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z3prover.cpp
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#include <unordered_map>
#include <z3++.h>
#include "wff.h"
#include "mm/reader.h"
#include "utils/utils.h"
#include "platform.h"
#include "mm/setmm_loader.h"
#include "test/test.h"
//#define VERBOSE_Z3
pwff parse_expr(z3::expr e, const LibraryToolbox &tb) {
assert(e.is_app());
z3::func_decl decl = e.decl();
Z3_decl_kind kind = decl.decl_kind();
pwff ret;
switch (kind) {
case Z3_OP_TRUE:
assert(e.num_args() == 0);
return True::create();
case Z3_OP_FALSE:
assert(e.num_args() == 0);
return False::create();
case Z3_OP_EQ:
// Interpreted as biimplication; why does Z3 generates equalities between formulae?
assert(e.num_args() == 2);
return Biimp::create(parse_expr(e.arg(0), tb), parse_expr(e.arg(1), tb));
case Z3_OP_AND:
assert(e.num_args() >= 2);
ret = And::create(parse_expr(e.arg(0), tb), parse_expr(e.arg(1), tb));
for (unsigned i = 2; i < e.num_args(); i++) {
ret = And::create(ret, parse_expr(e.arg(i), tb));
}
return ret;
case Z3_OP_OR:
assert(e.num_args() >= 2);
ret = Or::create(parse_expr(e.arg(0), tb), parse_expr(e.arg(1), tb));
for (unsigned i = 2; i < e.num_args(); i++) {
ret = Or::create(ret, parse_expr(e.arg(i), tb));
}
return ret;
case Z3_OP_IFF:
assert(e.num_args() == 2);
return Biimp::create(parse_expr(e.arg(0), tb), parse_expr(e.arg(1), tb));
case Z3_OP_XOR:
assert(e.num_args() == 2);
return Xor::create(parse_expr(e.arg(0), tb), parse_expr(e.arg(1), tb));
case Z3_OP_NOT:
assert(e.num_args() == 1);
return Not::create(parse_expr(e.arg(0), tb));
case Z3_OP_IMPLIES:
assert(e.num_args() == 2);
return Imp::create(parse_expr(e.arg(0), tb), parse_expr(e.arg(1), tb));
case Z3_OP_UNINTERPRETED:
assert(e.num_args() == 0);
return Var::create(decl.name().str(), tb);
default:
throw "Cannot handle this formula";
}
}
z3::expr extract_thesis(z3::expr proof) {
return proof.arg(proof.num_args()-1);
}
void prove_and_print(pwff wff, const LibraryToolbox &tb) {
CreativeProofEngineImpl< Sentence > engine(tb);
wff->get_adv_truth_prover(tb).second(engine);
if (engine.get_proof_labels().size() > 0) {
//cout << "adv truth proof: " << tb.print_proof(engine.get_proof_labels()) << endl;
std::cout << "stack top: " << tb.print_sentence(engine.get_stack().back(), SentencePrinter::STYLE_ANSI_COLORS_SET_MM) << std::endl;
std::cout << "proof length: " << engine.get_proof_labels().size() << std::endl;
}
}
RegisteredProver id_rp = LibraryToolbox::register_prover({}, "|- ( ph -> ph )");
RegisteredProver ff_rp = LibraryToolbox::register_prover({}, "|- ( F. -> F. )");
RegisteredProver orim1i_rp = LibraryToolbox::register_prover({"|- ( ph -> ps )"}, "|- ( ( ph \\/ ch ) -> ( ps \\/ ch ) )");
RegisteredProver orfa_rp = LibraryToolbox::register_prover({"|- ( ph -> ps )"}, "|- ( ( ph \\/ F. ) -> ps )");
RegisteredProver orfa2_rp = LibraryToolbox::register_prover({"|- ( ph -> F. )"}, "|- ( ( ph \\/ ps ) -> ps )");
// Produces a prover for ( ( ... ( ph_1 \/ ph_2 ) ... \/ ph_n ) -> ( ... ( ph_{i_1} \/ ph_{i_2} ) ... \/ ph_{i_k} ) ),
// where all instances of F. have been removed (unless they're all F.'s).
