Language Primitives and Type Discipline for Structured Communication-Based Programming Revisited: Two Systems for Higher-Order Session Communication

AbstractSession primitives and types provide a flexible programming style for structured interaction, and are used to statically check the safe and consistent composition of protocols in communication-centric distributed software. Unfortunately authors working on session types have recently realised that some of the previously published systems fail to satisfy the basic theorems of Subject Reduction and Type Safety.This report discusses the issues involved in higher-order session communication, presents a formulation of the recursive types as well as proofs of the Subject Reduction and Type Safety Theorems of the original session typing system by Honda-Vasconcelos-Kubo in ESOP'98. It also proposes a variant which allows a more liberal higher-order session communication, based on an idea of Gay and Hole

LeoPARD --- A Generic Platform for the Implementation of Higher-Order Reasoners

LeoPARD supports the implementation of knowledge representation and reasoning tools for higher-order logic(s). It combines a sophisticated data structure layer (polymorphically typed {\lambda}-calculus with nameless spine notation, explicit substitutions, and perfect term sharing) with an ambitious multi-agent blackboard architecture (supporting prover parallelism at the term, clause, and search level). Further features of LeoPARD include a parser for all TPTP dialects, a command line interpreter, and generic means for the integration of external reasoners.Comment: 6 pages, to appear in the proceedings of CICM'2015 conferenc

Termination in Concurrency, Revisited

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 variety of type systems that enforce termination by typing have been developed. In this paper, we rigorously compare several type systems for $\pi$-calculus processes from the unifying perspective of termination. Adopting session types as reference framework, we consider two different type systems: one follows Deng and Sangiorgi's weight-based approach; the other is Caires and Pfenning's Curry-Howard correspondence between linear logic and session types. Our technical results precisely connect these very different type systems, and shed light on the classes of client/server interactions they admit as correct

Session Communication and Integration

The scenario-based specification of a large distributed system is usually naturally decomposed into various modules. The integration of specification modules contrasts to the parallel composition of program components, and includes various ways such as scenario concatenation, choice, and nesting. The recent development of multiparty session types for process calculi provides useful techniques to accommodate the protocol modularisation, by encoding fragments of communication protocols in the usage of private channels for a class of agents. In this paper, we extend forgoing session type theories by enhancing the session integration mechanism. More specifically, we propose a novel synchronous multiparty session type theory, in which sessions are separated into the communicating and integrating levels. Communicating sessions record the message-based communications between multiple agents, whilst integrating sessions describe the integration of communicating ones. A two-level session type system is developed for pi-calculus with syntactic primitives for session establishment, and several key properties of the type system are studied. Applying the theory to system description, we show that a channel safety property and a session conformance property can be analysed. Also, to improve the utility of the theory, a process slicing method is used to help identify the violated sessions in the type checking.Comment: A short version of this paper is submitted for revie

A dependent nominal type theory

Nominal abstract syntax is an approach to representing names and binding pioneered by Gabbay and Pitts. So far nominal techniques have mostly been studied using classical logic or model theory, not type theory. Nominal extensions to simple, dependent and ML-like polymorphic languages have been studied, but decidability and normalization results have only been established for simple nominal type theories. We present a LF-style dependent type theory extended with name-abstraction types, prove soundness and decidability of beta-eta-equivalence checking, discuss adequacy and canonical forms via an example, and discuss extensions such as dependently-typed recursion and induction principles

A New Type Assignment for Strongly Normalizable Terms

We consider an operator definable in the intuitionistic theory of monadic predicates and we axiomatize some of its properties in a definitional extension of that monadic logic. The axiomatization lends itself to a natural deduction formulation to which the Curry-Howard isomorphism can be applied. The resulting Church style type system has the property that an untyped term is typable if and only if it is strongly normalizable

Language Primitives and Type Discipline for Structured Communication-Based Programming, Subject Reduction and Type Safety Theorems

Session primitives and types provide a flexible programming style for structural interaction, and are used to statically check the safe and consistent composition of protocols in communication-centric distributed software. Unfortunately authors working on session types have recently realised that some of the previously published systems fail to satisfy the basic theorems of Subject Reduction and Type Safety. This report discusses the issues involved in higher-order session communication, presents a formulation of the recursive types as well as proofs of the Subject Reduction and Type Safety Theorems of the original session typing system by Honda-Vasconcelos-Kubo in ESOP'98. It also proposes a new session typing system which allows a more liberal higher-order session communication based on an idea of Gay and Hole