2009/1/17 Andrew Coppin
Cory Knapp wrote:
Actually, that was part of my point: When I mention Haskell to people, and when I start describing it, they're generally frightened enough by the focus on pure code and lazy evaluation-- add to this the inherently abstract nature, and we can name typeclasses "cuddlyKitten", and the language is still going to scare J. R. Programmer. By "inherently mathematical nature", I didn't mean names like "monoid" and "functor", I meant *concepts* like monoid and functor. Not that either of them are actually terribly difficult; the problem is that they are terribly abstract. That draws a lot of people (especially mathematicians), but most people who aren' drawn by that are hugely put off-- whatever the name is. So, I guess my point is that the name is irrelevant: the language is going to intimidate a lot of people who are intimidated by the vocabulary.
Oh, I don't know. I have no idea what the mathematical definition of "functor" is, but as far as I can tell, the Haskell typeclass merely allows you to apply a function simultaneously to all elements of a collection. That's pretty concrete - and trivial. If it weren't for the seemingly cryptic name, nobody would think twice about it. (Not sure exactly what you'd call it though...)
No, a functor is a more wide notion than that, it has nothing to do with collections. An explanation more close to truth would be "A structure is a functor if it provides a way to convert a structure over X to a structure over Y, given a function X -> Y, while preserving the underlying 'structure'", where preserving structure means being compatible with composition and identity. Collections are one particular case. Another case is just functions with fixed domain A: given a "structure" of type [A->]X and a function of type X -> Y, you may build an [A->]Y. Yet another case are monads (actually, the example above is the Reader monad): given a monadic computation of type 'm a' and a function a -> b, you may get a computation of type m b: instance (Monad m) => Functor m where fmap f ma = do a <- ma; return (f a) There are extremely many other examples of functors; they are as ubiquitous as monoids and monads :) -- Eugene Kirpichov