I’ve just finished a draft of a paper called Denotational design with type class morphisms, for submission to ICFP 2009. The paper is on a theme I’ve explored in several posts, which is semantics-based design, guided by type class morphisms.
I’d love to get some readings and feedback. Pointers to related work would be particularly appreciated, as well as what’s unclear and what could be cut. It’s an entire page over the limit, so I’ll have to do some trimming before submitting.
Type classes provide a mechanism for varied implementations of standard interfaces. Many of these interfaces are founded in mathematical tradition and so have regularity not only of types but also of properties (laws) that must hold. Types and properties give strong guidance to the library implementor, while leaving freedom as well. Some of the remaining freedom is in how the implementation works, and some is in what it accomplishes.
To give additional guidance to the what, without impinging on the how, this paper proposes a principle of type class morphisms (TCMs), which further refines the compositional style of denotational semantics. The TCM idea is simply that the instance’s meaning is the meaning’s instance. This principle determines the meaning of each type class instance, and hence defines correctness of implementation. In some cases, it also provides a systematic guide to implementation, and in some cases, valuable design feedback.
The paper is illustrated with several examples of type, meanings, and morphisms.
The submission deadline is March 2, so comments before then are most helpful to me.
Enjoy, and thanks!