Examples with Expressions com.sri.ai.expresso.helper.Expressions used on opensource projects

Example 6 with Expressions

use of com.sri.ai.expresso.helper.Expressions 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 7 with Expressions

use of com.sri.ai.expresso.helper.Expressions in project aic-expresso by aic-sri-international.

the class NumberOfDistinctExpressionsStepSolverTest method test.

@Test
public void test() {
    TheoryTestingSupport theoryTestingSupport = TheoryTestingSupport.make(makeRandom(), new EqualityTheory(true, true));
    Context context = theoryTestingSupport.makeContextWithTestingInformation();
    String contextString = "X != Y and X != a and X != b and Y != b";
    List<String> elementsStrings = list("X", "Y", "a", "b", "c");
    context = context.conjoin(parse(contextString), context);
    ArrayList<Expression> list = mapIntoArrayList(elementsStrings, Expressions::parse);
    NumberOfDistinctExpressionsStepSolver stepSolver = new NumberOfDistinctExpressionsStepSolver(list);
    Step step = stepSolver.step(context);
    assertEquals(true, step.itDepends());
    assertEquals(parse("X = c"), step.getSplitter());
    ExpressionLiteralSplitterStepSolver stepSolverIfXEqualsC = step.getStepSolverForWhenSplitterIsTrue();
    ExpressionLiteralSplitterStepSolver stepSolverIfXIsDifferentFromC = step.getStepSolverForWhenSplitterIsFalse();
    // if X = c, the number of distinct values can be 3 or 4, depending on whether Y = a, or Y = b
    step = stepSolverIfXEqualsC.step(context);
    assertEquals(true, step.itDepends());
    assertEquals(parse("Y = a"), step.getSplitter());
    ExpressionLiteralSplitterStepSolver stepSolverIfXEqualsCAndYEqualsA = step.getStepSolverForWhenSplitterIsTrue();
    ExpressionLiteralSplitterStepSolver stepSolverIfXEqualsCAndYIsDifferentFromA = step.getStepSolverForWhenSplitterIsFalse();
    // if X = c and Y = a, the number of distinct values is 3 (a, b, c)
    step = stepSolverIfXEqualsCAndYEqualsA.step(context);
    assertEquals(false, step.itDepends());
    assertEquals(parse("3"), step.getValue());
    // if X = c and Y != a, the number of distinct values is 3 or 4, depending on Y = c
    step = stepSolverIfXEqualsCAndYIsDifferentFromA.step(context);
    assertEquals(true, step.itDepends());
    assertEquals(parse("Y = c"), step.getSplitter());
    ExpressionLiteralSplitterStepSolver stepSolverIfXEqualsCAndYIsDifferentFromAAndYEqualsC = step.getStepSolverForWhenSplitterIsTrue();
    ExpressionLiteralSplitterStepSolver stepSolverIfXEqualsCAndYIsDifferentFromAAndYIsDifferentFromC = step.getStepSolverForWhenSplitterIsFalse();
    // if X = c and Y != a and Y = c, the number of distinct values is 3
    step = stepSolverIfXEqualsCAndYIsDifferentFromAAndYEqualsC.step(context);
    assertEquals(false, step.itDepends());
    assertEquals(parse("3"), step.getValue());
    // if X = c and Y != a and Y != c, the number of distinct values is 4
    step = stepSolverIfXEqualsCAndYIsDifferentFromAAndYIsDifferentFromC.step(context);
    assertEquals(false, step.itDepends());
    assertEquals(parse("4"), step.getValue());
    // if X = c and Y = a, the number of distinct values is 3 (a, b, c)
    step = stepSolverIfXEqualsCAndYEqualsA.step(context);
    assertEquals(false, step.itDepends());
    assertEquals(parse("3"), step.getValue());
    // using again just to make sure it produces the same result
    step = stepSolverIfXEqualsCAndYEqualsA.step(context);
    assertEquals(false, step.itDepends());
    assertEquals(parse("3"), step.getValue());
    // if X != c, the number of distinct value will now depend on Y = a
    step = stepSolverIfXIsDifferentFromC.step(context);
    assertEquals(true, step.itDepends());
    assertEquals(parse("Y = a"), step.getSplitter());
    // using again just to make sure it produces the same result
    step = stepSolverIfXIsDifferentFromC.step(context);
    assertEquals(true, step.itDepends());
    assertEquals(parse("Y = a"), step.getSplitter());
    // if X != c, the number of distinct values can be 4 or 5, depending on whether Y = a, or Y = b
    step = stepSolverIfXIsDifferentFromC.step(context);
    assertEquals(true, step.itDepends());
    assertEquals(parse("Y = a"), step.getSplitter());
    ExpressionLiteralSplitterStepSolver stepSolverIfXIsDifferentFromCAndYEqualsA = step.getStepSolverForWhenSplitterIsTrue();
    ExpressionLiteralSplitterStepSolver stepSolverIfXIsDifferentFromCAndYIsDifferentFromA = step.getStepSolverForWhenSplitterIsFalse();
    step = stepSolverIfXIsDifferentFromCAndYEqualsA.step(context);
    assertEquals(false, step.itDepends());
    assertEquals(parse("4"), step.getValue());
    // if however Y != a, limit will depend on Y = c
    step = stepSolverIfXIsDifferentFromCAndYIsDifferentFromA.step(context);
    assertEquals(true, step.itDepends());
    assertEquals(parse("Y = c"), step.getSplitter());
    ExpressionLiteralSplitterStepSolver stepSolverIfXIsDifferentFromCAndYIsDifferentFromAAndYIsEqualToC = step.getStepSolverForWhenSplitterIsTrue();
    ExpressionLiteralSplitterStepSolver stepSolverIfXIsDifferentFromCAndYIsDifferentFromAAndYIsDifferentFromC = step.getStepSolverForWhenSplitterIsFalse();
    // if Y = c, then there are 4 distinct values
    step = stepSolverIfXIsDifferentFromCAndYIsDifferentFromAAndYIsEqualToC.step(context);
    assertEquals(false, step.itDepends());
    assertEquals(parse("4"), step.getValue());
    // if Y != c, then Y is also unique and the number of distinct values is 5
    step = stepSolverIfXIsDifferentFromCAndYIsDifferentFromAAndYIsDifferentFromC.step(context);
    assertEquals(false, step.itDepends());
    assertEquals(parse("5"), step.getValue());
}

