I'm investigating rational numbers with Haskell. This is the source I've found
data Ratio a = !a :% !a deriving (Eq)
reduce :: (Integral a) => a -> a -> Ratio a
{-# SPECIALISE reduce :: Integer -> Integer -> Rational #-}
reduce _ 0 = ratioZeroDenominatorError
reduce x y = (x `quot` d) :% (y `quot` d)
where d = gcd x y
(%) :: (Integral a) => a -> a -> Ratio a
x % y = reduce (x * signum y) (abs y)
The Ratio data type would seem to be a parameterized type with two parameters of the same type that must be "settled" in that they're not to be lazily dealt with. Then the :% is the data constructor, the : meaning it's a data constructor and not just an operation function. So this could have been
data Ratio a = :% !a !a deriving (Eq)
correct? But then what confuses me is in reduce, why
reduce x y = (x `quot` d) :% (y `quot` d)
and not just %? We have :% defined in the data type and then (%) defined as a function. What is going on here?
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Lawrence Bottorff
Grand Marais, MN, USA