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<title>src/Control/Monad/Trans/Free/Church.hs</title>
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<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE CPP #-}</span>
<a name="line-2"></a><span class='hs-comment'>{-# LANGUAGE FlexibleInstances #-}</span>
<a name="line-3"></a><span class='hs-comment'>{-# LANGUAGE MultiParamTypeClasses #-}</span>
<a name="line-4"></a><span class='hs-comment'>{-# LANGUAGE RankNTypes #-}</span>
<a name="line-5"></a><span class='hs-comment'>{-# LANGUAGE UndecidableInstances #-}</span>
<a name="line-6"></a>
<a name="line-7"></a><span class='hs-cpp'>#ifndef MIN_VERSION_base</span>
<a name="line-8"></a><span class='hs-cpp'>#define MIN_VERSION_base(x,y,z) 1</span>
<a name="line-9"></a><span class='hs-cpp'>#endif</span>
<a name="line-10"></a>
<a name="line-11"></a><span class='hs-cpp'>#ifndef MIN_VERSION_mtl</span>
<a name="line-12"></a><span class='hs-cpp'>#define MIN_VERSION_mtl(x,y,z) 1</span>
<a name="line-13"></a><span class='hs-cpp'>#endif</span>
<a name="line-14"></a>
<a name="line-15"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-16"></a><span class='hs-comment'>-- |</span>
<a name="line-17"></a><span class='hs-comment'>-- Module : Control.Monad.Trans.Free.Church</span>
<a name="line-18"></a><span class='hs-comment'>-- Copyright : (C) 2008-2014 Edward Kmett</span>
<a name="line-19"></a><span class='hs-comment'>-- License : BSD-style (see the file LICENSE)</span>
<a name="line-20"></a><span class='hs-comment'>--</span>
<a name="line-21"></a><span class='hs-comment'>-- Maintainer : Edward Kmett <ekmett@gmail.com></span>
<a name="line-22"></a><span class='hs-comment'>-- Stability : provisional</span>
<a name="line-23"></a><span class='hs-comment'>-- Portability : non-portable (rank-2 polymorphism, MTPCs)</span>
<a name="line-24"></a><span class='hs-comment'>--</span>
<a name="line-25"></a><span class='hs-comment'>-- Church-encoded free monad transformer.</span>
<a name="line-26"></a><span class='hs-comment'>--</span>
<a name="line-27"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-28"></a><span class='hs-keyword'>module</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'>Trans</span><span class='hs-varop'>.</span><span class='hs-conid'>Free</span><span class='hs-varop'>.</span><span class='hs-conid'>Church</span>
<a name="line-29"></a> <span class='hs-layout'>(</span>
<a name="line-30"></a> <span class='hs-comment'>-- * The free monad transformer</span>
<a name="line-31"></a> <span class='hs-conid'>FT</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-32"></a> <span class='hs-comment'>-- * The free monad</span>
<a name="line-33"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>F</span><span class='hs-layout'>,</span> <span class='hs-varid'>free</span><span class='hs-layout'>,</span> <span class='hs-varid'>runF</span>
<a name="line-34"></a> <span class='hs-comment'>-- * Operations</span>
<a name="line-35"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>improveT</span>
<a name="line-36"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>toFT</span><span class='hs-layout'>,</span> <span class='hs-varid'>fromFT</span>
<a name="line-37"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>iterT</span>
<a name="line-38"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>iterTM</span>
<a name="line-39"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>hoistFT</span>
<a name="line-40"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>transFT</span>
<a name="line-41"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>joinFT</span>
<a name="line-42"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>cutoff</span>
<a name="line-43"></a> <span class='hs-comment'>-- * Operations of free monad</span>
<a name="line-44"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>improve</span>
<a name="line-45"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>fromF</span><span class='hs-layout'>,</span> <span class='hs-varid'>toF</span>
<a name="line-46"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>retract</span>
<a name="line-47"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>retractT</span>
<a name="line-48"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>iter</span>
<a name="line-49"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>iterM</span>
<a name="line-50"></a> <span class='hs-comment'>-- * Free Monads With Class</span>
<a name="line-51"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>MonadFree</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-52"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>liftF</span>
<a name="line-53"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-54"></a>
<a name="line-55"></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-56"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Category</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varop'><<<</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'>>>></span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-57"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Monad</span>
<a name="line-58"></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'>Catch</span> <span class='hs-layout'>(</span><span class='hs-conid'>MonadCatch</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-conid'>MonadThrow</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-59"></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'>Identity</span>
<a name="line-60"></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'>Trans</span><span class='hs-varop'>.</span><span class='hs-conid'>Class</span>
<a name="line-61"></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'>IO</span><span class='hs-varop'>.</span><span class='hs-conid'>Class</span>
<a name="line-62"></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'>Reader</span><span class='hs-varop'>.</span><span class='hs-conid'>Class</span>
<a name="line-63"></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'>Class</span>
<a name="line-64"></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'>Class</span>
<a name="line-65"></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'>Error</span><span class='hs-varop'>.</span><span class='hs-conid'>Class</span>
<a name="line-66"></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'>Cont</span><span class='hs-varop'>.</span><span class='hs-conid'>Class</span>
<a name="line-67"></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'>Free</span><span class='hs-varop'>.</span><span class='hs-conid'>Class</span>
