Try zero

[chriseth]

This PR extends the check for "are we finished?" such that it still works if there are unknown variables left, but they are not constrained given the current state.

[georgwiese]

Hmm, I'm not sure I agree with this: For example, if a block machine output is not constrained, don't we want the entire process to fail? To catch soundness bugs?

Also, wouldn't this lead to the can_process_call implementation? For example, if I have a machine that receives $(a, b, c)$ and has the constraint $c = a + b$, would it now say that it can process a call where $a$ is known to be $0$ and $b$ and $c$ are unknown?

[chriseth]

Hm, interesting! I was looking at this in the context of https://github.com/powdr-labs/powdr/pull/2357/files#diff-18909377b8656c5e03adf2051ea1b22bfbe3fcfcf95357c630319b99f6356f59R368 - where I think that we certainly need it (and I also think that such things occur as well).

So essentially this is concerning constraints that are deactivated by some flags. Another example is a VM where an assignment register is not used by an instruction.

[chriseth]

Ok, maybe the solution for the case where the instruction does not use an assignment register is that assignment registers actually should not be assumed to be known on the previous row and should not be required to be computed in the next row.

[chriseth]

And the solution for the case where "operation_id = 0" is nonsensical would be that we either require it to be nonzero or we get an input constraint that disallows it. But the latter means that we need to provide input constraints for codegen, which extends the input space. Maybe we can try without input constraints first, and re-try with input constraints if it doesn't work?

[georgwiese]

But the latter means that we need to provide input constraints for codegen, which extends the input space

Not sure what you mean by that!

I do think it makes sense to treat the operation ID like an input.