Natural numbers defined inductively in Elm

nat.elm

module Nat exposing (..)

-- Example of inductively defined data type.
type Nat = O | S Nat

toNat : Int -> Nat
toNat n = case n of
            0  -> O
            sn -> S (toNat (sn - 1))

fromNat : Nat -> Int
fromNat n = case n of
              O    -> 0
              S np -> 1 + (fromNat np)

-- Nat.toNat 3 evaluates to S (S (S O)) : Nat
-- Nat.fromNat (Nat.toNat 10) evaluates to 10

-- Nat.S Nat.O == Nat.S Nat.O