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prove your first finite set theorem

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2025-10-15 18:33:22 +02:00
parent 30878541c8
commit 4225f1a0f1
3 changed files with 84 additions and 34 deletions
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112
src/smt/theory_finite_set.cpp
View file

@ -33,13 +33,13 @@ namespace smt {
// Setup the add_clause callback for axioms
std::function<void(expr_ref_vector const &)> add_clause_fn =
[this](expr_ref_vector const& clause) {
this->m_lemmas.push_back(clause);
this->add_clause(clause);
};
m_axioms.set_add_clause(add_clause_fn);
}
bool theory_finite_set::internalize_atom(app * atom, bool gate_ctx) {
// TRACE(finite_set, tout << "internalize_atom: " << mk_pp(atom, m) << "\n";);
TRACE(finite_set, tout << "internalize_atom: " << mk_pp(atom, m) << "\n";);
internalize_term(atom);
@ -57,7 +57,7 @@ namespace smt {
}
bool theory_finite_set::internalize_term(app * term) {
// TRACE("finite_set", tout << "internalize_term: " << mk_pp(term, m) << "\n";);
TRACE(finite_set, tout << "internalize_term: " << mk_pp(term, m) << "\n";);
// Internalize all arguments first
for (expr* arg : *term)
@ -84,32 +84,35 @@ namespace smt {
}
void theory_finite_set::new_eq_eh(theory_var v1, theory_var v2) {
// TRACE("finite_set", tout << "new_eq_eh: v" << v1 << " = v" << v2 << "\n";);
TRACE(finite_set, tout << "new_eq_eh: v" << v1 << " = v" << v2 << "\n";);
// When two sets are equal, propagate membership constraints
// This is handled by congruence closure, so no additional work needed here
}
void theory_finite_set::new_diseq_eh(theory_var v1, theory_var v2) {
// TRACE("finite_set", tout << "new_diseq_eh: v" << v1 << " != v" << v2 << "\n";);
TRACE(finite_set, tout << "new_diseq_eh: v" << v1 << " != v" << v2 << "\n";);
// Disequalities could trigger extensionality axioms
// For now, we rely on the final_check to handle this
}
final_check_status theory_finite_set::final_check_eh() {
// TRACE("finite_set", tout << "final_check_eh\n";);
TRACE(finite_set, tout << "final_check_eh\n";);
// walk all parents of elem in congruence table.
// if a parent is of the form elem' in S u T, or similar.
// create clauses for elem in S u T.
expr* elem1 = nullptr, *set1 = nullptr;
m_lemmas.reset();
for (auto elem : m_elements) {
if (!ctx.is_relevant(elem))
continue;
for (auto p : enode::parents(elem)) {
if (!u.is_in(p->get_expr(), elem1, set1))
continue;
if (elem->get_root() != p->get_arg(0)->get_root())
continue; // elem is then equal to set1 but not elem1. This is a different case.
if (!ctx.is_relevant(p))
continue;
for (auto sib : *p->get_arg(1))
instantiate_axioms(elem->get_expr(), sib->get_expr());
}
@ -125,8 +128,21 @@ namespace smt {
}
void theory_finite_set::instantiate_axioms(expr* elem, expr* set) {
// TRACE("finite_set", tout << "instantiate_axioms: " << mk_pp(elem, m) << " in " << mk_pp(set, m) << "\n";);
TRACE(finite_set, tout << "instantiate_axioms: " << mk_pp(elem, m) << " in " << mk_pp(set, m) << "\n";);
struct insert_obj_pair_table : public trail {
obj_pair_hashtable<expr, expr> &table;
expr *a, *b;
insert_obj_pair_table(obj_pair_hashtable<expr, expr> &t, expr *a, expr *b) :
table(t), a(a), b(b) {}
void undo() override {
table.erase({a, b});
}
};
if (m_lemma_exprs.contains({elem, set}))
return;
m_lemma_exprs.insert({elem, set});
ctx.push_trail(insert_obj_pair_table(m_lemma_exprs, elem, set));
// Instantiate appropriate axiom based on set structure
if (u.is_empty(set)) {
m_axioms.in_empty_axiom(elem);
@ -162,21 +178,9 @@ namespace smt {
}
void theory_finite_set::add_clause(expr_ref_vector const& clause) {
//TRACE("finite_set",
// tout << "add_clause: " << clause << "\n");
// Convert expressions to literals and assert the clause
literal_vector lits;
for (expr* e : clause) {
ctx.internalize(e, false);
literal lit = ctx.get_literal(e);
lits.push_back(lit);
}
if (!lits.empty()) {
scoped_trace_stream _sts(*this, lits);
ctx.mk_th_axiom(get_id(), lits);
}
TRACE(finite_set, tout << "add_clause: " << clause << "\n");
ctx.push_trail(push_back_vector(m_lemmas));
m_lemmas.push_back(clause);
}
theory * theory_finite_set::mk_fresh(context * new_ctx) {
@ -188,13 +192,13 @@ namespace smt {
}
void theory_finite_set::init_model(model_generator & mg) {
// TRACE("finite_set", tout << "init_model\n";);
TRACE(finite_set, tout << "init_model\n";);
// Model generation will use default interpretation for sets
// The model will be constructed based on the membership literals that are true
}
model_value_proc * theory_finite_set::mk_value(enode * n, model_generator & mg) {
// TRACE("finite_set", tout << "mk_value: " << mk_pp(n->get_expr(), m) << "\n";);
TRACE(finite_set, tout << "mk_value: " << mk_pp(n->get_expr(), m) << "\n";);
// For now, return nullptr to use default model construction
// A complete implementation would construct explicit set values
@ -203,16 +207,56 @@ namespace smt {
}
bool theory_finite_set::instantiate_false_lemma() {
// Implementation for instantiating false lemma
return false;
}
bool theory_finite_set::instantiate_unit_propagation() {
// Implementation for instantiating unit propagation
return false;
}
bool theory_finite_set::instantiate_free_lemma() {
// Implementation for instantiating free lemma
for (auto const& clause : m_lemmas) {
bool all_false = all_of(clause, [&](expr *e) { return ctx.find_assignment(e) == l_false; });
if (!all_false)
continue;
assert_clause(clause);
return true;
}
return false;
}
bool theory_finite_set::instantiate_unit_propagation() {
for (auto const &clause : m_lemmas) {
expr *undef = nullptr;
bool is_unit_propagating = true;
for (auto e : clause) {
switch (ctx.find_assignment(e)) {
case l_false: continue;
case l_true: is_unit_propagating = false; break;
case l_undef:
if (undef != nullptr)
is_unit_propagating = false;
undef = e;
break;
}
if (!is_unit_propagating)
break;
}
if (!is_unit_propagating || undef == nullptr)
continue;
assert_clause(clause);
return true;
}
return false;
}
bool theory_finite_set::instantiate_free_lemma() {
for (auto const& clause : m_lemmas) {
if (any_of(clause, [&](expr *e) { return ctx.find_assignment(e) == l_true; }))
continue;
assert_clause(clause);
return true;
}
return false;
}
void theory_finite_set::assert_clause(expr_ref_vector const &clause) {
literal_vector lclause;
for (auto e : clause)
lclause.push_back(mk_literal(e));
ctx.mk_th_axiom(get_id(), lclause);
}
} // namespace smt

