编写构造一个lr(0)分析器

LR(0)语法分析器的构造过程如下：

1. 对文法进行扩展，添加一个新的起始符号和一个新的产生式，使其成为SLR(1)语法。

2. 构造LR(0)自动机，包括所有可能的状态和转换。

3. 对于每个状态，计算LR(0)项目集并构造相应的分析表。对于每个项目，如果其后面有一个非终结符，则添加一个新的项目到项目集中。

4. 使用构造的分析表对输入的符号串进行分析，最终得到语法分析结果。

以下是一个示例文法和其LR(0)分析器的Python实现：

文法：
S -> E
E -> E + T | T
T -> T * F | F
F -> ( E ) | id

LR(0)分析器实现：

# 定义文法
grammar = {
    'S': ['E'],
    'E': ['E + T', 'T'],
    'T': ['T * F', 'F'],
    'F': ['( E )', 'id']
}

# 构造LR(0)自动机
def closure(items, grammar):
    """
    计算LR(0)项目集闭包
    """
    while True:
        new_items = items.copy()
        for item in items:
            pos = item.index('.')
            if pos == len(item) - 1:
                continue
            symbol = item[pos+1]
            if symbol in grammar:
                for production in grammar[symbol]:
                    new_item = symbol + '->.' + production
                    if new_item not in new_items:
                        new_items.append(new_item)
        if new_items == items:
            break
        items = new_items
    return items

def goto(items, symbol, grammar):
    """
    计算LR(0)项目集的GOTO集合
    """
    new_items = []
    for item in items:
        pos = item.index('.')
        if pos == len(item) - 1:
            continue
        if item[pos+1] == symbol:
            new_item = item[:pos] + symbol + '.' + item[pos+2:]
            new_items.append(new_item)
    return closure(new_items, grammar)

def construct_lr0_automaton(grammar):
    """
    构造LR(0)自动机
    """
    automaton = {}
    start_item = 'S->.E'
    start_state = closure([start_item], grammar)
    automaton[0] = start_state
    state_count = 1
    state_dict = {str(start_state): 0}
    state_queue = [start_state]
    while state_queue:
        state = state_queue.pop(0)
        for symbol in grammar.keys():
            next_state = goto(state, symbol, grammar)
            if not next_state:
                continue
            if str(next_state) not in state_dict:
                state_dict[str(next_state)] = state_count
                automaton[state_count] = next_state
                state_queue.append(next_state)
                state_count += 1
            automaton[state_dict[str(state)]][symbol] = state_dict[str(next_state)]
    return automaton

# 构造LR(0)分析表
def construct_lr0_table(automaton, grammar):
    """
    构造LR(0)分析表
    """
    table = {}
    for state, items in automaton.items():
        for item in items:
            pos = item.index('.')
            if pos == len(item) - 1:
                for i, symbol in enumerate(grammar.keys()):
                    if symbol == item[0]:
                        table[(state, symbol)] = ('acc', None)
                        break
                continue
            symbol = item[pos+1]
            if symbol in grammar:
                goto_state = automaton[state][symbol]
                table[(state, symbol)] = ('shift', goto_state)
            else:
                for production in grammar[item[0]]:
                    if production == 'epsilon':
                        follow_set = grammar[item[0]]
                    else:
                        follow_set = set(production)
                    for follow_symbol in follow_set:
                        table[(state, follow_symbol)] = ('reduce', item[0]+'->'+production)
    return table

# LR(0)分析器
def lr0_parser(input_string, automaton, table):
    """
    LR(0)分析器
    """
    input_list = input_string.split()
    stack = [0]
    output = []
    input_pos = 0
    while True:
        state = stack[-1]
        symbol = input_list[input_pos] if input_pos < len(input_list) else '$'
        action, value = table.get((state, symbol), (None, None))
        if action == 'shift':
            stack.append(value)
            input_pos += 1
        elif action == 'reduce':
            production = value
            lhs, rhs = production.split('->')
            rhs_len = len(rhs)
            for i in range(rhs_len):
                stack.pop()
            state = stack[-1]
            stack.append(automaton[state][lhs])
            output.append(production)
        elif action == 'acc':
            return output
        else:
            raise ValueError('Invalid input string')

使用示例：

automaton = construct_lr0_automaton(grammar)
table = construct_lr0_table(automaton, grammar)
input_string = 'id + id * id'
output = lr0_parser(input_string, automaton, table)
print(output)  # ['S->E', 'E->T', 'T->F', 'F->id', 'T->T*F', 'F->id', 'E->E+T', 'T->T*F', 'F->id']

以上就是LR(0)分析器的构造过程和Python实现，希望对你有所帮助！