{-# htermination (enumFromThenRatio :: Ratio MyInt -> Ratio MyInt -> (List (Ratio MyInt))) #-} import qualified Prelude data MyBool = MyTrue | MyFalse data List a = Cons a (List a) | Nil data MyInt = Pos Nat | Neg Nat ; data Nat = Succ Nat | Zero ; data Ordering = LT | EQ | GT ; data Ratio a = CnPc a a; iterate :: (a -> a) -> a -> (List a); iterate f x = Cons x (iterate f (f x)); primNegInt :: MyInt -> MyInt; primNegInt (Pos x) = Neg x; primNegInt (Neg x) = Pos x; negateMyInt :: MyInt -> MyInt negateMyInt = primNegInt; negateRatio :: Ratio MyInt -> Ratio MyInt negateRatio (CnPc x y) = CnPc (negateMyInt x) y; primMinusNat :: Nat -> Nat -> MyInt; primMinusNat Zero Zero = Pos Zero; primMinusNat Zero (Succ y) = Neg (Succ y); primMinusNat (Succ x) Zero = Pos (Succ x); primMinusNat (Succ x) (Succ y) = primMinusNat x y; primPlusNat :: Nat -> Nat -> Nat; primPlusNat Zero Zero = Zero; primPlusNat Zero (Succ y) = Succ y; primPlusNat (Succ x) Zero = Succ x; primPlusNat (Succ x) (Succ y) = Succ (Succ (primPlusNat x y)); primPlusInt :: MyInt -> MyInt -> MyInt; primPlusInt (Pos x) (Neg y) = primMinusNat x y; primPlusInt (Neg x) (Pos y) = primMinusNat y x; primPlusInt (Neg x) (Neg y) = Neg (primPlusNat x y); primPlusInt (Pos x) (Pos y) = Pos (primPlusNat x y); psMyInt :: MyInt -> MyInt -> MyInt psMyInt = primPlusInt; primEqNat :: Nat -> Nat -> MyBool; primEqNat Zero Zero = MyTrue; primEqNat Zero (Succ y) = MyFalse; primEqNat (Succ x) Zero = MyFalse; primEqNat (Succ x) (Succ y) = primEqNat x y; primEqInt :: MyInt -> MyInt -> MyBool; primEqInt (Pos (Succ x)) (Pos (Succ y)) = primEqNat x y; primEqInt (Neg (Succ x)) (Neg (Succ y)) = primEqNat x y; primEqInt (Pos Zero) (Neg Zero) = MyTrue; primEqInt (Neg Zero) (Pos Zero) = MyTrue; primEqInt (Neg Zero) (Neg Zero) = MyTrue; primEqInt (Pos Zero) (Pos Zero) = MyTrue; primEqInt xv xw = MyFalse; esEsMyInt :: MyInt -> MyInt -> MyBool esEsMyInt = primEqInt; fromIntMyInt :: MyInt -> MyInt fromIntMyInt x = x; stop :: MyBool -> a; stop MyFalse = stop MyFalse; error :: a; error = stop MyTrue; otherwise :: MyBool; otherwise = MyTrue; primMinusNatS :: Nat -> Nat -> Nat; primMinusNatS (Succ x) (Succ y) = primMinusNatS x y; primMinusNatS Zero (Succ y) = Zero; primMinusNatS x Zero = x; primDivNatS0 x y MyTrue = Succ (primDivNatS (primMinusNatS x y) (Succ y)); primDivNatS0 x y MyFalse = Zero; primGEqNatS :: Nat -> Nat -> MyBool; primGEqNatS (Succ x) Zero = MyTrue; primGEqNatS (Succ x) (Succ y) = primGEqNatS x y; primGEqNatS Zero (Succ x) = MyFalse; primGEqNatS Zero Zero = MyTrue; primDivNatS :: Nat -> Nat -> Nat; primDivNatS Zero Zero = error; primDivNatS (Succ x) Zero = error; primDivNatS (Succ x) (Succ y) = primDivNatS0 x y (primGEqNatS x y); primDivNatS Zero (Succ x) = Zero; primQuotInt :: MyInt -> MyInt -> MyInt; primQuotInt (Pos x) (Pos (Succ y)) = Pos (primDivNatS x (Succ y)); primQuotInt (Pos x) (Neg (Succ y)) = Neg (primDivNatS x (Succ y)); primQuotInt (Neg x) (Pos (Succ y)) = Neg (primDivNatS x (Succ y)); primQuotInt (Neg x) (Neg (Succ y)) = Pos (primDivNatS x (Succ y)); primQuotInt wz xu = error; quotMyInt :: MyInt -> MyInt -> MyInt quotMyInt = primQuotInt; absReal0 x MyTrue = negateMyInt x; absReal1 x MyTrue = x; absReal1 x MyFalse = absReal0 x otherwise; primCmpNat :: Nat -> Nat -> Ordering; primCmpNat Zero Zero = EQ; primCmpNat Zero (Succ y) = LT; primCmpNat (Succ x) Zero = GT; primCmpNat (Succ x) (Succ y) = primCmpNat x y; primCmpInt :: MyInt -> MyInt -> Ordering; primCmpInt (Pos Zero) (Pos Zero) = EQ; primCmpInt (Pos Zero) (Neg Zero) = EQ; primCmpInt (Neg Zero) (Pos Zero) = EQ; primCmpInt (Neg Zero) (Neg