categories-chapter-1.elm

{-|
Solutions in Elm for challenges 1, 2 and 3 from
http://bartoszmilewski.com/2014/11/04/category-the-essence-of-composition/
-}

import Graphics.Element exposing (show)

{- id is called identity i elm-core -}
id : a -> a
id x =
  x

{- Same as (>>) infix operator in elm-core -}
compose : (a -> b) -> (b -> c) -> a -> c
compose f g x =
  g (f x)

addOne : number -> number
addOne x =
  x + 1

addOneWithId : number -> number
addOneWithId =
  compose addOne id

idWithAddOne : number -> number
idWithAddOne =
  compose id addOne

main = show [ addOneWithId 41 == addOne 41
            , idWithAddOne 41 == addOne 41
            ]