lr0分析程序的设计与实现

LR(0)分析程序是一种语法分析方法，它通过建立文法的DFA状态转移图，来确定输入的符号串是否可以被该文法所接受。LR(0)分析程序的设计与实现可以大致分为以下几个步骤：

1. 文法预处理：将输入的文法转换为一些易于处理的形式。比如，将文法转换为扩充文法、消除左递归、消除公共左因子等。

2. 构造项集：根据扩充文法，构建出LR(0)项集族。一个项集包含了一些项，每个项表示了一条可能的规约或移进的路径。

3. 构造DFA：基于项集族构建出DFA状态转移图。DFA中的每个状态都是由一个项集生成的，每个转移条件都是由一个文法符号生成的。

4. 构造分析表：对于DFA中的每个状态，构造出对应的分析表，其中包含了移进、规约以及错误处理等操作。这些操作根据当前状态和下一个输入符号来进行。

5. 解析过程：利用构造好的分析表，解析输入的符号串，得到最终的分析结果。如果输入符号串可以被该文法所接受，则输出“accept”；否则输出“error”。

相关问题

LR0分析程序的设计与实现代码

以下是一个简单的 LR(0) 分析程序的设计与实现代码，用 Python 语言实现：

# LR(0) 分析程序

# 标识符常量
SHIFT = 1
REDUCE = 2
ACCEPT = 3
ERROR = 4

# 产生式类
class Production:
    def __init__(self, head, body):
        self.head = head
        self.body = body

# 项目类
class Item:
    def __init__(self, production, dot):
        self.production = production
        self.dot = dot

    def __eq__(self, other):
        return self.production == other.production and self.dot == other.dot

    def __hash__(self):
        return hash(str(self.production) + str(self.dot))

# LR(0) 分析表类
class LR0Table:
    def __init__(self, grammar):
        self.grammar = grammar
        self.actions = {}
        self.gotos = {}

        # 构造项目集规范族
        self.canonical_collection = self.build_canonical_collection()

        # 构造 LR(0) 分析表
        self.build_table()

    # 构造项目集规范族
    def build_canonical_collection(self):
        # 第一步：初始化
        start_production = self.grammar.productions[0]
        start_item = Item(start_production, 0)
        closure = self.closure(set([start_item]))
        current_state = frozenset(closure)
        canonical_collection = {current_state: closure}

        # 第二步：循环直到项目集规范族没有变化
        while True:
            for item in current_state:
                # 对于每个项目 A -> α·Bβ，进行 GOTO 操作
                if not item.dot == len(item.production.body):
                    symbol = item.production.body[item.dot]
                    goto = self.goto(current_state, symbol)
                    if not goto in canonical_collection:
                        closure = self.closure(goto)
                        canonical_collection[goto] = closure

            # 如果项目集规范族没有变化，则退出循环
            if len(canonical_collection) == len(current_state):
                break
            else:
                current_state = list(canonical_collection.keys())[-1]

        return canonical_collection

    # 求闭包
    def closure(self, items):
        closure = set(items)
        while True:
            new_items = set()
            for item in closure:
                # 对于每个项目 A -> α·Bβ，将 B -> γ 加入 new_items
                if not item.dot == len(item.production.body):
                    symbol = item.production.body[item.dot]
                    if symbol in self.grammar.non_terminals:
                        for production in self.grammar.productions:
                            if production.head == symbol:
                                new_item = Item(production, 0)
                                if not new_item in closure:
                                    new_items.add(new_item)
            if not new_items:
                break
            closure |= new_items

        return closure

    # 求 GOTO(A -> α·Bβ, b)
    def goto(self, items, symbol):
        goto = set()
        for item in items:
            if not item.dot == len(item.production.body) and item.production.body[item.dot] == symbol:
                goto.add(Item(item.production, item.dot + 1))
        return frozenset(self.closure(goto))

    # 构造 LR(0) 分析表
    def build_table(self):
        for i, state in enumerate(self.canonical_collection):
            # 对于每个项目 A -> α·，将 ACTION[s, a] 设为 SHIFT(t)，其中 t = GOTO[s, a]
            for item in state:
                if item.dot == len(item.production.body):
                    if item.production.head == self.grammar.start_symbol:
                        self.actions[(i, '$')] = (ACCEPT, None)
                    else:
                        for symbol in self.grammar.follow(item.production.head):
                            self.actions[(i, symbol)] = (REDUCE, item.production)
                else:
                    symbol = item.production.body[item.dot]
                    goto = self.goto(state, symbol)
                    if symbol in self.grammar.terminals:
                        self.actions[(i, symbol)] = (SHIFT, goto)
                    else:
                        self.gotos[(i, symbol)] = goto

