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LR.py
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LR.py
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from collections import defaultdict
from FiniteAutomata import *
class LR:
def __init__(self):
self.projects = defaultdict(defaultdict) # e.g. 1. S' -> ·S: projects[S'][·S] = 1 记录所有项目及编号
self.sorted_projects = dict() # e.g. 1. S' -> ·S: sorted_projects[1] = (S', ·S) 根据编号查找项目
self.projectSet = dict() # 项目集
self.production = [] # 产生式
# e.g. 3. A -> ·aA, 1. A -> aA: production_numdict[A][·aA] = 1 项目对应的产生式编号
self.production_numdict = defaultdict(defaultdict)
self.dfa = FA()
self.projects_num = 0
self.startsymbol = None
self.nonterminals = []
def setStart(self, startsy):
self.startsymbol = startsy
self.nonterminals.append(startsy)
def addNonterminals(self, symbol):
if symbol in Upper:
if symbol not in self.nonterminals:
self.nonterminals.append(symbol)
return True
return False
def addProjects(self, fromexp, toexp):
tmp = ''
for ch in toexp:
if ch != epsilon:
tmp += ch
toexp = tmp
for cut in range(0, len(toexp) + 1):
tmp = toexp[:cut] + dot + toexp[cut:]
self.projects_num += 1
self.production_numdict[fromexp][tmp] = len(self.production)
self.projects[fromexp][tmp] = self.projects_num
self.sorted_projects[self.projects_num] = (fromexp, tmp)
self.production.append((fromexp, toexp))
def scan(self, filetxt):
lines = filetxt.readlines()
if lines[0][0] not in Upper:
return False
self.setStart('S\'')
self.addProjects('S\'', lines[0][0]) # add augmented grammar 添加拓广文法
self.projectSet[0] = {(self.startsymbol, dot + lines[0][0])}
for line in lines:
if not self.addNonterminals(line[0]):
return False
if '\n' in line:
line = line[:-1]
fromexp = line[0]
tmp = ''
for s in line[3:]:
if s == '|':
self.addProjects(fromexp, tmp)
tmp = ''
continue
tmp += s
self.dfa.addSymbol(s)
self.addProjects(fromexp, tmp)
def getClosure(self, fromexp):
pst = set()
for toexp in self.projects[fromexp]:
if toexp.find(dot) == 0:
pst.add((fromexp, toexp))
return pst
def getProjectSet(self, pst): # 获得整个项目集
vis = set()
while len(vis) != len(pst):
for pj in pst:
if pj in vis:
continue
vis.add(pj)
nxtpos = pj[1].find(dot) + 1
if nxtpos == len(pj[1]) or pj[1][nxtpos] not in Upper:
continue
pst = pst.union(self.getClosure(pj[1][nxtpos]))
return pst
def getNxtStateId(self, fromst, sy): # get next project set id 根据当前项目集编号和获得符号获得下一个项目集编号
if fromst not in self.sy2stat or sy not in self.sy2stat[fromst]:
self.projectset_num += 1
self.sy2stat[fromst][sy] = self.projectset_num
stnum = self.projectset_num
else:
return self.sy2stat[fromst][sy], False
return stnum, True
def addProjectSet(self, Iid, project):
if isinstance(project, tuple):
project = set([project])
if Iid in self.projectSet:
self.projectSet[Iid] = self.projectSet[Iid].union(project)
else:
self.projectSet[Iid] = project
def BuildSimpleDFA(self): # do not contain lookahead terminals
self.sy2stat = defaultdict(defaultdict) # sy2stat[next_project_set_i_id][get_one_symbol] = next_project_set_j_id
self.projectset_num = 0
self.dfa.setStart(0)
q = [0]
while len(q):
Iid = q.pop()
self.projectSet[Iid] = self.getProjectSet(self.projectSet[Iid])
tmpdict = dict() # get one symbol and move to next project set, tmpdict[symbol] = next_project_set
for pj in self.projectSet[Iid]:
