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by dr0wsy 2527 days ago
> You don't need to know category theory. You just need to understand a few things that came from it, like `Maybe`, which is the most obviously useful and trivially easy monad. Just forget about the fact that it's a monad and any general rules about monads and just learn how to use `Maybe`.

I didn't convey my question clearly. What I'm wondering is how I should express programs, or part of them, using mathematical notation when I don't see them being mathematical in nature to begin with?

An example:

  def hello(name):
      if (name == "Bob"):
          print("Hello, " + name)
      else:
          print("Hello, World!")
How could I express this easily using mathematical notation?

It just feels weird that to convey this simple program on paper both I and the person I try to communicate with needs to have a grounding in category theory.

Hope you're able to understand my question. :)
1 comments
naturlich 2527 days ago
That was the second part of my answer: a graph on paper. Draw nodes of execution and represent the branch as two arrows coming from the node and heading to new nodes. Label the arrows with the predicates of the branch.

This is both definitely useful and definitely math.

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dr0wsy 2525 days ago
> That was the second part of my answer: a graph on paper. Draw nodes of execution and represent the branch as two arrows coming from the node and heading to new nodes. Label the arrows with the predicates of the branch.

Thanks! You don't happen to have some learning resources for modelling programs as state machines? I can't find anything when I search.

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naturlich 2525 days ago
This is more of a practical writeup on state machines than a theoretical one: http://gameprogrammingpatterns.com/state.html

You might also know these as flowcharts when applied to program flow control.

I don't think I answered the original question well. I just wanted to point out that math is more than just equations. Others have done a much better job in this thread.

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jcora 2525 days ago
This isn't about modelling rather a programming technique, but check out Idris for its dependent typing. It lets you encode state machines in types, which means your programs literally will not typecheck if you try for example to withdraw money from an unauthorized ATM, or candy from an empty store. You can make verified network protocols and drivers like this.
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