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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html>
<head>
<!-- Generated by HsColour, http://code.haskell.org/~malcolm/hscolour/ -->
<title>TypeLevel/Number/Int.hs</title>
<link type='text/css' rel='stylesheet' href='hscolour.css' />
</head>
<body>
<pre><a name="line-1"></a><span class='hs-comment'>{-# OPTIONS_GHC  -fno-warn-orphans #-}</span>
<a name="line-2"></a>
<a name="line-3"></a><span class='hs-comment'>{-# LANGUAGE DeriveDataTypeable    #-}</span>
<a name="line-4"></a><span class='hs-comment'>{-# LANGUAGE GADTs                 #-}</span>
<a name="line-5"></a><span class='hs-comment'>{-# LANGUAGE RankNTypes            #-}</span>
<a name="line-6"></a><span class='hs-comment'>{-# LANGUAGE EmptyDataDecls        #-}</span>
<a name="line-7"></a><span class='hs-comment'>{-# LANGUAGE FlexibleInstances     #-}</span>
<a name="line-8"></a><span class='hs-comment'>{-# LANGUAGE FlexibleContexts      #-}</span>
<a name="line-9"></a><span class='hs-comment'>{-# LANGUAGE UndecidableInstances  #-}</span>
<a name="line-10"></a><span class='hs-comment'>{-# LANGUAGE MultiParamTypeClasses #-}</span>
<a name="line-11"></a><span class='hs-comment'>{-# LANGUAGE TypeFamilies          #-}</span>
<a name="line-12"></a><span class='hs-comment'>{-# LANGUAGE TemplateHaskell       #-}</span>
<a name="line-13"></a><span class='hs-comment'>{-# LANGUAGE ScopedTypeVariables   #-}</span>
<a name="line-14"></a><span class='hs-comment'>-- |</span>
<a name="line-15"></a><span class='hs-comment'>-- Module      : TypeLevel.Number.Int</span>
<a name="line-16"></a><span class='hs-comment'>-- Copyright   : Alexey Khudyakov</span>
<a name="line-17"></a><span class='hs-comment'>-- License     : BSD3-style (see LICENSE)</span>
<a name="line-18"></a><span class='hs-comment'>--</span>
<a name="line-19"></a><span class='hs-comment'>-- Maintainer  : Alexey Khudyakov &lt;alexey.skladnoy@gmail.com&gt;</span>
<a name="line-20"></a><span class='hs-comment'>-- Stability   : unstable</span>
<a name="line-21"></a><span class='hs-comment'>-- Portability : unportable (GHC only)</span>
<a name="line-22"></a><span class='hs-comment'>--</span>
<a name="line-23"></a><span class='hs-comment'>-- Type level signed integer numbers are implemented using balanced</span>
<a name="line-24"></a><span class='hs-comment'>-- ternary encoding much in the same way as natural numbers.</span>
<a name="line-25"></a><span class='hs-comment'>--</span>
<a name="line-26"></a><span class='hs-comment'>-- Currently following operations are supported: Next, Prev, Add, Sub,</span>
<a name="line-27"></a><span class='hs-comment'>-- Mul.</span>
<a name="line-28"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>TypeLevel</span><span class='hs-varop'>.</span><span class='hs-conid'>Number</span><span class='hs-varop'>.</span><span class='hs-conid'>Int</span> <span class='hs-layout'>(</span> <span class='hs-comment'>-- * Integer numbers</span>
<a name="line-29"></a>                          <span class='hs-conid'>ZZ</span>
<a name="line-30"></a>                        <span class='hs-layout'>,</span> <span class='hs-conid'>Dn</span>
<a name="line-31"></a>                        <span class='hs-layout'>,</span> <span class='hs-conid'>D0</span>
<a name="line-32"></a>                        <span class='hs-layout'>,</span> <span class='hs-conid'>D1</span>
<a name="line-33"></a>                        <span class='hs-layout'>,</span> <span class='hs-conid'>IntT</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-34"></a>                          <span class='hs-comment'>-- ** Lifting</span>
<a name="line-35"></a>                        <span class='hs-layout'>,</span> <span class='hs-conid'>SomeInt</span>
<a name="line-36"></a>                        <span class='hs-layout'>,</span> <span class='hs-varid'>withInt</span>
<a name="line-37"></a>                          <span class='hs-comment'>-- * Template haskell utilities</span>
<a name="line-38"></a>                        <span class='hs-layout'>,</span> <span class='hs-varid'>intT</span>
<a name="line-39"></a>                        <span class='hs-layout'>,</span> <span class='hs-keyword'>module</span> <span class='hs-conid'>TypeLevel</span><span class='hs-varop'>.</span><span class='hs-conid'>Number</span><span class='hs-varop'>.</span><span class='hs-conid'>Classes</span>
<a name="line-40"></a>                        <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-41"></a>
<a name="line-42"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Typeable</span> <span class='hs-layout'>(</span><span class='hs-conid'>Typeable</span><span class='hs-layout'>)</span>
<a name="line-43"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Language</span><span class='hs-varop'>.</span><span class='hs-conid'>Haskell</span><span class='hs-varop'>.</span><span class='hs-conid'>TH</span>
<a name="line-44"></a>
<a name="line-45"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>TypeLevel</span><span class='hs-varop'>.</span><span class='hs-conid'>Number</span><span class='hs-varop'>.</span><span class='hs-conid'>Classes</span>
<a name="line-46"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>TypeLevel</span><span class='hs-varop'>.</span><span class='hs-conid'>Number</span><span class='hs-varop'>.</span><span class='hs-conid'>Int</span><span class='hs-varop'>.</span><span class='hs-conid'>Types</span>
<a name="line-47"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>TypeLevel</span><span class='hs-varop'>.</span><span class='hs-conid'>Util</span>
<a name="line-48"></a>
<a name="line-49"></a>
<a name="line-50"></a><a name="splitToTrits"></a><span class='hs-definition'>splitToTrits</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Integer</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Int</span><span class='hs-keyglyph'>]</span>
<a name="line-51"></a><span class='hs-definition'>splitToTrits</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>[]</span>
<a name="line-52"></a><span class='hs-definition'>splitToTrits</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>n</span> <span class='hs-varop'>==</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span>  <span class='hs-num'>0</span> <span class='hs-conop'>:</span> <span class='hs-varid'>splitToTrits</span>  <span class='hs-varid'>rest</span>
<a name="line-53"></a>               <span class='hs-keyglyph'>|</span> <span class='hs-varid'>n</span> <span class='hs-varop'>==</span> <span class='hs-num'>1</span> <span class='hs-keyglyph'>=</span>  <span class='hs-num'>1</span> <span class='hs-conop'>:</span> <span class='hs-varid'>splitToTrits</span>  <span class='hs-varid'>rest</span>
<a name="line-54"></a>               <span class='hs-keyglyph'>|</span> <span class='hs-varid'>n</span> <span class='hs-varop'>==</span> <span class='hs-num'>2</span> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>-</span><span class='hs-num'>1</span> <span class='hs-conop'>:</span> <span class='hs-varid'>splitToTrits</span> <span class='hs-layout'>(</span><span class='hs-varid'>rest</span> <span class='hs-varop'>+</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span>
