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
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