#13038: implementation of Modus ponens and Modus tollens -------------------------------------+------------------------------------- Reporter: vanto | Owner: 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: | -------------------------------------+------------------------------------- Comment (by vanto): The truth tables for mod_ponens and mod_tollens are the same as the truth table of logical implication. For mod_ponens the entrance is at a=1 and the exit is at b=1. For mod_tollens the entrance is at b=0 and the exit is at a=0. mod_ponens is not like a conjonction likewise mod_tollens is not like a negative disjonction. They are rules of inference.[[BR]] Read mod_ponens like this: From A and (A implies B), infer B.[[BR]] And for mod_tollens read this: From (not B) and (A implies B), infer (not A).[[BR]] If you want more details read the Hilbert system which is a deductive reasoning, please.[[BR]] I looked in the archive mailing list about logical implication. Sometimes people get confused about the logical implication. If we write "if...then..." into a piece of code it is not a logical implication. If we talk and say "if...then..." we can suppose and deduce a logical implication. Do you understand the difference?[[BR]] In Haskell we can consider two things. Give a name to the function or name the function using a symbol. The name may be "imply" or "implies" or "impl" or other. The symbol can be ->. or -. or -|> or -|>. or -| or -|. or ->| or other.[[BR]] I am not running a second discussion on the logical implication. If the committee agree with the logical implication to be put in Haskell then it is ok and you can submit a patch instead of me. If the committee agree with mod_ponens and mod_tollens, idem. From my point of view, these three things have their place in the Haskell language.[[BR]] Happy new year! -- Ticket URL: http://ghc.haskell.org/trac/ghc/ticket/13038#comment:4 GHC http://www.haskell.org/ghc/ The Glasgow Haskell Compiler