9f1b358c04
git-svn-id: https://yap.svn.sf.net/svnroot/yap/trunk@1486 b08c6af1-5177-4d33-ba66-4b1c6b8b522a
371 lines
8.1 KiB
Plaintext
371 lines
8.1 KiB
Plaintext
|
|
:- object(translator).
|
|
|
|
:- info([
|
|
version is 1.0,
|
|
date is 2004/6/8,
|
|
author is 'Paulo Moura',
|
|
comment is 'Translator of logic propostions to clauses in conjunctive normal form.',
|
|
source is 'Code partially based on an example found on the Clocksin and Mellish Prolog book.']).
|
|
|
|
:- public(translate/2).
|
|
:- mode(translate(+nonvar, -list), zero_or_one).
|
|
:- info(translate/2, [
|
|
comment is 'Translates a proposition to a list of clauses.',
|
|
argnames is ['Propostion', 'Clauses']]).
|
|
|
|
:- public(step_by_step/2).
|
|
:- mode(step_by_step(+nonvar, -list), zero_or_one).
|
|
:- info(step_by_step/2, [
|
|
comment is 'Translates a proposition to a list of clauses, printing the result of each translation step.',
|
|
argnames is ['Propostion', 'Clauses']]).
|
|
|
|
:- dynamic(gensym_counter_/1).
|
|
|
|
|
|
:- op(10, fy, ~ ). % negation
|
|
:- op(20, yfx, & ). % conjunction
|
|
:- op(30, yfx, v ). % disjunction
|
|
:- op(40, xfx, =>). % implication
|
|
:- op(40, xfx, <=>). % equivalence
|
|
|
|
|
|
translate(P, Cs) :-
|
|
remove_implications(P, P2),
|
|
distribute_negation(P2, P3),
|
|
remove_existential_quantifiers(P3, P4),
|
|
convert_to_prenex_normal_form(P4, P5),
|
|
remove_universal_quantifiers(P5, P6),
|
|
convert_to_conjunctive_normal_form(P6, P7),
|
|
convert_to_clauses(P7, Cs),
|
|
print_clauses(Cs).
|
|
|
|
|
|
step_by_step(P, Cs) :-
|
|
nl, write('Processing proposition: '), write(P), nl, nl,
|
|
write(' 1. Remove implications: '),
|
|
remove_implications(P, P2),
|
|
write(P2), nl,
|
|
write(' 2. Distribute negation: '),
|
|
distribute_negation(P2, P3),
|
|
write(P3), nl,
|
|
write(' 3. Remove existential quantifiers: '),
|
|
remove_existential_quantifiers(P3, P4),
|
|
write(P4), nl,
|
|
write(' 4. Convert to prenex normal form: '),
|
|
convert_to_prenex_normal_form(P4, P5),
|
|
write(P5), nl,
|
|
write(' 5. Remove universal quantifiers: '),
|
|
remove_universal_quantifiers(P5, P6),
|
|
write(P6), nl,
|
|
write(' 6. Convert to conjunctive normal form: '),
|
|
convert_to_conjunctive_normal_form(P6, P7),
|
|
write(P7), nl,
|
|
write(' 7. Convert to clauses: '),
|
|
convert_to_clauses(P7, Cs),
|
|
write(Cs), nl, nl,
|
|
write('Clauses in Prolog-like notation:'), nl,
|
|
print_clauses(Cs).
|
|
|
|
|
|
remove_implications(all(X, P), all(X, P2)) :-
|
|
!,
|
|
remove_implications(P, P2).
|
|
|
|
remove_implications(exists(X, P), exists(X, P2)) :-
|
|
!,
|
|
remove_implications(P, P2).
|
|
|
|
remove_implications(P <=> Q, P2 & Q2 v ~P2 & ~Q2) :-
|
|
!,
|
|
remove_implications(P, P2),
|
|
remove_implications(Q, Q2).
|
|
|
|
remove_implications(P => Q, ~P2 v Q2) :-
|
|
!,
|
|
remove_implications(P, P2),
|
|
remove_implications(Q, Q2).
|
|
|
|
remove_implications(P & Q, P2 & Q2) :-
|
|
!,
|
|
remove_implications(P, P2),
|
|
remove_implications(Q, Q2).
|
|
|
|
remove_implications(P v Q, P2 v Q2) :-
|
|
!,
|
|
remove_implications(P, P2),
|
|
remove_implications(Q, Q2).
|
|
|
|
remove_implications(~P, ~P2) :-
|
|
!,
|
|
remove_implications(P, P2).
|
|
|
|
remove_implications(P, P).
|
|
|
|
|
|
distribute_negation(all(X, P), all(X, P2)) :-
|
|
!,
|
|
distribute_negation(P, P2).
|
|
|
|
distribute_negation(exists(X, P), exists(X, P2)) :-
|
|
!,
|
|
distribute_negation(P, P2).