<a name="line-55"></a>               <span class='hs-keyword'>where</span>
<a name="line-56"></a>                 <span class='hs-layout'>(</span><span class='hs-varid'>rest</span><span class='hs-layout'>,</span><span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>divMod</span> <span class='hs-varid'>x</span> <span class='hs-num'>3</span>
<a name="line-57"></a><span class='hs-definition'>splitToTrits</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>error</span> <span class='hs-str'>"Internal error"</span>
<a name="line-58"></a>
<a name="line-59"></a><a name="intT"></a><span class='hs-comment'>-- | Generate type for integer number.</span>
<a name="line-60"></a><span class='hs-definition'>intT</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Integer</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>TypeQ</span>
<a name="line-61"></a><span class='hs-definition'>intT</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>foldr</span> <span class='hs-varid'>appT</span> <span class='hs-layout'>(</span><span class='hs-varid'>conT</span> <span class='hs-chr'>'</span><span class='hs-chr'>'</span><span class='hs-conid'>ZZ</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span> <span class='hs-varid'>map</span> <span class='hs-varid'>con</span> <span class='hs-varop'>.</span> <span class='hs-varid'>splitToTrits</span>
<a name="line-62"></a>  <span class='hs-keyword'>where</span>
<a name="line-63"></a>    <span class='hs-varid'>con</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>conT</span> <span class='hs-chr'>'</span><span class='hs-chr'>'</span><span class='hs-conid'>Dn</span>
<a name="line-64"></a>    <span class='hs-varid'>con</span>   <span class='hs-num'>0</span>  <span class='hs-keyglyph'>=</span> <span class='hs-varid'>conT</span> <span class='hs-chr'>'</span><span class='hs-chr'>'</span><span class='hs-conid'>D0</span>
<a name="line-65"></a>    <span class='hs-varid'>con</span>   <span class='hs-num'>1</span>  <span class='hs-keyglyph'>=</span> <span class='hs-varid'>conT</span> <span class='hs-chr'>'</span><span class='hs-chr'>'</span><span class='hs-conid'>D1</span>
<a name="line-66"></a>    <span class='hs-varid'>con</span>   <span class='hs-varid'>x</span>  <span class='hs-keyglyph'>=</span> <span class='hs-varid'>error</span> <span class='hs-varop'>$</span> <span class='hs-str'>"Strange trit: "</span> <span class='hs-varop'>++</span> <span class='hs-varid'>show</span> <span class='hs-varid'>x</span>
<a name="line-67"></a>
<a name="line-68"></a><span class='hs-comment'>----------------------------------------------------------------</span>
<a name="line-69"></a><span class='hs-comment'>--</span>
<a name="line-70"></a>
<a name="line-71"></a><span class='hs-comment'>-- | Type class for type level integers. Only numbers without leading</span>
<a name="line-72"></a><span class='hs-comment'>-- zeroes are members of the class.</span>
<a name="line-73"></a><span class='hs-keyword'>class</span> <span class='hs-conid'>IntT</span> <span class='hs-varid'>n</span> <span class='hs-keyword'>where</span>
<a name="line-74"></a>  <span class='hs-comment'>-- | Convert natural number to integral value. It's not checked</span>
<a name="line-75"></a>  <span class='hs-comment'>-- whether value could be represented.</span>
<a name="line-76"></a>  <span class='hs-varid'>toInt</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Integral</span> <span class='hs-varid'>i</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>i</span>
<a name="line-77"></a>
<a name="line-78"></a><a name="instance%20IntT%20ZZ"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>IntT</span>     <span class='hs-conid'>ZZ</span>  <span class='hs-keyword'>where</span> <span class='hs-varid'>toInt</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span>  <span class='hs-num'>0</span>
<a name="line-79"></a><a name="instance%20IntT%20(D1%20ZZ)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>IntT</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-conid'>ZZ</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>toInt</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span>  <span class='hs-num'>1</span>
<a name="line-80"></a><a name="instance%20IntT%20(Dn%20ZZ)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>IntT</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-conid'>ZZ</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>toInt</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>-</span><span class='hs-num'>1</span>
<a name="line-81"></a>
<a name="line-82"></a><a name="instance%20IntT%20(Dn%20(Dn%20n))"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>IntT</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>IntT</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>toInt</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>-</span><span class='hs-num'>1</span> <span class='hs-varop'>+</span> <span class='hs-num'>3</span> <span class='hs-varop'>*</span> <span class='hs-varid'>toInt'</span> <span class='hs-varid'>n</span>
<a name="line-83"></a><a name="instance%20IntT%20(D0%20(Dn%20n))"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>IntT</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>IntT</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>toInt</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span>  <span class='hs-num'>0</span> <span class='hs-varop'>+</span> <span class='hs-num'>3</span> <span class='hs-varop'>*</span> <span class='hs-varid'>toInt'</span> <span class='hs-varid'>n</span>
<a name="line-84"></a><a name="instance%20IntT%20(D1%20(Dn%20n))"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>IntT</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>IntT</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>toInt</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span>  <span class='hs-num'>1</span> <span class='hs-varop'>+</span> <span class='hs-num'>3</span> <span class='hs-varop'>*</span> <span class='hs-varid'>toInt'</span> <span class='hs-varid'>n</span>
<a name="line-85"></a><a name="instance%20IntT%20(Dn%20(D0%20n))"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>IntT</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>IntT</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>toInt</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>-</span><span class='hs-num'>1</span> <span class='hs-varop'>+</span> <span class='hs-num'>3</span> <span class='hs-varop'>*</span> <span class='hs-varid'>toInt'</span> <span class='hs-varid'>n</span>
