We develop a new Low-level, First-order Probabilistic Programming Language (LF-PPL) suited for models containing a mix of continuous, discrete, and/or piecewise-continuous variables. The key success of this language and its compilation scheme is in its ability to automatically distinguish parameters the density function is discontinuous with respect to, while further providing runtime checks for boundary crossings. This enables the introduction of new inference engines that are able to exploit gradient information, while remaining efficient for models which are not everywhere differentiable. We demonstrate this ability by incorporating a discontinuous Hamiltonian Monte Carlo (DHMC) inference engine that is able to deliver automated and efficient inference for non-differentiable models. Our system is backed up by a mathematical formalism that ensures that any model expressed in this language has a density with measure zero discontinuities to maintain the validity of the inference engine.

我们开发了一种新的低级、一阶概率编程语言（LF-PPL），适用于包含连续、离散和/或分段连续变量的模型，在能够自动区分与密度函数不连续有关的参数的同时，提供运行时检查边界交叉的编译方案。通过将不连续的哈密尔顿蒙特卡洛（DHMC）推断引擎整合进去，我们证明了该语言的能力，可以提供自动和高效的非可微模型推断。同时，我们的系统还有数学形式主义来确保任何表达在该语言中的模型具有密度，且在测度上具有零间断，以维护推断引擎的有效性。

LF-PPL：用于不可微分模型的低级一阶概率编程语言