From 9fc197af672fd2a237d80efa987f5e840341091f Mon Sep 17 00:00:00 2001
From: Hsiao-Wei Wang <hwwang156@gmail.com>
Date: Mon, 10 Jun 2019 11:10:13 -0400
Subject: [PATCH 01/21] class Bytes32

---
 scripts/build_spec.py                            |  7 ++++---
 .../pyspec/eth2spec/utils/ssz/ssz_typing.py      | 16 ++++++++++++++++
 2 files changed, 20 insertions(+), 3 deletions(-)

diff --git a/scripts/build_spec.py b/scripts/build_spec.py
index 7a51970e38..087a88f983 100644
--- a/scripts/build_spec.py
+++ b/scripts/build_spec.py
@@ -25,7 +25,8 @@
 )
 from eth2spec.utils.ssz.ssz_typing import (
     # unused: uint8, uint16, uint32, uint128, uint256,
-    uint64, Container, Vector, BytesN
+    uint64, Container, Vector,
+    Bytes4, Bytes32, Bytes48, Bytes96,
 )
 from eth2spec.utils.bls import (
     bls_aggregate_pubkeys,
@@ -52,7 +53,8 @@
 )
 from eth2spec.utils.ssz.ssz_typing import (
     # unused: uint8, uint16, uint32, uint128, uint256,
-    uint64, Container, Vector, BytesN
+    uint64, Container, Vector,
+    Bytes4, Bytes32, Bytes48, Bytes96,
 )
 from eth2spec.utils.bls import (
     bls_aggregate_pubkeys,
@@ -132,7 +134,6 @@ def objects_to_spec(functions: Dict[str, str],
     """
     new_type_definitions = \
         '\n'.join(['''%s = NewType('%s', %s)''' % (key, key, value) for key, value in new_types.items()])
-    new_type_definitions += '\n' + '\n'.join(['Bytes%s = BytesN[%s]' % (n, n) for n in byte_types])
     functions_spec = '\n\n'.join(functions.values())
     constants_spec = '\n'.join(map(lambda x: '%s = %s' % (x, constants[x]), constants))
     ssz_objects_instantiation_spec = '\n\n'.join(ssz_objects.values())
diff --git a/test_libs/pyspec/eth2spec/utils/ssz/ssz_typing.py b/test_libs/pyspec/eth2spec/utils/ssz/ssz_typing.py
index 368041f90a..e40c904cad 100644
--- a/test_libs/pyspec/eth2spec/utils/ssz/ssz_typing.py
+++ b/test_libs/pyspec/eth2spec/utils/ssz/ssz_typing.py
@@ -390,6 +390,22 @@ def hash_tree_root(self):
         return hash_tree_root(self, self.__class__)
 
 
+class Bytes4(BytesN):
+    length = 4
+
+
+class Bytes32(BytesN):
+    length = 32
+
+
+class Bytes48(BytesN):
+    length = 48
+
+
+class Bytes96(BytesN):
+    length = 96
+
+
 # SSZ Defaults
 # -----------------------------
 def get_zero_value(typ):

From 8b64f37d225bf0d5971735bd8088418dd68b096c Mon Sep 17 00:00:00 2001
From: Hsiao-Wei Wang <hwwang156@gmail.com>
Date: Mon, 10 Jun 2019 23:16:59 -0400
Subject: [PATCH 02/21] Make uint64 be `class` for type hinting

---
 scripts/build_spec.py                         | 36 +++++++++++--------
 .../pyspec/eth2spec/utils/ssz/ssz_typing.py   | 21 ++++++-----
 2 files changed, 34 insertions(+), 23 deletions(-)

diff --git a/scripts/build_spec.py b/scripts/build_spec.py
index 087a88f983..0ede5f1d98 100644
--- a/scripts/build_spec.py
+++ b/scripts/build_spec.py
@@ -15,7 +15,6 @@
     Any,
     Dict,
     List,
-    NewType,
     Tuple,
 )
 
@@ -41,7 +40,6 @@
     Any,
     Dict,
     List,
-    NewType,
     Tuple,
 )
 
@@ -65,11 +63,11 @@
 from eth2spec.utils.hash_function import hash
 '''
 NEW_TYPES = {
-    'Slot': 'int',
-    'Epoch': 'int',
-    'Shard': 'int',
-    'ValidatorIndex': 'int',
-    'Gwei': 'int',
+    'Slot': 'uint64',
+    'Epoch': 'uint64',
+    'Shard': 'uint64',
+    'ValidatorIndex': 'uint64',
+    'Gwei': 'uint64',
 }
 BYTE_TYPES = [4, 32, 48, 96]
 SUNDRY_FUNCTIONS = '''
@@ -79,7 +77,7 @@ def get_ssz_type_by_name(name: str) -> Container:
 
 # Monkey patch validator compute committee code
 _compute_committee = compute_committee
-committee_cache = {}
+committee_cache = {}  # type: Dict[Tuple[Bytes32, Bytes32, ValidatorIndex, int], List[ValidatorIndex]]
 
 
 def compute_committee(indices: List[ValidatorIndex], seed: Bytes32, index: int, count: int) -> List[ValidatorIndex]:
@@ -95,10 +93,10 @@ def compute_committee(indices: List[ValidatorIndex], seed: Bytes32, index: int,
 
 # Monkey patch hash cache
 _hash = hash
-hash_cache = {}
+hash_cache: Dict[bytes, Bytes32] = {}
 
 
-def hash(x):
+def hash(x: bytes) -> Bytes32:
     if x in hash_cache:
         return hash_cache[x]
     else:
@@ -108,7 +106,7 @@ def hash(x):
 
 
 # Access to overwrite spec constants based on configuration
-def apply_constants_preset(preset: Dict[str, Any]):
+def apply_constants_preset(preset: Dict[str, Any]) -> None:
     global_vars = globals()
     for k, v in preset.items():
         global_vars[k] = v
@@ -132,20 +130,28 @@ def objects_to_spec(functions: Dict[str, str],
     """
     Given all the objects that constitute a spec, combine them into a single pyfile.
     """
-    new_type_definitions = \
-        '\n'.join(['''%s = NewType('%s', %s)''' % (key, key, value) for key, value in new_types.items()])
+    new_type_definitions = (
+        '\n\n'.join(
+            [
+                f"class {key}({value}):\n"
+                f"    def __init__(self, _x: uint64) -> None:\n"
+                f"        ...\n"
+                for key, value in new_types.items()
+            ]
+        )
+    )
     functions_spec = '\n\n'.join(functions.values())
     constants_spec = '\n'.join(map(lambda x: '%s = %s' % (x, constants[x]), constants))
     ssz_objects_instantiation_spec = '\n\n'.join(ssz_objects.values())
     ssz_objects_reinitialization_spec = (
-        'def init_SSZ_types():\n    global_vars = globals()\n\n    '
+        'def init_SSZ_types() -> None:\n    global_vars = globals()\n\n    '
         + '\n\n    '.join([re.sub(r'(?!\n\n)\n', r'\n    ', value[:-1]) for value in ssz_objects.values()])
         + '\n\n'
         + '\n'.join(map(lambda x: '    global_vars[\'%s\'] = %s' % (x, x), ssz_objects.keys()))
     )
     spec = (
         imports
-        + '\n' + new_type_definitions
+        + '\n\n' + new_type_definitions
         + '\n\n' + constants_spec
         + '\n\n\n' + ssz_objects_instantiation_spec
         + '\n\n' + functions_spec
diff --git a/test_libs/pyspec/eth2spec/utils/ssz/ssz_typing.py b/test_libs/pyspec/eth2spec/utils/ssz/ssz_typing.py
index e40c904cad..cde1586c14 100644
--- a/test_libs/pyspec/eth2spec/utils/ssz/ssz_typing.py
+++ b/test_libs/pyspec/eth2spec/utils/ssz/ssz_typing.py
@@ -46,8 +46,13 @@ def __new__(cls, value, *args, **kwargs):
         return super().__new__(cls, value)
 
 
-# We simply default to uint64. But do give it a name, for readability
-uint64 = NewType('uint64', int)
+class uint64(uint):
+    byte_len = 8
+
+    def __new__(cls, value, *args, **kwargs):
+        if value.bit_length() > 64:
+            raise ValueError("value out of bounds for uint128")
+        return super().__new__(cls, value)
 
 
 class uint128(uint):
@@ -409,12 +414,12 @@ class Bytes96(BytesN):
 # SSZ Defaults
 # -----------------------------
 def get_zero_value(typ):
-    if is_uint_type(typ):
-        return 0
-    elif is_list_type(typ):
+    if is_list_type(typ):
         return []
     elif is_bool_type(typ):
         return False
+    elif is_uint_type(typ):
+        return uint64(0)
     elif is_vector_type(typ):
         return typ()
     elif is_bytesn_type(typ):
@@ -432,12 +437,12 @@ def get_zero_value(typ):
 
 
 def infer_type(obj):
-    if is_uint_type(obj.__class__):
-        return obj.__class__
-    elif isinstance(obj, int):
+    if isinstance(obj, int):
         return uint64
     elif isinstance(obj, list):
         return List[infer_type(obj[0])]
+    elif is_uint_type(obj.__class__):
+        return obj.__class__
     elif isinstance(obj, (Vector, Container, bool, BytesN, bytes)):
         return obj.__class__
     else:

From 9f454185f8448772a9cea4bc19a71f7b3808c7f2 Mon Sep 17 00:00:00 2001
From: Hsiao-Wei Wang <hwwang156@gmail.com>
Date: Tue, 11 Jun 2019 00:15:52 -0400
Subject: [PATCH 03/21] WIP!

1. Use custom types in SSZ declaration
2. Casting
---
 scripts/build_spec.py                         |   9 +-
 specs/core/0_beacon-chain.md                  | 172 +++++++++---------
 .../pyspec/eth2spec/utils/ssz/ssz_typing.py   |   2 +-
 3 files changed, 95 insertions(+), 88 deletions(-)

diff --git a/scripts/build_spec.py b/scripts/build_spec.py
index 0ede5f1d98..f396d3b9c5 100644
--- a/scripts/build_spec.py
+++ b/scripts/build_spec.py
@@ -15,6 +15,7 @@
     Any,
     Dict,
     List,
+    Set,
     Tuple,
 )
 
@@ -40,6 +41,7 @@
     Any,
     Dict,
     List,
+    Set,
     Tuple,
 )
 
@@ -77,10 +79,13 @@ def get_ssz_type_by_name(name: str) -> Container:
 
 # Monkey patch validator compute committee code
 _compute_committee = compute_committee
-committee_cache = {}  # type: Dict[Tuple[Bytes32, Bytes32, ValidatorIndex, int], List[ValidatorIndex]]
+committee_cache: Dict[Tuple[Bytes32, Bytes32, int, int], List[ValidatorIndex]] = {}
 
 
-def compute_committee(indices: List[ValidatorIndex], seed: Bytes32, index: int, count: int) -> List[ValidatorIndex]:
+def compute_committee(indices: List[ValidatorIndex],  # type: ignore
+                      seed: Bytes32,
+                      index: int,
+                      count: int) -> List[ValidatorIndex]:
     param_hash = (hash_tree_root(indices), seed, index, count)
 
     if param_hash in committee_cache:
diff --git a/specs/core/0_beacon-chain.md b/specs/core/0_beacon-chain.md
index a6d9d23c58..a6bfd5e1ac 100644
--- a/specs/core/0_beacon-chain.md
+++ b/specs/core/0_beacon-chain.md
@@ -180,18 +180,18 @@ These configurations are updated for releases, but may be out of sync during `de
 
 | Name | Value | Unit |
 | - | - | :-: |
-| `MIN_DEPOSIT_AMOUNT` | `2**0 * 10**9` (= 1,000,000,000) | Gwei |
-| `MAX_EFFECTIVE_BALANCE` | `2**5 * 10**9` (= 32,000,000,000) | Gwei |
-| `EJECTION_BALANCE` | `2**4 * 10**9` (= 16,000,000,000) | Gwei |
-| `EFFECTIVE_BALANCE_INCREMENT` | `2**0 * 10**9` (= 1,000,000,000) | Gwei |
+| `MIN_DEPOSIT_AMOUNT` | `Gwei(2**0 * 10**9)` (= 1,000,000,000) | Gwei |
+| `MAX_EFFECTIVE_BALANCE` | `Gwei(2**5 * 10**9)` (= 32,000,000,000) | Gwei |
+| `EJECTION_BALANCE` | `Gwei(2**4 * 10**9)` (= 16,000,000,000) | Gwei |
+| `EFFECTIVE_BALANCE_INCREMENT` | `Gwei(2**0 * 10**9)` (= 1,000,000,000) | Gwei |
 
 ### Initial values
 
 | Name | Value |
 | - | - |
-| `GENESIS_SLOT` | `0` |
-| `GENESIS_EPOCH` | `0` |
-| `FAR_FUTURE_EPOCH` | `2**64 - 1` |
+| `GENESIS_SLOT` | `Slot(0)` |
+| `GENESIS_EPOCH` | `Epoch(0)` |
+| `FAR_FUTURE_EPOCH` | `Epoch(2**64 - 1)` |
 | `ZERO_HASH` | `b'\x00' * 32` |
 | `BLS_WITHDRAWAL_PREFIX` | `0` |
 
@@ -272,7 +272,7 @@ class Fork(Container):
     # Current fork version
     current_version: Bytes4
     # Fork epoch number
-    epoch: uint64
+    epoch: Epoch
 ```
 
 #### `Validator`
@@ -284,17 +284,17 @@ class Validator(Container):
     # Withdrawal credentials
     withdrawal_credentials: Bytes32
     # Epoch when became eligible for activation
-    activation_eligibility_epoch: uint64
+    activation_eligibility_epoch: Epoch
     # Epoch when validator activated
-    activation_epoch: uint64
+    activation_epoch: Epoch
     # Epoch when validator exited
-    exit_epoch: uint64
+    exit_epoch: Epoch
     # Epoch when validator is eligible to withdraw
-    withdrawable_epoch: uint64
+    withdrawable_epoch: Epoch
     # Was the validator slashed
     slashed: bool
     # Effective balance
-    effective_balance: uint64
+    effective_balance: Gwei
 ```
 
