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<title>src/Data/TypeLevel/Num/Reps.hs</title>
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<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE EmptyDataDecls, TypeOperators, DeriveDataTypeable,
<a name="line-2"></a> ScopedTypeVariables, TemplateHaskell #-}</span>
<a name="line-3"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-4"></a><span class='hs-comment'>-- |</span>
<a name="line-5"></a><span class='hs-comment'>-- Module : Data.TypeLevel.Num.Reps</span>
<a name="line-6"></a><span class='hs-comment'>-- Copyright : (c) 2008 Alfonso Acosta, Oleg Kiselyov, Wolfgang Jeltsch</span>
<a name="line-7"></a><span class='hs-comment'>-- and KTH's SAM group </span>
<a name="line-8"></a><span class='hs-comment'>-- License : BSD-style (see the file LICENSE)</span>
<a name="line-9"></a><span class='hs-comment'>-- </span>
<a name="line-10"></a><span class='hs-comment'>-- Maintainer : alfonso.acosta@gmail.com</span>
<a name="line-11"></a><span class='hs-comment'>-- Stability : experimental</span>
<a name="line-12"></a><span class='hs-comment'>-- Portability : non-portable (TypeOperators)</span>
<a name="line-13"></a><span class='hs-comment'>--</span>
<a name="line-14"></a><span class='hs-comment'>-- Type-level numerical representations. Currently, only decimals are </span>
<a name="line-15"></a><span class='hs-comment'>-- supported.</span>
<a name="line-16"></a><span class='hs-comment'>-- </span>
<a name="line-17"></a><span class='hs-comment'>----------------------------------------------------------------------------</span>
<a name="line-18"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>TypeLevel</span><span class='hs-varop'>.</span><span class='hs-conid'>Num</span><span class='hs-varop'>.</span><span class='hs-conid'>Reps</span> <span class='hs-layout'>(</span>
<a name="line-19"></a> <span class='hs-comment'>-- * Decimal representation</span>
<a name="line-20"></a> <span class='hs-comment'>-- $decdescription</span>
<a name="line-21"></a> <span class='hs-comment'>-- ** Digits</span>
<a name="line-22"></a> <span class='hs-conid'>D0</span><span class='hs-layout'>,</span> <span class='hs-conid'>D1</span><span class='hs-layout'>,</span> <span class='hs-conid'>D2</span><span class='hs-layout'>,</span> <span class='hs-conid'>D3</span><span class='hs-layout'>,</span> <span class='hs-conid'>D4</span><span class='hs-layout'>,</span> <span class='hs-conid'>D5</span><span class='hs-layout'>,</span> <span class='hs-conid'>D6</span><span class='hs-layout'>,</span> <span class='hs-conid'>D7</span><span class='hs-layout'>,</span> <span class='hs-conid'>D8</span><span class='hs-layout'>,</span> <span class='hs-conid'>D9</span><span class='hs-layout'>,</span>
<a name="line-23"></a> <span class='hs-comment'>-- ** Connective</span>
<a name="line-24"></a> <span class='hs-layout'>(</span><span class='hs-conop'>:*</span><span class='hs-layout'>)</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span>
<a name="line-25"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-26"></a>
<a name="line-27"></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-28"></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><span class='hs-varop'>.</span><span class='hs-conid'>Syntax</span> <span class='hs-layout'>(</span><span class='hs-conid'>Lift</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-29"></a>
<a name="line-30"></a><span class='hs-comment'>-------------------------</span>
<a name="line-31"></a><span class='hs-comment'>-- Decimal Representation</span>
<a name="line-32"></a><span class='hs-comment'>-------------------------</span>
<a name="line-33"></a>
<a name="line-34"></a><span class='hs-comment'>-- $decdescription </span>
<a name="line-35"></a><span class='hs-comment'>-- Decimals are represented using a different type (@Dx@) for each digit and a </span>
<a name="line-36"></a><span class='hs-comment'>-- binary infix connective (@:*@) to enable forming arbitrary precision </span>
<a name="line-37"></a><span class='hs-comment'>-- multidigit numbers. For example @D0@ represents number 0, @D4 :* D2@ </span>
<a name="line-38"></a><span class='hs-comment'>-- represents number 42, @D1 :* D0 :* D0@ represents 100, etc ... Obviously, </span>
<a name="line-39"></a><span class='hs-comment'>-- negative numbers cannot be represented.</span>
<a name="line-40"></a>
<a name="line-41"></a><a name="D0"></a><span class='hs-comment'>-- | Decimal digit zero</span>
<a name="line-42"></a><a name="D0"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>D0</span> <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Typeable</span>
<a name="line-43"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Show</span> <span class='hs-conid'>D0</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"</span>
<a name="line-44"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Lift</span> <span class='hs-conid'>D0</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>lift</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-keyglyph'>|</span> <span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>D0</span> <span class='hs-keyglyph'>|</span><span class='hs-keyglyph'>]</span>
<a name="line-45"></a><a name="D1"></a><span class='hs-comment'>-- | Decimal digit one</span>
<a name="line-46"></a><a name="D1"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>D1</span> <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Typeable</span>
<a name="line-47"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Show</span> <span class='hs-conid'>D1</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'>"1"</span>
<a name="line-48"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Lift</span> <span class='hs-conid'>D1</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>lift</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-keyglyph'>|</span> <span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>D1</span> <span class='hs-keyglyph'>|</span><span class='hs-keyglyph'>]</span>
<a name="line-49"></a><a name="D2"></a><span class='hs-comment'>-- | Decimal digit two</span>
<a name="line-50"></a><a name="D2"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>D2</span> <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Typeable</span>
<a name="line-51"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Show</span> <span class='hs-conid'>D2</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'>"2"</span>
<a name="line-52"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Lift</span> <span class='hs-conid'>D2</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>lift</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-keyglyph'>|</span> <span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>D2</span> <span class='hs-keyglyph'>|</span><span class='hs-keyglyph'>]</span>
<a name="line-53"></a><a name="D3"></a><span class='hs-comment'>-- | Decimal digit three </span>
<a name="line-54"></a><a name="D3"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>D3</span> <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Typeable</span>
<a name="line-55"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Show</span> <span class='hs-conid'>D3</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'>"3"</span>
<a name="line-56"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Lift</span> <span class='hs-conid'>D3</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>lift</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-keyglyph'>|</span> <span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>D3</span> <span class='hs-keyglyph'>|</span><span class='hs-keyglyph'>]</span>
