Formalizing a Broader Recursion Coverage in SQL

SQL is the de facto standard language for relational databases and has evolved by introducing new resources and expressive capabilities, such as recursive definitions in queries and views. Recursion was included in the SQL-99 standard, but this approach is limited as only linear recursion is allowed, mutual recursion is not supported, and negation cannot be combined with recursion. In this work, we propose a new approach, called R-SQL, aimed to overcome these limitations and others, allowing in particular cycles in recursive definitions of graphs and mutually recursive relation definitions. In order to combine recursion and negation, we import ideas from the deductive database field, such as stratified negation, based on the definition of a dependency graph between relations involved in the database. We develop a formal framework using a stratified fixpoint semantics and introduce a proof-of-concept implementation.