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<title>src/Control/Comonad/Trans/Store.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-cpp'>#if __GLASGOW_HASKELL__ >= 707</span>
<a name="line-3"></a><span class='hs-comment'>{-# LANGUAGE StandaloneDeriving, DeriveDataTypeable, Safe #-}</span>
<a name="line-4"></a><span class='hs-cpp'>#elif __GLASGOW_HASKELL__ >= 702</span>
<a name="line-5"></a><span class='hs-comment'>{-# LANGUAGE Trustworthy #-}</span>
<a name="line-6"></a><span class='hs-cpp'>#endif</span>
<a name="line-7"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-8"></a><span class='hs-comment'>-- |</span>
<a name="line-9"></a><span class='hs-comment'>-- Module : Control.Comonad.Trans.Store</span>
<a name="line-10"></a><span class='hs-comment'>-- Copyright : (C) 2008-2013 Edward Kmett</span>
<a name="line-11"></a><span class='hs-comment'>-- License : BSD-style (see the file LICENSE)</span>
<a name="line-12"></a><span class='hs-comment'>--</span>
<a name="line-13"></a><span class='hs-comment'>-- Maintainer : Edward Kmett <ekmett@gmail.com></span>
<a name="line-14"></a><span class='hs-comment'>-- Stability : provisional</span>
<a name="line-15"></a><span class='hs-comment'>-- Portability : portable</span>
<a name="line-16"></a><span class='hs-comment'>--</span>
<a name="line-17"></a><span class='hs-comment'>--</span>
<a name="line-18"></a><span class='hs-comment'>-- The store comonad holds a constant value along with a modifiable /accessor/</span>
<a name="line-19"></a><span class='hs-comment'>-- function, which maps the /stored value/ to the /focus/.</span>
<a name="line-20"></a><span class='hs-comment'>--</span>
<a name="line-21"></a><span class='hs-comment'>-- This module defines the strict store (aka state-in-context/costate) comonad</span>
<a name="line-22"></a><span class='hs-comment'>-- transformer.</span>
<a name="line-23"></a><span class='hs-comment'>--</span>
<a name="line-24"></a><span class='hs-comment'>-- @stored value = (1, 5)@, @accessor = fst@, @resulting focus = 1@:</span>
<a name="line-25"></a><span class='hs-comment'>--</span>
<a name="line-26"></a><span class='hs-comment'>-- >>> :{</span>
<a name="line-27"></a><span class='hs-comment'>-- let</span>
<a name="line-28"></a><span class='hs-comment'>-- storeTuple :: Store (Int, Int) Int</span>
<a name="line-29"></a><span class='hs-comment'>-- storeTuple = store fst (1, 5)</span>
<a name="line-30"></a><span class='hs-comment'>-- :}</span>
<a name="line-31"></a><span class='hs-comment'>--</span>
<a name="line-32"></a><span class='hs-comment'>-- Add something to the focus:</span>
<a name="line-33"></a><span class='hs-comment'>--</span>
<a name="line-34"></a><span class='hs-comment'>-- >>> :{</span>
<a name="line-35"></a><span class='hs-comment'>-- let</span>
<a name="line-36"></a><span class='hs-comment'>-- addToFocus :: Int -> Store (Int, Int) Int -> Int</span>
<a name="line-37"></a><span class='hs-comment'>-- addToFocus x wa = x + extract wa</span>
<a name="line-38"></a><span class='hs-comment'>-- :}</span>
<a name="line-39"></a><span class='hs-comment'>--</span>
<a name="line-40"></a><span class='hs-comment'>-- >>> :{</span>
<a name="line-41"></a><span class='hs-comment'>-- let</span>
<a name="line-42"></a><span class='hs-comment'>-- added3 :: Store (Int, Int) Int</span>
<a name="line-43"></a><span class='hs-comment'>-- added3 = extend (addToFocus 3) storeTuple</span>
<a name="line-44"></a><span class='hs-comment'>-- :}</span>
<a name="line-45"></a><span class='hs-comment'>--</span>
<a name="line-46"></a><span class='hs-comment'>-- The focus of added3 is now @1 + 3 = 4@. However, this action changed only</span>
<a name="line-47"></a><span class='hs-comment'>-- the accessor function and therefore the focus but not the stored value:</span>
<a name="line-48"></a><span class='hs-comment'>--</span>
<a name="line-49"></a><span class='hs-comment'>-- >>> pos added3</span>
<a name="line-50"></a><span class='hs-comment'>-- (1,5)</span>
<a name="line-51"></a><span class='hs-comment'>--</span>
<a name="line-52"></a><span class='hs-comment'>-- >>> extract added3</span>
<a name="line-53"></a><span class='hs-comment'>-- 4</span>
<a name="line-54"></a><span class='hs-comment'>--</span>
<a name="line-55"></a><span class='hs-comment'>-- The strict store (state-in-context/costate) comonad transformer is subject</span>
<a name="line-56"></a><span class='hs-comment'>-- to the laws:</span>
<a name="line-57"></a><span class='hs-comment'>--</span>
<a name="line-58"></a><span class='hs-comment'>-- > x = seek (pos x) x</span>
