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Specifying Concurrent Programs in Separation Logic: Morphisms and Simulations
[article]
2019
arXiv
pre-print
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In addition to pre- and postconditions, program specifications in recent separation logics for concurrency have employed an algebraic structure of resources---a form of state transition system---to describe ...
In this paper we introduce a novel notion of resource morphism, i.e. structure-preserving function on resources, and show how to effectively integrate it into separation logic, using an associated notion ...
Any opinions, findings, and conclusions or recommendations expressed in the material are those of the authors and do not necessarily reflect the views of the funding agencies. ...
arXiv:1904.07136v3
fatcat:o4nsiyhvg5bvdhwrnmx5isopb4
On Algebraic Abstractions for Concurrent Separation Logics
[article]
2020
arXiv
pre-print
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Morphisms of structures are a standard concept in algebra and category theory, but haven't seen ubiquitous use in separation logic before. ...
This paper provides an algebraic formalization of ownership transfer in concurrent separation logic by means of structure-preserving partial functions (i.e., morphisms) between PCMs, and an associated ...
Any opinions, findings, and conclusions or recommendations expressed in the material are those of the authors and do not necessarily reflect the views of the funding agencies. ...
arXiv:2010.12686v1
fatcat:kjuklc2l7vhexmkwqboab227ry
Comparing logics for rewriting: rewriting logic, action calculi and tile logic
2002
Theoretical Computer Science
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The large di usion of concurrent and distributed systems has spawned in recent years a variety of new formalisms, equipped with features for supporting an easy speciÿcation of such systems. ...
The aim of our paper is to analyze three proposals, namely rewriting logic, action calculi and tile logic, chosen among those formalisms designed for the description of rule-based systems. ...
This corresponds to considering sequents in rewriting logic with source s; b and to applying a rewrite step that simulates a tile computation with initial conÿguration s and e ect b. ...
doi:10.1016/s0304-3975(01)00362-0
fatcat:kg2dg7fptrgllaeunxvzgqwglq
Concurrent Separation Logic Meets Template Games
[article]
2020
arXiv
pre-print
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programs, and Hoare logic for concurrent programs with shared memory and locks. ...
In this paper, we establish a deep and unexpected connection between two recent lines of work on concurrent separation logic (CSL) and on template game semantics for differential linear logic (DiLL). ...
ACKNOWLEDGMENTS We thank Nicolas Behr and Tom Hirschowitz for the nice and instructive discussions we had with them, and the anonymous reviewers for their helpful remarks. ...
arXiv:2005.04453v1
fatcat:npkbdkzwjnfvnf3t6jbmu25xr4
Dynamic structural operational semantics
2019
Journal of Logical and Algebraic Methods in Programming
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and Creol, which supports dynamic class upgrades in the setting of concurrent objects. ...
The important feature of Modular SOS (MSOS) that we exploit in DSOS is the sharp separation of the program execution code from the additional (data) structures needed at run-time. ...
Acknowledgements We are grateful to Martin Churchill and Martin Steffen (and several anonymous reviewers) for helping us to improve the paper. ...
doi:10.1016/j.jlamp.2019.05.006
fatcat:mdu5gkmaxff37a5s6fmcnwdudq
Twenty years of rewriting logic
2012
The Journal of Logic and Algebraic Programming
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Rewriting logic is a simple computational logic that can naturally express both concurrent computation and logical deduction with great generality. ...
; (ii) its semantic framework and logical framework uses; (iii) its language implementations and its formal tools; and (iv) its many applications to automated deduction, software and hardware specification ...
As already mentioned, I feel a debt of gratitude to the many gifted researchers who have made important contributions to the rewriting logic research program. ...
doi:10.1016/j.jlap.2012.06.003
fatcat:5tx4a5uxlvapfpf5fajozkbboi
Twenty Years of Rewriting Logic
[chapter]
2010
Lecture Notes in Computer Science
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Rewriting logic is a simple computational logic that can naturally express both concurrent computation and logical deduction with great generality. ...
; (ii) its semantic framework and logical framework uses; (iii) its language implementations and its formal tools; and (iv) its many applications to automated deduction, software and hardware specification ...
As already mentioned, I feel a debt of gratitude to the many gifted researchers who have made important contributions to the rewriting logic research program. ...
doi:10.1007/978-3-642-16310-4_2
fatcat:ho7s76r67nc63bndpoptbh5k4e
Conditional rewriting logic as a unified model of concurrency
1992
Theoretical Computer Science
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Concurrent rewriting coincides with logical deduction in conditional rewriting logic, a logic of actions whose models are concurrent systems. This logic is sound and complete and has initial models. ...
