/usr/share/doc/libghc-type-level-doc/html/Data-TypeLevel-Num-Ops.html is in libghc-type-level-doc 0.2.4-7.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 | <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /><title>Data.TypeLevel.Num.Ops</title><link href="ocean.css" rel="stylesheet" type="text/css" title="Ocean" /><script src="haddock-util.js" type="text/javascript"></script><script type="text/javascript">//<![CDATA[
window.onload = function () {pageLoad();setSynopsis("mini_Data-TypeLevel-Num-Ops.html");};
//]]>
</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Data-TypeLevel-Num-Ops.html">Source</a></li><li><a href="index.html">Contents</a></li><li><a href="doc-index.html">Index</a></li></ul><p class="caption">type-level-0.2.4: Type-level programming library</p></div><div id="content"><div id="module-header"><table class="info"><tr><th>Portability</th><td>non-portable (MPTC, non-standard instances)</td></tr><tr><th>Stability</th><td>experimental</td></tr><tr><th>Maintainer</th><td>alfonso.acosta@gmail.com</td></tr><tr><th>Safe Haskell</th><td>None</td></tr></table><p class="caption">Data.TypeLevel.Num.Ops</p></div><div id="table-of-contents"><p class="caption">Contents</p><ul><li><a href="#g:1">Successor/Predecessor
</a></li><li><a href="#g:2">Addition/Subtraction
</a></li><li><a href="#g:3">Multiplication/Division
</a><ul><li><a href="#g:4">Special efficiency cases
</a></li></ul></li><li><a href="#g:5">Exponientiation/Logarithm
</a><ul><li><a href="#g:6">Special efficiency cases
</a></li></ul></li><li><a href="#g:7">Comparison assertions
</a><ul><li><a href="#g:8">General comparison assertion
</a><ul><li><a href="#g:9">Type-level values denoting comparison results
</a></li></ul></li><li><a href="#g:10">Abbreviated comparison assertions
</a></li></ul></li><li><a href="#g:11">Maximum/Minimum
</a></li><li><a href="#g:12">Greatest Common Divisor
</a></li></ul></div><div id="description"><p class="caption">Description</p><div class="doc"><p>Type-level numerical operations and its value-level reflection functions.
</p></div></div><div id="synopsis"><p id="control.syn" class="caption expander" onclick="toggleSection('syn')">Synopsis</p><ul id="section.syn" class="hide" onclick="toggleSection('syn')"><li class="src short"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> x, <a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> y) => <a href="#t:Succ">Succ</a> x y | x -> y, y -> x</li><li class="src short"><a href="#v:succ">succ</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Succ">Succ</a> x y => x -> y</li><li class="src short"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> x, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> y) => <a href="#t:Pred">Pred</a> x y | x -> y, y -> x</li><li class="src short"><a href="#v:pred">pred</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Pred">Pred</a> x y => x -> y</li><li class="src short"><span class="keyword">class</span> (Add' x y z, Add' y x z) => <a href="#t:Add">Add</a> x y z | x y -> z, z x -> y, z y -> x</li><li class="src short"><a href="#v:-43-">(+)</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Add">Add</a> x y z => x -> y -> z</li><li class="src short"><span class="keyword">class</span> <a href="#t:Sub">Sub</a> x y z | x y -> z, z x -> y, z y -> x</li><li class="src short"><a href="#v:-45-">(-)</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Sub">Sub</a> x y z => x -> y -> z</li><li class="src short"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> x, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> y, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> z) => <a href="#t:Mul">Mul</a> x y z | x y -> z</li><li class="src short"><a href="#v:-42-">(*)</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> x y z => x -> y -> z</li><li class="src short"><span class="keyword">class</span> <a href="#t:Div">Div</a> x y z | x y -> z, x z -> y, y z -> x</li><li class="src short"><a href="#v:div">div</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Div">Div</a> x y z => x -> y -> z</li><li class="src short"><span class="keyword">class</span> <a href="#t:Mod">Mod</a> x y r | x y -> r</li><li class="src short"><a href="#v:mod">mod</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Mod">Mod</a> x y r => x -> y -> r</li><li class="src short"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> x, <a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> y) => <a href="#t:DivMod">DivMod</a> x y q r | x y -> q r</li><li class="src short"><a href="#v:divMod">divMod</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:DivMod">DivMod</a> x y q r => x -> y -> (q, r)</li><li class="src short"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> d, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> x) => <a href="#t:IsDivBy">IsDivBy</a> d x </li><li class="src short"><a href="#v:isDivBy">isDivBy</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:IsDivBy">IsDivBy</a> d x => d -> x</li><li class="src short"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> x, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> q) => <a href="#t:Mul10">Mul10</a> x q | x -> q, q -> x</li><li class="src short"><a href="#v:mul10">mul10</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Mul10">Mul10</a> x q => x -> q</li><li class="src short"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> x, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> q) => <a href="#t:Div10">Div10</a> x q | x -> q, q -> x</li><li class="src short"><a href="#v:div10">div10</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Div10">Div10</a> x q => x -> q</li><li class="src short"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> i, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> x) => <a href="#t:DivMod10">DivMod10</a> x i l | i l -> x, x -> i l</li><li class="src short"><a href="#v:divMod10">divMod10</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> x q r => x -> (q, r)</li><li class="src short"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> b, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> e, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> r) => <a href="#t:ExpBase">ExpBase</a> b e r | b e -> r</li><li class="src short"><a href="#v:-94-">(^)</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:ExpBase">ExpBase</a> b e r => b -> e -> r</li><li class="src short"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> b, b <a href="Data-TypeLevel-Num-Ops.html#t::-62--61-:">:>=:</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a>, <a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> x, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> e) => <a href="#t:LogBase">LogBase</a> b x e | b x -> e</li><li class="src short"><a href="#v:logBase">logBase</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:LogBaseF">LogBaseF</a> b x e f => b -> x -> e</li><li class="src short"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> b, b <a