Session Type Isomorphisms

Abstract

There has been a considerable amount of work on retrieving functions in function libraries using their type as search key. The availability of rich component specifications, in the form of behavioral types, enables similar queries where one can search a component library using the behavioral type of a component as the search key. Just like for function libraries, however, component libraries will contain components whose type differs from the searched one in the order of messages or in the position of the branching points. Thus, it makes sense to also look for those components whose type is different from, but isomorphic to, the searched one.In this article we give semantic and axiomatic characterizations of isomorphic session types. The theory of session type isomorphisms turns out to be subtle. In part this is due to the fact that it relies on a non-standard notion of equivalence between processes. In addition, we do not know whether the axiomatization is complete. It is known that the isomorphisms for arrow, product and sum types are not finitely axiomatisable, but it is not clear yet whether this negative results holds also for the family of types we consider in this work.

Behavioural Types for Heterogeneous Systems (Position Paper)

“…• Message Insertion / Reordering It may be that a component supports a compatible variation of its role in a protocol, but does not match the protocol exactly (for example, due to a version upgrade). In this case, the session IR can describe message reorderings (inspired by theoretical work on session type isomorphisms [5,15]), or insertions of messages at a given point. This would enable migrating components to new versions with a different but compatible behaviour.…”

Service Equivalence via Multiparty Session Type Isomorphisms

“…We build upon earlier work to axiomatise session type isomorphisms through behavioral adaptation. The first such attempt to investigate session type isomorphisms, following the theory of type isomorphisms [5] and finite hereditary permutations, was presented in [8] and described combinators for binary session types isomorphisms corresponding to adjacent processes. Interpretation of linear logic propositions as session types for communicating processes explains how type isomorphisms resulting from linear logic equivalences are realised by coercions between interface types of session-based concurrent systems [13].…”

“…We follow the approach developed in [8]. In that work, the notion of session type isomorphisms was initially explored.…”

C3Q: A Specification Model for Web Services Within Virtual Organizations

“…Session types, which can be assigned to endpoint processes, describe the user view of an interaction. In [7], the authors have specified component behavior as session types showing that session types can also describe the behavioral signature of services.…”