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Monads

module Main where

We begin by defining a plain wrapper, that does nothing besides get in our way.

data M a = M a deriving Show

The operator ∘ composes two functions whose return values are wrapped by M. For comparison, recall the type of (.).

(.) ∷ (b → c) → (a → b) → a → c

infixr 9 ∘

(∘) ∷ (b → M c) → (a → M b) → a → M c
(∘) p q x = p y where M y = q x

Note that M wraps its argument. We can think of M as a wrapped identity function; M is the identity element for the composition law ∘.

M ∷ a → M a

f and g are wrapped functions.

f, g ∷ String → M String

f x = M ('F' : x)
g x = M ('G' : x)

main ∷ IO ()
main = mapM_ (print . ($ "x"))
   [ M
   , f ∘ M
   , M ∘ f
   , f ∘ g
   , g ∘ f
   , f ∘ M ∘ g
   ]

M "x"
M "Fx"
M "Fx"
M "FGx"
M "GFx"
M "FGx"

Main.hs