[GHC] #11207: GHC cannot infer injectivity on type family operating on GHC.TypeLits' Nat, but can for equivalent type family operating on user-defined Nat kind

[GHC]

#11207: GHC cannot infer injectivity on type family operating on GHC.TypeLits' Nat,
but can for equivalent type family operating on user-defined Nat kind
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           Reporter:  duairc         |             Owner:
               Type:  bug            |            Status:  new
           Priority:  normal         |         Milestone:
          Component:  Compiler       |           Version:  7.10.2
           Keywords:                 |  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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 The following does not work:

 {{{#!hs
 {-# LANGUAGE DataKinds, PolyKinds, TypeFamilies, TypeOperators,
 UndecidableInstances #-}

 import GHC.TypeLits (Nat, type (-))

 type family Replicate (n :: Nat) (a :: k) = (r :: [k]) | r -> n where
     Replicate 0 a = '[]
     Replicate n a = a ': Replicate (n - 1) a
 }}}

 It fails to compile with the following error:

 {{{
 error:
     • Type family equation violates injectivity annotation.
       Type variable ‘n’ cannot be inferred from the right-hand side.
       In the type family equation:
         forall (k :: BOX) (n :: Nat) (a :: k).
           Replicate n a = a : Replicate (n - 1) a
     • In the equations for closed type family ‘Replicate’
       In the type family declaration for ‘Replicate’
 Failed, modules loaded: none.
 }}}

 However, the following does:

 {{{#!hs
 {-# LANGUAGE DataKinds, PolyKinds, TypeFamilies, TypeOperators,
 UndecidableInstances #-}

 data Nat = Zero | Succ Nat

 type family Replicate (n :: Nat) (a :: k) = (r :: [k]) | r -> n where
     Replicate Zero a = '[]
     Replicate (Succ n) a = a ': Replicate n a
 }}}

 Sure GHC.TypeLits' built-in Nat type is isomorphic to the one defined
 above, and thus GHC should be able to infer injectivity for Replicate?

--
Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/11207>
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