|
|
|
|
distribute_negation(P & Q, P2 & Q2) :-
|
|
!,
|
|
distribute_negation(P, P2),
|
|
distribute_negation(Q, Q2).
|
|
|
|
distribute_negation(P v Q, P2 v Q2) :-
|
|
!,
|
|
distribute_negation(P, P2),
|
|
distribute_negation(Q, Q2).
|
|
|
|
distribute_negation(~P, P2) :-
|
|
!,
|
|
apply_negation(P, P2).
|
|
|
|
distribute_negation(P, P).
|
|
|
|
|
|
apply_negation(all(X, P), exists(X, P2)) :-
|
|
!,
|
|
apply_negation(P, P2).
|
|
|
|
apply_negation(exists(X, P), all(X, P2)) :-
|
|
!,
|
|
apply_negation(P, P2).
|
|
|
|
apply_negation(P & Q, P2 v Q2) :-
|
|
!,
|
|
apply_negation(P, P2),
|
|
apply_negation(Q, Q2).
|
|
|
|
apply_negation(P v Q, P2 & Q2) :-
|
|
!,
|
|
apply_negation(P, P2),
|
|
apply_negation(Q, Q2).
|
|
|
|
apply_negation(~P, P2) :-
|
|
!,
|
|
distribute_negation(P, P2).
|
|
|
|
apply_negation(P, ~P).
|
|
|
|
|
|
remove_existential_quantifiers(P, P2) :-
|
|
remove_existential_quantifiers(P, P2, []).
|
|
|
|
remove_existential_quantifiers(all(X, P), all(X, P2), Vars) :-
|
|
!,
|
|
remove_existential_quantifiers(P, P2, [X| Vars]).
|
|
|
|
remove_existential_quantifiers(exists(X, P), P2, Vars) :-
|
|
!,
|
|
gensym(f, F),
|
|
X =.. [F| Vars],
|
|
remove_existential_quantifiers(P, P2, Vars).
|
|
|
|
remove_existential_quantifiers(P & Q, P2 & Q2, Vars) :-
|
|
!,
|
|
remove_existential_quantifiers(P, P2, Vars),
|
|
remove_existential_quantifiers(Q, Q2, Vars).
|
|
|
|
remove_existential_quantifiers(P v Q, P2 v Q2, Vars) :-
|
|
!,
|
|
remove_existential_quantifiers(P, P2, Vars),
|
|
remove_existential_quantifiers(Q, Q2, Vars).
|
|
|
|
remove_existential_quantifiers(P, P, _).
|
|
|
|
|
|
convert_to_prenex_normal_form(P, P2) :-
|
|
collect_vars(P, P1, [], Vars),
|
|
add_vars_at_front(Vars, P1, P2).
|
|
|
|
collect_vars(all(X, P), P2, Acc, Vars) :-
|
|
!,
|
|
collect_vars(P, P2, [X| Acc], Vars).
|
|
|
|
collect_vars(P & Q, P2 & Q2, Acc, Vars) :-
|
|
!,
|
|
collect_vars(P, P2, Acc, Acc2),
|
|
collect_vars(Q, Q2, Acc2, Vars).
|
|
|
|
collect_vars(P v Q, P2 v Q2, Acc, Vars) :-
|
|
!,
|
|
collect_vars(P, P2, Acc, Acc2),
|
|
collect_vars(Q, Q2, Acc2, Vars).
|
|
|
|
collect_vars(P, P, Vars, Vars).
|
|
|
|
|
|
add_vars_at_front([], P, P).
|
|
|
|
add_vars_at_front([X| Vars], P, P2) :-
|
|
add_vars_at_front(Vars, all(X, P), P2).
|
|
|
|
|
|
remove_universal_quantifiers(all(_, P), P2) :-
|
|
!,
|
|
remove_universal_quantifiers(P, P2).
|
|
|
|
remove_universal_quantifiers(P & Q, P2 & Q2) :-
|
|
!,
|
|
remove_universal_quantifiers(P, P2),
|
|
remove_universal_quantifiers(Q, Q2).
|
|
|
|
remove_universal_quantifiers(P v Q, P2 v Q2) :-
|
|
!,
|
|
remove_universal_quantifiers(P, P2),
|
|
remove_universal_quantifiers(Q, Q2).
|
|
|
|
remove_universal_quantifiers(P, P).
|
|
|
|
|
|
convert_to_conjunctive_normal_form(P v Q, R) :-
|
|
!,
|
|
convert_to_conjunctive_normal_form(P, P2),
|
|
convert_to_conjunctive_normal_form(Q, Q2),
|
|
distribute_disjunction(P2 v Q2, R).
|
|
|
|
convert_to_conjunctive_normal_form(P & Q, P2 & Q2) :-
|
|
!,
|
|
convert_to_conjunctive_normal_form(P, P2),
|
|
convert_to_conjunctive_normal_form(Q, Q2).
