[GHC] #13797: Mark negation injective

[GHC]

#13797: Mark negation injective
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           Reporter:  Iceland_jack   |             Owner:  (none)
               Type:  bug            |            Status:  new
           Priority:  normal         |         Milestone:
          Component:  Compiler       |           Version:  8.0.1
           Keywords:                 |  Operating System:  Unknown/Multiple
  InjectiveFamilies                  |
       Architecture:                 |   Type of failure:  None/Unknown
  Unknown/Multiple                   |
          Test Case:                 |        Blocked By:
           Blocking:                 |   Related Tickets:
Differential Rev(s):                 |         Wiki Page:
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 {{{#!hs
 {-# Language DataKinds, TypeOperators, TypeFamilyDependencies,
 UndecidableInstances #-}

 import GHC.TypeLits

 data N = O | S N

 type family
   U (a :: Nat) = (res :: N) | res -> a where
   U 0 = O
   U n = S (U (n-1))
 }}}

 gives

 {{{
 olates injectivity annotation.
       Type variable ‘n’ cannot be inferred from the right-hand side.
       In the type family equation:
         U n = 'S (U (n - 1)) -- Defined at /tmp/a.hs:37:3
     • In the equations for closed type family ‘U’
       In the type family declaration for ‘U’
 Failed, modules loaded: none.
 }}}

 I expect this to work, this depends on making `(-)` injective which
 depends on
 [https://ghc.haskell.org/trac/ghc/wiki/InjectiveTypeFamilies#Futureplansandideas
 "generalized injectivity"]?

 {{{#!hs
 type family
   (a :: Nat) - (b :: Nat) = (res :: Nat) | a b -> res, res a -> b, res b
 -> a where
   {- built in -}
 }}}

--
Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/13797>
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