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A symmetric modal lambda calculus for distributed computing

2004
*
Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.
*

We present

doi:10.1109/lics.2004.1319623
dblp:conf/lics/VIICHP04
fatcat:viye6kymrne6zc5wzqexqgwx5e
*a*foundational language*for**distributed*programming, called*Lambda*5, that addresses both mobility of code and locality of resources. ... Specifically, we take the possible worlds of the intuitionistic*modal*logic IS5 to be nodes on*a*network, and the connectives P and Q to reflect mobility and locality, respectively. ... Related Work Others have also used*modal*logic*for**distributed**computing*. ...##
###
A Symmetric Modal Lambda Calculus for Distributed Computing

2018

We present

doi:10.1184/r1/6602738.v1
fatcat:fpvhv7fmpngubglffaf34i3h5q
*a*foundational language*for**distributed*programming, called*Lambda*5, that addresses both mobility of code and locality of resources. ... Specifically, we take the possible worlds of the intuitionistic*modal*logic IS5 to be nodes on*a*network, and the connectives to reflect mobility and locality, respectively. ... Related Work Others have also used*modal*logic*for**distributed**computing*. ...##
###
Distributed Control Flow with Classical Modal Logic
[chapter]

2005
*
Lecture Notes in Computer Science
*

In previous work we presented

doi:10.1007/11538363_6
fatcat:af2mr4uynng77mrj63gouftijm
*a*foundational*calculus**for*spatially*distributed**computing*based on intuitionistic*modal*logic. ... This work investigates issues in*distributed*control flow through*a*similar propositions-as-types interpretation of classical*modal*logic. ... We build on our previous intuitionistic*calculus*,*Lambda*5 [8] , which is*a*simple programming language (and associated logic)*for**distributed**computing*. ...##
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Modality via Iterated Enrichment
[article]

2018
*
arXiv
*
pre-print

Finally, we show that the change-of-base semantics can be naturally extended to multi-staged effectful

arXiv:1804.02809v2
fatcat:kw5onsgl7vd5lezi7i6irb2b5u
*computation*and generalized contextual*modality**a*la Nanevski et al. ... Interestingly, this interpretation suggests the fact that Fitch-style*modal*type theory is the right adjoint of dual-context*calculus*. ... Acknowledgement The authors thank their colleague Hiroki Kobayashi*for*helpful discussions and comments to an early draft of this paper. ...##
###
From Linear Logic to Cyclic Sharing

2019
*
Electronic Proceedings in Theoretical Computer Science
*

We present

doi:10.4204/eptcs.292.3
fatcat:cznwpsweuvfnrlguxy4dzdaepy
*a*translation from Multiplicative Exponential Linear Logic to*a*simply-typed*lambda**calculus*with cyclic sharing. ... This translation is derived from*a*simple observation on the Int-construction on traced monoidal categories. ... Acknowledgements I thank Ken Sakayori and Takeshi Tsukada*for*stimulating discussions related to this work. ...##
###
Semantics of Linear Continuation-Passing in Call-by-Name
[chapter]

2004
*
Lecture Notes in Computer Science
*

Its semantic interpretation into

doi:10.1007/978-3-540-24754-8_17
fatcat:ehx7zccbaffv3belzzcd5nobyi
*a*category of linear continuations then amounts to the call-by-name continuation-passing style (CPS) transformation into*a*linear*lambda**calculus*with sum types. ... We show that our*calculus*is sound*for*this CPS semantics, hence*for*models given by the categories of linear continuations. ... Acknowledgements I thank Oliver Danvy*for*asking me how linear CPS*for*callby-name can be semantically understood, and anonymous reviewers*for*helpful comments. ...##
###
Page 562 of Mathematical Reviews Vol. , Issue 2003A
[page]

2003
*
Mathematical Reviews
*

Kok, Infinite intersection and union types

*for*the lazy*lambda**calculus*(448- 458); Yoriyuki Yamagata, Strong normalization of second order*symmetric**lambda*-mu*calculus*(459-467); Philip Wadler, The Girard-Reynolds ... in*distributed**computation*(64-81); Martin Abadi and Jan Jiirjens, Formal eavesdropping and its computa- tional interpretation (82-94); Kazunori Ueda, Resource-passing concurrent programming (95-126); ...##
###
Categorical and Algebraic Aspects of the Intuitionistic Modal Logic IEL^- and its predicate extensions
[article]

