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Propositions as sessions

Philip Wadler
2012 SIGPLAN notices  
logic correspond to session types.  ...  Continuing a line of work by Abramsky (1994) , by Bellin and Scott (1994) , and by Caires and Pfenning (2010), among others, this paper presents CP, a calculus in which propositions of classical linear  ...  Propositions as Sessions 15 The additive units are 0 for ⊕ and for .  ... 
doi:10.1145/2398856.2364568 fatcat:hjycyt6hzreqhfkbikuqn54aru

Propositions as sessions

PHILIP WADLER
2014 Journal of functional programming  
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.  ...  correspond to session types.  ...  We interpret ∃X.B as the session type of a channel that instantiates propositional variable X to a given proposition, and interpret ∀X.B as the session type of a process that generalises over X.  ... 
doi:10.1017/s095679681400001x fatcat:c5xwbb4lmjbvjjlfo5zzrqszjq

Sessions as Propositions

Sam Lindley, J. Garrett Morris
2014 Electronic Proceedings in Theoretical Computer Science  
We propose an extension of GV, called HGV, and give translations showing that it is as expressive as CP.  ...  Recently, Wadler presented a continuation-passing translation from a session-typed functional language, GV, to a process calculus based on classical linear logic, 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

Propositions as sessions

Philip Wadler
2012 Proceedings of the 17th ACM SIGPLAN international conference on Functional programming - ICFP '12  
logic correspond to session types.  ...  Continuing a line of work by Abramsky (1994) , by Bellin and Scott (1994) , and by Caires and Pfenning (2010), among others, this paper presents CP, a calculus in which propositions of classical linear  ...  We interpret ∃X.B as the session type of a process that instantiates propositional variable X to a given proposition, and interpret ∀X.B as the session type of a process that generalises over X.  ... 
doi:10.1145/2364527.2364568 dblp:conf/icfp/Wadler12 fatcat:56asdlyqrva75iudjx7l3hgmju

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  ...  and properties of session types.  ...  Functions as Session-Typed Processes. 15th International Conference on Foundations of Software Science and Computation Structures, FoS-SaCS'12, 346-360, 2012 P. Wadler. Propositions as sessions.  ... 
doi:10.1017/s0960129514000218 fatcat:2xrvjo5vynbtbeqq3fcfjl342m

Session Types as Intuitionistic Linear Propositions [chapter]

Luís Caires, Frank Pfenning
2010 Lecture Notes in Computer Science  
Our type system is based on a new interpretation of linear propositions as session types, and provides the first purely logical account of all (both shared and linear) features of session types.  ...  We then have x y .P (send y on x and proceeds as P ), x(y).P (receive a name z on x and proceed as P with the input parameter y replaced by z), and !  ...  An object of type A ⊗ B denotes a session that first sends a session channel of type A and afterwards behaves as B.  ... 
doi:10.1007/978-3-642-15375-4_16 fatcat:fsnrwcvslzga3isvvtrzhb3q2i

A Semantics for Propositions as Sessions [chapter]

Sam Lindley, J. Garrett Morris
2015 Lecture Notes in Computer Science  
Recently, Caires, Pfenning, and Toninho, and Wadler, have developed a correspondence between propositions of linear logic and session typed π-calculus processes.  ...  Session types  ...  -We connect GV to the interpretation of session types as linear logic propositions, by establishing a correspondence between the semantics of GV and that of CP. We begin by introducing CP ( §3.1).  ... 
doi:10.1007/978-3-662-46669-8_23 fatcat:s6gsygb3ubh73bvqydtzsquwmi

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

A Bunch of Sessions: A Propositions-as-Sessions Interpretation of Bunched Implications in Channel-Based Concurrency [article]

Dan Frumin, Emanuele D'Osualdo, Bas van den Heuvel, Jorge A. Pérez
2022 arXiv   pre-print
The emergence of propositions-as-sessions, a Curry-Howard correspondence between propositions of Linear Logic and session types for concurrent processes, has settled the logical foundations of message-passing  ...  We identify O'Hearn and Pym's Logic of Bunched Implications (BI) as a fruitful basis for an interpretation of the logic as a concurrent programming language.  ...  These correspondences are often collectively referred to as propositions-as-sessions.  ... 
arXiv:2209.05421v1 fatcat:fp6fn77m5favrlvpfc3lpcwcyq

Session Types as Intuitionistic Linear Propositions

Luis Caires, Frank Pfenning
2018
Our type system is based on a new interpretation of linear propositions as session types, and provides the first purely logical account of all (both shared and linear) features of session types.  ...  We show that our type discipline is useful from a programming perspective, and ensures session fidelity, absence of deadlocks, and a tight operational correspondence between π-calculus reductions and cut  ...  The system DILL as presented does not admit atomic formulas, and hence has no true initial sequents. However, the correspondence mentioned above yields an explicit identity theorem: Proposition 4.2.  ... 
doi:10.1184/r1/6609467 fatcat:7j3qs7kqhfg5dcawyavdjpybru

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.  ...  we can compose P and Q as (νx)(P | Q) :: −:1 using the above proposition and the cut rule.  ... 
doi:10.1184/r1/6606974 fatcat:g26hj6mq3nbslaxnzoc6mvvvui

A multi-agent bilateral bargaining model with endogenous protocol

Sang-Chul Suh, Quan Wen
2008 Economic Theory  
The ine±ciency in equilibrium remains even as the discount factor goes to one. JEL Numbers: C72 and C78  ...  Consider a multilateral bargaining problem where negotiation is conducted by a sequence of bilateral bargaining sessions.  ...  Appendix Proof of Proposition 1: As we argued, the continuation equilibrium in the second session is unique so we will concentrate on the players' strategies during the¯rst session.  ... 
doi:10.1007/s00199-008-0365-5 fatcat:jgvhtrz4ovb7vfcf7s5zpz3o24

Text and graphics: manipulating nutrition brochures to maximize recall

K. L. Clark
1999 Health Education Research  
Participants completed recalled materials from the assigned brochures (the no treatment control group did not include a brochure) at two different sessions, 30 days apart.  ...  Third, the same number of paragraphs were developed that had as near as possible the same number of sentences and propositions.  ...  At the second session, control group women recorded a similar number of propositions as women who read brochures, with the exception of women who read CC brochures.  ... 
doi:10.1093/her/14.4.555 pmid:10557525 fatcat:t2r2pzvunzhkpdbzhzapadz55e

Collaborative recall in face-to-face and electronic groups

Justina Ohaeri Ekeocha, Susan E. Brennan
2008 Memory  
Although groups (Session 2) recalled a higher quantity of propositions than did individuals in Session 1, individuals in Session 3 recalled just as many propositions as had their groups (when face-toface  ...  both media conditions recalled just as many propositions during Session 2.  ... 
doi:10.1080/09658210701807480 pmid:18324550 fatcat:gb6u5eq6m5gr7ehz2qkehmwyfq

Page 85 of Journal of Pharmaceutical Sciences Vol. 26, Issue 1 [page]

1937 Journal of Pharmaceutical Sciences  
Proposition 3—Issue a Correction Sheet as suggested in Proposition 1 and a new revision of the National Formulary, to be known as N. F.  ...  “‘As Proposition No. 3 embraces Proposition No. 1 we really have eight who approve of  ... 
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