コンパイル原理実験 3: 演算子優先度分析アルゴリズムの設計と実装 (Python)

目的

演算子優先解析法によれば、式を解析することにより、式が正しいかどうかを判断することができる。演算子優先の解析手法の実践を通じて、ボトムアップ構文解析手法の理解を深めます。

実験内容

1. 文法を入力します。これは、次の算術式の文法になります (必要に応じて変更できます):
E→E+T|ET|T
T→T*F|T/F|F
F→(E)|i
2.与えられた式を解析し、式が正しいかどうかの判定を出力します。
プログラム入出力例：
入力：1+2、
出力：正しい
入力：(1+2)/3+4-(5+6/7)、
出力：正しい
入力：((1-2)/3+4
出力：エラー
入力：1+2-3+(*4/5)
出力：エラー

実験手順

(1) 文法読み込み、データ前処理
ファイルから文法、終端記号、非終端記号を読み込みます。この部分の処理は実験2の文法の読み方と一致しています。

def data_input():  # 读取文法
    with open("input2.txt", 'r+', encoding="utf-8") as f:
        temp = f.readlines()
    for i in temp:
        line = str(i.strip("\n"))
        formules.append(line)
        if line[0] not in non_ter:
            non_ter.append(line[0])
            grammarElement.setdefault(line[0], line[5:])
        else:
            grammarElement[line[0]] += "|" + line[5:]
    for i in temp:
        line = str(i.strip("\n")).replace(" -> ", "")
        for j in line:
            if j not in non_ter and j not in terSymblo:
                terSymblo.append(j)
    if 'ε' in terSymblo: terSymblo.remove('ε')

(2) 最初の VT セットを見つけます。

def get_fistVT(formule):
    x = formule[0]
    ind = non_ter.index(x)
    index = []
    i = 5
    if formule[i] in terSymblo and formule[i] not in firstVT[x]:  # 首位为终结符 P->a...
        firstVT[x] += formule[i]
    elif formule[i] in non_ter:  # 首位为非终结符
        for f in firstVT[formule[i]]:
            if f not in firstVT[x]:
                firstVT[x] += f
        if i + 1 < len(formule):
            if formule[i + 1] in terSymblo and formule[i + 1] not in firstVT[x]:  # P->Q..
                firstVT[x] += formule[i + 1]

(3) 最後の VT セットを見つける

def get_lastVT(formule):
    x = formule[0]
    i = len(formule) - 1
    if formule[i] in terSymblo and formule[i] not in lastVT[x]:
        lastVT[x] += formule[i]
    elif formule[i] in non_ter:
        for f in lastVT[formule[i]]:
            if f not in lastVT[x]:
                lastVT[x] += f
        if formule[i - 1] in terSymblo and formule[i - 1] not in lastVT[x]:
            lastVT[x] += formule[i - 1]

(4) 演算子優先度分析テーブル
も格納用に2次元辞書を使用し、最初に2次元辞書の更新関数を記述する

def addtodict2(thedict, key_a, key_b, val):  # 设置二维字典的函数
    if key_a in thedict.keys():
        thedict[key_a].update({
    
    key_b: val})
    else:
        thedict.update({
    
    key_a: {
    
    key_b: val}})

次に、オペレータ優先度分析テーブルを見つけます。

def analy(formule): #算符优先分析表
    start = 5
    end = len(formule) - 2
    if start == end: return
    for i in range(start, end):
        if formule[i] in terSymblo and formule[i + 1] in terSymblo:
            addtodict2(data, formule[i], formule[i + 1], "=")
        if formule[i] in terSymblo and formule[i + 1] in non_ter and formule[i + 2] in terSymblo:
            addtodict2(data, formule[i], formule[i + 2], "=")
        if formule[i] in terSymblo and formule[i + 1] in non_ter:
            for j in firstVT[formule[i + 1]]:
                addtodict2(data, formule[i], j, "<")
        if formule[i] in non_ter and formule[i + 1] in terSymblo:
            for j in lastVT[formule[i]]:
                addtodict2(data, j, formule[i + 1], ">")
        if formule[i + 1] in terSymblo and formule[i + 2] in non_ter:
            for j in firstVT[formule[i + 2]]:
                addtodict2(data, formule[i + 1], j, "<")
        if formule[i + 1] in non_ter and formule[i + 2] in terSymblo:
            for j in lastVT[formule[i + 1]]:
                addtodict2(data, j, formule[i + 2], ">")

