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Nominal games and full abstraction for the nu-calculus

S. Abramsky, D.R. Ghica, A.S. Murawski, C.-H.L. Ong, I.D.B. Stark
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

J. Laird
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

Nikos Tzevelekos
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

J. Laird
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

Nikos Tzevelekos, Luke Ong
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

David Baelde, Kaustuv Chaudhuri, Andrew Gacek, Dale Miller, Gopalan Nadathur, Alwen Tiu, Yuting Wang
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

Andrzej S. Murawski, Nikos Tzevelekos
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]

Uli Fahrenberg, Axel Legay, Louis-Marie Traonouez
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]

Uli Fahrenberg and Axel Legay and Louis-Marie Traonouez
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]

Nick Benton, Martin Hofmann, Vivek Nigam
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]

Nick Benton, Martin Hofmann, Vivek Nigam
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

Nikos Tzevelekos
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]

Emmanuel Beffara
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

EMMANUEL BEFFARA
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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