##// END OF EJS Templates
Merge pull request #7561 from minrk/nbformat-doc...
Merge pull request #7561 from minrk/nbformat-doc describe what constitutes a minor revision to nbformat

File last commit:

r18336:ed94683b
r20138:9be4df70 merge
Show More
session.py
873 lines | 30.6 KiB | text/x-python | PythonLexer
"""Session object for building, serializing, sending, and receiving messages in
IPython. The Session object supports serialization, HMAC signatures, and
metadata on messages.
Also defined here are utilities for working with Sessions:
* A SessionFactory to be used as a base class for configurables that work with
Sessions.
* A Message object for convenience that allows attribute-access to the msg dict.
"""
# Copyright (c) IPython Development Team.
# Distributed under the terms of the Modified BSD License.
import hashlib
import hmac
import logging
import os
import pprint
import random
import uuid
import warnings
from datetime import datetime
try:
import cPickle
pickle = cPickle
except:
cPickle = None
import pickle
try:
# We are using compare_digest to limit the surface of timing attacks
from hmac import compare_digest
except ImportError:
# Python < 2.7.7: When digests don't match no feedback is provided,
# limiting the surface of attack
def compare_digest(a,b): return a == b
import zmq
from zmq.utils import jsonapi
from zmq.eventloop.ioloop import IOLoop
from zmq.eventloop.zmqstream import ZMQStream
from IPython.core.release import kernel_protocol_version
from IPython.config.configurable import Configurable, LoggingConfigurable
from IPython.utils import io
from IPython.utils.importstring import import_item
from IPython.utils.jsonutil import extract_dates, squash_dates, date_default
from IPython.utils.py3compat import (str_to_bytes, str_to_unicode, unicode_type,
iteritems)
from IPython.utils.traitlets import (CBytes, Unicode, Bool, Any, Instance, Set,
DottedObjectName, CUnicode, Dict, Integer,
TraitError,
)
from IPython.utils.pickleutil import PICKLE_PROTOCOL
from IPython.kernel.adapter import adapt
from IPython.kernel.zmq.serialize import MAX_ITEMS, MAX_BYTES
#-----------------------------------------------------------------------------
# utility functions
#-----------------------------------------------------------------------------
def squash_unicode(obj):
"""coerce unicode back to bytestrings."""
if isinstance(obj,dict):
for key in obj.keys():
obj[key] = squash_unicode(obj[key])
if isinstance(key, unicode_type):
obj[squash_unicode(key)] = obj.pop(key)
elif isinstance(obj, list):
for i,v in enumerate(obj):
obj[i] = squash_unicode(v)
elif isinstance(obj, unicode_type):
obj = obj.encode('utf8')
return obj
#-----------------------------------------------------------------------------
# globals and defaults
#-----------------------------------------------------------------------------
# ISO8601-ify datetime objects
# allow unicode
# disallow nan, because it's not actually valid JSON
json_packer = lambda obj: jsonapi.dumps(obj, default=date_default,
ensure_ascii=False, allow_nan=False,
)
json_unpacker = lambda s: jsonapi.loads(s)
pickle_packer = lambda o: pickle.dumps(squash_dates(o), PICKLE_PROTOCOL)
pickle_unpacker = pickle.loads
default_packer = json_packer
default_unpacker = json_unpacker
DELIM = b"<IDS|MSG>"
# singleton dummy tracker, which will always report as done
DONE = zmq.MessageTracker()
#-----------------------------------------------------------------------------
# Mixin tools for apps that use Sessions
#-----------------------------------------------------------------------------
session_aliases = dict(
ident = 'Session.session',
user = 'Session.username',
keyfile = 'Session.keyfile',
)
session_flags = {
'secure' : ({'Session' : { 'key' : str_to_bytes(str(uuid.uuid4())),
'keyfile' : '' }},
"""Use HMAC digests for authentication of messages.
Setting this flag will generate a new UUID to use as the HMAC key.
"""),
'no-secure' : ({'Session' : { 'key' : b'', 'keyfile' : '' }},
"""Don't authenticate messages."""),
}
def default_secure(cfg):
"""Set the default behavior for a config environment to be secure.
If Session.key/keyfile have not been set, set Session.key to
a new random UUID.
