430 lines
14 KiB
Python
430 lines
14 KiB
Python
from emis_funky_funktions import *
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from dataclasses import dataclass
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from enum import auto, IntEnum
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from functools import reduce
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from re import compile, Pattern
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from lex import Lexeme, tokenize
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from parse import Action
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from typing import Any, Callable, Collection, Mapping, Sequence, Tuple, TypeAlias
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# Grammar
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# S := <P> Eof
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# P := <M> + <P>
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# P := <M>
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# M := <T> * <M>
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# M := <T>
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# T := Letter
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# T := Number
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# T := ( <P> )
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class TrivialTok(IntEnum):
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"A set of tokens for a trivial grammar used for testing"
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EOF = auto()
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"Special token: End of file"
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ADD = auto()
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"Addition (+)"
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MUL = auto()
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"Multiplication (*)"
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LTR = auto()
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"A single letter (x)"
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NUM = auto()
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"A number (3)"
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OPN = auto()
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"An open paren, i.e. '('"
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CLS = auto()
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"An close paren, i.e. ')'"
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NUL = auto()
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"Whitespace ( )"
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def __repr__(self):
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return self._name_
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TRIVIAL_LEX_TABLE: Collection[Tuple[Pattern[str], TrivialTok]] = [
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(compile(r"\+" ), TrivialTok.ADD),
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(compile(r"\*" ), TrivialTok.MUL),
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(compile(r"[a-zA-Z]"), TrivialTok.LTR),
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(compile("\d+" ), TrivialTok.NUM),
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(compile("\(" ), TrivialTok.OPN),
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(compile("\)" ), TrivialTok.CLS),
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(compile("\s+" ), TrivialTok.NUL),
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]
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"""
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A mapping of regexs to the tokens the identify in a trivial grammar for testing
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Tokens earlier on in the list should be regarded as higher priority, even if a match lower
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on the list also matches. All unicode strings should be matched by at least one token.
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"""
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lex_trivial: Callable[[str], List[Lexeme[TrivialTok]]] =\
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c(unwrap_r, p(tokenize, TRIVIAL_LEX_TABLE, [TrivialTok.NUL], TrivialTok.EOF)) #type: ignore
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"""
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A lexer for the trivial grammar defined above
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Throws an error if the lex fails.
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>>> lex_trivial("1 + 3") #doctest: +NORMALIZE_WHITESPACE
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[[NUM: '1']@(1, 1-1),
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[ADD: '+']@(1, 3-3),
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[NUM: '3']@(1, 5-5),
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[EOF: '']@(1, 6-6)]
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"""
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############# Combinator Parsing ################
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Out = TypeVar('Out')
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Out1 = TypeVar('Out1')
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Out2 = TypeVar('Out2')
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TokN = TypeVar('TokN')
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LexStream: TypeAlias = Sequence[Lexeme[TokN]]
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ParserResult: TypeAlias = Result[Collection[Tuple[Out, LexStream[TokN]]], Collection[Tuple[Lexeme[TokN], TokN]]]
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@dataclass(frozen=True)
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class Parser(Generic[Out, TokN]):
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"""
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A parser which consumes a token stream and produces a series of possible parses
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Each possible parse consists of the subsection of the input stream left over after the
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parse, along with the output of that parse.
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If the parse fails, the error returned will be a series of two-tuples, each containing
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the lexeme at which the error occurred and the token which was expected in its stead.
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By the nature of combinator parsing, parsers can be built and tested in small pieces.
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To this end, each combinator method on this class comes with a small example
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demonstrating how to build a trivial parser using that method. However, in the
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following section, we also provide an example for a grammar that is still trivial, but
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slightly less so.
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### Example: Arithmetic Grammar
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Let us define the following grammar for basic additive and multiplicative arithmetic
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```
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S := <P> Eof
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P := <M> + <P>
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P := <M>
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M := <T> * <M>
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M := <T>
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T := Number
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T := ( <P> )
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```
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As with the rest of the examples in this class, we will use the `TrivialTok` token
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class to build this parser.
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Working our way from the bottom up, we start with defining a parser for T. For the
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parenthetical production, we use a lazy parser to refer to the parser for P, which
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hasn't been constructed yet.
