2100 lines
74 KiB
Python
2100 lines
74 KiB
Python
"""This is a small helper library to generate LR parser tables.
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The primary inspiration for this library is tree-sitter, which also generates
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LR parsers for grammars written in a turing-complete language. Like that, we
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write grammars in a language, only we do it in Python instead of JavaScript.
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Why Python? Because Python 3 is widely pre-installed on MacOS and Linux. This
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library requires nothing more than the basic standard library, and not even a
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new version of it. Therefore, it turns out to be a pretty light dependency for
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a rust or C++ or something kind of project. (Tree-sitter, on the other hand,
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requires node, which is a far less stable and available runtime in 2024.)
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The parser tables can really be used to power anything. I prefer to make
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concrete syntax trees (again, see tree-sitter), and there is no facility at all
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for actions or custom ASTs or whatnot. Any such processing needs to be done by
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the thing that processes the tables.
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## Making Grammars
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To get started, create a grammar that derives from the `Grammar` class. Create
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one method per nonterminal, decorated with the `rule` decorator. Here's an
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example:
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PLUS = Terminal('+')
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LPAREN = Terminal('(')
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RPAREN = Terminal(')')
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ID = Terminal('id')
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class SimpleGrammar(Grammar):
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@rule
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def expression(self):
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return seq(self.expression, PLUS, self.term) | self.term
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@rule
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def term(self):
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return seq(LPAREN, self.expression, RPAREN) | ID
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## Using grammars
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TODO
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## Representation Choices
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The SimpleGrammar class might seem a little verbose compared to a dense
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structure like:
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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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or
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grammar_simple = {
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'E': [
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['E', '+', 'T'],
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['T'],
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],
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'T': [
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['(', 'E', ')'],
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['id'],
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],
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}
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The advantage that the class has over a table like this is that you get to have
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all of your Python tools help you make sure your grammar is good, if you want
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them. e.g., if you're working with an LSP or something, the members give you
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autocomplete and jump-to-definition and possibly even type-checking.
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At the very least, if you mis-type the name of a nonterminal, or forget to
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implement it, we will immediately raise an error that *INCLUDES THE LOCATION IN
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THE SOURCE WHERE THE ERROR WAS MADE.* With tables, we can tell you that you
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made a mistake but it's up to you to figure out where you did it.
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### Aside: What about a custom DSL/EBNF like thing?
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Yeah, OK, there's a rich history of writing your grammar in a domain-specific
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language. YACC did it, ANTLR does it, GRMTools.... just about everybody except
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Tree-Sitter does this.
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But look, I've got several reasons for not doing it.
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First, I'm lazy, and don't want to write yet another parser for my parser. What
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tools should I use to write my parser generator parser? I guess I don't have my
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parser generator parser yet, so probably a hand-written top down parser? Some
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other python parser generator? Ugh!
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As an add-on to that, if I make my own format then I need to make tooling for
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*that* too: syntax highlighters, jump to definition, the works. Yuck. An
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existing language, and a format that builds on an existing language, gets me the
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tooling that comes along with that language. If you can leverage that
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effictively (and I think I have) then you start way ahead in terms of tooling.
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Second, this whole thing is supposed to be easy to include in an existing
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project, and adding a custom compiler doesn't seem to be that. Adding two python
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files seems to be about the right speed.
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Thirdly, and this is just hypothetical, it's probably pretty easy to write your
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own tooling around a grammar if it's already in Python. If you want to make
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railroad diagrams or EBNF pictures or whatever, all the productions are already
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right there in data structures for you to process. I've tried to keep them
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accessible and at least somewhat easy to work with. There's nothing that says a
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DSL-based system *has* to produce unusable intermediate data- certainly there
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are some tools that *try*- but with this approach the accessibility and the
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ergonomics of the tool go hand in hand.
