"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ &lt; 710</span>
<a name="line-122"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Type</span><span class='hs-varop'>.</span><span class='hs-conid'>Coercion</span>
<a name="line-123"></a><span class='hs-cpp'>#endif</span>
<a name="line-124"></a><span class='hs-cpp'>#endif</span>
<a name="line-125"></a>
<a name="line-126"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ &gt;= 710</span>
<a name="line-127"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</span> <span class='hs-conid'>GHC</span><span class='hs-varop'>.</span><span class='hs-conid'>Exts</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>Exts</span>
<a name="line-128"></a><span class='hs-cpp'>#endif</span>
<a name="line-129"></a>
<a name="line-130"></a><span class='hs-cpp'>#ifdef HLINT</span>
<a name="line-131"></a><span class='hs-comment'>{-# ANN module "HLint: ignore Use on" #-}</span>
<a name="line-132"></a><span class='hs-cpp'>#endif</span>
<a name="line-133"></a>
<a name="line-134"></a><span class='hs-comment'>-- $setup</span>
<a name="line-135"></a><span class='hs-comment'>-- &gt;&gt;&gt; :set -XNoOverloadedStrings</span>
<a name="line-136"></a><span class='hs-comment'>-- &gt;&gt;&gt; import Control.Lens</span>
<a name="line-137"></a><span class='hs-comment'>-- &gt;&gt;&gt; import Data.Map as Map</span>
<a name="line-138"></a><span class='hs-comment'>-- &gt;&gt;&gt; import Data.Foldable</span>
<a name="line-139"></a><span class='hs-comment'>-- &gt;&gt;&gt; import Data.Monoid</span>
<a name="line-140"></a>
<a name="line-141"></a><span class='hs-comment'>----------------------------------------------------------------------------</span>
<a name="line-142"></a><span class='hs-comment'>-- Isomorphisms</span>
<a name="line-143"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-144"></a>
<a name="line-145"></a><a name="AnIso"></a><span class='hs-comment'>-- | When you see this as an argument to a function, it expects an 'Iso'.</span>
<a name="line-146"></a><a name="AnIso"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>AnIso</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Exchange</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-varid'>a</span> <span class='hs-layout'>(</span><span class='hs-conid'>Identity</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Exchange</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-varid'>s</span> <span class='hs-layout'>(</span><span class='hs-conid'>Identity</span> <span class='hs-varid'>t</span><span class='hs-layout'>)</span>
<a name="line-147"></a>
<a name="line-148"></a><a name="AnIso'"></a><span class='hs-comment'>-- | A 'Simple' 'AnIso'.</span>
<a name="line-149"></a><a name="AnIso'"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>AnIso'</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>AnIso</span> <span class='hs-varid'>s</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span>
<a name="line-150"></a>
<a name="line-151"></a>
<a name="line-152"></a><a name="iso"></a><span class='hs-comment'>-- | Build a simple isomorphism from a pair of inverse functions.</span>
<a name="line-153"></a><span class='hs-comment'>--</span>
<a name="line-154"></a><span class='hs-comment'>-- @</span>
<a name="line-155"></a><span class='hs-comment'>-- 'Control.Lens.Getter.view' ('iso' f g) ≡ f</span>
<a name="line-156"></a><span class='hs-comment'>-- 'Control.Lens.Getter.view' ('Control.Lens.Iso.from' ('iso' f g)) ≡ g</span>
<a name="line-157"></a><span class='hs-comment'>-- 'Control.Lens.Setter.over' ('iso' f g) h ≡ g '.' h '.' f</span>
<a name="line-158"></a><span class='hs-comment'>-- 'Control.Lens.Setter.over' ('Control.Lens.Iso.from' ('iso' f g)) h ≡ f '.' h '.' g</span>
<a name="line-159"></a><span class='hs-comment'>-- @</span>
<a name="line-160"></a><span class='hs-definition'>iso</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-varid'>s</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>t</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Iso</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span>
<a name="line-161"></a><span class='hs-definition'>iso</span> <span class='hs-varid'>sa</span> <span class='hs-varid'>bt</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>dimap</span> <span class='hs-varid'>sa</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>bt</span><span class='hs-layout'>)</span>
<a name="line-162"></a><span class='hs-comment'>{-# INLINE iso #-}</span>
<a name="line-163"></a>
<a name="line-164"></a><span class='hs-comment'>----------------------------------------------------------------------------</span>
<a name="line-165"></a><span class='hs-comment'>-- Consuming Isomorphisms</span>
<a name="line-166"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-167"></a>
<a name="line-168"></a><a name="from"></a><span class='hs-comment'>-- | Invert an isomorphism.</span>
<a name="line-169"></a><span class='hs-comment'>--</span>
<a name="line-170"></a><span class='hs-comment'>-- @</span>
<a name="line-171"></a><span class='hs-comment'>-- 'from' ('from' l) ≡ l</span>
<a name="line-172"></a><span class='hs-comment'>-- @</span>
<a name="line-173"></a><span class='hs-definition'>from</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>AnIso</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Iso</span> <span class='hs-varid'>b</span> <span class='hs-varid'>a</span> <span class='hs-varid'>t</span> <span class='hs-varid'>s</span>
<a name="line-174"></a><span class='hs-definition'>from</span> <span class='hs-varid'>l</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>withIso</span> <span class='hs-varid'>l</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span> <span class='hs-varid'>sa</span> <span class='hs-varid'>bt</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>iso</span> <span class='hs-varid'>bt</span> <span class='hs-varid'>sa</span>
<a name="line-175"></a><span class='hs-comment'>{-# INLINE from #-}</span>
<a name="line-176"></a>
<a name="line-177"></a><a name="withIso"></a><span class='hs-comment'>-- | Extract the two functions, one from @s -&gt; a@ and</span>
<a name="line-178"></a><span class='hs-comment'>-- one from @b -&gt; t@ that characterize an 'Iso'.</span>
<a name="line-179"></a><span class='hs-definition'>withIso</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>AnIso</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varid'>s</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>t</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>r</span>
<a name="line-180"></a><span class='hs-definition'>withIso</span> <span class='hs-varid'>ai</span> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>ai</span> <span class='hs-layout'>(</span><span class='hs-conid'>Exchange</span> <span class='hs-varid'>id</span> <span class='hs-conid'>Identity</span><span class='hs-layout'>)</span> <span class='hs-keyword'>of</span>
<a name="line-181"></a>  <span class='hs-conid'>Exchange</span> <span class='hs-varid'>sa</span> <span class='hs-varid'>bt</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>k</span> <span class='hs-varid'>sa</span> <span class='hs-layout'>(</span><span class='hs-varid'>runIdentity</span> <span class='hs-cpp'>#.</span> <span class='hs-varid'>bt</span><span class='hs-layout'>)</span>
<a name="line-182"></a><span class='hs-comment'>{-# INLINE withIso #-}</span>
<a name="line-183"></a>
<a name="line-184"></a><a name="cloneIso"></a><span class='hs-comment'>-- | Convert from 'AnIso' back to any 'Iso'.</span>
<a name="line-185"></a><span class='hs-comment'>--</span>
<a name="line-186"></a><span class='hs-comment'>-- This is useful when you need to store an isomorphism as a data type inside a container</span>
<a name="line-187"></a><span class='hs-comment'>-- and later reconstitute it as an overloaded function.</span>
<a name="line-188"></a><span class='hs-comment'>--</span>
<a name="line-189"></a><span class='hs-comment'>-- See 'Control.Lens.Lens.cloneLens' or 'Control.Lens.Traversal.cloneTraversal' for more information on why you might want to do this.</span>
<a name="line-190"></a><span class='hs-definition'>cloneIso</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>AnIso</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Iso</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span>
<a name="line-191"></a><span class='hs-definition'>cloneIso</span> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>withIso</span> <span class='hs-varid'>k</span> <span class='hs-varid'>iso</span>
<a name="line-192"></a><span class='hs-comment'>{-# INLINE cloneIso #-}</span>
<a name="line-193"></a>
<a name="line-194"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-195"></a><span class='hs-comment'>-- Isomorphisms families as Lenses</span>
<a name="line-196"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-197"></a>
