Using the infix syntax

Let’s implement a simple expression grammar with the following operators:

Expression: BinaryExpr;

infix BinaryExpr on PrimaryExpression:
    right assoc '^'
    > '*' | '/'
    > '+' | '-'
    ;

PrimaryExpression: '(' expr=Expression ')' | value=Number;

In addition to better readability, the new notation also makes use of performance optimizations to speed up expression parsing by roughly 50% compared to the typical way of writing expressions.

The PrimaryExpression rule defines the basic building blocks of our expressions, which can be (for example) a parenthesized expression, an unary expression, or a number literal.

Expression: BinaryExpr;

infix BinaryExpr on PrimaryExpression:
    ...
    ;

PrimaryExpression: '(' expr=Expression ')' | '-' value=PrimaryExpression | value=Number | ...;

Use the > operator to define precedence levels. Operators listed after a > have lower precedence than those before it. In the example above, ^ has the highest precedence, followed by * and /, and finally + and - with the lowest precedence.

infix BinaryExpr on ...:
    A > B > C
    //A has higher precedence than B, B higher than C
    ;

If you have multiple operators with the same precedence, list them on the same line separated by |.

The default associativity for infix operators is left associative. To specify right associativity, use the assoc keyword preceded by right before the operator.

infix BinaryExpr on ...:
    ...> right assoc '^' >...
    ;