"""
if 'Session' in cfg:
if 'key' in cfg.Session or 'keyfile' in cfg.Session:
return
# key/keyfile not specified, generate new UUID:
cfg.Session.key = str_to_bytes(str(uuid.uuid4()))
#-----------------------------------------------------------------------------
# Classes
#-----------------------------------------------------------------------------
class SessionFactory(LoggingConfigurable):
"""The Base class for configurables that have a Session, Context, logger,
and IOLoop.
"""
logname = Unicode('')
def _logname_changed(self, name, old, new):
self.log = logging.getLogger(new)
# not configurable:
context = Instance('zmq.Context')
def _context_default(self):
return zmq.Context.instance()
session = Instance('IPython.kernel.zmq.session.Session')
loop = Instance('zmq.eventloop.ioloop.IOLoop', allow_none=False)
def _loop_default(self):
return IOLoop.instance()
def __init__(self, **kwargs):
super(SessionFactory, self).__init__(**kwargs)
if self.session is None:
# construct the session
self.session = Session(**kwargs)
class Message(object):
"""A simple message object that maps dict keys to attributes.
A Message can be created from a dict and a dict from a Message instance
simply by calling dict(msg_obj)."""
def __init__(self, msg_dict):
dct = self.__dict__
for k, v in iteritems(dict(msg_dict)):
if isinstance(v, dict):
v = Message(v)
dct[k] = v
# Having this iterator lets dict(msg_obj) work out of the box.
def __iter__(self):
return iter(iteritems(self.__dict__))
def __repr__(self):
return repr(self.__dict__)
def __str__(self):
return pprint.pformat(self.__dict__)
def __contains__(self, k):
return k in self.__dict__
def __getitem__(self, k):
return self.__dict__[k]
def msg_header(msg_id, msg_type, username, session):
date = datetime.now()
version = kernel_protocol_version
return locals()
def extract_header(msg_or_header):
"""Given a message or header, return the header."""
if not msg_or_header:
return {}
try:
# See if msg_or_header is the entire message.
h = msg_or_header['header']
except KeyError:
try:
# See if msg_or_header is just the header
h = msg_or_header['msg_id']
except KeyError:
raise
else:
h = msg_or_header
if not isinstance(h, dict):
h = dict(h)
return h
class Session(Configurable):
"""Object for handling serialization and sending of messages.
The Session object handles building messages and sending them
with ZMQ sockets or ZMQStream objects. Objects can communicate with each
other over the network via Session objects, and only need to work with the
dict-based IPython message spec. The Session will handle
serialization/deserialization, security, and metadata.
Sessions support configurable serialization via packer/unpacker traits,
and signing with HMAC digests via the key/keyfile traits.
Parameters
----------
debug : bool
whether to trigger extra debugging statements
packer/unpacker : str : 'json', 'pickle' or import_string
importstrings for methods to serialize message parts. If just
'json' or 'pickle', predefined JSON and pickle packers will be used.
Otherwise, the entire importstring must be used.
The functions must accept at least valid JSON input, and output *bytes*.
For example, to use msgpack:
packer = 'msgpack.packb', unpacker='msgpack.unpackb'
pack/unpack : callables
You can also set the pack/unpack callables for serialization directly.
session : bytes
the ID of this Session object. The default is to generate a new UUID.
username : unicode
username added to message headers. The default is to ask the OS.
key : bytes
The key used to initialize an HMAC signature. If unset, messages
will not be signed or checked.
keyfile : filepath
The file containing a key. If this is set, `key` will be initialized
to the contents of the file.
"""
debug=Bool(False, config=True, help="""Debug output in the Session""")
packer = DottedObjectName('json',config=True,
help="""The name of the packer for serializing messages.
Should be one of 'json', 'pickle', or an import name
for a custom callable serializer.""")
def _packer_changed(self, name, old, new):
if new.lower() == 'json':
self.pack = json_packer
self.unpack = json_unpacker
self.unpacker = new
elif new.lower() == 'pickle':
self.pack = pickle_packer
self.unpack = pickle_unpacker
self.unpacker = new
else:
self.pack = import_item(str(new))
unpacker = DottedObjectName('json', config=True,
help="""The name of the unpacker for unserializing messages.
