Here are some of the more practical insights for medium/large-scale software design that have stuck with me. They apply regardless of whether I'm working in a language that lets me easily express categorical-ish stuff in the type system:
- Triviality
The most trivial cases are actually the most important. If I build a little DSL, I give it an explicit "identity" construction in the internal representation, and use it liberally in the implementation, transformation phases, and tests, even though obviously its denotation as a no-op will be optimized away by my little DSL compiler, and it may not even be exposed as an atomic construct in the user-facing representation.
- Free constructions
When it's difficult to separate a model from an implementation, when simple interfaces are not enough because the model and implementation are substantially complex, multilayered systems on their own, often the answer is to use a free construction.
Free constructions are a killer tool for allowing the late-binding of rather complex concerns, while allowing for reasoning, transformation, and testing of the underlying components without worrying about that late-bound behavior. "Late-bound" here does not have to mean OO-style dynamic dispatch -- in fact now you have more expressive power to fuse some behaviors together in a staged manner with no runtime indirection, or to make other behaviors legitimately dynamic, differing from one call to the next. Tradeoffs in the flexibility/performance space are easier to make, to change, and to self-document.
This is particularly useful when you need to start addressing "meta" concerns as actual user-facing concerns -- when your project matures from a simple application that does Foo into a suite of tools for manipulating and reasoning about Foo and Fooness. Your Foo engine currently just does Foo, but now you want it to not just do Foo, but return a description of all the sub-Foo tasks it performed -- but only if the configuration has requested those details, because sometimes the user just wants to Foo. So you embed the basic, non-meta-level entities representing the actual component tasks in a free construction, compose them within that free construction, and implement the configurable details of that composition elsewhere.
- "Sameness"
Making clear distinctions between different notions of sameness is important. Identity, equality, isomorphism, adjointness -- sure, you might never explicitly implement an adjunction, but these are important notions to keep separate, at least conceptually if not concretely in source code entities, as a piece of software grows more complex. If you treat two things as fundamentally the same in more ways than they really are, you reach a point where you now can no longer recover crucial information in a later phase of computation. In an indexed/fibered construction, this X may be basically the same as that X, but this X, viewed as the image of a transformation applied to Y is quite different from that X, viewed as the image of a transformation applied to Z, although the images are equal. So can I just pass my X's around everywhere, or do I need to pass or at least store somewhere the references to Y and Z? What if computationally I can only get an X as the result of applying a function to Y, but conceptually the functional dependency (that is, as a mathematical function) points the other way around, from X to Y? Paying attention to these easy-to-miss distinctions can save you from code-architecting yourself into a corner. You may discover that the true reserve currency of the problem domain is Y when it looks like X, or vice versa.
