derrickturk/oban.ebnf

## oban.ebnf
(* Copyright 2020 Derrick W. Turk / terminus data science, LLC

   Licensed under the Apache License, Version 2.0 (the "License");
   you may not use this file except in compliance with the License.
   You may obtain a copy of the License at

       http://www.apache.org/licenses/LICENSE-2.0

   Unless required by applicable law or agreed to in writing, software
   distributed under the License is distributed on an "AS IS" BASIS,
   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   See the License for the specific language governing permissions and
   limitations under the License. *)

digit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9";
number = digit, { digit };
any_character = ? any UTF-8 code point ?
string = "<<", { (any_character - ">") | ("^", any_character) }, ">>"
triboolean = "True" | "False" | "FileNotFound";
expression = number | string | triboolean | congregation | callout
congregation = "(", [ expression, { ",", expression } ], ")"
callout = "{", [ string, "!", expression, { "&", string, "!", expression } ], "}"

## oban_pc_basic.py
#  Copyright 2020 Derrick W. Turk / terminus data science, LLC

#  Licensed under the Apache License, Version 2.0 (the "License");
#  you may not use this file except in compliance with the License.
#  You may obtain a copy of the License at

#      http://www.apache.org/licenses/LICENSE-2.0

#  Unless required by applicable law or agreed to in writing, software
#  distributed under the License is distributed on an "AS IS" BASIS,
#  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
#  See the License for the specific language governing permissions and
#  limitations under the License.

import sys
from enum import Enum, auto
from typing import Any, Callable, Dict, List, NamedTuple, Tuple, TypeVar, Union

# data types we need for OBAN:

class TriBool(Enum):
    FALSE = auto()
    TRUE = auto()
    FILENOTFOUND = auto()

# there's no way to write a recursive type alias:
# we'd prefer
# Expression = Union[int, str, TriBool, List[Expression], Dict[str, Expression]]
# but we can't, so we'll wrap it in a class
class Expression:
    # type alias for what we can wrap into an expression
    Wrappable = Union[
        int,
        str,
        TriBool,
        List['Expression'],
        Dict[str, 'Expression']
    ]

    def __init__(self, value: Wrappable):
        self.value = value

    def __repr__(self):
        return f'Expression({repr(self.value)})'

# here's how we'd represent:
# { <<first>> ! (1, FileNotFound)
# & <<second>> ! <<some <<text^>^>>>
# & <<third>> ! { <<nested>> ! True }
# }
example: Expression
example = Expression({
    'first': Expression([Expression(1), Expression(TriBool.FILENOTFOUND)]),
    'second': Expression('some <<text>>'),
    'third': Expression({ 'nested': Expression(TriBool.TRUE) })
})

# now, a parser

_T = TypeVar('_T')
ParseResult = Union[Tuple[_T, str], None]
Parser = Callable[[str], ParseResult[_T]]

# a parser which can't fail
InfallibleParser = Callable[[str], Tuple[_T, str]]

# some tools for building 'primitive' parsers

# the simplest parser: 'match exactly this string'
def exactly(match: str) -> Parser[str]:
    def parser(input: str) -> ParseResult[str]:
        if input.startswith(match):
            return match, input[len(match):]
        return None
    return parser

# another basic one: succeeds at end of input; fails otherwise
# eof: Parser[None]
eof: Parser[None]
eof = lambda input: (None, input) if len(input) == 0 else None

# a parser which consumes a single character, if available
char: Parser[str]
char = lambda input: (input[0], input[1:]) if len(input) > 0 else None

# an 'infallible' parser which consumes characters matching a predicate
def chars_while(p: Callable[[str], bool]) -> InfallibleParser[str]:
    def parser(input: str) -> Tuple[str, str]:
        split_at = 0
        while split_at < len(input) and p(input[split_at]):
            split_at += 1
        return input[:split_at], input[split_at:]
    return parser

# use it to build a "consume whitespace" parser
whitespace: Parser[str]
whitespace = chars_while(str.isspace)

# some basic combinators for parsers
_U = TypeVar('_U')

# map a function over a parser's result, if it succeeds
def pmap(f: Callable[[_T], _U], p: Parser[_T]) -> Parser[_U]:
    def parser(input: str) -> ParseResult[_U]:
        res = p(input)
        if res is None:
            return None
        x, rest = res
        return f(x), rest
    return parser

# a parser which always succeeds by producing a constant
def pure(x: _T) -> InfallibleParser[_T]:
    return lambda input: (x, input)

# the opposite - a parser which always fails
# it's really a Parser[_T] for all _T, but we'll use Any since mypy
#   isn't that sharp
fail: Parser[Any]
fail = lambda _: None

# replace a successful result by a constant
def cmap(x: _T, p: Parser[_U]) -> Parser[_T]:
    return pmap(lambda _: x, p)

# these are harder to type in Python - we can do them for the fixed-arity case,
#   but it's just too damn convenient to let these take *args

# chain multiple parsers together and produce a tuple of their results,
#   if all succeed
def chain(*parsers: Parser[Any]) -> Parser[Tuple[Any, ...]]:
    def parser(input: str) -> ParseResult[Tuple[Any, ...]]:
        results = list()
        for p in parsers:
            res = p(input)
            if res is None:
                return None
            val, input = res
            results.append(val)
        return tuple(results), input
    return parser

