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
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