int main() {
ExprManager em;
SmtEngine smt(&em);
// Prove that for integers x and y:
// x > 0 AND y > 0 => 2x + y >= 3
Type integer = em.integerType();
Expr x = em.mkVar("x", integer);
Expr y = em.mkVar("y", integer);
Expr zero = em.mkConst(Rational(0));
Expr x_positive = em.mkExpr(kind::GT, x, zero);
Expr y_positive = em.mkExpr(kind::GT, y, zero);
Expr two = em.mkConst(Rational(2));
Expr twox = em.mkExpr(kind::MULT, two, x);
Expr twox_plus_y = em.mkExpr(kind::PLUS, twox, y);
Expr three = em.mkConst(Rational(3));
Expr twox_plus_y_geq_3 = em.mkExpr(kind::GEQ, twox_plus_y, three);
Expr formula =
em.mkExpr(kind::AND, x_positive, y_positive).
impExpr(twox_plus_y_geq_3);
cout << "Checking validity of formula " << formula << " with CVC4." << endl;
cout << "CVC4 should report VALID." << endl;
cout << "Result from CVC4 is: " << smt.query(formula) << endl;
return 0;
}
Expr Tptp::convertRatToUnsorted(Expr expr) {
ExprManager* em = getExprManager();
// Create the conversion function If they doesn't exists
if (d_rtu_op.isNull()) {
Type t;
// Conversion from rational to unsorted
t = em->mkFunctionType(em->realType(), d_unsorted);
d_rtu_op = em->mkVar("$$rtu", t);
preemptCommand(new DeclareFunctionCommand("$$rtu", d_rtu_op, t));
// Conversion from unsorted to rational
t = em->mkFunctionType(d_unsorted, em->realType());
d_utr_op = em->mkVar("$$utr", t);
preemptCommand(new DeclareFunctionCommand("$$utr", d_utr_op, t));
}
// Add the inverse in order to show that over the elements that
// appear in the problem there is a bijection between unsorted and
// rational
Expr ret = em->mkExpr(kind::APPLY_UF, d_rtu_op, expr);
if (d_r_converted.find(expr) == d_r_converted.end()) {
d_r_converted.insert(expr);
Expr eq = em->mkExpr(kind::EQUAL, expr,
em->mkExpr(kind::APPLY_UF, d_utr_op, ret));
preemptCommand(new AssertCommand(eq));
}
return ret;
}
int main() {
ExprManager em;
Options opts;
SmtEngine smt(&em);
smt.setOption("incremental", SExpr("true"));
Expr x = em.mkVar("x", em.integerType());
Expr y = em.mkVar("y", em.integerType());
smt.assertFormula(em.mkExpr(kind::GT, em.mkExpr(kind::PLUS, x, y), em.mkConst(Rational(5))));
Expr q = em.mkExpr(kind::GT, x, em.mkConst(Rational(0)));
Result r = smt.query(q);
if(r != Result::INVALID) {
exit(1);
}
Statistics stats = smt.getStatistics();
for(Statistics::iterator i = stats.begin(); i != stats.end(); ++i) {
cout << "stat " << (*i).first << " is " << (*i).second << endl;
}
smt.assertFormula(em.mkExpr(kind::LT, y, em.mkConst(Rational(5))));
r = smt.query(q);
Statistics stats2 = smt.getStatistics();
bool different = false;
for(Statistics::iterator i = stats2.begin(); i != stats2.end(); ++i) {
cout << "stat1 " << (*i).first << " is " << stats.getStatistic((*i).first) << endl;
cout << "stat2 " << (*i).first << " is " << (*i).second << endl;
if(smt.getStatistic((*i).first) != (*i).second) {
cout << "SMT engine reports different value for statistic "
<< (*i).first << ": " << smt.getStatistic((*i).first) << endl;
exit(1);
}
different = different || stats.getStatistic((*i).first) != (*i).second;
}
#ifdef CVC4_STATISTICS_ON
if(!different) {
cout << "stats are the same! bailing.." << endl;
exit(1);
}
#endif /* CVC4_STATISTICS_ON */
return r == Result::VALID ? 0 : 1;
}
int main() {
ExprManager em;
