Arguably then, anything which is an instance of Monad should be a monad.
I would certainly argue strongly for that.
If it ain't true, then small, irrelevant changes in a piece of code could break. For example, is it safe to make this change:
do f y ==> do x <- f y return x
I'd hope it would be. (And the change might be useful if I want to insert a check or a debugging printf in the code.)
I'm afraid it isn't true that all instances of Monad respect the monad laws, due to our old friend seq. See: http://www.haskell.org/pipermail/haskell/2002-May/009622.html I don't want this discussion to get out of hand. The only point I'm making here is that the Haskell definition doesn't *require* that every instance of (==) be equality, in the same way that it doesn't *require* that all Monad instances are monads, and all '+'s are additions etc. Libraries might rely on properties of these methods, but as far as is practical those assumptions should be documented. Cheers, Simon