z3-src 503.3.0

Source distribution of the Z3 SMT solver, for use as a build dependency
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142

/*++
Copyright (c) 2026 Microsoft Corporation

--*/

#include "util/util.h"
#include "ast/euf/euf_egraph.h"
#include "ast/euf/euf_seq_plugin.h"
#include "ast/reg_decl_plugins.h"

namespace {

    class seq_euf_test {
        ast_manager m;
        seq_util seq;
        euf::egraph g;
        unsigned next_var = 0;

        static ast_manager& initialize(ast_manager& m) {
            reg_decl_plugins(m);
            return m;
        }

        euf::enode* node_core(expr* e) {
            if (auto* n = g.find(e))
                return n;
            euf::enode_vector args;
            for (expr* arg : *to_app(e))
                args.push_back(node_core(arg));
            auto* n = g.mk(e, 0, args.size(), args.data());
            if (seq.is_seq(e))
                g.add_th_var(n, next_var++, seq.get_family_id());
            return n;
        }

    public:
        seq_euf_test():
            seq(initialize(m)),
            g(m) {
            g.add_plugin(alloc(euf::seq_plugin, g));
        }

        expr_ref variable(char const* name, sort* s) {
            return expr_ref(m.mk_const(symbol(name), s), m);
        }

        expr_ref unit(expr* e) {
            return expr_ref(seq.str.mk_unit(e), m);
        }

        expr_ref concat(expr* a, expr* b) {
            return expr_ref(seq.str.mk_concat(a, b), m);
        }

        sort* element_sort() { return m.mk_uninterpreted_sort(symbol("E")); }
        sort* sequence_sort(sort* e) { return seq.str.mk_seq(e); }
        euf::enode* node(expr* e) { return node_core(e); }
        euf::egraph& egraph() { return g; }
    };

    void test_sequence_associativity() {
        seq_euf_test t;
        sort* e = t.element_sort();
        expr_ref ea = t.variable("a", e), eb = t.variable("b", e), ec = t.variable("c", e);
        expr_ref a = t.unit(ea), b = t.unit(eb), c = t.unit(ec);
        auto* left = t.node(t.concat(t.concat(a, b), c));
        auto* right = t.node(t.concat(a, t.concat(b, c)));
        auto* ab = t.node(t.concat(a, b));
        auto* ba = t.node(t.concat(b, a));
        t.egraph().propagate();
        TRACE(seq, tout << "sequence associativity\n" << t.egraph() << "\n";);
        ENSURE(left->get_root() == right->get_root());
        ENSURE(ab->get_root() != ba->get_root());
    }

    void test_sequence_completion() {
        seq_euf_test t;
        sort* e = t.element_sort();
        expr_ref ea = t.variable("a", e), eb = t.variable("b", e), ec = t.variable("c", e);
        expr_ref eu = t.variable("u", e), ev = t.variable("v", e);
        expr_ref a = t.unit(ea), b = t.unit(eb), c = t.unit(ec);
        expr_ref u = t.unit(eu), v = t.unit(ev);
        auto* ab = t.node(t.concat(a, b));
        auto* bc = t.node(t.concat(b, c));
        auto* nu = t.node(u);
        auto* nv = t.node(v);
        auto* uc = t.node(t.concat(u, c));
        auto* av = t.node(t.concat(a, v));
        t.egraph().merge(ab, nu, nullptr);
        t.egraph().merge(bc, nv, nullptr);
        t.egraph().propagate();
        TRACE(seq, tout << "sequence completion\n" << t.egraph() << "\n";);
        ENSURE(uc->get_root() == av->get_root());
    }

    void test_sequence_variable_simplification() {
        seq_euf_test t;
        sort* e = t.element_sort();
        sort* s = t.sequence_sort(e);
        expr_ref ea = t.variable("a", e), eb = t.variable("b", e), ec = t.variable("c", e);
        expr_ref a = t.unit(ea), b = t.unit(eb), c = t.unit(ec);
        expr_ref x = t.variable("x", s);
        auto* nx = t.node(x);
        auto* ab = t.node(t.concat(a, b));
        auto* xc = t.node(t.concat(x, c));
        auto* abc = t.node(t.concat(t.concat(a, b), c));
        t.egraph().merge(nx, ab, nullptr);
        t.egraph().propagate();
        TRACE(seq, tout << "sequence variable simplification\n" << t.egraph() << "\n";);
        ENSURE(xc->get_root() == abc->get_root());
    }

    void test_sequence_backtracking() {
        seq_euf_test t;
        sort* e = t.element_sort();
        sort* s = t.sequence_sort(e);
        expr_ref ea = t.variable("a", e), eb = t.variable("b", e), ec = t.variable("c", e);
        expr_ref a = t.unit(ea), b = t.unit(eb), c = t.unit(ec);
        expr_ref x = t.variable("x", s);
        auto* nx = t.node(x);
        auto* ab = t.node(t.concat(a, b));
        auto* xc = t.node(t.concat(x, c));
        auto* abc = t.node(t.concat(t.concat(a, b), c));
        t.egraph().propagate();
        ENSURE(xc->get_root() != abc->get_root());
        t.egraph().push();
        t.egraph().merge(nx, ab, nullptr);
        t.egraph().propagate();
        TRACE(seq, tout << "sequence backtracking before pop\n" << t.egraph() << "\n";);
        ENSURE(xc->get_root() == abc->get_root());
        t.egraph().pop(1);
        TRACE(seq, tout << "sequence backtracking after pop\n" << t.egraph() << "\n";);
        ENSURE(xc->get_root() != abc->get_root());
    }
}

void tst_euf_seq_plugin() {
    test_sequence_associativity();
    test_sequence_completion();
    test_sequence_variable_simplification();
    test_sequence_backtracking();
}