<?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/full/Agda/Termination/Lexicographic.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-comment'>-- | Lexicographic order search, more or less as defined in</span>
<a name="line-3"></a><span class='hs-comment'>-- \"A Predicative Analysis of Structural Recursion\" by</span>
<a name="line-4"></a><span class='hs-comment'>-- Andreas Abel and Thorsten Altenkirch.</span>
<a name="line-5"></a>
<a name="line-6"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Termination</span><span class='hs-varop'>.</span><span class='hs-conid'>Lexicographic</span>
<a name="line-7"></a> <span class='hs-layout'>(</span> <span class='hs-conid'>LexOrder</span>
<a name="line-8"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>RecBehaviour</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-9"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Column</span>
<a name="line-10"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>recBehaviourInvariant</span>
<a name="line-11"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>fromDiagonals</span>
<a name="line-12"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>lexOrder</span>
<a name="line-13"></a> <span class='hs-layout'>,</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Termination</span><span class='hs-varop'>.</span><span class='hs-conid'>Lexicographic</span><span class='hs-varop'>.</span><span class='hs-varid'>tests</span>
<a name="line-14"></a> <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-15"></a>
<a name="line-16"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Utils</span><span class='hs-varop'>.</span><span class='hs-conid'>QuickCheck</span>
<a name="line-17"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Termination</span><span class='hs-varop'>.</span><span class='hs-conid'>Matrix</span> <span class='hs-layout'>(</span><span class='hs-conid'>Size</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-18"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Termination</span><span class='hs-varop'>.</span><span class='hs-conid'>Matrix</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>M</span>
<a name="line-19"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Utils</span><span class='hs-varop'>.</span><span class='hs-conid'>Either</span>
<a name="line-20"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Utils</span><span class='hs-varop'>.</span><span class='hs-conid'>List</span>
<a name="line-21"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Utils</span><span class='hs-varop'>.</span><span class='hs-conid'>TestHelpers</span>
<a name="line-22"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Agda</span><span class='hs-varop'>.</span><span class='hs-conid'>Termination</span><span class='hs-varop'>.</span><span class='hs-conid'>CallGraph</span>
<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'>Arrow</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'>List</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'>Map</span> <span class='hs-layout'>(</span><span class='hs-conid'>Map</span><span class='hs-layout'>,</span> <span class='hs-layout'>(</span><span class='hs-varop'>!</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-26"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Map</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>Map</span>
<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'>Array</span> <span class='hs-layout'>(</span><span class='hs-conid'>Array</span><span class='hs-layout'>,</span> <span class='hs-conid'>Ix</span><span class='hs-layout'>)</span>
<a name="line-28"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Array</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>Array</span>
<a name="line-29"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Set</span> <span class='hs-layout'>(</span><span class='hs-conid'>Set</span><span class='hs-layout'>)</span>
<a name="line-30"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Set</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>Set</span>
<a name="line-31"></a>
<a name="line-32"></a><span class='hs-comment'>-- | A lexicographic ordering for the recursion behaviour of a</span>
<a name="line-33"></a><span class='hs-comment'>-- given function is a permutation of the argument indices which can</span>
<a name="line-34"></a><span class='hs-comment'>-- be used to show that the function terminates. See the paper</span>
<a name="line-35"></a><span class='hs-comment'>-- referred to above for more details.</span>
<a name="line-36"></a>
<a name="line-37"></a><a name="LexOrder"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>LexOrder</span> <span class='hs-varid'>arg</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyglyph'>[</span><span class='hs-varid'>arg</span><span class='hs-keyglyph'>]</span>
<a name="line-38"></a>
<a name="line-39"></a><span class='hs-comment'>-- | A recursion behaviour expresses how a certain function calls</span>
<a name="line-40"></a><span class='hs-comment'>-- itself (transitively). For every argument position there is a value</span>
<a name="line-41"></a><span class='hs-comment'>-- ('Column') describing how the function calls itself for that</span>
<a name="line-42"></a><span class='hs-comment'>-- particular argument. See also 'recBehaviourInvariant'.</span>
<a name="line-43"></a>
<a name="line-44"></a><a name="RecBehaviour"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>RecBehaviour</span> <span class='hs-varid'>arg</span> <span class='hs-varid'>call</span> <span class='hs-keyglyph'>=</span>