(5) オペレータ優先アルゴリズムの解析プロセス
まず、プロセスで使用するプロセス関数です。

def reverseString(string):
    return string[::-1]

2 つのスタックを初期化する

def initStack(string):
   # 分析栈，入栈#
   analysisStack = "#"
   # 当前输入串入栈，即string逆序入栈
   currentStack = reverseString(string)
   # 调用分析函数
   toAnalyze(analysisStack, currentStack)

分析スタックの最上位の終端要素を検索し、その要素とその添字を返します。

def findVTele(string):
    ele = '\0'
    ele_index = 0
    for i in range(len(string)):
        if (string[i] in terSymblo):
            ele = string[i]
            ele_index = i
    return ele, ele_index
    ```
然后才是具体分析过程
根据栈中内容进行分析
```python
def toAnalyze(analysisStack, currentStack):
    global analyzeResult
    global analyzeStep
    analyzeStep += 1
    analysisStack_top, analysisStack_index = findVTele(analysisStack)  # 分析栈最顶终结符元素及下标
    currentStack_top = currentStack[-1]  # 当前输入串栈顶
    relation = data[analysisStack_top][currentStack_top]
    if relation == '<':
        print(" {:^5} {:^15} {:^9} {:^15} {:^12} ".format(analyzeStep, analysisStack, relation,
                                                          reverseString(currentStack), '移进'))
        analysisStack += currentStack_top
        currentStack = currentStack[:-1]
        toAnalyze(analysisStack, currentStack)
    elif relation == '>':
        print(" {:^5} {:^15} {:^9} {:^15} {:^12} ".format(analyzeStep, analysisStack, relation,
                                                          reverseString(currentStack), '归约'))
        currenChar = analysisStack_top
        temp_string = ""
        for i in range(len(analysisStack) - 1, -1, -1):
            if (analysisStack[i] >= 'A' and analysisStack[i] <= 'Z'):
                temp_string = analysisStack[i] + temp_string
                continue
            elif (data[analysisStack[i]][currenChar] == '<'):
                break;
            temp_string = analysisStack[i] + temp_string
            currenChar = analysisStack[i]
        if (temp_string in sentencePattern):
            analysisStack = analysisStack[0:i + 1]
            analysisStack += 'N'
            toAnalyze(analysisStack, currentStack)
        else:
            print("归约出错！待归约串为：", temp_string, "--->产生式右部无此句型！")
            analyzeResult = False
            return
    elif (relation == '='):
        if (analysisStack_top == '#' and currentStack_top == '#'):
            print(" {:^5} {:^15} {:^9} {:^15} {:^12} ".format(analyzeStep, analysisStack, relation,
                                                              reverseString(currentStack), '完成'))
            analyzeResult = True
            return
        else:
            print(" {:^5} {:^15} {:^9} {:^15} {:^12} ".format(analyzeStep, analysisStack, relation,
                                                              reverseString(currentStack), '移进'))
            analysisStack += currentStack_top
            currentStack = currentStack[:-1]
            toAnalyze(analysisStack, currentStack)
    elif (relation == None):
        print(" {:^5} {:^15} {:^9} {:^15} {:^12} ".format(analyzeStep, analysisStack, 'None',
                                                          reverseString(currentStack), '报错'))
        analyzeResult = False
        return

(6) その後はメインプログラムであり、各プログラムの動作と解析プロセスの出力を制御します。

data_input()
data = dict()
for i in non_ter:
    firstVT.setdefault(i, "")
    lastVT.setdefault(i, "")
for i in terSymblo:
    for j in terSymblo:
        addtodict2(data, i, j, '')
#print(data)
sym = non_ter + terSymblo

for n in range(10):
    for i in formules:
        get_fistVT(i)
        get_lastVT(i)
print("firstVT集合：")
for i in non_ter:
    print(i+" : "+firstVT[i])
print("lastVT集合：")
for i in non_ter:
    print(i+" : "+lastVT[i])

temp2 = Start +" -> #" +Start+"#"
formules.append(temp2)
for i in formules:
    analy(i)
print("算符优先分析表")
for i in terSymblo:
    print("\t" + i.ljust(4), end="")
print()
for i in terSymblo:
    print(i.ljust(4), end="")
    for j in terSymblo:
        if j in data[i]:
