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lrparsers/parser/parser.py
John Doty 76ef85483e Accept is single-valued, the multi-value thing didn't ever make sense 
I mean, it did when we thought we were going to weave NFA states as we
were building them but we ended up not doing that and instead just
using the fancy EdgeList splitting magic when building DFAs from the
NFA. It has the same power and is simpler code, and also means that
we'll *never* be asked to have multiple Terminals be accepted from a
single NFA state.
2024-08-27 15:43:01 -07:00

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"""This is a small helper library to generate LR parser tables.
The primary inspiration for this library is tree-sitter, which also generates
LR parsers for grammars written in a turing-complete language. Like that, we
write grammars in a language, only we do it in Python instead of JavaScript.
Why Python? Because Python 3 is widely pre-installed on MacOS and Linux. This
library requires nothing more than the basic standard library, and not even a
new version of it. Therefore, it turns out to be a pretty light dependency for
a rust or C++ or something kind of project. (Tree-sitter, on the other hand,
requires node, which is a far less stable and available runtime in 2024.)
The parser tables can really be used to power anything. I prefer to make
concrete syntax trees (again, see tree-sitter), and there is no facility at all
for actions or custom ASTs or whatnot. Any such processing needs to be done by
the thing that processes the tables.
## Making Grammars
To get started, create a grammar that derives from the `Grammar` class. Create
one method per nonterminal, decorated with the `rule` decorator. Here's an
example:
class SimpleGrammar(Grammar):
@rule
def expression(self):
return seq(self.expression, self.PLUS, self.term) | self.term
@rule
def term(self):
return seq(self.LPAREN, self.expression, self.RPAREN) | self.ID
PLUS = Terminal('+')
LPAREN = Terminal('(')
RPAREN = Terminal(')')
ID = Terminal('id')
## Using grammars
TODO
## Representation Choices
The SimpleGrammar class might seem a little verbose compared to a dense
structure like:
grammar_simple = [
('E', ['E', '+', 'T']),
('E', ['T']),
('T', ['(', 'E', ')']),
('T', ['id']),
]
or
grammar_simple = {
'E': [
['E', '+', 'T'],
['T'],
],
'T': [
['(', 'E', ')'],
['id'],
],
}
The advantage that the class has over a table like this is that you get to have
all of your Python tools help you make sure your grammar is good, if you want
them. e.g., if you're working with an LSP or something, the members give you
autocomplete and jump-to-definition and possibly even type-checking.
At the very least, if you mis-type the name of a nonterminal, or forget to
implement it, we will immediately raise an error that *INCLUDES THE LOCATION IN
THE SOURCE WHERE THE ERROR WAS MADE.* With tables, we can tell you that you
made a mistake but it's up to you to figure out where you did it.
### Aside: What about a custom DSL/EBNF like thing?
Yeah, OK, there's a rich history of writing your grammar in a domain-specific
language. YACC did it, ANTLR does it, GRMTools.... just about everybody except
Tree-Sitter does this.
But look, I've got several reasons for not doing it.
First, I'm lazy, and don't want to write yet another parser for my parser. What
tools should I use to write my parser generator parser? I guess I don't have my
parser generator parser yet, so probably a hand-written top down parser? Some
other python parser generator? Ugh!
As an add-on to that, if I make my own format then I need to make tooling for
*that* too: syntax highlighters, jump to definition, the works. Yuck. An
existing language, and a format that builds on an existing language, gets me the
tooling that comes along with that language. If you can leverage that
effictively (and I think I have) then you start way ahead in terms of tooling.
Second, this whole thing is supposed to be easy to include in an existing
project, and adding a custom compiler doesn't seem to be that. Adding two python
files seems to be about the right speed.
Thirdly, and this is just hypothetical, it's probably pretty easy to write your
own tooling around a grammar if it's already in Python. If you want to make
railroad diagrams or EBNF pictures or whatever, all the productions are already
right there in data structures for you to process. I've tried to keep them
accessible and at least somewhat easy to work with. There's nothing that says a
DSL-based system *has* to produce unusable intermediate data- certainly there
are some tools that *try*- but with this approach the accessibility and the
ergonomics of the tool go hand in hand.
## Some History
The first version of this code was written as an idle exercise to learn how LR
parser table generation even worked. It was... very simple, fairly easy to
follow, and just *incredibly* slow. Like, mind-bogglingly slow. Unusably slow
for anything but the most trivial grammar.
As a result, when I decided I wanted to use it for a larger grammar, I found that
I just couldn't. So this has been hacked and significantly improved from that
version, now capable of building tables for nontrivial grammars. It could still
be a lot faster, but it meets my needs for now.
(BTW, the notes I read to learn how all this works are at
http://dragonbook.stanford.edu/lecture-notes/Stanford-CS143/. Specifically,
I started with handout 8, 'Bottom-up-parsing', and went from there. (I did
eventually have to backtrack a little into handout 7, since that's where
First() and Follow() are covered.)
May 2024
"""
import abc
import bisect
import collections
import dataclasses
import enum
import functools
import inspect
import json
import typing
###############################################################################
# LR0
#
# We start with LR0 parsers, because they form the basis of everything else.
###############################################################################
class ConfigurationCore(typing.NamedTuple):
name: int
symbols: typing.Tuple[int, ...]
position: int
next: int | None
@classmethod
def from_rule(cls, name: int, symbols: typing.Tuple[int, ...]):
if len(symbols) == 0:
next = None
else:
next = symbols[0]
return ConfigurationCore(
name=name,
symbols=symbols,
position=0,
next=next,
)
@property
def at_end(self) -> bool:
return self.position == len(self.symbols)
def replace_position(self, new_position):
if new_position == len(self.symbols):
next = None
else:
next = self.symbols[new_position]
return ConfigurationCore(
name=self.name,
symbols=self.symbols,
position=new_position,
next=next,
)
@property
def rest(self) -> typing.Tuple[int, ...]:
return self.symbols[(self.position + 1) :]
def __repr__(self) -> str:
return "{name} -> {bits}".format(
name=self.name,
bits=" ".join(
[
("* " + str(sym)) if i == self.position else str(sym)
for i, sym in enumerate(self.symbols)
]
)
+ (" *" if self.at_end else ""),
)
def format(self, alphabet: list[str]) -> str:
return "{name} -> {bits}".format(
name=alphabet[self.name],
bits=" ".join(
[
"* " + alphabet[sym] if i == self.position else alphabet[sym]
for i, sym in enumerate(self.symbols)
]
)
+ (" *" if self.at_end else ""),
)
class Configuration(typing.NamedTuple):
"""A rule being tracked in a state. That is, a specific position within a
specific rule, with an associated lookahead state.
We make a *lot* of these and we need/want to pre-cache a ton of things we
ask about so we need to override __init__, otherwise it's immutable and
fixed and doesn't have a dict to save space.
It also supports hashing and equality and comparison, so it can be sorted
and whatnot. This really is the workhorse data structure of the whole thing.
If you can improve this you can improve the performance of everything probably.
(Note: technically, lookahead isn't used until we get to LR(1) parsers,
but if left at its default it's harmless. Ignore it until you get to
the part about LR(1).)
"""
core: ConfigurationCore
lookahead: typing.Tuple[int, ...]
@classmethod
def from_rule(cls, name: int, symbols: typing.Tuple[int, ...], lookahead=()):
# Consider adding at_end and next to the namedtuple.
return Configuration(
core=ConfigurationCore.from_rule(name, symbols),
lookahead=lookahead,
)
@property
def at_end(self) -> bool:
return self.core.next is None
def replace_position(self, new_position):
return Configuration(
core=self.core.replace_position(new_position),
lookahead=self.lookahead,
)
@property
def rest(self):
return self.core.symbols[(self.core.position + 1) :]
def __repr__(self) -> str:
la = ", " + str(self.lookahead) if self.lookahead != () else ""
return f"{repr(self.core)}{la}"
def format(self, alphabet: list[str]) -> str:
if self.lookahead != ():
la = " {" + ",".join(alphabet[i] for i in self.lookahead) + "}"
else:
la = ""
return f"{self.core.format(alphabet)}{la}"
class CoreSet(frozenset[ConfigurationCore]):
pass
class ConfigSet(frozenset[Configuration]):
pass
class ConfigurationSetInfo:
"""When we build a grammar into a table, the first thing we need to do is
generate all the configuration sets and their successors.
(A configuration set is what it sounds like: an unordered set of
Configuration structures. But we use Tuple because it's hashable and
immutable and small and we order the Tuples so that we get repeatable
results.)
*This* is structure that tracks the result of that computation.
(Different generators vary in the details of how they generate this
structure, but they all compute this information.)