<a name="line-86"></a><a name="instance%20IntT%20(D0%20(D0%20n))"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>IntT</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>IntT</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>toInt</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span>  <span class='hs-num'>0</span> <span class='hs-varop'>+</span> <span class='hs-num'>3</span> <span class='hs-varop'>*</span> <span class='hs-varid'>toInt'</span> <span class='hs-varid'>n</span>
<a name="line-87"></a><a name="instance%20IntT%20(D1%20(D0%20n))"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>IntT</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>IntT</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>toInt</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span>  <span class='hs-num'>1</span> <span class='hs-varop'>+</span> <span class='hs-num'>3</span> <span class='hs-varop'>*</span> <span class='hs-varid'>toInt'</span> <span class='hs-varid'>n</span>
<a name="line-88"></a><a name="instance%20IntT%20(Dn%20(D1%20n))"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>IntT</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>IntT</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>toInt</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-comment'>-</span><span class='hs-num'>1</span> <span class='hs-varop'>+</span> <span class='hs-num'>3</span> <span class='hs-varop'>*</span> <span class='hs-varid'>toInt'</span> <span class='hs-varid'>n</span>
<a name="line-89"></a><a name="instance%20IntT%20(D0%20(D1%20n))"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>IntT</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>IntT</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>toInt</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span>  <span class='hs-num'>0</span> <span class='hs-varop'>+</span> <span class='hs-num'>3</span> <span class='hs-varop'>*</span> <span class='hs-varid'>toInt'</span> <span class='hs-varid'>n</span>
<a name="line-90"></a><a name="instance%20IntT%20(D1%20(D1%20n))"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>IntT</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>IntT</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>toInt</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span>  <span class='hs-num'>1</span> <span class='hs-varop'>+</span> <span class='hs-num'>3</span> <span class='hs-varop'>*</span> <span class='hs-varid'>toInt'</span> <span class='hs-varid'>n</span>
<a name="line-91"></a>
<a name="line-92"></a><a name="toInt'"></a><span class='hs-definition'>toInt'</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>IntT</span> <span class='hs-varid'>n</span><span class='hs-layout'>,</span> <span class='hs-conid'>Integral</span> <span class='hs-varid'>i</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-varid'>t</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>i</span>
<a name="line-93"></a><span class='hs-definition'>toInt'</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toInt</span> <span class='hs-varop'>.</span> <span class='hs-varid'>cdr</span>
<a name="line-94"></a>
<a name="line-95"></a>
<a name="line-96"></a><a name="instance%20Show%20ZZ"></a><span class='hs-keyword'>instance</span>                <span class='hs-conid'>Show</span>    <span class='hs-conid'>ZZ</span>  <span class='hs-keyword'>where</span> <span class='hs-varid'>show</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-str'>"[0:Z]"</span>
<a name="line-97"></a><a name="instance%20Show%20(Dn%20n)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>IntT</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Show</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>show</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-str'>"["</span><span class='hs-varop'>++</span><span class='hs-varid'>show</span> <span class='hs-layout'>(</span><span class='hs-varid'>toInt</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Integer</span><span class='hs-layout'>)</span><span class='hs-varop'>++</span><span class='hs-str'>":Z]"</span>
<a name="line-98"></a><a name="instance%20Show%20(D0%20n)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>IntT</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Show</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>show</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-str'>"["</span><span class='hs-varop'>++</span><span class='hs-varid'>show</span> <span class='hs-layout'>(</span><span class='hs-varid'>toInt</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Integer</span><span class='hs-layout'>)</span><span class='hs-varop'>++</span><span class='hs-str'>":Z]"</span>
<a name="line-99"></a><a name="instance%20Show%20(D1%20n)"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>IntT</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-conid'>Show</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>show</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-str'>"["</span><span class='hs-varop'>++</span><span class='hs-varid'>show</span> <span class='hs-layout'>(</span><span class='hs-varid'>toInt</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Integer</span><span class='hs-layout'>)</span><span class='hs-varop'>++</span><span class='hs-str'>":Z]"</span>
<a name="line-100"></a>
<a name="line-101"></a>
<a name="line-102"></a><span class='hs-comment'>-- | Some natural number</span>
<a name="line-103"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>SomeInt</span> <span class='hs-keyword'>where</span>
<a name="line-104"></a>  <span class='hs-conid'>SomeInt</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>IntT</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>SomeInt</span>
<a name="line-105"></a>  <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Typeable</span>
<a name="line-106"></a>
<a name="line-107"></a><a name="instance%20Show%20SomeInt"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Show</span> <span class='hs-conid'>SomeInt</span> <span class='hs-keyword'>where</span>
<a name="line-108"></a>  <span class='hs-varid'>showsPrec</span> <span class='hs-varid'>d</span> <span class='hs-layout'>(</span><span class='hs-conid'>SomeInt</span> <span class='hs-varid'>n</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'>&gt;</span> <span class='hs-num'>10</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span>
<a name="line-109"></a>    <span class='hs-varid'>showString</span> <span class='hs-str'>"withInt SomeInt "</span> <span class='hs-varop'>.</span> <span class='hs-varid'>shows</span> <span class='hs-layout'>(</span><span class='hs-varid'>toInt</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Integer</span><span class='hs-layout'>)</span>
<a name="line-110"></a>
<a name="line-111"></a>
<a name="line-112"></a>
<a name="line-113"></a><a name="withInt"></a><span class='hs-comment'>-- | Apply function which could work with any 'Nat' value only know at runtime.</span>
