Session Types in a Linearly Typed Multi-Threaded Lambda-Calculus

We present a formalization of session types in a multi-threaded lambda-calculus (MTLC) equipped with a linear type system, establishing for the MTLC both type preservation and global progress. The latter (global progress) implies that the evaluation of a well-typed program in the MTLC can never reach a deadlock. As this formulated MTLC can be readily embedded into ATS, a full-fledged language with a functional programming core that supports both dependent types (of DML-style) and linear types, we obtain a direct implementation of session types in ATS. In addition, we gain immediate support for a form of dependent session types based on this embedding into ATS. Compared to various existing formalizations of session types, we see the one given in this paper is unique in its closeness to concrete implementation. In particular, we report such an implementation ready for practical use that generates Erlang code from well-typed ATS source (making use of session types), thus taking great advantage of the infrastructural support for distributed computing in Erlang.Comment: This is the original version of the paper on supporting programming with dyadic session types in AT

Session types in a linearly typed multi-threaded lambda-calculus

We present a formalization of session types in a multi-threaded lambda-calculus (MTLC) equipped with a linear type system, establishing for the MTLC both type preservation and global progress. The latter (global progress) implies that the evaluation of a well-typed program in the MTLC can never reach a deadlock. As this formulated MTLC can be readily embedded into ATS, a full-fledged language with a functional programming core that supports both dependent types (of DML-style) and linear types, we obtain a direct implementation of session types in ATS. In addition, we gain immediate support for a form of dependent session types based on this embedding into ATS. Compared to various existing formalizations of session types, we see the one given in this paper is unique in its closeness to concrete implementation. In particular, we report such an implementation ready for practical use that generates Erlang code from well-typed ATS source (making use of session types), thus taking great advantage of the infrastructural support for distributed computing in Erlang.First author draf

Linearly Typed Dyadic Group Sessions for Building Multiparty Sessions

Traditionally, each party in a (dyadic or multiparty) session implements exactly one role specified in the type of the session. We refer to this kind of session as an individual session (i-session). As a generalization of i-session, a group session (g-session) is one in which each party may implement a group of roles based on one channel. In particular, each of the two parties involved in a dyadic g-session implements either a group of roles or its complement. In this paper, we present a formalization of g-sessions in a multi-threaded lambda-calculus (MTLC) equipped with a linear type system, establishing for the MTLC both type preservation and global progress. As this formulated MTLC can be readily embedded into ATS, a full-fledged language with a functional programming core that supports both dependent types (of DML-style) and linear types, we obtain a direct implementation of linearly typed g-sessions in ATS. The primary contribution of the paper lies in both of the identification of g-sessions as a fundamental building block for multiparty sessions and the theoretical development in support of this identification.Comment: This paper can be seen as the pre-sequel to classical linear multirole logic (CLML). arXiv admin note: substantial text overlap with arXiv:1603.0372

Linearly typed dyadic group sessions for building multiparty sessions

Traditionally, each party in a (dyadic or multiparty) session implements exactly one role specified in the type of the session. We refer to this kind of session as an individual session (i-session). As a generalization of i-session, a group session (g-session) is one in which each party may implement a group of roles based on one channel. In particular, each of the two parties involved in a dyadic g-session implements either a group of roles or its complement. In this paper, we present a formalization of g-sessions in a multi-threaded lambda-calculus (MTLC) equipped with a linear type system, establishing for the MTLC both type preservation and global progress. As this formulated MTLC can be readily embedded into ATS, a full-fledged language with a functional programming core that supports both dependent types (of DML-style) and linear types, we obtain a direct implementation of linearly typed g-sessions in ATS. The primary contribution of the paper lies in both of the identification of g-sessions as a fundamental building block for multiparty sessions and the theoretical development in support of this identification.First author draf

Multirole Logic and Multiparty Channels

We identify multirole logic as a new form of logic in which conjunction/disjunction is interpreted as an ultrafilter on some underlying set of roles and the notion of negation is generalized to endomorphisms on this set. We formulate both multirole logic (MRL) and linear multirole logic (LMRL) as natural generalizations of classical logic (CL) and classical linear logic (CLL), respectively. Among various meta-properties established for MRL and LMRL, we obtain one named multiparty cut-elimination stating that every cut involving one or more sequents (as a generalization of a binary cut involving exactly two sequents) can be eliminated, thus extending the celebrated result of cut-elimination by Gentzen. As a side note, we also give an ultrafilter-based interpretation for intuitionism, formulating MRLJ as a natural generalization of intuitionistic logic (IL). An immediate application of LMRL can be found in a formulation of session types for channels that support multiparty communication in distributed programming. We present a multi-threaded lambda-calculus (MTLC) where threads communicate on linearly typed multiparty channels that are directly rooted in LMRL, establishing for MTLC both type preservation and global progress. The primary contribution of the paper consists of both identifying multirole logic as a new form of logic and establishing a theoretical foundation for it, and the secondary contribution lies in applying multirole logic to the practical domain of distributed programming.Comment: arXiv admin note: text overlap with arXiv:1604.0302

Multirole logic and multiparty channels

We identify multirole logic as a new form of logic in which conjunction/disjunction is interpreted as an ultrafilter on the power set of some underlying set (of roles), and the notion of negation is generalized to endomorphisms on this underlying set. In this talk, we present linear multirole logic (LMRL) as a natural generalization of classical linear logic (CLL). Among various meta-properties established for LMRL, we obtain one named multiparty cut-elimination stating that every cut involving one or more sequents (as a generalization of a binary cut involving exactly two sequents) can be eliminated, thus extending the celebrated result of cut-elimination by Gentzen. An immediate application of LMRL can be found in a formulation of session types for channels that support multiparty communication in distributed programming. Guided by LMRL, we give an interesting interpretation to linear multiplicative conjunction/disjunction as session type constructors that encompasses certain seemingly contradictory ones found in the literature

Multirole Logic (Extended Abstract)

We identify multirole logic as a new form of logic in which conjunction/disjunction is interpreted as an ultrafilter on the power set of some underlying set (of roles) and the notion of negation is generalized to endomorphisms on this underlying set. We formalize both multirole logic (MRL) and linear multirole logic (LMRL) as natural generalizations of classical logic (CL) and classical linear logic (CLL), respectively, and also present a filter-based interpretation for intuitionism in multirole logic. Among various meta-properties established for MRL and LMRL, we obtain one named multiparty cut-elimination stating that every cut involving one or more sequents (as a generalization of a (binary) cut involving exactly two sequents) can be eliminated, thus extending the celebrated result of cut-elimination by Gentzen

08061 Abstracts Collection -- Types, Logics and Semantics for State

From 3 February to 8 February 2008, the Dagstuhl Seminar 08061 ``Types, Logics and Semantics for State\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available