A fully abstract game semantics for countable nondeterminism

W. John Gowers, James D. Laird

Research output: Chapter or section in a book/report/conference proceedingChapter in a published conference proceeding

1 Citation (SciVal)


The concept of fairness for a concurrent program means that the program must be able to exhibit an unbounded amount of nondeterminism without diverging. Game semantics models of nondeterminism show that this is hard to implement; for example, Harmer and McCusker's model only admits infinite nondeterminism if there is also the possibility of divergence. We solve a long standing problem by giving a fully abstract game semantics for a simple stateful language with a countably infinite nondeterminism primitive. We see that doing so requires us to keep track of infinitary information about strategies, as well as their finite behaviours. The unbounded nondeterminism gives rise to further problems, which can be formalized as a lack of continuity in the language. In order to prove adequacy for our model (which usually requires continuity), we develop a new technique in which we simulate the nondeterminism using a deterministic stateful construction, and then use combinatorial techniques to transfer the result to the nondeterministic language. Lastly, we prove full abstraction for the model; because of the lack of continuity, we cannot deduce this from definability of compact elements in the usual way, and we have to use a stronger universality result instead. We discuss how our techniques yield proofs of adequacy for models of nondeterministic PCF, such as those given by Tsukada and Ong.

Original languageEnglish
Title of host publicationComputer Science Logic 2018, CSL 2018
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Print)9783959770880
Publication statusPublished - 1 Aug 2018
Event27th Annual EACSL Conference Computer Science Logic, CSL 2018 - Birmingham, UK United Kingdom
Duration: 4 Sept 20187 Sept 2018


Conference27th Annual EACSL Conference Computer Science Logic, CSL 2018
Country/TerritoryUK United Kingdom


  • Games and logic
  • Nondeterminism
  • Semantics

ASJC Scopus subject areas

  • Software


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