Refactor BER decoder into a suspendable coroutine

The goal of this change is to make the decoder stopping on input
data starvation and resuming from where it stopped whenever the
caller decides to try again (hopefully making sure that some more
input becomes available).

This change makes it possible for the decoder to operate on streams
of data (meaning that the entire DER blob might not be immediately
available on input).

On top of that, the decoder yields partially reconstructed ASN.1
object on input starvation making it possible for the caller to
inspect what has been decoded so far and possibly consume partial
ASN.1 data.

All these new feature are natively available through
`StreamingDecoder` class. Previously published API is implemented
as a thin wrapper on top of that ensuring backward compatibility.

18 files changed, 1605 insertions, 902 deletions

diff --git a/CHANGES.rst b/CHANGES.rst
index 9b4c3af..9297c9b 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -1,7 +1,27 @@
 
-Revision 0.4.8, released XX-09-2019
+Revision 0.5.0, released XX-09-2019
 -----------------------------------
 
+- Refactor BER/CER/DER decoder into a coroutine.
+
+  The goal of this change is to make the decoder stopping on input
+  data starvation and resuming from where it stopped whenever the
+  caller decides to try again (hopefully making sure that some more
+  input becomes available).
+
+  This change makes it possible for the decoder to operate on streams
+  of data (meaning that the entire DER blob might not be immediately
+  available on input).
+
+  On top of that, the decoder yields partially reconstructed ASN.1
+  object on input starvation making it possible for the caller to
+  inspect what has been decoded so far and possibly consume partial
+  ASN.1 data.
+
+  All these new feature are natively available through
+  `StreamingDecoder` class. Previously published API is implemented
+  as a thin wrapper on top of that ensuring backward compatibility.
+
 - Added ability of combining `SingleValueConstraint` and
   `PermittedAlphabetConstraint` objects into one for proper modeling
   `FROM ... EXCEPT ...` ASN.1 clause.
diff --git a/README.md b/README.md
index e36324b..b01801b 100644
--- a/README.md
+++ b/README.md
@@ -18,6 +18,7 @@ Features
 
 * Generic implementation of ASN.1 types (X.208)
 * Standards compliant BER/CER/DER codecs
+* Can operate on streams of serialized data
 * Dumps/loads ASN.1 structures from Python types
 * 100% Python, works with Python 2.4 up to Python 3.7
 * MT-safe
diff --git a/pyasn1/codec/ber/decoder.py b/pyasn1/codec/ber/decoder.py
index 2a6448e..d3de8ff 100644
--- a/pyasn1/codec/ber/decoder.py
+++ b/pyasn1/codec/ber/decoder.py
@@ -5,15 +5,14 @@
 # License: http://snmplabs.com/pyasn1/license.html
 #
 import os
-import sys
-from io import BytesIO, BufferedReader, IOBase, DEFAULT_BUFFER_SIZE
 
 from pyasn1 import debug
 from pyasn1 import error
+from pyasn1.codec import streaming
 from pyasn1.codec.ber import eoo
 from pyasn1.compat.integer import from_bytes
 from pyasn1.compat.octets import oct2int, octs2ints, ints2octs, null
-from pyasn1.error import PyAsn1Error, UnsupportedSubstrateError
+from pyasn1.error import PyAsn1Error
 from pyasn1.type import base
 from pyasn1.type import char
 from pyasn1.type import tag
@@ -22,165 +21,16 @@ from pyasn1.type import univ
 from pyasn1.type import useful
 
 
-__all__ = ['decodeStream', 'decode']
+__all__ = ['StreamingDecoder', 'Decoder', 'decode']
 
 LOG = debug.registerLoggee(__name__, flags=debug.DEBUG_DECODER)
 
 noValue = base.noValue
 
+SubstrateUnderrunError = error.SubstrateUnderrunError
 
-_PY2 = sys.version_info < (3,)
 
-
-class _CachingStreamWrapper(IOBase):
-    """Wrapper around non-seekable streams.
-
-    Note that the implementation is tied to the decoder,
-    not checking for dangerous arguments for the sake
-    of performance.
-
-    The read bytes are kept in an internal cache until
-    setting _markedPosition which may reset the cache.
-    """
-    def __init__(self, raw):
-        self._raw = raw
-        self._cache = BytesIO()
-        self._markedPosition_ = 0
-
-    def peek(self, n):
-        result = self.read(n)
-        self._cache.seek(-len(result), os.SEEK_CUR)
-        return result
-
-    def seekable(self):
-        return True
-
-    def seek(self, n=-1, whence=os.SEEK_SET):
-        # Note that this not safe for seeking forward.
-        return self._cache.seek(n, whence)
-
-    def read(self, n=-1):
-        read_from_cache = self._cache.read(n)
-        if n != -1:
-            n -= len(read_from_cache)
-            if not n:  # 0 bytes left to read
-                return read_from_cache
-
-        read_from_raw = self._raw.read(n)
-        self._cache.write(read_from_raw)
-        return read_from_cache + read_from_raw
-
-    @property
-    def _markedPosition(self):
-        """Position where the currently processed element starts.
-
-        This is used for back-tracking in Decoder.__call__
-        and (indefLen)ValueDecoder and should not be used for other purposes.
-        The client is not supposed to ever seek before this position.
-        """
-        return self._markedPosition_
-
-    @_markedPosition.setter
-    def _markedPosition(self, value):
-        # By setting the value, we ensure we won't seek back before it.
-        # `value` should be the same as the current position
-        # We don't check for this for performance reasons.
-        self._markedPosition_ = value
-
-        # Whenever we set _marked_position, we know for sure
-        # that we will not return back, and thus it is
-        # safe to drop all cached data.
-        if self._cache.tell() > DEFAULT_BUFFER_SIZE:
-            self._cache = BytesIO(self._cache.read())
-            self._markedPosition_ = 0
-
-    def tell(self):
-        return self._cache.tell()
-
-
-def _asSeekableStream(substrate):
-    """Convert object to seekable byte-stream.
-
-    Parameters
-    ----------
-    substrate: :py:class:`bytes` or :py:class:`io.IOBase` or :py:class:`univ.OctetString`
-
-    Returns
-    -------
-    : :py:class:`io.IOBase`
-
-    Raises
-    ------
-    ~pyasn1.error.PyAsn1Error
-        If the supplied substrate cannot be converted to a seekable stream.
-    """
-    if isinstance(substrate, bytes):
-        return BytesIO(substrate)
-    elif isinstance(substrate, univ.OctetString):
-        return BytesIO(substrate.asOctets())
-    try:
-        if _PY2 and isinstance(substrate, file):  # Special case (it is not possible to set attributes)
-            return BufferedReader(substrate)
-        elif substrate.seekable():  # Will fail for most invalid types
-            return substrate
-        else:
-            return _CachingStreamWrapper(substrate)
-    except AttributeError:
-        raise UnsupportedSubstrateError("Cannot convert " + substrate.__class__.__name__ + " to a seekable bit stream.")
-
-
-def _endOfStream(substrate):
-    """Check whether we have reached the end of a stream.
-
-    Although it is more effective to read and catch exceptions, this
-    function
-
-    Parameters
-    ----------
-    substrate: :py:class:`IOBase`
-        Stream to check
-
-    Returns
-    -------
-    : :py:class:`bool`
-    """
-    if isinstance(substrate, BytesIO):
-        cp = substrate.tell()
-        substrate.seek(0, os.SEEK_END)
-        result = substrate.tell() == cp
-        substrate.seek(cp, os.SEEK_SET)
-        return result
-    else:
-        return not substrate.peek(1)
-
-
-def _peek(substrate, size=-1):
-    """Peek the stream.
-
-    Parameters
-    ----------
-    substrate: :py:class:`IOBase`
-        Stream to read from.
-
-    size: :py:class:`int`
-        How many bytes to peek (-1 = all available)
-
-    Returns
-    -------
-    : :py:class:`bytes` or :py:class:`str`
-        The return type depends on Python major version
-    """
-    if hasattr(substrate, "peek"):
-        return substrate.peek(size)
-    else:
-        current_position = substrate.tell()
-        try:
-            return substrate.read(size)
-        finally:
-            substrate.seek(current_position)
-
-
-class AbstractDecoder(object):
+class AbstractPayloadDecoder(object):
     protoComponent = None
 
     def valueDecoder(self, substrate, asn1Spec,
@@ -189,10 +39,9 @@ class AbstractDecoder(object):
                      **options):
         """Decode value with fixed byte length.
 
-        If the decoder does not consume a precise byte length,
-        it is considered an error.
+        The decoder is allowed to consume as many bytes as necessary.
         """
-        raise error.PyAsn1Error('Decoder not implemented for %s' % (tagSet,))  # TODO: Seems more like an NotImplementedError?
+        raise error.PyAsn1Error('SingleItemDecoder not implemented for %s' % (tagSet,))  # TODO: Seems more like an NotImplementedError?
 
     def indefLenValueDecoder(self, substrate, asn1Spec,
                              tagSet=None, length=None, state=None,
@@ -204,11 +53,19 @@ class AbstractDecoder(object):
         """
         raise error.PyAsn1Error('Indefinite length mode decoder not implemented for %s' % (tagSet,)) # TODO: Seems more like an NotImplementedError?
 
+    @staticmethod
+    def _passAsn1Object(asn1Object, options):
+        if 'asn1Object' not in options:
+            options['asn1Object'] = asn1Object
+
+        return options
+
 
-class AbstractSimpleDecoder(AbstractDecoder):
+class AbstractSimplePayloadDecoder(AbstractPayloadDecoder):
     @staticmethod
-    def substrateCollector(asn1Object, substrate, length):
-        return substrate.read(length)
+    def substrateCollector(asn1Object, substrate, length, options):
+        for chunk in streaming.read(substrate, length, options):
+            yield chunk
 
     def _createComponent(self, asn1Spec, tagSet, value, **options):
         if options.get('native'):
@@ -221,7 +78,7 @@ class AbstractSimpleDecoder(AbstractDecoder):
             return asn1Spec.clone(value)
 
 
-class ExplicitTagDecoder(AbstractSimpleDecoder):
+class RawPayloadDecoder(AbstractSimplePayloadDecoder):
     protoComponent = univ.Any('')
 
     def valueDecoder(self, substrate, asn1Spec,
@@ -229,43 +86,45 @@ class ExplicitTagDecoder(AbstractSimpleDecoder):
                      decodeFun=None, substrateFun=None,
                      **options):
         if substrateFun:
-            return substrateFun(
-                self._createComponent(asn1Spec, tagSet, '', **options),
-                substrate, length
-            )
-        value = decodeFun(substrate, asn1Spec, tagSet, length, **options)
+            asn1Object = self._createComponent(asn1Spec, tagSet, '', **options)
+
+            for chunk in substrateFun(asn1Object, substrate, length, options):
+                yield chunk
 
-        # TODO:
-        # if LOG:
-        #    LOG('explicit tag container carries %d octets of trailing payload '
-        #        '(will be lost!): %s' % (len(_), debug.hexdump(_)))
+            return
 
-        return value
+        for value in decodeFun(substrate, asn1Spec, tagSet, length, **options):
+            yield value
 
     def indefLenValueDecoder(self, substrate, asn1Spec,
                              tagSet=None, length=None, state=None,
                              decodeFun=None, substrateFun=None,
                              **options):
         if substrateFun:
-            return substrateFun(
-                self._createComponent(asn1Spec, tagSet, '', **options),
-                substrate, length
-            )
+            asn1Object = self._createComponent(asn1Spec, tagSet, '', **options)
 
-        value = decodeFun(substrate, asn1Spec, tagSet, length, **options)
+            for chunk in substrateFun(asn1Object, substrate, length, options):
+                yield chunk
 
-        eooMarker = decodeFun(substrate, allowEoo=True, **options)
+            return
 
-        if eooMarker is eoo.endOfOctets:
-            return value
-        else:
-            raise error.PyAsn1Error('Missing end-of-octets terminator')
+        while True:
+            for value in decodeFun(
+                    substrate, asn1Spec, tagSet, length,
+                    allowEoo=True, **options):
+                if value is eoo.endOfOctets:
+                    break
+
+                yield value
+
+            if value is eoo.endOfOctets:
+                break
 
 
-explicitTagDecoder = ExplicitTagDecoder()
+rawPayloadDecoder = RawPayloadDecoder()
 
 
-class IntegerDecoder(AbstractSimpleDecoder):
+class IntegerPayloadDecoder(AbstractSimplePayloadDecoder):
     protoComponent = univ.Integer(0)
 
     def valueDecoder(self, substrate, asn1Spec,
@@ -276,24 +135,27 @@ class IntegerDecoder(AbstractSimpleDecoder):
         if tagSet[0].tagFormat != tag.tagFormatSimple:
             raise error.PyAsn1Error('Simple tag format expected')
 
-        the_bytes = substrate.read(length)
-        if not the_bytes:
-            return self._createComponent(asn1Spec, tagSet, 0, **options)
+        for chunk in streaming.read(substrate, length, options):
+            if isinstance(chunk, SubstrateUnderrunError):
+                yield chunk
 
-        value = from_bytes(the_bytes, signed=True)
+        if not chunk:
+            yield self._createComponent(asn1Spec, tagSet, 0, **options)
 
-        return self._createComponent(asn1Spec, tagSet, value, **options)
+        value = from_bytes(chunk, signed=True)
 
+        yield self._createComponent(asn1Spec, tagSet, value, **options)
 
-class BooleanDecoder(IntegerDecoder):
+
+class BooleanPayloadDecoder(IntegerPayloadDecoder):
     protoComponent = univ.Boolean(0)
 
     def _createComponent(self, asn1Spec, tagSet, value, **options):
-        return IntegerDecoder._createComponent(
+        return IntegerPayloadDecoder._createComponent(
             self, asn1Spec, tagSet, value and 1 or 0, **options)
 
 
-class BitStringDecoder(AbstractSimpleDecoder):
+class BitStringPayloadDecoder(AbstractSimplePayloadDecoder):
     protoComponent = univ.BitString(())
     supportConstructedForm = True
 
@@ -303,24 +165,45 @@ class BitStringDecoder(AbstractSimpleDecoder):
                      **options):
 
         if substrateFun:
-            return substrateFun(self._createComponent(
-                asn1Spec, tagSet, noValue, **options), substrate, length)
+            asn1Object = self._createComponent(asn1Spec, tagSet, noValue, **options)
+
+            for chunk in substrateFun(asn1Object, substrate, length, options):
+                yield chunk
+
+            return
 
-        if not length or _endOfStream(substrate):
+        if not length:
+            raise error.PyAsn1Error('Empty BIT STRING substrate')
+
+        for chunk in streaming.isEndOfStream(substrate):
+            if isinstance(chunk, SubstrateUnderrunError):
+                yield chunk
+
+        if chunk:
             raise error.PyAsn1Error('Empty BIT STRING substrate')
 
         if tagSet[0].tagFormat == tag.tagFormatSimple:  # XXX what tag to check?
 
