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. 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 ν of names as the flat arena whose move-set is N . This approach leads to a clean and
more » ... ecise 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. 1 A model of a programming language is fully abstract if observational equivalence coincides with the equational theory induced by the model.
doi:10.1109/lics.2004.1319609 dblp:conf/lics/AbramskyGMOS04 fatcat:yrv2dgyks5c6dgym5mhs2jfq4a