Kleisli Categories

  Bartosz Milewski's Programming Cafe

In the previous installment of Categories for Programmers, Categories Great and Small, I gave a few examples of simple categories. In this installment we’ll work through a more advanced example. If you’re new to the series, here’s the Table of Contents.

Composition of Logs

You’ve seen how to model types and pure functions as a category. I also mentioned that there is a way to model side effects, or non-pure functions, in category theory. Let’s have a look at one such example: functions that log or trace their execution. Something that, in an imperative language, would likely be implemented by mutating some global state, as in:

string logger;

bool negate(bool b) {
     logger += "Not so! ";
     return !b;
}

You know that this is not a pure function, because its memoized version would fail to produce a log. This function has side effects.

In modern programming…

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