A Very Modal Model of a Modern, Major, General Type System

Authors

Andrew W. Appel, Paul-André Melličs, Christopher D. Richards, Jérôme Vouillon

Abstract

We present a clean and powerful model of recursive and impredicatively quantified types with mutable references. We interpret in this model all of the type constructors needed for typed intermediate languages and typed assembly languages used for object-oriented and functional languages. We establish in this purely semantic fashion a soundness proof of the typing systems underlying these TILs and TALs—ensuring that every well-typed program is safe. The technique is generic, and applies to any small-step semantics including λ-calculus, labeled transition systems, and von Neumann machines. It is also simple, and reduces mainly to defining a Kripke semantics of the Gödel-Löb logic of provability. We have machine-checked proofs in Coq.

Proofs

• Summary of the proofs (including definitions and lemmas, but omitting the proof details)
• Full proof script