Lambda the Ultimate

Type soundness and freedom for Mezzo,
Thibaut Balabonski, François Pottier, and Jonathan Protzenko,
2014

Full paper
Presentation slides

The programming language Mezzo is equipped with a rich type system that controls aliasing and access to mutable memory. We incorporate shared-memory concurrency into Mezzo and present a modular formalization of its core type system, in the form of a concurrent λ-calculus, which we extend with references and locks. We prove that well-typed programs do not go wrong and are data-race free. Our definitions and proofs are machine-checked.

The Mezzo programming language has been mentioned recently on LtU. The article above is however not so much about the practice of Mezzo or justification of its design choices (for this, see Programming with Permissions in Mezzo, François Pottier and Jonathan Protzenko, 2013), but a presentation of its soundness proof.

I think this paper is complementary to more practice-oriented ones, and remarkable for at least two reasons:

• It is remarkably simple, for a complete soundness proof (and race-freeness) of a programming language with higher-order functions, mutable states, strong update, linear types, and dynamic borrowing. This is one more confirmation of the simplifying effect of mechanized theorem proving.
• It is the first soundness proof of a programming language that is strongly inspired by Separation Logic. (Concurrent) Separation Logic has been a revolution in the field of programming logics, but it had until now not be part of a full-fledged language design, and this example is bound to be followed by many others. I expect the structure of this proof to be reused many times in the future.