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Full abstraction for nominal Scott domains

Published:23 January 2013Publication History
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Abstract

We develop a domain theory within nominal sets and present programming language constructs and results that can be gained from this approach. The development is based on the concept of orbit-finite subset, that is, a subset of a nominal sets that is both finitely supported and contained in finitely many orbits. This concept appears prominently in the recent research programme of Bojanczyk et al. on automata over infinite languages, and our results establish a connection between their work and a characterisation of topological compactness discovered, in a quite different setting, by Winskel and Turner as part of a nominal domain theory for concurrency. We use this connection to derive a notion of Scott domain within nominal sets. The functionals for existential quantification over names and `definite description' over names turn out to be compact in the sense appropriate for nominal Scott domains. Adding them, together with parallel-or, to a programming language for recursively defined higher-order functions with name abstraction and locally scoped names, we prove a full abstraction result for nominal Scott domains analogous to Plotkin's classic result about PCF and conventional Scott domains: two program phrases have the same observable operational behaviour in all contexts if and only if they denote equal elements of the nominal Scott domain model. This is the first full abstraction result we know of for higher-order functions with local names that uses a domain theory based on ordinary extensional functions, rather than using the more intensional approach of game semantics.

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        • Published in

          cover image ACM SIGPLAN Notices
          ACM SIGPLAN Notices  Volume 48, Issue 1
          POPL '13
          January 2013
          561 pages
          ISSN:0362-1340
          EISSN:1558-1160
          DOI:10.1145/2480359
          Issue’s Table of Contents
          • cover image ACM Conferences
            POPL '13: Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
            January 2013
            586 pages
            ISBN:9781450318327
            DOI:10.1145/2429069

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          • Published: 23 January 2013

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