Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMultiparty Sessions based on Proof Nets
102
0
0.0
(
0
)
Added by
EPTCS
Publication date
2014
fields
Informatics Engineering
and research's language is
English
Authors
Dimitris Mostrous
Ask ChatGPT about the research
No Arabic abstract
We interpret Linear Logic Proof Nets in a term language based on Solos calculus. The system includes a synchronisation mechanism, obtained by a conservative extension of the logic, that enables to define non-deterministic behaviours and multiparty sessions.
rate research
Read More
Reversible interactions model different scenarios, like biochemical systems and human as well as automatic negotiations. We abstract interactions via multiparty sessions enriched with named checkpoints. Computations can either go forward or roll back to some checkpoints, where possibly different choices may be taken. In this way communications can be undone and different conversations may be tried. Interactions are typed with global types, which control also rollbacks. Typeability of session participants in agreement with global types ensures session fidelity and progress of reversible communications.
We propose an interpretation of multiparty sessions with asynchronous communication as Flow Event Structures. We introduce a new notion of global type for asynchronous multiparty sessions, ensuring the expected properties for sessions, including progress. Our global types, which reflect asynchrony more directly than standard global types and are more permissive, are themselves interpreted as Prime Event Structures. The main result is that the Event Structure interpretation of a session is equivalent, when the session is typable, to the Event Structure interpretation of its global type.
RedPRL is an experimental proof assistant based on Cartesian cubical computational type theory, a new type theory for higher-dimensional constructions inspired by homotopy type theory. In the style of Nuprl, RedPRL users employ tactics to establish behavioral properties of cubical functional programs embodying the constructive content of proofs. Notably, RedPRL implements a two-level type theory, allowing an extensional, proof-irrelevant notion of exact equality to coexist with a higher-dimensional proof-relevant notion of paths.
The Abella interactive theorem prover has proven to be an effective vehicle for reasoning about relational specifications. However, the system has a limitation that arises from the fact that it is based on a simply typed logic: formalizations that are identical except in the respect that they apply to different types have to be repeated at each type. We develop an approach that overcomes this limitation while preserving the logical underpinnings of the system. In this approach object constructors, formulas and other relevant logical notions are allowed to be parameterized by types, with the interpretation that they stand for the (infinite) collection of corresponding constructs that are obtained by instantiating the type parameters. The proof structures that we consider for formulas that are schematized in this fashion are limited to ones whose type instances are valid proofs in the simply typed logic. We develop schematic proof rules that ensure this property, a task that is complicated by the fact that type information influences the notion of unification that plays a key role in the logic. Our ideas, which have been implemented in an updated version of the system, accommodate schematic polymorphism both in the core logic of Abella and in the executable specification logic that it embeds.
This paper is a survey of two kinds of compressed proof schemes, the emph{matrix method} and emph{proof nets}, as applied to a variety of logics ranging along the substructural hierarchy from classical all the way down to the nonassociative Lambek system. A novel treatment of proof nets for the latter is provided. Descriptions of proof nets and matrices are given in a uniform notation based on sequents, so that the properties of the schemes for the various logics can be easily compared.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
