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Nominal games and full abstraction for the nu-calculus
2004
Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004.
We introduce nominal games for modelling programming languages with dynamically generated local names, as exemplified by Pitts and Stark's nu-calculus. ...
The main result is the construction of the first fully-abstract model for the nu-calculus. 1 A model of a programming language is fully abstract if observational equivalence coincides with the equational ...
We thank Andy Pitts for helpful advice on FM-sets, EPSRC for financial support (GR/R88861), and Merton College, Oxford for a Visiting Research Fellowship (for Stark). ...
doi:10.1109/lics.2004.1319609
dblp:conf/lics/AbramskyGMOS04
fatcat:yrv2dgyks5c6dgym5mhs2jfq4a
Sequentiality and the CPS Semantics of Fresh Names
2007
Electronical Notes in Theoretical Computer Science
This is the target of a fully abstract CPS translation from the nu-calculus with first-class continuations. ...
We describe a notion of "FM-categorical" model for our calculus, with a simple interpretation of name generation due to Shinwell and Pitts. ...
[7] , the FM-cpo CPS models of mini-FreshML [6] , and games models [3] and [1] , also based on nominal sets. ...
doi:10.1016/j.entcs.2007.02.035
fatcat:jwm76rz7wvhdzkr6czhmdpb2uq
Full abstraction for nominal general references
2007
22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)
Thus nominal games can capture the essential features of nominal computation and, in particular, they model the ν-calculus. ...
TZEVELEKOS FULL ABSTRACTION FOR NOMINAL GENERAL REFERENCES 7 2.2. Strong support. ...
I would also like to thank Andy Pitts, Andrzej Murawski, Dan Ghica, Ian Stark, Luke Ong, Guy McCusker, Jim Laird, Paul Levy, Sam Sanjabi and the anonymous reviewers for fruitful discussions, suggestions ...
doi:10.1109/lics.2007.21
dblp:conf/lics/Tzevelekos07
fatcat:ho2qj34gzbdo7ev3xhvsmjcdhq
A game semantics of names and pointers
2008
Annals of Pure and Applied Logic
We describe a model of the call-by-value λ-calculus (a closed Freyd category) based on these games, and show that it can be used to interpret the nu-calculus of Pitts and Stark. ...
Using factorization and decomposition techniques, we show that the compact elements of our model are definable as terms, and hence it is fully abstract. ...
Acknowledgements This research was supported by the UK EPSRC grant GR/S72181. ...
doi:10.1016/j.apal.2007.10.006
fatcat:twc3zxtizvajvnwhvrdn3sqgsi
Full abstraction for nominal general references
2009
Logical Methods in Computer Science
Recently, nominal games have been proposed for modelling functional languages with names. These are ordinary, stateful games cast in the theory of nominal sets developed by Pitts and Gabbay. ...
Here we take nominal games one step further, by developing a fully abstract semantics for a language with nominal general references. ...
I would also like to thank Andy Pitts, Andrzej Murawski, Dan Ghica, Ian Stark, Luke Ong, Guy McCusker, Jim Laird, Paul Levy, Sam Sanjabi and the anonymous reviewers for fruitful discussions, suggestions ...
doi:10.2168/lmcs-5(3:8)2009
fatcat:jlnxwvncvjbpxjt6e472e4am2u
Abella: A System for Reasoning about Relational Specifications
2015
Journal of Formalized Reasoning
quantifier, and nominal constants for reasoning about these representations. ...
Along the way, we show how Abella can be used prove theorems involving natural numbers, lists, and automata, as well as involving typed and untyped λ-calculi and the π-calculus. ...
Acknowledgements: We thank Andrea Asperti, Roberto Blanco, Zakaria Chihani and Claudio Sacerdoti Coen for their comments on drafts of this tutorial. ...
doi:10.6092/issn.1972-5787/4650
dblp:journals/jfrea/BaeldeCGMNTW14
fatcat:k7smnc5yjjfkrit66vn7qp6uqa
Game Semantics for Good General References
2011
2011 IEEE 26th Annual Symposium on Logic in Computer Science
In contrast to the previous model by Abramsky, Honda and McCusker [3], it provides a faithful account of reference types, and the full abstraction result does not rely on the availability of spurious constructs ...
We present a new fully abstract and effectively presentable denotational model for RefML, a paradigmatic higherorder programming language combining call-by-value evaluation and general references in the ...
