Examples with IntensionalSet com.sri.ai.expresso.api.IntensionalSet used on opensource projects

Example 21 with IntensionalSet

use of com.sri.ai.expresso.api.IntensionalSet in project aic-expresso by aic-sri-international.

the class InversionPerformanceEvaluationTest method computeSize.

private Rational computeSize(Expression functionOnIntensionalSet, Rational resultSoFar, Context context) {
    IntensionalSet intensionalSet = (IntensionalSet) functionOnIntensionalSet.get(0);
    IndexExpressionsSet indexExpressionsSet = intensionalSet.getIndexExpressions();
    List<Expression> indices = IndexExpressions.getIndices(indexExpressionsSet);
    if (indices.size() != 1) {
        throw new UnsupportedOperationException("Currently only support singular indices");
    }
    Expression index = indices.get(0);
    Context intensionalSetContext = context.extendWith(indexExpressionsSet);
    Type type = GrinderUtil.getTypeOfExpression(index, intensionalSetContext);
    Rational result = resultSoFar.multiply(type.cardinality().rationalValue());
    Expression head = intensionalSet.getHead();
    if (Expressions.isFunctionApplicationWithArguments(head) && Sets.isIntensionalSet(head.get(0))) {
        result = computeSize(head, result, intensionalSetContext);
    }
    return result;
}

Example 22 with IntensionalSet

use of com.sri.ai.expresso.api.IntensionalSet in project aic-expresso by aic-sri-international.

the class AbstractIntensionalSet method replaceSymbol.

@Override
public Expression replaceSymbol(Expression symbol, Expression newSymbol, Registry registry) {
    IntensionalSet result = this;
    IndexExpressionsSet newIndexExpressions = getIndexExpressions().replaceSymbol(symbol, newSymbol, registry);
    Expression newHead = getHead().replaceSymbol(symbol, newSymbol, registry);
    Expression newCondition = getCondition().replaceSymbol(symbol, newSymbol, registry);
    result = replaceIfNeeded(newIndexExpressions, newHead, newCondition);
    return result;
}

Example 23 with IntensionalSet

use of com.sri.ai.expresso.api.IntensionalSet in project aic-expresso by aic-sri-international.

the class GrinderUtil method getTypeExpression.

