Lists of fixed length and type literals

Question

I\'m trying to define a type for lists of fixed length in Haskell. When I use the standard way to encode natural numbers as types in unary, everything works fine. However, w

Answer 1

Type level number literals don't yet have a structure on which we can do induction, and the built-in constraint solver can only figure out the simplest cases. Currently it's better to stick with Peano naturals.

However, we can still use the literals as syntactic sugar.

{-# LANGUAGE
  UndecidableInstances,
  DataKinds, TypeOperators, TypeFamilies #-}

import qualified GHC.TypeLits as Lit

data Nat = Z | S Nat

type family Lit n where
    Lit 0 = Z
    Lit n = S (Lit (n Lit.- 1))

Now you can write List (Lit 3) a instead of List (S (S (S Z))) a.