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arXiv 1502.06095cs.LO
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逻辑程序设计的双代数语义

Bialgebraic Semantics for Logic Programming

Filippo Bonchi, Fabio Zanasi

摘要:

双代数提供了一个抽象框架,包含不同类型的计算模型的语义。在本文中,我们提出了一个双代数方法的语义逻辑程序设计。我们的方法是研究逻辑程序作为反应系统,并利用抽象技术开发的设置。首先,我们使用饱和度模型的操作语义的逻辑程序作为余代数上的预层。然后,利用预层上的双代数,明确了其代数结构。由此产生的语义原来是组合方面的连接和长期替代。此外,它还编码了一个并行计算模型,其可靠性由不同线程之间的内置同步概念保证。

英文摘要:

Bialgebrae provide an abstract framework encompassing the semantics of different kinds of computational models. In this paper we propose a bialgebraic approach to the semantics of logic programming. Our methodology is to study logic programs as reactive systems and exploit abstract techniques developed in that setting. First we use saturation to model the operational semantics of logic programs as coalgebrae on presheaves. Then, we make explicit the underlying algebraic structure by using bialgebrae on presheaves. The resulting semantics turns out to be compositional with respect to conjunction and term substitution. Also, it encodes a parallel model of computation, whose soundness is guaranteed by a built-in notion of synchronisation between different threads.

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