<a name="line-45"></a> <span class='hs-conid'>RB</span> <span class='hs-layout'>{</span> <span class='hs-varid'>columns</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Map</span> <span class='hs-varid'>arg</span> <span class='hs-layout'>(</span><span class='hs-conid'>Column</span> <span class='hs-varid'>call</span><span class='hs-layout'>)</span>
<a name="line-46"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>calls</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Set</span> <span class='hs-varid'>call</span>
<a name="line-47"></a> <span class='hs-comment'>-- ^ The indices to the columns.</span>
<a name="line-48"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>size</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Size</span> <span class='hs-conid'>Integer</span>
<a name="line-49"></a> <span class='hs-layout'>}</span>
<a name="line-50"></a> <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Show</span>
<a name="line-51"></a>
<a name="line-52"></a><span class='hs-comment'>-- | A column expresses how the size of a certain argument changes in</span>
<a name="line-53"></a><span class='hs-comment'>-- the various recursive calls a function makes to itself</span>
<a name="line-54"></a><span class='hs-comment'>-- (transitively).</span>
<a name="line-55"></a>
<a name="line-56"></a><a name="Column"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>Column</span> <span class='hs-varid'>call</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Map</span> <span class='hs-varid'>call</span> <span class='hs-conid'>Order</span>
<a name="line-57"></a>
<a name="line-58"></a><span class='hs-comment'>-- | 'RecBehaviour' invariant: the size must match the real size of</span>
<a name="line-59"></a><span class='hs-comment'>-- the recursion behaviour, and all columns must have the same</span>
<a name="line-60"></a><span class='hs-comment'>-- indices.</span>
<a name="line-61"></a>
<a name="line-62"></a><a name="recBehaviourInvariant"></a><span class='hs-definition'>recBehaviourInvariant</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Eq</span> <span class='hs-varid'>call</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>RecBehaviour</span> <span class='hs-varid'>arg</span> <span class='hs-varid'>call</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-63"></a><span class='hs-definition'>recBehaviourInvariant</span> <span class='hs-varid'>rb</span> <span class='hs-keyglyph'>=</span>
<a name="line-64"></a> <span class='hs-varid'>genericLength</span> <span class='hs-layout'>(</span><span class='hs-conid'>Map</span><span class='hs-varop'>.</span><span class='hs-varid'>elems</span> <span class='hs-varop'>$</span> <span class='hs-varid'>columns</span> <span class='hs-varid'>rb</span><span class='hs-layout'>)</span> <span class='hs-varop'>==</span> <span class='hs-varid'>cols</span> <span class='hs-layout'>(</span><span class='hs-varid'>size</span> <span class='hs-varid'>rb</span><span class='hs-layout'>)</span>
<a name="line-65"></a> <span class='hs-varop'>&&</span>
<a name="line-66"></a> <span class='hs-varid'>all</span> <span class='hs-layout'>(</span><span class='hs-varop'>==</span> <span class='hs-varid'>rows</span> <span class='hs-layout'>(</span><span class='hs-varid'>size</span> <span class='hs-varid'>rb</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-67"></a> <span class='hs-layout'>(</span><span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-varid'>genericLength</span> <span class='hs-varop'>.</span> <span class='hs-conid'>Map</span><span class='hs-varop'>.</span><span class='hs-varid'>elems</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Map</span><span class='hs-varop'>.</span><span class='hs-varid'>elems</span> <span class='hs-varop'>$</span> <span class='hs-varid'>columns</span> <span class='hs-varid'>rb</span><span class='hs-layout'>)</span>
<a name="line-68"></a> <span class='hs-varop'>&&</span>
<a name="line-69"></a> <span class='hs-varid'>allEqual</span> <span class='hs-layout'>(</span><span class='hs-varid'>calls</span> <span class='hs-varid'>rb</span> <span class='hs-conop'>:</span> <span class='hs-layout'>(</span><span class='hs-varid'>map</span> <span class='hs-conid'>Map</span><span class='hs-varop'>.</span><span class='hs-varid'>keysSet</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Map</span><span class='hs-varop'>.</span><span class='hs-varid'>elems</span> <span class='hs-varop'>$</span> <span class='hs-varid'>columns</span> <span class='hs-varid'>rb</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-70"></a>
<a name="line-71"></a><span class='hs-comment'>-- Generates a recursion behaviour.</span>
<a name="line-72"></a>
<a name="line-73"></a><a name="instance%20Arbitrary%20(RecBehaviour%20call%20arg)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>Arbitrary</span> <span class='hs-varid'>call</span><span class='hs-layout'>,</span> <span class='hs-conid'>Arbitrary</span> <span class='hs-varid'>arg</span><span class='hs-layout'>,</span> <span class='hs-conid'>Ord</span> <span class='hs-varid'>arg</span><span class='hs-layout'>,</span> <span class='hs-conid'>Ord</span> <span class='hs-varid'>call</span><span class='hs-layout'>)</span>
<a name="line-74"></a> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Arbitrary</span> <span class='hs-layout'>(</span><span class='hs-conid'>RecBehaviour</span> <span class='hs-varid'>call</span> <span class='hs-varid'>arg</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-75"></a> <span class='hs-varid'>arbitrary</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span>
<a name="line-76"></a> <span class='hs-varid'>calls</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>fmap</span> <span class='hs-varid'>nub</span> <span class='hs-varop'>$</span> <span class='hs-varid'>listOf</span> <span class='hs-varid'>arbitrary</span>
