[GHC] #13038: implementation of Modus ponens and Modus tollens

[GHC]

#13038: implementation of Modus ponens and Modus tollens
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        Reporter:  vanto             |                Owner:  (none)
            Type:  feature request   |               Status:  infoneeded
        Priority:  normal            |            Milestone:
       Component:  libraries/base    |              Version:  8.0.1
      Resolution:                    |             Keywords:
Operating System:  Unknown/Multiple  |         Architecture:
                                     |  Unknown/Multiple
 Type of failure:  None/Unknown      |            Test Case:
      Blocked By:                    |             Blocking:
 Related Tickets:                    |  Differential Rev(s):
       Wiki Page:                    |
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Comment (by Iceland_jack):

 Regarding adding `implies` (`(==>)`),
 [https://ghc.haskell.org/trac/ghc/ticket/10592#comment:12 here is the
 hierarchy] I'm most intrigued by

 {{{#!hs
 class Boolean (Logic a) => Eq a where
   type Logic a :: Type
   (==) :: a -> a -> Logic a

 class Eq a => POrd a where
   inf :: a -> a -> a

 class POrd a => MinBound a where
   minBound :: a

 class POrd a => Lattice a where
   sup :: a -> a -> a

 class (Lattice a, MinBound a) => Bounded a where
   maxBound :: a

 class Bounded a => Complemented a where
   not :: a -> a

 class Bounded a => Heyting a where
   infixr 3 ==>
   (==>) :: a -> a -> a

 class (Complemented a, Heyting a) => Boolean a
 }}}

--
Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/13038#comment:6>
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