Removal of indirect left recursion (I don't understand formal symbols)

Question

I've tried looking for answers to my solution but I can't seem to wrap my head around the generalized solutions. It doesn't help that I can't figure out which of my elements map to capital letters and which are supposed to be represented by small letters.

This is part of my grammar in Antlr:

expression
    : literal
    | unaryExpression
    | binaryExpression
    | priorityExpression
    | invocation
    ;

binaryExpression: expression binaryOperator expression;

binaryOperator
    : ADD
    | SUBTRACT
    | DIVIDE
    | CONCAT
    | EQUALS
    | NOT_EQUALS
    | LESS_THAN
    | GREATER_THAN
    | MULTIPLY
    ;

How would I go about removing the recursion in binaryExpression?

Bart Kiers · Accepted Answer · 2018-06-17T20:59:54.627

By simply removing binaryExpression and using expression binaryOperator expression directly in expression:

expression
    : literal
    | unaryExpression
    | expression binaryOperator expression
    | priorityExpression
    | invocation
    ;

binaryOperator
    : ADD
    | SUBTRACT
    | DIVIDE
    | CONCAT
    | EQUALS
    | NOT_EQUALS
    | LESS_THAN
    | GREATER_THAN
    | MULTIPLY
    ;

EDIT

but now I lose the binary expression node in the AST and I have to detect it later in code

Then use labels:

expression
    : literal                              #literalExpr
    | unaryExpression                      #unaryExpr
    | expression binaryOperator expression #binaryExpr
    | priorityExpression                   #priorityExpr
    | invocation                           #invocationExpr
    ;

binaryOperator
    : ADD
    | SUBTRACT
    | DIVIDE
    | CONCAT
    | EQUALS
    | NOT_EQUALS
    | LESS_THAN
    | GREATER_THAN
    | MULTIPLY
    ;

Also, I'd like to gain a better understanding of how to remove this recursion instead of offloading it to Antlr

You can't. ANTLR simply doesn't allow such indirect left recursive rules. Only direct left recursion.

yes, but now I lose the binary expression node in the AST and I have to detect it later in code, effectively delaying that part of the parsing. Also, I'd like to gain a better understanding of how to remove this recursion instead of offloading it to Antlr — markonius, Jun 17 '18 at 19:56
In addition to Bart's solution, here is an anwser from me where I describe an [algorithm to remove direct left recursion](https://stackoverflow.com/questions/41788100/antlr4-mutual-left-recursion-grammar/41789097#41789097). — Mike Lischke, Jun 18 '18 at 06:45

Removal of indirect left recursion (I don't understand formal symbols)

1 Answers1

EDIT