clean up secondary circuit

[porcuquine]

This PR tries to tease apart usages of the supernova TrivialTestCircuit:

• create a new TrivialSecondaryCircuit for use in NIVC generally.
• leave the existing test circuit, but remove references to ROM.
• modify uses of program counter on the secondary circuit from the NIVC mechanism, so secondary circuits are not required to provide it
• add some initial support for CircuitSet type to formalize what an NIVC user will need to provide

I think it may be possible (and if so, probably desirable) to just use a normal trivial StepCircuit (not supernova) for the secondary circuit. However, trying to do this maximally led me into problems I could not debug. Hopefully as the implementation undergoes ongoing crypto review and refactoring/extension it will become clear which parts of the initial scaffolding can be pared back.

[huitseeker]

This overall LGTM, but I have a few questions inline.

[huitseeker]

Why a panic rather than SynthesisError::AssignementMissing?

[porcuquine]

It's because of the extremely confusing convention of how Option is overloaded in the bellman line of circuit-generation (phrased thus because maybe bellpepper will eventually help clean this up). Specifically, if inputs are missing (meaning we are synthesizing a blank shape), then the .get()? on line 185 will indeed result in the SynthesisError::AssignmentMissing. However, if that doesn't happen and inputs have been supplied, then those inputs are either for a primary or secondary circuit. In the secondary case, the program counter will not be present. However, in this code branch, we are specifically handling a primary circuit — so we require the actual value for the witness.

[huitseeker]

Nice 👍

[huitseeker]

Are you looking for an heterogeneous list (or more likely ExactSizeIterator) of dyn StepCircuit<F>, where F: Primefield?

[porcuquine]

Maybe, but this trait will end up doing some heavy lifting, and it's not really clear yet what it needs to look like. The above is just a first foot in the door. I will iterate in future revisions and bear your ideas in mind.