In that case, when do two domains that both derive from default_domain conflict? They have a common ancestor, namely default_domain. Or should default_domain be special in that regard, with a rule such as "if the merger of two domains is default_domain but one of them isn't default_domain, replace the result with not_a_domain"?
Close. Yes, default_domain is special. If the merger of two domains is default_domain and /neither of them/ is default_domain, the result is not_a_domain. Otherwise, the one that's not default_domain dominates. So, if lambda_domain is a sub-domain of default_domain, it is stronger than default_domain and should dominate. I.e., "_1 + 42" should be a lambda expression.
default_domain should *never* be the answer when any domain is not default_domain.
What about in the case of two different domains that both derive from default_domain but have no other ancestors in common? I see not_a_domain in your test cases. What about two different domains that each derive from DD0 (in your test case)? What should the result of combining them be? For non-default_domain domains I use the least common ancestor (which is what it seemed like you wanted). -- Jeremiah Willcock