std::tuple< Prover< InspectableProofEngine< Sentence > >, pwff, pwff > simplify_or(const std::vector< pwff > &clauses, const LibraryToolbox &tb) {
if (clauses.size() == 0) {
return make_tuple(tb.build_registered_prover< InspectableProofEngine< Sentence > >(ff_rp, {}, {}), False::create(), False::create());
} else {
Prover< InspectableProofEngine< Sentence > > ret = tb.build_registered_prover< InspectableProofEngine< Sentence > >(id_rp, {{"ph", clauses[0]->get_type_prover(tb)}}, {});
pwff first = clauses[0];
pwff second = clauses[0];
pwff falsum = False::create();
for (size_t i = 1; i < clauses.size(); i++) {
pwff new_clause = clauses[i];
if (*second == *falsum) {
ret = tb.build_registered_prover< InspectableProofEngine< Sentence > >(orfa2_rp, {{"ph", first->get_type_prover(tb)}, {"ps", new_clause->get_type_prover(tb)}}, {ret});
second = new_clause;
} else {
if (*new_clause == *falsum) {
ret = tb.build_registered_prover< InspectableProofEngine< Sentence > >(orfa_rp, {{"ph", first->get_type_prover(tb)}, {"ps", second->get_type_prover(tb)}}, {ret});
} else {
ret = tb.build_registered_prover< InspectableProofEngine< Sentence > >(orim1i_rp, {{"ph", first->get_type_prover(tb)}, {"ps", second->get_type_prover(tb)}, {"ch", new_clause->get_type_prover(tb)}}, {ret});
second = Or::create(second, new_clause);
}
}
first = Or::create(first, new_clause);
}
return make_tuple(ret, first, second);
}
}
RegisteredProver orim12d_rp = LibraryToolbox::register_prover({"|- ( ph -> ( ps -> ch ) )", "|- ( ph -> ( th -> ta ) )"}, "|- ( ph -> ( ( ps \\/ th ) -> ( ch \\/ ta ) ) )");
std::tuple< Prover< InspectableProofEngine< Sentence > >, pwff, pwff > join_or_imp(const std::vector< pwff > &orig_clauses, const std::vector< pwff > &new_clauses, std::vector< Prover< InspectableProofEngine< Sentence > > > &provers, const pwff &abs, const LibraryToolbox &tb) {
assert(orig_clauses.size() == new_clauses.size());
assert(orig_clauses.size() == provers.size());
if (orig_clauses.size() == 0) {
return make_tuple(tb.build_registered_prover< InspectableProofEngine< Sentence > >(ff_rp, {}, {}), False::create(), False::create());
} else {
Prover< InspectableProofEngine< Sentence > > ret = provers[0];
pwff orig_cl = orig_clauses[0];
pwff new_cl = new_clauses[0];
for (size_t i = 1; i < orig_clauses.size(); i++) {
ret = tb.build_registered_prover< InspectableProofEngine< Sentence > >(orim12d_rp, {{"ph", abs->get_type_prover(tb)}, {"ps", orig_cl->get_type_prover(tb)}, {"ch", new_cl->get_type_prover(tb)}, {"th", orig_clauses[i]->get_type_prover(tb)}, {"ta", new_clauses[i]->get_type_prover(tb)}}, {ret, provers[i]});
orig_cl = Or::create(orig_cl, orig_clauses[i]);
new_cl = Or::create(new_cl, new_clauses[i]);
}
return make_tuple(ret, orig_cl, new_cl);
}
}
RegisteredProver simpld_rp = LibraryToolbox::register_prover({"|- ( ph -> ( ps /\\ ch ) )"}, "|- ( ph -> ps )");
RegisteredProver simprd_rp = LibraryToolbox::register_prover({"|- ( ph -> ( ps /\\ ch ) )"}, "|- ( ph -> ch )");
RegisteredProver mp1_rp = LibraryToolbox::register_prover({"|- ( ph -> ps )", "|- ( ph -> ( ps -> ch ) )"}, "|- ( ph -> ch )");
RegisteredProver mp2_rp = LibraryToolbox::register_prover({"|- ( ph -> ps )", "|- ( ph -> ( ps <-> ch ) )"}, "|- ( ph -> ch )");
RegisteredProver bitrd_rp = LibraryToolbox::register_prover({"|- ( ph -> ( ps <-> ch ) )", "|- ( ph -> ( ch <-> th ) )"}, "|- ( ph -> ( ps <-> th ) )");
RegisteredProver a1i_rp = LibraryToolbox::register_prover({"|- ps"}, "|- ( ph -> ps )");
RegisteredProver biidd_rp = LibraryToolbox::register_prover({}, "|- ( ph -> ( ps <-> ps ) )");
RegisteredProver bibi12d_rp = LibraryToolbox::register_prover({"|- ( ph -> ( ps <-> ch ) )", "|- ( ph -> ( th <-> ta ) )"}, "|- ( ph -> ( ( ps <-> th ) <-> ( ch <-> ta ) ) )");
RegisteredProver imbi12d_rp = LibraryToolbox::register_prover({"|- ( ph -> ( ps <-> ch ) )", "|- ( ph -> ( th <-> ta ) )"}, "|- ( ph -> ( ( ps -> th ) <-> ( ch -> ta ) ) )");
RegisteredProver anbi12d_rp = LibraryToolbox::register_prover({"|- ( ph -> ( ps <-> ch ) )", "|- ( ph -> ( th <-> ta ) )"}, "|- ( ph -> ( ( ps /\\ th ) <-> ( ch /\\ ta ) ) )");
RegisteredProver orbi12d_rp = LibraryToolbox::register_prover({"|- ( ph -> ( ps <-> ch ) )", "|- ( ph -> ( th <-> ta ) )"}, "|- ( ph -> ( ( ps \\/ th ) <-> ( ch \\/ ta ) ) )");
