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
143
144
145
146
147
148
|
/******************************************************************************
* Top contributors (to current version):
* Yoni Zohar
*
* This file is part of the cvc5 project.
*
* Copyright (c) 2009-2021 by the authors listed in the file AUTHORS
* in the top-level source directory and their institutional affiliations.
* All rights reserved. See the file COPYING in the top-level source
* directory for licensing information.
* ****************************************************************************
*
* A simple demonstration of the api capabilities of cvc5.
*
*/
import io.github.cvc5.api.*;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
public class QuickStart
{
public static void main(String args[]) throws CVC5ApiException
{
// Create a solver
try (Solver solver = new Solver())
{
// We will ask the solver to produce models and unsat cores,
// hence these options should be turned on.
solver.setOption("produce-models", "true");
solver.setOption("produce-unsat-cores", "true");
// The simplest way to set a logic for the solver is to choose "ALL".
// This enables all logics in the solver.
// Alternatively, "QF_ALL" enables all logics without quantifiers.
// To optimize the solver's behavior for a more specific logic,
// use the logic name, e.g. "QF_BV" or "QF_AUFBV".
// Set the logic
solver.setLogic("ALL");
// In this example, we will define constraints over reals and integers.
// Hence, we first obtain the corresponding sorts.
Sort realSort = solver.getRealSort();
Sort intSort = solver.getIntegerSort();
// x and y will be real variables, while a and b will be integer variables.
// Formally, their cpp type is Term,
// and they are called "constants" in SMT jargon:
Term x = solver.mkConst(realSort, "x");
Term y = solver.mkConst(realSort, "y");
Term a = solver.mkConst(intSort, "a");
Term b = solver.mkConst(intSort, "b");
// Our constraints regarding x and y will be:
//
// (1) 0 < x
// (2) 0 < y
// (3) x + y < 1
// (4) x <= y
//
// Formally, constraints are also terms. Their sort is Boolean.
// We will construct these constraints gradually,
// by defining each of their components.
// We start with the constant numerals 0 and 1:
Term zero = solver.mkReal(0);
Term one = solver.mkReal(1);
// Next, we construct the term x + y
Term xPlusY = solver.mkTerm(Kind.PLUS, x, y);
// Now we can define the constraints.
// They use the operators +, <=, and <.
// In the API, these are denoted by PLUS, LEQ, and LT.
// A list of available operators is available in:
// src/api/cpp/cvc5_kind.h
Term constraint1 = solver.mkTerm(Kind.LT, zero, x);
Term constraint2 = solver.mkTerm(Kind.LT, zero, y);
Term constraint3 = solver.mkTerm(Kind.LT, xPlusY, one);
Term constraint4 = solver.mkTerm(Kind.LEQ, x, y);
// Now we assert the constraints to the solver.
solver.assertFormula(constraint1);
solver.assertFormula(constraint2);
solver.assertFormula(constraint3);
solver.assertFormula(constraint4);
// Check if the formula is satisfiable, that is,
// are there real values for x and y that satisfy all the constraints?
Result r1 = solver.checkSat();
// The result is either SAT, UNSAT, or UNKNOWN.
// In this case, it is SAT.
System.out.println("expected: sat");
System.out.println("result: " + r1);
// We can get the values for x and y that satisfy the constraints.
Term xVal = solver.getValue(x);
Term yVal = solver.getValue(y);
// It is also possible to get values for compound terms,
// even if those did not appear in the original formula.
Term xMinusY = solver.mkTerm(Kind.MINUS, x, y);
Term xMinusYVal = solver.getValue(xMinusY);
// Further, we can convert the values to java types,
Pair<BigInteger, BigInteger> xRational = xVal.getRealValue();
Pair<BigInteger, BigInteger> yRational = yVal.getRealValue();
System.out.println("value for x: " + xRational.first + "/" + xRational.second);
System.out.println("value for y: " + yRational.first + "/" + yRational.second);
// Next, we will check satisfiability of the same formula,
// only this time over integer variables a and b.
// We start by resetting assertions added to the solver.
solver.resetAssertions();
// Next, we assert the same assertions above with integers.
// This time, we inline the construction of terms
// to the assertion command.
solver.assertFormula(solver.mkTerm(Kind.LT, solver.mkInteger(0), a));
solver.assertFormula(solver.mkTerm(Kind.LT, solver.mkInteger(0), b));
solver.assertFormula(
solver.mkTerm(Kind.LT, solver.mkTerm(Kind.PLUS, a, b), solver.mkInteger(1)));
solver.assertFormula(solver.mkTerm(Kind.LEQ, a, b));
// We check whether the revised assertion is satisfiable.
Result r2 = solver.checkSat();
// This time the formula is unsatisfiable
System.out.println("expected: unsat");
System.out.println("result: " + r2);
// We can query the solver for an unsatisfiable core, i.e., a subset
// of the assertions that is already unsatisfiable.
List<Term> unsatCore = Arrays.asList(solver.getUnsatCore());
System.out.println("unsat core size: " + unsatCore.size());
System.out.println("unsat core: ");
for (Term t : unsatCore)
{
System.out.println(t);
}
}
}
}
|