On Sat, 2009-01-17 at 12:04 +0000, Andrew Coppin wrote:
Eugene Kirpichov wrote:
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.
As far as I'm aware, constraints like "while preserving the underlying structure" are not expressible in Haskell.
instance (Monad m) => Functor m where fmap f ma = do a <- ma; return (f a)
While that's quite interesting from a mathematical point of view, how is this "useful" for programming purposes?
Good Lord. fmap (as above) is *at least* useful enough to be in the standard library! (Control.Monad.liftM). Contrary to what some people seem to think, every single function in Haskell's standard library was included because enough people found it actually *useful* enough to add. Here's the first example I found, searching the source code for my macro language interpreter:[1] Macro-call interpolation has syntax §(expression), parsed by do char '§' lexParens $ Interpolation <$> parseExpr = do char '§' lexParens $ fmap Interpolation $ parseExpr = do [2] char '§' fmap Interpolation $ lexParens $ parseExpr Useful enough? jcc [1] The only simplifications applied were (a) ignoring an interpolation syntax substantially more complicated, and (b) re-naming the relevant constructor. [2] Valid because lexParens is a natural transformation.