A history_proof is a Skip_list.cell that stores multiple hashes. Skip_list.content history_proof gives the hash of this cell, while Skip_list.back_pointers history_proof is an array of hashes of earlier history_proofs in the inbox.

On the one hand, we think of this type as representing the whole Merkle structure of an inbox at a given level---it is the part of t above that can actually be used to prove things (it cannot be forged by a malicious node because it much match the hash stored by the L1).

On the other hand, we think of this type as representing a single proof-step back through the history of the inbox; given a hash that appears at some point later in the inbox this type proves that that hash points to this particular combination of a level tree and further back-pointers.

In terms of size, this type is a small set of hashes; one for the current level tree and `O(log2(ix))` in the back-pointers, where ix is the index of the cell in the skip list. That is, ix is the number of non-empty levels between now and the origination level of the rollup.

The type of the inbox for a smart-contract rollup as stored by the protocol in the context. Values that inhabit this type only act as fingerprint for inboxes and contain:

• level : the inbox level ;
• old_levels_messages : a witness of the inbox history.

inbox_level inbox returns the maximum level of message insertion in inbox or its initial level.

A History.t is basically a lookup table of history_proofs. We need this if we want to produce inbox proofs because it allows us to dereference the 'pointer' hashes in any of the history_proofs. This deref function is passed to Skip_list.back_path or Skip_list.search to allow these functions to construct valid paths back through the skip list.

old_levels_messages inbox returns the latest skip list cell of the inbox history that is not up to change (i.e. not the current level tree).

current_witness inbox returns the current witness of the inbox, i.e. the merkelized payload hash.