David Cachera, Thomas P. Jensen, David Pichardie, Vlad Rusu. Extracting a Data Flow Analyser in Constructive Logic. In David A. Schmidt, editor, Programming Languages and Systems, 13th European Symposium on Programming, ESOP 2004, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2004, Barcelona, Spain, March 29 - April 2, 2004, Proceedings. Volume 2986 of Lecture Notes in Computer Science, pages 385-400, Springer, 2004. [doi]
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.
Available at http://hal.inria.fr/docs/00/56/46/33/PDF/extractDataFlow-ESOP-nospringerlogo.pdf