Clean up light client spec

specs/light_client/merkle_proofs.md

@@ -20,10 +20,10 @@ In a binary Merkle tree, we define a "generalized index" of a node as `2**depth
 Note that the generalized index has the convenient property that the two children of node `k` are `2k` and `2k+1`, and also that it equals the position of a node in the linear representation of the Merkle tree that's computed by this function:
 
 ```python
-def merkle_tree(leaves):
+def merkle_tree(leaves: List[Bytes32]) -> List[Bytes32]:
     o = [0] * len(leaves) + leaves
-    for i in range(len(leaves)-1, 0, -1):
-        o[i] = hash(o[i*2] + o[i*2+1])
+    for i in range(len(leaves) - 1, 0, -1):
+        o[i] = hash(o[i * 2] + o[i * 2 + 1])
     return o
 ```
 
@@ -47,33 +47,33 @@ y_data_root  len(y)
 We can now define a concept of a "path", a way of describing a function that takes as input an SSZ object and outputs some specific (possibly deeply nested) member. For example, `foo -> foo.x` is a path, as are `foo -> len(foo.y)` and `foo -> foo.y[5].w`. We'll describe paths as lists, which can have two representations. In "human-readable form", they are `["x"]`, `["y", "__len__"]` and `["y", 5, "w"]` respectively. In "encoded form", they are lists of `uint64` values, in these cases (assuming the fields of `foo` in order are `x` then `y`, and `w` is the first field of `y[i]`) `[0]`, `[1, 2**64-1]`, `[1, 5, 0]`.
 
 ```python
-def path_to_encoded_form(obj: Any, path: List[str or int]) -> List[int]:
+def path_to_encoded_form(obj: Any, path: List[Union[str, int]]) -> List[int]:
     if len(path) == 0:
         return []
-    if isinstance(path[0], "__len__"):
+    elif isinstance(path[0], "__len__"):
         assert len(path) == 1
         return [LENGTH_FLAG]
     elif isinstance(path[0], str) and hasattr(obj, "fields"):
         return [list(obj.fields.keys()).index(path[0])] + path_to_encoded_form(getattr(obj, path[0]), path[1:])
-    elif isinstance(obj, (StaticList, DynamicList)):
+    elif isinstance(obj, (Vector, List)):
         return [path[0]] + path_to_encoded_form(obj[path[0]], path[1:])
     else:
         raise Exception("Unknown type / path")
 ```
 
-We can now define a function `get_generalized_indices(object: Any, path: List[int], root=1: int) -> int` that converts an object and a path to a set of generalized indices (note that for constant-sized objects, there is only one generalized index and it only depends on the path, but for dynamically sized objects the indices may depend on the object itself too). For dynamically-sized objects, the set of indices will have more than one member because of the need to access an array's length to determine the correct generalized index for some array access.
+We can now define a function `get_generalized_indices(object: Any, path: List[int], root: int=1) -> List[int]` that converts an object and a path to a set of generalized indices (note that for constant-sized objects, there is only one generalized index and it only depends on the path, but for dynamically sized objects the indices may depend on the object itself too). For dynamically-sized objects, the set of indices will have more than one member because of the need to access an array's length to determine the correct generalized index for some array access.
 
 ```python
-def get_generalized_indices(obj: Any, path: List[int], root=1) -> List[int]:
+def get_generalized_indices(obj: Any, path: List[int], root: int=1) -> List[int]:
     if len(path) == 0:
         return [root]
-    elif isinstance(obj, StaticList):
+    elif isinstance(obj, Vector):
         items_per_chunk = (32 // len(serialize(x))) if isinstance(x, int) else 1
         new_root = root * next_power_of_2(len(obj) // items_per_chunk) + path[0] // items_per_chunk
         return get_generalized_indices(obj[path[0]], path[1:], new_root)
-    elif isinstance(obj, DynamicList) and path[0] == LENGTH_FLAG:
+    elif isinstance(obj, List) and path[0] == LENGTH_FLAG:
         return [root * 2 + 1]
-    elif isinstance(obj, DynamicList) and isinstance(path[0], int):
+    elif isinstance(obj, List) and isinstance(path[0], int):
         assert path[0] < len(obj)
         items_per_chunk = (32 // len(serialize(x))) if isinstance(x, int) else 1
         new_root = root * 2 * next_power_of_2(len(obj) // items_per_chunk) + path[0] // items_per_chunk
@@ -99,27 +99,20 @@ x x . . . . x *
 
 . are unused nodes, * are used nodes, x are the values we are trying to prove. Notice how despite being a multiproof for 3 values, it requires only 3 auxiliary nodes, only one node more than would be required to prove a single value. Normally the efficiency gains are not quite that extreme, but the savings relative to individual Merkle proofs are still significant. As a rule of thumb, a multiproof for k nodes at the same level of an n-node tree has size `k * (n/k + log(n/k))`.
 
-Here is code for creating and verifying a multiproof. First a helper:
-
-```python
-def log2(x):
-    return 0 if x == 1 else 1 + log2(x//2)
-```
-
-First, a method for computing the generalized indices of the auxiliary tree nodes that a proof of a given set of generalized indices will require:
+Here is code for creating and verifying a multiproof. First, a method for computing the generalized indices of the auxiliary tree nodes that a proof of a given set of generalized indices will require:
 
