Haskell Partition for a Number Class

Question

I am trying to define a function toVal :: (Num a) => (Fraction a) -> a. The function takes a fraction and evaluates its numerical value. But since a function uses division, I can do the following, since division is defined by various functions in subclasses Num a:

data Fraction a = Constant a
    |Rational{numerator :: (Fraction a), denominator :: (Fraction a)}


toVal1 :: (Integral a) => (Fraction a) -> a
toVal1 (Constant a) = a
toVal1 (Rational num den) = (toVal1 num) `div` (toVal1 den)

toVal2 :: (Fractional a) => (Fraction a) -> a
toVal2 (Constant a) = a
toVal2 (Rational num den) = (toVal2 num) / (toVal2 den)

Is there a way to combine two functions so that I can have a common function toVal :: (Num a) => (Fraction a) -> a?

Answer 1

No, because it Numdoesn’t have the concept of division, or, in terms of C ++, because it’s not dynamic_cast<...>in Haskell.

You can enter your own style:

class HasDivOp a where
  divOp :: a -> a -> a

instance HasDivOp Int     where divOp = div
instance HasDivOp Integer where divOp = div
instance HasDivOp Double  where divOp = (/)
instance HasDivOp Float   where divOp = (/)

And then you have the only function that takes the correct one divOp:

toVal :: (Num a, HasDivOp a) => (Fraction a) -> a
toVal (Constant a)   = a
toVal (Rational a b) = toVal a `divOp` toVal b

- :

divG :: (a -> b) -> (a -> a -> b) -> Fraction a -> b
divG p _ (Constant x)       = p x
divG p f (Rational num den) = f (divG p f num) (divF p f den)

a b divF, a b a b, Fraction a b. a = b, :

divF :: (a -> a -> a) -> Fraction a -> a
divF = divG id

toVal1, toVal2 divF:

toVal1 :: Integral n => Fraction n -> Fraction n -> n
toVal1 = divF div

toVal2 :: Fractional n => Fraction n -> Fraction n -> n
toVal2 = divF (/)

toVal toVal1 :

toVal1 (Rational (Rational 2 3) (Rational 2 3)) = 0 :: Int

x div x 1 x /= 0. Fraction, :

rationalDiv :: Integral n => Fraction a -> Fraction a -> Fraction a
rationalDiv (Constant a  ) (Constant c  ) = Rational a       c
rationalDiv (Constant a  ) (Rational c d) = Rational (a * d) c
rationalDiv (Rational a b) (Constant c  ) = Rational a       (b * c)
rationalDiv (Rational a b) (Rational c d) = Rational (a * d) (b * c)

, Fraction * Num. , :

toVal3 :: Integral n => Fraction n -> n
toVal3 = divF div . divF rationalDiv

1 . : , Num , , .