what does the word "algebraic" mean when used in the context of programming langs?
- a random tweet
I'd wondered the same thing about "Algebraic Effects", and was excited to find a talk on YouTube titled What's Algebraic About Algebraic Effects and Handlers? Unfortunately, I'm not the target audience. As an engineer that doesn't shy away from math, it was still out of my depth.
I found some time this past spring looking into Algebraic Effects, and I think I have a decent answer to the question.
Algebra in the context of programming
My view of "Algebra" in the context of programming is a particular kind of compositionality, where there's a structure.
In contrast, mainstream developers often talk about compositionality as just two obj/function that can interoperate due to the same interface, but not much more can be inferred about properties of the interop between the two obj/functions.
So often times, we get some collection of objects/functions that go together in an arbitrary way according to the taste of the developer that wrote it. If they're any good, it feels intuitive. But more often than not, it feels arbitrary. The effect is magnified if you look into the codebase. To a newcomer, it feels like a mess, in the same way that a house built by piling stones high feels like a mess: there's no apparent or easily recognizable structure.
A tangential detour into abstract algebra
In abstract algebra, structure is often where you take some math object 𝛂 (like an int, or matrix), and you pair it with an operation, (like + or *), and you say: integers can be composed with op `+`, but we can ALSO infer properties in these combos--or laws.
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