Monad Comprehensions: A Versatile Representation for Queries

Summary

This chapter is an exploration of the possibilities that open up if we consistently adopt a style of database query and collection processing which allows us to look inside collections and thus enables us to play with atomic constructors instead of the monolithic collection values they build.

This comprehension of values goes well together with a completely functional style of query formulation: queries map between the constructors of different collection types. It turns out that a single uniform type of mapping, the catamorphism, is sufficient to embrace the functionality of today’s database query languages, like SQL, OQL, but also XPath. Monad comprehensions provide just the right amount of syntactic sugar to express these mappings in a style that is similar to relational calculus (but goes beyond its expressiveness).

The major portion of this chapter, however, demonstrates how monad comprehensions enable a succinct yet deep understanding of database queries. We will revisit a number of problems in the advanced query processing domain to see how monad comprehensions can (a) provide remarkably concise proofs of correctness for earlier work, (b) clarify and then broaden the applicability of existing query optimisation techniques, and (c) enable query transformations which otherwise require extensive sets of rewriting rules.