A rational number represents a ratio of integers exactly, making it a practical choice when fractional values must remain precise. In Haskell, Rational is an alias for Ratio Integer, while Ratio can use other integral types. section 10.4.2 section 10.1.1
Use the Ratio API to construct and calculate with rational values:
- Write numerator % denominator; the operator accepts Integral values, such as Int, Integer, or Natural, but not Double. section 10.4.2
- Use ordinary Num operations for arithmetic, including addition, subtraction, and multiplication. section 10.4.2
- Choose Natural when a domain value must be nonnegative, but guard calculations because subtracting too far can throw an exception. section 10.4.2
Representing musical note lengths
import Data.Ratio (Ratio, (%)) import Numeric.Natural (Natural) type Notelength = Ratio Natural whole, half, quarter :: Notelength whole = 1 % 1 half = 1 % 2 quarter = 1 % 4 dotted :: Notelength -> Notelength dotted x = x + x * (1 % 2) triplet :: Notelength -> Notelength triplet x = x * (2 % 3) A half note becomes 3 % 4 when dotted and 1 % 3 when treated as a triplet. section 10.4.2
ghci> import Data.Ratio ghci> :k Ratio Ratio :: * -> * ghci> 1 % 2 :: Ratio Int 1 % 2 ghci> 3 % 2 + 1 % 2 :: Ratio Int 2 % 1 ghci> 4 % 5 - 2 % 10 :: Ratio Int 3 % 5
Try constructing and calculating Ratio values directly in GHCi to see normalization and inferred kinds. section 10.4.2
