Quickstart Guide

First, create a cvc5 Solver instance:

Solver solver;

We will ask the solver to produce models and unsat cores in the following, and for this we have to enable the following options.

solver.setOption("produce-models", "true");
solver.setOption("produce-unsat-cores", "true");

Next we set the logic. 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" .

solver.setLogic("ALL");

In the following, we will define constraints of reals and integers. For this, we first query the solver for the corresponding sorts.

Sort realSort = solver.getRealSort();
Sort intSort = solver.getIntegerSort();

Now, we create two constants x and y of sort Real , and two constants a and b of sort Integer . Notice that these are symbolic constants, but not actual values.

Term x = solver.mkConst(realSort, "x");
Term y = solver.mkConst(realSort, "y");
Term a = solver.mkConst(intSort, "a");
Term b = solver.mkConst(intSort, "b");

We define the following constraints regarding x and y :

\[(0 < x) \wedge (0 < y) \wedge (x + y < 1) \wedge (x \leq y)\]

We construct the required terms and assert them as follows:

// 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::ADD, {x, y});

// Now we can define the constraints.
// They use the operators +, <=, and <.
// In the API, these are denoted by ADD, 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);

Now we check if the asserted formula is satisfiable, that is, we check if there exist values of sort Real for x and y that satisfy all the constraints.

Result r1 = solver.checkSat();

The result we get from this satisfiability check is either sat , unsat or unknown . It’s status can be queried via cvc5::Result::isSat() , cvc5::Result::isUnsat() and cvc5::Result::isSatUnknown() . Alternatively, it can also be printed.

std::cout << "expected: sat" << std::endl;
std::cout << "result: " << r1 << std::endl;

This will print:

expected: sat
result: sat

Now, we query the solver for 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 terms that do not appear in the original formula.

Term xMinusY = solver.mkTerm(Kind::SUB, {x, y});
Term xMinusYVal = solver.getValue(xMinusY);

We can retrieve the string representation of these values as follows.

std::string xStr = xVal.getRealValue();
std::string yStr = yVal.getRealValue();
std::string xMinusYStr = xMinusYVal.getRealValue();

std::cout << "value for x: " << xStr << std::endl;
std::cout << "value for y: " << yStr << std::endl;
std::cout << "value for x - y: " << xMinusYStr << std::endl;

This will print the following:

value for x: 1/6
value for y: 1/6
value for x - y: 0.0

We can convert these values to C++ types.

// Further, we can convert the values to cpp types
std::pair<int64_t, uint64_t> xPair = xVal.getReal64Value();
std::pair<int64_t, uint64_t> yPair = yVal.getReal64Value();
std::pair<int64_t, uint64_t> xMinusYPair = xMinusYVal.getReal64Value();

std::cout << "value for x: " << xPair.first << "/" << xPair.second
          << std::endl;
std::cout << "value for y: " << yPair.first << "/" << yPair.second
          << std::endl;
std::cout << "value for x - y: " << xMinusYPair.first << "/"
          << xMinusYPair.second << std::endl;

Another way to independently compute the value of x - y would be to perform the (rational) arithmetic manually. However, for more complex terms, it is easier to let the solver do the evaluation.

std::pair<int64_t, uint64_t> xMinusYComputed = {
  xPair.first * yPair.second - xPair.second * yPair.first,
  xPair.second * yPair.second
};
uint64_t g = std::gcd(xMinusYComputed.first, xMinusYComputed.second);
xMinusYComputed = { xMinusYComputed.first / g, xMinusYComputed.second / g };
if (xMinusYComputed == xMinusYPair)
{
  std::cout << "computed correctly" << std::endl;
}
else
{
  std::cout << "computed incorrectly" << std::endl;
}

This will print:

computed correctly

Next, we will check satisfiability of the same formula, only this time over integer variables a and b . For this, we first reset the assertions added to the solver.

solver.resetAssertions();

Next, we assert the same assertions as above, but 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::ADD, {a, b}), solver.mkInteger(1)}));
solver.assertFormula(solver.mkTerm(Kind::LEQ, {a, b}));

Now, we check whether the revised assertion is satisfiable.

Result r2 = solver.checkSat();
std::cout << "expected: unsat" << std::endl;
std::cout << "result: " << r2 << std::endl;

This time the asserted formula is unsatisfiable:

expected: unsat
result: unsat

We can query the solver for an unsatisfiable core, that is, a subset of the assertions that is already unsatisfiable.

std::vector<Term> unsatCore = solver.getUnsatCore();
std::cout << "unsat core size: " << unsatCore.size() << std::endl;
std::cout << "unsat core: " << std::endl;
for (const Term& t : unsatCore)
{
  std::cout << t << std::endl;
}

This will print:

unsat core size: 3
unsat core:
(< 0 a)
(< 0 b)
(< (+ a b) 1)

