549 lines
18 KiB
Python
549 lines
18 KiB
Python
# This is doty playing with parser tables.
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from collections import namedtuple
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class Configuration(
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namedtuple('Configuration', ['name', 'symbols', 'position'])
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):
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"""A rule being tracked in a state."""
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__slots__ = ()
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@classmethod
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def from_rule(cls, rule):
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return Configuration(name=rule[0], symbols=rule[1], position=0)
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@property
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def at_end(self):
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return self.position == len(self.symbols)
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@property
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def next(self):
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return self.symbols[self.position] if not self.at_end else None
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def at_symbol(self, symbol):
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return self.next == symbol
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def replace(self, **kwargs):
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return self._replace(**kwargs)
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def __str__(self):
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return "{name} -> {bits}".format(
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name=self.name,
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bits=' '.join([
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'* ' + sym if i == self.position else sym
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for i, sym in enumerate(self.symbols)
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]) + (' *' if self.at_end else '')
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)
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class GenerateLR0(object):
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"""Generate parser tables for an LR0 parser.
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Grammars are of the form:
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grammar_simple = [
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('E', ['E', '+', 'T']),
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('E', ['T']),
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('T', ['(', 'E', ')']),
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('T', ['id']),
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]
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Which is to say, they are a list of productions. Each production is a
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tuple where the first element of the tuple is the name of the
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non-terminal being added, and the second elment of the tuple is the
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list of terminals and non-terminals that make up the production.
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Don't name anything with double-underscores; those are reserved for
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the generator. Don't add '$' either, as it is reserved to mean
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end-of-stream. Use an empty list to indicate nullability, that is:
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('O', []),
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means that O can be matched with nothing.
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Note that this is implemented in the dumbest way possible, in order to be
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the most understandable it can be. I built this to learn, and I want to
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make sure I can keep learning with it.
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"""
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def __init__(self, start, grammar):
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"""Initialize the parser generator with the specified grammar and
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start symbol.
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"""
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# We always store the "augmented" grammar, which contains an initial
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# production for the start state. grammar[0] is always the start
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# rule, and in the set of states and table and whatever the first
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# element is always the starting state/position.
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self.grammar = [('__start', start)] + grammar
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self.nonterminals = set(rule[0] for rule in grammar)
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self.terminals = set(
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sym
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for name, symbols in grammar
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for sym in symbols
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if sym not in self.nonterminals
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)
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self.alphabet = self.terminals | self.nonterminals
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# Check to make sure they didn't use anything that will give us
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# heartburn later.
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reserved = [a for a in self.alphabet if a.startswith('__') or a == '$']
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if reserved:
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raise ValueError(
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"Can't use {symbols} in grammars, {what} reserved.".format(
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symbols=' or '.join(reserved),
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what="it's" if len(reserved) == 1 else "they're",
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)
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)
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self.terminals.add('$')
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self.alphabet.add('$')
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def gen_closure_next(self, config):
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"""Return the next set of configurations in the closure for
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config.
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If the position for config is just before a non-terminal, then the
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next set of configurations is configurations for all of the
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productions for that non-terminal, with the position at the
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beginning. (If the position for config is just before a terminal,
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or at the end of the production, then the next set is empty.)
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"""
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if config.at_end:
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return ()
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else:
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return tuple(
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Configuration.from_rule(rule)
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for rule in self.grammar
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if rule[0] == config.next
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)
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def gen_closure(self, config, closure):
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"""Compute the closure for the specified config and unify it with the
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existing closure.
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If the provided config is already in the closure then nothing is
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done.
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"""
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if config in closure:
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return closure
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else:
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new_closure = tuple(closure) + (config,)
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for next_config in self.gen_closure_next(config):
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new_closure = self.gen_closure(next_config, new_closure)
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return new_closure
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def gen_successor(self, config_set, symbol):
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"""Compute the successor state for the given config set and the
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given symbol.
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The successor represents the next state of the parser after seeing
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the symbol.
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"""
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seeds = [
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config.replace(position=config.position + 1)
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for config in config_set
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if config.at_symbol(symbol)
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]
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closure = ()
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for seed in seeds:
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closure = self.gen_closure(seed, closure)
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return closure
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def gen_all_successors(self, config_set):
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"""Return all of the non-empty successors for the given config set."""
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next = []
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for symbol in self.alphabet:
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successor = self.gen_successor(config_set, symbol)
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if len(successor) > 0:
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next.append(successor)
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return tuple(next)
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def gen_sets(self, config_set, F):
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"""Recursively generate all configuration sets starting from the
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provided set, and merge them with the provided set 'F'.
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"""
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if config_set in F:
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return F
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else:
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new_F = F + (config_set,)
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for successor in self.gen_all_successors(config_set):
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new_F = self.gen_sets(successor, new_F)
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return new_F
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def gen_all_sets(self):
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"""Generate all of the configuration sets for the grammar."""
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initial_set = self.gen_closure(
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Configuration.from_rule(self.grammar[0]),
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(),
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)
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return self.gen_sets(initial_set, ())
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def find_set_index(self, sets, set):
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"""Find the specified set in the set of sets, and return the
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index, or None if it is not found.