-            trailingBits = ord(substrate.read(1))
+            for trailingBits in streaming.read(substrate, 1, options):
+                if isinstance(trailingBits, SubstrateUnderrunError):
+                    yield trailingBits
+
+            trailingBits = ord(trailingBits)
             if trailingBits > 7:
                 raise error.PyAsn1Error(
                     'Trailing bits overflow %s' % trailingBits
                 )
 
+            for chunk in streaming.read(substrate, length - 1, options):
+                if isinstance(chunk, SubstrateUnderrunError):
+                    yield chunk
+
             value = self.protoComponent.fromOctetString(
-                substrate.read(length - 1), internalFormat=True, padding=trailingBits)
+                chunk, internalFormat=True, padding=trailingBits)
+
+            yield self._createComponent(asn1Spec, tagSet, value, **options)
 
-            return self._createComponent(asn1Spec, tagSet, value, **options)
+            return
 
         if not self.supportConstructedForm:
             raise error.PyAsn1Error('Constructed encoding form prohibited '
@@ -337,8 +220,11 @@ class BitStringDecoder(AbstractSimpleDecoder):
         current_position = substrate.tell()
 
         while substrate.tell() - current_position < length:
-            component = decodeFun(substrate, self.protoComponent,
-                                        substrateFun=substrateFun, **options)
+            for component in decodeFun(
+                    substrate, self.protoComponent, substrateFun=substrateFun,
+                    **options):
+                if isinstance(component, SubstrateUnderrunError):
+                    yield component
 
             trailingBits = oct2int(component[0])
             if trailingBits > 7:
@@ -351,7 +237,7 @@ class BitStringDecoder(AbstractSimpleDecoder):
                 prepend=bitString, padding=trailingBits
             )
 
-        return self._createComponent(asn1Spec, tagSet, bitString, **options)
+        yield self._createComponent(asn1Spec, tagSet, bitString, **options)
 
     def indefLenValueDecoder(self, substrate, asn1Spec,
                              tagSet=None, length=None, state=None,
@@ -359,21 +245,32 @@ class BitStringDecoder(AbstractSimpleDecoder):
                              **options):
 
         if substrateFun:
-            return substrateFun(self._createComponent(asn1Spec, tagSet, noValue, **options), substrate, length)
+            asn1Object = self._createComponent(asn1Spec, tagSet, noValue, **options)
+
+            for chunk in substrateFun(asn1Object, substrate, length, options):
+                yield chunk
+
+            return
 
         # All inner fragments are of the same type, treat them as octet string
         substrateFun = self.substrateCollector
 
         bitString = self.protoComponent.fromOctetString(null, internalFormat=True)
 
-        while True:
-            component = decodeFun(substrate, self.protoComponent,
-                                  substrateFun=substrateFun,
-                                  allowEoo=True, **options)
+        while True:  # loop over fragments
+
+            for component in decodeFun(
+                    substrate, self.protoComponent, substrateFun=substrateFun,
+                    allowEoo=True, **options):
+
+                if isinstance(component, SubstrateUnderrunError):
+                    yield component
+
+                if component is eoo.endOfOctets:
+                    break
+
             if component is eoo.endOfOctets:
                 break
-            if component is None:
-                raise error.SubstrateUnderrunError('No EOO seen before substrate ends')
 
             trailingBits = oct2int(component[0])
             if trailingBits > 7:
@@ -386,10 +283,10 @@ class BitStringDecoder(AbstractSimpleDecoder):
                 prepend=bitString, padding=trailingBits
             )
 
-        return self._createComponent(asn1Spec, tagSet, bitString, **options)
+        yield self._createComponent(asn1Spec, tagSet, bitString, **options)
 
 
-class OctetStringDecoder(AbstractSimpleDecoder):
+class OctetStringPayloadDecoder(AbstractSimplePayloadDecoder):
     protoComponent = univ.OctetString('')
     supportConstructedForm = True
 
@@ -398,11 +295,21 @@ class OctetStringDecoder(AbstractSimpleDecoder):
                      decodeFun=None, substrateFun=None,
                      **options):
         if substrateFun:
-            return substrateFun(self._createComponent(asn1Spec, tagSet, noValue, **options),
-                                substrate, length)
+            asn1Object = self._createComponent(asn1Spec, tagSet, noValue, **options)
+
+            for chunk in substrateFun(asn1Object, substrate, length, options):
+                yield chunk
+
+            return
 
         if tagSet[0].tagFormat == tag.tagFormatSimple:  # XXX what tag to check?
-            return self._createComponent(asn1Spec, tagSet, substrate.read(length), **options)
+            for chunk in streaming.read(substrate, length, options):
+                if isinstance(chunk, SubstrateUnderrunError):
+                    yield chunk
+
+            yield self._createComponent(asn1Spec, tagSet, chunk, **options)
+
+            return
 
         if not self.supportConstructedForm:
             raise error.PyAsn1Error('Constructed encoding form prohibited at %s' % self.__class__.__name__)
@@ -418,12 +325,15 @@ class OctetStringDecoder(AbstractSimpleDecoder):
         original_position = substrate.tell()
         # head = popSubstream(substrate, length)
         while substrate.tell() - original_position < length:
-            component = decodeFun(substrate, self.protoComponent,
-                                        substrateFun=substrateFun,
-                                        **options)
+            for component in decodeFun(
+                    substrate, self.protoComponent, substrateFun=substrateFun,
+                    **options):
+                if isinstance(component, SubstrateUnderrunError):
+                    yield component
+
             header += component
 
-        return self._createComponent(asn1Spec, tagSet, header, **options)
+        yield self._createComponent(asn1Spec, tagSet, header, **options)
 
     def indefLenValueDecoder(self, substrate, asn1Spec,
                              tagSet=None, length=None, state=None,
@@ -431,31 +341,38 @@ class OctetStringDecoder(AbstractSimpleDecoder):
                              **options):
         if substrateFun and substrateFun is not self.substrateCollector:
             asn1Object = self._createComponent(asn1Spec, tagSet, noValue, **options)
-            return substrateFun(asn1Object, substrate, length)
+
+            for chunk in substrateFun(asn1Object, substrate, length, options):
+                yield chunk
+
+            return
 
         # All inner fragments are of the same type, treat them as octet string
         substrateFun = self.substrateCollector
 
         header = null
 
-        while True:
-            component = decodeFun(substrate,
-                                             self.protoComponent,
-                                             substrateFun=substrateFun,
-                                             allowEoo=True, **options)
+        while True:  # loop over fragments
+
+            for component in decodeFun(
+                    substrate, self.protoComponent, substrateFun=substrateFun,
+                    allowEoo=True, **options):
+
+                if isinstance(component, SubstrateUnderrunError):
+                    yield component
+
+                if component is eoo.endOfOctets:
+                    break
+
             if component is eoo.endOfOctets:
                 break
-            if not component:
-                raise error.SubstrateUnderrunError(
-                    'No EOO seen before substrate ends'
-                )
 
             header += component
 
-        return self._createComponent(asn1Spec, tagSet, header, **options)
+        yield self._createComponent(asn1Spec, tagSet, header, **options)
 
 
-class NullDecoder(AbstractSimpleDecoder):
+class NullPayloadDecoder(AbstractSimplePayloadDecoder):
     protoComponent = univ.Null('')
 
     def valueDecoder(self, substrate, asn1Spec,
@@ -466,17 +383,19 @@ class NullDecoder(AbstractSimpleDecoder):
         if tagSet[0].tagFormat != tag.tagFormatSimple:
             raise error.PyAsn1Error('Simple tag format expected')
 
-        head = substrate.read(length)
+        for chunk in streaming.read(substrate, length, options):
+            if isinstance(chunk, SubstrateUnderrunError):
+                yield chunk
 
         component = self._createComponent(asn1Spec, tagSet, '', **options)
 
-        if head:
+        if chunk:
             raise error.PyAsn1Error('Unexpected %d-octet substrate for Null' % length)
 
-        return component
+        yield component
 
 
-class ObjectIdentifierDecoder(AbstractSimpleDecoder):
+class ObjectIdentifierPayloadDecoder(AbstractSimplePayloadDecoder):
     protoComponent = univ.ObjectIdentifier(())
 
     def valueDecoder(self, substrate, asn1Spec,
@@ -486,17 +405,20 @@ class ObjectIdentifierDecoder(AbstractSimpleDecoder):
         if tagSet[0].tagFormat != tag.tagFormatSimple:
             raise error.PyAsn1Error('Simple tag format expected')
 
-        head = substrate.read(length)
-        if not head:
+        for chunk in streaming.read(substrate, length, options):
+            if isinstance(chunk, SubstrateUnderrunError):
+                yield chunk
+
+        if not chunk:
             raise error.PyAsn1Error('Empty substrate')
 
-        head = octs2ints(head)
+        chunk = octs2ints(chunk)
 
         oid = ()
         index = 0
-        substrateLen = len(head)
+        substrateLen = len(chunk)
         while index < substrateLen:
-            subId = head[index]
+            subId = chunk[index]
             index += 1
             if subId < 128:
                 oid += (subId,)
@@ -510,7 +432,7 @@ class ObjectIdentifierDecoder(AbstractSimpleDecoder):
                         raise error.SubstrateUnderrunError(
                             'Short substrate for sub-OID past %s' % (oid,)
                         )
-                    nextSubId = head[index]
+                    nextSubId = chunk[index]
                     index += 1
                 oid += ((subId << 7) + nextSubId,)
             elif subId == 128:
@@ -528,12 +450,12 @@ class ObjectIdentifierDecoder(AbstractSimpleDecoder):
         elif oid[0] >= 80:
             oid = (2, oid[0] - 80) + oid[1:]
         else:
-            raise error.PyAsn1Error('Malformed first OID octet: %s' % head[0])
+            raise error.PyAsn1Error('Malformed first OID octet: %s' % chunk[0])
 
-        return self._createComponent(asn1Spec, tagSet, oid, **options)
+        yield self._createComponent(asn1Spec, tagSet, oid, **options)
 
 
-class RealDecoder(AbstractSimpleDecoder):
+class RealPayloadDecoder(AbstractSimplePayloadDecoder):
     protoComponent = univ.Real()
 
     def valueDecoder(self, substrate, asn1Spec,
@@ -543,15 +465,18 @@ class RealDecoder(AbstractSimpleDecoder):
         if tagSet[0].tagFormat != tag.tagFormatSimple:
             raise error.PyAsn1Error('Simple tag format expected')
 
-        head = substrate.read(length)
+        for chunk in streaming.read(substrate, length, options):
+            if isinstance(chunk, SubstrateUnderrunError):
+                yield chunk
 
-        if not head:
-            return self._createComponent(asn1Spec, tagSet, 0.0, **options)
+        if not chunk:
+            yield self._createComponent(asn1Spec, tagSet, 0.0, **options)
+            return
 
-        fo = oct2int(head[0])
-        head = head[1:]
+        fo = oct2int(chunk[0])
+        chunk = chunk[1:]
         if fo & 0x80:  # binary encoding
-            if not head:
+            if not chunk:
                 raise error.PyAsn1Error("Incomplete floating-point value")
 
             if LOG:
@@ -560,12 +485,12 @@ class RealDecoder(AbstractSimpleDecoder):
             n = (fo & 0x03) + 1
 
             if n == 4:
-                n = oct2int(head[0])
-                head = head[1:]
+                n = oct2int(chunk[0])
+                chunk = chunk[1:]
 
-            eo, head = head[:n], head[n:]
+            eo, chunk = chunk[:n], chunk[n:]
 
-            if not eo or not head:
+            if not eo or not chunk:
                 raise error.PyAsn1Error('Real exponent screwed')
 
             e = oct2int(eo[0]) & 0x80 and -1 or 0
@@ -587,10 +512,10 @@ class RealDecoder(AbstractSimpleDecoder):
                 e *= 4
             p = 0
 
-            while head:  # value
+            while chunk:  # value
                 p <<= 8
-                p |= oct2int(head[0])
-                head = head[1:]
+                p |= oct2int(chunk[0])
+                chunk = chunk[1:]
 
             if fo & 0x40:  # sign bit
                 p = -p
@@ -606,7 +531,7 @@ class RealDecoder(AbstractSimpleDecoder):
             value = fo & 0x01 and '-inf' or 'inf'
 
         elif fo & 0xc0 == 0:  # character encoding
-            if not head:
+            if not chunk:
                 raise error.PyAsn1Error("Incomplete floating-point value")
 
             if LOG:
@@ -614,13 +539,13 @@ class RealDecoder(AbstractSimpleDecoder):
 
             try:
                 if fo & 0x3 == 0x1:  # NR1
-                    value = (int(head), 10, 0)
+                    value = (int(chunk), 10, 0)
 
                 elif fo & 0x3 == 0x2:  # NR2
-                    value = float(head)
+                    value = float(chunk)
 
                 elif fo & 0x3 == 0x3:  # NR3
-                    value = float(head)
+                    value = float(chunk)
 
                 else:
                     raise error.SubstrateUnderrunError(
@@ -637,14 +562,14 @@ class RealDecoder(AbstractSimpleDecoder):
                 'Unknown encoding (tag %s)' % fo
             )
 
-        return self._createComponent(asn1Spec, tagSet, value, **options)
+        yield self._createComponent(asn1Spec, tagSet, value, **options)
 
 
-class AbstractConstructedDecoder(AbstractDecoder):
+class AbstractConstructedPayloadDecoder(AbstractPayloadDecoder):
     protoComponent = None
 
 
-class UniversalConstructedTypeDecoder(AbstractConstructedDecoder):
+class ConstructedPayloadDecoderBase(AbstractConstructedPayloadDecoder):
     protoRecordComponent = None
     protoSequenceComponent = None
 
@@ -654,36 +579,43 @@ class UniversalConstructedTypeDecoder(AbstractConstructedDecoder):
     def _getComponentPositionByType(self, asn1Object, tagSet, idx):
         raise NotImplementedError()
 
-    def _decodeComponents(self, substrate, tagSet=None, decodeFun=None, **options):
+    def _decodeComponentsSchemaless(
+            self, substrate, tagSet=None, decodeFun=None,
+            length=None, **options):
+
+        asn1Object = None
+
         components = []
         componentTypes = set()
 
-        while True:
-            component = decodeFun(substrate, **options)
-            if component is eoo.endOfOctets:
-                break
-            if component is None:
-                # TODO: Not an error in this case?
+        original_position = substrate.tell()
+
+        while length == -1 or substrate.tell() < original_position + length:
+            for component in decodeFun(substrate, **options):
+                if isinstance(component, SubstrateUnderrunError):
+                    yield component
+
+            if length == -1 and component is eoo.endOfOctets:
                 break
 
             components.append(component)
             componentTypes.add(component.tagSet)
 
-        # Now we have to guess is it SEQUENCE/SET or SEQUENCE OF/SET OF
-        # The heuristics is:
-        # * 1+ components of different types -> likely SEQUENCE/SET
-        # * otherwise -> likely SEQUENCE OF/SET OF
-        if len(componentTypes) > 1:
-            protoComponent = self.protoRecordComponent
+            # Now we have to guess is it SEQUENCE/SET or SEQUENCE OF/SET OF
+            # The heuristics is:
+            # * 1+ components of different types -> likely SEQUENCE/SET
+            # * otherwise -> likely SEQUENCE OF/SET OF
+            if len(componentTypes) > 1:
+                protoComponent = self.protoRecordComponent
 
