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<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE CPP #-}</span>
<a name="line-2"></a><span class='hs-comment'>{-# LANGUAGE Rank2Types #-}</span>
<a name="line-3"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ >= 710</span>
<a name="line-4"></a><span class='hs-comment'>{-# LANGUAGE PatternSynonyms #-}</span>
<a name="line-5"></a><span class='hs-comment'>{-# LANGUAGE ViewPatterns #-}</span>
<a name="line-6"></a><span class='hs-cpp'>#endif</span>
<a name="line-7"></a><span class='hs-comment'>--------------------------------------------------------------------------------</span>
<a name="line-8"></a><span class='hs-comment'>-- |</span>
<a name="line-9"></a><span class='hs-comment'>-- Module : Numeric.Lens</span>
<a name="line-10"></a><span class='hs-comment'>-- Copyright : (C) 2012-15 Edward Kmett</span>
<a name="line-11"></a><span class='hs-comment'>-- License : BSD-style (see the file LICENSE)</span>
<a name="line-12"></a><span class='hs-comment'>-- Maintainer : Edward Kmett <ekmett@gmail.com></span>
<a name="line-13"></a><span class='hs-comment'>-- Stability : provisional</span>
<a name="line-14"></a><span class='hs-comment'>-- Portability : portable</span>
<a name="line-15"></a><span class='hs-comment'>-------------------------------------------------------------------------------</span>
<a name="line-16"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Numeric</span><span class='hs-varop'>.</span><span class='hs-conid'>Lens</span>
<a name="line-17"></a> <span class='hs-layout'>(</span> <span class='hs-varid'>base</span>
<a name="line-18"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>integral</span>
<a name="line-19"></a> <span class='hs-comment'>-- * Predefined bases</span>
<a name="line-20"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>binary</span>
<a name="line-21"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>octal</span>
<a name="line-22"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>decimal</span>
<a name="line-23"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>hex</span>
<a name="line-24"></a> <span class='hs-comment'>-- * Arithmetic lenses</span>
<a name="line-25"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>adding</span>
<a name="line-26"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>subtracting</span>
<a name="line-27"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>multiplying</span>
<a name="line-28"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>dividing</span>
<a name="line-29"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>exponentiating</span>
<a name="line-30"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>negated</span>
<a name="line-31"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ >= 710</span>
<a name="line-32"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>pattern</span> <span class='hs-conid'>Integral</span>
<a name="line-33"></a><span class='hs-cpp'>#endif</span>
<a name="line-34"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-35"></a>
<a name="line-36"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Lens</span>
<a name="line-37"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Char</span> <span class='hs-layout'>(</span><span class='hs-varid'>chr</span><span class='hs-layout'>,</span> <span class='hs-varid'>ord</span><span class='hs-layout'>,</span> <span class='hs-varid'>isAsciiLower</span><span class='hs-layout'>,</span> <span class='hs-varid'>isAsciiUpper</span><span class='hs-layout'>,</span> <span class='hs-varid'>isDigit</span><span class='hs-layout'>)</span>
<a name="line-38"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Maybe</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromMaybe</span><span class='hs-layout'>)</span>
<a name="line-39"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Numeric</span> <span class='hs-layout'>(</span><span class='hs-varid'>readInt</span><span class='hs-layout'>,</span> <span class='hs-varid'>showIntAtBase</span><span class='hs-layout'>)</span>
<a name="line-40"></a>
<a name="line-41"></a><span class='hs-comment'>-- $setup</span>
<a name="line-42"></a><span class='hs-comment'>-- >>> :set -XNoOverloadedStrings</span>
<a name="line-43"></a><span class='hs-comment'>-- >>> import Data.Monoid (Sum(..))</span>
<a name="line-44"></a>
<a name="line-45"></a><a name="integral"></a><span class='hs-comment'>-- | This 'Prism' can be used to model the fact that every 'Integral'</span>
<a name="line-46"></a><span class='hs-comment'>-- type is a subset of 'Integer'.</span>
