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<title>src/Darcs/Witnesses/Sealed.hs</title>
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<pre><a name="line-1"></a><span class='hs-comment'>-- Copyright (C) 2007 David Roundy, 2009 Ganesh Sittampalam</span>
<a name="line-2"></a><span class='hs-comment'>--</span>
<a name="line-3"></a><span class='hs-comment'>-- This program is free software; you can redistribute it and/or modify</span>
<a name="line-4"></a><span class='hs-comment'>-- it under the terms of the GNU General Public License as published by</span>
<a name="line-5"></a><span class='hs-comment'>-- the Free Software Foundation; either version 2, or (at your option)</span>
<a name="line-6"></a><span class='hs-comment'>-- any later version.</span>
<a name="line-7"></a><span class='hs-comment'>--</span>
<a name="line-8"></a><span class='hs-comment'>-- This program is distributed in the hope that it will be useful,</span>
<a name="line-9"></a><span class='hs-comment'>-- but WITHOUT ANY WARRANTY; without even the implied warranty of</span>
<a name="line-10"></a><span class='hs-comment'>-- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the</span>
<a name="line-11"></a><span class='hs-comment'>-- GNU General Public License for more details.</span>
<a name="line-12"></a><span class='hs-comment'>--</span>
<a name="line-13"></a><span class='hs-comment'>-- You should have received a copy of the GNU General Public License</span>
<a name="line-14"></a><span class='hs-comment'>-- along with this program; see the file COPYING. If not, write to</span>
<a name="line-15"></a><span class='hs-comment'>-- the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,</span>
<a name="line-16"></a><span class='hs-comment'>-- Boston, MA 02110-1301, USA.</span>
<a name="line-17"></a>
<a name="line-18"></a><span class='hs-comment'>{-# LANGUAGE CPP, FlexibleInstances #-}</span>
<a name="line-19"></a>
<a name="line-20"></a><span class='hs-cpp'>#include "gadts.h"</span>
<a name="line-21"></a>
<a name="line-22"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Darcs</span><span class='hs-varop'>.</span><span class='hs-conid'>Witnesses</span><span class='hs-varop'>.</span><span class='hs-conid'>Sealed</span> <span class='hs-layout'>(</span> <span class='hs-conid'>Sealed</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'>seal</span><span class='hs-layout'>,</span> <span class='hs-varid'>unseal</span><span class='hs-layout'>,</span> <span class='hs-varid'>mapSeal</span><span class='hs-layout'>,</span>
<a name="line-23"></a> <span class='hs-varid'>unsafeUnseal</span><span class='hs-layout'>,</span> <span class='hs-varid'>unsafeUnsealFlipped</span><span class='hs-layout'>,</span> <span class='hs-varid'>unsafeUnseal2</span><span class='hs-layout'>,</span>
<a name="line-24"></a> <span class='hs-conid'>Sealed2</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'>seal2</span><span class='hs-layout'>,</span> <span class='hs-varid'>unseal2</span><span class='hs-layout'>,</span> <span class='hs-varid'>mapSeal2</span><span class='hs-layout'>,</span>
<a name="line-25"></a> <span class='hs-conid'>FlippedSeal</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'>flipSeal</span><span class='hs-layout'>,</span> <span class='hs-varid'>unsealFlipped</span><span class='hs-layout'>,</span> <span class='hs-varid'>mapFlipped</span><span class='hs-layout'>,</span>
<a name="line-26"></a> <span class='hs-varid'>unsealM</span><span class='hs-layout'>,</span> <span class='hs-varid'>liftSM</span><span class='hs-layout'>,</span>
<a name="line-27"></a> <span class='hs-conid'>Gap</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'>FreeLeft</span><span class='hs-layout'>,</span> <span class='hs-varid'>unFreeLeft</span><span class='hs-layout'>,</span> <span class='hs-conid'>FreeRight</span><span class='hs-layout'>,</span> <span class='hs-varid'>unFreeRight</span>
<a name="line-28"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-29"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Darcs</span><span class='hs-varop'>.</span><span class='hs-conid'>Witnesses</span><span class='hs-varop'>.</span><span class='hs-conid'>Eq</span> <span class='hs-layout'>(</span> <span class='hs-conid'>MyEq</span><span class='hs-layout'>,</span> <span class='hs-conid'>EqCheck</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span> <span class='hs-layout'>)</span>
<a name="line-30"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Darcs</span><span class='hs-varop'>.</span><span class='hs-conid'>Witnesses</span><span class='hs-varop'>.</span><span class='hs-conid'>Show</span>