-        else:
-            protoComponent = self.protoSequenceComponent
+            else:
+                protoComponent = self.protoSequenceComponent
 
-        asn1Object = protoComponent.clone(
-            # construct tagSet from base tag from prototype ASN.1 object
-            # and additional tags recovered from the substrate
-            tagSet=tag.TagSet(protoComponent.tagSet.baseTag, *tagSet.superTags)
-        )
+            asn1Object = protoComponent.clone(
+                # construct tagSet from base tag from prototype ASN.1 object
+                # and additional tags recovered from the substrate
+                tagSet=tag.TagSet(protoComponent.tagSet.baseTag, *tagSet.superTags)
+            )
 
         if LOG:
             LOG('guessed %r container type (pass `asn1Spec` to guide the '
@@ -696,7 +628,7 @@ class UniversalConstructedTypeDecoder(AbstractConstructedDecoder):
                 matchTags=False, matchConstraints=False
             )
 
-        return asn1Object
+        yield asn1Object
 
     def valueDecoder(self, substrate, asn1Spec,
                      tagSet=None, length=None, state=None,
@@ -707,7 +639,7 @@ class UniversalConstructedTypeDecoder(AbstractConstructedDecoder):
 
         original_position = substrate.tell()
 
-        if substrateFun is not None:
+        if substrateFun:
             if asn1Spec is not None:
                 asn1Object = asn1Spec.clone()
 
@@ -717,24 +649,36 @@ class UniversalConstructedTypeDecoder(AbstractConstructedDecoder):
             else:
                 asn1Object = self.protoRecordComponent, self.protoSequenceComponent
 
-            return substrateFun(asn1Object, substrate, length)
+            for chunk in substrateFun(asn1Object, substrate, length, options):
+                yield chunk
+
+            return
 
         if asn1Spec is None:
-            asn1Object = self._decodeComponents(
-                substrate, tagSet=tagSet, decodeFun=decodeFun, **options
-            )
+            for asn1Object in self._decodeComponentsSchemaless(
+                    substrate, tagSet=tagSet, decodeFun=decodeFun,
+                    length=length, **options):
+                if isinstance(asn1Object, SubstrateUnderrunError):
+                    yield asn1Object
 
             if substrate.tell() < original_position + length:
                 if LOG:
-                    trailing = substrate.read()
+                    for trailing in streaming.read(substrate, context=options):
+                        if isinstance(trailing, SubstrateUnderrunError):
+                            yield trailing
+
                     LOG('Unused trailing %d octets encountered: %s' % (
                         len(trailing), debug.hexdump(trailing)))
 
-            return asn1Object
+            yield asn1Object
+
+            return
 
         asn1Object = asn1Spec.clone()
         asn1Object.clear()
 
+        options = self._passAsn1Object(asn1Object, options)
+
         if asn1Spec.typeId in (univ.Sequence.typeId, univ.Set.typeId):
 
             namedTypes = asn1Spec.componentType
@@ -772,7 +716,9 @@ class UniversalConstructedTypeDecoder(AbstractConstructedDecoder):
                             'Excessive components decoded at %r' % (asn1Spec,)
                         )
 
-                component = decodeFun(substrate, componentType, **options)
+                for component in decodeFun(substrate, componentType, **options):
+                    if isinstance(component, SubstrateUnderrunError):
+                        yield component
 
                 if not isDeterministic and namedTypes:
                     if isSetType:
@@ -859,18 +805,20 @@ class UniversalConstructedTypeDecoder(AbstractConstructedDecoder):
                                 for pos, containerElement in enumerate(
                                         containerValue):
 
-                                    component = decodeFun(
-                                        _asSeekableStream(containerValue[pos].asOctets()),
-                                        asn1Spec=openType, **options
-                                    )
+                                    stream = streaming.asSeekableStream(containerValue[pos].asOctets())
+
+                                    for component in decodeFun(stream, asn1Spec=openType, **options):
+                                        if isinstance(component, SubstrateUnderrunError):
+                                            yield component
 
                                     containerValue[pos] = component
 
                             else:
-                                component = decodeFun(
-                                    _asSeekableStream(asn1Object.getComponentByPosition(idx).asOctets()),
-                                    asn1Spec=openType, **options
-                                )
+                                stream = streaming.asSeekableStream(asn1Object.getComponentByPosition(idx).asOctets())
+
+                                for component in decodeFun(stream, asn1Spec=openType, **options):
+                                    if isinstance(component, SubstrateUnderrunError):
+                                        yield component
 
                                 asn1Object.setComponentByPosition(idx, component)
 
@@ -880,9 +828,6 @@ class UniversalConstructedTypeDecoder(AbstractConstructedDecoder):
                     raise inconsistency
 
         else:
-            asn1Object = asn1Spec.clone()
-            asn1Object.clear()
-
             componentType = asn1Spec.componentType
 
             if LOG:
@@ -891,7 +836,10 @@ class UniversalConstructedTypeDecoder(AbstractConstructedDecoder):
             idx = 0
 
             while substrate.tell() - original_position < length:
-                component = decodeFun(substrate, componentType, **options)
+                for component in decodeFun(substrate, componentType, **options):
+                    if isinstance(component, SubstrateUnderrunError):
+                        yield component
+
                 asn1Object.setComponentByPosition(
                     idx, component,
                     verifyConstraints=False,
@@ -900,7 +848,7 @@ class UniversalConstructedTypeDecoder(AbstractConstructedDecoder):
 
                 idx += 1
 
-        return asn1Object
+        yield asn1Object
 
     def indefLenValueDecoder(self, substrate, asn1Spec,
                              tagSet=None, length=None, state=None,
@@ -919,17 +867,27 @@ class UniversalConstructedTypeDecoder(AbstractConstructedDecoder):
             else:
                 asn1Object = self.protoRecordComponent, self.protoSequenceComponent
 
-            return substrateFun(asn1Object, substrate, length)
+            for chunk in substrateFun(asn1Object, substrate, length, options):
+                yield chunk
+
+            return
 
         if asn1Spec is None:
-            return self._decodeComponents(
-                substrate, tagSet=tagSet, decodeFun=decodeFun,
-                **dict(options, allowEoo=True)
-            )
+            for asn1Object in self._decodeComponentsSchemaless(
+                    substrate, tagSet=tagSet, decodeFun=decodeFun,
+                    length=length, **dict(options, allowEoo=True)):
+                if isinstance(asn1Object, SubstrateUnderrunError):
+                    yield asn1Object
+
+            yield asn1Object
+
+            return
 
         asn1Object = asn1Spec.clone()
         asn1Object.clear()
 
+        options = self._passAsn1Object(asn1Object, options)
+
         if asn1Spec.typeId in (univ.Sequence.typeId, univ.Set.typeId):
 
             namedTypes = asn1Object.componentType
@@ -943,8 +901,10 @@ class UniversalConstructedTypeDecoder(AbstractConstructedDecoder):
                     asn1Spec))
 
             seenIndices = set()
+
             idx = 0
-            while True:  #not endOfStream(substrate):
+
+            while True:  # loop over components
                 if len(namedTypes) <= idx:
                     asn1Spec = None
 
@@ -967,17 +927,21 @@ class UniversalConstructedTypeDecoder(AbstractConstructedDecoder):
                             'Excessive components decoded at %r' % (asn1Object,)
                         )
 
-                component = decodeFun(substrate, asn1Spec, allowEoo=True, **options)
+                for component in decodeFun(substrate, asn1Spec, allowEoo=True, **options):
+
+                    if isinstance(component, SubstrateUnderrunError):
+                        yield component
+
+                    if component is eoo.endOfOctets:
+                        break
+
                 if component is eoo.endOfOctets:
                     break
-                if component is None:
-                    raise error.SubstrateUnderrunError(
-                        'No EOO seen before substrate ends'
-                    )
 
                 if not isDeterministic and namedTypes:
                     if isSetType:
                         idx = namedTypes.getPositionByType(component.effectiveTagSet)
+
                     elif namedTypes[idx].isOptional or namedTypes[idx].isDefaulted:
                         idx = namedTypes.getPositionNearType(component.effectiveTagSet, idx)
 
@@ -995,7 +959,9 @@ class UniversalConstructedTypeDecoder(AbstractConstructedDecoder):
 
             if namedTypes:
                 if not namedTypes.requiredComponents.issubset(seenIndices):
-                    raise error.PyAsn1Error('ASN.1 object %s has uninitialized components' % asn1Object.__class__.__name__)
+                    raise error.PyAsn1Error(
+                        'ASN.1 object %s has uninitialized '
+                        'components' % asn1Object.__class__.__name__)
 
                 if namedTypes.hasOpenTypes:
 
@@ -1057,20 +1023,28 @@ class UniversalConstructedTypeDecoder(AbstractConstructedDecoder):
                                 for pos, containerElement in enumerate(
                                         containerValue):
 
-                                    component = decodeFun(
-                                        _asSeekableStream(containerValue[pos].asOctets()),
-                                        asn1Spec=openType, **dict(options, allowEoo=True)
-                                    )
+                                    stream = streaming.asSeekableStream(containerValue[pos].asOctets())
+
+                                    for component in decodeFun(stream, asn1Spec=openType,
+                                                               **dict(options, allowEoo=True)):
+                                        if isinstance(component, SubstrateUnderrunError):
+                                            yield component
+
+                                        if component is eoo.endOfOctets:
+                                            break
 
                                     containerValue[pos] = component
 
                             else:
-                                component = decodeFun(
-                                    _asSeekableStream(asn1Object.getComponentByPosition(idx).asOctets()),
-                                    asn1Spec=openType, **dict(options, allowEoo=True)
-                                )
+                                stream = streaming.asSeekableStream(asn1Object.getComponentByPosition(idx).asOctets())
+                                for component in decodeFun(stream, asn1Spec=openType,
+                                                           **dict(options, allowEoo=True)):
+                                    if isinstance(component, SubstrateUnderrunError):
+                                        yield component
+
+                                    if component is eoo.endOfOctets:
+                                        break
 
-                                if component is not eoo.endOfOctets:
                                     asn1Object.setComponentByPosition(idx, component)
 
                 else:
@@ -1079,9 +1053,6 @@ class UniversalConstructedTypeDecoder(AbstractConstructedDecoder):
                         raise inconsistency
 
         else:
-            asn1Object = asn1Spec.clone()
-            asn1Object.clear()
-
             componentType = asn1Spec.componentType
 
             if LOG:
@@ -1090,14 +1061,18 @@ class UniversalConstructedTypeDecoder(AbstractConstructedDecoder):
             idx = 0
 
             while True:
-                component = decodeFun(substrate, componentType, allowEoo=True, **options)
+
+                for component in decodeFun(
+                        substrate, componentType, allowEoo=True, **options):
+
+                    if isinstance(component, SubstrateUnderrunError):
+                        yield component
+
+                    if component is eoo.endOfOctets:
+                        break
 
                 if component is eoo.endOfOctets:
                     break
-                if component is None:
-                    raise error.SubstrateUnderrunError(
-                        'No EOO seen before substrate ends'
-                    )
 
                 asn1Object.setComponentByPosition(
                     idx, component,
@@ -1107,38 +1082,36 @@ class UniversalConstructedTypeDecoder(AbstractConstructedDecoder):
 
                 idx += 1
 
+        yield asn1Object
 
-        return asn1Object
 
-
-class SequenceOrSequenceOfDecoder(UniversalConstructedTypeDecoder):
+class SequenceOrSequenceOfPayloadDecoder(ConstructedPayloadDecoderBase):
     protoRecordComponent = univ.Sequence()
     protoSequenceComponent = univ.SequenceOf()
 
 
-class SequenceDecoder(SequenceOrSequenceOfDecoder):
+class SequencePayloadDecoder(SequenceOrSequenceOfPayloadDecoder):
     protoComponent = univ.Sequence()
 
 
-class SequenceOfDecoder(SequenceOrSequenceOfDecoder):
+class SequenceOfPayloadDecoder(SequenceOrSequenceOfPayloadDecoder):
     protoComponent = univ.SequenceOf()
 
 
-class SetOrSetOfDecoder(UniversalConstructedTypeDecoder):
+class SetOrSetOfPayloadDecoder(ConstructedPayloadDecoderBase):
     protoRecordComponent = univ.Set()
     protoSequenceComponent = univ.SetOf()
 
 
-class SetDecoder(SetOrSetOfDecoder):
+class SetPayloadDecoder(SetOrSetOfPayloadDecoder):
     protoComponent = univ.Set()
 
 
-
-class SetOfDecoder(SetOrSetOfDecoder):
+class SetOfPayloadDecoder(SetOrSetOfPayloadDecoder):
     protoComponent = univ.SetOf()
 
 
-class ChoiceDecoder(AbstractConstructedDecoder):
+class ChoicePayloadDecoder(ConstructedPayloadDecoderBase):
     protoComponent = univ.Choice()
 
     def valueDecoder(self, substrate, asn1Spec,
@@ -1154,24 +1127,31 @@ class ChoiceDecoder(AbstractConstructedDecoder):
             asn1Object = asn1Spec.clone()
 
         if substrateFun:
-            return substrateFun(asn1Object, substrate, length)
+            for chunk in substrateFun(asn1Object, substrate, length, options):
+                yield chunk
+
+            return
+
+        options = self._passAsn1Object(asn1Object, options)
 
         if asn1Object.tagSet == tagSet:
             if LOG:
                 LOG('decoding %s as explicitly tagged CHOICE' % (tagSet,))
 
-            component = decodeFun(
-                substrate, asn1Object.componentTagMap, **options
-            )
+            for component in decodeFun(
+                    substrate, asn1Object.componentTagMap, **options):
+                if isinstance(component, SubstrateUnderrunError):
+                    yield component
 
         else:
             if LOG:
                 LOG('decoding %s as untagged CHOICE' % (tagSet,))
 
-            component = decodeFun(
-                substrate, asn1Object.componentTagMap,
-                tagSet, length, state, **options
-            )
+            for component in decodeFun(
+                    substrate, asn1Object.componentTagMap, tagSet, length,
+                    state, **options):
+                if isinstance(component, SubstrateUnderrunError):
+                    yield component
 
         effectiveTagSet = component.effectiveTagSet
 
@@ -1185,7 +1165,7 @@ class ChoiceDecoder(AbstractConstructedDecoder):
             innerFlag=False
         )
 
-        return asn1Object
+        yield asn1Object
 
     def indefLenValueDecoder(self, substrate, asn1Spec,
                              tagSet=None, length=None, state=None,
@@ -1193,53 +1173,67 @@ class ChoiceDecoder(AbstractConstructedDecoder):
                              **options):
         if asn1Spec is None:
             asn1Object = self.protoComponent.clone(tagSet=tagSet)
+
         else:
             asn1Object = asn1Spec.clone()
 
         if substrateFun:
-            return substrateFun(asn1Object, substrate, length)
+            for chunk in substrateFun(asn1Object, substrate, length, options):
+                yield chunk
 
