STEP-INDEXED RELATIONAL REASONING FOR COUNTABLE NONDETERMINISM

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.