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<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE CPP #-}</span>
<a name="line-2"></a><span class='hs-comment'>{-# LANGUAGE Rank2Types #-}</span>
<a name="line-3"></a><span class='hs-comment'>{-# LANGUAGE GADTs #-}</span>
<a name="line-4"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ >= 707</span>
<a name="line-5"></a><span class='hs-comment'>{-# LANGUAGE DeriveDataTypeable #-}</span>
<a name="line-6"></a><span class='hs-cpp'>#endif</span>
<a name="line-7"></a><span class='hs-comment'>{-# OPTIONS_GHC -Wall #-}</span>
<a name="line-8"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-9"></a><span class='hs-comment'>-- |</span>
<a name="line-10"></a><span class='hs-comment'>-- Module : Control.Applicative.Trans.Free</span>
<a name="line-11"></a><span class='hs-comment'>-- Copyright : (C) 2012-2013 Edward Kmett</span>
<a name="line-12"></a><span class='hs-comment'>-- License : BSD-style (see the file LICENSE)</span>
<a name="line-13"></a><span class='hs-comment'>--</span>
<a name="line-14"></a><span class='hs-comment'>-- Maintainer : Edward Kmett <ekmett@gmail.com></span>
<a name="line-15"></a><span class='hs-comment'>-- Stability : provisional</span>
<a name="line-16"></a><span class='hs-comment'>-- Portability : GADTs, Rank2Types</span>
<a name="line-17"></a><span class='hs-comment'>--</span>
<a name="line-18"></a><span class='hs-comment'>-- 'Applicative' functor transformers for free</span>
<a name="line-19"></a><span class='hs-comment'>----------------------------------------------------------------------------</span>
<a name="line-20"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Applicative</span><span class='hs-varop'>.</span><span class='hs-conid'>Trans</span><span class='hs-varop'>.</span><span class='hs-conid'>Free</span>
<a name="line-21"></a> <span class='hs-layout'>(</span>
<a name="line-22"></a> <span class='hs-comment'>-- | Compared to the free monad transformers, they are less expressive. However, they are also more</span>
<a name="line-23"></a> <span class='hs-comment'>-- flexible to inspect and interpret, as the number of ways in which</span>
<a name="line-24"></a> <span class='hs-comment'>-- the values can be nested is more limited.</span>
<a name="line-25"></a> <span class='hs-comment'>--</span>
<a name="line-26"></a> <span class='hs-comment'>-- See <<a href="http://paolocapriotti.com/assets/applicative.pdf">http://paolocapriotti.com/assets/applicative.pdf</a> Free Applicative Functors>,</span>
<a name="line-27"></a> <span class='hs-comment'>-- by Paolo Capriotti and Ambrus Kaposi, for some applications.</span>
<a name="line-28"></a> <span class='hs-conid'>ApT</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-29"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>ApF</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-30"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>liftApT</span>
<a name="line-31"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>liftApO</span>
<a name="line-32"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>runApT</span>
<a name="line-33"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>runApF</span>
<a name="line-34"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>runApT_</span>
<a name="line-35"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>hoistApT</span>
<a name="line-36"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>hoistApF</span>
<a name="line-37"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>transApT</span>
<a name="line-38"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>transApF</span>
<a name="line-39"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>joinApT</span>
<a name="line-40"></a> <span class='hs-comment'>-- * Free Applicative</span>
<a name="line-41"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Ap</span>
<a name="line-42"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>runAp</span>
<a name="line-43"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>runAp_</span>
<a name="line-44"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>retractAp</span>
<a name="line-45"></a> <span class='hs-comment'>-- * Free Alternative</span>
<a name="line-46"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Alt</span>
<a name="line-47"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>runAlt</span>
<a name="line-48"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-49"></a>
<a name="line-50"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Applicative</span>
<a name="line-51"></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-layout'>(</span><span class='hs-varid'>liftM</span><span class='hs-layout'>)</span>
<a name="line-52"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Functor</span><span class='hs-varop'>.</span><span class='hs-conid'>Apply</span>
<a name="line-53"></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-54"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Typeable</span>
<a name="line-55"></a><span class='hs-cpp'>#if !(MIN_VERSION_base(4,8,0))</span>
<a name="line-56"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Monoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>Monoid</span><span class='hs-layout'>)</span>