-        if asn1Object.tagSet == tagSet:
-            if LOG:
-                LOG('decoding %s as explicitly tagged CHOICE' % (tagSet,))
+            return
 
-            component = decodeFun(
-                substrate, asn1Object.componentType.tagMapUnique, **options
-            )
+        options = self._passAsn1Object(asn1Object, options)
 
-            # eat up EOO marker
-            eooMarker = decodeFun(
-                substrate, allowEoo=True, **options
-            )
+        isTagged = asn1Object.tagSet == tagSet
 
-            if eooMarker is not eoo.endOfOctets:
-                raise error.PyAsn1Error('No EOO seen before substrate ends')
+        if LOG:
+            LOG('decoding %s as %stagged CHOICE' % (
+                tagSet, isTagged and 'explicitly ' or 'un'))
 
-        else:
-            if LOG:
-                LOG('decoding %s as untagged CHOICE' % (tagSet,))
+        while True:
 
-            component = decodeFun(
-                substrate, asn1Object.componentType.tagMapUnique,
-                tagSet, length, state, **options
-            )
+            if isTagged:
+                iterator = decodeFun(
+                    substrate, asn1Object.componentType.tagMapUnique,
+                    **dict(options, allowEoo=True))
 
-        effectiveTagSet = component.effectiveTagSet
+            else:
+                iterator = decodeFun(
+                    substrate, asn1Object.componentType.tagMapUnique,
+                    tagSet, length, state, **dict(options, allowEoo=True))
 
-        if LOG:
-            LOG('decoded component %s, effective tag set %s' % (component, effectiveTagSet))
+            for component in iterator:
 
-        asn1Object.setComponentByType(
-            effectiveTagSet, component,
-            verifyConstraints=False,
-            matchTags=False, matchConstraints=False,
-            innerFlag=False
-        )
+                if isinstance(component, SubstrateUnderrunError):
+                    yield component
 
-        return asn1Object
+                if component is eoo.endOfOctets:
+                    break
 
+                effectiveTagSet = component.effectiveTagSet
+
+                if LOG:
+                    LOG('decoded component %s, effective tag set '
+                        '%s' % (component, effectiveTagSet))
 
-class AnyDecoder(AbstractSimpleDecoder):
+                asn1Object.setComponentByType(
+                    effectiveTagSet, component,
+                    verifyConstraints=False,
+                    matchTags=False, matchConstraints=False,
+                    innerFlag=False
+                )
+
+                if not isTagged:
+                    break
+
+            if not isTagged or component is eoo.endOfOctets:
+                break
+
+        yield asn1Object
+
+
+class AnyPayloadDecoder(AbstractSimplePayloadDecoder):
     protoComponent = univ.Any()
 
     def valueDecoder(self, substrate, asn1Spec,
@@ -1256,22 +1250,32 @@ class AnyDecoder(AbstractSimpleDecoder):
             isUntagged = tagSet != asn1Spec.tagSet
 
         if isUntagged:
-            fullPosition = substrate._markedPosition
+            fullPosition = substrate.markedPosition
             currentPosition = substrate.tell()
 
             substrate.seek(fullPosition, os.SEEK_SET)
-            length += (currentPosition - fullPosition)
+            length += currentPosition - fullPosition
 
             if LOG:
-                LOG('decoding as untagged ANY, substrate %s' % debug.hexdump(_peek(substrate, length)))
+                for chunk in streaming.peek(substrate, length):
+                    if isinstance(chunk, SubstrateUnderrunError):
+                        yield chunk
+                LOG('decoding as untagged ANY, substrate '
+                    '%s' % debug.hexdump(chunk))
 
         if substrateFun:
-            return substrateFun(self._createComponent(asn1Spec, tagSet, noValue, **options),
-                                substrate, length)
+            for chunk in substrateFun(
+                    self._createComponent(asn1Spec, tagSet, noValue, **options),
+                    substrate, length, options):
+                yield chunk
+
+            return
 
-        head = substrate.read(length)
+        for chunk in streaming.read(substrate, length, options):
+            if isinstance(chunk, SubstrateUnderrunError):
+                yield chunk
 
-        return self._createComponent(asn1Spec, tagSet, head, **options)
+        yield self._createComponent(asn1Spec, tagSet, chunk, **options)
 
     def indefLenValueDecoder(self, substrate, asn1Spec,
                              tagSet=None, length=None, state=None,
@@ -1288,28 +1292,36 @@ class AnyDecoder(AbstractSimpleDecoder):
 
         if isTagged:
             # tagged Any type -- consume header substrate
-            header = null
+            chunk = null
 
             if LOG:
                 LOG('decoding as tagged ANY')
 
         else:
             # TODO: Seems not to be tested
-            fullPosition = substrate._markedPosition
+            fullPosition = substrate.markedPosition
             currentPosition = substrate.tell()
 
             substrate.seek(fullPosition, os.SEEK_SET)
-            header = substrate.read(currentPosition - fullPosition)
+            for chunk in streaming.read(substrate, currentPosition - fullPosition, options):
+                if isinstance(chunk, SubstrateUnderrunError):
+                    yield chunk
 
             if LOG:
-                LOG('decoding as untagged ANY, header substrate %s' % debug.hexdump(header))
+                LOG('decoding as untagged ANY, header substrate %s' % debug.hexdump(chunk))
 
         # Any components do not inherit initial tag
         asn1Spec = self.protoComponent
 
         if substrateFun and substrateFun is not self.substrateCollector:
-            asn1Object = self._createComponent(asn1Spec, tagSet, noValue, **options)
-            return substrateFun(asn1Object, header + substrate, length + len(header))
+            asn1Object = self._createComponent(
+                asn1Spec, tagSet, noValue, **options)
+
+            for chunk in substrateFun(
+                    asn1Object, chunk + substrate, length + len(chunk), options):
+                yield chunk
+
+            return
 
         if LOG:
             LOG('assembling constructed serialization')
@@ -1317,130 +1329,134 @@ class AnyDecoder(AbstractSimpleDecoder):
         # All inner fragments are of the same type, treat them as octet string
         substrateFun = self.substrateCollector
 
-        while True:
-            component = decodeFun(substrate, asn1Spec,
-                                             substrateFun=substrateFun,
-                                             allowEoo=True, **options)
+        while True:  # loop over fragments
+
+            for component in decodeFun(
+                    substrate, asn1Spec, substrateFun=substrateFun,
+                    allowEoo=True, **options):
+
+                if isinstance(component, SubstrateUnderrunError):
+                    yield component
+
+                if component is eoo.endOfOctets:
+                    break
+
             if component is eoo.endOfOctets:
                 break
-            if not component:
-                raise error.SubstrateUnderrunError(
-                    'No EOO seen before substrate ends'
-                )
 
-            header += component
+            chunk += component
 
         if substrateFun:
-            return header  # TODO: Weird
+            yield chunk  # TODO: Weird
 
         else:
-            return self._createComponent(asn1Spec, tagSet, header, **options)
+            yield self._createComponent(asn1Spec, tagSet, chunk, **options)
 
 
 # character string types
-class UTF8StringDecoder(OctetStringDecoder):
+class UTF8StringPayloadDecoder(OctetStringPayloadDecoder):
     protoComponent = char.UTF8String()
 
 
-class NumericStringDecoder(OctetStringDecoder):
+class NumericStringPayloadDecoder(OctetStringPayloadDecoder):
     protoComponent = char.NumericString()
 
 
-class PrintableStringDecoder(OctetStringDecoder):
+class PrintableStringPayloadDecoder(OctetStringPayloadDecoder):
     protoComponent = char.PrintableString()
 
 
-class TeletexStringDecoder(OctetStringDecoder):
+class TeletexStringPayloadDecoder(OctetStringPayloadDecoder):
     protoComponent = char.TeletexString()
 
 
-class VideotexStringDecoder(OctetStringDecoder):
+class VideotexStringPayloadDecoder(OctetStringPayloadDecoder):
     protoComponent = char.VideotexString()
 
 
-class IA5StringDecoder(OctetStringDecoder):
+class IA5StringPayloadDecoder(OctetStringPayloadDecoder):
     protoComponent = char.IA5String()
 
 
-class GraphicStringDecoder(OctetStringDecoder):
+class GraphicStringPayloadDecoder(OctetStringPayloadDecoder):
     protoComponent = char.GraphicString()
 
 
-class VisibleStringDecoder(OctetStringDecoder):
+class VisibleStringPayloadDecoder(OctetStringPayloadDecoder):
     protoComponent = char.VisibleString()
 
 
-class GeneralStringDecoder(OctetStringDecoder):
+class GeneralStringPayloadDecoder(OctetStringPayloadDecoder):
     protoComponent = char.GeneralString()
 
 
-class UniversalStringDecoder(OctetStringDecoder):
+class UniversalStringPayloadDecoder(OctetStringPayloadDecoder):
     protoComponent = char.UniversalString()
 
 
-class BMPStringDecoder(OctetStringDecoder):
+class BMPStringPayloadDecoder(OctetStringPayloadDecoder):
     protoComponent = char.BMPString()
 
 
 # "useful" types
-class ObjectDescriptorDecoder(OctetStringDecoder):
+class ObjectDescriptorPayloadDecoder(OctetStringPayloadDecoder):
     protoComponent = useful.ObjectDescriptor()
 
 
-class GeneralizedTimeDecoder(OctetStringDecoder):
+class GeneralizedTimePayloadDecoder(OctetStringPayloadDecoder):
     protoComponent = useful.GeneralizedTime()
 
 
-class UTCTimeDecoder(OctetStringDecoder):
+class UTCTimePayloadDecoder(OctetStringPayloadDecoder):
     protoComponent = useful.UTCTime()
 
 
-tagMap = {
-    univ.Integer.tagSet: IntegerDecoder(),
-    univ.Boolean.tagSet: BooleanDecoder(),
-    univ.BitString.tagSet: BitStringDecoder(),
-    univ.OctetString.tagSet: OctetStringDecoder(),
-    univ.Null.tagSet: NullDecoder(),
-    univ.ObjectIdentifier.tagSet: ObjectIdentifierDecoder(),
-    univ.Enumerated.tagSet: IntegerDecoder(),
-    univ.Real.tagSet: RealDecoder(),
-    univ.Sequence.tagSet: SequenceOrSequenceOfDecoder(),  # conflicts with SequenceOf
-    univ.Set.tagSet: SetOrSetOfDecoder(),  # conflicts with SetOf
-    univ.Choice.tagSet: ChoiceDecoder(),  # conflicts with Any
+TAG_MAP = {
+    univ.Integer.tagSet: IntegerPayloadDecoder(),
+    univ.Boolean.tagSet: BooleanPayloadDecoder(),
+    univ.BitString.tagSet: BitStringPayloadDecoder(),
+    univ.OctetString.tagSet: OctetStringPayloadDecoder(),
+    univ.Null.tagSet: NullPayloadDecoder(),
+    univ.ObjectIdentifier.tagSet: ObjectIdentifierPayloadDecoder(),
+    univ.Enumerated.tagSet: IntegerPayloadDecoder(),
+    univ.Real.tagSet: RealPayloadDecoder(),
+    univ.Sequence.tagSet: SequenceOrSequenceOfPayloadDecoder(),  # conflicts with SequenceOf
+    univ.Set.tagSet: SetOrSetOfPayloadDecoder(),  # conflicts with SetOf
+    univ.Choice.tagSet: ChoicePayloadDecoder(),  # conflicts with Any
     # character string types
-    char.UTF8String.tagSet: UTF8StringDecoder(),
-    char.NumericString.tagSet: NumericStringDecoder(),
-    char.PrintableString.tagSet: PrintableStringDecoder(),
-    char.TeletexString.tagSet: TeletexStringDecoder(),
-    char.VideotexString.tagSet: VideotexStringDecoder(),
-    char.IA5String.tagSet: IA5StringDecoder(),
-    char.GraphicString.tagSet: GraphicStringDecoder(),
-    char.VisibleString.tagSet: VisibleStringDecoder(),
-    char.GeneralString.tagSet: GeneralStringDecoder(),
-    char.UniversalString.tagSet: UniversalStringDecoder(),
-    char.BMPString.tagSet: BMPStringDecoder(),
+    char.UTF8String.tagSet: UTF8StringPayloadDecoder(),
+    char.NumericString.tagSet: NumericStringPayloadDecoder(),
+    char.PrintableString.tagSet: PrintableStringPayloadDecoder(),
+    char.TeletexString.tagSet: TeletexStringPayloadDecoder(),
+    char.VideotexString.tagSet: VideotexStringPayloadDecoder(),
+    char.IA5String.tagSet: IA5StringPayloadDecoder(),
+    char.GraphicString.tagSet: GraphicStringPayloadDecoder(),
+    char.VisibleString.tagSet: VisibleStringPayloadDecoder(),
+    char.GeneralString.tagSet: GeneralStringPayloadDecoder(),
+    char.UniversalString.tagSet: UniversalStringPayloadDecoder(),
+    char.BMPString.tagSet: BMPStringPayloadDecoder(),
     # useful types
-    useful.ObjectDescriptor.tagSet: ObjectDescriptorDecoder(),
-    useful.GeneralizedTime.tagSet: GeneralizedTimeDecoder(),
-    useful.UTCTime.tagSet: UTCTimeDecoder()
+    useful.ObjectDescriptor.tagSet: ObjectDescriptorPayloadDecoder(),
+    useful.GeneralizedTime.tagSet: GeneralizedTimePayloadDecoder(),
+    useful.UTCTime.tagSet: UTCTimePayloadDecoder()
 }
 
 # Type-to-codec map for ambiguous ASN.1 types
-typeMap = {
-    univ.Set.typeId: SetDecoder(),
-    univ.SetOf.typeId: SetOfDecoder(),
-    univ.Sequence.typeId: SequenceDecoder(),
-    univ.SequenceOf.typeId: SequenceOfDecoder(),
-    univ.Choice.typeId: ChoiceDecoder(),
-    univ.Any.typeId: AnyDecoder()
+TYPE_MAP = {
+    univ.Set.typeId: SetPayloadDecoder(),
+    univ.SetOf.typeId: SetOfPayloadDecoder(),
+    univ.Sequence.typeId: SequencePayloadDecoder(),
+    univ.SequenceOf.typeId: SequenceOfPayloadDecoder(),
+    univ.Choice.typeId: ChoicePayloadDecoder(),
+    univ.Any.typeId: AnyPayloadDecoder()
 }
 
 # Put in non-ambiguous types for faster codec lookup
-for typeDecoder in tagMap.values():
+for typeDecoder in TAG_MAP.values():
     if typeDecoder.protoComponent is not None:
         typeId = typeDecoder.protoComponent.__class__.typeId
-        if typeId is not None and typeId not in typeMap:
-            typeMap[typeId] = typeDecoder
+        if typeId is not None and typeId not in TYPE_MAP:
+            TYPE_MAP[typeId] = typeDecoder
 
