C# 算术表达式的LR解析

我有LR语法和LR表，用于（1+1），1+（a+1）等表达式

0:E'->E

1:E->E+T

2:E->T

3:T->T*F

4:T->F

5:F->（E）

6:F->id

string[,] ActionTable = 
   //+         *       (       )       id   end     E      T       F 
 {   

 {""     ,""     ,"S4"   ,""     ,"S5"   ,""    ,"1"    ,"2"    ,"3"}, // 0
 {"S6"   ,""     ,""     ,""     ,""     ,"AC"  ,""     ,""     ,"" }, // 1
 {"R2"   ,"S7"   ,""     ,"R2"   ,""     ,"R2"  ,""     ,""      ,""},//2                                                              
 {"R4"   ,"R4"   ,""     ,"R4"   ,""     ,"R4"  ,""     ,""     ,""},  // 3                                
 {""     ,""     ,"S4"   ,""     ,"S5"   ,""    ,"8"    ,"2"    ,"3"}, // 4                                
 {"R6"   ,"R6"   ,""     ,"R6"   ,""     ,"R6"  ,""     ,""     ,""},  // 5                               
 {""     ,""     ,"S4"   ,""     ,"S5"   ,""    ,""     ,"9"    ,"3"}, // 6                                
 {""     ,""     ,"S4"   ,""     ,"S5"   ,""    ,""     ,""     ,"10"},// 7                                
 {"S6"   ,""     ,""     ,"S11"  ,""     ,""    ,""     ,""     ,""},  // 8                                
 {"R1"   ,"S7"   ,""     ,"R1"   ,"R1"   ,""    ,""     ,""     ,""},  // 9                                
  {"R3"   ,"R3"   ,""     ,"R3"   ,"R3"   ,""    ,""     ,""     ,""},  //10                                                               
 {"R5"   ,"R5"   ,""     ,"R5"   ,"R5"   ,""    ,""     ,""     ,""}   //11
                        };

我试图检查像1+1或1+（1*a）+1这样的表达式，但解析器说这个表达式不正确

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我能用我的语法做些什么来修复它呢？

你没有数字的产生式规则。

关于E->E+t，t->F，F->id呢？这是一个很好的观点。假设

id

只映射到变量。也许我应该更改语法？