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## Some History
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The first version of this code was written as an idle exercise to learn how LR
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parser table generation even worked. It was... very simple, fairly easy to
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follow, and just *incredibly* slow. Like, mind-bogglingly slow. Unusably slow
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for anything but the most trivial grammar.
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As a result, when I decided I wanted to use it for a larger grammar, I found that
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I just couldn't. So this has been hacked and significantly improved from that
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version, now capable of building tables for nontrivial grammars. It could still
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be a lot faster, but it meets my needs for now.
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(BTW, the notes I read to learn how all this works are at
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http://dragonbook.stanford.edu/lecture-notes/Stanford-CS143/. Specifically,
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I started with handout 8, 'Bottom-up-parsing', and went from there. (I did
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eventually have to backtrack a little into handout 7, since that's where
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First() and Follow() are covered.)
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May 2024
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"""
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import abc
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import collections
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import dataclasses
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import enum
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import functools
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import inspect
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import sys
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import typing
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###############################################################################
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# LR0
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#
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# We start with LR0 parsers, because they form the basis of everything else.
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###############################################################################
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class Configuration:
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"""A rule being tracked in a state. That is, a specific position within a
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specific rule, with an associated lookahead state.
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We make a *lot* of these and we need/want to pre-cache a ton of things we
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ask about so we need to override __init__, otherwise it's immutable and
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fixed and doesn't have a dict to save space.
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It also supports hashing and equality and comparison, so it can be sorted
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and whatnot. This really is the workhorse data structure of the whole thing.
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If you can improve this you can improve the performance of everything probably.
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(Note: technically, lookahead isn't used until we get to LR(1) parsers,
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but if left at its default it's harmless. Ignore it until you get to
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the part about LR(1).)
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"""
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__slots__ = (
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"name",
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"symbols",
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"position",
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"lookahead",
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"next",
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"at_end",
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"_vals",
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"_hash",
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)
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name: int
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symbols: typing.Tuple[int, ...]
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position: int
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lookahead: typing.Tuple[int, ...]
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next: int | None
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at_end: bool
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_vals: typing.Tuple
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_hash: int
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def __init__(self, name, symbols, position, lookahead) -> None:
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self.name = name
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self.symbols = symbols
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self.position = position
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self.lookahead = lookahead
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at_end = position == len(symbols)
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self.at_end = at_end
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self.next = symbols[position] if not at_end else None
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self._vals = (name, symbols, position, lookahead)
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self._hash = hash(self._vals)
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@classmethod
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def from_rule(cls, name: int, symbols: typing.Tuple[int, ...], lookahead=()):
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return Configuration(
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name=name,
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symbols=symbols,
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position=0,
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lookahead=lookahead,
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)
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def __hash__(self) -> int:
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return self._hash
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def __eq__(self, value: typing.Any, /) -> bool:
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if value is self:
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return True
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return (
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value._hash == self._hash
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and value.name == self.name
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and value.position == self.position
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and value.symbols == self.symbols
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and value.lookahead == self.lookahead
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)
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def __lt__(self, value) -> bool:
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if not isinstance(value, Configuration):
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return NotImplemented
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return self._vals < value._vals
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def __gt__(self, value) -> bool:
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if not isinstance(value, Configuration):
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return NotImplemented
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return self._vals > value._vals
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def __le__(self, value) -> bool:
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if not isinstance(value, Configuration):
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return NotImplemented
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return self._vals <= value._vals
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def __ge__(self, value) -> bool:
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if not isinstance(value, Configuration):
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return NotImplemented
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return self._vals >= value._vals
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def replace_position(self, new_position):
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return Configuration(
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name=self.name,
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symbols=self.symbols,
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position=new_position,
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lookahead=self.lookahead,
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)
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def clear_lookahead(self):
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return Configuration(
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name=self.name,
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symbols=self.symbols,
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position=self.position,
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lookahead=(),
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)
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def replace_lookahead(self, lookahead: typing.Tuple[int, ...]):
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return Configuration(
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name=self.name,
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symbols=self.symbols,
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position=self.position,
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lookahead=lookahead,
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)
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@property
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def rest(self):
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return self.symbols[(self.position + 1) :]
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def __repr__(self) -> str:
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la = ", " + str(self.lookahead) if self.lookahead != () else ""
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return "{name} -> {bits}{lookahead}".format(
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name=self.name,
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bits=" ".join(
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[
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("* " + str(sym)) if i == self.position else str(sym)
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for i, sym in enumerate(self.symbols)
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]
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)
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+ (" *" if self.at_end else ""),
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lookahead=la,
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)
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def format(self, alphabet: list[str]) -> str:
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la = ", " + str(tuple(alphabet[i] for i in self.lookahead)) if self.lookahead != () else ""
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return "{name} -> {bits}{lookahead}".format(
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name=alphabet[self.name],
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bits=" ".join(
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[
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"* " + alphabet[sym] if i == self.position else alphabet[sym]
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for i, sym in enumerate(self.symbols)
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]
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)
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+ (" *" if self.at_end else ""),
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lookahead=la,
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)
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# ConfigSet = typing.Tuple[Configuration, ...]