<a name="line-57"></a><span class='hs-cpp'>#endif</span>
<a name="line-58"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Foldable</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>F</span>
<a name="line-59"></a>
<a name="line-60"></a><a name="ApF"></a><span class='hs-comment'>-- | The free 'Applicative' for a 'Functor' @f@.</span>
<a name="line-61"></a><a name="ApF"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>ApF</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-varid'>a</span> <span class='hs-keyword'>where</span>
<a name="line-62"></a> <span class='hs-conid'>Pure</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>ApF</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-varid'>a</span>
<a name="line-63"></a> <span class='hs-conid'>Ap</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>ApT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>ApF</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-varid'>b</span>
<a name="line-64"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ >= 707</span>
<a name="line-65"></a> <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Typeable</span>
<a name="line-66"></a><span class='hs-cpp'>#endif</span>
<a name="line-67"></a>
<a name="line-68"></a><a name="ApT"></a><span class='hs-comment'>-- | The free 'Applicative' transformer for a 'Functor' @f@ over</span>
<a name="line-69"></a><a name="ApT"></a><span class='hs-comment'>-- 'Applicative' @g@.</span>
<a name="line-70"></a><a name="ApT"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>ApT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ApT</span> <span class='hs-layout'>{</span> <span class='hs-varid'>getApT</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>g</span> <span class='hs-layout'>(</span><span class='hs-conid'>ApF</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>}</span>
<a name="line-71"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ >= 707</span>
<a name="line-72"></a> <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Typeable</span>
<a name="line-73"></a><span class='hs-cpp'>#endif</span>
<a name="line-74"></a>
<a name="line-75"></a><a name="instance%20Functor%20(ApF%20f%20g)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Functor</span> <span class='hs-layout'>(</span><span class='hs-conid'>ApF</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-76"></a> <span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Pure</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Pure</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-77"></a> <span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Ap</span> <span class='hs-varid'>x</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span> <span class='hs-varop'>`Ap`</span> <span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varop'>.</span><span class='hs-layout'>)</span> <span class='hs-varid'>g</span>
<a name="line-78"></a>
<a name="line-79"></a><a name="instance%20Functor%20(ApT%20f%20g)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Functor</span> <span class='hs-layout'>(</span><span class='hs-conid'>ApT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-80"></a> <span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>ApT</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ApT</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-varop'><$></span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span>
<a name="line-81"></a>
<a name="line-82"></a><a name="instance%20Applicative%20(ApF%20f%20g)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Applicative</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Applicative</span> <span class='hs-layout'>(</span><span class='hs-conid'>ApF</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-83"></a> <span class='hs-varid'>pure</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Pure</span>
<a name="line-84"></a> <span class='hs-comment'>{-# INLINE pure #-}</span>
<a name="line-85"></a> <span class='hs-conid'>Pure</span> <span class='hs-varid'>f</span> <span class='hs-varop'><*></span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>y</span> <span class='hs-comment'>-- fmap</span>
<a name="line-86"></a> <span class='hs-varid'>y</span> <span class='hs-varop'><*></span> <span class='hs-conid'>Pure</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-varop'>$</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-varid'>y</span> <span class='hs-comment'>-- interchange</span>
<a name="line-87"></a> <span class='hs-conid'>Ap</span> <span class='hs-varid'>a</span> <span class='hs-varid'>f</span> <span class='hs-varop'><*></span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>a</span> <span class='hs-varop'>`Ap`</span> <span class='hs-layout'>(</span><span class='hs-varid'>flip</span> <span class='hs-varop'><$></span> <span class='hs-varid'>f</span> <span class='hs-varop'><*></span> <span class='hs-conid'>ApT</span> <span class='hs-layout'>(</span><span class='hs-varid'>pure</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-88"></a> <span class='hs-comment'>{-# INLINE (<*>) #-}</span>
<a name="line-89"></a>