/**
	 * Returns the type of given expression according to registry.
	 */
public static Expression getTypeExpression(Expression expression, Registry registry) {
    Expression result;
    if (FormulaUtil.isApplicationOfBooleanConnective(expression)) {
        result = makeSymbol("Boolean");
    } else if (expression.getSyntacticFormType().equals(FunctionApplication.SYNTACTIC_FORM_TYPE) && list(SUM, PRODUCT, MAX).contains(expression.getFunctor().toString())) {
        Expression argument = expression.get(0);
        if (argument.getSyntacticFormType().equals(IntensionalSet.SYNTACTIC_FORM_TYPE)) {
            IntensionalSet intensionalSetArgument = (IntensionalSet) argument;
            Expression head = intensionalSetArgument.getHead();
            // NOTE: Need to extend the registry as the index expressions in the quantifier may
            // declare new types (i.e. function types).
            Registry headRegistry = registry.extendWith(intensionalSetArgument.getIndexExpressions());
            result = getTypeExpression(head, headRegistry);
        } else if (argument.getSyntacticFormType().equals(ExtensionalSets.SYNTACTIC_FORM_TYPE)) {
            List<Expression> arguments = ((AbstractExtensionalSet) argument).getElementsDefinitions();
            result = getTypeOfCollectionOfNumericExpressionsWithDefaultInteger(arguments, registry);
        } else if (expression.hasFunctor(MAX)) {
            // MAX can also be applied to a bunch of numbers
            result = getTypeOfCollectionOfNumericExpressionsWithDefaultInteger(expression.getArguments(), registry);
        } else {
            throw new Error(expression.getFunctor() + " defined for sets only but got " + expression.get(0));
        }
    } else if (Equality.isEquality(expression) || Disequality.isDisequality(expression)) {
        result = makeSymbol("Boolean");
    } else if (expression.equals(FunctorConstants.REAL_INTERVAL_CLOSED_CLOSED) || expression.equals(FunctorConstants.REAL_INTERVAL_CLOSED_OPEN) || expression.equals(FunctorConstants.REAL_INTERVAL_OPEN_CLOSED) || expression.equals(FunctorConstants.REAL_INTERVAL_OPEN_OPEN)) {
        result = FunctionType.make(parse("Set"), parse("Number"), parse("Number"));
    } else if (IfThenElse.isIfThenElse(expression)) {
        Expression thenType = getTypeExpression(IfThenElse.thenBranch(expression), registry);
        Expression elseType = getTypeExpression(IfThenElse.elseBranch(expression), registry);
        if (thenType != null && elseType != null && (thenType.equals("Number") && isIntegerOrReal(elseType) || isIntegerOrReal(thenType) && elseType.equals("Number"))) {
            result = makeSymbol("Number");
        } else if (thenType != null && elseType != null && (thenType.equals("Integer") && elseType.equals("Real") || thenType.equals("Real") && elseType.equals("Integer"))) {
            result = makeSymbol("Real");
        } else if (thenType != null && (elseType == null || thenType.equals(elseType))) {
            result = thenType;
        } else if (elseType != null && (thenType == null || elseType.equals(thenType))) {
            result = elseType;
        } else if (thenType == null) {
            throw new Error("Could not determine the types of then and else branches of '" + expression + "'.");
        } else if (thenType.equals("Integer") && elseType.hasFunctor(INTEGER_INTERVAL)) {
            // TODO: I know, I know, this treatment of integers and interval is terrible... will fix at some point
            result = thenType;
        } else if (thenType.hasFunctor(INTEGER_INTERVAL) && elseType.equals("Integer")) {
            result = elseType;
        } else if (thenType.hasFunctor(INTEGER_INTERVAL) && elseType.hasFunctor(INTEGER_INTERVAL)) {
            IntegerInterval thenInterval = (IntegerInterval) thenType;
            IntegerInterval elseInterval = (IntegerInterval) elseType;
            Expression minimumLowerBound = LessThan.simplify(apply(LESS_THAN, thenInterval.getNonStrictLowerBound(), elseInterval.getNonStrictLowerBound()), registry).booleanValue() ? thenInterval.getNonStrictLowerBound() : elseInterval.getNonStrictLowerBound();
            Expression maximumUpperBound = GreaterThan.simplify(apply(GREATER_THAN, thenInterval.getNonStrictUpperBound(), elseInterval.getNonStrictUpperBound()), registry).booleanValue() ? thenInterval.getNonStrictUpperBound() : elseInterval.getNonStrictUpperBound();
            if (minimumLowerBound.equals(MINUS_INFINITY) && maximumUpperBound.equals(INFINITY)) {
                result = makeSymbol("Integer");
            } else {
                result = apply(INTEGER_INTERVAL, minimumLowerBound, maximumUpperBound);
