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Ph.D de

Group : Verification of Algorithms, Languages and Systems

Development and verification of arbitrary-precision integer arithmetic libraries

Starts on 01/10/2017
Advisor : MELQUIOND, Guillaume

Funding : Convention industrielle de formation par la recherche
Affiliation : Université Paris-Saclay
Laboratory : LRI - VALS & TrustInSoft

Defended on 03/11/2020, committee :
Rapporteurs :
- Karthikeyan Bhargavan, Directeur de recherche, Inria Paris
- Paul Zimmermann, Directeur de recherche, Inria Nancy

- Patricia Bouyer, Directrice de recherche, CNRS
- Catherine Dubois, Professeure, ENSIIE
- Xavier Leroy, Professeur, Collège de France
- Micaela Mayero, Maître de conférences, Université Paris-Nord

Directeur de thèse
- Guillaume Melquiond, Chargé de recherche, Inria Saclay

Co-encadrant de thèse
- Pascal Cuoq, Directeur scientifique, TrustInSoft

Research activities :

Abstract :
Arbitrary-precision integer arithmetic algorithms are used in contexts where both their performance and their correctness are critical, such as cryptographic software or computer algebra systems. GMP is a very widely-used arbitrary-precision integer arithmetic library. It features state-of-the-art algorithms that are intricate enough that their formal verification is both justified and difficult. This thesis tackles the formal verification of the functional correctness of a large fragment of GMP using the Why3 deductive verification platform.

In order to make this verification possible, I have made several additions to Why3 that enable the verification of C programs. Why3 features a functional programming and specification language called WhyML. I have developed models of the memory management and datatypes of the C language, allowing me to reimplement GMP's algorithms in WhyML and formally verify them. I have also extended Why3's extraction mechanism so that WhyML programs can be compiled to idiomatic C code, where only OCaml used to be supported.

The compilation of my WhyML algorithms results in a verified C library called WhyMP. It implements many state-of-the-art algorithms from GMP, with almost all of the optimization tricks preserved. WhyMP is compatible with GMP and performance-competitive with the assembly-free version. It goes far beyond existing verified arbitrary-precision arithmetic libraries, and is arguably the most ambitious existing Why3 development in terms of size and proof effort.

In an attempt to increase the degree of automation of my proofs, I have also added to Why3 a framework for proofs by reflection. It enables Why3 users to easily write dedicated decision procedures that are formally verified programs and make full use of WhyML's imperative features. Using this new framework, I was able to replace hundreds of handwritten proof annotations in my GMP verification by automated proofs.

Ph.D. dissertations & Faculty habilitations


The topic of this habilitation is the study of very small data visualizations, micro visualizations, in display contexts that can only dedicate minimal rendering space for data representations. For several years, together with my collaborators, I have been studying human perception, interaction, and analysis with micro visualizations in multiple contexts. In this document I bring together three of my research streams related to micro visualizations: data glyphs, where my joint research focused on studying the perception of small-multiple micro visualizations, word-scale visualizations, where my joint research focused on small visualizations embedded in text-documents, and small mobile data visualizations for smartwatches or fitness trackers. I consider these types of small visualizations together under the umbrella term ``micro visualizations.'' Micro visualizations are useful in multiple visualization contexts and I have been working towards a better understanding of the complexities involved in designing and using micro visualizations. Here, I define the term micro visualization, summarize my own and other past research and design guidelines and outline several design spaces for different types of micro visualizations based on some of the work I was involved in since my PhD.