On the Taylor Expansion of Probabilistic $\lambda$-Terms (Long Version)

Abstract

We generalise Ehrhard and Regnier's Taylor expansion from pure to probabilistic $\lambda$-terms through notions of probabilistic resource terms and explicit Taylor expansion. We prove that the Taylor expansion is adequate when seen as a way to give semantics to probabilistic $\lambda$-terms, and that there is a precise correspondence with probabilistic B\"ohm trees, as introduced by the second author.