diff --git a/specs/core/1_shard-data-chains.md b/specs/core/1_shard-data-chains.md
index 7cb4bd78b..aed570b80 100644
--- a/specs/core/1_shard-data-chains.md
+++ b/specs/core/1_shard-data-chains.md
@@ -217,7 +217,7 @@ def get_shard_header(block: ShardBlock) -> ShardBlockHeader:
 def verify_shard_attestation_signature(state: BeaconState,
                                        attestation: ShardAttestation) -> None:
     data = attestation.data
-    persistent_committee = get_persistent_committee(state, data.crosslink.shard, data.slot)
+    persistent_committee = get_persistent_committee(state, data.shard, data.slot)
     assert verify_bitfield(attestation.aggregation_bitfield, len(persistent_committee))
     pubkeys = []
     for i, index in enumerate(persistent_committee):
@@ -227,7 +227,7 @@ def verify_shard_attestation_signature(state: BeaconState,
             pubkeys.append(validator.pubkey)
     assert bls_verify(
         pubkey=bls_aggregate_pubkeys(pubkeys),
-        message_hash=data.crosslink.shard_block_root,
+        message_hash=data.shard_block_root,
         signature=attestation.aggregate_signature,
         domain=get_domain(state, slot_to_epoch(data.slot), DOMAIN_SHARD_ATTESTER)
     )
@@ -282,22 +282,22 @@ def is_valid_shard_block(beacon_blocks: List[BeaconBlock],
             return True
 
     # Check slot number
-    assert block.slot >= PHASE_1_GENESIS_SLOT
+    assert candidate.slot >= PHASE_1_GENESIS_SLOT
     assert unix_time >= beacon_state.genesis_time + (block.slot - GENESIS_SLOT) * SECONDS_PER_SLOT
 
     # Check shard number
-    assert block.shard <= SHARD_COUNT
+    assert candidate.shard <= SHARD_COUNT
 
     # Check beacon block
-    beacon_block = beacon_blocks[block.slot]
-    assert block.beacon_block_root == signing_root(beacon_block)
-    assert beacon_block.slot <= block.slot
+    beacon_block = beacon_blocks[candidate.slot]
+    assert candidate.beacon_block_root == signing_root(beacon_block)
+    assert beacon_block.slot <= candidate.slot:
 
     # Check state root
-    assert block.state_root == ZERO_HASH  # [to be removed in phase 2]
+    assert candidate.state_root == ZERO_HASH  # [to be removed in phase 2]
 
     # Check parent block
-    if block.slot == PHASE_1_GENESIS_SLOT:
+    if candidate.slot == PHASE_1_GENESIS_SLOT:
         assert candidate.parent_root == ZERO_HASH
     else:
         parent_block = next(
@@ -305,26 +305,26 @@ def is_valid_shard_block(beacon_blocks: List[BeaconBlock],
             signing_root(block) == candidate.parent_root)
         , None)
         assert parent_block != None
-        assert parent_block.shard == block.shard
-        assert parent_block.slot < block.slot
+        assert parent_block.shard == candidate.shard
+        assert parent_block.slot < candidate.slot
         assert signing_root(beacon_blocks[parent_block.slot]) == parent_block.beacon_chain_root
 
     # Check attestations
-    assert len(block.attestations) <= MAX_SHARD_ATTESTIONS
-    for _, attestation in enumerate(block.attestations):
-        assert max(GENESIS_SHARD_SLOT, block.slot - SLOTS_PER_EPOCH) <= attestation.data.slot
-        assert attestation.data.slot <= block.slot - MIN_ATTESTATION_INCLUSION_DELAY
-        assert attestation.data.crosslink.shard == block.shard
+    assert len(candidate.attestations) <= MAX_SHARD_ATTESTIONS
+    for _, attestation in enumerate(candidate.attestations):
+        assert max(GENESIS_SHARD_SLOT, candidate.slot - SLOTS_PER_EPOCH) <= attestation.data.slot
+        assert attestation.data.slot <= candidate.slot - MIN_ATTESTATION_INCLUSION_DELAY
+        assert attestation.data.crosslink.shard == candidate.shard
         verify_shard_attestation_signature(beacon_state, attestation)
 
     # Check signature
-    proposer_index = get_shard_proposer_index(beacon_state, block.shard, block.slot)
+    proposer_index = get_shard_proposer_index(beacon_state, candidate.shard, candidate.slot)
     assert proposer_index is not None
     assert bls_verify(
         pubkey=validators[proposer_index].pubkey,
         message_hash=signing_root(block),
-        signature=block.signature,
-        domain=get_domain(beacon_state, slot_to_epoch(block.slot), DOMAIN_SHARD_PROPOSER)
+        signature=candidate.signature,
+        domain=get_domain(beacon_state, slot_to_epoch(candidate.slot), DOMAIN_SHARD_PROPOSER)
     )
 
     return True
@@ -341,18 +341,18 @@ Let:
 ```python
 def is_valid_shard_attestation(valid_shard_blocks: List[ShardBlock],
                                beacon_state: BeaconState,
-                               candidate: Attestation) -> bool:
+                               candidate: ShardAttestation) -> bool:
     # Check shard block
     shard_block = next(
-        (block for block in valid_shard_blocks if
-        signing_root(block) == candidate.attestation.data.crosslink.shard_block_root)
+        block for block in valid_shard_blocks if
+        signing_root(block) == candidate.data.shard_block_root
     , None)
     assert shard_block != None
-    assert shard_block.slot == attestation.data.slot
-    assert shard_block.shard == attestation.data.crosslink.shard
+    assert shard_block.slot == candidate.data.slot
+    assert shard_block.shard == candidate.data.shard
 
     # Check signature
-    verify_shard_attestation_signature(beacon_state, attestation)
+    verify_shard_attestation_signature(beacon_state, candidate)
 
     return True
 ```