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. 2021 Mar 23;12648:348–374. doi: 10.1007/978-3-030-72019-3_13

Complete trace models of state and control

Guilhem Jaber 9,✉, Andrzej S Murawski 10,✉
Editor: Nobuko Yoshida1
PMCID: PMC7984571

Abstract

We consider a hierarchy of four typed call-by-value languages with either higher-order or ground-type references and with either call/cc or no control operator.

Our first result is a fully abstract trace model for the most expressive setting, featuring both higher-order references and call/cc, constructed in the spirit of operational game semantics. Next we examine the impact of suppressing higher-order references and callcc in contexts and provide an operational explanation for the game-semantic conditions known as visibility and bracketing respectively. This allows us to refine the original model to provide fully abstract trace models of interaction with contexts that need not use higher-order references or call/cc. Along the way, we discuss the relationship between error- and termination-based contextual testing in each case, and relate the two to trace and complete trace equivalence respectively.

Overall, the paper provides a systematic development of operational game semantics for all four cases, which represent the state-based face of the so-called semantic cube.

Keywords: contextual equivalence, operational game semantics, higher-order references, control operators

Footnotes

The full version is available at https://hal.archives-ouvertes.fr/hal-03116698.

Contributor Information

Nobuko Yoshida, Email: tenko.yoshida@gmail.com.

Guilhem Jaber, Email: guilhem.jaber@univ-nantes.fr.

Andrzej S. Murawski, Email: andrzej.murawski@cs.ox.ac.uk

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