nxtpos = pj[1].find(dot) + 1
if nxtpos == len(pj[1]):
continue
nxtsy = pj[1][nxtpos]
nxtpj = pj[1][:nxtpos - 1] + nxtsy + dot + pj[1][nxtpos + 1: ] # moving dot behind next symbol 将·后移一个符号
if nxtsy in tmpdict:
tmpdict[nxtsy].add((pj[0], nxtpj))
else:
tmpdict[nxtsy] = set([(pj[0], nxtpj)])
for nxtsy in tmpdict:
tmpdict[nxtsy] = self.getProjectSet(tmpdict[nxtsy])
if tmpdict[nxtsy] in self.projectSet.values():
nxtIid = list(self.projectSet.keys())[list(self.projectSet.values()).index(tmpdict[nxtsy])]
self.dfa.addTransition(Iid, nxtIid, nxtsy)
self.sy2stat[Iid][nxtsy] = nxtIid
continue
nxtIid, flag = self.getNxtStateId(Iid, nxtsy)
if flag:
q.append(nxtIid)
self.addProjectSet(nxtIid, tmpdict[nxtsy])
self.dfa.addTransition(Iid, nxtIid, nxtsy)
def addAction(self, stateid, sy, operation):
if isinstance(operation, str):
operation = set([operation])
if stateid in self.action and sy in self.action[stateid]:
self.action[stateid][sy] = self.action[stateid][sy].union(operation)
else:
self.action[stateid][sy] = operation
def addGoto(self, stateid, sy, operation):
if isinstance(operation, int):
operation = set([operation])
if stateid in self.goto and sy in self.goto[stateid]:
self.goto[stateid][sy] = self.goto[stateid][sy].union(operation)
else:
self.goto[stateid][sy] = operation
def GO(self, state, sy):
return self.sy2stat[state][sy]
def BuildLR0AnalyseTable(self):
self.action = defaultdict(defaultdict)
self.goto = defaultdict(defaultdict)
for Iid in self.projectSet:
for pj in self.projectSet[Iid]:
nxtpos = pj[1].find(dot) + 1
if nxtpos == len(pj[1]):
if self.projects[pj[0]][pj[1]] == 2:
self.addAction(Iid, '#', 'acc')
else:
op = 'r' + str(self.production_numdict[pj[0]][pj[1]])
if self.production_numdict[pj[0]][pj[1]] == 0:
continue
self.addAction(Iid, '#', op)
for sy in self.dfa.symbol:
self.addAction(Iid, sy, op)
continue
nxtsy = pj[1][nxtpos]
op = 'S' + str(self.GO(Iid, nxtsy))
if nxtsy not in Upper:
self.addAction(Iid, nxtsy, op)
else:
self.addGoto(Iid, nxtsy, int(op[1:]))
for stat in self.action:
for sy in self.action[stat]:
if len(self.action[stat][sy]) > 1:
print("It's not a LR(0) grammar.")
return False
print("It's a LR(0) grammar.")
return True
def addFirst(self, nt, sy):
if isinstance(sy, str):
sy = set([sy])
if nt in self.First:
self.First[nt] = self.First[nt].union(sy)
else:
self.First[nt] = sy
def getFirst(self, nt):
if nt in self.First:
return self.First[nt]
for pro in self.production:
if len(pro[1]) == 0:
continue
if pro[0] == nt:
if pro[1][0] not in Upper:
self.addFirst(nt, pro[1][0])
else:
if len(pro[1]) == 1:
self.addFirst(nt, self.getFirst(pro[1]))
else:
l = len(pro[1])
for sy in range(0, l):
if pro[1][sy] == pro[0]:
continue
if sy == l - 1:
self.addFirst(nt, self.getFirst(pro[1]))
elif pro[1][sy] in Upper:
tmp = self.getFirst(pro[1][sy])
if epsilon in tmp:
tmp.remove(epsilon)
self.addFirst(nt, tmp)
else:
self.addFirst(nt, tmp)
break
else:
self.addFirst(nt, pro[1][sy])
break
return self.First[nt]
def addFollow(self, nt, sy):
if isinstance(sy, str):
sy = set([sy])
if nt in self.Follow:
self.Follow[nt] = self.Follow[nt].union(sy)
else:
self.Follow[nt] = sy
def getFollow(self, nt):
if nt in self.Follow:
return self.Follow[nt]
for pro in self.production:
pos = pro[1].find(nt)
if pos == -1:
continue
if pos + 1 == len(pro[1]):
