Out of curiosity, what should the kind of (->) be? Both the argument and result kind of (->) can be either * or #, but we can't make the argument kind levity polymorphic due to [1], right? How would you encode that in a kind signature?
Ryan S. ----- [1] https://ghc.haskell.org/trac/ghc/ticket/11473 On Thu, Feb 4, 2016 at 4:15 PM, Richard Eisenberg <e...@cis.upenn.edu> wrote: > I agree with everything that's been said in this thread, including the > unstated "that type for ($) is sure ugly". > > Currently, saturated (a -> b) is like a language construct, and it has its > own typing rule, independent of the type of the type constructor (->). But > reading the comment that Ben linked to, I think that comment is out of date. > Now that we have levity polymorphism, we can probably to the Right Thing and > make the kind of (->) more flexible. > > Richard > > On Feb 4, 2016, at 3:27 PM, Ryan Scott <ryan.gl.sc...@gmail.com> wrote: > >>> My understanding was that the implicitly polymorphic levity, did (->) not >>> change because it's a type constructor? >> >> The kind of (->) as GHCi reports it is technically correct. As a kind >> constructor, (->) has precisely the kind * -> * -> *. What's special >> about (->) is that when you have a saturated application of it, it >> takes on a levity-polymorphic kind. For example, this: >> >> :k (->) Int# Int# >> >> would yield a kind error, but >> >> :k Int# -> Int# >> >> is okay. Now, if you want an explanation as to WHY that's the case, I >> don't think I could give one, as I simply got this information from >> [1] (see the fourth bullet point, for OpenKind). Perhaps SPJ or >> Richard Eisenberg could give a little insight here. >> >>> Also does this encapsulate the implicit impredicativity of ($) for making >>> runST $ work? I don't presently see how it would. >> >> You're right, the impredicativity hack is a completely different >> thing. So while you won't be able to define your own ($) and be able >> to (runST $ do ...), you can at least define your own ($) and have it >> work with unlifted return types. :) >> >> Ryan S. >> ----- >> [1] https://ghc.haskell.org/trac/ghc/wiki/NoSubKinds >> >> On Thu, Feb 4, 2016 at 2:53 PM, Christopher Allen <c...@bitemyapp.com> wrote: >>> My understanding was that the implicitly polymorphic levity, did (->) not >>> change because it's a type constructor? >>> >>> Prelude> :info (->) >>> data (->) a b -- Defined in ‘GHC.Prim’ >>> Prelude> :k (->) >>> (->) :: * -> * -> * >>> >>> Basically I'm asking why ($) changed and (->) did not when (->) had similar >>> properties WRT * and #. >>> >>> Also does this encapsulate the implicit impredicativity of ($) for making >>> runST $ work? I don't presently see how it would. >>> >>> Worry not about the book, we already hand-wave FTP effectively. One more >>> type shouldn't change much. >>> >>> Thank you very much for answering, this has been very helpful already :) >>> >>> --- Chris >>> >>> >>> On Thu, Feb 4, 2016 at 12:52 PM, Ryan Scott <ryan.gl.sc...@gmail.com> wrote: >>>> >>>> Hi Chris, >>>> >>>> The change to ($)'s type is indeed intentional. The short answer is >>>> that ($)'s type prior to GHC 8.0 was lying a little bit. If you >>>> defined something like this: >>>> >>>> unwrapInt :: Int -> Int# >>>> unwrapInt (I# i) = i >>>> >>>> You could write an expression like (unwrapInt $ 42), and it would >>>> typecheck. But that technically shouldn't be happening, since ($) :: >>>> (a -> b) -> a -> b, and we all know that polymorphic types have to >>>> live in kind *. But if you look at unwrapInt :: Int -> Int#, the type >>>> Int# certainly doesn't live in *. So why is this happening? >>>> >>>> The long answer is that prior to GHC 8.0, in the type signature ($) :: >>>> (a -> b) -> a -> b, b actually wasn't in kind *, but rather OpenKind. >>>> OpenKind is an awful hack that allows both lifted (kind *) and >>>> unlifted (kind #) types to inhabit it, which is why (unwrapInt $ 42) >>>> typechecks. To get rid of the hackiness of OpenKind, Richard Eisenberg >>>> extended the type system with levity polymorphism [1] to indicate in >>>> the type signature where these kind of scenarios are happening. >>>> >>>> So in the "new" type signature for ($): >>>> >>>> ($) :: forall (w :: Levity) a (b :: TYPE w). (a -> b) -> a -> b >>>> >>>> The type b can either live in kind * (which is now a synonym for TYPE >>>> 'Lifted) or kind # (which is a synonym for TYPE 'Unlifted), which is >>>> indicated by the fact that TYPE w is polymorphic in its levity type w. >>>> >>>> Truth be told, there aren't that many Haskell functions that actually >>>> levity polymorphic, since normally having an argument type that could >>>> live in either * or # would wreak havoc with the RTS (otherwise, how >>>> would it know if it's dealing with a pointer or a value on the >>>> stack?). But as it turns out, it's perfectly okay to have a levity >>>> polymorphic type in a non-argument position [2]. Indeed, in the few >>>> levity polymorphic functions that I can think of: >>>> >>>> ($) :: forall (w :: Levity) a (b :: TYPE w). (a -> b) -> a -> b >>>> error :: forall (v :: Levity) (a :: TYPE v). HasCallStack => >>>> [Char] -> a >>>> undefined :: forall (v :: Levity) (a :: TYPE v). HasCallStack => a >>>> >>>> The levity polymorphic type never appears directly to the left of an >>>> arrow. >>>> >>>> The downside of all this is, of course, that the type signature of ($) >>>> might look a lot scarier to beginners. I'm not sure how you'd want to >>>> deal with this, but for 99% of most use cases, it's okay to lie and >>>> state that ($) :: (a -> b) -> a -> b. You might have to include a >>>> disclaimer that if they type :t ($) into GHCi, they should be prepared >>>> for some extra information! >>>> >>>> Ryan S. >>>> ----- >>>> [1] https://ghc.haskell.org/trac/ghc/wiki/NoSubKinds >>>> [2] https://ghc.haskell.org/trac/ghc/ticket/11473 >>>> _______________________________________________ >>>> ghc-devs mailing list >>>> ghc-devs@haskell.org >>>> http://mail.haskell.org/cgi-bin/mailman/listinfo/ghc-devs >>> >>> >>> >>> >>> -- >>> Chris Allen >>> Currently working on http://haskellbook.com >> _______________________________________________ >> ghc-devs mailing list >> ghc-devs@haskell.org >> http://mail.haskell.org/cgi-bin/mailman/listinfo/ghc-devs >> > _______________________________________________ ghc-devs mailing list ghc-devs@haskell.org http://mail.haskell.org/cgi-bin/mailman/listinfo/ghc-devs
