[Haskell-cafe] How do you describe systems in general with Haskell?

[Grigory Sarnitskiy]

If you are to describe a system, which consists of several subsystems, how do you approach the problem? What types, classes, functions whatever do you introduce?

I guess it is a common problem, is there a general method? Just to describe, not to solve (though if the description implies the solution then it is wonderful).

Obviously this is not just a haskell-specific problem, but I think there might be people who are aware of the best current solution (category theory?).

For a dummy example, how would you describe the system from a fox, goose and bag of beans puzzle (wolf, goat and cabbage)?