<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"> <!--Rendered using the Haskell Html Library v0.2--> <HTML ><HEAD ><META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=UTF-8" ><TITLE >Data.TypeLevel.Num.Ops</TITLE ><LINK HREF="haddock.css" REL="stylesheet" TYPE="text/css" ><SCRIPT SRC="haddock-util.js" TYPE="text/javascript" ></SCRIPT ><SCRIPT TYPE="text/javascript" >window.onload = function () {setSynopsis("mini_Data-TypeLevel-Num-Ops.html")};</SCRIPT ></HEAD ><BODY ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="topbar" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD ><IMG SRC="haskell_icon.gif" WIDTH="16" HEIGHT="16" ALT=" " ></TD ><TD CLASS="title" >type-level-0.2.4: Type-level programming library</TD ><TD CLASS="topbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html" >Source code</A ></TD ><TD CLASS="topbut" ><A HREF="index.html" >Contents</A ></TD ><TD CLASS="topbut" ><A HREF="doc-index.html" >Index</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="modulebar" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD ><FONT SIZE="6" >Data.TypeLevel.Num.Ops</FONT ></TD ><TD ALIGN="right" ><TABLE CLASS="narrow" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="infohead" >Portability</TD ><TD CLASS="infoval" >non-portable (MPTC, non-standard instances)</TD ></TR ><TR ><TD CLASS="infohead" >Stability</TD ><TD CLASS="infoval" >experimental</TD ></TR ><TR ><TD CLASS="infohead" >Maintainer</TD ><TD CLASS="infoval" >alfonso.acosta@gmail.com</TD ></TR ></TABLE ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="section4" ><B >Contents</B ></TD ></TR ><TR ><TD ><DL ><DT ><A HREF="#1" >Successor/Predecessor </A ></DT ><DT ><A HREF="#2" >Addition/Subtraction </A ></DT ><DT ><A HREF="#3" >Multiplication/Division </A ></DT ><DD ><DL ><DT ><A HREF="#4" >Special efficiency cases </A ></DT ></DL ></DD ><DT ><A HREF="#5" >Exponientiation/Logarithm </A ></DT ><DD ><DL ><DT ><A HREF="#6" >Special efficiency cases </A ></DT ></DL ></DD ><DT ><A HREF="#7" >Comparison assertions </A ></DT ><DD ><DL ><DT ><A HREF="#8" >General comparison assertion </A ></DT ><DD ><DL ><DT ><A HREF="#9" >Type-level values denoting comparison results </A ></DT ></DL ></DD ><DT ><A HREF="#10" >Abbreviated comparison assertions </A ></DT ></DL ></DD ><DT ><A HREF="#11" >Maximum/Minimum </A ></DT ><DT ><A HREF="#12" >Greatest Common Divisor </A ></DT ></DL ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="section1" >Description</TD ></TR ><TR ><TD CLASS="doc" >Type-level numerical operations and its value-level reflection functions. </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="section1" >Synopsis</TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > y) => <A HREF="#t%3ASucc" >Succ</A > x y | x -> y, y -> x</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3Asucc" >succ</A > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3ASucc" >Succ</A > x y => x -> y</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > y) => <A HREF="#t%3APred" >Pred</A > x y | x -> y, y -> x</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3Apred" >pred</A > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3APred" >Pred</A > x y => x -> y</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > (Add' x y z, Add' y x z) => <A HREF="#t%3AAdd" >Add</A > x y z | x y -> z, z x -> y, z y -> x</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3A%2B" >(+)</A > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3AAdd" >Add</A > x y z => x -> y -> z</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > <A HREF="#t%3ASub" >Sub</A > x y z | x y -> z, z x -> y, z y -> x</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3A-" >(-)</A > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3ASub" >Sub</A > x y z => x -> y -> z</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > y, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > z) => <A HREF="#t%3AMul" >Mul</A > x y z | x y -> z</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3A%2A" >(*)</A > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > x y z => x -> y -> z</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > <A HREF="#t%3ADiv" >Div</A > x y z | x y -> z, x z -> y, y z -> x</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3Adiv" >div</A > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADiv" >Div</A > x y z => x -> y -> z</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > <A HREF="#t%3AMod" >Mod</A > x y r | x y -> r</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3Amod" >mod</A > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMod" >Mod</A > x y r => x -> y -> r</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > y) => <A HREF="#t%3ADivMod" >DivMod</A > x y q r | x y -> q r</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3AdivMod" >divMod</A > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod" >DivMod</A > x y q r => x -> y -> (q, r)</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > d, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x) => <A HREF="#t%3AIsDivBy" >IsDivBy</A > d x </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3AisDivBy" >isDivBy</A > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3AIsDivBy" >IsDivBy</A > d x => d -> x</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > q) => <A HREF="#t%3AMul10" >Mul10</A > x q | x -> q, q -> x</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3Amul10" >mul10</A > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul10" >Mul10</A > x q => x -> q</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > q) => <A HREF="#t%3ADiv10" >Div10</A > x q | x -> q, q -> x</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3Adiv10" >div10</A > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADiv10" >Div10</A > x q => x -> q</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > i, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x) => <A HREF="#t%3ADivMod10" >DivMod10</A > x i l | i l -> x, x -> i l</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3AdivMod10" >divMod10</A > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > x q r => x -> (q, r)</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > b, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > e, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > r) => <A HREF="#t%3AExpBase" >ExpBase</A > b e r | b e -> r</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3A%5E" >(^)</A > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3AExpBase" >ExpBase</A > b e r => b -> e -> r</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > b, b <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3E%3D%3A" >:>=:</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A >, <A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > e) => <A HREF="#t%3ALogBase" >LogBase</A > b x e | b x -> e</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3AlogBase" >logBase</A > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALogBaseF" >LogBaseF</A > b x e f => b -> x -> e</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > b, b <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3E%3D%3A" >:>=:</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A >, <A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > e, <A HREF="Data-TypeLevel-Bool.html#t%3ABool" >Bool</A > f) => <A HREF="#t%3ALogBaseF" >LogBaseF</A > b x e f | b x -> e f</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3AlogBaseF" >logBaseF</A > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALogBaseF" >LogBaseF</A > b x e f => b -> x -> (e, f)</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > b, b <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3E%3D%3A" >:>=:</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A >, <A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > x) => <A HREF="#t%3AIsPowOf" >IsPowOf</A > b x </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3AisPowOf" >isPowOf</A > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3AIsPowOf" >IsPowOf</A > b x => b -> x -> <A HREF="/usr/share/doc/ghc/html/libraries/ghc-prim-0.2.0.0/GHC-Unit.html#t%3A%28%29" >()</A ></TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > y) => <A HREF="#t%3AExp10" >Exp10</A > x y | x -> y, y -> x</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3Aexp10" >exp10</A > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3AExp10" >Exp10</A > x y => x -> y</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > y) => <A HREF="#t%3ALog10" >Log10</A > x y | x -> y</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3Alog10" >log10</A > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALog10" >Log10</A > x y => x -> y</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > y) => <A HREF="#t%3ATrich" >Trich</A > x y r | x y -> r</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3Atrich" >trich</A > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > x y r => z -> x -> r</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >data</SPAN > <A HREF="#t%3ALT" >LT</A > </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >data</SPAN > <A HREF="#t%3AEQ" >EQ</A > </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >data</SPAN > <A HREF="#t%3AGT" >GT</A > </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > x <A HREF="#t%3A%3A%3D%3D%3A" >:==:</A > y </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > x <A HREF="#t%3A%3A%3E%3A" >:>:</A > y </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > x <A HREF="#t%3A%3A%3C%3A" >:<:</A > y </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > x <A HREF="#t%3A%3A%3E%3D%3A" >:>=:</A > y </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > x <A HREF="#t%3A%3A%3C%3D%3A" >:<=:</A > y </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3A%3D%3D" >(==)</A > :: x <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3D%3D%3A" >:==:</A > y => x -> y -> <A HREF="/usr/share/doc/ghc/html/libraries/ghc-prim-0.2.0.0/GHC-Unit.html#t%3A%28%29" >()</A ></TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3A%3E" >(>)</A > :: x <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3E%3A" >:>:</A > y => x -> y -> <A HREF="/usr/share/doc/ghc/html/libraries/ghc-prim-0.2.0.0/GHC-Unit.html#t%3A%28%29" >()</A ></TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3A%3C" >(<)</A > :: x <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3C%3A" >:<:</A > y => x -> y -> <A HREF="/usr/share/doc/ghc/html/libraries/ghc-prim-0.2.0.0/GHC-Unit.html#t%3A%28%29" >()</A ></TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3A%3E%3D" >(>=)</A > :: x <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3E%3D%3A" >:>=:</A > y => x -> y -> <A HREF="/usr/share/doc/ghc/html/libraries/ghc-prim-0.2.0.0/GHC-Unit.html#t%3A%28%29" >()</A ></TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3A%3C%3D" >(<=)</A > :: x <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3C%3D%3A" >:<=:</A > y => x -> y -> <A HREF="/usr/share/doc/ghc/html/libraries/ghc-prim-0.2.0.0/GHC-Unit.html#t%3A%28%29" >()</A ></TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > <A HREF="#t%3AMax" >Max</A > x y z | x y -> z</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3Amax" >max</A > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMax" >Max</A > x y z => x -> y -> z</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > <A HREF="#t%3AMin" >Min</A > x y z | x y -> z</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3Amin" >min</A > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMin" >Min</A > x y z => x -> y -> z</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > y, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > gcd) => <A HREF="#t%3AGCD" >GCD</A > x y gcd | x y -> gcd</TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="#v%3Agcd" >gcd</A > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGCD" >GCD</A > x y z => x -> y -> z</TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="section1" ><A NAME="1" ><A NAME="1" >Successor/Predecessor </A ></A ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > y) => <A NAME="t:Succ" ><A NAME="t%3ASucc" ></A ></A ><B >Succ</B > x y | x -> y, y -> x</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#Succ" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Successor type-level relation. <TT >Succ x y</TT > establishes that <TT >succ x = y</TT >. </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Succ')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:Succ" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > y, IsZero y yz, <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > x xi xl, Succ' xi xl yi yl yz, <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > y yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ASucc" >Succ</A > x y</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:succ" ><A NAME="v%3Asucc" ></A ></A ><B >succ</B > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3ASucc" >Succ</A > x y => x -> y</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#succ" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for the <TT ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ASucc" >Succ</A ></TT > type-level relation </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > y) => <A NAME="t:Pred" ><A NAME="t%3APred" ></A ></A ><B >Pred</B > x y | x -> y, y -> x</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#Pred" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Predecessor type-level relation. <TT >Pred x y</TT > establishes that <TT >pred x = y</TT >. </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Pred')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:Pred" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ASucc" >Succ</A > x y => <A HREF="Data-TypeLevel-Num-Ops.html#t%3APred" >Pred</A > y x</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:pred" ><A NAME="v%3Apred" ></A ></A ><B >pred</B > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3APred" >Pred</A > x y => x -> y</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#pred" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for the <TT ><A HREF="Data-TypeLevel-Num-Ops.html#t%3APred" >Pred</A ></TT > type-level relation </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="section1" ><A NAME="2" ><A NAME="2" >Addition/Subtraction </A ></A ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > (Add' x y z, Add' y x z) => <A NAME="t:Add" ><A NAME="t%3AAdd" ></A ></A ><B >Add</B > x y z | x y -> z, z x -> y, z y -> x</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#Add" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Addition type-level relation. <TT >Add x y z</TT > establishes that <TT >x + y = z</TT >. </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Add')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:Add" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" >(Add' x y z, Add' y x z) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AAdd" >Add</A > x y z</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:+" ><A