====== Truth table ======
{{tag>operators logic}}
===== Description =====
Prolog program for calculating and displaying truth tables for boolean expressions involving 'and', 'or', and 'not'.

**Source**:  PrologTutorial	(on-line tutorial)
===== Download =====
Program source code: {{truth_table.pl}}
===== Listing =====
<code prolog>
/* prolog tutorial  2.13 Truth table maker */

:- op(1000,xfy,'and').
:- op(1000,xfy,'or').
:- op(900,fy,'not').

find_vars(N,V,V) :- member(N,[0,1]),!.    /* Boolean constants in expression */
find_vars(X,Vin,Vout) :- atom(X), 
                         (member(X,Vin) -> Vout = Vin ;   /* already have  */
                            Vout = [X|Vin]).                 /* include           */
find_vars(X and Y,Vin,Vout) :- find_vars(X,Vin,Vtemp),
                               find_vars(Y,Vtemp,Vout).
find_vars(X or Y,Vin,Vout) :-  find_vars(X,Vin,Vtemp),
                               find_vars(Y,Vtemp,Vout).
find_vars(not X,Vin,Vout) :-   find_vars(X,Vin,Vout).

initial_assign([],[]).
initial_assign([X|R],[0|S]) :- initial_assign(R,S).

successor(A,S) :- reverse(A,R),
                  next(R,N),
                  reverse(N,S).

next([0|R],[1|R]).
next([1|R],[0|S]) :- next(R,S).

truth_value(N,_,_,N) :- member(N,[0,1]).
truth_value(X,Vars,A,Val) :- atom(X),
                             lookup(X,Vars,A,Val).
truth_value(X and Y,Vars,A,Val) :- truth_value(X,Vars,A,VX),
                                   truth_value(Y,Vars,A,VY),
                                   boole_and(VX,VY,Val).
truth_value(X or Y,Vars,A,Val) :-  truth_value(X,Vars,A,VX),
                                   truth_value(Y,Vars,A,VY),
                                   boole_or(VX,VY,Val).
truth_value(not X,Vars,A,Val) :-   truth_value(X,Vars,A,VX),
                                   boole_not(VX,Val).

lookup(X,[X|_],[V|_],V).
lookup(X,[_|Vars],[_|A],V) :- lookup(X,Vars,A,V).

tt(E) :- find_vars(E,[],V),
         reverse(V,Vars),
         initial_assign(Vars,A),
         write('  '), write(Vars), write('    '), write(E), nl,
         write('-----------------------------------------'), nl,
         write_row(E,Vars,A),
         write('-----------------------------------------'), nl.

write_row(E,Vars,A) :- write('  '), write(A), write('        '), 
                       truth_value(E,Vars,A,V), write(V), nl,
                       (successor(A,N) -> write_row(E,Vars,N) ; true).


boole_and(0,0,0).      
boole_or(0,0,0).      
boole_not(0,1).
boole_and(0,1,0).      
boole_or(0,1,1).      
boole_not(1,0).
boole_and(1,0,0).      
boole_or(1,0,1).
boole_and(1,1,1).      
boole_or(1,1,1).

% ?- tt(x or (not y  and z)).
</code>
===== Comments =====