"""
core_key: dict[ConfigSet, int] # Map a ConfigSet into am index
config_set_key: dict[ConfigSet, int] # Map a ConfigSet into am index
sets: list[ConfigSet] # Map the index back into a set
closures: list[ConfigSet | None] # Track closures
# All the sucessors for all of the sets. `successors[i]` is the mapping
# from grammar symbol to the index of the set you get by processing that
# symbol.
successors: list[dict[int, int]]
def __init__(self):
self.core_key = {}
self.config_set_key = {}
self.sets = []
self.closures = []
self.successors = []
def register_core(self, c: ConfigSet) -> typing.Tuple[int, bool]:
"""Potentially add a new config set to the set of sets. Returns the
canonical ID of the set within this structure, along with a boolean
indicating whether the set was just added or not.
(You can use this integer to get the set back, if you need it, and
also access the successors table.)
"""
existing = self.core_key.get(c)
if existing is not None:
return existing, False
index = len(self.sets)
self.sets.append(c)
self.closures.append(None)
self.successors.append({})
self.core_key[c] = index
return index, True
def register_config_closure(self, c_id: int, closure: ConfigSet):
assert self.closures[c_id] is None
self.closures[c_id] = closure
self.config_set_key[closure] = c_id
def add_successor(self, c_id: int, symbol: int, successor: int):
"""Register sucessor(`c_id`, `symbol`) -> `successor`, where c_id
is the id of the set in this structure, and symbol is the id of a
symbol in the alphabet of the grammar.
"""
self.successors[c_id][symbol] = successor
def dump_state(self, alphabet: list[str]) -> str:
return json.dumps(
{
str(set_index): {
"configs": [c.format(alphabet) for c in config_set],
"successors": {
alphabet[k]: str(v) for k, v in self.successors[set_index].items()
},
}
for set_index, config_set in enumerate(self.sets)
},
indent=4,
sort_keys=True,
)
def find_path_to_set(self, target_set: ConfigSet) -> list[int]:
"""Trace the path of grammar symbols from the first set (which always
set 0) to the target set. This is useful in conflict reporting,
because we'll be *at* a ConfigSet and want to show the grammar symbols
that get us to where we found the conflict.
The return value is a list of grammar symbols to get to the specified
ConfigSet.
This function raises KeyError if no path is found.
"""
target_index = self.config_set_key[target_set]
visited = set()
queue: collections.deque = collections.deque()
# NOTE: Set 0 is always the first set, the one that contains the
# start symbol.
queue.appendleft((0, []))
while len(queue) > 0:
set_index, path = queue.pop()
if set_index == target_index:
return path
if set_index in visited:
continue
visited.add(set_index)
for symbol, successor in self.successors[set_index].items():
queue.appendleft((successor, path + [symbol]))
raise KeyError("Unable to find a path to the target set!")
class Assoc(enum.Enum):
"""Associativity of a rule."""
NONE = 0
LEFT = 1
RIGHT = 2
@dataclasses.dataclass
class Action:
pass
@dataclasses.dataclass
class Reduce(Action):
name: str
count: int
transparent: bool
@dataclasses.dataclass
class Shift(Action):
state: int
@dataclasses.dataclass
class Accept(Action):
pass
@dataclasses.dataclass
class Error(Action):
pass
ParseAction = Reduce | Shift | Accept | Error
@dataclasses.dataclass
class PossibleAction:
name: str
rule: str
action_str: str
def __str__(self):
return f"We are in the rule `{self.name}: {self.rule}` and we should {self.action_str}"
@dataclasses.dataclass
class Ambiguity:
path: str
symbol: str
actions: typing.Tuple[PossibleAction]
def __str__(self):
lines = []
lines.append(
f"When we have parsed '{self.path}' and see '{self.symbol}' we don't know whether:"
)
lines.extend(f"- {action}" for action in self.actions)
return "\n".join(lines)
class AmbiguityError(Exception):
ambiguities: list[Ambiguity]
def __init__(self, ambiguities):
self.ambiguities = ambiguities
def __str__(self):
return f"{len(self.ambiguities)} ambiguities:\n\n" + "\n\n".join(
str(ambiguity) for ambiguity in self.ambiguities
)
class ErrorCollection:
"""A collection of errors. The errors are grouped by config set and alphabet
symbol, so that we can group the error strings appropriately when we format
the error.
"""
errors: dict[ConfigSet, dict[int, dict[Configuration, Action]]]
def __init__(self):
self.errors = {}
def any(self) -> bool:
"""Return True if there are any errors in this collection."""
return len(self.errors) > 0
def add_error(
self,
config_set: ConfigSet,
symbol: int,
config: Configuration,
action: Action,
):
"""Add an error to the collection.
config_set is the set with the error.
symbol is the symbol we saw when we saw the error.
config is the configuration that we were in when we saw the error.
action is what we were trying to do.
(This all makes more sense from inside the TableBuilder.)
"""
set_errors = self.errors.get(config_set)
if set_errors is None:
set_errors = {}
self.errors[config_set] = set_errors
symbol_errors = set_errors.get(symbol)
if symbol_errors is None:
symbol_errors = {}
set_errors[symbol] = symbol_errors
symbol_errors[config] = action
def gen_exception(
self,
alphabet: list[str],
all_sets: ConfigurationSetInfo,
) -> AmbiguityError | None:
"""Format all the errors into an error, or return None if there are no
errors.
We need the alphabet to turn all these integers into something human
readable, and all the sets to trace a path to where the errors were
encountered.
"""
if len(self.errors) == 0:
return None
# with open("ambiguity.json", mode="w", encoding="utf-8") as aj:
# aj.write(all_sets.dump_state(alphabet))
errors = []
for config_set, set_errors in self.errors.items():
path = all_sets.find_path_to_set(config_set)
path_str = " ".join(alphabet[s] for s in path)
for symbol, symbol_errors in set_errors.items():
actions = []
for config, action in symbol_errors.items():
core = config.core
name = alphabet[core.name]
rule = " ".join(
f"{'* ' if core.position == i else ''}{alphabet[s]}"
for i, s in enumerate(core.symbols)
)
if config.at_end:
rule += " *"
match action:
case Reduce(name=name, count=count, transparent=transparent):
name_str = name if not transparent else f"transparent node ({name})"
action_str = f"pop {count} values off the stack and make a {name_str}"
case Shift():
action_str = "consume the token and keep going"
case Accept():
action_str = "accept the parse"
case _:
raise Exception(f"unknown action type {action}")
actions.append(PossibleAction(name, rule, action_str))
errors.append(
Ambiguity(path=path_str, symbol=alphabet[symbol], actions=tuple(actions))
)
return AmbiguityError(errors)
@dataclasses.dataclass
class ParseTable:
actions: list[dict[str, ParseAction]]
gotos: list[dict[str, int]]
trivia: set[str]
def format(self):
"""Format a parser table so pretty."""
def format_action(actions: dict[str, ParseAction], terminal: str):
action = actions.get(terminal)
match action:
case Accept():
return "accept"
case Shift(state=state):
return f"s{state}"
case Reduce(count=count):
return f"r{count}"
case _:
return ""
def format_goto(gotos: dict[str, int], nt: str):
index = gotos.get(nt)
if index is None:
return ""
else:
return str(index)
terminals = list(sorted({k for row in self.actions for k in row.keys()}))
nonterminals = list(sorted({k for row in self.gotos for k in row.keys()}))
header = " | {terms} | {nts}".format(
terms=" ".join(f"{terminal: <6}" for terminal in terminals),
nts=" ".join(f"{nt: <5}" for nt in nonterminals),
)
lines = [
header,
"-" * len(header),
] + [
"{index: <4} | {actions} | {gotos}".format(
index=i,
actions=" ".join(
"{0: <6}".format(format_action(actions, terminal)) for terminal in terminals
),
gotos=" ".join("{0: <5}".format(format_goto(gotos, nt)) for nt in nonterminals),
)
for i, (actions, gotos) in enumerate(zip(self.actions, self.gotos))
]
return "\n".join(lines)
class TableBuilder(object):
"""A helper object to assemble actions into build parse tables.
This is a builder type thing: call `new_row` at the start of
each row, then `flush` when you're done with the last row.
"""
errors: ErrorCollection
actions: list[dict[str, ParseAction]]
gotos: list[dict[str, int]]
alphabet: list[str]
precedence: typing.Tuple[typing.Tuple[Assoc, int], ...]
transparents: set[str]
action_row: None | list[typing.Tuple[None | ParseAction, None | Configuration]]
goto_row: None | list[None | int]
def __init__(
self,
alphabet: list[str],
precedence: typing.Tuple[typing.Tuple[Assoc, int], ...],
transparents: set[str],
):
self.errors = ErrorCollection()
self.actions = []
self.gotos = []
self.alphabet = alphabet
self.precedence = precedence
self.transparents = transparents
self.action_row = None
self.goto_row = None
def flush(self, all_sets: ConfigurationSetInfo) -> ParseTable:
"""Finish building the table and return it.
Raises ValueError if there were any conflicts during construction.
