Infinite Trace Equivalence

Abstract

We solve a longstanding problem by providing a denotational model for nondeterministic programs that identifies two programs iff they have the same range of possible behaviours. We discuss the difficulties with traditional approaches, where divergence is bottom or where a term denotes a function from a set of environments. We see that making forcing explicit, in the manner of game semantics, allows us to avoid these problems.We begin by modelling a first-order language with sequential I/O and unbounded nondeterminism (no harder to model, using this method, than finite nondeterminism). Then we extend the semantics to higher-order and recursive types by adapting earlier game models. Traditional adequacy proofs using logical relations are not applicable, so we use instead a novel hiding argument.