Split Semiring into Semiring and Dioid #305

Activity

1. JordanMartinez

   changed the title [-]Revamp Semiring[/-] [+]Split Semiring into Semiring and Dioid[/+] on Jul 20, 2023
2. mikesol commented on Jul 20, 2023

   

   mikesol

   on Jul 20, 2023

   More actions

   See also https://encyclopediaofmath.org/wiki/Idempotent_semi-ring, which is where they redirect from dioid.
3. MonoidMusician commented on Jul 20, 2023

   

   MonoidMusician

   on Jul 20, 2023

   More actions

   Idempotent semi-ring is the wrong concept. We don't want something that requires idempotence.
4. mikesol commented on Jul 20, 2023

   

   mikesol

   on Jul 20, 2023

   More actions

   @MonoidMusician, in general, does the idea seem interesting, or do you see any pitfalls in there?
5. MonoidMusician commented on Jul 20, 2023

   

   MonoidMusician

   on Jul 20, 2023

   More actions

   I'd want to see a use-case for the extra generality before making a breaking change. I personally don't have use for it.
6. mikesol commented on Jul 20, 2023

   

   mikesol

   on Jul 20, 2023

   More actions

   The thought came up when I was working on a shader compiler for WebGPU.

   WebGPU shaders have tons of overloaded primitive operations, for example multiplying a vector by a float. That expressivity is really nice when writing shaders and is industry-standard stuff: it gets unergonomic if you can't do that because of how often you're doing vector and matrix transforms.

   Obviously, mul a b in PureScript will fail if a is a Number and b is a Vec3 Number. But, I could use a custom Prelude with:

   class Bisemiring a b c | a b -> c where
     add :: a -> b -> c
     mul :: a -> b -> c
   
   instance Bisemiring Number (Vec3 Number) (Vec3 Number) where...
   instance Bisemiring (Vec3 Number) Number (Vec3 Number) where...
   instance Bisemiring (Vec3 Number) (Vec3 Number) (Vec3 Number) where...
   instance Bisemiring Number Number Number where...

   Without Dioid, it gets klunky to define one and zero. If Dioid existed separately, I could just import it and use the one and zero instances from that, but now I have to import Semiring, hide add and mul, etc.

   It's a minor nit, but hopefully you can see the line of thinking that got me there.