[GHC] #10832: Generalize injective type families

[GHC]

#10832: Generalize injective type families
-------------------------------------+-------------------------------------
              Reporter:  jstolarek   |             Owner:  jstolarek
                  Type:  feature     |            Status:  new
  request                            |
              Priority:  normal      |         Milestone:
             Component:  Compiler    |           Version:  7.11
  (Type checker)                     |
              Keywords:              |  Operating System:  Unknown/Multiple
          Architecture:              |   Type of failure:  None/Unknown
  Unknown/Multiple                   |
             Test Case:              |        Blocked By:
              Blocking:              |   Related Tickets:
Differential Revisions:              |
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 With injective type families we can now declare that type family result
 determines the arguments. But ITFs are not yet as expressive as functional
 dependencies. For example with FDs I can say:

 {{{#!hs
 data Nat = Zero | Succ a

 class Add a b r | a b -> r, r a -> b
 instance                Add Zero     b b
 instance (Add a b r) => Add (Succ a) b (Succ r)
 }}}
 Here we declare that the result and the first argument taken together
 uniquely determine the second argument. This is not currently possible
 with ITFs:

 {{{#!hs
 type family AddTF a b = r | r a -> b where
      AddTF Zero     b = b
      AddTF (Succ a) b = Succ (AddTF a b)
 }}}
 But we want to be able to say that.

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Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/10832>
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