Resumptions, Weak Bisimilarity and Big-Step Semantics for While with Interactive I/O: An Exercise in Mixed Induction-Coinduction

Keiko Nakata
(Institute of Cybernetics, Tallinn University of Technology, Estonia)
Tarmo Uustalu
(Institute of Cybernetics, Tallinn University of Technology, Estonia)

We look at the operational semantics of languages with interactive I/O through the glasses of constructive type theory. Following on from our earlier work on coinductive trace-based semantics for While, we define several big-step semantics for While with interactive I/O, based on resumptions and termination-sensitive weak bisimilarity. These require nesting inductive definitions in coinductive definitions, which is interesting both mathematically and from the point-of-view of implementation in a proof assistant.

After first defining a basic semantics of statements in terms of resumptions with explicit internal actions (delays), we introduce a semantics in terms of delay-free resumptions that essentially removes finite sequences of delays on the fly from those resumptions that are responsive. Finally, we also look at a semantics in terms of delay-free resumptions supplemented with a silent divergence option. This semantics hinges on decisions between convergence and divergence and is only equivalent to the basic one classically.

We have fully formalized our development in Coq.

In Luca Aceto and Paweł Sobociński: Proceedings Seventh Workshop on Structural Operational Semantics (SOS 2010), Paris, France, 30 August 2010, Electronic Proceedings in Theoretical Computer Science 32, pp. 57–75.
Published: 11th August 2010.

ArXived at: bibtex PDF

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