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Data-Complex-Lens.html
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Data-Complex-Lens.html
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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>src/Data/Complex/Lens.hs</title>
<link type='text/css' rel='stylesheet' href='hscolour.css' />
</head>
<body>
<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE CPP #-}</span>
<a name="line-2"></a><span class='hs-cpp'>#ifndef MIN_VERSION_base</span>
<a name="line-3"></a><span class='hs-cpp'>#define MIN_VERSION_base(x,y,z) 1</span>
<a name="line-4"></a><span class='hs-cpp'>#endif</span>
<a name="line-5"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-6"></a><span class='hs-comment'>-- |</span>
<a name="line-7"></a><span class='hs-comment'>-- Module : Data.Complex.Lens</span>
<a name="line-8"></a><span class='hs-comment'>-- Copyright : (C) 2012 Edward Kmett</span>
<a name="line-9"></a><span class='hs-comment'>-- License : BSD-style (see the file LICENSE)</span>
<a name="line-10"></a><span class='hs-comment'>-- Maintainer : Edward Kmett <ekmett@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 : Rank2Types</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'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Complex</span><span class='hs-varop'>.</span><span class='hs-conid'>Lens</span>
<a name="line-16"></a> <span class='hs-layout'>(</span> <span class='hs-varid'>real</span><span class='hs-layout'>,</span> <span class='hs-varid'>imaginary</span><span class='hs-layout'>,</span> <span class='hs-varid'>polarize</span>
<a name="line-17"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>traverseComplex</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'>Control</span><span class='hs-varop'>.</span><span class='hs-conid'>Applicative</span>
<a name="line-21"></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-22"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Complex</span>
<a name="line-23"></a>
<a name="line-24"></a><span class='hs-comment'>-- | Access the 'realPart' of a 'Complex' number</span>
<a name="line-25"></a><span class='hs-comment'>--</span>
<a name="line-26"></a><span class='hs-comment'>-- >>> (1.0 :+ 0.0)^.real</span>
<a name="line-27"></a><span class='hs-comment'>-- 1.0</span>
<a name="line-28"></a><span class='hs-comment'>--</span>
<a name="line-29"></a><span class='hs-comment'>-- @'real' :: 'Functor' f => (a -> f a) -> 'Complex' a -> f ('Complex' a)@</span>
<a name="line-30"></a><span class='hs-cpp'>#if MIN_VERSION_base(4,4,0)</span>
<a name="line-31"></a><a name="real"></a><span class='hs-definition'>real</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Simple</span> <span class='hs-conid'>Lens</span> <span class='hs-layout'>(</span><span class='hs-conid'>Complex</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span>
<a name="line-32"></a><span class='hs-cpp'>#else</span>
<a name="line-33"></a><span class='hs-definition'>real</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>RealFloat</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Simple</span> <span class='hs-conid'>Lens</span> <span class='hs-layout'>(</span><span class='hs-conid'>Complex</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span>
<a name="line-34"></a><span class='hs-cpp'>#endif</span>
<a name="line-35"></a><span class='hs-definition'>real</span> <span class='hs-varid'>f</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-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conop'>:+</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-varop'><$></span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span>
<a name="line-36"></a>
<a name="line-37"></a><span class='hs-comment'>-- | Access the 'imaginaryPart' of a 'Complex' number</span>
<a name="line-38"></a><span class='hs-comment'>--</span>
<a name="line-39"></a><span class='hs-comment'>-- >>> (0.0 :+ 1.0)^.imaginary</span>
<a name="line-40"></a><span class='hs-comment'>-- 1.0</span>
<a name="line-41"></a><span class='hs-comment'>--</span>
<a name="line-42"></a><span class='hs-comment'>-- @'imaginary' :: 'Functor' f => (a -> f a) -> 'Complex' a -> f ('Complex' a)@</span>
<a name="line-43"></a><span class='hs-cpp'>#if MIN_VERSION_base(4,4,0)</span>
<a name="line-44"></a><a name="imaginary"></a><span class='hs-definition'>imaginary</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Simple</span> <span class='hs-conid'>Lens</span> <span class='hs-layout'>(</span><span class='hs-conid'>Complex</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span>
