Generate function of given arity in Haskell using type numbers

Question

Assume I have encoded the natural numbers in Haskell types, and that I have a way of adding and subtracting from them:

data Zero
data Succ n
-- ...

Answer 1

I see your functional-dependency multiparameter empty-datatype flexibly scoped type variables and raise you a Haskell 98 version! It uses HoleyMonoid which is available on hackage:

{-# LANGUAGE NoMonomorphismRestriction #-}

import Prelude hiding (id, (.))
import Control.Category
import Data.HoleyMonoid

suc n = later (:[]) . n

zero  = id
one   = suc zero
two   = suc one
three = suc two

buildList = run

Testing (feel free to omit any type signatures):

> run three "one" "two" "three"
["one","two","three"]