<a name="line-68"></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'>Trans</span><span class='hs-varop'>.</span><span class='hs-conid'>Free</span> <span class='hs-layout'>(</span><span class='hs-conid'>FreeT</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-conid'>FreeF</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-conid'>Free</span><span class='hs-layout'>)</span>
<a name="line-69"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</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'>Trans</span><span class='hs-varop'>.</span><span class='hs-conid'>Free</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>FreeT</span>
<a name="line-70"></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-71"></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'>Traversable</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>T</span>
<a name="line-72"></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'>Bind</span> <span class='hs-varid'>hiding</span> <span class='hs-layout'>(</span><span class='hs-varid'>join</span><span class='hs-layout'>)</span>
<a name="line-73"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Function</span>
<a name="line-74"></a>
<a name="line-75"></a><span class='hs-cpp'>#if !(MIN_VERSION_base(4,8,0))</span>
<a name="line-76"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Foldable</span> <span class='hs-layout'>(</span><span class='hs-conid'>Foldable</span><span class='hs-layout'>)</span>
<a name="line-77"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Traversable</span> <span class='hs-layout'>(</span><span class='hs-conid'>Traversable</span><span class='hs-layout'>)</span>
<a name="line-78"></a><span class='hs-cpp'>#endif</span>
<a name="line-79"></a>
<a name="line-80"></a><a name="FT"></a><span class='hs-comment'>-- | The \"free monad transformer\" for a functor @f@</span>
<a name="line-81"></a><a name="FT"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>FT</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-conid'>FT</span> <span class='hs-layout'>{</span> <span class='hs-varid'>runFT</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyword'>forall</span> <span class='hs-varid'>r</span><span class='hs-varop'>.</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-varid'>r</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-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-varid'>r</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-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-varid'>r</span> <span class='hs-layout'>}</span>
<a name="line-82"></a>
<a name="line-83"></a><a name="instance%20Eq%20(FT%20f%20m%20a)"></a><span class='hs-keyword'>instance</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'>Monad</span> <span class='hs-varid'>m</span><span class='hs-layout'>,</span> <span class='hs-conid'>Eq</span> <span class='hs-layout'>(</span><span class='hs-conid'>FreeT</span> <span class='hs-varid'>f</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-keyglyph'>=></span> <span class='hs-conid'>Eq</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>f</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-84"></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> <span class='hs-varop'>`on`</span> <span class='hs-varid'>fromFT</span>
<a name="line-85"></a>
<a name="line-86"></a><a name="instance%20Ord%20(FT%20f%20m%20a)"></a><span class='hs-keyword'>instance</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'>Monad</span> <span class='hs-varid'>m</span><span class='hs-layout'>,</span> <span class='hs-conid'>Ord</span> <span class='hs-layout'>(</span><span class='hs-conid'>FreeT</span> <span class='hs-varid'>f</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-keyglyph'>=></span> <span class='hs-conid'>Ord</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>f</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-87"></a> <span class='hs-varid'>compare</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>compare</span> <span class='hs-varop'>`on`</span> <span class='hs-varid'>fromFT</span>
<a name="line-88"></a>
<a name="line-89"></a><a name="instance%20Functor%20(FT%20f%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Functor</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-90"></a> <span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>k</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FT</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-varid'>fr</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>k</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varid'>fr</span>
<a name="line-91"></a>
<a name="line-92"></a><a name="instance%20Apply%20(FT%20f%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Apply</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-93"></a> <span class='hs-layout'>(</span><span class='hs-varop'><.></span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varop'><*></span><span class='hs-layout'>)</span>
<a name="line-94"></a>
<a name="line-95"></a><a name="instance%20Applicative%20(FT%20f%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Applicative</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-96"></a> <span class='hs-varid'>pure</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FT</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>k</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>k</span> <span class='hs-varid'>a</span>
<a name="line-97"></a> <span class='hs-conid'>FT</span> <span class='hs-varid'>fk</span> <span class='hs-varop'><*></span> <span class='hs-conid'>FT</span> <span class='hs-varid'>ak</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FT</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>b</span> <span class='hs-varid'>fr</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>fk</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>e</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>ak</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>d</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span> <span class='hs-layout'>(</span><span class='hs-varid'>e</span> <span class='hs-varid'>d</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-varid'>fr</span><span class='hs-layout'>)</span> <span class='hs-varid'>fr</span>
<a name="line-98"></a>
<a name="line-99"></a><a name="instance%20Bind%20(FT%20f%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Bind</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-100"></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-101"></a>
<a name="line-102"></a><a name="instance%20Monad%20(FT%20f%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Monad</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-103"></a> <span class='hs-varid'>return</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pure</span>
