[GHC] #15235: GHCi's claim of infixr 0 (->) is a lie

[GHC]

#15235: GHCi's claim of infixr 0 (->) is a lie
-------------------------------------+-------------------------------------
           Reporter:  RyanGlScott    |             Owner:  (none)
               Type:  bug            |            Status:  new
           Priority:  normal         |         Milestone:  8.6.1
          Component:  Compiler       |           Version:  8.4.3
           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:
-------------------------------------+-------------------------------------
 Currently, if you query the `:info` for `(->)` in GHCi, it will give you:

 {{{
 $ ghci
 GHCi, version 8.4.3: http://www.haskell.org/ghc/  :? for help
 Loaded GHCi configuration from /home/ryanglscott/.ghci
 λ> :i (->)
 data (->) (a :: TYPE q) (b :: TYPE r)   -- Defined in ‘GHC.Prim’
 infixr 0 `(->)`
 <instances elided>
 }}}

 This fixity information appears to be plain wrong, as the following
 program demonstrates:

 {{{#!hs
 {-# LANGUAGE TypeOperators #-}
 module Bug where

 import Data.Type.Equality

 type (~>) = (->)
 infixr 0 ~>

 f :: (a ~> b -> c) :~: (a ~> (b -> c))
 f = Refl
 }}}

 Since `(~>)` and `(->)` are both `infixr 0`, I would expect `a ~> b -> c`
 to associate as `a ~> (b -> c)`, like the type signature for `f` wants to
 prove. However, GHC believes otherwise:

 {{{
 $ ghc Bug.hs
 [1 of 1] Compiling Bug              ( Bug.hs, Bug.o )

 Bug.hs:10:5: error:
     • Occurs check: cannot construct the infinite type: a ~ a ~> b
       Expected type: ((a ~> b) -> c) :~: (a ~> (b -> c))
         Actual type: ((a ~> b) -> c) :~: ((a ~> b) -> c)
     • In the expression: Refl
       In an equation for ‘f’: f = Refl
     • Relevant bindings include
         f :: ((a ~> b) -> c) :~: (a ~> (b -> c)) (bound at Bug.hs:10:1)
    |
 10 | f = Refl
    |     ^^^^
 }}}

 Reading the error message above, it appears that GHC gives `(->)` an even
 //lower// precedence than 0, since it associates `a ~> b -> c` as `(a ~>
 b) -> c`.

 I'm not sure how to reconcile these two facts. There are at least a couple
 of options I can think of:

 1. Claim `(->)` has a negative fixity.
 2. Try to change GHC so that `(->)` really is `infixr 0`.

-- 
Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/15235>
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