I will take the chance to speak about work with Jeremy Siek and Dale Miller (INRIA).
In this talk, I will set forth the idea that “well-typed languages are sound”, the idea of treating language specifications as expressions and that the appropriate typing discipline over these specifications guarantees the type soundness of the language.
The first contribution is a discipline for organizing and restricting languages that guarantees the validity of the progress theorem. This discipline is not novel but it makes explicit the way language designers have been organizing a certain class of languages for long time. We make the discipline formal and prove that, indeed, it ensures the validity of the progress theorem for the language at hand.
To be more precise, we represent language specifications as logic programs and we devise a meta type system over logic programs that enforces the mentioned organization and discipline. I have then proved that when such specifications are well-typed, the progress theorem holds for that language.
Next, we offer an analogous methodology and meta type system for guaranteeing the type preservation lemma. Ultimately, languages that conform to our meta type systems are guaranteed to be type sound, hence: well-typed languages are sound.
These theoretical results have been implemented in the TypeSoundnessCertifier, a tool that takes specifications of the Abella interactive theorem prover and automatically generates the full mechanized proof of type soundness for those specifications that successfully pass our type checkers.
We have applied TypeSoundnessCertifier to a plethora of programming languages and we have automatically produced the machine-checked proof of type soundness for over a hundred of languages, including full fledged languages with recursive types, universal types, letrec, exceptions, lists and other common types and operators.