code: def test_invalid_expressions(self) -> None:
      # double ellipsis should raise an error
      ParsedExpression("... a b c d")
      with self.assertRaises(ValueError):
          ParsedExpression("... a b c d ...")
      with self.assertRaises(ValueError):
          ParsedExpression("... a b c (d ...)")
      with self.assertRaises(ValueError):
          ParsedExpression("(... a) b c (d ...)")
  
      # double/missing/enclosed parenthesis
      ParsedExpression("(a) b c (d ...)")
      with self.assertRaises(ValueError):
          ParsedExpression("(a)) b c (d ...)")
      with self.assertRaises(ValueError):
          ParsedExpression("(a b c (d ...)")
      with self.assertRaises(ValueError):
          ParsedExpression("(a) (()) b c (d ...)")
      with self.assertRaises(ValueError):
          ParsedExpression("(a) ((b c) (d ...))")
  
      # invalid identifiers
      ParsedExpression("camelCase under_scored cApiTaLs ß ...")
      with self.assertRaises(ValueError):
          ParsedExpression("1a")
      with self.assertRaises(ValueError):
          ParsedExpression("_pre")
      with self.assertRaises(ValueError):
          ParsedExpression("...pre")
      with self.assertRaises(ValueError):
          ParsedExpression("pre...")
  
imports: from typing import Any, Callable, Dict
  from unittest import mock
  from functorch.einops._parsing import AnonymousAxis, ParsedExpression, parse_pattern, validate_rearrange_expressions, _ellipsis
  from torch.testing._internal.common_utils import TestCase, run_tests
label_desc: Use image node_id 2 for calling the TestParsedExpression obj's underlying member method code with example usage: obj.test_invalid_expressions() without return types