<a name="line-104"></a> <span class='hs-conid'>FT</span> <span class='hs-varid'>fk</span> <span class='hs-varop'>>>=</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FT</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>b</span> <span class='hs-varid'>fr</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>fk</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>d</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>runFT</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>d</span><span class='hs-layout'>)</span> <span class='hs-varid'>b</span> <span class='hs-varid'>fr</span><span class='hs-layout'>)</span> <span class='hs-varid'>fr</span>
<a name="line-105"></a>
<a name="line-106"></a><a name="instance%20MonadFree%20f%20(FT%20f%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>MonadFree</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-107"></a> <span class='hs-varid'>wrap</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FT</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>kp</span> <span class='hs-varid'>kf</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>kf</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>ft</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>runFT</span> <span class='hs-varid'>ft</span> <span class='hs-varid'>kp</span> <span class='hs-varid'>kf</span><span class='hs-layout'>)</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span>
<a name="line-108"></a>
<a name="line-109"></a><a name="instance%20MonadTrans%20(FT%20f)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>MonadTrans</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-110"></a> <span class='hs-varid'>lift</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FT</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-varop'>>>=</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-111"></a>
<a name="line-112"></a><a name="instance%20Alternative%20(FT%20f%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Alternative</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Alternative</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-113"></a> <span class='hs-varid'>empty</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FT</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>empty</span><span class='hs-layout'>)</span>
<a name="line-114"></a> <span class='hs-conid'>FT</span> <span class='hs-varid'>k1</span> <span class='hs-varop'><|></span> <span class='hs-conid'>FT</span> <span class='hs-varid'>k2</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FT</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-varid'>fr</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>k1</span> <span class='hs-varid'>a</span> <span class='hs-varid'>fr</span> <span class='hs-varop'><|></span> <span class='hs-varid'>k2</span> <span class='hs-varid'>a</span> <span class='hs-varid'>fr</span>
<a name="line-115"></a>
<a name="line-116"></a><a name="instance%20MonadPlus%20(FT%20f%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>MonadPlus</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>MonadPlus</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-117"></a> <span class='hs-varid'>mzero</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FT</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>mzero</span><span class='hs-layout'>)</span>
<a name="line-118"></a> <span class='hs-varid'>mplus</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>k1</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>k2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FT</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>a</span> <span class='hs-varid'>fr</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>k1</span> <span class='hs-varid'>a</span> <span class='hs-varid'>fr</span> <span class='hs-varop'>`mplus`</span> <span class='hs-varid'>k2</span> <span class='hs-varid'>a</span> <span class='hs-varid'>fr</span>
<a name="line-119"></a>
<a name="line-120"></a><a name="instance%20Foldable%20(FT%20f%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Foldable</span> <span class='hs-varid'>f</span><span class='hs-layout'>,</span> <span class='hs-conid'>Foldable</span> <span class='hs-varid'>m</span><span class='hs-layout'>,</span> <span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Foldable</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-121"></a> <span class='hs-varid'>foldr</span> <span class='hs-varid'>f</span> <span class='hs-varid'>r</span> <span class='hs-varid'>xs</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-varop'><<<</span><span class='hs-layout'>)</span> <span class='hs-varid'>id</span> <span class='hs-varid'>inner</span> <span class='hs-varid'>r</span>
<a name="line-122"></a> <span class='hs-keyword'>where</span>
<a name="line-123"></a> <span class='hs-varid'>inner</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>runFT</span> <span class='hs-varid'>xs</span> <span class='hs-layout'>(</span><span class='hs-varid'>return</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-keyglyph'>\</span><span class='hs-varid'>xg</span> <span class='hs-varid'>xf</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-varid'>liftM2</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'>xg</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>return</span> <span class='hs-varid'>id</span><span class='hs-layout'>)</span> <span class='hs-varid'>xf</span><span class='hs-layout'>)</span>
<a name="line-124"></a> <span class='hs-comment'>{-# INLINE foldr #-}</span>
<a name="line-125"></a>
<a name="line-126"></a><span class='hs-cpp'>#if MIN_VERSION_base(4,6,0)</span>
<a name="line-127"></a> <span class='hs-varid'>foldl'</span> <span class='hs-varid'>f</span> <span class='hs-varid'>z</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>F</span><span class='hs-varop'>.</span><span class='hs-varid'>foldl'</span> <span class='hs-layout'>(</span><span class='hs-varop'>!>>></span><span class='hs-layout'>)</span> <span class='hs-varid'>id</span> <span class='hs-varid'>inner</span> <span class='hs-varid'>z</span>
<a name="line-128"></a> <span class='hs-keyword'>where</span>
<a name="line-129"></a> <span class='hs-layout'>(</span><span class='hs-varop'>!>>></span><span class='hs-layout'>)</span> <span class='hs-varid'>h</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>r</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>g</span> <span class='hs-varop'>$!</span> <span class='hs-varid'>h</span> <span class='hs-varid'>r</span>
