Extended Addressing Machines, explicit substitutions, PCF, definability, full abstraction

06/23/2023

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by   Benedetto Intrigila, et al.

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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.