unsigned compute_degree(ExprManager& exprManager, const Expr& term) {
unsigned n = term.getNumChildren();
unsigned degree = 0;
// boolean stuff
if (term.getType() == exprManager.booleanType()) {
for (unsigned i = 0; i < n; ++ i) {
degree = std::max(degree, compute_degree(exprManager, term[i]));
}
return degree;
}
// terms
if (n == 0) {
if (term.getKind() == kind::CONST_RATIONAL) {
return 0;
} else {
return 1;
}
} else {
unsigned degree = 0;
if (term.getKind() == kind::MULT) {
for (unsigned i = 0; i < n; ++ i) {
degree += std::max(degree, compute_degree(exprManager, term[i]));
}
} else {
for (unsigned i = 0; i < n; ++ i) {
degree = std::max(degree, compute_degree(exprManager, term[i]));
}
}
return degree;
}
}
void Tptp::addTheory(Theory theory) {
ExprManager * em = getExprManager();
switch(theory) {
case THEORY_CORE:
//TPTP (CNF and FOF) is unsorted so we define this common type
{
std::string d_unsorted_name = "$$unsorted";
d_unsorted = em->mkSort(d_unsorted_name);
preemptCommand( new DeclareTypeCommand(d_unsorted_name, 0, d_unsorted) );
}
// propositionnal
defineType("Bool", em->booleanType());
defineVar("$true", em->mkConst(true));
defineVar("$false", em->mkConst(false));
addOperator(kind::AND);
addOperator(kind::EQUAL);
addOperator(kind::IMPLIES);
//addOperator(kind::ITE); //only for tff thf
addOperator(kind::NOT);
addOperator(kind::OR);
addOperator(kind::XOR);
addOperator(kind::APPLY_UF);
//Add quantifiers?
break;
default:
std::stringstream ss;
ss << "internal error: Tptp::addTheory(): unhandled theory " << theory;
throw ParserException(ss.str());
}
}
int main() {
ExprManager em;
Expr helloworld = em.mkVar("Hello World!", em.booleanType());
SmtEngine smt(&em);
std::cout << helloworld << " is " << smt.query(helloworld) << std::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;
}
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;
}