Store equality sets in AcirContext

[kevaundray]

Problem

There are many operations which enforce an equivalence relation between AcirVars, the explicit one being assert_eq_var.

This assert_eq means that we can replace lhs with rhs wherever we see fit. This is useful in the context, where lhs might be an Expression whereas rhs is a Witness and instead of creating an extra gate to convert lhs to a Witness, we can instead use rhs

Happy Case

Create a Map in AcirContext to store equivalence relations. As noted above the obvious case is assert_eq_var however, whenever a constrain is called there is opportunity to capture an equivalnce relation and whenever get_or_create_witness is called, there is an opportunity to capture an equivalence relation.

Alternatives Considered

No response

Additional Context

No response

Would you like to submit a PR for this Issue?

No

Support Needs

No response

[TomAFrench]

This is partially resolved in #2378 but doesn't account for transitive equivalences.