<a name="line-114"></a><span class='hs-definition'>withInt</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyword'>forall</span> <span class='hs-varid'>i</span> <span class='hs-varid'>a</span><span class='hs-varop'>.</span> <span class='hs-layout'>(</span><span class='hs-conid'>Integral</span> <span class='hs-varid'>i</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-layout'>(</span><span class='hs-keyword'>forall</span> <span class='hs-varid'>n</span><span class='hs-varop'>.</span> <span class='hs-conid'>IntT</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>i</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span>
<a name="line-115"></a><span class='hs-definition'>withInt</span> <span class='hs-varid'>f</span> <span class='hs-varid'>i0</span>
<a name="line-116"></a>  <span class='hs-keyglyph'>|</span> <span class='hs-varid'>i0</span> <span class='hs-varop'>==</span> <span class='hs-num'>0</span>   <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>ZZ</span><span class='hs-layout'>)</span>
<a name="line-117"></a>  <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>cont</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromIntegral</span> <span class='hs-varid'>i0</span><span class='hs-layout'>)</span> <span class='hs-varid'>f</span> <span class='hs-varid'>f</span> <span class='hs-varid'>f</span>
<a name="line-118"></a>  <span class='hs-keyword'>where</span>
<a name="line-119"></a>    <span class='hs-varid'>cont</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Integer</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-keyword'>forall</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span><span class='hs-varop'>.</span> <span class='hs-layout'>(</span><span class='hs-conid'>IntT</span> <span class='hs-varid'>n</span><span class='hs-layout'>,</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>~</span> <span class='hs-conid'>Dn</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-120"></a>                    <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-keyword'>forall</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span><span class='hs-varop'>.</span> <span class='hs-layout'>(</span><span class='hs-conid'>IntT</span> <span class='hs-varid'>n</span><span class='hs-layout'>,</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>~</span> <span class='hs-conid'>D0</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-121"></a>                    <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-keyword'>forall</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span><span class='hs-varop'>.</span> <span class='hs-layout'>(</span><span class='hs-conid'>IntT</span> <span class='hs-varid'>n</span><span class='hs-layout'>,</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>~</span> <span class='hs-conid'>D1</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span>
<a name="line-122"></a>    <span class='hs-varid'>cont</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varid'>kN</span> <span class='hs-keyword'>_</span>  <span class='hs-keyword'>_</span>  <span class='hs-keyglyph'>=</span> <span class='hs-varid'>kN</span> <span class='hs-layout'>(</span><span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Dn</span> <span class='hs-conid'>ZZ</span><span class='hs-layout'>)</span>
<a name="line-123"></a>    <span class='hs-varid'>cont</span>   <span class='hs-num'>1</span>  <span class='hs-keyword'>_</span>  <span class='hs-keyword'>_</span>  <span class='hs-varid'>k1</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>k1</span> <span class='hs-layout'>(</span><span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>D1</span> <span class='hs-conid'>ZZ</span><span class='hs-layout'>)</span>
<a name="line-124"></a>    <span class='hs-varid'>cont</span>   <span class='hs-varid'>i</span>  <span class='hs-varid'>kN</span> <span class='hs-varid'>k0</span> <span class='hs-varid'>k1</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>cont</span> <span class='hs-varid'>i'</span> <span class='hs-varid'>kN'</span> <span class='hs-varid'>k0'</span> <span class='hs-varid'>k1'</span>
<a name="line-125"></a>      <span class='hs-keyword'>where</span>
<a name="line-126"></a>        <span class='hs-layout'>(</span><span class='hs-varid'>i'</span><span class='hs-layout'>,</span><span class='hs-varid'>bit</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>divMod</span> <span class='hs-varid'>i</span> <span class='hs-num'>3</span> <span class='hs-keyword'>of</span>
<a name="line-127"></a>                     <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-layout'>,</span><span class='hs-num'>2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-varop'>+</span><span class='hs-num'>1</span><span class='hs-layout'>,</span><span class='hs-comment'>-</span><span class='hs-num'>1</span><span class='hs-layout'>)</span>
<a name="line-128"></a>                     <span class='hs-varid'>x</span>     <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>x</span>
<a name="line-129"></a>        <span class='hs-varid'>kN'</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyword'>forall</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span><span class='hs-varop'>.</span> <span class='hs-layout'>(</span><span class='hs-conid'>IntT</span> <span class='hs-varid'>n</span><span class='hs-layout'>,</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>~</span> <span class='hs-conid'>Dn</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span>
<a name="line-130"></a>        <span class='hs-varid'>kN'</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>bit</span> <span class='hs-varop'>==</span> <span class='hs-comment'>-</span><span class='hs-num'>1</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>kN</span> <span class='hs-layout'>(</span><span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-131"></a>              <span class='hs-keyglyph'>|</span> <span class='hs-varid'>bit</span> <span class='hs-varop'>==</span>  <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>k0</span> <span class='hs-layout'>(</span><span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-132"></a>              <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>k1</span> <span class='hs-layout'>(</span><span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-133"></a>        <span class='hs-varid'>k0'</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyword'>forall</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span><span class='hs-varop'>.</span> <span class='hs-layout'>(</span><span class='hs-conid'>IntT</span> <span class='hs-varid'>n</span><span class='hs-layout'>,</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>~</span> <span class='hs-conid'>D0</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span>
