{-# htermination (maxFloat :: Float -> Float -> Float) #-} import qualified Prelude data MyBool = MyTrue | MyFalse data List a = Cons a (List a) | Nil data Float = Float MyInt MyInt ; data MyInt = Pos Nat | Neg Nat ; data Nat = Succ Nat | Zero ; data Ordering = LT | EQ | GT ; 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; 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)); 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; primCmpFloat :: Float -> Float -> Ordering; primCmpFloat (Float x1 x2) (Float y1 y2) = compareMyInt (srMyInt x1 y1) (srMyInt x2 y2); compareFloat :: Float -> Float -> Ordering compareFloat = primCmpFloat; 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); ltEsFloat :: Float -> Float -> MyBool ltEsFloat x y = fsEsOrdering (compareFloat x y) GT; max0 x y MyTrue = x; otherwise :: MyBool; otherwise = MyTrue; max1 x y MyTrue = y; max1 x y MyFalse = max0 x y otherwise; max2 x y = max1 x y (ltEsFloat x y); maxFloat :: Float -> Float -> Float maxFloat x y = max2 x y;