self.addFollow(nt, self.getFollow(pro[0]))
self.addFollow(nt, '#')
elif pro[1][pos + 1] not in Upper:
self.addFollow(nt, pro[1][pos + 1])
else:
l = len(pro[1])
for i in range(pos + 1, l):
if pro[1][i] in Upper:
tmp = self.getFirst(pro[1][i])
if epsilon in tmp:
tmp.remove(epsilon)
self.addFollow(nt, tmp)
if i == l - 1:
self.addFollow(nt, self.getFollow(pro[0]))
else:
self.addFollow(nt, tmp)
break
else:
self.addFollow(nt, pro[1][i])
break
if nt in self.Follow:
return self.Follow[nt]
else:
return set()
def changeAction(self, stateid, sy, operation):
if operation == '':
self.action[stateid].pop(sy)
return
if isinstance(operation, str):
operation = set([operation])
self.action[stateid][sy] = operation
def BuildSLR1AnalyseTable(self):
problem_set = set()
for stat in self.action:
for sy in self.action[stat]:
if len(self.action[stat][sy]) > 1:
problem_set.add(stat)
self.First = dict()
self.Follow = dict()
movein = set()
reduction = []
for stat in problem_set:
for pj in self.projectSet[stat]:
pos = pj[1].find(dot) + 1
if pos == len(pj[1]):
reduction.append((self.production_numdict[pj[0]][pj[1]], self.getFollow(pj[0])))
else:
if pj[1][pos] in Upper:
movein = movein.union(self.getFirst(pj[1][pos]))
else:
movein.add(pj[1][pos])
reduction.append(movein)
l = len(reduction)
for i in range(0, l):
for j in range(0, l):
if i == j:
continue
if isinstance(reduction[i], tuple):
followi = reduction[i][1]
else:
followi = reduction[i]
if isinstance(reduction[j], tuple):
followj = reduction[j][1]
else:
followj = reduction[j]
if len(followi.intersection(followj)):
print("It's not a SLR(1) grammar.")
return False
reduction.pop()
for sy in self.dfa.symbol.union(set('#')):
if sy in movein:
self.changeAction(stat, sy, 'S' + str(self.GO(stat, sy)))
else:
flag = 1
for fol in reduction:
if sy in fol[1]:
self.changeAction(stat, sy, 'r' + str(fol[0]))
flag = 0
break
if flag:
self.changeAction(stat, sy, '')
movein = set()
reduction = []
print("It's a SLR(1) grammar.")
return True
def addLATerminal(self, set_num, project, sy):
if isinstance(sy, str):
sy = set([sy])
if set_num in self.LATerminal and project in self.LATerminal[set_num]:
self.LATerminal[set_num][project] = self.LATerminal[set_num][project].union(sy)
else:
self.LATerminal[set_num][project] = sy
def getClosureLATerminal(self, fromexp, setnum, searchsy):
pst, simple_pst = set(), set()
for toexp in self.projects[fromexp]:
if toexp.find(dot) == 0:
pst.add((fromexp, toexp, tuple(searchsy)))
simple_pst.add((fromexp, toexp))
self.addLATerminal(setnum, (fromexp, toexp), searchsy)
return pst, simple_pst
def getProjectSetLATerminal(self, pst, simple_pst, setnum):
vis = set()
while len(vis) != len(pst):
for pj in pst:
tpj = (pj[0], pj[1])
if pj in vis:
continue
vis.add(pj)
nxtpos = pj[1].find(dot) + 1
if nxtpos == len(pj[1]) or pj[1][nxtpos] not in Upper:
continue
nxtposLA = nxtpos + 1
if nxtposLA == len(pj[1]):
if setnum not in self.LATerminal or tpj not in self.LATerminal[setnum]:
vis.remove(pj)
continue
sy = self.LATerminal[setnum][tpj]
elif pj[1][nxtposLA] not in Upper:
sy = pj[1][nxtposLA]
else:
sy = self.getFirst(pj[1][nxtpos])
tmpst, stmpst = self.getClosureLATerminal(pj[1][nxtpos], setnum, sy)
pst = pst.union(tmpst)
simple_pst = simple_pst.union(stmpst)
return pst, simple_pst
def addSimpleProjectSet(self, Iid, project):
