## Expand description

An interactive protocol for proving/verifying evaluation claims on virtual polynomials.

A virtual polynomial evaluation claim can either be proven directly with a single opening proof per batched polynomial commitment, or with a sumcheck reduction to further evaluation claims. The definitions of the virtual polynomials determine how many rounds of sumcheck reductions are required before the polynomial commitment openings. The number of rounds is guaranteed to be finite because the graph of virtual polynomial definitions is acyclic.

The greedy evalcheck protocol runs the full sequence of alternating evalcheck and sumcheck protocols to reduce several evaluation claims to a single PCS opening per batch.