Publication details

Saarland University Computer Science

Step-indexed Relational Reasoning for Countable Nondeterminism

Jan Schwinghammer, Lars Birkedal

Submitted, February 2012

Programming languages with countable nondeterministic choice are computationally interesting since countable nondeterminism arises when modeling fairness for concurrent systems. Because countable choice introduces non-continuous behaviour, it is well-known that developing semantic models for programming languages with countable nondeterminism is challenging. We present a step-indexed logical relations model of a higher-order functional programming language with countable nondeterminism and demonstrate how it can be used to reason about contextually defined may- and must-equivalence. In earlier step-indexed models, the indices have been drawn from omega. Here the step-indexed relations for must-equivalence are indexed over an ordinal greater than omega. Finally, we define step-indexed logical relations for showing the adequacy of a continuation-passing-style transformation of the language.

A preliminary version of this work has been presented at CSL'11. The present version includes more proofs, and a section with a new application of step-indexed relational reasoning for showing the adequacy of a cps-transformation of our language.

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