FSCD 2017 invited talks

Abstract: Relational program verification is a variant of program verification where one focuses on guaranteeing properties about the executions of two programs, and as a special case about two executions of a single program on different inputs. Relational verification becomes particularly interesting when non-functional aspects of a computation, like probabilities or resource cost, are considered. Several approached to relational program verification have been developed, from relational program logics to relational abstract interpretation. In this talk, I will introduce two approaches to relational program verification for higher-order computations based on the use of type systems. The first approach consists in developing powerful type system where a rich language of assertions can be used to express complex relations between two programs. The second approach consists in developing more restrictive type systems enriched with effects expressing in a lightweight way relations between different runs of the same program. I will discuss the pros and cons of these two approaches on a concrete example: relational cost analysis, which aims at giving a bound on the difference in cost of running two programs, and as a special case the difference in cost of two executions of a single program on different inputs.

Abstract: In this talk, I'll describe how rewriting techniques can be successfully employed to built state-of-the-art automated resource analysis tools which favourably compare to other approaches. Furthermore I'll sketch the genesis of a uniform framework for resource analysis, emphasising success stories, without hiding intricate weaknesses. The talk ends with the discussion of open problems.

Abstract: Concurrent Kleene Algebra (CKA) is a mathematical formalism to study programs that exhibit concurrent behaviour. As with previous extensions of Kleene Algebra, characterizing the free model is crucial in order to develop the foundations of the theory and potential applications. For CKA, this has been an open question for a few years and this talk will overview why the problem is so difficult. We will then pave the way towards a solution, by presenting a new automaton model and a Kleene-like theorem for CKA. More precisely, we connect a relaxed version of CKA to series-parallel pomset languages, which are a natural candidate for the free model. There are two substantial differences with previous work: from expressions to automata, we use Brzozowski derivatives, which enable a direct construction of the automaton; from automata to expressions, we provide a syntactic characterization of the automata that denote valid CKA behaviours. We also survey how the present work can be used to to extend the network specification language NetKAT with primitives for concurrency so as to model and reason about concurrency within networks. This is joint work with Tobias Kappe, Paul Brunet, Bas Luttik, and Fabio Zanasi.

Abstract: Probabilistic programming has many applications in statistics, physics,... so that all programming languages have been equipped with probabilistic library. However, there is a need in developing semantical tools in order to formalize higher order and recursive probabilistic languages. Indeed, it is well known that categories of measurable spaces are not Cartesian closed. We have been studying quantitative semantics of probabilistic spaces to fill this gap. A first step has been to focus on probabilistic programming languages with discrete types such as integers and booleans. In this setting, probabilistic programs can be seen as linear combinations of deterministic programs. Probabilistic Coherent Spaces constitute a Cartesian closed category that is fully abstract with respect to probabilistic Call-By-Push-Value. Moreover, this toy language is endowed with a memorization operator that allow to encode most discrete probabilistic programs. The second step is to move on probabilistic programming with continuous types representing for instance reals endowed with Lebesgue measurable sets. We introduce the category of cones and stable functions which is Cartesian closed. The trick is to enlarge the category of measurable spaces to gain closeness and to embrace measurable spaces. Besides, the category of cones is a sound and adequate model of a higher order and recursive probabilistic language in which most classical distributions and probabilistic tools can be encoded. This is joint work with Thomas Ehrhard and Michele Pagani.