On the Representation of References in the pi-calculus

Daniel Hirschkoff (1, 2, 3) , Enguerrand Prebet (1, 2, 3) , Davide Sangiorgi (4, 5)

1 ENS de Lyon - École normale supérieure de Lyon
2 LIP - Laboratoire de l'Informatique du Parallélisme
3 PLUME - Preuves et Langages
4 FOCUS - Foundations of Component-based Ubiquitous Systems
5 UNIBO - Alma Mater Studiorum Università di Bologna = University of Bologna

The π-calculus has been advocated as a model to interpret, and give semantics to, languages withhigher-order features. Often these languages make use of forms of references (and hence viewing astore as set of references). While translations of references in π-calculi (and CCS) have appeared,the precision of such translations has not been fully investigated. In this paper we address this issue.We focus on the asynchronous π-calculus (Aπ), where translations of references are simpler. Wefirst define π ref , an extension of Aπ with references and operators to manipulate them, and illustrateexamples of the subtleties of behavioural equivalence in π ref . We then consider a translation ofπ ref into Aπ. References of π ref are mapped onto names of Aπ belonging to a dedicated "reference"type. We show how the presence of reference names affects the definition of barbed congruence. Weestablish full abstraction of the translation w.r.t. barbed congruence and barbed equivalence in thetwo calculi. We investigate proof techniques for barbed equivalence in Aπ, based on two forms oflabelled bisimilarities. For one bisimilarity we derive both soundness and completeness; for another,more efficient and involving an inductive ‘game’ on reference names, we derive soundness, leavingcompleteness open. Finally, we discuss examples of uses of the bisimilarities.

Mots clés: Asynchrony; Bisimulation; Imperative programming; Process calculus

Domaines: Logique en informatique [cs.LO]

Daniel Hirschkoff, Enguerrand Prebet, Davide Sangiorgi. On the Representation of References in the pi-calculus. 2020. ⟨hal-02895654v2⟩