 #### `Crosslink`
@@ -302,10 +302,10 @@ class Validator(Container):
 ```python
 class Crosslink(Container):
     # Shard number
-    shard: uint64
+    shard: Shard
     # Crosslinking data from epochs [start....end-1]
-    start_epoch: uint64
-    end_epoch: uint64
+    start_epoch: Epoch
+    end_epoch: Epoch
     # Root of the previous crosslink
     parent_root: Bytes32
     # Root of the crosslinked shard data since the previous crosslink
@@ -320,9 +320,9 @@ class AttestationData(Container):
     beacon_block_root: Bytes32
 
     # FFG vote
-    source_epoch: uint64
+    source_epoch: Epoch
     source_root: Bytes32
-    target_epoch: uint64
+    target_epoch: Epoch
     target_root: Bytes32
 
     # Crosslink vote
@@ -344,8 +344,8 @@ class AttestationDataAndCustodyBit(Container):
 ```python
 class IndexedAttestation(Container):
     # Validator indices
-    custody_bit_0_indices: List[uint64]
-    custody_bit_1_indices: List[uint64]
+    custody_bit_0_indices: List[ValidatorIndex]
+    custody_bit_1_indices: List[ValidatorIndex]
     # Attestation data
     data: AttestationData
     # Aggregate signature
@@ -363,7 +363,7 @@ class PendingAttestation(Container):
     # Inclusion delay
     inclusion_delay: uint64
     # Proposer index
-    proposer_index: uint64
+    proposer_index: ValidatorIndex
 ```
 
 #### `Eth1Data`
@@ -397,7 +397,7 @@ class DepositData(Container):
     # Withdrawal credentials
     withdrawal_credentials: Bytes32
     # Amount in Gwei
-    amount: uint64
+    amount: Gwei
     # Container self-signature
     signature: Bytes96
 ```
@@ -406,7 +406,7 @@ class DepositData(Container):
 
 ```python
 class BeaconBlockHeader(Container):
-    slot: uint64
+    slot: Slot
     parent_root: Bytes32
     state_root: Bytes32
     body_root: Bytes32
@@ -420,7 +420,7 @@ class BeaconBlockHeader(Container):
 ```python
 class ProposerSlashing(Container):
     # Proposer index
-    proposer_index: uint64
+    proposer_index: ValidatorIndex
     # First block header
     header_1: BeaconBlockHeader
     # Second block header
@@ -466,9 +466,9 @@ class Deposit(Container):
 ```python
 class VoluntaryExit(Container):
     # Minimum epoch for processing exit
-    epoch: uint64
+    epoch: Epoch
     # Index of the exiting validator
-    validator_index: uint64
+    validator_index: ValidatorIndex
     # Validator signature
     signature: Bytes96
 ```
@@ -478,15 +478,15 @@ class VoluntaryExit(Container):
 ```python
 class Transfer(Container):
     # Sender index
-    sender: uint64
+    sender: ValidatorIndex
     # Recipient index
-    recipient: uint64
+    recipient: ValidatorIndex
     # Amount in Gwei
-    amount: uint64
+    amount: Gwei
     # Fee in Gwei for block proposer
-    fee: uint64
+    fee: Gwei
     # Inclusion slot
-    slot: uint64
+    slot: Slot
     # Sender withdrawal pubkey
     pubkey: Bytes48
     # Sender signature
@@ -515,7 +515,7 @@ class BeaconBlockBody(Container):
 ```python
 class BeaconBlock(Container):
     # Header
-    slot: uint64
+    slot: Slot
     parent_root: Bytes32
     state_root: Bytes32
     body: BeaconBlockBody
@@ -529,24 +529,24 @@ class BeaconBlock(Container):
 ```python
 class BeaconState(Container):
     # Misc
-    slot: uint64
+    slot: Slot
     genesis_time: uint64
     fork: Fork  # For versioning hard forks
     # Validator registry
     validator_registry: List[Validator]
-    balances: List[uint64]
+    balances: List[Gwei]
     # Randomness and committees
     latest_randao_mixes: Vector[Bytes32, LATEST_RANDAO_MIXES_LENGTH]
-    latest_start_shard: uint64
+    latest_start_shard: Shard
     # Finality
     previous_epoch_attestations: List[PendingAttestation]
     current_epoch_attestations: List[PendingAttestation]
-    previous_justified_epoch: uint64
-    current_justified_epoch: uint64
+    previous_justified_epoch: Epoch
+    current_justified_epoch: Epoch
     previous_justified_root: Bytes32
     current_justified_root: Bytes32
     justification_bitfield: uint64
-    finalized_epoch: uint64
+    finalized_epoch: Epoch
     finalized_root: Bytes32
     # Recent state
     current_crosslinks: Vector[Crosslink, SHARD_COUNT]
@@ -554,7 +554,7 @@ class BeaconState(Container):
     latest_block_roots: Vector[Bytes32, SLOTS_PER_HISTORICAL_ROOT]
     latest_state_roots: Vector[Bytes32, SLOTS_PER_HISTORICAL_ROOT]
     latest_active_index_roots: Vector[Bytes32, LATEST_ACTIVE_INDEX_ROOTS_LENGTH]
-    latest_slashed_balances: Vector[uint64, LATEST_SLASHED_EXIT_LENGTH]
+    latest_slashed_balances: Vector[Gwei, LATEST_SLASHED_EXIT_LENGTH]
     latest_block_header: BeaconBlockHeader
     historical_roots: List[Bytes32]
     # Ethereum 1.0 chain data
@@ -619,7 +619,7 @@ def slot_to_epoch(slot: Slot) -> Epoch:
     """
     Return the epoch number of the given ``slot``.
     """
-    return slot // SLOTS_PER_EPOCH
+    return Epoch(slot // SLOTS_PER_EPOCH)
 ```
 
 ### `get_previous_epoch`
@@ -631,7 +631,7 @@ def get_previous_epoch(state: BeaconState) -> Epoch:
     Return the current epoch if it's genesis epoch.
     """
     current_epoch = get_current_epoch(state)
-    return GENESIS_EPOCH if current_epoch == GENESIS_EPOCH else current_epoch - 1
+    return GENESIS_EPOCH if current_epoch == GENESIS_EPOCH else Epoch(current_epoch - 1)
 ```
 
 ### `get_current_epoch`
@@ -651,7 +651,7 @@ def get_epoch_start_slot(epoch: Epoch) -> Slot:
     """
     Return the starting slot of the given ``epoch``.
     """
-    return epoch * SLOTS_PER_EPOCH
+    return Slot(epoch * SLOTS_PER_EPOCH)
 ```
 
 ### `is_active_validator`
@@ -681,7 +681,7 @@ def get_active_validator_indices(state: BeaconState, epoch: Epoch) -> List[Valid
     """
     Get active validator indices at ``epoch``.
     """
-    return [i for i, v in enumerate(state.validator_registry) if is_active_validator(v, epoch)]
+    return [ValidatorIndex(i) for i, v in enumerate(state.validator_registry) if is_active_validator(v, epoch)]
 ```
 
 ### `increase_balance`
@@ -737,10 +737,10 @@ def get_shard_delta(state: BeaconState, epoch: Epoch) -> int:
 def get_epoch_start_shard(state: BeaconState, epoch: Epoch) -> Shard:
     assert epoch <= get_current_epoch(state) + 1
     check_epoch = get_current_epoch(state) + 1
-    shard = (state.latest_start_shard + get_shard_delta(state, get_current_epoch(state))) % SHARD_COUNT
+    shard = Shard((state.latest_start_shard + get_shard_delta(state, get_current_epoch(state))) % SHARD_COUNT)
     while check_epoch > epoch:
         check_epoch -= 1
-        shard = (shard + SHARD_COUNT - get_shard_delta(state, check_epoch)) % SHARD_COUNT
+        shard = Shard((shard + SHARD_COUNT - get_shard_delta(state, Epoch(check_epoch))) % SHARD_COUNT)
     return shard
 ```
 
@@ -750,7 +750,7 @@ def get_epoch_start_shard(state: BeaconState, epoch: Epoch) -> Shard:
 def get_attestation_data_slot(state: BeaconState, data: AttestationData) -> Slot:
     committee_count = get_epoch_committee_count(state, data.target_epoch)
     offset = (data.crosslink.shard + SHARD_COUNT - get_epoch_start_shard(state, data.target_epoch)) % SHARD_COUNT
-    return get_epoch_start_slot(data.target_epoch) + offset // (committee_count // SLOTS_PER_EPOCH)
+    return Slot(get_epoch_start_slot(data.target_epoch) + offset // (committee_count // SLOTS_PER_EPOCH))
 ```
 
 ### `get_block_root_at_slot`
@@ -810,7 +810,7 @@ def generate_seed(state: BeaconState,
     Generate a seed for the given ``epoch``.
     """
     return hash(
-        get_randao_mix(state, epoch + LATEST_RANDAO_MIXES_LENGTH - MIN_SEED_LOOKAHEAD) +
+        get_randao_mix(state, Epoch(epoch + LATEST_RANDAO_MIXES_LENGTH - MIN_SEED_LOOKAHEAD)) +
         get_active_index_root(state, epoch) +
         int_to_bytes(epoch, length=32)
     )
@@ -826,7 +826,7 @@ def get_beacon_proposer_index(state: BeaconState) -> ValidatorIndex:
     epoch = get_current_epoch(state)
     committees_per_slot = get_epoch_committee_count(state, epoch) // SLOTS_PER_EPOCH
     offset = committees_per_slot * (state.slot % SLOTS_PER_EPOCH)
-    shard = (get_epoch_start_shard(state, epoch) + offset) % SHARD_COUNT
+    shard = Shard((get_epoch_start_shard(state, epoch) + offset) % SHARD_COUNT)
     first_committee = get_crosslink_committee(state, epoch, shard)
     MAX_RANDOM_BYTE = 2**8 - 1
     seed = generate_seed(state, epoch)
@@ -836,7 +836,7 @@ def get_beacon_proposer_index(state: BeaconState) -> ValidatorIndex:
         random_byte = hash(seed + int_to_bytes(i // 32, length=8))[i % 32]
         effective_balance = state.validator_registry[candidate_index].effective_balance
         if effective_balance * MAX_RANDOM_BYTE >= MAX_EFFECTIVE_BALANCE * random_byte:
-            return candidate_index
+            return ValidatorIndex(candidate_index)
         i += 1
 ```
 
@@ -860,7 +860,7 @@ def verify_merkle_branch(leaf: Bytes32, proof: List[Bytes32], depth: int, index:
 ### `get_shuffled_index`
 
 ```python
-def get_shuffled_index(index: ValidatorIndex, index_count: int, seed: Bytes32) -> ValidatorIndex:
+def get_shuffled_index(index: int, index_count: int, seed: Bytes32) -> ValidatorIndex:
     """
     Return the shuffled validator index corresponding to ``seed`` (and ``index_count``).
     """
@@ -869,16 +869,16 @@ def get_shuffled_index(index: ValidatorIndex, index_count: int, seed: Bytes32) -
 
     # Swap or not (https://link.springer.com/content/pdf/10.1007%2F978-3-642-32009-5_1.pdf)
     # See the 'generalized domain' algorithm on page 3
-    for round in range(SHUFFLE_ROUND_COUNT):
-        pivot = bytes_to_int(hash(seed + int_to_bytes(round, length=1))[0:8]) % index_count
+    for current_round in range(SHUFFLE_ROUND_COUNT):
+        pivot = bytes_to_int(hash(seed + int_to_bytes(current_round, length=1))[0:8]) % index_count
         flip = (pivot + index_count - index) % index_count
         position = max(index, flip)
-        source = hash(seed + int_to_bytes(round, length=1) + int_to_bytes(position // 256, length=4))
+        source = hash(seed + int_to_bytes(current_round, length=1) + int_to_bytes(position // 256, length=4))
         byte = source[(position % 256) // 8]
         bit = (byte >> (position % 8)) % 2
         index = flip if bit else index
 
-    return index
+    return ValidatorIndex(index)
 ```
 
 ### `compute_committee`
@@ -887,7 +887,7 @@ def get_shuffled_index(index: ValidatorIndex, index_count: int, seed: Bytes32) -
 def compute_committee(indices: List[ValidatorIndex], seed: Bytes32, index: int, count: int) -> List[ValidatorIndex]:
     start = (len(indices) * index) // count
     end = (len(indices) * (index + 1)) // count
-    return [indices[get_shuffled_index(i, len(indices), seed)] for i in range(start, end)]
+    return [indices[get_shuffled_index(ValidatorIndex(i), len(indices), seed)] for i in range(start, end)]
 ```
 
 ### `get_crosslink_committee`
@@ -937,7 +937,7 @@ def get_total_balance(state: BeaconState, indices: List[ValidatorIndex]) -> Gwei
     """
     Return the combined effective balance of the ``indices``. (1 Gwei minimum to avoid divisions by zero.)
     """
-    return max(sum([state.validator_registry[index].effective_balance for index in indices]), 1)
+    return Gwei(max(sum([state.validator_registry[index].effective_balance for index in indices]), 1))
 ```
 
 ### `get_domain`
@@ -945,7 +945,7 @@ def get_total_balance(state: BeaconState, indices: List[ValidatorIndex]) -> Gwei
 ```python
 def get_domain(state: BeaconState,
                domain_type: int,
-               message_epoch: int=None) -> int:
+               message_epoch: Epoch=None) -> int:
     """
     Return the signature domain (fork version concatenated with domain type) of a message.
     """
@@ -1072,7 +1072,7 @@ def get_delayed_activation_exit_epoch(epoch: Epoch) -> Epoch:
     """
     Return the epoch at which an activation or exit triggered in ``epoch`` takes effect.
     """
-    return epoch + 1 + ACTIVATION_EXIT_DELAY
+    return Epoch(epoch + 1 + ACTIVATION_EXIT_DELAY)
 ```
 
 ### `get_churn_limit`
@@ -1121,11 +1121,11 @@ def initiate_validator_exit(state: BeaconState, index: ValidatorIndex) -> None:
     exit_queue_epoch = max(exit_epochs + [get_delayed_activation_exit_epoch(get_current_epoch(state))])
     exit_queue_churn = len([v for v in state.validator_registry if v.exit_epoch == exit_queue_epoch])
     if exit_queue_churn >= get_churn_limit(state):
-        exit_queue_epoch += 1
+        exit_queue_epoch += Epoch(1)
 
