[Haskell-cafe] category design approach for inconvenient concepts

[Christopher Howard]

Recently I read this article I happened across, about the categorical
design pattern:

http://www.haskellforall.com/2012/08/the-category-design-pattern.html

Barely understood it, of course, but it was a rather intriguing concept.
So now I'm looking at all my programming problems trying to make types
that can be composed and that seem to fit the idea of a "category".

However, what I'm wondering about is ideas that can be "composed" but
that don't seem to fit the idea of "category", because they don't obey
the associativity law. To give a specific example (pseudo code like,
without any idea here of implementation or proper syntax):

Say you created a type called "Component" (C for short), the idea being
to compose Components out of other Components. Every C has zero or more
connectors on it. Two Cs can be connected to form a new C using some
kind of composition operator (say, <.>), provided there are enough
connectors (one on each). Presumably you would need a "Fail" constructor
of some kind to represent the situation when there is not enough connectors.

Say you had a C (coupler) with two connectors, a C (thing) with one
connector, and a C (gadget) with one connector.

So you could have...

(coupler <.> thing) <.> gadget

Because the coupler and the thing would combine to create a component
with one spare connector. This would then combine with the gadget to
make the final component. However, if you did...

coupler <.> (thing <.> gadget)

Then thing and gadget combine to make a component with no spare
connectors. And so the new component and the coupler then fail to
combine. Associativity law broken.

So, can I adjust my idea to fit the "category" concept? Or is it just
not applicable here? Or am I just misunderstanding the whole concept?

-- 
frigidcode.com

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