Example

examples/api/cpp/quickstart.cpp

  1/******************************************************************************
  2 * Top contributors (to current version):
  3 *   Yoni Zohar, Gereon Kremer, Mathias Preiner
  4 *
  5 * This file is part of the cvc5 project.
  6 *
  7 * Copyright (c) 2009-2022 by the authors listed in the file AUTHORS
  8 * in the top-level source directory and their institutional affiliations.
  9 * All rights reserved.  See the file COPYING in the top-level source
 10 * directory for licensing information.
 11 * ****************************************************************************
 12 *
 13 * A simple demonstration of the api capabilities of cvc5.
 14 *
 15 */
 16
 17#include <cvc5/cvc5.h>
 18
 19#include <iostream>
 20#include <numeric>
 21
 22using namespace cvc5;
 23
 24int main()
 25{
 26  // Create a solver
 27  //! [docs-cpp-quickstart-1 start]
 28  Solver solver;
 29  //! [docs-cpp-quickstart-1 end]
 30
 31  // We will ask the solver to produce models and unsat cores,
 32  // hence these options should be turned on.
 33  //! [docs-cpp-quickstart-2 start]
 34  solver.setOption("produce-models", "true");
 35  solver.setOption("produce-unsat-cores", "true");
 36  //! [docs-cpp-quickstart-2 end]
 37
 38  // The simplest way to set a logic for the solver is to choose "ALL".
 39  // This enables all logics in the solver.
 40  // Alternatively, "QF_ALL" enables all logics without quantifiers.
 41  // To optimize the solver's behavior for a more specific logic,
 42  // use the logic name, e.g. "QF_BV" or "QF_AUFBV".
 43
 44  // Set the logic
 45  //! [docs-cpp-quickstart-3 start]
 46  solver.setLogic("ALL");
 47  //! [docs-cpp-quickstart-3 end]
 48
 49  // In this example, we will define constraints over reals and integers.
 50  // Hence, we first obtain the corresponding sorts.
 51  //! [docs-cpp-quickstart-4 start]
 52  Sort realSort = solver.getRealSort();
 53  Sort intSort = solver.getIntegerSort();
 54  //! [docs-cpp-quickstart-4 end]
 55
 56  // x and y will be real variables, while a and b will be integer variables.
 57  // Formally, their cpp type is Term,
 58  // and they are called "constants" in SMT jargon:
 59  //! [docs-cpp-quickstart-5 start]
 60  Term x = solver.mkConst(realSort, "x");
 61  Term y = solver.mkConst(realSort, "y");
 62  Term a = solver.mkConst(intSort, "a");
 63  Term b = solver.mkConst(intSort, "b");
 64  //! [docs-cpp-quickstart-5 end]
 65
 66  // Our constraints regarding x and y will be:
 67  //
 68  //   (1)  0 < x
 69  //   (2)  0 < y
 70  //   (3)  x + y < 1
 71  //   (4)  x <= y
 72  //
 73
 74  //! [docs-cpp-quickstart-6 start]
 75  // Formally, constraints are also terms. Their sort is Boolean.
 76  // We will construct these constraints gradually,
 77  // by defining each of their components.
 78  // We start with the constant numerals 0 and 1:
 79  Term zero = solver.mkReal(0);
 80  Term one = solver.mkReal(1);
 81
 82  // Next, we construct the term x + y
 83  Term xPlusY = solver.mkTerm(Kind::ADD, {x, y});
 84
 85  // Now we can define the constraints.
 86  // They use the operators +, <=, and <.
 87  // In the API, these are denoted by ADD, LEQ, and LT.
 88  // A list of available operators is available in:
 89  // src/api/cpp/cvc5_kind.h
 90  Term constraint1 = solver.mkTerm(Kind::LT, {zero, x});
 91  Term constraint2 = solver.mkTerm(Kind::LT, {zero, y});
 92  Term constraint3 = solver.mkTerm(Kind::LT, {xPlusY, one});
 93  Term constraint4 = solver.mkTerm(Kind::LEQ, {x, y});
 94
 95  // Now we assert the constraints to the solver.
 96  solver.assertFormula(constraint1);
 97  solver.assertFormula(constraint2);
 98  solver.assertFormula(constraint3);
 99  solver.assertFormula(constraint4);
100  //! [docs-cpp-quickstart-6 end]
101
102  // Check if the formula is satisfiable, that is,
103  // are there real values for x and y that satisfy all the constraints?
104  //! [docs-cpp-quickstart-7 start]
105  Result r1 = solver.checkSat();
106  //! [docs-cpp-quickstart-7 end]
107
108  // The result is either SAT, UNSAT, or UNKNOWN.
109  // In this case, it is SAT.
110  //! [docs-cpp-quickstart-8 start]
111  std::cout << "expected: sat" << std::endl;
112  std::cout << "result: " << r1 << std::endl;
113  //! [docs-cpp-quickstart-8 end]
