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

Example 16 with IntensionalSet

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

the class IntensionalUnionIntersectionEqualToEmptySetSimplifier method standardizeApart.

private static IntensionalSet standardizeApart(IntensionalSet intensionalSet, List<Expression> forAllsSoFar, Context context) {
    IntensionalSet result = intensionalSet;
    if (forAllsSoFar.size() > 0) {
        // May need to standardize apart
        List<Expression> tupleArgs = new ArrayList<>();
        for (Expression forAll : forAllsSoFar) {
            tupleArgs.add(ForAll.getIndexExpression(forAll));
            tupleArgs.add(ForAll.getBody(forAll));
        }
        Expression tupleOfForAlls = Expressions.makeTuple(tupleArgs);
        List<Expression> originalIndexes = IndexExpressions.getIndices(intensionalSet.getIndexExpressions());
        List<Expression> saIndexes = new ArrayList<>();
        for (Expression index : originalIndexes) {
            Expression saIndex = Expressions.primedUntilUnique(index, tupleOfForAlls, context);
            saIndexes.add(saIndex);
        }
        if (!originalIndexes.equals(saIndexes)) {
            // We need to update intensional set with standardized apart indices
            IndexExpressionsSet saIndexExpressionsSet = intensionalSet.getIndexExpressions();
            Expression saHead = intensionalSet.getHead();
            Expression saCondition = intensionalSet.getCondition();
            Context intensionalSetContext = context.extendWith(saIndexExpressionsSet);
            for (int i = 0; i < originalIndexes.size(); i++) {
                Expression originalIndex = originalIndexes.get(i);
                Expression saIndex = saIndexes.get(i);
                if (!originalIndex.equals(saIndex)) {
                    saIndexExpressionsSet = saIndexExpressionsSet.replaceSymbol(originalIndex, saIndex, context);
                    saHead = saHead.replaceAllOccurrences(originalIndex, saIndex, intensionalSetContext);
                    saCondition = saCondition.replaceAllOccurrences(originalIndex, saIndex, intensionalSetContext);
                }
            }
            result = (IntensionalSet) IntensionalSet.intensionalSetOfSameKindAs(intensionalSet, saIndexExpressionsSet, saHead, saCondition);
        }
    }
    return result;
}

Example 17 with IntensionalSet

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

the class IntensionalUnionIntersectionEqualToEmptySetSimplifier method intensionalSetToForAllAndPhi.

private static Expression[] intensionalSetToForAllAndPhi(IntensionalSet intensionalSet, List<Expression> forAllsSoFar, Context context) {
    IntensionalSet saIntensionalSet = standardizeApart(intensionalSet, forAllsSoFar, context);
    Expression forAll = ForAll.make(saIntensionalSet.getIndexExpressions(), saIntensionalSet.getCondition());
    Expression phi = saIntensionalSet.getHead();
    Expression[] result = new Expression[] { forAll, phi };
    return result;
}

Example 18 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;
}

Example 19 with IntensionalSet

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

the class IntensionalUnionToUnionsOfIntensionalSetsOfBaseTypeSimplifier method simplify.

public static Expression simplify(Expression expression, Context context) {
    Expression result = expression;
    if (Sets.isIntensionalUnion(expression)) {
        IntensionalSet intensionalMultiSet = (IntensionalSet) expression.get(0);
        Expression intensionalHead = intensionalMultiSet.getHead();
        // TODO - base case set is an extensional uniset?
        if (Sets.isExtensionalSet(intensionalHead) && intensionalHead.numberOfArguments() == 1) {
            Expression baseTypeHead = intensionalHead.get(0);
            result = IntensionalSet.intensionalMultiSet(intensionalMultiSet.getIndexExpressions(), baseTypeHead, intensionalMultiSet.getCondition());
        } else // Determine if recursive case
        if (intensionalHead.hasFunctor(FunctorConstants.UNION)) {
            // Union( {{ (on I)   Set1 union ... union Set_m : C }} )
            // --->
            // recurse(Union( {{ (on I) Set1 : C }} ))
            // union ... union
            // recurse(Union( {{ (on I) Set_m : C }} ))
            List<Expression> recursedUnionArgs = new ArrayList<>();
            for (Expression setI : intensionalHead.getArguments()) {
                Expression setIUnionArg = IntensionalSet.intensionalMultiSet(intensionalMultiSet.getIndexExpressions(), setI, intensionalMultiSet.getCondition());
                Expression setIUnion = Expressions.apply(FunctorConstants.INTENSIONAL_UNION, setIUnionArg);
                Expression setIRecurseResult = simplify(setIUnion, context);
                recursedUnionArgs.add(setIRecurseResult);
            }
            result = Sets.makeUnion(recursedUnionArgs.toArray(new Expression[recursedUnionArgs.size()]));
        }
    }
    return result;
}

Example 20 with IntensionalSet

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

the class InversionSimplifier method isFunctionOnIntensionalSetWithSingleIndex.

private static boolean isFunctionOnIntensionalSetWithSingleIndex(Object functor, Expression expression) {
    boolean result = false;
    if (((functor == null && Expressions.isFunctionApplicationWithArguments(expression)) || expression.hasFunctor(functor)) && expression.numberOfArguments() == 1) {
        Expression expressionArg1 = expression.get(0);
        if (Sets.isIntensionalSet(expressionArg1)) {
            IntensionalSet intensionalSet = (IntensionalSet) expressionArg1;
            IndexExpressionsSet indexExpressionsSet = intensionalSet.getIndexExpressions();
            List<Expression> indices = IndexExpressions.getIndices(indexExpressionsSet);
            if (indices.size() == 1) {
                result = true;
            }
        }
    }
    return result;
}