Zero) = EQ; primCmpInt (Pos x) (Pos y) = primCmpNat x y; primCmpInt (Pos x) (Neg y) = GT; primCmpInt (Neg x) (Pos y) = LT; primCmpInt (Neg x) (Neg y) = primCmpNat y x; compareMyInt :: MyInt -> MyInt -> Ordering compareMyInt = primCmpInt; esEsOrdering :: Ordering -> Ordering -> MyBool esEsOrdering LT LT = MyTrue; esEsOrdering LT EQ = MyFalse; esEsOrdering LT GT = MyFalse; esEsOrdering EQ LT = MyFalse; esEsOrdering EQ EQ = MyTrue; esEsOrdering EQ GT = MyFalse; esEsOrdering GT LT = MyFalse; esEsOrdering GT EQ = MyFalse; esEsOrdering GT GT = MyTrue; not :: MyBool -> MyBool; not MyTrue = MyFalse; not MyFalse = MyTrue; fsEsOrdering :: Ordering -> Ordering -> MyBool fsEsOrdering x y = not (esEsOrdering x y); gtEsMyInt :: MyInt -> MyInt -> MyBool gtEsMyInt x y = fsEsOrdering (compareMyInt x y) LT; absReal2 x = absReal1 x (gtEsMyInt x (fromIntMyInt (Pos Zero))); absReal x = absReal2 x; absMyInt :: MyInt -> MyInt absMyInt = absReal; primModNatS0 x y MyTrue = primModNatS (primMinusNatS x (Succ y)) (Succ (Succ y)); primModNatS0 x y MyFalse = Succ x; primModNatS :: Nat -> Nat -> Nat; primModNatS Zero Zero = error; primModNatS Zero (Succ x) = Zero; primModNatS (Succ x) Zero = error; primModNatS (Succ x) (Succ Zero) = Zero; primModNatS (Succ x) (Succ (Succ y)) = primModNatS0 x y (primGEqNatS x (Succ y)); primRemInt :: MyInt -> MyInt -> MyInt; primRemInt (Pos x) (Pos (Succ y)) = Pos (primModNatS x (Succ y)); primRemInt (Pos x) (Neg (Succ y)) = Pos (primModNatS x (Succ y)); primRemInt (Neg x) (Pos (Succ y)) = Neg (primModNatS x (Succ y)); primRemInt (Neg x) (Neg (Succ y)) = Neg (primModNatS x (Succ y)); primRemInt wx wy = error; remMyInt :: MyInt -> MyInt -> MyInt remMyInt = primRemInt; gcd0Gcd'0 x y = gcd0Gcd' y (remMyInt x y); gcd0Gcd'1 MyTrue x xx = x; gcd0Gcd'1 xy xz yu = gcd0Gcd'0 xz yu; gcd0Gcd'2 x xx = gcd0Gcd'1 (esEsMyInt xx (fromIntMyInt (Pos Zero))) x xx; gcd0Gcd'2 yv yw = gcd0Gcd'0 yv yw; gcd0Gcd' x xx = gcd0Gcd'2 x xx; gcd0Gcd' x y = gcd0Gcd'0 x y; gcd0 x y = gcd0Gcd' (absMyInt x) (absMyInt y); gcd1 MyTrue yx yy = error; gcd1 yz zu zv = gcd0 zu zv; gcd2 MyTrue yx yy = gcd1 (esEsMyInt yy (fromIntMyInt (Pos Zero))) yx yy; gcd2 zw zx zy = gcd0 zx zy; gcd3 yx yy = gcd2 (esEsMyInt yx (fromIntMyInt (Pos Zero))) yx yy; gcd3 zz vuu = gcd0 zz vuu; gcd yx yy = gcd3 yx yy; gcd x y = gcd0 x y; reduce2D vuv vuw = gcd vuv vuw; reduce2Reduce0 vuv vuw x y MyTrue = CnPc (quotMyInt x (reduce2D vuv vuw)) (quotMyInt y (reduce2D vuv vuw)); reduce2Reduce1 vuv vuw x y MyTrue = error; reduce2Reduce1 vuv vuw x y MyFalse = reduce2Reduce0 vuv vuw x y otherwise; reduce2 x y = reduce2Reduce1 x y x y (esEsMyInt y (fromIntMyInt (Pos Zero))); reduce x y = reduce2 x y; primMulNat :: Nat -> Nat -> Nat; primMulNat Zero Zero = Zero; primMulNat Zero (Succ y) = Zero; primMulNat (Succ x) Zero = Zero; primMulNat (Succ x) (Succ y) = primPlusNat (primMulNat x (Succ y)) (Succ y); primMulInt :: MyInt -> MyInt -> MyInt; primMulInt (Pos x) (Pos y) = Pos (primMulNat x y); primMulInt (Pos x) (Neg y) = Neg (primMulNat x y); primMulInt (Neg x) (Pos y) = Neg (primMulNat x y); primMulInt (Neg x) (Neg y) = Pos (primMulNat x y); srMyInt :: MyInt -> MyInt -> MyInt srMyInt = primMulInt; psRatio :: Ratio MyInt -> Ratio MyInt -> Ratio MyInt psRatio (CnPc x y) (CnPc x' y') = reduce (psMyInt (srMyInt x y') (srMyInt x' y)) (srMyInt y y'); msRatio :: Ratio MyInt -> Ratio MyInt -> Ratio MyInt msRatio x y = psRatio x (negateRatio y); numericEnumFromThen n m = iterate (psRatio (msRatio m n)) n; enumFromThenRatio :: Ratio MyInt -> Ratio MyInt -> (List (Ratio MyInt)) enumFromThenRatio = numericEnumFromThen;