Oren> On Mon, Aug 26, 2002 at 03:51:13PM -0400, Andrew Koenig wrote: Oren> Can you give a more concrete example of what could a cartesian Oren> product of type predicates actually stand for in Python?
Consider my TotallyOrdered suggestion from before. I would like to have a way of saying that for any two types T1 and T2 (where T1 might equal T2) chosen from the set {int, long, float}, < imposes a total ordering on values of those types.
Come to think of it, that's not really a Cartesian product. Rather, it's a claim about the members of the set union(int,union(long, float)).
Oren> Isn't it easier to just spell it union(int, long, float)? Yes but I have a cold today so I'm not thinking clearly. Oren> Your example helped me make the distinction between two very Oren> types of type categories: Oren> 1. Type categories based on form: presence of methods, call signatures, etc. Oren> 2. Type categories based on semantics. Oren> Semantic categories only live within a single form category. A Oren> method call cannot possibly be semantically correct if it isn't Oren> well-formed: it will cause a runtime error. But a method call Oren> that is well-formed may or may not be semantically correct. Yes. Oren> A language *can* verify well-formedness. It cannot verify Oren> semantical correctness but it can provide tools to help Oren> developers communicate their semantic expectations. Yes. Oren> Form-based categories may be used to convey semantic categories: Oren> just add a dummy method or member to serve as a marker. It can Oren> force an interface with an otherwise identical form to be Oren> intentionally incompatible to help you detect semantic Oren> categorization errors. Remember that one thing I consider important is the ability to claim that classes written by others belong to a category defined by me. I do not want to have to modify those classes in order to do so. So, for example, if I want to say that int is TotallyOrdered, I do not want to have to modify the definition of int to do so. Oren> The opposite is not true: semantic categories cannot be used to Oren> enforce well-formedness. You can mark a class as implementing Oren> the "TotallyOrdered" interface when it doesn't even have a Oren> comparison method. Yes. But semantic categories are useful anyway. Oren> A similar case can happen when using inheritance for Oren> categorization: a subclass may modify the call signatures, Oren> making the class form-incompatible but it still retains its Oren> ancestry which may be interpreted in some cases as a marker of a Oren> semantic category. Right. And several people have noted that it can be desirable for subclasses sometimes not to be members of all of their base classes' categories.