1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
|
"""This module builds a LALR(1) transition-table for lalr_parser.py
For now, shift/reduce conflicts are automatically resolved as shifts.
"""
# Author: Erez Shinan (2017)
# Email : erezshin@gmail.com
from collections import defaultdict
from ..utils import classify, classify_bool, bfs, fzset, Enumerator, logger
from ..exceptions import GrammarError
from .grammar_analysis import GrammarAnalyzer, Terminal, LR0ItemSet
from ..grammar import Rule
###{standalone
class Action:
def __init__(self, name):
self.name = name
def __str__(self):
return self.name
def __repr__(self):
return str(self)
Shift = Action('Shift')
Reduce = Action('Reduce')
class ParseTable:
def __init__(self, states, start_states, end_states):
self.states = states
self.start_states = start_states
self.end_states = end_states
def serialize(self, memo):
tokens = Enumerator()
rules = Enumerator()
states = {
state: {tokens.get(token): ((1, arg.serialize(memo)) if action is Reduce else (0, arg))
for token, (action, arg) in actions.items()}
for state, actions in self.states.items()
}
return {
'tokens': tokens.reversed(),
'states': states,
'start_states': self.start_states,
'end_states': self.end_states,
}
@classmethod
def deserialize(cls, data, memo):
tokens = data['tokens']
states = {
state: {tokens[token]: ((Reduce, Rule.deserialize(arg, memo)) if action==1 else (Shift, arg))
for token, (action, arg) in actions.items()}
for state, actions in data['states'].items()
}
return cls(states, data['start_states'], data['end_states'])
class IntParseTable(ParseTable):
@classmethod
def from_ParseTable(cls, parse_table):
enum = list(parse_table.states)
state_to_idx = {s:i for i,s in enumerate(enum)}
int_states = {}
for s, la in parse_table.states.items():
la = {k:(v[0], state_to_idx[v[1]]) if v[0] is Shift else v
for k,v in la.items()}
int_states[ state_to_idx[s] ] = la
start_states = {start:state_to_idx[s] for start, s in parse_table.start_states.items()}
end_states = {start:state_to_idx[s] for start, s in parse_table.end_states.items()}
return cls(int_states, start_states, end_states)
###}
# digraph and traverse, see The Theory and Practice of Compiler Writing
# computes F(x) = G(x) union (union { G(y) | x R y })
# X: nodes
# R: relation (function mapping node -> list of nodes that satisfy the relation)
# G: set valued function
def digraph(X, R, G):
F = {}
S = []
N = {}
for x in X:
N[x] = 0
for x in X:
# this is always true for the first iteration, but N[x] may be updated in traverse below
if N[x] == 0:
traverse(x, S, N, X, R, G, F)
return F
# x: single node
# S: stack
# N: weights
# X: nodes
# R: relation (see above)
# G: set valued function
# F: set valued function we are computing (map of input -> output)
def traverse(x, S, N, X, R, G, F):
S.append(x)
d = len(S)
N[x] = d
F[x] = G[x]
for y in R[x]:
if N[y] == 0:
traverse(y, S, N, X, R, G, F)
n_x = N[x]
assert(n_x > 0)
n_y = N[y]
assert(n_y != 0)
if (n_y > 0) and (n_y < n_x):
N[x] = n_y
F[x].update(F[y])
if N[x] == d:
f_x = F[x]
while True:
z = S.pop()
N[z] = -1
F[z] = f_x
if z == x:
break
class LALR_Analyzer(GrammarAnalyzer):
def __init__(self, parser_conf, debug=False):
GrammarAnalyzer.__init__(self, parser_conf, debug)
self.nonterminal_transitions = []
self.directly_reads = defaultdict(set)
self.reads = defaultdict(set)
self.includes = defaultdict(set)
self.lookback = defaultdict(set)
def compute_lr0_states(self):
self.lr0_states = set()
# map of kernels to LR0ItemSets
cache = {}
def step(state):
_, unsat = classify_bool(state.closure, lambda rp: rp.is_satisfied)
d = classify(unsat, lambda rp: rp.next)
for sym, rps in d.items():
kernel = fzset({rp.advance(sym) for rp in rps})
new_state = cache.get(kernel, None)
if new_state is None:
closure = set(kernel)
for rp in kernel:
if not rp.is_satisfied and not rp.next.is_term:
closure |= self.expand_rule(rp.next, self.lr0_rules_by_origin)
