[GHC] #13879: Strange interaction between higher-rank kinds and type synonyms

[GHC]

#13879: Strange interaction between higher-rank kinds and type synonyms
-------------------------------------+-------------------------------------
           Reporter:  RyanGlScott    |             Owner:  (none)
               Type:  bug            |            Status:  new
           Priority:  normal         |         Milestone:
          Component:  Compiler       |           Version:  8.0.1
  (Type checker)                     |
           Keywords:  TypeInType     |  Operating System:  Unknown/Multiple
       Architecture:                 |   Type of failure:  GHC rejects
  Unknown/Multiple                   |  valid program
          Test Case:                 |        Blocked By:
           Blocking:                 |   Related Tickets:
Differential Rev(s):                 |         Wiki Page:
-------------------------------------+-------------------------------------
 Here's some code with typechecks with GHC 8.0.1, 8.0.2, 8.2.1, and HEAD:

 {{{#!hs
 {-# LANGUAGE GADTs #-}
 {-# LANGUAGE RankNTypes #-}
 {-# LANGUAGE ScopedTypeVariables #-}
 {-# LANGUAGE TypeFamilies #-}
 {-# LANGUAGE TypeInType #-}
 {-# LANGUAGE TypeOperators #-}
 module Bug where

 import Data.Kind

 data family Sing (a :: k)

 data (a :: j) :~~: (b :: k) where
   HRefl :: a :~~: a

 data instance Sing (z :: a :~~: b) where
   SHRefl :: Sing HRefl

 (%:~~:->) :: forall (j :: Type) (k :: Type) (a :: j) (b :: k) (r :: a :~~:
 b) (p :: forall (z :: Type) (y :: z). a :~~: y -> Type).
              Sing r
           -> p HRefl
           -> p r
 (%:~~:->) SHRefl pHRefl = pHRefl

 type App f x = f x
 type HRApp (f :: forall (z :: Type) (y :: z). a :~~: y -> Type) (x :: a
 :~~: b) = f x
 }}}

 Now I want to refactor this so that I use `App`:

 {{{#!hs
 (%:~~:->) :: forall (j :: Type) (k :: Type) (a :: j) (b :: k) (r :: a :~~:
 b) (p :: forall (z :: Type) (y :: z). a :~~: y -> Type).
              Sing r
           -> App p HRefl
           -> App p r
 }}}

 However, GHC doesn't like that:

 {{{
 $ /opt/ghc/8.2.1/bin/ghci Bug.hs -fprint-explicit-kinds -fprint-explicit-
 foralls
 GHCi, version 8.2.0.20170623: http://www.haskell.org/ghc/  :? for help
 Loaded GHCi configuration from /home/rgscott/.ghci
 [1 of 1] Compiling Bug              ( Bug.hs, interpreted )

 Bug.hs:21:20: error:
     • Expected kind ‘(:~~:) j z a a’,
         but ‘'HRefl j a’ has kind ‘(:~~:) j j a a’
     • In the second argument of ‘App’, namely ‘HRefl’
       In the type signature:
         (%:~~:->) :: forall (j :: Type)
                             (k :: Type)
                             (a :: j)
                             (b :: k)
                             (r :: a :~~: b)
                             (p :: forall (z :: Type) (y :: z). a :~~: y ->
 Type).
                      Sing r -> App p HRefl -> App p r
    |
 21 |           -> App p HRefl
    |                    ^^^^^

 Bug.hs:22:20: error:
     • Expected kind ‘(:~~:) j z a b’, but ‘r’ has kind ‘(:~~:) j k a b’
     • In the second argument of ‘App’, namely ‘r’
       In the type signature:
         (%:~~:->) :: forall (j :: Type)
                             (k :: Type)
                             (a :: j)
                             (b :: k)
                             (r :: a :~~: b)
                             (p :: forall (z :: Type) (y :: z). a :~~: y ->
 Type).
                      Sing r -> App p HRefl -> App p r
    |
 22 |           -> App p r
    |                    ^
 }}}

 These errors are surprising to me, since it appears that the two higher-
 rank types, `z` and `y`, are behaving differently here: `y` appears to be
 willing to unify with other types in applications of `p`, but `z` isn't! I
 would expect //both// to be willing to unify in applications of `p`.

 Out of desperation, I tried this other formulation of `(%:~~:->)` which
 uses `HRApp` instead of `App`:

 {{{#!hs
 (%:~~:->) :: forall (j :: Type) (k :: Type) (a :: j) (b :: k) (r :: a :~~:
 b) (p :: forall (z :: Type) (y :: z). a :~~: y -> Type).
              Sing r
           -> HRApp p HRefl
           -> HRApp p r
 }}}

 But now I get an even stranger error message:

 {{{
 $ /opt/ghc/8.2.1/bin/ghci Bug.hs -fprint-explicit-kinds -fprint-explicit-
 foralls
 GHCi, version 8.2.0.20170623: http://www.haskell.org/ghc/  :? for help
 Loaded GHCi configuration from /home/rgscott/.ghci
 [1 of 1] Compiling Bug              ( Bug.hs, interpreted )

 Bug.hs:21:20: error:
     • Expected kind ‘forall z (y :: z). (:~~:) j z a y -> *’,
         but ‘p’ has kind ‘forall z (y :: z). (:~~:) j z a y -> *’
     • In the first argument of ‘HRApp’, namely ‘p’
       In the type signature:
         (%:~~:->) :: forall (j :: Type)
                             (k :: Type)
                             (a :: j)
                             (b :: k)
                             (r :: a :~~: b)
                             (p :: forall (z :: Type) (y :: z). a :~~: y ->
 Type).
                      Sing r -> HRApp p HRefl -> HRApp p r
    |
 21 |           -> HRApp p HRefl
    |                    ^

 Bug.hs:21:20: error:
     • Expected kind ‘forall z (y :: z). (:~~:) j z a y -> *’,
         but ‘p’ has kind ‘forall z (y :: z). (:~~:) j z a y -> *’
     • In the first argument of ‘HRApp’, namely ‘p’
       In the type signature:
         (%:~~:->) :: forall (j :: Type)
                             (k :: Type)
                             (a :: j)
                             (b :: k)
                             (r :: a :~~: b)
                             (p :: forall (z :: Type) (y :: z). a :~~: y ->
 Type).
                      Sing r -> HRApp p HRefl -> HRApp p r
    |
 21 |           -> HRApp p HRefl
    |                    ^

 Bug.hs:22:20: error:
     • Expected kind ‘forall z (y :: z). (:~~:) j z a y -> *’,
         but ‘p’ has kind ‘forall z (y :: z). (:~~:) j z a y -> *’
     • In the first argument of ‘HRApp’, namely ‘p’
       In the type signature:
         (%:~~:->) :: forall (j :: Type)
                             (k :: Type)
                             (a :: j)
                             (b :: k)
                             (r :: a :~~: b)
                             (p :: forall (z :: Type) (y :: z). a :~~: y ->
 Type).
                      Sing r -> HRApp p HRefl -> HRApp p r
    |
 22 |           -> HRApp p r
    |                    ^
 }}}

 That's right, it can't match the kinds:

 * `forall z (y :: z). (:~~:) j z a y -> *`, and
 * `forall z (y :: z). (:~~:) j z a y -> *`

 Uh... what? Those are the same kind!

--
Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/13879>
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