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class ConfigSet(frozenset):
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pass
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class ConfigurationSetInfo:
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"""When we build a grammar into a table, the first thing we need to do is
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generate all the configuration sets and their successors.
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(A configuration set is what it sounds like: an unordered set of
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Configuration structures. But we use Tuple because it's hashable and
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immutable and small and we order the Tuples so that we get repeatable
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results.)
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*This* is structure that tracks the result of that computation.
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(Different generators vary in the details of how they generate this
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structure, but they all compute this information.)
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"""
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config_set_key: dict[ConfigSet, int] # Map a ConfigSet into am index
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sets: list[ConfigSet] # Map the index back into a set
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# All the sucessors for all of the sets. `successors[i]` is the mapping
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# from grammar symbol to the index of the set you get by processing that
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# symbol.
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successors: list[dict[int, int]]
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def __init__(self):
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self.config_set_key = {}
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self.sets = []
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self.successors = []
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def register_config_set(self, c: ConfigSet) -> typing.Tuple[int, bool]:
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"""Potentially add a new config set to the set of sets. Returns the
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canonical ID of the set within this structure, along with a boolean
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indicating whether the set was just added or not.
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(You can use this integer to get the set back, if you need it, and
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also access the successors table.)
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"""
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existing = self.config_set_key.get(c)
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if existing is not None:
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return existing, False
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index = len(self.sets)
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self.sets.append(c)
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self.successors.append({})
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self.config_set_key[c] = index
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return index, True
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def add_successor(self, c_id: int, symbol: int, successor: int):
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"""Register sucessor(`c_id`, `symbol`) -> `successor`, where c_id
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is the id of the set in this structure, and symbol is the id of a
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symbol in the alphabet of the grammar.
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"""
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self.successors[c_id][symbol] = successor
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def find_path_to_set(self, target_set: ConfigSet) -> list[int]:
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"""Trace the path of grammar symbols from the first set (which always
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set 0) to the target set. This is useful in conflict reporting,
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because we'll be *at* a ConfigSet and want to show the grammar symbols
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that get us to where we found the conflict.
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The return value is a list of grammar symbols to get to the specified
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ConfigSet.
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This function raises KeyError if no path is found.
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"""
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target_index = self.config_set_key[target_set]
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visited = set()
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queue: collections.deque = collections.deque()
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queue.appendleft((0, []))
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while len(queue) > 0:
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set_index, path = queue.pop()
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if set_index == target_index:
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return path
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if set_index in visited:
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continue
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visited.add(set_index)
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for symbol, successor in self.successors[set_index].items():
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queue.appendleft((successor, path + [symbol]))
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raise KeyError("Unable to find a path to the target set!")
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class Assoc(enum.Enum):
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"""Associativity of a rule."""