<a name="line-134"></a>        <span class='hs-varid'>k0'</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>bit</span> <span class='hs-varop'>==</span> <span class='hs-comment'>-</span><span class='hs-num'>1</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>kN</span> <span class='hs-layout'>(</span><span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-135"></a>              <span class='hs-keyglyph'>|</span> <span class='hs-varid'>bit</span> <span class='hs-varop'>==</span>  <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>k0</span> <span class='hs-layout'>(</span><span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-136"></a>              <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>k1</span> <span class='hs-layout'>(</span><span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-137"></a>
<a name="line-138"></a>        <span class='hs-varid'>k1'</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyword'>forall</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span><span class='hs-varop'>.</span> <span class='hs-layout'>(</span><span class='hs-conid'>IntT</span> <span class='hs-varid'>n</span><span class='hs-layout'>,</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>~</span> <span class='hs-conid'>D1</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span>
<a name="line-139"></a>        <span class='hs-varid'>k1'</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>bit</span> <span class='hs-varop'>==</span> <span class='hs-comment'>-</span><span class='hs-num'>1</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>kN</span> <span class='hs-layout'>(</span><span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-140"></a>              <span class='hs-keyglyph'>|</span> <span class='hs-varid'>bit</span> <span class='hs-varop'>==</span>  <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>k0</span> <span class='hs-layout'>(</span><span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-141"></a>              <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>k1</span> <span class='hs-layout'>(</span><span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-142"></a>
<a name="line-143"></a><span class='hs-comment'>----------------------------------------------------------------</span>
<a name="line-144"></a><span class='hs-comment'>-- Number normalization</span>
<a name="line-145"></a>
<a name="line-146"></a><a name="AddBit"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>family</span>   <span class='hs-conid'>AddBit</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>::</span> <span class='hs-varop'>*</span>
<a name="line-147"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>AddBit</span>    <span class='hs-conid'>ZZ</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ZZ</span>
<a name="line-148"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>AddBit</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D0</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-149"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>AddBit</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D0</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-150"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>AddBit</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D0</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-151"></a>
<a name="line-152"></a>
<a name="line-153"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Normalized</span>     <span class='hs-conid'>ZZ</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ZZ</span>
<a name="line-154"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Normalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Dn</span>     <span class='hs-layout'>(</span><span class='hs-conid'>Normalized</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-155"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Normalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>AddBit</span> <span class='hs-layout'>(</span><span class='hs-conid'>Normalized</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-156"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Normalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D1</span>     <span class='hs-layout'>(</span><span class='hs-conid'>Normalized</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-157"></a>
<a name="line-158"></a><span class='hs-comment'>----------------------------------------------------------------</span>
<a name="line-159"></a><span class='hs-comment'>-- Next Number</span>
<a name="line-160"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Next</span>     <span class='hs-conid'>ZZ</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D1</span> <span class='hs-conid'>ZZ</span>
<a name="line-161"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Next</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Normalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-162"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Next</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D1</span> <span class='hs-varid'>n</span>
<a name="line-163"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Next</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Normalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-layout'>(</span><span class='hs-conid'>Next</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-164"></a>
<a name="line-165"></a><span class='hs-comment'>----------------------------------------------------------------</span>
<a name="line-166"></a><span class='hs-comment'>-- Previous number</span>
<a name="line-167"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Prev</span>     <span class='hs-conid'>ZZ</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Dn</span> <span class='hs-conid'>ZZ</span>
<a name="line-168"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Prev</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Normalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-layout'>(</span><span class='hs-conid'>Prev</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-169"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Prev</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span>
<a name="line-170"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Prev</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Normalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-171"></a>
<a name="line-172"></a><span class='hs-comment'>----------------------------------------------------------------</span>
<a name="line-173"></a><span class='hs-comment'>-- Negate number</span>
<a name="line-174"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Negate</span>    <span class='hs-conid'>ZZ</span>  <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ZZ</span>
<a name="line-175"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Negate</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D1</span> <span class='hs-layout'>(</span><span class='hs-conid'>Negate</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-176"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Negate</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D0</span> <span class='hs-layout'>(</span><span class='hs-conid'>Negate</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-177"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Negate</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Dn</span> <span class='hs-layout'>(</span><span class='hs-conid'>Negate</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-178"></a>