<a name="line-198"></a><a name="au"></a><span class='hs-comment'>-- | Based on 'Control.Lens.Wrapped.ala' from Conor McBride's work on Epigram.</span>
<a name="line-199"></a><span class='hs-comment'>--</span>
<a name="line-200"></a><span class='hs-comment'>-- This version is generalized to accept any 'Iso', not just a @newtype@.</span>
<a name="line-201"></a><span class='hs-comment'>--</span>
<a name="line-202"></a><span class='hs-comment'>-- &gt;&gt;&gt; au (_Wrapping Sum) foldMap [1,2,3,4]</span>
<a name="line-203"></a><span class='hs-comment'>-- 10</span>
<a name="line-204"></a><span class='hs-comment'>--</span>
<a name="line-205"></a><span class='hs-comment'>-- You may want to think of this combinator as having the following, simpler type:</span>
<a name="line-206"></a><span class='hs-comment'>--</span>
<a name="line-207"></a><span class='hs-comment'>-- @</span>
<a name="line-208"></a><span class='hs-comment'>-- au :: AnIso s t a b -&gt; ((b -&gt; t) -&gt; e -&gt; s) -&gt; e -&gt; a</span>
<a name="line-209"></a><span class='hs-comment'>-- @</span>
<a name="line-210"></a><span class='hs-definition'>au</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>AnIso</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>t</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>f</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span>
<a name="line-211"></a><span class='hs-definition'>au</span> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>withIso</span> <span class='hs-varid'>k</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span> <span class='hs-varid'>sa</span> <span class='hs-varid'>bt</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>fmap</span> <span class='hs-varid'>sa</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>bt</span><span class='hs-layout'>)</span>
<a name="line-212"></a><span class='hs-comment'>{-# INLINE au #-}</span>
<a name="line-213"></a>
<a name="line-214"></a><a name="auf"></a><span class='hs-comment'>-- | Based on @ala'@ from Conor McBride's work on Epigram.</span>
<a name="line-215"></a><span class='hs-comment'>--</span>
<a name="line-216"></a><span class='hs-comment'>-- This version is generalized to accept any 'Iso', not just a @newtype@.</span>
<a name="line-217"></a><span class='hs-comment'>--</span>
<a name="line-218"></a><span class='hs-comment'>-- For a version you pass the name of the @newtype@ constructor to, see 'Control.Lens.Wrapped.alaf'.</span>
<a name="line-219"></a><span class='hs-comment'>--</span>
<a name="line-220"></a><span class='hs-comment'>-- &gt;&gt;&gt; auf (_Unwrapping Sum) (foldMapOf both) Prelude.length ("hello","world")</span>
<a name="line-221"></a><span class='hs-comment'>-- 10</span>
<a name="line-222"></a><span class='hs-comment'>--</span>
<a name="line-223"></a><span class='hs-comment'>-- Mnemonically, the German /auf/ plays a similar role to /à la/, and the combinator</span>
<a name="line-224"></a><span class='hs-comment'>-- is 'au' with an extra function argument:</span>
<a name="line-225"></a><span class='hs-comment'>--</span>
<a name="line-226"></a><span class='hs-comment'>-- @</span>
<a name="line-227"></a><span class='hs-comment'>-- 'auf' :: 'Iso' s t a b -&gt; ((r -&gt;  a) -&gt; e -&gt; b) -&gt; (r -&gt; s) -&gt; e -&gt; t</span>
<a name="line-228"></a><span class='hs-comment'>-- @</span>
<a name="line-229"></a><span class='hs-comment'>--</span>
<a name="line-230"></a><span class='hs-comment'>-- but the signature is general.</span>
<a name="line-231"></a><span class='hs-definition'>auf</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Optic</span> <span class='hs-layout'>(</span><span class='hs-conid'>Costar</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varid'>g</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>g</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>f</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>g</span> <span class='hs-varid'>t</span>
<a name="line-232"></a><span class='hs-definition'>auf</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>coerce</span>
<a name="line-233"></a><span class='hs-comment'>{-# INLINE auf #-}</span>
<a name="line-234"></a>
<a name="line-235"></a><a name="under"></a><span class='hs-comment'>-- | The opposite of working 'Control.Lens.Setter.over' a 'Setter' is working 'under' an isomorphism.</span>
<a name="line-236"></a><span class='hs-comment'>--</span>
<a name="line-237"></a><span class='hs-comment'>-- @</span>
<a name="line-238"></a><span class='hs-comment'>-- 'under' ≡ 'Control.Lens.Setter.over' '.' 'from'</span>
<a name="line-239"></a><span class='hs-comment'>-- @</span>
<a name="line-240"></a><span class='hs-comment'>--</span>
<a name="line-241"></a><span class='hs-comment'>-- @</span>
<a name="line-242"></a><span class='hs-comment'>-- 'under' :: 'Iso' s t a b -&gt; (t -&gt; s) -&gt; b -&gt; a</span>
<a name="line-243"></a><span class='hs-comment'>-- @</span>
<a name="line-244"></a><span class='hs-definition'>under</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>AnIso</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>t</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span>
<a name="line-245"></a><span class='hs-definition'>under</span> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>withIso</span> <span class='hs-varid'>k</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span> <span class='hs-varid'>sa</span> <span class='hs-varid'>bt</span> <span class='hs-varid'>ts</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>sa</span> <span class='hs-varop'>.</span> <span class='hs-varid'>ts</span> <span class='hs-varop'>.</span> <span class='hs-varid'>bt</span>
<a name="line-246"></a><span class='hs-comment'>{-# INLINE under #-}</span>
<a name="line-247"></a>
<a name="line-248"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-249"></a><span class='hs-comment'>-- Isomorphisms</span>
<a name="line-250"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-251"></a>
<a name="line-252"></a><a name="enum"></a><span class='hs-comment'>-- | This isomorphism can be used to convert to or from an instance of 'Enum'.</span>
<a name="line-253"></a><span class='hs-comment'>--</span>
<a name="line-254"></a><span class='hs-comment'>-- &gt;&gt;&gt; LT^.from enum</span>
<a name="line-255"></a><span class='hs-comment'>-- 0</span>
<a name="line-256"></a><span class='hs-comment'>--</span>
<a name="line-257"></a><span class='hs-comment'>-- &gt;&gt;&gt; 97^.enum :: Char</span>
<a name="line-258"></a><span class='hs-comment'>-- 'a'</span>
<a name="line-259"></a><span class='hs-comment'>--</span>
<a name="line-260"></a><span class='hs-comment'>-- Note: this is only an isomorphism from the numeric range actually used</span>
<a name="line-261"></a><span class='hs-comment'>-- and it is a bit of a pleasant fiction, since there are questionable</span>
<a name="line-262"></a><span class='hs-comment'>-- 'Enum' instances for 'Double', and 'Float' that exist solely for</span>
<a name="line-263"></a><span class='hs-comment'>-- @[1.0 .. 4.0]@ sugar and the instances for those and 'Integer' don't</span>
<a name="line-264"></a><span class='hs-comment'>-- cover all values in their range.</span>
<a name="line-265"></a><span class='hs-definition'>enum</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Enum</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Iso'</span> <span class='hs-conid'>Int</span> <span class='hs-varid'>a</span>
<a name="line-266"></a><span class='hs-definition'>enum</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iso</span> <span class='hs-varid'>toEnum</span> <span class='hs-varid'>fromEnum</span>
<a name="line-267"></a><span class='hs-comment'>{-# INLINE enum #-}</span>
<a name="line-268"></a>
<a name="line-269"></a><a name="mapping"></a><span class='hs-comment'>-- | This can be used to lift any 'Iso' into an arbitrary 'Functor'.</span>
<a name="line-270"></a><span class='hs-definition'>mapping</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Functor</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>AnIso</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Iso</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>g</span> <span class='hs-varid'>t</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>g</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-271"></a><span class='hs-definition'>mapping</span> <span class='hs-varid'>k</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>withIso</span> <span class='hs-varid'>k</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span> <span class='hs-varid'>sa</span> <span class='hs-varid'>bt</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>iso</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>sa</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>bt</span><span class='hs-layout'>)</span>
