<?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>Data/IntTrie.hs</title> <link type='text/css' rel='stylesheet' href='hscolour.css' /> </head> <body> <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 : Data.IntTrie</span> <a name="line-4"></a><span class='hs-comment'>-- Copyright : (c) Luke Palmer 2010</span> <a name="line-5"></a><span class='hs-comment'>-- License : BSD3</span> <a name="line-6"></a><span class='hs-comment'>--</span> <a name="line-7"></a><span class='hs-comment'>-- Maintainer : Luke Palmer <lrpalmer@gmail.com></span> <a name="line-8"></a><span class='hs-comment'>-- Stability : experimental</span> <a name="line-9"></a><span class='hs-comment'>-- Portability : Haskell 2010</span> <a name="line-10"></a><span class='hs-comment'>--</span> <a name="line-11"></a><span class='hs-comment'>-- Provides a minimal infinite, lazy trie for integral types.</span> <a name="line-12"></a><span class='hs-comment'>-- It intentionally leaves out ideas such as delete and</span> <a name="line-13"></a><span class='hs-comment'>-- emptiness so that it can be used lazily, eg. as the target</span> <a name="line-14"></a><span class='hs-comment'>-- of an infinite foldr. Essentially its purpose is to be an</span> <a name="line-15"></a><span class='hs-comment'>-- efficient implementation of a function from integral type,</span> <a name="line-16"></a><span class='hs-comment'>-- given point-at-a-time modifications.</span> <a name="line-17"></a><span class='hs-comment'>-------------------------------------------------------------</span> <a name="line-18"></a> <a name="line-19"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>IntTrie</span> <a name="line-20"></a> <span class='hs-layout'>(</span> <span class='hs-conid'>IntTrie</span><span class='hs-layout'>,</span> <span class='hs-varid'>identity</span><span class='hs-layout'>,</span> <span class='hs-varid'>apply</span><span class='hs-layout'>,</span> <span class='hs-varid'>modify</span><span class='hs-layout'>,</span> <span class='hs-varid'>modify'</span><span class='hs-layout'>,</span> <span class='hs-varid'>overwrite</span> <span class='hs-layout'>)</span> <a name="line-21"></a><span class='hs-keyword'>where</span> <a name="line-22"></a> <a name="line-23"></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-24"></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-25"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Function</span> <span class='hs-layout'>(</span><span class='hs-varid'>fix</span><span class='hs-layout'>)</span> <a name="line-26"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Monoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>Monoid</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <a name="line-27"></a> <a name="line-28"></a><a name="IntTrie"></a><span class='hs-comment'>-- | A trie from integers to values of type a. </span> <a name="line-29"></a><a name="IntTrie"></a><span class='hs-comment'>-- </span> <a name="line-30"></a><a name="IntTrie"></a><span class='hs-comment'>-- Semantics: [[IntTrie a]] = Integer -> a</span> <a name="line-31"></a><a name="IntTrie"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>IntTrie</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>IntTrie</span> <span class='hs-layout'>(</span><span class='hs-conid'>BitTrie</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-conid'>BitTrie</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-comment'>-- negative, 0, positive</span> <a name="line-32"></a> <a name="line-33"></a><a name="BitTrie"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>BitTrie</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>BitTrie</span> <span class='hs-varid'>a</span> <span class='hs-layout'>(</span><span class='hs-conid'>BitTrie</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>BitTrie</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <a name="line-34"></a> <a name="line-35"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Functor</span> <span class='hs-conid'>BitTrie</span> <span class='hs-keyword'>where</span> <a name="line-36"></a> <span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>BitTrie</span> <span class='hs-varid'>x</span> <span class='hs-varid'>l</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>BitTrie</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>l</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>r</span><span class='hs-layout'>)</span> <a name="line-37"></a> <a name="line-38"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Applicative</span> <span class='hs-conid'>BitTrie</span> <span class='hs-keyword'>where</span> <a name="line-39"></a> <span class='hs-varid'>pure</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fix</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>g</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>BitTrie</span> <span class='hs-varid'>x</span> <span class='hs-varid'>g</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span> <a name="line-40"></a> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>BitTrie</span> <span class='hs-varid'>f</span> <span class='hs-varid'>fl</span> <span class='hs-varid'>fr</span><span class='hs-layout'>)</span> <span class='hs-varop'><*></span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>BitTrie</span> <span class='hs-varid'>x</span> <span class='hs-varid'>xl</span> <span class='hs-varid'>xr</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>BitTrie</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>fl</span> <span class='hs-varop'><*></span> <span class='hs-varid'>xl</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>fr</span> <span class='hs-varop'><*></span> <span class='hs-varid'>xr</span><span class='hs-layout'>)</span> <a name="line-41"></a> <a name="line-42"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Monoid</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Monoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>BitTrie</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <a name="line-43"></a> <span class='hs-varid'>mempty</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pure</span> <span