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
|
/********************* */
/*! \file sets.cpp
** \verbatim
** Original author: Kshitij Bansal
** Major contributors: none
** Minor contributors (to current version): none
** This file is part of the CVC4 project.
** Copyright (c) 2009-2014 New York University and The University of Iowa
** See the file COPYING in the top-level source directory for licensing
** information.\endverbatim
**
** \brief Reasoning about sets with CVC4.
**
** A simple demonstration of reasoning about sets with CVC4.
**/
#include <iostream>
//#include <cvc4/cvc4.h> // use this after CVC4 is properly installed
#include "smt/smt_engine.h"
using namespace std;
using namespace CVC4;
int main() {
ExprManager em;
SmtEngine smt(&em);
// Optionally, set the logic. We need at least UF for equality predicate,
// integers (LIA) and sets (FS).
smt.setLogic("QF_UFLIAFS");
// Produce models
smt.setOption("produce-models", true);
// Set output language to SMTLIB2
cout << Expr::setlanguage(language::output::LANG_SMTLIB_V2);
Type integer = em.integerType();
Type set = em.mkSetType(integer);
// Verify union distributions over intersection
// (A union B) intersection C = (A intersection C) union (B intersection C)
{
Expr A = em.mkVar("A", set);
Expr B = em.mkVar("B", set);
Expr C = em.mkVar("C", set);
Expr unionAB = em.mkExpr(kind::UNION, A, B);
Expr lhs = em.mkExpr(kind::INTERSECTION, unionAB, C);
Expr intersectionAC = em.mkExpr(kind::INTERSECTION, A, C);
Expr intersectionBC = em.mkExpr(kind::INTERSECTION, B, C);
Expr rhs = em.mkExpr(kind::UNION, intersectionAC, intersectionBC);
Expr theorem = em.mkExpr(kind::EQUAL, lhs, rhs);
cout << "CVC4 reports: " << theorem << " is " << smt.query(theorem) << "." << endl;
}
// Verify emptset is a subset of any set
{
Expr A = em.mkVar("A", set);
Expr emptyset = em.mkConst(EmptySet(set));
Expr theorem = em.mkExpr(kind::SUBSET, emptyset, A);
cout << "CVC4 reports: " << theorem << " is " << smt.query(theorem) << "." << endl;
}
// Find me an element in {1, 2} intersection {2, 3}, if there is one.
{
Expr one = em.mkConst(Rational(1));
Expr two = em.mkConst(Rational(2));
Expr three = em.mkConst(Rational(3));
Expr singleton_one = em.mkExpr(kind::SINGLETON, one);
Expr singleton_two = em.mkExpr(kind::SINGLETON, two);
Expr singleton_three = em.mkExpr(kind::SINGLETON, three);
Expr one_two = em.mkExpr(kind::UNION, singleton_one, singleton_two);
Expr two_three = em.mkExpr(kind::UNION, singleton_two, singleton_three);
Expr intersection = em.mkExpr(kind::INTERSECTION, one_two, two_three);
Expr x = em.mkVar("x", integer);
Expr e = em.mkExpr(kind::MEMBER, x, intersection);
Result result = smt.checkSat(e);
cout << "CVC4 reports: " << e << " is " << result << "." << endl;
if(result == Result::SAT) {
cout << "For instance, " << smt.getValue(x) << " is a member." << endl;
}
}
}
|
