On Tue, 05 Jun 2007, at 00:41, Tony Morris wrote:
I would like to know if all 16 possible functions that accept two boolean arguments have names in First-Order Logic. I know they have Haskell function names (e.g. \p -> \_ -> id p, \_ -> \_ -> const True), but I'm hoping there is a more general name that is recognised by anyone with a feel for logic, but not necessarily Haskell.
I have listed all sixteen of these functions below using Haskell (named a to p) along with the name of those that I am aware of having a name as a comment.
Thanks for any tips.
{-
p q | a b c d e f g h i j k l m n o p 0 0 | 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 | 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 0 | 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 1 | 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
-}
Common Lisp has names for them. See: http://www.cs.cmu.edu/Groups/AI/html/cltl/clm/ node131.html#SECTION001670000000000000000 and then search for (boole boole-and x y) == (logand x y) and look at the table just before that. ---Frank