SmtEngine smt(&em);
smt.setLogic("QF_BV"); // Set the logic
Type bitvector32 = em.mkBitVectorType(32);
Expr x = em.mkVar("a", bitvector32);
Expr ext_31_1 = em.mkConst(CVC4::BitVectorExtract(31,1));
Expr x_31_1 = em.mkExpr(ext_31_1, x);
Expr ext_30_0 = em.mkConst(CVC4::BitVectorExtract(30,0));
Expr x_30_0 = em.mkExpr(ext_30_0, x);
Expr ext_31_31 = em.mkConst(CVC4::BitVectorExtract(31,31));
Expr x_31_31 = em.mkExpr(ext_31_31, x);
Expr ext_0_0 = em.mkConst(CVC4::BitVectorExtract(0,0));
Expr x_0_0 = em.mkExpr(ext_0_0, x);
Expr eq = em.mkExpr(kind::EQUAL, x_31_1, x_30_0);
cout << " Asserting: " << eq << endl;
smt.assertFormula(eq);
Expr eq2 = em.mkExpr(kind::EQUAL, x_31_31, x_0_0);
cout << " Querying: " << eq2 << endl;
cout << " Expect valid. " << endl;
cout << " CVC4: " << smt.query(eq2) << endl;
return 0;
}
int main() {
ExprManager em;
SmtEngine smt(&em);
smt.setOption("produce-models", true); // Produce Models
smt.setOption("output-language", "cvc4"); // Set the output-language to CVC's
smt.setOption("default-dag-thresh", 0); //Disable dagifying the output
smt.setLogic(string("QF_UFLIRA"));
// Sorts
SortType u = em.mkSort("u");
Type integer = em.integerType();
Type boolean = em.booleanType();
Type uToInt = em.mkFunctionType(u, integer);
Type intPred = em.mkFunctionType(integer, boolean);
// Variables
Expr x = em.mkVar("x", u);
Expr y = em.mkVar("y", u);
// Functions
Expr f = em.mkVar("f", uToInt);
Expr p = em.mkVar("p", intPred);
// Constants
Expr zero = em.mkConst(Rational(0));
Expr one = em.mkConst(Rational(1));
// Terms
Expr f_x = em.mkExpr(kind::APPLY_UF, f, x);
Expr f_y = em.mkExpr(kind::APPLY_UF, f, y);
Expr sum = em.mkExpr(kind::PLUS, f_x, f_y);
Expr p_0 = em.mkExpr(kind::APPLY_UF, p, zero);
Expr p_f_y = em.mkExpr(kind::APPLY_UF, p, f_y);
// Construct the assumptions
Expr assumptions =
em.mkExpr(kind::AND,
em.mkExpr(kind::LEQ, zero, f_x), // 0 <= f(x)
em.mkExpr(kind::LEQ, zero, f_y), // 0 <= f(y)
em.mkExpr(kind::LEQ, sum, one), // f(x) + f(y) <= 1
p_0.notExpr(), // not p(0)
p_f_y); // p(f(y))
smt.assertFormula(assumptions);
cout << "Given the following assumptions:" << endl
<< assumptions << endl
<< "Prove x /= y is valid. "
<< "CVC4 says: " << smt.query(em.mkExpr(kind::DISTINCT, x, y))
<< "." << endl;
cout << "Now we call checksat on a trivial query to show that" << endl
<< "the assumptions are satisfiable: "
<< smt.checkSat(em.mkConst(true)) << "."<< endl;
cout << "Finally, after a SAT call, we recursively call smt.getValue(...) on"
<< "all of the assumptions to see what the satisfying model looks like."
<< endl;
prefixPrintGetValue(smt, assumptions);
return 0;
}
int main() {
ExprManager em;
SmtEngine smt(&em);
smt.setLogic("QF_BV"); // Set the logic
// The following example has been adapted from the book A Hacker's Delight by
// Henry S. Warren.
//
// Given a variable x that can only have two values, a or b. We want to
// assign to x a value other than the current one. The straightforward code
// to do that is:
//
//(0) if (x == a ) x = b;
// else x = a;
//
// Two more efficient yet equivalent methods are:
//
//(1) x = a ⊕ b ⊕ x;
//
//(2) x = a + b - x;
//
// We will use CVC4 to prove that the three pieces of code above are all
// equivalent by encoding the problem in the bit-vector theory.
