"""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()
