VmProcessor does not work for more complex information flow

[georgwiese]

Consider this example:

let N = 4;

namespace Test(N);
    col fixed ISLAST(i) { if i == N - 1 { 1 } else { 0 } };
    col fixed INDEX(i) { i };
    col witness w, sum;

    // Compute the witness from the index
    w = INDEX + 1;

    // The sum should be the sum of all witnesses, op to the current row.
    sum' = (1 - ISLAST) * sum + w';

    // Note that adding this equivalent constraint resolves the issue.
    // sum' = (1 - ISLAST) * sum + (INDEX' + 1);

This can be solved by running the following steps:

• Process w = INDEX + 1 in row 0:
  • -> Set w[0] = 1
• Process sum' = (1 - ISLAST) * sum + w' on row 3:
  • -> Set sum[0] = 1
• Process w = INDEX + 1 in row 1:
  • -> Set w[1] = 2
• Process sum' = (1 - ISLAST) * sum + w' on row 0:
  • -> Set sum[1] = 3
• ...

Instead, the VM processor never figures our a value of sum and eventually sets it to 0, violating the constraints. To see that, run:
cargo run pil test.pil -o output -f --export-witness-csv --prove-with mock

The reason is that w = INDEX + 1 needs to processed on the next row before sum' = (1 - ISLAST) * sum + w can be completed on the current row.