<a name="line-77"></a> <span class='hs-varid'>args</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>fmap</span> <span class='hs-varid'>nub</span> <span class='hs-varop'>$</span> <span class='hs-varid'>listOf</span> <span class='hs-varid'>arbitrary</span>
<a name="line-78"></a> <span class='hs-keyword'>let</span> <span class='hs-varid'>rows</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>genericLength</span> <span class='hs-varid'>calls</span>
<a name="line-79"></a> <span class='hs-varid'>cols</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>genericLength</span> <span class='hs-varid'>args</span>
<a name="line-80"></a> <span class='hs-varid'>sz</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Size</span> <span class='hs-layout'>{</span> <span class='hs-varid'>rows</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>rows</span><span class='hs-layout'>,</span> <span class='hs-varid'>cols</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>cols</span> <span class='hs-layout'>}</span>
<a name="line-81"></a> <span class='hs-varid'>colGen</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span>
<a name="line-82"></a> <span class='hs-varid'>col</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>vectorOf</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromIntegral</span> <span class='hs-varid'>rows</span><span class='hs-layout'>)</span> <span class='hs-varid'>arbitrary</span>
<a name="line-83"></a> <span class='hs-varid'>return</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Map</span><span class='hs-varop'>.</span><span class='hs-varid'>fromList</span> <span class='hs-layout'>(</span><span class='hs-varid'>zip</span> <span class='hs-varid'>calls</span> <span class='hs-varid'>col</span><span class='hs-layout'>)</span>
<a name="line-84"></a> <span class='hs-varid'>cols</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-varid'>zip</span> <span class='hs-varid'>args</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>vectorOf</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromIntegral</span> <span class='hs-varid'>cols</span><span class='hs-layout'>)</span> <span class='hs-varid'>colGen</span>
<a name="line-85"></a> <span class='hs-varid'>return</span> <span class='hs-varop'>$</span> <span class='hs-conid'>RB</span> <span class='hs-layout'>{</span> <span class='hs-varid'>columns</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Map</span><span class='hs-varop'>.</span><span class='hs-varid'>fromList</span> <span class='hs-varid'>cols</span>
<a name="line-86"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>calls</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Set</span><span class='hs-varop'>.</span><span class='hs-varid'>fromList</span> <span class='hs-varid'>calls</span>
<a name="line-87"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>size</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>sz</span> <span class='hs-layout'>}</span>
<a name="line-88"></a>
<a name="line-89"></a><a name="instance%20CoArbitrary%20(RecBehaviour%20call%20arg)"></a><span class='hs-keyword'>instance</span> <span class='hs-layout'>(</span><span class='hs-conid'>CoArbitrary</span> <span class='hs-varid'>call</span><span class='hs-layout'>,</span> <span class='hs-conid'>CoArbitrary</span> <span class='hs-varid'>arg</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>CoArbitrary</span> <span class='hs-layout'>(</span><span class='hs-conid'>RecBehaviour</span> <span class='hs-varid'>call</span> <span class='hs-varid'>arg</span><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-90"></a> <span class='hs-varid'>coarbitrary</span> <span class='hs-layout'>(</span><span class='hs-conid'>RB</span> <span class='hs-varid'>c</span> <span class='hs-varid'>cs</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-91"></a> <span class='hs-varid'>coarbitrary</span> <span class='hs-layout'>(</span><span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-varid'>id</span> <span class='hs-varop'>***</span> <span class='hs-conid'>Map</span><span class='hs-varop'>.</span><span class='hs-varid'>toList</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Map</span><span class='hs-varop'>.</span><span class='hs-varid'>toList</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span>
<a name="line-92"></a> <span class='hs-varid'>coarbitrary</span> <span class='hs-layout'>(</span><span class='hs-conid'>Set</span><span class='hs-varop'>.</span><span class='hs-varid'>toList</span> <span class='hs-varid'>cs</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span>
<a name="line-93"></a> <span class='hs-varid'>coarbitrary</span> <span class='hs-varid'>s</span>
<a name="line-94"></a>
<a name="line-95"></a><a name="prop_recBehaviour_Arbitrary"></a><span class='hs-definition'>prop_recBehaviour_Arbitrary</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>RecBehaviour</span> <span class='hs-conid'>Integer</span> <span class='hs-conid'>Integer</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-96"></a><span class='hs-definition'>prop_recBehaviour_Arbitrary</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>recBehaviourInvariant</span>
<a name="line-97"></a>
<a name="line-98"></a><span class='hs-comment'>-- | Checks whether there are any calls left in the recursion</span>
<a name="line-99"></a><span class='hs-comment'>-- behaviour.</span>
<a name="line-100"></a>
<a name="line-101"></a><a name="noCallsLeft"></a><span class='hs-definition'>noCallsLeft</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>RecBehaviour</span> <span class='hs-varid'>arg</span> <span class='hs-varid'>call</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-102"></a><span class='hs-definition'>noCallsLeft</span> <span class='hs-varid'>rb</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>rows</span> <span class='hs-layout'>(</span><span class='hs-varid'>size</span> <span class='hs-varid'>rb</span><span class='hs-layout'>)</span> <span class='hs-varop'>==</span> <span class='hs-num'>0</span>