if isinstance(project, tuple):
project = set([project])
if Iid in self.simple_projectSet:
self.simple_projectSet[Iid] = self.simple_projectSet[Iid].union(project)
else:
self.simple_projectSet[Iid] = project
def deDuplication(self, pst):
# de-duplication and merge
# e.g. i: ('F', '·d', ('#',)), j: ('F', '·d', (',',)) -> ('F', '·d', ('#', ','))
for pji in pst:
for pjj in pst:
if pji == pjj:
pj = pji
pst = pst.difference(set([pji]))
pst = pst.union(set([pj]))
continue
if pji[0] == pjj[0] and pji[1] == pjj[1]:
pj = (pji[0], pji[1], tuple(set(pji[2]).union(set(pjj[2]))))
pst = pst.difference(set([pji]))
pst = pst.difference(set([pjj]))
pst = pst.union(set([pj]))
return pst
def getTempProjectSetLASearch(self, pst):
vis = set()
while len(vis) != len(pst):
for pj in pst:
if pj in vis:
continue
vis.add(pj)
nxtpos = pj[1].find(dot) + 1
if nxtpos == len(pj[1]) or pj[1][nxtpos] not in Upper:
continue
tmpst = self.getClosure(pj[1][nxtpos])
for tmpj in tmpst:
pst = pst.union(set([(tmpj[0], tmpj[1], pj[2])]))
return pst
def BuildDFA(self): # DFA that contains lookahead terminals
self.sy2stat = defaultdict(defaultdict)
self.projectSet = dict()
# without lookahead terminals, makes it easy to find the set of items with concentric items
# 不含向前搜索符，方便之后查找同心集
self.simple_projectSet = dict()
self.transitions = dict()
# lookahead terminals 向前搜索符 LATerminal[project_set_num][project] = symbol_set
self.LATerminal = defaultdict(defaultdict)
self.projectset_num = 0
self.dfa = FA()
self.dfa.setStart(0)
q = [0]
self.addLATerminal(0, self.sorted_projects[1], '#')
self.projectSet[0] = {(self.sorted_projects[1][0], self.sorted_projects[1][1], ('#',))}
self.simple_projectSet[0] = {(self.sorted_projects[1][0], self.sorted_projects[1][1])}
while len(q):
Iid = q.pop()
self.projectSet[Iid], self.simple_projectSet[Iid] = self.getProjectSetLATerminal(self.projectSet[Iid], self.simple_projectSet[Iid], Iid)
self.projectSet[Iid] = self.deDuplication(self.projectSet[Iid])
tmpdict, simple_tmpdict = dict(), dict()
tmp_LATerminal = defaultdict(defaultdict) # 记录项目间转移时的向前搜索符
for pj in self.projectSet[Iid]:
nxtpos = pj[1].find(dot) + 1
if nxtpos == len(pj[1]):
continue
nxtsy = pj[1][nxtpos]
nxtpj = pj[1][:nxtpos - 1] + nxtsy + dot + pj[1][nxtpos + 1: ]
tpj = (pj[0], pj[1])
if nxtsy in tmpdict:
tmpdict[nxtsy].add((pj[0], nxtpj, tuple(self.LATerminal[Iid][tpj])))
simple_tmpdict[nxtsy].add((pj[0], nxtpj))
else:
tmpdict[nxtsy] = set([(pj[0], nxtpj, tuple(self.LATerminal[Iid][tpj]))])
simple_tmpdict[nxtsy] = set([(pj[0], nxtpj)])
if nxtsy in tmp_LATerminal and (pj[0], nxtpj) in tmp_LATerminal[nxtsy]:
tmp_LATerminal[nxtsy][(pj[0], nxtpj)] = tmp_LATerminal[nxtsy][(pj[0], nxtpj)].union(self.LATerminal[Iid][tpj])
else:
tmp_LATerminal[nxtsy][(pj[0], nxtpj)] = self.LATerminal[Iid][tpj]
for nxtsy in tmpdict:
tmpdict[nxtsy], simple_tmpdict[nxtsy] = self.getTempProjectSetLASearch(tmpdict[nxtsy]), self.getProjectSet(simple_tmpdict[nxtsy])
tmpdict[nxtsy] = self.deDuplication(tmpdict[nxtsy])
if tmpdict[nxtsy] in self.projectSet.values():
nxtIid = list(self.projectSet.keys())[list(self.projectSet.values()).index(tmpdict[nxtsy])]
self.dfa.addTransition(Iid, nxtIid, nxtsy)
self.sy2stat[Iid][nxtsy] = nxtIid
continue
nxtIid, flag = self.getNxtStateId(Iid, nxtsy)
if flag:
q.append(nxtIid)
