On the Expressiveness of Joining

The expressiveness of communication primitives has been explored in a common framework based on the pi-calculus by considering four features: synchronism (asynchronous vs synchronous), arity (monadic vs polyadic data), communication medium (shared dataspaces vs channel-based), and pattern-matching (binding to a name vs testing name equality vs intensionality). Here another dimension coordination is considered that accounts for the number of processes required for an interaction to occur. Coordination generalises binary languages such as pi-calculus to joining languages that combine inputs such as the Join Calculus and general rendezvous calculus. By means of possibility/impossibility of encodings, this paper shows coordination is unrelated to the other features. That is, joining languages are more expressive than binary languages, and no combination of the other features can encode a joining language into a binary language. Further, joining is not able to encode any of the other features unless they could be encoded otherwise.Comment: In Proceedings ICE 2015, arXiv:1508.04595. arXiv admin note: substantial text overlap with arXiv:1408.145

An Algebra of Hierarchical Graphs

We define an algebraic theory of hierarchical graphs, whose axioms characterise graph isomorphism: two terms are equated exactly when they represent the same graph. Our algebra can be understood as a high-level language for describing graphs with a node-sharing, embedding structure, and it is then well suited for defining graphical representations of software models where nesting and linking are key aspects

Session Types for Broadcasting

Up to now session types have been used under the assumptions of point to point communication, to ensure the linearity of session endpoints, and reliable communication, to ensure send/receive duality. In this paper we define a session type theory for broadcast communication semantics that by definition do not assume point to point and reliable communication. Our session framework lies on top of the parametric framework of broadcasting psi-calculi, giving insights on developing session types within a parametric framework. Our session type theory enjoys the properties of soundness and safety. We further believe that the solutions proposed will eventually provide a deeper understanding of how session types principles should be applied in the general case of communication semantics.Comment: In Proceedings PLACES 2014, arXiv:1406.331

Counterpart semantics for a second-order mu-calculus

We propose a novel approach to the semantics of quantified μ-calculi, considering models where states are algebras; the evolution relation is given by a counterpart relation (a family of partial homomorphisms), allowing for the creation, deletion, and merging of components; and formulas are interpreted over sets of state assignments (families of substitutions, associating formula variables to state components). Our proposal avoids the limitations of existing approaches, usually enforcing restrictions of the evolution relation: the resulting semantics is a streamlined and intuitively appealing one, yet it is general enough to cover most of the alternative proposals we are aware of

Mixin Composition Synthesis based on Intersection Types

We present a method for synthesizing compositions of mixins using type inhabitation in intersection types. First, recursively defined classes and mixins, which are functions over classes, are expressed as terms in a lambda calculus with records. Intersection types with records and record-merge are used to assign meaningful types to these terms without resorting to recursive types. Second, typed terms are translated to a repository of typed combinators. We show a relation between record types with record-merge and intersection types with constructors. This relation is used to prove soundness and partial completeness of the translation with respect to mixin composition synthesis. Furthermore, we demonstrate how a translated repository and goal type can be used as input to an existing framework for composition synthesis in bounded combinatory logic via type inhabitation. The computed result is a class typed by the goal type and generated by a mixin composition applied to an existing class

Shapely monads and analytic functors

In this paper, we give precise mathematical form to the idea of a structure whose data and axioms are faithfully represented by a graphical calculus; some prominent examples are operads, polycategories, properads, and PROPs. Building on the established presentation of such structures as algebras for monads on presheaf categories, we describe a characteristic property of the associated monads---the shapeliness of the title---which says that "any two operations of the same shape agree". An important part of this work is the study of analytic functors between presheaf categories, which are a common generalisation of Joyal's analytic endofunctors on sets and of the parametric right adjoint functors on presheaf categories introduced by Diers and studied by Carboni--Johnstone, Leinster and Weber. Our shapely monads will be found among the analytic endofunctors, and may be characterised as the submonads of a universal analytic monad with "exactly one operation of each shape". In fact, shapeliness also gives a way to define the data and axioms of a structure directly from its graphical calculus, by generating a free shapely monad on the basic operations of the calculus. In this paper we do this for some of the examples listed above; in future work, we intend to do so for graphical calculi such as Milner's bigraphs, Lafont's interaction nets, or Girard's multiplicative proof nets, thereby obtaining canonical notions of denotational model

Hierarchical models for service-oriented systems

We present our approach to the denotation and representation of hierarchical graphs: a suitable algebra of hierarchical graphs and two domains of interpretations. Each domain of interpretation focuses on a particular perspective of the graph hierarchy: the top view (nested boxes) is based on a notion of embedded graphs while the side view (tree hierarchy) is based on gs-graphs. Our algebra can be understood as a high-level language for describing such graphical models, which are well suited for defining graphical representations of service-oriented systems where nesting (e.g. sessions, transactions, locations) and linking (e.g. shared channels, resources, names) are key aspects