<a name="line-31"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Darcs</span><span class='hs-varop'>.</span><span class='hs-conid'>Witnesses</span><span class='hs-varop'>.</span><span class='hs-conid'>Eq</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-32"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Darcs</span><span class='hs-varop'>.</span><span class='hs-conid'>Witnesses</span><span class='hs-varop'>.</span><span class='hs-conid'>Unsafe</span> <span class='hs-layout'>(</span> <span class='hs-varid'>unsafeCoerceP1</span><span class='hs-layout'>,</span> <span class='hs-varid'>unsafeCoerceP</span> <span class='hs-layout'>)</span>
<a name="line-33"></a>
<a name="line-34"></a><a name="Sealed"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>Sealed</span> <span class='hs-varid'>a</span> <span class='hs-keyword'>where</span>
<a name="line-35"></a> <span class='hs-conid'>Sealed</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Sealed</span> <span class='hs-varid'>a</span>
<a name="line-36"></a>
<a name="line-37"></a><a name="seal"></a><span class='hs-definition'>seal</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Sealed</span> <span class='hs-varid'>a</span>
<a name="line-38"></a><span class='hs-definition'>seal</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Sealed</span>
<a name="line-39"></a>
<a name="line-40"></a><a name="instance%20Eq%20(Sealed%20(a%20C(x%20)))"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>MyEq</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Eq</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sealed</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-41"></a> <span class='hs-conid'>Sealed</span> <span class='hs-varid'>x</span> <span class='hs-varop'>==</span> <span class='hs-conid'>Sealed</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>|</span> <span class='hs-conid'>IsEq</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>x</span> <span class='hs-varop'>=\/=</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>True</span>
<a name="line-42"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span>
<a name="line-43"></a>
<a name="line-44"></a><a name="Sealed2"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>Sealed2</span> <span class='hs-varid'>a</span> <span class='hs-keyword'>where</span>
<a name="line-45"></a> <span class='hs-conid'>Sealed2</span> <span class='hs-keyglyph'>::</span> <span class='hs-varop'>!</span><span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Sealed2</span> <span class='hs-varid'>a</span>
<a name="line-46"></a>
<a name="line-47"></a><a name="seal2"></a><span class='hs-definition'>seal2</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Sealed2</span> <span class='hs-varid'>a</span>
<a name="line-48"></a><span class='hs-definition'>seal2</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Sealed2</span>
<a name="line-49"></a>
<a name="line-50"></a><a name="FlippedSeal"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>FlippedSeal</span> <span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-51"></a> <span class='hs-conid'>FlippedSeal</span> <span class='hs-keyglyph'>::</span> <span class='hs-varop'>!</span><span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FlippedSeal</span> <span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>y</span><span class='hs-layout'>)</span>
<a name="line-52"></a>
<a name="line-53"></a><a name="flipSeal"></a><span class='hs-definition'>flipSeal</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FlippedSeal</span> <span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>y</span><span class='hs-layout'>)</span>
<a name="line-54"></a><span class='hs-definition'>flipSeal</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FlippedSeal</span>
<a name="line-55"></a>
<a name="line-56"></a><a name="unsafeUnseal"></a><span class='hs-definition'>unsafeUnseal</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Sealed</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>)</span>
<a name="line-57"></a><span class='hs-definition'>unsafeUnseal</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sealed</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unsafeCoerceP1</span> <span class='hs-varid'>a</span>
<a name="line-58"></a>
<a name="line-59"></a><a name="unsafeUnsealFlipped"></a><span class='hs-definition'>unsafeUnsealFlipped</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>FlippedSeal</span> <span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span>
<a name="line-60"></a><span class='hs-definition'>unsafeUnsealFlipped</span> <span class='hs-layout'>(</span><span class='hs-conid'>FlippedSeal</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unsafeCoerceP</span> <span class='hs-varid'>a</span>
<a name="line-61"></a>
<a name="line-62"></a><a name="unsafeUnseal2"></a><span class='hs-definition'>unsafeUnseal2</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Sealed2</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span>
