An inflationary fixed point operator in XQuery

We introduce a controlled form of recursion in XQuery, an inflationary fixed point operator, familiar from the context of relational databases. This operator imposes restrictions on the expressible types of recursion, but we show that it is sufficiently versatile to capture a wide range of interesting use cases, including Regular XPath and its core transitive closure operator.
While the optimization of general user-defined recursive functions in XQuery appears elusive, we describe how inflationary fixed points can be efficiently evaluated, provided that the recursive XQuery expressions are distributive. We test distributivity syntactically and algebraically, and provide experimental evidence that XQuery processors can benefit substantially from this mode of evaluation.