Deeper constant optimization

[TurtlePU]

For now, only "explicit constants" are optimized away -- that is, created with fromConstant :: a -> var in MonadCircuit and with embed :: Symbolic c => f (BaseField c) -> c f. More can be optimized:

• [ ] Calls to newAssigned where witness is evidently constant (e.g. the result of fromConstant x * fromConstant y) (#324)
• [ ] Variables whose constraints force them to be constant (e.g. those k for which there is a constraint k - 1 == 0) (#355)

[vlasin]

It seems, the first item can be solved by modifying the constraint function instance for ArithmeticCircuit.

[TurtlePU]

Not the constraint, but the newAssigned function, I guess, as constraint is not able to change any variable

But yeah, the first point is doable without running any specific optimization passes

[vlasin]

As for the second item, we could do more if we make a reasonable assumption about the set of polynomial equations that are admissible constraints. Specifically, if we assume that any substitution of the form $x \rightarrow a_1 x_1 + a_2 x_2 + b$ does not make a valid constraint invalid, then we could eliminate all equations of the form $a_1 x_1 + a_2 x_2 + a_3 x_3 + b = 0$.

It holds true for Plonk and PlonkUp and, in general, is a pretty reasonable assumption, but it should be possible to turn it off if needed, I think. And, we should be careful with input variables.