<a name="line-103"></a>
<a name="line-104"></a><span class='hs-comment'>-- | Constructs a recursion behaviour from a list of matrix diagonals</span>
<a name="line-105"></a><span class='hs-comment'>-- (\"rows\"). Note that the @call@ indices do not need to be</span>
<a name="line-106"></a><span class='hs-comment'>-- distinct, since they are paired up with unique 'Integer's.</span>
<a name="line-107"></a><span class='hs-comment'>--</span>
<a name="line-108"></a><span class='hs-comment'>-- Precondition: all arrays should have the same bounds.</span>
<a name="line-109"></a>
<a name="line-110"></a><a name="fromDiagonals"></a><span class='hs-definition'>fromDiagonals</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Ord</span> <span class='hs-varid'>call</span><span class='hs-layout'>,</span> <span class='hs-conid'>Ix</span> <span class='hs-varid'>arg</span><span class='hs-layout'>)</span>
<a name="line-111"></a> <span class='hs-keyglyph'>=></span> <span class='hs-keyglyph'>[</span><span class='hs-layout'>(</span><span class='hs-varid'>call</span><span class='hs-layout'>,</span> <span class='hs-conid'>Array</span> <span class='hs-varid'>arg</span> <span class='hs-conid'>Order</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>RecBehaviour</span> <span class='hs-varid'>arg</span> <span class='hs-layout'>(</span><span class='hs-conid'>Integer</span><span class='hs-layout'>,</span> <span class='hs-varid'>call</span><span class='hs-layout'>)</span>
<a name="line-112"></a><span class='hs-definition'>fromDiagonals</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>RB</span> <span class='hs-layout'>{</span> <span class='hs-varid'>columns</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Map</span><span class='hs-varop'>.</span><span class='hs-varid'>fromList</span> <span class='hs-conid'>[]</span>
<a name="line-113"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>calls</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Set</span><span class='hs-varop'>.</span><span class='hs-varid'>empty</span>
<a name="line-114"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>size</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Size</span> <span class='hs-num'>0</span> <span class='hs-num'>0</span> <span class='hs-layout'>}</span>
<a name="line-115"></a><span class='hs-definition'>fromDiagonals</span> <span class='hs-varid'>rows</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>RB</span> <span class='hs-layout'>{</span> <span class='hs-varid'>columns</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Map</span><span class='hs-varop'>.</span><span class='hs-varid'>fromList</span> <span class='hs-varop'>$</span> <span class='hs-varid'>zip</span> <span class='hs-varid'>args</span> <span class='hs-varid'>cols</span>
<a name="line-116"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>calls</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Set</span><span class='hs-varop'>.</span><span class='hs-varid'>fromList</span> <span class='hs-varid'>calls</span>
<a name="line-117"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>size</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Size</span> <span class='hs-layout'>{</span> <span class='hs-varid'>rows</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>genericLength</span> <span class='hs-varid'>rows</span>
<a name="line-118"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>cols</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>genericLength</span> <span class='hs-varid'>cols</span> <span class='hs-layout'>}</span>
<a name="line-119"></a> <span class='hs-layout'>}</span>
<a name="line-120"></a> <span class='hs-keyword'>where</span>
<a name="line-121"></a> <span class='hs-varid'>calls</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>zip</span> <span class='hs-keyglyph'>[</span><span class='hs-num'>1</span> <span class='hs-keyglyph'>..</span><span class='hs-keyglyph'>]</span> <span class='hs-varop'>$</span> <span class='hs-varid'>map</span> <span class='hs-varid'>fst</span> <span class='hs-varid'>rows</span>
<a name="line-122"></a> <span class='hs-varid'>cols</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>map</span> <span class='hs-conid'>Map</span><span class='hs-varop'>.</span><span class='hs-varid'>fromList</span> <span class='hs-varop'>$</span> <span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-varid'>zip</span> <span class='hs-varid'>calls</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>transpose</span> <span class='hs-varop'>$</span>
<a name="line-123"></a> <span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-conid'>Array</span><span class='hs-varop'>.</span><span class='hs-varid'>elems</span> <span class='hs-varop'>.</span> <span class='hs-varid'>snd</span><span class='hs-layout'>)</span> <span class='hs-varid'>rows</span>
<a name="line-124"></a> <span class='hs-varid'>args</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Array</span><span class='hs-varop'>.</span><span class='hs-varid'>range</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Array</span><span class='hs-varop'>.</span><span class='hs-varid'>bounds</span> <span class='hs-varop'>$</span> <span class='hs-varid'>snd</span> <span class='hs-varop'>$</span> <span class='hs-varid'>head</span> <span class='hs-varid'>rows</span>
<a name="line-125"></a>
<a name="line-126"></a><a name="prop_fromDiagonals"></a><span class='hs-definition'>prop_fromDiagonals</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span>
