Lambda calculus serves as a foundation for all sorts of functional languages and its various extensions are compiler targets for languages like Haskell, ML, etc. So what is the equivalent for object oriented languages? Is there a minimal object calculus that serves as the foundation for object oriented languages?
So what is the equivalent for object oriented languages?
I mean, there is Cardelli's object calculus (and a handful of derivatives), but in general, there's nothing fancy about object oriented languages that requires a new approach to computation.
It's well known (see TaPL for example) how to extend/encode Records and Mutation (and sub-typing/dispatch) onto/in lambda calculus. The underlying structures don't need to change, even though there are often layers above it that add semantic restriction and make things more usable (member access, implied
this, object layouts, etc).
While not really an answer to your specific question, I will suggest that those OO langs that do have lambdas (or specifically do not) usually do so for practical reasons. The recent inclusion of lambdas/closures in Java 8 is a case-in-point.
This generated a lot of discussion, even well before Java 8. There is a dense website dedicated to this specific implementation that has a lot of technical and theoretical discussion that might be of interest?
Specifically, check out Bloch's "Controversy" slides.