Basing on an original Coq implementation of unbounded linear search for partially decidable predicates, we study the computational contents of μ-recursive functions via their syntactic representation, and a correct by construction Coq interpreter for this abstract syntax. When this interpreter is extracted, we claim the resulting OCaml code to be the natural combination of the implementation of the μ-recursive schemes of composition, primitive recursion and unbounded minimization of partial (i.e., possibly non-terminating) functions. At the level of the fully specified Coq terms, this implies the representation of higher-order functions of which some of the arguments are themselves partial functions. We handle this issue using some techniques coming from the Braga method. Hence we get a faithful embedding of μ-recursive algorithms into Coq preserving not only their extensional meaning but also their intended computational behavior. We put a strong focus on the quality of the Coq artifact which is both self contained and with a line of code count of less than 1k in total.

We introduce a static analysis and two program transformations for Datalog to circumvent performance ssues that arise with the implementation of primitive predicates, notably in the framework of a large scale telecommunication application. To this effect, we introduce a new trace semantics for Datalog with a verified mechanization. This work can be seen as both a first step and a proof of concept for the creation of a full-blown library of verified Datalog optimizations, on top of an existing Coq/MathComp formalization of Datalog towards the development of a realistic environment for certified data centric applications.

This paper introduces CertiCAN, a tool produced using the Coq proof assistant for the formal certification of CAN analysis results. Result certification is a process that is light-weight and flexible compared to tool certification, which makes it a practical choice for industrial purposes. The analysis underlying CertiCAN, which is based on a combined use of two well-known CAN analysis techniques, is computationally efficient. Experiments demonstrate that CertiCAN is faster than the corresponding certified combined analysis. More importantly, it is able to certify the results of RTaW-Pegase, an industrial CAN analysis tool, even for large systems. This result paves the way for a broader acceptance of formal tools for the certification of real-time systems analysis results.

This paper presents a generic proof of Typical Worst-Case Analysis (TWCA), an analysis technique for weakly-hard real-time uniprocessor systems. TWCA was originally introduced for systems with fixed priority preemptive (FPP) schedulers and has since been extended to fixed-priority nonpreemptive (FPNP) and earliest-deadline-first (EDF) schedulers. Our generic analysis is based on an abstract model that characterizes the exact properties needed to make TWCA applicable to any system model. Our results are formalized and checked using the Coq proof assistant along with the Prosa schedulability analysis library. Our experience with formalizing real-time systems analyses shows that this is not only a way to increase confidence in our claimed results: The discipline required to obtain machine checked proofs helps understanding the exact assumptions required by a given analysis, its key intermediate steps and how this analysis can be generalized.

This paper presents the first steps toward a formally proven tool for schedulability analysis of tasks with offsets. We formalize and verify the seminal response time analysis of Tindell by extending the Prosa proof library, which is based on the Coq proof assistant. Thanks to Coq's extraction capabilities, this will allow us to easily obtain a certified analyzer. Additionally, we want to build a Coq certifier that can verify the correctness of results obtained using related (but uncertified), already existing analyzers. Our objective is to investigate the advantages and drawbacks of both approaches, namely the certified analysis and the certifier. The work described in this paper as well as its continuation is intended to enrich the Prosa library.

Data centric languages, such as recursive rule based languages, have been proposed to program distributed applications over networks. They greatly simplify the code, while still admitting efficient distributed execution, including on sensor networks. From previous work [1], we know that they also provide a promising approach to another tough issue about distributed protocols: their formal verification. Indeed, we can take advantage of their data centric orientation, which allows us to explicitly handle global structures such as the topology of the network. We illustrate here our approach on two non-trivial protocols and discuss its Coq implementation.

Population protocols are an elegant model recently introduced for distributed algorithms running in large and unreliable networks of tiny mobile agents. Correctness proofs of such protocols involve subtle arguments on infinite sequences of events. We propose a general formalization of self-stabilizing population protocols with the Coq proof assistant. It is used in reasoning about a concrete protocol for leader election in complete graphs. The protocol is formally proved to be correct for networks of arbitrarily large size. To this end we develop an appropriate theory of infinite sequences, including results for reasoning on abstractions. In addition, we provide a constructive correctness proof for a leader election protocol in directed rings. An advantage of using a constructive setting is that we get more informative proofs on the scenarios that converge to the desired configurations.

The development of a simulator, called Veda, is described. Veda is a software tool to help designers in protocol modeling and validation. It is oriented towards the rapid prototyping of distributed algorithms. Algorithms are described using an ISO (International Organisation for Standardization) formal description technique, called Estelle. The development of Veda and its internal structure is presented, emphasizing the use of Prolog as a software engineering tool. Typical uses of Veda are discussed.>