On Sep 11, 2015, at 4:28 AM, Roman Cheplyaka
On 11/09/15 06:22, Carter Schonwald wrote:
Would this allow having a strict monoid instance for maybe, given the right hinting at the use site?
That's a fantastic idea, especially if it could be generalized to Applicative functors, where the problem of "inner laziness" is pervasive.
But that'd be tricky, because functions have the Lifted kind, and so <*> would have to be crazily levity-polymorphic. (Or is this not crazy?)
No more crazy than other things. Right now, we have (<*>) :: forall (a :: *) (b :: *) (f :: * -> *). Applicative f => f (a -> b) -> f a -> f b Under this proposal, we would have (ignore the Boxity stuff) (<*>) :: forall (v1 :: Levity) (v2 :: Levity) (v3 :: Levity) (a :: TYPE v1) (b :: TYPE v2) (f :: forall (v4 :: Levity). TYPE v4 -> TYPE v3). Applicative f => f @'Lifted (a -> b) -> f @v1 a -> f @v2 b The higher-rank levity-polymorphism is necessary in case `a` and `b` have different levities. This may be getting wildly out-of-hand, but I don't think it's actually breaking. I would like to point out that using forall here is really quite wrong. As others have pointed out, levity polymorphism is ad-hoc polymorphism, not parametric. Using 'pi' would be much closer to it, but it implies the existence of more dependent types than we really need for this. Richard
Roman
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