href="Data-TypeLevel-Num-Ops.html#t::-62--61-:">:>=:</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a>, <a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> x, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> e, <a href="Data-TypeLevel-Bool.html#t:Bool">Bool</a> f) => <a href="#t:LogBaseF">LogBaseF</a> b x e f | b x -> e f</li><li class="src short"><a href="#v:logBaseF">logBaseF</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:LogBaseF">LogBaseF</a> b x e f => b -> x -> (e, f)</li><li class="src short"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> b, b <a href="Data-TypeLevel-Num-Ops.html#t::-62--61-:">:>=:</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a>, <a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> x) => <a href="#t:IsPowOf">IsPowOf</a> b x </li><li class="src short"><a href="#v:isPowOf">isPowOf</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:IsPowOf">IsPowOf</a> b x => b -> x -> ()</li><li class="src short"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> x, <a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> y) => <a href="#t:Exp10">Exp10</a> x y | x -> y, y -> x</li><li class="src short"><a href="#v:exp10">exp10</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Exp10">Exp10</a> x y => x -> y</li><li class="src short"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> x, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> y) => <a href="#t:Log10">Log10</a> x y | x -> y</li><li class="src short"><a href="#v:log10">log10</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Log10">Log10</a> x y => x -> y</li><li class="src short"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> x, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> y) => <a href="#t:Trich">Trich</a> x y r | x y -> r</li><li class="src short"><a href="#v:trich">trich</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> x y r => z -> x -> r</li><li class="src short"><span class="keyword">data</span> <a href="#t:LT">LT</a> </li><li class="src short"><span class="keyword">data</span> <a href="#t:EQ">EQ</a> </li><li class="src short"><span class="keyword">data</span> <a href="#t:GT">GT</a> </li><li class="src short"><span class="keyword">class</span> x <a href="#t::-61--61-:">:==:</a> y </li><li class="src short"><span class="keyword">class</span> x <a href="#t::-62-:">:>:</a> y </li><li class="src short"><span class="keyword">class</span> x <a href="#t::-60-:">:<:</a> y </li><li class="src short"><span class="keyword">class</span> x <a href="#t::-62--61-:">:>=:</a> y </li><li class="src short"><span class="keyword">class</span> x <a href="#t::-60--61-:">:<=:</a> y </li><li class="src short"><a href="#v:-61--61-">(==)</a> :: x <a href="Data-TypeLevel-Num-Ops.html#t::-61--61-:">:==:</a> y => x -> y -> ()</li><li class="src short"><a href="#v:-62-">(>)</a> :: x <a href="Data-TypeLevel-Num-Ops.html#t::-62-:">:>:</a> y => x -> y -> ()</li><li class="src short"><a href="#v:-60-">(<)</a> :: x <a href="Data-TypeLevel-Num-Ops.html#t::-60-:">:<:</a> y => x -> y -> ()</li><li class="src short"><a href="#v:-62--61-">(>=)</a> :: x <a href="Data-TypeLevel-Num-Ops.html#t::-62--61-:">:>=:</a> y => x -> y -> ()</li><li class="src short"><a href="#v:-60--61-">(<=)</a> :: x <a href="Data-TypeLevel-Num-Ops.html#t::-60--61-:">:<=:</a> y => x -> y -> ()</li><li class="src short"><span class="keyword">class</span> <a href="#t:Max">Max</a> x y z | x y -> z</li><li class="src short"><a href="#v:max">max</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Max">Max</a> x y z => x -> y -> z</li><li class="src short"><span class="keyword">class</span> <a href="#t:Min">Min</a> x y z | x y -> z</li><li class="src short"><a href="#v:min">min</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Min">Min</a> x y z => x -> y -> z</li><li class="src short"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> x, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> y, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> gcd) => <a href="#t:GCD">GCD</a> x y gcd | x y -> gcd</li><li class="src short"><a href="#v:gcd">gcd</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:GCD">GCD</a> x y z => x -> y -> z</li></ul></div><div id="interface"><h1 id="g:1">Successor/Predecessor
</h1><div class="top"><p class="src"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> x, <a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> y) => <a name="t:Succ" class="def">Succ</a> x y | x -> y, y -> x<a href="src/Data-TypeLevel-Num-Ops.html#Succ" class="link">Source</a></p><div class="doc"><p>Successor type-level relation. <code>Succ x y</code> establishes
that <code>succ x = y</code>.
</p></div><div class="subs instances"><p id="control.i:Succ" class="caption collapser" onclick="toggleSection('i:Succ')">Instances</p><div id="section.i:Succ" class="show"><table><tr><td class="src">(<a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> y, IsZero y yz, <a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> x xi xl, Succ' xi xl yi yl yz, <a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> y yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Succ">Succ</a> x y</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:succ" class="def">succ</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Succ">Succ</a> x y => x -> y<a href="src/Data-TypeLevel-Num-Ops.html#succ" class="link">Source</a></p><div class="doc"><p>value-level reflection function for the <code><a href="Data-TypeLevel-Num-Ops.html#t:Succ">Succ</a></code> type-level relation
</p></div></div><div class="top"><p class="src"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> x, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> y) => <a name="t:Pred" class="def">Pred</a> x y | x -> y, y -> x<a href="src/Data-TypeLevel-Num-Ops.html#Pred" class="link">Source</a></p><div class="doc"><p>Predecessor type-level relation. <code>Pred x y</code> establishes
that <code>pred x = y</code>.
</p></div><div class="subs instances"><p id="control.i:Pred" class="caption collapser" onclick="toggleSection('i:Pred')">Instances</p><div id="section.i:Pred" class="show"><table><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Succ">Succ</a> x y => <a href="Data-TypeLevel-Num-Ops.html#t:Pred">Pred</a> y x</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:pred" class="def">pred</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Pred">Pred</a> x y => x -> y<a href="src/Data-TypeLevel-Num-Ops.html#pred" class="link">Source</a></p><div class="doc"><p>value-level reflection function for the <code><a href="Data-TypeLevel-Num-Ops.html#t:Pred">Pred</a></code> type-level relation
</p></div></div><h1 id="g:2">Addition/Subtraction
</h1><div class="top"><p class="src"><span class="keyword">class</span> (Add' x y z, Add' y x z) => <a name="t:Add" class="def">Add</a> x y z | x y -> z, z x -> y, z y -> x<a href="src/Data-TypeLevel-Num-Ops.html#Add" class="link">Source</a></p><div class="doc"><p>Addition type-level relation. <code>Add x y z</code> establishes
that <code>x + y = z</code>.