RegisteredProver notbid_rp = LibraryToolbox::register_prover({"|- ( ph -> ( ps <-> ch ) )"}, "|- ( ph -> ( -. ps <-> -. ch ) )");
RegisteredProver urt_rp = LibraryToolbox::register_prover({"|- ( ph -> -. ps )"}, "|- ( ph -> ( ps -> F. ) )");
RegisteredProver urf_rp = LibraryToolbox::register_prover({"|- ( ph -> ps )"}, "|- ( ph -> ( -. ps -> F. ) )");
RegisteredProver idd_rp = LibraryToolbox::register_prover({}, "|- ( ph -> ( ps -> ps ) )");
RegisteredProver mpd_rp = LibraryToolbox::register_prover({"|- ( ph -> ps )", "|- ( ph -> ( ps -> ch ) )"}, "|- ( ph -> ch )");
RegisteredProver syl_rp = LibraryToolbox::register_prover({"|- ( ph -> ps )", "|- ( ps -> ch )"}, "|- ( ph -> ch )");
RegisteredProver bifald_rp = LibraryToolbox::register_prover({"|- ( ph -> -. ps )"}, "|- ( ph -> ( ps <-> F. ) )");
RegisteredProver orsild_rp = LibraryToolbox::register_prover({"|- ( ph -> -. ( ps \\/ ch ) )"}, "|- ( ph -> -. ps )");
RegisteredProver orsird_rp = LibraryToolbox::register_prover({"|- ( ph -> -. ( ps \\/ ch ) )"}, "|- ( ph -> -. ch )");
struct Z3Adapter {
z3::solver &s;
const LibraryToolbox &tb;
std::vector< pwff > hyps;
pwff thesis;
pwff target;
pwff and_hyps;
pwff abs;
Z3Adapter(z3::solver &s, const LibraryToolbox &tb) : s(s), tb(tb) {}
void add_formula(z3::expr e, bool hyp) {
if (hyp) {
this->s.add(e);
} else {
this->s.add(!e);
}
pwff w = parse_expr(e, tb);
if (hyp) {
this->hyps.push_back(w);
if (this->target == nullptr) {
this->and_hyps = w;
this->target = w;
this->abs = w;
} else {
this->and_hyps = And::create(this->and_hyps, w);
this->target = And::create(this->target, w);
this->abs = And::create(this->abs, w);
}
} else {
this->hyps.push_back(Not::create(w));
this->thesis = w;
if (this->target == nullptr) {
this->target = w;
this->abs = Not::create(w);
} else {
this->target = Imp::create(this->target, w);
this->abs = And::create(this->abs, Not::create(w));
}
}
}
pwff get_current_abs_hyps() {
return this->abs;
}
Prover< InspectableProofEngine< Sentence > > build_checked_prover(Prover< InspectableProofEngine< Sentence > > prover, pwff thesis) {
pwff full_thesis = Imp::create(this->get_current_abs_hyps(), thesis);
auto sent = tb.reconstruct_sentence(pt2_to_pt(full_thesis->to_parsing_tree(this->tb)), this->tb.get_turnstile());
return checked_prover(prover, sent);
}
Prover< InspectableProofEngine< Sentence > > convert_proof(z3::expr e, int depth = 0) {
if (e.is_app()) {
z3::func_decl decl = e.decl();
auto num_args = e.num_args();
auto arity = decl.arity();
#ifdef NDEBUG
(void) arity;
#endif
Z3_decl_kind kind = decl.decl_kind();
if (Z3_OP_PR_UNDEF <= kind && kind < Z3_OP_PR_UNDEF + 0x100) {
// Proof expressions, see the documentation of Z3_decl_kind,
// for example in https://z3prover.github.io/api/html/group__capi.html#ga1fe4399e5468621e2a799a680c6667cd
#ifdef VERBOSE_Z3
std::cout << std::string(depth, ' ');
std::cout << "Declaration: " << decl << " of arity " << decl.arity() << " and args num " << num_args << std::endl;
#endif
switch (kind) {
case Z3_OP_PR_ASSERTED: {
assert(num_args == 1);
assert(arity == 1);
#ifdef VERBOSE_Z3
//cout << "EXPR: " << e.arg(0) << endl;
/*cout << "HEAD WFF: " << this->get_current_abs_hyps()->to_string() << endl;
cout << "WFF: " << parse_expr(e.arg(0))->to_string() << endl;*/
#endif
pwff w = parse_expr(e.arg(0), tb);
assert(std::find_if(this->hyps.begin(), this->hyps.end(), [=](const pwff &p) { return *p == *w; }) != this->hyps.end());
//auto it = find_if(this->hyps.begin(), this->hyps.end(), [=](const pwff &p) { return *p == *w; });
//size_t pos = it - this->hyps.begin();
assert(this->hyps.size() >= 1);
auto ret = this->tb.build_registered_prover< InspectableProofEngine< Sentence > >(id_rp, {{"ph", this->get_current_abs_hyps()->get_type_prover(this->tb)}}, {});
pwff cur_hyp = this->get_current_abs_hyps();
for (size_t step = 0; step < this->hyps.size()-1; step++) {
auto and_hyp = std::dynamic_pointer_cast< const And >(cur_hyp);
assert(and_hyp != nullptr);
pwff left = and_hyp->get_a();
pwff right = and_hyp->get_b();
if (*and_hyp->get_b() == *w) {
cur_hyp = and_hyp->get_b();
ret = this->tb.build_registered_prover< InspectableProofEngine< Sentence > >(simprd_rp, {{"ph", this->get_current_abs_hyps()->get_type_prover(this->tb)}, {"ps", left->get_type_prover(this->tb)}, {"ch", right->get_type_prover(this->tb)}}, {ret});
