Related papers: Duality of Session Types: The Final Cut

Sessions are a fundamental notion in message-passing systems. A session is an abstract notion of communication between parties where each one owns an endpoint. Session types are types that are assigned to the endpoints and that are used to…

We (re)define session types as projections of process behaviors with respect to the communication channels they use. In this setting, we give session types a semantics based on fair testing. The outcome is a unified theory of behavioral…

Session types model structured communication-based programming. In particular, binary session types for the pi-calculus describe communication between exactly two participants in a distributed scenario. Adding sessions to the pi-calculus…

Session types are used to describe communication protocols in distributed systems and, as usual in type theories, session subtyping characterizes substitutability of the communicating processes. We investigate the (un)decidability of…

Timed session types formalise timed communication protocols between two participants at the endpoints of a session. They feature a decidable compliance relation, which generalises to the timed setting the progress-based compliance between…

Session types capture precise protocol structure in concurrent programming, but do not specify properties of the exchanged values beyond their basic type. Refinement types are a form of dependent types that can address this limitation,…

We propose a semantically grounded theory of session types which relies on intersection and union types. We argue that intersection and union types are natural candidates for modeling branching points in session types and we show that the…

Session types describe the structure of communications implemented by channels. In particular, they prescribe the sequence of communications, whether they are input or output actions, and the type of value exchanged. Crucial to any language…

Session types are behavioural types for guaranteeing that concurrent programs are free from basic communication errors. Recent work has shown that asynchronous session subtyping is undecidable. However, since session types have become…

We define the notion of duality categories as generalization of duality groups. Two examples are treated. The first is the Serre duality in the categories of strict polynomial functors. The second concerns finite complexes. We show in…

This is the written version of a series of lectures reviewing the basics of duality as applied to p-forms and sigma-models. The ideas are introduced by way of worked examples, often quite detailed. Our approach is very pedestrian and the…

Multiparty Session Types (MPST) are a well-established typing discipline for message-passing processes interacting on sessions involving two or more participants. Session typing can ensure desirable properties: absence of communication…

Suitable duals of multimodules are introduced and used to provide transposition contravariant right semi-adjunctions (and dualitites under reflexivity). Several additional notions on multimodules are discussed: generalized morphisms and…

We study the notion of subtyping for session types in a logical setting, where session types are propositions of multiplicative/additive linear logic extended with least and greatest fixed points. The resulting subtyping relation admits a…

Termination is a central property in sequential programming models: a term is terminating if all its reduction sequences are finite. Termination is also important in concurrency in general, and for message-passing programs in particular. A…

Duality, the equivalence between seemingly distinct quantum systems, is a curious property that has been known for at least three quarters of a century. In the past two decades it has played a central role in mapping out the structure of…

Session types offer a type-based discipline for enforcing communication protocols in distributed programming. We have previously formalized simple session types in the setting of multi-threaded $\lambda$-calculus with linear types. In this…

This paper proposes bimorphic recursion, which is restricted polymorphic recursion such that every recursive call in the body of a function definition has the same type. Bimorphic recursion allows us to assign two different types to a…

There are several notions of duality between lines and points. In this note, it is shown that all these can be studied in a unified way. Most interesting properties are independent of specific choices. It is also shown that either dual…

It is shown that there exists a duality among fields. If a field is dual to another field, the solution of the field can be obtained from the dual field by the duality transformation. We give a general result on the dual fields. Different…