Ratio package:numhask

data Ratio a

A rational number, represented as the ratio of two Integral numbers.

type Rational = Ratio Integer

Ratio of two integers

module NumHask.Data.Rational

Rational classes

class FromRatio a b

Fractional in base splits into fromRatio and Field

>>> fromRatio (5 :% 2 :: Ratio Integer) :: Double
2.5

class FromRational a

fromRational is special in two ways:

numeric decimal literals (like "53.66") are interpreted as exactly "fromRational (53.66 :: GHC.Real.Ratio Integer)". The prelude version, GHC.Real.fromRational is used as default (or whatever is in scope if RebindableSyntax is set).
The default rules in haskell2010 specify that contraints on fromRational need to be in a form C v, where v is a Num or a subclass of Num.

So a type synonym of `type FromRational a = FromRatio a Integer` doesn't work well with type defaulting; hence the need for a separate class.

class ToRatio a b

toRatio is equivalent to Real in base, but is polymorphic in the Integral type.

>>> toRatio (3.1415927 :: Float) :: Ratio Integer
13176795 :% 4194304