A Parametric Framework for Reversible Pi-Calculi

Abstract

This paper presents a study of causality in a reversible, concurrent setting. There exist various notions of causality in π-calculus, which differ in the treatment of parallel extrusions of the same name. In this paper we present a uniform framework for reversible π-calculi that is parametric with respect to a data structure that stores information about an extrusion of a name. Different data structures yield different approaches to the parallel extrusion problem. We map three well-known causal semantics into our framework. We show that the (parametric) reversibility induced by our framework is causallyconsistent and prove a causal correspondence between an appropriate instance of the framework and Boreale and Sangiorgi's causal semantics. * This work was partially supported by COST Action IC1405 "Reversible computation -extending horizons of computing", the input action on a depends on the output on b. In the case of parallel extrusions of the same name, for example νa (ba | ca | a(z)), there exist different interpretations of which extrusion will cause the action a(z). In what follows, we consider three approaches.The classical and the most used approach to causality in the π-calculus is the one where the order of extrusions matters and the first one of them is the cause of the action a(z). Some of the causal semantics representing this idea are [15,6,8] and all of them are defined for standard (forward-only) π-calculus. In [15] the authors claim that, after abstracting away from the technique used to record causal dependences, the final order between the actions in their semantics coincides with the ones introduced in [6, 8]. Hence we group these semantics together as a single approach to causality. Secondly, in [9], action a(z) in the example above depends on one of the extruders, but there is no need to keep track of which one exactly. This causal semantics is defined for the forward-only π-calculus.Finally, the first compositional causal semantics for the reversible π-calculus is introduced in [10]. In the above example, parallel extrusions are concurrent and the action a(z) will record dependence on one of them (exactly which one is decided by the context). This causal semantics enjoys certain correctness properties which are not satisfied by other semantics.Here we present a framework for reversible π-calculus that is parametric with respect to the data structure that stores information about an extrusion of a name. Different data structures will lead to different approaches to the parallel extrusion problem, including the three described above. Our framework allows us to add reversibility to semantics where it was not previously defined. By varying the parameters, different orderings of the causally-consistent backward steps are allowed. Our intention is to develop a causal behavioural theory for the framework, in order to better understand different interpretations of reversibility in the π-calculus, and to use this understanding for causal analysis of concurrent programs.A preliminary discussion of the...

A parametric framework for reversible π-calculi

“…To show the correspondence between the mentioned semantics and our framework, we shall consider it in a late (rather than early, as originally given) version. The precise definition is given in [24]. The authors distinguish between two types of causality: subject and the object.…”

“…We prove causal correspondence between Boreale and Sangiorgi's late semantics (rather than early, as originally given) and the framework when memory ∆ is instantiated with Γ w . The precise definitions and the proofs are given in [24]; here we shall give just a brief presentation of the idea.…”

“…Hence, we need to provide a connection between sets of structural causes in these two semantics. Let us briefly explain our method; more details can be found in [24].…”

“…The main results are given in Section 4, and Section 5 concludes the paper. Proofs are omitted for space reasons; they can be found in the extended version [24].…”

Reversing P/T Nets

“…Intuitively, this notion stipulates that any event can be undone provided that all its consequences, if any, are undone beforehand. The interplay between reversibility and concurrency has been widely studied in process calculi [6,21,12,4,17], event structures [22,5,26,8] and lately Petri Nets [19,1]. Despite being a very basic model of concurrency, Petri nets still lack a satisfactory causally-consistent reversible semantics.…”