Question

Importance of isomorphism in functional programming

Answer 1

Answer:

I'm trying to draw some analogs between functional programming and concepts in Category Theory based off of some of the lingo I hear from time-to-time. Essentially I'm trying to "unpackage" that lingo into something concrete I can then expand on. I'll then be able to use the lingo with an understanding of just-what-the-heck-I'm-talking about. Which is always nice.

One of these terms I hear all the time is Isomorphism, I gather this is about reasoning about equivalence between functions or function compositions. I was wondering if someone could provide some insights into some common patterns where the property of isomorphism comes in handy (in functional programming), and any by-products gained, such as compiler optimizations from reasoning about isomorphic functions.

Answer 2

When programming, you can often express the same concept in multiple ways. If you can losslessly translate between two alternatives, it's an isomorphism. An introduction for object-oriented programmers. ... In any case, one term from category theory that occasionally makes the rounds is isomorphism.