An indexed model of recursive types for foundational proof-carrying code

Abstract

The proofs of "traditional" proof carrying code (PCC) are type-specialized in the sense that they require axioms about a specific type system. In contrast, the proofs of foundational PCC explicitly define all required types and explicitly prove all the required properties of those types assuming only a fixed foundation of mathematics such as higher-order logic. Foundational PCC is both more flexible and more secure than type-specialized PCC. For foundational PCC we need semantic models of type systems on von Neumann machines. Previous models have been either too weak (lacking general recursive types and first-class function-pointers), too complex (requiring machine-checkable proofs of large bodies of computability theory), or not obviously applicable to von Neumann machines. Our new model is strong, simple, and works either in λ-calculus or on Pentiums. Categories and Subject Descriptors: F.3.1 [Logics and Meanings of Programs]: Specifying and Verifying and Reasoning about Programs - Mechanical verification; F.3.2 [Logics and Meanings of Programs]: Semantics of Programming Languages.