The Idea of statebox (From glancing over the paper on their homepage) is that you draw architectural diagrams. And then these Petrinets have some kind of category-theoretical encoding. Which allows us to interpret the high level architectural diagram to a low level program, by telling what exactly the nodes and arrows do. These interpretations then fill in the gaps on whatever the architectural diagram has (like error handling, UI drawing, whatever).
This is similar to free monads, where the choice of specific interpretation of the DSL is delayed, and even multiple interpreters can exist
> ...you draw architectural diagrams. ...Which allows us to interpret the high level architectural diagram to a low level program, by telling what exactly the nodes and arrows do
This is not a new idea at all - I'm strongly reminded of the whole Model Driven Architecture brouhaha back in the 1990s and early 2000s. Needless to say, it didn't work. You can't do "code generation" from a high-level architectural diagram and expect to end up with a functioning system! At best, if you really do it right, the high-level design might enable you to specify type-like properties that constrain the low-level implementation in a broadly helpful way[1]. But you still have to write all the low-level code!
[1] And this is in actuality incredibly optimistic - MDA and UML didn't even manage that! Instead, all the pretty diagrams (1) were inherently fuzzy, so they did not embody any actual constraints on the implementation, and (2) even in the best of cases, got immediately out of sync with the ground-level truth of the actual implementation.
yep UML and such don't have what we think of as sensible semantics.
> if you really do it right, the high-level design might enable you to specify type-like properties that constrain the low-level implementation in a broadly helpful way
so this is exactly what we do. we have a general way to specify boxes and wires and if you give me some sort of type system and a functor and voila, we can produce some well behaved code. nothing is hand-wavy about it, or "complex", like specialized flags or properties of boxes, just some simple mappings
This is similar to free monads, where the choice of specific interpretation of the DSL is delayed, and even multiple interpreters can exist