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arXiv 1707.06901cs.PLcs.LOmath.PR
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概率密度函数的一种验证算法

A Verified Compiler for Probability Density Functions

Manuel Eberl, Johannes Hölzl, Tobias Nipkow

摘要:

Bhat等人开发了一个归纳编译器,它可以用简单的概率函数语言计算概率空间的密度函数。在这项工作中,我们实现了这样一个编译器的修改后的版本,这种语言的定理证明器伊莎贝尔,并给出了一个正式的证明其可靠性w.r.t.源语言和目标语言的语义。与Isabelle的归纳谓词代码生成一起,这产生了一个完全验证的、可执行的密度编译器。使用标准的精化方法,证明分两步完成:首先,定义一个抽象编译器,使用直接在定理证明器的逻辑中建模的抽象函数,并证明其正确性。然后,这个编译器被细化为返回目标语言表达式的具体版本。

英文摘要:

Bhat et al. developed an inductive compiler that computes density functions for probability spaces described by programs in a simple probabilistic functional language. In this work, we implement such a compiler for a modified version of this language within the theorem prover Isabelle and give a formal proof of its soundness w.r.t. the semantics of the source and target language. Together with Isabelle's code generation for inductive predicates, this yields a fully verified, executable density compiler. The proof is done in two steps, using a standard refinement approach: first, an abstract compiler working with abstract functions modelled directly in the theorem prover's logic is defined and proven sound. Then, this compiler is refined to a concrete version that returns a target-language expression.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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