AI 中文总结
研究不精确概率编程，通过分级单子、BDD和半环参数推理实现可信集。引入Haskell嵌入式DSL Imp，利用分级单子恢复交换性，且相同编译BDD支持多种推理，展示不精确概率编程的新方法及优势。
AI 中文摘要
不精确概率通过用一组可能分布的凸集替换单个分布来推广标准概率论。我们表明，这种推广无需改变离散概率语言使用的标准BDD编译和加权模型计数流程。不精确抛硬币只是一个权重未固定而是自由的BDD变量。我们引入了Imp，一种用于不精确概率编程的Haskell嵌入式DSL。由有限的认知不确定性命名源集索引的分级单子恢复了标准凸幂集单子所缺乏的交换性，并且GHC的类型系统在编译时强制执行此特性。加权模型计数在半环中是参数化的，因此相同的编译BDD支持精确、可微和区间有界推理。
英文摘要
Imprecise probability generalizes standard probability theory by replacing a single distribution with a convex set of possible distributions. We show that this generalization requires no change to the standard BDD compilation and weighted model counting pipeline used by discrete probabilistic languages. An imprecise coin flip is simply a BDD variable whose weight is left free rather than fixed. We introduce Imp, a Haskell-embedded DSL for imprecise probabilistic programming. A graded monad, indexed by finite sets of named sources of epistemic uncertainty, restores the commutativity that the standard convex powerset monad lacks, and GHC's type system enforces this at compile time. Weighted model counting is parametric in the semiring, so the same compiled BDD supports exact, differentiable, and interval-bounded inference.
Journal refProc. ACM Program. Lang. 10, ICFP, Article 300 (2026)
DOI：10.1145/3828698
