On coinductive equivalences for higher-order probabilistic functional programs

Ugo Dal Lago, D. Sangiorgi, Michele Alberti
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引用次数: 59

Abstract

We study bisimulation and context equivalence in a probabilistic lambda-calculus. The contributions of this paper are threefold. Firstly we show a technique for proving congruence of probabilistic applicative bisimilarity. While the technique follows Howe's method, some of the technicalities are quite different, relying on non-trivial "disentangling" properties for sets of real numbers. Secondly we show that, while bisimilarity is in general strictly finer than context equivalence, coincidence between the two relations is attained on pure lambda-terms. The resulting equality is that induced by Levy-Longo trees, generally accepted as the finest extensional equivalence on pure lambda-terms under a lazy regime. Finally, we derive a coinductive characterisation of context equivalence on the whole probabilistic language, via an extension in which terms akin to distributions may appear in redex position. Another motivation for the extension is that its operational semantics allows us to experiment with a different congruence technique, namely that of logical bisimilarity.
高阶概率泛函规划的协归纳等价
我们研究了概率λ演算中的双模拟和上下文等价。本文的贡献有三个方面。首先给出了一种概率应用双相似度的同余证明方法。虽然这项技术沿用了Howe的方法,但一些技术上的差异很大,它依赖于实数集的非平凡“解纠缠”特性。其次,我们表明,虽然双相似性一般严格优于上下文等价,但在纯lambda项上,两种关系之间的重合是可以实现的。所得的等式是由Levy-Longo树推导出来的,通常被认为是惰性状态下纯λ项上最优的扩展等价。最后,我们推导了整个概率语言上上下文等价的协归纳特征,通过一个扩展,其中类似于分布的项可能出现在索引位置。扩展的另一个动机是,它的操作语义允许我们试验不同的同余技术,即逻辑双相似性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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