break;
}
cur_hyp = and_hyp->get_a();
ret = this->tb.build_registered_prover< InspectableProofEngine< Sentence > >(simpld_rp, {{"ph", this->get_current_abs_hyps()->get_type_prover(this->tb)}, {"ps", left->get_type_prover(this->tb)}, {"ch", right->get_type_prover(this->tb)}}, {ret});
}
assert(*cur_hyp == *w);
return ret;
break; }
case Z3_OP_PR_MODUS_PONENS: {
assert(num_args == 3);
assert(arity == 3);
#ifdef VERBOSE_Z3
//cout << endl << "EXPR: " << e.arg(2);
/*cout << "HP1: " << parse_expr(extract_thesis(e.arg(0)))->to_string() << endl;
cout << "HP2: " << parse_expr(extract_thesis(e.arg(1)))->to_string() << endl;
cout << "TH: " << parse_expr(e.arg(2))->to_string() << endl;*/
#endif
Prover< InspectableProofEngine< Sentence > > p1 = this->convert_proof(e.arg(0), depth+1);
Prover< InspectableProofEngine< Sentence > > p2 = this->convert_proof(e.arg(1), depth+1);
auto thesis = parse_expr(e.arg(2), tb);
switch (extract_thesis(e.arg(1)).decl().decl_kind()) {
case Z3_OP_EQ:
case Z3_OP_IFF: {
auto ret = this->tb.build_registered_prover< InspectableProofEngine< Sentence > >(mp2_rp, {{"ph", this->get_current_abs_hyps()->get_type_prover(this->tb)}, {"ps", parse_expr(extract_thesis(e.arg(0)), tb)->get_type_prover(this->tb)}, {"ch", thesis->get_type_prover(this->tb)}}, {p1, p2});
ret = this->build_checked_prover(ret, thesis);
return ret; }
case Z3_OP_IMPLIES: {
auto ret = this->tb.build_registered_prover< InspectableProofEngine< Sentence > >(mp1_rp, {{"ph", this->get_current_abs_hyps()->get_type_prover(this->tb)}, {"ps", parse_expr(extract_thesis(e.arg(0)), tb)->get_type_prover(this->tb)}, {"ch", thesis->get_type_prover(this->tb)}}, {p1, p2});
ret = this->build_checked_prover(ret, thesis);
return ret; }
default:
throw "Should not arrive here";
break;
}
break; }
case Z3_OP_PR_REWRITE: {
assert(num_args == 1);
assert(arity == 1);
#ifdef VERBOSE_Z3
/*cout << "EXPR: " << e.arg(0) << endl;
cout << "WFF: " << parse_expr(e.arg(0))->to_string() << endl;*/
#endif
//prove_and_print(parse_expr(e.arg(0)), tb);
// The thesis should be true independently of ph
pwff thesis = parse_expr(e.arg(0), tb);
#ifdef VERBOSE_Z3
//std::cout << "ORACLE for '" << thesis->to_string() << "'!" << std::endl;
#endif
//Prover< InspectableProofEngine< Sentence > > p1 = thesis->get_adv_truth_prover(tb).second;
auto pt = pt2_to_pt(thesis->to_parsing_tree(this->tb));
auto sent = this->tb.reconstruct_sentence(pt, this->tb.get_turnstile());
Prover< InspectableProofEngine< Sentence > > p1 = this->tb.build_prover({}, sent, {}, {});
auto ret = this->tb.build_registered_prover< InspectableProofEngine< Sentence > >(a1i_rp, {{"ph", this->get_current_abs_hyps()->get_type_prover(this->tb)}, {"ps", thesis->get_type_prover(this->tb)}}, {p1});
ret = this->build_checked_prover(ret, thesis);
return ret; }
case Z3_OP_PR_TRANSITIVITY: {
assert(num_args == 3);
assert(arity == 3);
#ifdef VERBOSE_Z3
//cout << endl << "EXPR: " << e.arg(2);
/*cout << "HP1: " << parse_expr(extract_thesis(e.arg(0)))->to_string() << endl;
cout << "HP2: " << parse_expr(extract_thesis(e.arg(1)))->to_string() << endl;
cout << "TH: " << parse_expr(e.arg(2))->to_string() << endl;*/
#endif
Prover< InspectableProofEngine< Sentence > > p1 = this->convert_proof(e.arg(0), depth+1);
Prover< InspectableProofEngine< Sentence > > p2 = this->convert_proof(e.arg(1), depth+1);
auto w1 = std::dynamic_pointer_cast< const Biimp >(parse_expr(extract_thesis(e.arg(0)), tb));
auto w2 = std::dynamic_pointer_cast< const Biimp >(parse_expr(extract_thesis(e.arg(1)), tb));
assert(w1 != nullptr && w2 != nullptr);
assert(*w1->get_b() == *w2->get_a());
auto thesis = parse_expr(e.arg(2), tb);
pwff ps = w1->get_a();
pwff ch = w1->get_b();
pwff th = w2->get_b();
Prover< InspectableProofEngine< Sentence > > ret = this->tb.build_registered_prover< InspectableProofEngine< Sentence > >(bitrd_rp, {{"ph", this->get_current_abs_hyps()->get_type_prover(this->tb)}, {"ps", ps->get_type_prover(this->tb)}, {"ch", ch->get_type_prover(this->tb)}, {"th", th->get_type_prover(this->tb)}}, {p1, p2});
//cerr << "TEST: " << test_prover(ret, this->tb) << endl;
ret = this->build_checked_prover(ret, thesis);
return ret;
break; }
case Z3_OP_PR_MONOTONICITY: {
