#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