<a name="line-179"></a>
<a name="line-180"></a><span class='hs-comment'>----------------------------------------------------------------</span>
<a name="line-181"></a><span class='hs-comment'>-- Addition</span>
<a name="line-182"></a>
<a name="line-183"></a><a name="Add'"></a><span class='hs-comment'>-- Type class which actually implement addtition of natural numbers</span>
<a name="line-184"></a><a name="Add'"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>family</span> <span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-varid'>carry</span> <span class='hs-keyglyph'>::</span> <span class='hs-varop'>*</span>
<a name="line-185"></a>
<a name="line-186"></a><a name="CarryN"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>CarryN</span>
<a name="line-187"></a><a name="Carry0"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>Carry0</span>
<a name="line-188"></a><a name="Carry1"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>Carry1</span>
<a name="line-189"></a>
<a name="line-190"></a><span class='hs-comment'>-- Special cases with ZZ</span>
<a name="line-191"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span>     <span class='hs-conid'>ZZ</span>     <span class='hs-conid'>ZZ</span> <span class='hs-conid'>Carry0</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ZZ</span>
<a name="line-192"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span>     <span class='hs-conid'>ZZ</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry0</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-193"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span>     <span class='hs-conid'>ZZ</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry0</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-194"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span>     <span class='hs-conid'>ZZ</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry0</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-195"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>     <span class='hs-conid'>ZZ</span> <span class='hs-conid'>Carry0</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-196"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>     <span class='hs-conid'>ZZ</span> <span class='hs-conid'>Carry0</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-197"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>     <span class='hs-conid'>ZZ</span> <span class='hs-conid'>Carry0</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-198"></a><span class='hs-comment'>--</span>
<a name="line-199"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span>     <span class='hs-conid'>ZZ</span>     <span class='hs-conid'>ZZ</span> <span class='hs-conid'>CarryN</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Dn</span> <span class='hs-conid'>ZZ</span>
<a name="line-200"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span>     <span class='hs-conid'>ZZ</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-conid'>CarryN</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Prev</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-201"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span>     <span class='hs-conid'>ZZ</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-conid'>CarryN</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-202"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span>     <span class='hs-conid'>ZZ</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-conid'>CarryN</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-203"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>     <span class='hs-conid'>ZZ</span> <span class='hs-conid'>CarryN</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Prev</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-204"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>     <span class='hs-conid'>ZZ</span> <span class='hs-conid'>CarryN</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-205"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>     <span class='hs-conid'>ZZ</span> <span class='hs-conid'>CarryN</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-206"></a><span class='hs-comment'>--</span>
<a name="line-207"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span>     <span class='hs-conid'>ZZ</span>     <span class='hs-conid'>ZZ</span> <span class='hs-conid'>Carry1</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D1</span> <span class='hs-conid'>ZZ</span>
<a name="line-208"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span>     <span class='hs-conid'>ZZ</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry1</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-209"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span>     <span class='hs-conid'>ZZ</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry1</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-210"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span>     <span class='hs-conid'>ZZ</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry1</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Next</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-211"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>     <span class='hs-conid'>ZZ</span> <span class='hs-conid'>Carry1</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-212"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>     <span class='hs-conid'>ZZ</span> <span class='hs-conid'>Carry1</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-213"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>     <span class='hs-conid'>ZZ</span> <span class='hs-conid'>Carry1</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Next</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-214"></a>
<a name="line-215"></a><span class='hs-comment'>-- == General recursion ==</span>
<a name="line-216"></a><span class='hs-comment'>-- No carry</span>
<a name="line-217"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry0</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D1</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>CarryN</span><span class='hs-layout'>)</span>
<a name="line-218"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry0</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Dn</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-219"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry0</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D0</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-220"></a><span class='hs-comment'>--</span>
