[GHC] #12199: GHC is oblivious to injectivity when a type family is used in a GADT type

[GHC]

#12199: GHC is oblivious to injectivity when a type family is used in a GADT type
-------------------------------------+-------------------------------------
           Reporter:  RyanGlScott    |             Owner:
               Type:  bug            |            Status:  new
           Priority:  normal         |         Milestone:
          Component:  Compiler       |           Version:  8.0.1
  (Type checker)                     |
           Keywords:  TypeFamilies,  |  Operating System:  Unknown/Multiple
  Injective                          |
       Architecture:                 |   Type of failure:  GHC rejects
  Unknown/Multiple                   |  valid program
          Test Case:                 |        Blocked By:
           Blocking:                 |   Related Tickets:
Differential Rev(s):                 |         Wiki Page:
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 [https://www.reddit.com/r/haskell/comments/4oeidw/type_family_dependencies_and_gadts/
 A reddit post] points out a limitation of injective type families:

 {{{#!hs
 {-# LANGUAGE GADTs                  #-}
 {-# LANGUAGE KindSignatures         #-}
 {-# LANGUAGE TypeFamilyDependencies #-}

 type family Foo a = b | b -> a where
   Foo Int = Bool

 data Bar :: * -> * where
   Bar :: a -> Bar (Foo a)

 oink :: Bar Bool -> Int
 oink (Bar x) = x  -- type error
 }}}

 Compiling this fails with:

 {{{
 Could not deduce: a ~ Int
 from the context: Bool ~ Foo a
 }}}

 Which seems odd, given that `Bool ~ Foo a` should imply `a ~ Int` by
 injectivity. Even if you change the type signature of `oink` to `Bar (Foo
 Int) -> Int`, it fails with:

 {{{
 Could not deduce: a ~ Int
 from the context: Foo Int ~ Foo a
 }}}

 which makes it even more apparent that it isn't aware of the fact that
 `Foo` is injective.

--
Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/12199>
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