public void Test3()
{
ObjectVariableTerm x = new ObjectVariable('x');
IndividualConstantTerm <RationalNumber> half =
(IndividualConstant <RationalNumber>)(new RationalNumber(1, 2));
IndividualConstantTerm <RationalNumber>
one = (IndividualConstant <RationalNumber>)(new RationalNumber(1, 1));
var pr1 = new PredicateFormula(Predicates.More, x, half);
var pr2 = new PredicateFormula(Predicates.Less, x, one);
var f1 = new PropositionalConnectiveFormula(Conjunction.GetInstance(), pr1, pr2);
var f2 = new QuantifierFormula(ExistentialQuantifier.GetInstance(), x, f1);
IndividualConstantTerm <int> twoConst = new IndividualConstant <int>(2);
var xSqr = new FunctionTerm(Functions.Pow, x, twoConst);
var pr3 = new PredicateFormula(Predicates.MoreZero, xSqr);
var pr4 = new PredicateFormula(Predicates.EqualZero, x);
var f3 = new PropositionalConnectiveFormula(Disjunction.GetInstance(), pr3, pr4);
var f4 = new QuantifierFormula(UniversalQuantifier.GetInstance(), x, f3);
var f = new PropositionalConnectiveFormula(Conjunction.GetInstance(), f2, f4);
var actual = SimpleTarskiAlgorithm.QuantifiersElimination(f);
Formula expected = new PredicateFormula(True.GetInstance());
Assert.AreEqual(expected, actual);
}
private static Symbol SpecialSymbol(string str, ref int index)
{
++index;
if (index >= str.Length)
{
throw new ArgumentException(
$"a tag was expected, but there is no tag before the symbol \\ with the number {index - 1}");
}
var tag = GetTag(str, ref index);
if (tag.Length == 0)
{
throw new ArgumentException(
$"a tag was expected, but there is no tag before the symbol \\ with the number {index - 1}");
}
return(tag switch
{
"lnot" => Negation.GetInstance(),
"lor" => Disjunction.GetInstance(),
"land" => Conjunction.GetInstance(),
"to" => Implication.GetInstance(),
"forall" => UniversalQuantifier.GetInstance(),
"exists" => ExistentialQuantifier.GetInstance(),
"over" => Division.GetInstance(),
"func" => GetFunction(str, ref index), // \func{name arity}
"pr" => GetPredicate(str, ref index), // \pr{name arity}
_ => throw new ArgumentException($"unknown tag {tag} before the symbol with the number {index}")
});
public void ZeroEqualZero()
{
ObjectVariableTerm x = new ObjectVariable('x');
IndividualConstantTerm <int> zero = (IndividualConstant <int>) 0;
var pr = new PredicateFormula(Predicates.Equal, zero, zero);
var f = new QuantifierFormula(UniversalQuantifier.GetInstance(), x, pr);
var actual = SimpleTarskiAlgorithm.QuantifiersElimination(f);
var expected = new PredicateFormula(True.GetInstance());
Assert.AreEqual(expected, actual);
}