2020
*
arXiv
*
pre-print

We also provide

arXiv:2005.01135v3
fatcat:7f3qvt33dzgmtdl4rcztcv7me4
*a*categorical interpretation of this*modal**lambda**calculus*considering coalgebras associated with*a*monoidal functor on*a*cartesian closed category. ... We construct the*modal**lambda**calculus*which is Curry-Howard isomorphic to IEL^- as the type-theoretical representation of applicative*computation*widely known in functional programming. ... Some of the results were presented at the conference Logical Foundations in*Computer*Science 2020. ...##
###
Relational Reasoning for Markov Chains in a Probabilistic Guarded Lambda Calculus
[chapter]

2018
*
Lecture Notes in Computer Science
*

We extend the simply-typed guarded λ-

doi:10.1007/978-3-319-89884-1_8
fatcat:dq4oqbtembbmloqadvtwexdx7q
*calculus*with discrete probabilities and endow it with*a*program logic*for*reasoning about relational properties of guarded probabilistic*computations*. ... This provides*a*framework*for*programming and reasoning about infinite stochastic processes like Markov chains. ... This research was supported in part by the ModuRes Sapere Aude Advanced Grant from The Danish Council*for*Independent Research*for*the Natural Sciences (FNU), by*a*research grant (12386, Guarded Homotopy ...##
###
Classical Copying versus Quantum Entanglement in Natural Language: The Case of VP-ellipsis

2018
*
Electronic Proceedings in Theoretical Computer Science
*

We then develop two different compositional models of

doi:10.4204/eptcs.283.8
fatcat:h7b5buuhpjfedazeqnm35arsce
*distributional*meaning*for*this*calculus*. ... Following the line of research in compositional*distributional*semantics set out by (Coecke et al., 2010) we develop an extension of the Lambek*calculus*which admits*a*controlled form of contraction to ... Acknowledgements The authors are thankful*for*the anonymous reviewers' comments. The first author gratefully acknowledges support from*a*Queen Mary Principal Studentship. ...##
###
A Lambda Calculus for Gödel–Dummett Logic Capturing Waitfreedom
[chapter]

2012
*
Lecture Notes in Computer Science
*

We propose

doi:10.1007/978-3-642-29822-6_14
fatcat:bmt6blzkmnbx7bdsf45laba7cu
*a*typed*lambda**calculus*based on Avron's hypersequent*calculus**for*Gödel-Dummett logic. This*calculus*turns out to model waitfree*computation*. ... The*calculus*is not only proof theoretically interesting, but also valuable as*a*basis*for**distributed*programming languages. ... This work is encouraged by feedbacks from ACAN (Algebraic and Coalgebraic Approaches to Non-Classical Logics Workshop) and OPLSS'11 participants, supported by Grant-in-Aid*for*JSPS Fellows 23-6978, and ...##
###
Page 5739 of Mathematical Reviews Vol. , Issue 95j
[page]

1995
*
Mathematical Reviews
*

Bystrov,

*A*nonstandard method of constructing tableaux*for**modal*and relevant logics (156-170); I.*A*. Gerasi- mova,*Distributed*systems from the point of view of epistemic logic (171-180);*A*. S. ...*calculus*(278-290);*A*. ...##
###
A categorical reduction system for linear logic
[article]

2020
*
arXiv
*
pre-print

*A*simple way to this end is to reform

*a*concerned category into

*a*

*calculus*, where the instructions

*for*the diagram chasing are given in the form of rewriting rules. ... We build

*a*

*calculus*directly on the free category of the semantics. It enables us to perform diagram chasing as essentially one-way

*computations*led by the rewriting rules. ... We thank an anonymous referee

*for*

*a*number of helpful suggestions to improve the presentation. Of course, it is completely our responsibility if there remain poor presentations yet. ...

##
###
Page 2809 of Mathematical Reviews Vol. , Issue 93e
[page]

1993
*
Mathematical Reviews
*

*Comput*. Sci. 100 (1992), no. 1, 253-265. Summary: “We consider size-depth tradeoffs

*for*threshold circuits

*computing*

*symmetric*functions. ... Finally, it is demonstrated that

*a*wide range of models of con- currency (labelled transition systems,

*lambda*

*calculus*, Petri nets and others) can be viewed as special cases of conditional rewriting logic ...

##
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Von Neumann Algebras form a Model for the Quantum Lambda Calculus
[article]

2016
*
arXiv
*
pre-print

We present

arXiv:1603.02133v1
fatcat:nwhasor5mracnf36a4nnze2p4m
*a*model of Selinger and Valiron's quantum*lambda**calculus*based on von Neumann algebras, and show that the model is adequate with respect to the operational semantics. ... Acknowledgements We thank Chris Heunen*for*spotting*a*typo. ... [36, 37] proposed*a*typed 1*lambda**calculus**for*quantum*computation*, and they studied it in*a*series of papers [38] [39] [40] . ...
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