<a name="line-90"></a><a name="instance%20Applicative%20(ApT%20f%20g)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Applicative</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Applicative</span> <span class='hs-layout'>(</span><span class='hs-conid'>ApT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-91"></a> <span class='hs-varid'>pure</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ApT</span> <span class='hs-varop'>.</span> <span class='hs-varid'>pure</span> <span class='hs-varop'>.</span> <span class='hs-varid'>pure</span>
<a name="line-92"></a> <span class='hs-comment'>{-# INLINE pure #-}</span>
<a name="line-93"></a> <span class='hs-conid'>ApT</span> <span class='hs-varid'>xs</span> <span class='hs-varop'><*></span> <span class='hs-conid'>ApT</span> <span class='hs-varid'>ys</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ApT</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varop'><*></span><span class='hs-layout'>)</span> <span class='hs-varop'><$></span> <span class='hs-varid'>xs</span> <span class='hs-varop'><*></span> <span class='hs-varid'>ys</span><span class='hs-layout'>)</span>
<a name="line-94"></a> <span class='hs-comment'>{-# INLINE (<*>) #-}</span>
<a name="line-95"></a>
<a name="line-96"></a><a name="instance%20Apply%20(ApF%20f%20g)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Applicative</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Apply</span> <span class='hs-layout'>(</span><span class='hs-conid'>ApF</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-97"></a> <span class='hs-layout'>(</span><span class='hs-varop'><.></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varop'><*></span><span class='hs-layout'>)</span>
<a name="line-98"></a> <span class='hs-comment'>{-# INLINE (<.>) #-}</span>
<a name="line-99"></a>
<a name="line-100"></a><a name="instance%20Apply%20(ApT%20f%20g)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Applicative</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Apply</span> <span class='hs-layout'>(</span><span class='hs-conid'>ApT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-101"></a> <span class='hs-layout'>(</span><span class='hs-varop'><.></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varop'><*></span><span class='hs-layout'>)</span>
<a name="line-102"></a> <span class='hs-comment'>{-# INLINE (<.>) #-}</span>
<a name="line-103"></a>
<a name="line-104"></a><a name="instance%20Alternative%20(ApT%20f%20g)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Alternative</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Alternative</span> <span class='hs-layout'>(</span><span class='hs-conid'>ApT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-105"></a> <span class='hs-varid'>empty</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ApT</span> <span class='hs-varid'>empty</span>
<a name="line-106"></a> <span class='hs-comment'>{-# INLINE empty #-}</span>
<a name="line-107"></a> <span class='hs-conid'>ApT</span> <span class='hs-varid'>g</span> <span class='hs-varop'><|></span> <span class='hs-conid'>ApT</span> <span class='hs-varid'>h</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ApT</span> <span class='hs-layout'>(</span><span class='hs-varid'>g</span> <span class='hs-varop'><|></span> <span class='hs-varid'>h</span><span class='hs-layout'>)</span>
<a name="line-108"></a> <span class='hs-comment'>{-# INLINE (<|>) #-}</span>
<a name="line-109"></a>
<a name="line-110"></a><a name="liftApT"></a><span class='hs-comment'>-- | A version of 'lift' that can be used with no constraint for @f@.</span>
<a name="line-111"></a><span class='hs-definition'>liftApT</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Applicative</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>ApT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-varid'>a</span>
<a name="line-112"></a><span class='hs-definition'>liftApT</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ApT</span> <span class='hs-layout'>(</span><span class='hs-varid'>pure</span> <span class='hs-layout'>(</span><span class='hs-conid'>Ap</span> <span class='hs-varid'>x</span> <span class='hs-layout'>(</span><span class='hs-varid'>pure</span> <span class='hs-varid'>id</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-113"></a>
<a name="line-114"></a><a name="liftApO"></a><span class='hs-comment'>-- | Lift an action of the \"outer\" 'Functor' @g a@ to @'ApT' f g a@.</span>
<a name="line-115"></a><span class='hs-definition'>liftApO</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>g</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>ApT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-varid'>a</span>
<a name="line-116"></a><span class='hs-definition'>liftApO</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ApT</span> <span class='hs-layout'>(</span><span class='hs-conid'>Pure</span> <span class='hs-varop'><$></span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span>
<a name="line-117"></a>
<a name="line-118"></a><a name="runApF"></a><span class='hs-comment'>-- | Given natural transformations @f ~> h@ and @g . h ~> h@ this gives</span>
<a name="line-119"></a><span class='hs-comment'>-- a natural transformation @ApF f g ~> h@.</span>