            print(data[i][j].ljust(8), end="")
        else:
            print("\t\t", end="")
    print()

sentencePattern = ["N+N", "N*N", "N/N", "(N)", "i","N^N","N,N","a"]
analyzeResult = False
analyzeStep = 0
print("请输入待分析的字符串：")
string = input()
string = string.replace(" ", "")
string+="#"
print(" {:^4} {:^13} {:^6} {:^12} {:^10} ".format('步骤', '分析栈', '优先关系', '当前输入串', '移进或归约'))
initStack(string)
if (analyzeResult):
    print("该字符串是文法的合法句子。\n")
else:
    print("该字符串不是文法的合法句子。\n")

トータルプログラム

import re

grammarElement = {
    
    }
terSymblo = ['#']
non_ter = []
Start = 'S'
allSymbol = []  # 所有符号
firstVT = {
    
    }  # FIRSTVT集
lastVT = {
    
    }  # lastVT集
formules = []

def data_input():  # 读取文法
    with open("input2.txt", 'r+', encoding="utf-8") as f:
        temp = f.readlines()
    for i in temp:
        line = str(i.strip("\n"))
        formules.append(line)
        if line[0] not in non_ter:
            non_ter.append(line[0])
            grammarElement.setdefault(line[0], line[5:])
        else:
            grammarElement[line[0]] += "|" + line[5:]
    for i in temp:
        line = str(i.strip("\n")).replace(" -> ", "")
        for j in line:
            if j not in non_ter and j not in terSymblo:
                terSymblo.append(j)
    if 'ε' in terSymblo: terSymblo.remove('ε')


def get_fistVT(formule):
    x = formule[0]
    ind = non_ter.index(x)
    index = []
    i = 5
    if formule[i] in terSymblo and formule[i] not in firstVT[x]:  # 首位为终结符 P->a...
        firstVT[x] += formule[i]
    elif formule[i] in non_ter:  # 首位为非终结符
        for f in firstVT[formule[i]]:
            if f not in firstVT[x]:
                firstVT[x] += f
        if i + 1 < len(formule):
            if formule[i + 1] in terSymblo and formule[i + 1] not in firstVT[x]:  # P->Q..
                firstVT[x] += formule[i + 1]

def get_lastVT(formule):
    x = formule[0]
    i = len(formule) - 1
    if formule[i] in terSymblo and formule[i] not in lastVT[x]:
        lastVT[x] += formule[i]
    elif formule[i] in non_ter:
        for f in lastVT[formule[i]]:
            if f not in lastVT[x]:
                lastVT[x] += f
        if formule[i - 1] in terSymblo and formule[i - 1] not in lastVT[x]:
            lastVT[x] += formule[i - 1]

def addtodict2(thedict, key_a, key_b, val):  # 设置二维字典的函数
    if key_a in thedict.keys():
        thedict[key_a].update({
    
    key_b: val})
    else:
        thedict.update({
    
    key_a: {
    
    key_b: val}})

def analy(formule): #算符优先分析表
    start = 5
    end = len(formule) - 2
    if start == end: return
    for i in range(start, end):
        if formule[i] in terSymblo and formule[i + 1] in terSymblo:
            addtodict2(data, formule[i], formule[i + 1], "=")
        if formule[i] in terSymblo and formule[i + 1] in non_ter and formule[i + 2] in terSymblo:
            addtodict2(data, formule[i], formule[i + 2], "=")
        if formule[i] in terSymblo and formule[i + 1] in non_ter:
            for j in firstVT[formule[i + 1]]:
                addtodict2(data, formule[i], j, "<")
        if formule[i] in non_ter and formule[i + 1] in terSymblo:
            for j in lastVT[formule[i]]:
                addtodict2(data, j, formule[i + 1], ">")
        if formule[i + 1] in terSymblo and formule[i + 2] in non_ter:
            for j in firstVT[formule[i + 2]]:
                addtodict2(data, formule[i + 1], j, "<")
        if formule[i + 1] in non_ter and formule[i + 2] in terSymblo:
            for j in lastVT[formule[i + 1]]:
                addtodict2(data, j, formule[i + 2], ">")

def reverseString(string):
    return string[::-1]

# 初始化两个栈
def initStack(string):
    # 分析栈，入栈#
    analysisStack = "#"
    # 当前输入串入栈，即string逆序入栈
    currentStack = reverseString(string)
    # 调用分析函数
    toAnalyze(analysisStack, currentStack)

# 寻找分析栈最顶终结符元素，返回该元素及其下标
def findVTele(string):
    ele = '\0'
    ele_index = 0
    for i in range(len(string)):
        if (string[i] in terSymblo):
