Contributions. Our contribution consists of the following points. In Sect. 2 we study a calculus for contracting processes. Compared to the calculus in [1], the one in this paper differs in the treatment of the main primitives fuse and join, which have a simplified semantics. Moreover, we also provide here a reduction semantics, and compare it to the labelled one. In Sect. 3 we show our calculus suitable for modelling complex interactions of contracting parties. In Sect. 4 we substantiate a statement made in [1], by showing how to actually encode into our calculus some common concurrency idioms, among which the π-calculus [19] and graph rewriting [21]. In Sect. 5 we discuss further differences between the two calculi, and compare them with other frameworks. We now define our calculus of contracting processes. The calculus is similar to that in [1], yet it diverges in the treatment of the crucial primitives fuse and join . We will detail the differences between the two versions in Sect. 5. Our calculus features both names, ranged over by n, m, . . . , and variables, ranged over by x, y, Constraints are terms over variables and names, and include a special element ⊥; the set of constraints D is ranged over by c, d. Our calculus is parametric with respect to an arbitrary constraint system (D, ⊢) (Def. 1). Definition 1 (Constraint system [24]) A constraint system is a pair (D, ⊢), where D is a countable set, and ⊢⊆ P(D) × D is a relation satisfying: (i) C ⊢ c whenever c ∈ C; (ii) C ⊢ c whenever for all c′ ∈ C′ we have C ⊢ c′, and C′ ⊢ c; (iii) for any c, C ⊢ c whenever C ⊢ ⊥. Syntax. Names in our calculus behave similarly to the names in the π-calculus: that is, distinct names represent distinct concrete objects. Instead, variables behave as the names in the fusion calculus: that is, distinct variables can be bound to the same concrete object, so they can be fused. A fusion σ is a substitution that maps a set of variables to a single name. We write σ = {n/→x} for the fusion that replaces each variable in →x with the name n. We use metavariables a, b, to range over both names and variables.
Contributions. Our contribution consists of the following points. In Sect. 2 we study a calculus for contracting processes. Compared to the calculus in [2], the one in this paper differs in the treatment of the main primitives fuse and join, which have a simplified semantics. Moreover, we also provide here a reduction semantics, and compare it to the labelled one. In Sect. 3 we show our calculus suitable for modelling complex interactions of contracting parties. In Sect. 4 we substantiate a statement made in [2], by showing how to actually encode into our calculus some common concurrency idioms, among which the π-calculus [19] and graph rewriting [21]. In Sect. 5 we discuss further differences between the two calculi, and compare them with other frameworks.
Contributions. Authors Corresponding author Clinical expert External Reviewers Acknowledgements
Contributions. We propose a unified framework for modelling distributed systems that base their interactions on contracts. Technically, our contribution consists of the following points: • We devise a minimal set of properties which are desirable in any logical formalization of contracts. • We define a logic to model contracts, and to infer the duties deriving from those. Our logic satisfies all the properties identified above as desirable. Further, we support the logic with several examples. • We study the proof theory of our logic. In particular, we show that our logic is consistent and decidable. • We define a calculus for contracting processes, which exploits the logic to drive synchronizations between processes. • We show that our calculus is suitable for modelling complex interactions of contracting parties. We also show how to embed the π-calculus and graph rewriting in our calculus.
Contributions. 5.1 The Projects, as detailed in the Annexes, with a total cost of 902 000 Euros will be financed by the Regional Government of Lombardy.