            }
        } else {
            throw new Error("'" + expression + "' then and else branches have different types (" + thenType + " and " + elseType + " respectively).");
        }
    } else if (isCardinalityExpression(expression)) {
        result = makeSymbol("Integer");
    } else if (isNumericFunctionApplication(expression)) {
        List<Expression> argumentTypes = mapIntoList(expression.getArguments(), e -> getTypeExpression(e, registry));
        int firstNullArgumentTypeIndexIfAny = Util.getIndexOfFirstSatisfyingPredicateOrMinusOne(argumentTypes, t -> t == null);
        if (firstNullArgumentTypeIndexIfAny != -1) {
            throw new Error("Cannot determine type of " + expression.getArguments().get(firstNullArgumentTypeIndexIfAny) + ", which is needed for determining type of " + expression);
        }
        /**
			 * commonDomain is the co-domain shared by all argument function types, or empty tuple for arguments that are not function-typed.
			 * Therefore, if no argument is function-typed, it will be equal to the empty tuple.
			 */
        Expression commonDomain = getCommonDomainIncludingConversionOfNonFunctionTypesToNullaryFunctions(argumentTypes, registry);
        if (commonDomain == null) {
            throw new Error("Operator " + expression.getFunctor() + " applied to arguments of non-compatible types: " + expression + ", types of arguments are " + argumentTypes);
        }
        boolean noArgumentIsFunctionTyped = commonDomain.equals(EMPTY_TUPLE) && !thereExists(argumentTypes, t -> t.hasFunctor(FunctorConstants.FUNCTION_TYPE));
        Expression resultCoDomain;
        if (thereExists(argumentTypes, t -> Util.equals(getCoDomainOrItself(t), "Number"))) {
            resultCoDomain = makeSymbol("Number");
        } else if (thereExists(argumentTypes, t -> Util.equals(getCoDomainOrItself(t), "Real"))) {
            resultCoDomain = makeSymbol("Real");
        } else if (thereExists(argumentTypes, t -> isRealInterval(getCoDomainOrItself(t)))) {
            resultCoDomain = makeSymbol("Real");
        } else {
            resultCoDomain = makeSymbol("Integer");
        }
        if (noArgumentIsFunctionTyped) {
            result = resultCoDomain;
        } else {
            result = apply(FUNCTION_TYPE, commonDomain, resultCoDomain);
        }
    } else if (expression.hasFunctor(FunctorConstants.INTEGER_INTERVAL) || expression.hasFunctor(FunctorConstants.REAL_INTERVAL_CLOSED_CLOSED) || expression.hasFunctor(FunctorConstants.REAL_INTERVAL_OPEN_CLOSED) || expression.hasFunctor(FunctorConstants.REAL_INTERVAL_CLOSED_OPEN) || expression.hasFunctor(FunctorConstants.REAL_INTERVAL_OPEN_OPEN)) {
        result = makeSymbol("Set");
    } else if (isComparisonFunctionApplication(expression)) {
        result = makeSymbol("Boolean");
    } else if (expression.hasFunctor(FunctorConstants.FUNCTION_TYPE)) {
        // very vague type for now
        result = apply(FUNCTION_TYPE, makeSymbol("Set"), makeSymbol("Set"));
    } else if (Sets.isIntensionalMultiSet(expression)) {
        IntensionalSet set = (IntensionalSet) expression;
        // NOTE: Need to extend the registry as the index expressions in the quantifier may
        // declare new types (i.e. function types).
        Registry headRegistry = registry.extendWith(set.getIndexExpressions());
        Expression headType = getTypeExpression(set.getHead(), headRegistry);
        result = new DefaultIntensionalMultiSet(list(), headType, TRUE);
    } else if (Sets.isExtensionalSet(expression)) {
        // very vague type for now
        result = apply(FUNCTION_TYPE, makeSymbol("Set"));
    } else if (expression.hasFunctor(FunctorConstants.INTERSECTION) || expression.hasFunctor(FunctorConstants.UNION) || expression.hasFunctor(FunctorConstants.INTENSIONAL_UNION)) {
        // very vague type for now
        result = apply(FUNCTION_TYPE, makeSymbol("Set"));
    } else if (expression.getSyntacticFormType().equals(Symbol.SYNTACTIC_FORM_TYPE)) {
        if (expression.getValue() instanceof Integer) {
            result = makeSymbol("Integer");
        } else if (expression.getValue() instanceof Double) {
            result = makeSymbol("Real");
        } else if (expression.getValue() instanceof Rational) {
            Rational rational = (Rational) expression.getValue();
            boolean isInteger = rational.isInteger();
            result = makeSymbol(isInteger ? "Integer" : "Real");
        } else if (expression.getValue() instanceof Number) {
            result = makeSymbol("Number");