<a name="line-127"></a> <span class='hs-varid'>forAll</span> <span class='hs-layout'>(</span><span class='hs-varid'>vectorOf</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromIntegral</span> <span class='hs-varop'>$</span> <span class='hs-varid'>rows</span> <span class='hs-varop'>$</span> <span class='hs-conid'>M</span><span class='hs-varop'>.</span><span class='hs-varid'>size</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-varid'>arbitrary</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>calls</span> <span class='hs-keyglyph'>-></span>
<a name="line-128"></a> <span class='hs-keyword'>let</span> <span class='hs-varid'>oss</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>zip</span> <span class='hs-varid'>calls</span> <span class='hs-varop'>$</span>
<a name="line-129"></a> <span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-conid'>Array</span><span class='hs-varop'>.</span><span class='hs-varid'>listArray</span> <span class='hs-layout'>(</span><span class='hs-num'>1</span><span class='hs-layout'>,</span> <span class='hs-varid'>cols</span> <span class='hs-varop'>$</span> <span class='hs-conid'>M</span><span class='hs-varop'>.</span><span class='hs-varid'>size</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span>
<a name="line-130"></a> <span class='hs-conid'>M</span><span class='hs-varop'>.</span><span class='hs-varid'>toLists</span> <span class='hs-varid'>m</span>
<a name="line-131"></a> <span class='hs-varid'>rb</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fromDiagonals</span> <span class='hs-varid'>oss</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>RecBehaviour</span> <span class='hs-conid'>Integer</span> <span class='hs-layout'>(</span><span class='hs-conid'>Integer</span><span class='hs-layout'>,</span> <span class='hs-conid'>Bool</span><span class='hs-layout'>)</span>
<a name="line-132"></a> <span class='hs-keyword'>in</span>
<a name="line-133"></a> <span class='hs-varid'>recBehaviourInvariant</span> <span class='hs-varid'>rb</span>
<a name="line-134"></a> <span class='hs-varop'>&&</span>
<a name="line-135"></a> <span class='hs-keyword'>if</span> <span class='hs-varid'>rows</span> <span class='hs-layout'>(</span><span class='hs-conid'>M</span><span class='hs-varop'>.</span><span class='hs-varid'>size</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-varop'>==</span> <span class='hs-num'>0</span> <span class='hs-keyword'>then</span>
<a name="line-136"></a> <span class='hs-varid'>rows</span> <span class='hs-layout'>(</span><span class='hs-varid'>size</span> <span class='hs-varid'>rb</span><span class='hs-layout'>)</span> <span class='hs-varop'>==</span> <span class='hs-num'>0</span>
<a name="line-137"></a> <span class='hs-keyword'>else</span>
<a name="line-138"></a> <span class='hs-varid'>size</span> <span class='hs-varid'>rb</span> <span class='hs-varop'>==</span> <span class='hs-conid'>M</span><span class='hs-varop'>.</span><span class='hs-varid'>size</span> <span class='hs-varid'>m</span>
<a name="line-139"></a>
<a name="line-140"></a><span class='hs-comment'>-- | Checks if this \"column\" is well-behaved (all calls decreasing,</span>
<a name="line-141"></a><span class='hs-comment'>-- at least one strictly decreasing).</span>
<a name="line-142"></a>
<a name="line-143"></a><a name="okColumn"></a><span class='hs-definition'>okColumn</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Column</span> <span class='hs-varid'>call</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-144"></a><span class='hs-definition'>okColumn</span> <span class='hs-varid'>col</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>any</span> <span class='hs-varid'>decreasing</span> <span class='hs-varid'>col'</span> <span class='hs-varop'>&&</span> <span class='hs-varid'>all</span> <span class='hs-layout'>(</span><span class='hs-varop'>/=</span> <span class='hs-varid'>unknown</span><span class='hs-layout'>)</span> <span class='hs-varid'>col'</span>
<a name="line-145"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>col'</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Map</span><span class='hs-varop'>.</span><span class='hs-varid'>elems</span> <span class='hs-varid'>col</span>
<a name="line-146"></a>
<a name="line-147"></a><span class='hs-comment'>-- | @'newBehaviour' n rb@ computes a new recursion behaviour from</span>
<a name="line-148"></a><span class='hs-comment'>-- @rb@ by removing all \"rows\" (calls) for which the @n@-th element</span>
<a name="line-149"></a><span class='hs-comment'>-- is 'decreasing', and also completely removing the @n@-th column.</span>
<a name="line-150"></a><span class='hs-comment'>--</span>
<a name="line-151"></a><span class='hs-comment'>-- Precondition: there has to be an @n@-th column.</span>
<a name="line-152"></a>
<a name="line-153"></a><a name="newBehaviour"></a><span class='hs-definition'>newBehaviour</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Ord</span> <span class='hs-varid'>arg</span><span class='hs-layout'>,</span> <span class='hs-conid'>Ord</span> <span class='hs-varid'>call</span><span class='hs-layout'>)</span>
<a name="line-154"></a> <span class='hs-keyglyph'>=></span> <span class='hs-varid'>arg</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>RecBehaviour</span> <span class='hs-varid'>arg</span> <span class='hs-varid'>call</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>RecBehaviour</span> <span class='hs-varid'>arg</span> <span class='hs-varid'>call</span>
<a name="line-155"></a><span class='hs-definition'>newBehaviour</span> <span class='hs-varid'>n</span> <span class='hs-varid'>rb</span> <span class='hs-keyglyph'>=</span>
