docs: Yellow paper rollup circuits and state update (AztecProtocol#3558)

PR looking to fix AztecProtocol#3148, AztecProtocol#3149 and AztecProtocol#3150.

---------

Co-authored-by: Rahul Kothari <rahul.kothari.201@gmail.com>
Co-authored-by: Jan Beneš <janbenes1234@gmail.com>
Co-authored-by: esau <152162806+sklppy88@users.noreply.github.com>

Author: 4 people

yellow-paper/docs/contracts/index.md

@@ -0,0 +1,343 @@
+---
+title: Base Rollup
+sidebar_position: 2
+---
+
+The base rollup circuit is the most complex of the rollup circuits, as it has to interpret the output data of a kernel proof and perform the state updates and transaction validation. While this makes the data structures complex to follow, the goal of the circuit is fairly straight forward: 
+
+Take `BaseRollupInputs` as an input value, and transform it to `BaseOrMergeRollupPublicInputs` as an output value while making sure that the validity conditions are met.
+
+```mermaid
+graph LR
+A[BaseRollupInputs] --> C[BaseRollupCircuit] --> B[BaseOrMergeRollupPublicInputs]
+```
+
+## Overview
+
+Below is a subset of the figure from [earlier](./index.md) (granted, not much is removed). The figure shows the data structures related to the Base Rollup circuit.
+
+```mermaid
+classDiagram
+direction TB
+
+
+class PartialStateReference {
+    note_hash_tree: Snapshot
+    nullifier_tree: Snapshot
+    contract_tree: Snapshot
+    public_data_tree: Snapshot
+}
+
+class StateReference {
+    l1_to_l2_message_tree: Snapshot
+    partial: PartialStateReference
+}
+StateReference *-- PartialStateReference: partial
+
+class GlobalVariables {
+    block_number: Fr
+    timestamp: Fr
+    version: Fr
+    chain_id: Fr
+    coinbase: Address
+}
+
+class Header {
+    last_archive: Snapshot
+    content_hash: Fr[2]
+    state: StateReference
+    global_variables: GlobalVariables
+}
+Header *.. Body : content_hash
+Header *-- StateReference : state
+Header *-- GlobalVariables : global_variables
+
+class ContractData {
+    leaf: Fr
+    address: Address
+    portal: EthAddress
+}
+
+class Logs {
+    private: EncryptedLogs
+    public: UnencryptedLogs
+}
+
+class PublicDataWrite {
+    index: Fr
+    value: Fr
+}
+
+class TxEffect {
+    note_hashes: List~Fr~
+    nullifiers: List~Fr~
+    l2_to_l1_msgs: List~Fr~
+    contracts: List~ContractData~
+    public_writes: List~PublicDataWrite~
+    logs: Logs
+}
+TxEffect *-- "m" ContractData: contracts
+TxEffect *-- "m" PublicDataWrite: public_writes
+TxEffect *-- Logs : logs
+
+class Body {
+    l1_to_l2_messages: List~Fr~
+    tx_effects: List~TxEffect~
+}
+Body *-- "m" TxEffect
+
+class ProvenBlock { 
+    archive: Snapshot
+    header: Header
+    body: Body
+}
+
+ProvenBlock *-- Header : header
+ProvenBlock *-- Body : body
+
+class ConstantRollupData {
+  last_archive: Snapshot
+  base_rollup_vk_hash: Fr,
+  merge_rollup_vk_hash: Fr,
+  global_variables: GlobalVariables
+}
+ConstantRollupData *-- GlobalVariables : global_variables
+
+class PublicDataUpdateRequest {
+    index: Fr
+    old_value: Fr
+    new_value: Fr
+}
+
+class PublicDataRead {
+    index: Fr
+    value: Fr
+}
+
+class NewContractData {
+    function_tree_root: Fr
+    address: Address
+    portal: EthAddress
+}
+
+class CombinedAccumulatedData {
+    aggregation_object: AggregationObject
+    read_requests: List~Fr~
+    pending_read_requests: List~Fr~
+    note_hashes: List~Fr~
+    nullifiers: List~Fr~
+    nullified_note_hashes: List~Fr~
+
