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https://github.com/Z3Prover/z3
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add interpretations when there are ranges
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner
parent
65f38eac16
commit
2e4402c8f3
8 changed files with 427 additions and 158 deletions
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@ -19,6 +19,7 @@ Revision History:
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--*/
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#include "ast/ast.h"
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#include "ast/ast_pp.h"
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#include "ast/finite_set_decl_plugin.h"
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#include "ast/arith_decl_plugin.h"
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#include "ast/array_decl_plugin.h"
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@ -38,8 +39,8 @@ void finite_set_axioms::in_empty_axiom(expr *x) {
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expr_ref empty_set(u.mk_empty(elem_sort), m);
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expr_ref x_in_empty(u.mk_in(x, empty_set), m);
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theory_axiom ax(m, "in-empty");
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ax.clause.push_back(m.mk_not(x_in_empty));
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theory_axiom* ax = alloc(theory_axiom, m, "in-empty");
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ax->clause.push_back(m.mk_not(x_in_empty));
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m_add_clause(ax);
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}
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@ -50,27 +51,28 @@ void finite_set_axioms::in_union_axiom(expr *x, expr *a) {
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if (!u.is_union(a, b, c))
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return;
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theory_axiom ax(m, "in-union");
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expr_ref x_in_a(u.mk_in(x, a), m);
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expr_ref x_in_b(u.mk_in(x, b), m);
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expr_ref x_in_c(u.mk_in(x, c), m);
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// (x in a) => (x in b) or (x in c)
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ax.clause.push_back(m.mk_not(x_in_a));
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ax.clause.push_back(x_in_b);
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ax.clause.push_back(x_in_c);
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m_add_clause(ax);
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theory_axiom *ax1 = alloc(theory_axiom, m, "in-union");
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ax1->clause.push_back(m.mk_not(x_in_a));
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ax1->clause.push_back(x_in_b);
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ax1->clause.push_back(x_in_c);
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m_add_clause(ax1);
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// (x in b) => (x in a)
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theory_axiom ax2(m, "in-union");
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ax2.clause.push_back(m.mk_not(x_in_b));
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ax2.clause.push_back(x_in_a);
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theory_axiom* ax2 = alloc(theory_axiom, m, "in-union");
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ax2->clause.push_back(m.mk_not(x_in_b));
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ax2->clause.push_back(x_in_a);
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m_add_clause(ax2);
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// (x in c) => (x in a)
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theory_axiom ax3(m, "in-union");
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ax3.clause.push_back(m.mk_not(x_in_c));
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ax3.clause.push_back(x_in_a);
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theory_axiom* ax3 = alloc(theory_axiom, m, "in-union");
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ax3->clause.push_back(m.mk_not(x_in_c));
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ax3->clause.push_back(x_in_a);
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m_add_clause(ax3);
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}
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@ -86,22 +88,22 @@ void finite_set_axioms::in_intersect_axiom(expr *x, expr *a) {
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expr_ref x_in_c(u.mk_in(x, c), m);
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// (x in a) => (x in b)
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theory_axiom ax1(m, "in-intersect");
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ax1.clause.push_back(m.mk_not(x_in_a));
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ax1.clause.push_back(x_in_b);
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theory_axiom* ax1 = alloc(theory_axiom, m, "in-intersect");
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ax1->clause.push_back(m.mk_not(x_in_a));
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ax1->clause.push_back(x_in_b);
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m_add_clause(ax1);
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// (x in a) => (x in c)
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theory_axiom ax2(m, "in-intersect");
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ax2.clause.push_back(m.mk_not(x_in_a));
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ax2.clause.push_back(x_in_c);
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theory_axiom* ax2 = alloc(theory_axiom, m, "in-intersect");
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ax2->clause.push_back(m.mk_not(x_in_a));
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ax2->clause.push_back(x_in_c);
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m_add_clause(ax2);
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// (x in b) and (x in c) => (x in a)
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theory_axiom ax3(m, "in-intersect");
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ax3.clause.push_back(m.mk_not(x_in_b));
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ax3.clause.push_back(m.mk_not(x_in_c));
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ax3.clause.push_back(x_in_a);