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NONE = 0
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LEFT = 1
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RIGHT = 2
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@dataclasses.dataclass
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class Action:
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pass
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@dataclasses.dataclass
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class Reduce(Action):
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name: str
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count: int
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transparent: bool
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@dataclasses.dataclass
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class Shift(Action):
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state: int
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@dataclasses.dataclass
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class Accept(Action):
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pass
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@dataclasses.dataclass
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class Error(Action):
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pass
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@dataclasses.dataclass
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class PossibleAction:
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name: str
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rule: str
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action_str: str
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def __str__(self):
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return f"We are in the rule `{self.name}: {self.rule}` and we should {self.action_str}"
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@dataclasses.dataclass
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class Ambiguity:
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path: str
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symbol: str
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actions: typing.Tuple[PossibleAction]
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def __str__(self):
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lines = []
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lines.append(
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f"When we have parsed '{self.path}' and see '{self.symbol}' we don't know whether:"
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)
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lines.extend(f"- {action}" for action in self.actions)
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return "\n".join(lines)
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class AmbiguityError(Exception):
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ambiguities: list[Ambiguity]
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def __init__(self, ambiguities):
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self.ambiguities = ambiguities
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def __str__(self):
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return "The grammar is ambiguous:\n\n" + "\n\n".join(
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str(ambiguity) for ambiguity in self.ambiguities
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)
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class ErrorCollection:
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"""A collection of errors. The errors are grouped by config set and alphabet
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symbol, so that we can group the error strings appropriately when we format
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the error.
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"""
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errors: dict[ConfigSet, dict[int, dict[Configuration, Action]]]
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def __init__(self):
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self.errors = {}
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def any(self) -> bool:
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"""Return True if there are any errors in this collection."""
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return len(self.errors) > 0
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def add_error(
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self,
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config_set: ConfigSet,
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symbol: int,
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config: Configuration,
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action: Action,
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):
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"""Add an error to the collection.
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config_set is the set with the error.
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symbol is the symbol we saw when we saw the error.
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config is the configuration that we were in when we saw the error.
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action is what we were trying to do.
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(This all makes more sense from inside the TableBuilder.)
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"""
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set_errors = self.errors.get(config_set)
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if set_errors is None:
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set_errors = {}
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self.errors[config_set] = set_errors
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symbol_errors = set_errors.get(symbol)
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if symbol_errors is None:
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symbol_errors = {}
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set_errors[symbol] = symbol_errors
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symbol_errors[config] = action
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def gen_exception(
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self,
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alphabet: list[str],
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all_sets: ConfigurationSetInfo,
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) -> AmbiguityError | None:
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"""Format all the errors into a string, or return None if there are no
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errors.
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We need the alphabet to turn all these integers into something human
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readable, and all the sets to trace a path to where the errors were
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encountered.
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"""
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if len(self.errors) == 0:
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return None
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errors = []
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for config_set, set_errors in self.errors.items():
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path = all_sets.find_path_to_set(config_set)
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path_str = " ".join(alphabet[s] for s in path)
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for symbol, symbol_errors in set_errors.items():
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actions = []
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for config, action in symbol_errors.items():
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name = alphabet[config.name]
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rule = " ".join(
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f"{'* ' if config.position == i else ''}{alphabet[s]}"
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for i, s in enumerate(config.symbols)
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)
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if config.next is None:
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rule += " *"
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match action:
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case Reduce(name=name, count=count, transparent=transparent):
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name_str = name if not transparent else f"transparent node ({name})"
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action_str = f"pop {count} values off the stack and make a {name_str}"
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case Shift():
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action_str = "consume the token and keep going"
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case Accept():
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action_str = "accept the parse"
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case _:
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raise Exception(f"unknown action type {action}")
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actions.append(PossibleAction(name, rule, action_str))
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errors.append(
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Ambiguity(path=path_str, symbol=alphabet[symbol], actions=tuple(actions))
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)
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return AmbiguityError(errors)
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@dataclasses.dataclass
|
|
class ParseTable:
|
|
actions: list[dict[str, Action]]
|
|
gotos: list[dict[str, int]]
|
|
|
|
def format(self):
|
|
"""Format a parser table so pretty."""
