Logics and Models for Concurrency and Type Theory

Abstract

Abstract : The goal was to contribute useful new concepts and results in two very active areas of research within semantics of computation, namely concurrency and type theory. The technical method of approach used logic and category theory and aimed at a conceptual unification of concurrency and constructive type theory. Section 2 summarizes the accomplishments attained under this contract and explains the specific ways in which the research goals were met. Several topics were supported by the contract, and there are important connections between these different topics. General logics, often in the particular form of categorical logics, form a common semantic framework for all these investigations; they are discussed in Section 2.1. Work on concurrency models is discussed in Section 2.2. Rewriting logic, its role in unifying models of concurrency, and the Maude language are discussed in Section 2.3. The connections between linear logic and concurrency as well as models for linear logic are discussed in Section 2.4. Sections 2.5, 2.6, and 2.7 cover work on different aspects of type theory, namely models of polymorphism, constructors and selectors, and higher-order subtypes.