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theory_axiom* ax3 = alloc(theory_axiom, m, "in-intersect");
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ax3->clause.push_back(m.mk_not(x_in_b));
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ax3->clause.push_back(m.mk_not(x_in_c));
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ax3->clause.push_back(x_in_a);
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m_add_clause(ax3);
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}
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@ -117,22 +119,22 @@ void finite_set_axioms::in_difference_axiom(expr *x, expr *a) {
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expr_ref x_in_c(u.mk_in(x, c), m);
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// (x in a) => (x in b)
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theory_axiom ax1(m, "in-difference");
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ax1.clause.push_back(m.mk_not(x_in_a));
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ax1.clause.push_back(x_in_b);
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theory_axiom* ax1 = alloc(theory_axiom, m, "in-difference");
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ax1->clause.push_back(m.mk_not(x_in_a));
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ax1->clause.push_back(x_in_b);
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m_add_clause(ax1);
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// (x in a) => not (x in c)
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theory_axiom ax2(m, "in-difference");
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ax2.clause.push_back(m.mk_not(x_in_a));
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ax2.clause.push_back(m.mk_not(x_in_c));
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theory_axiom* ax2 = alloc(theory_axiom, m, "in-difference");
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ax2->clause.push_back(m.mk_not(x_in_a));
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ax2->clause.push_back(m.mk_not(x_in_c));
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m_add_clause(ax2);
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// (x in b) and not (x in c) => (x in a)
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theory_axiom ax3(m, "in-difference");
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ax3.clause.push_back(m.mk_not(x_in_b));
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ax3.clause.push_back(x_in_c);
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ax3.clause.push_back(x_in_a);
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theory_axiom* ax3 = alloc(theory_axiom, m, "in-difference");
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ax3->clause.push_back(m.mk_not(x_in_b));
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ax3->clause.push_back(x_in_c);
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ax3->clause.push_back(x_in_a);
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m_add_clause(ax3);
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}
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@ -145,11 +147,11 @@ void finite_set_axioms::in_singleton_axiom(expr *x, expr *a) {
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expr_ref x_in_a(u.mk_in(x, a), m);
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theory_axiom ax(m, "in-singleton");
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theory_axiom* ax = alloc(theory_axiom, m, "in-singleton");
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if (x == b) {
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// If x and b are syntactically identical, then (x in a) is always true
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ax.clause.push_back(x_in_a);
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ax->clause.push_back(x_in_a);
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m_add_clause(ax);
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return;
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}
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@ -157,17 +159,42 @@ void finite_set_axioms::in_singleton_axiom(expr *x, expr *a) {
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expr_ref x_eq_b(m.mk_eq(x, b), m);
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// (x in a) => (x == b)
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ax.clause.push_back(m.mk_not(x_in_a));
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ax.clause.push_back(x_eq_b);
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ax->clause.push_back(m.mk_not(x_in_a));
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ax->clause.push_back(x_eq_b);
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m_add_clause(ax);
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ax.clause.reset();
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ax = alloc(theory_axiom, m, "in-singleton");
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// (x == b) => (x in a)
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ax.clause.push_back(m.mk_not(x_eq_b));
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ax.clause.push_back(x_in_a);
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ax->clause.push_back(m.mk_not(x_eq_b));
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ax->clause.push_back(x_in_a);
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m_add_clause(ax);
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}
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void finite_set_axioms::in_singleton_axiom(expr* a) {
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expr *b = nullptr;
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if (!u.is_singleton(a, b))
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return;
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arith_util arith(m);
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expr_ref b_in_a(u.mk_in(b, a), m);
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auto ax = alloc(theory_axiom, m, "in-singleton");
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ax->clause.push_back(b_in_a);
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m_add_clause(ax);
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ax = alloc(theory_axiom, m, "in-singleton");
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expr_ref bm1_in_a(u.mk_in(arith.mk_add(b, arith.mk_int(-1)), a), m);
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ax->clause.push_back(m.mk_not(bm1_in_a));
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m_add_clause(ax);
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ax = alloc(theory_axiom, m, "in-singleton");
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expr_ref bp1_in_a(u.mk_in(arith.mk_add(b, arith.mk_int(1)), a), m);