|
|
|
|
convert_to_conjunctive_normal_form(P, P).
|
|
|
|
|
|
distribute_disjunction(P & Q v R, P2 & Q2) :-
|
|
!,
|
|
convert_to_conjunctive_normal_form(P v R, P2),
|
|
convert_to_conjunctive_normal_form(Q v R, Q2).
|
|
|
|
distribute_disjunction(P v Q & R, P2 & Q2) :-
|
|
!,
|
|
convert_to_conjunctive_normal_form(P v Q, P2),
|
|
convert_to_conjunctive_normal_form(P v R, Q2).
|
|
|
|
distribute_disjunction(P, P).
|
|
|
|
|
|
convert_to_clauses(P, Cs) :-
|
|
convert_to_clauses(P, [], Cs).
|
|
|
|
|
|
convert_to_clauses(P & Q, Acc, Cs) :-
|
|
!,
|
|
convert_to_clauses(Q, Acc, Acc2),
|
|
convert_to_clauses(P, Acc2, Cs).
|
|
|
|
convert_to_clauses(P, Acc, [cl(Pos, Negs)| Acc]) :-
|
|
convert_to_clauses(P, [], Pos, [], Negs),
|
|
!.
|
|
|
|
convert_to_clauses(_, Cs, Cs).
|
|
|
|
|
|
convert_to_clauses(P v Q, AccPos, Pos, AccNegs, Negs) :-
|
|
!,
|
|
convert_to_clauses(Q, AccPos, AccPos2, AccNegs, AccNegs2),
|
|
convert_to_clauses(P, AccPos2, Pos, AccNegs2, Negs).
|
|
|
|
convert_to_clauses(~P, Pos, Pos, AccNegs, [P| AccNegs]) :-
|
|
!,
|
|
not_member_of(P, Pos).
|
|
|
|
convert_to_clauses(P, AccPos, [P| AccPos], Negs, Negs) :-
|
|
!,
|
|
not_member_of(P, Negs).
|
|
|
|
/*
|
|
convert_to_clauses(P & Q, {P2, Q2}) :-
|
|
!,
|
|
convert_to_clauses(P, P2),
|
|
convert_to_clauses(Q, Q2).
|
|
|
|
convert_to_clauses(P v Q, R) :-
|
|
!,
|
|
convert_to_clause(P v Q, R).
|
|
|
|
convert_to_clauses(P, {P}).
|
|
|
|
|
|
convert_to_clause(P & Q, R) :-
|
|
!,
|
|
convert_to_clauses(P & Q, {R}).
|
|
|
|
convert_to_clause(P v Q, {P2, Q}) :-
|
|
!,
|
|
convert_to_clause(P, P2).
|
|
|
|
convert_to_clause(P, P).
|
|
*/
|
|
|
|
not_member_of(P, [P| _]) :-
|
|
!,
|
|
fail.
|
|
|
|
not_member_of(P, [_| Ps]) :-
|
|
!,
|
|
not_member_of(P, Ps).
|
|
|
|
not_member_of(_, []).
|
|
|
|
|
|
print_clauses([]) :-
|
|
nl.
|
|
|
|
print_clauses([cl(Pos, Negs)| Cs]) :-
|
|
print_clause(Pos, Negs), nl,
|
|
print_clauses(Cs).
|
|
|
|
print_clause(Pos, []) :-
|
|
!,
|
|
print_disjunctions(Pos), write(' :- .').
|
|
|
|
print_clause([], Negs) :-
|
|
!,
|
|
write(':- '), print_conjunctions(Negs), write('.').
|
|
|
|
print_clause(Pos, Negs) :-
|
|
!,
|
|
print_disjunctions(Pos), write(' :- '),
|
|
print_conjunctions(Negs), write('.').
|
|
|
|
|
|
print_disjunctions([P]) :-
|
|
!,
|
|
write(P).
|
|
|
|
print_disjunctions([P| Ps]) :-
|
|
!,
|
|
write(P), write('; '),
|
|
print_disjunctions(Ps).
|
|
|
|
|
|
print_conjunctions([P]) :-
|
|
!,
|
|
write(P).
|
|
|
|
print_conjunctions([P| Ps]) :-
|
|
!,
|
|
write(P), write(', '),
|
|
print_conjunctions(Ps).
|
|
|
|
|
|
gensym_counter_(0).
|
|
|
|
|
|
gensym(Base, Atom) :-
|
|
retract(gensym_counter_(Counter)),
|
|
Counter2 is Counter + 1,
|
|
number_codes(Counter2, Codes2),
|
|
atom_codes(Number, Codes2),
|
|
atom_concat(Base, Number, Atom),
|
|
assertz(gensym_counter_(Counter2)).
|
|
|
|
|
|
:- end_object.
|