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<pre><a name="line-1"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-2"></a><span class='hs-comment'>-- |</span>
<a name="line-3"></a><span class='hs-comment'>-- Module : Numeric.Natural.Internal</span>
<a name="line-4"></a><span class='hs-comment'>-- Copyright : (C) 2011 Edward Kmett,</span>
<a name="line-5"></a><span class='hs-comment'>-- License : BSD-style (see the file LICENSE)</span>
<a name="line-6"></a><span class='hs-comment'>--</span>
<a name="line-7"></a><span class='hs-comment'>-- Maintainer : Edward Kmett <ekmett@gmail.com></span>
<a name="line-8"></a><span class='hs-comment'>-- Stability : provisional</span>
<a name="line-9"></a><span class='hs-comment'>-- Portability : portable</span>
<a name="line-10"></a><span class='hs-comment'>--</span>
<a name="line-11"></a><span class='hs-comment'>-- This module exposes the potentially unsafe operations that are sometimes</span>
<a name="line-12"></a><span class='hs-comment'>-- needed for efficiency: The Natural data constructor and unsafePred.</span>
<a name="line-13"></a><span class='hs-comment'>--</span>
<a name="line-14"></a><span class='hs-comment'>----------------------------------------------------------------------------</span>
<a name="line-15"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Numeric</span><span class='hs-varop'>.</span><span class='hs-conid'>Natural</span><span class='hs-varop'>.</span><span class='hs-conid'>Internal</span>
<a name="line-16"></a> <span class='hs-layout'>(</span> <span class='hs-conid'>Natural</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-17"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Whole</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-18"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-19"></a>
<a name="line-20"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Word</span>
<a name="line-21"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Bits</span>
<a name="line-22"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Text</span><span class='hs-varop'>.</span><span class='hs-conid'>Read</span>
<a name="line-23"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Ix</span>
<a name="line-24"></a>
<a name="line-25"></a><a name="Natural"></a><span class='hs-keyword'>newtype</span> <span class='hs-conid'>Natural</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-layout'>{</span> <span class='hs-varid'>runNatural</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Integer</span> <span class='hs-layout'>}</span> <span class='hs-keyword'>deriving</span> <span class='hs-layout'>(</span><span class='hs-conid'>Eq</span><span class='hs-layout'>,</span><span class='hs-conid'>Ord</span><span class='hs-layout'>,</span><span class='hs-conid'>Ix</span><span class='hs-layout'>)</span>
<a name="line-26"></a>
<a name="line-27"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Show</span> <span class='hs-conid'>Natural</span> <span class='hs-keyword'>where</span>
<a name="line-28"></a> <span class='hs-varid'>showsPrec</span> <span class='hs-varid'>d</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>showsPrec</span> <span class='hs-varid'>d</span> <span class='hs-varid'>n</span>
<a name="line-29"></a>
<a name="line-30"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Read</span> <span class='hs-conid'>Natural</span> <span class='hs-keyword'>where</span>
<a name="line-31"></a> <span class='hs-varid'>readPrec</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fmap</span> <span class='hs-conid'>Natural</span> <span class='hs-varop'>$</span> <span class='hs-varid'>step</span> <span class='hs-varid'>readPrec</span>
<a name="line-32"></a>
<a name="line-33"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Num</span> <span class='hs-conid'>Natural</span> <span class='hs-keyword'>where</span>
<a name="line-34"></a> <span class='hs-conid'>Natural</span> <span class='hs-varid'>n</span> <span class='hs-varop'>+</span> <span class='hs-conid'>Natural</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span> <span class='hs-varop'>+</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span>
<a name="line-35"></a> <span class='hs-conid'>Natural</span> <span class='hs-varid'>n</span> <span class='hs-varop'>*</span> <span class='hs-conid'>Natural</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span> <span class='hs-varop'>*</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span>
<a name="line-36"></a> <span class='hs-conid'>Natural</span> <span class='hs-varid'>n</span> <span class='hs-comment'>-</span> <span class='hs-conid'>Natural</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>result</span> <span class='hs-varop'><</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>error</span> <span class='hs-str'>"Natural.(-): negative result"</span>
<a name="line-37"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-varid'>result</span>
<a name="line-38"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>result</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>n</span> <span class='hs-comment'>-</span> <span class='hs-varid'>m</span>
<a name="line-39"></a> <span class='hs-varid'>abs</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-varid'>n</span>
<a name="line-40"></a> <span class='hs-varid'>signum</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-layout'>(</span><span class='hs-varid'>signum</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-41"></a> <span class='hs-varid'>fromInteger</span> <span class='hs-varid'>n</span>
<a name="line-42"></a> <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-conid'>Natural</span> <span class='hs-varid'>n</span>
