Modern data analytics applications, such as knowledge graph reasoning and machine learning, typically involve recursion through aggregation. Such computations pose great challenges to both system builders and theoreticians: first, to derive simple yet powerful abstractions for these computations; second, to define and study the semantics for the abstractions; third, to devise optimization techniques for these computations.

In recent work we presented a generalization of Datalog called Datalog, which addresses these challenges. Datalog is a simple abstraction, which allows aggregates to be interleaved with recursion, and retains much of the simplicity and elegance of Datalog. We define its formal semantics based on an algebraic structure called Partially Ordered Pre-Semirings, and illustrate through several examples how Datalog can be used for a variety of applications. Finally, we describe a new optimization rule for Datalog, called the FGH-rule, then illustrate the FGH-rule on several examples, including a simple magic-set rewriting, generalized semi-naïve evaluation, and a bill-of-material example, and briefly discuss the implementation of the FGH-rule and present some experimental validation of its effectiveness.

现代数据分析应用程序，例如知识图推理和机器学习，通常涉及通过聚合进行递归。这样的计算对系统构建者和理论家都提出了巨大的挑战：首先，为这些计算推导简单而强大的抽象；第二，定义和研究抽象的语义；第三，为这些计算设计优化技术。

在最近的工作中，我们提出了一种称为 Datalog 的 Datalog 的概括，它解决了这些挑战。Datalog 是一个简单的抽象，它允许聚合与递归交错，并保留了 Datalog 的大部分简单和优雅。我们基于称为 Partially Ordered Pre-Semirings 的代数结构定义其形式语义，并通过几个示例说明 Datalog 如何用于各种应用程序。最后，我们描述了一个新的 Datalog 优化规则，称为 FGH 规则，然后在几个示例中说明了 FGH 规则，包括一个简单的魔术集重写、广义的半朴素评估和一个物料清单示例，并简要讨论 FGH 规则的实施，并对其有效性进行一些实验验证。