<a name="line-120"></a><span class='hs-definition'>runApF</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Applicative</span> <span class='hs-varid'>h</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'>=></span> <span class='hs-layout'>(</span><span class='hs-keyword'>forall</span> <span class='hs-varid'>a</span><span class='hs-varop'>.</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>h</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-keyword'>forall</span> <span class='hs-varid'>a</span><span class='hs-varop'>.</span> <span class='hs-varid'>g</span> <span class='hs-layout'>(</span><span class='hs-varid'>h</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>h</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>ApF</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>h</span> <span class='hs-varid'>b</span>
<a name="line-121"></a><span class='hs-definition'>runApF</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-layout'>(</span><span class='hs-conid'>Pure</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pure</span> <span class='hs-varid'>x</span>
<a name="line-122"></a><span class='hs-definition'>runApF</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-layout'>(</span><span class='hs-conid'>Ap</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span> <span class='hs-varop'><**></span> <span class='hs-varid'>runApT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-varid'>y</span>
<a name="line-123"></a>
<a name="line-124"></a><a name="runApT"></a><span class='hs-comment'>-- | Given natural transformations @f ~> h@ and @g . h ~> h@ this gives</span>
<a name="line-125"></a><span class='hs-comment'>-- a natural transformation @ApT f g ~> h@.</span>
<a name="line-126"></a><span class='hs-definition'>runApT</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Applicative</span> <span class='hs-varid'>h</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'>=></span> <span class='hs-layout'>(</span><span class='hs-keyword'>forall</span> <span class='hs-varid'>a</span><span class='hs-varop'>.</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>h</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-keyword'>forall</span> <span class='hs-varid'>a</span><span class='hs-varop'>.</span> <span class='hs-varid'>g</span> <span class='hs-layout'>(</span><span class='hs-varid'>h</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>h</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>ApT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>h</span> <span class='hs-varid'>b</span>
<a name="line-127"></a><span class='hs-definition'>runApT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-layout'>(</span><span class='hs-conid'>ApT</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>g</span> <span class='hs-layout'>(</span><span class='hs-varid'>runApF</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-varop'><$></span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-128"></a>
<a name="line-129"></a><a name="runApT_"></a><span class='hs-comment'>-- | Perform a monoidal analysis over @'ApT' f g b@ value.</span>
<a name="line-130"></a><span class='hs-comment'>--</span>
<a name="line-131"></a><span class='hs-comment'>-- Examples:</span>
<a name="line-132"></a><span class='hs-comment'>--</span>
<a name="line-133"></a><span class='hs-comment'>-- @</span>
<a name="line-134"></a><span class='hs-comment'>-- height :: ('Functor' g, 'F.Foldable' g) => 'ApT' f g a -> 'Int'</span>
<a name="line-135"></a><span class='hs-comment'>-- height = 'getSum' . runApT_ (\_ -> 'Sum' 1) 'F.maximum'</span>
<a name="line-136"></a><span class='hs-comment'>-- @</span>
<a name="line-137"></a><span class='hs-comment'>--</span>
<a name="line-138"></a><span class='hs-comment'>-- @</span>
<a name="line-139"></a><span class='hs-comment'>-- size :: ('Functor' g, 'F.Foldable' g) => 'ApT' f g a -> 'Int'</span>
<a name="line-140"></a><span class='hs-comment'>-- size = 'getSum' . runApT_ (\_ -> 'Sum' 1) 'F.fold'</span>
<a name="line-141"></a><span class='hs-comment'>-- @</span>
<a name="line-142"></a><span class='hs-definition'>runApT_</span> <span class='hs-keyglyph'>::</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-conid'>Monoid</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-keyword'>forall</span> <span class='hs-varid'>a</span><span class='hs-varop'>.</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-varid'>g</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>ApT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span>
<a name="line-143"></a><span class='hs-definition'>runApT_</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>getConst</span> <span class='hs-varop'>.</span> <span class='hs-varid'>runApT</span> <span class='hs-layout'>(</span><span class='hs-conid'>Const</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Const</span> <span class='hs-varop'>.</span> <span class='hs-varid'>g</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fmap</span> <span class='hs-varid'>getConst</span><span class='hs-layout'>)</span>
<a name="line-144"></a>
<a name="line-145"></a><a name="hoistApF"></a><span class='hs-comment'>-- | Given a natural transformation from @f@ to @f'@ this gives a monoidal natural transformation from @ApF f g@ to @ApF f' g@.</span>
