In UFL code contributed from the Firedrake team, there are some comments I'd like to address: The __eq__ operator of any Python object is used to compare for equality in set and dict if __hash__ compares equal. The __lt__ operator is used to define sorting, e.g. sorted(myobjects) will use this operator. Together these operators allow e.g. sorted(set(myobjects)) to get a sorted unique list. It's not necessarily important for the sorting to have any meaning, however it is important that it is deterministic between runs and platforms. Raising custom exceptions (including calling error()) in a Python special function is always a bug. The correct behaviour is to "return NotImplemented", which allows Python to follow its regular protocols. E.g. when writing A < B, if A.__lt__(B) returns NotImplemented, Python will try B.__lt__(A). If any of this was news and you're writing significant Python code, I recommend reading more here: https://docs.python.org/2/reference/datamodel.html Martin