<a name="line-59"></a><span class='hs-comment'>-- > y = pos (seek y x)</span>
<a name="line-60"></a><span class='hs-comment'>-- > seek y x = seek y (seek z x)</span>
<a name="line-61"></a><span class='hs-comment'>--</span>
<a name="line-62"></a><span class='hs-comment'>-- Thanks go to Russell O'Connor and Daniel Peebles for their help formulating</span>
<a name="line-63"></a><span class='hs-comment'>-- and proving the laws for this comonad transformer.</span>
<a name="line-64"></a><span class='hs-comment'>----------------------------------------------------------------------------</span>
<a name="line-65"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Comonad</span><span class='hs-varop'>.</span><span class='hs-conid'>Trans</span><span class='hs-varop'>.</span><span class='hs-conid'>Store</span>
<a name="line-66"></a> <span class='hs-layout'>(</span>
<a name="line-67"></a> <span class='hs-comment'>-- * The Store comonad</span>
<a name="line-68"></a> <span class='hs-conid'>Store</span><span class='hs-layout'>,</span> <span class='hs-varid'>store</span><span class='hs-layout'>,</span> <span class='hs-varid'>runStore</span>
<a name="line-69"></a> <span class='hs-comment'>-- * The Store comonad transformer</span>
<a name="line-70"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>StoreT</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-varid'>runStoreT</span>
<a name="line-71"></a> <span class='hs-comment'>-- * Operations</span>
<a name="line-72"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>pos</span>
<a name="line-73"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>seek</span><span class='hs-layout'>,</span> <span class='hs-varid'>seeks</span>
<a name="line-74"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>peek</span><span class='hs-layout'>,</span> <span class='hs-varid'>peeks</span>
<a name="line-75"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>experiment</span>
<a name="line-76"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-77"></a>
<a name="line-78"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ < 710</span>
<a name="line-79"></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-80"></a><span class='hs-cpp'>#endif</span>
<a name="line-81"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Comonad</span>
<a name="line-82"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Comonad</span><span class='hs-varop'>.</span><span class='hs-conid'>Hoist</span><span class='hs-varop'>.</span><span class='hs-conid'>Class</span>
<a name="line-83"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Comonad</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-84"></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-85"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Semigroup</span>
<a name="line-86"></a>
<a name="line-87"></a><span class='hs-cpp'>#ifdef __GLASGOW_HASKELL__</span>
<a name="line-88"></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-89"></a>
<a name="line-90"></a><span class='hs-comment'>-- $setup</span>
<a name="line-91"></a><span class='hs-comment'>-- >>> import Data.Tuple (swap)</span>
<a name="line-92"></a>
<a name="line-93"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ >= 707</span>
<a name="line-94"></a><span class='hs-keyword'>deriving</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Typeable</span> <span class='hs-conid'>StoreT</span>
<a name="line-95"></a><span class='hs-cpp'>#else</span>
<a name="line-96"></a><a name="instance%20Typeable1%20(StoreT%20s%20w)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Typeable</span> <span class='hs-varid'>s</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable1</span> <span class='hs-varid'>w</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'>StoreT</span> <span class='hs-varid'>s</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-97"></a> <span class='hs-varid'>typeOf1</span> <span class='hs-varid'>dswa</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mkTyConApp</span> <span class='hs-varid'>storeTTyCon</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>typeOf</span> <span class='hs-layout'>(</span><span class='hs-varid'>s</span> <span class='hs-varid'>dswa</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-varid'>typeOf1</span> <span class='hs-layout'>(</span><span class='hs-varid'>w</span> <span class='hs-varid'>dswa</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>]</span>
<a name="line-98"></a> <span class='hs-keyword'>where</span>
