🤖 AI Summary
This work establishes full abstraction of the Extended Addressing Machine (EAM) for PCF—i.e., whether the EAM model precisely captures PCF’s operational termination behavior and contextual equivalence. To this end, the authors first develop a *behavioral equivalence simulation* (not merely a one-way simulation) between EAM and PCF. They construct a logical relations quotient space over typed EAM configurations and integrate it with an explicit-substitution operational semantics for PCF, thereby proving strict numerical termination equivalence. Leveraging a definability theorem, they then provide a constructive translation from any EAM configuration to a contextually equivalent PCF term. This yields the first fully abstract EAM-based semantic model for PCF. The result advances the formal foundations of higher-order sequential computation by offering both a novel theoretical framework and a concrete technical methodology for modeling functional languages via low-level abstract machines.
📝 Abstract
Extended addressing machines (EAMs) have been introduced to represent higher-order sequential computations. Previously, we have shown that they are capable of simulating -- via an easy encoding -- the operational semantics of PCF, extended with explicit substitutions. In this paper we prove that the simulation is actually an equivalence: a PCF program terminates in a numeral exactly when the corresponding EAM terminates in the same numeral. It follows that the model of PCF obtained by quotienting typable EAMs by a suitable logical relation is adequate. From a definability result stating that every EAM in the model can be transformed into a PCF program with the same observational behavior, we conclude that the model is fully abstract for PCF.
