Andrew Butterfield wrote:
let m denote the "list monad" (hypothetically). Let's instantiate:
return :: x -> [x] return x = [x,x]
(>>=) :: [x] -> (x -> [y]) -> [y] xs >>= f = concat ((map f) xs)
Let g n = [show n]
Here (return 1 >>= g ) [1,2,3] = ["1","1","1","1","1","1"] but g[1,2,3] = ["1","2","3"], thus violating the first monad law | return http://haskell.org/ghc/docs/latest/html/libraries/base/Prelude.html#v:return a >>= http://haskell.org/ghc/docs/latest/html/libraries/base/Prelude.html#v:>>= f = f a
I messed this up - I was trying for the simplest example I could get ! Apologies. Start over: Program ---------------------------------------------------- module BadMonad where import Monad newtype MyList t = MyList [t] instance Show t => Show (MyList t) where show (MyList xs) = show xs unmylist (MyList xs) = xs myconcat xs = MyList (concat (map unmylist xs)) instance Monad MyList where return x = MyList [x,x] (MyList xs) >>= f = myconcat ((map f) xs) i2s :: Int -> MyList Char i2s x = MyList (show x) m = i2s 9 Hugs transcript ---------------------------------------- BadMonad> m "9" :: MyList Char BadMonad> m >>= return "99" :: MyList Char We violate the second law (Right Identity, m = m >>= return ) -- -------------------------------------------------------------------- Andrew Butterfield Tel: +353-1-896-2517 Fax: +353-1-677-2204 Foundations and Methods Research Group Director. Course Director, B.A. (Mod.) in CS and ICT degrees, Year 4. Department of Computer Science, Room F.13, O'Reilly Institute, Trinity College, University of Dublin, Ireland. http://www.cs.tcd.ie/Andrew.Butterfield/ --------------------------------------------------------------------