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Linear logic propositions as session types

LUÍS CAIRES, FRANK PFENNING, BERNARDO TONINHO
2014 Mathematical Structures in Computer Science  
that corresponds to a standard sequent calculus presentation of intuitionistic linear logic, interpreting linear propositions as session types and thus providing a purely logical account of all key features  ...  We also discuss an alternative presentation of linear session types based on classical linear logic, and compare our development with other more traditional session type systems.  ...  Intuitionistic Linear Logic as Session Types In this section, we detail our main contribution of interpreting a dyadic sequent calculus formulation of intuitionistic linear logic DILLas a session typing  ... 
doi:10.1017/s0960129514000218 fatcat:2xrvjo5vynbtbeqq3fcfjl342m

Propositions in Linear Multirole Logic as Multiparty Session Types [article]

Hongwei Xi, Hanwen Wu
2016 arXiv   pre-print
We identify multirole logic as a new form of logic and formalize linear multirole logic (LMRL) as a natural generalization of classical linear logic (CLL).  ...  We also present a variant of π-calculus for multiparty sessions that demonstrates a tight correspondence between process communication in this variant and multi-cut elimination in LMRL, thus extending  ...  between process communication in this variant and multi-cut elimination in LMRL, thus extending some recent results on encoding session types as propositions in linear logic (Caires and Pfenning 2010  ... 
arXiv:1611.08888v1 fatcat:c2lrjcfozjc7pa3g5q27nhrg4y

Linear Logic Propositions as Session Types

Luis Caires, Frank Pfenning, Bernardo Toninho
2018
This paper proposes a type system for the π-calculus that corresponds to a standard sequent calculus presentation of intuitionistic linear logic, interpreting linear propositions as session types and thus  ...  We also discuss an alternative presentation of linear session types based on classical linear logic, and compare our development with other more traditional session type systems.  ...  Intuitionistic Linear Logic as Session Types In this section, we detail our main contribution of interpreting a sequent calculus formulation of dual intuitionistic linear logic as a session typing discipline  ... 
doi:10.1184/r1/6606974 fatcat:g26hj6mq3nbslaxnzoc6mvvvui

Session Type Systems based on Linear Logic: Classical versus Intuitionistic

Bas van den Heuvel, Jorge A. Pérez
2020 Electronic Proceedings in Theoretical Computer Science  
Session type systems have been given logical foundations via Curry-Howard correspondences based on both intuitionistic and classical linear logic.  ...  We develop United Linear Logic (ULL), a logic encompassing both classical and intuitionistic linear logic.  ...  Caires and Pfenning discovered a Curry-Howard correspondence between a form of session types for the π-calculus and Girard's linear logic [8] : session types correspond to linear logic propositions, type  ... 
doi:10.4204/eptcs.314.1 fatcat:rmzwlrlxgzbjvlb6r7gxtablei

Linear Logical Relations for Session-Based Concurrency [chapter]

Jorge A. Pérez, Luís Caires, Frank Pfenning, Bernardo Toninho
2012 Lecture Notes in Computer Science  
In prior work we proposed an interpretation of intuitionistic linear logic propositions as session types for concurrent processes.  ...  As applications, we prove that all proof conversions induced by the logic interpretation actually express observational equivalences, and explain how type isomorphisms resulting from linear logic equivalences  ...  Another interpretation of session types as linear logic propositions is proposed in [7] . It is based on soft linear logic [15] , and so the exponential "!"  ... 
doi:10.1007/978-3-642-28869-2_27 fatcat:gpkpmr5bgncxnbk3b3pn2nzjb4

Polarized Substructural Session Types [chapter]

Frank Pfenning, Dennis Griffith
2015 Lecture Notes in Computer Science  
The deep connection between session-typed concurrency and linear logic is embodied in the language SILL that integrates functional and message-passing concurrent programming.  ...  We show how polarizing the propositions into positive and negative connectives allows us to elegantly express synchronization in the type instead of encoding it by extra-logical means.  ...  Linear Logic and Session Types We give here only the briefest review of linear logic and its deep connection to session types.  ... 
doi:10.1007/978-3-662-46678-0_1 fatcat:4a3fs7vv45hdjnhyyxdosef3si

Propositions as types

Philip Wadler
2015 Communications of the ACM  
The principle of Propositions as Types describes a fundamental connection between logic and computation which views propositions as types, proofs as programs, and normalisation of proofs as evaluation  ...  It is suitable for students in both logic and computing, presuming no previous knowledge of either, though familiarity with logic and computing will be helpful.  ...  Propositions as Types is a notion with breadth. It applies to a range of logics including propositional, predicate, second-order, intuitionistic, classical, modal, and linear.  ... 
doi:10.1145/2699407 fatcat:2egom54z3zagzcywzgynnwfcw4

