Section: New Results

Program Verification and Formal Languages

Participant : Arthur Charguéraud.

• Armaël Guéneau, a PhD student advised by A. Charguéraud and F. Pottier (Cambium), has developed a formal proof of the functional correctness and the asymptotic complexity of a state-of-the-art incremental cycle detection algorithm due to Bender, Fineman, Gilbert, and Tarjan. This work moreover proposes a simple change that allows the algorithm to be regarded as genuinely online. The verification proof is carried out by exploiting Separation Logic with Time Credits, in the CFML tool, to simultaneously verify the correctness and the worst-case amortized asymptotic complexity of the modified algorithm. This work was published at ITP'19 [17]. It leverages previous work on the extension of the CFML verification tool to allow the specification of the asymptotic complexity of higher-order, imperative programs [55], and shows that this framework scales up to larger, more complex programs.

• Arthur Charguéraud, together with Jean-Christophe Filliâtre and Cláudio Lourenço (CNRS, Inria and Université Paris Saclay), and Mário Pereira (NOVA LINCS & DI, Universidade Nova de Lisboa), developed a behavioral specification language for OCaml, called GOSPEL. It is designed to enable modular verification of data structures and algorithms. Compared with writing specifications directly in Separation Logic, it provides a high-level syntax that greatly improves conciseness and makes it accessible to programmers with no familiarity with Separation Logic. GOSPEL is applied to the development of a formally verified library of general-purpose OCaml data structures. This work was published at the World Congress on Formal Methods (FM) 2019 [15].