<a name="line-272"></a><span class='hs-comment'>{-# INLINE mapping #-}</span>
<a name="line-273"></a>
<a name="line-274"></a><a name="non"></a><span class='hs-comment'>-- | If @v@ is an element of a type @a@, and @a'@ is @a@ sans the element @v@, then @'non' v@ is an isomorphism from</span>
<a name="line-275"></a><span class='hs-comment'>-- @'Maybe' a'@ to @a@.</span>
<a name="line-276"></a><span class='hs-comment'>--</span>
<a name="line-277"></a><span class='hs-comment'>-- @</span>
<a name="line-278"></a><span class='hs-comment'>-- 'non' ≡ 'non'' '.' 'only'</span>
<a name="line-279"></a><span class='hs-comment'>-- @</span>
<a name="line-280"></a><span class='hs-comment'>--</span>
<a name="line-281"></a><span class='hs-comment'>-- Keep in mind this is only a real isomorphism if you treat the domain as being @'Maybe' (a sans v)@.</span>
<a name="line-282"></a><span class='hs-comment'>--</span>
<a name="line-283"></a><span class='hs-comment'>-- This is practically quite useful when you want to have a 'Data.Map.Map' where all the entries should have non-zero values.</span>
<a name="line-284"></a><span class='hs-comment'>--</span>
<a name="line-285"></a><span class='hs-comment'>-- &gt;&gt;&gt; Map.fromList [("hello",1)] &amp; at "hello" . non 0 +~ 2</span>
<a name="line-286"></a><span class='hs-comment'>-- fromList [("hello",3)]</span>
<a name="line-287"></a><span class='hs-comment'>--</span>
<a name="line-288"></a><span class='hs-comment'>-- &gt;&gt;&gt; Map.fromList [("hello",1)] &amp; at "hello" . non 0 -~ 1</span>
<a name="line-289"></a><span class='hs-comment'>-- fromList []</span>
<a name="line-290"></a><span class='hs-comment'>--</span>
<a name="line-291"></a><span class='hs-comment'>-- &gt;&gt;&gt; Map.fromList [("hello",1)] ^. at "hello" . non 0</span>
<a name="line-292"></a><span class='hs-comment'>-- 1</span>
<a name="line-293"></a><span class='hs-comment'>--</span>
<a name="line-294"></a><span class='hs-comment'>-- &gt;&gt;&gt; Map.fromList [] ^. at "hello" . non 0</span>
<a name="line-295"></a><span class='hs-comment'>-- 0</span>
<a name="line-296"></a><span class='hs-comment'>--</span>
<a name="line-297"></a><span class='hs-comment'>-- This combinator is also particularly useful when working with nested maps.</span>
<a name="line-298"></a><span class='hs-comment'>--</span>
<a name="line-299"></a><span class='hs-comment'>-- /e.g./ When you want to create the nested 'Data.Map.Map' when it is missing:</span>
<a name="line-300"></a><span class='hs-comment'>--</span>
<a name="line-301"></a><span class='hs-comment'>-- &gt;&gt;&gt; Map.empty &amp; at "hello" . non Map.empty . at "world" ?~ "!!!"</span>
<a name="line-302"></a><span class='hs-comment'>-- fromList [("hello",fromList [("world","!!!")])]</span>
<a name="line-303"></a><span class='hs-comment'>--</span>
<a name="line-304"></a><span class='hs-comment'>-- and when have deleting the last entry from the nested 'Data.Map.Map' mean that we</span>
<a name="line-305"></a><span class='hs-comment'>-- should delete its entry from the surrounding one:</span>
<a name="line-306"></a><span class='hs-comment'>--</span>
<a name="line-307"></a><span class='hs-comment'>-- &gt;&gt;&gt; fromList [("hello",fromList [("world","!!!")])] &amp; at "hello" . non Map.empty . at "world" .~ Nothing</span>
<a name="line-308"></a><span class='hs-comment'>-- fromList []</span>
<a name="line-309"></a><span class='hs-comment'>--</span>
<a name="line-310"></a><span class='hs-comment'>-- It can also be used in reverse to exclude a given value:</span>
<a name="line-311"></a><span class='hs-comment'>--</span>
<a name="line-312"></a><span class='hs-comment'>-- &gt;&gt;&gt; non 0 # rem 10 4</span>
<a name="line-313"></a><span class='hs-comment'>-- Just 2</span>
<a name="line-314"></a><span class='hs-comment'>--</span>
<a name="line-315"></a><span class='hs-comment'>-- &gt;&gt;&gt; non 0 # rem 10 5</span>
<a name="line-316"></a><span class='hs-comment'>-- Nothing</span>
<a name="line-317"></a><span class='hs-definition'>non</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Eq</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Iso'</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-varid'>a</span>
<a name="line-318"></a><span class='hs-definition'>non</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>non'</span> <span class='hs-varop'>.</span> <span class='hs-varid'>only</span>
<a name="line-319"></a><span class='hs-comment'>{-# INLINE non #-}</span>
<a name="line-320"></a>
<a name="line-321"></a><a name="non'"></a><span class='hs-comment'>-- | @'non'' p@ generalizes @'non' (p # ())@ to take any unit 'Prism'</span>
<a name="line-322"></a><span class='hs-comment'>--</span>
<a name="line-323"></a><span class='hs-comment'>-- This function generates an isomorphism between @'Maybe' (a | 'isn't' p a)@ and @a@.</span>
<a name="line-324"></a><span class='hs-comment'>--</span>
<a name="line-325"></a><span class='hs-comment'>-- &gt;&gt;&gt; Map.singleton "hello" Map.empty &amp; at "hello" . non' _Empty . at "world" ?~ "!!!"</span>
<a name="line-326"></a><span class='hs-comment'>-- fromList [("hello",fromList [("world","!!!")])]</span>
<a name="line-327"></a><span class='hs-comment'>--</span>
<a name="line-328"></a><span class='hs-comment'>-- &gt;&gt;&gt; fromList [("hello",fromList [("world","!!!")])] &amp; at "hello" . non' _Empty . at "world" .~ Nothing</span>
<a name="line-329"></a><span class='hs-comment'>-- fromList []</span>
<a name="line-330"></a><span class='hs-definition'>non'</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>APrism'</span> <span class='hs-varid'>a</span> <span class='hs-conid'>()</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Iso'</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-varid'>a</span>
<a name="line-331"></a><span class='hs-definition'>non'</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iso</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromMaybe</span> <span class='hs-varid'>def</span><span class='hs-layout'>)</span> <span class='hs-varid'>go</span> <span class='hs-keyword'>where</span>
<a name="line-332"></a>  <span class='hs-varid'>def</span>                           <span class='hs-keyglyph'>=</span> <span class='hs-varid'>review</span> <span class='hs-layout'>(</span><span class='hs-varid'>clonePrism</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <span class='hs-conid'>()</span>
<a name="line-333"></a>  <span class='hs-varid'>go</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>has</span> <span class='hs-layout'>(</span><span class='hs-varid'>clonePrism</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <span class='hs-varid'>b</span>   <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Nothing</span>
<a name="line-334"></a>       <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span>              <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Just</span> <span class='hs-varid'>b</span>
<a name="line-335"></a><span class='hs-comment'>{-# INLINE non' #-}</span>
<a name="line-336"></a>
<a name="line-337"></a><a name="anon"></a><span class='hs-comment'>-- | @'anon' a p@ generalizes @'non' a@ to take any value and a predicate.</span>
<a name="line-338"></a><span class='hs-comment'>--</span>
<a name="line-339"></a><span class='hs-comment'>-- This function assumes that @p a@ holds @'True'@ and generates an isomorphism between @'Maybe' (a | 'not' (p a))@ and @a@.</span>
<a name="line-340"></a><span class='hs-comment'>--</span>
<a name="line-341"></a><span class='hs-comment'>-- &gt;&gt;&gt; Map.empty &amp; at "hello" . anon Map.empty Map.null . at "world" ?~ "!!!"</span>
<a name="line-342"></a><span class='hs-comment'>-- fromList [("hello",fromList [("world","!!!")])]</span>
<a name="line-343"></a><span class='hs-comment'>--</span>
<a name="line-344"></a><span class='hs-comment'>-- &gt;&gt;&gt; fromList [("hello",fromList [("world","!!!")])] &amp; at "hello" . anon Map.empty Map.null . at "world" .~ Nothing</span>
<a name="line-345"></a><span class='hs-comment'>-- fromList []</span>
<a name="line-346"></a><span class='hs-definition'>anon</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Bool</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Iso'</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-varid'>a</span>
<a name="line-347"></a><span class='hs-definition'>anon</span> <span class='hs-varid'>a</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iso</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromMaybe</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-varid'>go</span> <span class='hs-keyword'>where</span>
<a name="line-348"></a>  <span class='hs-varid'>go</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>p</span> <span class='hs-varid'>b</span>       <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Nothing</span>