<a name="line-146"></a><span class='hs-definition'>hoistApF</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-keyword'>forall</span> <span class='hs-varid'>a</span><span class='hs-varop'>.</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f'</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>ApF</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>ApF</span> <span class='hs-varid'>f'</span> <span class='hs-varid'>g</span> <span class='hs-varid'>b</span>
<a name="line-147"></a><span class='hs-definition'>hoistApF</span> <span class='hs-keyword'>_</span> <span class='hs-layout'>(</span><span class='hs-conid'>Pure</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Pure</span> <span class='hs-varid'>x</span>
<a name="line-148"></a><span class='hs-definition'>hoistApF</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Ap</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span> <span class='hs-varop'>`Ap`</span> <span class='hs-varid'>hoistApT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>y</span>
<a name="line-149"></a>
<a name="line-150"></a><a name="hoistApT"></a><span class='hs-comment'>-- | Given a natural transformation from @f@ to @f'@ this gives a monoidal natural transformation from @ApT f g@ to @ApT f' g@.</span>
<a name="line-151"></a><span class='hs-definition'>hoistApT</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-keyword'>forall</span> <span class='hs-varid'>a</span><span class='hs-varop'>.</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f'</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>ApT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>ApT</span> <span class='hs-varid'>f'</span> <span class='hs-varid'>g</span> <span class='hs-varid'>b</span>
<a name="line-152"></a><span class='hs-definition'>hoistApT</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>ApT</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ApT</span> <span class='hs-layout'>(</span><span class='hs-varid'>hoistApF</span> <span class='hs-varid'>f</span> <span class='hs-varop'><$></span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span>
<a name="line-153"></a>
<a name="line-154"></a><a name="transApF"></a><span class='hs-comment'>-- | Given a natural transformation from @g@ to @g'@ this gives a monoidal natural transformation from @ApF f g@ to @ApF f g'@.</span>
<a name="line-155"></a><span class='hs-definition'>transApF</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-keyword'>forall</span> <span class='hs-varid'>a</span><span class='hs-varop'>.</span> <span class='hs-varid'>g</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>g'</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>ApF</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>ApF</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g'</span> <span class='hs-varid'>b</span>
<a name="line-156"></a><span class='hs-definition'>transApF</span> <span class='hs-keyword'>_</span> <span class='hs-layout'>(</span><span class='hs-conid'>Pure</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Pure</span> <span class='hs-varid'>x</span>
<a name="line-157"></a><span class='hs-definition'>transApF</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Ap</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x</span> <span class='hs-varop'>`Ap`</span> <span class='hs-varid'>transApT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>y</span>
<a name="line-158"></a>
<a name="line-159"></a><a name="transApT"></a><span class='hs-comment'>-- | Given a natural transformation from @g@ to @g'@ this gives a monoidal natural transformation from @ApT f g@ to @ApT f g'@.</span>
<a name="line-160"></a><span class='hs-definition'>transApT</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-keyword'>forall</span> <span class='hs-varid'>a</span><span class='hs-varop'>.</span> <span class='hs-varid'>g</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>g'</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>ApT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>ApT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g'</span> <span class='hs-varid'>b</span>
<a name="line-161"></a><span class='hs-definition'>transApT</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>ApT</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ApT</span> <span class='hs-varop'>$</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>transApF</span> <span class='hs-varid'>f</span> <span class='hs-varop'><$></span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span>
<a name="line-162"></a>
<a name="line-163"></a><a name="joinApT"></a><span class='hs-comment'>-- | Pull out and join @m@ layers of @'ApT' f m a@.</span>
<a name="line-164"></a><span class='hs-definition'>joinApT</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>ApT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-conid'>Ap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-165"></a><span class='hs-definition'>joinApT</span> <span class='hs-layout'>(</span><span class='hs-conid'>ApT</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>m</span> <span class='hs-varop'>>>=</span> <span class='hs-varid'>joinApF</span>
<a name="line-166"></a> <span class='hs-keyword'>where</span>
