A theorem prover / proof assistant supporting (multiple) subtyping / subclassing [closed]

Question

In short, I am looking for a theorem prover which its underlying logic supports multiple subtyping / subclassing mechanism.( I tried to use Isabelle, but it does not seem to provide a first class support for subtyping. see this )

I would like to define a couple of types among which some are subclasses / subtypes of others. Furthermore, each type might be subtype of more than one type. For example:

Type A
Type B
Type C
Type E
Type F

C is subtype of A
C is also subtype of B
E and F are subtypes of B

PS: I am editing this question again to be more specific (because of a complains about being of-topic!): I am looking for a theorem prover / proof assistance in which I can define the above structure in a straight forward manner (not with workarounds as it is kindly described by some respectable answers here). If I take the types as classes then It seems above subtypings could be easily formulated in C++! So I am looking for a formal system / tool that I can define such a subtyping structure there and I can reason?

Many thanks

Answer 1

PVS has traditionally emphasized "predicate subtyping" a lot, but the system is a bit old-fashioned these days and has fallen behind the other big players that are more active: Coq, Isabelle/HOL, Agda, other HOLs, ACL2.

You did not make your application clear. I reckon that any of the big systems could be applied to the problem, one way or the other. Formalization is a matter to phrase your problem in a suitable way within the given logical environment. Logics are not programming languages, but have the real power of mathematics. Thus with some experience in a particular logic, you will be able to do great and amazing things that you did not expect at first sight.

When choosing your system, lists of particular low-level features are not so relevant. It is more important that you like the general style and culture of the system, before you make a commitment. You can compare that to learning a foreign language. Before you spend months or years to study do you collect features of the grammar? I don't think so.