Update 0_beacon-chain.md

specs/core/0_beacon-chain.md

@@ -69,7 +69,7 @@
             - [`get_shuffling`](#get_shuffling)
             - [`get_previous_epoch_committee_count_per_slot`](#get_previous_epoch_committee_count_per_slot)
             - [`get_current_epoch_committee_count_per_slot`](#get_current_epoch_committee_count_per_slot)
-            - [`get_shard_committees_at_slot`](#get_shard_committees_at_slot)
+            - [`get_crosslink_committees_at_slot`](#get_crosslink_committees_at_slot)
             - [`get_block_root`](#get_block_root)
             - [`get_randao_mix`](#get_randao_mix)
             - [`get_beacon_proposer_index`](#get_beacon_proposer_index)
@@ -927,10 +927,10 @@ def get_current_epoch_committee_count_per_slot(state: BeaconState) -> int:
     return get_committee_count_per_slot(len(current_active_validators))
 ```
 
-#### `get_shard_committees_at_slot`
+#### `get_crosslink_committees_at_slot`
 
 ```python
-def get_shard_committees_at_slot(state: BeaconState,
+def get_crosslink_committees_at_slot(state: BeaconState,
                                  slot: int) -> List[Tuple[List[int], int]]:
     """
     Returns the list of ``(committee, shard)`` tuples for the ``slot``.
@@ -980,7 +980,7 @@ def get_block_root(state: BeaconState,
     return state.latest_block_roots[slot % LATEST_BLOCK_ROOTS_LENGTH]
 ```
 
-`get_block_root(_, s)` should always return `hash_tree_root` of the block in the beacon chain at slot `s`, and `get_shard_committees_at_slot(_, s)` should not change unless the [validator](#dfn-validator) registry changes.
+`get_block_root(_, s)` should always return `hash_tree_root` of the block in the beacon chain at slot `s`, and `get_crosslink_committees_at_slot(_, s)` should not change unless the [validator](#dfn-validator) registry changes.
 
 #### `get_randao_mix`
 
@@ -1003,7 +1003,7 @@ def get_beacon_proposer_index(state: BeaconState,
     """
     Returns the beacon proposer index for the ``slot``.
     """
-    first_committee, _ = get_shard_committees_at_slot(state, slot)[0]
+    first_committee, _ = get_crosslink_committees_at_slot(state, slot)[0]
     return first_committee[slot % len(first_committee)]
 ```
 
@@ -1031,15 +1031,15 @@ def get_attestation_participants(state: BeaconState,
     """
 
     # Find the committee in the list with the desired shard
-    shard_committees = get_shard_committees_at_slot(state, attestation_data.slot)
+    crosslink_committees = get_crosslink_committees_at_slot(state, attestation_data.slot)
     
-    assert attestation.shard in [shard for _, shard in shard_committees]
-    shard_committee = [committee for committee, shard in shard_committees if shard == attestation_data.shard][0]
+    assert attestation.shard in [shard for _, shard in crosslink_committees]
+    crosslink_committee = [committee for committee, shard in crosslink_committees if shard == attestation_data.shard][0]
     assert len(participation_bitfield) == (len(committee) + 7) // 8
 
     # Find the participating attesters in the committee
     participants = []
-    for i, validator_index in enumerate(shard_committee):
+    for i, validator_index in enumerate(crosslink_committee):
         participation_bit = (participation_bitfield[i//8] >> (7 - (i % 8))) % 2
         if participation_bit == 1:
             participants.append(validator_index)
@@ -1616,14 +1616,14 @@ All [validators](#dfn-validator):
 
 **Note**: `previous_epoch_boundary_attesting_balance` balance might be marginally different than `current_epoch_boundary_attesting_balance` during the previous epoch transition. Due to the tight bound on validator churn each epoch and small per-epoch rewards/penalties, the potential balance difference is very low and only marginally affects consensus safety.
 
-For every `slot in range(state.slot - 2 * EPOCH_LENGTH, state.slot)`, let `shard_committee_at_slot = get_shard_committees_at_slot(slot)`. For every `(shard_committee, shard)` in `shard_committee_at_slot`, compute:
+For every `slot in range(state.slot - 2 * EPOCH_LENGTH, state.slot)`, let `crosslink_committee_at_slot = get_crosslink_committees_at_slot(slot)`. For every `(crosslink_committee, shard)` in `crosslink_committee_at_slot`, compute:
 
 * Let `shard_block_root` be `state.latest_crosslinks[shard].shard_block_root`
-* Let `attesting_validator_indices(shard_committee, shard_block_root)` be the union of the [validator](#dfn-validator) index sets given by `[get_attestation_participants(state, a.data, a.participation_bitfield) for a in current_epoch_attestations + previous_epoch_attestations if a.shard == shard and a.shard_block_root == shard_block_root]`.
-* Let `winning_root(shard_committee)` be equal to the value of `shard_block_root` such that `sum([get_effective_balance(state, i) for i in attesting_validator_indices(shard_committee, shard_block_root)])` is maximized (ties broken by favoring lower `shard_block_root` values).
-* Let `attesting_validators(shard_committee)` be equal to `attesting_validator_indices(shard_committee, winning_root(shard_committee))` for convenience.
-* Let `total_attesting_balance(shard_committee) = sum([get_effective_balance(state, i) for i in attesting_validators(shard_committee)])`.
-* Let `total_balance(shard_committee) = sum([get_effective_balance(state, i) for i in shard_committee])`.
+* Let `attesting_validator_indices(crosslink_committee, shard_block_root)` be the union of the [validator](#dfn-validator) index sets given by `[get_attestation_participants(state, a.data, a.participation_bitfield) for a in current_epoch_attestations + previous_epoch_attestations if a.shard == shard and a.shard_block_root == shard_block_root]`.
+* Let `winning_root(crosslink_committee)` be equal to the value of `shard_block_root` such that `sum([get_effective_balance(state, i) for i in attesting_validator_indices(crosslink_committee, shard_block_root)])` is maximized (ties broken by favoring lower `shard_block_root` values).
+* Let `attesting_validators(crosslink_committee)` be equal to `attesting_validator_indices(crosslink_committee, winning_root(crosslink_committee))` for convenience.
+* Let `total_attesting_balance(crosslink_committee) = sum([get_effective_balance(state, i) for i in attesting_validators(crosslink_committee)])`.
+* Let `total_balance(crosslink_committee) = sum([get_effective_balance(state, i) for i in crosslink_committee])`.
 
 Define the following helpers to process attestation inclusion rewards and inclusion distance reward/penalty. For every attestation `a` in `previous_epoch_attestations`:
 
@@ -1652,9 +1652,9 @@ Set `state.finalized_slot = state.previous_justified_slot` if any of the followi
 
 ### Crosslinks
 
-For every `slot in range(state.slot - 2 * EPOCH_LENGTH, state.slot)`, let `shard_committee_at_slot = get_shard_committees_at_slot(slot)`. For every `(shard_committee, shard)` in `shard_committee_at_slot`, compute:
+For every `slot in range(state.slot - 2 * EPOCH_LENGTH, state.slot)`, let `crosslink_committee_at_slot = get_crosslink_committees_at_slot(slot)`. For every `(crosslink_committee, shard)` in `crosslink_committee_at_slot`, compute:
 
-* Set `state.latest_crosslinks[shard] = CrosslinkRecord(slot=state.slot, shard_block_root=winning_root(shard_committee))` if `3 * total_attesting_balance(shard_committee) >= 2 * total_balance(shard_committee)`.
+* Set `state.latest_crosslinks[shard] = CrosslinkRecord(slot=state.slot, shard_block_root=winning_root(crosslink_committee))` if `3 * total_attesting_balance(crosslink_committee) >= 2 * total_balance(crosslink_committee)`.
 
 ### Rewards and penalties
 
@@ -1698,10 +1698,10 @@ For each `index` in `previous_epoch_attester_indices`, we determine the proposer
 
 #### Crosslinks
 
-For every `i in range(state.slot - 2 * EPOCH_LENGTH, state.slot - EPOCH_LENGTH)`, let `shard_committee_at_slot, start_shard = get_shard_committees_at_slot(i)`. For every `j in range(len(shard_committee_at_slot))`, let `shard_committee = shard_committee_at_slot[j]`, `shard = (start_shard + j) % SHARD_COUNT`, and compute:
+For every `i in range(state.slot - 2 * EPOCH_LENGTH, state.slot - EPOCH_LENGTH)`, let `crosslink_committee_at_slot, start_shard = get_crosslink_committees_at_slot(i)`. For every `j in range(len(crosslink_committee_at_slot))`, let `crosslink_committee = crosslink_committee_at_slot[j]`, `shard = (start_shard + j) % SHARD_COUNT`, and compute:
 
-* If `index in attesting_validators(shard_committee)`, `state.validator_balances[index] += base_reward(state, index) * total_attesting_balance(shard_committee) // total_balance(shard_committee))`.
-* If `index not in attesting_validators(shard_committee)`, `state.validator_balances[index] -= base_reward(state, index)`.
+* If `index in attesting_validators(crosslink_committee)`, `state.validator_balances[index] += base_reward(state, index) * total_attesting_balance(crosslink_committee) // total_balance(crosslink_committee))`.
+* If `index not in attesting_validators(crosslink_committee)`, `state.validator_balances[index] -= base_reward(state, index)`.
 
 ### Ejections