Retractable Contracts

Abstract

In calculi for modelling communication protocols, internal and external choices play dual roles. Two external choices can be viewed naturally as dual too, as they represent an agreement between the communicating parties. If the interaction fails, the past agreements are good candidates as points where to roll back, in order to take a different agreement. We propose a variant of contracts with synchronous rollbacks to agreement points in case of deadlock. The new calculus is equipped with a compliance relation which is shown to be decidable.

Retractable and Speculative Contracts

“…It is possible to show that all the relations on our retractable and speculative contracts (rsC) are conservative extensions of corresponding notions on (firstorder) session contracts (SC) as defined in [3,10], and on the retractable session contracts (rC) as defined in [7]. As previously said, it is not difficult to check that session contracts SC are a subset of retractable session contracts rC, which, in turn, are a subset of the contracts rsC we are presently investigating, namely: SC rC rsC.…”

“…Unlike the retractable session contracts of [7], in the present setting it is possible to get a natural notion of duality. The dual σ of an element σ of rsC is obtained, as for session contracts, by interchanging any name a with a and + with ⊕.…”

“…It can be obtained from the syntax of session contracts of [3,10] (called first-order session behaviors in [3]), that we dub here SC, just adding external retractable/speculative choice among outputs and internal choice among inputs. As a matter of fact our contracts can also be seen as an extension of the retractable session contracts of [7], that we dub here rC, simply adding internal choice among inputs. Basics of session contracts and retractable session contracts are recalled in the companion technical report [8].…”

“…While this operator has limited practical impact, it makes the model more symmetric and the mathematical treatment simpler. A few preliminary results on the topic of this paper have been presented in a workshop paper [7], which considers retractable session contracts, i.e., retractable contracts without internal choice among inputs. The main result of [7] is the decidability of the compliance relation (while we study here also the complexity), which was obtained via an algorithm that we now know to be exponential.…”

“…Here we present a more refined, polynomial one ( Figure 7). In [7] the subcontract relation and the dual contract were not studied, and indeed the dual contract did not exist due to the absence of internal choice among inputs.…”