Isaac Dupree wrote:
Heinrich Apfelmus wrote:
However, in a sense, one can interpret the pure in purely functional as a property of the type constructor (->) , i.e. a function of type (a -> b) is guaranteed to not have side effects. In this light, ML and Scheme are lacking a very important type: they only have functions with side effects.
Or more precisely, their type system does not distinguish between functions with and without side effects.
that's not actually more precise! Haskell doesn't entirely do that either. consider: f :: Int -> IO Int f x = return (x + 1) No side effects! But other ->IO typed values do yield side-effects.
It is exactly as if ML and Scheme contain only the type of (->) composed with IO. (Well, actually Scheme is dynamically typed so it's a bit silly to say so..) (and Scheme allows functions with zero arguments, which are different from its non-side-effecting values.. not sure about ML)
Yes, "distinguish" in the sense of "optional distinction by annotation" instead of "automatically detect whether a function has side effects or not". (By the way, in a sense it is possible to detect that f has no side effects. Namely, it's most general type is polymorphic in the monad: f :: Monad m => Int -> m Int ) This is much like Java lacking (having lacked?) types whose values cannot be null , compared to a vs Maybe a in Haskell. Regards, Heinrich Apfelmus -- http://apfelmus.nfshost.com