Proof-of-Concept: Structured I/O, Numeric Hierarchy with (Semi)Euclidean + (Semi)Integral, Optimized Constants, Map-of-Maps multivariate polynomials

[echatav]

Proof-of-Concept draft reference demonstrating:

• Structured Circuit I/O
• Numeric/Algebraic typeclass hierarchy with
  • (Semi)Euclidean & (Semi)Integral
  • optimizable scalar combine and evalMonomial methods
  • Mod int n parametrizable by a SemiIntegral int and a KnownNat n or Prime n.
• Map-of-maps definition of multivariate Polynomials
• Optimization of constant variables.

[vlasin]

We've recently added a new type of constraints called range constraints to the Circuit type. An input or output variable can be constrained to an interval of the form [0, a]. I think it would make sense to consider it in this draft.

Additionally, we will have constraints of the form (x_1, ..., x_k) \in T sometime soon. Just a heads up.

[TurtlePU]

I think we salvaged the ideas from this PoC in #154, #214 and in #217, so we can close this. @echatav, what do you think?

[echatav]

I just want to keep it open as a reference, not to merge. There are still lots of things here as proof of concepts that are relevant to proposals that I want to merge back in their own PRs. I will add a label if it helps.