"""
self._flush_row()
error = self.errors.gen_exception(self.alphabet, all_sets)
if error is not None:
raise error
return ParseTable(actions=self.actions, gotos=self.gotos, trivia=set())
def new_row(self, config_set: ConfigSet):
"""Start a new row, processing the given config set. Call this before
doing anything else.
"""
self._flush_row()
self.action_row = [(None, None) for _ in self.alphabet]
self.goto_row = [None for _ in self.alphabet]
self.current_config_set = config_set
def _flush_row(self):
if self.action_row:
actions = {
self.alphabet[sym]: e[0]
for sym, e in enumerate(self.action_row)
if e[0] is not None
}
self.actions.append(actions)
if self.goto_row:
gotos = {self.alphabet[sym]: e for sym, e in enumerate(self.goto_row) if e is not None}
self.gotos.append(gotos)
def set_table_reduce(self, symbol: int, config: Configuration):
"""Mark a reduce of the given configuration for the given symbol in the
current row.
"""
name = self.alphabet[config.core.name]
transparent = name in self.transparents
action = Reduce(name, len(config.core.symbols), transparent)
self._set_table_action(symbol, action, config)
def set_table_accept(self, symbol: int, config: Configuration):
"""Mark a accept of the given configuration for the given symbol in the
current row.
"""
self._set_table_action(symbol, Accept(), config)
def set_table_shift(self, symbol: int, index: int, config: Configuration):
"""Mark a shift in the current row of the given given symbol to the
given index. The configuration here provides debugging informtion for
conflicts.
"""
self._set_table_action(symbol, Shift(index), config)
def set_table_goto(self, symbol: int, index: int):
"""Set the goto for the given nonterminal symbol in the current row."""
assert self.goto_row is not None
assert self.goto_row[symbol] is None # ?
self.goto_row[symbol] = index
def _action_precedence(self, symbol: int, action: Action, config: Configuration):
if isinstance(action, Shift):
return self.precedence[symbol]
else:
return self.precedence[config.core.name]
def _set_table_action(self, symbol_id: int, action: ParseAction, config: Configuration | None):
"""Set the action for 'symbol' in the table row to 'action'.
This is destructive; it changes the table. It records an error if
there is already an action for the symbol in the row.
"""
assert isinstance(symbol_id, int)
assert self.action_row is not None
existing, existing_config = self.action_row[symbol_id]
if existing is not None and existing != action:
assert existing_config is not None
assert config is not None
existing_assoc, existing_prec = self._action_precedence(
symbol_id, existing, existing_config
)
new_assoc, new_prec = self._action_precedence(symbol_id, action, config)
if existing_prec > new_prec:
# Precedence of the action in the table already wins, do nothing.
return
elif existing_prec == new_prec:
# It's an actual conflict, use associativity if we can.
# If there's a conflict in associativity then it's a real conflict!
assoc = Assoc.NONE
if existing_assoc == Assoc.NONE:
assoc = new_assoc
elif new_assoc == Assoc.NONE:
assoc = existing_assoc
elif new_assoc == existing_assoc:
assoc = new_assoc
resolved = False
if assoc == Assoc.LEFT:
# Prefer reduce over shift
if isinstance(action, Shift) and isinstance(existing, Reduce):
action = existing
resolved = True
elif isinstance(action, Reduce) and isinstance(existing, Shift):
resolved = True
elif assoc == Assoc.RIGHT:
# Prefer shift over reduce
if isinstance(action, Shift) and isinstance(existing, Reduce):
resolved = True
elif isinstance(action, Reduce) and isinstance(existing, Shift):
action = existing
resolved = True
if not resolved:
# Record the conflicts.
self.errors.add_error(
self.current_config_set, symbol_id, existing_config, existing
)
self.errors.add_error(self.current_config_set, symbol_id, config, action)
else:
# Precedence of the new action is greater than the existing
# action, just allow the overwrite with no change.
pass
self.action_row[symbol_id] = (action, config)
class GenerateLR0:
"""Generate parser tables for an LR0 parser."""
# Internally we use integers as symbols, not strings. Mostly this is fine,
# but when we need to map back from integer to string we index this list.
alphabet: list[str]
# The grammar we work with. The outer list is indexed by grammar symbol,
# terminal *and* non-terminal. The inner list is the list of productions
# for the given nonterminal symbol. (If you have a terminal `t` and look it
# up you'll just get an empty list.)
grammar: list[list[typing.Tuple[int, ...]]]
# nonterminal[i] is True if alphabet[i] is a nonterminal.
nonterminal: typing.Tuple[bool, ...]
# The complement of nonterminal. terminal[i] is True if alphabet[i] is a
# terminal.
terminal: typing.Tuple[bool, ...]
# The precedence of every symbol. If no precedence was explicitly provided
# for a symbol, then its entry in this tuple will be (NONE, 0).
precedence: typing.Tuple[typing.Tuple[Assoc, int], ...]
# The set of symbols for which we should reduce "transparently." This doesn't
# affect state generation at all, only the generation of the final table.
transparents: set[str]
# The lookup that maps a particular symbol to an integer. (Only really used
# for debugging.)
symbol_key: dict[str, int]
# The start symbol of the grammar.
start_symbol: int
# The end symbol of the grammar.
end_symbol: int
config_sets_key: dict[ConfigSet, int]
successors: list[set[int]]
def __init__(
self,
start: str,
grammar: list[typing.Tuple[str, list[str]]],
precedence: None | dict[str, typing.Tuple[Assoc, int]] = None,
transparents: None | set[str] = None,
):
"""Initialize the parser generator with the specified grammar and
start symbol.
The input grammars are of the form:
grammar_simple = [
('E', ['E', '+', 'T']),
('E', ['T']),
('T', ['(', 'E', ')']),
('T', ['id']),
]
Which is to say, they are a list of productions. Each production is a
tuple where the first element of the tuple is the name of the
non-terminal being added, and the second elment of the tuple is the
list of terminals and non-terminals that make up the production.
There is currently no support for custom actions or alternation or
anything like that. If you want alternations that you'll have to lower
the grammar by hand into the simpler form first.
Don't name anything with double-underscores; those are reserved for
the generator. Don't add '$' either, as it is reserved to mean
end-of-stream. Use an empty list to indicate nullability, that is:
('O', []),
means that O can be matched with nothing.
This isn't a *great* way to author these things, but it is very simple
and flexible. You probably don't want to author this on your own; see
the Grammar class for a high-level API.
The precedence dictionary, if provided, maps a given symbol to an
associativity and a precedence. Any symbol not in the dictionary is
presumed to have an associativity of NONE and a precedence of zero.
"""
# Work out the alphabet.
alphabet = set()
for name, rule in grammar:
alphabet.add(name)
alphabet.update(symbol for symbol in rule)
# Check to make sure they didn't use anything that will give us
# heartburn later.
reserved = [a for a in alphabet if a.startswith("__") or a == "$"]
if reserved:
raise ValueError(
"Can't use {symbols} in grammars, {what} reserved.".format(
symbols=" or ".join(reserved),
what="it's" if len(reserved) == 1 else "they're",
)
)
alphabet.add("__start")
alphabet.add("$")
self.alphabet = list(sorted(alphabet))
symbol_key = {symbol: index for index, symbol in enumerate(self.alphabet)}
start_symbol = symbol_key["__start"]
end_symbol = symbol_key["$"]
assert self.alphabet[start_symbol] == "__start"
assert self.alphabet[end_symbol] == "$"
# Turn the incoming grammar into a dictionary, indexed by nonterminal.
#
# We count on python dictionaries retaining the insertion order, like
# it or not.
full_grammar: list[list] = [list() for _ in self.alphabet]
terminal: list[bool] = [True for _ in self.alphabet]
assert terminal[end_symbol]
nonterminal = [False for _ in self.alphabet]
for name, rule in grammar:
name_symbol = symbol_key[name]
terminal[name_symbol] = False
nonterminal[name_symbol] = True
rules = full_grammar[name_symbol]
rules.append(tuple(symbol_key[symbol] for symbol in rule))
self.grammar = full_grammar
self.grammar[start_symbol].append((symbol_key[start],))
terminal[start_symbol] = False
nonterminal[start_symbol] = True
self.terminal = tuple(terminal)
self.nonterminal = tuple(nonterminal)
assert self.terminal[end_symbol]
assert self.nonterminal[start_symbol]
if precedence is None:
precedence = {}
self.precedence = tuple(precedence.get(a, (Assoc.NONE, 0)) for a in self.alphabet)
if transparents is None:
transparents = set()
self.transparents = transparents
self.symbol_key = symbol_key
self.start_symbol = start_symbol
self.end_symbol = end_symbol
@functools.cache
def gen_closure_next(self, config: Configuration):
"""Return the next set of configurations in the closure for config.
