New type of ($) operator in GHC 8.0 is problematic

[Richard Eisenberg]

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 But reading the comment that Ben linked to, I think that comment is out of date.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.scott at 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 ($) and have it
> work with unlifted return types. :)
> 
> Ryan S.
> -----
> [1] https://ghc.haskell.org/trac/ghc/wiki/NoSubKinds
> 
> On Thu, Feb 4, 2016 at 2:53 PM, Christopher Allen <cma at bitemyapp.com> wrote:
>> My understanding was that the implicitly polymorphic levity, did (->) not
>> change because it's a type constructor?
>> 
>> Prelude> :info (->)
>> data (->) a b -- Defined in ‘GHC.Prim’
>> Prelude> :k (->)
>> (->) :: * -> * -> *
>> 
>> Basically I'm asking why ($) 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.scott at 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 at haskell.org
>>> http://mail.haskell.org/cgi-bin/mailman/listinfo/ghc-devs
>> 
>> 
>> 
>> 
>> --
>> Chris Allen
>> Currently working on http://haskellbook.com
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