Building Certified Static Analysers by Modular Construction of Well-founded Lattices

Abstract

This paper presents fixpoint calculations on lattice structures as example of highly modular programming in a dependently typed functional language. We propose a library of Coq module functors for constructing complex lattices using efficient data structures. The lattice signature contains a well-foundedness proof obligation which ensures termination of generic fixpoint iteration algorithms. With this library, complex well-foundedness proofs can hence be constructed in a functorial fashion. This paper demonstrates the ability of the recent Coq module system in manipulating algebraic structures and extracting efficient Ocaml implementations from them. The second contribution of this work is a generic result, based on the constructive notion of accessibility predicate, about preservation of accessibility properties when combining relations.

Verified Abstract Interpretation Techniques for Disassembling Low-level Self-modifying Code

“…On the one hand, a direct proof of the fixpoint iterator would be very hard: in particular, it would require difficult proofs over the widening operators of all abstract domains [29]. On the other hand, we can adapt the iteration strategy, optimize the algorithm and so on with no additional proof effort.…”

“…Using the Coq proof assistant and following the orthodox approach based on Galois connections, he runs into difficulties with α abstraction functions being nonconstructive, and with the calculation of abstract operators being poorly supported by Coq. Later, Pichardie's Ph.D. thesis [28,30] mechanizes the γ -only presentation of abstract interpretation that we use.…”

Certified Information Flow Analysis of Service Implementations

“…First approaches to verifying static analyses with Coq considered the classical monotone data flow analysis framework, including the groundbreaking work on analyses supporting optimizations in the CompCert optimizing compiler [24]. Mechanized verification of the more general abstract interpretation has later been studied [25]- [27]. The presentations in [3], [12] provide introductions into the approach and are accompanied by basic Coq developments for standard analyses, including, e.g., liveness analysis and interval analysis.…”

Certified Abstract Interpretation with Pretty-Big-Step Semantics

“…The formalization of Galois connections in proof assistants has been studied in previous work by several authors (e.g., [5,18]), and we have relied on existing libraries of constructors for building abstract domains.…”