Maude provides a simple unification of concurrent programming with functional and object-oriented programming and supports high level declarative programming of concurrent systems. ...
being used for simulating concurrent interactions between objects in the real world. ...
doi:10.1016/0304-3975(92)90182-f
fatcat:sqyjuly6rzambma4e6zmomrogm
Reflection in membership equational logic, many-sorted equational logic, Horn logic with equality, and rewriting logic
2007
Theoretical Computer Science
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and rewrites in the conditions is reflective. ...
These results provide logical foundations for reflective languages and tools based on these logics. ...
Acknowledgments We thank Narciso Martí-Oliet for many discussions on the topic of reflection in rewriting logic, and for his detailed and very helpful comments on earlier drafts of this paper. ...
doi:10.1016/j.tcs.2006.12.009
fatcat:aoc4r7kdvfglrhddwx3hmhnzfa
Quantales and Observational Semantics
[chapter]
2000
Current Research in Operational Quantum Logic
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We illustrate the idea that quantales can be regarded as algebras of experimental observations on physical systems, and we give a survey of some research in computer science where this idea has been used ...
We extend the mathematical framework hitherto available so that it can be applied to more general systems than before, in particular to quantum systems and systems whose behaviour is partially unobservable ...
The research of the author is also partially supported by FCT, the PRAXIS XXI Program under grant 2/2.1/TIT/1658/95, and by the ESPRIT IV Working Group 22704. ...
doi:10.1007/978-94-017-1201-9_11
fatcat:7gyqd2a2mncqbeolnh2lrl5ywu
Concurrency Theory: A Historical Perspective on Coinduction and Process Calculi
[chapter]
2014
Handbook of the History of Logic
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Acknowledgements The authors are grateful to Luca Aceto and Rob van Glabbeek for comments on an earlier draft of the paper. ...
So, behavior considered in computer science is discrete, takes place at separate moments in time, and we can observe separate things happening consecutively, different actions are separated in time. ...
Non-deterministic and concurrent programs or, more generally, programs whose computations are described by trees rather than sequences, are mentioned in the conclusions for future work. ...
doi:10.1016/b978-0-444-51624-4.50009-5
fatcat:o4fvjxxppvf2pkpjkcpj3erfym
Logical Relations as Types: Proof-Relevant Parametricity for Program Modules
[article]
2021
arXiv
pre-print
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2021 pre-print arXiv:2010.08599v2 fatcat:zcxxze6nnzhazgypfq23gq5yamOther Versions
Using the insight that logical relations/parametricity is itself a form of phase distinction between the syntactic and the semantic, we contribute a new synthetic approach to phase separated parametricity ...
Our main result is a (significant) proof-relevant and phase-sensitive generalization of the Reynolds abstraction theorem for a calculus of program modules, based on a new kind of logical relation called ...
. is work was supported in part by AFOSR under grants MURI FA ---and FA ---. ...
arXiv:2010.08599v3
fatcat:egvxsje5qbhzbgguct6cv47sjy
Verification of graph grammars using a logical approach
2012
Science of Computer Programming
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This work proposes a relational and logical approach to graph grammars that allows formal verification of systems using mathematical induction. ...
an attribute data part) and in which the behavior involves a large amount of parallelism and can be described as reactions to stimuli that can be observed in the state of the system. ...
Additionally to the complex states and reactive behavior, concurrency and non-determinism play an essential role in this area of applications: many events may happen concurrently, if they all are enabled ...
doi:10.1016/j.scico.2010.02.006
fatcat:fgtfde4jsjdqjmkxvzrcrckchq
Amalgamation of domain specific languages with behaviour
2017
Journal of Logical and Algebraic Methods in Programming
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Given a graph-grammar formalisation of DSLs, in this paper, we build on graph transformation system morphisms to define parameterized DSLs and their instantiation by an amalgamation construction. ...
Results on the protection of the behaviour along the induced morphisms allow us to safely reuse and combine definitions of DSLs to build more complex ones. ...
Acknowledgements We would like to thank the anonymous reviewers for their careful reading of our work and the comments made, which we found very useful in order to improve the quality and clarity of our ...
doi:10.1016/j.jlamp.2015.09.005
fatcat:4dsp6mvpincb7l3vgjmloffsp4
Towards an embedding of Graph Transformation in Intuitionistic Linear Logic
2009
Electronic Proceedings in Theoretical Computer Science
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Linear logics have been shown to be able to embed both rewriting-based approaches and process calculi in a single, declarative framework. ...
In this paper we are exploring the embedding of double-pushout graph transformations into quantified linear logic, leading to a Curry-Howard style isomorphism between graphs and transformations on one ...
Unlike operational formalisms, linear logics are not bound to any particular programming or modelling paradigm and thus have a potential for integrating and comparing different such paradigms through embeddings ...
doi:10.4204/eptcs.12.7
fatcat:edkaqyhzvjfzbcon7fq6mu4zue
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