I have a draft paper some of you might enjoy, called "Denotational design with type class morphisms".
Abstract:
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.
You'll find the paper at
http://conal.net/papers/type-class-morphisms/ .
I'd sure appreciate feedback on it, especially if in time for the *March 2* ICFP deadline. Pointers to related work would be particularly appreciated, as well as what's unclear and what could be cut. This draft is an entire page over the limit, so I'll have to do some trimming before submitting.
Enjoy, and thanks!
- Conal