NAME="v%3A%2B" ></A ></A ><B >(+)</B > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3AAdd" >Add</A > x y z => x -> y -> z</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#%2B" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for the <TT ><A HREF="Data-TypeLevel-Num-Ops.html#t%3AAdd" >Add</A ></TT > type-level relation </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > <A NAME="t:Sub" ><A NAME="t%3ASub" ></A ></A ><B >Sub</B > x y z | x y -> z, z x -> y, z y -> x</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#Sub" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Subtraction type-level relation. <TT >Sub x y z</TT > establishes that <TT >x - y = z</TT > </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Sub')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:Sub" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3AAdd" >Add</A > x y z => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ASub" >Sub</A > z y x</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:-" ><A NAME="v%3A-" ></A ></A ><B >(-)</B > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3ASub" >Sub</A > x y z => x -> y -> z</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#-" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for the <TT ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ASub" >Sub</A ></TT > type-level relation </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="section1" ><A NAME="3" ><A NAME="3" >Multiplication/Division </A ></A ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > y, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > z) => <A NAME="t:Mul" ><A NAME="t%3AMul" ></A ></A ><B >Mul</B > x y z | x y -> z</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#Mul" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Multiplication type-level relation. <TT >Mul x y z</TT > establishes that <TT >x * y = z</TT >. 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) </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Mul')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:Mul" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Ops.html#t%3AAdd" >Add</A > z y z', <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > y z) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > y z'</TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Ops.html#t%3AAdd" >Add</A > z y z', <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > y z) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > y z'</TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Ops.html#t%3AAdd" >Add</A > z y z', <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > y z) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > y z'</TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Ops.html#t%3AAdd" >Add</A > z y z', <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > y z) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > y z'</TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Ops.html#t%3AAdd" >Add</A > z y z', <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > y z) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > y z'</TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Ops.html#t%3AAdd" >Add</A > z y z', <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > y z) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > y z'</TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Ops.html#t%3AAdd" >Add</A > z y z', <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > y z) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > y z'</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3AAdd" >Add</A > y y z => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > y z</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > y => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > y y</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > y => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > y <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A ></TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > xi xl), <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > y, <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > xi y z, <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul10" >Mul10</A > z z10, <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > xl y dy, <A HREF="Data-TypeLevel-Num-Ops.html#t%3AAdd" >Add</A > dy z10 z') => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > xi xl) y z'</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:*" ><A NAME="v%3A%2A" ></A ></A ><B >(*)</B > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > x y z => x -> y -> z</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#%2A" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for the multiplication type-level relation </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > <A NAME="t:Div" ><A NAME="t%3ADiv" ></A ></A ><B >Div</B > x y z | x y -> z, x z -> y, y z -> x</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#Div" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Division type-level relation. Remainder-discarding version of <TT ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod" >DivMod</A ></TT >. Note it is not relational (due to DivMod not being relational) </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Div')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:Div" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod" >DivMod</A > x y q r => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADiv" >Div</A > x y q</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:div" ><A NAME="v%3Adiv" ></A ></A ><B >div</B > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADiv" >Div</A > x y z => x -> y -> z</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#div" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for the <TT ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ADiv" >Div</A ></TT > type-level relation </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > <A NAME="t:Mod" ><A NAME="t%3AMod" ></A ></A ><B >Mod</B > x y r | x y -> r</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#Mod" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Remainder of division, type-level relation. <TT >Mod x y r</TT > establishes that <TT >r</TT > is the reminder of dividing <TT >x</TT > by <TT >y</TT >. </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Mod')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:Mod" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod" >DivMod</A > x y q r => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMod" >Mod</A > x y r</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:mod" ><A NAME="v%3Amod" ></A ></A ><B >mod</B > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMod" >Mod</A > x y r => x -> y -> r</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#mod" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for the <TT ><A HREF="Data-TypeLevel-Num-Ops.html#t%3AMod" >Mod</A ></TT > type-level relation </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > y) => <A NAME="t:DivMod" ><A NAME="t%3ADivMod" ></A ></A ><B >DivMod</B > x y q r | x y -> q r</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#DivMod" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Division and Remainder type-level relation. <TT >DivMod x y q r</TT > establishes that <TT >x<EM >y = q + r</EM >y</TT > Note it is not relational (i.e. its inverse cannot be used for multiplication). </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:DivMod')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:DivMod" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > y, <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > x y cmp, DivMod' x y q r cmp) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod" >DivMod</A > x y q r</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:divMod" ><A NAME="v%3AdivMod" ></A ></A ><B >divMod</B > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod" >DivMod</A > x y q r => x -> y -> (q, r)</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#divMod" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for the <TT ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod" >DivMod</A ></TT > type-level relation </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > d, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x) => <A NAME="t:IsDivBy" ><A NAME="t%3AIsDivBy" ></A ></A ><B >IsDivBy</B > d x </TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#IsDivBy" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Is-divisible-by type-level assertion. e.g <TT >IsDivBy d x</TT > establishes that <TT >x</TT > is divisible by <TT >d</TT >. </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:IsDivBy')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:IsDivBy" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod" >DivMod</A > x d q <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AIsDivBy" >IsDivBy</A > d x</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:isDivBy" ><A NAME="v%3AisDivBy" ></A ></A ><B >isDivBy</B > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3AIsDivBy" >IsDivBy</A > d x => d -> x</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#isDivBy" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for IsDivBy </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="section2" ><A NAME="4" ><A NAME="4" >Special efficiency cases </A ></A ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > q) => <A NAME="t:Mul10" ><A NAME="t%3AMul10" ></A ></A ><B >Mul10</B > x q | x -> q, q -> x</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#Mul10" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Multiplication by 10 type-level relation (based on <TT ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A ></TT >). <TT >Mul10 x y</TT > establishes that <TT >10 * x = y</TT >. </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Mul10')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:Mul10" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > x q <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul10" >Mul10</A > q x</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:mul10" ><A NAME="v%3Amul10" ></A ></A ><B >mul10</B > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul10" >Mul10</A > x q => x -> q</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#mul10" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for <TT ><A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul10" >Mul10</A ></TT > </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > q) => <A NAME="t:Div10" ><A NAME="t%3ADiv10" ></A ></A ><B >Div10</B > x q | x -> q, q -> x</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#Div10" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Division by 10 type-level relation (based on DivMod10) </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Div10')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:Div10" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > x q r => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADiv10" >Div10</A > x q</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:div10" ><A NAME="v%3Adiv10" ></A ></A ><B >div10</B > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADiv10" >Div10</A > x q => x -> q</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#div10" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for Mul10 </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > i, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x) => <A NAME="t:DivMod10" ><A NAME="t%3ADivMod10" ></A ></A ><B >DivMod10</B > x i l | i l -> x, x -> i l</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#DivMod10" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" ><P >Division by 10 and Remainer type-level relation (similar to <TT ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod" >DivMod</A ></TT >). </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 <TT ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod" >DivMod</A ></TT >, <TT ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A ></TT > is relational (it can be used to multiply by 10) </P ></TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:DivMod10')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:DivMod10" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > l) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > l) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > l</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > l) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > l) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > l</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > l) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > l) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > l</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > l) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > l) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > l</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > l) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > l) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > l</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > l) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > l) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > l</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > l) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > l) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > l</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > l) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > l) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > l</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > l) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > l) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > l</TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > x l), <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > x l) l')) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > x l) l') (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > x l) l'</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:divMod10" ><A NAME="v%3AdivMod10" ></A ></A ><B >divMod10</B > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod10" >DivMod10</A > x q r => x -> (q, r)</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#divMod10" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for DivMod10 </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="section1" ><A NAME="5" ><A NAME="5" >Exponientiation/Logarithm </A ></A ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > b, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > e, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > r) => <A NAME="t:ExpBase" ><A NAME="t%3AExpBase" ></A ></A ><B >ExpBase</B > b e r | b e -> r</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#ExpBase" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Exponentation type-level relation. <TT >ExpBase b e r</TT > establishes that <TT >b^e = r</TT > Note it is not relational (i.e. it cannot be used to express