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]) Supposedly a reactive system is a system which may not take a message (the Maybe), or do take it and respond with an updated version of itself, and a sequence of outgoing messages. For example, a copying machine might be defined as: id:R m id m = Just (id, [m]) 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) where id is defined as id::Meally a a id m = (id, m) I like the formalization because (a) it is concise, (b) structural composition operators can be defined trivially, (c) hides the state of a machine, (d) might possibly, in the long run, somewhere, even work out equally well as a monadic approach. Does it make sense? Are there any known references to this approach? Cheers, l4t3r PS: Actually, I just realized this might be the co-algebraic approach, so I guess I am asking for a haskell which allows co-algebraic types. _________________________________________________________________ The new MSN 8: smart spam protection and 2 months FREE* http://join.msn.com/?page=features/junkmail