new_state = LR0ItemSet(kernel, closure)
cache[kernel] = new_state
state.transitions[sym] = new_state
yield new_state
self.lr0_states.add(state)
for _ in bfs(self.lr0_start_states.values(), step):
pass
def compute_reads_relations(self):
# handle start state
for root in self.lr0_start_states.values():
assert(len(root.kernel) == 1)
for rp in root.kernel:
assert(rp.index == 0)
self.directly_reads[(root, rp.next)] = set([ Terminal('$END') ])
for state in self.lr0_states:
seen = set()
for rp in state.closure:
if rp.is_satisfied:
continue
s = rp.next
# if s is a not a nonterminal
if s not in self.lr0_rules_by_origin:
continue
if s in seen:
continue
seen.add(s)
nt = (state, s)
self.nonterminal_transitions.append(nt)
dr = self.directly_reads[nt]
r = self.reads[nt]
next_state = state.transitions[s]
for rp2 in next_state.closure:
if rp2.is_satisfied:
continue
s2 = rp2.next
# if s2 is a terminal
if s2 not in self.lr0_rules_by_origin:
dr.add(s2)
if s2 in self.NULLABLE:
r.add((next_state, s2))
def compute_includes_lookback(self):
for nt in self.nonterminal_transitions:
state, nonterminal = nt
includes = []
lookback = self.lookback[nt]
for rp in state.closure:
if rp.rule.origin != nonterminal:
continue
# traverse the states for rp(.rule)
state2 = state
for i in range(rp.index, len(rp.rule.expansion)):
s = rp.rule.expansion[i]
nt2 = (state2, s)
state2 = state2.transitions[s]
if nt2 not in self.reads:
continue
for j in range(i + 1, len(rp.rule.expansion)):
if not rp.rule.expansion[j] in self.NULLABLE:
break
else:
includes.append(nt2)
# state2 is at the final state for rp.rule
if rp.index == 0:
for rp2 in state2.closure:
if (rp2.rule == rp.rule) and rp2.is_satisfied:
lookback.add((state2, rp2.rule))
for nt2 in includes:
self.includes[nt2].add(nt)
def compute_lookaheads(self):
read_sets = digraph(self.nonterminal_transitions, self.reads, self.directly_reads)
follow_sets = digraph(self.nonterminal_transitions, self.includes, read_sets)
for nt, lookbacks in self.lookback.items():
for state, rule in lookbacks:
for s in follow_sets[nt]:
state.lookaheads[s].add(rule)
def compute_lalr1_states(self):
m = {}
reduce_reduce = []
for state in self.lr0_states:
actions = {}
for la, next_state in state.transitions.items():
actions[la] = (Shift, next_state.closure)
for la, rules in state.lookaheads.items():
if len(rules) > 1:
# Try to resolve conflict based on priority
p = [(r.options.priority or 0, r) for r in rules]
p.sort(key=lambda r: r[0], reverse=True)
best, second_best = p[:2]
if best[0] > second_best[0]:
rules = [best[1]]
else:
reduce_reduce.append((state, la, rules))
if la in actions:
if self.debug:
logger.warning('Shift/Reduce conflict for terminal %s: (resolving as shift)', la.name)
logger.warning(' * %s', list(rules)[0])
else:
actions[la] = (Reduce, list(rules)[0])
m[state] = { k.name: v for k, v in actions.items() }
if reduce_reduce:
msgs = []
for state, la, rules in reduce_reduce:
msg = 'Reduce/Reduce collision in %s between the following rules: %s' % (la, ''.join([ '\n\t- ' + str(r) for r in rules ]))
if self.debug:
msg += '\n collision occurred in state: {%s\n }' % ''.join(['\n\t' + str(x) for x in state.closure])
msgs.append(msg)
raise GrammarError('\n\n'.join(msgs))
states = { k.closure: v for k, v in m.items() }
# compute end states
end_states = {}
for state in states:
for rp in state:
for start in self.lr0_start_states:
if rp.rule.origin.name == ('$root_' + start) and rp.is_satisfied:
assert(not start in end_states)
end_states[start] = state
_parse_table = ParseTable(states, { start: state.closure for start, state in self.lr0_start_states.items() }, end_states)
if self.debug:
self.parse_table = _parse_table
else:
self.parse_table = IntParseTable.from_ParseTable(_parse_table)
def compute_lalr(self):
self.compute_lr0_states()
self.compute_reads_relations()
self.compute_includes_lookback()
self.compute_lookaheads()
self.compute_lalr1_states()
|