 
 (stDecodeTag,
@@ -1455,16 +1471,19 @@ for typeDecoder in tagMap.values():
  stStop) = [x for x in range(10)]
 
 
-class Decoder(object):
+class SingleItemDecoder(object):
     defaultErrorState = stErrorCondition
     #defaultErrorState = stDumpRawValue
-    defaultRawDecoder = AnyDecoder()
+    defaultRawDecoder = AnyPayloadDecoder()
+
     supportIndefLength = True
 
-    # noinspection PyDefaultArgument
-    def __init__(self, tagMap, typeMap={}):
-        self.__tagMap = tagMap
-        self.__typeMap = typeMap
+    TAG_MAP = TAG_MAP
+    TYPE_MAP = TYPE_MAP
+
+    def __init__(self, tagMap=None, typeMap=None):
+        self.__tagMap = tagMap or self.TAG_MAP
+        self.__typeMap = typeMap or self.TYPE_MAP
         # Tag & TagSet objects caches
         self.__tagCache = {}
         self.__tagSetCache = {}
@@ -1475,29 +1494,37 @@ class Decoder(object):
                  decodeFun=None, substrateFun=None,
                  **options):
 
-        if LOG:
-            LOG('decoder called at scope %s with state %d, working with up to %s octets of substrate: %s' % (debug.scope, state, length, substrate))
-
         allowEoo = options.pop('allowEoo', False)
 
+        if LOG:
+            LOG('decoder called at scope %s with state %d, working with up '
+                'to %s octets of substrate: '
+                '%s' % (debug.scope, state, length, substrate))
+
         # Look for end-of-octets sentinel
         if allowEoo and self.supportIndefLength:
-            eoo_candidate = substrate.read(2)
+
+            for eoo_candidate in streaming.read(substrate, 2, options):
+                if isinstance(eoo_candidate, SubstrateUnderrunError):
+                    yield eoo_candidate
+
             if eoo_candidate == self.__eooSentinel:
                 if LOG:
                     LOG('end-of-octets sentinel found')
-                return eoo.endOfOctets
+                yield eoo.endOfOctets
+                return
+
             else:
                 substrate.seek(-2, os.SEEK_CUR)
 
-        value = noValue
-
         tagMap = self.__tagMap
         typeMap = self.__typeMap
         tagCache = self.__tagCache
         tagSetCache = self.__tagSetCache
 
-        substrate._markedPosition = substrate.tell()
+        value = noValue
+
+        substrate.markedPosition = substrate.tell()
 
         while state is not stStop:
 
@@ -1505,9 +1532,9 @@ class Decoder(object):
                 # Decode tag
                 isShortTag = True
 
-                firstByte = substrate.read(1)
-                if not firstByte:
-                    return None
+                for firstByte in streaming.read(substrate, 1, options):
+                    if isinstance(firstByte, SubstrateUnderrunError):
+                        yield firstByte
 
                 firstOctet = ord(firstByte)
 
@@ -1526,15 +1553,20 @@ class Decoder(object):
                         tagId = 0
 
                         while True:
-                            integerByte = substrate.read(1)
+                            for integerByte in streaming.read(substrate, 1, options):
+                                if isinstance(integerByte, SubstrateUnderrunError):
+                                    yield integerByte
+
                             if not integerByte:
                                 raise error.SubstrateUnderrunError(
                                     'Short octet stream on long tag decoding'
                                 )
+
                             integerTag = ord(integerByte)
                             lengthOctetIdx += 1
                             tagId <<= 7
                             tagId |= (integerTag & 0x7F)
+
                             if not integerTag & 0x80:
                                 break
 
@@ -1568,12 +1600,11 @@ class Decoder(object):
 
             if state is stDecodeLength:
                 # Decode length
-                try:
-                    firstOctet = ord(substrate.read(1))
-                except:
-                    raise error.SubstrateUnderrunError(
-                        'Short octet stream on length decoding'
-                    )
+                for firstOctet in streaming.read(substrate, 1, options):
+                    if isinstance(firstOctet, SubstrateUnderrunError):
+                        yield firstOctet
+
+                firstOctet = ord(firstOctet)
 
                 if firstOctet < 128:
                     length = firstOctet
@@ -1581,7 +1612,10 @@ class Decoder(object):
                 elif firstOctet > 128:
                     size = firstOctet & 0x7F
                     # encoded in size bytes
-                    encodedLength = list(substrate.read(size))
+                    for encodedLength in streaming.read(substrate, size, options):
+                        if isinstance(encodedLength, SubstrateUnderrunError):
+                            yield encodedLength
+                    encodedLength = list(encodedLength)
                     # missing check on maximum size, which shouldn't be a
                     # problem, we can handle more than is possible
                     if len(encodedLength) != size:
@@ -1726,25 +1760,30 @@ class Decoder(object):
                 original_position = substrate.tell()
 
                 if length == -1:  # indef length
-                    value = concreteDecoder.indefLenValueDecoder(
-                        substrate, asn1Spec,
-                        tagSet, length, stGetValueDecoder,
-                        self, substrateFun,
-                        **options
-                    )
+                    for value in concreteDecoder.indefLenValueDecoder(
+                            substrate, asn1Spec,
+                            tagSet, length, stGetValueDecoder,
+                            self, substrateFun, **options):
+                        if isinstance(value, SubstrateUnderrunError):
+                            yield value
+
                 else:
-                    value = concreteDecoder.valueDecoder(
-                        substrate, asn1Spec,
-                        tagSet, length, stGetValueDecoder,
-                        self, substrateFun,
-                        **options
-                    )
-                    bytes_read = substrate.tell() - original_position
-                    if bytes_read != length:
-                        raise PyAsn1Error("Read %s bytes instead of expected %s." % (bytes_read, length))
+                    for value in concreteDecoder.valueDecoder(
+                            substrate, asn1Spec,
+                            tagSet, length, stGetValueDecoder,
+                            self, substrateFun, **options):
+                        if isinstance(value, SubstrateUnderrunError):
+                            yield value
+
+                    bytesRead = substrate.tell() - original_position
+                    if bytesRead != length:
+                        raise PyAsn1Error(
+                            "Read %s bytes instead of expected %s." % (bytesRead, length))
 
                 if LOG:
-                   LOG('codec %s yields type %s, value:\n%s\n...' % (concreteDecoder.__class__.__name__, value.__class__.__name__, isinstance(value, base.Asn1Item) and value.prettyPrint() or value))
+                   LOG('codec %s yields type %s, value:\n%s\n...' % (
+                       concreteDecoder.__class__.__name__, value.__class__.__name__,
+                       isinstance(value, base.Asn1Item) and value.prettyPrint() or value))
 
                 state = stStop
                 break
@@ -1754,7 +1793,7 @@ class Decoder(object):
                         tagSet[0].tagFormat == tag.tagFormatConstructed and
                         tagSet[0].tagClass != tag.tagClassUniversal):
                     # Assume explicit tagging
-                    concreteDecoder = explicitTagDecoder
+                    concreteDecoder = rawPayloadDecoder
                     state = stDecodeValue
 
                 else:
@@ -1781,25 +1820,187 @@ class Decoder(object):
             debug.scope.pop()
             LOG('decoder left scope %s, call completed' % debug.scope)
 
-        return value
+        yield value
 
 
-_decode = Decoder(tagMap, typeMap)
+class StreamingDecoder(object):
+    """Create an iterator that turns BER/CER/DER byte stream into ASN.1 objects.
 
+    On each iteration, consume whatever BER/CER/DER serialization is
+    available in the `substrate` stream-like object and turns it into
+    one or more, possibly nested, ASN.1 objects.
 
-def decodeStream(substrate, asn1Spec=None, **kwargs):
-    """Iterator of objects in a substrate."""
-    # TODO: This should become `decode` after API-breaking approved
-    try:
-        substrate = _asSeekableStream(substrate)
-    except TypeError:
-        raise PyAsn1Error
-    while True:
-        result = _decode(substrate, asn1Spec, **kwargs)
-        if result is None:
-            break
-        yield result
-        # TODO: Check about eoo.endOfOctets?
+    Parameters
+    ----------
+    substrate: :py:class:`file`, :py:class:`io.BytesIO`
+        BER/CER/DER serialization in form of a byte stream
+
+    Keyword Args
+    ------------
+    asn1Spec: :py:class:`~pyasn1.type.base.PyAsn1Item`
+        A pyasn1 type object to act as a template guiding the decoder.
+        Depending on the ASN.1 structure being decoded, `asn1Spec` may
+        or may not be required. One of the reasons why `asn1Spec` may
+        me required is that ASN.1 structure is encoded in the *IMPLICIT*
+        tagging mode.
+
+    Yields
+    ------
+    : :py:class:`~pyasn1.type.base.PyAsn1Item`, :py:class:`~pyasn1.error.SubstrateUnderrunError`
+        Decoded ASN.1 object (possibly, nested) or
+        :py:class:`~pyasn1.error.SubstrateUnderrunError` object indicating
+        insufficient BER/CER/DER serialization on input to fully recover ASN.1
+        objects from it.
+        
+        In the latter case the caller is advised to ensure some more data in
+        the input stream, then call the iterator again. The decoder will resume
+        the decoding process using the newly arrived data.
+
+        The `context` property of :py:class:`~pyasn1.error.SubstrateUnderrunError`
+        object might hold a reference to the partially populated ASN.1 object
+        being reconstructed.
+
+    Raises
+    ------
+    ~pyasn1.error.PyAsn1Error, ~pyasn1.error.EndOfStreamError
+        `PyAsn1Error` on deserialization error, `EndOfStreamError` on
+         premature stream closure.
+
+    Examples
+    --------
+    Decode BER serialisation without ASN.1 schema
+
+    .. code-block:: pycon
+
+        >>> stream = io.BytesIO(
+        ...    b'0\t\x02\x01\x01\x02\x01\x02\x02\x01\x03')
+        >>>
+        >>> for asn1Object in StreamingDecoder(stream):
+        ...     print(asn1Object)
+        >>>
+        SequenceOf:
+         1 2 3
+
+    Decode BER serialisation with ASN.1 schema
+
+    .. code-block:: pycon
+
+        >>> stream = io.BytesIO(
+        ...    b'0\t\x02\x01\x01\x02\x01\x02\x02\x01\x03')
+        >>>
+        >>> schema = SequenceOf(componentType=Integer())
+        >>>
+        >>> decoder = StreamingDecoder(stream, asn1Spec=schema)
+        >>> for asn1Object in decoder:
+        ...     print(asn1Object)
+        >>>
+        SequenceOf:
+         1 2 3
+    """
+
+    SINGLE_ITEM_DECODER = SingleItemDecoder
+
+    def __init__(self, substrate, asn1Spec=None, **kwargs):
+        self._substrate = streaming.asSeekableStream(substrate)
+        self._asn1Spec = asn1Spec
+        self._options = kwargs
+        self._decoder = self.SINGLE_ITEM_DECODER()
+
+    def __iter__(self):
+        while True:
+            for asn1Object in self._decoder(
+                    self._substrate, self._asn1Spec, **self._options):
+                yield asn1Object
+
+            for chunk in streaming.isEndOfStream(self._substrate):
+                if isinstance(chunk, SubstrateUnderrunError):
+                    yield
+
+                break
+
+            if chunk:
+                break
+
+
+class Decoder(object):
+    """Create a BER decoder object.
+
+    Parse BER/CER/DER octet-stream into one, possibly nested, ASN.1 object.
+    """
+    STREAMING_DECODER = StreamingDecoder
+
+    @classmethod
+    def __call__(cls, substrate, asn1Spec=None, **kwargs):
+        """Turns BER/CER/DER octet stream into an ASN.1 object.
+
+        Takes BER/CER/DER octet-stream in form of :py:class:`bytes` (Python 3)
+        or :py:class:`str` (Python 2) and decode it into an ASN.1 object
+        (e.g. :py:class:`~pyasn1.type.base.PyAsn1Item` derivative) which
+        may be a scalar or an arbitrary nested structure.
+
+        Parameters
+        ----------
+        substrate: :py:class:`bytes` (Python 3) or :py:class:`str` (Python 2)
+            BER/CER/DER octet-stream to parse
+
+        Keyword Args
+        ------------
+        asn1Spec: :py:class:`~pyasn1.type.base.PyAsn1Item`
+            A pyasn1 type object (:py:class:`~pyasn1.type.base.PyAsn1Item`
+            derivative) to act as a template guiding the decoder.
+            Depending on the ASN.1 structure being decoded, `asn1Spec` may or
+            may not be required. Most common reason for it to require is that
+            ASN.1 structure is encoded in *IMPLICIT* tagging mode.
+
+        Returns
+        -------
+        : :py:class:`tuple`
+            A tuple of :py:class:`~pyasn1.type.base.PyAsn1Item` object
+            recovered from BER/CER/DER substrate and the unprocessed trailing
+            portion of the `substrate` (may be empty)
+
+        Raises
+        ------
+        : :py:class:`~pyasn1.error.PyAsn1Error`
+            :py:class:`~pyasn1.error.SubstrateUnderrunError` on insufficient
+            input or :py:class:`~pyasn1.error.PyAsn1Error` on decoding error.
+
+        Examples
+        --------
+        Decode BER/CER/DER serialisation without ASN.1 schema
+
+        .. code-block:: pycon
+
+           >>> s, unprocessed = decode(b'0\t\x02\x01\x01\x02\x01\x02\x02\x01\x03')
+           >>> str(s)
+           SequenceOf:
+            1 2 3
+
+        Decode BER/CER/DER serialisation with ASN.1 schema
+
+        .. code-block:: pycon
+
+           >>> seq = SequenceOf(componentType=Integer())
+           >>> s, unprocessed = decode(
+                b'0\t\x02\x01\x01\x02\x01\x02\x02\x01\x03', asn1Spec=seq)
+           >>> str(s)
+           SequenceOf:
+            1 2 3
+
+        """
+        substrate = streaming.asSeekableStream(substrate)
+
+        for asn1Object in cls.STREAMING_DECODER(substrate, asn1Spec, **kwargs):
+            if isinstance(asn1Object, SubstrateUnderrunError):
+                raise error.SubstrateUnderrunError('Short substrate on input')
+
+            try:
+                tail = next(streaming.read(substrate))
+
+            except error.EndOfStreamError:
+                tail = null
+
+            return asn1Object, tail
 
 
 #: Turns BER octet stream into an ASN.1 object.
@@ -1831,6 +2032,11 @@ def decodeStream(substrate, asn1Spec=None, **kwargs):
 #: ~pyasn1.error.PyAsn1Error, ~pyasn1.error.SubstrateUnderrunError
 #:     On decoding errors
 #:
+#: Notes
+#: -----
+#: This function is deprecated. Please use :py:class:`Decoder` or
+#: :py:class:`StreamingDecoder` class instance.
+#:
 #: Examples
 #: --------
 #: Decode BER serialisation without ASN.1 schema
@@ -1852,13 +2058,4 @@ def decodeStream(substrate, asn1Spec=None, **kwargs):
 #:    SequenceOf:
 #:     1 2 3
 #:
-def decode(substrate, asn1Spec=None, **kwargs):
-    # TODO: Temporary solution before merging with upstream
-    #   It preserves the original API
-    substrate = _asSeekableStream(substrate)
-    value = _decode(substrate, asn1Spec=asn1Spec, **kwargs)
-    return value, substrate.read()
-
-
-# XXX
-# non-recursive decoding; return position rather than substrate
+decode = Decoder()
diff --git a/pyasn1/codec/ber/encoder.py b/pyasn1/codec/ber/encoder.py
index 778aa86..6b77b70 100644
--- a/pyasn1/codec/ber/encoder.py
+++ b/pyasn1/codec/ber/encoder.py
@@ -17,7 +17,7 @@ from pyasn1.type import tag
 from pyasn1.type import univ
 from pyasn1.type import useful
 
