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streamline axioms

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2025-10-27 18:58:45 +01:00
parent 4464ab9431
commit c0ca3b5a0a
2 changed files with 49 additions and 92 deletions
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135
src/ast/rewriter/finite_set_axioms.cpp
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@ -12,14 +12,13 @@ Abstract:
Author:
GitHub Copilot Agent 2025
Revision History:
nbjorner October 2025
--*/
#include "ast/ast.h"
#include "ast/ast_pp.h"
#include "ast/ast_util.h"
#include "ast/finite_set_decl_plugin.h"
#include "ast/arith_decl_plugin.h"
#include "ast/array_decl_plugin.h"
@ -64,16 +63,10 @@ void finite_set_axioms::in_union_axiom(expr *x, expr *a) {
m_add_clause(ax1);
// (x in b) => (x in a)
theory_axiom* ax2 = alloc(theory_axiom, m, "in-union", x, a);
ax2->clause.push_back(m.mk_not(x_in_b));
ax2->clause.push_back(x_in_a);
m_add_clause(ax2);
add_binary("in-union", x, a, m.mk_not(x_in_b), x_in_a);
// (x in c) => (x in a)
theory_axiom* ax3 = alloc(theory_axiom, m, "in-union", x, a);
ax3->clause.push_back(m.mk_not(x_in_c));
ax3->clause.push_back(x_in_a);
m_add_clause(ax3);
add_binary("in-union", x, a, m.mk_not(x_in_c), x_in_a);
}
// a := set.intersect(b, c)
@ -86,25 +79,18 @@ void finite_set_axioms::in_intersect_axiom(expr *x, expr *a) {
expr_ref x_in_a(u.mk_in(x, a), m);
expr_ref x_in_b(u.mk_in(x, b), m);
expr_ref x_in_c(u.mk_in(x, c), m);
expr_ref nx_in_a(m.mk_not(x_in_a), m);
expr_ref nx_in_b(m.mk_not(x_in_b), m);
expr_ref nx_in_c(m.mk_not(x_in_c), m);
// (x in a) => (x in b)
theory_axiom* ax1 = alloc(theory_axiom, m, "in-intersect", x, a);
ax1->clause.push_back(m.mk_not(x_in_a));
ax1->clause.push_back(x_in_b);
m_add_clause(ax1);
add_binary("in-intersect", x, a, nx_in_a, x_in_b);
// (x in a) => (x in c)
theory_axiom* ax2 = alloc(theory_axiom, m, "in-intersect", x, a);
ax2->clause.push_back(m.mk_not(x_in_a));
ax2->clause.push_back(x_in_c);
m_add_clause(ax2);
add_binary("in-intersect", x, a, nx_in_a, x_in_c);
// (x in b) and (x in c) => (x in a)
theory_axiom* ax3 = alloc(theory_axiom, m, "in-intersect", x, a);
ax3->clause.push_back(m.mk_not(x_in_b));
ax3->clause.push_back(m.mk_not(x_in_c));
ax3->clause.push_back(x_in_a);
m_add_clause(ax3);
add_ternary("in-intersect", x, a, nx_in_b, nx_in_c, x_in_a);
}
// a := set.difference(b, c)
@ -117,25 +103,18 @@ void finite_set_axioms::in_difference_axiom(expr *x, expr *a) {
expr_ref x_in_a(u.mk_in(x, a), m);
expr_ref x_in_b(u.mk_in(x, b), m);
expr_ref x_in_c(u.mk_in(x, c), m);
expr_ref nx_in_a(m.mk_not(x_in_a), m);
expr_ref nx_in_b(m.mk_not(x_in_b), m);
expr_ref nx_in_c(m.mk_not(x_in_c), m);
// (x in a) => (x in b)
theory_axiom* ax1 = alloc(theory_axiom, m, "in-difference", x, a);
ax1->clause.push_back(m.mk_not(x_in_a));
ax1->clause.push_back(x_in_b);
m_add_clause(ax1);
add_binary("in-difference", x, a, nx_in_a, x_in_b);