<a name="line-349"></a>       <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Just</span> <span class='hs-varid'>b</span>
<a name="line-350"></a><span class='hs-comment'>{-# INLINE anon #-}</span>
<a name="line-351"></a>
<a name="line-352"></a><a name="curried"></a><span class='hs-comment'>-- | The canonical isomorphism for currying and uncurrying a function.</span>
<a name="line-353"></a><span class='hs-comment'>--</span>
<a name="line-354"></a><span class='hs-comment'>-- @</span>
<a name="line-355"></a><span class='hs-comment'>-- 'curried' = 'iso' 'curry' 'uncurry'</span>
<a name="line-356"></a><span class='hs-comment'>-- @</span>
<a name="line-357"></a><span class='hs-comment'>--</span>
<a name="line-358"></a><span class='hs-comment'>-- &gt;&gt;&gt; (fst^.curried) 3 4</span>
<a name="line-359"></a><span class='hs-comment'>-- 3</span>
<a name="line-360"></a><span class='hs-comment'>--</span>
<a name="line-361"></a><span class='hs-comment'>-- &gt;&gt;&gt; view curried fst 3 4</span>
<a name="line-362"></a><span class='hs-comment'>-- 3</span>
<a name="line-363"></a><span class='hs-definition'>curried</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Iso</span> <span class='hs-layout'>(</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'>-&gt;</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</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'>-&gt;</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>d</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>e</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span>
<a name="line-364"></a><span class='hs-definition'>curried</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iso</span> <span class='hs-varid'>curry</span> <span class='hs-varid'>uncurry</span>
<a name="line-365"></a><span class='hs-comment'>{-# INLINE curried #-}</span>
<a name="line-366"></a>
<a name="line-367"></a><a name="uncurried"></a><span class='hs-comment'>-- | The canonical isomorphism for uncurrying and currying a function.</span>
<a name="line-368"></a><span class='hs-comment'>--</span>
<a name="line-369"></a><span class='hs-comment'>-- @</span>
<a name="line-370"></a><span class='hs-comment'>-- 'uncurried' = 'iso' 'uncurry' 'curry'</span>
<a name="line-371"></a><span class='hs-comment'>-- @</span>
<a name="line-372"></a><span class='hs-comment'>--</span>
<a name="line-373"></a><span class='hs-comment'>-- @</span>
<a name="line-374"></a><span class='hs-comment'>-- 'uncurried' = 'from' 'curried'</span>
<a name="line-375"></a><span class='hs-comment'>-- @</span>
<a name="line-376"></a><span class='hs-comment'>--</span>
<a name="line-377"></a><span class='hs-comment'>-- &gt;&gt;&gt; ((+)^.uncurried) (1,2)</span>
<a name="line-378"></a><span class='hs-comment'>-- 3</span>
<a name="line-379"></a><span class='hs-definition'>uncurried</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Iso</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>d</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>e</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</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'>-&gt;</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</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'>-&gt;</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span>
<a name="line-380"></a><span class='hs-definition'>uncurried</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iso</span> <span class='hs-varid'>uncurry</span> <span class='hs-varid'>curry</span>
<a name="line-381"></a><span class='hs-comment'>{-# INLINE uncurried #-}</span>
<a name="line-382"></a>
<a name="line-383"></a><a name="flipped"></a><span class='hs-comment'>-- | The isomorphism for flipping a function.</span>
<a name="line-384"></a><span class='hs-comment'>--</span>
<a name="line-385"></a><span class='hs-comment'>-- &gt;&gt;&gt;((,)^.flipped) 1 2</span>
<a name="line-386"></a><span class='hs-comment'>-- (2,1)</span>
<a name="line-387"></a><span class='hs-definition'>flipped</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Iso</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>a'</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>b'</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>c'</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>b'</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a'</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>c'</span><span class='hs-layout'>)</span>
<a name="line-388"></a><span class='hs-definition'>flipped</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iso</span> <span class='hs-varid'>flip</span> <span class='hs-varid'>flip</span>
<a name="line-389"></a><span class='hs-comment'>{-# INLINE flipped #-}</span>
<a name="line-390"></a>
<a name="line-391"></a><a name="Swapped"></a><span class='hs-comment'>-- | This class provides for symmetric bifunctors.</span>
<a name="line-392"></a><a name="Swapped"></a><span class='hs-keyword'>class</span> <span class='hs-conid'>Bifunctor</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Swapped</span> <span class='hs-varid'>p</span> <span class='hs-keyword'>where</span>
<a name="line-393"></a>  <span class='hs-comment'>-- |</span>
<a name="line-394"></a>  <span class='hs-comment'>-- @</span>
<a name="line-395"></a>  <span class='hs-comment'>-- 'swapped' '.' 'swapped' ≡ 'id'</span>
<a name="line-396"></a>  <span class='hs-comment'>-- 'first' f '.' 'swapped' = 'swapped' '.' 'second' f</span>
<a name="line-397"></a>  <span class='hs-comment'>-- 'second' g '.' 'swapped' = 'swapped' '.' 'first' g</span>
<a name="line-398"></a>  <span class='hs-comment'>-- 'bimap' f g '.' 'swapped' = 'swapped' '.' 'bimap' g f</span>
<a name="line-399"></a>  <span class='hs-comment'>-- @</span>
<a name="line-400"></a>  <span class='hs-comment'>--</span>
<a name="line-401"></a>  <span class='hs-comment'>-- &gt;&gt;&gt; (1,2)^.swapped</span>
<a name="line-402"></a>  <span class='hs-comment'>-- (2,1)</span>
<a name="line-403"></a>  <span class='hs-varid'>swapped</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Iso</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span> <span class='hs-varid'>c</span> <span class='hs-varid'>d</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span> <span class='hs-varid'>b</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span> <span class='hs-varid'>d</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span>
<a name="line-404"></a>
<a name="line-405"></a><a name="instance%20Swapped%20(,)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Swapped</span> <span class='hs-conid'>(,)</span> <span class='hs-keyword'>where</span>
<a name="line-406"></a>  <span class='hs-varid'>swapped</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iso</span> <span class='hs-varid'>swap</span> <span class='hs-varid'>swap</span>
<a name="line-407"></a>
<a name="line-408"></a><a name="instance%20Swapped%20Either"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Swapped</span> <span class='hs-conid'>Either</span> <span class='hs-keyword'>where</span>
<a name="line-409"></a>  <span class='hs-varid'>swapped</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iso</span> <span class='hs-layout'>(</span><span class='hs-varid'>either</span> <span class='hs-conid'>Right</span> <span class='hs-conid'>Left</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>either</span> <span class='hs-conid'>Right</span> <span class='hs-conid'>Left</span><span class='hs-layout'>)</span>
<a name="line-410"></a>
<a name="line-411"></a><a name="Strict"></a><span class='hs-comment'>-- | Ad hoc conversion between \"strict\" and \"lazy\" versions of a structure,</span>
<a name="line-412"></a><a name="Strict"></a><span class='hs-comment'>-- such as 'StrictT.Text' or 'StrictB.ByteString'.</span>
<a name="line-413"></a><a name="Strict"></a><span class='hs-keyword'>class</span> <span class='hs-conid'>Strict</span> <span class='hs-varid'>lazy</span> <span class='hs-varid'>strict</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>lazy</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>strict</span><span class='hs-layout'>,</span> <span class='hs-varid'>strict</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>lazy</span> <span class='hs-keyword'>where</span>
<a name="line-414"></a>  <span class='hs-varid'>strict</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Iso'</span> <span class='hs-varid'>lazy</span> <span class='hs-varid'>strict</span>
<a name="line-415"></a>
<a name="line-416"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ &gt;= 710</span>
<a name="line-417"></a><a name="pattern"></a><span class='hs-definition'>pattern</span> <span class='hs-conid'>Strict</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>&lt;-</span> <span class='hs-layout'>(</span><span class='hs-varid'>view</span> <span class='hs-varid'>strict</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-418"></a>  <span class='hs-conid'>Strict</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>review</span> <span class='hs-varid'>strict</span> <span class='hs-varid'>a</span>