<a name="line-63"></a><span class='hs-definition'>unsafeUnseal2</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sealed2</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unsafeCoerceP</span> <span class='hs-varid'>a</span>
<a name="line-64"></a>
<a name="line-65"></a><a name="unseal"></a><span class='hs-definition'>unseal</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>FORALL</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Sealed</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span>
<a name="line-66"></a><span class='hs-definition'>unseal</span> <span class='hs-varid'>f</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>unsafeUnseal</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span>
<a name="line-67"></a>
<a name="line-68"></a><span class='hs-comment'>-- laziness property:</span>
<a name="line-69"></a><span class='hs-comment'>-- unseal (const True) undefined == True</span>
<a name="line-70"></a>
<a name="line-71"></a><a name="unsealM"></a><span class='hs-definition'>unsealM</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-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sealed</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-conid'>FORALL</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-varid'>b</span>
<a name="line-72"></a><span class='hs-definition'>unsealM</span> <span class='hs-varid'>m1</span> <span class='hs-varid'>m2</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span> <span class='hs-varid'>sx</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>m1</span>
<a name="line-73"></a> <span class='hs-varid'>unseal</span> <span class='hs-varid'>m2</span> <span class='hs-varid'>sx</span>
<a name="line-74"></a>
<a name="line-75"></a><a name="liftSM"></a><span class='hs-definition'>liftSM</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-conid'>FORALL</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>m</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sealed</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'>b</span>
<a name="line-76"></a><span class='hs-definition'>liftSM</span> <span class='hs-varid'>f</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span> <span class='hs-varid'>sx</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>m</span>
<a name="line-77"></a> <span class='hs-varid'>return</span> <span class='hs-layout'>(</span><span class='hs-varid'>unseal</span> <span class='hs-varid'>f</span> <span class='hs-varid'>sx</span><span class='hs-layout'>)</span>
<a name="line-78"></a>
<a name="line-79"></a><a name="mapSeal"></a><span class='hs-definition'>mapSeal</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>FORALL</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Sealed</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Sealed</span> <span class='hs-varid'>b</span>
<a name="line-80"></a><span class='hs-definition'>mapSeal</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unseal</span> <span class='hs-layout'>(</span><span class='hs-varid'>seal</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span>
<a name="line-81"></a>
<a name="line-82"></a><a name="mapFlipped"></a><span class='hs-definition'>mapFlipped</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>FORALL</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varid'>z</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FlippedSeal</span> <span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FlippedSeal</span> <span class='hs-varid'>b</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>z</span><span class='hs-layout'>)</span>
<a name="line-83"></a><span class='hs-definition'>mapFlipped</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>FlippedSeal</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FlippedSeal</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span>
<a name="line-84"></a>
<a name="line-85"></a><a name="unseal2"></a><span class='hs-definition'>unseal2</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>FORALL</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Sealed2</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span>
<a name="line-86"></a><span class='hs-definition'>unseal2</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-layout'>(</span><span class='hs-varid'>unsafeUnseal2</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-87"></a>
<a name="line-88"></a><a name="mapSeal2"></a><span class='hs-definition'>mapSeal2</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>FORALL</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Sealed2</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Sealed2</span> <span class='hs-varid'>b</span>
<a name="line-89"></a><span class='hs-definition'>mapSeal2</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unseal2</span> <span class='hs-layout'>(</span><span class='hs-varid'>seal2</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span><span class='hs-layout'>)</span>
