Note [Injectivity annotation]

Language/Haskell/Syntax/Decls.hs:685 compiler

A user can declare a type family to be injective:

   type family Id a = r | r -> a where ...

 * The part after the "|" is called "injectivity annotation".
 * "r -> a" part is called "injectivity condition"; at the moment terms
   "injectivity annotation" and "injectivity condition" are synonymous
   because we only allow a single injectivity condition.
 * "r" is the "LHS of injectivity condition". LHS can only contain the
   variable naming the result of a type family.

 * "a" is the "RHS of injectivity condition". RHS contains space-separated
   type and kind variables representing the arguments of a type
   family. Variables can be omitted if a type family is not injective in
   these arguments. Example:
         type family Foo a b c = d | d -> a c where ...

Note that:
 (a) naming of type family result is required to provide injectivity
     annotation
 (b) for associated types if the result was named then injectivity annotation
     is mandatory. Otherwise result type variable is indistinguishable from
     associated type default.

It is possible that in the future this syntax will be extended to support
more complicated injectivity annotations. For example we could declare that
if we know the result of Plus and one of its arguments we can determine the
other argument:

   type family Plus a b = (r :: Nat) | r a -> b, r b -> a where ...

Here injectivity annotation would consist of two comma-separated injectivity
conditions.

See also Note [Injective type families] in GHC.Core.TyCon

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