<a name="line-419"></a>
<a name="line-420"></a><span class='hs-definition'>pattern</span> <span class='hs-conid'>Lazy</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>&lt;-</span> <span class='hs-layout'>(</span><span class='hs-varid'>view</span> <span class='hs-varid'>lazy</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-421"></a>  <span class='hs-conid'>Lazy</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>review</span> <span class='hs-varid'>lazy</span> <span class='hs-varid'>a</span>
<a name="line-422"></a>
<a name="line-423"></a><span class='hs-definition'>pattern</span> <span class='hs-conid'>Swapped</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>&lt;-</span> <span class='hs-layout'>(</span><span class='hs-varid'>view</span> <span class='hs-varid'>swapped</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-424"></a>  <span class='hs-conid'>Swapped</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>review</span> <span class='hs-varid'>swapped</span> <span class='hs-varid'>a</span>
<a name="line-425"></a>
<a name="line-426"></a><span class='hs-definition'>pattern</span> <span class='hs-conid'>Reversed</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>&lt;-</span> <span class='hs-layout'>(</span><span class='hs-varid'>view</span> <span class='hs-varid'>reversed</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-427"></a>  <span class='hs-conid'>Reversed</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>review</span> <span class='hs-varid'>reversed</span> <span class='hs-varid'>a</span>
<a name="line-428"></a><span class='hs-cpp'>#endif</span>
<a name="line-429"></a>
<a name="line-430"></a><a name="instance%20Strict%20LazyB.ByteString%20StrictB.ByteString"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Strict</span> <span class='hs-conid'>LazyB</span><span class='hs-varop'>.</span><span class='hs-conid'>ByteString</span> <span class='hs-conid'>StrictB</span><span class='hs-varop'>.</span><span class='hs-conid'>ByteString</span> <span class='hs-keyword'>where</span>
<a name="line-431"></a><span class='hs-cpp'>#if MIN_VERSION_bytestring(0,10,0)</span>
<a name="line-432"></a>  <span class='hs-varid'>strict</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iso</span> <span class='hs-conid'>LazyB</span><span class='hs-varop'>.</span><span class='hs-varid'>toStrict</span> <span class='hs-conid'>LazyB</span><span class='hs-varop'>.</span><span class='hs-varid'>fromStrict</span>
<a name="line-433"></a><span class='hs-cpp'>#else</span>
<a name="line-434"></a>  <span class='hs-varid'>strict</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iso</span> <span class='hs-layout'>(</span><span class='hs-conid'>StrictB</span><span class='hs-varop'>.</span><span class='hs-varid'>concat</span> <span class='hs-varop'>.</span> <span class='hs-conid'>LazyB</span><span class='hs-varop'>.</span><span class='hs-varid'>toChunks</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>LazyB</span><span class='hs-varop'>.</span><span class='hs-varid'>fromChunks</span> <span class='hs-varop'>.</span> <span class='hs-varid'>return</span><span class='hs-layout'>)</span>
<a name="line-435"></a><span class='hs-cpp'>#endif</span>
<a name="line-436"></a>  <span class='hs-comment'>{-# INLINE strict #-}</span>
<a name="line-437"></a>
<a name="line-438"></a><a name="instance%20Strict%20LazyT.Text%20StrictT.Text"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Strict</span> <span class='hs-conid'>LazyT</span><span class='hs-varop'>.</span><span class='hs-conid'>Text</span> <span class='hs-conid'>StrictT</span><span class='hs-varop'>.</span><span class='hs-conid'>Text</span> <span class='hs-keyword'>where</span>
<a name="line-439"></a>  <span class='hs-varid'>strict</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iso</span> <span class='hs-conid'>LazyT</span><span class='hs-varop'>.</span><span class='hs-varid'>toStrict</span> <span class='hs-conid'>LazyT</span><span class='hs-varop'>.</span><span class='hs-varid'>fromStrict</span>
<a name="line-440"></a>  <span class='hs-comment'>{-# INLINE strict #-}</span>
<a name="line-441"></a>
<a name="line-442"></a><a name="instance%20Strict%20(Lazy.StateT%20s%20m%20a)%20(Strict.StateT%20s%20m%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Strict</span> <span class='hs-layout'>(</span><span class='hs-conid'>Lazy</span><span class='hs-varop'>.</span><span class='hs-conid'>StateT</span> <span class='hs-varid'>s</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Strict</span><span class='hs-varop'>.</span><span class='hs-conid'>StateT</span> <span class='hs-varid'>s</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-443"></a>  <span class='hs-varid'>strict</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iso</span> <span class='hs-layout'>(</span><span class='hs-conid'>Strict</span><span class='hs-varop'>.</span><span class='hs-conid'>StateT</span> <span class='hs-varop'>.</span> <span class='hs-conid'>Lazy</span><span class='hs-varop'>.</span><span class='hs-varid'>runStateT</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Lazy</span><span class='hs-varop'>.</span><span class='hs-conid'>StateT</span> <span class='hs-varop'>.</span> <span class='hs-conid'>Strict</span><span class='hs-varop'>.</span><span class='hs-varid'>runStateT</span><span class='hs-layout'>)</span>
<a name="line-444"></a>  <span class='hs-comment'>{-# INLINE strict #-}</span>
<a name="line-445"></a>
<a name="line-446"></a><a name="instance%20Strict%20(Lazy.WriterT%20w%20m%20a)%20(Strict.WriterT%20w%20m%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Strict</span> <span class='hs-layout'>(</span><span class='hs-conid'>Lazy</span><span class='hs-varop'>.</span><span class='hs-conid'>WriterT</span> <span class='hs-varid'>w</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Strict</span><span class='hs-varop'>.</span><span class='hs-conid'>WriterT</span> <span class='hs-varid'>w</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-447"></a>  <span class='hs-varid'>strict</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iso</span> <span class='hs-layout'>(</span><span class='hs-conid'>Strict</span><span class='hs-varop'>.</span><span class='hs-conid'>WriterT</span> <span class='hs-varop'>.</span> <span class='hs-conid'>Lazy</span><span class='hs-varop'>.</span><span class='hs-varid'>runWriterT</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Lazy</span><span class='hs-varop'>.</span><span class='hs-conid'>WriterT</span> <span class='hs-varop'>.</span> <span class='hs-conid'>Strict</span><span class='hs-varop'>.</span><span class='hs-varid'>runWriterT</span><span class='hs-layout'>)</span>
<a name="line-448"></a>  <span class='hs-comment'>{-# INLINE strict #-}</span>
<a name="line-449"></a>
<a name="line-450"></a><a name="instance%20Strict%20(Lazy.RWST%20r%20w%20s%20m%20a)%20(Strict.RWST%20r%20w%20s%20m%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Strict</span> <span class='hs-layout'>(</span><span class='hs-conid'>Lazy</span><span class='hs-varop'>.</span><span class='hs-conid'>RWST</span> <span class='hs-varid'>r</span> <span class='hs-varid'>w</span> <span class='hs-varid'>s</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Strict</span><span class='hs-varop'>.</span><span class='hs-conid'>RWST</span> <span class='hs-varid'>r</span> <span class='hs-varid'>w</span> <span class='hs-varid'>s</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-451"></a>  <span class='hs-varid'>strict</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iso</span> <span class='hs-layout'>(</span><span class='hs-conid'>Strict</span><span class='hs-varop'>.</span><span class='hs-conid'>RWST</span> <span class='hs-varop'>.</span> <span class='hs-conid'>Lazy</span><span class='hs-varop'>.</span><span class='hs-varid'>runRWST</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Lazy</span><span class='hs-varop'>.</span><span class='hs-conid'>RWST</span> <span class='hs-varop'>.</span> <span class='hs-conid'>Strict</span><span class='hs-varop'>.</span><span class='hs-varid'>runRWST</span><span class='hs-layout'>)</span>
<a name="line-452"></a>  <span class='hs-comment'>{-# INLINE strict #-}</span>
<a name="line-453"></a>
<a name="line-454"></a><a name="lazy"></a><span class='hs-comment'>-- | An 'Iso' between the strict variant of a structure and its lazy</span>
<a name="line-455"></a><span class='hs-comment'>-- counterpart.</span>
<a name="line-456"></a><span class='hs-comment'>--</span>
<a name="line-457"></a><span class='hs-comment'>-- @</span>