<a name="line-47"></a><span class='hs-comment'>--</span>
<a name="line-48"></a><span class='hs-comment'>-- Embedding through the 'Prism' only succeeds if the 'Integer' would pass</span>
<a name="line-49"></a><span class='hs-comment'>-- through unmodified when re-extracted.</span>
<a name="line-50"></a><span class='hs-definition'>integral</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Integral</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Integral</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Prism</span> <span class='hs-conid'>Integer</span> <span class='hs-conid'>Integer</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span>
<a name="line-51"></a><span class='hs-definition'>integral</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>prism</span> <span class='hs-varid'>toInteger</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span> <span class='hs-varid'>i</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>let</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fromInteger</span> <span class='hs-varid'>i</span> <span class='hs-keyword'>in</span>
<a name="line-52"></a> <span class='hs-keyword'>if</span> <span class='hs-varid'>toInteger</span> <span class='hs-varid'>a</span> <span class='hs-varop'>==</span> <span class='hs-varid'>i</span>
<a name="line-53"></a> <span class='hs-keyword'>then</span> <span class='hs-conid'>Right</span> <span class='hs-varid'>a</span>
<a name="line-54"></a> <span class='hs-keyword'>else</span> <span class='hs-conid'>Left</span> <span class='hs-varid'>i</span>
<a name="line-55"></a>
<a name="line-56"></a><span class='hs-cpp'>#if __GLASGOW_HASKELL__ >= 710</span>
<a name="line-57"></a><a name="pattern"></a><span class='hs-definition'>pattern</span> <span class='hs-conid'>Integral</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'><-</span> <span class='hs-layout'>(</span><span class='hs-varid'>preview</span> <span class='hs-varid'>integral</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Just</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-58"></a> <span class='hs-conid'>Integral</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>review</span> <span class='hs-varid'>integral</span> <span class='hs-varid'>a</span>
<a name="line-59"></a><span class='hs-cpp'>#endif</span>
<a name="line-60"></a>
<a name="line-61"></a><a name="base"></a><span class='hs-comment'>-- | A prism that shows and reads integers in base-2 through base-36</span>
<a name="line-62"></a><span class='hs-comment'>--</span>
<a name="line-63"></a><span class='hs-comment'>-- Note: This is an improper prism, since leading 0s are stripped when reading.</span>
<a name="line-64"></a><span class='hs-comment'>--</span>
<a name="line-65"></a><span class='hs-comment'>-- >>> "100" ^? base 16</span>
<a name="line-66"></a><span class='hs-comment'>-- Just 256</span>
<a name="line-67"></a><span class='hs-comment'>--</span>
<a name="line-68"></a><span class='hs-comment'>-- >>> 1767707668033969 ^. re (base 36)</span>
<a name="line-69"></a><span class='hs-comment'>-- "helloworld"</span>
<a name="line-70"></a><span class='hs-definition'>base</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Integral</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Int</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Prism'</span> <span class='hs-conid'>String</span> <span class='hs-varid'>a</span>
<a name="line-71"></a><span class='hs-definition'>base</span> <span class='hs-varid'>b</span>
<a name="line-72"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>b</span> <span class='hs-varop'><</span> <span class='hs-num'>2</span> <span class='hs-varop'>||</span> <span class='hs-varid'>b</span> <span class='hs-varop'>></span> <span class='hs-num'>36</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>error</span> <span class='hs-layout'>(</span><span class='hs-str'>"base: Invalid base "</span> <span class='hs-varop'>++</span> <span class='hs-varid'>show</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</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-varid'>prism</span> <span class='hs-varid'>intShow</span> <span class='hs-varid'>intRead</span>
<a name="line-74"></a> <span class='hs-keyword'>where</span>
<a name="line-75"></a> <span class='hs-varid'>intShow</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>showSigned'</span> <span class='hs-layout'>(</span><span class='hs-varid'>showIntAtBase</span> <span class='hs-layout'>(</span><span class='hs-varid'>toInteger</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-varid'>intToDigit'</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>toInteger</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-str'>""</span>
