Functionality inside Trace
to obtain relation columns used in lookups
#2334
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This PR supports a new functionality inside the
Trace
struct to extract the columns used in lookups, which shall be used in the delayed lookup argument.The rough idea is to recurse over the values of each lookup expression for each instruction/step variant, so that upon initialization of the decomposed traces, the lookup-related columns are identified. This means "collecting" them has no impact on the witness generation code.
Note that columns are extracted in generic shape. If we wanted to have them in alias shape, then we would need to create all the expressions in alias shape and then before calling the prover, convert them into generic shape.