# run multiple parsers, recovering from errors, until one succeeds;
#   fail if all parsers fail
def alt(*parsers: Parser[Any]) -> Parser[Any]:
    def parser(input: str) -> ParseResult[Any]:
        for p in parsers:
            res = p(input)
            if res is not None:
                return res
        return None
    return parser

# capture zero or more repetitions of a parser
def many(p: Parser[_T]) -> InfallibleParser[List[_T]]:
    def parser(input: str) -> Tuple[List[_T], str]:
        results: List[_T] = list()
        while True:
            res = p(input)
            if res is None:
                return results, input
            val, input = res
            results.append(val)
    return parser

# we can use alt to define an "optional" parser combinator, which allows but does
#   not require its base parser to match
def optional(p: Parser[_T]) -> Parser[Union[_T, None]]:
    return alt(p, pure(None))

# finally, a way to "decide" the next parser based on
#   the result of the previous - this is what makes Parser a monad
def bind(p: Parser[_T], f: Callable[[_T], Parser[_U]]) -> Parser[_U]:
    def parser(input: str) -> ParseResult[_U]:
        res = p(input)
        if res is None:
            return None
        x, input = res
        return f(x)(input)
    return parser

# we can use bind to build some interesting extensions to previous
#   parsers

# like chars_while, but requires there to be at least one matching char
def chars_while1(p: Callable[[str], bool]) -> Parser[str]:
    return bind(chars_while(p), lambda c: fail if len(c) == 0 else pure(c))

# use it to build a "run of digits" parser
digits: Parser[str]
digits = chars_while1(str.isdigit)

# use it to build an "unsigned integer" parser
integer: Parser[int]
integer = pmap(int, digits)

# capture one or more repetitions of a parser
def some(p: Parser[_T]) -> Parser[List[_T]]:
    return bind(many(p), lambda r: fail if len(r) == 0 else pure(r))

# now we can start building some more interesting combinators

# mypy hates type-checking lambdas as arguments to pmap, so we'll need some
#   tuple-extractor functions
def first(t: Tuple[Any, ...]) -> Any:
    return t[0]

def second(t: Tuple[Any, ...]) -> Any:
    return t[1]

# "only" p - match what p matches, then insist on end-of-input
def only(p: Parser[_T]) -> Parser[_T]:
    return pmap(first, chain(p, eof))

# match p, followed by optional whitespace
def lexeme(p: Parser[_T]) -> Parser[_T]:
    return pmap(first, chain(p, whitespace))

# match zero or more p, separated by sep
def sep_by(p: Parser[_T], sep: Parser[_U]) -> Parser[List[_T]]:
    # mypy hates this thing's type
    # it should be:
    # def extract(t: Union[Tuple[_T, List[Tuple[_U, _T]]], None]) -> List[_T]:
    # but that fails inference when we use it as an argument to pmap
    def extract(t):
        if t is None:
            return []
        return [t[0]] + [u[1] for u in t[1]]
    return pmap(
            extract,
            optional(chain(p, many(chain(sep, p)))))

# now we can write our recursive descent parser for OBAN

# we already have `integer`

tribool: Parser[TriBool]
tribool = alt(
    cmap(TriBool.FALSE, exactly('False')),
    cmap(TriBool.TRUE, exactly('True')),
    cmap(TriBool.FILENOTFOUND, exactly('FileNotFound'))
)

# again, mypy isn't smart enough to follow the type of this "lambda"
def _string_extract(t):
    _1, parts, _2 = t
    return ''.join(p[1] if isinstance(p, tuple) else p for p in parts)

string: Parser[str]
string = pmap(
    _string_extract,
    chain(
        exactly('<<'),
        many(alt(
            chars_while1(lambda c: c != '>' and c != '^'),
            chain(exactly('^'), char)
        )),
        exactly('>>')
    ))

# there's a circular dependency between congregation, callout, and expression
# we'll break it in expression, by making it a "proper" function
def expression(input: str) -> ParseResult[Expression]:
    parser = pmap(
        Expression,
        lexeme(alt(integer, tribool, string, congregation, callout)))
    return parser(input)

# in a lazier world, this would work:
# expression: Parser[Expression]
# expression = pmap(
#     Expression,
#     lexeme(alt(integer, tribool, string, congregation, callout)))

congregation: Parser[List[Expression]]
congregation = pmap(
    second,
    chain(
        lexeme(exactly('(')),
        sep_by(expression, lexeme(exactly(','))),
        lexeme(exactly(')'))
    ))

def _callout_extract(t):
    return { kv[0]: kv[2] for kv in t[1] }

callout: Parser[Dict[str, Expression]]
callout = pmap(
    _callout_extract,
    chain(
        lexeme(exactly('{')),
        sep_by(chain(
                lexeme(string),
                lexeme(exactly('!')),
                expression
            ),
            lexeme(exactly('&'))),
        lexeme(exactly('}'))
    ))

# since `lexeme` skips trailing whitespace, we need to allow leading whitespace
#   before a document explicitly, then ensure end-of-input
document: Parser[Expression]
document = pmap(second, chain(whitespace, only(expression)))

def main(argv: List[str]) -> int:
    for line in sys.stdin:
        res = document(line)
        if res is None:
            print('> parse error', file=sys.stderr)
        else:
            x, _ = res
            print(f'> {x}')
    return 0

if __name__ == '__main__':
    sys.exit(main(sys.argv))

## oban_pc_improved.py
#  Copyright 2020 Derrick W. Turk / terminus data science, LLC

#  Licensed under the Apache License, Version 2.0 (the "License");
#  you may not use this file except in compliance with the License.
#  You may obtain a copy of the License at

#      http://www.apache.org/licenses/LICENSE-2.0

#  Unless required by applicable law or agreed to in writing, software
#  distributed under the License is distributed on an "AS IS" BASIS,
#  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
#  See the License for the specific language governing permissions and
#  limitations under the License.

import sys
from enum import Enum, auto
from typing import Any, Callable, Dict, List, NamedTuple, Tuple, TypeVar, Union

# OBAN AST definitions

class TriBool(Enum):
    FALSE = auto()
    TRUE = auto()
    FILENOTFOUND = auto()

class Expression:
    Wrappable = Union[
        int,
        str,
        TriBool,
        List['Expression'],
        Dict[str, 'Expression']
    ]

    def __init__(self, value: Wrappable):
        self.value = value

    def __repr__(self):
        return f'Expression({repr(self.value)})'

# this time, we'll parse into a monad with state, context,
#   and a richer notion of failure

class ParserState(NamedTuple):
    pos: int = 0

    # methods for producing updated states

    def advance(self, chars: int) -> 'ParserState':
        return self._replace(pos = self.pos + chars)

    # is the parser at the end of input?
    def is_eof(self, input: str) -> bool:
        return self.pos >= len(input)

    # examine the next n chars from the input, starting at pos
    def slice(self, input: str, chars: int) -> str:
        return input[self.pos : self.pos + chars]

    # fail at the current pos with a given 'expected' message
    def fail(self, expected: str, committed: bool = False) -> 'ParseError':
        return ParseError(self.pos, expected, committed)

class ParseError(NamedTuple):
    pos: int
    expected: str
    committed: bool = False # is this error "un-backtrackable"? see `alt`.

_T = TypeVar('_T')
ParseResult = Union[Tuple[_T, ParserState], ParseError]
Parser = Callable[[str, ParserState], ParseResult[_T]]

# a parser which can't fail
InfallibleParser = Callable[[str, ParserState], Tuple[_T, ParserState]]

def exactly(match: str) -> Parser[str]:
    def parser(input: str, state: ParserState) -> ParseResult[str]:
        if state.slice(input, len(match)) == match:
            return match, state.advance(len(match))
        return state.fail(f'"{match}"')
    return parser

eof: Parser[None]
eof = lambda input, state: (
    (None, state) if state.is_eof(input)
    else state.fail('end of input')
)

char: Parser[str]
char = lambda input, state: (
    (state.slice(input, 1), state.advance(1)) if not state.is_eof(input)
    else state.fail('any character')
)

# we could build this with char, but we'll write it more efficiently by
#   directly inspecting the input one character at a time
def chars_while(p: Callable[[str], bool]) -> InfallibleParser[str]:
    def parser(input: str, state: ParserState) -> Tuple[str, ParserState]:
        chars: int = 0
        while state.pos + chars < len(input) and p(input[state.pos + chars]):
            chars += 1
        return state.slice(input, chars), state.advance(chars)
    return parser

whitespace: Parser[str]
whitespace = chars_while(str.isspace)

# combinators work like before - but there will be a little more plumbing
#   in the error case
_U = TypeVar('_U')

# map a function over a parser's result, if it succeeds
def pmap(f: Callable[[_T], _U], p: Parser[_T]) -> Parser[_U]:
    def parser(input: str, state: ParserState) -> ParseResult[_U]:
        res = p(input, state)
        if isinstance(res, ParseError):
            return res
        x, new_state = res
        return f(x), new_state
    return parser

# a parser which always succeeds by producing a constant
def pure(x: _T) -> InfallibleParser[_T]:
    return lambda _, state: (x, state)

# the opposite - a parser which always fails (with a given "expected" message)
def fail(expected: str) -> Parser[_T]:
    return lambda _, state: state.fail(expected)

# replace a successful result by a constant
def cmap(x: _T, p: Parser[_U]) -> Parser[_T]:
    return pmap(lambda _: x, p)

# these are harder to type in Python - we can do them for the fixed-arity case,
#   but it's just too convenient to let these take *args

# chain multiple parsers together and produce a tuple of their results,
#   if all succeed
def chain(*parsers: Parser[Any]) -> Parser[Tuple[Any, ...]]:
    def parser(input: str, state: ParserState) -> ParseResult[Tuple[Any, ...]]:
        results = list()
        for p in parsers:
            res = p(input, state)
            if isinstance(res, ParseError):
                return res
            val, state = res
            results.append(val)
        return tuple(results), state
    return parser

# run multiple parsers, recovering from errors, until one succeeds;
#   fail if all parsers fail
# this parser introduces a new issue: "unbacktrackable" errors
# we usually want `alt` to backtrack when a sub-parser fails, so that it can
#   try the next parser in the sequence without consuming any input.
# however, sometimes a sub-parser "knows" that the expected grammar is locked
#   in, and we want `alt` to fail if that parser fails.
# consider parsing Python's `x if y else z`: once we see `if`, we know that
#   we're inside a conditional expression - if we get a subsequent parse error,
#   we would not want to go back and try parsing the whole thing as, say, a list
#   comprehension!
def alt(*parsers: Parser[Any]) -> Parser[Any]:
    def parser(input: str, state: ParserState) -> ParseResult[Any]:
        expected: List[str] = list()
        for p in parsers:
            res = p(input, state)
            if not isinstance(res, ParseError):
                return res
            if res.committed:
                return res # these errors can't be backtracked
            expected.append(res.expected)
        # take a crack at an "expected" message by combining sub-parser messages
        return state.fail(', or '.join(expected))
    return parser