    # 执行 LR(0) 分析
    def parse(self, input):
        stack = [0]
        output = []
        while True:
            state = stack[-1]
            symbol = input[0]
            if (state, symbol) in self.actions:
                action, arg = self.actions[(state, symbol)]
                if action == SHIFT:
                    stack.append(arg)
                    input = input[1:]
                elif action == REDUCE:
                    head = arg.head
                    body = arg.body
                    output.append(arg)
                    for i in range(len(body)):
                        stack.pop()
                    state = stack[-1]
                    stack.append(self.gotos[(state, head)])
                elif action == ACCEPT:
                    output.append(arg)
                    return output
                else:
                    raise Exception('Syntax error')
            else:
                raise Exception('Syntax error')

此代码实现了 LR(0) 分析程序的主要功能，包括构造项目集规范族、构造 LR(0) 分析表和执行 LR(0) 分析。使用时需要提供一个文法对象（包括产生式和起始符号）和一个输入串。输出为分析树或语法错误。

LR0分析程序的设计与实现代码，使用C语言

以下是一个简单的LR(0)分析程序的设计和实现代码，使用了C语言：

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#define MAX_STATES 100
#define MAX_SYMBOLS 100
#define MAX_PRODUCTIONS 100

// 定义文法
char *grammar[] = {
    "S->E",
    "E->E+T",
    "E->T",
    "T->T*F",
    "T->F",
    "F->(E)",
    "F->id"
};
int num_symbols = 5;

// 定义项目
char *closure(char **I, int n) {
    char **J = I;
    int m = n;
    while (1) {
        int item_added = 0;
        for (int i = 0; i < m; i++) {
            char *item = J[i];
            int dot_pos = strchr(item, '.') - item;
            if (dot_pos == strlen(item) - 1) {
                continue;
            }
            char next_symbol = item[dot_pos + 1];
            if (next_symbol >= 'A' && next_symbol <= 'Z') {
                for (int j = 0; j < num_symbols; j++) {
                    if (grammar[j][0] == next_symbol) {
                        char *new_item = malloc(strlen(grammar[j]) + 4);
                        sprintf(new_item, "%c->.%s", next_symbol, grammar[j] + 3);
                        if (!strstr(J[0], new_item) && !strstr(J[m-1], new_item)) {
                            J[m++] = new_item;
                            item_added = 1;
                        } else {
                            free(new_item);
                        }
                    }
                }
            }
        }
        if (!item_added) {
            break;
        }
    }
    char *closure = malloc(m * (strlen(grammar[0]) + 1));
    strcpy(closure, J[0]);
    for (int i = 1; i < m; i++) {
        strcat(closure, "/");
        strcat(closure, J[i]);
    }
    return closure;
}

// 定义goto函数
int goto(char **I, int n, char X, char **J) {
    int m = 0;
    for (int i = 0; i < n; i++) {
        char *item = I[i];
        int dot_pos = strchr(item, '.') - item;
        if (dot_pos == strlen(item) - 1) {
            continue;
        }
        char next_symbol = item[dot_pos + 1];
        if (next_symbol == X) {
            char *new_item = malloc(strlen(item) + 1);
            strcpy(new_item, item);
            new_item[dot_pos] = next_symbol;
            new_item[dot_pos + 1] = '.';
            J[m++] = new_item;
        }
    }
    char *closure_J = closure(J, m);
    int ret = 1;
    for (int i = 0; i < n; i++) {
        if (strcmp(I[i], closure_J) == 0) {
            ret = 0;
            break;
        }
    }
    if (ret) {
        strcpy(I[n], closure_J);
    }
    free(closure_J);
    return ret ? n + 1 : -1;
}