class='hs-varid'>mempty</span> <a name="line-44"></a> <span class='hs-varid'>mappend</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftA2</span> <span class='hs-varid'>mappend</span> <a name="line-45"></a> <a name="line-46"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Functor</span> <span class='hs-conid'>IntTrie</span> <span class='hs-keyword'>where</span> <a name="line-47"></a> <span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>IntTrie</span> <span class='hs-varid'>neg</span> <span class='hs-varid'>z</span> <span class='hs-varid'>pos</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>IntTrie</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>neg</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>z</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>f</span> <span class='hs-varid'>pos</span><span class='hs-layout'>)</span> <a name="line-48"></a> <a name="line-49"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Applicative</span> <span class='hs-conid'>IntTrie</span> <span class='hs-keyword'>where</span> <a name="line-50"></a> <span class='hs-varid'>pure</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>IntTrie</span> <span class='hs-layout'>(</span><span class='hs-varid'>pure</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-varid'>x</span> <span class='hs-layout'>(</span><span class='hs-varid'>pure</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <a name="line-51"></a> <span class='hs-conid'>IntTrie</span> <span class='hs-varid'>fneg</span> <span class='hs-varid'>fz</span> <span class='hs-varid'>fpos</span> <span class='hs-varop'><*></span> <span class='hs-conid'>IntTrie</span> <span class='hs-varid'>xneg</span> <span class='hs-varid'>xz</span> <span class='hs-varid'>xpos</span> <span class='hs-keyglyph'>=</span> <a name="line-52"></a> <span class='hs-conid'>IntTrie</span> <span class='hs-layout'>(</span><span class='hs-varid'>fneg</span> <span class='hs-varop'><*></span> <span class='hs-varid'>xneg</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>fz</span> <span class='hs-varid'>xz</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>fpos</span> <span class='hs-varop'><*></span> <span class='hs-varid'>xpos</span><span class='hs-layout'>)</span> <a name="line-53"></a> <a name="line-54"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Monoid</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Monoid</span> <span class='hs-layout'>(</span><span class='hs-conid'>IntTrie</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span> <a name="line-55"></a> <span class='hs-varid'>mempty</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pure</span> <span class='hs-varid'>mempty</span> <a name="line-56"></a> <span class='hs-varid'>mappend</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>liftA2</span> <span class='hs-varid'>mappend</span> <a name="line-57"></a> <a name="line-58"></a><a name="apply"></a><span class='hs-comment'>-- | Apply the trie to an argument. This is the semantic map.</span> <a name="line-59"></a><span class='hs-definition'>apply</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Ord</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-conid'>Num</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-conid'>Bits</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>IntTrie</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <a name="line-60"></a><span class='hs-definition'>apply</span> <span class='hs-layout'>(</span><span class='hs-conid'>IntTrie</span> <span class='hs-varid'>neg</span> <span class='hs-varid'>z</span> <span class='hs-varid'>pos</span><span class='hs-layout'>)</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <a name="line-61"></a> <span class='hs-keyword'>case</span> <span class='hs-varid'>compare</span> <span class='hs-varid'>x</span> <span class='hs-num'>0</span> <span class='hs-keyword'>of</span> <a name="line-62"></a> <span class='hs-conid'>LT</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>applyPositive</span> <span class='hs-varid'>neg</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-varid'>x</span><span class='hs-layout'>)</span> <a name="line-63"></a> <span class='hs-conid'>EQ</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>z</span> <a name="line-64"></a> <span class='hs-conid'>GT</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>applyPositive</span> <span class='hs-varid'>pos</span> <span class='hs-varid'>x</span> <a name="line-65"></a> <a name="line-66"></a><a name="applyPositive"></a><span class='hs-definition'>applyPositive</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Num</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-conid'>Bits</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>BitTrie</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <a name="line-67"></a><span class='hs-definition'>applyPositive</span> <span class='hs-layout'>(</span><span class='hs-conid'>BitTrie</span> <span class='hs-varid'>one</span> <span class='hs-varid'>even</span> <span class='hs-varid'>odd</span><span class='hs-layout'>)</span> <span class='hs-varid'>x</span> <a name="line-68"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>x</span> <span class='hs-varop'>==</span> <span class='hs-num'>1</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>one</span> <a name="line-69"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>testBit</span> <span class='hs-varid'>x</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>applyPositive</span> <span class='hs-varid'>odd</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'>`shiftR`</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <a name="line-70"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>applyPositive</span> <span class='hs-varid'>even</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'>`shiftR`</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <a name="line-71"></a> <a name="line-72"></a><a name="identity"></a><span class='hs-comment'>-- | The identity trie. </span> <a name="line-73"></a><span