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>>> parse_parens = Parser.token(TrivialTok.OPN)\\
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... .bind(k(Parser.lazy(lambda: parse_p)))\\
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... .seq_ignore_tok(TrivialTok.CLS)
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>>> parse_num = Parser.token(TrivialTok.NUM)\\
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... .map(c(int, Lexeme.get_match))
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>>> parse_t = parse_parens.or_(parse_num)
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For multiplication, we use `Parser.many()` to represent any number of "* <T>" matches
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and combine them together. This is a slight departure from how our grammar is
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written above. The set of accepted inputs will be the same, but our implementation
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will be left-associative. It is possible to implement this grammar as it is written,
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but this will result in a right-associative structure. Of course, multiplication and
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addition are associative, so in this case it doesn't matter.
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>>> parse_times = Parser.token(TrivialTok.MUL)\\
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... .map(k(lambda x: lambda y: x * y))\\
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... .fapply(parse_t)\\
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... .many(lambda l: lambda r: c(l, r), lambda x: x)
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>>> parse_m = parse_t.fapply_r(parse_times)
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Addition is largely the same as multiplication:
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>>> parse_plus = Parser.token(TrivialTok.ADD)\\
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... .map(k(lambda x: lambda y: x + y))\\
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... .fapply(parse_m)\\
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... .many(lambda l: lambda r: c(l, r), lambda x: x)
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>>> parse_p = parse_m.fapply_r(parse_plus)
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And finally, we expect and EOF after the end of the term, to ensure that we've reached
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the end of the input.
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>>> parse_s = parse_p.seq_ignore_tok(TrivialTok.EOF)
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And now, for a few sample runs:
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>>> parse_s.parse(lex_trivial('1'))
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Ok([(1, [])])
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>>> parse_s.parse(lex_trivial('1 + 2'))
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Ok([(3, [])])
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>>> parse_s.parse(lex_trivial('1 + 2 * 3 + 4'))
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Ok([(11, [])])
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>>> parse_s.parse(lex_trivial('(1 + 2) * (3 + 4)'))
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Ok([(21, [])])
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>>> parse_s.parse(lex_trivial('(1 + 2 * 3) * (4 + 5) + 6'))
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Ok([(69, [])])
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"""
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parse: Callable[[LexStream[TokN]], ParserResult[Out, TokN]]
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@staticmethod
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def epsilon(ret: Out) -> 'Parser[Out, TokN]':
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"""
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Parse an empty string, then return a constant
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Always succeeds, and always produces exactly one possibility
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>>> Parser.epsilon(100).parse(lex_trivial("+"))
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Ok(((100, [[ADD: '+']@(1, 1-1), [EOF: '']@(1, 2-2)]),))
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"""
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return Parser(lambda s: Ok(((ret, s),)))
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@staticmethod
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def token(t: TokN) -> 'Parser[Lexeme[TokN], TokN]':
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"""
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Parser that only accepts a single token, and returns the parsed lexeme
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The first argument is a function which, given a lexeme, returns the token that
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that lexeme instantiates. The second argument is a token which this parser should
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accept
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>>> parse_num = Parser.token(TrivialTok.NUM)
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>>> parse_num.parse(lex_trivial('3'))
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Ok((([NUM: '3']@(1, 1-1), [[EOF: '']@(1, 2-2)]),))
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>>> parse_num.parse(lex_trivial('x'))
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Err((([LTR: 'x']@(1, 1-1), NUM),))
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"""
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def parse_single(input: LexStream) -> ParserResult[Lexeme[TokN], TokN]:
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match input:
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case [lexeme, *rest] if lexeme.token == t:
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return Ok(((lexeme, rest),))
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case [bad_lexeme, *rest]:
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return Err(((bad_lexeme, t),))
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case []:
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raise Exception('Bad grammar! Reached an empty input')
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raise Exception('Unreachable')
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return Parser(parse_single)
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@staticmethod
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def lazy(
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gen: 'Callable[[], Parser[Out, TokN]]',
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) -> 'Parser[Out, TokN]':
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"""
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A stand-in parser which will only be actually computed when called
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"""
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return Parser(lambda s: gen().parse(s))
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def bind(self, f: 'Callable[[Out], Parser[Out2, TokN]]') -> 'Parser[Out2, TokN]':
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"""
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A monadic bind operator - allows a parser to be generated from its precenent
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### Example
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We generate a parser which reads a number then accepts exactly that many plus
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tokens, returning the last one.
