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add assume-eqs and extensionality

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2025-10-17 09:37:11 +02:00
parent 981c7d27ea
commit df62e5e9e6
6 changed files with 98 additions and 22 deletions
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3
src/ast/finite_set_decl_plugin.cpp
View file

@ -70,6 +70,8 @@ void finite_set_decl_plugin::init() {
m_sigs[OP_FINITE_SET_MAP] = alloc(polymorphism::psig, m, "set.map", 2, 2, arrABsetA, setB);
m_sigs[OP_FINITE_SET_SELECT] = alloc(polymorphism::psig, m, "set.select", 1, 2, arrABoolsetA, setA);
m_sigs[OP_FINITE_SET_RANGE] = alloc(polymorphism::psig, m, "set.range", 0, 2, intintT, setInt);
m_sigs[OP_FINITE_SET_DIFF] = alloc(polymorphism::psig, m, "set.diff", 1, 2, setAsetA, A);
// m_sigs[OP_FINITE_SET_MAP_INVERSE] = alloc(polymorphism::psig, m, "set.map_inverse", 2, 3, arrABsetBsetA, A);
}
sort * finite_set_decl_plugin::mk_sort(decl_kind k, unsigned num_parameters, parameter const * parameters) {
@ -152,6 +154,7 @@ func_decl * finite_set_decl_plugin::mk_func_decl(decl_kind k, unsigned num_param
case OP_FINITE_SET_MAP:
case OP_FINITE_SET_SELECT:
case OP_FINITE_SET_RANGE:
case OP_FINITE_SET_DIFF:
return mk_finite_set_op(k, arity, domain, range);
default:
return nullptr;

3
src/ast/finite_set_decl_plugin.h
View file

@ -23,6 +23,7 @@ Operators:
set.map : (S -> T) (FiniteSet S) -> (FiniteSet T)
set.select : (S -> Bool) (FiniteSet S) -> (FiniteSet S)
set.range : Int Int -> (FiniteSet Int)
set.diff : (FiniteSet S) (FiniteSet S) -> S
--*/
#pragma once
@ -46,6 +47,8 @@ enum finite_set_op_kind {
OP_FINITE_SET_MAP,
OP_FINITE_SET_SELECT,
OP_FINITE_SET_RANGE,
OP_FINITE_SET_DIFF,
OP_FINITE_SET_MAP_INVERSE,
LAST_FINITE_SET_OP
};

15
src/ast/rewriter/finite_set_axioms.cpp
View file

@ -298,4 +298,19 @@ void finite_set_axioms::subset_axiom(expr* a) {
clause2.push_back(a);
clause2.push_back(m.mk_not(eq));
m_add_clause(clause2);
}
void finite_set_axioms::extensionality_axiom(expr *a, expr* b) {
// a != b => set.in (set.diff(a, b) a) != set.in (set.diff(a, b) b)
expr_ref diff_ab(u.mk_difference(a, b), m);
expr_ref a_eq_b(m.mk_eq(a, b), m);
expr_ref diff_in_a(u.mk_in(diff_ab, a), m);
expr_ref diff_in_b(u.mk_in(diff_ab, b), m);
// (a != b) => (x in diff_ab != x in diff_ba)
expr_ref_vector clause(m);
clause.push_back(a_eq_b);
clause.push_back(m.mk_not(m.mk_iff(diff_in_a, diff_in_b)));
m_add_clause(clause);
}

3
src/ast/rewriter/finite_set_axioms.h
View file

@ -69,4 +69,7 @@ public:
// set.size(a) = 1
void size_singleton_axiom(expr *a);
// a != b => set.in (set.diff(a, b) a) != set.in (set.diff(a, b) b)
void extensionality_axiom(expr *a, expr *b);
};

