Various categories have been proposed as targets for the denotational semantics of higher-order probabilistic programming languages. One such proposal involves joint probability distributions (couplings) used in Bayesian statistical models with conditioning. In previous treatments, composition of joint measures was performed by disintegrating to obtain Markov kernels, composing the kernels, then reintegrating to obtain a joint measure. Disintegrations exist only under certain restrictions on the underlying spaces. In this paper we propose a category whose morphisms are joint finite measures in which composition is defined without reference to disintegration, allowing its application to a broader class of spaces. The category is symmetric monoidal with a pleasing symmetry in which the dagger structure is a simple transpose.

翻译：针对高阶概率编程语言的指称语义，已有多种范畴被提出作为目标。其中一种方案涉及贝叶斯统计模型中用于条件化的联合概率分布（耦合）。在以往的处理中，联合测度的复合需通过解积分得到马尔可夫核，对核进行复合后再重新积分以获得联合测度。解积分仅当基础空间满足特定限制条件时才存在。本文提出一个范畴，其态射为联合有限测度，其中复合的定义无需依赖解积分，从而可将其应用于更广泛的空间类。该范畴是对称幺半范畴，具有优美的对称性，其dagger结构为简单的转置运算。