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})"


def parse(tokens: list):
    """Parse a token list into an AST.

    Grammar:
        expr    → term   (('+' | '-') term)*
        term    → unary  (('*' | '/') unary)*
        unary   → '-' unary | primary
        primary → NUMBER | '(' expr ')'

    Returns the root Node.  Raises ParseError on malformed input.
    """
    pos = 0

    def peek():
        return tokens[pos]

    def consume(kind=None):
        nonlocal pos
        tok = tokens[pos]
        if kind and tok.kind != kind:
            raise ParseError(f"expected {kind}, got {tok.kind!r}")
        pos += 1
        return tok

    def expr():
        left = term()
        while peek().kind in ('PLUS', 'MINUS'):
            op = consume().kind
            right = term()
            left = BinOp(op, left, right)
        return left

    def term():
        left = unary()
        while peek().kind in ('STAR', 'SLASH'):
            op = consume().kind
            right = unary()
            left = BinOp(op, left, right)
        return left

    def unary():
        if peek().kind == 'MINUS':
            op = consume().kind
            operand = unary()
            return Unary(op, operand)
        return primary()

    def primary():
        tok = peek()
        if tok.kind == 'NUMBER':
            consume()
            return Num(tok.value)
        if tok.kind == 'LPAREN':
            consume()
            node = expr()
            if peek().kind != 'RPAREN':
                raise ParseError(f"expected ')', got {peek().kind!r}")
            consume()
            return node
        raise ParseError(f"unexpected token {tok.kind!r}")

    node = expr()
    if peek().kind != 'EOF':
        raise ParseError(f"unexpected token {peek().kind!r} after expression")
    return node