<a name="line-90"></a>
<a name="line-91"></a><a name="unsealFlipped"></a><span class='hs-definition'>unsealFlipped</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>FORALL</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FlippedSeal</span> <span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>z</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span>
<a name="line-92"></a><span class='hs-definition'>unsealFlipped</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>FlippedSeal</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span>
<a name="line-93"></a>
<a name="line-94"></a><a name="instance%20Show%20(Sealed%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Show1</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Show</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sealed</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-95"></a> <span class='hs-varid'>showsPrec</span> <span class='hs-varid'>d</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sealed</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>showParen</span> <span class='hs-layout'>(</span><span class='hs-varid'>d</span> <span class='hs-varop'>></span> <span class='hs-varid'>appPrec</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>showString</span> <span class='hs-str'>"Sealed "</span> <span class='hs-varop'>.</span> <span class='hs-varid'>showsPrec1</span> <span class='hs-layout'>(</span><span class='hs-varid'>appPrec</span> <span class='hs-varop'>+</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varid'>x</span>
<a name="line-96"></a><a name="instance%20Show%20(Sealed2%20a)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Show2</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Show</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sealed2</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-97"></a> <span class='hs-varid'>showsPrec</span> <span class='hs-varid'>d</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sealed2</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>showParen</span> <span class='hs-layout'>(</span><span class='hs-varid'>d</span> <span class='hs-varop'>></span> <span class='hs-varid'>appPrec</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>showString</span> <span class='hs-str'>"Sealed2 "</span> <span class='hs-varop'>.</span> <span class='hs-varid'>showsPrec2</span> <span class='hs-layout'>(</span><span class='hs-varid'>appPrec</span> <span class='hs-varop'>+</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varid'>x</span>
<a name="line-98"></a>
<a name="line-99"></a><a name="Poly"></a><span class='hs-comment'>-- |'Poly' is similar to 'Sealed', but the type argument is</span>
<a name="line-100"></a><a name="Poly"></a><span class='hs-comment'>-- universally quantified instead of being existentially quantified.</span>
<a name="line-101"></a><a name="Poly"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>Poly</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Poly</span> <span class='hs-layout'>{</span> <span class='hs-varid'>unPoly</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>FORALL</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>}</span>
<a name="line-102"></a>
<a name="line-103"></a><a name="Stepped"></a><span class='hs-comment'>-- |'Stepped' is a type level composition operator.</span>
<a name="line-104"></a><a name="Stepped"></a><span class='hs-comment'>-- For example, 'Stepped Sealed p' is equivalent to 'lambda x . Sealed (p x)'</span>
<a name="line-105"></a><a name="Stepped"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>Stepped</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>SEALEDPATCHKIND</span> <span class='hs-keyglyph'>-></span> <span class='hs-varop'>*</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Stepped</span> <span class='hs-layout'>{</span> <span class='hs-varid'>unStepped</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-layout'>}</span>
<a name="line-106"></a>
<a name="line-107"></a><a name="FreeLeft"></a><span class='hs-comment'>-- |'FreeLeft p' is '\forall x . \exists y . p x y'</span>
<a name="line-108"></a><a name="FreeLeft"></a><span class='hs-comment'>-- In other words the caller is free to specify the left witness,</span>
<a name="line-109"></a><a name="FreeLeft"></a><span class='hs-comment'>-- and then the right witness is an existential.</span>
<a name="line-110"></a><a name="FreeLeft"></a><span class='hs-comment'>-- Note that the order of the type constructors is important for ensuring</span>
<a name="line-111"></a><a name="FreeLeft"></a><span class='hs-comment'>-- that 'y' is dependent on the 'x' that is supplied.</span>
<a name="line-112"></a><a name="FreeLeft"></a><span class='hs-comment'>-- This is why 'Stepped' is needed, rather than writing the more obvious</span>
