Nat.elm

module Main exposing (main)

import Html exposing (Html, text)


main : Html msg
main =
    multiply
        (fromInt 9)
        (fromInt 5)
        |> toInt
        |> toString
        |> text


type Nat
    = Zero
    | S Nat
    
    
add : Nat -> Nat -> Nat
add x y =
    case x of
        Zero ->
            y
            
        S s ->
            add s (S y)
            

multiply : Nat -> Nat -> Nat
multiply x y =
    case y of
        Zero ->
            y
            
        S s ->
            add x (multiply x s)

    
fromInt : Int -> Nat
fromInt int =
    case int of
        0 ->
            Zero
            
        _ ->
            S (fromInt (int - 1))
            
toInt : Nat -> Int
toInt nat =
    case nat of
        Zero ->
            0
            
        S s ->
            1 + toInt s