fin

Nat and Fin: peano naturals and finite numbers

BSD-3-Clause licensed by Oleg Grenrus

Maintained by Oleg.Grenrus

This version can be pinned in stack with:fin-0.2.1@sha256:10964c36ebdba53bc53fce5e439dc04839b0c02c55934d226bf00d863cbf6119,3955

Depends on 8 packages(full list with versions):

Used by 3 packages in nightly-2022-01-15(full list with versions):

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.

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.

Changes

Add boring instances
Explicitly implement >= and > for Nat.
<=, >= and min for Nat are lazier
Add NFData (SNat n) instance
Add GEq, GCompare, GNFData, GShow (from some package) instances for SNat.

SNat is now what was called InlineInduction. To migrate code from fin-0.1 to fin-0.2 it’s often enough to replace InlineInduction with SNatI, and inlineInduction with induction.
Explicitly mark all modules as Safe or Trustworthy.

Rename Fin constructors to FZ and FS. Now you can have both Nat and Fin imported unqualified in a single module.

Add Data.Type.Nat.LE, Data.Type.Nat.LT and Data.Type.Nat.LE.ReflStep modules
Add withSNat and discreteNat