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ax->clause.push_back(m.mk_not(bp1_in_a));
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}
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// a := set.range(lo, hi)
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// (x in a) <=> (lo <= x <= hi)
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void finite_set_axioms::in_range_axiom(expr *x, expr *a) {
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@ -177,29 +204,58 @@ void finite_set_axioms::in_range_axiom(expr *x, expr *a) {
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arith_util arith(m);
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expr_ref x_in_a(u.mk_in(x, a), m);
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expr_ref lo_le_x(arith.mk_le(lo, x), m);
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expr_ref x_le_hi(arith.mk_le(x, hi), m);
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expr_ref lo_le_x(arith.mk_le(arith.mk_sub(lo, x), arith.mk_int(0)), m);
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expr_ref x_le_hi(arith.mk_le(arith.mk_sub(x, hi), arith.mk_int(0)), m);
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m_rewriter(lo_le_x);
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m_rewriter(x_le_hi);
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// (x in a) => (lo <= x)
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theory_axiom ax1(m, "in-range");
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ax1.clause.push_back(m.mk_not(x_in_a));
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ax1.clause.push_back(lo_le_x);
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theory_axiom* ax1 = alloc(theory_axiom, m, "in-range");
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ax1->clause.push_back(m.mk_not(x_in_a));
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ax1->clause.push_back(lo_le_x);
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m_add_clause(ax1);
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// (x in a) => (x <= hi)
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theory_axiom ax2(m, "in-range");
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ax2.clause.push_back(m.mk_not(x_in_a));
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ax2.clause.push_back(x_le_hi);
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theory_axiom* ax2 = alloc(theory_axiom, m, "in-range");
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ax2->clause.push_back(m.mk_not(x_in_a));
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ax2->clause.push_back(x_le_hi);
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m_add_clause(ax2);
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// (lo <= x) and (x <= hi) => (x in a)
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theory_axiom ax3(m, "in-range");
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ax3.clause.push_back(m.mk_not(lo_le_x));
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ax3.clause.push_back(m.mk_not(x_le_hi));
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ax3.clause.push_back(x_in_a);
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theory_axiom* ax3 = alloc(theory_axiom, m, "in-range");
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ax3->clause.push_back(m.mk_not(lo_le_x));
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ax3->clause.push_back(m.mk_not(x_le_hi));
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ax3->clause.push_back(x_in_a);
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m_add_clause(ax3);
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}
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// a := set.range(lo, hi)
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// (not (set.in (- lo 1) r))
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// (not (set.in (+ hi 1) r))
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// (set.in lo r)
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// (set.in hi r)
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void finite_set_axioms::in_range_axiom(expr* r) {
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expr *lo = nullptr, *hi = nullptr;
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if (!u.is_range(r, lo, hi))
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return;
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theory_axiom* ax = alloc(theory_axiom, m, "range-bounds");
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ax->clause.push_back(u.mk_in(lo, r));
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m_add_clause(ax);
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ax = alloc(theory_axiom, m, "range-bounds");
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ax->clause.push_back(u.mk_in(hi, r));
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m_add_clause(ax);
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arith_util a(m);
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ax = alloc(theory_axiom, m, "range-bounds");
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ax->clause.push_back(m.mk_not(u.mk_in(a.mk_add(hi, a.mk_int(1)), r)));
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m_add_clause(ax);
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ax = alloc(theory_axiom, m, "range-bounds");
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ax->clause.push_back(m.mk_not(u.mk_in(a.mk_add(lo, a.mk_int(-1)), r)));
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m_add_clause(ax);
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}
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// a := set.map(f, b)
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// (x in a) <=> set.map_inverse(f, x, b) in b
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void finite_set_axioms::in_map_axiom(expr *x, expr *a) {
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@ -228,9 +284,9 @@ void finite_set_axioms::in_map_image_axiom(expr *x, expr *a) {
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expr_ref fx_in_a(u.mk_in(fx, a), m);
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// (x in b) => f(x) in a
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theory_axiom ax(m, "in-map-image");
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ax.clause.push_back(m.mk_not(x_in_b));
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ax.clause.push_back(fx_in_a);
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theory_axiom* ax = alloc(theory_axiom, m, "in-map-image");
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ax->clause.push_back(m.mk_not(x_in_b));
