What is the mathematical model of a Python's class?

Question

I understand that the classical model from the lambda-papers is not valid for Python.

And the closures are not the mathematical model of the implementation of the Python system.

So which model is it?

Answer 1

The main difference between Python and models from classical papers on the lambda calculus is that Python is a multi-paradigm language. Most papers which consider the lambda calculus consider a pure functional language, without the complexities involved by adding other paradigms (like OOP or logical programming).

From the question and your comments, I take it that you are interested in the foundations of such multi-paradigm languages. In that case, I can highly suggest Concepts, Techniques, and Models of Computer Programming by Peter van Roy and Seif Haridi. The book is mainly about the Mozart/Oz language, which in itself is a rather academic language. However, the book very clearly demonstrates how to start off with a very small core language and build object-orientation, functional, and logic programming on top of it (and all within the same core language).

As for the actual mathematical model, most programming languages have only an informal or semi-formal specification. Seldom do you find one that has a proper theory like the lambda calculus as its foundation. There are a lot of different mathematical models that have been invented and are more or less applicable. What's interesting is that there is a general distinction into the different approaches to how programming semantics are modeled: semantics can be described denotationally, operationally, or algebraically. If you want to go even deeper, then reading up a little about the Unifying Theories of Programming is a start, albeit a tough one with a steep learning curve.