Brent Yorgey wrote:
"Computation" does not really have any technical meaning, it's just supposed to be an intuition. But the term "computation" is often used to refer to things of type (m a) where m is a Monad. You can clearly see from the types that something of type (m a) is different than something of type (a -> b). The former takes no inputs and somehow produces value(s) of type a; the latter takes something of type a as input and produces something of type b as output.
However, you could also legitimately thing of things of type (a -> b) as "computations"; more interestingly, you can think of things of type (a -> m b) as "parameterized computations" which can be composed in nice ways.
Don't rely too heavily on the "computation" idea; monads certainly don't "revolve around computations", it's only one particular way of giving intuition for monads which does.
Thanks. That helps a lot. It looks to me that one could replace the word "computation" everywhere in the article with "monadic type" (where again, "monadic type" is just an intuition for "m a" where m is a Monad) and the article would be equally correct. Am I right? The Wikipedia article seems to use "monadic type" for the same things that ertes calls "computation". I can't decide which term gives better intuition. The term "computation" makes binding more intuitive: The computation (m a) returns a value of type "a" can then be fed into a function of type (a -> m b). On the other hand, "monadic type" is more intuitive when you write "Maybe Int" or "IO String". Anyways, thanks for the help. I'm (slowly) making progress. Cheers, Daniel.