</p></div><div class="subs instances"><p id="control.i:Add" class="caption collapser" onclick="toggleSection('i:Add')">Instances</p><div id="section.i:Add" class="show"><table><tr><td class="src">(Add' x y z, Add' y x z) => <a href="Data-TypeLevel-Num-Ops.html#t:Add">Add</a> x y z</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:-43-" class="def">(+)</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Add">Add</a> x y z => x -> y -> z<a href="src/Data-TypeLevel-Num-Ops.html#%2B" class="link">Source</a></p><div class="doc"><p>value-level reflection function for the <code><a href="Data-TypeLevel-Num-Ops.html#t:Add">Add</a></code> type-level relation
</p></div></div><div class="top"><p class="src"><span class="keyword">class</span> <a name="t:Sub" class="def">Sub</a> x y z | x y -> z, z x -> y, z y -> x<a href="src/Data-TypeLevel-Num-Ops.html#Sub" class="link">Source</a></p><div class="doc"><p>Subtraction type-level relation. <code>Sub x y z</code> establishes
that <code>x - y = z</code>
</p></div><div class="subs instances"><p id="control.i:Sub" class="caption collapser" onclick="toggleSection('i:Sub')">Instances</p><div id="section.i:Sub" class="show"><table><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Add">Add</a> x y z => <a href="Data-TypeLevel-Num-Ops.html#t:Sub">Sub</a> z y x</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:-45-" class="def">(-)</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Sub">Sub</a> x y z => x -> y -> z<a href="src/Data-TypeLevel-Num-Ops.html#-" class="link">Source</a></p><div class="doc"><p>value-level reflection function for the <code><a href="Data-TypeLevel-Num-Ops.html#t:Sub">Sub</a></code> type-level relation
</p></div></div><h1 id="g:3">Multiplication/Division
</h1><div class="top"><p class="src"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> x, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> y, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> z) => <a name="t:Mul" class="def">Mul</a> x y z | x y -> z<a href="src/Data-TypeLevel-Num-Ops.html#Mul" class="link">Source</a></p><div class="doc"><p>Multiplication type-level relation. <code>Mul x y z</code> establishes
that <code>x * y = z</code>.
Note it isn't relational (i.e. its inverse cannot be used for division,
however, even if it could, the resulting division would only
work for zero-remainder divisions)
</p></div><div class="subs instances"><p id="control.i:Mul" class="caption collapser" onclick="toggleSection('i:Mul')">Instances</p><div id="section.i:Mul" class="show"><table><tr><td class="src">(<a href="Data-TypeLevel-Num-Ops.html#t:Add">Add</a> z y z', <a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> y z) => <a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> y z'</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-TypeLevel-Num-Ops.html#t:Add">Add</a> z y z', <a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> y z) => <a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> y z'</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-TypeLevel-Num-Ops.html#t:Add">Add</a> z y z', <a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> y z) => <a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> y z'</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-TypeLevel-Num-Ops.html#t:Add">Add</a> z y z', <a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> y z) => <a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> y z'</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-TypeLevel-Num-Ops.html#t:Add">Add</a> z y z', <a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> y z) => <a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> y z'</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-TypeLevel-Num-Ops.html#t:Add">Add</a> z y z', <a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> y z) => <a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> y z'</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-TypeLevel-Num-Ops.html#t:Add">Add</a> z y z', <a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> y z) => <a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> y z'</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Add">Add</a> y y z => <a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> y z</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> y => <a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> y y</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> y => <a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> y <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a></td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> xi xl), <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> y, <a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> xi y z, <a href="Data-TypeLevel-Num-Ops.html#t:Mul10">Mul10</a> z z10, <a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> xl y dy, <a href="Data-TypeLevel-Num-Ops.html#t:Add">Add</a> dy z10 z') => <a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> xi xl) y z'</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:-42-" class="def">(*)</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> x y z => x -> y -> z<a href="src/Data-TypeLevel-Num-Ops.html#%2A" class="link">Source</a></p><div class="doc"><p>value-level reflection function for the multiplication type-level relation
</p></div></div><div class="top"><p class="src"><span class="keyword">class</span> <a name="t:Div" class="def">Div</a> x y z | x y -> z, x z -> y, y z -> x<a href="src/Data-TypeLevel-Num-Ops.html#Div" class="link">Source</a></p><div class="doc"><p>Division type-level relation. Remainder-discarding version of <code><a href="Data-TypeLevel-Num-Ops.html#t:DivMod">DivMod</a></code>.
Note it is not relational (due to DivMod not being relational)
</p></div><div class="subs instances"><p id="control.i:Div" class="caption collapser" onclick="toggleSection('i:Div')">Instances</p><div id="section.i:Div" class="show"><table><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:DivMod">DivMod</a> x y q r => <a href="Data-TypeLevel-Num-Ops.html#t:Div">Div</a> x y q</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:div" class="def">div</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Div">Div</a> x y z => x -> y -> z<a href="src/Data-TypeLevel-Num-Ops.html#div" class="link">Source</a></p><div class="doc"><p>value-level reflection function for the <code><a href="Data-TypeLevel-Num-Ops.html#t:Div">Div</a></code> type-level relation
</p></div></div><div class="top"><p class="src"><span class="keyword">class</span> <a name="t:Mod" class="def">Mod</a> x y r | x y -> r<a href="src/Data-TypeLevel-Num-Ops.html#Mod" class="link">Source</a></p><div class="doc"><p>Remainder of division, type-level relation. <code>Mod x y r</code> establishes that
<code>r</code> is the reminder of dividing <code>x</code> by <code>y</code>.