     # Set validator exit epoch and withdrawable epoch
     validator.exit_epoch = exit_queue_epoch
-    validator.withdrawable_epoch = validator.exit_epoch + MIN_VALIDATOR_WITHDRAWABILITY_DELAY
+    validator.withdrawable_epoch = Epoch(validator.exit_epoch + MIN_VALIDATOR_WITHDRAWABILITY_DELAY)
 ```
 
 #### `slash_validator`
@@ -1140,15 +1140,15 @@ def slash_validator(state: BeaconState,
     current_epoch = get_current_epoch(state)
     initiate_validator_exit(state, slashed_index)
     state.validator_registry[slashed_index].slashed = True
-    state.validator_registry[slashed_index].withdrawable_epoch = current_epoch + LATEST_SLASHED_EXIT_LENGTH
+    state.validator_registry[slashed_index].withdrawable_epoch = Epoch(current_epoch + LATEST_SLASHED_EXIT_LENGTH)
     slashed_balance = state.validator_registry[slashed_index].effective_balance
     state.latest_slashed_balances[current_epoch % LATEST_SLASHED_EXIT_LENGTH] += slashed_balance
 
     proposer_index = get_beacon_proposer_index(state)
     if whistleblower_index is None:
         whistleblower_index = proposer_index
-    whistleblowing_reward = slashed_balance // WHISTLEBLOWING_REWARD_QUOTIENT
-    proposer_reward = whistleblowing_reward // PROPOSER_REWARD_QUOTIENT
+    whistleblowing_reward = Gwei(slashed_balance // WHISTLEBLOWING_REWARD_QUOTIENT)
+    proposer_reward = Gwei(whistleblowing_reward // PROPOSER_REWARD_QUOTIENT)
     increase_balance(state, proposer_index, proposer_reward)
     increase_balance(state, whistleblower_index, whistleblowing_reward - proposer_reward)
     decrease_balance(state, slashed_index, whistleblowing_reward)
@@ -1226,7 +1226,7 @@ def process_slots(state: BeaconState, slot: Slot) -> None:
         # Process epoch on the first slot of the next epoch
         if (state.slot + 1) % SLOTS_PER_EPOCH == 0:
             process_epoch(state)
-        state.slot += 1
+        state.slot += Slot(1)
 ```
 
 ```python
@@ -1293,7 +1293,7 @@ def get_matching_head_attestations(state: BeaconState, epoch: Epoch) -> List[Pen
 ```python
 def get_unslashed_attesting_indices(state: BeaconState,
                                     attestations: List[PendingAttestation]) -> List[ValidatorIndex]:
-    output = set()
+    output = set()  # type: Set[ValidatorIndex]
     for a in attestations:
         output = output.union(get_attesting_indices(state, a.data, a.aggregation_bitfield))
     return sorted(filter(lambda index: not state.validator_registry[index].slashed, list(output)))
@@ -1379,7 +1379,7 @@ def process_crosslinks(state: BeaconState) -> None:
     state.previous_crosslinks = [c for c in state.current_crosslinks]
     for epoch in (get_previous_epoch(state), get_current_epoch(state)):
         for offset in range(get_epoch_committee_count(state, epoch)):
-            shard = (get_epoch_start_shard(state, epoch) + offset) % SHARD_COUNT
+            shard = Shard((get_epoch_start_shard(state, epoch) + offset) % SHARD_COUNT)
             crosslink_committee = get_crosslink_committee(state, epoch, shard)
             winning_crosslink, attesting_indices = get_winning_crosslink_and_attesting_indices(state, epoch, shard)
             if 3 * get_total_balance(state, attesting_indices) >= 2 * get_total_balance(state, crosslink_committee):
@@ -1392,17 +1392,17 @@ def process_crosslinks(state: BeaconState) -> None:
 def get_base_reward(state: BeaconState, index: ValidatorIndex) -> Gwei:
     total_balance = get_total_active_balance(state)
     effective_balance = state.validator_registry[index].effective_balance
-    return effective_balance * BASE_REWARD_FACTOR // integer_squareroot(total_balance) // BASE_REWARDS_PER_EPOCH
+    return Gwei(effective_balance * BASE_REWARD_FACTOR // integer_squareroot(total_balance) // BASE_REWARDS_PER_EPOCH)
 ```
 
 ```python
 def get_attestation_deltas(state: BeaconState) -> Tuple[List[Gwei], List[Gwei]]:
     previous_epoch = get_previous_epoch(state)
     total_balance = get_total_active_balance(state)
-    rewards = [0 for _ in range(len(state.validator_registry))]
-    penalties = [0 for _ in range(len(state.validator_registry))]
+    rewards = [Gwei(0) for index in range(len(state.validator_registry))]
+    penalties = [Gwei(0) for index in range(len(state.validator_registry))]
     eligible_validator_indices = [
-        index for index, v in enumerate(state.validator_registry)
+        ValidatorIndex(index) for index, v in enumerate(state.validator_registry)
         if is_active_validator(v, previous_epoch) or (v.slashed and previous_epoch + 1 < v.withdrawable_epoch)
     ]
 
@@ -1421,21 +1421,23 @@ def get_attestation_deltas(state: BeaconState) -> Tuple[List[Gwei], List[Gwei]]:
 
     # Proposer and inclusion delay micro-rewards
     for index in get_unslashed_attesting_indices(state, matching_source_attestations):
+        index = ValidatorIndex(index)
         attestation = min([
             a for a in matching_source_attestations
             if index in get_attesting_indices(state, a.data, a.aggregation_bitfield)
         ], key=lambda a: a.inclusion_delay)
-        rewards[attestation.proposer_index] += get_base_reward(state, index) // PROPOSER_REWARD_QUOTIENT
-        rewards[index] += get_base_reward(state, index) * MIN_ATTESTATION_INCLUSION_DELAY // attestation.inclusion_delay
+        rewards[attestation.proposer_index] += Gwei(get_base_reward(state, index) // PROPOSER_REWARD_QUOTIENT)
+        rewards[index] += Gwei(get_base_reward(state, index) * MIN_ATTESTATION_INCLUSION_DELAY // attestation.inclusion_delay)
 
     # Inactivity penalty
     finality_delay = previous_epoch - state.finalized_epoch
     if finality_delay > MIN_EPOCHS_TO_INACTIVITY_PENALTY:
         matching_target_attesting_indices = get_unslashed_attesting_indices(state, matching_target_attestations)
         for index in eligible_validator_indices:
-            penalties[index] += BASE_REWARDS_PER_EPOCH * get_base_reward(state, index)
+            index = ValidatorIndex(index)
+            penalties[index] += Gwei(BASE_REWARDS_PER_EPOCH * get_base_reward(state, index))
             if index not in matching_target_attesting_indices:
-                penalties[index] += (
+                penalties[index] += Gwei(
                     state.validator_registry[index].effective_balance * finality_delay // INACTIVITY_PENALTY_QUOTIENT
                 )
 
@@ -1444,11 +1446,11 @@ def get_attestation_deltas(state: BeaconState) -> Tuple[List[Gwei], List[Gwei]]:
 
 ```python
 def get_crosslink_deltas(state: BeaconState) -> Tuple[List[Gwei], List[Gwei]]:
-    rewards = [0 for index in range(len(state.validator_registry))]
-    penalties = [0 for index in range(len(state.validator_registry))]
+    rewards = [Gwei(0) for index in range(len(state.validator_registry))]
+    penalties = [Gwei(0) for index in range(len(state.validator_registry))]
     epoch = get_previous_epoch(state)
     for offset in range(get_epoch_committee_count(state, epoch)):
-        shard = (get_epoch_start_shard(state, epoch) + offset) % SHARD_COUNT
+        shard = Shard((get_epoch_start_shard(state, epoch) + offset) % SHARD_COUNT)
         crosslink_committee = get_crosslink_committee(state, epoch, shard)
         winning_crosslink, attesting_indices = get_winning_crosslink_and_attesting_indices(state, epoch, shard)
         attesting_balance = get_total_balance(state, attesting_indices)
@@ -1469,9 +1471,9 @@ def process_rewards_and_penalties(state: BeaconState) -> None:
 
     rewards1, penalties1 = get_attestation_deltas(state)
     rewards2, penalties2 = get_crosslink_deltas(state)
-    for i in range(len(state.validator_registry)):
-        increase_balance(state, i, rewards1[i] + rewards2[i])
-        decrease_balance(state, i, penalties1[i] + penalties2[i])
+    for index in range(len(state.validator_registry)):
+        increase_balance(state, ValidatorIndex(index), rewards1[index] + rewards2[index])
+        decrease_balance(state, ValidatorIndex(index), penalties1[index] + penalties2[index])
 ```
 
 #### Registry updates
@@ -1487,7 +1489,7 @@ def process_registry_updates(state: BeaconState) -> None:
             validator.activation_eligibility_epoch = get_current_epoch(state)
 
         if is_active_validator(validator, get_current_epoch(state)) and validator.effective_balance <= EJECTION_BALANCE:
-            initiate_validator_exit(state, index)
+            initiate_validator_exit(state, ValidatorIndex(index))
 
     # Queue validators eligible for activation and not dequeued for activation prior to finalized epoch
     activation_queue = sorted([
@@ -1520,7 +1522,7 @@ def process_slashings(state: BeaconState) -> None:
                 validator.effective_balance * min(total_penalties * 3, total_balance) // total_balance,
                 validator.effective_balance // MIN_SLASHING_PENALTY_QUOTIENT
             )
-            decrease_balance(state, index, penalty)
+            decrease_balance(state, ValidatorIndex(index), penalty)
 ```
 
 #### Final updates
@@ -1539,11 +1541,11 @@ def process_final_updates(state: BeaconState) -> None:
         if balance < validator.effective_balance or validator.effective_balance + 3 * HALF_INCREMENT < balance:
             validator.effective_balance = min(balance - balance % EFFECTIVE_BALANCE_INCREMENT, MAX_EFFECTIVE_BALANCE)
     # Update start shard
-    state.latest_start_shard = (state.latest_start_shard + get_shard_delta(state, current_epoch)) % SHARD_COUNT
+    state.latest_start_shard = Shard((state.latest_start_shard + get_shard_delta(state, current_epoch)) % SHARD_COUNT)
     # Set active index root
     index_root_position = (next_epoch + ACTIVATION_EXIT_DELAY) % LATEST_ACTIVE_INDEX_ROOTS_LENGTH
     state.latest_active_index_roots[index_root_position] = hash_tree_root(
-        get_active_validator_indices(state, next_epoch + ACTIVATION_EXIT_DELAY)
+        get_active_validator_indices(state, Epoch(next_epoch + ACTIVATION_EXIT_DELAY))
     )
     # Set total slashed balances
     state.latest_slashed_balances[next_epoch % LATEST_SLASHED_EXIT_LENGTH] = (
@@ -1771,7 +1773,7 @@ def process_deposit(state: BeaconState, deposit: Deposit) -> None:
         state.balances.append(amount)
     else:
         # Increase balance by deposit amount
-        index = validator_pubkeys.index(pubkey)
+        index = ValidatorIndex(validator_pubkeys.index(pubkey))
         increase_balance(state, index, amount)
 ```
 
diff --git a/test_libs/pyspec/eth2spec/utils/ssz/ssz_typing.py b/test_libs/pyspec/eth2spec/utils/ssz/ssz_typing.py
index cde1586c14..25851f331b 100644
--- a/test_libs/pyspec/eth2spec/utils/ssz/ssz_typing.py
+++ b/test_libs/pyspec/eth2spec/utils/ssz/ssz_typing.py
@@ -254,7 +254,7 @@ def __init__(self, *args: Iterable):
         # cannot check non-type objects, or parametrized types
         if isinstance(cls.elem_type, type) and not hasattr(cls.elem_type, '__args__'):
             for i, item in enumerate(self.items):
-                if not issubclass(type(item), cls.elem_type):
+                if not issubclass(cls.elem_type, type(item)):
                     raise TypeError("Typed vector cannot hold differently typed value"
                                     " at index %d. Got type: %s, expected type: %s" % (i, type(item), cls.elem_type))
 

From 6f526add79d904f6230400eff7dbcb6dbab0c8b3 Mon Sep 17 00:00:00 2001
From: Hsiao-Wei Wang <hwwang156@gmail.com>
Date: Tue, 11 Jun 2019 00:40:07 -0400
Subject: [PATCH 04/21] flake8 length

---
 specs/core/0_beacon-chain.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/specs/core/0_beacon-chain.md b/specs/core/0_beacon-chain.md
index a6bfd5e1ac..57bc2673f1 100644
--- a/specs/core/0_beacon-chain.md
+++ b/specs/core/0_beacon-chain.md
@@ -1427,7 +1427,9 @@ def get_attestation_deltas(state: BeaconState) -> Tuple[List[Gwei], List[Gwei]]:
             if index in get_attesting_indices(state, a.data, a.aggregation_bitfield)
         ], key=lambda a: a.inclusion_delay)
         rewards[attestation.proposer_index] += Gwei(get_base_reward(state, index) // PROPOSER_REWARD_QUOTIENT)
-        rewards[index] += Gwei(get_base_reward(state, index) * MIN_ATTESTATION_INCLUSION_DELAY // attestation.inclusion_delay)
+        rewards[index] += Gwei(
+            get_base_reward(state, index) * MIN_ATTESTATION_INCLUSION_DELAY // attestation.inclusion_delay
+        )
 
     # Inactivity penalty
     finality_delay = previous_epoch - state.finalized_epoch

From f2c33529df6c7d724277fb4329c3cf623444ca4a Mon Sep 17 00:00:00 2001
From: Hsiao-Wei Wang <hwwang156@gmail.com>
Date: Tue, 11 Jun 2019 00:40:25 -0400
Subject: [PATCH 05/21] Add mypy check in CI