<a name="line-167"></a> <span class='hs-varid'>joinApF</span> <span class='hs-layout'>(</span><span class='hs-conid'>Pure</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>return</span> <span class='hs-layout'>(</span><span class='hs-varid'>pure</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span>
<a name="line-168"></a> <span class='hs-varid'>joinApF</span> <span class='hs-layout'>(</span><span class='hs-conid'>Ap</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>liftApT</span> <span class='hs-varid'>x</span> <span class='hs-varop'><**></span><span class='hs-layout'>)</span> <span class='hs-varop'>`liftM`</span> <span class='hs-varid'>joinApT</span> <span class='hs-varid'>y</span>
<a name="line-169"></a>
<a name="line-170"></a><a name="Ap"></a><span class='hs-comment'>-- | The free 'Applicative' for a 'Functor' @f@.</span>
<a name="line-171"></a><a name="Ap"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>Ap</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ApT</span> <span class='hs-varid'>f</span> <span class='hs-conid'>Identity</span>
<a name="line-172"></a>
<a name="line-173"></a><a name="runAp"></a><span class='hs-comment'>-- | Given a natural transformation from @f@ to @g@, this gives a canonical monoidal natural transformation from @'Ap' f@ to @g@.</span>
<a name="line-174"></a><span class='hs-comment'>--</span>
<a name="line-175"></a><span class='hs-comment'>-- prop> runAp t == retractApp . hoistApp t</span>
<a name="line-176"></a><span class='hs-definition'>runAp</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Applicative</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-keyword'>forall</span> <span class='hs-varid'>x</span><span class='hs-varop'>.</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>g</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Ap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>g</span> <span class='hs-varid'>a</span>
<a name="line-177"></a><span class='hs-definition'>runAp</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>runApT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>runIdentity</span>
<a name="line-178"></a>
<a name="line-179"></a><a name="runAp_"></a><span class='hs-comment'>-- | Perform a monoidal analysis over free applicative value.</span>
<a name="line-180"></a><span class='hs-comment'>--</span>
<a name="line-181"></a><span class='hs-comment'>-- Example:</span>
<a name="line-182"></a><span class='hs-comment'>--</span>
<a name="line-183"></a><span class='hs-comment'>-- @</span>
<a name="line-184"></a><span class='hs-comment'>-- count :: 'Ap' f a -> 'Int'</span>
<a name="line-185"></a><span class='hs-comment'>-- count = 'getSum' . runAp_ (\\_ -> 'Sum' 1)</span>
<a name="line-186"></a><span class='hs-comment'>-- @</span>
<a name="line-187"></a><span class='hs-definition'>runAp_</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Monoid</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-keyword'>forall</span> <span class='hs-varid'>x</span><span class='hs-varop'>.</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Ap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span>
<a name="line-188"></a><span class='hs-definition'>runAp_</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>runApT_</span> <span class='hs-varid'>f</span> <span class='hs-varid'>runIdentity</span>
<a name="line-189"></a>
<a name="line-190"></a><a name="retractAp"></a><span class='hs-comment'>-- | Interprets the free applicative functor over f using the semantics for</span>
<a name="line-191"></a><span class='hs-comment'>-- `pure` and `<*>` given by the Applicative instance for f.</span>
<a name="line-192"></a><span class='hs-comment'>--</span>
<a name="line-193"></a><span class='hs-comment'>-- prop> retractApp == runAp id</span>
<a name="line-194"></a><span class='hs-definition'>retractAp</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Applicative</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Ap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span>
<a name="line-195"></a><span class='hs-definition'>retractAp</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>runAp</span> <span class='hs-varid'>id</span>
<a name="line-196"></a>
<a name="line-197"></a><a name="Alt"></a><span class='hs-comment'>-- | The free 'Alternative' for a 'Functor' @f@.</span>
<a name="line-198"></a><a name="Alt"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>Alt</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ApT</span> <span class='hs-varid'>f</span> <span class='hs-conid'>[]</span>
<a name="line-199"></a>
<a name="line-200"></a><a name="runAlt"></a><span class='hs-comment'>-- | Given a natural transformation from @f@ to @g@, this gives a canonical monoidal natural transformation from @'Alt' f@ to @g@.</span>
<a name="line-201"></a><span class='hs-definition'>runAlt</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Alternative</span> <span class='hs-varid'>g</span><span class='hs-layout'>,</span> <span class='hs-conid'>F</span><span class='hs-varop'>.</span><span class='hs-conid'>Foldable</span> <span class='hs-varid'>t</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-keyword'>forall</span> <span class='hs-varid'>x</span><span class='hs-varop'>.</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>g</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>ApT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>t</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>g</span> <span class='hs-varid'>a</span>
