On the algorithmic structure of Dialectica programs

Abstract: We explore the Dialectica interpretation from the perspective of programming languages, by presenting it as a collection of rules in the style of Hoare logic. This allows us to add a while loop construct for Dialectica realizers, which offers an elegant description of programs extracted from nonconstructive principles. We characterise Dialectica realizers in terms of a generalised backpropagation procedure, whose forward component can be regarded as a `stateful' program in the usual sense. We propose several directions in which the work we present here can be developed in future.