uncomment Nat examples

Comparison.scala

@@ -1,19 +1,34 @@
 sealed trait Comparison {
-	type gt = Match[False, False, True, Bool]
-	type ge = Match[False, True, True, Bool]
-	type eq = Match[False, True, False, Bool]
-	type le = Match[True, True, False, Bool]
-	type lt = Match[True, False, False, Bool]
+	type gt <: Bool
+	type ge <: Bool
+	type eq <: Bool
+	type le <: Bool
+	type lt <: Bool
 	type Match[IfLT <: Up, IfEQ <: Up, IfGT <: Up, Up] <: Up
 }
 sealed trait GT extends Comparison {
 	type Match[IfLT <: Up, IfEQ <: Up, IfGT <: Up, Up] = IfGT
+	type eq = False
+	type gt = True
+	type lt = False
+	type le = False
+	type ge = True
 }
 sealed trait LT extends Comparison {
 	type Match[IfLT <: Up, IfEQ <: Up, IfGT <: Up, Up] = IfLT
+	type eq = False
+	type gt = False
+	type lt = True
+	type le = True
+	type ge = False
 }
 sealed trait EQ extends Comparison {
 	type Match[IfLT <: Up, IfEQ <: Up, IfGT <: Up, Up] = IfEQ
+	type eq = True
+	type gt = False
+	type lt = False
+	type le = True
+	type ge = True
 }
 object Comparison {
 	def show[C <: Comparison](implicit rep: ComparisonRep[C]): String = rep.value

Nat.scala

@@ -51,7 +51,7 @@ sealed trait Nat0 extends Nat {
 	type Compare[N <: Nat] = N#Match[ConstLT, EQ, Comparison]
 }
 sealed trait Succ[N <: Nat] extends Nat {
-	type FoldR[Init <: Type, Type, F <: Fold[Nat, Type]] = F#Apply[Succ[N], N#FoldR[Init, Type, F]]//N#FoldR[F#Apply[Succ[N],Init], Type, F]
+	type FoldR[Init <: Type, Type, F <: Fold[Nat, Type]] = F#Apply[Succ[N], N#FoldR[Init, Type, F]]
 	type FoldL[Init <: Type, Type, F <: Fold[Nat, Type]] = N#FoldL[F#Apply[Succ[N],Init], Type, F]
 	type Match[NonZero[N <: Nat] <: Up, IfZero <: Up, Up] = NonZero[N]
 	type Compare[O <: Nat] = O#Match[N#Compare, GT, Comparison]

NatTest.scala

@@ -4,8 +4,8 @@ import Bool._
 object NatTest
 {
 	val true = toBoolean[ Sq[_9] === ( _1 + (_8 x _10) )]
-	//val true = toBoolean[ Eq[ Sq[Sq[_9]], Sq[Add[_1,Mult[_8,_10]]] ] ]
-	//val true = toBoolean[ Eq[ Mod[ Exp[_9,_4], _6], _3] ]
-	//val true = toInt[ Mod[ Sq[_9], _6] ] == 81 % 6
+	val true = toBoolean[ Sq[Sq[_9]] === Sq[_1 + (_8 x _10) ] ]
+	val true = toBoolean[ ( (_9 ^ _4) % _6) === _3 ]
+	val true = toInt[ ( Sq[_9] % _6 ) ] == 81 % 6
 	def run() {}
 }