Full abstraction for nominal general references

Game semantics has been used with considerable success in formulating fully abstract semantics for languages with higher-order procedures and a wide range of computational effects. Recently, nominal games have been proposed for modeling functional languages with names. These are ordinary 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.

[1]  Andrew M. Pitts,et al.  A new approach to abstract syntax involving binders , 1999, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158).

[2]  S. Lane.  Categories for the Working Mathematician , 1971 .

[3]  Peter J. Freyd,et al.  Recursive types reduced to inductive types , 1990, [1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science.

[4]  Philip Wadler,et al.  The essence of functional programming , 1992, POPL '92.

[5]  Radha Jagadeesan,et al.  Full Abstraction for PCF , 1994, Inf. Comput..

[6]  Guy McCusker.  Games and Full Abstraction for FPC , 2000, Inf. Comput..

[7]  Julian Rathke,et al.  A fully abstract may testing semantics for concurrent objects , 2005, Theor. Comput. Sci..

[8]  Nobuko Yoshida,et al.  Game-Theoretic Analysis of Call-by-Value Computation , 1997, Theor. Comput. Sci..

[9]  Ulrich Schöpp.  Names and binding in type theory , 2006 .

[10]  Gordon D. Plotkin,et al.  The category-theoretic solution of recursive domain equations , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[11]  John C. Reynolds,et al.  The essence of ALGOL , 1997 .

[12]  Andrzej S. Murawski,et al.  Full Abstraction for Reduced ML , 2009, FoSSaCS.

[13]  James Laird.  Game Semantics for Higher-Order Concurrency , 2006, FSTTCS.

[14]  James Laird.  A Fully Abstract Trace Semantics for General References , 2007, ICALP.

[15]  Samson Abramsky.  Axioms for definability and full completeness , 2000, Proof, Language, and Interaction.

[16]  Ian Stark.  Categorical models for local names , 1996, LISP Symb. Comput..

[17]  Stephen Brookes,et al.  Monads and Comonads in Intensional Semantics , 1993 .

[18]  J. van Leeuwen,et al.  Theoretical Computer Science , 2003, Lecture Notes in Computer Science.

[19]  Andrew M. Pitts,et al.  Observable Properties of Higher Order Functions that Dynamically Create Local Names, or What's new? , 1993, MFCS.

[20]  Thomas Ehrhard,et al.  Believe it or not, AJM's games model is a model of classical linear logic , 1997, Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science.

[21]  Samson Abramsky.  Linearity‚ Sharing and State: a fully abstract game semantics for Idealized Algol , 1997 .

[22]  Guy McCusker.  Games and Full Abstraction for a Functional Metalanguage with Recursive Types , 1998, Distinguished Dissertations.

[23]  Andrew M. Pitts,et al.  A New Approach to Abstract Syntax with Variable Binding , 2002, Formal Aspects of Computing.

[24]  Gordon D. Plotkin,et al.  Notions of Computation Determine Monads , 2002, FoSSaCS.

[25]  James Laird.  A Categorical Semantics of Higher Order Store , 2002, CTCS.

[26]  Michael Barr,et al.  Category theory for computing science , 1995, Prentice Hall International Series in Computer Science.

[27]  Nikos Tzevelekos.  Full abstraction for nominal exceptions and general references , 2007 .

[28]  Dan R. Ghica,et al.  Reasoning about Idealized ALGOL Using Regular Languages , 2000, ICALP.

[29]  C.-H. Luke Ong.  Observational equivalence of 3rd-order Idealized Algol is decidable , 2002, Proceedings 17th Annual IEEE Symposium on Logic in Computer Science.

[30]  C.-H. Luke Ong,et al.  Fully abstract semantics of additive aspects by translation , 2007, AOSD.

[31]  S. Brookes,et al.  Applications of Categories in Computer Science: Computational comonads and intensional semantics , 1992 .

[32]  Russell Harmer.  Games and full abstraction for non-deterministic languages , 1999 .

[33]  James Laird.  A game semantics of names and pointers , 2008, Ann. Pure Appl. Log..

[34]  Dana S. Scott,et al.  A Type-Theoretical Alternative to ISWIM, CUCH, OWHY , 1993, Theor. Comput. Sci..

[35]  Robin Milner,et al.  Definition of standard ML , 1990 .

[36]  Andrzej S. Murawski.  On program equivalence in languages with ground-type references , 2003, 18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings..

[37]  Peyton Jones,et al.  Haskell 98 language and libraries : the revised report , 2003 .

[38]  Radha Jagadeesan,et al.  Games and Full Completeness for Multiplicative Linear Logic , 1994, J. Symb. Log..

[39]  Andrew M. Pitts,et al.  Nominal Logic: A First Order Theory of Names and Binding , 2001, TACS.

[40]  Karl-Heinz Niggl.  Momega Considered as a Programming Language , 1999, Ann. Pure Appl. Log..

[41]  Ian David Bede Stark,et al.  Names and higher-order functions , 1994 .

[42]  G.D. Plotkin,et al.  LCF Considered as a Programming Language , 1977, Theor. Comput. Sci..

[43]  Rasmus Ejlers Møgelberg,et al.  Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science , 2007 .

[44]  James Laird.  A fully abstract game semantics of local exceptions , 2001, Proceedings 16th Annual IEEE Symposium on Logic in Computer Science.

[45]  C.-H. Luke Ong,et al.  On Full Abstraction for PCF: I, II, and III , 2000, Inf. Comput..

[46]  James Laird.  A Game Semantics of Local Names and Good Variables , 2004, FoSSaCS.

[47]  Nikos Tzevelekos.  Full abstraction for nominal general references , 2007, LICS.

[48]  Eugenio Moggi,et al.  Computational lambda-calculus and monads , 1989, [1989] Proceedings. Fourth Annual Symposium on Logic in Computer Science.

[49]  Samson Abramsky,et al.  A fully abstract game semantics for general references , 1998, Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226).

[50]  Radha Jagadeesan,et al.  Full Abstraction for PCF , 2000, Inf. Comput..

[51]  Andrzej S. Murawski,et al.  Nominal games and full abstraction for the nu-calculus , 2004, Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004..

[52]  Eugenio Moggi,et al.  Notions of Computation and Monads , 1991, Inf. Comput..