<a name="line-130"></a> <span class='hs-varid'>inner</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>runFT</span> <span class='hs-varid'>xs</span> <span class='hs-layout'>(</span><span class='hs-varid'>return</span> <span class='hs-varop'>.</span> <span class='hs-varid'>flip</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>xg</span> <span class='hs-varid'>xf</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-varid'>liftM2</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'>xg</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>return</span> <span class='hs-varid'>id</span><span class='hs-layout'>)</span> <span class='hs-varid'>xf</span><span class='hs-layout'>)</span>
<a name="line-131"></a> <span class='hs-comment'>{-# INLINE foldl' #-}</span>
<a name="line-132"></a><span class='hs-cpp'>#endif</span>
<a name="line-133"></a>
<a name="line-134"></a><a name="instance%20Traversable%20(FT%20f%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span><span class='hs-layout'>,</span> <span class='hs-conid'>Traversable</span> <span class='hs-varid'>m</span><span class='hs-layout'>,</span> <span class='hs-conid'>Traversable</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Traversable</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-135"></a> <span class='hs-varid'>traverse</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>k</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-varid'>join</span> <span class='hs-varop'>.</span> <span class='hs-varid'>lift</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span> <span class='hs-conid'>T</span><span class='hs-varop'>.</span><span class='hs-varid'>sequenceA</span> <span class='hs-varop'>$</span> <span class='hs-varid'>k</span> <span class='hs-varid'>traversePure</span> <span class='hs-varid'>traverseFree</span>
<a name="line-136"></a> <span class='hs-keyword'>where</span>
<a name="line-137"></a> <span class='hs-varid'>traversePure</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>return</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fmap</span> <span class='hs-varid'>return</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span>
<a name="line-138"></a> <span class='hs-varid'>traverseFree</span> <span class='hs-varid'>xg</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>return</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-varid'>wrap</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-varid'>join</span> <span class='hs-varop'>.</span> <span class='hs-varid'>lift</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span> <span class='hs-conid'>T</span><span class='hs-varop'>.</span><span class='hs-varid'>traverse</span> <span class='hs-layout'>(</span><span class='hs-conid'>T</span><span class='hs-varop'>.</span><span class='hs-varid'>sequenceA</span> <span class='hs-varop'>.</span> <span class='hs-varid'>xg</span><span class='hs-layout'>)</span>
<a name="line-139"></a>
<a name="line-140"></a><a name="instance%20MonadIO%20(FT%20f%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>MonadIO</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>MonadIO</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-141"></a> <span class='hs-varid'>liftIO</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>lift</span> <span class='hs-varop'>.</span> <span class='hs-varid'>liftIO</span>
<a name="line-142"></a> <span class='hs-comment'>{-# INLINE liftIO #-}</span>
<a name="line-143"></a>
<a name="line-144"></a><a name="instance%20MonadError%20e%20(FT%20f%20m)"></a><span class='hs-keyword'>instance</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'>MonadError</span> <span class='hs-varid'>e</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>MonadError</span> <span class='hs-varid'>e</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-145"></a> <span class='hs-varid'>throwError</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>lift</span> <span class='hs-varop'>.</span> <span class='hs-varid'>throwError</span>
<a name="line-146"></a> <span class='hs-comment'>{-# INLINE throwError #-}</span>
<a name="line-147"></a> <span class='hs-varid'>m</span> <span class='hs-varop'>`catchError`</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toFT</span> <span class='hs-varop'>$</span> <span class='hs-varid'>fromFT</span> <span class='hs-varid'>m</span> <span class='hs-varop'>`catchError`</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromFT</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span>
<a name="line-148"></a>
<a name="line-149"></a><a name="instance%20MonadCont%20(FT%20f%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>MonadCont</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>MonadCont</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-150"></a> <span class='hs-varid'>callCC</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>join</span> <span class='hs-varop'>.</span> <span class='hs-varid'>lift</span> <span class='hs-varop'>$</span> <span class='hs-varid'>callCC</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>k</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>return</span> <span class='hs-varop'>$</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>lift</span> <span class='hs-varop'>.</span> <span class='hs-varid'>k</span> <span class='hs-varop'>.</span> <span class='hs-varid'>return</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-151"></a>
<a name="line-152"></a><a name="instance%20MonadReader%20r%20(FT%20f%20m)"></a><span class='hs-keyword'>instance</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'>MonadReader</span> <span class='hs-varid'>r</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>MonadReader</span> <span class='hs-varid'>r</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-153"></a> <span class='hs-varid'>ask</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>lift</span> <span class='hs-varid'>ask</span>
<a name="line-154"></a> <span class='hs-comment'>{-# INLINE ask #-}</span>
<a name="line-155"></a> <span class='hs-varid'>local</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>hoistFT</span> <span class='hs-layout'>(</span><span class='hs-varid'>local</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span>
<a name="line-156"></a> <span class='hs-comment'>{-# INLINE local #-}</span>
<a name="line-157"></a>
<a name="line-158"></a><a name="instance%20MonadWriter%20w%20(FT%20f%20m)"></a><span class='hs-keyword'>instance</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'>MonadWriter</span> <span class='hs-varid'>w</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>MonadWriter</span> <span class='hs-varid'>w</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-159"></a> <span class='hs-varid'>tell</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>lift</span> <span class='hs-varop'>.</span> <span class='hs-varid'>tell</span>
<a name="line-160"></a> <span class='hs-comment'>{-# INLINE tell #-}</span>
<a name="line-161"></a> <span class='hs-varid'>listen</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toFT</span> <span class='hs-varop'>.</span> <span class='hs-varid'>listen</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fromFT</span>