<a name="line-458"></a><span class='hs-comment'>-- 'lazy' = 'from' 'strict'</span>
<a name="line-459"></a><span class='hs-comment'>-- @</span>
<a name="line-460"></a><span class='hs-comment'>--</span>
<a name="line-461"></a><span class='hs-comment'>-- See &lt;<a href="http://hackage.haskell.org/package/strict-base-types">http://hackage.haskell.org/package/strict-base-types</a>&gt; for an example</span>
<a name="line-462"></a><span class='hs-comment'>-- use.</span>
<a name="line-463"></a><span class='hs-definition'>lazy</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Strict</span> <span class='hs-varid'>lazy</span> <span class='hs-varid'>strict</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Iso'</span> <span class='hs-varid'>strict</span> <span class='hs-varid'>lazy</span>
<a name="line-464"></a><span class='hs-definition'>lazy</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>from</span> <span class='hs-varid'>strict</span>
<a name="line-465"></a>
<a name="line-466"></a><a name="reversed"></a><span class='hs-comment'>-- | An 'Iso' between a list, 'ByteString', 'Text' fragment, etc. and its reversal.</span>
<a name="line-467"></a><span class='hs-comment'>--</span>
<a name="line-468"></a><span class='hs-comment'>-- &gt;&gt;&gt; "live" ^. reversed</span>
<a name="line-469"></a><span class='hs-comment'>-- "evil"</span>
<a name="line-470"></a><span class='hs-comment'>--</span>
<a name="line-471"></a><span class='hs-comment'>-- &gt;&gt;&gt; "live" &amp; reversed %~ ('d':)</span>
<a name="line-472"></a><span class='hs-comment'>-- "lived"</span>
<a name="line-473"></a><span class='hs-definition'>reversed</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Reversing</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Iso'</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span>
<a name="line-474"></a><span class='hs-definition'>reversed</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>involuted</span> <span class='hs-conid'>Iso</span><span class='hs-varop'>.</span><span class='hs-varid'>reversing</span>
<a name="line-475"></a>
<a name="line-476"></a><a name="involuted"></a><span class='hs-comment'>-- | Given a function that is its own inverse, this gives you an 'Iso' using it in both directions.</span>
<a name="line-477"></a><span class='hs-comment'>--</span>
<a name="line-478"></a><span class='hs-comment'>-- @</span>
<a name="line-479"></a><span class='hs-comment'>-- 'involuted' ≡ 'Control.Monad.join' 'iso'</span>
<a name="line-480"></a><span class='hs-comment'>-- @</span>
<a name="line-481"></a><span class='hs-comment'>--</span>
<a name="line-482"></a><span class='hs-comment'>-- &gt;&gt;&gt; "live" ^. involuted reverse</span>
<a name="line-483"></a><span class='hs-comment'>-- "evil"</span>
<a name="line-484"></a><span class='hs-comment'>--</span>
<a name="line-485"></a><span class='hs-comment'>-- &gt;&gt;&gt; "live" &amp; involuted reverse %~ ('d':)</span>
<a name="line-486"></a><span class='hs-comment'>-- "lived"</span>
<a name="line-487"></a><span class='hs-definition'>involuted</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Iso'</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span>
<a name="line-488"></a><span class='hs-definition'>involuted</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iso</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span>
<a name="line-489"></a><span class='hs-comment'>{-# INLINE involuted #-}</span>
<a name="line-490"></a>
<a name="line-491"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ &gt;= 710</span>
<a name="line-492"></a><span class='hs-definition'>pattern</span> <span class='hs-conid'>List</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>&lt;-</span> <span class='hs-layout'>(</span><span class='hs-conid'>Exts</span><span class='hs-varop'>.</span><span class='hs-varid'>toList</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-493"></a>  <span class='hs-conid'>List</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Exts</span><span class='hs-varop'>.</span><span class='hs-varid'>fromList</span> <span class='hs-varid'>a</span>
<a name="line-494"></a><span class='hs-cpp'>#endif</span>
<a name="line-495"></a>
<a name="line-496"></a><span class='hs-comment'>------------------------------------------------------------------------------</span>
<a name="line-497"></a><span class='hs-comment'>-- Magma</span>
<a name="line-498"></a><span class='hs-comment'>------------------------------------------------------------------------------</span>
<a name="line-499"></a>
<a name="line-500"></a><a name="magma"></a><span class='hs-comment'>-- | This isomorphism can be used to inspect a 'Traversal' to see how it associates</span>
<a name="line-501"></a><span class='hs-comment'>-- the structure and it can also be used to bake the 'Traversal' into a 'Magma' so</span>
<a name="line-502"></a><span class='hs-comment'>-- that you can traverse over it multiple times.</span>
<a name="line-503"></a><span class='hs-definition'>magma</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>LensLike</span> <span class='hs-layout'>(</span><span class='hs-conid'>Mafic</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Iso</span> <span class='hs-varid'>s</span> <span class='hs-varid'>u</span> <span class='hs-layout'>(</span><span class='hs-conid'>Magma</span> <span class='hs-conid'>Int</span> <span class='hs-varid'>t</span> <span class='hs-varid'>b</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Magma</span> <span class='hs-varid'>j</span> <span class='hs-varid'>u</span> <span class='hs-varid'>c</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span>
<a name="line-504"></a><span class='hs-definition'>magma</span> <span class='hs-varid'>l</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iso</span> <span class='hs-layout'>(</span><span class='hs-varid'>runMafic</span> <span class='hs-varop'>`rmap`</span> <span class='hs-varid'>l</span> <span class='hs-varid'>sell</span><span class='hs-layout'>)</span> <span class='hs-varid'>runMagma</span>
<a name="line-505"></a><span class='hs-comment'>{-# INLINE magma #-}</span>
<a name="line-506"></a>
<a name="line-507"></a><a name="imagma"></a><span class='hs-comment'>-- | This isomorphism can be used to inspect an 'IndexedTraversal' to see how it associates</span>
<a name="line-508"></a><span class='hs-comment'>-- the structure and it can also be used to bake the 'IndexedTraversal' into a 'Magma' so</span>
<a name="line-509"></a><span class='hs-comment'>-- that you can traverse over it multiple times with access to the original indices.</span>
<a name="line-510"></a><span class='hs-definition'>imagma</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Over</span> <span class='hs-layout'>(</span><span class='hs-conid'>Indexed</span> <span class='hs-varid'>i</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Molten</span> <span class='hs-varid'>i</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Iso</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t'</span> <span class='hs-layout'>(</span><span class='hs-conid'>Magma</span> <span class='hs-varid'>i</span> <span class='hs-varid'>t</span> <span class='hs-varid'>b</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Magma</span> <span class='hs-varid'>j</span> <span class='hs-varid'>t'</span> <span class='hs-varid'>c</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span>
<a name="line-511"></a><span class='hs-definition'>imagma</span> <span class='hs-varid'>l</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iso</span> <span class='hs-layout'>(</span><span class='hs-varid'>runMolten</span> <span class='hs-cpp'>#.</span> <span class='hs-varid'>l</span> <span class='hs-varid'>sell</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>iextract</span> <span class='hs-varop'>.#</span> <span class='hs-conid'>Molten</span><span class='hs-layout'>)</span>
<a name="line-512"></a><span class='hs-comment'>{-# INLINE imagma #-}</span>
<a name="line-513"></a>
<a name="line-514"></a><span class='hs-comment'>------------------------------------------------------------------------------</span>
<a name="line-515"></a><span class='hs-comment'>-- Contravariant</span>
<a name="line-516"></a><span class='hs-comment'>------------------------------------------------------------------------------</span>
<a name="line-517"></a>
<a name="line-518"></a><a name="contramapping"></a><span class='hs-comment'>-- | Lift an 'Iso' into a 'Contravariant' functor.</span>
<a name="line-519"></a><span class='hs-comment'>--</span>
<a name="line-520"></a><span class='hs-comment'>-- @</span>
<a name="line-521"></a><span class='hs-comment'>-- contramapping :: 'Contravariant' f =&gt; 'Iso' s t a b -&gt; 'Iso' (f a) (f b) (f s) (f t)</span>
<a name="line-522"></a><span class='hs-comment'>-- contramapping :: 'Contravariant' f =&gt; 'Iso'' s a -&gt; 'Iso'' (f a) (f s)</span>
