> Perhaps rocky1138 thinks this because they have experience answering this question by doing so?
They have experience with their problem solving style, they don't have experience with every problem solving style, or even necessarily with my problem solving style. You can't infer much from that, and certainly not that typing is "not great when prototyping".
> Just to be clear, I'm talking about recognizing the monads or functors or what have you. Even the general mathematician doesn't start by drawing the right diagram.
Absolutely. But you define the type that seems to match part of the problem, then realize it doesn't fit another aspect, and you refactor it until it covers all of the properties you need. Sometimes this involves writing some code to ensure you've captured the right properties for the problem when there's an algorithmic part, certainly, but to think you've captured anything meaningful or coherent without type checking is bizarre.
Like you later say, "abstracting partial solutions" is probably a pretty common approach, but those partial solutions only come together in a coherent whole if they're typed. Otherwise they likely won't mesh well, and you're left with a mishmash of partial solutions, not a solution.