<a name="line-76"></a>
<a name="line-77"></a> <span class='hs-varid'>intRead</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=</span>
<a name="line-78"></a> <span class='hs-keyword'>case</span> <span class='hs-varid'>readSigned'</span> <span class='hs-layout'>(</span><span class='hs-varid'>readInt</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromIntegral</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>isDigit'</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-varid'>digitToInt'</span><span class='hs-layout'>)</span> <span class='hs-varid'>s</span> <span class='hs-keyword'>of</span>
<a name="line-79"></a> <span class='hs-keyglyph'>[</span><span class='hs-layout'>(</span><span class='hs-varid'>n</span><span class='hs-layout'>,</span><span class='hs-str'>""</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Right</span> <span class='hs-varid'>n</span>
<a name="line-80"></a> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Left</span> <span class='hs-varid'>s</span>
<a name="line-81"></a><span class='hs-comment'>{-# INLINE base #-}</span>
<a name="line-82"></a>
<a name="line-83"></a><a name="intToDigit'"></a><span class='hs-comment'>-- | Like 'Data.Char.intToDigit', but handles up to base-36</span>
<a name="line-84"></a><span class='hs-definition'>intToDigit'</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Int</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Char</span>
<a name="line-85"></a><span class='hs-definition'>intToDigit'</span> <span class='hs-varid'>i</span>
<a name="line-86"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>i</span> <span class='hs-varop'>>=</span> <span class='hs-num'>0</span> <span class='hs-varop'>&&</span> <span class='hs-varid'>i</span> <span class='hs-varop'><</span> <span class='hs-num'>10</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>chr</span> <span class='hs-layout'>(</span><span class='hs-varid'>ord</span> <span class='hs-chr'>'0'</span> <span class='hs-varop'>+</span> <span class='hs-varid'>i</span><span class='hs-layout'>)</span>
<a name="line-87"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>i</span> <span class='hs-varop'>>=</span> <span class='hs-num'>10</span> <span class='hs-varop'>&&</span> <span class='hs-varid'>i</span> <span class='hs-varop'><</span> <span class='hs-num'>36</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>chr</span> <span class='hs-layout'>(</span><span class='hs-varid'>ord</span> <span class='hs-chr'>'a'</span> <span class='hs-varop'>+</span> <span class='hs-varid'>i</span> <span class='hs-comment'>-</span> <span class='hs-num'>10</span><span class='hs-layout'>)</span>
<a name="line-88"></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-layout'>(</span><span class='hs-str'>"intToDigit': Invalid int "</span> <span class='hs-varop'>++</span> <span class='hs-varid'>show</span> <span class='hs-varid'>i</span><span class='hs-layout'>)</span>
<a name="line-89"></a>
<a name="line-90"></a><a name="digitToInt'"></a><span class='hs-comment'>-- | Like 'Data.Char.digitToInt', but handles up to base-36</span>
<a name="line-91"></a><span class='hs-definition'>digitToInt'</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Char</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Int</span>
<a name="line-92"></a><span class='hs-definition'>digitToInt'</span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fromMaybe</span> <span class='hs-layout'>(</span><span class='hs-varid'>error</span> <span class='hs-layout'>(</span><span class='hs-str'>"digitToInt': Invalid digit "</span> <span class='hs-varop'>++</span> <span class='hs-varid'>show</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-93"></a> <span class='hs-layout'>(</span><span class='hs-varid'>digitToIntMay</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span>
<a name="line-94"></a>
<a name="line-95"></a><a name="digitToIntMay"></a><span class='hs-comment'>-- | A safe variant of 'digitToInt''</span>
<a name="line-96"></a><span class='hs-definition'>digitToIntMay</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Char</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Maybe</span> <span class='hs-conid'>Int</span>
<a name="line-97"></a><span class='hs-definition'>digitToIntMay</span> <span class='hs-varid'>c</span>