If the position for config is just before a non-terminal, then the
next set of configurations is configurations for all of the
productions for that non-terminal, with the position at the
beginning. (If the position for config is just before a terminal,
or at the end of the production, then the next set is empty.)
"""
next = config.core.next
if next is None:
return ()
else:
return tuple(Configuration.from_rule(next, rule) for rule in self.grammar[next])
def gen_closure(self, seeds: typing.Iterable[Configuration]) -> ConfigSet:
"""Compute the closure for the specified configs. The closure is all
of the configurations we could be in. Specifically, if the position
for a config is just before a non-terminal then we must also consider
configurations where the rule is the rule for the non-terminal and
the position is just before the beginning of the rule.
(We have replaced a recursive version with an iterative one.)
"""
closure = set()
pending = list(seeds)
pending_next = []
while len(pending) > 0:
for config in pending:
if config in closure:
continue
closure.add(config)
pending_next.extend(self.gen_closure_next(config))
temp = pending
pending = pending_next
pending_next = temp
pending_next.clear()
return ConfigSet(closure)
def gen_all_successors(
self, config_set: typing.Iterable[Configuration]
) -> list[typing.Tuple[int, ConfigSet]]:
"""Return all of the non-empty successors for the given config set.
(That is, given the config set, pretend we see all the symbols we
could possibly see, and figure out which configs sets we get from
those symbols. Those are the successors of this set.)
"""
possible = {config.core.next for config in config_set if config.core.next is not None}
next = []
for symbol in possible:
seeds = ConfigSet(
config.replace_position(config.core.position + 1)
for config in config_set
if config.core.next == symbol
)
if len(seeds) > 0:
next.append((symbol, seeds))
return next
def gen_sets(self, seeds: list[Configuration]) -> ConfigurationSetInfo:
"""Generate all configuration sets starting from the provided seeds."""
result = ConfigurationSetInfo()
successors = []
pending = [ConfigSet(seeds)]
pending_next = []
while len(pending) > 0:
for core in pending:
id, is_new = result.register_core(core)
if is_new:
config_set = self.gen_closure(core)
result.register_config_closure(id, config_set)
for symbol, successor in self.gen_all_successors(config_set):
successors.append((id, symbol, successor))
pending_next.append(successor)
temp = pending
pending = pending_next
pending_next = temp
pending_next.clear()
for id, symbol, successor in successors:
result.add_successor(id, symbol, result.core_key[successor])
return result
def gen_all_sets(self) -> ConfigurationSetInfo:
"""Generate all of the configuration sets for the grammar."""
seeds = [
Configuration.from_rule(self.start_symbol, rule)
for rule in self.grammar[self.start_symbol]
]
return self.gen_sets(seeds)
def gen_reduce_set(self, config: Configuration) -> typing.Iterable[int]:
"""Return the set of symbols that indicate we should reduce the given
configuration.
In an LR0 parser, this is just the set of all terminals.
"""
del config
return [index for index, value in enumerate(self.terminal) if value]
def gen_table(self) -> ParseTable:
"""Generate the parse table.
The parse table is a list of states. The first state in the list is
the starting state. Each state is a dictionary that maps a symbol to an
action. Each action is a tuple. The first element of the tuple is a
string describing what to do:
- 'shift': The second element of the tuple is the state
number. Consume the input and push that state onto the stack.
- 'reduce': The second element is the name of the non-terminal being
reduced, and the third element is the number of states to remove
from the stack. Don't consume the input; just remove the specified
number of things from the stack, and then consult the table again,
this time using the new top-of-stack as the current state and the
name of the non-terminal to find out what to do.
- 'goto': The second element is the state number to push onto the
stack. In the literature, these entries are treated distinctly from
the actions, but we mix them here because they never overlap with the
other actions. (These are always associated with non-terminals, and
the other actions are always associated with terminals.)
- 'accept': Accept the result of the parse, it worked.
Anything missing from the row indicates an error.
"""
config_sets = self.gen_all_sets()
builder = TableBuilder(self.alphabet, self.precedence, self.transparents)
for config_set_id, config_set in enumerate(config_sets.closures):
assert config_set is not None
builder.new_row(config_set)
successors = config_sets.successors[config_set_id]
for config in config_set:
config_next = config.core.next
if config_next is None:
if config.core.name != self.start_symbol:
for a in self.gen_reduce_set(config):
builder.set_table_reduce(a, config)
else:
builder.set_table_accept(self.end_symbol, config)
elif self.terminal[config_next]:
index = successors[config_next]
builder.set_table_shift(config_next, index, config)
# Gotos
for symbol, index in successors.items():
if self.nonterminal[symbol]:
builder.set_table_goto(symbol, index)
return builder.flush(config_sets)
###############################################################################
# SLR(1)
###############################################################################
def update_changed(items: set[int], other: set[int]) -> bool:
"""Merge the `other` set into the `items` set, and return True if this
changed the items set.
"""
old_len = len(items)
items.update(other)
return old_len != len(items)
@dataclasses.dataclass(frozen=True)
class FirstInfo:
"""A structure that tracks the first set of a grammar. (Or, as it is
commonly styled in textbooks, FIRST.)
firsts[s] is the set of first terminals of any particular nonterminal s.
(For a terminal , firsts[s] == s.)
is_epsilon[s] is True if the nonterminal s can be empty, that is, if
it can match zero symbols.
For example, consider following grammar:
[
('x', ['y', 'A']),
('y', ['z']),
('y', ['B', 'x']),
('y', []),
('z', ['C']),
('z', ['D', x]),
]
For this grammar, FIRST['z'] is ('C', 'D').
FIRST['y'] is ('B', 'C', 'D'). For the first production, 'z' is first, and
since 'z' is a nonterminal we need to include all of its symbols too,
transitively. For the second production, 'B' is first, and so that gets
added to the set. The last production doesn't have anything in it, so it
doesn't contribute to FIRST['y'], but it does set `is_epsilon` to True.
Finally, FIRST['x'] is ('A', 'B', 'C', 'D'). ('B', 'C', 'D') comes from
FIRST['y'], as 'y' is first in our only production. But the 'A' comes from
the fact that is_epsilon['y'] is True: since 'y' can match empty input,
it is also legal for 'x' to begin with 'A'.
"""
firsts: list[set[int]]
is_epsilon: list[bool]
@classmethod
def from_grammar(
cls,
grammar: list[list[typing.Tuple[int, ...]]],
terminal: typing.Tuple[bool, ...],
) -> "FirstInfo":
"""Construct a new FirstInfo from the specified grammar.
terminal[s] is True if symbol s is a terminal symbol.
"""
# Add all terminals to their own firsts
firsts: list[set[int]] = []
for index, is_terminal in enumerate(terminal):
firsts.append(set())
if is_terminal:
firsts[index].add(index)
# Because we're working with recursive and mutually recursive rules, we
# need to make sure we terminate once we've actually found all the first
# symbols. Naive recursion will go forever, and recursion with a visited
# set to halt recursion ends up revisiting the same symbols over and
# over, running *very* slowly. Strangely, iteration to fixed-point turns
# out to be reasonably quick in practice, and is what every other parser
# generator uses in the end.
epsilons = [False for _ in terminal]
changed = True
while changed:
changed = False
for name, rules in enumerate(grammar):
f = firsts[name]
for rule in rules:
if len(rule) == 0:
changed = changed or not epsilons[name]
epsilons[name] = True
continue
for index, symbol in enumerate(rule):
other_firsts = firsts[symbol]
changed = update_changed(f, other_firsts) or changed
is_last = index == len(rule) - 1
if is_last and epsilons[symbol]:
# If this is the last symbol and the last
# symbol can be empty then I can be empty
# too! :P
changed = changed or not epsilons[name]
epsilons[name] = True
if not epsilons[symbol]:
# If we believe that there is at least one
# terminal in the first set of this
# nonterminal then I don't have to keep
# looping through the symbols in this rule.
break
return FirstInfo(firsts=firsts, is_epsilon=epsilons)
@dataclasses.dataclass(frozen=True)
class FollowInfo:
"""A structure that tracks the follow set of a grammar. (Or, again, as the
textbooks would have it, FOLLOW.)
The follow set for a nonterminal is the set of terminals that can follow the
nonterminal in a valid sentence. The resulting set never contains epsilon
and is never empty, since we should always at least ground out at '$', which
is the end-of-stream marker.
In order to compute follow, we need to find every place that a given
nonterminal appears in the grammar, and look at the first set of the symbol
that follows it. But if the first set of the symbol that follows it includes
epsilon, then we need to include the first of the symbol after *that*, and
so forth, until we finally either get to the end of the rule or we find some
symbol whose first doesn't include epsilon.
If we get to the end of the rule before finding a symbol that doesn't include
epsilon, then we also need to include the follow of the nonterminal that
contains the rule itself. (Anything that follows this rule can follow the
symbol we're considering.)