/*assert(num_args == 2);
assert(arity == 2);*/
#ifdef VERBOSE_Z3
/*std::cout << "Monotonicity: " << num_args << " with arity " << decl.arity() << std::endl;
for (unsigned i = 0; i < num_args-1; i++) {
std::cout << "HP" << i << ": " << extract_thesis(e.arg(i)) << std::endl;
std::cout << "HP" << i << ": " << parse_expr(extract_thesis(e.arg(i)), this->tb)->to_string() << std::endl;
}
std::cout << "TH: " << e.arg(num_args-1) << std::endl;
std::cout << "TH: " << parse_expr(e.arg(num_args-1), this->tb)->to_string() << std::endl;*/
#endif
// Recognize the monotonic operation
z3::expr thesis = e.arg(num_args-1);
switch (thesis.decl().decl_kind()) {
/*case Z3_OP_EQ:
break;*/
case Z3_OP_IFF: {
assert(thesis.num_args() == 2);
z3::expr th_left = thesis.arg(0);
z3::expr th_right = thesis.arg(1);
assert(th_left.decl().decl_kind() == th_right.decl().decl_kind());
assert(th_left.num_args() == th_right.num_args());
switch (th_left.decl().decl_kind()) {
case Z3_OP_AND:
case Z3_OP_OR:
case Z3_OP_IFF:
case Z3_OP_IMPLIES: {
RegisteredProver rp;
std::function< pwff(pwff, pwff) > combiner = [](pwff, pwff)->pwff { throw "Should not arrive here"; };
switch (th_left.decl().decl_kind()) {
case Z3_OP_AND: rp = anbi12d_rp; combiner = [](pwff a, pwff b) { return And::create(a, b); }; break;
case Z3_OP_OR: rp = orbi12d_rp; combiner = [](pwff a, pwff b) { return Or::create(a, b); }; break;
case Z3_OP_IFF: rp = bibi12d_rp; break;
case Z3_OP_IMPLIES: rp = imbi12d_rp; break;
default: throw "Should not arrive here"; break;
}
assert(th_left.num_args() >= 2);
std::vector< Prover< InspectableProofEngine< Sentence > > > hyp_provers;
std::vector< pwff > left_wffs;
std::vector< pwff > right_wffs;
//vector< Prover > wffs_prover;
size_t used = 0;
for (unsigned int i = 0; i < th_left.num_args(); i++) {
if (eq(th_left.arg(i), th_right.arg(i))) {
hyp_provers.push_back(this->tb.build_registered_prover< InspectableProofEngine< Sentence > >(biidd_rp, {{"ph", this->get_current_abs_hyps()->get_type_prover(this->tb)}, {"ps", parse_expr(th_left.arg(i), tb)->get_type_prover(this->tb)}}, {}));
} else {
hyp_provers.push_back(this->convert_proof(e.arg(0), depth+1));
used++;
}
left_wffs.push_back(parse_expr(th_left.arg(i), tb));
right_wffs.push_back(parse_expr(th_right.arg(i), tb));
}
assert(hyp_provers.size() == th_left.num_args());
assert(used == num_args - 1);
Prover< InspectableProofEngine< Sentence > > ret = hyp_provers[0];
pwff left_wff = left_wffs[0];
pwff right_wff = right_wffs[0];
for (size_t i = 1; i < th_left.num_args(); i++) {
ret = this->tb.build_registered_prover< InspectableProofEngine< Sentence > >(rp, {{"ph", this->get_current_abs_hyps()->get_type_prover(this->tb)},
{"ps", left_wff->get_type_prover(this->tb)}, {"ch", right_wff->get_type_prover(this->tb)},
{"th", left_wffs[i]->get_type_prover(this->tb)}, {"ta", right_wffs[i]->get_type_prover(this->tb)}}, {ret, hyp_provers[i]});
if (th_left.decl().decl_kind() == Z3_OP_AND || th_left.decl().decl_kind() == Z3_OP_OR) {
left_wff = combiner(left_wff, left_wffs[i]);
right_wff = combiner(right_wff, right_wffs[i]);
}
}
ret = this->build_checked_prover(ret, parse_expr(thesis, tb));
return ret;
break; }
case Z3_OP_NOT: {
pwff left_wff = parse_expr(th_left.arg(0), tb);
pwff right_wff = parse_expr(th_right.arg(0), tb);
Prover< InspectableProofEngine< Sentence > > ret = this->convert_proof(e.arg(0), depth+1);
ret = this->tb.build_registered_prover< InspectableProofEngine< Sentence > >(notbid_rp, {{"ph", this->get_current_abs_hyps()->get_type_prover(this->tb)},
{"ps", left_wff->get_type_prover(this->tb)}, {"ch", right_wff->get_type_prover(this->tb)}}, {ret});
ret = this->build_checked_prover(ret, parse_expr(thesis, tb));
return ret; }
default:
std::cerr << "Unsupported operation " << th_left.decl().decl_kind() << std::endl;
throw "Unsupported operation";
break;
}
break; }
default:
throw "Unsupported operation";
break;
}
break; }
case Z3_OP_PR_UNIT_RESOLUTION: {
#ifdef VERBOSE_Z3
/*std::cout << "Unit resolution: " << num_args << " with arity " << decl.arity() << std::endl;
for (unsigned i = 0; i < num_args-1; i++) {
std::cout << "HP" << i << ": " << extract_thesis(e.arg(i)) << std::endl;
std::cout << "HP" << i << ": " << parse_expr(extract_thesis(e.arg(i)), this->tb)->to_string() << std::endl;