-__all__ = ['encode']
+__all__ = ['Encoder', 'encode']
 
 LOG = debug.registerLoggee(__name__, flags=debug.DEBUG_ENCODER)
 
@@ -706,7 +706,7 @@ class AnyEncoder(OctetStringEncoder):
         return value, not options.get('defMode', True), True
 
 
-tagMap = {
+TAG_MAP = {
     eoo.endOfOctets.tagSet: EndOfOctetsEncoder(),
     univ.Boolean.tagSet: BooleanEncoder(),
     univ.Integer.tagSet: IntegerEncoder(),
@@ -739,7 +739,7 @@ tagMap = {
 }
 
 # Put in ambiguous & non-ambiguous types for faster codec lookup
-typeMap = {
+TYPE_MAP = {
     univ.Boolean.typeId: BooleanEncoder(),
     univ.Integer.typeId: IntegerEncoder(),
     univ.BitString.typeId: BitStringEncoder(),
@@ -774,14 +774,16 @@ typeMap = {
 }
 
 
-class Encoder(object):
+class SingleItemEncoder(object):
     fixedDefLengthMode = None
     fixedChunkSize = None
 
-    # noinspection PyDefaultArgument
-    def __init__(self, tagMap, typeMap={}):
-        self.__tagMap = tagMap
-        self.__typeMap = typeMap
+    TAG_MAP = TAG_MAP
+    TYPE_MAP = TYPE_MAP
+
+    def __init__(self, tagMap=None, typeMap=None):
+        self.__tagMap = tagMap or self.TAG_MAP
+        self.__typeMap = typeMap or self.TYPE_MAP
 
     def __call__(self, value, asn1Spec=None, **options):
         try:
@@ -795,8 +797,11 @@ class Encoder(object):
                                     'and "asn1Spec" not given' % (value,))
 
         if LOG:
-            LOG('encoder called in %sdef mode, chunk size %s for '
-                   'type %s, value:\n%s' % (not options.get('defMode', True) and 'in' or '', options.get('maxChunkSize', 0), asn1Spec is None and value.prettyPrintType() or asn1Spec.prettyPrintType(), value))
+            LOG('encoder called in %sdef mode, chunk size %s for type %s, '
+                'value:\n%s' % (not options.get('defMode', True) and 'in' or '',
+                                options.get('maxChunkSize', 0),
+                                asn1Spec is None and value.prettyPrintType() or
+                                asn1Spec.prettyPrintType(), value))
 
         if self.fixedDefLengthMode is not None:
             options.update(defMode=self.fixedDefLengthMode)
@@ -804,12 +809,12 @@ class Encoder(object):
         if self.fixedChunkSize is not None:
             options.update(maxChunkSize=self.fixedChunkSize)
 
-
         try:
             concreteEncoder = self.__typeMap[typeId]
 
             if LOG:
-                LOG('using value codec %s chosen by type ID %s' % (concreteEncoder.__class__.__name__, typeId))
+                LOG('using value codec %s chosen by type ID '
+                    '%s' % (concreteEncoder.__class__.__name__, typeId))
 
         except KeyError:
             if asn1Spec is None:
@@ -827,15 +832,28 @@ class Encoder(object):
                 raise error.PyAsn1Error('No encoder for %r (%s)' % (value, tagSet))
 
             if LOG:
-                LOG('using value codec %s chosen by tagSet %s' % (concreteEncoder.__class__.__name__, tagSet))
+                LOG('using value codec %s chosen by tagSet '
+                    '%s' % (concreteEncoder.__class__.__name__, tagSet))
 
         substrate = concreteEncoder.encode(value, asn1Spec, self, **options)
 
         if LOG:
-            LOG('codec %s built %s octets of substrate: %s\nencoder completed' % (concreteEncoder, len(substrate), debug.hexdump(substrate)))
+            LOG('codec %s built %s octets of substrate: %s\nencoder '
+                'completed' % (concreteEncoder, len(substrate),
+                               debug.hexdump(substrate)))
 
         return substrate
 
+
+class Encoder(object):
+    SINGLE_ITEM_ENCODER = SingleItemEncoder
+
+    @classmethod
+    def __call__(cls, pyObject, asn1Spec=None, **options):
+        singleItemEncoder = cls.SINGLE_ITEM_ENCODER()
+        return singleItemEncoder(pyObject, asn1Spec=asn1Spec, **options)
+
+
 #: Turns ASN.1 object into BER octet stream.
 #:
 #: Takes any ASN.1 object (e.g. :py:class:`~pyasn1.type.base.PyAsn1Item` derivative)
@@ -887,4 +905,4 @@ class Encoder(object):
 #:    >>> encode(seq)
 #:    b'0\t\x02\x01\x01\x02\x01\x02\x02\x01\x03'
 #:
-encode = Encoder(tagMap, typeMap)
+encode = Encoder()
diff --git a/pyasn1/codec/cer/decoder.py b/pyasn1/codec/cer/decoder.py
index b709313..08f9ec8 100644
--- a/pyasn1/codec/cer/decoder.py
+++ b/pyasn1/codec/cer/decoder.py
@@ -4,79 +4,89 @@
 # Copyright (c) 2005-2019, Ilya Etingof <etingof@gmail.com>
 # License: http://snmplabs.com/pyasn1/license.html
 #
-from io import BytesIO
-
 from pyasn1 import error
+from pyasn1.codec import streaming
 from pyasn1.codec.ber import decoder
-from pyasn1.codec.ber.decoder import _asSeekableStream
 from pyasn1.compat.octets import oct2int
 from pyasn1.type import univ
 
-__all__ = ['decode', 'decodeStream']
+__all__ = ['decode', 'StreamingDecoder']
+
+SubstrateUnderrunError = error.SubstrateUnderrunError
 
 
-class BooleanDecoder(decoder.AbstractSimpleDecoder):
+class BooleanPayloadDecoder(decoder.AbstractSimplePayloadDecoder):
     protoComponent = univ.Boolean(0)
 
     def valueDecoder(self, substrate, asn1Spec,
                      tagSet=None, length=None, state=None,
                      decodeFun=None, substrateFun=None,
                      **options):
-        head = substrate.read(1)
-        if not head or length != 1:
+
+        if length != 1:
             raise error.PyAsn1Error('Not single-octet Boolean payload')
-        byte = oct2int(head[0])
+
+        for chunk in streaming.read(substrate, length, options):
+            if isinstance(chunk, SubstrateUnderrunError):
+                yield chunk
+
+        byte = oct2int(chunk[0])
+
         # CER/DER specifies encoding of TRUE as 0xFF and FALSE as 0x0, while
         # BER allows any non-zero value as TRUE; cf. sections 8.2.2. and 11.1 
         # in https://www.itu.int/ITU-T/studygroups/com17/languages/X.690-0207.pdf
         if byte == 0xff:
             value = 1
+
         elif byte == 0x00:
             value = 0
+
         else:
             raise error.PyAsn1Error('Unexpected Boolean payload: %s' % byte)
-        return self._createComponent(asn1Spec, tagSet, value, **options)
+
+        yield self._createComponent(asn1Spec, tagSet, value, **options)
+
 
 # TODO: prohibit non-canonical encoding
-BitStringDecoder = decoder.BitStringDecoder
-OctetStringDecoder = decoder.OctetStringDecoder
-RealDecoder = decoder.RealDecoder
-
-tagMap = decoder.tagMap.copy()
-tagMap.update(
-    {univ.Boolean.tagSet: BooleanDecoder(),
-     univ.BitString.tagSet: BitStringDecoder(),
-     univ.OctetString.tagSet: OctetStringDecoder(),
-     univ.Real.tagSet: RealDecoder()}
+BitStringPayloadDecoder = decoder.BitStringPayloadDecoder
+OctetStringPayloadDecoder = decoder.OctetStringPayloadDecoder
+RealPayloadDecoder = decoder.RealPayloadDecoder
+
+TAG_MAP = decoder.TAG_MAP.copy()
+TAG_MAP.update(
+    {univ.Boolean.tagSet: BooleanPayloadDecoder(),
+     univ.BitString.tagSet: BitStringPayloadDecoder(),
+     univ.OctetString.tagSet: OctetStringPayloadDecoder(),
+     univ.Real.tagSet: RealPayloadDecoder()}
 )
 
-typeMap = decoder.typeMap.copy()
+TYPE_MAP = decoder.TYPE_MAP.copy()
 
 # Put in non-ambiguous types for faster codec lookup
-for typeDecoder in tagMap.values():
+for typeDecoder in TAG_MAP.values():
     if typeDecoder.protoComponent is not None:
         typeId = typeDecoder.protoComponent.__class__.typeId
-        if typeId is not None and typeId not in typeMap:
-            typeMap[typeId] = typeDecoder
+        if typeId is not None and typeId not in TYPE_MAP:
+            TYPE_MAP[typeId] = typeDecoder
 
 
-class Decoder(decoder.Decoder):
-    pass
+class SingleItemDecoder(decoder.SingleItemDecoder):
+    __doc__ = decoder.SingleItemDecoder.__doc__
+
+    TAG_MAP = TAG_MAP
+    TYPE_MAP = TYPE_MAP
 
 
-_decode = Decoder(tagMap, typeMap)
+class StreamingDecoder(decoder.StreamingDecoder):
+    __doc__ = decoder.StreamingDecoder.__doc__
 
+    SINGLE_ITEM_DECODER = SingleItemDecoder
+
+
+class Decoder(decoder.Decoder):
+    __doc__ = decoder.Decoder.__doc__
 
-def decodeStream(substrate, asn1Spec=None, **kwargs):
-    """Iterator of objects in a substrate."""
-    # TODO: This should become `decode` after API-breaking approved
-    substrate = _asSeekableStream(substrate)
-    while True:
-        result = _decode(substrate, asn1Spec, **kwargs)
-        if result is None:
-            break
-        yield result
-        # TODO: Check about eoo.endOfOctets?
+    STREAMING_DECODER = StreamingDecoder
 
 
 #: Turns CER octet stream into an ASN.1 object.
@@ -129,9 +139,4 @@ def decodeStream(substrate, asn1Spec=None, **kwargs):
 #:    SequenceOf:
 #:     1 2 3
 #:
-def decode(substrate, asn1Spec=None, **kwargs):
-    # TODO: Temporary solution before merging with upstream
-    #   It preserves the original API
-    substrate = _asSeekableStream(substrate)
-    value = _decode(substrate, asn1Spec=asn1Spec, **kwargs)
-    return value, substrate.read()
+decode = Decoder()
diff --git a/pyasn1/codec/cer/encoder.py b/pyasn1/codec/cer/encoder.py
index 935b696..9e6cdac 100644
--- a/pyasn1/codec/cer/encoder.py
+++ b/pyasn1/codec/cer/encoder.py
@@ -10,7 +10,7 @@ from pyasn1.compat.octets import str2octs, null
 from pyasn1.type import univ
 from pyasn1.type import useful
 
-__all__ = ['encode']
+__all__ = ['Encoder', 'encode']
 
 
 class BooleanEncoder(encoder.IntegerEncoder):
@@ -234,8 +234,9 @@ class SequenceEncoder(encoder.SequenceEncoder):
     omitEmptyOptionals = True
 
 
-tagMap = encoder.tagMap.copy()
-tagMap.update({
+TAG_MAP = encoder.TAG_MAP.copy()
+
+TAG_MAP.update({
     univ.Boolean.tagSet: BooleanEncoder(),
     univ.Real.tagSet: RealEncoder(),
     useful.GeneralizedTime.tagSet: GeneralizedTimeEncoder(),
@@ -245,8 +246,9 @@ tagMap.update({
     univ.Sequence.typeId: SequenceEncoder()
 })
 
-typeMap = encoder.typeMap.copy()
-typeMap.update({
+TYPE_MAP = encoder.TYPE_MAP.copy()
+
+TYPE_MAP.update({
     univ.Boolean.typeId: BooleanEncoder(),
     univ.Real.typeId: RealEncoder(),
     useful.GeneralizedTime.typeId: GeneralizedTimeEncoder(),
@@ -259,10 +261,18 @@ typeMap.update({
 })
 
 
-class Encoder(encoder.Encoder):
+class SingleItemEncoder(encoder.SingleItemEncoder):
     fixedDefLengthMode = False
     fixedChunkSize = 1000
 
+    TAG_MAP = TAG_MAP
+    TYPE_MAP = TYPE_MAP
+
+
+class Encoder(encoder.Encoder):
+    SINGLE_ITEM_ENCODER = SingleItemEncoder
+
+
 #: Turns ASN.1 object into CER octet stream.
 #:
 #: Takes any ASN.1 object (e.g. :py:class:`~pyasn1.type.base.PyAsn1Item` derivative)
@@ -308,6 +318,6 @@ class Encoder(encoder.Encoder):
 #:    >>> encode(seq)
 #:    b'0\x80\x02\x01\x01\x02\x01\x02\x02\x01\x03\x00\x00'
 #:
-encode = Encoder(tagMap, typeMap)
+encode = Encoder()
 
 # EncoderFactory queries class instance and builds a map of tags -> encoders
diff --git a/pyasn1/codec/der/decoder.py b/pyasn1/codec/der/decoder.py
index e339970..b9526c3 100644
--- a/pyasn1/codec/der/decoder.py
+++ b/pyasn1/codec/der/decoder.py
@@ -4,59 +4,59 @@
 # Copyright (c) 2005-2019, Ilya Etingof <etingof@gmail.com>
 # License: http://snmplabs.com/pyasn1/license.html
 #
-from io import BytesIO
-
-from pyasn1.codec.ber.decoder import _asSeekableStream
 from pyasn1.codec.cer import decoder
 from pyasn1.type import univ
 
-__all__ = ['decode', 'decodeStream']
+__all__ = ['decode', 'StreamingDecoder']
 
 
-class BitStringDecoder(decoder.BitStringDecoder):
+class BitStringPayloadDecoder(decoder.BitStringPayloadDecoder):
     supportConstructedForm = False
 
 
-class OctetStringDecoder(decoder.OctetStringDecoder):
+class OctetStringPayloadDecoder(decoder.OctetStringPayloadDecoder):
     supportConstructedForm = False
 
+
 # TODO: prohibit non-canonical encoding
-RealDecoder = decoder.RealDecoder
+RealPayloadDecoder = decoder.RealPayloadDecoder
 