<a name="line-98"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>isDigit</span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Just</span> <span class='hs-layout'>(</span><span class='hs-varid'>ord</span> <span class='hs-varid'>c</span> <span class='hs-comment'>-</span> <span class='hs-varid'>ord</span> <span class='hs-chr'>'0'</span><span class='hs-layout'>)</span>
<a name="line-99"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>isAsciiLower</span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Just</span> <span class='hs-layout'>(</span><span class='hs-varid'>ord</span> <span class='hs-varid'>c</span> <span class='hs-comment'>-</span> <span class='hs-varid'>ord</span> <span class='hs-chr'>'a'</span> <span class='hs-varop'>+</span> <span class='hs-num'>10</span><span class='hs-layout'>)</span>
<a name="line-100"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>isAsciiUpper</span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Just</span> <span class='hs-layout'>(</span><span class='hs-varid'>ord</span> <span class='hs-varid'>c</span> <span class='hs-comment'>-</span> <span class='hs-varid'>ord</span> <span class='hs-chr'>'A'</span> <span class='hs-varop'>+</span> <span class='hs-num'>10</span><span class='hs-layout'>)</span>
<a name="line-101"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Nothing</span>
<a name="line-102"></a>
<a name="line-103"></a><a name="isDigit'"></a><span class='hs-comment'>-- | Select digits that fall into the given base</span>
<a name="line-104"></a><span class='hs-definition'>isDigit'</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Int</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Char</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-105"></a><span class='hs-definition'>isDigit'</span> <span class='hs-varid'>b</span> <span class='hs-varid'>c</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>digitToIntMay</span> <span class='hs-varid'>c</span> <span class='hs-keyword'>of</span>
<a name="line-106"></a> <span class='hs-conid'>Just</span> <span class='hs-varid'>i</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>i</span> <span class='hs-varop'><</span> <span class='hs-varid'>b</span>
<a name="line-107"></a> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>False</span>
<a name="line-108"></a>
<a name="line-109"></a><a name="showSigned'"></a><span class='hs-comment'>-- | A simpler variant of 'Numeric.showSigned' that only prepends a dash and</span>
<a name="line-110"></a><span class='hs-comment'>-- doesn't know about parentheses</span>
<a name="line-111"></a><span class='hs-definition'>showSigned'</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Real</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>ShowS</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>ShowS</span>
<a name="line-112"></a><span class='hs-definition'>showSigned'</span> <span class='hs-varid'>f</span> <span class='hs-varid'>n</span>
<a name="line-113"></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-varid'>showChar</span> <span class='hs-chr'>'-'</span> <span class='hs-varop'>.</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-varid'>negate</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-114"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varid'>n</span>
<a name="line-115"></a>
<a name="line-116"></a><a name="readSigned'"></a><span class='hs-comment'>-- | A simpler variant of 'Numeric.readSigned' that supports any base, only</span>
<a name="line-117"></a><span class='hs-comment'>-- recognizes an initial dash and doesn't know about parentheses</span>
<a name="line-118"></a><span class='hs-definition'>readSigned'</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Real</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>ReadS</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>ReadS</span> <span class='hs-varid'>a</span>
<a name="line-119"></a><span class='hs-definition'>readSigned'</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-chr'>'-'</span><span class='hs-conop'>:</span><span class='hs-varid'>xs</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varid'>xs</span> <span class='hs-varop'>&</span> <span class='hs-varid'>mapped</span> <span class='hs-varop'>.</span> <span class='hs-sel'>_1</span> <span class='hs-varop'>%~</span> <span class='hs-varid'>negate</span>
<a name="line-120"></a><span class='hs-definition'>readSigned'</span> <span class='hs-varid'>f</span> <span class='hs-varid'>xs</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>f</span> <span class='hs-varid'>xs</span>
<a name="line-121"></a>
<a name="line-122"></a><a name="binary"></a><span class='hs-comment'>-- | @'binary' = 'base' 2@</span>