+    l2_to_l1_messages: List~Fr~
+    contracts: List~NewContractData~
+    public_update_requests: List~PublicDataUpdateRequest~
+    public_reads: List~PublicDataRead~
+    logs: Logs
+
+    private_call_stack: List~CallRequest~
+    public_call_stack: List~CallRequest~
+    start_public_data_root: Fr
+    end_public_data_root: Fr
+}
+CombinedAccumulatedData *-- "m" NewContractData: contracts
+CombinedAccumulatedData *-- "m" PublicDataUpdateRequest: public_update_requests
+CombinedAccumulatedData *-- "m" PublicDataRead: public_reads
+CombinedAccumulatedData *-- Logs : logs
+
+class ContractDeploymentData {
+    deployer_public_key: Point
+    constructor_vk_hash: Fr
+    constructor_args_hash: Fr
+    function_tree_root: Fr
+    salt: Fr
+    portal_address: Fr
+}
+
+class TxContext {
+    fee_context: FeeContext
+    is_contract_deployment: bool
+    chain_id: Fr
+    version: Fr
+    contract_deployment_data: ContractDeploymentData
+}
+TxContext *-- ContractDeploymentData: contract_deployment_data
+
+class CombinedConstantData { 
+    historical_header: Header
+    tx_context: TxContext
+}
+CombinedConstantData *-- Header : historical_header
+CombinedConstantData *-- TxContext : tx_context
+
+class KernelPublicInputs {
+  is_private: bool
+  end: CombinedAccumulatedData
+  constants: CombinedConstantData
+}
+KernelPublicInputs *-- CombinedAccumulatedData : end
+KernelPublicInputs *-- CombinedConstantData : constants
+
+class KernelData {
+  proof: Proof
+  public_inputs: KernelPublicInputs
+}
+KernelData *-- KernelPublicInputs : public_inputs
+
+class StateDiffHints {
+  nullifier_predecessor_preimages: List~NullifierLeafPreimage~
+  nullifier_predecessor_membership_witnesses: List~NullifierMembershipWitness~
+  sorted_nullifiers: List~Fr~
+  sorted_nullifier_indexes: List~Fr~
+  note_hash_subtree_sibling_path: List~Fr~,
+  nullifier_subtree_sibling_path: List~Fr~,
+  contract_subtree_sibling_path: List~Fr~,
+  public_data_sibling_path: List~Fr~,
+}
+
+class BaseRollupInputs {
+  historical_header_membership_witnesses: List~HeaderMembershipWitness~
+  kernel_data: List~KernelData~
+  partial: PartialStateReference
+  state_diff_hints: StateDiffHints
+}
+BaseRollupInputs *-- "m" KernelData : kernelData
+BaseRollupInputs *-- PartialStateReference : partial
+BaseRollupInputs *-- StateDiffHints : state_diff_hints
+BaseRollupInputs *-- ConstantRollupData : constants
+
+class BaseOrMergeRollupPublicInputs {
+    type: Fr
+    height_in_block_tree: Fr
+    aggregation_object: AggregationObject
+    txs_hash: Fr[2]
+    out_hash: Fr[2]
+    constants: ConstantRollupData
+    start: PartialStateReference
+    end: PartialStateReference
+}
+BaseOrMergeRollupPublicInputs *-- ConstantRollupData : constants
+BaseOrMergeRollupPublicInputs *-- PartialStateReference : start
+BaseOrMergeRollupPublicInputs *-- PartialStateReference : end
+```
+
+:::warning TODO  
+Fee structs and contract deployment structs will need to be revised, in line with newer ideas.  
+:::
+
+### Validity Conditions
+
+```python
+def BaseRollupCircuit(
+  state_diff_hints: StateDiffHints,
+  historical_header_membership_witnesses: HeaderMembershipWitness[],
+  kernel_data: KernelData[],
+  partial: PartialStateReference,
+  constants: ConstantRollupData,
+) -> BaseOrMergeRollupPublicInputs:
+
+  tx_hashes = Fr[][2]
+  contracts = Fr[]
+  public_data_tree_root = partial.public_data_tree
+  for i in len(kernel_data):
+    tx_hash, _c, public_data_tree_root = kernel_checks(
