numeric-prelude-0.1.1: An experimental alternative hierarchy of numeric type classes Source code Contents Index

Number.ResidueClass.Check

Synopsis

data T a = Cons { modulus :: !a representative :: !a } factorPrec :: Int (/:) :: C a => a -> a -> T a isCompatible :: Eq a => T a -> T a -> Bool maybeCompatible :: Eq a => T a -> T a -> Maybe a fromRepresentative :: C a => a -> a -> T a lift1 :: Eq a => (a -> a -> a) -> T a -> T a lift2 :: Eq a => (a -> a -> a -> a) -> T a -> T a -> T a errIncompat :: a zero :: C a => a -> T a one :: C a => a -> T a fromInteger :: C a => a -> Integer -> T a

Documentation

data T a Source

The best solution seems to let modulus be part of the type. This could happen with a phantom type for modulus and a run function like Control.Monad.ST.runST. Then operations with non-matching moduli could be detected at compile time and zero and one could be generated with the correct modulus. An alternative trial can be found in module ResidueClassMaybe. Constructors Cons modulus :: !a representative :: !a Instances Eq a => Eq (T a) (Read a, C a) => Read (T a) Show a => Show (T a) (Eq a, C a) => C (T a) (Eq a, C a) => C (T a) C a => C (T a) (Eq a, C a) => C (T a)

factorPrec :: Int Source

(/:) :: C a => a -> a -> T a Source

r /: m is the residue class containing r with respect to the modulus m

isCompatible :: Eq a => T a -> T a -> Bool Source

Check if two residue classes share the same modulus

maybeCompatible :: Eq a => T a -> T a -> Maybe a Source

fromRepresentative :: C a => a -> a -> T a Source

lift1 :: Eq a => (a -> a -> a) -> T a -> T a Source

lift2 :: Eq a => (a -> a -> a -> a) -> T a -> T a -> T a Source

errIncompat :: a Source

zero :: C a => a -> T a Source

one :: C a => a -> T a Source

fromInteger :: C a => a -> Integer -> T a Source

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