</p></div><div class="subs instances"><p id="control.i:Mod" class="caption collapser" onclick="toggleSection('i:Mod')">Instances</p><div id="section.i:Mod" class="show"><table><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:DivMod">DivMod</a> x y q r => <a href="Data-TypeLevel-Num-Ops.html#t:Mod">Mod</a> x y r</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:mod" class="def">mod</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Mod">Mod</a> x y r => x -> y -> r<a href="src/Data-TypeLevel-Num-Ops.html#mod" class="link">Source</a></p><div class="doc"><p>value-level reflection function for the <code><a href="Data-TypeLevel-Num-Ops.html#t:Mod">Mod</a></code> type-level relation
</p></div></div><div class="top"><p class="src"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> x, <a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> y) => <a name="t:DivMod" class="def">DivMod</a> x y q r | x y -> q r<a href="src/Data-TypeLevel-Num-Ops.html#DivMod" class="link">Source</a></p><div class="doc"><p>Division and Remainder type-level relation. <code>DivMod x y q r</code> establishes
that <code>x<em>y = q + r</em>y</code>
Note it is not relational (i.e. its inverse cannot be used
for multiplication).
</p></div><div class="subs instances"><p id="control.i:DivMod" class="caption collapser" onclick="toggleSection('i:DivMod')">Instances</p><div id="section.i:DivMod" class="show"><table><tr><td class="src">(<a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> y, <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> x y cmp, DivMod' x y q r cmp) => <a href="Data-TypeLevel-Num-Ops.html#t:DivMod">DivMod</a> x y q r</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:divMod" class="def">divMod</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:DivMod">DivMod</a> x y q r => x -> y -> (q, r)<a href="src/Data-TypeLevel-Num-Ops.html#divMod" class="link">Source</a></p><div class="doc"><p>value-level reflection function for the <code><a href="Data-TypeLevel-Num-Ops.html#t:DivMod">DivMod</a></code> type-level relation
</p></div></div><div class="top"><p class="src"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> d, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> x) => <a name="t:IsDivBy" class="def">IsDivBy</a> d x <a href="src/Data-TypeLevel-Num-Ops.html#IsDivBy" class="link">Source</a></p><div class="doc"><p>Is-divisible-by type-level assertion. e.g <code>IsDivBy d x</code> establishes that
<code>x</code> is divisible by <code>d</code>.
</p></div><div class="subs instances"><p id="control.i:IsDivBy" class="caption collapser" onclick="toggleSection('i:IsDivBy')">Instances</p><div id="section.i:IsDivBy" class="show"><table><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:DivMod">DivMod</a> x d q <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> => <a href="Data-TypeLevel-Num-Ops.html#t:IsDivBy">IsDivBy</a> d x</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:isDivBy" class="def">isDivBy</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:IsDivBy">IsDivBy</a> d x => d -> x<a href="src/Data-TypeLevel-Num-Ops.html#isDivBy" class="link">Source</a></p><div class="doc"><p>value-level reflection function for IsDivBy
</p></div></div><h2 id="g:4">Special efficiency cases
</h2><div class="top"><p class="src"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> x, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> q) => <a name="t:Mul10" class="def">Mul10</a> x q | x -> q, q -> x<a href="src/Data-TypeLevel-Num-Ops.html#Mul10" class="link">Source</a></p><div class="doc"><p>Multiplication by 10 type-level relation (based on <code><a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a></code>).
<code>Mul10 x y</code> establishes that <code>10 * x = y</code>.
</p></div><div class="subs instances"><p id="control.i:Mul10" class="caption collapser" onclick="toggleSection('i:Mul10')">Instances</p><div id="section.i:Mul10" class="show"><table><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> x q <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> => <a href="Data-TypeLevel-Num-Ops.html#t:Mul10">Mul10</a> q x</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:mul10" class="def">mul10</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Mul10">Mul10</a> x q => x -> q<a href="src/Data-TypeLevel-Num-Ops.html#mul10" class="link">Source</a></p><div class="doc"><p>value-level reflection function for <code><a href="Data-TypeLevel-Num-Ops.html#t:Mul10">Mul10</a></code>
</p></div></div><div class="top"><p class="src"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> x, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> q) => <a name="t:Div10" class="def">Div10</a> x q | x -> q, q -> x<a href="src/Data-TypeLevel-Num-Ops.html#Div10" class="link">Source</a></p><div class="doc"><p>Division by 10 type-level relation (based on DivMod10)
</p></div><div class="subs instances"><p id="control.i:Div10" class="caption collapser" onclick="toggleSection('i:Div10')">Instances</p><div id="section.i:Div10" class="show"><table><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> x q r => <a href="Data-TypeLevel-Num-Ops.html#t:Div10">Div10</a> x q</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:div10" class="def">div10</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Div10">Div10</a> x q => x -> q<a href="src/Data-TypeLevel-Num-Ops.html#div10" class="link">Source</a></p><div class="doc"><p>value-level reflection function for Mul10
</p></div></div><div class="top"><p class="src"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> i, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> x) => <a name="t:DivMod10" class="def">DivMod10</a> x i l | i l -> x, x -> i l<a href="src/Data-TypeLevel-Num-Ops.html#DivMod10" class="link">Source</a></p><div class="doc"><p>Division by 10 and Remainer type-level relation (similar to <code><a href="Data-TypeLevel-Num-Ops.html#t:DivMod">DivMod</a></code>).
</p><p>This operation is much faster than DivMod. Furthermore, it is
the general, non-structural, constructor/deconstructor since it
splits a decimal numeral into its initial digits and last digit.
Thus, it allows to inspect the structure of a number and is normally
used to create type-level operations.
