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Journal Articles Proceedings of the ACM on Programming Languages Year : 2022

On Feller continuity and full abstraction


We study the nature of applicative bisimilarity in λ-calculi endowed with operators for sampling from contin- uous distributions. On the one hand, we show that bisimilarity, logical equivalence, and testing equivalence all coincide with contextual equivalence when real numbers can be manipulated through continuous functions only. The key ingredient towards this result is a notion of Feller-continuity for labelled Markov processes, which we believe of independent interest, giving rise a broad class of LMPs for which coinductive and logically inspired equivalences coincide. On the other hand, we show that if no constraint is put on the way real numbers are manipulated, characterizing contextual equivalence turns out to be hard, and most of the aforementioned notions of equivalence are even unsound.
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hal-03923488 , version 1 (04-01-2023)



Gilles Barthe, Raphaëlle Crubillé, Ugo Dal Lago, Francesco Gavazzo. On Feller continuity and full abstraction. Proceedings of the ACM on Programming Languages, 2022, 6 (ICFP), pp.826-854. ⟨10.1145/3547651⟩. ⟨hal-03923488⟩
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