# run a parser, but make any errors "committed"/"unbacktrackable"
def commit(p: Parser[_T]) -> Parser[_T]:
    def parser(input: str, state: ParserState) -> ParseResult:
        res = p(input, state)
        if isinstance(res, ParseError):
            return res._replace(committed=True)
        return res
    return parser

# capture zero or more repetitions of a parser
# the end-of-loop condition is a form of backtracking, so we need to check
#   for a committed error
def many(p: Parser[_T]) -> Parser[List[_T]]:
    def parser(input: str, state: ParserState) -> ParseResult[List[_T]]:
        results: List[_T] = list()
        while True:
            res = p(input, state)
            if isinstance(res, ParseError):
                if res.committed:
                    return res
                return results, state
            val, state = res
            results.append(val)
    return parser

# we can use alt to define an "optional" parser combinator, which allows but does
#   not require its base parser to match
def optional(p: Parser[_T]) -> Parser[Union[_T, None]]:
    return alt(p, pure(None))

# finally, a way to "decide" the next parser based on
#   the result of the previous - this is what makes Parser a monad
def bind(p: Parser[_T], f: Callable[[_T], Parser[_U]]) -> Parser[_U]:
    def parser(input: str, state: ParserState) -> ParseResult[_U]:
        res = p(input, state)
        if isinstance(res, ParseError):
            return res
        x, state = res
        return f(x)(input, state)
    return parser

# we can use bind to build some interesting extensions to previous
#   parsers

# like chars_while, but requires there to be at least one matching char
# rather than "guess" an expected message, take it as an argument
def chars_while1(p: Callable[[str], bool], expected: str) -> Parser[str]:
    return bind(chars_while(p), lambda c: (
        pure(c) if len(c) > 0 else fail(expected)
    ))

# use it to build a "run of digits" parser
digits: Parser[str]
digits = chars_while1(str.isdigit, 'digits')

# use it to build an "unsigned integer" parser
integer: Parser[int]
integer = pmap(int, digits)

# capture one or more repetitions of a parser
def some(p: Parser[_T], expected: str) -> Parser[List[_T]]:
    return bind(many(p), lambda c: (
        pure(c) if len(c) > 0 else fail(expected)
    ))

# now we can start building some more interesting combinators

# mypy hates type-checking lambdas as arguments to pmap, so we'll need some
#   tuple-extractor functions
def first(t: Tuple[Any, ...]) -> Any:
    return t[0]

def second(t: Tuple[Any, ...]) -> Any:
    return t[1]

# "only" p - match what p matches, then insist on end-of-input
def only(p: Parser[_T]) -> Parser[_T]:
    return pmap(first, chain(p, eof))

# match p, followed by optional whitespace
def lexeme(p: Parser[_T]) -> Parser[_T]:
    return pmap(first, chain(p, whitespace))

# match zero or more p, separated by sep
def sep_by(p: Parser[_T], sep: Parser[_U]) -> Parser[List[_T]]:
    # mypy hates this thing's type
    # it should be:
    # def extract(t: Union[Tuple[_T, List[Tuple[_U, _T]]], None]) -> List[_T]:
    # but that fails inference when we use it as an argument to pmap
    def extract(t):
        if t is None:
            return []
        return [t[0]] + [u[1] for u in t[1]]
    return pmap(
            extract,
            optional(chain(p, many(chain(sep, commit(p))))))

# now we can write our recursive descent parser for OBAN

# we already have `integer`

tribool: Parser[TriBool]
tribool = alt(
    cmap(TriBool.FALSE, exactly('False')),
    cmap(TriBool.TRUE, exactly('True')),
    cmap(TriBool.FILENOTFOUND, exactly('FileNotFound'))
)

# again, mypy isn't smart enough to follow the type of this "lambda"
def _string_extract(t):
    _1, (parts, _2) = t
    return ''.join(p[1] if isinstance(p, tuple) else p for p in parts)

string: Parser[str]
string = pmap(
    _string_extract,
    chain(
        exactly('<<'),
        commit(chain(
            many(alt(
                chars_while1(lambda c: c != '>' and c != '^',
                    'non-escape characters'),
                chain(exactly('^'), char)
            )),
            exactly('>>')
        ))
    ))

# there's a circular dependency between congregation, callout, and expression
# we'll break it in expression, by making it a "proper" function
def expression(input: str, state: ParserState) -> ParseResult[Expression]:
    parser = pmap(
        Expression,
        lexeme(alt(integer, tribool, string, congregation, callout)))
    return parser(input, state)

# in a lazier world, this would work:
# expression: Parser[Expression]
# expression = pmap(
#     Expression,
#     lexeme(alt(integer, tribool, string, congregation, callout)))

def _congregation_extract(t):
    return t[1][0]

congregation: Parser[List[Expression]]
congregation = pmap(
    _congregation_extract,
    chain(
        lexeme(exactly('(')),
        commit(chain(
            sep_by(expression, lexeme(exactly(','))),
            lexeme(exactly(')'))))
    ))

def _callout_extract(t):
    return { kv[0]: kv[2] for kv in t[1][0] }

callout: Parser[Dict[str, Expression]]
callout = pmap(
    _callout_extract,
    chain(
        lexeme(exactly('{')),
        commit(chain(
            sep_by(chain(
                    lexeme(string),
                    lexeme(exactly('!')),
                    expression
                ),
                lexeme(exactly('&'))),
            lexeme(exactly('}'))
        ))
    ))