<a name="line-113"></a><a name="FreeLeft"></a><span class='hs-comment'>-- 'Sealed (Poly p)' which would notionally have the same quantification</span>
<a name="line-114"></a><a name="FreeLeft"></a><span class='hs-comment'>-- of the type witnesses.</span>
<a name="line-115"></a><a name="FreeLeft"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>FreeLeft</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FLInternal</span> <span class='hs-layout'>(</span><span class='hs-conid'>Poly</span> <span class='hs-layout'>(</span><span class='hs-conid'>Stepped</span> <span class='hs-conid'>Sealed</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-116"></a>
<a name="line-117"></a><a name="FreeRight"></a><span class='hs-comment'>-- |'FreeLeft p' is '\forall y . \exists x . p x y'</span>
<a name="line-118"></a><a name="FreeRight"></a><span class='hs-comment'>-- In other words the caller is free to specify the right witness,</span>
<a name="line-119"></a><a name="FreeRight"></a><span class='hs-comment'>-- and then the left witness is an existential.</span>
<a name="line-120"></a><a name="FreeRight"></a><span class='hs-comment'>-- Note that the order of the type constructors is important for ensuring</span>
<a name="line-121"></a><a name="FreeRight"></a><span class='hs-comment'>-- that 'x' is dependent on the 'y' that is supplied.</span>
<a name="line-122"></a><a name="FreeRight"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>FreeRight</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FRInternal</span> <span class='hs-layout'>(</span><span class='hs-conid'>Poly</span> <span class='hs-layout'>(</span><span class='hs-conid'>FlippedSeal</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-123"></a>
<a name="line-124"></a><a name="unFreeLeft"></a><span class='hs-comment'>-- |Unwrap a 'FreeLeft' value</span>
<a name="line-125"></a><span class='hs-definition'>unFreeLeft</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>FreeLeft</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Sealed</span> <span class='hs-layout'>(</span><span class='hs-varid'>p</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-126"></a><span class='hs-definition'>unFreeLeft</span> <span class='hs-layout'>(</span><span class='hs-conid'>FLInternal</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unStepped</span> <span class='hs-layout'>(</span><span class='hs-varid'>unPoly</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span>
<a name="line-127"></a>
<a name="line-128"></a><a name="unFreeRight"></a><span class='hs-comment'>-- |Unwrap a 'FreeRight' value</span>
<a name="line-129"></a><span class='hs-definition'>unFreeRight</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>FreeRight</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FlippedSeal</span> <span class='hs-varid'>p</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>)</span>
<a name="line-130"></a><span class='hs-definition'>unFreeRight</span> <span class='hs-layout'>(</span><span class='hs-conid'>FRInternal</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>unPoly</span> <span class='hs-varid'>x</span>
<a name="line-131"></a>
<a name="line-132"></a><a name="Gap"></a><span class='hs-comment'>-- |'Gap' abstracts over 'FreeLeft' and 'FreeRight' for code constructing these values</span>
<a name="line-133"></a><a name="Gap"></a><span class='hs-keyword'>class</span> <span class='hs-conid'>Gap</span> <span class='hs-varid'>w</span> <span class='hs-keyword'>where</span>
<a name="line-134"></a> <span class='hs-comment'>-- |An empty 'Gap', e.g. 'NilFL' or 'NilRL'</span>
<a name="line-135"></a> <span class='hs-varid'>emptyGap</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>FORALL</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-varid'>p</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>p</span>
<a name="line-136"></a> <span class='hs-comment'>-- |A 'Gap' constructed from a completely polymorphic value, for example the constructors</span>
<a name="line-137"></a> <span class='hs-comment'>-- for primitive patches</span>
<a name="line-138"></a> <span class='hs-varid'>freeGap</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>FORALL</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-varid'>p</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>p</span>
<a name="line-139"></a>
<a name="line-140"></a> <span class='hs-comment'>-- |Compose two 'Gap' values together in series, e.g. 'joinGap (+>+)' or 'joinGap (:>:)'</span>