Example 8 with Expressions

use of com.sri.ai.expresso.helper.Expressions in project aic-expresso by aic-sri-international.

the class GrinderUtil method fromTypeExpressionToItsIntrinsicMeaning.

/**
 * A method mapping type expressions to their intrinsic {@link Type} objects,
 * where "intrinsic" means there is only one possible {@link Type} object
 * for them in the registry of grinder
 * (therefore, it cannot be used for, say, categorical types defined
 * by the user and registered in the registry by name only).
 * Current recognized type expressions are
 * <code>Boolean</code>, <code>Integer</code>, and function applications
 * of the type <code>model..n</code>.
 * If there is no such meaning, the method returns <code>null</code>.
 * @param typeExpression
 * @param registry TODO
 * @return
 */
public static Type fromTypeExpressionToItsIntrinsicMeaning(Expression typeExpression, Registry registry) throws Error {
    Type type;
    if (typeExpression.equals("Boolean")) {
        type = BOOLEAN_TYPE;
    } else if (typeExpression.equals("Integer")) {
        type = INTEGER_TYPE;
    } else if (typeExpression.equals("Real")) {
        type = REAL_TYPE;
    } else if (typeExpression.hasFunctor(INTEGER_INTERVAL) && typeExpression.numberOfArguments() == 2) {
        type = new IntegerInterval(typeExpression.get(0), typeExpression.get(1));
    } else if ((typeExpression.hasFunctor(FunctorConstants.REAL_INTERVAL_CLOSED_CLOSED) || typeExpression.hasFunctor(FunctorConstants.REAL_INTERVAL_OPEN_CLOSED) || typeExpression.hasFunctor(FunctorConstants.REAL_INTERVAL_CLOSED_OPEN) || typeExpression.hasFunctor(FunctorConstants.REAL_INTERVAL_OPEN_OPEN)) && typeExpression.numberOfArguments() == 2) {
        type = new RealInterval(typeExpression.toString());
    } else if (FunctionType.isFunctionType(typeExpression)) {
        Function<Expression, Type> getType = e -> registry.getTypeFromTypeExpression(e);
        Type codomain = getType.apply(FunctionType.getCodomain(typeExpression));
        List<Expression> argumentTypeExpressions = FunctionType.getArgumentList(typeExpression);
        ArrayList<Type> argumentTypes = mapIntoArrayList(argumentTypeExpressions, getType);
        Type[] argumentTypesArray = new Type[argumentTypes.size()];
        type = new FunctionType(codomain, argumentTypes.toArray(argumentTypesArray));
    } else if (TupleType.isTupleType(typeExpression)) {
        List<Type> elementTypes = typeExpression.getArguments().stream().map(elementTypeExpression -> registry.getTypeFromTypeExpression(elementTypeExpression)).collect(Collectors.toList());
        type = new TupleType(elementTypes);
    } else {
        type = null;
    }
    return type;
}

Example 9 with Expressions

use of com.sri.ai.expresso.helper.Expressions in project aic-expresso by aic-sri-international.

the class GrinderUtil method getTypeExpressionOfExpression.

/**
 * Returns the type of given expression according to registry.
 */
public static Expression getTypeExpressionOfExpression(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 = getTypeExpressionOfExpression(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 = getTypeExpressionOfExpression(IfThenElse.thenBranch(expression), registry);
        Expression elseType = getTypeExpressionOfExpression(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 -> getTypeExpressionOfExpression(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 = getTypeExpressionOfExpression(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.getTypeExpressionOfRegisteredSymbol(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 = getTypeExpressionOfExpression(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 = getTypeExpressionOfExpression(expression.getFunctor(), registry);
        if (functionType == null) {
            throw new Error("Type of '" + expression.getFunctor() + "' required but unknown.");
        }
        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.getTypeFromTypeExpression(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 -> getTypeExpressionOfExpression(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 = getTypeExpressionOfExpression(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 = getTypeExpressionOfExpression(lambdaExpression.getBody(), lambdaExpressionWithABodyRegistry);
        result = Expressions.apply(FUNCTION_TYPE, domain, coDomain);
    } else if (expression instanceof AbstractExpressionWrapper) {
        Expression innerExpression = ((AbstractExpressionWrapper) expression).getInnerExpression();
        result = getTypeExpressionOfExpression(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;
}