Section: New Results

Software specification and verification

Step-indexing in program logics

Participant : Filip Sieczkowski.

Filip Sieczkowski pursued a line of work focused on techniques for formal reasoning about programs, in joint work with Lars Birkedal (Aarhus University) and Kasper Svendsen (Cambridge University). A modern and successful approach to grounding programs logics is to rely on so-called step-indexed models. Filip and his co-authors solved a problem that arises in most step-indexed models, due to a tight coupling between the unfoldings of a recursive domain equation and evaluation steps. Their approach is based on the use of transfinite step-indexing. This work appeared at ESOP 2016 [29].

TLA+

Participants : Damien Doligez, Leslie Lamport [Microsoft Research] , Martin Riener [team VeriDis] , Stephan Merz [team VeriDis] .

Damien Doligez is head of the “Tools for Proofs” team in the Microsoft-Inria Joint Centre. The aim of this project is to extend the TLA+ language with a formal language for hierarchical proofs, formalizing Lamport's ideas [48], and to build tools for writing TLA+ specifications and mechanically checking the proofs.

Our rewrite of the TLAPS tools is almost done and we hope to do a first release in the first quarter of 2017.

Hash tables and iterators: a case study in program verification

Participant : François Pottier.

In the setting of the Vocal ANR project, François Pottier developed the the specification and proof of an (imperative, sequential) hash table implementation, as found in the module Hashtbl of OCaml's standard library. This data structure supports the usual dictionary operations (insertion, lookup, and so on), as well as iteration via folds and iterators. The code was verified using higher-order separation logic, embedded in Coq, via Charguéraud's CFML tool and library. This work was presented at CPP 2017 [27]. It can be viewed as a case study that should help prepare the way for verifying other modules in the Vocal library.

Read-only permissions in separation logic

Participants : Arthur Charguéraud, François Pottier.

Separation Logic, as currently implemented in Charguéraud's CFML tool and library, imposes a simple ownership discipline on mutable heap-allocated data structures: a thread either has full read-write access to a data structure, or has no access at all. This implies, for instance, that two threads cannot temporarily share read-only access to a data structure. There exist more flexible disciplines in the literature, such as “fractional permissions” and “share algebras”, but they are much more complex.

In the setting of the Vocal ANR project, Arthur Charguéraud and François Pottier noted that it would be desirable to define an extension of Separation Logic that allows temporary shared read-only access, yet remains very simple. They proposed a general mechanism for temporarily converting any assertion (or “permission”) to a read-only form. The metatheory of this proposal has been verified in Coq. This work will be presented at ESOP 2017 [42].

Charguéraud and Pottier believe that this mechanism should allow more concise specifications and proofs. This remains to be confirmed, in future work, via an implementation in CFML and case studies in the Vocal project.

Formal reasoning about asymptotic complexity

Participants : Armaël Guéneau, Arthur Charguéraud, François Pottier.

Armaël Guéneau started his Ph.D. at Gallium in September 2016, supervised by Arthur Charguéraud and François Pottier. In the line of his previous M2 internship at Gallium, he continued his work on asymptotic reasoning in Coq. The challenge is to give a formal definition of the well-known big-$O$ notation, covering both single-variable and multiple-variable scenarios, to establish its fundamental properties, and to define tactics that make asymptotic reasoning as convenient in Coq as it seemingly is on paper. The ultimate goal is to apply these techniques to machine-checked proofs of the asymptotic time complexity of programs.

Certified distributed algorithms for autonomous mobile robots

Participant : Pierre Courtieu.

The variety and complexity of the tasks that can be performed by autonomous robots are increasing. Many applications envision groups of mobile robots that self-organise and cooperate toward the resolution of common objectives, in the absence of any central coordinating authority.

Pierre Courtieu is elaborating a verification platform, based on Coq, for distributed algorithms for autonomous robots. (This is joint work with Xavier Urbain, Sebastien Tixeuil and Lionel Rieg.) As part of this effort, Pierre Courtieu designed and verified a protocol for mobile robots that achieves the “gathering” task in all cases where it has not been proved impossible [34], [35].