|
|
|
|
def format_action(actions: dict[str, Action], 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, Action]]
|
|
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 | Action, 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)
|
|
|
|
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.name]
|
|
transparent = name in self.transparents
|
|
action = Reduce(name, len(config.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.name]
|
|
|
|
def _set_table_action(self, symbol_id: int, action: Action, 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.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)
|
|
for next_config in self.gen_closure_next(config):
|
|
pending_next.append(next_config)
|
|
|
|
temp = pending
|
|
pending = pending_next
|
|
pending_next = temp
|
|
pending_next.clear()
|
|
|
|
return ConfigSet(closure) # TODO: Why tuple?
|
|
|
|
def gen_successor(self, config_set: typing.Iterable[Configuration], symbol: int) -> ConfigSet:
|
|
"""Compute the successor state for the given config set and the
|
|
given symbol.
|
|
|
|
The successor represents the next state of the parser after seeing
|
|
the symbol.
|
|
"""
|
|
seeds = tuple(
|
|
config.replace_position(config.position + 1)
|
|
for config in config_set
|
|
if config.next == symbol
|
|
)
|
|
|
|
closure = self.gen_closure(seeds)
|
|
return 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.next for config in config_set if config.next is not None}
|
|
|
|
next = []
|
|
for symbol in possible:
|
|
successor = self.gen_successor(config_set, symbol)
|
|
if len(successor) > 0:
|
|
next.append((symbol, successor))
|
|
|
|
return next
|
|
|
|
def gen_sets(self, config_set: ConfigSet) -> ConfigurationSetInfo:
|
|
"""Generate all configuration sets starting from the provided set."""
|
|
result = ConfigurationSetInfo()
|
|
|
|
successors = []
|
|
pending = [config_set]
|
|
pending_next = []
|
|
while len(pending) > 0:
|
|
for config_set in pending:
|
|
id, is_new = result.register_config_set(config_set)
|
|
if is_new:
|
|
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.config_set_key[successor])
|
|
|
|
return result
|
|
|
|
def gen_all_sets(self) -> ConfigurationSetInfo:
|
|
"""Generate all of the configuration sets for the grammar."""
|
|
seeds = tuple(
|
|
Configuration.from_rule(self.start_symbol, rule)
|
|
for rule in self.grammar[self.start_symbol]
|
|
)
|
|
initial_set = self.gen_closure(seeds)
|
|
return self.gen_sets(initial_set)
|
|
|
|
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.sets):
|
|
builder.new_row(config_set)
|
|
successors = config_sets.successors[config_set_id]
|
|
|
|
for config in config_set:
|
|
config_next = config.next
|
|
if config_next is None:
|
|
if config.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)
|
|
|
|
|
|
def parse(table: ParseTable, input, trace=False):
|
|
"""Parse the input with the generated parsing table and return the
|
|
concrete syntax tree.
|
|
|
|
The parsing table can be generated by GenerateLR0.gen_table() or by any
|
|
of the other generators below. The parsing mechanism never changes, only
|
|
the table generation mechanism.
|
|
|
|
input is a list of tokens. Don't stick an end-of-stream marker, I'll stick
|
|
one on for you.
|
|
|
|
This is not a *great* parser, it's really just a demo for what you can
|
|
do with the table.
