Simplification pass for ACIR

[guipublic]

Related issue(s)

Resolves #573

Description

Summary of changes

Add a simplification pass which removes gates of the form x=field value, by replacing x by its value in all the other gates.
The simplification is done on the fly, every-time a gate is added to the circuit. If it can be simplified, we update the previous gates using the solved value until nothing is solved. Usually only one pass is needed (so two in total to see that the second one did not solve anything)

Checklist

• I have tested the changes locally.
• I have formatted the changes with Prettier and/or cargo fmt with default settings.
• I have linked this PR to the issue(s) that it resolves.
• I have reviewed the changes on GitHub, line by line.
• I have ensured all changes are covered in the description.

[kevaundray]

For reference, why is this done on the fly instead of at the end like the other passes?

(Doing it on the fly seems to have made a lot of the code now need to take a Result)

[guipublic]

For reference, why is this done on the fly instead of at the end like the other passes?

This is done in order to minimise the impact of the simplification. If we do it at the end, we need to reprocess the whole circuit again and again until nothing is solved, and the circuit can be big. Here, when we add a gate and if it can be solved, then usually the solved witness is defined by the gate and so we don't need to perform another pass on the circuit.
When the solved witness is not defined by the gate we need to do a full pass over the circuit (but the circuit is not complete so it is smaller) and because all the gates were previously solved, in practice only one is needed. With all the integration tests, there is only one case where more than one pass is needed.

[kevaundray]

There's been quite a bit of merge conflicts on this, that I will resolve

[jfecher]

What is the status on this PR? Do we want to try to fix the conflicts and merge it, restart it, or abandon it?

[guipublic]

What is the status on this PR? Do we want to try to fix the conflicts and merge it, restart it, or abandon it?

I think the acvm changes are too big for solving the conflicts. I will create another PR (probably we need two now) and then we can abandon this one.

[TomAFrench]

Closing in favour of noir-lang/acvm#151