So getting the value out of the monad is not a pure function (extract :: Monad m => m a -> a). I think I stated that, already, in my previous post. I'd even say that the monadic values alone can be completely meaningless. They often have a meaning only relative to some environment, thus are (usually) _effectful_ computations. But we already knew that, didn't we?
It may help to remember that, in the mathematical context where monads where born (AKA category theory), a monad is generally defined as a functor with a join and a unit (satisfying some laws that I would have to look up). The unit should be familiar (it's spelled 'return' in haskell), but join may not be. Its type is join :: Monad m => m (m a) -> m a which is a lot like extract, except with one more "monad layer" wrapped around it. IIRC the relevant identity here is: x >>= f === join (fmap f x) and with f specialzed to id: join (fmap id x) === x >>= id join x === x >>= id I'm not sure why (>>=) is taken as basic in Haskell. At any rate, my point is that I think your questions might be better framed in terms of the behavior of 'fmap'.
The real question (the one that bugs me, anyway) is if one can give a precise meaning to the informal argument that if the definition of bind is to be non-trivial then its second argument must be applied to some non-trivial value at one point (but not, of course, in all cases, nor necessarily only once), and that this implies that the computation represented by the first argument must somehow be 'run' (in some environment) in order to produce such a value. -- And, of course, whether this is actually true in the first place. Would you say that your examples above are counter-examples to this statement (imprecise as it is, unfortunately)?
Ben
-- Rob Dockins Talk softly and drive a Sherman tank. Laugh hard, it's a long way to the bank. -- TMBG