|
|
"""
|
|
assert "$" not in input
|
|
input = input + ["$"]
|
|
input_index = 0
|
|
|
|
# Our stack is a stack of tuples, where the first entry is the state number
|
|
# and the second entry is the 'value' that was generated when the state was
|
|
# pushed.
|
|
stack: list[typing.Tuple[int, typing.Any]] = [(0, None)]
|
|
while True:
|
|
current_state = stack[-1][0]
|
|
current_token = input[input_index]
|
|
|
|
action = table.actions[current_state].get(current_token, Error())
|
|
if trace:
|
|
print(
|
|
"{stack: <20} {input: <50} {action: <5}".format(
|
|
stack=repr([s[0] for s in stack]),
|
|
input=repr(input[input_index:]),
|
|
action=repr(action),
|
|
)
|
|
)
|
|
|
|
match action:
|
|
case Accept():
|
|
return stack[-1][1]
|
|
|
|
case Reduce(name=name, count=size, transparent=transparent):
|
|
children = []
|
|
for _, c in stack[-size:]:
|
|
if isinstance(c, tuple) and c[0] is None:
|
|
children.extend(c[1])
|
|
else:
|
|
children.append(c)
|
|
|
|
value = (name if not transparent else None, tuple(children))
|
|
stack = stack[:-size]
|
|
|
|
goto = table.gotos[stack[-1][0]].get(name)
|
|
assert goto is not None
|
|
stack.append((goto, value))
|
|
|
|
case Shift(state):
|
|
stack.append((state, (current_token, ())))
|
|
input_index += 1
|
|
|
|
case Error():
|
|
raise ValueError(
|
|
"Syntax error: unexpected symbol {sym}".format(
|
|
sym=current_token,
|
|
),
|
|
)
|
|
|
|
|
|
###############################################################################
|
|
# 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 '$', which is the end-of-stream marker.
|
|
|
|
See FollowInfo for more information on how this is determined.
|
|
"""
|
|
return self._follows.follows[symbol]
|
|
|
|
def gen_reduce_set(self, config: Configuration) -> typing.Iterable[int]:
|
|
"""Return the set of symbols that indicate we should reduce the given
|
|
config.
|
|
|
|
In an SLR1 parser, this is the follow set of the config nonterminal.
|
|
"""
|
|
return self.gen_follow(config.name)
|
|
|
|
|
|
class GenerateLR1(GenerateSLR1):
|
|
"""Generate parse tables for LR1, or "canonical LR" grammars.
|
|
|
|
LR1 parsers can recognize more than SLR parsers. Like SLR parsers, they
|
|
are choosier about when they reduce. But unlike SLR parsers, they specify
|
|
the terminals on which they reduce by carrying a 'lookahead' terminal in
|
|
the configuration. The lookahead of a configuration is computed as the
|
|
closure of a configuration set is computed, so see gen_closure_next for
|
|
details. (Except for the start configuration, which has '$' 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.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(sorted(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 = tuple(
|
|
Configuration.from_rule(self.start_symbol, rule, lookahead=(self.end_symbol,))
|
|
for rule in self.grammar[self.start_symbol]
|
|
)
|
|
initial_set = self.gen_closure(seeds)
|
|
return self.gen_sets(initial_set)
|
|
|
|
|
|
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, config_set: ConfigSet) -> 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[ConfigSet, list[ConfigSet]] = {}
|
|
seen: set[ConfigSet] = set()
|
|
successors: list[typing.Tuple[ConfigSet, int, ConfigSet]] = []
|
|
pending = [config_set]
|
|
while len(pending) > 0:
|
|
config_set = pending.pop()
|
|
if config_set in seen:
|
|
continue
|
|
seen.add(config_set)
|
|
|
|
config_set_no_la = ConfigSet(s.clear_lookahead() for s in config_set)
|
|
|
|
existing = F.get(config_set_no_la)
|
|
if existing is not None:
|
|
existing.append(config_set)
|
|
else:
|
|
F[config_set_no_la] = [config_set]
|
|
|
|
for symbol, successor in self.gen_all_successors(config_set):
|
|
successor_no_la = ConfigSet(s.clear_lookahead() for s in successor)
|
|
successors.append((config_set_no_la, symbol, successor_no_la))
|
|
pending.append(successor)