<a name="line-43"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>error</span> <span class='hs-str'>"Natural.fromInteger: negative"</span>
<a name="line-44"></a>
<a name="line-45"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Bits</span> <span class='hs-conid'>Natural</span> <span class='hs-keyword'>where</span>
<a name="line-46"></a> <span class='hs-conid'>Natural</span> <span class='hs-varid'>n</span> <span class='hs-varop'>.&.</span> <span class='hs-conid'>Natural</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span> <span class='hs-varop'>.&.</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span>
<a name="line-47"></a> <span class='hs-conid'>Natural</span> <span class='hs-varid'>n</span> <span class='hs-varop'>.|.</span> <span class='hs-conid'>Natural</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span> <span class='hs-varop'>.|.</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span>
<a name="line-48"></a> <span class='hs-varid'>xor</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-layout'>(</span><span class='hs-varid'>xor</span> <span class='hs-varid'>n</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span>
<a name="line-49"></a> <span class='hs-varid'>complement</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>error</span> <span class='hs-str'>"Bits.complement: Natural complement undefined"</span>
<a name="line-50"></a> <span class='hs-varid'>shift</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-varop'>.</span> <span class='hs-varid'>shift</span> <span class='hs-varid'>n</span>
<a name="line-51"></a> <span class='hs-varid'>rotate</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-varop'>.</span> <span class='hs-varid'>rotate</span> <span class='hs-varid'>n</span>
<a name="line-52"></a> <span class='hs-varid'>bit</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-varop'>.</span> <span class='hs-varid'>bit</span>
<a name="line-53"></a> <span class='hs-varid'>setBit</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-varop'>.</span> <span class='hs-varid'>setBit</span> <span class='hs-varid'>n</span>
<a name="line-54"></a> <span class='hs-varid'>clearBit</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-varop'>.</span> <span class='hs-varid'>clearBit</span> <span class='hs-varid'>n</span>
<a name="line-55"></a> <span class='hs-varid'>complementBit</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-varop'>.</span> <span class='hs-varid'>complementBit</span> <span class='hs-varid'>n</span>
<a name="line-56"></a> <span class='hs-varid'>testBit</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>testBit</span> <span class='hs-varop'>.</span> <span class='hs-varid'>runNatural</span>
<a name="line-57"></a> <span class='hs-varid'>bitSize</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>bitSize</span> <span class='hs-varop'>.</span> <span class='hs-varid'>runNatural</span>
<a name="line-58"></a> <span class='hs-varid'>isSigned</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>False</span>
<a name="line-59"></a> <span class='hs-varid'>shiftL</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-varop'>.</span> <span class='hs-varid'>shiftL</span> <span class='hs-varid'>n</span>
<a name="line-60"></a> <span class='hs-varid'>shiftR</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-varop'>.</span> <span class='hs-varid'>shiftR</span> <span class='hs-varid'>n</span>
<a name="line-61"></a> <span class='hs-varid'>rotateL</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-varop'>.</span> <span class='hs-varid'>rotateL</span> <span class='hs-varid'>n</span>
<a name="line-62"></a> <span class='hs-varid'>rotateR</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-varop'>.</span> <span class='hs-varid'>rotateR</span> <span class='hs-varid'>n</span>
<a name="line-63"></a>
<a name="line-64"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Real</span> <span class='hs-conid'>Natural</span> <span class='hs-keyword'>where</span>
<a name="line-65"></a> <span class='hs-varid'>toRational</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>toRational</span> <span class='hs-varid'>a</span>
<a name="line-66"></a>
<a name="line-67"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Enum</span> <span class='hs-conid'>Natural</span> <span class='hs-keyword'>where</span>
<a name="line-68"></a> <span class='hs-varid'>pred</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-num'>0</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>error</span> <span class='hs-str'>"Natural.pred: 0"</span>
<a name="line-69"></a> <span class='hs-varid'>pred</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-layout'>(</span><span class='hs-varid'>pred</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-70"></a> <span class='hs-varid'>succ</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-layout'>(</span><span class='hs-varid'>succ</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-71"></a> <span class='hs-varid'>fromEnum</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fromEnum</span> <span class='hs-varid'>n</span>
<a name="line-72"></a> <span class='hs-varid'>toEnum</span> <span class='hs-varid'>n</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-varid'>error</span> <span class='hs-str'>"Natural.toEnum: negative"</span>
<a name="line-73"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-layout'>(</span><span class='hs-varid'>toEnum</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-74"></a>
<a name="line-75"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Integral</span> <span class='hs-conid'>Natural</span> <span class='hs-keyword'>where</span>
