Biblio

The area of secure compilation aims to design compilers which produce hardened code that can withstand attacks from low-level co-linked components. So far, there is no formal correctness criterion for secure compilers that comes with a clear understanding of what security properties the criterion actually provides. Ideally, we would like a criterion that, if fulfilled by a compiler, guarantees that large classes of security properties of source language programs continue to hold in the compiled program, even as the compiled program is run against adversaries with low-level attack capabilities. This paper provides such a novel correctness criterion for secure compilers, called trace-preserving compilation (TPC). We show that TPC preserves a large class of security properties, namely all safety hyperproperties. Further, we show that TPC preserves more properties than full abstraction, the de-facto criterion used for secure compilation. Then, we show that several fully abstract compilers described in literature satisfy an additional, common property, which implies that they also satisfy TPC. As an illustration, we prove that a fully abstract compiler from a typed source language to an untyped target language satisfies TPC.

Homotopy type theory is an interpretation of Martin-L¨of’s constructive type theory into abstract homotopy theory. There results a link between constructive mathematics and algebraic topology, providing topological semantics for intensional systems of type theory as well as a computational approach to algebraic topology via type theory-based proof assistants such as Coq. The present work investigates inductive types in this setting. Modified rules for inductive types, including types of well-founded trees, or W-types, are presented, and the basic homotopical semantics of such types are determined. Proofs of all results have been formally verified by the Coq proof assistant, and the proof scripts for this verification form an essential component of this research.