</p><p>Note that contrary to <code><a href="Data-TypeLevel-Num-Ops.html#t:DivMod">DivMod</a></code>, <code><a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a></code> is relational (it can be used to
multiply by 10)
</p></div><div class="subs instances"><p id="control.i:DivMod10" class="caption collapser" onclick="toggleSection('i:DivMod10')">Instances</p><div id="section.i:DivMod10" class="show"><table><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> l) => <a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> l) <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> l</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> l) => <a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> l) <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> l</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> l) => <a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> l) <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> l</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> l) => <a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> l) <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> l</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> l) => <a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> l) <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> l</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> l) => <a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> l) <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> l</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> l) => <a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> l) <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> l</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> l) => <a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> l) <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> l</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> l) => <a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> l) <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> l</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> x l), <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> x l) l')) => <a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> x l) l') (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> x l) l'</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:divMod10" class="def">divMod10</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:DivMod10">DivMod10</a> x q r => x -> (q, r)<a href="src/Data-TypeLevel-Num-Ops.html#divMod10" class="link">Source</a></p><div class="doc"><p>value-level reflection function for DivMod10
</p></div></div><h1 id="g:5">Exponientiation/Logarithm
</h1><div class="top"><p class="src"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> b, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> e, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> r) => <a name="t:ExpBase" class="def">ExpBase</a> b e r | b e -> r<a href="src/Data-TypeLevel-Num-Ops.html#ExpBase" class="link">Source</a></p><div class="doc"><p>Exponentation type-level relation. <code>ExpBase b e r</code> establishes
that <code>b^e = r</code>
Note it is not relational (i.e. it cannot be used to express logarithms)
</p></div><div class="subs instances"><p id="control.i:ExpBase" class="caption collapser" onclick="toggleSection('i:ExpBase')">Instances</p><div id="section.i:ExpBase" class="show"><table><tr><td class="src">(<a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> r b r', <a href="Data-TypeLevel-Num-Ops.html#t:ExpBase">ExpBase</a> b <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> r) => <a href="Data-TypeLevel-Num-Ops.html#t:ExpBase">ExpBase</a> b <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> r'</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> r b r', <a href="Data-TypeLevel-Num-Ops.html#t:ExpBase">ExpBase</a> b <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> r) => <a href="Data-TypeLevel-Num-Ops.html#t:ExpBase">ExpBase</a> b <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> r'</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> r b r', <a href="Data-TypeLevel-Num-Ops.html#t:ExpBase">ExpBase</a> b <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> r) => <a href="Data-TypeLevel-Num-Ops.html#t:ExpBase">ExpBase</a> b <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> r'</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> r b r', <a href="Data-TypeLevel-Num-Ops.html#t:ExpBase">ExpBase</a> b <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> r) => <a href="Data-TypeLevel-Num-Ops.html#t:ExpBase">ExpBase</a> b <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> r'</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> r b r', <a href="Data-TypeLevel-Num-Ops.html#t:ExpBase">ExpBase</a> b <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> r) => <a href="Data-TypeLevel-Num-Ops.html#t:ExpBase">ExpBase</a> b <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> r'</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> r b r', <a href="Data-TypeLevel-Num-Ops.html#t:ExpBase">ExpBase</a> b <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> r) => <a href="Data-TypeLevel-Num-Ops.html#t:ExpBase">ExpBase</a> b <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> r'</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> r b r', <a href="Data-TypeLevel-Num-Ops.html#t:ExpBase">ExpBase</a> b <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> r) => <a href="Data-TypeLevel-Num-Ops.html#t:ExpBase">ExpBase</a> b <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> r'</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> b b r => <a href="Data-TypeLevel-Num-Ops.html#t:ExpBase">ExpBase</a> b <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> r</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> b => <a href="Data-TypeLevel-Num-Ops.html#t:ExpBase">ExpBase</a> b <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> b</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> b => <a href="Data-TypeLevel-Num-Ops.html#t:ExpBase">ExpBase</a> b <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a></td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> b, <a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> ei el), <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> r, <a href="Data-TypeLevel-Num-Ops.html#t:Mul">Mul</a> b r r', <a href="Data-TypeLevel-Num-Ops.html#t:Pred">Pred</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> ei el) e', <a href="Data-TypeLevel-Num-Ops.html#t:ExpBase">ExpBase</a> b e' r) => <a href="Data-TypeLevel-Num-Ops.html#t:ExpBase">ExpBase</a> b (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> ei el) r'</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:-94-" class="def">(^)</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:ExpBase">ExpBase</a> b e r => b -> e -> r<a href="src/Data-TypeLevel-Num-Ops.html#%5E" class="link">Source</a></p><div class="doc"><p>value-level reflection function for the ExpBase type-level relation
</p></div></div><div class="top"><p class="src"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> b, b <a href="Data-TypeLevel-Num-Ops.html#t::-62--61-:">:>=:</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a>, <a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> x, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> e) => <a name="t:LogBase" class="def">LogBase</a> b x e | b x -> e<a href="src/Data-TypeLevel-Num-Ops.html#LogBase" class="link">Source</a></p><div class="subs instances"><p id="control.i:LogBase" class="caption collapser" onclick="toggleSection('i:LogBase')">Instances</p><div id="section.i:LogBase" class="show"><table><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:LogBaseF">LogBaseF</a> b x e f => <a href="Data-TypeLevel-Num-Ops.html#t:LogBase">LogBase</a> b x e</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:logBase" class="def">logBase</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:LogBaseF">LogBaseF</a> b x e f => b -> x -> e<a href="src/Data-TypeLevel-Num-Ops.html#logBase" class="link">Source</a></p><div class="doc"><p>value-level reflection function for LogBase
</p></div></div><div class="top"><p class="src"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> b, b <a href="Data-TypeLevel-Num-Ops.html#t::-62--61-:">:>=:</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a>, <a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> x, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> e, <a href="Data-TypeLevel-Bool.html#t:Bool">Bool</a> f) => <a name="t:LogBaseF" class="def">LogBaseF</a> b x e f | b x -> e f<a href="src/Data-TypeLevel-Num-Ops.html#LogBaseF" class="link">Source</a></p><div class="doc"><p>Version of LogBase which also outputs if the logarithm
calculated was exact.
