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

[GHC]

#13038: implementation of Modus ponens and Modus tollens
-------------------------------------+-------------------------------------
           Reporter:  vanto          |             Owner:
               Type:  feature        |            Status:  new
  request                            |
           Priority:  normal         |         Milestone:
          Component:                 |           Version:  8.0.1
  libraries/base                     |
           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:
-------------------------------------+-------------------------------------
 Can we have in Prelude - Booleans, Modus ponens and Modus tollens
 implemented? Or in another module?

 reminder:[[BR]]

 P is a proposition and v(p) is the logic value of P.[[BR]]

 P is true, v(P) = 1[[BR]]

 P is false, v(P) = 0[[BR]]

 P -> Q is always true in propositional logic.

 Modus ponens:[[BR]]
 v(P) = 1[[BR]]

 v(P -> Q) = 1[[BR]]

 v(Q) = 1[[BR]]

 v(P) and v(P -> q) are premiss, v(q) is the conclusion.[[BR]]
 or in a more general form[[BR]]

 P        : X is A[[BR]]

 P -> Q   : A -> B[[BR]]

 Q        : X is B[[BR]]

 Modus tollens:[[BR]]
 v(Q) = 0[[BR]]

 v(P -> Q) = 1[[BR]]

 v(P) = 0[[BR]]

 v(Q) and v(P -> Q) are premiss, v(P) is the conclusion.[[BR]]
 or in a more general form[[BR]]

 not Q  : X is not B[[BR]]

 P -> Q : A -> B[[BR]]

 not P  : X is not A[[BR]][[BR]]

 As well as using the numbers 0 and 1 for the respective values false and
 true, we'll use the letters F for False and T for True.[[BR]]

 We are always:[[BR]]
 v(F) = 0[[BR]]

 v(T) = 1[[BR]]

 v(P -> Q) = 1[[BR]]

--
Ticket URL: <http://ghc.haskell.org/trac/ghc/ticket/13038>
GHC <http://www.haskell.org/ghc/>
The Glasgow Haskell Compiler