<a name="line-141"></a> <span class='hs-varid'>joinGap</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>FORALL</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-varid'>z</span><span class='hs-layout'>)</span> <span class='hs-varid'>p</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>q</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>y</span> <span class='hs-varid'>z</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>r</span> <span class='hs-conid'>C</span><span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varid'>z</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>q</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>w</span> <span class='hs-varid'>r</span>
<a name="line-142"></a>
<a name="line-143"></a><a name="instance%20Gap%20FreeLeft"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Gap</span> <span class='hs-conid'>FreeLeft</span> <span class='hs-keyword'>where</span>
<a name="line-144"></a> <span class='hs-varid'>emptyGap</span> <span class='hs-varid'>e</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FLInternal</span> <span class='hs-layout'>(</span><span class='hs-conid'>Poly</span> <span class='hs-layout'>(</span><span class='hs-conid'>Stepped</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sealed</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-145"></a> <span class='hs-varid'>freeGap</span> <span class='hs-varid'>e</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FLInternal</span> <span class='hs-layout'>(</span><span class='hs-conid'>Poly</span> <span class='hs-layout'>(</span><span class='hs-conid'>Stepped</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sealed</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-146"></a> <span class='hs-varid'>joinGap</span> <span class='hs-varid'>op</span> <span class='hs-layout'>(</span><span class='hs-conid'>FLInternal</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>FLInternal</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span>
<a name="line-147"></a> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FLInternal</span> <span class='hs-layout'>(</span><span class='hs-conid'>Poly</span> <span class='hs-layout'>(</span><span class='hs-keyword'>case</span> <span class='hs-varid'>unPoly</span> <span class='hs-varid'>p</span> <span class='hs-keyword'>of</span> <span class='hs-conid'>Stepped</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sealed</span> <span class='hs-varid'>p'</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-varid'>unPoly</span> <span class='hs-varid'>q</span> <span class='hs-keyword'>of</span> <span class='hs-conid'>Stepped</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sealed</span> <span class='hs-varid'>q'</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Stepped</span> <span class='hs-layout'>(</span><span class='hs-conid'>Sealed</span> <span class='hs-layout'>(</span><span class='hs-varid'>p'</span> <span class='hs-varop'>`op`</span> <span class='hs-varid'>q'</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-148"></a>
<a name="line-149"></a><a name="instance%20Gap%20FreeRight"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Gap</span> <span class='hs-conid'>FreeRight</span> <span class='hs-keyword'>where</span>
<a name="line-150"></a> <span class='hs-varid'>emptyGap</span> <span class='hs-varid'>e</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FRInternal</span> <span class='hs-layout'>(</span><span class='hs-conid'>Poly</span> <span class='hs-layout'>(</span><span class='hs-conid'>FlippedSeal</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-151"></a> <span class='hs-varid'>freeGap</span> <span class='hs-varid'>e</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FRInternal</span> <span class='hs-layout'>(</span><span class='hs-conid'>Poly</span> <span class='hs-layout'>(</span><span class='hs-conid'>FlippedSeal</span> <span class='hs-varid'>e</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-152"></a> <span class='hs-varid'>joinGap</span> <span class='hs-varid'>op</span> <span class='hs-layout'>(</span><span class='hs-conid'>FRInternal</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>FRInternal</span> <span class='hs-varid'>q</span><span class='hs-layout'>)</span>
<a name="line-153"></a> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>FRInternal</span> <span class='hs-layout'>(</span><span class='hs-conid'>Poly</span> <span class='hs-layout'>(</span><span class='hs-keyword'>case</span> <span class='hs-varid'>unPoly</span> <span class='hs-varid'>q</span> <span class='hs-keyword'>of</span> <span class='hs-conid'>FlippedSeal</span> <span class='hs-varid'>q'</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-varid'>unPoly</span> <span class='hs-varid'>p</span> <span class='hs-keyword'>of</span> <span class='hs-conid'>FlippedSeal</span> <span class='hs-varid'>p'</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>FlippedSeal</span> <span class='hs-layout'>(</span><span class='hs-varid'>p'</span> <span class='hs-varop'>`op`</span> <span class='hs-varid'>q'</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
</pre></body>
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