Abstract superclass of all expression nodes.

Correct operator precedence and associativity is enforced by the parameter types of the various child classes. For example, consider the following simple expression:

1 + 2 * 3

Because multiplication has higher precedence than addition, the correct syntax tree for this expression is:

SumOperation {
    leftOperand = IntegerLiteral("1");
    rightOperand = ProductOperation {
        leftOperand = IntegerLiteral("2");
        rightOperand = IntegerLiteral("3");
    };
}

A very simple, strictly left-associative parser that doesn’t respect operator precedence might instead try to produce:

ProductOperation {
    leftFactor = SumOperation {
        leftSummand = IntegerLiteral("1");
        rightSummand = IntegerLiteral("2");
    };
    rightFactor = IntegerLiteral("3");
}

However, this is not well-typed (the parser would likely have an assertion failure at runtime), because the types of ProductOperation’s child nodes are crafted such that only nodes with correct precedence and associativity can be created.

To ensure this, there is one type alias for each precedence level, specified as the union type of

• the next higher level’s alias, and
• all operator types on this level.

For example, there is MultiplyingExpression for multiplicative expressions and AddingExpression for summative expressions. ProductOperation.leftFactor then has type MultiplyingExpression, which does not include SumOperation. ProductOperation.rightFactor has the next higher level’s type UnioningExpression, reflecting the left-associativity of product operations: Instead of

ProductOperation {
    leftFactor = IntegerLiteral("1");
    rightFactor = ProductOperation {
        leftFactor = IntegerLiteral("2");
        rightFactor = IntegerLiteral("3");
    };
}

you should have

ProductOperation {
    leftFactor = ProductOperation {
        leftFactor = IntegerLiteral("1");
        rightFactor = IntegerLiteral("2");
    };
    rightFactor = IntegerLiteral("3");
}

These aliases are, from highest to lowest precedence:

• PrePostfixingExpression
• ExponentiatingExpression
• InvertingExpression
• IntersectingExpression
• UnioningExpression
• MultiplyingExpression
• ScalingExpression
• AddingExpression
• SpanningExpression
• ExistsNonemptyExpression
• ComparingExpression
• EquatingExpression
• NegatingExpression
• ConjoiningExpression
• DisjoiningExpression
• ThenElseExpression
• AssigningExpression