<a name="line-156"></a> <span class='hs-conid'>RB</span> <span class='hs-layout'>{</span> <span class='hs-varid'>columns</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Map</span><span class='hs-varop'>.</span><span class='hs-varid'>map</span> <span class='hs-varid'>remove</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Map</span><span class='hs-varop'>.</span><span class='hs-varid'>delete</span> <span class='hs-varid'>n</span> <span class='hs-varop'>$</span> <span class='hs-varid'>columns</span> <span class='hs-varid'>rb</span>
<a name="line-157"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>calls</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Set</span><span class='hs-varop'>.</span><span class='hs-varid'>difference</span> <span class='hs-layout'>(</span><span class='hs-varid'>calls</span> <span class='hs-varid'>rb</span><span class='hs-layout'>)</span>
<a name="line-158"></a> <span class='hs-layout'>(</span><span class='hs-conid'>Set</span><span class='hs-varop'>.</span><span class='hs-varid'>fromList</span> <span class='hs-varid'>indicesToRemove</span><span class='hs-layout'>)</span>
<a name="line-159"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>size</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Size</span> <span class='hs-layout'>{</span> <span class='hs-varid'>rows</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>rows</span> <span class='hs-layout'>(</span><span class='hs-varid'>size</span> <span class='hs-varid'>rb</span><span class='hs-layout'>)</span> <span class='hs-comment'>-</span>
<a name="line-160"></a> <span class='hs-varid'>genericLength</span> <span class='hs-varid'>indicesToRemove</span>
<a name="line-161"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>cols</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>cols</span> <span class='hs-layout'>(</span><span class='hs-varid'>size</span> <span class='hs-varid'>rb</span><span class='hs-layout'>)</span> <span class='hs-comment'>-</span> <span class='hs-num'>1</span> <span class='hs-layout'>}</span>
<a name="line-162"></a> <span class='hs-layout'>}</span>
<a name="line-163"></a> <span class='hs-keyword'>where</span>
<a name="line-164"></a> <span class='hs-conid'>Just</span> <span class='hs-varid'>colN</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Map</span><span class='hs-varop'>.</span><span class='hs-varid'>lookup</span> <span class='hs-varid'>n</span> <span class='hs-varop'>$</span> <span class='hs-varid'>columns</span> <span class='hs-varid'>rb</span>
<a name="line-165"></a> <span class='hs-varid'>indicesToRemove</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>map</span> <span class='hs-varid'>fst</span> <span class='hs-varop'>$</span> <span class='hs-varid'>filter</span> <span class='hs-layout'>(</span><span class='hs-varid'>decreasing</span> <span class='hs-varop'>.</span> <span class='hs-varid'>snd</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Map</span><span class='hs-varop'>.</span><span class='hs-varid'>toList</span> <span class='hs-varid'>colN</span>
<a name="line-166"></a> <span class='hs-varid'>remove</span> <span class='hs-varid'>colJ</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>foldr</span> <span class='hs-conid'>Map</span><span class='hs-varop'>.</span><span class='hs-varid'>delete</span> <span class='hs-varid'>colJ</span> <span class='hs-varid'>indicesToRemove</span>
<a name="line-167"></a>
<a name="line-168"></a><a name="prop_newBehaviour"></a><span class='hs-definition'>prop_newBehaviour</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>RecBehaviour</span> <span class='hs-conid'>Integer</span> <span class='hs-conid'>Integer</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Property</span>
<a name="line-169"></a><span class='hs-definition'>prop_newBehaviour</span> <span class='hs-varid'>rb</span> <span class='hs-keyglyph'>=</span>
<a name="line-170"></a> <span class='hs-varid'>not</span> <span class='hs-layout'>(</span><span class='hs-varid'>cols</span> <span class='hs-layout'>(</span><span class='hs-varid'>size</span> <span class='hs-varid'>rb</span><span class='hs-layout'>)</span> <span class='hs-varop'>==</span> <span class='hs-num'>0</span><span class='hs-layout'>)</span> <span class='hs-varop'>==></span>
<a name="line-171"></a> <span class='hs-varid'>forAll</span> <span class='hs-layout'>(</span><span class='hs-varid'>elements</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Map</span><span class='hs-varop'>.</span><span class='hs-varid'>keys</span> <span class='hs-varop'>$</span> <span class='hs-varid'>columns</span> <span class='hs-varid'>rb</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>n</span> <span class='hs-keyglyph'>-></span>
<a name="line-172"></a> <span class='hs-varid'>recBehaviourInvariant</span> <span class='hs-layout'>(</span><span class='hs-varid'>newBehaviour</span> <span class='hs-varid'>n</span> <span class='hs-varid'>rb</span><span class='hs-layout'>)</span>
<a name="line-173"></a>
<a name="line-174"></a><span class='hs-comment'>-- | @'correctLexOrder' rs ps@ checks that the permutation @ps@ really</span>
<a name="line-175"></a><span class='hs-comment'>-- induces a lexicographic ordering which shows that the function</span>
<a name="line-176"></a><span class='hs-comment'>-- represented by the recursion behaviour @rs@ terminates.</span>
<a name="line-177"></a>
<a name="line-178"></a><a name="correctLexOrder"></a><span class='hs-definition'>correctLexOrder</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Ord</span> <span class='hs-varid'>arg</span><span class='hs-layout'>,</span> <span class='hs-conid'>Ord</span> <span class='hs-varid'>call</span><span class='hs-layout'>)</span>
<a name="line-179"></a> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>RecBehaviour</span> <span class='hs-varid'>arg</span> <span class='hs-varid'>call</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>LexOrder</span> <span class='hs-varid'>arg</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Bool</span>