---
 Makefile                                  | 4 +++-
 test_libs/pyspec/requirements-testing.txt | 1 +
 2 files changed, 4 insertions(+), 1 deletion(-)

diff --git a/Makefile b/Makefile
index f79b89dada..87439559fd 100644
--- a/Makefile
+++ b/Makefile
@@ -49,7 +49,9 @@ citest: $(PY_SPEC_ALL_TARGETS)
 
 lint: $(PY_SPEC_ALL_TARGETS)
 	cd $(PY_SPEC_DIR); . venv/bin/activate; \
-	flake8  --ignore=E252,W504,W503 --max-line-length=120 ./eth2spec;
+	flake8  --ignore=E252,W504,W503 --max-line-length=120 ./eth2spec; \
+	cd ./eth2spec; \
+	mypy --follow-imports=silent --warn-unused-ignores --ignore-missing-imports --check-untyped-defs --disallow-incomplete-defs --disallow-untyped-defs --disallow-any-generics -p phase0
 
 install_deposit_contract_test: $(PY_SPEC_ALL_TARGETS)
 	cd $(DEPOSIT_CONTRACT_DIR); python3 -m venv venv; . venv/bin/activate; pip3 install -r requirements-testing.txt
diff --git a/test_libs/pyspec/requirements-testing.txt b/test_libs/pyspec/requirements-testing.txt
index 331d0fa284..1ae21a2f24 100644
--- a/test_libs/pyspec/requirements-testing.txt
+++ b/test_libs/pyspec/requirements-testing.txt
@@ -2,3 +2,4 @@
 pytest>=3.6,<3.7
 ../config_helpers
 flake8==3.7.7
+mypy==0.701

From 7a366828baf1a3a1ba34074b45becc01cbedd2e8 Mon Sep 17 00:00:00 2001
From: Hsiao-Wei Wang <hwwang156@gmail.com>
Date: Wed, 12 Jun 2019 14:54:00 -0400
Subject: [PATCH 06/21] Make phase0 pass

---
 scripts/build_spec.py                             |  2 ++
 specs/core/0_beacon-chain.md                      |  6 +++---
 test_libs/pyspec/eth2spec/utils/ssz/ssz_typing.py | 12 ++++++------
 3 files changed, 11 insertions(+), 9 deletions(-)

diff --git a/scripts/build_spec.py b/scripts/build_spec.py
index f396d3b9c5..a4a97ab575 100644
--- a/scripts/build_spec.py
+++ b/scripts/build_spec.py
@@ -13,6 +13,7 @@
 
 PHASE0_IMPORTS = '''from typing import (
     Any,
+    Callable,
     Dict,
     List,
     Set,
@@ -39,6 +40,7 @@
 '''
 PHASE1_IMPORTS = '''from typing import (
     Any,
+    Callable,
     Dict,
     List,
     Set,
diff --git a/specs/core/0_beacon-chain.md b/specs/core/0_beacon-chain.md
index 57bc2673f1..86c22c9764 100644
--- a/specs/core/0_beacon-chain.md
+++ b/specs/core/0_beacon-chain.md
@@ -1634,15 +1634,15 @@ def process_operations(state: BeaconState, body: BeaconBlockBody) -> None:
     assert len(body.deposits) == min(MAX_DEPOSITS, state.latest_eth1_data.deposit_count - state.deposit_index)
     # Verify that there are no duplicate transfers
     assert len(body.transfers) == len(set(body.transfers))
-
-    for operations, max_operations, function in (
+    all_operations = [
         (body.proposer_slashings, MAX_PROPOSER_SLASHINGS, process_proposer_slashing),
         (body.attester_slashings, MAX_ATTESTER_SLASHINGS, process_attester_slashing),
         (body.attestations, MAX_ATTESTATIONS, process_attestation),
         (body.deposits, MAX_DEPOSITS, process_deposit),
         (body.voluntary_exits, MAX_VOLUNTARY_EXITS, process_voluntary_exit),
         (body.transfers, MAX_TRANSFERS, process_transfer),
-    ):
+    ]  # type: List[Tuple[List[Container], int, Callable]]
+    for operations, max_operations, function in all_operations:
         assert len(operations) <= max_operations
         for operation in operations:
             function(state, operation)
diff --git a/test_libs/pyspec/eth2spec/utils/ssz/ssz_typing.py b/test_libs/pyspec/eth2spec/utils/ssz/ssz_typing.py
index 25851f331b..b75a40403a 100644
--- a/test_libs/pyspec/eth2spec/utils/ssz/ssz_typing.py
+++ b/test_libs/pyspec/eth2spec/utils/ssz/ssz_typing.py
@@ -414,12 +414,12 @@ class Bytes96(BytesN):
 # SSZ Defaults
 # -----------------------------
 def get_zero_value(typ):
-    if is_list_type(typ):
+    if is_uint_type(typ):
+        return uint64(0)
+    elif is_list_type(typ):
         return []
     elif is_bool_type(typ):
         return False
-    elif is_uint_type(typ):
-        return uint64(0)
     elif is_vector_type(typ):
         return typ()
     elif is_bytesn_type(typ):
@@ -437,12 +437,12 @@ def get_zero_value(typ):
 
 
 def infer_type(obj):
-    if isinstance(obj, int):
+    if is_uint_type(obj.__class__):
+        return obj.__class__
+    elif isinstance(obj, int):
         return uint64
     elif isinstance(obj, list):
         return List[infer_type(obj[0])]
-    elif is_uint_type(obj.__class__):
-        return obj.__class__
     elif isinstance(obj, (Vector, Container, bool, BytesN, bytes)):
         return obj.__class__
     else:

From 8a54203796503a873780377e180c8c19d143ec6a Mon Sep 17 00:00:00 2001
From: Hsiao-Wei Wang <hwwang156@gmail.com>
Date: Wed, 12 Jun 2019 16:50:49 -0400
Subject: [PATCH 07/21] Modify the mypy config

---
 Makefile | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Makefile b/Makefile
index 87439559fd..26fe3a3876 100644
--- a/Makefile
+++ b/Makefile
@@ -51,7 +51,7 @@ lint: $(PY_SPEC_ALL_TARGETS)
 	cd $(PY_SPEC_DIR); . venv/bin/activate; \
 	flake8  --ignore=E252,W504,W503 --max-line-length=120 ./eth2spec; \
 	cd ./eth2spec; \
-	mypy --follow-imports=silent --warn-unused-ignores --ignore-missing-imports --check-untyped-defs --disallow-incomplete-defs --disallow-untyped-defs --disallow-any-generics -p phase0
+	mypy --follow-imports=silent --warn-unused-ignores --ignore-missing-imports --check-untyped-defs --disallow-incomplete-defs --disallow-untyped-defs -p phase0
 
 install_deposit_contract_test: $(PY_SPEC_ALL_TARGETS)
 	cd $(DEPOSIT_CONTRACT_DIR); python3 -m venv venv; . venv/bin/activate; pip3 install -r requirements-testing.txt

From 48e8164e28aeb73d7bc9108a89c40bff60ef2e42 Mon Sep 17 00:00:00 2001
From: Hsiao-Wei Wang <hwwang156@gmail.com>
Date: Wed, 12 Jun 2019 20:08:19 -0400
Subject: [PATCH 08/21] Add phase1 type hinting checks and fix many bugs

---
 scripts/build_spec.py             |  1 +
 specs/core/1_custody-game.md      | 62 ++++++++++++++++---------------
 specs/core/1_shard-data-chains.md | 34 ++++++++---------
 3 files changed, 51 insertions(+), 46 deletions(-)

diff --git a/scripts/build_spec.py b/scripts/build_spec.py
index a4a97ab575..3fb1dda7ea 100644
--- a/scripts/build_spec.py
+++ b/scripts/build_spec.py
@@ -43,6 +43,7 @@
     Callable,
     Dict,
     List,
+    Optional,
     Set,
     Tuple,
 )
diff --git a/specs/core/1_custody-game.md b/specs/core/1_custody-game.md
index 6c89ef8531..9e8414a427 100644
--- a/specs/core/1_custody-game.md
+++ b/specs/core/1_custody-game.md
@@ -184,7 +184,7 @@ class CustodyResponse(Container):
 ```python
 class CustodyKeyReveal(Container):
     # Index of the validator whose key is being revealed
-    revealer_index: uint64
+    revealer_index: ValidatorIndex
     # Reveal (masked signature)
     reveal: Bytes96
 ```
@@ -198,7 +198,7 @@ class EarlyDerivedSecretReveal(Container):
     # Index of the validator whose key is being revealed
     revealed_index: uint64
     # RANDAO epoch of the key that is being revealed
-    epoch: uint64
+    epoch: Epoch
     # Reveal (masked signature)
     reveal: Bytes96
     # Index of the validator who revealed (whistleblower)
@@ -251,7 +251,7 @@ class BeaconBlockBody(Container):
 ### `ceillog2`
 
 ```python
-def ceillog2(x):
+def ceillog2(x: int) -> int:
     return x.bit_length()
 ```
 
@@ -269,7 +269,7 @@ def get_custody_chunk_count(crosslink: Crosslink) -> int:
 ```python
 def get_custody_chunk_bit(key: Bytes96, chunk: bytes) -> bool:
     # TODO: Replace with something MPC-friendly, e.g. the Legendre symbol
-    return get_bitfield_bit(hash(key + chunk), 0)
+    return bool(get_bitfield_bit(hash(key + chunk), 0))
 ```
 
 ### `get_chunk_bits_root`
@@ -288,7 +288,7 @@ def get_chunk_bits_root(chunk_bitfield: bytes) -> Bytes32:
 ```python
 def get_randao_epoch_for_custody_period(period: int, validator_index: ValidatorIndex) -> Epoch:
     next_period_start = (period + 1) * EPOCHS_PER_CUSTODY_PERIOD - validator_index % EPOCHS_PER_CUSTODY_PERIOD
-    return next_period_start + CUSTODY_PERIOD_TO_RANDAO_PADDING
+    return Epoch(next_period_start + CUSTODY_PERIOD_TO_RANDAO_PADDING)
 ```
 
 ### `get_validators_custody_reveal_period`
@@ -372,7 +372,11 @@ def process_custody_key_reveal(state: BeaconState,
 
     # Reward Block Preposer
     proposer_index = get_beacon_proposer_index(state)
-    increase_balance(state, proposer_index, get_base_reward(state, reveal.revealer_index) // MINOR_REWARD_QUOTIENT)
+    increase_balance(
+        state,
+        proposer_index,
+        Gwei(get_base_reward(state, reveal.revealer_index) // MINOR_REWARD_QUOTIENT)
+    )
 ```
 
 #### Early derived secret reveals
@@ -433,7 +437,7 @@ def process_early_derived_secret_reveal(state: BeaconState,
             // len(get_active_validator_indices(state, get_current_epoch(state)))
             // PROPOSER_REWARD_QUOTIENT
         )
-        penalty = (
+        penalty = Gwei(
             max_proposer_slot_reward
             * EARLY_DERIVED_SECRET_REVEAL_SLOT_REWARD_MULTIPLE
             * (len(state.exposed_derived_secrets[derived_secret_location]) + 1)
@@ -442,8 +446,8 @@ def process_early_derived_secret_reveal(state: BeaconState,
         # Apply penalty
         proposer_index = get_beacon_proposer_index(state)
         whistleblower_index = reveal.masker_index
-        whistleblowing_reward = penalty // WHISTLEBLOWING_REWARD_QUOTIENT
-        proposer_reward = whistleblowing_reward // PROPOSER_REWARD_QUOTIENT
+        whistleblowing_reward = Gwei(penalty // WHISTLEBLOWING_REWARD_QUOTIENT)
+        proposer_reward = Gwei(whistleblowing_reward // PROPOSER_REWARD_QUOTIENT)
         increase_balance(state, proposer_index, proposer_reward)
         increase_balance(state, whistleblower_index, whistleblowing_reward - proposer_reward)
         decrease_balance(state, reveal.revealed_index, penalty)
@@ -512,7 +516,7 @@ def process_bit_challenge(state: BeaconState,
         pubkey=challenger.pubkey,
         message_hash=signing_root(challenge),
         signature=challenge.signature,
-        domain=get_domain(state, get_current_epoch(state), DOMAIN_CUSTODY_BIT_CHALLENGE),
+        domain=get_domain(state, DOMAIN_CUSTODY_BIT_CHALLENGE, get_current_epoch(state)),
     )
     assert is_slashable_validator(challenger, get_current_epoch(state))
 
@@ -535,8 +539,8 @@ def process_bit_challenge(state: BeaconState,
     # Verify the responder is a valid custody key
     epoch_to_sign = get_randao_epoch_for_custody_period(
         get_validators_custody_reveal_period(
-            state=state,
-            index=challenge.responder_index,
+            state,
+            challenge.responder_index,
             epoch=slot_to_epoch(attestation.data.slot)),
         challenge.responder_index
     )
@@ -610,7 +614,7 @@ def process_chunk_challenge_response(state: BeaconState,
     # Verify the chunk matches the crosslink data root
     assert verify_merkle_branch(
         leaf=hash_tree_root(response.chunk),
-        branch=response.data_branch,
+        proof=response.data_branch,
         depth=challenge.depth,
         index=response.chunk_index,
         root=challenge.data_root,
@@ -620,7 +624,7 @@ def process_chunk_challenge_response(state: BeaconState,
     records[records.index(challenge)] = CustodyChunkChallengeRecord()
     # Reward the proposer
     proposer_index = get_beacon_proposer_index(state)
-    increase_balance(state, proposer_index, get_base_reward(state, proposer_index) // MINOR_REWARD_QUOTIENT)
+    increase_balance(state, proposer_index, Gwei(get_base_reward(state, proposer_index) // MINOR_REWARD_QUOTIENT))
 ```
 
 ```python
@@ -635,7 +639,7 @@ def process_bit_challenge_response(state: BeaconState,
     # Verify the chunk matches the crosslink data root
     assert verify_merkle_branch(
         leaf=hash_tree_root(response.chunk),
-        branch=response.data_branch,
+        proof=response.data_branch,
         depth=ceillog2(challenge.chunk_count),
         index=response.chunk_index,
         root=challenge.data_root,
@@ -643,7 +647,7 @@ def process_bit_challenge_response(state: BeaconState,
     # Verify the chunk bit leaf matches the challenge data
     assert verify_merkle_branch(
         leaf=response.chunk_bits_leaf,
-        branch=response.chunk_bits_branch,
+        proof=response.chunk_bits_branch,
         depth=ceillog2(challenge.chunk_count) >> 8,
         index=response.chunk_index // 256,
         root=challenge.chunk_bits_merkle_root
@@ -671,8 +675,8 @@ Run `process_reveal_deadlines(state)` immediately after `process_registry_update
 def process_reveal_deadlines(state: BeaconState) -> None:
     for index, validator in enumerate(state.validator_registry):
         deadline = validator.next_custody_reveal_period + (CUSTODY_RESPONSE_DEADLINE // EPOCHS_PER_CUSTODY_PERIOD)
-        if get_validators_custody_reveal_period(state, index) > deadline:
-            slash_validator(state, index)
+        if get_validators_custody_reveal_period(state, ValidatorIndex(index)) > deadline:
+            slash_validator(state, ValidatorIndex(index))
 ```
 
