Add support for Noir as frontend

[Savio-Sou]

Add to sonobe the ability to parse Noir (more accurately ACIR, Noir's intermediate representation of choice) and specifically its folding opcode; hence the ability to fold, prove and generate verifiers for circuits written in Noir.

Relevant links:

• Noir repo: https://github.com/noir-lang/noir
• ACIR folder: https://github.com/noir-lang/noir/tree/master/acvm-repo
• Reference Noir --> proving backend (e.g. bb) workflow: https://noir-lang.org/docs/dev/getting_started/hello_noir/
• Noir PR adding #[fold] attribute: feat(acir_gen): Fold attribute at compile-time and initial non inlined ACIR AztecProtocol/aztec-packages#5341
• Barretenberg PR adding ability to fold ACIR: feat: fold acir programs AztecProtocol/aztec-packages#6563

[dmpierre]

Hey, thanks for suggesting this, we would indeed like to tackle this. Let me have a look!

[dmpierre]

(small update: waiting for the aztec noir team to circle back on a few questions)

[Savio-Sou]

Additional reference: Closest pointer to ACIR --> R1CS would be arkworks_bridge, which does conversion of ACIR opcodes but to a new data structure instead of R1CS (as in the circom_compat struct).

Note that conversion is incomplete, where only AssertZero ACIR opcodes are handled as they can be converted into R1CS cleanly, while other opcodes would fail.

A possible approach could be building a converter which:

1. Decomposes every ACIR opcode into AssertZero opcodes (a la acvm_stdlib)
2. Uses ACVM to perform witness generation on this ACIR
3. Converts this ACIR into R1CS

Follows by witness generation, which can either be witness generation on the ACIR or custom witness generation on the R1CS output.

(Credit @TomAFrench for insights)

[dmpierre]

It seems like this approach is working. With a few modifications, I managed to test it for a circuit with a shape similar to what sonobe expects. I will work on integrating this modified version of the arkworks_bridge into the lib now!