<a name="line-180"></a><span class='hs-definition'>correctLexOrder</span> <span class='hs-varid'>rb</span> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>noCallsLeft</span> <span class='hs-varid'>rb</span>
<a name="line-181"></a><span class='hs-definition'>correctLexOrder</span> <span class='hs-varid'>rb</span> <span class='hs-layout'>(</span><span class='hs-varid'>p0</span> <span class='hs-conop'>:</span> <span class='hs-varid'>ps</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-182"></a> <span class='hs-varid'>okColumn</span> <span class='hs-layout'>(</span><span class='hs-varid'>columns</span> <span class='hs-varid'>rb</span> <span class='hs-varop'>!</span> <span class='hs-varid'>p0</span><span class='hs-layout'>)</span> <span class='hs-varop'>&&</span> <span class='hs-varid'>correctLexOrder</span> <span class='hs-layout'>(</span><span class='hs-varid'>newBehaviour</span> <span class='hs-varid'>p0</span> <span class='hs-varid'>rb</span><span class='hs-layout'>)</span> <span class='hs-varid'>ps</span>
<a name="line-183"></a>
<a name="line-184"></a><span class='hs-comment'>-- | Tries to compute a lexicographic ordering for the given recursion</span>
<a name="line-185"></a><span class='hs-comment'>-- behaviour. This algorithm should be complete.</span>
<a name="line-186"></a><span class='hs-comment'>--</span>
<a name="line-187"></a><span class='hs-comment'>-- If no lexicographic ordering can be found, then two sets are</span>
<a name="line-188"></a><span class='hs-comment'>-- returned:</span>
<a name="line-189"></a><span class='hs-comment'>--</span>
<a name="line-190"></a><span class='hs-comment'>-- * A set of argument positions which are not properly decreasing, and</span>
<a name="line-191"></a><span class='hs-comment'>--</span>
<a name="line-192"></a><span class='hs-comment'>-- * the calls where these problems show up.</span>
<a name="line-193"></a>
<a name="line-194"></a><a name="lexOrder"></a><span class='hs-definition'>lexOrder</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Ord</span> <span class='hs-varid'>arg</span><span class='hs-layout'>,</span> <span class='hs-conid'>Ord</span> <span class='hs-varid'>call</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span>
<a name="line-195"></a> <span class='hs-conid'>RecBehaviour</span> <span class='hs-varid'>arg</span> <span class='hs-varid'>call</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Either</span> <span class='hs-layout'>(</span><span class='hs-conid'>Set</span> <span class='hs-varid'>arg</span><span class='hs-layout'>,</span> <span class='hs-conid'>Set</span> <span class='hs-varid'>call</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>LexOrder</span> <span class='hs-varid'>arg</span><span class='hs-layout'>)</span>
<a name="line-196"></a><span class='hs-definition'>lexOrder</span> <span class='hs-varid'>rb</span> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>noCallsLeft</span> <span class='hs-varid'>rb</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Right</span> <span class='hs-conid'>[]</span>
<a name="line-197"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>okColumns</span> <span class='hs-keyword'>of</span>
<a name="line-198"></a> <span class='hs-conid'>[]</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Left</span> <span class='hs-layout'>(</span><span class='hs-conid'>Map</span><span class='hs-varop'>.</span><span class='hs-varid'>keysSet</span> <span class='hs-varop'>$</span> <span class='hs-varid'>columns</span> <span class='hs-varid'>rb</span><span class='hs-layout'>,</span> <span class='hs-varid'>calls</span> <span class='hs-varid'>rb</span><span class='hs-layout'>)</span>
<a name="line-199"></a> <span class='hs-layout'>(</span><span class='hs-varid'>n</span> <span class='hs-conop'>:</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-varid'>lexOrder</span> <span class='hs-layout'>(</span><span class='hs-varid'>newBehaviour</span> <span class='hs-varid'>n</span> <span class='hs-varid'>rb</span><span class='hs-layout'>)</span> <span class='hs-keyword'>of</span>
<a name="line-200"></a> <span class='hs-conid'>Left</span> <span class='hs-varid'>err</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Left</span> <span class='hs-varid'>err</span>
<a name="line-201"></a> <span class='hs-conid'>Right</span> <span class='hs-varid'>ps</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Right</span> <span class='hs-varop'>$</span> <span class='hs-varid'>n</span> <span class='hs-conop'>:</span> <span class='hs-varid'>ps</span>
<a name="line-202"></a> <span class='hs-keyword'>where</span>
<a name="line-203"></a> <span class='hs-varid'>okColumns</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>map</span> <span class='hs-varid'>fst</span> <span class='hs-varop'>$</span> <span class='hs-varid'>filter</span> <span class='hs-varid'>snd</span> <span class='hs-varop'>$</span>
<a name="line-204"></a> <span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-varid'>id</span> <span class='hs-varop'>***</span> <span class='hs-varid'>okColumn</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span>
<a name="line-205"></a> <span class='hs-conid'>Map</span><span class='hs-varop'>.</span><span class='hs-varid'>toList</span> <span class='hs-varop'>$</span> <span class='hs-varid'>columns</span> <span class='hs-varid'>rb</span>
<a name="line-206"></a>
<a name="line-207"></a><a name="prop_lexOrder"></a><span class='hs-definition'>prop_lexOrder</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>RecBehaviour</span> <span class='hs-conid'>Integer</span> <span class='hs-conid'>Integer</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Property</span>
