GHCi's claim of infixr 0 (->) is a lie

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:

{-# 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.

Trac metadata

Trac field	Value
Version	8.4.3
Type	Bug
TypeOfFailure	OtherFailure
Priority	normal
Resolution	Unresolved
Component	Compiler
Test case
Differential revisions
BlockedBy
Related
Blocking
CC
Operating system
Architecture