linear VS polysemy

Linear.Quaternion.Quaterion from the linear package has a Num instance, and quaternion multiplication is noncommutative.

That's pretty much exactly the abstraction used in the 'linear' package's Affine class, in which we find points separated by vectors.

Linear algebra: hmatrix again with its own array type (and linear but this is restricted to low dimensions)

This is very niche, but something I've wanted to do for a while is to generate some cool physics example on the surface of a sphere with https://hackage.haskell.org/package/hamilton, and display it with https://reanimate.github.io/ (using https://hackage.haskell.org/package/linear for the projection)

Do check out the linear package. It has some complicated parts, but the types work out very nicely. Your Coords type is called V3 in that package, it has a huge list of instances for all kinds of different type classes.

I've come to love the linear approach, where instead of working with Naperian (Representable) functors, you work with Distributive functors.

See also the linear library, it contains types like data V3 a = V3 a a a with all of the useful instances.

Thirdly, composing arbitrary effects without losing state is really, really difficult. Things are fine when you limit yourself to State and Reader, sure, but once you start with nondeterminism you’ll discover it’s shockingly easy to produce behaviors that are baffling unless you’ve spent a preposterous amount of time thinking about this stuff. (I’ve been bitten in prod by silent state-dropping bugs, and rarely have I been more flummoxed.) Consider this example, which produces silent changes in the semantics of <|> depending on whether you use it inside or outside of a higher-order effect. Every single effect library (besides the still-unreleased eff) gets certain combinations of effects + nondeterminism wrong. You could make the argument that most people don’t use nondeterministic monads, but eDSLs really shine when you have access to them, as you can turn a concrete interpreter to an abstract one fairly easily.

Looking for a few projects that make use of it, I found accelerate, hawk, polysemy and pretty-simple, so I'll be interested to poke around in their code and see how they have things set up.

Right, I think I'll just give it a shot to see. Polysemy is nice but I'm still having trouble getting what I want out of it (which may very well be entirely a fault of my own understanding)

Languages such as Koka only support algebraic effects, not scoping operations such as catch and listen. The Effect Handlers in Scope paper introduces scoping operations, which lead to the Haskell libraries fused-effects and polysemy, but they turned out to have some weird semantics. eff is her effort to fix that.

Looking at the interpreter for Reader might give some clues if this doesn't work. https://github.com/polysemy-research/polysemy/blob/master/src/Polysemy/Reader.hs#L38-L45

*But I'm not terribly well versed in Scala's other DI offerings. I came from Haskell and didn't find anything in Scala that clicked with me until I found ZIO. It reminded me a lot of my favorite way of writing Haskell programs (https://github.com/polysemy-research/polysemy)—albeit with a completely different implementation.