We present a technique to study normalizing strategies when termination is asymptotic, that is, it appears as a limit, as opposite to reaching a normal form in a finite number of steps. Asymptotic termination occurs in several settings, such as effectful, and in particular probabilistic computation -- where the limits are distributions over the possible outputs -- or infinitary lambda-calculi -- where the limits are infinitary normal forms such as Boehm trees. As a concrete application, we obtain a result which is of independent interest: a normalization theorem for Call-by-Value (and -- in a uniform way -- for Call-by-Name) probabilistic lambda-calculus.

翻译：当终止是无症状时,我们提出一种研究使战略正常化的方法,也就是说,它似乎是一种限制,而不是在一定数量的步骤中达到一种正常的形式。在几种情况下,例如有效,特别是概率计算 -- -- 限制是可能产出的分布 -- -- 或无止境的羊羔-卡库里 -- -- 限制是无穷的正常形式,如博埃姆树。作为一个具体应用,我们取得了一种独立利益的结果:按价计算(和 -- -- 以统一的方式 -- -- 逐名计算)的正常化理论,即按单调计算(和 -- -- 以统一的方式 -- -- 逐名计算)的羊驼-卡库卢斯(aball-by-Value)的概率。