<a name="line-123"></a><span class='hs-definition'>binary</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Integral</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Prism'</span> <span class='hs-conid'>String</span> <span class='hs-varid'>a</span>
<a name="line-124"></a><span class='hs-definition'>binary</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>base</span> <span class='hs-num'>2</span>
<a name="line-125"></a>
<a name="line-126"></a><a name="octal"></a><span class='hs-comment'>-- | @'octal' = 'base' 8@</span>
<a name="line-127"></a><span class='hs-definition'>octal</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Integral</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Prism'</span> <span class='hs-conid'>String</span> <span class='hs-varid'>a</span>
<a name="line-128"></a><span class='hs-definition'>octal</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>base</span> <span class='hs-num'>8</span>
<a name="line-129"></a>
<a name="line-130"></a><a name="decimal"></a><span class='hs-comment'>-- | @'decimal' = 'base' 10@</span>
<a name="line-131"></a><span class='hs-definition'>decimal</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Integral</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Prism'</span> <span class='hs-conid'>String</span> <span class='hs-varid'>a</span>
<a name="line-132"></a><span class='hs-definition'>decimal</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>base</span> <span class='hs-num'>10</span>
<a name="line-133"></a>
<a name="line-134"></a><a name="hex"></a><span class='hs-comment'>-- | @'hex' = 'base' 16@</span>
<a name="line-135"></a><span class='hs-definition'>hex</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Integral</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Prism'</span> <span class='hs-conid'>String</span> <span class='hs-varid'>a</span>
<a name="line-136"></a><span class='hs-definition'>hex</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>base</span> <span class='hs-num'>16</span>
<a name="line-137"></a>
<a name="line-138"></a><a name="adding"></a><span class='hs-comment'>-- | @'adding' n = 'iso' (+n) (subtract n)@</span>
<a name="line-139"></a><span class='hs-comment'>--</span>
<a name="line-140"></a><span class='hs-comment'>-- >>> [1..3]^..traverse.adding 1000</span>
<a name="line-141"></a><span class='hs-comment'>-- [1001,1002,1003]</span>
<a name="line-142"></a><span class='hs-definition'>adding</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Num</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Iso'</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span>
<a name="line-143"></a><span class='hs-definition'>adding</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iso</span> <span class='hs-layout'>(</span><span class='hs-varop'>+</span><span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>subtract</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-144"></a>
<a name="line-145"></a><a name="subtracting"></a><span class='hs-comment'>-- | @</span>
<a name="line-146"></a><span class='hs-comment'>-- 'subtracting' n = 'iso' (subtract n) ((+n)</span>
<a name="line-147"></a><span class='hs-comment'>-- 'subtracting' n = 'from' ('adding' n)</span>
<a name="line-148"></a><span class='hs-comment'>-- @</span>
<a name="line-149"></a><span class='hs-definition'>subtracting</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Num</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Iso'</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span>
<a name="line-150"></a><span class='hs-definition'>subtracting</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iso</span> <span class='hs-layout'>(</span><span class='hs-varid'>subtract</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varop'>+</span><span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-151"></a>
<a name="line-152"></a><a name="multiplying"></a><span class='hs-comment'>-- | @'multiplying' n = iso (*n) (/n)@</span>
<a name="line-153"></a><span class='hs-comment'>--</span>
<a name="line-154"></a><span class='hs-comment'>-- Note: This errors for n = 0</span>
<a name="line-155"></a><span class='hs-comment'>--</span>
<a name="line-156"></a><span class='hs-comment'>-- >>> 5 & multiplying 1000 +~ 3</span>
<a name="line-157"></a><span class='hs-comment'>-- 5.003</span>
<a name="line-158"></a><span class='hs-comment'>--</span>
<a name="line-159"></a><span class='hs-comment'>-- >>> let fahrenheit = multiplying (9/5).adding 32 in 230^.from fahrenheit</span>
<a name="line-160"></a><span class='hs-comment'>-- 110.0</span>
