[GHC] #12176: Failure of bidirectional type inference at the kind level

[GHC]

#12176: Failure of bidirectional type inference at the kind level
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           Reporter:  goldfire       |             Owner:  goldfire
               Type:  bug            |            Status:  new
           Priority:  normal         |         Milestone:
          Component:  Compiler       |           Version:  8.0.1
           Keywords:  TypeInType     |  Operating System:  Unknown/Multiple
       Architecture:                 |   Type of failure:  None/Unknown
  Unknown/Multiple                   |
          Test Case:                 |        Blocked By:
           Blocking:                 |   Related Tickets:
Differential Rev(s):                 |         Wiki Page:
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 I'm feeling particularly sadistic towards GHC at the moment, and so I fed
 it this:

 {{{
 import Data.Kind

 data Proxy :: forall k. k -> Type where
   MkProxy :: forall k (a :: k). Proxy a

 data X where
   MkX :: forall (k :: Type) (a :: k). Proxy a -> X

 type Expr = (MkX :: forall (a :: Bool). Proxy a -> X)

 type family Foo (x :: forall (a :: k). Proxy a -> X) where
   Foo (MkX :: forall (a :: k). Proxy a -> X) = (MkProxy :: Proxy k)
 }}}

 Incredibly, GHC accepts it! And it even means what I wish it to, with GHCi
 telling me the following (with `-fprint-explicit-kinds`):

 {{{
 λ> :i Foo
 type family Foo k (x :: forall (a :: k). Proxy k a -> X)
             :: Proxy * k
   where [k] Foo k ('MkX k) = 'MkProxy * k
 }}}

 That is, I wished to extract the kind parameter to `MkK`, matching against
 a partially-applied `MkX`, and GHC understood that intention.

 However, sadly, writing `Foo Expr` produces

 {{{
     • Expected kind ‘forall (a :: k0). Proxy k0 a -> X’,
         but ‘Expr a0’ has kind ‘Proxy Bool a0 -> X’
     • In the first argument of ‘Foo’, namely ‘Expr’
       In the type ‘Foo Expr’
       In the type family declaration for ‘XXX’
 }}}

 For some reason, `Expr` is getting instantiated when it shouldn't be.

 Perhaps there's a simpler test case demonstrating the bug, but I feel so
 gleeful that this chicanery is accepted at all that I wanted to post.

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Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/12176>
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