4
src/smt/theory_finite_set.h
View file

@ -88,6 +88,7 @@ theory_finite_set.cpp.
#include "ast/ast_pp.h"
#include "ast/finite_set_decl_plugin.h"
#include "ast/rewriter/finite_set_axioms.h"
#include "util/obj_pair_hashtable.h"
#include "smt/smt_theory.h"
namespace smt {
@ -97,6 +98,7 @@ namespace smt {
finite_set_axioms m_axioms;
obj_hashtable<enode> m_elements; // set of all 'x' where there is an 'x in S' atom
vector<expr_ref_vector> m_lemmas;
obj_pair_hashtable<expr, expr> m_lemma_exprs;
protected:
// Override relevant methods from smt::theory
@ -115,9 +117,11 @@ namespace smt {
// Helper methods for axiom instantiation
void instantiate_axioms(expr* elem, expr* set);
void add_clause(expr_ref_vector const& clause);
void assert_clause(expr_ref_vector const &clause);
bool instantiate_false_lemma();
bool instantiate_unit_propagation();
bool instantiate_free_lemma();
lbool truth_value(expr *e);
public:
theory_finite_set(context& ctx);

2
src/util/trace_tags.def
View file

@ -70,6 +70,8 @@ X(eq_der, top_sort, "top sort")
X(expr_substitution_simplifier, expr_substitution_simplifier, "expr substitution simplifier")
X(expr_substitution_simplifier, propagate_values, "propagate values")
X(finite_set, finite_set, "finite set")
X(fm_model_converter, fm_model_converter, "fm model converter")
X(fm_model_converter, fm_mc, "fm mc")