melpow is the crate that implements MelPoW, Themelio's version of non-interactive proofs of sequential work, which are just "Interactive Proofs of Sequential Work" by Cohen and Pietrzak subjected to a Fiat-Shamir transformation. MelPoW is used as the core mechanism behind Melmint, the algorithmic monetary policy system that stabilizes the mel.
Proof is the main interface to MelPoW. It represents a proof that a certain amount of sequential work, represented by a difficulty, has been done starting from a puzzle. The difficulty is exponential: a difficulty of N represents that O(2^N) work has been done.