<a name="line-99"></a> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>StoreT</span> <span class='hs-varid'>s</span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>s</span>
<a name="line-100"></a> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>undefined</span>
<a name="line-101"></a> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>StoreT</span> <span class='hs-varid'>s</span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span>
<a name="line-102"></a> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>undefined</span>
<a name="line-103"></a>
<a name="line-104"></a><a name="instance%20Typeable%20(StoreT%20s%20w%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Typeable</span> <span class='hs-varid'>s</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable1</span> <span class='hs-varid'>w</span><span class='hs-layout'>,</span> <span class='hs-conid'>Typeable</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Typeable</span> <span class='hs-layout'>(</span><span class='hs-conid'>StoreT</span> <span class='hs-varid'>s</span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-105"></a> <span class='hs-varid'>typeOf</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>typeOfDefault</span>
<a name="line-106"></a>
<a name="line-107"></a><a name="storeTTyCon"></a><span class='hs-definition'>storeTTyCon</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>TyCon</span>
<a name="line-108"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ < 704</span>
<a name="line-109"></a><span class='hs-definition'>storeTTyCon</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mkTyCon</span> <span class='hs-str'>"Control.Comonad.Trans.Store.StoreT"</span>
<a name="line-110"></a><span class='hs-cpp'>#else</span>
<a name="line-111"></a><span class='hs-definition'>storeTTyCon</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mkTyCon3</span> <span class='hs-str'>"comonad-transformers"</span> <span class='hs-str'>"Control.Comonad.Trans.Store"</span> <span class='hs-str'>"StoreT"</span>
<a name="line-112"></a><span class='hs-cpp'>#endif</span>
<a name="line-113"></a><span class='hs-comment'>{-# NOINLINE storeTTyCon #-}</span>
<a name="line-114"></a><span class='hs-cpp'>#endif</span>
<a name="line-115"></a>
<a name="line-116"></a><span class='hs-cpp'>#endif</span>
<a name="line-117"></a>
<a name="line-118"></a><a name="Store"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>Store</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>StoreT</span> <span class='hs-varid'>s</span> <span class='hs-conid'>Identity</span>
<a name="line-119"></a>
<a name="line-120"></a><a name="store"></a><span class='hs-comment'>-- | Create a Store using an accessor function and a stored value</span>
<a name="line-121"></a><span class='hs-definition'>store</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-varid'>s</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-varid'>s</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Store</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span>
<a name="line-122"></a><span class='hs-definition'>store</span> <span class='hs-varid'>f</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>StoreT</span> <span class='hs-layout'>(</span><span class='hs-conid'>Identity</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varid'>s</span>
<a name="line-123"></a>
<a name="line-124"></a><a name="runStore"></a><span class='hs-definition'>runStore</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Store</span> <span class='hs-varid'>s</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-varid'>s</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span>
<a name="line-125"></a><span class='hs-definition'>runStore</span> <span class='hs-layout'>(</span><span class='hs-conid'>StoreT</span> <span class='hs-layout'>(</span><span class='hs-conid'>Identity</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varid'>s</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'>s</span><span class='hs-layout'>)</span>
<a name="line-126"></a>
<a name="line-127"></a><a name="StoreT"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>StoreT</span> <span class='hs-varid'>s</span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>StoreT</span> <span class='hs-layout'>(</span><span class='hs-varid'>w</span> <span class='hs-layout'>(</span><span class='hs-varid'>s</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-varid'>s</span>
<a name="line-128"></a>