Only used with custom functions for `packer`.""")
def _unpacker_changed(self, name, old, new):
if new.lower() == 'json':
self.pack = json_packer
self.unpack = json_unpacker
self.packer = new
elif new.lower() == 'pickle':
self.pack = pickle_packer
self.unpack = pickle_unpacker
self.packer = new
else:
self.unpack = import_item(str(new))
session = CUnicode(u'', config=True,
help="""The UUID identifying this session.""")
def _session_default(self):
u = unicode_type(uuid.uuid4())
self.bsession = u.encode('ascii')
return u
def _session_changed(self, name, old, new):
self.bsession = self.session.encode('ascii')
# bsession is the session as bytes
bsession = CBytes(b'')
username = Unicode(str_to_unicode(os.environ.get('USER', 'username')),
help="""Username for the Session. Default is your system username.""",
config=True)
metadata = Dict({}, config=True,
help="""Metadata dictionary, which serves as the default top-level metadata dict for each message.""")
# if 0, no adapting to do.
adapt_version = Integer(0)
# message signature related traits:
key = CBytes(b'', config=True,
help="""execution key, for extra authentication.""")
def _key_changed(self):
self._new_auth()
signature_scheme = Unicode('hmac-sha256', config=True,
help="""The digest scheme used to construct the message signatures.
Must have the form 'hmac-HASH'.""")
def _signature_scheme_changed(self, name, old, new):
if not new.startswith('hmac-'):
raise TraitError("signature_scheme must start with 'hmac-', got %r" % new)
hash_name = new.split('-', 1)[1]
try:
self.digest_mod = getattr(hashlib, hash_name)
except AttributeError:
raise TraitError("hashlib has no such attribute: %s" % hash_name)
self._new_auth()
digest_mod = Any()
def _digest_mod_default(self):
return hashlib.sha256
auth = Instance(hmac.HMAC)
def _new_auth(self):
if self.key:
self.auth = hmac.HMAC(self.key, digestmod=self.digest_mod)
else:
self.auth = None
digest_history = Set()
digest_history_size = Integer(2**16, config=True,
help="""The maximum number of digests to remember.
The digest history will be culled when it exceeds this value.
"""
)
keyfile = Unicode('', config=True,
help="""path to file containing execution key.""")
def _keyfile_changed(self, name, old, new):
with open(new, 'rb') as f:
self.key = f.read().strip()
# for protecting against sends from forks
pid = Integer()
# serialization traits:
pack = Any(default_packer) # the actual packer function
def _pack_changed(self, name, old, new):
if not callable(new):
raise TypeError("packer must be callable, not %s"%type(new))
unpack = Any(default_unpacker) # the actual packer function
def _unpack_changed(self, name, old, new):
# unpacker is not checked - it is assumed to be
if not callable(new):
raise TypeError("unpacker must be callable, not %s"%type(new))
# thresholds:
copy_threshold = Integer(2**16, config=True,
help="Threshold (in bytes) beyond which a buffer should be sent without copying.")
buffer_threshold = Integer(MAX_BYTES, config=True,
help="Threshold (in bytes) beyond which an object's buffer should be extracted to avoid pickling.")
item_threshold = Integer(MAX_ITEMS, config=True,
help="""The maximum number of items for a container to be introspected for custom serialization.
Containers larger than this are pickled outright.
"""
)
def __init__(self, **kwargs):
"""create a Session object
Parameters
----------
debug : bool
whether to trigger extra debugging statements
packer/unpacker : str : 'json', 'pickle' or import_string
importstrings for methods to serialize message parts. If just
'json' or 'pickle', predefined JSON and pickle packers will be used.
Otherwise, the entire importstring must be used.
The functions must accept at least valid JSON input, and output
*bytes*.
For example, to use msgpack:
packer = 'msgpack.packb', unpacker='msgpack.unpackb'
pack/unpack : callables
You can also set the pack/unpack callables for serialization
directly.
session : unicode (must be ascii)
the ID of this Session object. The default is to generate a new
UUID.
bsession : bytes
The session as bytes
username : unicode
username added to message headers. The default is to ask the OS.
key : bytes
The key used to initialize an HMAC signature. If unset, messages
will not be signed or checked.
signature_scheme : str
The message digest scheme. Currently must be of the form 'hmac-HASH',
where 'HASH' is a hashing function available in Python's hashlib.
The default is 'hmac-sha256'.
This is ignored if 'key' is empty.
keyfile : filepath
The file containing a key. If this is set, `key` will be
initialized to the contents of the file.