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"""
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for i, s in enumerate(sets):
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if s == set:
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return i
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return None
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def gen_table(self):
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"""Generate the parse table.
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The parse table is a list of states. The first state in the list is
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the starting state. Each state is a dictionary that maps a symbol to an
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action. Each action is a tuple. The first element of the tuple is a
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string describing what to do:
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- 'shift': The second element of the tuple is the state
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number. Consume the input and push that state onto the stack.
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- 'reduce': The second element is the name of the non-terminal being
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reduced, and the third element is the number of states to remove
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from the stack. Don't consume the input; just remove the specified
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number of things from the stack, and then consult the table again,
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this time using the new top-of-stack as the current state and the
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name of the non-terminal to find out what to do.
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- 'goto': The second element is the state number to push onto the
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stack. In the literature, these entries are treated distinctly from
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the actions, but we mix them here because they never overlap with the
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other actions. (These are always associated with non-terminals, and
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the other actions are always associated with terminals.)
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- 'accept': Accept the result of the parse, it worked.
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Anything missing from the row indicates an error.
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"""
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action_table = []
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config_sets = self.gen_all_sets()
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for config_set in config_sets:
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actions = {}
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# Actions
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for config in config_set:
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if config.at_end:
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if config.name != '__start':
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for a in self.terminals:
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self.set_table_action(
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actions,
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a,
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('reduce', config.name, len(config.symbols)),
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config,
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)
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else:
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self.set_table_action(
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actions,
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'$',
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('accept',),
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config,
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)
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else:
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if config.next in self.terminals:
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successor = self.gen_successor(config_set, config.next)
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index = self.find_set_index(config_sets, successor)
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self.set_table_action(
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actions,
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config.next,
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('shift', index),
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config,
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)
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# Gotos
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for symbol in self.nonterminals:
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successor = self.gen_successor(config_set, symbol)
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index = self.find_set_index(config_sets, successor)
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if index is not None:
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self.set_table_action(
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actions,
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symbol,
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('goto', index),
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None,
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)
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# set_table_action stores the configs that generated the actions in
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# the table, for diagnostic purposes. This filters them out again
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# so that the parser has something clean to work with.
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actions = {k: self.get_table_action(actions, k) for k in actions}
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action_table.append(actions)
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return action_table
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def set_table_action(self, row, symbol, action, config):
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"""Set the action for 'symbol' in the table row to 'action'.
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This is destructive; it changes the table. It raises an error if
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there is already an action for the symbol in the row.
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"""
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existing, existing_config = row.get(symbol, (None, None))
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if existing is not None and existing != action:
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config_old = str(existing_config)
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config_new = str(config)
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max_len = max(len(config_old), len(config_new)) + 1
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error = (
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"Conflicting actions for {symbol}:\n"
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" {config_old: <{max_len}}: {old}\n"
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" {config_new: <{max_len}}: {new}\n".format(
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config_old=config_old,
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config_new=config_new,
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max_len=max_len,
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old=existing,
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new=action,
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symbol=symbol,
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)
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)
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raise ValueError(error)
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row[symbol] = (action, config)
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def get_table_action(self, row, symbol):
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return row[symbol][0]
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class GenerateSLR1(GenerateLR0):
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"""Generate parse tables for SLR1 grammars.
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boop
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"""
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def gen_first_symbol(self, symbol, visited):
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"""Compute the first set for a single symbol.
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The first set is the set of tokens that can appear as the first token
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for a given symbol. (Obviously, if the symbol is itself a token, then
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this is trivial.)
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'visited' is a set of already visited symbols, to stop infinite
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recursion on left-recursive grammars. That means that sometimes this
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function can return an empty tuple. Don't confuse that with a tuple
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containing epsilon: that's a tuple containing 'None', not an empty
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tuple.
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"""
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if symbol in self.terminals:
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return (symbol,)
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elif symbol in visited:
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return ()
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else:
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assert symbol in self.nonterminals
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visited.add(symbol)
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# All the firsts from all the productions.
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firsts = [
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self.gen_first(rule[1], visited)
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for rule in self.grammar
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if rule[0] == symbol
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]
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result = ()
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for fs in firsts:
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result = result + tuple(f for f in fs if f not in result)
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return result
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def gen_first(self, symbols, visited=None):
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"""Compute the first set for a sequence of symbols.
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The first set is the set of tokens that can appear as the first token
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for this sequence of symbols. The interesting wrinkle in computing the
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first set for a sequence of symbols is that we keep computing the first
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sets so long as Epsilon appears in the set. i.e., if we are computing
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for ['A', 'B', 'C'] and the first set of 'A' contains epsilon, then the
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first set for the *sequence* also contains the first set of ['B', 'C'],
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since 'A' could be missing entirely.
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An epsilon in the result is indicated by 'None'. There will always be
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at least one element in the result.
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The 'visited' parameter, if not None, is a set of symbols that are
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already in the process of being evaluated, to deal with left-recursive
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grammars. (See gen_first_symbol for more.)
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"""
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if len(symbols) == 0:
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return (None,) # Epsilon.