 ```python
 def get_proof_indices(tree_indices: List[int]) -> List[int]:
     # Get all indices touched by the proof
-    maximal_indices = set({})
+    maximal_indices = set()
     for i in tree_indices:
         x = i
         while x > 1:
             maximal_indices.add(x ^ 1)
             x //= 2
     maximal_indices = tree_indices + sorted(list(maximal_indices))[::-1]
     # Get indices that cannot be recalculated from earlier indices
-    redundant_indices = set({})
+    redundant_indices = set()
     proof = []
     for index in maximal_indices:
         if index not in redundant_indices:
@@ -130,26 +123,26 @@ def get_proof_indices(tree_indices: List[int]) -> List[int]:
                     break
                 index //= 2
     return [i for i in proof if i not in tree_indices]
-````
+```
 
 Generating a proof is simply a matter of taking the node of the SSZ hash tree with the union of the given generalized indices for each index given by `get_proof_indices`, and outputting the list of nodes in the same order.
 
 Here is the verification function:
 
 ```python
-def verify_multi_proof(root, indices, leaves, proof):
+def verify_multi_proof(root: Bytes32, indices: List[int], leaves: List[Bytes32], proof: List[bytes]) -> bool:
     tree = {}
     for index, leaf in zip(indices, leaves):
         tree[index] = leaf
-    for index, proofitem in zip(get_proof_indices(indices), proof):
-        tree[index] = proofitem
-    indexqueue = sorted(tree.keys())[:-1]
+    for index, proof_item in zip(get_proof_indices(indices), proof):
+        tree[index] = proof_item
+    index_queue = sorted(tree.keys())[:-1]
     i = 0
-    while i < len(indexqueue):
-        index = indexqueue[i]
-        if index >= 2 and index^1 in tree:
-            tree[index//2] = hash(tree[index - index%2] + tree[index - index%2 + 1])
-            indexqueue.append(index//2)
+    while i < len(index_queue):
+        index = index_queue[i]
+        if index >= 2 and index ^ 1 in tree:
+            tree[index // 2] = hash(tree[index - index % 2] + tree[index - index % 2 + 1])
+            index_queue.append(index // 2)
         i += 1
     return (indices == []) or (1 in tree and tree[1] == root)
 ```
@@ -158,7 +151,7 @@ def verify_multi_proof(root, indices, leaves, proof):
 
 We define:
 
-#### `MerklePartial`
+#### `SSZMerklePartial`
 
 
 ```python
@@ -172,6 +165,6 @@ We define:
 
 #### Proofs for execution
 
-We define `MerklePartial(f, arg1, arg2..., focus=0)` as being a `MerklePartial` object wrapping a Merkle multiproof of the set of nodes in the hash tree of the SSZ object `arg[focus]` that is needed to authenticate the parts of the object needed to compute `f(arg1, arg2...)`.
+We define `MerklePartial(f, arg1, arg2..., focus=0)` as being a `SSZMerklePartial` object wrapping a Merkle multiproof of the set of nodes in the hash tree of the SSZ object `arg[focus]` that is needed to authenticate the parts of the object needed to compute `f(arg1, arg2...)`.
 
-Ideally, any function which accepts an SSZ object should also be able to accept a `MerklePartial` object as a substitute.
+Ideally, any function which accepts an SSZ object should also be able to accept a `SSZMerklePartial` object as a substitute.

specs/light_client/sync_protocol.md

@@ -5,16 +5,19 @@ __NOTICE__: This document is a work-in-progress for researchers and implementers
 ## Table of Contents
 
 <!-- TOC -->
+
 - [Beacon Chain Light Client Syncing](#beacon-chain-light-client-syncing)
     - [Table of Contents](#table-of-contents)
-    - [Light client state](#light-client-state)
-    - [Updating the shuffled committee](#updating-the-shuffled-committee)
-    - [Computing the current committee](#computing-the-current-committee)  
-    - [Verifying blocks](#verifying-blocks)      
+    - [Preliminaries](#preliminaries)
+        - [Light client state](#light-client-state)
+        - [Updating the shuffled committee](#updating-the-shuffled-committee)
+    - [Computing the current committee](#computing-the-current-committee)
+    - [Verifying blocks](#verifying-blocks)
+
 <!-- /TOC -->
 
 
-### Preliminaries
+## Preliminaries
 
 We define an "expansion" of an object as an object where a field in an object that is meant to represent the `hash_tree_root` of another object is replaced by the object. Note that defining expansions is not a consensus-layer-change; it is merely a "re-interpretation" of the object. Particularly, the `hash_tree_root` of an expansion of an object is identical to that of the original object, and we can define expansions where, given a complete history, it is always possible to compute the expansion of any object in the history. The opposite of an expansion is a "summary" (eg. `BeaconBlockHeader` is a summary of `BeaconBlock`).
 
@@ -40,7 +43,7 @@ We add a data type `PeriodData` and four helpers:
 {
     'validator_count': 'uint64',
     'seed': 'bytes32',
-    'committee': [Validator]
+    'committee': [Validator],
 }
 ```
 
