Nominal games and full abstraction for the nu-calculus

• Published in: Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, 2004 pp. 150 - 159
• Main Authors: Abramsky, S., Ghica, D.R., Murawski, A.S., Ong, C.-H.L., Stark, I.D.B.
• Format: Conference Proceeding
• Language: English
• Published: Los Alamitos, Calif IEEE 2004; IEEE Computer Society
• Subjects: Applied sciences; Calculus; Computer languages; Computer science; control theory; systems; Exact sciences and technology; Joining processes; Logical, boolean and switching functions; Privacy; Runtime; Testing; Theoretical computing; Yarn; Type theory; Invariant; Modelling language; Programming language; Abstract interpretation; Logical programming; Abstraction
• ISBN: 9780769521923; 0769521924
• ISSN: 1043-6871; 2575-5528
• DOI: 10.1109/LICS.2004.1319609

We introduce nominal games for modelling programming languages with dynamically generated local names, as exemplified by Pitts and Stark's nu-calculus. Inspired by Pitts and Gabbay's recent work on nominal sets, we construct arenas and strategies in the world (or topos) of Fraenkel-Mostowski sets (or simply FM-sets). We fix an infinite set N of names to be the "atoms" of the FM-theory, and interpret the type v of names as the flat arena whose move-set is N. This approach leads to a clean and precise treatment of fresh names and standard game constructions (such as plays, views, innocent strategies, etc.) that are considered invariant under renaming. The main result is the construction of the first fully-abstract model for the nu-calculus.