# since `lexeme` skips trailing whitespace, we need to allow leading whitespace
#   before a document explicitly, then ensure end-of-input
document: Parser[Expression]
document = pmap(second, chain(whitespace, only(expression)))

def main(argv: List[str]) -> int:
    for line in sys.stdin:
        res = document(line.rstrip(), ParserState())
        if isinstance(res, ParseError):
            print(f"{' ' * res.pos}^ expected: {res.expected}", file=sys.stderr)
        else:
            x, _ = res
            print(f'> {x}')
    return 0

if __name__ == '__main__':
    sys.exit(main(sys.argv))

## oban_rec.py
#  Copyright 2020 Derrick W. Turk / terminus data science, LLC

#  Licensed under the Apache License, Version 2.0 (the "License");
#  you may not use this file except in compliance with the License.
#  You may obtain a copy of the License at

#      http://www.apache.org/licenses/LICENSE-2.0

#  Unless required by applicable law or agreed to in writing, software
#  distributed under the License is distributed on an "AS IS" BASIS,
#  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
#  See the License for the specific language governing permissions and
#  limitations under the License.

import sys
from enum import Enum, auto
from typing import Callable, Dict, List, NamedTuple, Tuple, TypeVar, Union

class ParserState(NamedTuple):
    input: str
    pos: int = 0

class ParseError(NamedTuple):
    expected: str
    pos: int
    # allow backtracking on failure (True), or commit to this error (False)?
    backtrack: bool = True

_T = TypeVar('_T')

ParseResult = Union[Tuple[_T, ParserState], ParseError]

# Parser = Callable[[ParserState], ParseResult[_T]]
# (useless, because we can't write
# p : Parser[int]
# def p(state: ParserState) -> ParseResult[int]:
#     ...
# )

def whitespace(state: ParserState) -> Tuple[None, ParserState]:
    pos = state.pos
    while pos < len(state.input) and state.input[pos].isspace():
        pos += 1
    return (None, ParserState(state.input, pos))

def integer(state: ParserState) -> ParseResult[int]:
    _, state = whitespace(state)
    pos = state.pos
    if not state.input[pos].isdigit():
        return ParseError('integer', pos)
    num = ''
    while pos < len(state.input) and state.input[pos].isdigit():
        num += state.input[pos]
        pos += 1
    return (int(num), ParserState(state.input, pos))

def string(state: ParserState) -> ParseResult[str]:
    _, state = whitespace(state)
    pos = state.pos
    if state.input[pos:pos+2] != '<<':
        return ParseError('<<', pos)
    pos += 2
    text = ''
    while pos < len(state.input):
        if state.input[pos] == '^':
            if pos + 1 >= len(state.input):
                return ParseError('any character', pos + 1, backtrack = False)
            text += state.input[pos+1]
            pos += 2
        elif state.input[pos:pos+2] == '>>':
            pos += 2
            return (text, ParserState(state.input, pos))
        else:
            text += state.input[pos]
            pos += 1
    return ParseError('>>', pos, backtrack = False)

class TriBool(Enum):
    FALSE = auto()
    TRUE = auto()
    FILENOTFOUND = auto()

def tribool(state: ParserState) -> ParseResult[TriBool]:
    _, state = whitespace(state)
    pos = state.pos
    if state.input[pos:pos+5] == 'False':
        pos += 5
        return (TriBool.FALSE, ParserState(state.input, pos))
    if state.input[pos:pos+4] == 'True':
        pos += 4
        return (TriBool.TRUE, ParserState(state.input, pos))
    if state.input[pos:pos+12] == 'FileNotFound':
        pos += 12
        return (TriBool.FILENOTFOUND, ParserState(state.input, pos))
    return ParseError('tribool', pos)

# there's no way to write a recursive type alias:
# we'd prefer
# Expression = Union[int, str, TriBool, List[Expression], Dict[str, Expression]]
# but we can't, so we'll wrap it in a class
class Expression:
    # type alias for what we can wrap into an expression
    Wrappable = Union[
        int,
        str,
        TriBool,
        List['Expression'],
        Dict[str, 'Expression']
    ]

    def __init__(self, value: Wrappable):
        self.value = value

    def __repr__(self):
        return f'Expression({repr(self.value)})'

def congregation(state: ParserState) -> ParseResult[List[Expression]]:
    _, state = whitespace(state)

    if state.pos >= len(state.input) or state.input[state.pos] != '(':
        return ParseError('(', state.pos)

    state = ParserState(state.input, state.pos + 1)
    _, state = whitespace(state)

    exprs: List[Expression] = list()