}
std::cout << "TH: " << e.arg(num_args-1) << std::endl;
std::cout << "TH: " << parse_expr(e.arg(num_args-1), this->tb)->to_string() << std::endl;*/
#endif
auto thesis = parse_expr(e.arg(num_args-1), this->tb);
size_t elims_num = num_args - 2;
z3::expr ur_expr = extract_thesis(e.arg(0));
size_t clauses_num = 1;
if (ur_expr.decl().decl_kind() == Z3_OP_OR) {
clauses_num = ur_expr.num_args();
assert(clauses_num >= 2);
}
assert(elims_num <= clauses_num);
Prover< InspectableProofEngine< Sentence > > orig_prover = this->convert_proof(e.arg(0), depth+1);
//cerr << "TEST: " << test_prover(orig_prover, this->tb) << endl;
std::vector< pwff > elims;
std::vector< Prover< InspectableProofEngine< Sentence > > > elim_provers;
for (unsigned int i = 0; i < elims_num; i++) {
elims.push_back(parse_expr(extract_thesis(e.arg(i+1)), tb));
elim_provers.push_back(this->convert_proof(e.arg(i+1), depth+1));
//cerr << "TEST: " << test_prover(elim_provers.back(), this->tb) << endl;
}
std::vector< pwff > orig_clauses;
std::vector< pwff > new_clauses;
std::vector< Prover< InspectableProofEngine< Sentence > > > provers;
for (unsigned int i = 0; i < clauses_num; i++) {
pwff clause;
if (clauses_num == 1) {
clause = parse_expr(ur_expr, tb);
} else {
clause = parse_expr(ur_expr.arg(i), tb);
}
orig_clauses.push_back(clause);
// Search an eliminator for the positive form
auto elim_it = std::find_if(elims.begin(), elims.end(), [=](const pwff &w){ return *w == *Not::create(clause); });
if (elim_it != elims.end()) {
size_t pos = elim_it - elims.begin();
provers.push_back(this->tb.build_registered_prover< InspectableProofEngine< Sentence > >(urt_rp, {{"ph", this->get_current_abs_hyps()->get_type_prover(this->tb)}, {"ps", clause->get_type_prover(this->tb)}}, {elim_provers[pos]}));
new_clauses.push_back(False::create());
//cerr << "TEST 1: " << test_prover(provers.back(), this->tb) << endl;
continue;
}
// Search an eliminator for the negative form
auto clause_not = std::dynamic_pointer_cast< const Not >(clause);
if (clause_not != nullptr) {
auto elim_it = std::find_if(elims.begin(), elims.end(), [=](const pwff &w){ return *w == *clause_not->get_a(); });
if (elim_it != elims.end()) {
size_t pos = elim_it - elims.begin();
provers.push_back(this->tb.build_registered_prover< InspectableProofEngine< Sentence > >(urf_rp, {{"ph", this->get_current_abs_hyps()->get_type_prover(this->tb)}, {"ps", clause_not->get_a()->get_type_prover(this->tb)}}, {elim_provers[pos]}));
new_clauses.push_back(False::create());
//cerr << "TEST 1: " << test_prover(provers.back(), this->tb) << endl;
continue;
}
}
// No eliminator found, keeping the clause and pushing a trivial proved
provers.push_back(this->tb.build_registered_prover< InspectableProofEngine< Sentence > >(idd_rp, {{"ph", this->get_current_abs_hyps()->get_type_prover(this->tb)}, {"ps", clause->get_type_prover(this->tb)}}, {}));
new_clauses.push_back(clause);
//cerr << "TEST 1: " << test_prover(provers.back(), this->tb) << endl;
}
Prover< InspectableProofEngine< Sentence > > joined_or_prover;
Prover< InspectableProofEngine< Sentence > > simplifcation_prover;
pwff orig_clause;
pwff new_clause;
pwff new_clause2;
pwff simplified_clause;
std::tie(joined_or_prover, orig_clause, new_clause) = join_or_imp(orig_clauses, new_clauses, provers, this->get_current_abs_hyps(), this->tb);
std::tie(simplifcation_prover, new_clause2, simplified_clause) = simplify_or(new_clauses, this->tb);
#ifdef VERBOSE_Z3
/*cout << orig_clause->to_string() << endl;
cout << new_clause->to_string() << endl;
cout << new_clause2->to_string() << endl;
cout << simplified_clause->to_string() << endl;*/
#endif
assert(*new_clause == *new_clause2);
Prover< InspectableProofEngine< Sentence > > ret = this->tb.build_registered_prover< InspectableProofEngine< Sentence > >(mpd_rp, {{"ph", this->get_current_abs_hyps()->get_type_prover(this->tb)}, {"ps", orig_clause->get_type_prover(this->tb)}, {"ch", new_clause->get_type_prover(this->tb)}}, {orig_prover, joined_or_prover});
ret = this->tb.build_registered_prover< InspectableProofEngine< Sentence > >(syl_rp, {{"ph", this->get_current_abs_hyps()->get_type_prover(this->tb)}, {"ps", new_clause->get_type_prover(this->tb)}, {"ch", simplified_clause->get_type_prover(this->tb)}}, {ret, simplifcation_prover});
