25 research outputs found
An Interpretation of CCS into Ludics
Abstract Starting from works aimed at extending the Curry-Howard correspondence to process calculi through linear logic, we give another Curry-Howard counterpart for Milner's Calculus of Communicating Systems (CCS) by taking Ludics as the target system. Indeed interaction, Ludics' dynamic, allows to fully represent both the non-determinism and non-confluence of the calculus. We give an interpretation of CCS processes into carefully defined behaviours of Ludics using a new construction, called directed behaviour, that allows controlled interaction paths by using pruned designs. We characterize the execution of processes as interaction on behaviours, by implicitly representing the causal order and conflict relation of event structures. As a direct consequence, we are also able to interpret deadlocked processes, and identify deadlock-free ones
Sequentiality vs. Concurrency in Games and Logic
Connections between the sequentiality/concurrency distinction and the
semantics of proofs are investigated, with particular reference to games and
Linear Logic.Comment: 35 pages, appeared in Mathematical Structures in Computer Scienc
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.Comment: In Proceedings ICE 2011, arXiv:1108.014
A Nice Labelling for Tree-Like Event Structures of Degree 3 (Extended Version)
We address the problem of finding nice labellings for event structures of
degree 3. We develop a minimum theory by which we prove that the labelling
number of an event structure of degree 3 is bounded by a linear function of the
height. The main theorem we present in this paper states that event structures
of degree 3 whose causality order is a tree have a nice labelling with 3
colors. Finally, we exemplify how to use this theorem to construct upper bounds
for the labelling number of other event structures of degree 3
Full Abstraction for the Resource Lambda Calculus with Tests, through Taylor Expansion
We study the semantics of a resource-sensitive extension of the lambda
calculus in a canonical reflexive object of a category of sets and relations, a
relational version of Scott's original model of the pure lambda calculus. This
calculus is related to Boudol's resource calculus and is derived from Ehrhard
and Regnier's differential extension of Linear Logic and of the lambda
calculus. We extend it with new constructions, to be understood as implementing
a very simple exception mechanism, and with a "must" parallel composition.
These new operations allow to associate a context of this calculus with any
point of the model and to prove full abstraction for the finite sub-calculus
where ordinary lambda calculus application is not allowed. The result is then
extended to the full calculus by means of a Taylor Expansion formula. As an
intermediate result we prove that the exception mechanism is not essential in
the finite sub-calculus
An intensionally fully-abstract sheaf model for π (expanded version)
International audienceFollowing previous work on CCS, we propose a compositional model for the π-calculus in which processes are interpreted as sheaves on certain simple sites. Such sheaves are a concurrent form of innocent strategies, in the sense of Hyland-Ong/Nickau game semantics. We define an analogue of fair testing equivalence in the model and show that our interpretation is intensionally fully abstract for it. That is, the interpretation preserves and reflects fair testing equivalence; and furthermore, any innocent strategy is fair testing equivalent to the interpretation of some process. The central part of our work is the construction of our sites, relying on a combinatorial presentation of π-calculus traces in the spirit of string diagrams