In this work we present a formalization, backed with a contrasted implementation, of a relational database language (called HR-SQL) that extends SQL in two aspects. On the one hand, including non-linear and mutual recursion. On the other hand, including hypothetical relations and queries. Regarding expressiveness, HR-SQL allows a novel form of hypothetical reasoning, completely integrated with recursive definitions. In addition, aggregate functions are added. Regarding formalization, the extended language is founded on a stratified fixpoint semantics based on logic programming techniques. We include results of the existence of such fixpoints. An algorithm that transforms a database containing hypothetical definitions into an equivalent one without hypothesis and its correctness proof are presented. Regarding the implementation, we introduce here a system that incorporates the aforementioned benefits and enhances former implementations in several areas. The current HR-SQL system is targeted to several state-of-the-art relational database systems, and could be used with any SQL-based system with minor modifications in the implementation.

在这项工作中，我们提出了一种关系数据库语言（称为HR-SQL）的形式化，并带有对比的实现，该关系数据库语言在两个方面扩展了SQL。一方面包括非线性和相互递归。另一方面，包括假设关系和查询。关于表达性，HR-SQL允许一种新颖的假设推理形式，与递归定义完全集成。另外，添加了聚合函数。关于形式化，扩展语言基于基于逻辑编程技术的分层定点语义建立。我们包括此类定点的存在的结果。提出了一种将包含假设定义的数据库转换为没有假设的等价数据库的算法及其正确性证明。关于实施，我们在这里介绍一种系统，该系统结合了上述优点并在多个方面增强了以前的实现。当前的HR-SQL系统针对多个最新的关系数据库系统，并且可以与任何基于SQL的系统一起使用，并且在实现中进行了一些小的修改。