/* 

  Boolean in Picat.

  From IF/Prolog boole.pro

  This Picat model was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/


% import util.
import cp.


main => go.


go =>
  Axiom=findall([X1,Y1,Z1],axiom(X1,Y1,Z1)),
  println(axiom=Axiom),

  Xor = findall([A1,B1],xor(A1,B1)),
  println(xor=Xor),

  Morgan1 = findall([A2,B2],morgan1(A2,B2)),
  println(morgan1=Morgan1),

  Morgan2 = findall([A3,B3],morgan2(A3,B3)),
  println(morgan2=Morgan2),
  
  nl.

axiom(X, Y, Z) =>
        X #^ 0 #<=> X,
        X #^ X #<=> 0,
        X #^ Y #<=> Y #^ X,
        (X #^ Y) #^ Z #<=> X #^ (Y #^ Z),
        X #/\ Y #<=> Y #/\ X,
        X #/\ (Y #/\ Z) #<=> (X #/\ Y) #/\ Z,
        X #/\ (Y #^ Z) #<=> (X #/\ Y) #^ (X #/\ Z),
        0 #/\ X #<=> 0,
        1 #/\ X #<=> X,
        X #/\ X #<=> X,

        solve([X,Y,Z]).


xor(A, B) =>
        A #^ B #<=> (A #/\ #~B) #\/ (#~A #/\ B), solve([A,B]).


morgan1(A, B) =>
        #~(A #/\ B) #<=> #~A #\/ #~B, solve([A,B]).

morgan2(A, B) =>
        #~(A #\/ B) #<=> #~A #/\ #~B, solve([A,B]).