<a name="line-221"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry0</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Dn</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-222"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry0</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D0</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-223"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry0</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D1</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-224"></a><span class='hs-comment'>--</span>
<a name="line-225"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry0</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D0</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-226"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry0</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D1</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-227"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry0</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Dn</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>Carry1</span><span class='hs-layout'>)</span>
<a name="line-228"></a><span class='hs-comment'>-- Carry '-'</span>
<a name="line-229"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>CarryN</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D0</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>CarryN</span><span class='hs-layout'>)</span>
<a name="line-230"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>CarryN</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D1</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>CarryN</span><span class='hs-layout'>)</span>
<a name="line-231"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>CarryN</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Dn</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-232"></a><span class='hs-comment'>--</span>
<a name="line-233"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>CarryN</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D1</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>CarryN</span><span class='hs-layout'>)</span>
<a name="line-234"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>CarryN</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Dn</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-235"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>CarryN</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D0</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-236"></a><span class='hs-comment'>--</span>
<a name="line-237"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>CarryN</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Dn</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-238"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>CarryN</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D0</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-239"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>CarryN</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D1</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-240"></a><span class='hs-comment'>-- Carry '+'</span>
<a name="line-241"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry1</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Dn</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-242"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry1</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D0</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-243"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry1</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D1</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-244"></a><span class='hs-comment'>--</span>
<a name="line-245"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry1</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D0</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-246"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry1</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D1</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-247"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry1</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Dn</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>Carry1</span><span class='hs-layout'>)</span>
<a name="line-248"></a><span class='hs-comment'>--</span>
<a name="line-249"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry1</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D1</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-250"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry1</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Dn</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>Carry1</span><span class='hs-layout'>)</span>
<a name="line-251"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry1</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>D0</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span> <span class='hs-conid'>Carry1</span><span class='hs-layout'>)</span>
<a name="line-252"></a>
<a name="line-253"></a><span class='hs-comment'>-- Instances for AddN</span>
<a name="line-254"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add</span>     <span class='hs-conid'>ZZ</span>     <span class='hs-conid'>ZZ</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ZZ</span>
<a name="line-255"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add</span>     <span class='hs-conid'>ZZ</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Normalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-256"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add</span>     <span class='hs-conid'>ZZ</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Normalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-257"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add</span>     <span class='hs-conid'>ZZ</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Normalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-258"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>     <span class='hs-conid'>ZZ</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Normalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-259"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>     <span class='hs-conid'>ZZ</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Normalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-260"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>     <span class='hs-conid'>ZZ</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Normalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-261"></a><span class='hs-comment'>--</span>
<a name="line-262"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Normalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-263"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Normalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-264"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Normalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-265"></a><span class='hs-comment'>--</span>
