from dataclasses import dataclass
from typing import Union


class ParseError(Exception):
    pass


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

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


@dataclass
class BinOp:
    op: str
    left: object
    right: object

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


@dataclass
class Unary:
    op: str
    operand: object

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


class _Parser:
    def __init__(self, tokens):
        self._tokens = tokens
        self._pos = 0

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

    def _advance(self):
        tok = self._tokens[self._pos]
        self._pos += 1
        return tok

    def _expect(self, kind):
        tok = self._peek()
        if tok.kind != kind:
            raise ParseError(f"expected {kind!r}, got {tok.kind!r} ({tok.value!r})")
        return self._advance()

    def parse(self):
        node = self._expr()
        tok = self._peek()
        if tok.kind != 'EOF':
            raise ParseError(f"unexpected token {tok.kind!r} ({tok.value!r})")
        return node

    def _expr(self):
        left = self._term()
        while self._peek().kind in ('PLUS', 'MINUS'):
            op = self._advance().value
            right = self._term()
            left = BinOp(op, left, right)
        return left

    def _term(self):
        left = self._factor()
        while self._peek().kind in ('STAR', 'SLASH'):
            op = self._advance().value
            right = self._factor()
            left = BinOp(op, left, right)
        return left

    def _factor(self):
        tok = self._peek()
        if tok.kind == 'MINUS':
            self._advance()
            operand = self._factor()
            return Unary('-', operand)
        if tok.kind == 'NUMBER':
            self._advance()
            return Num(tok.value)
        if tok.kind == 'LPAREN':
            self._advance()
            node = self._expr()
            self._expect('RPAREN')
            return node
        raise ParseError(f"unexpected token {tok.kind!r} ({tok.value!r})")


def parse(tokens):
    """Parse a token list from calc.lexer.tokenize() into an AST.

    AST node shapes:
      Num(value)              — a numeric literal (int or float)
      BinOp(op, left, right) — binary operation; op is '+', '-', '*', or '/'
      Unary(op, operand)     — unary minus; op is '-'

    Raises ParseError on malformed input.
    """
    return _Parser(tokens).parse()