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>>> some_n = Parser.token(TrivialTok.NUM)
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>>> n_plus = some_n.bind(lambda prev_result:
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... reduce(
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... lambda a, p: a.bind(k(p)),
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... [
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... Parser.token(TrivialTok.ADD)
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... for i in range(int(prev_result.matched_string))
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... ]
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... )
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... )
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**Sample Run 1**: We parse the string `3+++`. Since this is a three followed by
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exactly three plus signs, this should parse successfully. Sure enough, the result
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contains exactly one possibility, where the `3+++` has been consumed, leaving only
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the EOF, and returning the value of the last plus sign.
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>>> n_plus.parse(lex_trivial('3+++'))
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Ok([([ADD: '+']@(1, 4-4), [[EOF: '']@(1, 5-5)])])
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**Simple Run 2**: We parse the string `3++`. This only has two of the three plus
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signs, so we should expect it to fail. As expected, at does, correctly
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identifying that it saw an EOF while expecting an ADD.
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>>> n_plus.parse(lex_trivial('3++'))
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Err([([EOF: '']@(1, 4-4), ADD)])
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"""
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def handle_results(results: Collection[Tuple[Out, LexStream]]) -> ParserResult[Out2, TokN]:
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successes, errors = partition([
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f(out1).parse(stream)
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for (out1, stream) in results
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])
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if len(successes):
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return Ok([p for s in successes for p in s])
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else:
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return Err([e for errs in errors for e in errs])
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def inner(input: LexStream) -> ParserResult[Out2, TokN]:
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return self.parse(input) << handle_results
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return Parser(inner)
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def map(self, f: Callable[[Out], B]) -> 'Parser[B, TokN]':
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"""
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Transform the output of some parser with a function
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This is a particularly useful method, because it allows converting parsers which
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return lexemes (e.g. `Parser.token()`) into parsers that return other thing.
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As an example, here's a parser which parses a number, and returns it as a number.
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>>> parse_num = Parser.token(TrivialTok.NUM)\\
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... .map(lambda l: int(l.matched_string))
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>>> parse_num.parse(lex_trivial('3'))
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Ok([(3, [[EOF: '']@(1, 2-2)])])
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"""
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return self.bind(c(Parser.epsilon, f)) #type: ignore
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def fapply(self: 'Parser[Callable[[Out1], Out2], TokN]', arg: 'Parser[Out1, TokN]') -> 'Parser[Out2, TokN]':
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"""
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Apply the function which this returns to the value produced by another parser
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Equivalent to the fapply method of an applicative functor.
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"""
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return self.bind(p(Parser.map, arg)) #type: ignore
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def fapply_r(self: 'Parser[Out, TokN]', arg: 'Parser[Callable[[Out], Out2], TokN]') -> 'Parser[Out2, TokN]':
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"""
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A reversed version of `fapply()`
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Applies the function returned by the argument to the value returned by this.
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"""
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return self.bind(lambda v: arg.map(lambda f: f(v)))
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def seq_ignore(self, subsequent: 'Parser[Any, TokN]') -> 'Parser[Out, TokN]':
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"""
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Parses two things in series, ignoring the output of the second parser
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Example: Parse a number followed by any letter (ignored)
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>>> parse_num = Parser.token(TrivialTok.NUM)\\
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... .map(lambda l: int(l.matched_string))
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>>> parse_numlet = parse_num.seq_ignore(Parser.token(TrivialTok.LTR))
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>>> parse_numlet.parse(lex_trivial('4a'))
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Ok([(4, [[EOF: '']@(1, 3-3)])])
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"""
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return self.map(k).fapply(subsequent) #type:ignore
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def seq_ignore_tok(self, subsequent: TokN) -> 'Parser[Out, TokN]':
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"""
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A shorthand for calling `seq_ignore()` with `Parser.token`
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Example: Parse a number followed by any letter (ignored)
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>>> parse_num = Parser.token(TrivialTok.NUM)\\
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... .map(lambda l: int(l.matched_string))
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>>> parse_numlet = parse_num.seq_ignore_tok(TrivialTok.LTR)
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>>> parse_numlet.parse(lex_trivial('4a'))
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Ok([(4, [[EOF: '']@(1, 3-3)])])
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"""
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return self.seq_ignore(Parser.token(subsequent))
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def or_(self: 'Parser[Out, TokN]', *parsers: 'Parser[Out, TokN]') -> 'Parser[Out, TokN]':
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"""
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Returns a parser which succeeds if this or any arguments succeed
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**Example:** A parser which parses a letter or a number
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>>> parse_or = Parser.token(TrivialTok.NUM).or_(Parser.token(TrivialTok.LTR))
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>>> parse_or.parse(lex_trivial('a')) #doctest: +ELLIPSIS
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Ok(...)
