notElem_3.hs

contents

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

data MyInt = Pos Nat  | Neg Nat ;

data Nat = Succ Nat  | Zero ;

asAs :: MyBool  ->  MyBool  ->  MyBool;
asAs MyFalse x = MyFalse;
asAs MyTrue x = x;

foldr :: (a  ->  b  ->  b)  ->  b  ->  (List a)  ->  b;
foldr f z Nil = z;
foldr f z (Cons x xs) = f x (foldr f z xs);

and :: (List MyBool)  ->  MyBool;
and = foldr asAs MyTrue;

map :: (a  ->  b)  ->  (List a)  ->  (List b);
map f Nil = Nil;
map f (Cons x xs) = Cons (f x) (map f xs);

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

all :: (a  ->  MyBool)  ->  (List a)  ->  MyBool;
all p = pt and (map p);

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;

primEqChar :: Char  ->  Char  ->  MyBool;
primEqChar (Char x) (Char y) = primEqInt x y;

esEsChar :: Char  ->  Char  ->  MyBool
esEsChar = primEqChar;

not :: MyBool  ->  MyBool;
not MyTrue = MyFalse;
not MyFalse = MyTrue;

fsEsChar :: Char  ->  Char  ->  MyBool
fsEsChar x y = not (esEsChar x y);

notElemChar :: Char  ->  (List Char)  ->  MyBool
notElemChar = pt all fsEsChar;

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