Consider this nonsense grammar:
[
('s', ['x', 'A']),
('x', ['y', 'B']),
('x', ['y', 'z']),
('y', ['x', 'C']),
('z', ['D']),
('z', []),
]
In this grammar, FOLLOW['y'] is ('A', 'B', 'D'). 'B' comes from the first
production of 'x', that's easy. 'D' comes from the second production of 'x':
FIRST['z'] is ('D'), and so that goes into FOLLOW['y'].
'A' is the surprising one: it comes from the fact that FIRST['z'] contains
epsilon. Since 'z' can successfully match on empty input, we need to treat
'y' as if it were at the end of 'x'. Anything that can follow 'x' can also
follow 'y'. Since 'A' is in FOLLOW['x'] (from the production 's'), then 'A'
is also in FOLLOW['y'].
Note that the follow set of any nonterminal is never empty and never
contains epsilon: they all terminate at the end-of-stream marker eventually,
by construction. (The individual parser generators make sure to augment the
grammar so that this is true, and that's a main reason why they do it.)
"""
follows: list[set[int]]
@classmethod
def from_grammar(
cls,
grammar: list[list[typing.Tuple[int, ...]]],
terminal: typing.Tuple[bool, ...],
start_symbol: int,
end_symbol: int,
firsts: FirstInfo,
):
follows: list[set[int]] = [set() for _ in grammar]
follows[start_symbol].add(end_symbol)
# See the comment in FirstInfo for why this is the way it is, more or
# less. Iteration to fixed point handlily beats recursion with
# memoization. I'm as shocked and dismayed as you as you are, but it's
# nice to remember that fixed-point algorithms are good sometimes.
changed = True
while changed:
changed = False
for name, rules in enumerate(grammar):
for rule in rules:
# To do this more efficiently, we actually walk backwards
# through the rule. As long as we've still seen something
# with epsilon, then we need to add FOLLOW[name] to
# FOLLOW[symbol]. As soon as we see something *without*
# epsilon, we can stop doing that. (This is *way* more
# efficient than trying to figure out epsilon while walking
# forward.)
epsilon = True
prev_symbol = None
for symbol in reversed(rule):
f = follows[symbol]
if terminal[symbol]:
# This particular rule can't produce epsilon.
epsilon = False
prev_symbol = symbol
continue
# While epsilon is still set, update the follow of
# this nonterminal with the follow of the production
# we're processing. (This also means that the follow
# of the last symbol in the production is the follow
# of the entire production, as it should be.)
if epsilon:
changed = update_changed(f, follows[name]) or changed
# If we're not at the end of the list then the follow
# of the current symbol contains the first of the
# next symbol.
if prev_symbol is not None:
changed = update_changed(f, firsts.firsts[prev_symbol]) or changed
# Now if there's no epsilon in this symbol there's no
# more epsilon in the rest of the sequence.
if not firsts.is_epsilon[symbol]:
epsilon = False
prev_symbol = symbol
return FollowInfo(follows=follows)
class GenerateSLR1(GenerateLR0):
"""Generate parse tables for SLR1 grammars.
SLR1 parsers can recognize more than LR0 parsers, because they have a
little bit more information: instead of generating reduce actions for a
production on all possible inputs, as LR0 parsers do, they generate
reduce actions only for inputs that are in the 'follow' set of the
non-terminal.
That means SLR1 parsers need to know how to generate 'follow(A)', which
means they need to know how to generate 'first(A)'. See FirstInfo and
FollowInfo for the details on how this is computed.
"""
_firsts: FirstInfo
_follows: FollowInfo
def __init__(self, *args, **kwargs):
"""See the constructor of GenerateLR0 for an explanation of the
parameters to the constructor and what they mean.
"""
super().__init__(*args, **kwargs)
# We store the firsts not because we need them here, but because LR1
# and LALR need them.
self._firsts = FirstInfo.from_grammar(self.grammar, self.terminal)
self._follows = FollowInfo.from_grammar(
self.grammar,
self.terminal,
self.start_symbol,
self.end_symbol,
self._firsts,
)
def gen_follow(self, symbol: int) -> set[int]:
"""Generate the follow set for the given nonterminal.
The follow set for a nonterminal is the set of terminals that can
follow the nonterminal in a valid sentence. The resulting set never
contains epsilon and is never empty, since we should always at least
ground out at '$', which is the end-of-stream marker.
See FollowInfo for more information on how this is determined.
"""
return self._follows.follows[symbol]
def gen_reduce_set(self, config: Configuration) -> typing.Iterable[int]:
"""Return the set of symbols that indicate we should reduce the given
config.
In an SLR1 parser, this is the follow set of the config nonterminal.
"""
return self.gen_follow(config.core.name)
class GenerateLR1(GenerateSLR1):
"""Generate parse tables for LR1, or "canonical LR" grammars.
LR1 parsers can recognize more than SLR parsers. Like SLR parsers, they
are choosier about when they reduce. But unlike SLR parsers, they specify
the terminals on which they reduce by carrying a 'lookahead' terminal in
the configuration. The lookahead of a configuration is computed as the
closure of a configuration set is computed, so see gen_closure_next for
details. (Except for the start configuration, which has '$' as its
lookahead.)
"""
def gen_first(self, symbols: typing.Iterable[int]) -> typing.Tuple[set[int], bool]:
"""Return the first set for a *sequence* of symbols.
(This is more than FIRST: we need to know the first thing that can
happen in this particular sequence right here.)
Build the set by combining the first sets of the symbols from left to
right as long as epsilon remains in the first set. If we reach the end
and every symbol has had epsilon, then this set also has epsilon.
Otherwise we can stop as soon as we get to a non-epsilon first(), and
our result does not have epsilon.
"""
result = set()
for s in symbols:
result.update(self._firsts.firsts[s])
if not self._firsts.is_epsilon[s]:
return (result, False)
return (result, True)
def gen_reduce_set(self, config: Configuration) -> typing.Iterable[int]:
"""Return the set of symbols that indicate we should reduce the given
config.
In an LR1 parser, this is the lookahead of the configuration.
"""
return config.lookahead
@functools.cache
def gen_closure_next(self, config: Configuration):
"""Return the next set of configurations in the closure for config.
In LR1 parsers, we must compute the lookahead for the configurations
we're adding to the closure. The lookahead for the new configurations
is the first() of the rest of this config's production. If that
contains epsilon, then the lookahead *also* contains the lookahead we
already have. (This lookahead was presumably generated by the same
process, so in some sense it is a 'parent' lookahead, or a lookahead
from an upstream production in the grammar.)
(See the documentation in GenerateLR0 for more information on how
this function fits into the whole process, specifically `gen_closure`.)
"""
config_next = config.core.next
if config_next is None:
return ()
else:
next = []
for rule in self.grammar[config_next]:
lookahead, epsilon = self.gen_first(config.rest)
if epsilon:
lookahead.update(config.lookahead)
lookahead_tuple = tuple(sorted(lookahead))
next.append(Configuration.from_rule(config_next, rule, lookahead=lookahead_tuple))
return tuple(next)
def gen_all_sets(self):
"""Generate all of the configuration sets for the grammar.
In LR1 parsers, we must remember to set the lookahead of the start
symbol to '$'.
"""
seeds = [
Configuration.from_rule(self.start_symbol, rule, lookahead=(self.end_symbol,))
for rule in self.grammar[self.start_symbol]
]
return self.gen_sets(seeds)
class GenerateLALR(GenerateLR1):
"""Generate tables for LALR.
LALR is smaller than LR(1) but bigger than SLR(1). It works by generating
the LR(1) configuration sets, but merging configuration sets which are
equal in everything but their lookaheads. This works in that it doesn't
generate any shift/reduce conflicts that weren't already in the LR(1)
grammar. It can, however, introduce new reduce/reduce conflicts, because
it does lose information. The advantage is that the number of parser
states is much much smaller in LALR than in LR(1).
If you can get away with generating LALR tables for a grammar than you
should do it.
(Note that because we use immutable state everywhere this generator does
a lot of copying and allocation. This particular generator could still
use a bunch of improvement, probably.)
"""
def gen_sets(self, seeds: list[Configuration]) -> ConfigurationSetInfo:
"""Recursively generate all configuration sets starting from the
provided set.
The difference between this method and the one in GenerateLR0, where
this comes from, is that we're going to be keeping track of states
that we found that are equivalent in lookahead.
