Extracting a Data Flow Analyser in Constructive Logic

Abstract

Abstract. We show how to formalise a constraint-based data flow analysis in the specification language of the Coq proof assistant. This involves defining a dependent type of lattices together with a library of lattice functors for modular construction of complex abstract domains. Constraints are expressed in an intermediate representation that allows for both efficient constraint resolution and correctness proof of the analysis with respect to an operational semantics. The proof of existence of a correct, minimal solution to the constraints is constructive which means that the extraction mechanism of Coq provides a provably correct data flow analyser in ocaml. The library of lattices together with the intermediate representation of constraints are defined in an analysis-independent fashion that provides a basis for a generic framework for proving and extracting static analysers in Coq.

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

“…Most of the previous works on mechanized verification of static analyzes focused on standard data-flow frameworks [4,8,15,23] or abstract interpretation for small imperative structured languages [3,10,27]. Klein and Nipkow instantiate such a framework for inference of Java bytecode types [23]; Coupet-Grimal and Delobel [15] and Bertot et al [4] for compiler optimizations, and Cachera et al [8] for data-flow analysis.…”

“…Klein and Nipkow instantiate such a framework for inference of Java bytecode types [23]; Coupet-Grimal and Delobel [15] and Bertot et al [4] for compiler optimizations, and Cachera et al [8] for data-flow analysis.…”

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

“…In earlier work, we already introduced the lattice library [4]. However, we mainly discussed the semantic proofs required for certified analyses.…”

“…In our previous work [4] we considered the ascending chain condition but in this work we are interested in more general criterion: the existence of a widening operator.…”

“…We use the extraction mechanism of the Coq proof assistant to extract Ocaml programs from constructive proofs. In earlier work, we presented a lattice library which allows the construction of complex lattices in a modular fashion [4]. It was shown how this library was used to construct large termination proofs based on the ascending chain condition.…”