<a name="line-162"></a> <span class='hs-varid'>pass</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toFT</span> <span class='hs-varop'>.</span> <span class='hs-varid'>pass</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fromFT</span>
<a name="line-163"></a><span class='hs-cpp'>#if MIN_VERSION_mtl(2,1,1)</span>
<a name="line-164"></a> <span class='hs-varid'>writer</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>lift</span> <span class='hs-layout'>(</span><span class='hs-varid'>writer</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span>
<a name="line-165"></a> <span class='hs-comment'>{-# INLINE writer #-}</span>
<a name="line-166"></a><span class='hs-cpp'>#endif</span>
<a name="line-167"></a>
<a name="line-168"></a><a name="instance%20MonadState%20s%20(FT%20f%20m)"></a><span class='hs-keyword'>instance</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'>MonadState</span> <span class='hs-varid'>s</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>MonadState</span> <span class='hs-varid'>s</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-169"></a> <span class='hs-varid'>get</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>lift</span> <span class='hs-varid'>get</span>
<a name="line-170"></a> <span class='hs-comment'>{-# INLINE get #-}</span>
<a name="line-171"></a> <span class='hs-varid'>put</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>lift</span> <span class='hs-varop'>.</span> <span class='hs-varid'>put</span>
<a name="line-172"></a> <span class='hs-comment'>{-# INLINE put #-}</span>
<a name="line-173"></a><span class='hs-cpp'>#if MIN_VERSION_mtl(2,1,1)</span>
<a name="line-174"></a> <span class='hs-varid'>state</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>lift</span> <span class='hs-layout'>(</span><span class='hs-varid'>state</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span>
<a name="line-175"></a> <span class='hs-comment'>{-# INLINE state #-}</span>
<a name="line-176"></a><span class='hs-cpp'>#endif</span>
<a name="line-177"></a>
<a name="line-178"></a><a name="instance%20MonadThrow%20(FT%20f%20m)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>MonadThrow</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>MonadThrow</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-179"></a> <span class='hs-varid'>throwM</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>lift</span> <span class='hs-varop'>.</span> <span class='hs-varid'>throwM</span>
<a name="line-180"></a> <span class='hs-comment'>{-# INLINE throwM #-}</span>
<a name="line-181"></a>
<a name="line-182"></a><a name="instance%20MonadCatch%20(FT%20f%20m)"></a><span class='hs-keyword'>instance</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'>MonadCatch</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>MonadCatch</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-183"></a> <span class='hs-varid'>catch</span> <span class='hs-varid'>m</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toFT</span> <span class='hs-varop'>$</span> <span class='hs-varid'>fromFT</span> <span class='hs-varid'>m</span> <span class='hs-varop'>`</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'>Catch</span><span class='hs-varop'>.</span><span class='hs-varid'>catch</span><span class='hs-varop'>`</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromFT</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span>
<a name="line-184"></a> <span class='hs-comment'>{-# INLINE catch #-}</span>
<a name="line-185"></a>
<a name="line-186"></a><a name="toFT"></a><span class='hs-comment'>-- | Generate a Church-encoded free monad transformer from a 'FreeT' monad</span>
<a name="line-187"></a><span class='hs-comment'>-- transformer.</span>
<a name="line-188"></a><span class='hs-definition'>toFT</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'>FreeT</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-conid'>FT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span>
<a name="line-189"></a><span class='hs-definition'>toFT</span> <span class='hs-layout'>(</span><span class='hs-conid'>FreeT</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FT</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>ka</span> <span class='hs-varid'>kfr</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>do</span>
<a name="line-190"></a> <span class='hs-varid'>freef</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>f</span>
<a name="line-191"></a> <span class='hs-keyword'>case</span> <span class='hs-varid'>freef</span> <span class='hs-keyword'>of</span>
<a name="line-192"></a> <span class='hs-conid'>Pure</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>ka</span> <span class='hs-varid'>a</span>
<a name="line-193"></a> <span class='hs-conid'>Free</span> <span class='hs-varid'>fb</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>kfr</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>x</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>runFT</span> <span class='hs-layout'>(</span><span class='hs-varid'>toFT</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-varid'>ka</span> <span class='hs-varid'>kfr</span><span class='hs-layout'>)</span> <span class='hs-varid'>fb</span>
<a name="line-194"></a>
<a name="line-195"></a><a name="fromFT"></a><span class='hs-comment'>-- | Convert to a 'FreeT' free monad representation.</span>
<a name="line-196"></a><span class='hs-definition'>fromFT</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Monad</span> <span class='hs-varid'>m</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-keyglyph'>=></span> <span class='hs-conid'>FT</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-conid'>FreeT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span>
<a name="line-197"></a><span class='hs-definition'>fromFT</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>k</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FreeT</span> <span class='hs-varop'>$</span> <span class='hs-varid'>k</span> <span class='hs-layout'>(</span><span class='hs-varid'>return</span> <span class='hs-varop'>.</span> <span class='hs-conid'>Pure</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>xg</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>runFreeT</span> <span class='hs-varop'>.</span> <span class='hs-varid'>wrap</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-conid'>FreeT</span> <span class='hs-varop'>.</span> <span class='hs-varid'>xg</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-198"></a>
<a name="line-199"></a><a name="F"></a><span class='hs-comment'>-- | The \"free monad\" for a functor @f@.</span>
