{-# htermination (ceilingRatio :: Ratio MyInt -> MyInt) #-} import qualified Prelude data MyBool = MyTrue | MyFalse data List a = Cons a (List a) | Nil data Tup2 a b = Tup2 a b ; data Integer = Integer MyInt ; data MyInt = Pos Nat | Neg Nat ; data Nat = Succ Nat | Zero ; data Ordering = LT | EQ | GT ; data Ratio a = CnPc a a; ceilingN0 xv (Tup2 n vw) = n; fromIntegerMyInt :: Integer -> MyInt fromIntegerMyInt (Integer x) = x; pt :: (c -> b) -> (a -> c) -> a -> b; pt f g x = f (g x); toIntegerMyInt :: MyInt -> Integer toIntegerMyInt x = Integer x; fromIntegral = pt fromIntegerMyInt toIntegerMyInt; properFractionQ1 xw xx (Tup2 q vx) = q; stop :: MyBool -> a; stop MyFalse = stop MyFalse; error :: a; error = stop 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 wx wy = error; 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 vz wu = error; primQrmInt :: MyInt -> MyInt -> Tup2 MyInt MyInt; primQrmInt x y = Tup2 (primQuotInt x y) (primRemInt x y); quotRemMyInt :: MyInt -> MyInt -> Tup2 MyInt MyInt quotRemMyInt = primQrmInt; properFractionVu30 xw xx = quotRemMyInt xw xx; properFractionQ xw xx = properFractionQ1 xw xx (properFractionVu30 xw xx); properFractionR1 xw xx (Tup2 vy r) = r; properFractionR xw xx = properFractionR1 xw xx (properFractionVu30 xw xx); properFractionRatio :: Ratio MyInt -> Tup2 MyInt (Ratio MyInt) properFractionRatio (CnPc x y) = Tup2 (fromIntegral (properFractionQ x y)) (CnPc (properFractionR x y) y); ceilingVu8 xv = properFractionRatio xv;
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