-tagMap = decoder.tagMap.copy()
-tagMap.update(
-    {univ.BitString.tagSet: BitStringDecoder(),
-     univ.OctetString.tagSet: OctetStringDecoder(),
-     univ.Real.tagSet: RealDecoder()}
+TAG_MAP = decoder.TAG_MAP.copy()
+TAG_MAP.update(
+    {univ.BitString.tagSet: BitStringPayloadDecoder(),
+     univ.OctetString.tagSet: OctetStringPayloadDecoder(),
+     univ.Real.tagSet: RealPayloadDecoder()}
 )
 
-typeMap = decoder.typeMap.copy()
+TYPE_MAP = decoder.TYPE_MAP.copy()
 
 # Put in non-ambiguous types for faster codec lookup
-for typeDecoder in tagMap.values():
+for typeDecoder in TAG_MAP.values():
     if typeDecoder.protoComponent is not None:
         typeId = typeDecoder.protoComponent.__class__.typeId
-        if typeId is not None and typeId not in typeMap:
-            typeMap[typeId] = typeDecoder
+        if typeId is not None and typeId not in TYPE_MAP:
+            TYPE_MAP[typeId] = typeDecoder
 
 
-class Decoder(decoder.Decoder):
+class SingleItemDecoder(decoder.SingleItemDecoder):
+    __doc__ = decoder.SingleItemDecoder.__doc__
+
+    TAG_MAP = TAG_MAP
+    TYPE_MAP = TYPE_MAP
+
     supportIndefLength = False
 
 
-_decode = Decoder(tagMap, decoder.typeMap)
+class StreamingDecoder(decoder.StreamingDecoder):
+    __doc__ = decoder.StreamingDecoder.__doc__
+
+    SINGLE_ITEM_DECODER = SingleItemDecoder
 
 
-def decodeStream(substrate, asn1Spec=None, **kwargs):
-    """Iterator of objects in a substrate."""
-    # TODO: This should become `decode` after API-breaking approved
-    substrate = _asSeekableStream(substrate)
-    while True:
-        result = _decode(substrate, asn1Spec, **kwargs)
-        if result is None:
-            break
-        yield result
-        # TODO: Check about eoo.endOfOctets?
+class Decoder(decoder.Decoder):
+    __doc__ = decoder.Decoder.__doc__
+
+    STREAMING_DECODER = StreamingDecoder
 
 
 #: Turns DER octet stream into an ASN.1 object.
@@ -109,9 +109,4 @@ def decodeStream(substrate, asn1Spec=None, **kwargs):
 #:    SequenceOf:
 #:     1 2 3
 #:
-def decode(substrate, asn1Spec=None, **kwargs):
-    # TODO: Temporary solution before merging with upstream
-    #   It preserves the original API
-    substrate = _asSeekableStream(substrate)
-    value = _decode(substrate, asn1Spec=asn1Spec, **kwargs)
-    return value, substrate.read()
\ No newline at end of file
+decode = Decoder()
diff --git a/pyasn1/codec/der/encoder.py b/pyasn1/codec/der/encoder.py
index 90e982d..1a6af82 100644
--- a/pyasn1/codec/der/encoder.py
+++ b/pyasn1/codec/der/encoder.py
@@ -8,7 +8,7 @@ from pyasn1 import error
 from pyasn1.codec.cer import encoder
 from pyasn1.type import univ
 
-__all__ = ['encode']
+__all__ = ['Encoder', 'encode']
 
 
 class SetEncoder(encoder.SetEncoder):
@@ -42,23 +42,34 @@ class SetEncoder(encoder.SetEncoder):
         else:
             return compType.tagSet
 
-tagMap = encoder.tagMap.copy()
-tagMap.update({
+
+TAG_MAP = encoder.TAG_MAP.copy()
+
+TAG_MAP.update({
     # Set & SetOf have same tags
     univ.Set.tagSet: SetEncoder()
 })
 
-typeMap = encoder.typeMap.copy()
-typeMap.update({
+TYPE_MAP = encoder.TYPE_MAP.copy()
+
+TYPE_MAP.update({
     # Set & SetOf have same tags
     univ.Set.typeId: SetEncoder()
 })
 
 
-class Encoder(encoder.Encoder):
+class SingleItemEncoder(encoder.SingleItemEncoder):
     fixedDefLengthMode = True
     fixedChunkSize = 0
 
+    TAG_MAP = TAG_MAP
+    TYPE_MAP = TYPE_MAP
+
+
+class Encoder(encoder.Encoder):
+    SINGLE_ITEM_ENCODER = SingleItemEncoder
+
+
 #: Turns ASN.1 object into DER octet stream.
 #:
 #: Takes any ASN.1 object (e.g. :py:class:`~pyasn1.type.base.PyAsn1Item` derivative)
@@ -104,4 +115,4 @@ class Encoder(encoder.Encoder):
 #:    >>> encode(seq)
 #:    b'0\t\x02\x01\x01\x02\x01\x02\x02\x01\x03'
 #:
-encode = Encoder(tagMap, typeMap)
+encode = Encoder()
diff --git a/pyasn1/codec/native/decoder.py b/pyasn1/codec/native/decoder.py
index 104b92e..ecb1b16 100644
--- a/pyasn1/codec/native/decoder.py
+++ b/pyasn1/codec/native/decoder.py
@@ -17,17 +17,17 @@ __all__ = ['decode']
 LOG = debug.registerLoggee(__name__, flags=debug.DEBUG_DECODER)
 
 
-class AbstractScalarDecoder(object):
+class AbstractScalarPayloadDecoder(object):
     def __call__(self, pyObject, asn1Spec, decodeFun=None, **options):
         return asn1Spec.clone(pyObject)
 
 
-class BitStringDecoder(AbstractScalarDecoder):
+class BitStringPayloadDecoder(AbstractScalarPayloadDecoder):
     def __call__(self, pyObject, asn1Spec, decodeFun=None, **options):
         return asn1Spec.clone(univ.BitString.fromBinaryString(pyObject))
 
 
-class SequenceOrSetDecoder(object):
+class SequenceOrSetPayloadDecoder(object):
     def __call__(self, pyObject, asn1Spec, decodeFun=None, **options):
         asn1Value = asn1Spec.clone()
 
@@ -40,7 +40,7 @@ class SequenceOrSetDecoder(object):
         return asn1Value
 
 
-class SequenceOfOrSetOfDecoder(object):
+class SequenceOfOrSetOfPayloadDecoder(object):
     def __call__(self, pyObject, asn1Spec, decodeFun=None, **options):
         asn1Value = asn1Spec.clone()
 
@@ -50,7 +50,7 @@ class SequenceOfOrSetOfDecoder(object):
         return asn1Value
 
 
-class ChoiceDecoder(object):
+class ChoicePayloadDecoder(object):
     def __call__(self, pyObject, asn1Spec, decodeFun=None, **options):
         asn1Value = asn1Spec.clone()
 
@@ -64,87 +64,92 @@ class ChoiceDecoder(object):
         return asn1Value
 
 
-tagMap = {
-    univ.Integer.tagSet: AbstractScalarDecoder(),
-    univ.Boolean.tagSet: AbstractScalarDecoder(),
-    univ.BitString.tagSet: BitStringDecoder(),
-    univ.OctetString.tagSet: AbstractScalarDecoder(),
-    univ.Null.tagSet: AbstractScalarDecoder(),
-    univ.ObjectIdentifier.tagSet: AbstractScalarDecoder(),
-    univ.Enumerated.tagSet: AbstractScalarDecoder(),
-    univ.Real.tagSet: AbstractScalarDecoder(),
-    univ.Sequence.tagSet: SequenceOrSetDecoder(),  # conflicts with SequenceOf
-    univ.Set.tagSet: SequenceOrSetDecoder(),  # conflicts with SetOf
-    univ.Choice.tagSet: ChoiceDecoder(),  # conflicts with Any
+TAG_MAP = {
+    univ.Integer.tagSet: AbstractScalarPayloadDecoder(),
+    univ.Boolean.tagSet: AbstractScalarPayloadDecoder(),
+    univ.BitString.tagSet: BitStringPayloadDecoder(),
+    univ.OctetString.tagSet: AbstractScalarPayloadDecoder(),
+    univ.Null.tagSet: AbstractScalarPayloadDecoder(),
+    univ.ObjectIdentifier.tagSet: AbstractScalarPayloadDecoder(),
+    univ.Enumerated.tagSet: AbstractScalarPayloadDecoder(),
+    univ.Real.tagSet: AbstractScalarPayloadDecoder(),
+    univ.Sequence.tagSet: SequenceOrSetPayloadDecoder(),  # conflicts with SequenceOf
+    univ.Set.tagSet: SequenceOrSetPayloadDecoder(),  # conflicts with SetOf
+    univ.Choice.tagSet: ChoicePayloadDecoder(),  # conflicts with Any
     # character string types
-    char.UTF8String.tagSet: AbstractScalarDecoder(),
-    char.NumericString.tagSet: AbstractScalarDecoder(),
-    char.PrintableString.tagSet: AbstractScalarDecoder(),
-    char.TeletexString.tagSet: AbstractScalarDecoder(),
-    char.VideotexString.tagSet: AbstractScalarDecoder(),
-    char.IA5String.tagSet: AbstractScalarDecoder(),
-    char.GraphicString.tagSet: AbstractScalarDecoder(),
-    char.VisibleString.tagSet: AbstractScalarDecoder(),
-    char.GeneralString.tagSet: AbstractScalarDecoder(),
-    char.UniversalString.tagSet: AbstractScalarDecoder(),
-    char.BMPString.tagSet: AbstractScalarDecoder(),
+    char.UTF8String.tagSet: AbstractScalarPayloadDecoder(),
+    char.NumericString.tagSet: AbstractScalarPayloadDecoder(),
+    char.PrintableString.tagSet: AbstractScalarPayloadDecoder(),
+    char.TeletexString.tagSet: AbstractScalarPayloadDecoder(),
+    char.VideotexString.tagSet: AbstractScalarPayloadDecoder(),
+    char.IA5String.tagSet: AbstractScalarPayloadDecoder(),
+    char.GraphicString.tagSet: AbstractScalarPayloadDecoder(),
+    char.VisibleString.tagSet: AbstractScalarPayloadDecoder(),
+    char.GeneralString.tagSet: AbstractScalarPayloadDecoder(),
+    char.UniversalString.tagSet: AbstractScalarPayloadDecoder(),
+    char.BMPString.tagSet: AbstractScalarPayloadDecoder(),
     # useful types
-    useful.ObjectDescriptor.tagSet: AbstractScalarDecoder(),
-    useful.GeneralizedTime.tagSet: AbstractScalarDecoder(),
-    useful.UTCTime.tagSet: AbstractScalarDecoder()
+    useful.ObjectDescriptor.tagSet: AbstractScalarPayloadDecoder(),
+    useful.GeneralizedTime.tagSet: AbstractScalarPayloadDecoder(),
+    useful.UTCTime.tagSet: AbstractScalarPayloadDecoder()
 }
 
 # Put in ambiguous & non-ambiguous types for faster codec lookup
-typeMap = {
-    univ.Integer.typeId: AbstractScalarDecoder(),
-    univ.Boolean.typeId: AbstractScalarDecoder(),
-    univ.BitString.typeId: BitStringDecoder(),
-    univ.OctetString.typeId: AbstractScalarDecoder(),
-    univ.Null.typeId: AbstractScalarDecoder(),
-    univ.ObjectIdentifier.typeId: AbstractScalarDecoder(),
-    univ.Enumerated.typeId: AbstractScalarDecoder(),
-    univ.Real.typeId: AbstractScalarDecoder(),
+TYPE_MAP = {
+    univ.Integer.typeId: AbstractScalarPayloadDecoder(),
+    univ.Boolean.typeId: AbstractScalarPayloadDecoder(),
+    univ.BitString.typeId: BitStringPayloadDecoder(),
+    univ.OctetString.typeId: AbstractScalarPayloadDecoder(),
+    univ.Null.typeId: AbstractScalarPayloadDecoder(),
+    univ.ObjectIdentifier.typeId: AbstractScalarPayloadDecoder(),
+    univ.Enumerated.typeId: AbstractScalarPayloadDecoder(),
+    univ.Real.typeId: AbstractScalarPayloadDecoder(),
     # ambiguous base types
-    univ.Set.typeId: SequenceOrSetDecoder(),
-    univ.SetOf.typeId: SequenceOfOrSetOfDecoder(),
-    univ.Sequence.typeId: SequenceOrSetDecoder(),
-    univ.SequenceOf.typeId: SequenceOfOrSetOfDecoder(),
-    univ.Choice.typeId: ChoiceDecoder(),
-    univ.Any.typeId: AbstractScalarDecoder(),
+    univ.Set.typeId: SequenceOrSetPayloadDecoder(),
+    univ.SetOf.typeId: SequenceOfOrSetOfPayloadDecoder(),
+    univ.Sequence.typeId: SequenceOrSetPayloadDecoder(),
+    univ.SequenceOf.typeId: SequenceOfOrSetOfPayloadDecoder(),
+    univ.Choice.typeId: ChoicePayloadDecoder(),
+    univ.Any.typeId: AbstractScalarPayloadDecoder(),
     # character string types
-    char.UTF8String.typeId: AbstractScalarDecoder(),
-    char.NumericString.typeId: AbstractScalarDecoder(),
-    char.PrintableString.typeId: AbstractScalarDecoder(),
-    char.TeletexString.typeId: AbstractScalarDecoder(),
-    char.VideotexString.typeId: AbstractScalarDecoder(),
-    char.IA5String.typeId: AbstractScalarDecoder(),
-    char.GraphicString.typeId: AbstractScalarDecoder(),
-    char.VisibleString.typeId: AbstractScalarDecoder(),
-    char.GeneralString.typeId: AbstractScalarDecoder(),
-    char.UniversalString.typeId: AbstractScalarDecoder(),
-    char.BMPString.typeId: AbstractScalarDecoder(),
+    char.UTF8String.typeId: AbstractScalarPayloadDecoder(),
+    char.NumericString.typeId: AbstractScalarPayloadDecoder(),
+    char.PrintableString.typeId: AbstractScalarPayloadDecoder(),
+    char.TeletexString.typeId: AbstractScalarPayloadDecoder(),
+    char.VideotexString.typeId: AbstractScalarPayloadDecoder(),
+    char.IA5String.typeId: AbstractScalarPayloadDecoder(),
+    char.GraphicString.typeId: AbstractScalarPayloadDecoder(),
+    char.VisibleString.typeId: AbstractScalarPayloadDecoder(),
+    char.GeneralString.typeId: AbstractScalarPayloadDecoder(),
+    char.UniversalString.typeId: AbstractScalarPayloadDecoder(),
+    char.BMPString.typeId: AbstractScalarPayloadDecoder(),
     # useful types
-    useful.ObjectDescriptor.typeId: AbstractScalarDecoder(),
-    useful.GeneralizedTime.typeId: AbstractScalarDecoder(),
-    useful.UTCTime.typeId: AbstractScalarDecoder()
+    useful.ObjectDescriptor.typeId: AbstractScalarPayloadDecoder(),
+    useful.GeneralizedTime.typeId: AbstractScalarPayloadDecoder(),
+    useful.UTCTime.typeId: AbstractScalarPayloadDecoder()
 }
 