<a name="line-161"></a><span class='hs-definition'>multiplying</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Fractional</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Eq</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Iso'</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span>
<a name="line-162"></a><span class='hs-definition'>multiplying</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>error</span> <span class='hs-str'>"Numeric.Lens.multiplying: factor 0"</span>
<a name="line-163"></a><span class='hs-definition'>multiplying</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iso</span> <span class='hs-layout'>(</span><span class='hs-varop'>*</span><span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varop'>/</span><span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-164"></a>
<a name="line-165"></a><a name="dividing"></a><span class='hs-comment'>-- | @</span>
<a name="line-166"></a><span class='hs-comment'>-- 'dividing' n = 'iso' (/n) (*n)</span>
<a name="line-167"></a><span class='hs-comment'>-- 'dividing' n = 'from' ('multiplying' n)@</span>
<a name="line-168"></a><span class='hs-comment'>--</span>
<a name="line-169"></a><span class='hs-comment'>-- Note: This errors for n = 0</span>
<a name="line-170"></a><span class='hs-definition'>dividing</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Fractional</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Eq</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Iso'</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span>
<a name="line-171"></a><span class='hs-definition'>dividing</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>error</span> <span class='hs-str'>"Numeric.Lens.dividing: divisor 0"</span>
<a name="line-172"></a><span class='hs-definition'>dividing</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iso</span> <span class='hs-layout'>(</span><span class='hs-varop'>/</span><span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varop'>*</span><span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-173"></a>
<a name="line-174"></a><a name="exponentiating"></a><span class='hs-comment'>-- | @'exponentiating' n = 'iso' (**n) (**recip n)@</span>
<a name="line-175"></a><span class='hs-comment'>--</span>
<a name="line-176"></a><span class='hs-comment'>-- Note: This errors for n = 0</span>
<a name="line-177"></a><span class='hs-comment'>--</span>
<a name="line-178"></a><span class='hs-comment'>-- >>> au (_Wrapping Sum . from (exponentiating 2)) (foldMapOf each) (3,4) == 5</span>
<a name="line-179"></a><span class='hs-comment'>-- True</span>
<a name="line-180"></a><span class='hs-definition'>exponentiating</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Floating</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Eq</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Iso'</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span>
<a name="line-181"></a><span class='hs-definition'>exponentiating</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>error</span> <span class='hs-str'>"Numeric.Lens.exponentiating: exponent 0"</span>
<a name="line-182"></a><span class='hs-definition'>exponentiating</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iso</span> <span class='hs-layout'>(</span><span class='hs-varop'>**</span><span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varop'>**</span><span class='hs-varid'>recip</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-183"></a>
<a name="line-184"></a>
<a name="line-185"></a><a name="negated"></a><span class='hs-comment'>-- | @'negated' = 'iso' 'negate' 'negate'@</span>
<a name="line-186"></a><span class='hs-comment'>--</span>
<a name="line-187"></a><span class='hs-comment'>-- >>> au (_Wrapping Sum . negated) (foldMapOf each) (3,4) == 7</span>
<a name="line-188"></a><span class='hs-comment'>-- True</span>
<a name="line-189"></a><span class='hs-comment'>--</span>
<a name="line-190"></a><span class='hs-comment'>-- >>> au (_Wrapping Sum) (foldMapOf (each.negated)) (3,4) == -7</span>
<a name="line-191"></a><span class='hs-comment'>-- True</span>
<a name="line-192"></a><span class='hs-definition'>negated</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Num</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Iso'</span> <span class='hs-varid'>a</span> <span class='hs-varid'>a</span>
<a name="line-193"></a><span class='hs-definition'>negated</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>iso</span> <span class='hs-varid'>negate</span> <span class='hs-varid'>negate</span>
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