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A symmetric modal lambda calculus for distributed computing

T. Murphy, K. Crary, R. Harper, F. Pfenning
2004 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.  
We present 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.  ... 
doi:10.1109/lics.2004.1319623 dblp:conf/lics/VIICHP04 fatcat:viye6kymrne6zc5wzqexqgwx5e

A Symmetric Modal Lambda Calculus for Distributed Computing

Tom Murphy, Karl Crary, Robert Harper, Frank Pfenning
2018
We present 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.  ... 
doi:10.1184/r1/6602738.v1 fatcat:fpvhv7fmpngubglffaf34i3h5q

Distributed Control Flow with Classical Modal Logic [chapter]

Tom Murphy VII, Karl Crary, Robert Harper
2005 Lecture Notes in Computer Science  
In previous work we presented 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.  ... 
doi:10.1007/11538363_6 fatcat:af2mr4uynng77mrj63gouftijm

Modality via Iterated Enrichment [article]

Yuichi Nishiwaki, Yoshihiko Kakutani, Yuito Murase
2018 arXiv   pre-print
Finally, we show that the change-of-base semantics can be naturally extended to multi-staged effectful 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.  ... 
arXiv:1804.02809v2 fatcat:kw5onsgl7vd5lezi7i6irb2b5u

From Linear Logic to Cyclic Sharing

Masahito Hasegawa
2019 Electronic Proceedings in Theoretical Computer Science  
We present 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.  ... 
doi:10.4204/eptcs.292.3 fatcat:cznwpsweuvfnrlguxy4dzdaepy

Semantics of Linear Continuation-Passing in Call-by-Name [chapter]

Masahito Hasegawa
2004 Lecture Notes in Computer Science  
Its semantic interpretation into 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.  ... 
doi:10.1007/978-3-540-24754-8_17 fatcat:ehx7zccbaffv3belzzcd5nobyi

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]

Daniel Rogozin
2020 arXiv   pre-print
We also provide 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.  ... 
arXiv:2005.01135v3 fatcat:7f3qvt33dzgmtdl4rcztcv7me4

Relational Reasoning for Markov Chains in a Probabilistic Guarded Lambda Calculus [chapter]

Alejandro Aguirre, Gilles Barthe, Lars Birkedal, Aleš Bizjak, Marco Gaboardi, Deepak Garg
2018 Lecture Notes in Computer Science  
We extend the simply-typed guarded λ-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  ... 
doi:10.1007/978-3-319-89884-1_8 fatcat:dq4oqbtembbmloqadvtwexdx7q

Classical Copying versus Quantum Entanglement in Natural Language: The Case of VP-ellipsis

Gijs Wijnholds, Mehrnoosh Sadrzadeh
2018 Electronic Proceedings in Theoretical Computer Science  
We then develop two different compositional models of 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.  ... 
doi:10.4204/eptcs.283.8 fatcat:h7b5buuhpjfedazeqnm35arsce

A Lambda Calculus for Gödel–Dummett Logic Capturing Waitfreedom [chapter]

Yoichi Hirai
2012 Lecture Notes in Computer Science  
We propose 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  ... 
doi:10.1007/978-3-642-29822-6_14 fatcat:bmt6blzkmnbx7bdsf45laba7cu

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]

Ryu Hasegawa
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.  ... 
arXiv:1912.00629v2 fatcat:3sbits7mtbeepm3ba5eewcsuvm

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  ... 

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

Kenta Cho, Abraham Westerbaan
2016 arXiv   pre-print
We present 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] .  ... 
arXiv:1603.02133v1 fatcat:nwhasor5mracnf36a4nnze2p4m
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