+      kernel_data[i], 
+      constants, 
+      public_data_tree_root,
+      historical_header_membership_witnesses[i],
+    )
+    tx_hashes.push(tx_hash)
+    contracts.push_array(_c)
+
+  note_hash_subtree = MerkleTree(
+    [...note_hashes for kernel_data.public_inputs.end.note_hashes in kernel_data]
+  )
+  note_hash_snapshot = merkle_insertion(
+    partial.note_hash_tree.root,
+    note_hash_subtree.root,
+    state_diff_hints.note_hash_subtree_sibling_path,
+    NOTE_HASH_SUBTREE_HEIGHT,
+    NOTE_HASH_TREE_HEIGHT,
+  )
+
+  # We can use the sorted nullifiers to simplify batch-insertion
+  # The sorting can be checked with a permutation 
+  nullifier_snapshot = successor_merkle_batch_insertion(
+    partial.nullifier_tree.root,
+    [...nullifiers for kernel_data.public_inputs.end.nullifiers in kernel_data],
+    state_diff_hints.sorted_nullifiers,
+    state_diff_hints.sorted_nullifier_indexes,
+    state_diff_hints.nullifier_subtree_sibling_path,
+    state_diff.nullifier_predecessor_preimages,
+    state_diff.nullifier_predecessor_membership_witnesses,
+    NULLIFIER_SUBTREE_HEIGHT,
+    NULLIFIER_TREE_HEIGHT,
+  )
+
+  contract_sub_tree = MerkleTree(contracts)
+  contract_snapshot = merkle_insertion(
+    partial.note_hash_tree.root,
+    note_hash_subtree.root,
+    state_diff_hints.contract_subtree_sibling_path,
+    CONTRACTS_SUBTREE_HEIGHT,
+    CONTRACTS_TREE_HEIGHT,
+  )
+
+  txs_hash = SHA256(tx_hashes)
+  out_hash = SHA256(
+    [...l2_to_l1_messages for kernel_data.public_inputs.end.l2_to_l1_messages in kernel_data]
+  )
+
+  return BaseOrMergeRollupPublicInputs(
+    type=0,
+    height_in_block_tree=0,
+    aggregation_object=
+    txs_hash=txs_hash
+    out_hash=out_hash
+    start=partial,
+    end=PartialStateReference(
+      note_hash_tree=note_hash_snapshot,
+      nullifier_tree=nullifier_snapshot,
+      contract_tree=contract_snapshot,
+      public_data_tree=public_data_tree_root,
+    ),
+  )
+
+def kernel_checks(
+  kernel: KernelData, 
+  constants: ConstantRollupData, 
+  public_data_tree_root: Fr,
+  historical_header_membership_witness: HeaderMembershipWitness
+) -> (Fr[2], Fr[], Fr):
+  assert public_data_tree_root == kernel.public_inputs.end.start_public_data_root
+  assert kernel.proof.verify(kernel.public_inputs)
+
+  tx_context = kernel.public_inputs.constants.tx_context
+  assert tx_context.chainid == constants.globalVariables.chainid
+  assert tx_context.version == constants.globalVariables.version
+
+  assert len(kernel.public_inputs.end.private_call_stack) == 0
+  assert len(kernel.public_inputs.end.public_call_stack) == 0
+
+  assert merkle_inclusion(
+    kernel.constants.historical_header.hash(), 
+    kernel.constants.historical_header.global_variables.block_number, 
+    historical_header_membership_witness, 
+    constants.last_archive
+  )
+
+  contracts = []
+  contract_datas = []
+  for preimage in kernel.public_inputs.end.contracts:
+    to_push = preimage.hash() if preimage.address == 0 else 0:
+    contracts.push(to_push)
+    contract_datas.push(ContractData(to_push, preimage.address, preimage.portal))
+
+  tx_hash = SHA256(
+    kernel.public_inputs.end.note_hashes |
+    kernel.public_inputs.end.nullifiers |
+    contract_datas | 
+    kernel.public_inputs.end.public_data_writes |
+    kernel.public_inputs.end.l2_to_l1_messages
+  )
+  return (tx_hash, contracts, kernel.public_inputs.end.end_public_data_root)
+```