"""
#
# First, do the actual walk. Don't merge yet: just keep track of all
# the config sets that need to be merged.
#
F: dict[CoreSet, list[ConfigSet]] = {}
seen: set[ConfigSet] = set()
closed_cores: dict[CoreSet, CoreSet] = {}
successors: list[typing.Tuple[CoreSet, int, CoreSet]] = []
pending = [(ConfigSet(seeds), CoreSet(s.core for s in seeds))]
while len(pending) > 0:
seed_set, seed_core = pending.pop()
if seed_set in seen:
continue
seen.add(seed_set)
closure = self.gen_closure(seed_set)
closure_core = CoreSet(s.core for s in closure)
closed_cores[seed_core] = closure_core
existing = F.get(closure_core)
if existing is not None:
existing.append(closure)
else:
F[closure_core] = [closure]
for symbol, successor in self.gen_all_successors(closure):
successor_seed_core = CoreSet(s.core for s in successor)
successors.append((closure_core, symbol, successor_seed_core))
pending.append((successor, successor_seed_core))
# Now we gathered the sets, merge them all.
final_sets: dict[CoreSet, ConfigSet] = {}
for key, config_sets in F.items():
la_merge: dict[ConfigurationCore, set[int]] = {}
for config_set in config_sets:
for config in config_set:
la_key = config.core
la_set = la_merge.get(la_key)
if la_set is None:
la_merge[la_key] = set(config.lookahead)
else:
la_set.update(config.lookahead)
final_set = ConfigSet(
Configuration(core=core, lookahead=tuple(sorted(la)))
for core, la in la_merge.items()
)
final_sets[key] = final_set
# Register all the actually merged, final config sets.
result = ConfigurationSetInfo()
for config_set in final_sets.values():
# Because we're building this so late we don't distinguish.
# This is probably a hack, and a sign the tracker should be better.
id, _ = result.register_core(config_set)
result.register_config_closure(id, config_set)
# Now record all the successors that we found. Of course, the actual
# sets that wound up in the ConfigurationSetInfo don't match anything
# we found during the previous phase.
#
# *Fortunately* we recorded the no-lookahead keys in the successors
# so we can find the final sets, then look them up in the registered
# sets, and actually register the successor.
for config_core, symbol, successor_seed_core in successors:
actual_config_set = final_sets[config_core]
from_index = result.config_set_key[actual_config_set]
successor_no_la = closed_cores[successor_seed_core]
actual_successor = final_sets[successor_no_la]
to_index = result.config_set_key[actual_successor]
result.add_successor(from_index, symbol, to_index)
return result
###############################################################################
# Sugar for constructing grammars
###############################################################################
# This is the "high level" API for constructing grammars.
class Rule:
"""A token (terminal), production (nonterminal), or some other
combination thereof. Rules are composed and then flattened into
productions.
"""
def __or__(self, other) -> "Rule":
return AlternativeRule(self, other)
def __add__(self, other) -> "Rule":
return SequenceRule(self, other)
@abc.abstractmethod
def flatten(self) -> typing.Generator[list["str | Terminal"], None, None]:
"""Convert this potentially nested and branching set of rules into a
series of nice, flat symbol lists.
e.g., if this rule is (X + (A | (B + C | D))) then flattening will
yield something like:
["X", "A"]
["X", "B", "C"]
["X", "B", "D"]
Isn't that nice?
Note that Token rules remain unchanged in the result: this is so we
can better distinguish terminals from nonterminals while processing
the grammar.
"""
raise NotImplementedError()
class Terminal(Rule):
"""A token, or terminal symbol in the grammar."""
value: str | None
pattern: "str | Re"
def __init__(self, pattern, *, name=None):
self.value = name
self.pattern = pattern
def flatten(self) -> typing.Generator[list["str | Terminal"], None, None]:
# We are just ourselves when flattened.
yield [self]
def __repr__(self) -> str:
return self.value or "???"
class NonTerminal(Rule):
"""A non-terminal, or a production, in the grammar.
You probably don't want to create this directly; instead you probably want
to use the `@rule` decorator to associate this with a function in your
grammar class.
"""
fn: typing.Callable[["Grammar"], Rule]
name: str
transparent: bool
def __init__(
self,
fn: typing.Callable[["Grammar"], Rule],
name: str | None = None,
transparent: bool = False,
):
"""Create a new NonTerminal.
`fn` is the function that will yield the `Rule` which is the
right-hand-side of this production; it will be flattened with `flatten`.
`name` is the name of the production- if unspecified (or `None`) it will
be replaced with the `__name__` of the provided fn.
"""
self.fn = fn
self.name = name or fn.__name__
self.transparent = transparent
def generate_body(self, grammar) -> list[list[str | Terminal]]:
"""Generate the body of the non-terminal.
We do this by first calling the associated function in order to get a
Rule, and then flattening the Rule into the associated set of
productions.
"""
return [rule for rule in self.fn(grammar).flatten()]
def flatten(self) -> typing.Generator[list[str | Terminal], None, None]:
# Although we contain multitudes, when flattened we're being asked in
# the context of some other production. Yield ourselves, and trust that
# in time we will be asked to generate our body.
yield [self.name]
class AlternativeRule(Rule):
"""A rule that matches if one or another rule matches."""
def __init__(self, left: Rule, right: Rule):
self.left = left
self.right = right
def flatten(self) -> typing.Generator[list[str | Terminal], None, None]:
# All the things from the left of the alternative, then all the things
# from the right, never intermingled.
yield from self.left.flatten()
yield from self.right.flatten()
class SequenceRule(Rule):
"""A rule that matches if a first part matches, followed by a second part.
Two things in order.
"""
def __init__(self, first: Rule, second: Rule):
self.first = first
self.second = second
def flatten(self) -> typing.Generator[list[str | Terminal], None, None]:
# All the things in the prefix....
for first in self.first.flatten():
# ...potentially followed by all the things in the suffix.
for second in self.second.flatten():
yield first + second
class NothingRule(Rule):
"""A rule that matches no input. Nothing, the void. Don't make a new one of
these, you're probably better off just using the singleton `Nothing`.
"""
def flatten(self) -> typing.Generator[list[str | Terminal], None, None]:
# It's quiet in here.
yield []
Nothing = NothingRule()
def seq(*args: Rule) -> Rule:
"""A rule that matches a sequence of rules.
(A helper function that combines its arguments into nested sequences.)
"""
result = args[0]
for rule in args[1:]:
result = SequenceRule(result, rule)
return result
@typing.overload
def rule(f: typing.Callable, /) -> Rule: ...
@typing.overload
def rule(
name: str | None = None, transparent: bool | None = None
) -> typing.Callable[[typing.Callable[[typing.Any], Rule]], Rule]: ...
def rule(
name: str | None | typing.Callable = None, transparent: bool | None = None
) -> Rule | typing.Callable[[typing.Callable[[typing.Any], Rule]], Rule]:
"""The decorator that marks a method in a Grammar object as a nonterminal
rule.
As with all the best decorators, it can be called with or without arguments.
If called with one argument, that argument is a name that overrides the name
of the nonterminal, which defaults to the name of the function.
"""
if callable(name):
return rule()(name)
def wrapper(f: typing.Callable[[typing.Any], Rule]):
nonlocal name
nonlocal transparent
if name is None:
name = f.__name__
assert isinstance(name, str)
if transparent is None:
transparent = name.startswith("_")
return NonTerminal(f, name, transparent)
return wrapper
PrecedenceList = list[typing.Tuple[Assoc, list[Rule]]]
class Grammar:
"""The base class for defining a grammar.
Inherit from this, and and define members for your nonterminals, and then
use the `build_tables` method to construct the parse tables.
Here's an example of a simple grammar:
class SimpleGrammar(Grammar):
@rule
def expression(self):
return seq(self.expression, self.PLUS, self.term) | self.term
@rule
def term(self):
return seq(self.LPAREN, self.expression, self.RPAREN) | self.ID
PLUS = Terminal('+')
LPAREN = Terminal('(')
RPAREN = Terminal(')')
ID = Terminal('id')
Not very exciting, perhaps, but it's something.
"""
_precedence: dict[str, typing.Tuple[Assoc, int]]
_start: str
_generator: type[GenerateLR0]
_terminals: list[Terminal]
_trivia: list[Terminal]
def __init__(
self,
start: str | None = None,
precedence: PrecedenceList | None = None,
generator: type[GenerateLR0] | None = None,
trivia: list[str | Terminal] | None = None,
):
if start is None:
start = getattr(self, "start", None)
if start is None:
raise ValueError(
"The default start rule must either be specified in the constructor or as an "
"attribute in the class."
