如何避免ANTLR 4中的相互左递归 [英] How to avoid mutual left-recursion in ANTLR 4

问题描述

我正在编写一种语法来处理标量和向量表达式.下面的语法经过简化以显示我所遇到的问题，其中标量表达式可以从矢量导出，而矢量可以从标量导出.例如，向量可以是文字[1, 2, 3]或标量与向量2 * [1, 2, 3]的乘积(等效于[2, 4, 6]).标量可以是文字2或向量[1, 2, 3][1]的索引(等效于2).

I am writing a grammar to handle scalar and vector expressions. The grammar below is simplified to show the problem I have where a scalar expression can be derived from a vector and a vector can be derived from a scalar. For example, a vector could be a literal [1, 2, 3] or the product of a scalar and a vector 2 * [1, 2, 3] (equivalent to [2, 4, 6]). A scalar could be a literal 2 or an index into a vector [1, 2, 3][1] (equivalent to 2).

grammar LeftRecursion;

Integer
    : [0-9]+
    ;

WhiteSpace
    : [ \t\r\n]+ -> skip
    ;

input
    : expression EOF;

expression
    : scalar
    | vector
    ;

scalar
    : Integer
    | vector '[' Integer ']'
    ;

vector
    : '[' Integer ',' Integer ',' Integer ']'
    | scalar '*' vector
    ;

ANTLR4给我错误:The following sets of rules are mutually left-recursive [scalar, vector].这是有道理的，因为scalar引用了vector，反之亦然，但是同时它应该是确定性的.

ANTLR4 gives me the error: The following sets of rules are mutually left-recursive [scalar, vector]. This makes sense because scalar references vector and vice-versa, but at the same time it should be deterministic.

我将如何重构该语法以避免相互(间接)左递归?我可以扩展其中一个术语，但是这会在完整语法中引入很多重复之处，其中有更多替代选择用于向量和标量.我也可以重构语法以使其具有主表达式，但是我不想允许scalar '*' scalar作为有效的vector替代.还有其他选择吗?

How would I refactor this grammar to avoid the mutual (indirect) left-recursion? I could expand one of the terms inplace, but that would introduce a lot of duplication in the full grammar where there are more alternatives for vector and scalar. I could also refactor the grammar to have a primary expression, but I don't want to allow scalar '*' scalar as a valid vector alternative. Are there other options?

推荐答案

AFAIK不能解决，只能扩展以消除间接递归规则:

AFAIK, there is no way around it but to expand to eliminate the indirect recursive rule:

expression
    : scalar
    | vector
    ;

scalar
    : '[' Integer ',' Integer ',' Integer ']' '[' Integer ']'
    | scalar '*' vector '[' Integer ']'
    | Integer
    ;

vector
    : '[' Integer ',' Integer ',' Integer ']'
    | scalar '*' vector
    ;

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