Polarized Substructural Session Types

Abstract

Abstract. The deep connection between session-typed concurrency and linear logic is embodied in the language SILL that integrates functional and message-passing concurrent programming. The exacting nature of linear typing provides strong guarantees, such as global progress, absence of deadlock, and race freedom, but it also requires explicit resource management by the programmer. This burden is alleviated in an affine type system where resources need not be used, relying on a simple form of garbage collection. In this paper we show how to effectively support both linear and affine typing in a single language, in addition to the already present unrestricted (intuitionistic) types. The approach, based on Benton's adjoint construction, suggests that the usual distinction between synchronous and asynchronous communication can be viewed through the lens of modal logic. We show how polarizing the propositions into positive and negative connectives allows us to elegantly express synchronization in the type instead of encoding it by extra-logical means.

Objects as session-typed processes

“…Shared channels [15,17,60], for example, are readily applicable to our work and can be easily integrated into CLOO in terms of the shifting operators defined in [52]. Whilst shared channels result in process replication, they could be combined with traditional locking primitives to share, for example, a database.…”

“…This formalization draws from existing work [55] that combines functional and message-passing concurrent computation based on linear logic. After those extensions and formalization, we would like to tackle the introduction of polymorphism in the sense of behavioral polymorphism [16] to facilitate generic data structures and affine types [52] to allow garbage collection of processes.…”

“…Those efforts have given rise to theories of behavioral polymorphism [16] and observational equivalence [51]. Most recently, an elegant integration of synchronous and asynchronous communication has been discovered [52]. Whereas all this research targets a purely functional setting, our work applies linear session types to an imperative, object-oriented setting.…”

Hybrid Session Verification Through Endpoint API Generation

“…New languages have also been developed from session type concepts. The design of SILL [33,40] is based on a Curry-Howard isomorphism between propositions in linear logic and session types, giving a language with powerful linear and session typing features, but that requires programmers to shape their data structures and algorithms according to this paradigm.…”

Benefits of session types for software development

“…Some examples would be Session J [9], or Mungo [11], both extending Java. New languages have also been developed based on session types, such as SILL [18]. A majority of research has been done on static session typing, with the contribution often being to develop a type system that types more programs, or to develop a type system that guarantees stronger properties of programs.…”