compiler-construction - LL(1) grammar and indexing operator [ ]

Question

I would like to learn how to solve transferring grammar to LL(1). I have following problem:

E -> E + E
E -> E * E
E -> E[ E ]
E -> int
E -> id

Regarding operators '+' and '*' I know the solution:

E -> TA
A -> + TA
A -> epsilon

T -> FB
B -> * FB
B -> epsilon

the problem is what to do with indexing operator while in the same time we have to avoid left recursion?

Does anybody know the solution?

Thanks.

Answer 1

（来自评论）：

基于算术运算符的建议解决方案：

E -> T A
A -> + T A
A -> epsilon

T -> F B
B -> * F B
B -> epsilon

我们可以添加几乎类似的：

F -> G C
F -> int
C -> [ E ] C
C -> epsilon

并完成：

G -> id
G -> ( E )

最后一行带括号的表达式不在原始问题中，但添加它似乎是合理的。该F节与其他两个节的不同之处在于它拒绝整数文字的索引表达式（3[x]例如），尽管目标语言可能允许（C例如，它允许）在这种情况下F -> int应该用原始的G -> int.