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>>> parse_or.parse(lex_trivial('1')) #doctest: +ELLIPSIS
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Ok(...)
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Notice that this can produce multiple successes. A simple example would be a
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parser which parses either a single number or an empty string (epsilon). When
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faced with an input stream starting with a number, it could either parse that
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number, returning the rest of the input stream, or parse the empty string,
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returning the input unchanged.
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>>> parse_maybe_num = Parser.token(TrivialTok.NUM)\\
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... .map(lambda l: int(l.matched_string))\\
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... .or_(Parser.epsilon(-1))
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>>> parse_maybe_num.parse(lex_trivial('3')) #doctest: +NORMALIZE_WHITESPACE
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Ok([(3, [[EOF: '']@(1, 2-2)]),
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(-1, [[NUM: '3']@(1, 1-1), [EOF: '']@(1, 2-2)])])
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"""
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all_parsers = (self, *parsers)
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def inner(input: LexStream) -> ParserResult[Out, TokN]:
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successes, failures = partition([p.parse(input) for p in all_parsers])
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if len(successes):
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return Ok([successful_path for success in successes for successful_path in success])
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else:
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return Err([expectation for failure in failures for expectation in failure])
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return Parser(inner)
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def opt(self, fallback: Out) -> 'Parser[Out, TokN]':
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"""
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Parse one or zero of this thing, returning fallback if not parsing it
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We can use this to write a simpler example of parse_maybe_num from the `or_()`
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example:
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>>> parse_maybe_num = Parser.token(TrivialTok.NUM)\\
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... .map(lambda l: int(l.matched_string))\\
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... .opt(-1)
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>>> parse_maybe_num.parse(lex_trivial('3')) #doctest: +NORMALIZE_WHITESPACE
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Ok([(3, [[EOF: '']@(1, 2-2)]),
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(-1, [[NUM: '3']@(1, 1-1), [EOF: '']@(1, 2-2)])])
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"""
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return self.or_(Parser.epsilon(fallback))
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def many(self, combine: Callable[[Out], Callable[[Out2], Out2]], default: Out2) -> 'Parser[Out2, TokN]':
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"""
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Create a new parser which accepts any number of instances of this parser
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The combine argument is a function which joins the result of this parser with the
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result of parsing the 0 or more identical parsers on the right. Think of this
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like a reduce.
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As an example, here's a parser which parses any number of numbers, and sums them
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all together.
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We start with the single number parser from the `map()` example.
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>>> parse_num = Parser.token(TrivialTok.NUM)\\
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... .map(lambda l: int(l.matched_string))
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Then we call `many()` on it. We also add the EOF parser to the end to force it to
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parse the whole input.
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>>> parse_nums = parse_num.many(lambda num: lambda sum: num + sum, 0)\\
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... .seq_ignore_tok(TrivialTok.EOF)
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**Sample Run 1:** Sum of the numbers 1, 2, and 3. This produces the operation (1
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+ (2 + (3 + 0))
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>>> parse_nums.parse(lex_trivial('1 2 3'))
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Ok([(6, [])])
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**Sample Run 2:** If attempting to sum no numbers, we get back the default
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argument, zero in this case.
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>>> parse_nums.parse(lex_trivial(''))
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Ok([(0, [])])
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"""
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return (self.map(combine)
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.fapply(Parser.lazy(p(self.many, combine, default))) #type: ignore
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.opt(default))
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if __name__ == '__main__':
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import doctest
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doctest.testmod() |