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else:
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if visited is None:
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visited = set()
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result = self.gen_first_symbol(symbols[0], visited)
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if None in result:
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result = tuple(set(s for s in result if s is not None))
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result = result + self.gen_first(symbols[1:], visited)
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return result
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def gen_follow(self, symbol):
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"""Generate the follow set for the given nonterminal."""
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if symbol == '__start':
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return tuple('$')
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assert symbol in self.nonterminals
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follow = ()
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for production in self.grammar:
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for index, prod_symbol in enumerate(production[1]):
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if prod_symbol != symbol:
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continue
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first = self.gen_first(production[1][index+1:])
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follow = follow + tuple(f for f in first if f is not None)
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if None in first:
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follow = follow + self.gen_follow(production[0])
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assert None not in follow # Should always ground out at __start
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return follow
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def parse(table, input, trace=False):
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"""Parse the input with the generated parsing table and return the
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concrete syntax tree.
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input is a list of tokens. Don't stick an end-of-stream marker, I'll stick
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one on for you.
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"""
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input = input + ['$']
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input_index = 0
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stack = [(0, None)]
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while True:
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current_state = stack[-1][0]
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current_token = input[input_index]
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action = table[current_state].get(current_token, ('error',))
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if trace:
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print("{stack: <20} {input: <50} {action: <5}".format(
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stack=[s[0] for s in stack],
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input=input[input_index:],
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action=action
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))
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if action[0] == 'accept':
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return stack[-1][1]
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elif action[0] == 'reduce':
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name = action[1]
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size = action[2]
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value = (name, tuple(s[1] for s in stack[-size:]))
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stack = stack[:-size]
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goto = table[stack[-1][0]].get(name, ('error',))
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if (goto[0] != 'goto'):
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raise ValueError('OH NOES GOTO')
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stack.append((goto[1], value))
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elif action[0] == 'shift':
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stack.append((action[1], (current_token, ())))
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input_index += 1
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elif action[0] == 'error':
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raise ValueError('OH NOES WAT')
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def format_node(node):
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"""Print out an indented concrete syntax tree, from parse()."""
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lines = [
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'{name}'.format(name=node[0])
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] + [
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' ' + line
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for child in node[1]
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for line in format_node(child).split('\n')
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]
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return '\n'.join(lines)
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def format_table(generator, table):
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"""Format a parser table so pretty."""
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def format_action(state, terminal):
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action = state.get(terminal, ('error',))
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if action[0] == 'accept':
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return 'accept'
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elif action[0] == 'shift':
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return 's' + str(action[1])
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elif action[0] == 'error':
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return ''
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elif action[0] == 'reduce':
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return 'r' + str(action[1])
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header = " | {terms} | {nts}".format(
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terms=' '.join(
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'{0: <6}'.format(terminal)
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for terminal in (generator.terminals)
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),
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nts=' '.join(
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'{0: <5}'.format(nt)
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for nt in generator.nonterminals
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),
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)
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lines = [
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header,
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'-' * len(header),
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] + [
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"{index} | {actions} | {gotos}".format(
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index=i,
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actions=' '.join(
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'{0: <6}'.format(format_action(row, terminal))
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for terminal in (generator.terminals)
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),
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gotos=' '.join(
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'{0: <5}'.format(row.get(nt, ('error', ''))[1])
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for nt in generator.nonterminals
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),
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)
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for i, row in enumerate(table)
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]
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return '\n'.join(lines)
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# OK, this is a very simple LR0 grammar.
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grammar_simple = [
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('E', ['E', '+', 'T']),
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('E', ['T']),
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('T', ['(', 'E', ')']),
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('T', ['id']),
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]
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gen = GenerateLR0('E', grammar_simple)
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table = gen.gen_table()
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tree = parse(table, ['id', '+', '(', 'id', ')'])
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print(format_node(tree) + "\n")
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# This one doesn't work with LR0, though, it has a shift/reduce conflict.
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grammar_lr0_shift_reduce = grammar_simple + [
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('T', ['id', '[', 'E', ']']),
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]
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try:
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gen = GenerateLR0('E', grammar_lr0_shift_reduce)
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table = gen.gen_table()
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assert False
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except ValueError as e:
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print(e)
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# Nor does this: it has a reduce/reduce conflict.
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grammar_lr0_reduce_reduce = grammar_simple + [
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('E', ['V', '=', 'E']),
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('V', ['id']),
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]
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try:
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gen = GenerateLR0('E', grammar_lr0_reduce_reduce)
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table = gen.gen_table()
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assert False
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except ValueError as e:
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print(e)
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# Nullable symbols just don't work with constructs like this, because you can't
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# look ahead to figure out if you should reduce an empty 'F' or not.
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grammar_nullable = [
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('E', ['F', 'boop']),
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('F', ['beep']),
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('F', []),
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]
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try:
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gen = GenerateLR0('E', grammar_nullable)
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table = gen.gen_table()
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assert False
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except ValueError as e:
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print(e)
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gen = GenerateSLR1('E', grammar_lr0_shift_reduce)
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print("First: {first}".format(first=str(gen.gen_first(['E']))))
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print("Follow: {follow}".format(follow=str(gen.gen_follow('E'))))
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