On the Taylor expansion of probabilistic λ-terms

We generalise Ehrhard and Regnier’s Taylor expansion from pure to probabilistic λ-terms. We prove that the Taylor expansion is adequate when seen as a way to give semantics to probabilistic λ-terms, and that there is a precise correspondence with probabilistic Böhm trees, as introduced by the second author. We prove this adequacy through notions of probabilistic resource terms and explicit Taylor expansion.