<a name="line-523"></a><span class='hs-comment'>-- @</span>
<a name="line-524"></a><span class='hs-definition'>contramapping</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Contravariant</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>AnIso</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Iso</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>t</span><span class='hs-layout'>)</span>
<a name="line-525"></a><span class='hs-definition'>contramapping</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>withIso</span> <span class='hs-varid'>f</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span> <span class='hs-varid'>sa</span> <span class='hs-varid'>bt</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>iso</span> <span class='hs-layout'>(</span><span class='hs-varid'>contramap</span> <span class='hs-varid'>sa</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>contramap</span> <span class='hs-varid'>bt</span><span class='hs-layout'>)</span>
<a name="line-526"></a><span class='hs-comment'>{-# INLINE contramapping #-}</span>
<a name="line-527"></a>
<a name="line-528"></a><span class='hs-comment'>------------------------------------------------------------------------------</span>
<a name="line-529"></a><span class='hs-comment'>-- Profunctor</span>
<a name="line-530"></a><span class='hs-comment'>------------------------------------------------------------------------------</span>
<a name="line-531"></a>
<a name="line-532"></a><a name="dimapping"></a><span class='hs-comment'>-- | Lift two 'Iso's into both arguments of a 'Profunctor' simultaneously.</span>
<a name="line-533"></a><span class='hs-comment'>--</span>
<a name="line-534"></a><span class='hs-comment'>-- @</span>
<a name="line-535"></a><span class='hs-comment'>-- dimapping :: 'Profunctor' p =&gt; 'Iso' s t a b -&gt; 'Iso' s' t' a' b' -&gt; 'Iso' (p a s') (p b t') (p s a') (p t b')</span>
<a name="line-536"></a><span class='hs-comment'>-- dimapping :: 'Profunctor' p =&gt; 'Iso'' s a -&gt; 'Iso'' s' a' -&gt; 'Iso'' (p a s') (p s a')</span>
<a name="line-537"></a><span class='hs-comment'>-- @</span>
<a name="line-538"></a><span class='hs-definition'>dimapping</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Profunctor</span> <span class='hs-varid'>p</span><span class='hs-layout'>,</span> <span class='hs-conid'>Profunctor</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>AnIso</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>AnIso</span> <span class='hs-varid'>s'</span> <span class='hs-varid'>t'</span> <span class='hs-varid'>a'</span> <span class='hs-varid'>b'</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Iso</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span> <span class='hs-varid'>a</span> <span class='hs-varid'>s'</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>q</span> <span class='hs-varid'>b</span> <span class='hs-varid'>t'</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a'</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>q</span> <span class='hs-varid'>t</span> <span class='hs-varid'>b'</span><span class='hs-layout'>)</span>
<a name="line-539"></a><span class='hs-definition'>dimapping</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>withIso</span> <span class='hs-varid'>f</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span> <span class='hs-varid'>sa</span> <span class='hs-varid'>bt</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>withIso</span> <span class='hs-varid'>g</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span> <span class='hs-varid'>s'a'</span> <span class='hs-varid'>b't'</span> <span class='hs-keyglyph'>-&gt;</span>
<a name="line-540"></a>  <span class='hs-varid'>iso</span> <span class='hs-layout'>(</span><span class='hs-varid'>dimap</span> <span class='hs-varid'>sa</span> <span class='hs-varid'>s'a'</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>dimap</span> <span class='hs-varid'>bt</span> <span class='hs-varid'>b't'</span><span class='hs-layout'>)</span>
<a name="line-541"></a><span class='hs-comment'>{-# INLINE dimapping #-}</span>
<a name="line-542"></a>
<a name="line-543"></a><a name="lmapping"></a><span class='hs-comment'>-- | Lift an 'Iso' contravariantly into the left argument of a 'Profunctor'.</span>
<a name="line-544"></a><span class='hs-comment'>--</span>
<a name="line-545"></a><span class='hs-comment'>-- @</span>
<a name="line-546"></a><span class='hs-comment'>-- lmapping :: 'Profunctor' p =&gt; 'Iso' s t a b -&gt; 'Iso' (p a x) (p b y) (p s x) (p t y)</span>
<a name="line-547"></a><span class='hs-comment'>-- lmapping :: 'Profunctor' p =&gt; 'Iso'' s a -&gt; 'Iso'' (p a x) (p s x)</span>
<a name="line-548"></a><span class='hs-comment'>-- @</span>
<a name="line-549"></a><span class='hs-definition'>lmapping</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Profunctor</span> <span class='hs-varid'>p</span><span class='hs-layout'>,</span> <span class='hs-conid'>Profunctor</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>AnIso</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Iso</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span> <span class='hs-varid'>a</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>q</span> <span class='hs-varid'>b</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span> <span class='hs-varid'>s</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>q</span> <span class='hs-varid'>t</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span>
<a name="line-550"></a><span class='hs-definition'>lmapping</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>withIso</span> <span class='hs-varid'>f</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span> <span class='hs-varid'>sa</span> <span class='hs-varid'>bt</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>iso</span> <span class='hs-layout'>(</span><span class='hs-varid'>lmap</span> <span class='hs-varid'>sa</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>lmap</span> <span class='hs-varid'>bt</span><span class='hs-layout'>)</span>
<a name="line-551"></a><span class='hs-comment'>{-# INLINE lmapping #-}</span>
<a name="line-552"></a>
<a name="line-553"></a><a name="rmapping"></a><span class='hs-comment'>-- | Lift an 'Iso' covariantly into the right argument of a 'Profunctor'.</span>
<a name="line-554"></a><span class='hs-comment'>--</span>
<a name="line-555"></a><span class='hs-comment'>-- @</span>
<a name="line-556"></a><span class='hs-comment'>-- rmapping :: 'Profunctor' p =&gt; 'Iso' s t a b -&gt; 'Iso' (p x s) (p y t) (p x a) (p y b)</span>
<a name="line-557"></a><span class='hs-comment'>-- rmapping :: 'Profunctor' p =&gt; 'Iso'' s a -&gt; 'Iso'' (p x s) (p x a)</span>
<a name="line-558"></a><span class='hs-comment'>-- @</span>
<a name="line-559"></a><span class='hs-definition'>rmapping</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Profunctor</span> <span class='hs-varid'>p</span><span class='hs-layout'>,</span> <span class='hs-conid'>Profunctor</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>AnIso</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Iso</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span> <span class='hs-varid'>x</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>q</span> <span class='hs-varid'>y</span> <span class='hs-varid'>t</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span> <span class='hs-varid'>x</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>q</span> <span class='hs-varid'>y</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-560"></a><span class='hs-definition'>rmapping</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>withIso</span> <span class='hs-varid'>g</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span> <span class='hs-varid'>sa</span> <span class='hs-varid'>bt</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>iso</span> <span class='hs-layout'>(</span><span class='hs-varid'>rmap</span> <span class='hs-varid'>sa</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>rmap</span> <span class='hs-varid'>bt</span><span class='hs-layout'>)</span>
<a name="line-561"></a><span class='hs-comment'>{-# INLINE rmapping #-}</span>
<a name="line-562"></a>
<a name="line-563"></a><span class='hs-comment'>------------------------------------------------------------------------------</span>
<a name="line-564"></a><span class='hs-comment'>-- Bifunctor</span>
<a name="line-565"></a><span class='hs-comment'>------------------------------------------------------------------------------</span>
<a name="line-566"></a>
<a name="line-567"></a><a name="bimapping"></a><span class='hs-comment'>-- | Lift two 'Iso's into both arguments of a 'Bifunctor'.</span>
<a name="line-568"></a><span class='hs-comment'>--</span>
<a name="line-569"></a><span class='hs-comment'>-- @</span>