114
115  // We can get the values for x and y that satisfy the constraints.
116  //! [docs-cpp-quickstart-9 start]
117  Term xVal = solver.getValue(x);
118  Term yVal = solver.getValue(y);
119  //! [docs-cpp-quickstart-9 end]
120
121  // It is also possible to get values for compound terms,
122  // even if those did not appear in the original formula.
123  //! [docs-cpp-quickstart-10 start]
124  Term xMinusY = solver.mkTerm(Kind::SUB, {x, y});
125  Term xMinusYVal = solver.getValue(xMinusY);
126  //! [docs-cpp-quickstart-10 end]
127
128  // We can now obtain the string representations of the values.
129  //! [docs-cpp-quickstart-11 start]
130  std::string xStr = xVal.getRealValue();
131  std::string yStr = yVal.getRealValue();
132  std::string xMinusYStr = xMinusYVal.getRealValue();
133
134  std::cout << "value for x: " << xStr << std::endl;
135  std::cout << "value for y: " << yStr << std::endl;
136  std::cout << "value for x - y: " << xMinusYStr << std::endl;
137  //! [docs-cpp-quickstart-11 end]
138
139  //! [docs-cpp-quickstart-12 start]
140  // Further, we can convert the values to cpp types
141  std::pair<int64_t, uint64_t> xPair = xVal.getReal64Value();
142  std::pair<int64_t, uint64_t> yPair = yVal.getReal64Value();
143  std::pair<int64_t, uint64_t> xMinusYPair = xMinusYVal.getReal64Value();
144
145  std::cout << "value for x: " << xPair.first << "/" << xPair.second
146            << std::endl;
147  std::cout << "value for y: " << yPair.first << "/" << yPair.second
148            << std::endl;
149  std::cout << "value for x - y: " << xMinusYPair.first << "/"
150            << xMinusYPair.second << std::endl;
151  //! [docs-cpp-quickstart-12 end]
152
153  // Another way to independently compute the value of x - y would be
154  // to perform the (rational) arithmetic manually.
155  // However, for more complex terms,
156  // it is easier to let the solver do the evaluation.
157  //! [docs-cpp-quickstart-13 start]
158  std::pair<int64_t, uint64_t> xMinusYComputed = {
159    xPair.first * yPair.second - xPair.second * yPair.first,
160    xPair.second * yPair.second
161  };
162  uint64_t g = std::gcd(xMinusYComputed.first, xMinusYComputed.second);
163  xMinusYComputed = { xMinusYComputed.first / g, xMinusYComputed.second / g };
164  if (xMinusYComputed == xMinusYPair)
165  {
166    std::cout << "computed correctly" << std::endl;
167  }
168  else
169  {
170    std::cout << "computed incorrectly" << std::endl;
171  }
172  //! [docs-cpp-quickstart-13 end]
173
174  // Next, we will check satisfiability of the same formula,
175  // only this time over integer variables a and b.
176
177  // We start by resetting assertions added to the solver.
178  //! [docs-cpp-quickstart-14 start]
179  solver.resetAssertions();
180  //! [docs-cpp-quickstart-14 end]
181
182  // Next, we assert the same assertions above with integers.
183  // This time, we inline the construction of terms
184  // to the assertion command.
185  //! [docs-cpp-quickstart-15 start]
186  solver.assertFormula(solver.mkTerm(Kind::LT, {solver.mkInteger(0), a}));
187  solver.assertFormula(solver.mkTerm(Kind::LT, {solver.mkInteger(0), b}));
188  solver.assertFormula(solver.mkTerm(
189      Kind::LT, {solver.mkTerm(Kind::ADD, {a, b}), solver.mkInteger(1)}));
190  solver.assertFormula(solver.mkTerm(Kind::LEQ, {a, b}));
191  //! [docs-cpp-quickstart-15 end]
192
193  // We check whether the revised assertion is satisfiable.
194  //! [docs-cpp-quickstart-16 start]
195  Result r2 = solver.checkSat();
196  //! [docs-cpp-quickstart-16 end]
197
198  // This time the formula is unsatisfiable
199  //! [docs-cpp-quickstart-17 start]
200  std::cout << "expected: unsat" << std::endl;
201  std::cout << "result: " << r2 << std::endl;
202  //! [docs-cpp-quickstart-17 end]
203
204  // We can query the solver for an unsatisfiable core, i.e., a subset
205  // of the assertions that is already unsatisfiable.
206  //! [docs-cpp-quickstart-18 start]
207  std::vector<Term> unsatCore = solver.getUnsatCore();
208  std::cout << "unsat core size: " << unsatCore.size() << std::endl;
209  std::cout << "unsat core: " << std::endl;
210  for (const Term& t : unsatCore)
211  {
212    std::cout << t << std::endl;
213  }
214  //! [docs-cpp-quickstart-18 end]
215
216  return 0;
217}