Disintegration is a relation on measures and a transformation on probabilistic programs that generalizes density calculation and conditioning, two operations widely used for exact and approximate inference. Existing program transformations that find a disintegration or density automatically are limited to a fixed base measure that is an independent product of Lebesgue and counting measures, so they are of no help in practical cases that require tricky reasoning about other base measures. We present the first disintegrator that handles variable base measures, including discrete-continuous mixtures , dependent products , and disjoint sums . By analogy with type inference, our disintegrator can check a given base measure as well as infer an unknown one that is principal. We derive the disintegrator and prove it sound by equational reasoning from semantic specifications. It succeeds in a variety of applications where disintegration and density calculation had not been previously mechanized.

中文翻译：

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各种基本措施的象征性解体

分解是度量的关系和概率程序的转换，它概括了密度计算和调节，这两种操作广泛用于精确和近似推理。自动找到分解或密度的现有程序转换仅限于固定的基本度量，该基本度量是 Lebesgue 和计数度量的独立乘积，因此在需要对其他基本度量进行复杂推理的实际案例中它们没有帮助。我们提出了第一个处理可变基础度量的分解器，包括离散-连续混合物,依赖产品， 和不相交的和. 通过与类型推断类比，我们的分解器可以检查给定的基本度量，并推断出一个未知的主要度量。我们推导出分解器并通过语义规范的等式推理证明它是合理的。它在以前没有机械化分解和密度计算的各种应用中取得了成功。