Propositions as sessions

Philip Wadler
2012 Proceedings of the 17th ACM SIGPLAN international conference on Functional programming - ICFP '12  
logic correspond to session types.  ...  The translation formalises for the first time a connection between a standard presentation of session types and linear logic, and shows how a modification to the standard presentation yield a language  ...  Classical linear logic as a process calculus This section presents CP, a session-typed process calculus.  ... 
doi:10.1145/2364527.2364568 dblp:conf/icfp/Wadler12 fatcat:56asdlyqrva75iudjx7l3hgmju

Sessions as Propositions

Sam Lindley, J. Garrett Morris
2014 Electronic Proceedings in Theoretical Computer Science  
Recently, Wadler presented a continuation-passing translation from a session-typed functional language, GV, to a process calculus based on classical linear logic, CP.  ...  We propose an extension of GV, called HGV, and give translations showing that it is as expressive as CP.  ...  Caires and Pfenning [3] give a propositions-as-types correspondence between intuitionistic linear logic and session types, interpreting linear logic propositions as session types for a restricted π-calculus  ... 
doi:10.4204/eptcs.155.2 fatcat:4o5pm7qfwjbzrc67edrfhkmazm

A New Linear Logic for Deadlock-Free Session-Typed Processes [chapter]

Ornela Dardha, Simon J. Gay
2018 Lecture Notes in Computer Science  
The first is the propositions-as-types approach by Caires and Pfenning, which provides a linear logic foundation for session types and guarantees deadlock-freedom by forbidding cyclic process connections  ...  This can be seen in three ways: (i) as a new linear logic in which cyclic structures can be derived and a Cycle-elimination theorem generalises Cut-elimination; (ii) as a logically-based session type system  ...  The Caires-Pfenning approach has been widely accepted as a propositions-as-types theory of concurrent programming, as well as providing a logical foundation for session types.  ... 
doi:10.1007/978-3-319-89366-2_5 fatcat:ehz7wogjh5gdpfjiufqv7lt56m

Propositions as sessions

Philip Wadler
2012 SIGPLAN notices  
logic correspond to session types.  ...  The translation formalises for the first time a connection between a standard presentation of session types and linear logic, and shows how a modification to the standard presentation yield a language  ...  CP, classical linear logic as a session-typed process calculus In ∃X.B and ∀X.B, propositional variable X is bound in B.  ... 
doi:10.1145/2398856.2364568 fatcat:hjycyt6hzreqhfkbikuqn54aru

Conflation Confers Concurrency [chapter]

Robert Atkey, Sam Lindley, J. Garrett Morris
2016 Lecture Notes in Computer Science  
Recent work has explored a correspondence between proof rules and cut reduction in linear logic and typing and evaluation of process calculi.  ...  Session types provide a static guarantee that concurrent programs respect communication protocols.  ...  This work was supported by the EPSRC grant: From Data Types to Session Types-A Basis for Concurrency and Distribution (EP/K034413/1).  ... 
doi:10.1007/978-3-319-30936-1_2 fatcat:rxizvecm4jczrlffhh67xysbq4

Linear logical relations and observational equivalences for session-based concurrency

Jorge A. Pérez, Luís Caires, Frank Pfenning, Bernardo Toninho
2014 Information and Computation  
The starting point for our study is an interpretation of linear logic propositions as session types for communicating processes, proposed in prior work.  ...  Linear logical relations and observational equivalences for session-based concurrency.  ...  Session types as intuitionistic linear logic propositions As anticipated in the introduction, the type structure coincides with intuitionistic linear logic [19, 2] , omitting atomic formulas and the additive  ... 
doi:10.1016/j.ic.2014.08.001 fatcat:jjd3f3lrbncg7hcm53tzb7e2iq

Propositions as sessions

PHILIP WADLER
2014 Journal of functional programming  
correspond to session types.  ...  These two formulations are related by the Curry-Howard correspondence, which takes propositions as types, proofs as programs, and normalisation of proofs as evaluation of programs.  ...  Classical linear logic as a process calculus This section presents CP, a session-typed process calculus.  ... 
doi:10.1017/s095679681400001x fatcat:c5xwbb4lmjbvjjlfo5zzrqszjq

Multiparty Dependent Session Types (Extended Abstract) [article]

Hanwen Wu, Hongwei Xi
2018 arXiv   pre-print
This work formalizes the first multiparty dependent session types as an expressive and practical type discipline for enforcing communication protocols.  ...  The type system is formulated in the setting of multi-threaded λ-calculus with inspirations from multirole logic, a generalization of classical logic we discovered earlier.  ...  -Discovered and formulated classical multirole logics (MRL) and linear multirole logic (LMRL) as generalizations of classical logic (LK) and classical linear logic (CLL).  ... 
arXiv:1808.00077v1 fatcat:xzms3ivryvaqvinjt7uozhwzu4
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