// 构造LR(0)自动机
char *states[MAX_STATES];
int num_states = 1;
char *queue[MAX_STATES];

void construct_LR0_automaton() {
    char *C = closure((char *[]){"S->.E"}, 1);
    states[0] = C;
    queue[0] = C;
    int head = 0, tail = 1;
    while (head < tail) {
        C = queue[head++];
        for (char symbol = 'A'; symbol <= 'Z'; symbol++) {
            char *J[MAX_PRODUCTIONS];
            int m = goto(C, strlen(C), symbol, J);
            if (m > 0) {
                states[num_states] = J[0];
                for (int i = 1; i < m; i++) {
                    strcat(states[num_states], "/");
                    strcat(states[num_states], J[i]);
                }
                queue[tail++] = states[num_states];
                num_states++;
            }
        }
    }
}

// 定义LR(0)分析表
enum Action {
    SHIFT,
    REDUCE,
    ACCEPT
};

struct TableEntry {
    enum Action action;
    int num;
};

struct TableEntry action[MAX_STATES][MAX_SYMBOLS];
int goto_table[MAX_STATES][MAX_SYMBOLS];

void construct_LR0_table() {
    for (int i = 0; i < num_states; i++) {
        for (int j = 0; j < MAX_SYMBOLS; j++) {
            action[i][j].action = -1;
            goto_table[i][j] = -1;
        }
    }
    for (int i = 0; i < num_states; i++) {
        char *C = states[i];
        char *item = strtok(C, "/");
        while (item) {
            int dot_pos = strchr(item, '.') - item;
            if (dot_pos == strlen(item) - 1) {
                for (int j = 0; j < num_symbols; j++) {
                    if (grammar[j][0] == item[0]) {
                        action[i]['$' - 'A'].action = ACCEPT;
                        action[i]['$' - 'A'].num = j;
                        break;
                    }
                }
            } else {
                char X = item[dot_pos + 1];
                if (X >= 'a' && X <= 'z') {
                    action[i][X - 'A'].action = SHIFT;
                    action[i][X - 'A'].num = goto(states, num_states, X, (char *[]){"", ""});
                } else if (X >= 'A' && X <= 'Z') {
                    int j;
                    for (j = 0; j < num_symbols; j++) {
                        if (grammar[j][0] == X) {
                            break;
                        }
                    }
                    action[i][j].action = REDUCE;
                    action[i][j].num = j;
                }
            }
            item = strtok(NULL, "/");
        }
    }
    for (int i = 0; i < num_states; i++) {
        char *C = states[i];
        char *item = strtok(C, "/");
        while (item) {
            int dot_pos = strchr(item, '.') - item;
            if (dot_pos < strlen(item) - 1) {
                char X = item[dot_pos + 1];
                if (X >= 'A' && X <= 'Z') {
                    goto_table[i][X - 'A'] = goto(states, num_states, X, (char *[]){"", ""});
                }
            }
            item = strtok(NULL, "/");
        }
    }
}

// 测试
int parse_LR0(char *string) {
    int stack[MAX_STATES];
    int top = 0;
    stack[top++] = 0;
    char *input_str = malloc(strlen(string) + 2);
    strcpy(input_str, string);
    strcat(input_str, "$");
    int output[MAX_PRODUCTIONS];
    int num_output = 0;
    while (1) {
        int state = stack[top - 1];
        char a = input_str[0];
        if (action[state][a - 'A'].action == -1) {
            printf("error\n");
            return -1;
        }
        switch (action[state][a - 'A'].action) {
            case SHIFT:
                stack[top++] = action[state][a - 'A'].num;
                input_str++;
                break;
            case REDUCE: {
                int num = action[state][a - 'A'].num;
                output[num_output++] = num;
                char *production = grammar[num];
                int len = strlen(production) - 3;
                for (int i = 0; i < len * 2; i++) {
                    top--;
                }
                state = stack[top - 1];
                stack[top++] = goto_table[state][production[0] - 'A'];
                break;
            }
            case ACCEPT:
                output[num_output++] = num_symbols;
                for (int i = 0; i < num_output; i++) {
                    printf("%s\n", grammar[output[i]]);
                }
                return 0;
        }
    }
}

int main() {
    construct_LR0_automaton();
    construct_LR0_table();
    parse_LR0("id+id*id");
    return 0;
}

这段代码实现了一个简单的LR(0)分析程序，包括构造LR(0)自动机和分析表，以及使用分析表进行语法分析的过程。