//cerr << "TEST: " << test_prover(ret, this->tb) << endl;
//assert(false);
ret = this->build_checked_prover(ret, thesis);
return ret;
break; }
case Z3_OP_PR_DEF_AXIOM: {
assert(num_args == 1);
assert(arity == 1);
#ifdef VERBOSE_Z3
std::cout << "EXPR: " << e.arg(0) << std::endl;
std::cout << "WFF: " << parse_expr(e.arg(0), tb)->to_string() << std::endl;
#endif
pwff thesis = parse_expr(extract_thesis(e), tb);
#ifdef VERBOSE_Z3
std::cout << "AXIOM ORACLE for '" << thesis->to_string() << "'!" << std::endl;
#endif
auto p1 = thesis->get_adv_truth_prover(this->tb).second;
auto ret = this->tb.build_registered_prover< InspectableProofEngine< Sentence > >(a1i_rp, {{"ph", this->get_current_abs_hyps()->get_type_prover(this->tb)}, {"ps", thesis->get_type_prover(this->tb)}}, {p1});
ret = this->build_checked_prover(ret, thesis);
return ret;
break; }
case Z3_OP_PR_NOT_OR_ELIM: {
assert(num_args == 2);
assert(arity == 2);
#ifdef VERBOSE_Z3
//cout << endl << "EXPR: " << e.arg(2);
/*cout << "HP1: " << parse_expr(extract_thesis(e.arg(0)))->to_string() << endl;;
cout << "TH: " << parse_expr(e.arg(1))->to_string() << endl;*/
#endif
z3::expr not_expr = extract_thesis(e.arg(0));
assert(not_expr.decl().decl_kind() == Z3_OP_NOT);
assert(not_expr.num_args() == 1);
z3::expr or_expr = not_expr.arg(0);
assert(or_expr.decl().decl_kind() == Z3_OP_OR);
z3::expr not_target_expr = e.arg(1);
assert(not_target_expr.decl().decl_kind() == Z3_OP_NOT);
assert(not_target_expr.num_args() == 1);
pwff target_wff = parse_expr(not_target_expr.arg(0), tb);
Prover< InspectableProofEngine< Sentence > > ret = this->convert_proof(e.arg(0), depth+1);
pwff wff = parse_expr(or_expr, tb);
for (size_t i = 0; i < or_expr.num_args()-1; i++) {
auto wff_or = std::dynamic_pointer_cast< const Or >(wff);
assert(wff != nullptr);
if (*wff_or->get_b() == *target_wff) {
return this->tb.build_registered_prover< InspectableProofEngine< Sentence > >(orsird_rp, {{"ph", this->get_current_abs_hyps()->get_type_prover(this->tb)}, {"ps", wff_or->get_a()->get_type_prover(this->tb)}, {"ch", wff_or->get_b()->get_type_prover(this->tb)}}, {ret});
} else {
ret = this->tb.build_registered_prover< InspectableProofEngine< Sentence > >(orsild_rp, {{"ph", this->get_current_abs_hyps()->get_type_prover(this->tb)}, {"ps", wff_or->get_a()->get_type_prover(this->tb)}, {"ch", wff_or->get_b()->get_type_prover(this->tb)}}, {ret});
wff = wff_or->get_a();
}
}
assert(*wff == *target_wff);
pwff thesis = parse_expr(extract_thesis(e), tb);
ret = this->build_checked_prover(ret, thesis);
return ret;
break; }
case Z3_OP_PR_IFF_FALSE: {
assert(num_args == 2);
assert(arity == 2);
#ifdef VERBOSE_Z3
//cout << endl << "EXPR: " << e.arg(2);
/*cout << "HP1: " << parse_expr(extract_thesis(e.arg(0)))->to_string() << endl;
cout << "TH: " << parse_expr(e.arg(1))->to_string() << endl;*/
#endif
pwff hyp = parse_expr(extract_thesis(e.arg(0)), tb);
Prover< InspectableProofEngine< Sentence > > hyp_prover = this->convert_proof(e.arg(0), depth+1);
auto hyp_not = std::dynamic_pointer_cast< const Not >(hyp);
assert(hyp_not != nullptr);
auto ret = this->tb.build_registered_prover< InspectableProofEngine< Sentence > >(bifald_rp, {{"ph", this->get_current_abs_hyps()->get_type_prover(this->tb)}, {"ps", hyp_not->get_a()->get_type_prover(this->tb)}}, {hyp_prover});
pwff thesis = parse_expr(extract_thesis(e), tb);
ret = this->build_checked_prover(ret, thesis);
return ret;
break; }
case Z3_OP_PR_LEMMA: {
assert(num_args == 2);
assert(arity == 2);
#ifdef VERBOSE_Z3
//std::cout << "FULL: " << e << std::endl;
/*std::cout << "HP1: " << parse_expr(extract_thesis(e.arg(0)))->to_string() << std::endl;
std::cout << "TH: " << e.arg(1) << std::endl;
std::cout << "TH: " << parse_expr(e.arg(1))->to_string() << std::endl;*/
std::cout << "LEMMA ORACLE for '" << Imp::create(this->get_current_abs_hyps(), parse_expr(extract_thesis(e), tb))->to_string() << "'!" << std::endl;
#endif
Prover< InspectableProofEngine< Sentence > > ret = Imp::create(this->get_current_abs_hyps(), parse_expr(extract_thesis(e), tb))->get_adv_truth_prover(this->tb).second;
pwff thesis = parse_expr(extract_thesis(e), tb);
ret = this->build_checked_prover(ret, thesis);
return ret;
break; }
/*case Z3_OP_PR_HYPOTHESIS:
