abs_1.hs

contents

{-# htermination (absRatio :: Ratio MyInt  ->  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;

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

negateMyInt :: MyInt  ->  MyInt
negateMyInt = primNegInt;

absReal0 x MyTrue = negateMyInt x;

otherwise :: MyBool;
otherwise = MyTrue;

absReal1 x MyTrue = x;
absReal1 x MyFalse = absReal0 x otherwise;

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

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;

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

fsEsOrdering :: Ordering  ->  Ordering  ->  MyBool
fsEsOrdering x y = not (esEsOrdering x y);

gtEsMyInt :: MyInt  ->  MyInt  ->  MyBool
gtEsMyInt x y = fsEsOrdering (compareMyInt x y) LT;

absReal2 x = absReal1 x (gtEsMyInt x (fromIntMyInt (Pos Zero)));

absReal x = absReal2 x;

absMyInt :: MyInt  ->  MyInt
absMyInt = absReal;

absRatio :: Ratio MyInt  ->  Ratio MyInt
absRatio (CnPc x y) = CnPc (absMyInt x) y;

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