 Run `process_challenge_deadlines(state)` immediately after `process_reveal_deadlines(state)`:
@@ -682,17 +686,17 @@ Run `process_challenge_deadlines(state)` immediately after `process_reveal_deadl
     process_challenge_deadlines(state)
 # end insert @process_challenge_deadlines
 def process_challenge_deadlines(state: BeaconState) -> None:
-    for challenge in state.custody_chunk_challenge_records:
-        if get_current_epoch(state) > challenge.inclusion_epoch + CUSTODY_RESPONSE_DEADLINE:
-            slash_validator(state, challenge.responder_index, challenge.challenger_index)
-            records = state.custody_chunk_challenge_records
-            records[records.index(challenge)] = CustodyChunkChallengeRecord()
-
-    for challenge in state.custody_bit_challenge_records:
-        if get_current_epoch(state) > challenge.inclusion_epoch + CUSTODY_RESPONSE_DEADLINE:
-            slash_validator(state, challenge.responder_index, challenge.challenger_index)
+    for custody_chunk_challenge in state.custody_chunk_challenge_records:
+        if get_current_epoch(state) > custody_chunk_challenge.inclusion_epoch + CUSTODY_RESPONSE_DEADLINE:
+            slash_validator(state, custody_chunk_challenge.responder_index, custody_chunk_challenge.challenger_index)
+            records = state.custody_chunk_challenge
+            records[records.index(custody_chunk_challenge)] = CustodyChunkChallengeRecord()
+
+    for custody_bit_challenge in state.custody_bit_challenge_records:
+        if get_current_epoch(state) > custody_bit_challenge.inclusion_epoch + CUSTODY_RESPONSE_DEADLINE:
+            slash_validator(state, custody_bit_challenge.responder_index, custody_bit_challenge.challenger_index)
             records = state.custody_bit_challenge_records
-            records[records.index(challenge)] = CustodyBitChallengeRecord()
+            records[records.index(custody_bit_challenge)] = CustodyBitChallengeRecord()
 ```
 
 Append this to `process_final_updates(state)`:
@@ -713,5 +717,5 @@ def after_process_final_updates(state: BeaconState) -> None:
     for index, validator in enumerate(state.validator_registry):
         if index not in validator_indices_in_records:
             if validator.exit_epoch != FAR_FUTURE_EPOCH and validator.withdrawable_epoch == FAR_FUTURE_EPOCH:
-                validator.withdrawable_epoch = validator.exit_epoch + MIN_VALIDATOR_WITHDRAWABILITY_DELAY
+                validator.withdrawable_epoch = Epoch(validator.exit_epoch + MIN_VALIDATOR_WITHDRAWABILITY_DELAY)
 ```
diff --git a/specs/core/1_shard-data-chains.md b/specs/core/1_shard-data-chains.md
index 21e08e7c96..ce6f0a6c28 100644
--- a/specs/core/1_shard-data-chains.md
+++ b/specs/core/1_shard-data-chains.md
@@ -79,8 +79,8 @@ class ShardBlockBody(Container):
 ```python
 class ShardAttestation(Container):
     class data(Container):
-        slot: uint64
-        shard: uint64
+        slot: Slot
+        shard: Shard
         shard_block_root: Bytes32
     aggregation_bitfield: bytes
     aggregate_signature: Bytes96
@@ -90,8 +90,8 @@ class ShardAttestation(Container):
 
 ```python
 class ShardBlock(Container):
-    slot: uint64
-    shard: uint64
+    slot: Slot
+    shard: Shard
     beacon_chain_root: Bytes32
     parent_root: Bytes32
     data: ShardBlockBody
@@ -104,8 +104,8 @@ class ShardBlock(Container):
 
 ```python
 class ShardBlockHeader(Container):
-    slot: uint64
-    shard: uint64
+    slot: Slot
+    shard: Shard
     beacon_chain_root: Bytes32
     parent_root: Bytes32
     body_root: Bytes32
@@ -138,8 +138,8 @@ def get_period_committee(state: BeaconState,
 ### `get_switchover_epoch`
 
 ```python
-def get_switchover_epoch(state: BeaconState, epoch: Epoch, index: ValidatorIndex):
-    earlier_start_epoch = epoch - (epoch % PERSISTENT_COMMITTEE_PERIOD) - PERSISTENT_COMMITTEE_PERIOD * 2
+def get_switchover_epoch(state: BeaconState, epoch: Epoch, index: ValidatorIndex) -> int:
+    earlier_start_epoch = Epoch(epoch - (epoch % PERSISTENT_COMMITTEE_PERIOD) - PERSISTENT_COMMITTEE_PERIOD * 2)
     return (bytes_to_int(hash(generate_seed(state, earlier_start_epoch) + int_to_bytes(index, length=3)[0:8]))
             % PERSISTENT_COMMITTEE_PERIOD)
 ```
@@ -154,19 +154,19 @@ def get_persistent_committee(state: BeaconState,
     Return the persistent committee for the given ``shard`` at the given ``slot``.
     """
     epoch = slot_to_epoch(slot)
-    earlier_start_epoch = epoch - (epoch % PERSISTENT_COMMITTEE_PERIOD) - PERSISTENT_COMMITTEE_PERIOD * 2
-    later_start_epoch = epoch - (epoch % PERSISTENT_COMMITTEE_PERIOD) - PERSISTENT_COMMITTEE_PERIOD
+    earlier_start_epoch = Epoch(epoch - (epoch % PERSISTENT_COMMITTEE_PERIOD) - PERSISTENT_COMMITTEE_PERIOD * 2)
+    later_start_epoch = Epoch(epoch - (epoch % PERSISTENT_COMMITTEE_PERIOD) - PERSISTENT_COMMITTEE_PERIOD)
 
     committee_count = max(
-        len(get_active_validator_indices(state.validator_registry, earlier_start_epoch)) //
+        len(get_active_validator_indices(state, earlier_start_epoch)) //
         (SHARD_COUNT * TARGET_COMMITTEE_SIZE),
-        len(get_active_validator_indices(state.validator_registry, later_start_epoch)) //
+        len(get_active_validator_indices(state, later_start_epoch)) //
         (SHARD_COUNT * TARGET_COMMITTEE_SIZE),
     ) + 1
 
     index = slot % committee_count
-    earlier_committee = get_period_committee(state, shard, earlier_start_epoch, index, committee_count)
-    later_committee = get_period_committee(state, shard, later_start_epoch, index, committee_count)
+    earlier_committee = get_period_committee(state, earlier_start_epoch, shard, index, committee_count)
+    later_committee = get_period_committee(state, later_start_epoch, shard, index, committee_count)
 
     # Take not-yet-cycled-out validators from earlier committee and already-cycled-in validators from
     # later committee; return a sorted list of the union of the two, deduplicated
@@ -181,7 +181,7 @@ def get_persistent_committee(state: BeaconState,
 ```python
 def get_shard_proposer_index(state: BeaconState,
                              shard: Shard,
-                             slot: Slot) -> ValidatorIndex:
+                             slot: Slot) -> Optional[ValidatorIndex]:
     # Randomly shift persistent committee
     persistent_committee = get_persistent_committee(state, shard, slot)
     seed = hash(state.current_shuffling_seed + int_to_bytes(shard, length=8) + int_to_bytes(slot, length=8))
@@ -231,7 +231,7 @@ def verify_shard_attestation_signature(state: BeaconState,
         pubkey=bls_aggregate_pubkeys(pubkeys),
         message_hash=data.shard_block_root,
         signature=attestation.aggregate_signature,
-        domain=get_domain(state, slot_to_epoch(data.slot), DOMAIN_SHARD_ATTESTER)
+        domain=get_domain(state, DOMAIN_SHARD_ATTESTER, slot_to_epoch(data.slot))
     )
 ```
 
@@ -328,7 +328,7 @@ def is_valid_shard_block(beacon_blocks: List[BeaconBlock],
         pubkey=beacon_state.validator_registry[proposer_index].pubkey,
         message_hash=signing_root(block),
         signature=candidate.signature,
-        domain=get_domain(beacon_state, slot_to_epoch(candidate.slot), DOMAIN_SHARD_PROPOSER),
+        domain=get_domain(beacon_state, DOMAIN_SHARD_PROPOSER, slot_to_epoch(candidate.slot)),
     )
 
     return True

From 8577cff72eedc2d99eec7e2cc288715834de8a36 Mon Sep 17 00:00:00 2001
From: Hsiao-Wei Wang <hwwang156@gmail.com>
Date: Wed, 12 Jun 2019 20:10:24 -0400
Subject: [PATCH 09/21] enable mypy check in CI

---
 Makefile | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/Makefile b/Makefile
index 26fe3a3876..ca59d6c8a9 100644
--- a/Makefile
+++ b/Makefile
@@ -51,7 +51,8 @@ lint: $(PY_SPEC_ALL_TARGETS)
 	cd $(PY_SPEC_DIR); . venv/bin/activate; \
 	flake8  --ignore=E252,W504,W503 --max-line-length=120 ./eth2spec; \
 	cd ./eth2spec; \
-	mypy --follow-imports=silent --warn-unused-ignores --ignore-missing-imports --check-untyped-defs --disallow-incomplete-defs --disallow-untyped-defs -p phase0
+	mypy --follow-imports=silent --warn-unused-ignores --ignore-missing-imports --check-untyped-defs --disallow-incomplete-defs --disallow-untyped-defs -p phase0; \
+	mypy --follow-imports=silent --warn-unused-ignores --ignore-missing-imports --check-untyped-defs --disallow-incomplete-defs --disallow-untyped-defs -p phase1
 
 install_deposit_contract_test: $(PY_SPEC_ALL_TARGETS)
 	cd $(DEPOSIT_CONTRACT_DIR); python3 -m venv venv; . venv/bin/activate; pip3 install -r requirements-testing.txt

From 00a68e28b50cb0c1067319d31c75d368b352b822 Mon Sep 17 00:00:00 2001
From: Hsiao-Wei Wang <hwwang156@gmail.com>
Date: Sat, 15 Jun 2019 16:57:50 -0400
Subject: [PATCH 10/21] Define Custom Types via function_puller

---
 scripts/build_spec.py                         | 17 ++++----
 scripts/function_puller.py                    | 22 +++++-----
 specs/core/0_beacon-chain.md                  | 40 +++++++++----------
 .../pyspec/eth2spec/utils/ssz/ssz_typing.py   |  2 +-
 4 files changed, 43 insertions(+), 38 deletions(-)

diff --git a/scripts/build_spec.py b/scripts/build_spec.py
index 3fb1dda7ea..6bcb04656d 100644
--- a/scripts/build_spec.py
+++ b/scripts/build_spec.py
@@ -128,11 +128,11 @@ def apply_constants_preset(preset: Dict[str, Any]) -> None:
 
 
 def objects_to_spec(functions: Dict[str, str],
+                    custom_types: Dict[str, str],
                     constants: Dict[str, str],
                     ssz_objects: Dict[str, str],
                     inserts: Dict[str, str],
                     imports: Dict[str, str],
-                    new_types: Dict[str, str],
                     byte_types: List[int],
                     ) -> str:
     """
@@ -144,7 +144,7 @@ def objects_to_spec(functions: Dict[str, str],
                 f"class {key}({value}):\n"
                 f"    def __init__(self, _x: uint64) -> None:\n"
                 f"        ...\n"
-                for key, value in new_types.items()
+                for key, value in custom_types.items()
             ]
         )
     )
@@ -225,18 +225,19 @@ def combine_spec_objects(spec0: SpecObject, spec1: SpecObject) -> SpecObject:
     """
     Takes in two spec variants (as tuples of their objects) and combines them using the appropriate combiner function.
     """
-    functions0, constants0, ssz_objects0, inserts0 = spec0
-    functions1, constants1, ssz_objects1, inserts1 = spec1
+    functions0, custom_types0, constants0, ssz_objects0, inserts0 = spec0
+    functions1, custom_types1, constants1, ssz_objects1, inserts1 = spec1
     functions = combine_functions(functions0, functions1)
+    custom_types = combine_constants(custom_types0, custom_types1)
     constants = combine_constants(constants0, constants1)
     ssz_objects = combine_ssz_objects(ssz_objects0, ssz_objects1)
     inserts = combine_inserts(inserts0, inserts1)
-    return functions, constants, ssz_objects, inserts
+    return functions, custom_types, constants, ssz_objects, inserts
 
 
 def build_phase0_spec(sourcefile: str, outfile: str=None) -> Optional[str]:
-    functions, constants, ssz_objects, inserts = get_spec(sourcefile)
-    spec = objects_to_spec(functions, constants, ssz_objects, inserts, PHASE0_IMPORTS, NEW_TYPES, BYTE_TYPES)
+    functions, custom_types, constants, ssz_objects, inserts = get_spec(sourcefile)
+    spec = objects_to_spec(functions, custom_types, constants, ssz_objects, inserts, PHASE0_IMPORTS, BYTE_TYPES)
     if outfile is not None:
         with open(outfile, 'w') as out:
             out.write(spec)
@@ -253,7 +254,7 @@ def build_phase1_spec(phase0_sourcefile: str,
     spec_objects = phase0_spec
     for value in [phase1_custody, phase1_shard_data]:
         spec_objects = combine_spec_objects(spec_objects, value)
-    spec = objects_to_spec(*spec_objects, PHASE1_IMPORTS, NEW_TYPES, BYTE_TYPES)
+    spec = objects_to_spec(*spec_objects, PHASE1_IMPORTS, BYTE_TYPES)
     if outfile is not None:
         with open(outfile, 'w') as out:
             out.write(spec)
diff --git a/scripts/function_puller.py b/scripts/function_puller.py
index 303d4ec2f5..4ad9eef57c 100644
--- a/scripts/function_puller.py
+++ b/scripts/function_puller.py
@@ -29,6 +29,7 @@ def get_spec(file_name: str) -> SpecObject:
     inserts = {}
     function_matcher = re.compile(FUNCTION_REGEX)
     inserts_matcher = re.compile(BEGIN_INSERT_REGEX)
+    custom_types = {}
     for linenum, line in enumerate(open(file_name).readlines()):
         line = line.rstrip()
         if pulling_from is None and len(line) > 0 and line[0] == '#' and line[-1] == '`':
@@ -64,7 +65,7 @@ def get_spec(file_name: str) -> SpecObject:
                     ssz_objects[current_name] = ssz_objects.get(current_name, '') + line + '\n'
                 else:
                     functions[current_name] = functions.get(current_name, '') + line + '\n'
-            # Handle constant table entries
+            # Handle constant and custom types table entries
             elif pulling_from is None and len(line) > 0 and line[0] == '|':
                 row = line[1:].split('|')
                 if len(row) >= 2:
@@ -72,12 +73,15 @@ def get_spec(file_name: str) -> SpecObject:
                         row[i] = row[i].strip().strip('`')
                         if '`' in row[i]:
                             row[i] = row[i][:row[i].find('`')]
-                    eligible = True
-                    if row[0][0] not in 'ABCDEFGHIJKLMNOPQRSTUVWXYZ_':
-                        eligible = False
-                    for c in row[0]:
-                        if c not in 'ABCDEFGHIJKLMNOPQRSTUVWXYZ_0123456789':
+                    if row[1].startswith('uint') or row[1].startswith('bytes'):
+                        custom_types[row[0]] = row[1]
+                    else:
+                        eligible = True
+                        if row[0][0] not in 'ABCDEFGHIJKLMNOPQRSTUVWXYZ_':
                             eligible = False
-                    if eligible:
-                        constants[row[0]] = row[1].replace('**TBD**', '0x1234567890123456789012345678901234567890')
-    return functions, constants, ssz_objects, inserts
+                        for c in row[0]:
+                            if c not in 'ABCDEFGHIJKLMNOPQRSTUVWXYZ_0123456789':
+                                eligible = False
+                        if eligible:
+                            constants[row[0]] = row[1].replace('**TBD**', '0x1234567890123456789012345678901234567890')
+    return functions, custom_types, constants, ssz_objects, inserts
diff --git a/specs/core/0_beacon-chain.md b/specs/core/0_beacon-chain.md
index 86c22c9764..8baba6928f 100644
--- a/specs/core/0_beacon-chain.md
+++ b/specs/core/0_beacon-chain.md
@@ -10,6 +10,7 @@
     - [Introduction](#introduction)
     - [Notation](#notation)
     - [Terminology](#terminology)
+    - [Custom types](#custom-types)
     - [Constants](#constants)
         - [Misc](#misc)
         - [Deposit contract](#deposit-contract)
@@ -45,7 +46,6 @@
             - [`BeaconBlock`](#beaconblock)
         - [Beacon state](#beacon-state)
             - [`BeaconState`](#beaconstate)
-    - [Custom types](#custom-types)
     - [Helper functions](#helper-functions)
         - [`xor`](#xor)
         - [`hash`](#hash)
@@ -150,6 +150,20 @@ Code snippets appearing in `this style` are to be interpreted as Python code.
 * **Withdrawal period**—the number of slots between a [validator](#dfn-validator) exit and the [validator](#dfn-validator) balance being withdrawable.
 * **Genesis time**—the Unix time of the genesis beacon chain block at slot 0.
 
+## Custom types
+
+We define the following Python custom types for type hinting and readability:
+
+| Name | SSZ equivalent | Description |
+| - | - | - |
+| `Slot` | `uint64` | a slot number |
+| `Epoch` | `uint64` | an epoch number |
+| `Shard` | `uint64` | a shard number |
+| `ValidatorIndex` | `uint64` | a validator registry index |
+| `Gwei` | `uint64` | an amount in Gwei |
+| `BLSPubkey` | `Bytes48` | a BLS12-381 public key |
+| `BLSSignature` | `Bytes96` | a BLS12-381 signature |
+
 ## Constants
 
 *Note*: The default mainnet values for the constants are included here for spec-design purposes.
@@ -178,12 +192,12 @@ These configurations are updated for releases, but may be out of sync during `de
 
 ### Gwei values
 
-| Name | Value | Unit |
+| Name | Value |
 | - | - | :-: |
-| `MIN_DEPOSIT_AMOUNT` | `Gwei(2**0 * 10**9)` (= 1,000,000,000) | Gwei |
-| `MAX_EFFECTIVE_BALANCE` | `Gwei(2**5 * 10**9)` (= 32,000,000,000) | Gwei |
-| `EJECTION_BALANCE` | `Gwei(2**4 * 10**9)` (= 16,000,000,000) | Gwei |
-| `EFFECTIVE_BALANCE_INCREMENT` | `Gwei(2**0 * 10**9)` (= 1,000,000,000) | Gwei |
+| `MIN_DEPOSIT_AMOUNT` | `Gwei(2**0 * 10**9)` (= 1,000,000,000) |
+| `MAX_EFFECTIVE_BALANCE` | `Gwei(2**5 * 10**9)` (= 32,000,000,000) |
+| `EJECTION_BALANCE` | `Gwei(2**4 * 10**9)` (= 16,000,000,000) |
+| `EFFECTIVE_BALANCE_INCREMENT` | `Gwei(2**0 * 10**9)` (= 1,000,000,000) |
 
 ### Initial values
 
@@ -563,20 +577,6 @@ class BeaconState(Container):
     deposit_index: uint64
 ```
 