93
src/smt/theory_finite_set.cpp
View file

@ -131,9 +131,18 @@ namespace smt {
}
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";);
// Disequalities could trigger extensionality axioms
// For now, we rely on the final_check to handle this
TRACE(finite_set, tout << "new_diseq_eh: v" << v1 << " != v" << v2 << "\n");
auto n1 = get_enode(v1);
auto n2 = get_enode(v2);
auto e1 = n1->get_expr();
auto e2 = n2->get_expr();
if (u.is_finite_set(e1) && u.is_finite_set(e2)) {
if (e1->get_id() > e2->get_id())
std::swap(e1, e2);
if (!is_new_axiom(e1, e2))
return;
m_axioms.extensionality_axiom(e1, e2);
}
}
/**
@ -143,7 +152,7 @@ namespace smt {
*
* It ensures saturation with respect to the theory axioms:
* - membership axioms
* - extensionality axioms
* - assume eqs axioms
*/
final_check_status theory_finite_set::final_check_eh() {
TRACE(finite_set, tout << "final_check_eh\n";);
@ -151,7 +160,7 @@ namespace smt {
if (add_membership_axioms())
return FC_CONTINUE;
if (add_extensionality_axioms())
if (assume_eqs())
return FC_CONTINUE;
return FC_DONE;
@ -219,32 +228,76 @@ namespace smt {
}
/**
* Saturate with respect to extensionality:
* Saturate with respect to equality sharing:
* - Sets corresponding to shared variables having the same interpretation should also be congruent
*/
bool theory_finite_set::add_extensionality_axioms() {
bool theory_finite_set::assume_eqs() {
collect_members();
expr_ref_vector trail(m); // make sure reference counts to union expressions are valid in this scope
obj_map<expr, enode*> set_reprs;
auto start = ctx.get_random_value();
auto sz = get_num_vars();
for (unsigned w = 0; w < sz; ++w) {
auto v = (w + start) % sz;
enode* n = get_enode(v);
if (!u.is_finite_set(n->get_expr()))
continue;
if (!is_relevant_and_shared(n))
continue;
auto r = n->get_root();
// Create a union expression that is canonical (sorted)
auto& set = *m_set_members[r];
ptr_vector<expr> elems;
for (auto e : set)
elems.push_back(e->get_expr());
std::sort(elems.begin(), elems.end(), [](expr *a, expr *b) { return a->get_id() < b->get_id(); });
expr* s = nullptr;
for (auto v : elems)
s = s ? u.mk_union(s, v) : v;
trail.push_back(s);
enode *n2 = nullptr;
if (!set_reprs.find(s, n2)) {
set_reprs.insert(s, n2);
continue;
}
if (n2->get_root() == r)
continue;
if (is_new_axiom(n->get_expr(), n2->get_expr()) && assume_eq(n, n2)) {
TRACE(finite_set,
tout << "assume " << mk_pp(n->get_expr(), m) << " = " << mk_pp(n2->get_expr(), m) << "\n";);
return true;
}
}
return false;
}
bool theory_finite_set::is_new_axiom(expr* a, expr* b) {
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({a, b}))
return false;
m_lemma_exprs.insert({a, b});
ctx.push_trail(insert_obj_pair_table(m_lemma_exprs, a, b));
return true;
}
/**
* Instantiate axioms for a given element in a set.
*/
void theory_finite_set::add_membership_axioms(expr *elem, expr *set) {
TRACE(finite_set, tout << "add_membership_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}))
if (!is_new_axiom(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);
@ -296,8 +349,6 @@ namespace smt {
collect_members();
}
void theory_finite_set::collect_members() {
// This method can be used to collect all elements that are members of sets
// and ensure that the model factory has values for them.

3
src/smt/theory_finite_set.h
View file

@ -128,7 +128,8 @@ namespace smt {
lbool truth_value(expr *e);
void add_immediate_axioms(app *atom);
bool add_membership_axioms();
bool add_extensionality_axioms();
bool assume_eqs();
bool is_new_axiom(expr *a, expr *b);
// model construction
void collect_members();