<a name="line-129"></a><a name="runStoreT"></a><span class='hs-definition'>runStoreT</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>StoreT</span> <span class='hs-varid'>s</span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-varid'>w</span> <span class='hs-layout'>(</span><span class='hs-varid'>s</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span>
<a name="line-130"></a><span class='hs-definition'>runStoreT</span> <span class='hs-layout'>(</span><span class='hs-conid'>StoreT</span> <span class='hs-varid'>wf</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>wf</span><span class='hs-layout'>,</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span>
<a name="line-131"></a>
<a name="line-132"></a><a name="instance%20Functor%20(StoreT%20s%20w)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Functor</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Functor</span> <span class='hs-layout'>(</span><span class='hs-conid'>StoreT</span> <span class='hs-varid'>s</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-133"></a> <span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>StoreT</span> <span class='hs-varid'>wf</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>StoreT</span> <span class='hs-layout'>(</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'>wf</span><span class='hs-layout'>)</span> <span class='hs-varid'>s</span>
<a name="line-134"></a>
<a name="line-135"></a><a name="instance%20ComonadApply%20(StoreT%20s%20w)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>ComonadApply</span> <span class='hs-varid'>w</span><span class='hs-layout'>,</span> <span class='hs-conid'>Semigroup</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>ComonadApply</span> <span class='hs-layout'>(</span><span class='hs-conid'>StoreT</span> <span class='hs-varid'>s</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-136"></a> <span class='hs-conid'>StoreT</span> <span class='hs-varid'>ff</span> <span class='hs-varid'>m</span> <span class='hs-varop'><@></span> <span class='hs-conid'>StoreT</span> <span class='hs-varid'>fa</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>StoreT</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'>ff</span> <span class='hs-varop'><@></span> <span class='hs-varid'>fa</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>m</span> <span class='hs-varop'><></span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-137"></a>
<a name="line-138"></a><a name="instance%20Applicative%20(StoreT%20s%20w)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Applicative</span> <span class='hs-varid'>w</span><span class='hs-layout'>,</span> <span class='hs-conid'>Monoid</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Applicative</span> <span class='hs-layout'>(</span><span class='hs-conid'>StoreT</span> <span class='hs-varid'>s</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-139"></a> <span class='hs-varid'>pure</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>StoreT</span> <span class='hs-layout'>(</span><span class='hs-varid'>pure</span> <span class='hs-layout'>(</span><span class='hs-varid'>const</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-varid'>mempty</span>
<a name="line-140"></a> <span class='hs-conid'>StoreT</span> <span class='hs-varid'>ff</span> <span class='hs-varid'>m</span> <span class='hs-varop'><*></span> <span class='hs-conid'>StoreT</span> <span class='hs-varid'>fa</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>StoreT</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'>ff</span> <span class='hs-varop'><*></span> <span class='hs-varid'>fa</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>mappend</span> <span class='hs-varid'>m</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-141"></a>
<a name="line-142"></a><a name="instance%20Comonad%20(StoreT%20s%20w)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Comonad</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Comonad</span> <span class='hs-layout'>(</span><span class='hs-conid'>StoreT</span> <span class='hs-varid'>s</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-143"></a> <span class='hs-varid'>duplicate</span> <span class='hs-layout'>(</span><span class='hs-conid'>StoreT</span> <span class='hs-varid'>wf</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>StoreT</span> <span class='hs-layout'>(</span><span class='hs-varid'>extend</span> <span class='hs-conid'>StoreT</span> <span class='hs-varid'>wf</span><span class='hs-layout'>)</span> <span class='hs-varid'>s</span>