-## Custom types
-
-We define the following Python custom types for type hinting and readability:
-
-| Name | SSZ equivalent | Description |
-| - | - | - |
-| `Slot` | `uint64` | a slot number |
-| `Epoch` | `uint64` | an epoch number |
-| `Shard` | `uint64` | a shard number |
-| `ValidatorIndex` | `uint64` | a validator registry index |
-| `Gwei` | `uint64` | an amount in Gwei |
-| `BLSPubkey` | `Bytes48` | a BLS12-381 public key |
-| `BLSSignature` | `Bytes96` | a BLS12-381 signature |
-
 ## Helper functions
 
 *Note*: The definitions below are for specification purposes and are not necessarily optimal implementations.
diff --git a/test_libs/pyspec/eth2spec/utils/ssz/ssz_typing.py b/test_libs/pyspec/eth2spec/utils/ssz/ssz_typing.py
index b75a40403a..cbd313d85f 100644
--- a/test_libs/pyspec/eth2spec/utils/ssz/ssz_typing.py
+++ b/test_libs/pyspec/eth2spec/utils/ssz/ssz_typing.py
@@ -51,7 +51,7 @@ class uint64(uint):
 
     def __new__(cls, value, *args, **kwargs):
         if value.bit_length() > 64:
-            raise ValueError("value out of bounds for uint128")
+            raise ValueError("value out of bounds for uint64")
         return super().__new__(cls, value)
 
 

From b772b03847d90e52b5c0f79df893f416b655fb6f Mon Sep 17 00:00:00 2001
From: Hsiao-Wei Wang <hwwang156@gmail.com>
Date: Sat, 15 Jun 2019 17:23:44 -0400
Subject: [PATCH 11/21] Handle `BLSPubkey` and `BLSSignature`

---
 scripts/build_spec.py        | 14 ++++++++------
 scripts/function_puller.py   |  2 +-
 specs/core/0_beacon-chain.md | 22 +++++++++++-----------
 3 files changed, 20 insertions(+), 18 deletions(-)

diff --git a/scripts/build_spec.py b/scripts/build_spec.py
index 6bcb04656d..8f0048b8f7 100644
--- a/scripts/build_spec.py
+++ b/scripts/build_spec.py
@@ -142,8 +142,10 @@ def objects_to_spec(functions: Dict[str, str],
         '\n\n'.join(
             [
                 f"class {key}({value}):\n"
-                f"    def __init__(self, _x: uint64) -> None:\n"
+                f"    def __init__(self, _x: {value}) -> None:\n"
                 f"        ...\n"
+                if value.startswith("uint")
+                else f"class {key}({value}):\n    pass\n"
                 for key, value in custom_types.items()
             ]
         )
@@ -185,7 +187,7 @@ def combine_constants(old_constants: Dict[str, str], new_constants: Dict[str, st
     return old_constants
 
 
-def dependency_order_ssz_objects(objects: Dict[str, str]) -> None:
+def dependency_order_ssz_objects(objects: Dict[str, str], custom_types: Dict[str, str]) -> None:
     """
     Determines which SSZ Object is depenedent on which other and orders them appropriately
     """
@@ -194,14 +196,14 @@ def dependency_order_ssz_objects(objects: Dict[str, str]) -> None:
         dependencies = re.findall(r'(: [A-Z][\w[]*)', value)
         dependencies = map(lambda x: re.sub(r'\W|Vector|List|Container|uint\d+|Bytes\d+|bytes', '', x), dependencies)
         for dep in dependencies:
-            if dep in NEW_TYPES or len(dep) == 0:
+            if dep in custom_types or len(dep) == 0:
                 continue
             key_list = list(objects.keys())
             for item in [dep, key] + key_list[key_list.index(dep)+1:]:
                 objects[item] = objects.pop(item)
 
 
-def combine_ssz_objects(old_objects: Dict[str, str], new_objects: Dict[str, str]) -> Dict[str, str]:
+def combine_ssz_objects(old_objects: Dict[str, str], new_objects: Dict[str, str], custom_types) -> Dict[str, str]:
     """
     Takes in old spec and new spec ssz objects, combines them,
     and returns the newer versions of the objects in dependency order.
@@ -213,7 +215,7 @@ def combine_ssz_objects(old_objects: Dict[str, str], new_objects: Dict[str, str]
             # remove leading variable name
             value = re.sub(r'^class [\w]*\(Container\):\n', '', value)
         old_objects[key] = old_objects.get(key, '') + value
-    dependency_order_ssz_objects(old_objects)
+    dependency_order_ssz_objects(old_objects, custom_types)
     return old_objects
 
 
@@ -230,7 +232,7 @@ def combine_spec_objects(spec0: SpecObject, spec1: SpecObject) -> SpecObject:
     functions = combine_functions(functions0, functions1)
     custom_types = combine_constants(custom_types0, custom_types1)
     constants = combine_constants(constants0, constants1)
-    ssz_objects = combine_ssz_objects(ssz_objects0, ssz_objects1)
+    ssz_objects = combine_ssz_objects(ssz_objects0, ssz_objects1, custom_types)
     inserts = combine_inserts(inserts0, inserts1)
     return functions, custom_types, constants, ssz_objects, inserts
 
diff --git a/scripts/function_puller.py b/scripts/function_puller.py
index 4ad9eef57c..0fd2fa4763 100644
--- a/scripts/function_puller.py
+++ b/scripts/function_puller.py
@@ -73,7 +73,7 @@ def get_spec(file_name: str) -> SpecObject:
                         row[i] = row[i].strip().strip('`')
                         if '`' in row[i]:
                             row[i] = row[i][:row[i].find('`')]
-                    if row[1].startswith('uint') or row[1].startswith('bytes'):
+                    if row[1].startswith('uint') or row[1].startswith('Bytes'):
                         custom_types[row[0]] = row[1]
                     else:
                         eligible = True
diff --git a/specs/core/0_beacon-chain.md b/specs/core/0_beacon-chain.md
index 8baba6928f..a45da28725 100644
--- a/specs/core/0_beacon-chain.md
+++ b/specs/core/0_beacon-chain.md
@@ -294,7 +294,7 @@ class Fork(Container):
 ```python
 class Validator(Container):
     # BLS public key
-    pubkey: Bytes48
+    pubkey: BLSPubkey
     # Withdrawal credentials
     withdrawal_credentials: Bytes32
     # Epoch when became eligible for activation
@@ -363,7 +363,7 @@ class IndexedAttestation(Container):
     # Attestation data
     data: AttestationData
     # Aggregate signature
-    signature: Bytes96
+    signature: BLSSignature
 ```
 
 #### `PendingAttestation`
@@ -407,13 +407,13 @@ class HistoricalBatch(Container):
 ```python
 class DepositData(Container):
     # BLS pubkey
-    pubkey: Bytes48
+    pubkey: BLSPubkey
     # Withdrawal credentials
     withdrawal_credentials: Bytes32
     # Amount in Gwei
     amount: Gwei
     # Container self-signature
-    signature: Bytes96
+    signature: BLSSignature
 ```
 
 #### `BeaconBlockHeader`
@@ -424,7 +424,7 @@ class BeaconBlockHeader(Container):
     parent_root: Bytes32
     state_root: Bytes32
     body_root: Bytes32
-    signature: Bytes96
+    signature: BLSSignature
 ```
 
 ### Beacon operations
@@ -462,7 +462,7 @@ class Attestation(Container):
     # Custody bitfield
     custody_bitfield: bytes
     # BLS aggregate signature
-    signature: Bytes96
+    signature: BLSSignature
 ```
 
 #### `Deposit`
@@ -484,7 +484,7 @@ class VoluntaryExit(Container):
     # Index of the exiting validator
     validator_index: ValidatorIndex
     # Validator signature
-    signature: Bytes96
+    signature: BLSSignature
 ```
 
 #### `Transfer`
@@ -502,9 +502,9 @@ class Transfer(Container):
     # Inclusion slot
     slot: Slot
     # Sender withdrawal pubkey
-    pubkey: Bytes48
+    pubkey: BLSPubkey
     # Sender signature
-    signature: Bytes96
+    signature: BLSSignature
 ```
 
 ### Beacon blocks
@@ -513,7 +513,7 @@ class Transfer(Container):
 
 ```python
 class BeaconBlockBody(Container):
-    randao_reveal: Bytes96
+    randao_reveal: BLSSignature
     eth1_data: Eth1Data
     graffiti: Bytes32
     proposer_slashings: List[ProposerSlashing]
@@ -533,7 +533,7 @@ class BeaconBlock(Container):
     parent_root: Bytes32
     state_root: Bytes32
     body: BeaconBlockBody
-    signature: Bytes96
+    signature: BLSSignature
 ```
 
 ### Beacon state

From 9b77ec11f8e091992b74258f39e5633663c5903e Mon Sep 17 00:00:00 2001
From: Hsiao-Wei Wang <hwwang156@gmail.com>
Date: Sat, 15 Jun 2019 17:32:52 -0400
Subject: [PATCH 12/21] Version: Bytes4