    # the first expression (no comma)
    expr_res = expression(state)
    if isinstance(expr_res, ParseError):
        if not expr_res.backtrack:
            return expr_res
        if state.pos < len(state.input) and state.input[state.pos] == ')':
            return (exprs, ParserState(state.input, state.pos + 1))
        else:
            return ParseError('expression or )', state.pos, backtrack = False)
    expr, state = expr_res
    exprs.append(expr)

    while True:
        _, state = whitespace(state)
        pos = state.pos

        if pos < len(state.input) and state.input[pos] == ')':
            pos += 1
            return (exprs, ParserState(state.input, pos))

        if pos < len(state.input) and state.input[pos] == ',':
            state = ParserState(state.input, pos + 1)
            _, state = whitespace(state)

            expr_res = expression(state)
            if isinstance(expr_res, ParseError):
                return expr_res._replace(backtrack = False)
            expr, state = expr_res
            exprs.append(expr)
        else:
            return ParseError(', or )', pos, backtrack = False)

def callout(state: ParserState) -> ParseResult[Dict[str, Expression]]:
    _, state = whitespace(state)

    if state.pos >= len(state.input) or state.input[state.pos] != '{':
        return ParseError('{', state.pos)

    state = ParserState(state.input, state.pos + 1)
    _, state = whitespace(state)

    exprs: Dict[str, Expression] = dict()

    # the first mapping (no &)
    label_res = string(state)
    if isinstance(label_res, ParseError):
        if not label_res.backtrack:
            return label_res
        if state.pos < len(state.input) and state.input[state.pos] == '}':
            return (exprs, ParserState(state.input, state.pos + 1))
        else:
            return ParseError('string or }', state.pos, backtrack = False)
    label, state = label_res

    _, state = whitespace(state)
    if state.pos < len(state.input) and state.input[state.pos] == '!':
        state = ParserState(state.input, state.pos + 1)
        _, state = whitespace(state)
    else:
        return ParseError('!', state.pos, backtrack = False)

    _, state = whitespace(state)
    expr_res = expression(state)
    if isinstance(expr_res, ParseError):
        return expr_res._replace(backtrack = False)
    expr, state = expr_res
    exprs[label] = expr

    while True:
        _, state = whitespace(state)
        pos = state.pos

        if pos < len(state.input) and state.input[pos] == '}':
            pos += 1
            return (exprs, ParserState(state.input, pos))

        if pos < len(state.input) and state.input[pos] == '&':
            state = ParserState(state.input, pos + 1)
            _, state = whitespace(state)

            label_res = string(state)
            if isinstance(label_res, ParseError):
                return label_res._replace(backtrack = False)
            label, state = label_res

            _, state = whitespace(state)
            if state.pos < len(state.input) and state.input[state.pos] == '!':
                state = ParserState(state.input, state.pos + 1)
                _, state = whitespace(state)
            else:
                return ParseError('!', state.pos, backtrack = False)

            _, state = whitespace(state)
            expr_res = expression(state)
            if isinstance(expr_res, ParseError):
                return expr_res._replace(backtrack = False)
            expr, state = expr_res
            exprs[label] = expr
        else:
            return ParseError('& or }', pos, backtrack = False)

def expression(state: ParserState) -> ParseResult[Expression]:
    _, state = whitespace(state)

    # first, try to parse as an integer
    int_res = integer(state)
    if not isinstance(int_res, ParseError):
        num, state = int_res
        return (Expression(num), state)
    elif not int_res.backtrack:
        return int_res

    # then, as a tribool
    tribool_res = tribool(state)
    if not isinstance(tribool_res, ParseError):
        tb, state = tribool_res
        return (Expression(tb), state)
    elif not tribool_res.backtrack:
        return tribool_res

    # then, as a string
    str_res = string(state)
    if not isinstance(str_res, ParseError):
        text, state = str_res
        return (Expression(text), state)
    elif not str_res.backtrack:
        return str_res

    # then, as a congregation
    cong_res = congregation(state)
    if not isinstance(cong_res, ParseError):
        cong, state = cong_res
        return (Expression(cong), state)
    elif not cong_res.backtrack:
        return cong_res

    # finally, as a callout
    call_res = callout(state)
    if not isinstance(call_res, ParseError):
        call, state = call_res
        return (Expression(call), state)
    elif not call_res.backtrack:
        return call_res

    return ParseError('expression', state.pos)

# one, and only one, expression
def document(state: ParserState) -> ParseResult[Expression]:
    res = expression(state)
    if isinstance(res, ParseError):
        return res
    expr, state = res
    _, state = whitespace(state)
    if state.pos != len(state.input):
        return ParseError('end of document', state.pos)
    return expr, state

def main(argv: List[str]) -> int:
    for line in sys.stdin:
        res = document(ParserState(line, 0))

        if isinstance(res, ParseError):
            print(f'{" " * res.pos}^ expected {res.expected}', file=sys.stderr)
            continue

        parsed, _ = res
        print(parsed)

    return 0

if __name__ == '__main__':
    sys.exit(main(sys.argv))

## z_LICENSE
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## z_NOTICE
OBAN grammar & parser code
Copyright 2020 Derrick W. Turk

This software contains code derived from "Irregular Expressions"
by Derrick W. Turk (https://usethe.computer/posts/18-irregular-expressions.html).
	(* Copyright 2020 Derrick W. Turk / terminus data science, LLC