self.addProjectSet(nxtIid, tmpdict[nxtsy])
self.addSimpleProjectSet(nxtIid, simple_tmpdict[nxtsy])
for sy in tmp_LATerminal:
for pj in tmp_LATerminal[sy]:
self.addLATerminal(nxtIid, pj, tmp_LATerminal[sy][pj])
self.dfa.addTransition(Iid, nxtIid, nxtsy)
def BuildLR1AnalyseTable(self):
self.action = defaultdict(defaultdict)
self.goto = defaultdict(defaultdict)
for Iid in self.projectSet:
for pj in self.projectSet[Iid]:
tpj = (pj[0], pj[1])
nxtpos = pj[1].find(dot) + 1
if nxtpos == len(pj[1]):
if self.projects[pj[0]][pj[1]] == 2:
self.addAction(Iid, '#', 'acc')
else:
op = 'r' + str(self.production_numdict[pj[0]][pj[1]])
if self.production_numdict[pj[0]][pj[1]] == 0:
continue
if '#' in self.LATerminal[Iid][tpj]:
self.addAction(Iid, '#', op)
for sy in self.dfa.symbol:
if sy in self.LATerminal[Iid][tpj]:
self.addAction(Iid, sy, op)
continue
nxtsy = pj[1][nxtpos]
op = 'S' + str(self.GO(Iid, nxtsy))
if nxtsy not in Upper:
self.addAction(Iid, nxtsy, op)
else:
self.addGoto(Iid, nxtsy, int(op[1:]))
for stat in self.action:
for sy in self.action[stat]:
if len(self.action[stat][sy]) > 1:
print("It's not a LR(1) grammar.")
return False
print("It's a LR(1) grammar.")
return True
def BuildLALR1AnalyseTable(self):
action, goto = self.action, self.goto
self.action, self.goto = defaultdict(defaultdict), defaultdict(defaultdict)
concentric, concentric_num = dict(), 0 # 存储同心集
f, f_num = dict(), 1 # saving state ID, after merging
cnt = len(self.projectSet) + 1
for i in range(1, cnt):
tmp = set(i)
for j in range(i + 1, cnt):
if j in f:
continue
if self.simple_projectSet[i] == self.simple_projectSet[j]:
tmp.add(j)
f[j] = f_num
if len(tmp) > 1:
concentric_num += 1
concentric[concentric_num] = tmp
f[i] = f_num
f_num += 1
if concentric_num == 0:
print("It's a LALR(1) grammar.")
return True
for Iid in self.projectSet:
for pj in self.projectSet[Iid]:
tpj = (pj[0], pj[1])
nxtpos = pj[1].find(dot) + 1
if nxtpos == len(pj[1]):
if self.projects[pj[0]][pj[1]] == 2:
self.addAction(f[Iid], '#', 'acc')
else:
op = 'r' + str(self.production_numdict[pj[0]][pj[1]])
if self.production_numdict[pj[0]][pj[1]] == 0:
continue
if '#' in self.LATerminal[Iid][tpj]:
self.addAction(f[Iid], '#', op)
for sy in self.dfa.symbol:
if sy in self.LATerminal[Iid][tpj]:
self.addAction(f[Iid], sy, op)
continue
nxtsy = pj[1][nxtpos]
op = 'S' + f[str(self.GO(Iid, nxtsy))]
if nxtsy not in Upper:
self.addAction(f[Iid], nxtsy, op)
else:
self.addGoto(f[Iid], nxtsy, int(op[1:]))
for stat in self.action:
for sy in self.action[stat]:
if len(self.action[stat][sy]) > 1:
self.action, self.goto = action, goto
print("It's not a LALR(1) grammar.")
return False
print("It's a LALR(1) grammar.")
def Analysis(self, sentence):
statstack = [0]
systack = ['#']
inpstack = '#' + sentence[::-1]
while True:
curstate = statstack[-1]
cursy = inpstack[-1]
if cursy not in self.action[curstate]:
return False
op = list(self.action[curstate][cursy])[0]
if op[0] == 'S':
systack.append(inpstack[-1])
inpstack = inpstack[:-1]
statstack.append(int(op[1:]))
elif op[0] == 'r':
production = self.production[int(op[1:])]
opnum = len(production[1])
statstack = statstack[:-opnum]
systack = systack[:-opnum]
statstack.append(list(self.goto[statstack[-1]][production[0]])[0])
systack.append(production[0])
elif op == 'acc':
return True