On Wed, Jul 16, 2003 at 02:01:36PM +0200, blaat blaat wrote:
Sorry if this mail starts a new thread. I am not subscribed to haskell-cafe and am new to hotmail.
Uhm, as far as the example goes. I was trying to define a small (shallow encoding of) a reactive systems language. Because I wanted to try something else than monads I defined the following recursive type for a reactive system.
type R m = m -> Maybe (R m, [m])
I don't think there's an extension of Haskell with regular type unification. It's certainly possible, but there's an equivalent in standard Haskell: newtype R m = MkR (m -> Maybe (R m, [m])) except for the nuisance of adding and removing the MkR constructor. Also, regular type trees would make type errors more hairy, and in Haskell one tends to write a lot of data's and newtype's anyway in order to define class instances. So co-algebraic programs are nothing special in Haskell, if you ignore that constructor.
A version for a ?Meally? machine embedding (always take an incoming message, and respond with one outgoing message) could be written as
type Meally i o = i -> (Meally i o, o)
This particular example is an instance of an arrow type, and is handy for simulating synchronous circuits, cf http://www.soi.city.ac.uk/~ross/papers/fop.html (look for "Simple automata" on the 3rd page) A more bizarre example is "hyperfunctions": newtype Hyper i o = Hyper (i -> Hyper o i) cf http://www.cse.ogi.edu/~krstic/psfiles/hyperfunctions.ps