---
 scripts/build_spec.py        | 7 -------
 specs/core/0_beacon-chain.md | 5 +++--
 2 files changed, 3 insertions(+), 9 deletions(-)

diff --git a/scripts/build_spec.py b/scripts/build_spec.py
index 8f0048b8f7..9f5d07b294 100644
--- a/scripts/build_spec.py
+++ b/scripts/build_spec.py
@@ -67,13 +67,6 @@
 
 from eth2spec.utils.hash_function import hash
 '''
-NEW_TYPES = {
-    'Slot': 'uint64',
-    'Epoch': 'uint64',
-    'Shard': 'uint64',
-    'ValidatorIndex': 'uint64',
-    'Gwei': 'uint64',
-}
 BYTE_TYPES = [4, 32, 48, 96]
 SUNDRY_FUNCTIONS = '''
 def get_ssz_type_by_name(name: str) -> Container:
diff --git a/specs/core/0_beacon-chain.md b/specs/core/0_beacon-chain.md
index a45da28725..8b0c51b044 100644
--- a/specs/core/0_beacon-chain.md
+++ b/specs/core/0_beacon-chain.md
@@ -161,6 +161,7 @@ We define the following Python custom types for type hinting and readability:
 | `Shard` | `uint64` | a shard number |
 | `ValidatorIndex` | `uint64` | a validator registry index |
 | `Gwei` | `uint64` | an amount in Gwei |
+| `Version` | `Bytes4` | a fork version number |
 | `BLSPubkey` | `Bytes48` | a BLS12-381 public key |
 | `BLSSignature` | `Bytes96` | a BLS12-381 signature |
 
@@ -282,9 +283,9 @@ The types are defined topologically to aid in facilitating an executable version
 ```python
 class Fork(Container):
     # Previous fork version
-    previous_version: Bytes4
+    previous_version: Version
     # Current fork version
-    current_version: Bytes4
+    current_version: Version
     # Fork epoch number
     epoch: Epoch
 ```

From e93ba51ef807e7ae87c5f793c385112da1b8c0ab Mon Sep 17 00:00:00 2001
From: Hsiao-Wei Wang <hwwang156@gmail.com>
Date: Sat, 15 Jun 2019 18:25:37 -0400
Subject: [PATCH 13/21] More clean up

---
 specs/core/1_custody-game.md        | 18 +++++++++---------
 specs/core/1_shard-data-chains.md   |  6 +++---
 specs/light_client/sync_protocol.md |  2 +-
 3 files changed, 13 insertions(+), 13 deletions(-)

diff --git a/specs/core/1_custody-game.md b/specs/core/1_custody-game.md
index 9e8414a427..315084c301 100644
--- a/specs/core/1_custody-game.md
+++ b/specs/core/1_custody-game.md
@@ -133,9 +133,9 @@ class CustodyBitChallenge(Container):
     responder_index: ValidatorIndex
     attestation: Attestation
     challenger_index: ValidatorIndex
-    responder_key: Bytes96
+    responder_key: BLSSignature
     chunk_bits: bytes
-    signature: Bytes96
+    signature: BLSSignature
 ```
 
 #### `CustodyChunkChallengeRecord`
@@ -162,7 +162,7 @@ class CustodyBitChallengeRecord(Container):
     data_root: Bytes32
     chunk_count: uint64
     chunk_bits_merkle_root: Bytes32
-    responder_key: Bytes96
+    responder_key: BLSSignature
 ```
 
 #### `CustodyResponse`
@@ -186,7 +186,7 @@ class CustodyKeyReveal(Container):
     # Index of the validator whose key is being revealed
     revealer_index: ValidatorIndex
     # Reveal (masked signature)
-    reveal: Bytes96
+    reveal: BLSSignature
 ```
 
 #### `EarlyDerivedSecretReveal`
@@ -196,13 +196,13 @@ Represents an early (punishable) reveal of one of the derived secrets, where der
 ```python
 class EarlyDerivedSecretReveal(Container):
     # Index of the validator whose key is being revealed
-    revealed_index: uint64
+    revealed_index: ValidatorIndex
     # RANDAO epoch of the key that is being revealed
     epoch: Epoch
     # Reveal (masked signature)
-    reveal: Bytes96
+    reveal: BLSSignature
     # Index of the validator who revealed (whistleblower)
-    masker_index: uint64
+    masker_index: ValidatorIndex
     # Mask used to hide the actual reveal signature (prevent reveal from being stolen)
     mask: Bytes32
 ```
@@ -232,7 +232,7 @@ class BeaconState(Container):
 
     # Future derived secrets already exposed; contains the indices of the exposed validator
     # at RANDAO reveal period % EARLY_DERIVED_SECRET_PENALTY_MAX_FUTURE_EPOCHS
-    exposed_derived_secrets: Vector[List[uint64], EARLY_DERIVED_SECRET_PENALTY_MAX_FUTURE_EPOCHS]
+    exposed_derived_secrets: Vector[List[ValidatorIndex], EARLY_DERIVED_SECRET_PENALTY_MAX_FUTURE_EPOCHS]
 ```
 
 #### `BeaconBlockBody`
@@ -267,7 +267,7 @@ def get_custody_chunk_count(crosslink: Crosslink) -> int:
 ### `get_custody_chunk_bit`
 
 ```python
-def get_custody_chunk_bit(key: Bytes96, chunk: bytes) -> bool:
+def get_custody_chunk_bit(key: BLSSignature, chunk: bytes) -> bool:
     # TODO: Replace with something MPC-friendly, e.g. the Legendre symbol
     return bool(get_bitfield_bit(hash(key + chunk), 0))
 ```
diff --git a/specs/core/1_shard-data-chains.md b/specs/core/1_shard-data-chains.md
index ce6f0a6c28..6b18d13f64 100644
--- a/specs/core/1_shard-data-chains.md
+++ b/specs/core/1_shard-data-chains.md
@@ -83,7 +83,7 @@ class ShardAttestation(Container):
         shard: Shard
         shard_block_root: Bytes32
     aggregation_bitfield: bytes
-    aggregate_signature: Bytes96
+    aggregate_signature: BLSSignature
 ```
 
 ### `ShardBlock`
@@ -97,7 +97,7 @@ class ShardBlock(Container):
     data: ShardBlockBody
     state_root: Bytes32
     attestations: List[ShardAttestation]
-    signature: Bytes96
+    signature: BLSSignature
 ```
 
 ### `ShardBlockHeader`
@@ -111,7 +111,7 @@ class ShardBlockHeader(Container):
     body_root: Bytes32
     state_root: Bytes32
     attestations: List[ShardAttestation]
-    signature: Bytes96
+    signature: BLSSignature
 ```
 
 ## Helper functions
diff --git a/specs/light_client/sync_protocol.md b/specs/light_client/sync_protocol.md
index 8501c58690..dc2ce397be 100644
--- a/specs/light_client/sync_protocol.md
+++ b/specs/light_client/sync_protocol.md
@@ -167,7 +167,7 @@ If a client wants to update its `finalized_header` it asks the network for a `Bl
 ```python
 {
     'header': BeaconBlockHeader,
-    'shard_aggregate_signature': 'bytes96',
+    'shard_aggregate_signature': BLSSignature,
     'shard_bitfield': 'bytes',
     'shard_parent_block': ShardBlock,
 }

From 18ebd2aa9093b16b708be7261f510f5d96e2d3bd Mon Sep 17 00:00:00 2001
From: Hsiao-Wei Wang <hwwang156@gmail.com>
Date: Mon, 17 Jun 2019 17:21:45 -0400
Subject: [PATCH 14/21] Bytes32 -> Hash

---
 scripts/build_spec.py        | 20 ++++------
 specs/core/0_beacon-chain.md | 71 ++++++++++++++++++------------------
 2 files changed, 44 insertions(+), 47 deletions(-)

diff --git a/scripts/build_spec.py b/scripts/build_spec.py
index 9f5d07b294..01bcac76e3 100644
--- a/scripts/build_spec.py
+++ b/scripts/build_spec.py
@@ -75,21 +75,19 @@ def get_ssz_type_by_name(name: str) -> Container:
 
 # Monkey patch validator compute committee code
 _compute_committee = compute_committee
-committee_cache: Dict[Tuple[Bytes32, Bytes32, int, int], List[ValidatorIndex]] = {}
+committee_cache: Dict[Tuple[Hash, Hash, int, int], List[ValidatorIndex]] = {}
 
 
 def compute_committee(indices: List[ValidatorIndex],  # type: ignore
-                      seed: Bytes32,
+                      seed: Hash,
                       index: int,
                       count: int) -> List[ValidatorIndex]:
     param_hash = (hash_tree_root(indices), seed, index, count)
 
-    if param_hash in committee_cache:
-        return committee_cache[param_hash]
-    else:
+    if param_hash not in committee_cache:
         ret = _compute_committee(indices, seed, index, count)
         committee_cache[param_hash] = ret
-        return ret
+    return committee_cache[param_hash]
 
 
 # Monkey patch hash cache
@@ -97,13 +95,11 @@ def compute_committee(indices: List[ValidatorIndex],  # type: ignore
 hash_cache: Dict[bytes, Bytes32] = {}
 
 
-def hash(x: bytes) -> Bytes32:
-    if x in hash_cache:
-        return hash_cache[x]
-    else:
+def hash(x: bytes) -> Hash:
+    if x not in hash_cache:
         ret = _hash(x)
-        hash_cache[x] = ret
-        return ret
+        hash_cache[x] = Hash(ret)
+    return hash_cache[x]
 
 
 # Access to overwrite spec constants based on configuration
diff --git a/specs/core/0_beacon-chain.md b/specs/core/0_beacon-chain.md
index 8b0c51b044..76dc6eb740 100644
--- a/specs/core/0_beacon-chain.md
+++ b/specs/core/0_beacon-chain.md
@@ -162,6 +162,7 @@ We define the following Python custom types for type hinting and readability:
 | `ValidatorIndex` | `uint64` | a validator registry index |
 | `Gwei` | `uint64` | an amount in Gwei |
 | `Version` | `Bytes4` | a fork version number |
+| `Hash` | `Bytes32` | a hashed result |
 | `BLSPubkey` | `Bytes48` | a BLS12-381 public key |
 | `BLSSignature` | `Bytes96` | a BLS12-381 signature |
 
@@ -297,7 +298,7 @@ class Validator(Container):
     # BLS public key
     pubkey: BLSPubkey
     # Withdrawal credentials
-    withdrawal_credentials: Bytes32
+    withdrawal_credentials: Hash
     # Epoch when became eligible for activation
     activation_eligibility_epoch: Epoch
     # Epoch when validator activated
@@ -322,9 +323,9 @@ class Crosslink(Container):
     start_epoch: Epoch
     end_epoch: Epoch
     # Root of the previous crosslink
-    parent_root: Bytes32
+    parent_root: Hash
     # Root of the crosslinked shard data since the previous crosslink
-    data_root: Bytes32
+    data_root: Hash
 ```
 
 #### `AttestationData`
@@ -332,13 +333,13 @@ class Crosslink(Container):
 ```python
 class AttestationData(Container):
     # LMD GHOST vote
-    beacon_block_root: Bytes32
+    beacon_block_root: Hash
 
     # FFG vote
     source_epoch: Epoch
-    source_root: Bytes32
+    source_root: Hash
     target_epoch: Epoch
-    target_root: Bytes32
+    target_root: Hash
 
     # Crosslink vote
     crosslink: Crosslink
@@ -386,11 +387,11 @@ class PendingAttestation(Container):
 ```python
 class Eth1Data(Container):
     # Root of the deposit tree
-    deposit_root: Bytes32
+    deposit_root: Hash
     # Total number of deposits
     deposit_count: uint64
     # Block hash
-    block_hash: Bytes32
+    block_hash: Hash
 ```
 
 #### `HistoricalBatch`
@@ -398,9 +399,9 @@ class Eth1Data(Container):
 ```python
 class HistoricalBatch(Container):
     # Block roots
-    block_roots: Vector[Bytes32, SLOTS_PER_HISTORICAL_ROOT]
+    block_roots: Vector[Hash, SLOTS_PER_HISTORICAL_ROOT]
     # State roots
-    state_roots: Vector[Bytes32, SLOTS_PER_HISTORICAL_ROOT]
+    state_roots: Vector[Hash, SLOTS_PER_HISTORICAL_ROOT]
 ```
 
 #### `DepositData`
@@ -410,7 +411,7 @@ class DepositData(Container):
     # BLS pubkey
     pubkey: BLSPubkey
     # Withdrawal credentials
-    withdrawal_credentials: Bytes32
+    withdrawal_credentials: Hash
     # Amount in Gwei
     amount: Gwei
     # Container self-signature
@@ -422,9 +423,9 @@ class DepositData(Container):
 ```python
 class BeaconBlockHeader(Container):
     slot: Slot
-    parent_root: Bytes32
-    state_root: Bytes32
-    body_root: Bytes32
+    parent_root: Hash
+    state_root: Hash
+    body_root: Hash
     signature: BLSSignature
 ```
 
