BANGBANG_1.hs

contents

{-# htermination (emEm :: (List a)  ->  MyInt  ->  a) #-} 
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 ;

stop :: MyBool  ->  a;
stop MyFalse = stop MyFalse;

error :: a;
error = stop MyTrue;

emEm0 Nil wu = error;

emEm1 (Cons vx vy) vz = error;
emEm1 wz xu = emEm0 wz xu;

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;

emEm2 vw xs n MyTrue = emEm xs (msMyInt n (Pos (Succ Zero)));
emEm2 vw xs n MyFalse = emEm1 (Cons vw xs) n;

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;

gtMyInt :: MyInt  ->  MyInt  ->  MyBool
gtMyInt x y = esEsOrdering (compareMyInt x y) GT;

emEm3 (Cons vw xs) n = emEm2 vw xs n (gtMyInt n (Pos Zero));
emEm3 xw xx = emEm1 xw xx;

emEm4 MyTrue (Cons x vv) xz = x;
emEm4 yu yv yw = emEm3 yv yw;

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 wv ww = MyFalse;

esEsMyInt :: MyInt  ->  MyInt  ->  MyBool

content may be truncated. 'popout' for larger text window.