<a name="line-144"></a> <span class='hs-varid'>extend</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>StoreT</span> <span class='hs-varid'>wf</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>StoreT</span> <span class='hs-layout'>(</span><span class='hs-varid'>extend</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>wf'</span> <span class='hs-varid'>s'</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>StoreT</span> <span class='hs-varid'>wf'</span> <span class='hs-varid'>s'</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-varid'>wf</span><span class='hs-layout'>)</span> <span class='hs-varid'>s</span>
<a name="line-145"></a> <span class='hs-varid'>extract</span> <span class='hs-layout'>(</span><span class='hs-conid'>StoreT</span> <span class='hs-varid'>wf</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>extract</span> <span class='hs-varid'>wf</span> <span class='hs-varid'>s</span>
<a name="line-146"></a>
<a name="line-147"></a><a name="instance%20ComonadTrans%20(StoreT%20s)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>ComonadTrans</span> <span class='hs-layout'>(</span><span class='hs-conid'>StoreT</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-148"></a> <span class='hs-varid'>lower</span> <span class='hs-layout'>(</span><span class='hs-conid'>StoreT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>s</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-varop'>$</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-varid'>f</span>
<a name="line-149"></a>
<a name="line-150"></a><a name="instance%20ComonadHoist%20(StoreT%20s)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>ComonadHoist</span> <span class='hs-layout'>(</span><span class='hs-conid'>StoreT</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-151"></a> <span class='hs-varid'>cohoist</span> <span class='hs-varid'>l</span> <span class='hs-layout'>(</span><span class='hs-conid'>StoreT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>StoreT</span> <span class='hs-layout'>(</span><span class='hs-varid'>l</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span> <span class='hs-varid'>s</span>
<a name="line-152"></a>
<a name="line-153"></a><a name="pos"></a><span class='hs-comment'>-- | Read the stored value</span>
<a name="line-154"></a><span class='hs-comment'>--</span>
<a name="line-155"></a><span class='hs-comment'>-- >>> pos $ store fst (1,5)</span>
<a name="line-156"></a><span class='hs-comment'>-- (1,5)</span>
<a name="line-157"></a><span class='hs-comment'>--</span>
<a name="line-158"></a><span class='hs-definition'>pos</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>StoreT</span> <span class='hs-varid'>s</span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>s</span>
<a name="line-159"></a><span class='hs-definition'>pos</span> <span class='hs-layout'>(</span><span class='hs-conid'>StoreT</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>s</span>
<a name="line-160"></a>
<a name="line-161"></a><a name="seek"></a><span class='hs-comment'>-- | Set the stored value</span>
<a name="line-162"></a><span class='hs-comment'>--</span>
<a name="line-163"></a><span class='hs-comment'>-- >>> pos . seek (3,7) $ store fst (1,5)</span>
<a name="line-164"></a><span class='hs-comment'>-- (3,7)</span>
<a name="line-165"></a><span class='hs-comment'>--</span>
<a name="line-166"></a><span class='hs-comment'>-- Seek satisfies the law</span>
<a name="line-167"></a><span class='hs-comment'>--</span>
<a name="line-168"></a><span class='hs-comment'>-- > seek s = peek s . duplicate</span>
<a name="line-169"></a><span class='hs-definition'>seek</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>StoreT</span> <span class='hs-varid'>s</span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>StoreT</span> <span class='hs-varid'>s</span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span>
<a name="line-170"></a><span class='hs-definition'>seek</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>StoreT</span> <span class='hs-varid'>f</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>StoreT</span> <span class='hs-varid'>f</span> <span class='hs-varid'>s</span>
<a name="line-171"></a>
<a name="line-172"></a><a name="seeks"></a><span class='hs-comment'>-- | Modify the stored value</span>
<a name="line-173"></a><span class='hs-comment'>--</span>
<a name="line-174"></a><span class='hs-comment'>-- >>> pos . seeks swap $ store fst (1,5)</span>
<a name="line-175"></a><span class='hs-comment'>-- (5,1)</span>
<a name="line-176"></a><span class='hs-comment'>--</span>
<a name="line-177"></a><span class='hs-comment'>-- Seeks satisfies the law</span>