<a name="line-570"></a><span class='hs-comment'>-- bimapping :: 'Bifunctor' p =&gt; 'Iso' s t a b -&gt; 'Iso' s' t' a' b' -&gt; 'Iso' (p s s') (p t t') (p a a') (p b b')</span>
<a name="line-571"></a><span class='hs-comment'>-- bimapping :: 'Bifunctor' p =&gt; 'Iso'' s a -&gt; 'Iso'' s' a' -&gt; 'Iso'' (p s s') (p a a')</span>
<a name="line-572"></a><span class='hs-comment'>-- @</span>
<a name="line-573"></a><span class='hs-definition'>bimapping</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Bifunctor</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Bifunctor</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>AnIso</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>AnIso</span> <span class='hs-varid'>s'</span> <span class='hs-varid'>t'</span> <span class='hs-varid'>a'</span> <span class='hs-varid'>b'</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Iso</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>s</span> <span class='hs-varid'>s'</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>g</span> <span class='hs-varid'>t</span> <span class='hs-varid'>t'</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a'</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>g</span> <span class='hs-varid'>b</span> <span class='hs-varid'>b'</span><span class='hs-layout'>)</span>
<a name="line-574"></a><span class='hs-definition'>bimapping</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>withIso</span> <span class='hs-varid'>f</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span> <span class='hs-varid'>sa</span> <span class='hs-varid'>bt</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>withIso</span> <span class='hs-varid'>g</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>s'a'</span> <span class='hs-varid'>b't'</span> <span class='hs-keyglyph'>-&gt;</span>
<a name="line-575"></a>  <span class='hs-varid'>iso</span> <span class='hs-layout'>(</span><span class='hs-varid'>bimap</span> <span class='hs-varid'>sa</span> <span class='hs-varid'>s'a'</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>bimap</span> <span class='hs-varid'>bt</span> <span class='hs-varid'>b't'</span><span class='hs-layout'>)</span>
<a name="line-576"></a><span class='hs-comment'>{-# INLINE bimapping #-}</span>
<a name="line-577"></a>
<a name="line-578"></a><a name="firsting"></a><span class='hs-comment'>-- | Lift an 'Iso' into the first argument of a 'Bifunctor'.</span>
<a name="line-579"></a><span class='hs-comment'>--</span>
<a name="line-580"></a><span class='hs-comment'>-- @</span>
<a name="line-581"></a><span class='hs-comment'>-- firsting :: 'Bifunctor' p =&gt; 'Iso' s t a b -&gt; 'Iso' (p s x) (p t y) (p a x) (p b y)</span>
<a name="line-582"></a><span class='hs-comment'>-- firsting :: 'Bifunctor' p =&gt; 'Iso'' s a -&gt; 'Iso'' (p s x) (p a x)</span>
<a name="line-583"></a><span class='hs-comment'>-- @</span>
<a name="line-584"></a><span class='hs-definition'>firsting</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Bifunctor</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Bifunctor</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>AnIso</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Iso</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>s</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>g</span> <span class='hs-varid'>t</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>g</span> <span class='hs-varid'>b</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span>
<a name="line-585"></a><span class='hs-definition'>firsting</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>withIso</span> <span class='hs-varid'>p</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span> <span class='hs-varid'>sa</span> <span class='hs-varid'>bt</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>iso</span> <span class='hs-layout'>(</span><span class='hs-varid'>first</span> <span class='hs-varid'>sa</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>first</span> <span class='hs-varid'>bt</span><span class='hs-layout'>)</span>
<a name="line-586"></a><span class='hs-comment'>{-# INLINE firsting #-}</span>
<a name="line-587"></a>
<a name="line-588"></a><a name="seconding"></a><span class='hs-comment'>-- | Lift an 'Iso' into the second argument of a 'Bifunctor'. This is</span>
<a name="line-589"></a><span class='hs-comment'>-- essentially the same as 'mapping', but it takes a 'Bifunctor p'</span>
<a name="line-590"></a><span class='hs-comment'>-- constraint instead of a 'Functor (p a)' one.</span>
<a name="line-591"></a><span class='hs-comment'>--</span>
<a name="line-592"></a><span class='hs-comment'>-- @</span>
<a name="line-593"></a><span class='hs-comment'>-- seconding :: 'Bifunctor' p =&gt; 'Iso' s t a b -&gt; 'Iso' (p x s) (p y t) (p x a) (p y b)</span>
<a name="line-594"></a><span class='hs-comment'>-- seconding :: 'Bifunctor' p =&gt; 'Iso'' s a -&gt; 'Iso'' (p x s) (p x a)</span>
<a name="line-595"></a><span class='hs-comment'>-- @</span>
<a name="line-596"></a><span class='hs-definition'>seconding</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Bifunctor</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Bifunctor</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>AnIso</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Iso</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>x</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>g</span> <span class='hs-varid'>y</span> <span class='hs-varid'>t</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>x</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>g</span> <span class='hs-varid'>y</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-597"></a><span class='hs-definition'>seconding</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>withIso</span> <span class='hs-varid'>p</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span> <span class='hs-varid'>sa</span> <span class='hs-varid'>bt</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>iso</span> <span class='hs-layout'>(</span><span class='hs-varid'>second</span> <span class='hs-varid'>sa</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>second</span> <span class='hs-varid'>bt</span><span class='hs-layout'>)</span>
<a name="line-598"></a><span class='hs-comment'>{-# INLINE seconding #-}</span>
<a name="line-599"></a>
<a name="line-600"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ &gt;= 708</span>
<a name="line-601"></a><a name="coerced"></a><span class='hs-comment'>-- | Data types that are representationally equal are isomorphic.</span>
<a name="line-602"></a><span class='hs-comment'>--</span>
<a name="line-603"></a><span class='hs-comment'>-- This is only available on GHC 7.8+</span>
<a name="line-604"></a><span class='hs-comment'>--</span>
<a name="line-605"></a><span class='hs-comment'>-- @since 4.13</span>
<a name="line-606"></a><span class='hs-definition'>coerced</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyword'>forall</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span><span class='hs-varop'>.</span> <span class='hs-layout'>(</span><span class='hs-conid'>Coercible</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Coercible</span> <span class='hs-varid'>t</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Iso</span> <span class='hs-varid'>s</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span>
<a name="line-607"></a><span class='hs-cpp'># if __GLASGOW_HASKELL__ &gt;= 710</span>
<a name="line-608"></a><span class='hs-definition'>coerced</span> <span class='hs-varid'>l</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>rmap</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>coerce'</span><span class='hs-layout'>)</span> <span class='hs-varid'>l</span> <span class='hs-varop'>.#</span> <span class='hs-varid'>coerce</span>
<a name="line-609"></a><span class='hs-cpp'># else</span>
<a name="line-610"></a><span class='hs-definition'>coerced</span> <span class='hs-varid'>l</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>sym</span> <span class='hs-conid'>Coercion</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Coercion</span> <span class='hs-varid'>a</span> <span class='hs-varid'>s</span> <span class='hs-keyword'>of</span>
<a name="line-611"></a>              <span class='hs-conid'>Coercion</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>rmap</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>coerce'</span><span class='hs-layout'>)</span> <span class='hs-varid'>l</span> <span class='hs-varop'>.#</span> <span class='hs-varid'>coerce</span>
<a name="line-612"></a><span class='hs-cpp'># endif</span>
<a name="line-613"></a><span class='hs-comment'>{-# INLINE coerced #-}</span>
<a name="line-614"></a><span class='hs-cpp'>#endif</span>
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