"""Recursive-descent parser for calc expressions.

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

All nodes implement __repr__ for easy shape inspection.

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

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]


def parse(tokens: list) -> Node:
    """Parse a token list into an AST. Raises ParseError on malformed input."""
    p = _Parser(tokens)
    tree = p.expr()
    if p.current().kind != "EOF":
        raise ParseError(f"unexpected token {p.current()!r} after expression")
    return tree


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

    def current(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!r} but got {tok.kind!r} ({tok.value!r})"
            )
        self._pos += 1
        return tok

    def expr(self) -> Node:
        node = self.term()
        while self.current().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.current().kind in ("STAR", "SLASH"):
            op = self.consume().value
            node = BinOp(op, node, self.unary())
        return node

    def unary(self) -> Node:
        if self.current().kind == "MINUS":
            self.consume("MINUS")
            return Unary("-", self.unary())
        return self.primary()

    def primary(self) -> Node:
        tok = self.current()
        if tok.kind == "NUMBER":
            self.consume("NUMBER")
            return Num(tok.value)
        if tok.kind == "LPAREN":
            self.consume("LPAREN")
            node = self.expr()
            if self.current().kind != "RPAREN":
                raise ParseError("unclosed '(' — expected ')'")
            self.consume("RPAREN")
            return node
        if tok.kind == "EOF":
            raise ParseError("unexpected end of input")
        raise ParseError(f"unexpected token {tok.kind!r} ({tok.value!r})")