	Licensed under the Apache License, Version 2.0 (the "License");
	you may not use this file except in compliance with the License.
	You may obtain a copy of the License at

	http://www.apache.org/licenses/LICENSE-2.0

	Unless required by applicable law or agreed to in writing, software
	distributed under the License is distributed on an "AS IS" BASIS,
	WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
	See the License for the specific language governing permissions and
	limitations under the License. *)

	digit = "0" \| "1" \| "2" \| "3" \| "4" \| "5" \| "6" \| "7" \| "8" \| "9";
	number = digit, { digit };
	any_character = ? any UTF-8 code point ?
	string = "<<", { (any_character - ">") \| ("^", any_character) }, ">>"
	triboolean = "True" \| "False" \| "FileNotFound";
	expression = number \| string \| triboolean \| congregation \| callout
	congregation = "(", [ expression, { ",", expression } ], ")"
	callout = "{", [ string, "!", expression, { "&", string, "!", expression } ], "}"
	# Copyright 2020 Derrick W. Turk / terminus data science, LLC

	# Licensed under the Apache License, Version 2.0 (the "License");
	# you may not use this file except in compliance with the License.
	# You may obtain a copy of the License at

	# http://www.apache.org/licenses/LICENSE-2.0

	# Unless required by applicable law or agreed to in writing, software
	# distributed under the License is distributed on an "AS IS" BASIS,
	# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
	# See the License for the specific language governing permissions and
	# limitations under the License.

	import sys
	from enum import Enum, auto
	from typing import Any, Callable, Dict, List, NamedTuple, Tuple, TypeVar, Union

	# data types we need for OBAN:

	class TriBool(Enum):
	FALSE = auto()
	TRUE = auto()
	FILENOTFOUND = auto()

	# there's no way to write a recursive type alias:
	# we'd prefer
	# Expression = Union[int, str, TriBool, List[Expression], Dict[str, Expression]]
	# but we can't, so we'll wrap it in a class
	class Expression:
	# type alias for what we can wrap into an expression
	Wrappable = Union[
	int,
	str,
	TriBool,
	List['Expression'],
	Dict[str, 'Expression']
	]

	def __init__(self, value: Wrappable):
	self.value = value

	def __repr__(self):
	return f'Expression({repr(self.value)})'

	# here's how we'd represent:
	# { <<first>> ! (1, FileNotFound)
	# & <<second>> ! <<some <<text^>^>>>
	# & <<third>> ! { <<nested>> ! True }
	# }
	example: Expression
	example = Expression({
	'first': Expression([Expression(1), Expression(TriBool.FILENOTFOUND)]),
	'second': Expression('some <<text>>'),
	'third': Expression({ 'nested': Expression(TriBool.TRUE) })
	})

	# now, a parser

	_T = TypeVar('_T')
	ParseResult = Union[Tuple[_T, str], None]
	Parser = Callable[[str], ParseResult[_T]]

	# a parser which can't fail
	InfallibleParser = Callable[[str], Tuple[_T, str]]

	# some tools for building 'primitive' parsers

	# the simplest parser: 'match exactly this string'
	def exactly(match: str) -> Parser[str]:
	def parser(input: str) -> ParseResult[str]:
	if input.startswith(match):
	return match, input[len(match):]
	return None
	return parser

	# another basic one: succeeds at end of input; fails otherwise
	# eof: Parser[None]
	eof: Parser[None]
	eof = lambda input: (None, input) if len(input) == 0 else None

	# a parser which consumes a single character, if available
	char: Parser[str]
	char = lambda input: (input[0], input[1:]) if len(input) > 0 else None

	# an 'infallible' parser which consumes characters matching a predicate
	def chars_while(p: Callable[[str], bool]) -> InfallibleParser[str]:
	def parser(input: str) -> Tuple[str, str]:
	split_at = 0
	while split_at < len(input) and p(input[split_at]):
	split_at += 1
	return input[:split_at], input[split_at:]
	return parser

	# use it to build a "consume whitespace" parser
	whitespace: Parser[str]
	whitespace = chars_while(str.isspace)

	# some basic combinators for parsers
	_U = TypeVar('_U')

	# map a function over a parser's result, if it succeeds
	def pmap(f: Callable[[_T], _U], p: Parser[_T]) -> Parser[_U]:
	def parser(input: str) -> ParseResult[_U]:
	res = p(input)
	if res is None:
	return None
	x, rest = res
	return f(x), rest
	return parser

	# a parser which always succeeds by producing a constant
	def pure(x: _T) -> InfallibleParser[_T]:
	return lambda input: (x, input)

	# the opposite - a parser which always fails
	# it's really a Parser[_T] for all _T, but we'll use Any since mypy
	# isn't that sharp
	fail: Parser[Any]
	fail = lambda _: None

	# replace a successful result by a constant
	def cmap(x: _T, p: Parser[_U]) -> Parser[_T]:
	return pmap(lambda _: x, p)

	# these are harder to type in Python - we can do them for the fixed-arity case,
	# but it's just too damn convenient to let these take *args

	# chain multiple parsers together and produce a tuple of their results,
	# if all succeed
	def chain(*parsers: Parser[Any]) -> Parser[Tuple[Any, ...]]:
	def parser(input: str) -> ParseResult[Tuple[Any, ...]]:
	results = list()
	for p in parsers:
	res = p(input)
	if res is None:
	return None
	val, input = res
	results.append(val)
	return tuple(results), input
	return parser

	# run multiple parsers, recovering from errors, until one succeeds;
	# fail if all parsers fail
	def alt(*parsers: Parser[Any]) -> Parser[Any]:
	def parser(input: str) -> ParseResult[Any]:
	for p in parsers:
	res = p(input)
	if res is not None:
	return res
	return None
	return parser

