Kevin Jardine
I think that we are having a terminology confusion here. For me, a pure function is one that does not operate inside a monad. Eg. ++, map, etc.
No, a pure function is one without any side effects.
It was at one point my belief that although code in monads could call pure functions, code in pure functions could not call functions that operated inside a monad.
Not at all. I can do something like "map (liftM succ) [Just 2, Nothing]", where liftM is a monadic function. The thing is that I'm applying it to a "pure" monad (i.e. the Maybe monad doesn't have side effects).
I was then introduced to functions such as execState and unsafePerformIO which appear to prove that my original belief was false.
unsafePerformIO is the wild-card here; it's whole purpose is to be able to say that "this IO action (usually linking to a C library or some such) is pure, promise!!!".
Currently I am in a state of deep confusion, but that is OK, because it means that I am learning something new!
The big point here that you seem to be tied up in is that Monad /= impure. I see three broad classifications of Monads: 1) Data structures that can be used as monads, such as [a] and Maybe a. 2) Special monadic wrappers/transformers such as State, Reader, etc. which allow you to act as if something is being done sequentially (which is the whole point of >>=) but is actually a pure function. The ST monad also appears to be able to be used like this if you use runST. 3) Side-effect monads: IO, STM, ST (used with stToIO), etc. The "classical" monads, so to speak which you seem to be thinking about. -- Ivan Lazar Miljenovic Ivan.Miljenovic@gmail.com IvanMiljenovic.wordpress.com