)
if precedence is None:
precedence = getattr(self, "precedence", [])
assert precedence is not None
if generator is None:
generator = getattr(self, "generator", GenerateLALR)
assert generator is not None
if trivia is None:
trivia = getattr(self, "trivia", [])
assert trivia is not None
# Fixup terminal names with the name of the member that declared it.
terminals = {}
for n, t in inspect.getmembers(self, lambda x: isinstance(x, Terminal)):
if t.value is None:
t.value = n
if n in terminals:
raise ValueError(f"More than one terminal has the name '{n}'")
terminals[n] = t
# Resolve the trivia declarations correctly.
resolved_trivia: list[Terminal] = []
for t in trivia:
if isinstance(t, str):
resolved = terminals.get(t)
if resolved is None:
raise ValueError(f"The trivia '{t}' is not a terminal name")
resolved_trivia.append(resolved)
else:
resolved_trivia.append(t)
# Fix up the precedence table.
precedence_table = {}
for prec, (associativity, symbols) in enumerate(precedence):
for symbol in symbols:
if isinstance(symbol, Terminal):
key = symbol.value
elif isinstance(symbol, NonTerminal):
key = symbol.name
else:
raise ValueError(f"{symbol} must be either a Token or a NonTerminal")
precedence_table[key] = (associativity, prec + 1)
self._precedence = precedence_table
self._start = start
self._generator = generator
self._terminals = list(terminals.values())
self._trivia = resolved_trivia
@property
def terminals(self) -> list[Terminal]:
return self._terminals
@property
def resolved_trivia(self) -> list[Terminal]:
return self._trivia
def generate_nonterminal_dict(
self, start: str | None = None
) -> typing.Tuple[dict[str, list[list[str | Terminal]]], set[str]]:
"""Convert the rules into a dictionary of productions.
Our table generators work on a very flat set of productions. This is the
first step in flattening the productions from the members: walk the rules
starting from the given start rule and flatten them, one by one, into a
dictionary that maps nonterminal rule name to its associated list of
productions.
"""
if start is None:
start = self._start
rules = inspect.getmembers(self, lambda x: isinstance(x, NonTerminal))
nonterminals = {rule.name: rule for _, rule in rules}
transparents = {rule.name for _, rule in rules if rule.transparent}
grammar = {}
rule = nonterminals.get(start)
if rule is None:
raise ValueError(f"Cannot find a rule named '{start}'")
queue = [rule]
while len(queue) > 0:
rule = queue.pop()
if rule.name in grammar:
continue
body = rule.generate_body(self)
for clause in body:
for symbol in clause:
if not isinstance(symbol, Terminal):
assert isinstance(symbol, str)
nonterminal = nonterminals.get(symbol)
if nonterminal is None:
raise ValueError(f"While processing {rule.name}: cannot find {symbol}")
queue.append(nonterminal)
grammar[rule.name] = body
return (grammar, transparents)
def desugar(
self, start: str | None = None
) -> typing.Tuple[list[typing.Tuple[str, list[str]]], set[str]]:
"""Convert the rules into a flat list of productions.
Our table generators work from a very flat set of productions. The form
produced by this function is one level flatter than the one produced by
generate_nonterminal_dict- less useful to people, probably, but it is
the input form needed by the Generator.
"""
temp_grammar, transparents = self.generate_nonterminal_dict(start)
grammar = []
for rule_name, clauses in temp_grammar.items():
for clause in clauses:
new_clause = []
for symbol in clause:
if isinstance(symbol, Terminal):
if symbol.value in temp_grammar:
raise ValueError(
f"'{symbol.value}' is the name of both a Terminal and a NonTerminal rule. This will cause problems."
)
new_clause.append(symbol.value)
else:
new_clause.append(symbol)
grammar.append((rule_name, new_clause))
return grammar, transparents
def build_table(self, start: str | None = None, generator=None) -> ParseTable:
"""Construct a parse table for this grammar, starting at the named
nonterminal rule.
"""
if start is None:
start = self._start
desugared, transparents = self.desugar(start)
if generator is None:
generator = self._generator
gen = generator(start, desugared, precedence=self._precedence, transparents=transparents)
table = gen.gen_table()
for t in self._trivia:
assert t.value is not None
table.trivia.add(t.value)
return table
###############################################################################
# Lexer support
###############################################################################
# For machine-generated lexers
@dataclasses.dataclass(frozen=True, slots=True)
class Span:
lower: int # inclusive
upper: int # exclusive
@classmethod
def from_str(cls, lower: str, upper: str | None = None) -> "Span":
lo = ord(lower)
if upper is None:
hi = lo + 1
else:
hi = ord(upper) + 1
return Span(lower=lo, upper=hi)
def __len__(self) -> int:
return self.upper - self.lower
def intersects(self, other: "Span") -> bool:
"""Determine if this span intersects the other span."""
return self.lower < other.upper and self.upper > other.lower
def split(self, other: "Span") -> tuple["Span|None", "Span|None", "Span|None"]:
"""Split two possibly-intersecting spans into three regions: a low
region, which covers just the lower part of the union, a mid region,
which covers the intersection, and a hi region, which covers just the
upper part of the union.
Together, low and high cover the union of the two spans. Mid covers
the intersection. The implication is that if both spans are identical
then the low and high regions will both be None and mid will be equal
to both.
Graphically, given two spans A and B:
[ B )
[ A )
[ lo )[ mid )[ hi )
If the lower bounds align then the `lo` region is empty:
[ B )
[ A )
[ mid )[ hi )
If the upper bounds align then the `hi` region is empty:
[ B )
[ A )
[ lo )[ mid )
If both bounds align then both are empty:
[ B )
[ A )
[ mid )
split is reflexive: it doesn't matter which order you split things in,
you will always get the same output spans, in the same order.
"""
if not self.intersects(other):
if self.lower < other.lower:
return (self, None, other)
else:
return (other, None, self)
first = min(self.lower, other.lower)
second = max(self.lower, other.lower)
third = min(self.upper, other.upper)
fourth = max(self.upper, other.upper)
low = Span(first, second) if first != second else None
mid = Span(second, third)
hi = Span(third, fourth) if third != fourth else None
return (low, mid, hi)
def __str__(self) -> str:
return f"[{self.lower}-{self.upper})"
ET = typing.TypeVar("ET")
class EdgeList[ET]:
"""A list of edge transitions, keyed by *span*."""
_edges: list[tuple[Span, list[ET]]]
def __init__(self):
self._edges = []
def __iter__(self) -> typing.Iterator[tuple[Span, list[ET]]]:
return iter(self._edges)
def __repr__(self) -> str:
return f"EdgeList[{','.join(str(s[0]) + '->' + repr(s[1]) for s in self._edges)}]"
def add_edge(self, c: Span, s: ET):
"""Add an edge for the given span to the list. If there are already
spans that overlap this one, split and generating multiple distinct
edges.
"""
our_targets = [s]
# Look to see where we would put this span based solely on a sort of
# lower bounds: find the lowest upper bound that is greater than the
# lower bound of the incoming span.
point = bisect.bisect_right(self._edges, c.lower, key=lambda x: x[0].upper)
# We might need to run this in multiple iterations because we keep
# splitting against the *lowest* matching span.
next_span: Span | None = c
while next_span is not None:
c = next_span
next_span = None
# print(f" incoming: {self} @ {point} <- {c}->[{s}]")
# Check to see if we've run off the end of the list of spans.
if point == len(self._edges):
self._edges.insert(point, (c, [s]))
# print(f" trivial end: {self}")
return
# Nope, pull out the span to the right of us.
right_span, right_targets = self._edges[point]
# Because we intersect at least a little bit we know that we need to
# split and keep processing.
del self._edges[point]
lo, mid, hi = c.split(right_span) # Remember the semantics
# print(f" -> {c} splits {right_span} -> {lo}, {mid}, {hi} @{point}")
# We do this from lo to hi, lo first.
if lo is not None:
# NOTE: lo will never intersect both no matter what.
if lo.intersects(right_span):
assert not lo.intersects(c)
targets = right_targets
else:
assert lo.intersects(c)
targets = our_targets
self._edges.insert(point, (lo, targets))
point += 1 # Adjust the insertion point, important for us to keep running.
if mid is not None:
# If mid exists it is known to intersect with both so we can just
# do it.
self._edges.insert(point, (mid, right_targets + our_targets))
point += 1 # Adjust the insertion point, important for us to keep running.
if hi is not None:
# NOTE: Just like lo, hi will never intersect both no matter what.
if hi.intersects(right_span):
# If hi intersects the right span then we're done, no
# need to keep running.
assert not hi.intersects(c)
self._edges.insert(point, (hi, right_targets))
else:
# BUT! If hi intersects the incoming span then what we
# need to do is to replace the incoming span with hi
# (having chopped off the lower part of the incoming
# span) and continue to execute with only the upper part
# of the incoming span.
#
# Why? Because the upper part of the incoming span might
# intersect *more* spans, in which case we need to keep
# splitting and merging targets.
assert hi.intersects(c)
next_span = hi
# print(f" result: {self}")
class NFAState:
"""An NFA state. A state can be an accept state if it has a Terminal
associated with it."""
