Universality of data retrieval languages

We consider the question of how powerful a relational query language should be and state two principles that we feel any query language should satisfy. We show that although relational algebra and relational calculus satisfy these principles, there are certain queries involving least fixed points that cannot be expressed by these languages, yet that also satisfy the principles. We then consider various extensions of relational algebra to enable it to answer such queries. Finally, we discuss our extensions to relational algebra in terms of a new programming language oriented model for queries.