        } else if (expression.getValue() instanceof String && expression.isStringLiteral()) {
            result = makeSymbol("String");
        } else if (expression.getValue() instanceof Boolean) {
            result = makeSymbol("Boolean");
        } else if (expression.equals(Expressions.INFINITY) || expression.equals(Expressions.MINUS_INFINITY)) {
            result = makeSymbol("Number");
        } else {
            result = registry.getTypeOfRegisteredSymbol(expression);
            if (result == null) {
                Type type = getFirstSatisfyingPredicateOrNull(registry.getTypes(), t -> t.contains(expression));
                if (type != null) {
                    result = parse(type.getName());
                }
            }
        }
    } else if (expression.hasFunctor(FunctorConstants.GET) && expression.numberOfArguments() == 2 && Expressions.isNumber(expression.get(1))) {
        Expression argType = getTypeExpression(expression.get(0), registry);
        if (TupleType.isTupleType(argType)) {
            TupleType tupleType = (TupleType) GrinderUtil.fromTypeExpressionToItsIntrinsicMeaning(argType, registry);
            result = parse(tupleType.getElementTypes().get(expression.get(1).intValue() - 1).toString());
        } else {
            throw new Error("get type from tuple for '" + expression + "' currently not supported.");
        }
    } else if (expression.hasFunctor(FunctorConstants.TUPLE_TYPE)) {
        // Is a type expression already.
        result = expression;
    } else if (expression.getSyntacticFormType().equals(FunctionApplication.SYNTACTIC_FORM_TYPE)) {
        Expression functionType = getTypeExpression(expression.getFunctor(), registry);
        if (functionType == null) {
            throw new Error("Type of '" + expression.getFunctor() + "' required, but unknown to registry.");
        }
        Expression coDomain = FunctionType.getCodomain(functionType);
        List<Expression> argumentsTypesList = FunctionType.getArgumentList(functionType);
        if (expression.getArguments().size() != argumentsTypesList.size()) {
            throw new Error("Function " + expression.getFunctor() + " is of type " + functionType + " but has incorrect number of arguments = " + expression.getArguments());
        }
        for (int idx = 0; idx < expression.getArguments().size(); idx++) {
            Expression arg = expression.get(idx);
            Expression argExprType = argumentsTypesList.get(idx);
            Type argType = registry.getType(argExprType);
            if (!isSubtypeOf(arg, argType, registry)) {
                throw new Error("Function " + expression.getFunctor() + " is of type " + functionType + " but has arguments that are not legal subtypes [#" + idx + "] = " + expression.getArguments());
            }
        }
        result = coDomain;
    } else if (Tuple.isTuple(expression)) {
        List<Expression> elementTypes = expression.getArguments().stream().map(element -> getTypeExpression(element, registry)).collect(Collectors.toList());
        result = TupleType.make(elementTypes);
    } else if (expression instanceof QuantifiedExpressionWithABody) {
        QuantifiedExpressionWithABody quantifiedExpressionWithABody = (QuantifiedExpressionWithABody) expression;
        // NOTE: Need to extend the registry as the index expressions in the quantifier may
        // declare new types (i.e. function types).
        Registry quantifiedExpressionWithABodyRegistry = registry.extendWith(quantifiedExpressionWithABody.getIndexExpressions());
        result = getTypeExpression(quantifiedExpressionWithABody.getBody(), quantifiedExpressionWithABodyRegistry);
    } else if (expression instanceof LambdaExpression) {
        LambdaExpression lambdaExpression = (LambdaExpression) expression;
        Collection<Expression> domain = IndexExpressions.getIndexDomainsOfQuantifiedExpression(lambdaExpression);
        IndexExpressionsSet indexExpressions = lambdaExpression.getIndexExpressions();
        Registry lambdaExpressionWithABodyRegistry = registry.extendWith(indexExpressions);
        Expression coDomain = getTypeExpression(lambdaExpression.getBody(), lambdaExpressionWithABodyRegistry);
        result = Expressions.apply(FUNCTION_TYPE, domain, coDomain);
    } else if (expression instanceof AbstractExpressionWrapper) {
        Expression innerExpression = ((AbstractExpressionWrapper) expression).getInnerExpression();
        result = getTypeExpression(innerExpression, registry);
    } else {
        throw new Error("GrinderUtil.getType does not yet know how to determine the type of this sort of expression: " + expression);
    }
    return result;
}

