[Haskell-cafe] Re: A question about "monad laws"

[Andrew Butterfield]

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:&gt;&gt;=> 
> 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 )


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Andrew Butterfield     Tel: +353-1-896-2517     Fax: +353-1-677-2204
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