class='hs-comment'>--</span> <a name="line-74"></a><span class='hs-comment'>-- > apply identity = id</span> <a name="line-75"></a><span class='hs-definition'>identity</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Num</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Bits</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>IntTrie</span> <span class='hs-varid'>a</span> <a name="line-76"></a><span class='hs-definition'>identity</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>IntTrie</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-varid'>negate</span> <span class='hs-varid'>identityPositive</span><span class='hs-layout'>)</span> <span class='hs-num'>0</span> <span class='hs-varid'>identityPositive</span> <a name="line-77"></a> <a name="line-78"></a><a name="identityPositive"></a><span class='hs-definition'>identityPositive</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Num</span> <span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-conid'>Bits</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>BitTrie</span> <span class='hs-varid'>a</span> <a name="line-79"></a><span class='hs-definition'>identityPositive</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>go</span> <a name="line-80"></a> <span class='hs-keyword'>where</span> <a name="line-81"></a> <span class='hs-varid'>go</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>BitTrie</span> <span class='hs-num'>1</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-varop'>`shiftL`</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varid'>go</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>n</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-varid'>n</span> <span class='hs-varop'>`shiftL`</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varop'>.|.</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varid'>go</span><span class='hs-layout'>)</span> <a name="line-82"></a> <a name="line-83"></a><a name="modify"></a><span class='hs-comment'>-- | Modify the function at one point</span> <a name="line-84"></a><span class='hs-comment'>--</span> <a name="line-85"></a><span class='hs-comment'>-- > apply (modify x f t) i | i == x = f (apply t i)</span> <a name="line-86"></a><span class='hs-comment'>-- > | otherwise = apply t i</span> <a name="line-87"></a><span class='hs-definition'>modify</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Ord</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-conid'>Num</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-conid'>Bits</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>b</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-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>IntTrie</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>IntTrie</span> <span class='hs-varid'>a</span> <a name="line-88"></a><span class='hs-definition'>modify</span> <span class='hs-varid'>x</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>IntTrie</span> <span class='hs-varid'>neg</span> <span class='hs-varid'>z</span> <span class='hs-varid'>pos</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <a name="line-89"></a> <span class='hs-keyword'>case</span> <span class='hs-varid'>compare</span> <span class='hs-varid'>x</span> <span class='hs-num'>0</span> <span class='hs-keyword'>of</span> <a name="line-90"></a> <span class='hs-conid'>LT</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>IntTrie</span> <span class='hs-layout'>(</span><span class='hs-varid'>modifyPositive</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-varid'>f</span> <span class='hs-varid'>neg</span><span class='hs-layout'>)</span> <span class='hs-varid'>z</span> <span class='hs-varid'>pos</span> <a name="line-91"></a> <span class='hs-conid'>EQ</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>IntTrie</span> <span class='hs-varid'>neg</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>z</span><span class='hs-layout'>)</span> <span class='hs-varid'>pos</span> <a name="line-92"></a> <span class='hs-conid'>GT</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>IntTrie</span> <span class='hs-varid'>neg</span> <span class='hs-varid'>z</span> <span class='hs-layout'>(</span><span class='hs-varid'>modifyPositive</span> <span class='hs-varid'>x</span> <span class='hs-varid'>f</span> <span class='hs-varid'>pos</span><span class='hs-layout'>)</span> <a name="line-93"></a> <a name="line-94"></a><a name="modifyPositive"></a><span class='hs-definition'>modifyPositive</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Num</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-conid'>Bits</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>b</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-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>BitTrie</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>BitTrie</span> <span class='hs-varid'>a</span> <a name="line-95"></a><span class='hs-definition'>modifyPositive</span> <span class='hs-varid'>x</span> <span class='hs-varid'>f</span> <span class='hs-keyglyph'>~</span><span class='hs-layout'>(</span><span class='hs-conid'>BitTrie</span> <span class='hs-varid'>one</span> <span class='hs-varid'>even</span> <span class='hs-varid'>odd</span><span class='hs-layout'>)</span> <a name="line-96"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>x</span> <span class='hs-varop'>==</span> <span class='hs-num'>1</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>BitTrie</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>one</span><span class='hs-layout'>)</span> <span class='hs-varid'>even</span> <span class='hs-varid'>odd</span> <a name="line-97"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>testBit</span> <span class='hs-varid'>x</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>BitTrie</span> <span class='hs-varid'>one</span> <span class='hs-varid'>even</span> <span class='hs-layout'>(</span><span class='hs-varid'>modifyPositive</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'>`shiftR`</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varid'>f</span> <span