We spell out the paradigm of exact conditioning as an intuitive and powerful way of conditioning on observations in probabilistic programs. This is contrasted with likelihood-based scoring known from languages such as Stan. We study exact conditioning in the cases of discrete and Gaussian probability, presenting prototypical languages for each case and giving semantics to them. We make use of categorical probability (namely Markov and CD categories) to give a general account of exact conditioning, which avoids limits and measure theory, instead focusing on restructuring dataflow and program equations. The correspondence between such categories and a class of programming languages is made precise by defining the internal language of a CD category.

我们将精确调节的范式阐明为在概率程序中对观察进行调节的直观且强大的方式。这与Stan等语言中已知的基于可能性的评分形成对比。我们研究离散概率和高斯概率情况下的精确条件，为每种情况提供原型语言并赋予它们语义。我们利用分类概率（即马尔可夫和 CD 类别）来给出精确条件的一般说明，避免限制和测度论，而是专注于重构数据流和程序方程。通过定义CD类别的内部语言，可以使这些类别与一类编程语言之间的对应关系变得精确。