概率相干空间对于概率PCF来说是完全抽象的

T. Ehrhard, C. Tasson, Michele Pagani
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引用次数: 78

摘要

概率相干空间(PCoh)产生高阶概率计算的语义,将类型解释为凸集,将程序解释为幂级数。我们证明了Pcoh中解释的相等性表征了具有随机原语的PCF中程序的操作不可区分性。这是对概率PCF语义进行完全抽象的第一个结果。关键因素是幂级数的规律性。在推导定理的过程中,我们设计了一个加权交型分配系统,给出了PCoh的逻辑表示。
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Probabilistic coherence spaces are fully abstract for probabilistic PCF
Probabilistic coherence spaces (PCoh) yield a semantics of higher-order probabilistic computation, interpreting types as convex sets and programs as power series. We prove that the equality of interpretations in Pcoh characterizes the operational indistinguishability of programs in PCF with a random primitive. This is the first result of full abstraction for a semantics of probabilistic PCF. The key ingredient relies on the regularity of power series. Along the way to the theorem, we design a weighted intersection type assignment system giving a logical presentation of PCoh.
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Session details: Verified systems Session details: Semantic models 2 Session details: Program analysis 3 Session details: Program analysis 1 Session details: Type system design
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