Example 24 with IntensionalSet

use of com.sri.ai.expresso.api.IntensionalSet in project aic-expresso by aic-sri-international.

the class IntersectionIntensionalSetsSimplifier method simplify.

public static Expression simplify(Expression expression, Context context) {
    Expression result = expression;
    if (expression.hasFunctor(FunctorConstants.INTERSECTION)) {
        List<Expression> intensionalMultiSetArgs = new ArrayList<>();
        List<Expression> nonIntensionalMultiSetArgs = new ArrayList<>();
        for (Expression arg : expression.getArguments()) {
            if (Sets.isIntensionalMultiSet(arg)) {
                intensionalMultiSetArgs.add(arg);
            } else {
                nonIntensionalMultiSetArgs.add(arg);
            }
        }
        if (intensionalMultiSetArgs.size() > 1) {
            boolean resultIsEmptySet = false;
            IntensionalSet intersectedMultiSet = (IntensionalSet) intensionalMultiSetArgs.get(0);
            for (int i = 1; i < intensionalMultiSetArgs.size() && !resultIsEmptySet; i++) {
                IntensionalSet otherMultiSet = standardizeApartIntensionalSets((IntensionalSet) intensionalMultiSetArgs.get(i), intersectedMultiSet, context);
                // {{ (on I1) H1 : C1 }} intersection {{ (on I2) H2 : C2 }}
                // ---->
                // {{ (on I1) H1 : C1 and evaluate(there exists I2 : C2 and H2 = H1) }}				
                IndexExpressionsSet i1 = intersectedMultiSet.getIndexExpressions();
                IndexExpressionsSet i2 = otherMultiSet.getIndexExpressions();
                Expression h1 = intersectedMultiSet.getHead();
                Expression h2 = otherMultiSet.getHead();
                Expression c1 = intersectedMultiSet.getCondition();
                Expression c2 = otherMultiSet.getCondition();
                Expression thereExists = ThereExists.make(i2, And.make(c2, Equality.make(h2, h1)));
                Context i1ExtendedContext = context.extendWith(i1);
                Expression thereExistsEvaluated = context.getTheory().evaluate(thereExists, i1ExtendedContext);
                if (thereExistsEvaluated.equals(false)) {
                    // They don't intersect, which means you have an empty
                    // set in the intersection, which means the whole thing
                    // results in the empty set.
                    resultIsEmptySet = true;
                } else if (!thereExistsEvaluated.equals(true)) {
                    // If we have a condition, other than false and true
                    // we will want to extend the current result by the condition
                    Expression extendedCondition = And.make(c1, thereExistsEvaluated);
                    intersectedMultiSet = (IntensionalSet) IntensionalSet.intensionalMultiSet(i1, h1, extendedCondition);
                    // Ensure we don't have a false condition.
                    Expression simplifiedIntersectedMultiSet = context.getTheory().evaluate(intersectedMultiSet, context);
                    if (Sets.isEmptySet(simplifiedIntersectedMultiSet)) {
                        resultIsEmptySet = true;
                    }
                }
            }
            if (resultIsEmptySet) {
                result = Sets.EMPTY_SET;
            } else if (nonIntensionalMultiSetArgs.size() > 0) {
                List<Expression> intersectedArgs = new ArrayList<>();
                intersectedArgs.add(intersectedMultiSet);
                intersectedArgs.addAll(nonIntensionalMultiSetArgs);
                result = Sets.makeIntersection(intersectedArgs.toArray(new Expression[intersectedArgs.size()]));
            } else {
                result = intersectedMultiSet;
            }
        }
    }
    return result;
}

Example 25 with IntensionalSet

use of com.sri.ai.expresso.api.IntensionalSet in project aic-expresso by aic-sri-international.

the class IntensionalUnionIntersectionEqualToEmptySetSimplifier method simplify.

public static Expression simplify(Expression expression, Context context) {
    Expression result = expression;
    if (Equality.isEquality(expression) && expression.numberOfArguments() == 2) {
        Expression intersection = null;
        Expression emptySet = null;
        for (Expression arg : expression.getArguments()) {
            if (Expressions.hasFunctor(arg, FunctorConstants.INTERSECTION)) {
                intersection = arg;
            } else if (Sets.isEmptySet(arg)) {
                emptySet = arg;
            }
        }
        if (intersection != null && emptySet != null) {
            // (&cup;<sub>i &isin; D:C</sub>&Phi;) &cap; (&cup;<sub>i' &isin; D':C'</sub>&Phi;') = &empty;
            if (intersection.getArguments().stream().allMatch(Sets::isIntensionalUnion)) {
                List<Expression> forAlls = new ArrayList<>();
                List<Expression> phis = new ArrayList<>();
                // &forall; i &isin; D : C &rArr; &forall; i' &isin; D' : C' &rArr;  (&Phi; &cap; &Phi;' = &empty;)
                for (Expression intensionalUnion : intersection.getArguments()) {
                    IntensionalSet intensionalSet = (IntensionalSet) intensionalUnion.get(0);
                    Expression[] forAllAndPhi = intensionalSetToForAllAndPhi(intensionalSet, forAlls, context);
                    Expression forAll = forAllAndPhi[0];
                    Expression phi = forAllAndPhi[1];
                    handleNestedForAlls(forAll, forAlls);
                    phis.add(phi);
                }
                result = Equality.make(Expressions.apply(FunctorConstants.INTERSECTION, phis), emptySet);
                for (int i = forAlls.size() - 1; i >= 0; i--) {
                    Expression forAll = forAlls.get(i);
                    Expression body = Implication.make(ForAll.getBody(forAll), result);
                    result = ForAll.make(ForAll.getIndexExpression(forAll), body);
                }
            }
        }
    }
    return result;
}