f indicates if the resulting logarithm has no fractional part (i.e.
tells if the result provided is exact)
</p></div><div class="subs instances"><p id="control.i:LogBaseF" class="caption collapser" onclick="toggleSection('i:LogBaseF')">Instances</p><div id="section.i:LogBaseF" class="show"><table><tr><td class="src">(<a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> x b cmp, LogBaseF' b x e f cmp) => <a href="Data-TypeLevel-Num-Ops.html#t:LogBaseF">LogBaseF</a> b x e f</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:logBaseF" class="def">logBaseF</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:LogBaseF">LogBaseF</a> b x e f => b -> x -> (e, f)<a href="src/Data-TypeLevel-Num-Ops.html#logBaseF" class="link">Source</a></p><div class="doc"><p>value-level reflection function for LogBaseF
</p></div></div><div class="top"><p class="src"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> b, b <a href="Data-TypeLevel-Num-Ops.html#t::-62--61-:">:>=:</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a>, <a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> x) => <a name="t:IsPowOf" class="def">IsPowOf</a> b x <a href="src/Data-TypeLevel-Num-Ops.html#IsPowOf" class="link">Source</a></p><div class="doc"><p>Assert that a number (<code>x</code>) can be expressed as the power of another one
(<code>b</code>) (i.e. the fractional part of <code>log_base_b x = 0</code>, or,
in a different way, <code>exists y . b^y = x</code>).
</p></div><div class="subs instances"><p id="control.i:IsPowOf" class="caption collapser" onclick="toggleSection('i:IsPowOf')">Instances</p><div id="section.i:IsPowOf" class="show"><table><tr><td class="src">(<a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> x b cmp, IsPowOf' b x cmp) => <a href="Data-TypeLevel-Num-Ops.html#t:IsPowOf">IsPowOf</a> b x</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:isPowOf" class="def">isPowOf</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:IsPowOf">IsPowOf</a> b x => b -> x -> ()<a href="src/Data-TypeLevel-Num-Ops.html#isPowOf" class="link">Source</a></p></div><h2 id="g:6">Special efficiency cases
</h2><div class="top"><p class="src"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> x, <a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> y) => <a name="t:Exp10" class="def">Exp10</a> x y | x -> y, y -> x<a href="src/Data-TypeLevel-Num-Ops.html#Exp10" class="link">Source</a></p><div class="doc"><p>Base-10 Exponentiation type-level relation
</p></div><div class="subs instances"><p id="control.i:Exp10" class="caption collapser" onclick="toggleSection('i:Exp10')">Instances</p><div id="section.i:Exp10" class="show"><table><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Exp10">Exp10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Exp10">Exp10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Exp10">Exp10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Exp10">Exp10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Exp10">Exp10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Exp10">Exp10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Exp10">Exp10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Exp10">Exp10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Exp10">Exp10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>)</td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Exp10">Exp10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>)</td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-TypeLevel-Num-Ops.html#t:Pred">Pred</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> xi xl) x', <a href="Data-TypeLevel-Num-Ops.html#t:Exp10">Exp10</a> x' (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> y <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>)) => <a href="Data-TypeLevel-Num-Ops.html#t:Exp10">Exp10</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> xi xl) (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> y <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a>)</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:exp10" class="def">exp10</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Exp10">Exp10</a> x y => x -> y<a href="src/Data-TypeLevel-Num-Ops.html#exp10" class="link">Source</a></p><div class="doc"><p>value-level reflection function for Exp10
</p></div></div><div class="top"><p class="src"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> x, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> y) => <a name="t:Log10" class="def">Log10</a> x y | x -> y<a href="src/Data-TypeLevel-Num-Ops.html#Log10" class="link">Source</a></p><div class="doc"><p>Base-10 logarithm type-level relation
Note it is not relational (cannot be used to express Exponentation to 10)
However, it works with any positive numeral (not just powers of 10)
</p></div><div class="subs instances"><p id="control.i:Log10" class="caption collapser" onclick="toggleSection('i:Log10')">Instances</p><div id="section.i:Log10" class="show"><table><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Log10">Log10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Log10">Log10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Log10">Log10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Log10">Log10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Log10">Log10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Log10">Log10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Log10">Log10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Log10">Log10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Log10">Log10</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a></td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> xi xl), <a href="Data-TypeLevel-Num-Ops.html#t:Pred">Pred</a> y y', <a href="Data-TypeLevel-Num-Ops.html#t:Log10">Log10</a> xi y') => <a href="Data-TypeLevel-Num-Ops.html#t:Log10">Log10</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> xi xl) y</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:log10" class="def">log10</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Log10">Log10</a> x y => x -> y<a href="src/Data-TypeLevel-Num-Ops.html#log10" class="link">Source</a></p><div class="doc"><p>value-level reflection function for <code><a href="Data-TypeLevel-Num-Ops.html#t:Log10">Log10</a></code>
</p></div></div><h1 id="g:7">Comparison assertions
</h1><h2 id="g:8">General comparison assertion
</h2><div class="top"><p class="src"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> x, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> y) => <a name="t:Trich" class="def">Trich</a> x y r | x y -> r<a href="src/Data-TypeLevel-Num-Ops.html#Trich" class="link">Source</a></p><div class="doc"><p>Trichotomy type-level relation. 'Trich x y r' establishes
the relation (<code>r</code>) between <code>x</code> and <code>y</code>. The obtained relation (<code>r</code>)
