[GHC] #14822: -XQuantifiedConstraints: Turn term-level entailments (:-) into constraints (=>)

[GHC]

#14822: -XQuantifiedConstraints: Turn term-level entailments (:-) into constraints
(=>)
-------------------------------------+-------------------------------------
        Reporter:  Iceland_jack      |                Owner:  (none)
            Type:  bug               |               Status:  closed
        Priority:  normal            |            Milestone:
       Component:  Compiler          |              Version:  8.5
      Resolution:  invalid           |             Keywords:
                                     |  QuantifiedConstraints, wipT2893
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 Iceland_jack):

 I don't make use of `Bool` being closed. I don't seek to discharge `forall
 b. C b` as you claim, rather `pi b. C b`.

 I found a way to emulate what I want with `unsafeCoerce`. Here is an
 example for the open kind `Type`:

 {{{#!hs
 {-# Language KindSignatures, GADTs, ConstraintKinds,
 QuantifiedConstraints, TypeOperators, MultiParamTypeClasses,
 FlexibleInstances, UndecidableInstances, AllowAmbiguousTypes,
 TypeApplications, ScopedTypeVariables, RankNTypes #-}

 import Data.Kind
 import Unsafe.Coerce

 -- constraints
 data Dict :: Constraint -> Type where
   Dict :: c => Dict c

 class    (a => b) => Implies a b
 instance (a => b) => Implies a b

 type a |- b = Dict (a `Implies` b)

 -- Representation of two types: Int and Bool
 data S :: Type -> Type where
   SInt  :: S Int
   SBool :: S Bool

 -- Can be passed explicitly
 class    SI a    where s :: S a
 instance SI Int  where s = SInt
 instance SI Bool where s = SBool

 -- Can be eliminated like with an if-then-else
 sElim :: S a -> (Int ~ a => res) -> (Bool ~ a => res) -> res
 sElim SInt  i _ = i
 sElim SBool _ b = b

 -- (SI a) entails (Str a)
 class    Str a    where str :: String
 instance Str Int  where str = "INT"
 instance Str Bool where str = "BOOL"

 newtype Wrap a = Wrap a

 instance SI a => Str (Wrap a) where
   str = sElim (s @a)
     (str @a)
     (str @a)

 wit :: forall ty. SI ty |- Str ty
 wit = wrapElim Dict where

   wrapElim :: (SI ty |- Str (Wrap ty))
            -> (SI ty |- Str ty)
   wrapElim = unsafeCoerce

 -- >> siStr @Int
 -- "INT!"
 -- >> siStr @Bool
 -- "BOOL!"
 siStr :: forall ty. SI ty => String
 siStr = go wit where

   go :: SI ty => (SI ty |- Str ty) -> String
   go Dict = str @ty ++ "!"
 }}}

-- 
Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/14822#comment:3>
GHC <http://www.haskell.org/ghc/>
The Glasgow Haskell Compiler