论文标题
马尔可夫内核和线性操作员的高阶语言
A Higher-Order Language for Markov Kernels and Linear Operators
论文作者
论文摘要
已经做了很多工作来为概率编程语言提供语义。近年来，用于推理概率程序的大多数语义分为两类：基于马尔可夫内核和基于线性操作员的语义的语义。 两种语义风格都在推理有关概率程序的推理中都有许多应用，但它们各自具有优点和缺点。尽管人们认为他们之间有联系，但没有语言可以处理两种编程样式。 在这项工作中，我们通过定义两级演算及其分类语义来解决这些问题，这使得可以使用两种语义进行编程。从事物的逻辑方面，我们将这种语言视为线性逻辑的替代资源解释，其中要保留的资源是采样而不是可变使用。
Much work has been done to give semantics to probabilistic programming languages. In recent years, most of the semantics used to reason about probabilistic programs fall in two categories: semantics based on Markov kernels and semantics based on linear operators. Both styles of semantics have found numerous applications in reasoning about probabilistic programs, but they each have their strengths and weaknesses. Though it is believed that there is a connection between them there are no languages that can handle both styles of programming. In this work we address these questions by defining a two-level calculus and its categorical semantics which makes it possible to program with both kinds of semantics. From the logical side of things we see this language as an alternative resource interpretation of linear logic, where the resource being kept track of is sampling instead of variable use.