"""
super(Session, self).__init__(**kwargs)
self._check_packers()
self.none = self.pack({})
# ensure self._session_default() if necessary, so bsession is defined:
self.session
self.pid = os.getpid()
@property
def msg_id(self):
"""always return new uuid"""
return str(uuid.uuid4())
def _check_packers(self):
"""check packers for datetime support."""
pack = self.pack
unpack = self.unpack
# check simple serialization
msg = dict(a=[1,'hi'])
try:
packed = pack(msg)
except Exception as e:
msg = "packer '{packer}' could not serialize a simple message: {e}{jsonmsg}"
if self.packer == 'json':
jsonmsg = "\nzmq.utils.jsonapi.jsonmod = %s" % jsonapi.jsonmod
else:
jsonmsg = ""
raise ValueError(
msg.format(packer=self.packer, e=e, jsonmsg=jsonmsg)
)
# ensure packed message is bytes
if not isinstance(packed, bytes):
raise ValueError("message packed to %r, but bytes are required"%type(packed))
# check that unpack is pack's inverse
try:
unpacked = unpack(packed)
assert unpacked == msg
except Exception as e:
msg = "unpacker '{unpacker}' could not handle output from packer '{packer}': {e}{jsonmsg}"
if self.packer == 'json':
jsonmsg = "\nzmq.utils.jsonapi.jsonmod = %s" % jsonapi.jsonmod
else:
jsonmsg = ""
raise ValueError(
msg.format(packer=self.packer, unpacker=self.unpacker, e=e, jsonmsg=jsonmsg)
)
# check datetime support
msg = dict(t=datetime.now())
try:
unpacked = unpack(pack(msg))
if isinstance(unpacked['t'], datetime):
raise ValueError("Shouldn't deserialize to datetime")
except Exception:
self.pack = lambda o: pack(squash_dates(o))
self.unpack = lambda s: unpack(s)
def msg_header(self, msg_type):
return msg_header(self.msg_id, msg_type, self.username, self.session)
def msg(self, msg_type, content=None, parent=None, header=None, metadata=None):
"""Return the nested message dict.
This format is different from what is sent over the wire. The
serialize/deserialize methods converts this nested message dict to the wire
format, which is a list of message parts.
"""
msg = {}
header = self.msg_header(msg_type) if header is None else header
msg['header'] = header
msg['msg_id'] = header['msg_id']
msg['msg_type'] = header['msg_type']
msg['parent_header'] = {} if parent is None else extract_header(parent)
msg['content'] = {} if content is None else content
msg['metadata'] = self.metadata.copy()
if metadata is not None:
msg['metadata'].update(metadata)
return msg
def sign(self, msg_list):
"""Sign a message with HMAC digest. If no auth, return b''.
Parameters
----------
msg_list : list
The [p_header,p_parent,p_content] part of the message list.
"""
if self.auth is None:
return b''
h = self.auth.copy()
for m in msg_list:
h.update(m)
return str_to_bytes(h.hexdigest())
def serialize(self, msg, ident=None):
"""Serialize the message components to bytes.
This is roughly the inverse of deserialize. The serialize/deserialize
methods work with full message lists, whereas pack/unpack work with
the individual message parts in the message list.
Parameters
----------
msg : dict or Message
The next message dict as returned by the self.msg method.
Returns
-------
msg_list : list
The list of bytes objects to be sent with the format::
[ident1, ident2, ..., DELIM, HMAC, p_header, p_parent,
p_metadata, p_content, buffer1, buffer2, ...]
In this list, the ``p_*`` entities are the packed or serialized
versions, so if JSON is used, these are utf8 encoded JSON strings.
"""
content = msg.get('content', {})
if content is None:
content = self.none
elif isinstance(content, dict):
content = self.pack(content)
elif isinstance(content, bytes):
# content is already packed, as in a relayed message
pass
elif isinstance(content, unicode_type):
# should be bytes, but JSON often spits out unicode
content = content.encode('utf8')
else:
raise TypeError("Content incorrect type: %s"%type(content))
real_message = [self.pack(msg['header']),
self.pack(msg['parent_header']),
self.pack(msg['metadata']),
content,
]
to_send = []
if isinstance(ident, list):
# accept list of idents
to_send.extend(ident)
elif ident is not None:
to_send.append(ident)
to_send.append(DELIM)
signature = self.sign(real_message)
to_send.append(signature)
to_send.extend(real_message)
return to_send
def send(self, stream, msg_or_type, content=None, parent=None, ident=None,
buffers=None, track=False, header=None, metadata=None):
"""Build and send a message via stream or socket.