// (x in a) => not (x in c)
theory_axiom* ax2 = alloc(theory_axiom, m, "in-difference", x, a);
ax2->clause.push_back(m.mk_not(x_in_a));
ax2->clause.push_back(m.mk_not(x_in_c));
m_add_clause(ax2);
add_binary("in-difference", x, a, nx_in_a, nx_in_c);
// (x in b) and not (x in c) => (x in a)
theory_axiom* ax3 = alloc(theory_axiom, m, "in-difference", x, a);
ax3->clause.push_back(m.mk_not(x_in_b));
ax3->clause.push_back(x_in_c);
ax3->clause.push_back(x_in_a);
m_add_clause(ax3);
add_ternary("in-difference", x, a, nx_in_b, x_in_c, x_in_a);
}
// a := set.singleton(b)
@ -147,7 +126,6 @@ void finite_set_axioms::in_singleton_axiom(expr *x, expr *a) {
expr_ref x_in_a(u.mk_in(x, a), m);
if (x == b) {
// If x and b are syntactically identical, then (x in a) is always true
theory_axiom* ax = alloc(theory_axiom, m, "in-singleton", x, a);
@ -192,6 +170,8 @@ void finite_set_axioms::in_range_axiom(expr *x, expr *a) {
expr_ref x_le_hi(arith.mk_le(arith.mk_sub(x, hi), arith.mk_int(0)), m);
m_rewriter(lo_le_x);
m_rewriter(x_le_hi);
expr_ref nx_le_hi(m.mk_not(x_le_hi), m);
expr_ref nlo_le_x(m.mk_not(lo_le_x), m);
// (x in a) => (lo <= x)
add_binary("in-range", x, a, m.mk_not(x_in_a), lo_le_x);
@ -200,11 +180,7 @@ void finite_set_axioms::in_range_axiom(expr *x, expr *a) {
add_binary("in-range", x, a, m.mk_not(x_in_a), x_le_hi);
// (lo <= x) and (x <= hi) => (x in a)
theory_axiom* ax3 = alloc(theory_axiom, m, "in-range", x, a);
ax3->clause.push_back(m.mk_not(lo_le_x));
ax3->clause.push_back(m.mk_not(x_le_hi));
ax3->clause.push_back(x_in_a);
m_add_clause(ax3);
add_ternary("in-range", x, a, nlo_le_x, nx_le_hi, x_in_a);
}
// a := set.range(lo, hi)
@ -216,19 +192,13 @@ void finite_set_axioms::in_range_axiom(expr* r) {
expr *lo = nullptr, *hi = nullptr;
if (!u.is_range(r, lo, hi))
return;
theory_axiom* ax = alloc(theory_axiom, m, "range-bounds");
arith_util a(m);
expr_ref lo_le_hi(a.mk_le(a.mk_sub(lo, hi), a.mk_int(0)), m);
m_rewriter(lo_le_hi);
ax->clause.push_back(m.mk_not(lo_le_hi));
ax->clause.push_back(u.mk_in(lo, r));
m_add_clause(ax);
ax = alloc(theory_axiom, m, "range-bounds", r);
ax->clause.push_back(m.mk_not(lo_le_hi));
ax->clause.push_back(u.mk_in(hi, r));
m_add_clause(ax);
add_binary("range-bounds", r, nullptr, m.mk_not(lo_le_hi), u.mk_in(lo, r));
add_binary("range-bounds", r, nullptr, m.mk_not(lo_le_hi), u.mk_in(hi, r));
add_unit("range-bounds", r, m.mk_not(u.mk_in(a.mk_add(hi, a.mk_int(1)), r)));
add_unit("range-bounds", r, m.mk_not(u.mk_in(a.mk_add(lo, a.mk_int(-1)), r)));
}
@ -245,10 +215,6 @@ void finite_set_axioms::in_map_axiom(expr *x, expr *a) {
expr_ref f2(u.mk_in(inv, b), m);
add_binary("map-inverse", x, a, m.mk_not(f1), f2);
add_binary("map-inverse", x, b, f1, m.mk_not(f2));
// For now, we provide a placeholder implementation
// The full implementation would require skolemization
// to express the inverse relationship properly.