<a name="line-45"></a><span class='hs-cpp'>#else</span>
<a name="line-46"></a><span class='hs-definition'>imaginary</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>RealFloat</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Simple</span> <span class='hs-conid'>Lens</span> <span class='hs-layout'>(</span><span class='hs-conid'>Complex</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span>
<a name="line-47"></a><span class='hs-cpp'>#endif</span>
<a name="line-48"></a><span class='hs-definition'>imaginary</span> <span class='hs-varid'>f</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-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-conop'>:+</span><span class='hs-layout'>)</span> <span class='hs-varop'><$></span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span>
<a name="line-49"></a>
<a name="line-50"></a><a name="polarize"></a><span class='hs-comment'>-- | This isn't /quite/ a legal lens. Notably the </span>
<a name="line-51"></a><span class='hs-comment'>--</span>
<a name="line-52"></a><span class='hs-comment'>-- @'view' l ('set' l b a) = b@</span>
<a name="line-53"></a><span class='hs-comment'>--</span>
<a name="line-54"></a><span class='hs-comment'>-- law is violated when you set a 'polar' value with 0 'magnitude' and non-zero 'phase'</span>
<a name="line-55"></a><span class='hs-comment'>-- as the 'phase' information is lost. So don't do that!</span>
<a name="line-56"></a><span class='hs-comment'>--</span>
<a name="line-57"></a><span class='hs-comment'>-- Otherwise, this is a perfectly cromulent 'Lens'.</span>
<a name="line-58"></a><span class='hs-definition'>polarize</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>RealFloat</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>RealFloat</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Iso</span> <span class='hs-layout'>(</span><span class='hs-conid'>Complex</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Complex</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span><span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span><span class='hs-layout'>,</span><span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-59"></a><span class='hs-definition'>polarize</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>isos</span> <span class='hs-varid'>polar</span> <span class='hs-layout'>(</span><span class='hs-varid'>uncurry</span> <span class='hs-varid'>mkPolar</span><span class='hs-layout'>)</span>
<a name="line-60"></a> <span class='hs-varid'>polar</span> <span class='hs-layout'>(</span><span class='hs-varid'>uncurry</span> <span class='hs-varid'>mkPolar</span><span class='hs-layout'>)</span>
<a name="line-61"></a>
<a name="line-62"></a><span class='hs-comment'>-- | Traverse both the real and imaginary parts of a 'Complex' number.</span>
<a name="line-63"></a><span class='hs-comment'>--</span>
<a name="line-64"></a><span class='hs-comment'>-- > traverseComplex :: Applicative f => (a -> f b) -> Complex a -> f (Complex b)</span>
<a name="line-65"></a><span class='hs-cpp'>#if MIN_VERSION_base(4,4,0)</span>
<a name="line-66"></a><a name="traverseComplex"></a><span class='hs-definition'>traverseComplex</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Traversal</span> <span class='hs-layout'>(</span><span class='hs-conid'>Complex</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Complex</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span>
<a name="line-67"></a><span class='hs-cpp'>#else</span>
<a name="line-68"></a><span class='hs-definition'>traverseComplex</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>RealFloat</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>RealFloat</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Traversal</span> <span class='hs-layout'>(</span><span class='hs-conid'>Complex</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Complex</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span>
<a name="line-69"></a><span class='hs-cpp'>#endif</span>
<a name="line-70"></a><span class='hs-definition'>traverseComplex</span> <span class='hs-varid'>f</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-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conop'>:+</span><span class='hs-layout'>)</span> <span class='hs-varop'><$></span> <span class='hs-varid'>f</span> <span class='hs-varid'>a</span> <span class='hs-varop'><*></span> <span class='hs-varid'>f</span> <span class='hs-varid'>b</span>
</pre></body>
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