Our plays do not feature information about the full content of the store, as this would reveal functional values and jeopardize full abstraction. ...
doi:10.1109/lics.2011.31
dblp:conf/lics/MurawskiT11
fatcat:kkrrxzjprbdzbhx6umcwufghni
Structural Refinement for the Modal nu-Calculus
[chapter]
2014
Lecture Notes in Computer Science
This shows that the modal nu-calculus supports composition and decomposition of specifications. ...
We introduce a new notion of structural refinement, a sound abstraction of logical implication, for the modal nucalculus. ...
For a finite set X of nominals, let L(X) be the set of formulae generated by the abstract syntax L(X) ∋ φ := tt | ff | a x | ¬φ | φ ∧ φ, for a ∈ Σ and x ∈ X. ...
doi:10.1007/978-3-319-10882-7_11
fatcat:tm2qhcuorrglnknmthfwc43wdq
Structural Refinement for the Modal nu-Calculus
[article]
2014
arXiv
pre-print
We introduce a new notion of structural refinement, a sound abstraction of logical implication, for the modal nu-calculus. ...
This shows that the modal nu-calculus supports composition and decomposition of specifications. ...
For a finite set X of nominals, let L(X) be the set of formulae generated by the abstract syntax L(X) ∋ φ := tt | ff | a x | ¬φ | φ ∧ φ, for a ∈ Σ and x ∈ X. ...
arXiv:1402.2143v2
fatcat:44d7c3dctrfxbbvuia4ety6m4e
Proof-Relevant Logical Relations for Name Generation
[chapter]
2013
Lecture Notes in Computer Science
Pitts and Stark's ν-calculus is a paradigmatic total language for studying the problem of contextual equivalence in higher-order languages with name generation. ...
If recursion is added to the language and one attempts to adapt the models from (nominal) sets to (nominal) domains, however, the direct-style construction of the allocation monad no longer works. ...
] and nominal game semantics [AGM + 04, Tze12]. ...
doi:10.1007/978-3-642-38946-7_6
fatcat:qxyfqkonajhilg4zc3pybwsehm
Proof-Relevant Logical Relations for Name Generation
[article]
2017
arXiv
pre-print
Pitts and Stark's ν-calculus is a paradigmatic total language for studying the problem of contextual equivalence in higher-order languages with name generation. ...
If recursion is added to the language and one attempts to adapt the models from (nominal) sets to (nominal) domains, however, the direct-style construction of the allocation monad no longer works. ...
] and nominal game semantics [AGM + 04, Tze12]. ...
arXiv:1708.05193v1
fatcat:7awf2fmvqbbbllgiblm74amf3m
Program equivalence with names
unpublished
The nu-calculus of Pitts and Stark was introduced as a paradig-matic functional language with a very basic local-state effect: references of unit type. ...
However, it was soon realised that the behaviour of nu-calculus programs is quite intricate , and program equivalence in particular is surprisingly difficult to capture. ...
Acknowledgements Many thanks to Vasilis Koutavas, Paul-Andre Mellies, Andrzej Murawski and Ian Stark for fruitful discussions, explanations and suggestions. ...
fatcat:4kjxugb4nvak3ozadsotjy5ur4
Order algebras: a quantitative model of interaction
[article]
2011
arXiv
pre-print
(in the sense that the internal workings of processes are ignored) and non-interleaving. ...
This algebraic structure is shown to provide faithful interpretations of finitary process algebras, for an extension of the standard notion of testing semantics, leading to a model that is both denotational ...
Simpler modifications of the calculus could lead to full abstraction, for instance by imposing a more structured naming discipline. ...
arXiv:0911.0630v3
fatcat:r2fny7kkyrdbzbr2y3rcfntw54
Order algebras: a quantitative model of interaction
2017
Mathematical Structures in Computer Science
(in the sense that the internal workings of processes are ignored) and non-interleaving. ...
This algebraic structure is shown to provide faithful interpretations of finitary process algebras, for an extension of the standard notion of testing semantics, leading to a model that is both denotational ...
Simpler modifications of the calculus could lead to full abstraction, for instance by imposing a more structured naming discipline. ...
doi:10.1017/s0960129516000360
fatcat:sjkv2oxoxbafhirrn6miwnbub4
Reviews and Descriptions of Tables and Books
1961
Mathematics of Computation
The preface states nominal reader requirements of "a course in calculus, with some elements of advanced calculus and rudimentary knowledge of matrix theory," but it also admits to "compromise in the presentation ...
He concludes with an introduction to abstract algebra.The numerical methods are developed for use with desk computers and are amply illustrated throughout the text. ...
doi:10.1090/s0025-5718-61-99213-4
fatcat:sevngcclonao3bf6gbvrdob6kq
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