Type level numbers using existing Nat functionality. Uses kind-polymorphic typeclasses and type families to facilitate more general code compatible with existing code using type-level Naturals.
Import either Data.TypeNums or Data.TypeLits instead of GHC.TypeLits. Some definitions conflict with GHC.TypeLits, so if you really must import it, use an explicit import list.
This library is intended to be used in a kind-polymorphic way, such that a type-level integer parameter can be written as a natural, and a rational can be written as either of the other two. As an example:
{-# LANGUAGE PolyKinds #-}
data SomeType (n :: k) = SomeType
useSomeType :: KnownInt n => SomeType n -> _
useSomeType = -- ...- Positive integers are written as natural numbers, as before. Optionally
they can also be written as
Pos n. - Negative integers are written as
Neg n. - Ratios are written as
n :% d, wherencan be a natural number,Pos n, orNeg n, anddis a natural number.
Addition, subtraction and multiplication at type level are all given as infix operators with standard notation, and are compatible with any combination of the above types. Equality and comparison constraints are likewise available for any combination of the above types.
N.B. The equality constraint conflicts with that in Data.Type.Equality. The (==) operator from Data.Type.Equality is re-exported as (==?) from both Data.TypeNums and Data.TypeLits.