arXiv subjects

Damien Pous

Publications and source records attributed to Damien Pous.

26 records · Page 2Linked to original sources

arXiv2012

Innocent strategies as presheaves and interactive equivalences for CCS (expanded version)

Seeking a general framework for reasoning about and comparing programming languages, we derive a new view of Milner's CCS. We construct a category E of 'plays', and a subcategory V of 'views'. We argue that presheaves on V adequately represent 'innocent' strategies, in the sense of game semantics. We equip innocent strategies with a simple notion of interaction. We then prove decomposition results for innocent strategies, and, restricting to presheaves of finite ordinals, prove that innocent strategies are a final coalgebra for a polynomial functor derived from the game. This leads to a translation of CCS with recursive equations. Finally, we propose a notion of 'interactive equivalence' for innocent strategies, which is close in spirit to Beffara's interpretation of testing equivalences in concurrency theory. In this framework, we consider analogues of fair testing and must testing. We show that must testing is strictly finer in our model than in CCS, since it avoids what we call 'spatial unfairness'. Still, it differs from fair testing, and we show that it coincides with a relaxed form of fair testing.

cs.LO↗

arXiv2012

Untyping Typed Algebras and Colouring Cyclic Linear Logic

We prove "untyping" theorems: in some typed theories (semirings, Kleene algebras, residuated lattices, involutive residuated lattices), typed equations can be derived from the underlying untyped equations. As a consequence, the corresponding untyped decision procedures can be extended for free to the typed settings. Some of these theorems are obtained via a detour through fragments of cyclic linear logic, and give rise to a substantial optimisation of standard proof search algorithms.

cs.LO↗

arXiv2012

Deciding Kleene Algebras in Coq

We present a reflexive tactic for deciding the equational theory of Kleene algebras in the Coq proof assistant. This tactic relies on a careful implementation of efficient finite automata algorithms, so that it solves casual equations instantaneously and properly scales to larger expressions. The decision procedure is proved correct and complete: correctness is established w.r.t. any model by formalising Kozen's initiality theorem; a counter-example is returned when the given equation does not hold. The correctness proof is challenging: it involves both a precise analysis of the underlying automata algorithms and a lot of algebraic reasoning. In particular, we have to formalise the theory of matrices over a Kleene algebra. We build on the recent addition of firstorder typeclasses in Coq in order to work efficiently with the involved algebraic structures.

cs.LO↗

arXiv2011

Tactics for Reasoning modulo AC in Coq

We present a set of tools for rewriting modulo associativity and commutativity (AC) in Coq, solving a long-standing practical problem. We use two building blocks: first, an extensible reflexive decision procedure for equality modulo AC; second, an OCaml plug-in for pattern matching modulo AC. We handle associative only operations, neutral elements, uninterpreted function symbols, and user-defined equivalence relations. By relying on type-classes for the reification phase, we can infer these properties automatically, so that end-users do not need to specify which operation is A or AC, or which constant is a neutral element.

cs.MS↗

arXiv2011

Innocent strategies as presheaves and interactive equivalences for CCS

Seeking a general framework for reasoning about and comparing programming languages, we derive a new view of Milner's CCS. We construct a category E of plays, and a subcategory V of views. We argue that presheaves on V adequately represent innocent strategies, in the sense of game semantics. We then equip innocent strategies with a simple notion of interaction. This results in an interpretation of CCS. Based on this, we propose a notion of interactive equivalence for innocent strategies, which is close in spirit to Beffara's interpretation of testing equivalences in concurrency theory. In this framework we prove that the analogues of fair and must testing equivalences coincide, while they differ in the standard setting.

cs.LO↗

arXiv2009

Encapsulation and Dynamic Modularity in the Pi-Calculus

We describe a process calculus featuring high level constructs for component-oriented programming in a distributed setting. We propose an extension of the higher-order pi-calculus intended to capture several important mechanisms related to component-based programming, such as dynamic update, reconfiguration and code migration. In this paper, we are primarily concerned with the possibility to build a distributed implementation of our calculus. Accordingly, we define a low-level calculus, that describes how the high-level constructs are implemented, as well as details of the data structures manipulated at runtime. We also discuss current and future directions of research in relation to our analysis of component-based programming.

cs.PL↗

arXiv2008

On characterising strong bisimilarity in a fragment of CCS with replication

We provide a characterisation of strong bisimilarity in a fragment of CCS that contains only prefix, parallel composition, synchronisation and a limited form of replication. The characterisation is not an axiomatisation, but is instead presented as a rewriting system. We discuss how our method allows us to derive a new congruence result in the $π$-calculus: congruence holds in the sub-calculus that does not include restriction nor sum, and features a limited form of replication. We have not formalised the latter result in all details.

cs.LO↗

arXiv2008

A Distribution Law for CCS and a New Congruence Result for the pi-calculus

We give an axiomatisation of strong bisimilarity on a small fragment of CCS that does not feature the sum operator. This axiomatisation is then used to derive congruence of strong bisimilarity in the finite pi-calculus in absence of sum. To our knowledge, this is the only nontrivial subcalculus of the pi-calculus that includes the full output prefix and for which strong bisimilarity is a congruence.

cs.LO↗