Applicative bisimiliarity is a coinductively-defined program equivalence in which programs are tested as argument-passing processes. Starting with the seminal work by Abramsky, applicative bisimiliarity has been proved to be a powerful technique for higher-order program equivalence. Recently, applicative bisimiliarity has also been generalised to lambda calculi with algebraic effects, and with discrete probabilistic choice in particular. In this paper, we show that applicative bisimiliarity behaves well in a lambda-calculus in which probabilistic choice is available in a more general form, namely through an operator for sampling of values from continuous distributions. Our main result shows that applicative bisimilarity is sound for contextual equivalence, hence providing a new reasoning principle for higher-order probabilistic languages.

Lago, U.D., Gavazzo, F. (2019). On Bisimilarity in Lambda Calculi with Continuous Probabilistic Choice [10.1016/j.entcs.2019.09.007].

On Bisimilarity in Lambda Calculi with Continuous Probabilistic Choice

Lago, Ugo Dal;Gavazzo, Francesco
2019

Abstract

Applicative bisimiliarity is a coinductively-defined program equivalence in which programs are tested as argument-passing processes. Starting with the seminal work by Abramsky, applicative bisimiliarity has been proved to be a powerful technique for higher-order program equivalence. Recently, applicative bisimiliarity has also been generalised to lambda calculi with algebraic effects, and with discrete probabilistic choice in particular. In this paper, we show that applicative bisimiliarity behaves well in a lambda-calculus in which probabilistic choice is available in a more general form, namely through an operator for sampling of values from continuous distributions. Our main result shows that applicative bisimilarity is sound for contextual equivalence, hence providing a new reasoning principle for higher-order probabilistic languages.
2019
Proceedings of the Thirty-Fifth Conference on the Mathematical Foundations of Programming Semantics, MFPS 2019.
121
141
Lago, U.D., Gavazzo, F. (2019). On Bisimilarity in Lambda Calculi with Continuous Probabilistic Choice [10.1016/j.entcs.2019.09.007].
Lago, Ugo Dal; Gavazzo, Francesco
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/732562
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