设计实现简单表达式的SLR(1)分析器

下面是设计实现简单表达式的SLR(1)分析器的具体步骤：

1. 构造文法的FIRST集和FOLLOW集。

假设文法为：

E -> E + T | T
T -> T * F | F
F -> ( E ) | id

其FIRST集和FOLLOW集如下：

- FIRST(E) = {(, id}
- FIRST(T) = {(, id}
- FIRST(F) = {(, id}
- FOLLOW(E) = {), $, +}
- FOLLOW(T) = {), $, +, *}
- FOLLOW(F) = {), $, +, *, id}

2. 构造DFA状态转移图。

首先，将S'->.E加入初始状态闭包中，即{S'->.E}。然后，对于每个状态，依次考虑每个文法符号X（包括终结符和非终结符），求出它的闭包，并将它们作为出边添加到DFA中。如果某个闭包已经存在于某个状态中，则不需要再次添加。

以状态{E->E+.T}为例：

- X = (，闭包为{E->.(E+T), T->.T*F, F->.(E), F->.id}，添加出边E->{E->(E.+T), T->.T*F, F->.(E), F->.id}
- X = id，闭包为{F->.id}，添加出边E->{F->id.}
- X = +，没有闭包，不添加出边
- X = *，没有闭包，不添加出边

最终得到的DFA状态转移图如下所示：

        +-------+    (    +-------+
        |   0   |-------->|   1   |
        +-------+          +---+---+
           | id             | F->id |
           |                +-------+
        +--+----+    E     +-------+
        |   2   |-------->|   3   |
        +-------+          +-+---+-+
           | (              | E->(E.+T)
           |                | T->.T*F
        +--+----+          | F->.(E)
        |   4   |    id    | F->.id
        +-------+----------> +-+-+
                             | E->E+.T
                             +---+

3. 构造ACTION和GOTO表。

根据DFA状态转移图，ACTION和GOTO表可以如下构造：

STATE | ACTION                            | GOTO
------+----------------------------------+------
  0   | ( -> shift 4, id -> shift 5       | E -> 2, T -> 6, F -> 7
      +----------------------------------+
  1   | + -> shift 8                      | 
      | ) -> reduce E -> T                |
      | $ -> reduce E -> T                |
      +----------------------------------+
  2   | + -> shift 9, $ -> accept         | 
      | ) -> reduce E -> T                |
      +----------------------------------+
  3   | + -> reduce T -> F                | 
      | * -> shift 10, ) -> reduce T -> F |
      | $ -> reduce T -> F                |
      +----------------------------------+
  4   | ( -> shift 4, id -> shift 5       | E -> 2, T -> 6, F -> 7
      +----------------------------------+
  5   | + -> reduce F -> id               | 
      | * -> reduce F -> id               |
      | ) -> reduce F -> id               |
      | $ -> reduce F -> id               |
      +----------------------------------+
  6   | + -> reduce E -> E+T              | 
      | * -> reduce E -> E+T              |
      | ) -> reduce E -> E+T              |
      | $ -> reduce E -> E+T              |
      +----------------------------------+
  7   | + -> reduce T -> F*               | 
      | * -> reduce T -> F*               |
      | ) -> reduce T -> F*               |
      | $ -> reduce T -> F*               |
      +----------------------------------+
  8   | ( -> shift 4, id -> shift 5       | T -> 11, F -> 7
      +----------------------------------+
  9   | ( -> shift 4, id -> shift 5       | T -> 12, F -> 7
      +----------------------------------+
  10  | ( -> shift 4, id -> shift 5       | F -> 13
      +----------------------------------+
  11  | + -> reduce F -> id               | 
      | * -> reduce F -> id               |
      | ) -> reduce F -> id               |
      | $ -> reduce F -> id               |
      +----------------------------------+
  12  | + -> reduce T -> T*F              | 
      | * -> reduce T -> T*F              |
      | ) -> reduce T -> T*F              |
      | $ -> reduce T -> T*F              |
      +----------------------------------+
  13  | + -> reduce F -> (E)              | 
      | * -> reduce F -> (E)              |
      | ) -> reduce F -> (E)              |
      | $ -> reduce F -> (E)              |
      +----------------------------------+

最后，将构造出的SLR(1)分析器实现为C语言程序即可。