Prefer commitment over root

[Mirko-von-Leipzig]

Originally raised as a concern in 0xPolygonMiden/miden-node#620 (comment).

Consider changing various xxx_root and xxx_hash fields into xxx_commitment where applicable e.g. in the block header.

Ideally root should only be used to describe fields representing the root of some tree. Take into account potential future changes e.g. just because the commitment is currently the root of some tree, does not mean it will always be. Commitments often change to encompass other tree roots, or combine other hashes which results in api churn and breaking changes.

Some of these changes could be contested, so I suggest submitting a list of proposed fields before embarking on a wider refactor.

[PhilippGackstatter]

Fully agree!

Adding AccountHeader to the list which uses root for the vault but commitment for storage and code:

miden-base/objects/src/accounts/header.rs

Lines 20 to 25 in 0e65f4f

	pub struct AccountHeader {
	id: AccountId,
	nonce: Felt,
	vault_root: Digest,
	storage_commitment: Digest,
	code_commitment: Digest,

But the method on the vault to get the "root" is called AssetVault::commitment, leading to assigning a commitment to a root which feels inconsistent:

miden-base/objects/src/accounts/header.rs

Lines 119 to 129 in 0e65f4f

	impl From<&Account> for AccountHeader {
	fn from(account: &Account) -> Self {
	Self {
	id: account.id(),
	nonce: account.nonce(),
	vault_root: account.vault().commitment(),
	storage_commitment: account.storage().commitment(),
	code_commitment: account.code().commitment(),
	}
	}
	}

This could be made more consistent by using commitment.