<a name="line-202"></a><span class='hs-definition'>runAlt</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>ApT</span> <span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>F</span><span class='hs-varop'>.</span><span class='hs-varid'>foldr</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>x</span> <span class='hs-varid'>acc</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>h</span> <span class='hs-varid'>x</span> <span class='hs-varop'><|></span> <span class='hs-varid'>acc</span><span class='hs-layout'>)</span> <span class='hs-varid'>empty</span> <span class='hs-varid'>xs</span>
<a name="line-203"></a> <span class='hs-keyword'>where</span>
<a name="line-204"></a> <span class='hs-varid'>h</span> <span class='hs-layout'>(</span><span class='hs-conid'>Pure</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pure</span> <span class='hs-varid'>x</span>
<a name="line-205"></a> <span class='hs-varid'>h</span> <span class='hs-layout'>(</span><span class='hs-conid'>Ap</span> <span class='hs-varid'>x</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span> <span class='hs-varop'><**></span> <span class='hs-varid'>runAlt</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span>
<a name="line-206"></a>
<a name="line-207"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ < 707</span>
<a name="line-208"></a><a name="instance%20Typeable1%20(ApT%20f%20g)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Typeable1</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable1</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Typeable1</span> <span class='hs-layout'>(</span><span class='hs-conid'>ApT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-209"></a> <span class='hs-varid'>typeOf1</span> <span class='hs-varid'>t</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mkTyConApp</span> <span class='hs-varid'>apTTyCon</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>typeOf1</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>t</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>]</span> <span class='hs-keyword'>where</span>
<a name="line-210"></a> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>ApT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>g</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-211"></a> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>undefined</span>
<a name="line-212"></a>
<a name="line-213"></a><a name="instance%20Typeable1%20(ApF%20f%20g)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Typeable1</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable1</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Typeable1</span> <span class='hs-layout'>(</span><span class='hs-conid'>ApF</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-214"></a> <span class='hs-varid'>typeOf1</span> <span class='hs-varid'>t</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mkTyConApp</span> <span class='hs-varid'>apFTyCon</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>typeOf1</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>t</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>]</span> <span class='hs-keyword'>where</span>
<a name="line-215"></a> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>ApF</span> <span class='hs-varid'>f</span> <span class='hs-varid'>g</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>g</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-216"></a> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>undefined</span>
<a name="line-217"></a>
<a name="line-218"></a><a name="apTTyCon"></a><span class='hs-definition'>apTTyCon</span><span class='hs-layout'>,</span> <span class='hs-varid'>apFTyCon</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>TyCon</span>
<a name="line-219"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ < 704</span>
<a name="line-220"></a><span class='hs-definition'>apTTyCon</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mkTyCon</span> <span class='hs-str'>"Control.Applicative.Trans.Free.ApT"</span>
<a name="line-221"></a><a name="apFTyCon"></a><span class='hs-definition'>apFTyCon</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mkTyCon</span> <span class='hs-str'>"Control.Applicative.Trans.Free.ApF"</span>
<a name="line-222"></a><span class='hs-cpp'>#else</span>
<a name="line-223"></a><span class='hs-definition'>apTTyCon</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mkTyCon3</span> <span class='hs-str'>"free"</span> <span class='hs-str'>"Control.Applicative.Trans.Free"</span> <span class='hs-str'>"ApT"</span>
<a name="line-224"></a><span class='hs-definition'>apFTyCon</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mkTyCon3</span> <span class='hs-str'>"free"</span> <span class='hs-str'>"Control.Applicative.Trans.Free"</span> <span class='hs-str'>"ApF"</span>
<a name="line-225"></a><span class='hs-cpp'>#endif</span>
<a name="line-226"></a><span class='hs-comment'>{-# NOINLINE apTTyCon #-}</span>
<a name="line-227"></a><span class='hs-comment'>{-# NOINLINE apFTyCon #-}</span>
<a name="line-228"></a><span class='hs-cpp'>#endif</span>
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