// Creating a bit-vector type of width 32
Type bitvector32 = em.mkBitVectorType(32);
// Variables
Expr x = em.mkVar("x", bitvector32);
Expr a = em.mkVar("a", bitvector32);
Expr b = em.mkVar("b", bitvector32);
// First encode the assumption that x must be equal to a or b
Expr x_eq_a = em.mkExpr(kind::EQUAL, x, a);
Expr x_eq_b = em.mkExpr(kind::EQUAL, x, b);
Expr assumption = em.mkExpr(kind::OR, x_eq_a, x_eq_b);
// Assert the assumption
smt.assertFormula(assumption);
// Introduce a new variable for the new value of x after assignment.
Expr new_x = em.mkVar("new_x", bitvector32); // x after executing code (0)
Expr new_x_ = em.mkVar("new_x_", bitvector32); // x after executing code (1) or (2)
// Encoding code (0)
// new_x = x == a ? b : a;
Expr ite = em.mkExpr(kind::ITE, x_eq_a, b, a);
Expr assignment0 = em.mkExpr(kind::EQUAL, new_x, ite);
// Assert the encoding of code (0)
cout << "Asserting " << assignment0 << " to CVC4 " << endl;
smt.assertFormula(assignment0);
cout << "Pushing a new context." << endl;
smt.push();
// Encoding code (1)
// new_x_ = a xor b xor x
Expr a_xor_b_xor_x = em.mkExpr(kind::BITVECTOR_XOR, a, b, x);
Expr assignment1 = em.mkExpr(kind::EQUAL, new_x_, a_xor_b_xor_x);
// Assert encoding to CVC4 in current context;
cout << "Asserting " << assignment1 << " to CVC4 " << endl;
smt.assertFormula(assignment1);
Expr new_x_eq_new_x_ = em.mkExpr(kind::EQUAL, new_x, new_x_);
cout << " Querying: " << new_x_eq_new_x_ << endl;
cout << " Expect valid. " << endl;
cout << " CVC4: " << smt.query(new_x_eq_new_x_) << endl;
cout << " Popping context. " << endl;
smt.pop();
// Encoding code (2)
// new_x_ = a + b - x
Expr a_plus_b = em.mkExpr(kind::BITVECTOR_PLUS, a, b);
Expr a_plus_b_minus_x = em.mkExpr(kind::BITVECTOR_SUB, a_plus_b, x);
Expr assignment2 = em.mkExpr(kind::EQUAL, new_x_, a_plus_b_minus_x);
// Assert encoding to CVC4 in current context;
cout << "Asserting " << assignment2 << " to CVC4 " << endl;
smt.assertFormula(assignment2);
cout << " Querying: " << new_x_eq_new_x_ << endl;
cout << " Expect valid. " << endl;
cout << " CVC4: " << smt.query(new_x_eq_new_x_) << endl;
return 0;
}
Expr add(SetType t, Expr e) {
if(setTypes.find(t) == setTypes.end() ) {
// mark as processed
setTypes.insert(t);
Type elementType = t.getElementType();
ostringstream oss_type;
oss_type << language::SetLanguage(language::output::LANG_SMTLIB_V2)
<< elementType;
string elementTypeAsString = oss_type.str();
elementTypeAsString.erase(
remove_if(elementTypeAsString.begin(), elementTypeAsString.end(), nonsense),
elementTypeAsString.end());
// define-sort
ostringstream oss_name;
oss_name << language::SetLanguage(language::output::LANG_SMTLIB_V2)
<< "(Set " << elementType << ")";
string name = oss_name.str();
Type newt = em->mkArrayType(t.getElementType(), em->booleanType());
mapTypes[t] = newt;
// diffent types
vector<Type> t_t;
t_t.push_back(t);
t_t.push_back(t);
vector<Type> elet_t;
elet_t.push_back(elementType);
elet_t.push_back(t);
if(!enableAxioms)
sout << "(define-fun emptyset" << elementTypeAsString << " "
<< " ()"
<< " " << name
<< " ( (as const " << name << ") false ) )" << endl;
setoperators[ make_pair(t, kind::EMPTYSET) ] =
em->mkVar( std::string("emptyset") + elementTypeAsString,
t);
if(!enableAxioms)
