<div dir="ltr">><span style="font-size:12.8px"> make the kind of (->) more flexible.</span><div><br></div><div>Can that wait until 8.2 so we don't have to edit the book as much in preparation for 8.0? :P</div></div><div class="gmail_extra"><br><div class="gmail_quote">On Thu, Feb 4, 2016 at 3:15 PM, Richard Eisenberg <span dir="ltr"><<a href="mailto:eir@cis.upenn.edu" target="_blank">eir@cis.upenn.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">I agree with everything that's been said in this thread, including the unstated "that type for ($) is sure ugly".<br>
<br>
Currently, saturated (a -> b) is like a language construct, and it has its own typing rule, independent of the type of the type constructor (->). But reading the comment that Ben linked to, I think that comment is out of date. Now that we have levity polymorphism, we can probably to the Right Thing and make the kind of (->) more flexible.<br>
<span class="HOEnZb"><font color="#888888"><br>
Richard<br>
</font></span><div class="HOEnZb"><div class="h5"><br>
On Feb 4, 2016, at 3:27 PM, Ryan Scott <<a href="mailto:ryan.gl.scott@gmail.com">ryan.gl.scott@gmail.com</a>> wrote:<br>
<br>
>> My understanding was that the implicitly polymorphic levity, did (->) not change because it's a type constructor?<br>
><br>
> The kind of (->) as GHCi reports it is technically correct. As a kind<br>
> constructor, (->) has precisely the kind * -> * -> *. What's special<br>
> about (->) is that when you have a saturated application of it, it<br>
> takes on a levity-polymorphic kind. For example, this:<br>
><br>
> :k (->) Int# Int#<br>
><br>
> would yield a kind error, but<br>
><br>
> :k Int# -> Int#<br>
><br>
> is okay. Now, if you want an explanation as to WHY that's the case, I<br>
> don't think I could give one, as I simply got this information from<br>
> [1] (see the fourth bullet point, for OpenKind). Perhaps SPJ or<br>
> Richard Eisenberg could give a little insight here.<br>
><br>
>> Also does this encapsulate the implicit impredicativity of ($) for making runST $ work? I don't presently see how it would.<br>
><br>
> You're right, the impredicativity hack is a completely different<br>
> thing. So while you won't be able to define your own ($) and be able<br>
> to (runST $ do ...), you can at least define your own ($) and have it<br>
> work with unlifted return types. :)<br>
><br>
> Ryan S.<br>
> -----<br>
> [1] <a href="https://ghc.haskell.org/trac/ghc/wiki/NoSubKinds" rel="noreferrer" target="_blank">https://ghc.haskell.org/trac/ghc/wiki/NoSubKinds</a><br>
><br>
> On Thu, Feb 4, 2016 at 2:53 PM, Christopher Allen <<a href="mailto:cma@bitemyapp.com">cma@bitemyapp.com</a>> wrote:<br>
>> My understanding was that the implicitly polymorphic levity, did (->) not<br>
>> change because it's a type constructor?<br>
>><br>
>> Prelude> :info (->)<br>
>> data (->) a b -- Defined in ‘GHC.Prim’<br>
>> Prelude> :k (->)<br>
>> (->) :: * -> * -> *<br>
>><br>
>> Basically I'm asking why ($) changed and (->) did not when (->) had similar<br>
>> properties WRT * and #.<br>
>><br>
>> Also does this encapsulate the implicit impredicativity of ($) for making<br>
>> runST $ work? I don't presently see how it would.<br>
>><br>
>> Worry not about the book, we already hand-wave FTP effectively. One more<br>
>> type shouldn't change much.<br>
>><br>
>> Thank you very much for answering, this has been very helpful already :)<br>
>><br>
>> --- Chris<br>
>><br>
>><br>
>> On Thu, Feb 4, 2016 at 12:52 PM, Ryan Scott <<a href="mailto:ryan.gl.scott@gmail.com">ryan.gl.scott@gmail.com</a>> wrote:<br>
>>><br>
>>> Hi Chris,<br>
>>><br>
>>> The change to ($)'s type is indeed intentional. The short answer is<br>
>>> that ($)'s type prior to GHC 8.0 was lying a little bit. If you<br>
>>> defined something like this:<br>
>>><br>
>>> unwrapInt :: Int -> Int#<br>
>>> unwrapInt (I# i) = i<br>
