Wouter Swierstra wrote:
In a sense, that's also the reason why stream fusion à la Duncan + Roman + Don uses an existential type
data Stream a where Stream :: ∀s. s -> (s -> Step a s) -> Stream a
data Step a s = Done | Yield a s | Skip s
I thought there was a deeper reason for this, but I might be wrong. [..]
data CoFix f = In (f (CoFix f))
Then the unfold producing a value of type CoFix f has type:
forall a . (a -> f a) -> a -> CoFix f
(exists a . (a -> f a, a)) -> CoFix f
Using the "co-Church encoding" of colists yields the above Stream data type, where "f" corresponds to the "Step" data type. (The Skip constructor is a bit of a fix to cope with filter and friends).
Yes. I mean, I want to say that the efficiency gain of fusion is based on the fact that the state (the "seed" a ) can be represented more compactly than the resulting CoFix f . I.e. while ∃a. (a -> f a, a) =~= CoFix f the former type may be a more compact representation than the latter, demonstrating that an existential type may have performance benefits compared to an isomorphic alternative. (This is even without sharing here, Ryan remark was about sharing issues) Regards, apfelmus