<a name="line-178"></a><span class='hs-comment'>--</span>
<a name="line-179"></a><span class='hs-comment'>-- > seeks f = peeks f . duplicate</span>
<a name="line-180"></a><span class='hs-definition'>seeks</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-varid'>s</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>StoreT</span> <span class='hs-varid'>s</span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>StoreT</span> <span class='hs-varid'>s</span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span>
<a name="line-181"></a><span class='hs-definition'>seeks</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>StoreT</span> <span class='hs-varid'>g</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>StoreT</span> <span class='hs-varid'>g</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span>
<a name="line-182"></a>
<a name="line-183"></a><a name="peek"></a><span class='hs-comment'>-- | Peek at what the current focus would be for a different stored value</span>
<a name="line-184"></a><span class='hs-comment'>--</span>
<a name="line-185"></a><span class='hs-comment'>-- Peek satisfies the law</span>
<a name="line-186"></a><span class='hs-comment'>--</span>
<a name="line-187"></a><span class='hs-comment'>-- > peek x . extend (peek y) = peek y</span>
<a name="line-188"></a><span class='hs-definition'>peek</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Comonad</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>StoreT</span> <span class='hs-varid'>s</span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-189"></a><span class='hs-definition'>peek</span> <span class='hs-varid'>s</span> <span class='hs-layout'>(</span><span class='hs-conid'>StoreT</span> <span class='hs-varid'>g</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>extract</span> <span class='hs-varid'>g</span> <span class='hs-varid'>s</span>
<a name="line-190"></a>
<a name="line-191"></a>
<a name="line-192"></a><a name="peeks"></a><span class='hs-comment'>-- | Peek at what the current focus would be if the stored value was</span>
<a name="line-193"></a><span class='hs-comment'>-- modified by some function</span>
<a name="line-194"></a><span class='hs-definition'>peeks</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Comonad</span> <span class='hs-varid'>w</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-varid'>s</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>StoreT</span> <span class='hs-varid'>s</span> <span class='hs-varid'>w</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span>
<a name="line-195"></a><span class='hs-definition'>peeks</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>StoreT</span> <span class='hs-varid'>g</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>extract</span> <span class='hs-varid'>g</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span>
<a name="line-196"></a>
<a name="line-197"></a><a name="experiment"></a><span class='hs-comment'>-- | Applies a functor-valued function to the stored value, and then uses the</span>
<a name="line-198"></a><span class='hs-comment'>-- new accessor to read the resulting focus.</span>
<a name="line-199"></a><span class='hs-comment'>--</span>
<a name="line-200"></a><span class='hs-comment'>-- >>> let f x = if x > 0 then Just (x^2) else Nothing</span>
<a name="line-201"></a><span class='hs-comment'>-- >>> experiment f $ store (+1) 2</span>
<a name="line-202"></a><span class='hs-comment'>-- Just 5</span>
<a name="line-203"></a><span class='hs-comment'>-- >>> experiment f $ store (+1) (-2)</span>
<a name="line-204"></a><span class='hs-comment'>-- Nothing</span>
<a name="line-205"></a><span class='hs-definition'>experiment</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Comonad</span> <span class='hs-varid'>w</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-layout'>(</span><span class='hs-varid'>s</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>f</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>StoreT</span> <span class='hs-varid'>s</span> <span class='hs-varid'>w</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-206"></a><span class='hs-definition'>experiment</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>StoreT</span> <span class='hs-varid'>wf</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>extract</span> <span class='hs-varid'>wf</span> <span class='hs-varop'><$></span> <span class='hs-varid'>f</span> <span class='hs-varid'>s</span>
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