On Tue, Jun 05, 2007 at 02:41:48PM +1000, 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.
There are way more than 16, if you count partial and lazy functions.
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
-}
I see P/Q notation used a lot
c :: Bool -> Bool -> Bool c False _ = False c _ q = not q
P∧¬Q Also AND-NOT, commonly seen in electronics circles as it is the logic function performed by a single transistor Stefan