<a name="line-200"></a><a name="F"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>F</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FT</span> <span class='hs-varid'>f</span> <span class='hs-conid'>Identity</span>
<a name="line-201"></a>
<a name="line-202"></a><a name="runF"></a><span class='hs-comment'>-- | Unwrap the 'Free' monad to obtain it's Church-encoded representation.</span>
<a name="line-203"></a><span class='hs-definition'>runF</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>F</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-keyword'>forall</span> <span class='hs-varid'>r</span><span class='hs-varop'>.</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>r</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span>
<a name="line-204"></a><span class='hs-definition'>runF</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>kp</span> <span class='hs-varid'>kf</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>runIdentity</span> <span class='hs-varop'>$</span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-varid'>return</span> <span class='hs-varop'>.</span> <span class='hs-varid'>kp</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>xg</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>return</span> <span class='hs-varop'>.</span> <span class='hs-varid'>kf</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-varid'>runIdentity</span> <span class='hs-varop'>.</span> <span class='hs-varid'>xg</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-205"></a>
<a name="line-206"></a><a name="free"></a><span class='hs-comment'>-- | Wrap a Church-encoding of a \"free monad\" as the free monad for a functor.</span>
<a name="line-207"></a><span class='hs-definition'>free</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-keyword'>forall</span> <span class='hs-varid'>r</span><span class='hs-varop'>.</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>r</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>F</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span>
<a name="line-208"></a><span class='hs-definition'>free</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FT</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>kp</span> <span class='hs-varid'>kf</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>return</span> <span class='hs-varop'>$</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>runIdentity</span> <span class='hs-varop'>.</span> <span class='hs-varid'>kp</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>runIdentity</span> <span class='hs-varop'>.</span> <span class='hs-varid'>kf</span> <span class='hs-varid'>return</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-209"></a>
<a name="line-210"></a><a name="iterT"></a><span class='hs-comment'>-- | Tear down a free monad transformer using iteration.</span>
<a name="line-211"></a><span class='hs-definition'>iterT</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'>Monad</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'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>m</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FT</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-varid'>a</span>
<a name="line-212"></a><span class='hs-definition'>iterT</span> <span class='hs-varid'>phi</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</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-varid'>return</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>xg</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>phi</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fmap</span> <span class='hs-varid'>xg</span><span class='hs-layout'>)</span>
<a name="line-213"></a><span class='hs-comment'>{-# INLINE iterT #-}</span>
<a name="line-214"></a>
<a name="line-215"></a><a name="iterTM"></a><span class='hs-comment'>-- | Tear down a free monad transformer using iteration over a transformer.</span>
<a name="line-216"></a><span class='hs-definition'>iterTM</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'>Monad</span> <span class='hs-varid'>m</span><span class='hs-layout'>,</span> <span class='hs-conid'>MonadTrans</span> <span class='hs-varid'>t</span><span class='hs-layout'>,</span> <span class='hs-conid'>Monad</span> <span class='hs-layout'>(</span><span class='hs-varid'>t</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>t</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>t</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FT</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'>t</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span>
<a name="line-217"></a><span class='hs-definition'>iterTM</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>join</span> <span class='hs-varop'>.</span> <span class='hs-varid'>lift</span> <span class='hs-varop'>$</span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-varid'>return</span> <span class='hs-varop'>.</span> <span class='hs-varid'>return</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>xg</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>return</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-varid'>join</span> <span class='hs-varop'>.</span> <span class='hs-varid'>lift</span> <span class='hs-varop'>.</span> <span class='hs-varid'>xg</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-218"></a>
<a name="line-219"></a><a name="hoistFT"></a><span class='hs-comment'>-- | Lift a monad homomorphism from @m@ to @n@ into a monad homomorphism from @'FT' f m@ to @'FT' f n@</span>
<a name="line-220"></a><span class='hs-comment'>--</span>
<a name="line-221"></a><span class='hs-comment'>-- @'hoistFT' :: ('Monad' m, 'Monad' n, 'Functor' f) => (m ~> n) -> 'FT' f m ~> 'FT' f n@</span>
<a name="line-222"></a><span class='hs-definition'>hoistFT</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span><span class='hs-layout'>,</span> <span class='hs-conid'>Monad</span> <span class='hs-varid'>n</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'>m</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>n</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>n</span> <span class='hs-varid'>b</span>
<a name="line-223"></a><span class='hs-definition'>hoistFT</span> <span class='hs-varid'>phi</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FT</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>kp</span> <span class='hs-varid'>kf</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>join</span> <span class='hs-varop'>.</span> <span class='hs-varid'>phi</span> <span class='hs-varop'>$</span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-varid'>return</span> <span class='hs-varop'>.</span> <span class='hs-varid'>kp</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>xg</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>return</span> <span class='hs-varop'>.</span> <span class='hs-varid'>kf</span> <span class='hs-layout'>(</span><span class='hs-varid'>join</span> <span class='hs-varop'>.</span> <span class='hs-varid'>phi</span> <span class='hs-varop'>.</span> <span class='hs-varid'>xg</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-224"></a>