accept: Terminal | None
epsilons: list["NFAState"]
_edges: EdgeList["NFAState"]
def __init__(self):
self.accept = None
self.epsilons = []
self._edges = EdgeList()
def __repr__(self):
return f"State{id(self)}"
def edges(self) -> typing.Iterable[tuple[Span, list["NFAState"]]]:
return self._edges
def add_edge(self, c: Span, s: "NFAState") -> "NFAState":
self._edges.add_edge(c, s)
return s
def dump_graph(self, name="nfa.dot"):
with open(name, "w", encoding="utf8") as f:
f.write("digraph G {\n")
stack: list[NFAState] = [self]
visited = set()
while len(stack) > 0:
state = stack.pop()
if state in visited:
continue
visited.add(state)
label = state.accept.value if state.accept is not None else ""
f.write(f' {id(state)} [label="{label}"];\n')
for target in state.epsilons:
stack.append(target)
f.write(f' {id(state)} -> {id(target)} [label="\u03B5"];\n')
for span, targets in state.edges():
label = str(span).replace('"', '\\"')
for target in targets:
stack.append(target)
f.write(f' {id(state)} -> {id(target)} [label="{label}"];\n')
f.write("}\n")
@dataclasses.dataclass
class Re:
def to_nfa(self) -> tuple[NFAState, list[NFAState]]:
raise NotImplementedError()
def __str__(self) -> str:
raise NotImplementedError()
@classmethod
def seq(cls, *values: "Re") -> "Re":
result = values[0]
for v in values[1:]:
result = ReSeq(result, v)
return result
@classmethod
def literal(cls, value: str) -> "Re":
return cls.seq(*[ReSet.from_ranges(c) for c in value])
@classmethod
def set(cls, *args: str | tuple[str, str]) -> "ReSet":
return ReSet.from_ranges(*args)
@classmethod
def any(cls) -> "ReSet":
return ReSet.any()
def plus(self) -> "Re":
return RePlus(self)
def star(self) -> "Re":
return ReStar(self)
def question(self) -> "Re":
return ReQuestion(self)
def __or__(self, value: "Re", /) -> "Re":
return ReAlt(self, value)
def __add__(self, value: "Re") -> "Re":
return ReSeq(self, value)
UNICODE_MAX_CP = 1114112
@dataclasses.dataclass
class ReSet(Re):
values: list[Span]
@classmethod
def from_ranges(cls, *args: str | tuple[str, str]) -> "ReSet":
values = []
for a in args:
if isinstance(a, str):
values.append(Span.from_str(a))
else:
values.append(Span.from_str(a[0], a[1]))
return ReSet(values)
@classmethod
def any(cls) -> "ReSet":
return ReSet(values=[Span(0, UNICODE_MAX_CP)])
def invert(self) -> "ReSet":
spans = []
lower = 0
for span in self.values:
upper = span.lower
if upper != lower:
assert lower < upper
spans.append(Span(lower, upper))
lower = span.upper
# What... is.... the top end here? Are we dealing with bytes? Are we
# dealing with unicode character ranges? In python we're dealing with
# "ord". I feel like this... here... is correct but might need to
# change when the state machine is converted for other languages.
#
upper = UNICODE_MAX_CP
if upper != lower:
assert lower < upper
spans.append(Span(lower, upper))
return ReSet(spans)
def __invert__(self) -> "ReSet":
return self.invert()
def to_nfa(self) -> tuple[NFAState, list[NFAState]]:
start = NFAState()
end = NFAState()
for span in self.values:
start.add_edge(span, end)
return (start, [end])
def __str__(self) -> str:
if len(self.values) == 1:
span = self.values[0]
if len(span) == 1:
return chr(span.lower)
ranges = []
for span in self.values:
start = chr(span.lower)
end = chr(span.upper - 1)
if start == end:
ranges.append(start)
else:
ranges.append(f"{start}-{end}")
return "[{}]".format("".join(ranges))
@dataclasses.dataclass
class RePlus(Re):
child: Re
def to_nfa(self) -> tuple[NFAState, list[NFAState]]:
start, ends = self.child.to_nfa()
end = NFAState()
for e in ends:
e.epsilons.append(end)
end.epsilons.append(start)
return (start, [end])
def __str__(self) -> str:
return f"({self.child})+"
@dataclasses.dataclass
class ReStar(Re):
child: Re
def to_nfa(self) -> tuple[NFAState, list[NFAState]]:
start = NFAState()
child_start, ends = self.child.to_nfa()
start.epsilons.append(child_start)
for end in ends:
end.epsilons.append(start)
# TODO: Do I need to make an explicit end state here?
return (start, [start])
def __str__(self) -> str:
return f"({self.child})*"
@dataclasses.dataclass
class ReQuestion(Re):
child: Re
def to_nfa(self) -> tuple[NFAState, list[NFAState]]:
start = NFAState()
child_start, ends = self.child.to_nfa()
start.epsilons.append(child_start)
ends.append(start)
return (start, ends)
def __str__(self) -> str:
return f"({self.child})?"
@dataclasses.dataclass
class ReSeq(Re):
left: Re
right: Re
def to_nfa(self) -> tuple[NFAState, list[NFAState]]:
left_start, left_ends = self.left.to_nfa()
right_start, right_ends = self.right.to_nfa()
for end in left_ends:
end.epsilons.append(right_start)
return (left_start, right_ends)
def __str__(self) -> str:
return f"{self.left}{self.right}"
@dataclasses.dataclass
class ReAlt(Re):
left: Re
right: Re
def to_nfa(self) -> tuple[NFAState, list[NFAState]]:
left_start, left_ends = self.left.to_nfa()
right_start, right_ends = self.right.to_nfa()
start = NFAState()
start.epsilons.append(left_start)
start.epsilons.append(right_start)
return (start, left_ends + right_ends)
def __str__(self) -> str:
return f"(({self.left})||({self.right}))"
LexerTable = list[tuple[Terminal | None, list[tuple[Span, int]]]]
class NFASuperState:
states: frozenset[NFAState]
def __init__(self, states: typing.Iterable[NFAState]):
# Close over the given states, including every state that is
# reachable by epsilon-transition.
stack = list(states)
result = set()
while len(stack) > 0:
st = stack.pop()
if st in result:
continue
result.add(st)
stack.extend(st.epsilons)
self.states = frozenset(result)
def __eq__(self, other):
if not isinstance(other, NFASuperState):
return False
return self.states == other.states
def __hash__(self) -> int:
return hash(self.states)
def edges(self) -> list[tuple[Span, "NFASuperState"]]:
working: EdgeList[list[NFAState]] = EdgeList()
for st in self.states:
for span, targets in st.edges():
working.add_edge(span, targets)
# EdgeList maps span to list[list[State]] which we want to flatten.
last_upper = None
result = []
for span, stateses in working:
if last_upper is not None:
assert last_upper <= span.lower
last_upper = span.upper
s: list[NFAState] = []
for states in stateses:
s.extend(states)
result.append((span, NFASuperState(s)))
if len(result) > 0:
for i in range(0, len(result) - 1):
span = result[i][0]
next_span = result[i + 1][0]
assert span.upper <= next_span.lower
# TODO: Merge spans that are adjacent and go to the same state.
return result
def accept_terminal(self) -> Terminal | None:
accept = None
for st in self.states:
if st.accept is None:
continue
if accept is None:
accept = st.accept
elif accept.value != st.accept.value:
if accept.regex and not st.accept.regex:
accept = st.accept
elif st.accept.regex and not accept.regex:
pass
else:
raise ValueError(
f"Lexer is ambiguous: cannot distinguish between {accept.value} ('{accept.pattern}') and {st.accept.value} ('{st.accept.pattern}')"
)
return accept
def compile_lexer(grammar: Grammar) -> LexerTable:
# Parse the terminals all together into a big NFA rooted at `NFA`.
NFA = NFAState()
for terminal in grammar.terminals:
pattern = terminal.pattern
if isinstance(pattern, Re):
start, ends = pattern.to_nfa()
for end in ends:
end.accept = terminal
NFA.epsilons.append(start)
else:
start = end = NFAState()
for c in pattern:
end = end.add_edge(Span.from_str(c), NFAState())
end.accept = terminal
NFA.epsilons.append(start)
NFA.dump_graph()
# Convert the NFA into a DFA in the most straightforward way (by tracking
# sets of state closures, called SuperStates.)
DFA: dict[NFASuperState, tuple[int, list[tuple[Span, NFASuperState]]]] = {}
stack = [NFASuperState([NFA])]
while len(stack) > 0:
ss = stack.pop()
if ss in DFA:
continue
edges = ss.edges()
DFA[ss] = (len(DFA), edges)
for _, target in edges:
stack.append(target)
return [
(
ss.accept_terminal(),
[(k, DFA[v][0]) for k, v in edges],
)
for ss, (_, edges) in DFA.items()
]
def dump_lexer_table(table: LexerTable, name: str = "lexer.dot"):
with open(name, "w", encoding="utf-8") as f:
f.write("digraph G {\n")
for index, (accept, edges) in enumerate(table):
label = accept.value if accept is not None else ""
f.write(f' {index} [label="{label}"];\n')
for span, target in edges:
label = str(span).replace('"', '\\"')
f.write(f' {index} -> {target} [label="{label}"];\n')
pass
f.write("}\n")
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