sout << "(define-fun singleton" << elementTypeAsString << " "
<< " ( (x " << elementType << ") )"
<< " " << name << ""
<< " (store emptyset" << elementTypeAsString << " x true) )" << endl;
setoperators[ make_pair(t, kind::SINGLETON) ] =
em->mkVar( std::string("singleton") + elementTypeAsString,
em->mkFunctionType( elementType, t ) );
if(!enableAxioms)
sout << "(define-fun union" << elementTypeAsString << " "
<< " ( (s1 " << name << ") (s2 " << name << ") )"
<< " " << name << ""
<< " ((_ map or) s1 s2))" << endl;
setoperators[ make_pair(t, kind::UNION) ] =
em->mkVar( std::string("union") + elementTypeAsString,
em->mkFunctionType( t_t, t ) );
if(!enableAxioms)
sout << "(define-fun intersection" << elementTypeAsString << ""
<< " ( (s1 " << name << ") (s2 " << name << ") )"
<< " " << name << ""
<< " ((_ map and) s1 s2))" << endl;
setoperators[ make_pair(t, kind::INTERSECTION) ] =
em->mkVar( std::string("intersection") + elementTypeAsString,
em->mkFunctionType( t_t, t ) );
if(!enableAxioms)
sout << "(define-fun setminus" << elementTypeAsString << " "
<< " ( (s1 " << name << ") (s2 " << name << ") )"
<< " " << name << ""
<< " (intersection" << elementTypeAsString << " s1 ((_ map not) s2)))" << endl;
setoperators[ make_pair(t, kind::SETMINUS) ] =
em->mkVar( std::string("setminus") + elementTypeAsString,
em->mkFunctionType( t_t, t ) );
if(!enableAxioms)
sout << "(define-fun member" << elementTypeAsString << " "
<< " ( (x " << elementType << ")" << " (s " << name << "))"
<< " Bool"
<< " (select s x) )" << endl;
setoperators[ make_pair(t, kind::MEMBER) ] =
em->mkVar( std::string("member") + elementTypeAsString,
em->mkPredicateType( elet_t ) );
if(!enableAxioms)
sout << "(define-fun subset" << elementTypeAsString << " "
<< " ( (s1 " << name << ") (s2 " << name << ") )"
<< " Bool"
<<" (= emptyset" << elementTypeAsString << " (setminus" << elementTypeAsString << " s1 s2)) )" << endl;
setoperators[ make_pair(t, kind::SUBSET) ] =
em->mkVar( std::string("subset") + elementTypeAsString,
em->mkPredicateType( t_t ) );
if(enableAxioms) {
int N = sizeof(setaxioms) / sizeof(setaxioms[0]);
for(int i = 0; i < N; ++i) {
string s = setaxioms[i];
ostringstream oss;
oss << language::SetLanguage(language::output::LANG_SMTLIB_V2) << elementType;
boost::replace_all(s, "HOLDA", elementTypeAsString);
boost::replace_all(s, "HOLDB", oss.str());
if( s == "" ) continue;
sout << s << endl;
}
}
}
Expr ret;
if(e.getKind() == kind::EMPTYSET) {
ret = setoperators[ make_pair(t, e.getKind()) ];
} else {
vector<Expr> children = e.getChildren();
children.insert(children.begin(), setoperators[ make_pair(t, e.getKind()) ]);
ret = em->mkExpr(kind::APPLY, children);
}
// cout << "returning " << ret << endl;
return ret;
}
int main() {
ExprManager em;
SmtEngine smt(&em);
smt.setOption("produce-models", true); // Produce Models
smt.setOption("output-language", "smtlib"); // output-language
smt.setLogic("QF_AUFBV"); // Set the logic
// Consider the following code (where size is some previously defined constant):
//
//
// Assert (current_array[0] > 0);
// for (unsigned i = 1; i < k; ++i) {
// current_array[i] = 2 * current_array[i - 1];
// Assert (current_array[i-1] < current_array[i]);
// }
//
// We want to check whether the assertion in the body of the for loop holds
// throughout the loop.
