SLR(1)分析表构建步骤及完整代码实现

SLR(1)分析表是编译原理中的重要概念，用于语法分析。以下是SLR(1)分析表的构建步骤及Python代码实现：

步骤：

计算FIRST集和FOLLOW集: - 对于每个非终结符A，求出A的FIRST集合和FOLLOW集合。 - 对于每个产生式A → α，将FIRST(α)中的所有终结符加入到A的FOLLOW集合中。
构建分析表: - 对于每个产生式A → α: - 对于FIRST(α)中的每个终结符a，将'A → α'加入到ACTION[A, a]中。 - 如果ε ∈ FIRST(α)，则对于FOLLOW(A)中的每个终结符a，将'A → α'加入到ACTION[A, a]中。 - 对于每个非终结符A，对于FOLLOW(A)中的每个终结符a，将'A → ε'加入到ACTION[A, a]中。 - 对于每个状态i，对于每个终结符a，如果GOTO[i, a] = j，则将GOTO[i, a]加入到GOTO表中。

**Python代码实现:**python# 计算某个符号的FIRST集合def first(symbol, productions, first_dict): if symbol in first_dict: return first_dict[symbol] if symbol.is_terminal(): return set([symbol]) result = set() for production in productions[symbol]: if production.is_empty(): result.add('ε') else: first_set = first(production[0], productions, first_dict) result |= first_set i = 1 while 'ε' in first_set and i < len(production): first_set = first(production[i], productions, first_dict) result |= (first_set - set(['ε'])) i += 1 if i == len(production) and 'ε' in first_set: result.add('ε') first_dict[symbol] = result return result

计算所有符号的FIRST集合def compute_first_set(start_symbol, productions): first_dict = {} for symbol in productions: first(symbol, productions, first_dict) return first_dict

计算某个非终结符的FOLLOW集合def follow(symbol, start_symbol, productions, first_dict, follow_dict): if symbol in follow_dict: return follow_dict[symbol] result = set() if symbol == start_symbol: result.add('$') for non_terminal in productions: for production in productions[non_terminal]: if symbol in production: i = production.index(symbol) if i == len(production) - 1: result |= follow(non_terminal, start_symbol, productions, first_dict, follow_dict) else: first_set = first(production[i + 1], productions, first_dict) result |= (first_set - set(['ε'])) if 'ε' in first_set: result |= follow(non_terminal, start_symbol, productions, first_dict, follow_dict) follow_dict[symbol] = result return result

计算所有非终结符的FOLLOW集合def compute_follow_set(start_symbol, productions, first_dict): follow_dict = {} for non_terminal in productions: follow(non_terminal, start_symbol, productions, first_dict, follow_dict) return follow_dict

构建SLR(1)分析表def build_slr1_table(start_symbol, productions, terminals, states, goto_dict): first_dict = compute_first_set(start_symbol, productions) follow_dict = compute_follow_set(start_symbol, productions, first_dict) table = {} for i, state in enumerate(states): for symbol in [start_symbol] + terminals: if symbol in goto_dict[i]: j = goto_dict[i][symbol] if symbol in terminals: table[(i, symbol)] = ('S', j) else: table[(i, symbol)] = ('G', j) for item in state: production = item.production if item.dot_index == len(production): for symbol in follow_dict[production.left]: if (i, symbol) in table: raise ValueError('Conflict in state {} with symbol {}'.format(i, symbol)) table[(i, symbol)] = ('R', production) elif production[item.dot_index].is_terminal(): symbol = production[item.dot_index] j = goto_dict[i][symbol] table[(i, symbol)] = ('S', j) return table

示例输入start_symbol = 'S'terminals = ['id', '+', '', '(', ')', '$']productions = { 'S': [['E']], 'E': [['E', '+', 'T'], ['T']], 'T': [['T', '', 'F'], ['F']], 'F': [['(', 'E', ')'], ['id']]}

示例状态集和GOTO函数 (需要根据具体文法计算)states = [ # ...]goto_dict = { # ...}

构建SLR(1)分析表table = build_slr1_table(start_symbol, productions, terminals, states, goto_dict)

打印分析表for (state, symbol), action in table.items(): print('({}, {}): {}'.format(state, symbol, action))

注意: 上述代码中的 states 和 goto_dict 需要根据具体文法计算得到，这里仅提供示例结构。

希望以上内容能够帮助您理解和掌握SLR(1)分析表的构建方法。