fin: Nat and Fin: peano naturals and finite numbers

This package provides two simple types, and some tools to work with them. Also on type level as DataKinds.

-- Peano naturals
data Nat = Z | S Nat

-- Finite naturals
data Fin (n :: Nat) where
    Z :: Fin ('S n)
    S :: Fin n -> Fin ('Nat.S n)

vec implements length-indexed (sized) lists using this package for indexes.

The Data.Fin.Enum module let's work generically with enumerations.

See Hasochism: the pleasure and pain of dependently typed haskell programming by Sam Lindley and Conor McBride for answers to how and why. Read APLicative Programming with Naperian Functors by Jeremy Gibbons for (not so) different ones.

Similar packages

• finite-typelits . Is a great package, but uses GHC.TypeLits.

• type-natural depends on singletons package. fin will try to stay light on the dependencies, and support as many GHC versions as practical.

• peano is very incomplete

• nat as well.

• PeanoWitnesses doesn't use DataKinds.

• type-combinators is big package too.

• Data
  • Data.Fin
    • Data.Fin.Enum
  • Data.Nat
  • Type
    • Data.Type.Nat
      • Data.Type.Nat.LE
        • Data.Type.Nat.LE.ReflStep
      • Data.Type.Nat.LT