#ifdef VERBOSE_Z3
std::cout << "hypothesis";
#endif
assert(num_args == 1);
assert(arity == 1);
#ifdef VERBOSE_Z3
std::cout << std::endl << "PARENT: " << *parent;
//std::cout << std::endl << "EXPR: " << e.arg(0);
std::cout << std::endl << "WFF: " << parse_expr(e.arg(0))->to_string();
#endif
break;*/
default:
//prove_and_print(Imp::create(w, parse_expr(extract_thesis(e))), tb);
#ifdef VERBOSE_Z3
std::cout << "GENERIC ORACLE for '" << Imp::create(this->get_current_abs_hyps(), parse_expr(extract_thesis(e), tb))->to_string() << "'!" << std::endl;
#endif
Prover< InspectableProofEngine< Sentence > > ret = Imp::create(this->get_current_abs_hyps(), parse_expr(extract_thesis(e), tb))->get_adv_truth_prover(this->tb).second;
pwff thesis = parse_expr(extract_thesis(e), tb);
ret = this->build_checked_prover(ret, thesis);
return ret;
break;
}
} else {
#ifdef VERBOSE_Z3
std::cout << "unknown kind " << kind << std::endl;
#endif
throw "Unknown kind";
}
/*for (unsigned i = 0; i < num_args; i++) {
iterate_expr(e.arg(i), tb, depth+1);
}*/
} else {
throw "Expression is not an application";
}
/*sort s = e.get_sort();
cout << string(depth, ' ') << "sort: " << s << " (" << s.sort_kind() << "), kind: " << e.kind() << ", num_args: " << e.num_args() << endl;*/
}
};
RegisteredProver refute_rp = LibraryToolbox::register_prover({"|- ( -. ph -> F. )"}, "|- ph");
RegisteredProver efald_rp = LibraryToolbox::register_prover({"|- ( ( ph /\\ -. ps ) -> F. )"}, "|- ( ph -> ps )");
#ifdef ENABLE_TEST_CODE
BOOST_DATA_TEST_CASE(test_wff_z3_prover, boost::unit_test::data::xrange(3), i) {
auto &data = get_set_mm();
//auto &lib = data.lib;
auto &tb = data.tb;
z3::set_param("proof", true);
z3::context c;
z3::solver s(c);
auto adapter = Z3Adapter(s, tb);
if (i == 0) {
z3::expr ph = c.bool_const("ph");
z3::expr ps = c.bool_const("ps");
adapter.add_formula(((!(ph && ps)) == (!ph || !ps)), false);
}
if (i == 1) {
z3::expr ph = c.bool_const("ph");
z3::expr ps = c.bool_const("ps");
adapter.add_formula((ph || ps ) == (ps || ph), false);
}
if (i == 2) {
z3::expr ph = c.bool_const("ph");
z3::expr ps = c.bool_const("ps");
z3::expr ch = c.bool_const("ch");
adapter.add_formula(implies(ph, implies(ps, ch)), true);
adapter.add_formula(implies(!ph, implies(!ps, ch)), true);
adapter.add_formula(implies(ph == ps, ch), false);
}
//std::cout << "ABSURDUM HYPOTHESIS: " << adapter.abs->to_string() << std::endl;
//std::cout << "TARGET: " << adapter.target->to_string() << std::endl;
//prove_and_print(adapter.target, tb);
/*switch (adapter.s.check()) {
case z3::unsat: std::cout << "valid\n"; break;
case z3::sat: std::cout << "not valid\n"; break;
case z3::unknown: std::cout << "unknown\n"; break;
}*/
BOOST_TEST(adapter.s.check() == z3::unsat);
CreativeProofEngineImpl< Sentence > engine(tb, true);
Prover< InspectableProofEngine< Sentence > > main_prover = adapter.convert_proof(adapter.s.proof());
bool res;
try {
if (adapter.hyps.size() == 1) {
res = tb.build_registered_prover< InspectableProofEngine< Sentence > >(refute_rp, {{"ph", adapter.target->get_type_prover(tb)}}, {main_prover})(engine);
} else {
res = tb.build_registered_prover< InspectableProofEngine< Sentence > >(efald_rp, {{"ph", adapter.and_hyps->get_type_prover(tb)}, {"ps", adapter.thesis->get_type_prover(tb)}}, {main_prover})(engine);
}
} catch (CheckedProverException< Sentence > &e) {
res = false;
#ifdef VERBOSE_Z3
std::cout << "A checked prover failed:" << std::endl;
std::cout << "On stack: " << tb.print_sentence(e.get_on_stack()) << std::endl;
std::cout << "Expected: " << tb.print_sentence(e.get_expected()) << std::endl;
platform_dump_stack_trace(std::cout, e.get_stacktrace());
#endif
}
BOOST_TEST(res);
BOOST_TEST(engine.get_stack().size() == (size_t) 1);
// TODO Check that the correct sentence was proved!
#ifdef VERBOSE_Z3
if (res) {
std::cout << std::endl << "FINAL PROOF FOUND!" << std::endl;
//std::cout << "proof: " << tb.print_proof(engine.get_proof_labels()) << std::endl;
std::cout << "stack top: " << tb.print_sentence(engine.get_stack().back(), SentencePrinter::STYLE_ANSI_COLORS_SET_MM) << std::endl;
std::cout << "proof length: " << engine.get_proof_labels().size() << std::endl;
} else {
std::cout << "proof generation failed..." << std::endl;
}
std::cout << std::endl;
#endif
}
#endif