>>><br>
>>> You could write an expression like (unwrapInt $ 42), and it would<br>
>>> typecheck. But that technically shouldn't be happening, since ($) ::<br>
>>> (a -> b) -> a -> b, and we all know that polymorphic types have to<br>
>>> live in kind *. But if you look at unwrapInt :: Int -> Int#, the type<br>
>>> Int# certainly doesn't live in *. So why is this happening?<br>
>>><br>
>>> The long answer is that prior to GHC 8.0, in the type signature ($) ::<br>
>>> (a -> b) -> a -> b, b actually wasn't in kind *, but rather OpenKind.<br>
>>> OpenKind is an awful hack that allows both lifted (kind *) and<br>
>>> unlifted (kind #) types to inhabit it, which is why (unwrapInt $ 42)<br>
>>> typechecks. To get rid of the hackiness of OpenKind, Richard Eisenberg<br>
>>> extended the type system with levity polymorphism [1] to indicate in<br>
>>> the type signature where these kind of scenarios are happening.<br>
>>><br>
>>> So in the "new" type signature for ($):<br>
>>><br>
>>> ($) :: forall (w :: Levity) a (b :: TYPE w). (a -> b) -> a -> b<br>
>>><br>
>>> The type b can either live in kind * (which is now a synonym for TYPE<br>
>>> 'Lifted) or kind # (which is a synonym for TYPE 'Unlifted), which is<br>
>>> indicated by the fact that TYPE w is polymorphic in its levity type w.<br>
>>><br>
>>> Truth be told, there aren't that many Haskell functions that actually<br>
>>> levity polymorphic, since normally having an argument type that could<br>
>>> live in either * or # would wreak havoc with the RTS (otherwise, how<br>
>>> would it know if it's dealing with a pointer or a value on the<br>
>>> stack?). But as it turns out, it's perfectly okay to have a levity<br>
>>> polymorphic type in a non-argument position [2]. Indeed, in the few<br>
>>> levity polymorphic functions that I can think of:<br>
>>><br>
>>> ($) :: forall (w :: Levity) a (b :: TYPE w). (a -> b) -> a -> b<br>
>>> error :: forall (v :: Levity) (a :: TYPE v). HasCallStack =><br>
>>> [Char] -> a<br>
>>> undefined :: forall (v :: Levity) (a :: TYPE v). HasCallStack => a<br>
>>><br>
>>> The levity polymorphic type never appears directly to the left of an<br>
>>> arrow.<br>
>>><br>
>>> The downside of all this is, of course, that the type signature of ($)<br>
>>> might look a lot scarier to beginners. I'm not sure how you'd want to<br>
>>> deal with this, but for 99% of most use cases, it's okay to lie and<br>
>>> state that ($) :: (a -> b) -> a -> b. You might have to include a<br>
>>> disclaimer that if they type :t ($) into GHCi, they should be prepared<br>
>>> for some extra information!<br>
>>><br>
>>> Ryan S.<br>
>>> -----<br>
>>> [1] <a href="https://ghc.haskell.org/trac/ghc/wiki/NoSubKinds" rel="noreferrer" target="_blank">https://ghc.haskell.org/trac/ghc/wiki/NoSubKinds</a><br>
>>> [2] <a href="https://ghc.haskell.org/trac/ghc/ticket/11473" rel="noreferrer" target="_blank">https://ghc.haskell.org/trac/ghc/ticket/11473</a><br>
>>> _______________________________________________<br>
>>> ghc-devs mailing list<br>
>>> <a href="mailto:ghc-devs@haskell.org">ghc-devs@haskell.org</a><br>
>>> <a href="http://mail.haskell.org/cgi-bin/mailman/listinfo/ghc-devs" rel="noreferrer" target="_blank">http://mail.haskell.org/cgi-bin/mailman/listinfo/ghc-devs</a><br>
>><br>
>><br>
>><br>
>><br>
>> --<br>
>> Chris Allen<br>
>> Currently working on <a href="http://haskellbook.com" rel="noreferrer" target="_blank">http://haskellbook.com</a><br>
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><br>
<br>
</div></div></blockquote></div><br><br clear="all"><div><br></div>-- <br><div class="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div dir="ltr">Chris Allen<br><div><span style="font-size:12.8000001907349px">Currently working on </span><a href="http://haskellbook.com" target="_blank">http://haskellbook.com</a></div></div></div></div></div></div>
</div>