from __future__ import annotations
from dataclasses import dataclass
from typing import Union


class ParseError(Exception):
    pass


@dataclass
class Num:
    value: Union[int, float]

    def __repr__(self) -> str:
        return f"Num({self.value!r})"


@dataclass
class BinOp:
    op: str
    left: "Node"
    right: "Node"

    def __repr__(self) -> str:
        return f"BinOp({self.op!r}, {self.left!r}, {self.right!r})"


@dataclass
class Unary:
    op: str
    operand: "Node"

    def __repr__(self) -> str:
        return f"Unary({self.op!r}, {self.operand!r})"


Node = Union[Num, BinOp, Unary]


class _Parser:
    def __init__(self, tokens: list) -> None:
        self._tokens = tokens
        self._pos = 0

    def _peek(self):
        return self._tokens[self._pos]

    def _consume(self, kind: str = None):
        tok = self._tokens[self._pos]
        if kind is not None and tok.kind != kind:
            raise ParseError(
                f"expected {kind}, got {tok.kind!r} ({tok.value!r})"
            )
        self._pos += 1
        return tok

    def parse(self) -> Node:
        if self._peek().kind == "EOF":
            raise ParseError("empty input")
        node = self._expr()
        if self._peek().kind != "EOF":
            tok = self._peek()
            raise ParseError(
                f"unexpected token {tok.kind!r} ({tok.value!r}) after expression"
            )
        return node

    def _expr(self) -> Node:
        node = self._term()
        while self._peek().kind in ("PLUS", "MINUS"):
            op = self._consume().value
            node = BinOp(op, node, self._term())
        return node

    def _term(self) -> Node:
        node = self._unary()
        while self._peek().kind in ("STAR", "SLASH"):
            op = self._consume().value
            node = BinOp(op, node, self._unary())
        return node

    def _unary(self) -> Node:
        if self._peek().kind == "MINUS":
            self._consume()
            return Unary("-", self._unary())
        return self._primary()

    def _primary(self) -> Node:
        tok = self._peek()
        if tok.kind == "NUMBER":
            self._consume()
            return Num(tok.value)
        if tok.kind == "LPAREN":
            self._consume()
            node = self._expr()
            if self._peek().kind != "RPAREN":
                raise ParseError("unclosed parenthesis")
            self._consume()
            return node
        raise ParseError(
            f"unexpected token {tok.kind!r} ({tok.value!r})"
        )


def parse(tokens: list) -> Node:
    """Parse a token list produced by calc.lexer.tokenize into an AST."""
    return _Parser(tokens).parse()