[Haskell-cafe] Request to review my attempt at understanding Monads

[Bas van Dijk]

On Tue, Dec 29, 2009 at 7:58 AM, CK Kashyap <ck_kashyap at yahoo.com> wrote:
> I'd appreciate answers to the following queries -
> 1. Comments about the functions I've written

{-# LANGUAGE UnicodeSyntax #-}

import Monad ( MonadPlus(..) )

data List α = Cons α (List α) | Empty
              deriving Show

If you look at your definitions of 'myMap', 'myAppend' and 'myConcat'
you will notice that they all follow a similar pattern which can be
abstracted in a so called "catamorphism" (or in normal Haskell a
"fold"):

myFoldr ∷ (α → β → β) → β → List α → β
myFoldr f z = myFoldr_f_z
    where
      myFoldr_f_z Empty = z
      myFoldr_f_z (Cons x xs) = f x $ myFoldr_f_z xs

myMap ∷ (α → β) → List α → List β
myMap f = myFoldr (Cons . f) Empty

myAppend ∷ List α → List α → List α
myAppend xs ys = myFoldr Cons ys xs

myConcat ∷ List (List α) → List α
myConcat = myFoldr myAppend Empty

instance Monad List where
    return a = Cons a Empty
    l >>= f = myConcat $ myMap f l

instance MonadPlus List where
    mplus = myAppend
    mzero = Empty

list2myList ∷ [α] → List α
list2myList = foldr Cons Empty

regards,

Bas