// Setting up the problem parameters
unsigned k = 4; // number of unrollings (should be a power of 2)
unsigned index_size = log2(k); // size of the index
// Types
Type elementType = em.mkBitVectorType(32);
Type indexType = em.mkBitVectorType(index_size);
Type arrayType = em.mkArrayType(indexType, elementType);
// Variables
Expr current_array = em.mkVar("current_array", arrayType);
// Making a bit-vector constant
Expr zero = em.mkConst(BitVector(index_size, 0u));
// Asserting that current_array[0] > 0
Expr current_array0 = em.mkExpr(kind::SELECT, current_array, zero);
Expr current_array0_gt_0 = em.mkExpr(kind::BITVECTOR_SGT, current_array0, em.mkConst(BitVector(32, 0u)));
smt.assertFormula(current_array0_gt_0);
// Building the assertions in the loop unrolling
Expr index = em.mkConst(BitVector(index_size, 0u));
Expr old_current = em.mkExpr(kind::SELECT, current_array, index);
Expr two = em.mkConst(BitVector(32, 2u));
std::vector<Expr> assertions;
for (unsigned i = 1; i < k; ++i) {
index = em.mkConst(BitVector(index_size, Integer(i)));
Expr new_current = em.mkExpr(kind::BITVECTOR_MULT, two, old_current);
// current[i] = 2 * current[i-1]
current_array = em.mkExpr(kind::STORE, current_array, index, new_current);
// current[i-1] < current [i]
Expr current_slt_new_current = em.mkExpr(kind::BITVECTOR_SLT, old_current, new_current);
assertions.push_back(current_slt_new_current);
old_current = em.mkExpr(kind::SELECT, current_array, index);
}
Expr query = em.mkExpr(kind::NOT, em.mkExpr(kind::AND, assertions));
cout << "Asserting " << query << " to CVC4 " << endl;
smt.assertFormula(query);
cout << "Expect sat. " << endl;
cout << "CVC4: " << smt.checkSat(em.mkConst(true)) << endl;
// Getting the model
cout << "The satisfying model is: " << endl;
cout << " current_array = " << smt.getValue(current_array) << endl;
cout << " current_array[0] = " << smt.getValue(current_array0) << endl;
return 0;
}
int main() {
ExprManager em;
SmtEngine smt(&em);
// Set the logic
smt.setLogic("S");
// Produce models
smt.setOption("produce-models", true);
// The option strings-exp is needed
smt.setOption("strings-exp", true);
// Set output language to SMTLIB2
std::cout << language::SetLanguage(language::output::LANG_SMTLIB_V2);
// String type
Type string = em.stringType();
// std::string
std::string std_str_ab("ab");
// CVC4::String
CVC4::String cvc4_str_ab(std_str_ab);
CVC4::String cvc4_str_abc("abc");
// String constants
Expr ab = em.mkConst(cvc4_str_ab);
Expr abc = em.mkConst(CVC4::String("abc"));
// String variables
Expr x = em.mkVar("x", string);
Expr y = em.mkVar("y", string);
Expr z = em.mkVar("z", string);
// String concatenation: x.ab.y
Expr lhs = em.mkExpr(kind::STRING_CONCAT, x, ab, y);
// String concatenation: abc.z
Expr rhs = em.mkExpr(kind::STRING_CONCAT, abc, z);
// x.ab.y = abc.z
Expr formula1 = em.mkExpr(kind::EQUAL, lhs, rhs);
// Length of y: |y|
Expr leny = em.mkExpr(kind::STRING_LENGTH, y);
// |y| >= 0
Expr formula2 = em.mkExpr(kind::GEQ, leny, em.mkConst(Rational(0)));
// Regular expression: (ab[c-e]*f)|g|h
Expr r = em.mkExpr(kind::REGEXP_UNION,
em.mkExpr(kind::REGEXP_CONCAT,
em.mkExpr(kind::STRING_TO_REGEXP, em.mkConst(String("ab"))),
em.mkExpr(kind::REGEXP_STAR,
em.mkExpr(kind::REGEXP_RANGE, em.mkConst(String("c")), em.mkConst(String("e")))),
em.mkExpr(kind::STRING_TO_REGEXP, em.mkConst(String("f")))),
em.mkExpr(kind::STRING_TO_REGEXP, em.mkConst(String("g"))),
em.mkExpr(kind::STRING_TO_REGEXP, em.mkConst(String("h"))));
// String variables
Expr s1 = em.mkVar("s1", string);
Expr s2 = em.mkVar("s2", string);
// String concatenation: s1.s2
Expr s = em.mkExpr(kind::STRING_CONCAT, s1, s2);
// s1.s2 in (ab[c-e]*f)|g|h
Expr formula3 = em.mkExpr(kind::STRING_IN_REGEXP, s, r);
// Make a query
Expr q = em.mkExpr(kind::AND,
formula1,
formula2,
formula3);
// check sat
Result result = smt.checkSat(q);
std::cout << "CVC4 reports: " << q << " is " << result << "." << std::endl;
if(result == Result::SAT) {
std::cout << " x = " << smt.getValue(x) << std::endl;
std::cout << " s1.s2 = " << smt.getValue(s) << std::endl;
}
}