<a name="line-266"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Normalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-267"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Normalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-268"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Normalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-269"></a><span class='hs-comment'>--</span>
<a name="line-270"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Normalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-271"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Normalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-272"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Add</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Normalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-273"></a>
<a name="line-274"></a>
<a name="line-275"></a><span class='hs-comment'>----------------------------------------------------------------</span>
<a name="line-276"></a><span class='hs-comment'>-- Subtraction.</span>
<a name="line-277"></a><span class='hs-comment'>--</span>
<a name="line-278"></a><span class='hs-comment'>-- Subtraction is much easier since is ise defined using</span>
<a name="line-279"></a><span class='hs-comment'>-- addition and negation</span>
<a name="line-280"></a>
<a name="line-281"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Sub</span>     <span class='hs-conid'>ZZ</span>     <span class='hs-conid'>ZZ</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ZZ</span>
<a name="line-282"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Sub</span>     <span class='hs-conid'>ZZ</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Negate</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-283"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Sub</span>     <span class='hs-conid'>ZZ</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Negate</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-284"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Sub</span>     <span class='hs-conid'>ZZ</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Negate</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-285"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Sub</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>     <span class='hs-conid'>ZZ</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-286"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Sub</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>     <span class='hs-conid'>ZZ</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-287"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Sub</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>     <span class='hs-conid'>ZZ</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-288"></a>
<a name="line-289"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Sub</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Add</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Negate</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-290"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Sub</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Add</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Negate</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-291"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Sub</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Add</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Negate</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-292"></a><span class='hs-comment'>--</span>
<a name="line-293"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Sub</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Add</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Negate</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-294"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Sub</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Add</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Negate</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-295"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Sub</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Add</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Negate</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-296"></a><span class='hs-comment'>--</span>
<a name="line-297"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Sub</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Add</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Negate</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-298"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Sub</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Add</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Negate</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-299"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Sub</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Add</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Negate</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-300"></a>
<a name="line-301"></a>
<a name="line-302"></a><span class='hs-comment'>----------------------------------------------------------------</span>
<a name="line-303"></a><span class='hs-comment'>-- Multiplication</span>
<a name="line-304"></a>
<a name="line-305"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Mul</span> <span class='hs-varid'>n</span>    <span class='hs-conid'>ZZ</span>  <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ZZ</span>
<a name="line-306"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Mul</span> <span class='hs-varid'>n</span> <span class='hs-layout'>(</span><span class='hs-conid'>Dn</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Normalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span> <span class='hs-layout'>(</span><span class='hs-conid'>Negate</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-layout'>(</span><span class='hs-conid'>Mul</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
<a name="line-307"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Mul</span> <span class='hs-varid'>n</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Normalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-layout'>(</span><span class='hs-conid'>Mul</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-308"></a><span class='hs-keyword'>type</span> <span class='hs-keyword'>instance</span> <span class='hs-conid'>Mul</span> <span class='hs-varid'>n</span> <span class='hs-layout'>(</span><span class='hs-conid'>D1</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Normalized</span> <span class='hs-layout'>(</span><span class='hs-conid'>Add'</span>         <span class='hs-varid'>n</span>  <span class='hs-layout'>(</span><span class='hs-conid'>D0</span> <span class='hs-layout'>(</span><span class='hs-conid'>Mul</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-conid'>Carry0</span><span class='hs-layout'>)</span>
</pre></body>
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