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This differs from vm1's merkle gadget in one primary way; the caller is meant to lookup on "end" instead of "start". This changes which inputs need dedicated columns and need to be propagated down during a merkle check. In vm1's implementation, the only thing that needed to be propagated down was
expected_root. In this vm2 implementation, we need to propagateleaf,leaf_index, andtree_height, but notexpected_root.I got close to reverting this primary difference but opted not to because it only saves one maybe two columns. If we decide that we should make that change, I'll do so when adding the merkle "write" functionality.
Here is a diagram comparing vm1 vs vm2 ways of doing things (also screenshotted here):
