Lambda Calculus and Probabilistic Computation

International audienceWe introduce two extensions of the λ-calculus with a probabilistic choice operator, Λcbv⊕ and Λcbn⊕, modeling respectively call-by-value and call-by-name probabilistic computation. We prove that both enjoys confluence and standardization, in an extended way: we revisit these two fundamental notions to take into account the asymptotic behaviour of terms.The common root of the two calculi is a further calculus based on Linear Logic, Λ!⊕, which allows for a fine control of the interaction between choice and copying, and which allows us to develop a unified, modular approach