// This would be: exists y. f(y) = x and y in b
}
// a := set.map(f, b)
@ -283,6 +249,8 @@ void finite_set_axioms::in_filter_axiom(expr *x, expr *a) {
// Apply predicate p to x using array select
array_util autil(m);
expr_ref px(autil.mk_select(p, x), m);
m_rewriter(px);
expr_ref npx(mk_not(m, px), m);
// (x in a) => (x in b)
add_binary("in-filter", x, a, m.mk_not(x_in_a), x_in_b);
@ -291,26 +259,30 @@ void finite_set_axioms::in_filter_axiom(expr *x, expr *a) {
add_binary("in-filter", x, a, m.mk_not(x_in_a), px);
// (x in b) and p(x) => (x in a)
theory_axiom* ax3 = alloc(theory_axiom, m, "in-filter", x, a);
ax3->clause.push_back(m.mk_not(x_in_b));
ax3->clause.push_back(m.mk_not(px));
ax3->clause.push_back(x_in_a);
m_add_clause(ax3);
add_ternary("in-filter", x, a, m.mk_not(x_in_b), npx, x_in_a);
}
void finite_set_axioms::add_unit(char const* name, expr* e, expr* unit) {
theory_axiom *ax = alloc(theory_axiom, m, name, e);
void finite_set_axioms::add_unit(char const* name, expr* p1, expr* unit) {
theory_axiom *ax = alloc(theory_axiom, m, name, p1);
ax->clause.push_back(unit);
m_add_clause(ax);
}
void finite_set_axioms::add_binary(char const* name, expr* x, expr* y, expr* f1, expr* f2) {
theory_axiom *ax = alloc(theory_axiom, m, name, x, y);
void finite_set_axioms::add_binary(char const* name, expr* p1, expr* p2, expr* f1, expr* f2) {
theory_axiom *ax = alloc(theory_axiom, m, name, p1, p2);
ax->clause.push_back(f1);
ax->clause.push_back(f2);
m_add_clause(ax);
}
void finite_set_axioms::add_ternary(char const *name, expr *p1, expr *p2, expr *f1, expr *f2, expr *f3) {
theory_axiom *ax = alloc(theory_axiom, m, name, p1, p2);
ax->clause.push_back(f1);
ax->clause.push_back(f2);
ax->clause.push_back(f3);
m_add_clause(ax);
}
// Auxiliary algebraic axioms to ease reasoning about set.size
// The axioms are not required for completenss for the base fragment
// as they are handled by creating semi-linear sets.
@ -369,20 +341,10 @@ void finite_set_axioms::size_lb_axiom(expr* e) {
void finite_set_axioms::subset_axiom(expr* a) {
expr *b = nullptr, *c = nullptr;
if (!u.is_subset(a, b, c))
return;
expr_ref intersect_bc(u.mk_intersect(b, c), m);
expr_ref eq(m.mk_eq(intersect_bc, b), m);
theory_axiom* ax1 = alloc(theory_axiom, m, "subset", a);
ax1->clause.push_back(m.mk_not(a));
ax1->clause.push_back(eq);
m_add_clause(ax1);
theory_axiom* ax2 = alloc(theory_axiom, m, "subset", a);
ax2->clause.push_back(a);
ax2->clause.push_back(m.mk_not(eq));
m_add_clause(ax2);
return;
expr_ref eq(m.mk_eq(u.mk_intersect(b, c), b), m);
add_binary("subset", a, nullptr, m.mk_not(a), eq);
add_binary("subset", a, nullptr, a, m.mk_not(eq));
}
void finite_set_axioms::extensionality_axiom(expr *a, expr* b) {
@ -392,17 +354,10 @@ void finite_set_axioms::extensionality_axiom(expr *a, expr* b) {
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);
expr_ref ndiff_in_a(m.mk_not(diff_in_a), m);
expr_ref ndiff_in_b(m.mk_not(diff_in_b), m);
// (a != b) => (x in diff_ab != x in diff_ba)
theory_axiom* ax = alloc(theory_axiom, m, "extensionality", a, b);
ax->clause.push_back(a_eq_b);
ax->clause.push_back(m.mk_not(diff_in_a));
ax->clause.push_back(m.mk_not(diff_in_b));
m_add_clause(ax);
ax = alloc(theory_axiom, m, "extensionality", a, b);
ax->clause.push_back(a_eq_b);
ax->clause.push_back(diff_in_a);
ax->clause.push_back(diff_in_b);
m_add_clause(ax);
add_ternary("extensionality", a, b, a_eq_b, ndiff_in_a, ndiff_in_b);
add_ternary("extensionality", a, b, a_eq_b, diff_in_a, diff_in_b);
}

6
src/ast/rewriter/finite_set_axioms.h
View file

@ -46,9 +46,11 @@ class finite_set_axioms {
std::function<void(theory_axiom *)> m_add_clause;
void add_unit(char const* name, expr* x, expr *e);
void add_unit(char const* name, expr* p1, expr *e);
void add_binary(char const *name, expr *x, expr *y, expr *f1, expr *f2);
void add_binary(char const *name, expr *p1, expr *p2, expr *f1, expr *f2);
void add_ternary(char const *name, expr *p1, expr *p2, expr *f1, expr *f2, expr *f3);
public: