% P46 (**) Truth tables for logical expressions.
% Define predicates and/2, or/2, nand/2, nor/2, xor/2, impl/2 
% and equ/2 (for logical equivalence) which succeed or
% fail according to the result of their respective operations; e.g.
% and(A,B) will succeed, if and only if both A and B succeed.
% Note that A and B can be Prolog goals (not only the constants
% true and fail).
% A logical expression in two variables can then be written in 
% prefix notation, as in the following example: and(or(A,B),nand(A,B)).
%
% Now, write a predicate table/3 which prints the truth table of a
% given logical expression in two variables.
%
% Example:
% ?- table(A,B,and(A,or(A,B))).
% true  true  true
% true  fail  true
% fail  true  fail
% fail  fail  fail
    
and(A,B) :- A, B.

or(A,_) :- A.
or(_,B) :- B.

equ(A,B) :- or(and(A,B), and(not(A),not(B))).

xor(A,B) :- not(equ(A,B)).

nor(A,B) :- not(or(A,B)).

nand(A,B) :- not(and(A,B)).

impl(A,B) :- or(not(A),B).

% bind(X) :- instantiate X to be true and false successively

bind(true).
bind(fail).

table(A,B,Expr) :- bind(A), bind(B), do(A,B,Expr), fail.

do(A,B,_) :- write(A), write('  '), write(B), write('  '), fail.
do(_,_,Expr) :- Expr, !, write(true), nl.
do(_,_,_) :- write(fail), nl.