Circular Proofs as Session-Typed Processes: A Local Validity Condition
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Published:2022-05-10
Issue:
Volume:Volume 18, Issue 2
Page:
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ISSN:1860-5974
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Container-title:Logical Methods in Computer Science
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language:en
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Short-container-title:
Author:
Derakhshan Farzaneh,Pfenning Frank
Abstract
Proof theory provides a foundation for studying and reasoning about
programming languages, most directly based on the well-known Curry-Howard
isomorphism between intuitionistic logic and the typed lambda-calculus. More
recently, a correspondence between intuitionistic linear logic and the
session-typed pi-calculus has been discovered. In this paper, we establish an
extension of the latter correspondence for a fragment of substructural logic
with least and greatest fixed points. We describe the computational
interpretation of the resulting infinitary proof system as session-typed
processes, and provide an effectively decidable local criterion to recognize
mutually recursive processes corresponding to valid circular proofs as
introduced by Fortier and Santocanale. We show that our algorithm imposes a
stricter requirement than Fortier and Santocanale's guard condition, but is
local and compositional and therefore more suitable as the basis for a
programming language.
Funder
National Science Foundation
Publisher
Centre pour la Communication Scientifique Directe (CCSD)
Subject
General Computer Science,Theoretical Computer Science
Cited by
2 articles.
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1. A Logical Account of Subtyping for Session Types;Electronic Proceedings in Theoretical Computer Science;2023-04-13
2. Nested Session Types;ACM Transactions on Programming Languages and Systems;2022-07-15