First-order full abstraction of the FGLS monad

Establish that the full ground local state monad is fully abstract at first-order types, so that observational equivalence of first-order terms implies equality of their denotations, and transfer this result to the finitary submonad.

Background

The paper studies Kammar et al.’s possible-worlds monad for full ground local state (FGLS), which models dynamically allocated mutable references capable of storing ground values and references. The authors construct a finitary submonad and prove adequacy of its semantics, but do not establish full abstraction.

Full abstraction at first-order types would mean that observationally equivalent terms without function types have equal denotations. Combined with the already available adequacy result, this would identify observational and denotational equality for first-order terms and support completeness of the model for compiler optimisations involving full ground references. The authors conjecture that the property holds for the FGLS monad and suggest that techniques inspired by game semantics could prove it; they further state that the result would transfer to the finitary submonad and could enable decision procedures for observational equivalence.