@@ -85,14 +88,13 @@ later_period_data = get_period_data(new_committee_proof, finalized_header, shard
 
 The maximum size of a proof is `128 * ((22-7) * 32 + 110) = 75520` bytes for validator records and `(22-7) * 32 + 128 * 8 = 1504` for the active index proof (much smaller because the relevant active indices are all beside each other in the Merkle tree). This needs to be done once per `PERSISTENT_COMMITTEE_PERIOD` epochs (2048 epochs / 9 days), or ~38 bytes per epoch.
 
-### Computing the current committee
+## Computing the current committee
 
 Here is a helper to compute the committee at a slot given the maximal earlier and later committees:
 
 ```python
 def compute_committee(header: BeaconBlockHeader,
-                      validator_memory: ValidatorMemory):
-
+                      validator_memory: ValidatorMemory) -> List[ValidatorIndex]:
     earlier_validator_count = validator_memory.earlier_period_data.validator_count
     later_validator_count = validator_memory.later_period_data.validator_count
     maximal_earlier_committee = validator_memory.earlier_period_data.committee
@@ -105,11 +107,13 @@ def compute_committee(header: BeaconBlockHeader,
         earlier_validator_count // (SHARD_COUNT * TARGET_COMMITTEE_SIZE),
         later_validator_count // (SHARD_COUNT * TARGET_COMMITTEE_SIZE),
     ) + 1
-
-    def get_offset(count, end:bool):
-        return get_split_offset(count,
-                                SHARD_COUNT * committee_count,
-                                validator_memory.shard_id * committee_count + (1 if end else 0))
+
+    def get_offset(count: int, end: bool) -> int:
+        return get_split_offset(
+            count,
+            SHARD_COUNT * committee_count,
+            validator_memory.shard_id * committee_count + (1 if end else 0),
+        )
 
     actual_earlier_committee = maximal_earlier_committee[
         0:get_offset(earlier_validator_count, True) - get_offset(earlier_validator_count, False)
@@ -129,21 +133,20 @@ def compute_committee(header: BeaconBlockHeader,
         [i for i in earlier_committee if epoch % PERSISTENT_COMMITTEE_PERIOD < get_switchover_epoch(i)] +
         [i for i in later_committee if epoch % PERSISTENT_COMMITTEE_PERIOD >= get_switchover_epoch(i)]
     )))
-
 ```
 
 Note that this method makes use of the fact that the committee for any given shard always starts and ends at the same validator index independently of the committee count (this is because the validator set is split into `SHARD_COUNT * committee_count` slices but the first slice of a shard is a multiple `committee_count * i`, so the start of the slice is `n * committee_count * i // (SHARD_COUNT * committee_count) = n * i // SHARD_COUNT`, using the slightly nontrivial algebraic identity `(x * a) // ab == x // b`).
 
-### Verifying blocks
+## Verifying blocks
 
 If a client wants to update its `finalized_header` it asks the network for a `BlockValidityProof`, which is simply:
 
 ```python
 {
-    'header': BlockHeader,
+    'header': BeaconBlockHeader,
     'shard_aggregate_signature': 'bytes96',
     'shard_bitfield': 'bytes',
-    'shard_parent_block': ShardBlock
+    'shard_parent_block': ShardBlock,
 }
 ```