Can be <code><a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></code> (if <code>x</code> is lower than <code>y</code>), <code><a href="Data-TypeLevel-Num-Ops.html#t:EQ">EQ</a></code> (if <code>x</code> equals <code>y</code>) or
<code><a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></code> (if <code>x</code> is greater than <code>y</code>)
</p></div><div class="subs instances"><p id="control.i:Trich" class="caption collapser" onclick="toggleSection('i:Trich')">Instances</p><div id="section.i:Trich" class="show"><table><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Ops.html#t:EQ">EQ</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Ops.html#t:EQ">EQ</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Ops.html#t:EQ">EQ</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Ops.html#t:EQ">EQ</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Ops.html#t:EQ">EQ</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Ops.html#t:EQ">EQ</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Ops.html#t:EQ">EQ</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Ops.html#t:EQ">EQ</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Ops.html#t:EQ">EQ</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Ops.html#t:EQ">EQ</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src">(<a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> xi xl), <a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl), <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> xl yl rl, <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> xi yi ri, CS ri rl r) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> xi xl) (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) r</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:trich" class="def">trich</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> x y r => z -> x -> r<a href="src/Data-TypeLevel-Num-Ops.html#trich" class="link">Source</a></p><div class="doc"><p>value-level reflection function for the comparison type-level assertion
</p></div></div><h3 id="g:9">Type-level values denoting comparison results
</h3><div class="top"><p class="src"><span class="keyword">data</span> <a name="t:LT" class="def">LT</a> <a href="src/Data-TypeLevel-Num-Ops.html#LT" class="link">Source</a></p><div class="doc"><p>Lower than
</p></div><div class="subs instances"><p id="control.i:LT" class="caption collapser" onclick="toggleSection('i:LT')">Instances</p><div id="section.i:LT" class="show"><table><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a></td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">data</span> <a name="t:EQ" class="def">EQ</a> <a href="src/Data-TypeLevel-Num-Ops.html#EQ" class="link">Source</a></p><div class="doc"><p>Equal
</p></div><div class="subs instances"><p id="control.i:EQ" class="caption collapser" onclick="toggleSection('i:EQ')">Instances</p><div id="section.i:EQ" class="show"><table><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Ops.html#t:EQ">EQ</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Ops.html#t:EQ">EQ</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Ops.html#t:EQ">EQ</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Ops.html#t:EQ">EQ</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Ops.html#t:EQ">EQ</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Ops.html#t:EQ">EQ</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Ops.html#t:EQ">EQ</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Ops.html#t:EQ">EQ</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Ops.html#t:EQ">EQ</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Ops.html#t:EQ">EQ</a></td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">data</span> <a name="t:GT" class="def">GT</a> <a href="src/Data-TypeLevel-Num-Ops.html#GT" class="link">Source</a></p><div class="doc"><p>Greater than
</p></div><div class="subs instances"><p id="control.i:GT" class="caption collapser" onclick="toggleSection('i:GT')">Instances</p><div id="section.i:GT" class="show"><table><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Reps.html#t:D9">D9</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Reps.html#t:D8">D8</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Reps.html#t:D7">D7</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Reps.html#t:D6">D6</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Reps.html#t:D5">D5</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Reps.html#t:D4">D4</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Reps.html#t:D3">D3</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Reps.html#t:D2">D2</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Reps.html#t:D1">D1</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr><tr><td class="src"><a href="Data-TypeLevel-Num-Sets.html#t:Pos">Pos</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) => <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> (<a href="Data-TypeLevel-Num-Reps.html#t::-42-">:*</a> yi yl) <a href="Data-TypeLevel-Num-Reps.html#t:D0">D0</a> <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a></td><td class="doc empty"> </td></tr></table></div></div></div><h2 id="g:10">Abbreviated comparison assertions
</h2><div class="top"><p class="src"><span class="keyword">class</span> x <a name="t::-61--61-:" class="def">:==:</a> y <a href="src/Data-TypeLevel-Num-Ops.html#%3A%3D%3D%3A" class="link">Source</a></p><div class="doc"><p>Equality abbreviated type-level assertion
</p></div><div class="subs instances"><p id="control.i::-61--61-:" class="caption collapser" onclick="toggleSection('i::-61--61-:')">Instances</p><div id="section.i::-61--61-:" class="show"><table><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> x y <a href="Data-TypeLevel-Num-Ops.html#t:EQ">EQ</a> => x <a href="Data-TypeLevel-Num-Ops.html#t::-61--61-:">:==:</a> y</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">class</span> x <a name="t::-62-:" class="def">:>:</a> y <a href="src/Data-TypeLevel-Num-Ops.html#%3A%3E%3A" class="link">Source</a></p><div class="doc"><p>Greater-than abbreviated type-level assertion
</p></div><div class="subs instances"><p id="control.i::-62-:" class="caption collapser" onclick="toggleSection('i::-62-:')">Instances</p><div id="section.i::-62-:" class="show"><table><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> x y <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a> => x <a href="Data-TypeLevel-Num-Ops.html#t::-62-:">:>:</a> y</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">class</span> x <a name="t::-60-:" class="def">:<:</a> y <a href="src/Data-TypeLevel-Num-Ops.html#%3A%3C%3A" class="link">Source</a></p><div class="doc"><p>Lower-than abbreviated type-level assertion