<a name="line-208"></a><span class='hs-definition'>prop_lexOrder</span> <span class='hs-varid'>rb</span> <span class='hs-keyglyph'>=</span>
<a name="line-209"></a> <span class='hs-keyword'>let</span> <span class='hs-varid'>mPerm</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>lexOrder</span> <span class='hs-varid'>rb</span>
<a name="line-210"></a> <span class='hs-conid'>Right</span> <span class='hs-varid'>perm</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>mPerm</span>
<a name="line-211"></a> <span class='hs-keyword'>in</span>
<a name="line-212"></a> <span class='hs-varid'>isRight</span> <span class='hs-varid'>mPerm</span> <span class='hs-varop'>==></span>
<a name="line-213"></a> <span class='hs-varid'>classify</span> <span class='hs-layout'>(</span><span class='hs-varid'>cols</span> <span class='hs-layout'>(</span><span class='hs-varid'>size</span> <span class='hs-varid'>rb</span><span class='hs-layout'>)</span> <span class='hs-varop'>>=</span> <span class='hs-num'>2</span><span class='hs-layout'>)</span> <span class='hs-str'>"interesting"</span> <span class='hs-varop'>$</span>
<a name="line-214"></a> <span class='hs-varid'>correctLexOrder</span> <span class='hs-varid'>rb</span> <span class='hs-varid'>perm</span>
<a name="line-215"></a>
<a name="line-216"></a><a name="prop_lexOrder_noArgs"></a><span class='hs-definition'>prop_lexOrder_noArgs</span> <span class='hs-keyglyph'>=</span>
<a name="line-217"></a> <span class='hs-varid'>forAll</span> <span class='hs-varid'>positive</span> <span class='hs-varop'>$</span> <span class='hs-keyglyph'>\</span><span class='hs-varid'>n</span> <span class='hs-keyglyph'>-></span>
<a name="line-218"></a> <span class='hs-varid'>isLeft</span> <span class='hs-layout'>(</span><span class='hs-varid'>lexOrder</span> <span class='hs-varop'>$</span> <span class='hs-varid'>rb</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span>
<a name="line-219"></a> <span class='hs-keyword'>where</span> <span class='hs-varid'>rb</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Integer</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>RecBehaviour</span> <span class='hs-conid'>Integer</span> <span class='hs-conid'>Integer</span>
<a name="line-220"></a> <span class='hs-varid'>rb</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>RB</span> <span class='hs-layout'>{</span> <span class='hs-varid'>columns</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Map</span><span class='hs-varop'>.</span><span class='hs-varid'>empty</span>
<a name="line-221"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>calls</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Set</span><span class='hs-varop'>.</span><span class='hs-varid'>fromList</span> <span class='hs-keyglyph'>[</span><span class='hs-num'>1</span> <span class='hs-keyglyph'>..</span> <span class='hs-varid'>n</span><span class='hs-keyglyph'>]</span>
<a name="line-222"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>size</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Size</span> <span class='hs-layout'>{</span> <span class='hs-varid'>rows</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>n</span><span class='hs-layout'>,</span> <span class='hs-varid'>cols</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>0</span> <span class='hs-layout'>}</span>
<a name="line-223"></a> <span class='hs-layout'>}</span>
<a name="line-224"></a>
<a name="line-225"></a><span class='hs-comment'>------------------------------------------------------------------------</span>
<a name="line-226"></a><span class='hs-comment'>-- All tests</span>
<a name="line-227"></a>
<a name="line-228"></a><a name="tests"></a><span class='hs-definition'>tests</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>IO</span> <span class='hs-conid'>Bool</span>
<a name="line-229"></a><span class='hs-definition'>tests</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>runTests</span> <span class='hs-str'>"Agda.Termination.Lexicographic"</span>
<a name="line-230"></a> <span class='hs-keyglyph'>[</span> <span class='hs-varid'>quickCheck'</span> <span class='hs-varid'>prop_recBehaviour_Arbitrary</span>
<a name="line-231"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>quickCheck'</span> <span class='hs-varid'>prop_fromDiagonals</span>
<a name="line-232"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>quickCheck'</span> <span class='hs-varid'>prop_newBehaviour</span>
<a name="line-233"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>quickCheckWith'</span> <span class='hs-varid'>stdArgs</span><span class='hs-layout'>{</span> <span class='hs-varid'>maxSuccess</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>50</span>
<a name="line-234"></a><span class='hs-cpp'>#if MIN_VERSION_QuickCheck(2,5,0)</span>
<a name="line-235"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>maxDiscardRatio</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>4</span>
<a name="line-236"></a><span class='hs-cpp'>#else</span>
<a name="line-237"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>maxDiscard</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>200</span>
<a name="line-238"></a><span class='hs-cpp'>#endif</span>
<a name="line-239"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>maxSize</span> <span class='hs-keyglyph'>=</span> <span class='hs-num'>20</span>
<a name="line-240"></a> <span class='hs-layout'>}</span>
<a name="line-241"></a> <span class='hs-varid'>prop_lexOrder</span>
<a name="line-242"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>quickCheck'</span> <span class='hs-varid'>prop_lexOrder_noArgs</span>
<a name="line-243"></a> <span class='hs-keyglyph'>]</span>
</pre></body>
</html>
