Comprehending Monoids with Class.

The design of embedded database query languages has long relied on monadic comprehension (and specifically list comprehension), a natural foundation for expressing queries over collections of data. We argue that monoid comprehension is an interesting alternative foundation for such languages. We show that a generalized version of the monoid comprehension calculus can be naturally encoded in languages with support for type classes, and that this unlocks a new kind of expressive power — among other things, it gives us a grouping construct for free and it allows queries mixing heterogeneous data types (lists, sets, multisets, infinite streams, maps, etc.), while using the type system to statically verify some desirable properties about these queries. We believe that these new directions have the potential of making language-integrated queries more pleasant to use, more expressive, and eventually easier to optimize. ACM Reference Format: Lionel Parreaux and Christoph E. Koch. 2018. Comprehending Monoids with Class (Extended Abstract) . In Proceedings of Type-Driven Development (TyDe’18). ACM, New York, NY, USA, 3 pages. https: