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

G'day all. Quoting askyle :

Yup: bind f = f <=< id -- whence you can say (>>=) = flip bind

Ah, yes.

My point is that (as far as I can see) you cannot prove the properties of bind by only assuming identity and associativity for (<=<).

One thing that may help is that if you can prove that fmap is sane: fmap (f . g) = fmap f . fmap g then the naturality of return is precisely its free theorem, and ditto for bind. So perhaps this law: (f <=< g) . h === f <=< (g . h) is actually the fmap law in disguise? Cheers, Andrew Bromage