<a name="line-225"></a><a name="transFT"></a><span class='hs-comment'>-- | Lift a natural transformation from @f@ to @g@ into a monad homomorphism from @'FT' f m@ to @'FT' g n@</span>
<a name="line-226"></a><span class='hs-definition'>transFT</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-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'>g</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FT</span> <span class='hs-varid'>g</span> <span class='hs-varid'>m</span> <span class='hs-varid'>b</span>
<a name="line-227"></a><span class='hs-definition'>transFT</span> <span class='hs-varid'>phi</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FT</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>kp</span> <span class='hs-varid'>kf</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-varid'>kp</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>xg</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>kf</span> <span class='hs-varid'>xg</span> <span class='hs-varop'>.</span> <span class='hs-varid'>phi</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-228"></a>
<a name="line-229"></a><a name="joinFT"></a><span class='hs-comment'>-- | Pull out and join @m@ layers of @'FreeT' f m a@.</span>
<a name="line-230"></a><span class='hs-definition'>joinFT</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span><span class='hs-layout'>,</span> <span class='hs-conid'>Traversable</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FT</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'>F</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-231"></a><span class='hs-definition'>joinFT</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</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-layout'>(</span><span class='hs-varid'>return</span> <span class='hs-varop'>.</span> <span class='hs-varid'>return</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>xg</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>liftM</span> <span class='hs-varid'>wrap</span> <span class='hs-varop'>.</span> <span class='hs-conid'>T</span><span class='hs-varop'>.</span><span class='hs-varid'>mapM</span> <span class='hs-varid'>xg</span><span class='hs-layout'>)</span>
<a name="line-232"></a>
<a name="line-233"></a><a name="cutoff"></a><span class='hs-comment'>-- | Cuts off a tree of computations at a given depth.</span>
<a name="line-234"></a><span class='hs-comment'>-- If the depth is 0 or less, no computation nor</span>
<a name="line-235"></a><span class='hs-comment'>-- monadic effects will take place.</span>
<a name="line-236"></a><span class='hs-comment'>--</span>
<a name="line-237"></a><span class='hs-comment'>-- Some examples (n ≥ 0):</span>
<a name="line-238"></a><span class='hs-comment'>--</span>
<a name="line-239"></a><span class='hs-comment'>-- prop> cutoff 0 _ == return Nothing</span>
<a name="line-240"></a><span class='hs-comment'>-- prop> cutoff (n+1) . return == return . Just</span>
<a name="line-241"></a><span class='hs-comment'>-- prop> cutoff (n+1) . lift == lift . liftM Just</span>
<a name="line-242"></a><span class='hs-comment'>-- prop> cutoff (n+1) . wrap == wrap . fmap (cutoff n)</span>
<a name="line-243"></a><span class='hs-comment'>--</span>
<a name="line-244"></a><span class='hs-comment'>-- Calling 'retract . cutoff n' is always terminating, provided each of the</span>
<a name="line-245"></a><span class='hs-comment'>-- steps in the iteration is terminating.</span>
<a name="line-246"></a><span class='hs-definition'>cutoff</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'>Monad</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Integer</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FT</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-conid'>FT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-conid'>Maybe</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-247"></a><span class='hs-definition'>cutoff</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toFT</span> <span class='hs-varop'>.</span> <span class='hs-conid'>FreeT</span><span class='hs-varop'>.</span><span class='hs-varid'>cutoff</span> <span class='hs-varid'>n</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fromFT</span>
<a name="line-248"></a>
<a name="line-249"></a><a name="retract"></a><span class='hs-comment'>-- |</span>
<a name="line-250"></a><span class='hs-comment'>-- 'retract' is the left inverse of 'liftF'</span>
<a name="line-251"></a><span class='hs-comment'>--</span>
<a name="line-252"></a><span class='hs-comment'>-- @</span>
<a name="line-253"></a><span class='hs-comment'>-- 'retract' . 'liftF' = 'id'</span>
<a name="line-254"></a><span class='hs-comment'>-- @</span>
<a name="line-255"></a><span class='hs-definition'>retract</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'>Monad</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>F</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-256"></a><span class='hs-definition'>retract</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>runF</span> <span class='hs-varid'>m</span> <span class='hs-varid'>return</span> <span class='hs-varid'>join</span>
<a name="line-257"></a><span class='hs-comment'>{-# INLINE retract #-}</span>
<a name="line-258"></a>
<a name="line-259"></a><a name="retractT"></a><span class='hs-comment'>-- | Tear down a free monad transformer using iteration over a transformer.</span>
<a name="line-260"></a><span class='hs-definition'>retractT</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>MonadTrans</span> <span class='hs-varid'>t</span><span class='hs-layout'>,</span> <span class='hs-conid'>Monad</span> <span class='hs-layout'>(</span><span class='hs-varid'>t</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-conid'>Monad</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>FT</span> <span class='hs-layout'>(</span><span class='hs-varid'>t</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>t</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span>