	# capture zero or more repetitions of a parser
	def many(p: Parser[_T]) -> InfallibleParser[List[_T]]:
	def parser(input: str) -> Tuple[List[_T], str]:
	results: List[_T] = list()
	while True:
	res = p(input)
	if res is None:
	return results, input
	val, input = res
	results.append(val)
	return parser

	# we can use alt to define an "optional" parser combinator, which allows but does
	# not require its base parser to match
	def optional(p: Parser[_T]) -> Parser[Union[_T, None]]:
	return alt(p, pure(None))

	# finally, a way to "decide" the next parser based on
	# the result of the previous - this is what makes Parser a monad
	def bind(p: Parser[_T], f: Callable[[_T], Parser[_U]]) -> Parser[_U]:
	def parser(input: str) -> ParseResult[_U]:
	res = p(input)
	if res is None:
	return None
	x, input = res
	return f(x)(input)
	return parser

	# we can use bind to build some interesting extensions to previous
	# parsers

	# like chars_while, but requires there to be at least one matching char
	def chars_while1(p: Callable[[str], bool]) -> Parser[str]:
	return bind(chars_while(p), lambda c: fail if len(c) == 0 else pure(c))

	# use it to build a "run of digits" parser
	digits: Parser[str]
	digits = chars_while1(str.isdigit)

	# use it to build an "unsigned integer" parser
	integer: Parser[int]
	integer = pmap(int, digits)

	# capture one or more repetitions of a parser
	def some(p: Parser[_T]) -> Parser[List[_T]]:
	return bind(many(p), lambda r: fail if len(r) == 0 else pure(r))

	# now we can start building some more interesting combinators

	# mypy hates type-checking lambdas as arguments to pmap, so we'll need some
	# tuple-extractor functions
	def first(t: Tuple[Any, ...]) -> Any:
	return t[0]

	def second(t: Tuple[Any, ...]) -> Any:
	return t[1]

	# "only" p - match what p matches, then insist on end-of-input
	def only(p: Parser[_T]) -> Parser[_T]:
	return pmap(first, chain(p, eof))

	# match p, followed by optional whitespace
	def lexeme(p: Parser[_T]) -> Parser[_T]:
	return pmap(first, chain(p, whitespace))

	# match zero or more p, separated by sep
	def sep_by(p: Parser[_T], sep: Parser[_U]) -> Parser[List[_T]]:
	# mypy hates this thing's type
	# it should be:
	# def extract(t: Union[Tuple[_T, List[Tuple[_U, _T]]], None]) -> List[_T]:
	# but that fails inference when we use it as an argument to pmap
	def extract(t):
	if t is None:
	return []
	return [t[0]] + [u[1] for u in t[1]]
	return pmap(
	extract,
	optional(chain(p, many(chain(sep, p)))))

	# now we can write our recursive descent parser for OBAN

	# we already have `integer`

	tribool: Parser[TriBool]
	tribool = alt(
	cmap(TriBool.FALSE, exactly('False')),
	cmap(TriBool.TRUE, exactly('True')),
	cmap(TriBool.FILENOTFOUND, exactly('FileNotFound'))
	)

	# again, mypy isn't smart enough to follow the type of this "lambda"
	def _string_extract(t):
	_1, parts, _2 = t
	return ''.join(p[1] if isinstance(p, tuple) else p for p in parts)

	string: Parser[str]
	string = pmap(
	_string_extract,
	chain(
	exactly('<<'),
	many(alt(
	chars_while1(lambda c: c != '>' and c != '^'),
	chain(exactly('^'), char)
	)),
	exactly('>>')
	))

	# there's a circular dependency between congregation, callout, and expression
	# we'll break it in expression, by making it a "proper" function
	def expression(input: str) -> ParseResult[Expression]:
	parser = pmap(
	Expression,
	lexeme(alt(integer, tribool, string, congregation, callout)))
	return parser(input)

	# in a lazier world, this would work:
	# expression: Parser[Expression]
	# expression = pmap(
	# Expression,
	# lexeme(alt(integer, tribool, string, congregation, callout)))

	congregation: Parser[List[Expression]]
	congregation = pmap(
	second,
	chain(
	lexeme(exactly('(')),
	sep_by(expression, lexeme(exactly(','))),
	lexeme(exactly(')'))
	))

	def _callout_extract(t):
	return { kv[0]: kv[2] for kv in t[1] }

	callout: Parser[Dict[str, Expression]]
	callout = pmap(
	_callout_extract,
	chain(
	lexeme(exactly('{')),
	sep_by(chain(
	lexeme(string),
	lexeme(exactly('!')),
	expression
	),
	lexeme(exactly('&'))),
	lexeme(exactly('}'))
	))

	# since `lexeme` skips trailing whitespace, we need to allow leading whitespace
	# before a document explicitly, then ensure end-of-input
	document: Parser[Expression]
	document = pmap(second, chain(whitespace, only(expression)))

	def main(argv: List[str]) -> int:
	for line in sys.stdin:
	res = document(line)
	if res is None:
	print('> parse error', file=sys.stderr)
	else:
	x, _ = res
	print(f'> {x}')
	return 0

	if __name__ == '__main__':
	sys.exit(main(sys.argv))
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	OBAN grammar & parser code
	Copyright 2020 Derrick W. Turk

	This software contains code derived from "Irregular Expressions"
	by Derrick W. Turk (https://usethe.computer/posts/18-irregular-expressions.html).