Section: Research Program

Introduction

In the former ProVal project, we have been working on the design of methods and tools for deductive verification of programs. One of our original skills was the ability to conduct proofs by using automatic provers and proof assistants at the same time, depending on the difficulty of the program, and specifically the difficulty of each particular verification condition. We thus believe that we are in a good position to propose a bridge between the two families of approaches of deductive verification presented above. Establishing this bridge is one of the goals of the Toccata project: we want to provide methods and tools for deductive program verification that can offer both a high amount of proof automation and a high guarantee of validity. Toward this objective, a new axis of research was proposed: the development of certified analysis tools that are themselves formally proved correct.

The reader should be aware that the word “certified” in this scientific programme means “verified by a formal specification and a formal proof that the program meets this specification”. This differs from the standard meaning of “certified” in an industrial context where it means a conformance to some rigorous process and/or norm. We believe this is the right term to use, as it was used for the Certified Compiler project [100], the new conference series Certified Programs and Proofs, and more generally the important topics of proof certificates.

In industrial applications, numerical calculations are very common (e.g. control software in transportation). Typically they involve floating-point numbers. Some of the members of Toccata have an internationally recognized expertise on deductive program verification involving floating-point computations. Our past work includes a new approach for proving behavioral properties of numerical C programs using Frama-C/Jessie [41], various examples of applications of that approach [61], the use of the Gappa solver for proving numerical algorithms [118], an approach to take architectures and compilers into account when dealing with floating-point programs [62], [111]. We also contributed to the Handbook of Floating-Point Arithmetic [110]. A representative case study is the analysis and the proof of both the method error and the rounding error of a numerical analysis program solving the one-dimension acoustic wave equation [4] [54]. Our experience led us to a conclusion that verification of numerical programs can benefit a lot from combining automatic and interactive theorem proving [56], [61]. Certification of numerical programs is the other main axis of Toccata.

Our scientific programme in structured into four objectives:

1. deductive program verification;

2. automated reasoning;

3. formalization and certification of languages, tools and systems;

4. proof of numerical programs.

We detail these objectives below.