class='hs-varid'>odd</span><span class='hs-layout'>)</span> <a name="line-98"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>BitTrie</span> <span class='hs-varid'>one</span> <span class='hs-layout'>(</span><span class='hs-varid'>modifyPositive</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'>`shiftR`</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varid'>f</span> <span class='hs-varid'>even</span><span class='hs-layout'>)</span> <span class='hs-varid'>odd</span> <a name="line-99"></a> <a name="line-100"></a> <a name="line-101"></a><a name="modify'"></a><span class='hs-comment'>-- | Modify the function at one point (strict version)</span> <a name="line-102"></a><span class='hs-definition'>modify'</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Ord</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-conid'>Num</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-conid'>Bits</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>b</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-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>IntTrie</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>IntTrie</span> <span class='hs-varid'>a</span> <a name="line-103"></a><span class='hs-definition'>modify'</span> <span class='hs-varid'>x</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>IntTrie</span> <span class='hs-varid'>neg</span> <span class='hs-varid'>z</span> <span class='hs-varid'>pos</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <a name="line-104"></a> <span class='hs-keyword'>case</span> <span class='hs-varid'>compare</span> <span class='hs-varid'>x</span> <span class='hs-num'>0</span> <span class='hs-keyword'>of</span> <a name="line-105"></a> <span class='hs-conid'>LT</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-conid'>IntTrie</span> <span class='hs-varop'>$!</span> <span class='hs-varid'>modifyPositive'</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-varid'>f</span> <span class='hs-varid'>neg</span><span class='hs-layout'>)</span> <span class='hs-varid'>z</span> <span class='hs-varid'>pos</span> <a name="line-106"></a> <span class='hs-conid'>EQ</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-conid'>IntTrie</span> <span class='hs-varid'>neg</span> <span class='hs-varop'>$!</span> <span class='hs-varid'>f</span> <span class='hs-varid'>z</span><span class='hs-layout'>)</span> <span class='hs-varid'>pos</span> <a name="line-107"></a> <span class='hs-conid'>GT</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>IntTrie</span> <span class='hs-varid'>neg</span> <span class='hs-varid'>z</span> <span class='hs-varop'>$!</span> <span class='hs-varid'>modifyPositive'</span> <span class='hs-varid'>x</span> <span class='hs-varid'>f</span> <span class='hs-varid'>pos</span> <a name="line-108"></a> <a name="line-109"></a><a name="modifyPositive'"></a><span class='hs-definition'>modifyPositive'</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Num</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-conid'>Bits</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-layout'>(</span><span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>BitTrie</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>BitTrie</span> <span class='hs-varid'>a</span> <a name="line-110"></a><span class='hs-definition'>modifyPositive'</span> <span class='hs-varid'>x</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>BitTrie</span> <span class='hs-varid'>one</span> <span class='hs-varid'>even</span> <span class='hs-varid'>odd</span><span class='hs-layout'>)</span> <a name="line-111"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>x</span> <span class='hs-varop'>==</span> <span class='hs-num'>1</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>BitTrie</span> <span class='hs-varop'>$!</span> <span class='hs-varid'>f</span> <span class='hs-varid'>one</span><span class='hs-layout'>)</span> <span class='hs-varid'>even</span> <span class='hs-varid'>odd</span> <a name="line-112"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>testBit</span> <span class='hs-varid'>x</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>BitTrie</span> <span class='hs-varid'>one</span> <span class='hs-varid'>even</span> <span class='hs-varop'>$!</span> <span class='hs-varid'>modifyPositive'</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'>`shiftR`</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varid'>f</span> <span class='hs-varid'>odd</span> <a name="line-113"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>BitTrie</span> <span class='hs-varid'>one</span> <span class='hs-varop'>$!</span> <span class='hs-varid'>modifyPositive'</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span> <span class='hs-varop'>`shiftR`</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span> <span class='hs-varid'>f</span> <span class='hs-varid'>even</span><span class='hs-layout'>)</span> <span class='hs-varid'>odd</span> <a name="line-114"></a> <a name="line-115"></a> <a name="line-116"></a><a name="overwrite"></a><span class='hs-comment'>-- | Overwrite the function at one point</span> <a name="line-117"></a><span class='hs-comment'>--</span> <a name="line-118"></a><span class='hs-comment'>-- > overwrite i x = modify i (const x)</span> <a name="line-119"></a><span class='hs-definition'>overwrite</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Ord</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-conid'>Num</span> <span class='hs-varid'>b</span><span class='hs-layout'>,</span> <span class='hs-conid'>Bits</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>IntTrie</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>IntTrie</span> <span class='hs-varid'>a</span> <a name="line-120"></a><span class='hs-definition'>overwrite</span> <span class='hs-varid'>i</span> <span class='hs-varid'>x</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>modify</span> <span class='hs-varid'>i</span> <span class='hs-layout'>(</span><span class='hs-varid'>const</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> </pre></body> </html>