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ax->clause.push_back(fx_in_a);
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m_add_clause(ax);
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}
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@ -249,22 +305,22 @@ void finite_set_axioms::in_filter_axiom(expr *x, expr *a) {
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expr_ref px(autil.mk_select(p, x), m);
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// (x in a) => (x in b)
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theory_axiom ax1(m, "in-filter");
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ax1.clause.push_back(m.mk_not(x_in_a));
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ax1.clause.push_back(x_in_b);
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theory_axiom* ax1 = alloc(theory_axiom, m, "in-filter");
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ax1->clause.push_back(m.mk_not(x_in_a));
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ax1->clause.push_back(x_in_b);
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m_add_clause(ax1);
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// (x in a) => p(x)
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theory_axiom ax2(m, "in-filter");
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ax2.clause.push_back(m.mk_not(x_in_a));
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ax2.clause.push_back(px);
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theory_axiom* ax2 = alloc(theory_axiom, m, "in-filter");
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ax2->clause.push_back(m.mk_not(x_in_a));
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ax2->clause.push_back(px);
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m_add_clause(ax2);
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// (x in b) and p(x) => (x in a)
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theory_axiom ax3(m, "in-filter");
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ax3.clause.push_back(m.mk_not(x_in_b));
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ax3.clause.push_back(m.mk_not(px));
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ax3.clause.push_back(x_in_a);
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theory_axiom* ax3 = alloc(theory_axiom, m, "in-filter");
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ax3->clause.push_back(m.mk_not(x_in_b));
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ax3->clause.push_back(m.mk_not(px));
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ax3->clause.push_back(x_in_a);
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m_add_clause(ax3);
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}
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@ -280,8 +336,8 @@ void finite_set_axioms::size_singleton_axiom(expr *a) {
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expr_ref one(arith.mk_int(1), m);
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expr_ref eq(m.mk_eq(size_a, one), m);
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theory_axiom ax(m, "size-singleton");
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ax.clause.push_back(eq);
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theory_axiom* ax = alloc(theory_axiom, m, "size-singleton");
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ax->clause.push_back(eq);
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m_add_clause(ax);
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}
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@ -293,14 +349,14 @@ void finite_set_axioms::subset_axiom(expr* a) {
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expr_ref intersect_bc(u.mk_intersect(b, c), m);
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expr_ref eq(m.mk_eq(intersect_bc, b), m);
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theory_axiom ax1(m, "subset");
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ax1.clause.push_back(m.mk_not(a));
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ax1.clause.push_back(eq);
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theory_axiom* ax1 = alloc(theory_axiom, m, "subset");
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ax1->clause.push_back(m.mk_not(a));
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ax1->clause.push_back(eq);
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m_add_clause(ax1);
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theory_axiom ax2(m, "subset");
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ax2.clause.push_back(a);
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ax2.clause.push_back(m.mk_not(eq));
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theory_axiom* ax2 = alloc(theory_axiom, m, "subset");
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ax2->clause.push_back(a);
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ax2->clause.push_back(m.mk_not(eq));
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m_add_clause(ax2);
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}
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@ -313,15 +369,15 @@ void finite_set_axioms::extensionality_axiom(expr *a, expr* b) {
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expr_ref diff_in_b(u.mk_in(diff_ab, b), m);
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// (a != b) => (x in diff_ab != x in diff_ba)
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theory_axiom ax(m, "extensionality");
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ax.clause.push_back(a_eq_b);
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ax.clause.push_back(m.mk_not(diff_in_a));
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ax.clause.push_back(m.mk_not(diff_in_b));
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theory_axiom* ax = alloc(theory_axiom, m, "extensionality");
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ax->clause.push_back(a_eq_b);
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ax->clause.push_back(m.mk_not(diff_in_a));
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ax->clause.push_back(m.mk_not(diff_in_b));
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m_add_clause(ax);
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||||
|
||||
theory_axiom ax2(m, "extensionality");
|
||||
ax2.clause.push_back(m.mk_not(a_eq_b));
|
||||
ax2.clause.push_back(diff_in_a);
|
||||
ax2.clause.push_back(diff_in_b);
|
||||
theory_axiom* ax2 = alloc(theory_axiom, m, "extensionality");
|
||||
ax2->clause.push_back(m.mk_not(a_eq_b));
|
||||
ax2->clause.push_back(diff_in_a);
|
||||
ax2->clause.push_back(diff_in_b);
|
||||
m_add_clause(ax2);
|
||||
}
|
||||
Loading…
Add table
Add a link
Reference in a new issue