@@ -471,7 +472,7 @@ class Attestation(Container):
 ```python
 class Deposit(Container):
     # Branch in the deposit tree
-    proof: Vector[Bytes32, DEPOSIT_CONTRACT_TREE_DEPTH]
+    proof: Vector[Hash, DEPOSIT_CONTRACT_TREE_DEPTH]
     # Data
     data: DepositData
 ```
@@ -531,8 +532,8 @@ class BeaconBlockBody(Container):
 class BeaconBlock(Container):
     # Header
     slot: Slot
-    parent_root: Bytes32
-    state_root: Bytes32
+    parent_root: Hash
+    state_root: Hash
     body: BeaconBlockBody
     signature: BLSSignature
 ```
@@ -551,27 +552,27 @@ class BeaconState(Container):
     validator_registry: List[Validator]
     balances: List[Gwei]
     # Randomness and committees
-    latest_randao_mixes: Vector[Bytes32, LATEST_RANDAO_MIXES_LENGTH]
+    latest_randao_mixes: Vector[Hash, LATEST_RANDAO_MIXES_LENGTH]
     latest_start_shard: Shard
     # Finality
     previous_epoch_attestations: List[PendingAttestation]
     current_epoch_attestations: List[PendingAttestation]
     previous_justified_epoch: Epoch
     current_justified_epoch: Epoch
-    previous_justified_root: Bytes32
-    current_justified_root: Bytes32
+    previous_justified_root: Hash
+    current_justified_root: Hash
     justification_bitfield: uint64
     finalized_epoch: Epoch
-    finalized_root: Bytes32
+    finalized_root: Hash
     # Recent state
     current_crosslinks: Vector[Crosslink, SHARD_COUNT]
     previous_crosslinks: Vector[Crosslink, SHARD_COUNT]
-    latest_block_roots: Vector[Bytes32, SLOTS_PER_HISTORICAL_ROOT]
-    latest_state_roots: Vector[Bytes32, SLOTS_PER_HISTORICAL_ROOT]
-    latest_active_index_roots: Vector[Bytes32, LATEST_ACTIVE_INDEX_ROOTS_LENGTH]
+    latest_block_roots: Vector[Hash, SLOTS_PER_HISTORICAL_ROOT]
+    latest_state_roots: Vector[Hash, SLOTS_PER_HISTORICAL_ROOT]
+    latest_active_index_roots: Vector[Hash, LATEST_ACTIVE_INDEX_ROOTS_LENGTH]
     latest_slashed_balances: Vector[Gwei, LATEST_SLASHED_EXIT_LENGTH]
     latest_block_header: BeaconBlockHeader
-    historical_roots: List[Bytes32]
+    historical_roots: List[Hash]
     # Ethereum 1.0 chain data
     latest_eth1_data: Eth1Data
     eth1_data_votes: List[Eth1Data]
@@ -597,11 +598,11 @@ The `hash` function is SHA256.
 
 ### `hash_tree_root`
 
-`def hash_tree_root(object: SSZSerializable) -> Bytes32` is a function for hashing objects into a single root utilizing a hash tree structure. `hash_tree_root` is defined in the [SimpleSerialize spec](../simple-serialize.md#merkleization).
+`def hash_tree_root(object: SSZSerializable) -> Hash` is a function for hashing objects into a single root utilizing a hash tree structure. `hash_tree_root` is defined in the [SimpleSerialize spec](../simple-serialize.md#merkleization).
 
 ### `signing_root`
 
-`def signing_root(object: Container) -> Bytes32` is a function defined in the [SimpleSerialize spec](../simple-serialize.md#self-signed-containers) to compute signing messages.
+`def signing_root(object: Container) -> Hash` is a function defined in the [SimpleSerialize spec](../simple-serialize.md#self-signed-containers) to compute signing messages.
 
 ### `bls_domain`
 
@@ -758,7 +759,7 @@ def get_attestation_data_slot(state: BeaconState, data: AttestationData) -> Slot
 
 ```python
 def get_block_root_at_slot(state: BeaconState,
-                           slot: Slot) -> Bytes32:
+                           slot: Slot) -> Hash:
     """
     Return the block root at a recent ``slot``.
     """
@@ -770,7 +771,7 @@ def get_block_root_at_slot(state: BeaconState,
 
 ```python
 def get_block_root(state: BeaconState,
-                   epoch: Epoch) -> Bytes32:
+                   epoch: Epoch) -> Hash:
     """
     Return the block root at a recent ``epoch``.
     """
@@ -781,7 +782,7 @@ def get_block_root(state: BeaconState,
 
 ```python
 def get_randao_mix(state: BeaconState,
-                   epoch: Epoch) -> Bytes32:
+                   epoch: Epoch) -> Hash:
     """
     Return the randao mix at a recent ``epoch``.
     ``epoch`` expected to be between (current_epoch - LATEST_RANDAO_MIXES_LENGTH, current_epoch].
@@ -793,7 +794,7 @@ def get_randao_mix(state: BeaconState,
 
 ```python
 def get_active_index_root(state: BeaconState,
-                          epoch: Epoch) -> Bytes32:
+                          epoch: Epoch) -> Hash:
     """
     Return the index root at a recent ``epoch``.
     ``epoch`` expected to be between
@@ -806,7 +807,7 @@ def get_active_index_root(state: BeaconState,
 
 ```python
 def generate_seed(state: BeaconState,
-                  epoch: Epoch) -> Bytes32:
+                  epoch: Epoch) -> Hash:
     """
     Generate a seed for the given ``epoch``.
     """
@@ -844,7 +845,7 @@ def get_beacon_proposer_index(state: BeaconState) -> ValidatorIndex:
 ### `verify_merkle_branch`
 
 ```python
-def verify_merkle_branch(leaf: Bytes32, proof: List[Bytes32], depth: int, index: int, root: Bytes32) -> bool:
+def verify_merkle_branch(leaf: Hash, proof: List[Hash], depth: int, index: int, root: Hash) -> bool:
     """
     Verify that the given ``leaf`` is on the merkle branch ``proof``
     starting with the given ``root``.
@@ -861,7 +862,7 @@ def verify_merkle_branch(leaf: Bytes32, proof: List[Bytes32], depth: int, index:
 ### `get_shuffled_index`
 
 ```python
-def get_shuffled_index(index: int, index_count: int, seed: Bytes32) -> ValidatorIndex:
+def get_shuffled_index(index: int, index_count: int, seed: Hash) -> ValidatorIndex:
     """
     Return the shuffled validator index corresponding to ``seed`` (and ``index_count``).
     """
@@ -885,7 +886,7 @@ def get_shuffled_index(index: int, index_count: int, seed: Bytes32) -> Validator
 ### `compute_committee`
 
 ```python
-def compute_committee(indices: List[ValidatorIndex], seed: Bytes32, index: int, count: int) -> List[ValidatorIndex]:
+def compute_committee(indices: List[ValidatorIndex], seed: Hash, index: int, count: int) -> List[ValidatorIndex]:
     start = (len(indices) * index) // count
     end = (len(indices) * (index + 1)) // count
     return [indices[get_shuffled_index(ValidatorIndex(i), len(indices), seed)] for i in range(start, end)]

From f4de5e3c72b1a178f55379a8fb6468d5f1a9eb52 Mon Sep 17 00:00:00 2001
From: protolambda <proto@protolambda.com>
Date: Tue, 18 Jun 2019 21:50:53 +0200
Subject: [PATCH 15/21] fix review comment: one line cache set

---
 scripts/build_spec.py | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/scripts/build_spec.py b/scripts/build_spec.py
index d672db419f..4890beaac9 100644
--- a/scripts/build_spec.py
+++ b/scripts/build_spec.py
@@ -85,8 +85,7 @@ def compute_committee(indices: List[ValidatorIndex],  # type: ignore
     param_hash = (hash_tree_root(indices), seed, index, count)
 
     if param_hash not in committee_cache:
-        ret = _compute_committee(indices, seed, index, count)
-        committee_cache[param_hash] = ret
+        committee_cache[param_hash] = _compute_committee(indices, seed, index, count)
     return committee_cache[param_hash]
 
 

From 207f632e1a4c609a3edd2724fc98f2fa341e94a6 Mon Sep 17 00:00:00 2001
From: protolambda <proto@protolambda.com>
Date: Tue, 18 Jun 2019 21:53:39 +0200
Subject: [PATCH 16/21] resolve other ret comment

---
 scripts/build_spec.py | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/scripts/build_spec.py b/scripts/build_spec.py
index 4890beaac9..b7605df60b 100644
--- a/scripts/build_spec.py
+++ b/scripts/build_spec.py
@@ -91,13 +91,12 @@ def compute_committee(indices: List[ValidatorIndex],  # type: ignore
 
 # Monkey patch hash cache
 _hash = hash
-hash_cache: Dict[bytes, Bytes32] = {}
+hash_cache: Dict[bytes, Hash] = {}
 
 
 def hash(x: bytes) -> Hash:
     if x not in hash_cache:
-        ret = _hash(x)
-        hash_cache[x] = Hash(ret)
+        hash_cache[x] = Hash(_hash(x))
     return hash_cache[x]
 
 

From f0e909c8d853b3db38dbe8bdef25c1f80a9e5b4c Mon Sep 17 00:00:00 2001
From: protolambda <proto@protolambda.com>
Date: Tue, 18 Jun 2019 21:54:00 +0200
Subject: [PATCH 17/21] add mypy cache to gitignore

---
 .gitignore | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/.gitignore b/.gitignore
index 16d39a4342..4dff5fbcb3 100644
--- a/.gitignore
+++ b/.gitignore
@@ -9,7 +9,9 @@ build/
 output/
 
 eth2.0-spec-tests/
+
 .pytest_cache
+.mypy_cache
 
 # Dynamically built from Markdown spec
 test_libs/pyspec/eth2spec/phase0/spec.py

From 346e61dfeb1d4924ec0921a91e99dc4450764041 Mon Sep 17 00:00:00 2001
From: protolambda <proto@protolambda.com>
Date: Tue, 18 Jun 2019 21:57:37 +0200
Subject: [PATCH 18/21] make epoch pattern similar to exit-epoch loop

---
 specs/core/0_beacon-chain.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/specs/core/0_beacon-chain.md b/specs/core/0_beacon-chain.md
index 6534ce4f2d..8e81566340 100644
--- a/specs/core/0_beacon-chain.md
+++ b/specs/core/0_beacon-chain.md
@@ -704,11 +704,11 @@ def get_shard_delta(state: BeaconState, epoch: Epoch) -> int:
 ```python
 def get_epoch_start_shard(state: BeaconState, epoch: Epoch) -> Shard:
     assert epoch <= get_current_epoch(state) + 1
-    check_epoch = get_current_epoch(state) + 1
+    check_epoch = Epoch(get_current_epoch(state) + 1)
     shard = Shard((state.start_shard + get_shard_delta(state, get_current_epoch(state))) % SHARD_COUNT)
     while check_epoch > epoch:
-        check_epoch -= 1
-        shard = Shard((shard + SHARD_COUNT - get_shard_delta(state, Epoch(check_epoch))) % SHARD_COUNT)
+        check_epoch -= Epoch(1)
+        shard = Shard((shard + SHARD_COUNT - get_shard_delta(state, check_epoch)) % SHARD_COUNT)
     return shard
 ```
 

From 060041945cc25c95a8ec477800abc11dda21af11 Mon Sep 17 00:00:00 2001
From: protolambda <proto@protolambda.com>
Date: Tue, 18 Jun 2019 22:00:22 +0200
Subject: [PATCH 19/21] remove unnecessary cast

---
 specs/core/0_beacon-chain.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/specs/core/0_beacon-chain.md b/specs/core/0_beacon-chain.md
index 8e81566340..3016b52d88 100644
--- a/specs/core/0_beacon-chain.md
+++ b/specs/core/0_beacon-chain.md
@@ -843,7 +843,7 @@ def get_shuffled_index(index: ValidatorIndex, index_count: int, seed: Hash) -> V
         position = max(index, flip)
         source = hash(
             seed + int_to_bytes(current_round, length=1) +
-            int_to_bytes(ValidatorIndex(position // 256), length=4)
+            int_to_bytes(position // 256, length=4)
         )
         byte = source[(position % 256) // 8]
         bit = (byte >> (position % 8)) % 2

From 7d2f0a9dc0df1c69fc8178160325043b06cbb92c Mon Sep 17 00:00:00 2001
From: Hsiao-Wei Wang <hwwang156@gmail.com>
Date: Tue, 18 Jun 2019 14:07:05 -0600
Subject: [PATCH 20/21] clean up

---
 scripts/build_spec.py | 6 ------
 1 file changed, 6 deletions(-)

diff --git a/scripts/build_spec.py b/scripts/build_spec.py
index b7605df60b..e209e2c56a 100644
--- a/scripts/build_spec.py
+++ b/scripts/build_spec.py
@@ -132,17 +132,11 @@ def objects_to_spec(functions: Dict[str, str],
                 f"    def __init__(self, _x: {value}) -> None:\n"
                 f"        ...\n"
                 if value.startswith("uint")
-                # else ""
-                # else f"{key} = {value}\n"
                 else f"class {key}({value}):\n    pass\n"
                 for key, value in custom_types.items()
             ]
         )
     )
-    # new_type_definitions += '\n'.join(['Bytes%s = BytesN[%s]' % (n, n) for n in byte_types])
-    # new_type_definitions += '\n' + '\n'.join(['Hash = Bytes32', 'BLSPubkey = Bytes48', 'BLSSignature = Bytes96'])
-    # new_type_definitions += \
-    #     '\n' + '\n'.join(['''%s = NewType('%s', %s)''' % (key, key, value) for key, value in new_types.items()])
     functions_spec = '\n\n'.join(functions.values())
     constants_spec = '\n'.join(map(lambda x: '%s = %s' % (x, constants[x]), constants))
     ssz_objects_instantiation_spec = '\n\n'.join(ssz_objects.values())

From 6df75ec3d479faf0eba764033e2d66822dba89f8 Mon Sep 17 00:00:00 2001
From: protolambda <proto@protolambda.com>
Date: Tue, 18 Jun 2019 22:16:21 +0200
Subject: [PATCH 21/21] cleanup unused byte part of builder

---
 scripts/build_spec.py | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/scripts/build_spec.py b/scripts/build_spec.py
index e209e2c56a..3a1b22efd3 100644
--- a/scripts/build_spec.py
+++ b/scripts/build_spec.py
@@ -120,7 +120,6 @@ def objects_to_spec(functions: Dict[str, str],
                     ssz_objects: Dict[str, str],
                     inserts: Dict[str, str],
                     imports: Dict[str, str],
-                    byte_types: List[int],
                     ) -> str:
     """
     Given all the objects that constitute a spec, combine them into a single pyfile.
@@ -226,7 +225,7 @@ def combine_spec_objects(spec0: SpecObject, spec1: SpecObject) -> SpecObject:
 
 def build_phase0_spec(sourcefile: str, outfile: str=None) -> Optional[str]:
     functions, custom_types, constants, ssz_objects, inserts = get_spec(sourcefile)
-    spec = objects_to_spec(functions, custom_types, constants, ssz_objects, inserts, PHASE0_IMPORTS, BYTE_TYPES)
+    spec = objects_to_spec(functions, custom_types, constants, ssz_objects, inserts, PHASE0_IMPORTS)
     if outfile is not None:
         with open(outfile, 'w') as out:
             out.write(spec)
@@ -243,7 +242,7 @@ def build_phase1_spec(phase0_sourcefile: str,
     spec_objects = phase0_spec
     for value in [phase1_custody, phase1_shard_data]:
         spec_objects = combine_spec_objects(spec_objects, value)
-    spec = objects_to_spec(*spec_objects, PHASE1_IMPORTS, BYTE_TYPES)
+    spec = objects_to_spec(*spec_objects, PHASE1_IMPORTS)
     if outfile is not None:
         with open(outfile, 'w') as out:
             out.write(spec)