<a name="line-76"></a> <span class='hs-varid'>quot</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-layout'>(</span><span class='hs-varid'>quot</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-77"></a> <span class='hs-varid'>rem</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-layout'>(</span><span class='hs-varid'>rem</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-78"></a> <span class='hs-varid'>div</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-layout'>(</span><span class='hs-varid'>div</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-79"></a> <span class='hs-varid'>mod</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-layout'>(</span><span class='hs-varid'>mod</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-80"></a> <span class='hs-varid'>divMod</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>q</span><span class='hs-layout'>,</span> <span class='hs-conid'>Natural</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <span class='hs-layout'>(</span><span class='hs-varid'>q</span><span class='hs-layout'>,</span><span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>divMod</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span>
<a name="line-81"></a> <span class='hs-varid'>quotRem</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>q</span><span class='hs-layout'>,</span> <span class='hs-conid'>Natural</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <span class='hs-layout'>(</span><span class='hs-varid'>q</span><span class='hs-layout'>,</span><span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>quotRem</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span>
<a name="line-82"></a> <span class='hs-varid'>toInteger</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>runNatural</span>
<a name="line-83"></a>
<a name="line-84"></a><a name="Whole"></a><span class='hs-comment'>-- | A refinement of Integral to represent types that do not contain negative numbers.</span>
<a name="line-85"></a><a name="Whole"></a><span class='hs-keyword'>class</span> <span class='hs-conid'>Integral</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Whole</span> <span class='hs-varid'>n</span> <span class='hs-keyword'>where</span>
<a name="line-86"></a> <span class='hs-varid'>toNatural</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Natural</span>
<a name="line-87"></a> <span class='hs-varid'>unsafePred</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>n</span>
<a name="line-88"></a>
<a name="line-89"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Whole</span> <span class='hs-conid'>Word</span> <span class='hs-keyword'>where</span>
<a name="line-90"></a> <span class='hs-varid'>toNatural</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-varop'>.</span> <span class='hs-varid'>toInteger</span>
<a name="line-91"></a> <span class='hs-varid'>unsafePred</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>n</span> <span class='hs-comment'>-</span> <span class='hs-num'>1</span>
<a name="line-92"></a>
<a name="line-93"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Whole</span> <span class='hs-conid'>Word8</span> <span class='hs-keyword'>where</span>
<a name="line-94"></a> <span class='hs-varid'>toNatural</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-varop'>.</span> <span class='hs-varid'>toInteger</span>
<a name="line-95"></a> <span class='hs-varid'>unsafePred</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>n</span> <span class='hs-comment'>-</span> <span class='hs-num'>1</span>
<a name="line-96"></a>
<a name="line-97"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Whole</span> <span class='hs-conid'>Word16</span> <span class='hs-keyword'>where</span>
<a name="line-98"></a> <span class='hs-varid'>toNatural</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-varop'>.</span> <span class='hs-varid'>toInteger</span>
<a name="line-99"></a> <span class='hs-varid'>unsafePred</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>n</span> <span class='hs-comment'>-</span> <span class='hs-num'>1</span>
<a name="line-100"></a>
<a name="line-101"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Whole</span> <span class='hs-conid'>Word32</span> <span class='hs-keyword'>where</span>
<a name="line-102"></a> <span class='hs-varid'>toNatural</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-varop'>.</span> <span class='hs-varid'>toInteger</span>
<a name="line-103"></a> <span class='hs-varid'>unsafePred</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>n</span> <span class='hs-comment'>-</span> <span class='hs-num'>1</span>
<a name="line-104"></a>
<a name="line-105"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Whole</span> <span class='hs-conid'>Word64</span> <span class='hs-keyword'>where</span>
<a name="line-106"></a> <span class='hs-varid'>toNatural</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-varop'>.</span> <span class='hs-varid'>toInteger</span>
<a name="line-107"></a> <span class='hs-varid'>unsafePred</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>n</span> <span class='hs-comment'>-</span> <span class='hs-num'>1</span>
<a name="line-108"></a>
<a name="line-109"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Whole</span> <span class='hs-conid'>Natural</span> <span class='hs-keyword'>where</span>
<a name="line-110"></a> <span class='hs-varid'>toNatural</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>id</span>
<a name="line-111"></a> <span class='hs-varid'>unsafePred</span> <span class='hs-layout'>(</span><span class='hs-conid'>Natural</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Natural</span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span> <span class='hs-comment'>-</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span>
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