[Haskell-cafe] Monad definition question

Does the definition of monad silently assume that if f and f' are equal in the sense that they return the same value for any argument o correct type then m >>= f = m >>= f' More specifically, the definition says x >>= return = x. How does one justify from this that x >>= (return . id) = x? Are values of type a -> b in general assumed to be maps from the set of values of type a into the set ov values of type b? (What bothers me is that the problem whether two lambda-expressions define the same map is clearly undecidable.) More generally, is some kind of logic without equality more appropriate for formalisation of Haskell then the usual kind(s) of logic with equality?