{-# htermination (divModMyInt :: MyInt -> MyInt -> Tup2 MyInt MyInt) #-} import qualified Prelude data MyBool = MyTrue | MyFalse data List a = Cons a (List a) | Nil data Tup2 a b = Tup2 a b ; data MyInt = Pos Nat | Neg Nat ; data Nat = Succ Nat | Zero ; data Ordering = LT | EQ | GT ; divModQ1 wx wy (Tup2 q vv) = q; stop :: MyBool -> a; stop MyFalse = stop MyFalse; error :: a; error = stop 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)); primQuotInt (Neg x) (Pos (Succ y)) = Neg (primDivNatS x (Succ y)); primQuotInt (Neg x) (Neg (Succ y)) = Pos (primDivNatS x (Succ y)); primQuotInt vz wu = error; primModNatS0 x y MyTrue = primModNatS (primMinusNatS x (Succ y)) (Succ (Succ y)); primModNatS0 x y MyFalse = Succ x; primModNatS :: Nat -> Nat -> Nat; primModNatS Zero Zero = error; primModNatS Zero (Succ x) = Zero; primModNatS (Succ x) Zero = error; primModNatS (Succ x) (Succ Zero) = Zero; primModNatS (Succ x) (Succ (Succ y)) = primModNatS0 x y (primGEqNatS x (Succ y)); primRemInt :: MyInt -> MyInt -> MyInt; primRemInt (Pos x) (Pos (Succ y)) = Pos (primModNatS x (Succ y)); primRemInt (Pos x) (Neg (Succ y)) = Pos (primModNatS x (Succ y)); primRemInt (Neg x) (Pos (Succ y)) = Neg (primModNatS x (Succ y)); primRemInt (Neg x) (Neg (Succ y)) = Neg (primModNatS x (Succ y)); primRemInt vx vy = error; primQrmInt :: MyInt -> MyInt -> Tup2 MyInt MyInt; primQrmInt x y = Tup2 (primQuotInt x y) (primRemInt x y); quotRemMyInt :: MyInt -> MyInt -> Tup2 MyInt MyInt quotRemMyInt = primQrmInt; divModVu5 wx wy = quotRemMyInt wx wy; divModQ wx wy = divModQ1 wx wy (divModVu5 wx wy); divModQr0 wx wy qr = qr; divModQr wx wy = divModQr0 wx wy (divModVu5 wx wy); divModR0 wx wy (Tup2 vw r) = r; divModR wx wy = divModR0 wx wy (divModVu5 wx wy); fromIntMyInt :: MyInt -> MyInt fromIntMyInt x = 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; 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; divModDivMod0 wx wy d MyTrue = Tup2 (msMyInt (divModQ wx wy) (fromIntMyInt (Pos (Succ Zero)))) (psMyInt (divModR wx wy) d); divModDivMod0 wx wy d MyFalse = divModQr wx wy; 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 esEsMyInt = primEqInt; primNegInt :: MyInt -> MyInt; primNegInt (Pos x) = Neg x; primNegInt (Neg x) = Pos x; negateMyInt :: MyInt -> MyInt negateMyInt = primNegInt; 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; otherwise :: MyBool; otherwise = MyTrue; signumReal0 x MyTrue = fromIntMyInt (Neg (Succ Zero)); signumReal1 x MyTrue = fromIntMyInt (Pos (Succ Zero)); signumReal1 x MyFalse = signumReal0 x otherwise; signumReal2 x MyTrue = fromIntMyInt (Pos Zero); signumReal2 x MyFalse = signumReal1 x (gtMyInt x (fromIntMyInt (Pos Zero))); signumReal3 x = signumReal2 x (esEsMyInt x (fromIntMyInt (Pos Zero))); signumReal x = signumReal3 x; signumMyInt :: MyInt -> MyInt signumMyInt = signumReal; divModMyInt :: MyInt -> MyInt -> Tup2 MyInt MyInt divModMyInt n d = divModDivMod0 n d d (esEsMyInt (signumMyInt (divModR n d)) (negateMyInt (signumMyInt d)));