The message format used by this function internally is as follows:
[ident1,ident2,...,DELIM,HMAC,p_header,p_parent,p_content,
buffer1,buffer2,...]
The serialize/deserialize methods convert the nested message dict into this
format.
Parameters
----------
stream : zmq.Socket or ZMQStream
The socket-like object used to send the data.
msg_or_type : str or Message/dict
Normally, msg_or_type will be a msg_type unless a message is being
sent more than once. If a header is supplied, this can be set to
None and the msg_type will be pulled from the header.
content : dict or None
The content of the message (ignored if msg_or_type is a message).
header : dict or None
The header dict for the message (ignored if msg_to_type is a message).
parent : Message or dict or None
The parent or parent header describing the parent of this message
(ignored if msg_or_type is a message).
ident : bytes or list of bytes
The zmq.IDENTITY routing path.
metadata : dict or None
The metadata describing the message
buffers : list or None
The already-serialized buffers to be appended to the message.
track : bool
Whether to track. Only for use with Sockets, because ZMQStream
objects cannot track messages.
Returns
-------
msg : dict
The constructed message.
"""
if not isinstance(stream, zmq.Socket):
# ZMQStreams and dummy sockets do not support tracking.
track = False
if isinstance(msg_or_type, (Message, dict)):
# We got a Message or message dict, not a msg_type so don't
# build a new Message.
msg = msg_or_type
buffers = buffers or msg.get('buffers', [])
else:
msg = self.msg(msg_or_type, content=content, parent=parent,
header=header, metadata=metadata)
if not os.getpid() == self.pid:
io.rprint("WARNING: attempted to send message from fork")
io.rprint(msg)
return
buffers = [] if buffers is None else buffers
if self.adapt_version:
msg = adapt(msg, self.adapt_version)
to_send = self.serialize(msg, ident)
to_send.extend(buffers)
longest = max([ len(s) for s in to_send ])
copy = (longest < self.copy_threshold)
if buffers and track and not copy:
# only really track when we are doing zero-copy buffers
tracker = stream.send_multipart(to_send, copy=False, track=True)
else:
# use dummy tracker, which will be done immediately
tracker = DONE
stream.send_multipart(to_send, copy=copy)
if self.debug:
pprint.pprint(msg)
pprint.pprint(to_send)
pprint.pprint(buffers)
msg['tracker'] = tracker
return msg
def send_raw(self, stream, msg_list, flags=0, copy=True, ident=None):
"""Send a raw message via ident path.
This method is used to send a already serialized message.
Parameters
----------
stream : ZMQStream or Socket
The ZMQ stream or socket to use for sending the message.
msg_list : list
The serialized list of messages to send. This only includes the
[p_header,p_parent,p_metadata,p_content,buffer1,buffer2,...] portion of
the message.
ident : ident or list
A single ident or a list of idents to use in sending.
"""
to_send = []
if isinstance(ident, bytes):
ident = [ident]
if ident is not None:
to_send.extend(ident)
to_send.append(DELIM)
to_send.append(self.sign(msg_list))
to_send.extend(msg_list)
stream.send_multipart(to_send, flags, copy=copy)
def recv(self, socket, mode=zmq.NOBLOCK, content=True, copy=True):
"""Receive and unpack a message.
Parameters
----------
socket : ZMQStream or Socket
The socket or stream to use in receiving.
Returns
-------
[idents], msg
[idents] is a list of idents and msg is a nested message dict of
same format as self.msg returns.
"""
if isinstance(socket, ZMQStream):
socket = socket.socket
try:
msg_list = socket.recv_multipart(mode, copy=copy)
except zmq.ZMQError as e:
if e.errno == zmq.EAGAIN:
# We can convert EAGAIN to None as we know in this case
# recv_multipart won't return None.
return None,None
else:
raise
# split multipart message into identity list and message dict
# invalid large messages can cause very expensive string comparisons
idents, msg_list = self.feed_identities(msg_list, copy)
try:
return idents, self.deserialize(msg_list, content=content, copy=copy)
except Exception as e:
# TODO: handle it
raise e
def feed_identities(self, msg_list, copy=True):
"""Split the identities from the rest of the message.
