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from collections import Counter, defaultdict
from ..utils import bfs, fzset, classify
from ..exceptions import GrammarError
from ..grammar import Rule, Terminal, NonTerminal
class RulePtr(object):
__slots__ = ('rule', 'index')
def __init__(self, rule, index):
assert isinstance(rule, Rule)
assert index <= len(rule.expansion)
self.rule = rule
self.index = index
def __repr__(self):
before = [x.name for x in self.rule.expansion[:self.index]]
after = [x.name for x in self.rule.expansion[self.index:]]
return '<%s : %s * %s>' % (self.rule.origin.name, ' '.join(before), ' '.join(after))
@property
def next(self):
return self.rule.expansion[self.index]
def advance(self, sym):
assert self.next == sym
return RulePtr(self.rule, self.index+1)
@property
def is_satisfied(self):
return self.index == len(self.rule.expansion)
def __eq__(self, other):
return self.rule == other.rule and self.index == other.index
def __hash__(self):
return hash((self.rule, self.index))
# state generation ensures no duplicate LR0ItemSets
class LR0ItemSet(object):
__slots__ = ('kernel', 'closure', 'transitions', 'lookaheads')
def __init__(self, kernel, closure):
self.kernel = fzset(kernel)
self.closure = fzset(closure)
self.transitions = {}
self.lookaheads = defaultdict(set)
def __repr__(self):
return '{%s | %s}' % (', '.join([repr(r) for r in self.kernel]), ', '.join([repr(r) for r in self.closure]))
def update_set(set1, set2):
if not set2 or set1 > set2:
return False
copy = set(set1)
set1 |= set2
return set1 != copy
def calculate_sets(rules):
"""Calculate FOLLOW sets.
Adapted from: http://lara.epfl.ch/w/cc09:algorithm_for_first_and_follow_sets"""
symbols = {sym for rule in rules for sym in rule.expansion} | {rule.origin for rule in rules}
# foreach grammar rule X ::= Y(1) ... Y(k)
# if k=0 or {Y(1),...,Y(k)} subset of NULLABLE then
# NULLABLE = NULLABLE union {X}
# for i = 1 to k
# if i=1 or {Y(1),...,Y(i-1)} subset of NULLABLE then
# FIRST(X) = FIRST(X) union FIRST(Y(i))
# for j = i+1 to k
# if i=k or {Y(i+1),...Y(k)} subset of NULLABLE then
# FOLLOW(Y(i)) = FOLLOW(Y(i)) union FOLLOW(X)
# if i+1=j or {Y(i+1),...,Y(j-1)} subset of NULLABLE then
# FOLLOW(Y(i)) = FOLLOW(Y(i)) union FIRST(Y(j))
# until none of NULLABLE,FIRST,FOLLOW changed in last iteration
NULLABLE = set()
FIRST = {}
FOLLOW = {}
for sym in symbols:
FIRST[sym]={sym} if sym.is_term else set()
FOLLOW[sym]=set()
# Calculate NULLABLE and FIRST
changed = True
while changed:
changed = False
for rule in rules:
if set(rule.expansion) <= NULLABLE:
if update_set(NULLABLE, {rule.origin}):
changed = True
for i, sym in enumerate(rule.expansion):
if set(rule.expansion[:i]) <= NULLABLE:
if update_set(FIRST[rule.origin], FIRST[sym]):
changed = True
else:
break
# Calculate FOLLOW
changed = True
while changed:
changed = False
for rule in rules:
for i, sym in enumerate(rule.expansion):
if i==len(rule.expansion)-1 or set(rule.expansion[i+1:]) <= NULLABLE:
if update_set(FOLLOW[sym], FOLLOW[rule.origin]):
changed = True
for j in range(i+1, len(rule.expansion)):
if set(rule.expansion[i+1:j]) <= NULLABLE:
if update_set(FOLLOW[sym], FIRST[rule.expansion[j]]):
changed = True
return FIRST, FOLLOW, NULLABLE
class GrammarAnalyzer(object):
def __init__(self, parser_conf, debug=False):
self.debug = debug
root_rules = {start: Rule(NonTerminal('$root_' + start), [NonTerminal(start), Terminal('$END')])
for start in parser_conf.start}
rules = parser_conf.rules + list(root_rules.values())
self.rules_by_origin = classify(rules, lambda r: r.origin)
if len(rules) != len(set(rules)):
duplicates = [item for item, count in Counter(rules).items() if count > 1]
raise GrammarError("Rules defined twice: %s" % ', '.join(str(i) for i in duplicates))
for r in rules:
for sym in r.expansion:
if not (sym.is_term or sym in self.rules_by_origin):
raise GrammarError("Using an undefined rule: %s" % sym)
self.start_states = {start: self.expand_rule(root_rule.origin)
for start, root_rule in root_rules.items()}
self.end_states = {start: fzset({RulePtr(root_rule, len(root_rule.expansion))})
for start, root_rule in root_rules.items()}
lr0_root_rules = {start: Rule(NonTerminal('$root_' + start), [NonTerminal(start)])
for start in parser_conf.start}
lr0_rules = parser_conf.rules + list(lr0_root_rules.values())
assert(len(lr0_rules) == len(set(lr0_rules)))
self.lr0_rules_by_origin = classify(lr0_rules, lambda r: r.origin)
# cache RulePtr(r, 0) in r (no duplicate RulePtr objects)
self.lr0_start_states = {start: LR0ItemSet([RulePtr(root_rule, 0)], self.expand_rule(root_rule.origin, self.lr0_rules_by_origin))
for start, root_rule in lr0_root_rules.items()}
self.FIRST, self.FOLLOW, self.NULLABLE = calculate_sets(rules)
def expand_rule(self, source_rule, rules_by_origin=None):
"Returns all init_ptrs accessible by rule (recursive)"
if rules_by_origin is None:
rules_by_origin = self.rules_by_origin
init_ptrs = set()
def _expand_rule(rule):
assert not rule.is_term, rule
for r in rules_by_origin[rule]:
init_ptr = RulePtr(r, 0)
init_ptrs.add(init_ptr)
if r.expansion: # if not empty rule
new_r = init_ptr.next
if not new_r.is_term:
yield new_r
for _ in bfs([source_rule], _expand_rule):
pass
return fzset(init_ptrs)
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