antlr4 json grammar and indirect left recursion - antlr4

Question

I read "The Definite ANTLR4 Reference" and it says
While ANTLR v4 can handle direct left recursion, it can’t handle indirect left
recursion.
on page 71.
But in json grammar on page 90 i see next
grammar JSON;
json: object
| array
;
object
: '{' pair (',' pair)* '}'
| '{' '}' // empty object
;
pair: STRING ':' value ;
array
: '[' value (',' value)* ']'
| '[' ']' // empty array
;
value
: STRING
| NUMBER
| object // indirect recursion
| array // indirec recursion
| 'true'
| 'false'
| 'null'
;
Is it correct?

Answer 1

The JSON grammar you mentioned is not a problem because it actually doesn't contain any indirect left recursion.
The rule value can produce array and array can again produce something which contains value, but not as it's leftmost part. (there is a [ preceding value)
The value rule would only be a problem if there would be some way to produce value folowed by any terminals and non-terminals.
From the book
A left-recursive rule is one that
either directly or indirectly invokes itself on the left edge of an alternative.
Example:
expr : expr '*' expr // match subexpressions joined with '*'
| expr '+' expr // match subexpressions joined with '+' operator
| INT // matches simple integer atom
;
It is left recursion because there is at least one alternative immediatly started with expr. Also it is direct left recursion.
Example of indirect left recursion:
expr : addition // indirectly invokes expr left recursively via addition
| ...
;
addition : expr '+' expr
;