Feed until DELIM is reached, then return the prefix as idents and
remainder as msg_list. This is easily broken by setting an IDENT to DELIM,
but that would be silly.
Parameters
----------
msg_list : a list of Message or bytes objects
The message to be split.
copy : bool
flag determining whether the arguments are bytes or Messages
Returns
-------
(idents, msg_list) : two lists
idents will always be a list of bytes, each of which is a ZMQ
identity. msg_list will be a list of bytes or zmq.Messages of the
form [HMAC,p_header,p_parent,p_content,buffer1,buffer2,...] and
should be unpackable/unserializable via self.deserialize at this
point.
"""
if copy:
idx = msg_list.index(DELIM)
return msg_list[:idx], msg_list[idx+1:]
else:
failed = True
for idx,m in enumerate(msg_list):
if m.bytes == DELIM:
failed = False
break
if failed:
raise ValueError("DELIM not in msg_list")
idents, msg_list = msg_list[:idx], msg_list[idx+1:]
return [m.bytes for m in idents], msg_list
def _add_digest(self, signature):
"""add a digest to history to protect against replay attacks"""
if self.digest_history_size == 0:
# no history, never add digests
return
self.digest_history.add(signature)
if len(self.digest_history) > self.digest_history_size:
# threshold reached, cull 10%
self._cull_digest_history()
def _cull_digest_history(self):
"""cull the digest history
Removes a randomly selected 10% of the digest history
"""
current = len(self.digest_history)
n_to_cull = max(int(current // 10), current - self.digest_history_size)
if n_to_cull >= current:
self.digest_history = set()
return
to_cull = random.sample(self.digest_history, n_to_cull)
self.digest_history.difference_update(to_cull)
def deserialize(self, msg_list, content=True, copy=True):
"""Unserialize a msg_list to a nested message dict.
This is roughly the inverse of serialize. The serialize/deserialize
methods work with full message lists, whereas pack/unpack work with
the individual message parts in the message list.
Parameters
----------
msg_list : list of bytes or Message objects
The list of message parts of the form [HMAC,p_header,p_parent,
p_metadata,p_content,buffer1,buffer2,...].
content : bool (True)
Whether to unpack the content dict (True), or leave it packed
(False).
copy : bool (True)
Whether to return the bytes (True), or the non-copying Message
object in each place (False).
Returns
-------
msg : dict
The nested message dict with top-level keys [header, parent_header,
content, buffers].
"""
minlen = 5
message = {}
if not copy:
for i in range(minlen):
msg_list[i] = msg_list[i].bytes
if self.auth is not None:
signature = msg_list[0]
if not signature:
raise ValueError("Unsigned Message")
if signature in self.digest_history:
raise ValueError("Duplicate Signature: %r" % signature)
self._add_digest(signature)
check = self.sign(msg_list[1:5])
if not compare_digest(signature, check):
raise ValueError("Invalid Signature: %r" % signature)
if not len(msg_list) >= minlen:
raise TypeError("malformed message, must have at least %i elements"%minlen)
header = self.unpack(msg_list[1])
message['header'] = extract_dates(header)
message['msg_id'] = header['msg_id']
message['msg_type'] = header['msg_type']
message['parent_header'] = extract_dates(self.unpack(msg_list[2]))
message['metadata'] = self.unpack(msg_list[3])
if content:
message['content'] = self.unpack(msg_list[4])
else:
message['content'] = msg_list[4]
message['buffers'] = msg_list[5:]
# adapt to the current version
return adapt(message)
def unserialize(self, *args, **kwargs):
warnings.warn(
"Session.unserialize is deprecated. Use Session.deserialize.",
DeprecationWarning,
)
return self.deserialize(*args, **kwargs)
def test_msg2obj():
am = dict(x=1)
ao = Message(am)
assert ao.x == am['x']
am['y'] = dict(z=1)
ao = Message(am)
assert ao.y.z == am['y']['z']
k1, k2 = 'y', 'z'
assert ao[k1][k2] == am[k1][k2]
am2 = dict(ao)
assert am['x'] == am2['x']
assert am['y']['z'] == am2['y']['z']