Lambda Calculus and Probabilistic Computation

We introduce two extensions of the λ -calculus with a probabilistic choice operator, Λ
_⊕
^cbv
and Λ
_⊕
^cbn
, 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 us to develop a unified, modular approach.