logarithms) </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:ExpBase')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:ExpBase" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > r b r', <A HREF="Data-TypeLevel-Num-Ops.html#t%3AExpBase" >ExpBase</A > b <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > r) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AExpBase" >ExpBase</A > b <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > r'</TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > r b r', <A HREF="Data-TypeLevel-Num-Ops.html#t%3AExpBase" >ExpBase</A > b <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > r) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AExpBase" >ExpBase</A > b <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > r'</TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > r b r', <A HREF="Data-TypeLevel-Num-Ops.html#t%3AExpBase" >ExpBase</A > b <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > r) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AExpBase" >ExpBase</A > b <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > r'</TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > r b r', <A HREF="Data-TypeLevel-Num-Ops.html#t%3AExpBase" >ExpBase</A > b <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > r) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AExpBase" >ExpBase</A > b <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > r'</TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > r b r', <A HREF="Data-TypeLevel-Num-Ops.html#t%3AExpBase" >ExpBase</A > b <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > r) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AExpBase" >ExpBase</A > b <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > r'</TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > r b r', <A HREF="Data-TypeLevel-Num-Ops.html#t%3AExpBase" >ExpBase</A > b <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > r) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AExpBase" >ExpBase</A > b <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > r'</TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > r b r', <A HREF="Data-TypeLevel-Num-Ops.html#t%3AExpBase" >ExpBase</A > b <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > r) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AExpBase" >ExpBase</A > b <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > r'</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > b b r => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AExpBase" >ExpBase</A > b <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > r</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > b => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AExpBase" >ExpBase</A > b <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > b</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > b => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AExpBase" >ExpBase</A > b <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A ></TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > b, <A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > ei el), <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > r, <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMul" >Mul</A > b r r', <A HREF="Data-TypeLevel-Num-Ops.html#t%3APred" >Pred</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > ei el) e', <A HREF="Data-TypeLevel-Num-Ops.html#t%3AExpBase" >ExpBase</A > b e' r) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AExpBase" >ExpBase</A > b (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > ei el) r'</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:^" ><A NAME="v%3A%5E" ></A ></A ><B >(^)</B > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3AExpBase" >ExpBase</A > b e r => b -> e -> r</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#%5E" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for the ExpBase type-level relation </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > b, b <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3E%3D%3A" >:>=:</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A >, <A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > e) => <A NAME="t:LogBase" ><A NAME="t%3ALogBase" ></A ></A ><B >LogBase</B > b x e | b x -> e</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#LogBase" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:LogBase')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:LogBase" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ALogBaseF" >LogBaseF</A > b x e f => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALogBase" >LogBase</A > b x e</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:logBase" ><A NAME="v%3AlogBase" ></A ></A ><B >logBase</B > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALogBaseF" >LogBaseF</A > b x e f => b -> x -> e</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#logBase" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for LogBase </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > b, b <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3E%3D%3A" >:>=:</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A >, <A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > e, <A HREF="Data-TypeLevel-Bool.html#t%3ABool" >Bool</A > f) => <A NAME="t:LogBaseF" ><A NAME="t%3ALogBaseF" ></A ></A ><B >LogBaseF</B > b x e f | b x -> e f</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#LogBaseF" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >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) </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:LogBaseF')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:LogBaseF" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > x b cmp, LogBaseF' b x e f cmp) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALogBaseF" >LogBaseF</A > b x e f</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:logBaseF" ><A NAME="v%3AlogBaseF" ></A ></A ><B >logBaseF</B > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALogBaseF" >LogBaseF</A > b x e f => b -> x -> (e, f)</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#logBaseF" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for LogBaseF </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > b, b <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3E%3D%3A" >:>=:</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A >, <A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > x) => <A NAME="t:IsPowOf" ><A NAME="t%3AIsPowOf" ></A ></A ><B >IsPowOf</B > b x </TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#IsPowOf" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Assert that a number (<TT >x</TT >) can be expressed as the power of another one (<TT >b</TT >) (i.e. the fractional part of <TT >log_base_b x = 0</TT >, or, in a different way, <TT >exists y . b^y = x</TT >). </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:IsPowOf')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:IsPowOf" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > x b cmp, IsPowOf' b x cmp) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AIsPowOf" >IsPowOf</A > b x</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:isPowOf" ><A NAME="v%3AisPowOf" ></A ></A ><B >isPowOf</B > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3AIsPowOf" >IsPowOf</A > b x => b -> x -> <A HREF="/usr/share/doc/ghc/html/libraries/ghc-prim-0.2.0.0/GHC-Unit.html#t%3A%28%29" >()</A ></TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#isPowOf" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="section2" ><A NAME="6" ><A NAME="6" >Special efficiency cases </A ></A ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > y) => <A NAME="t:Exp10" ><A NAME="t%3AExp10" ></A ></A ><B >Exp10</B > x y | x -> y, y -> x</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#Exp10" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Base-10 Exponentiation type-level relation </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Exp10')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:Exp10" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3AExp10" >Exp10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3AExp10" >Exp10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >)</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3AExp10" >Exp10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >)</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3AExp10" >Exp10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >)</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3AExp10" >Exp10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >)</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3AExp10" >Exp10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >)</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3AExp10" >Exp10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >)</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3AExp10" >Exp10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >)</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3AExp10" >Exp10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >)</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3AExp10" >Exp10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >)</TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Ops.html#t%3APred" >Pred</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > xi xl) x', <A HREF="Data-TypeLevel-Num-Ops.html#t%3AExp10" >Exp10</A > x' (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > y <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >)) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AExp10" >Exp10</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > xi xl) (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > y <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >)</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:exp10" ><A NAME="v%3Aexp10" ></A ></A ><B >exp10</B > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3AExp10" >Exp10</A > x y => x -> y</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#exp10" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for Exp10 </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > y) => <A NAME="t:Log10" ><A NAME="t%3ALog10" ></A ></A ><B >Log10</B > x y | x -> y</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#Log10" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >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) </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Log10')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:Log10" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ALog10" >Log10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ALog10" >Log10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ALog10" >Log10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ALog10" >Log10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ALog10" >Log10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ALog10" >Log10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ALog10" >Log10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ALog10" >Log10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ALog10" >Log10</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A ></TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > xi xl), <A HREF="Data-TypeLevel-Num-Ops.html#t%3APred" >Pred</A > y y', <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALog10" >Log10</A > xi y') => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALog10" >Log10</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > xi xl) y</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:log10" ><A NAME="v%3Alog10" ></A ></A ><B >log10</B > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALog10" >Log10</A > x y => x -> y</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#log10" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for <TT ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ALog10" >Log10</A ></TT > </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="section1" ><A NAME="7" ><A NAME="7" >Comparison assertions </A ></A ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="section2" ><A NAME="8" ><A NAME="8" >General comparison assertion </A ></A ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > y) => <A NAME="t:Trich" ><A NAME="t%3ATrich" ></A ></A ><B >Trich</B > x y r | x y -> r</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#Trich" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Trichotomy type-level relation. 'Trich x y r' establishes the relation (<TT >r</TT >) between <TT >x</TT > and <TT >y</TT >. The obtained relation (<TT >r</TT >) Can be <TT ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TT > (if <TT >x</TT > is lower than <TT >y</TT >), <TT ><A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A ></TT > (if <TT >x</TT > equals <TT >y</TT >) or <TT ><A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TT > (if <TT >x</TT > is greater than <TT >y</TT >) </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Trich')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:Trich" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A 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HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD 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HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > xi xl), <A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl), <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > xl yl rl, <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > xi yi ri, CS ri rl r) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > xi xl) (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) r</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:trich" ><A NAME="v%3Atrich" ></A ></A ><B >trich</B > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > x y r => z -> x -> r</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#trich" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for the comparison type-level assertion </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="section3" ><A NAME="9" ><A NAME="9" >Type-level values denoting comparison results </A ></A ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >data</SPAN > <A NAME="t:LT" ><A NAME="t%3ALT" ></A ></A ><B >LT</B > </TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#LT" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Lower than </TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:LT')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:LT" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" >CS <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A > r <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" >Max' x y <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A > y</TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > y, <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGCD" >GCD</A > y x gcd) => GCD' x y <A HREF="Data-TypeLevel-Bool.html#t%3AFalse" >False</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A > gcd</TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > b, b <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3E%3D%3A" >:>=:</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A >, <A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > x) => LogBaseF' b x <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Bool.html#t%3AFalse" >False</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > y) => DivMod' x y <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > x <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A ></TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >data</SPAN > <A NAME="t:EQ" ><A NAME="t%3AEQ" ></A ></A ><B >EQ</B > </TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#EQ" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Equal </TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:EQ')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:EQ" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" >CS <A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A > r r</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A ></TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > b, b <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3E%3D%3A" >:>=:</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A >) => IsPowOf' b b <A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A ></TD ></TR ><TR ><TD CLASS="decl" >Max' x y <A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A > y</TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x => GCD' x x <A HREF="Data-TypeLevel-Bool.html#t%3AFalse" >False</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A > x</TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > b, b <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3E%3D%3A" >:>=:</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A >) => LogBaseF' b b <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Bool.html#t%3ATrue" >True</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A ></TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > y) => DivMod' x y <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A ></TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >data</SPAN > <A NAME="t:GT" ><A NAME="t%3AGT" ></A ></A ><B >GT</B > </TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#GT" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Greater than </TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:GT')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:GT" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" >CS <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A > r <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > b, b <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3E%3D%3A" >:>=:</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A >, <A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > x, <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod" >DivMod</A > x b q <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A >, <A HREF="Data-TypeLevel-Num-Ops.html#t%3AIsPowOf" >IsPowOf</A > b q) => IsPowOf' b x <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" >Max' x y <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A > x</TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > y, <A HREF="Data-TypeLevel-Num-Ops.html#t%3ASub" >Sub</A > x y x', <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGCD" >GCD</A > x' y gcd) => GCD' x y <A HREF="Data-TypeLevel-Bool.html#t%3AFalse" >False</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A > gcd</TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > b, b <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3E%3D%3A" >:>=:</A > <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A >, <A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > x, <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod" >DivMod</A > x b q r, IsZero r rz, <A HREF="Data-TypeLevel-Bool.html#t%3AAnd" >And</A > rz f' f, <A HREF="Data-TypeLevel-Num-Ops.html#t%3APred" >Pred</A > e e', <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALogBaseF" >LogBaseF</A > b q e' f') => LogBaseF' b x e f <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > y, <A HREF="Data-TypeLevel-Num-Ops.html#t%3ASub" >Sub</A > x y x', <A HREF="Data-TypeLevel-Num-Ops.html#t%3APred" >Pred</A > q q', <A HREF="Data-TypeLevel-Num-Ops.html#t%3ADivMod" >DivMod</A > x' y q' r) => DivMod' x y q r <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD9" >D9</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD8" >D8</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD7" >D7</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD6" >D6</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD5" >D5</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD4" >D4</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD3" >D3</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD2" >D2</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD1" >D1</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Sets.html#t%3APos" >Pos</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > (<A HREF="Data-TypeLevel-Num-Reps.html#t%3A%3A%2A" >:*</A > yi yl) <A HREF="Data-TypeLevel-Num-Reps.html#t%3AD0" >D0</A > <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A ></TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="section2" ><A NAME="10" ><A NAME="10" >Abbreviated comparison assertions </A ></A ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > x <A NAME="t::==:" ><A NAME="t%3A%3A%3D%3D%3A" ></A ></A ><B >:==:</B > y </TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#%3A%3D%3D%3A" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Equality abbreviated type-level assertion </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:%3A%3D%3D%3A')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:%3A%3D%3D%3A" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > x y <A HREF="Data-TypeLevel-Num-Ops.html#t%3AEQ" >EQ</A > => x <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3D%3D%3A" >:==:</A > y</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > x <A NAME="t::>:" ><A NAME="t%3A%3A%3E%3A" ></A ></A ><B >:>:</B > y </TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#%3A%3E%3A" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Greater-than abbreviated type-level assertion </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:%3A%3E%3A')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:%3A%3E%3A" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > x y <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A > => x <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3E%3A" >:>:</A > y</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > x <A NAME="t::<:" ><A NAME="t%3A%3A%3C%3A" ></A ></A ><B >:<:</B > y </TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#%3A%3C%3A" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Lower-than abbreviated type-level assertion </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:%3A%3C%3A')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:%3A%3C%3A" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" ><A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > x y <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A > => x <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3C%3A" >:<:</A > y</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > x <A NAME="t::>=:" ><A NAME="t%3A%3A%3E%3D%3A" ></A ></A ><B >:>=:</B > y </TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#%3A%3E%3D%3A" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Greater-than or equal abbreviated type-level assertion </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:%3A%3E%3D%3A')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:%3A%3E%3D%3A" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Ops.html#t%3ASucc" >Succ</A > x x', <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > x' y <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGT" >GT</A >) => x <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3E%3D%3A" >:>=:</A > y</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > x <A NAME="t::<=:" ><A NAME="t%3A%3A%3C%3D%3A" ></A ></A ><B >:<=:</B > y </TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#%3A%3C%3D%3A" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Lower-than or equal abbreviated type-level assertion </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:%3A%3C%3D%3A')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:%3A%3C%3D%3A" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Ops.html#t%3ASucc" >Succ</A > x' x, <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > x' y <A HREF="Data-TypeLevel-Num-Ops.html#t%3ALT" >LT</A >) => x <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3C%3D%3A" >:<=:</A > y</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:==" ><A NAME="v%3A%3D%3D" ></A ></A ><B >(==)</B > :: x <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3D%3D%3A" >:==:</A > y => x -> y -> <A HREF="/usr/share/doc/ghc/html/libraries/ghc-prim-0.2.0.0/GHC-Unit.html#t%3A%28%29" >()</A ></TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#%3D%3D" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for the equality abbreviated type-level assertion </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:>" ><A NAME="v%3A%3E" ></A ></A ><B >(>)</B > :: x <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3E%3A" >:>:</A > y => x -> y -> <A HREF="/usr/share/doc/ghc/html/libraries/ghc-prim-0.2.0.0/GHC-Unit.html#t%3A%28%29" >()</A ></TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#%3E" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for the equality abbreviated type-level assertion </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:<" ><A NAME="v%3A%3C" ></A ></A ><B >(<)</B > :: x <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3C%3A" >:<:</A > y => x -> y -> <A HREF="/usr/share/doc/ghc/html/libraries/ghc-prim-0.2.0.0/GHC-Unit.html#t%3A%28%29" >()</A ></TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#%3C" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for the lower-than abbreviated type-level assertion </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:>=" ><A NAME="v%3A%3E%3D" ></A ></A ><B >(>=)</B > :: x <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3E%3D%3A" >:>=:</A > y => x -> y -> <A HREF="/usr/share/doc/ghc/html/libraries/ghc-prim-0.2.0.0/GHC-Unit.html#t%3A%28%29" >()</A ></TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#%3E%3D" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for the greater-than or equal abbreviated type-level assertion </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:<=" ><A NAME="v%3A%3C%3D" ></A ></A ><B >(<=)</B > :: x <A HREF="Data-TypeLevel-Num-Ops.html#t%3A%3A%3C%3D%3A" >:<=:</A > y => x -> y -> <A HREF="/usr/share/doc/ghc/html/libraries/ghc-prim-0.2.0.0/GHC-Unit.html#t%3A%28%29" >()</A ></TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#%3C%3D" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for the lower-than or equal abbreviated type-level assertion </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="section1" ><A NAME="11" ><A NAME="11" >Maximum/Minimum </A ></A ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > <A NAME="t:Max" ><A NAME="t%3AMax" ></A ></A ><B >Max</B > x y z | x y -> z</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#Max" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Maximum type-level relation </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Max')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:Max" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" >(Max' x y b z, <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > x y b) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMax" >Max</A > x y z</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:max" ><A NAME="v%3Amax" ></A ></A ><B >max</B > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMax" >Max</A > x y z => x -> y -> z</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#max" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for the maximum type-level relation </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > <A NAME="t:Min" ><A NAME="t%3AMin" ></A ></A ><B >Min</B > x y z | x y -> z</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#Min" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Minimum type-level relation </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:Min')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:Min" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" >(Max' y x b z, <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > x y b) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMin" >Min</A > x y z</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:min" ><A NAME="v%3Amin" ></A ></A ><B >min</B > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3AMin" >Min</A > x y z => x -> y -> z</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#min" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for the minimum type-level relation </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="section1" ><A NAME="12" ><A NAME="12" >Greatest Common Divisor </A ></A ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><SPAN CLASS="keyword" >class</SPAN > (<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > y, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > gcd) => <A NAME="t:GCD" ><A NAME="t%3AGCD" ></A ></A ><B >GCD</B > x y gcd | x y -> gcd</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#GCD" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="body" ><TABLE CLASS="vanilla" CELLSPACING="0" CELLPADDING="0" ><TR ><TD CLASS="ndoc" >Greatest Common Divisor type-level relation </TD ></TR ><TR ><TD CLASS="s8" ></TD ></TR ><TR ><TD CLASS="section4" ><IMG SRC="minus.gif" CLASS="coll" ONCLICK="toggle(this,'i:GCD')" ALT="show/hide" > Instances</TD ></TR ><TR ><TD CLASS="body" ><DIV ID="i:GCD" STYLE="display:block;" ><TABLE CLASS="vanilla" CELLSPACING="1" CELLPADDING="0" ><TR ><TD CLASS="decl" >(<A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > x, <A HREF="Data-TypeLevel-Num-Sets.html#t%3ANat" >Nat</A > y, <A HREF="Data-TypeLevel-Num-Ops.html#t%3ATrich" >Trich</A > x y cmp, IsZero y yz, GCD' x y yz cmp gcd) => <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGCD" >GCD</A > x y gcd</TD ></TR ></TABLE ></DIV ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="topdecl" ><TABLE CLASS="declbar" ><TR ><TD CLASS="declname" ><A NAME="v:gcd" ><A NAME="v%3Agcd" ></A ></A ><B >gcd</B > :: <A HREF="Data-TypeLevel-Num-Ops.html#t%3AGCD" >GCD</A > x y z => x -> y -> z</TD ><TD CLASS="declbut" ><A HREF="src/Data-TypeLevel-Num-Ops.html#gcd" >Source</A ></TD ></TR ></TABLE ></TD ></TR ><TR ><TD CLASS="doc" >value-level reflection function for the GCD type-level relation </TD ></TR ><TR ><TD CLASS="s15" ></TD ></TR ><TR ><TD CLASS="botbar" >Produced by <A HREF="http://www.haskell.org/haddock/" >Haddock</A > version 2.6.1</TD ></TR ></TABLE ></BODY ></HTML >