Initial selectorified API

[Fizzixnerd]

I have here a skeleton API for a selectorified API. This begins to address #2543 and #2545 (Perhaps? Comments?) by switching from the API used in o1vm/src/mips/interpreter.rs to that detailed in o1vmsrc/mips/singlestep.rs.

The main changes are:

• No use of mutability, instead using the "generator style" of a -> State -> (b, State)
• Significantly pared down API, will likely add to it as I realize it was needed, but for now start small!
• Instructions now "know" their arguments, by packing them in the enum fields with them. This allows the generator style to uniformly look like Instructions -> State -> (Witness, State) and for witness generation, without having to worry about different arities and register arguments. [Of course, the old instructions with their arguments can be relatively easily converted to this form -- to come].
• A small example of the API in use is below the API with a couple of test curves and an example instruction-set based on a significantly simplified MIPS instruction set, using just one of each of a small class of instructions, for parallel debugging and sanity-checking purposes.
• Simplified register set, again for debugging and sanity-checking
• Simplified ExampleS previously an implementor of InterpreterEnv (Env in witness.rs and the like) which will almost surely grow as the number of instructions returns to parity.

The point of these changes is to provide a basic test-bed for the selector changes to come.

[marcbeunardeau88]

I understand that you are re-creating from scratch
Shouldn't we rather build on top of https://github.com/o1-labs/proof-systems/blob/master/o1vm/src/mips/interpreter.rs ?
I would have expected a new function in interpreter similar to https://github.com/o1-labs/proof-systems/blob/master/o1vm/src/mips/interpreter.rs#L987C8-L987C23
But something done differently here : https://github.com/o1-labs/proof-systems/blob/master/o1vm/src/mips/interpreter.rs#L1047

[marcbeunardeau88]

I understand that variables are a way to index to positions in the plonk matrix.
Therfore, I would use something like unsigned integer, but not a crypto related object

[Fizzixnerd]

Yes, I changed to unsigned integer in the latest version.

Regarding the from-scratch approach shown here, this is mostly a playground where I can test out ideas which I will then port back to the regular interpreter, I think, without the full complexity of the regular interpreter. It didn't start out as that, mind you!

But I think you and Danny are right.

[dannywillems]

As discussed in PM, I would simply use an "iter" on the instructions with the constraint environment, multiplying by a selector, adding constraints on them on the way.
The selectors are added to a witness structure/proof structure. I'm not sure that we need a new trait.

[dannywillems]

C.f Arrabiata

[Fizzixnerd]

Closing as I decided on another approach.