pred_1.hs

contents

{-# htermination (predTup0 :: Tup0  ->  Tup0) #-} 
import qualified Prelude 
data MyBool = MyTrue | MyFalse 
data List a = Cons a (List a) | Nil 
data Tup0 = Tup0 ;

data MyInt = Pos Nat  | Neg Nat ;

data Nat = Succ Nat  | Zero ;

fromEnumTup0 :: Tup0  ->  MyInt
fromEnumTup0 Tup0 = Pos Zero;

pt :: (b  ->  a)  ->  (c  ->  b)  ->  c  ->  a;
pt f g x = f (g x);

flip :: (c  ->  b  ->  a)  ->  b  ->  c  ->  a;
flip f x y = f y x;

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));

primMinusInt :: MyInt  ->  MyInt  ->  MyInt;
primMinusInt (Pos x) (Neg y) = Pos (primPlusNat x y);
primMinusInt (Neg x) (Pos y) = Neg (primPlusNat x y);
primMinusInt (Neg x) (Neg y) = primMinusNat y x;
primMinusInt (Pos x) (Pos y) = primMinusNat x y;

msMyInt :: MyInt  ->  MyInt  ->  MyInt
msMyInt = primMinusInt;

subtractMyInt :: MyInt  ->  MyInt  ->  MyInt
subtractMyInt = flip msMyInt;

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 vv vw = MyFalse;

esEsMyInt :: MyInt  ->  MyInt  ->  MyBool
esEsMyInt = primEqInt;

toEnum0 MyTrue vx = Tup0;

toEnum1 vx = toEnum0 (esEsMyInt vx (Pos Zero)) vx;

toEnumTup0 :: MyInt  ->  Tup0
toEnumTup0 vx = toEnum1 vx;

predTup0 :: Tup0  ->  Tup0
predTup0 = pt toEnumTup0 (pt (subtractMyInt (Pos (Succ Zero))) fromEnumTup0);

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