|
|
|
|
# Now we gathered the sets, merge them all.
|
|
final_sets: dict[ConfigSet, ConfigSet] = {}
|
|
for key, config_sets in F.items():
|
|
la_merge: dict[Configuration, set[int]] = {}
|
|
for config_set in config_sets:
|
|
for config in config_set:
|
|
la_key = config.clear_lookahead()
|
|
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(
|
|
config.replace_lookahead(tuple(sorted(la))) for config, 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():
|
|
result.register_config_set(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_set_no_la, symbol, successor_no_la in successors:
|
|
actual_config_set = final_sets[config_set_no_la]
|
|
from_index = result.config_set_key[actual_config_set]
|
|
|
|
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
|
|
|
|
def __init__(self, value):
|
|
self.value = sys.intern(value)
|
|
|
|
def flatten(self) -> typing.Generator[list["str | Terminal"], None, None]:
|
|
# We are just ourselves when flattened.
|
|
yield [self]
|
|
|
|
|
|
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:
|
|
|
|
PLUS = Terminal('+')
|
|
LPAREN = Terminal('(')
|
|
RPAREN = Terminal(')')
|
|
ID = Terminal('id')
|
|
|
|
class SimpleGrammar(Grammar):
|
|
@rule
|
|
def expression(self):
|
|
return seq(self.expression, PLUS, self.term) | self.term
|
|
|
|
@rule
|
|
def term(self):
|
|
return seq(LPAREN, self.expression, RPAREN) | ID
|
|
|
|
Not very exciting, perhaps, but it's something.
|
|
"""
|
|
|
|
_precedence: dict[str, typing.Tuple[Assoc, int]]
|
|
_start: str
|
|
|
|
def __init__(self, start: str, precedence: PrecedenceList | None = None):
|
|
if precedence is None:
|
|
precedence = getattr(self, "precedence", [])
|
|
assert precedence is not None
|
|
|
|
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
|
|
|
|
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):
|
|
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, generator=GenerateLALR):
|
|
"""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)
|
|
|
|
gen = generator(start, desugared, precedence=self._precedence, transparents=transparents)
|
|
table = gen.gen_table()
|
|
return table
|
|
|
|
|
|
###############################################################################
|
|
# Formatting
|
|
###############################################################################
|
|
def format_node(node):
|
|
"""Print out an indented concrete syntax tree, from parse()."""
|
|
lines = ["{name}".format(name=node[0])] + [
|
|
" " + line for child in node[1] for line in format_node(child).split("\n")
|
|
]
|
|
return "\n".join(lines)
|
|
|
|
|
|
###############################################################################
|
|
# Examples
|
|
###############################################################################
|
|
def examples():
|
|
def dump_grammar(grammar):
|
|
for name, symbols in grammar:
|
|
print(f"{name} -> {symbols}")
|
|
print()
|
|
|
|
# OK, this is a very simple LR0 grammar.
|
|
print("grammar_simple:")
|
|
grammar_simple = [
|
|
("E", ["E", "+", "T"]),
|
|
("E", ["T"]),
|
|
("T", ["(", "E", ")"]),
|
|
("T", ["id"]),
|
|
]
|
|
|
|
gen = GenerateLR0("E", grammar_simple)
|
|
table = gen.gen_table()
|
|
print(table.format())
|
|
tree = parse(table, ["id", "+", "(", "id", ")"])
|
|
print(format_node(tree) + "\n")
|
|
print()
|
|
|
|
# This one doesn't work with LR0, though, it has a shift/reduce conflict.
|
|
print("grammar_lr0_shift_reduce (LR0):")
|
|
grammar_lr0_shift_reduce = grammar_simple + [
|
|
("T", ["id", "[", "E", "]"]),
|
|
]
|
|
try:
|
|
gen = GenerateLR0("E", grammar_lr0_shift_reduce)
|
|
table = gen.gen_table()
|
|
assert False
|
|
except ValueError as e:
|
|
print(e)
|
|
print()
