On Wed, Sep 30, 2009 at 9:54 AM, Peter Verswyvelen
I guess this is related to the expression problem. Suppose I have a datatype data Actor = Ball ... | Paddle ... | Wall ... and a function move (Ball ...) = move (Paddle ...) = move (Wall ...) = in Haskell one must put Actor and move into a single file. This is rather cumbersome if you work with multiple people or want to keep the files small and readable. Surely it is possible to use type classes, existentials, etc to split the data type into multiple ones, but that's already advanced stuff in a sense.
You can do it without type classes and existentials. The functionality you want is already supported by Haskell, you just have to let go of your syntactical expectations. The trick is that you should rewrite your data type not as an algebra (a set of constructors), but as a coalgebra (a set of projections). Let's say your two open functions are: move :: Actor -> Actor isAlive :: Actor -> Bool This gives rise to the definition of an Actor type: data Actor = Actor { move :: Actor, isAlive :: Bool } And then the alternatives of your open data type are just values of type Actor: ball :: Vector -> Vector -> Actor ball pos vel = Actor { move = ball (pos + vel) vel, isAlive = True } etc. This trick works well until you get to the encoding of functions that pattern match on multiple Actors at the same time. As far as I can tell, that cannot be encoded in this style in any reasonable way. Such functions must be rephrased in a coalgebraic style; i.e. instead of asking about constructors, using projection functions it knows are available. So for example instead of implementing "collide" by asking about pairs, add functions which report a shape function and a normal, or whatever your collide algorithm needs from shapes. You would probably end up having to do this anyway even with your proposed extension, because watch: partial data Actor = Ball ... collide (Ball ...) (Ball ...) = ... collide (Ball ...) x = ... We don't know about any other constructors, so the second line has to contain a pattern-free x. So you would have to use projection functions to get any information about it, exactly as you would when you're writing in the coalgebraic style. So, Yes! Haskell can do that! Luke