[GHC] #12119: Can't create injective type family equation with TypeError as the RHS

[GHC]

#12119: Can't create injective type family equation with TypeError as the RHS
-------------------------------------+-------------------------------------
        Reporter:  RyanGlScott       |                Owner:
            Type:  feature request   |               Status:  new
        Priority:  normal            |            Milestone:
       Component:  Compiler (Type    |              Version:  8.0.1
  checker)                           |             Keywords:
      Resolution:                    |  CustomTypeErrors, TypeFamilies,
                                     |  Injective
Operating System:  Unknown/Multiple  |         Architecture:
                                     |  Unknown/Multiple
 Type of failure:  None/Unknown      |            Test Case:
      Blocked By:                    |             Blocking:
 Related Tickets:                    |  Differential Rev(s):
       Wiki Page:                    |
-------------------------------------+-------------------------------------

Comment (by simonpj):

 That looks plausible to me.

 What is the consequences of declaring `Foo` to be injective?  Answer, only
 that if we have
 {{{
  [W] g1 : Foo t1 ~ Foo t2
 }}}
 where `[W]` means "wanted", a constraint we are trying to solve, then we
 try to prove
 {{{
  [W] g2: t1 ~ t2
 }}}
 Assuming we succeed, binding `g2 = <some coercion>`, then we can prove the
 first constraint by binding `g1 = Foo g2`.

 If `F` is not injective, this proof strategy is no unsound; but it may be
 incomplete.  Perhaps there are un-equal types `t1` and `t2` for which `Foo
 t1 ~ Foo t2`.

 In your example, it's true that `Foo Int ~ TypeError "boom" ~ Foo Bool`.
 So indeed there may be a solution to the constraint `Foo t1 ~ Foo t2` that
 does not require `t1 ~ t2`.  But if the proof goes via `TypeError`, as
 here, perhaps that particular sort of incompleteness doesn't matter.

 So it sounds plausible.  I don't really know how to formalise it though.

--
Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/12119#comment:1>
GHC <http://www.haskell.org/ghc/>
The Glasgow Haskell Compiler