<a name="line-261"></a><span class='hs-definition'>retractT</span> <span class='hs-layout'>(</span><span class='hs-conid'>FT</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>join</span> <span class='hs-varop'>.</span> <span class='hs-varid'>lift</span> <span class='hs-varop'>$</span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-varid'>return</span> <span class='hs-varop'>.</span> <span class='hs-varid'>return</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>xg</span> <span class='hs-varid'>xf</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>return</span> <span class='hs-varop'>$</span> <span class='hs-varid'>xf</span> <span class='hs-varop'>>>=</span> <span class='hs-varid'>join</span> <span class='hs-varop'>.</span> <span class='hs-varid'>lift</span> <span class='hs-varop'>.</span> <span class='hs-varid'>xg</span><span class='hs-layout'>)</span>
<a name="line-262"></a>
<a name="line-263"></a><a name="iter"></a><span class='hs-comment'>-- | Tear down an 'F' 'Monad' using iteration.</span>
<a name="line-264"></a><span class='hs-definition'>iter</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>F</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-265"></a><span class='hs-definition'>iter</span> <span class='hs-varid'>phi</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>runIdentity</span> <span class='hs-varop'>.</span> <span class='hs-varid'>iterT</span> <span class='hs-layout'>(</span><span class='hs-conid'>Identity</span> <span class='hs-varop'>.</span> <span class='hs-varid'>phi</span> <span class='hs-varop'>.</span> <span class='hs-varid'>fmap</span> <span class='hs-varid'>runIdentity</span><span class='hs-layout'>)</span>
<a name="line-266"></a><span class='hs-comment'>{-# INLINE iter #-}</span>
<a name="line-267"></a>
<a name="line-268"></a><a name="iterM"></a><span class='hs-comment'>-- | Like 'iter' for monadic values.</span>
<a name="line-269"></a><span class='hs-definition'>iterM</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'>Monad</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'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>m</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>F</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-varid'>a</span>
<a name="line-270"></a><span class='hs-definition'>iterM</span> <span class='hs-varid'>phi</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iterT</span> <span class='hs-varid'>phi</span> <span class='hs-varop'>.</span> <span class='hs-varid'>hoistFT</span> <span class='hs-layout'>(</span><span class='hs-varid'>return</span> <span class='hs-varop'>.</span> <span class='hs-varid'>runIdentity</span><span class='hs-layout'>)</span>
<a name="line-271"></a>
<a name="line-272"></a><a name="fromF"></a><span class='hs-comment'>-- | Convert to another free monad representation.</span>
<a name="line-273"></a><span class='hs-definition'>fromF</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'>MonadFree</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>F</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-varid'>a</span>
<a name="line-274"></a><span class='hs-definition'>fromF</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>runF</span> <span class='hs-varid'>m</span> <span class='hs-varid'>return</span> <span class='hs-varid'>wrap</span>
<a name="line-275"></a><span class='hs-comment'>{-# INLINE fromF #-}</span>
<a name="line-276"></a>
<a name="line-277"></a><a name="toF"></a><span class='hs-comment'>-- | Generate a Church-encoded free monad from a 'Free' monad.</span>
<a name="line-278"></a><span class='hs-definition'>toF</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Free</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>F</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span>
<a name="line-279"></a><span class='hs-definition'>toF</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toFT</span>
<a name="line-280"></a><span class='hs-comment'>{-# INLINE toF #-}</span>
<a name="line-281"></a>
<a name="line-282"></a><a name="improve"></a><span class='hs-comment'>-- | Improve the asymptotic performance of code that builds a free monad with only binds and returns by using 'F' behind the scenes.</span>
<a name="line-283"></a><span class='hs-comment'>--</span>
<a name="line-284"></a><span class='hs-comment'>-- This is based on the \"Free Monads for Less\" series of articles by Edward Kmett:</span>
<a name="line-285"></a><span class='hs-comment'>--</span>
<a name="line-286"></a><span class='hs-comment'>-- <<a href="http://comonad.com/reader/2011/free-monads-for-less/">http://comonad.com/reader/2011/free-monads-for-less/</a>></span>
<a name="line-287"></a><span class='hs-comment'>-- <<a href="http://comonad.com/reader/2011/free-monads-for-less-2/">http://comonad.com/reader/2011/free-monads-for-less-2/</a>></span>
<a name="line-288"></a><span class='hs-comment'>--</span>
<a name="line-289"></a><span class='hs-comment'>-- and \"Asymptotic Improvement of Computations over Free Monads\" by Janis Voightländer:</span>
<a name="line-290"></a><span class='hs-comment'>--</span>
<a name="line-291"></a><span class='hs-comment'>-- <<a href="http://www.iai.uni-bonn.de/~jv/mpc08.pdf">http://www.iai.uni-bonn.de/~jv/mpc08.pdf</a>></span>
<a name="line-292"></a><span class='hs-definition'>improve</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-keyword'>forall</span> <span class='hs-varid'>m</span><span class='hs-varop'>.</span> <span class='hs-conid'>MonadFree</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Free</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span>
<a name="line-293"></a><span class='hs-definition'>improve</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fromF</span> <span class='hs-varid'>m</span>
<a name="line-294"></a><span class='hs-comment'>{-# INLINE improve #-}</span>
<a name="line-295"></a>
<a name="line-296"></a><a name="improveT"></a><span class='hs-comment'>-- | Improve the asymptotic performance of code that builds a free monad transformer</span>
<a name="line-297"></a><span class='hs-comment'>-- with only binds and returns by using 'FT' behind the scenes.</span>
<a name="line-298"></a><span class='hs-comment'>--</span>
<a name="line-299"></a><span class='hs-comment'>-- Similar to 'improve'.</span>
<a name="line-300"></a><span class='hs-definition'>improveT</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'>Monad</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'>t</span><span class='hs-varop'>.</span> <span class='hs-conid'>MonadFree</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>t</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>t</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FreeT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span> <span class='hs-varid'>a</span>
<a name="line-301"></a><span class='hs-definition'>improveT</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fromFT</span> <span class='hs-varid'>m</span>
<a name="line-302"></a><span class='hs-comment'>{-# INLINE improveT #-}</span>
<a name="line-303"></a>
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