|
|
|
|
# Nor does this: it has a reduce/reduce conflict.
|
|
print("grammar_lr0_reduce_reduce (LR0):")
|
|
grammar_lr0_reduce_reduce = grammar_simple + [
|
|
("E", ["V", "=", "E"]),
|
|
("V", ["id"]),
|
|
]
|
|
try:
|
|
gen = GenerateLR0("E", grammar_lr0_reduce_reduce)
|
|
table = gen.gen_table()
|
|
assert False
|
|
except ValueError as e:
|
|
print(e)
|
|
print()
|
|
|
|
# Nullable symbols just don't work with constructs like this, because you can't
|
|
# look ahead to figure out if you should reduce an empty 'F' or not.
|
|
print("grammar_nullable (LR0):")
|
|
grammar_nullable = [
|
|
("E", ["F", "boop"]),
|
|
("F", ["beep"]),
|
|
("F", []),
|
|
]
|
|
try:
|
|
gen = GenerateLR0("E", grammar_nullable)
|
|
table = gen.gen_table()
|
|
assert False
|
|
except ValueError as e:
|
|
print(e)
|
|
print()
|
|
|
|
print("grammar_lr0_shift_reduce (SLR1):")
|
|
dump_grammar(grammar_lr0_shift_reduce)
|
|
gen = GenerateSLR1("E", grammar_lr0_shift_reduce)
|
|
print(f"Follow('E'): {str([gen.alphabet[f] for f in gen.gen_follow(gen.symbol_key['E'])])}")
|
|
table = gen.gen_table()
|
|
print(table.format())
|
|
tree = parse(table, ["id", "+", "(", "id", "[", "id", "]", ")"], trace=True)
|
|
print(format_node(tree) + "\n")
|
|
print()
|
|
|
|
# SLR1 can't handle this.
|
|
print("grammar_aho_ullman_1 (SLR1):")
|
|
grammar_aho_ullman_1 = [
|
|
("S", ["L", "=", "R"]),
|
|
("S", ["R"]),
|
|
("L", ["*", "R"]),
|
|
("L", ["id"]),
|
|
("R", ["L"]),
|
|
]
|
|
try:
|
|
gen = GenerateSLR1("S", grammar_aho_ullman_1)
|
|
table = gen.gen_table()
|
|
assert False
|
|
except ValueError as e:
|
|
print(e)
|
|
print()
|
|
|
|
# Here's an example with a full LR1 grammar, though.
|
|
print("grammar_aho_ullman_2 (LR1):")
|
|
grammar_aho_ullman_2 = [
|
|
("S", ["X", "X"]),
|
|
("X", ["a", "X"]),
|
|
("X", ["b"]),
|
|
]
|
|
gen = GenerateLR1("S", grammar_aho_ullman_2)
|
|
table = gen.gen_table()
|
|
print(table.format())
|
|
parse(table, ["b", "a", "a", "b"], trace=True)
|
|
print()
|
|
|
|
# What happens if we do LALR to it?
|
|
print("grammar_aho_ullman_2 (LALR):")
|
|
gen = GenerateLALR("S", grammar_aho_ullman_2)
|
|
table = gen.gen_table()
|
|
print(table.format())
|
|
print()
|
|
|
|
# A fun LALAR grammar.
|
|
print("grammar_lalr:")
|
|
grammar_lalr = [
|
|
("S", ["V", "E"]),
|
|
("E", ["F"]),
|
|
("E", ["E", "+", "F"]),
|
|
("F", ["V"]),
|
|
("F", ["int"]),
|
|
("F", ["(", "E", ")"]),
|
|
("V", ["id"]),
|
|
]
|
|
gen = GenerateLALR("S", grammar_lalr)
|
|
table = gen.gen_table()
|
|
print(table.format())
|
|
print()
|
|
|
|
|
|
if __name__ == "__main__":
|
|
examples()
|