            ele = string[i]
            ele_index = i
    return ele, ele_index

# 根据栈中内容进行分析
def toAnalyze(analysisStack, currentStack):
    global analyzeResult
    global analyzeStep
    analyzeStep += 1
    analysisStack_top, analysisStack_index = findVTele(analysisStack)  # 分析栈最顶终结符元素及下标
    currentStack_top = currentStack[-1]  # 当前输入串栈顶
    relation = data[analysisStack_top][currentStack_top]
    if relation == '<':
        print(" {:^5} {:^15} {:^9} {:^15} {:^12} ".format(analyzeStep, analysisStack, relation,
                                                          reverseString(currentStack), '移进'))
        analysisStack += currentStack_top
        currentStack = currentStack[:-1]
        toAnalyze(analysisStack, currentStack)
    elif relation == '>':
        print(" {:^5} {:^15} {:^9} {:^15} {:^12} ".format(analyzeStep, analysisStack, relation,
                                                          reverseString(currentStack), '归约'))
        currenChar = analysisStack_top
        temp_string = ""
        for i in range(len(analysisStack) - 1, -1, -1):
            if (analysisStack[i] >= 'A' and analysisStack[i] <= 'Z'):
                temp_string = analysisStack[i] + temp_string
                continue
            elif (data[analysisStack[i]][currenChar] == '<'):
                break;
            temp_string = analysisStack[i] + temp_string
            currenChar = analysisStack[i]
        if (temp_string in sentencePattern):
            analysisStack = analysisStack[0:i + 1]
            analysisStack += 'N'
            toAnalyze(analysisStack, currentStack)
        else:
            print("归约出错！待归约串为：", temp_string, "--->产生式右部无此句型！")
            analyzeResult = False
            return
    elif (relation == '='):
        if (analysisStack_top == '#' and currentStack_top == '#'):
            print(" {:^5} {:^15} {:^9} {:^15} {:^12} ".format(analyzeStep, analysisStack, relation,
                                                              reverseString(currentStack), '完成'))
            analyzeResult = True
            return
        else:
            print(" {:^5} {:^15} {:^9} {:^15} {:^12} ".format(analyzeStep, analysisStack, relation,
                                                              reverseString(currentStack), '移进'))
            analysisStack += currentStack_top
            currentStack = currentStack[:-1]
            toAnalyze(analysisStack, currentStack)
    elif (relation == None):
        print(" {:^5} {:^15} {:^9} {:^15} {:^12} ".format(analyzeStep, analysisStack, 'None',
                                                          reverseString(currentStack), '报错'))
        analyzeResult = False
        return

data_input()
data = dict()
for i in non_ter:
    firstVT.setdefault(i, "")
    lastVT.setdefault(i, "")
for i in terSymblo:
    for j in terSymblo:
        addtodict2(data, i, j, '')
#print(data)
sym = non_ter + terSymblo

for n in range(10):
    for i in formules:
        get_fistVT(i)
        get_lastVT(i)
print("firstVT集合：")
for i in non_ter:
    print(i+" : "+firstVT[i])
print("lastVT集合：")
for i in non_ter:
    print(i+" : "+lastVT[i])

temp2 = Start +" -> #" +Start+"#"
formules.append(temp2)
for i in formules:
    analy(i)
print("算符优先分析表")
for i in terSymblo:
    print("\t" + i.ljust(4), end="")
print()
for i in terSymblo:
    print(i.ljust(4), end="")
    for j in terSymblo:
        if j in data[i]:
            print(data[i][j].ljust(8), end="")
        else:
            print("\t\t", end="")
    print()

sentencePattern = ["N+N", "N*N", "N/N", "(N)", "i","N^N","N,N","a"]
analyzeResult = False
analyzeStep = 0
print("请输入待分析的字符串：")
string = input()
string = string.replace(" ", "")
string+="#"
print(" {:^4} {:^13} {:^6} {:^12} {:^10} ".format('步骤', '分析栈', '优先关系', '当前输入串', '移进或归约'))
initStack(string)
if (analyzeResult):
    print("该字符串是文法的合法句子。\n")
else:
    print("该字符串不是文法的合法句子。\n")

テスト

文法をテストする

S -> a
S -> ^
S -> (T)
T -> T,S
T -> S

終了