</p></div><div class="subs instances"><p id="control.i::-60-:" class="caption collapser" onclick="toggleSection('i::-60-:')">Instances</p><div id="section.i::-60-:" class="show"><table><tr><td class="src"><a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> x y <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a> => x <a href="Data-TypeLevel-Num-Ops.html#t::-60-:">:<:</a> y</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">class</span> x <a name="t::-62--61-:" class="def">:>=:</a> y <a href="src/Data-TypeLevel-Num-Ops.html#%3A%3E%3D%3A" class="link">Source</a></p><div class="doc"><p>Greater-than or equal abbreviated type-level assertion
</p></div><div class="subs instances"><p id="control.i::-62--61-:" class="caption collapser" onclick="toggleSection('i::-62--61-:')">Instances</p><div id="section.i::-62--61-:" class="show"><table><tr><td class="src">(<a href="Data-TypeLevel-Num-Ops.html#t:Succ">Succ</a> x x', <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> x' y <a href="Data-TypeLevel-Num-Ops.html#t:GT">GT</a>) => x <a href="Data-TypeLevel-Num-Ops.html#t::-62--61-:">:>=:</a> y</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><span class="keyword">class</span> x <a name="t::-60--61-:" class="def">:<=:</a> y <a href="src/Data-TypeLevel-Num-Ops.html#%3A%3C%3D%3A" class="link">Source</a></p><div class="doc"><p>Lower-than or equal abbreviated type-level assertion
</p></div><div class="subs instances"><p id="control.i::-60--61-:" class="caption collapser" onclick="toggleSection('i::-60--61-:')">Instances</p><div id="section.i::-60--61-:" class="show"><table><tr><td class="src">(<a href="Data-TypeLevel-Num-Ops.html#t:Succ">Succ</a> x' x, <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> x' y <a href="Data-TypeLevel-Num-Ops.html#t:LT">LT</a>) => x <a href="Data-TypeLevel-Num-Ops.html#t::-60--61-:">:<=:</a> y</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:-61--61-" class="def">(==)</a> :: x <a href="Data-TypeLevel-Num-Ops.html#t::-61--61-:">:==:</a> y => x -> y -> ()<a href="src/Data-TypeLevel-Num-Ops.html#%3D%3D" class="link">Source</a></p><div class="doc"><p>value-level reflection function for the equality abbreviated
type-level assertion
</p></div></div><div class="top"><p class="src"><a name="v:-62-" class="def">(>)</a> :: x <a href="Data-TypeLevel-Num-Ops.html#t::-62-:">:>:</a> y => x -> y -> ()<a href="src/Data-TypeLevel-Num-Ops.html#%3E" class="link">Source</a></p><div class="doc"><p>value-level reflection function for the equality abbreviated
type-level assertion
</p></div></div><div class="top"><p class="src"><a name="v:-60-" class="def">(<)</a> :: x <a href="Data-TypeLevel-Num-Ops.html#t::-60-:">:<:</a> y => x -> y -> ()<a href="src/Data-TypeLevel-Num-Ops.html#%3C" class="link">Source</a></p><div class="doc"><p>value-level reflection function for the lower-than abbreviated
type-level assertion
</p></div></div><div class="top"><p class="src"><a name="v:-62--61-" class="def">(>=)</a> :: x <a href="Data-TypeLevel-Num-Ops.html#t::-62--61-:">:>=:</a> y => x -> y -> ()<a href="src/Data-TypeLevel-Num-Ops.html#%3E%3D" class="link">Source</a></p><div class="doc"><p>value-level reflection function for the greater-than or equal abbreviated
type-level assertion
</p></div></div><div class="top"><p class="src"><a name="v:-60--61-" class="def">(<=)</a> :: x <a href="Data-TypeLevel-Num-Ops.html#t::-60--61-:">:<=:</a> y => x -> y -> ()<a href="src/Data-TypeLevel-Num-Ops.html#%3C%3D" class="link">Source</a></p><div class="doc"><p>value-level reflection function for the lower-than or equal abbreviated
type-level assertion
</p></div></div><h1 id="g:11">Maximum/Minimum
</h1><div class="top"><p class="src"><span class="keyword">class</span> <a name="t:Max" class="def">Max</a> x y z | x y -> z<a href="src/Data-TypeLevel-Num-Ops.html#Max" class="link">Source</a></p><div class="doc"><p>Maximum type-level relation
</p></div><div class="subs instances"><p id="control.i:Max" class="caption collapser" onclick="toggleSection('i:Max')">Instances</p><div id="section.i:Max" class="show"><table><tr><td class="src">(Max' x y b z, <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> x y b) => <a href="Data-TypeLevel-Num-Ops.html#t:Max">Max</a> x y z</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:max" class="def">max</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Max">Max</a> x y z => x -> y -> z<a href="src/Data-TypeLevel-Num-Ops.html#max" class="link">Source</a></p><div class="doc"><p>value-level reflection function for the maximum type-level relation
</p></div></div><div class="top"><p class="src"><span class="keyword">class</span> <a name="t:Min" class="def">Min</a> x y z | x y -> z<a href="src/Data-TypeLevel-Num-Ops.html#Min" class="link">Source</a></p><div class="doc"><p>Minimum type-level relation
</p></div><div class="subs instances"><p id="control.i:Min" class="caption collapser" onclick="toggleSection('i:Min')">Instances</p><div id="section.i:Min" class="show"><table><tr><td class="src">(Max' y x b z, <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> x y b) => <a href="Data-TypeLevel-Num-Ops.html#t:Min">Min</a> x y z</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:min" class="def">min</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:Min">Min</a> x y z => x -> y -> z<a href="src/Data-TypeLevel-Num-Ops.html#min" class="link">Source</a></p><div class="doc"><p>value-level reflection function for the minimum type-level relation
</p></div></div><h1 id="g:12">Greatest Common Divisor
</h1><div class="top"><p class="src"><span class="keyword">class</span> (<a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> x, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> y, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> gcd) => <a name="t:GCD" class="def">GCD</a> x y gcd | x y -> gcd<a href="src/Data-TypeLevel-Num-Ops.html#GCD" class="link">Source</a></p><div class="doc"><p>Greatest Common Divisor type-level relation
</p></div><div class="subs instances"><p id="control.i:GCD" class="caption collapser" onclick="toggleSection('i:GCD')">Instances</p><div id="section.i:GCD" class="show"><table><tr><td class="src">(<a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> x, <a href="Data-TypeLevel-Num-Sets.html#t:Nat">Nat</a> y, <a href="Data-TypeLevel-Num-Ops.html#t:Trich">Trich</a> x y cmp, IsZero y yz, GCD' x y yz cmp gcd) => <a href="Data-TypeLevel-Num-Ops.html#t:GCD">GCD</a> x y gcd</td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:gcd" class="def">gcd</a> :: <a href="Data-TypeLevel-Num-Ops.html#t:GCD">GCD</a> x y z => x -> y -> z<a href="src/Data-TypeLevel-Num-Ops.html#gcd" class="link">Source</a></p><div class="doc"><p>value-level reflection function for the GCD type-level relation
</p></div></div></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.13.2</p></div></body></html>
|