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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
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
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
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