enumFromThen_2.hs

contents

{-# htermination (enumFromThenRatio :: Ratio MyInt  ->  Ratio MyInt  ->  (List (Ratio MyInt))) #-} 
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 ;

data Ratio a = CnPc a a;

iterate :: (a  ->  a)  ->  a  ->  (List a);
iterate f x = Cons x (iterate f (f x));

primNegInt :: MyInt  ->  MyInt;
primNegInt (Pos x) = Neg x;
primNegInt (Neg x) = Pos x;

negateMyInt :: MyInt  ->  MyInt
negateMyInt = primNegInt;

negateRatio :: Ratio MyInt  ->  Ratio MyInt
negateRatio (CnPc x y) = CnPc (negateMyInt x) y;

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));

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

psMyInt :: MyInt  ->  MyInt  ->  MyInt
psMyInt = primPlusInt;

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 xv xw = MyFalse;

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

fromIntMyInt :: MyInt  ->  MyInt
fromIntMyInt x = x;

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

error :: a;
error = stop MyTrue;

otherwise :: MyBool;
otherwise = 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));

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