<a name="line-57"></a><a name="D4"></a><span class='hs-comment'>-- | Decimal digit four </span>
<a name="line-58"></a><a name="D4"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>D4</span> <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Typeable</span>
<a name="line-59"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Show</span> <span class='hs-conid'>D4</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'>"4"</span>
<a name="line-60"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Lift</span> <span class='hs-conid'>D4</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>lift</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-keyglyph'>|</span> <span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>D4</span> <span class='hs-keyglyph'>|</span><span class='hs-keyglyph'>]</span>
<a name="line-61"></a><a name="D5"></a><span class='hs-comment'>-- | Decimal digit five</span>
<a name="line-62"></a><a name="D5"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>D5</span> <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Typeable</span>
<a name="line-63"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Show</span> <span class='hs-conid'>D5</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'>"5"</span>
<a name="line-64"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Lift</span> <span class='hs-conid'>D5</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>lift</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-keyglyph'>|</span> <span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>D5</span> <span class='hs-keyglyph'>|</span><span class='hs-keyglyph'>]</span>
<a name="line-65"></a><a name="D6"></a><span class='hs-comment'>-- | Decimal digit six</span>
<a name="line-66"></a><a name="D6"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>D6</span> <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Typeable</span>
<a name="line-67"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Lift</span> <span class='hs-conid'>D6</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>lift</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-keyglyph'>|</span> <span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>D6</span> <span class='hs-keyglyph'>|</span><span class='hs-keyglyph'>]</span>
<a name="line-68"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Show</span> <span class='hs-conid'>D6</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'>"6"</span>
<a name="line-69"></a><a name="D7"></a><span class='hs-comment'>-- | Decimal digit seven</span>
<a name="line-70"></a><a name="D7"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>D7</span> <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Typeable</span>
<a name="line-71"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Show</span> <span class='hs-conid'>D7</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'>"7"</span>
<a name="line-72"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Lift</span> <span class='hs-conid'>D7</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>lift</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-keyglyph'>|</span> <span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>D7</span> <span class='hs-keyglyph'>|</span><span class='hs-keyglyph'>]</span>
<a name="line-73"></a><a name="D8"></a><span class='hs-comment'>-- | Decimal digit eight</span>
<a name="line-74"></a><a name="D8"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>D8</span> <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Typeable</span>
<a name="line-75"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Show</span> <span class='hs-conid'>D8</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'>"8"</span>
<a name="line-76"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Lift</span> <span class='hs-conid'>D8</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>lift</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-keyglyph'>|</span> <span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>D8</span> <span class='hs-keyglyph'>|</span><span class='hs-keyglyph'>]</span>
<a name="line-77"></a><a name="D9"></a><span class='hs-comment'>-- | Decimal digit nine</span>
<a name="line-78"></a><a name="D9"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>D9</span> <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Typeable</span>
<a name="line-79"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Show</span> <span class='hs-conid'>D9</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'>"9"</span>
<a name="line-80"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Lift</span> <span class='hs-conid'>D9</span> <span class='hs-keyword'>where</span> <span class='hs-varid'>lift</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-keyglyph'>|</span> <span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>D9</span> <span class='hs-keyglyph'>|</span><span class='hs-keyglyph'>]</span>
<a name="line-81"></a>
<a name="line-82"></a><span class='hs-comment'>-- | Connective to glue digits together.</span>
<a name="line-83"></a><span class='hs-comment'>-- For example, @D1 :* D0 :* D0@ represents the decimal number 100</span>
<a name="line-84"></a><span class='hs-keyword'>data</span> <span class='hs-varid'>a</span> <span class='hs-conop'>:*</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>a</span> <span class='hs-conop'>:*</span> <span class='hs-varid'>b</span> <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Typeable</span>
<a name="line-85"></a>
<a name="line-86"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Show</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Show</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Show</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-conop'>:*</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-87"></a> <span class='hs-varid'>show</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>show</span> <span class='hs-layout'>(</span><span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-varop'>++</span> <span class='hs-layout'>(</span><span class='hs-varid'>show</span> <span class='hs-layout'>(</span><span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-88"></a>
<a name="line-89"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Lift</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Lift</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Lift</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-conop'>:*</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-90"></a> <span class='hs-varid'>lift</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-keyglyph'>|</span> <span class='hs-varop'>$</span><span class='hs-layout'>(</span><span class='hs-varid'>lift</span> <span class='hs-layout'>(</span><span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span><span class='hs-varid'>a</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-conop'>:*</span> <span class='hs-varop'>$</span><span class='hs-layout'>(</span><span class='hs-varid'>lift</span> <span class='hs-layout'>(</span><span class='hs-varid'>undefined</span> <span class='hs-keyglyph'>::</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-layout'>)</span> <span class='hs-keyglyph'>|</span><span class='hs-keyglyph'>]</span>
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