 
-class Decoder(object):
+class SingleItemDecoder(object):
+
+    TAG_MAP = TAG_MAP
+    TYPE_MAP = TYPE_MAP
 
-    # noinspection PyDefaultArgument
-    def __init__(self, tagMap, typeMap):
-        self.__tagMap = tagMap
-        self.__typeMap = typeMap
+    def __init__(self, tagMap=None, typeMap=None):
+        self.__tagMap = tagMap or self.TAG_MAP
+        self.__typeMap = typeMap or self.TYPE_MAP
 
     def __call__(self, pyObject, asn1Spec, **options):
 
         if LOG:
             debug.scope.push(type(pyObject).__name__)
-            LOG('decoder called at scope %s, working with type %s' % (debug.scope, type(pyObject).__name__))
+            LOG('decoder called at scope %s, working with '
+                'type %s' % (debug.scope, type(pyObject).__name__))
 
         if asn1Spec is None or not isinstance(asn1Spec, base.Asn1Item):
-            raise error.PyAsn1Error('asn1Spec is not valid (should be an instance of an ASN.1 Item, not %s)' % asn1Spec.__class__.__name__)
+            raise error.PyAsn1Error(
+                'asn1Spec is not valid (should be an instance of an ASN.1 '
+                'Item, not %s)' % asn1Spec.__class__.__name__)
 
         try:
             valueDecoder = self.__typeMap[asn1Spec.typeId]
@@ -155,21 +160,35 @@ class Decoder(object):
 
             try:
                 valueDecoder = self.__tagMap[baseTagSet]
+
             except KeyError:
                 raise error.PyAsn1Error('Unknown ASN.1 tag %s' % asn1Spec.tagSet)
 
         if LOG:
-            LOG('calling decoder %s on Python type %s <%s>' % (type(valueDecoder).__name__, type(pyObject).__name__, repr(pyObject)))
+            LOG('calling decoder %s on Python type %s '
+                '<%s>' % (type(valueDecoder).__name__,
+                          type(pyObject).__name__, repr(pyObject)))
 
         value = valueDecoder(pyObject, asn1Spec, self, **options)
 
         if LOG:
-            LOG('decoder %s produced ASN.1 type %s <%s>' % (type(valueDecoder).__name__, type(value).__name__, repr(value)))
+            LOG('decoder %s produced ASN.1 type %s '
+                '<%s>' % (type(valueDecoder).__name__,
+                          type(value).__name__, repr(value)))
             debug.scope.pop()
 
         return value
 
 
+class Decoder(object):
+    SINGLE_ITEM_DECODER = SingleItemDecoder
+
+    @classmethod
+    def __call__(cls, pyObject, asn1Spec=None, **kwargs):
+        singleItemDecoder = cls.SINGLE_ITEM_DECODER()
+        return singleItemDecoder(pyObject, asn1Spec=asn1Spec, **kwargs)
+
+
 #: Turns Python objects of built-in types into ASN.1 objects.
 #:
 #: Takes Python objects of built-in types and turns them into a tree of
@@ -210,4 +229,4 @@ class Decoder(object):
 #:    SequenceOf:
 #:     1 2 3
 #:
-decode = Decoder(tagMap, typeMap)
+decode = Decoder()
diff --git a/pyasn1/codec/native/encoder.py b/pyasn1/codec/native/encoder.py
index 4318abd..a3e17a9 100644
--- a/pyasn1/codec/native/encoder.py
+++ b/pyasn1/codec/native/encoder.py
@@ -107,7 +107,7 @@ class AnyEncoder(AbstractItemEncoder):
         return value.asOctets()
 
 
-tagMap = {
+TAG_MAP = {
     univ.Boolean.tagSet: BooleanEncoder(),
     univ.Integer.tagSet: IntegerEncoder(),
     univ.BitString.tagSet: BitStringEncoder(),
@@ -140,7 +140,7 @@ tagMap = {
 
 
 # Put in ambiguous & non-ambiguous types for faster codec lookup
-typeMap = {
+TYPE_MAP = {
     univ.Boolean.typeId: BooleanEncoder(),
     univ.Integer.typeId: IntegerEncoder(),
     univ.BitString.typeId: BitStringEncoder(),
@@ -175,20 +175,24 @@ typeMap = {
 }
 
 
-class Encoder(object):
+class SingleItemEncoder(object):
+
+    TAG_MAP = TAG_MAP
+    TYPE_MAP = TYPE_MAP
 
-    # noinspection PyDefaultArgument
-    def __init__(self, tagMap, typeMap={}):
-        self.__tagMap = tagMap
-        self.__typeMap = typeMap
+    def __init__(self, tagMap=None, typeMap=None):
+        self.__tagMap = tagMap or self.TAG_MAP
+        self.__typeMap = typeMap or self.TYPE_MAP
 
     def __call__(self, value, **options):
         if not isinstance(value, base.Asn1Item):
-            raise error.PyAsn1Error('value is not valid (should be an instance of an ASN.1 Item)')
+            raise error.PyAsn1Error(
+                'value is not valid (should be an instance of an ASN.1 Item)')
 
         if LOG:
             debug.scope.push(type(value).__name__)
-            LOG('encoder called for type %s <%s>' % (type(value).__name__, value.prettyPrint()))
+            LOG('encoder called for type %s '
+                '<%s>' % (type(value).__name__, value.prettyPrint()))
 
         tagSet = value.tagSet
 
@@ -197,7 +201,8 @@ class Encoder(object):
 
         except KeyError:
             # use base type for codec lookup to recover untagged types
-            baseTagSet = tag.TagSet(value.tagSet.baseTag, value.tagSet.baseTag)
+            baseTagSet = tag.TagSet(
+                value.tagSet.baseTag, value.tagSet.baseTag)
 
             try:
                 concreteEncoder = self.__tagMap[baseTagSet]
@@ -206,17 +211,28 @@ class Encoder(object):
                 raise error.PyAsn1Error('No encoder for %s' % (value,))
 
         if LOG:
-            LOG('using value codec %s chosen by %s' % (concreteEncoder.__class__.__name__, tagSet))
+            LOG('using value codec %s chosen by '
+                '%s' % (concreteEncoder.__class__.__name__, tagSet))
 
         pyObject = concreteEncoder.encode(value, self, **options)
 
         if LOG:
-            LOG('encoder %s produced: %s' % (type(concreteEncoder).__name__, repr(pyObject)))
+            LOG('encoder %s produced: '
+                '%s' % (type(concreteEncoder).__name__, repr(pyObject)))
             debug.scope.pop()
 
         return pyObject
 
 
+class Encoder(object):
+    SINGLE_ITEM_ENCODER = SingleItemEncoder
+
+    @classmethod
+    def __call__(cls, pyObject, asn1Spec=None, **kwargs):
+        singleItemEncoder = cls.SINGLE_ITEM_ENCODER()
+        return singleItemEncoder(pyObject, asn1Spec=asn1Spec, **kwargs)
+
+
 #: Turns ASN.1 object into a Python built-in type object(s).
 #:
 #: Takes any ASN.1 object (e.g. :py:class:`~pyasn1.type.base.PyAsn1Item` derivative)
@@ -253,4 +269,4 @@ class Encoder(object):
 #:    >>> encode(seq)
 #:    [1, 2, 3]
 #:
-encode = Encoder(tagMap, typeMap)
+encode = SingleItemEncoder()
diff --git a/pyasn1/codec/streaming.py b/pyasn1/codec/streaming.py
new file mode 100644
index 0000000..1889677
--- /dev/null
+++ b/pyasn1/codec/streaming.py
@@ -0,0 +1,240 @@
+#
+# This file is part of pyasn1 software.
+#
+# Copyright (c) 2005-2019, Ilya Etingof <etingof@gmail.com>
+# License: http://snmplabs.com/pyasn1/license.html
+#
+import io
+import os
+import sys
+
+from pyasn1 import error
+from pyasn1.type import univ
+
+_PY2 = sys.version_info < (3,)
+
+
+class CachingStreamWrapper(io.IOBase):
+    """Wrapper around non-seekable streams.
+
+    Note that the implementation is tied to the decoder,
+    not checking for dangerous arguments for the sake
+    of performance.
+
+    The read bytes are kept in an internal cache until
+    setting _markedPosition which may reset the cache.
+    """
+    def __init__(self, raw):
+        self._raw = raw
+        self._cache = io.BytesIO()
+        self._markedPosition = 0
+
+    def peek(self, n):
+        result = self.read(n)
+        self._cache.seek(-len(result), os.SEEK_CUR)
+        return result
+
+    def seekable(self):
+        return True
+
+    def seek(self, n=-1, whence=os.SEEK_SET):
+        # Note that this not safe for seeking forward.
+        return self._cache.seek(n, whence)
+
+    def read(self, n=-1):
+        read_from_cache = self._cache.read(n)
+        if n != -1:
+            n -= len(read_from_cache)
+            if not n:  # 0 bytes left to read
+                return read_from_cache
+
+        read_from_raw = self._raw.read(n)
+
+        self._cache.write(read_from_raw)
+
+        return read_from_cache + read_from_raw
+
+    @property
+    def markedPosition(self):
+        """Position where the currently processed element starts.
+
+        This is used for back-tracking in SingleItemDecoder.__call__
+        and (indefLen)ValueDecoder and should not be used for other purposes.
+        The client is not supposed to ever seek before this position.
+        """
+        return self._markedPosition
+
+    @markedPosition.setter
+    def markedPosition(self, value):
+        # By setting the value, we ensure we won't seek back before it.
+        # `value` should be the same as the current position
+        # We don't check for this for performance reasons.
+        self._markedPosition = value
+
+        # Whenever we set _marked_position, we know for sure
+        # that we will not return back, and thus it is
+        # safe to drop all cached data.
+        if self._cache.tell() > io.DEFAULT_BUFFER_SIZE:
+            self._cache = io.BytesIO(self._cache.read())
+            self._markedPosition = 0
+
+    def tell(self):
+        return self._cache.tell()
+
+
+def asSeekableStream(substrate):
+    """Convert object to seekable byte-stream.
+
+    Parameters
+    ----------
+    substrate: :py:class:`bytes` or :py:class:`io.IOBase` or :py:class:`univ.OctetString`
+
+    Returns
+    -------
+    : :py:class:`io.IOBase`
+
+    Raises
+    ------
+    : :py:class:`~pyasn1.error.PyAsn1Error`
+        If the supplied substrate cannot be converted to a seekable stream.
+    """
+    if isinstance(substrate, bytes):
+        return io.BytesIO(substrate)
+
+    elif isinstance(substrate, univ.OctetString):
+        return io.BytesIO(substrate.asOctets())
+
+    try:
+        # Special case: impossible to set attributes on `file` built-in
+        if _PY2 and isinstance(substrate, file):
+            return io.BufferedReader(substrate)
+
+        elif substrate.seekable():  # Will fail for most invalid types
+            return substrate
+
+        else:
+            return CachingStreamWrapper(substrate)
+
+    except AttributeError:
+        raise error.UnsupportedSubstrateError(
+            "Cannot convert " + substrate.__class__.__name__ +
+            " to a seekable bit stream.")
+
+
+def isEndOfStream(substrate):
+    """Check whether we have reached the end of a stream.
+
+    Although it is more effective to read and catch exceptions, this
+    function
+
+    Parameters
+    ----------
+    substrate: :py:class:`IOBase`
+        Stream to check
+
+    Returns
+    -------
+    : :py:class:`bool`
+    """
+    if isinstance(substrate, io.BytesIO):
+        cp = substrate.tell()
+        substrate.seek(0, os.SEEK_END)
+        result = substrate.tell() == cp
+        substrate.seek(cp, os.SEEK_SET)
+        yield result
+
+    else:
+        received = substrate.read(1)
+        if received is None:
+            yield
+
+        if received:
+            substrate.seek(-1, os.SEEK_CUR)
+
+        yield not received
+
+
+def peek(substrate, size=-1):
+    """Peek the stream.
+
+    Parameters
+    ----------
+    substrate: :py:class:`IOBase`
+        Stream to read from.
+
+    size: :py:class:`int`
+        How many bytes to peek (-1 = all available)
+
+    Returns
+    -------
+    : :py:class:`bytes` or :py:class:`str`
+        The return type depends on Python major version
+    """
+    if hasattr(substrate, "peek"):
+        received = substrate.peek(size)
+        if received is None:
+            yield
+
+        while len(received) < size:
+            yield
+
+        yield received
+
+    else:
+        current_position = substrate.tell()
+        try:
+            for chunk in read(substrate, size):
+                yield chunk
+
+        finally:
+            substrate.seek(current_position)
+
+
+def read(substrate, size=-1, context=None):
+    """Read from the stream.
+
+    Parameters
+    ----------
+    substrate: :py:class:`IOBase`
+        Stream to read from.
+
+    Keyword parameters
+    ------------------
+    size: :py:class:`int`
+        How many bytes to read (-1 = all available)
+
+    context: :py:class:`dict`
+        Opaque caller context will be attached to exception objects created
+        by this function.
+
+    Yields
+    ------
+    : :py:class:`bytes` or :py:class:`str` or None
+        Returns read data or :py:class:`~pyasn1.error.SubstrateUnderrunError`
+        object if no `size` bytes is readily available in the stream. The
+        data type depends on Python major version
+
+    Raises
+    ------
+    : :py:class:`~pyasn1.error.EndOfStreamError`
+        Input stream is exhausted
+    """
+    while True:
+        # this will block unless stream is non-blocking
+        received = substrate.read(size)
+        if received is None:  # non-blocking stream can do this
+            yield error.SubstrateUnderrunError(context=context)
+
+        elif size != 0 and not received:  # end-of-stream
+            raise error.EndOfStreamError(context=context)
+
+        elif len(received) < size:
+            substrate.seek(-len(received), os.SEEK_CUR)
+
+            # behave like a non-blocking stream
+            yield error.SubstrateUnderrunError(context=context)
+
+        else:
+            break
+
+    yield received
diff --git a/pyasn1/error.py b/pyasn1/error.py
index 85a31ff..08ec1b3 100644
--- a/pyasn1/error.py
+++ b/pyasn1/error.py
@@ -12,7 +12,36 @@ class PyAsn1Error(Exception):
     `PyAsn1Error` is the base exception class (based on
     :class:`Exception`) that represents all possible ASN.1 related
     errors.
+
+    Parameters
+    ----------
+    args:
+        Opaque positional parameters
+
+    Keyword Args
+    ------------
+    kwargs:
+        Opaque keyword parameters
+
     """
+    def __init__(self, *args, **kwargs):
+        self._args = args
+        self._kwargs = kwargs
+
+    @property
+    def context(self):
+        """Return exception context
+
+        When exception object is created, the caller can supply some opaque
+        context for the upper layers to better understand the cause of the
+        exception.
+
+        Returns
+        -------
+        : :py:class:`dict`
+            Dict holding context specific data
+        """
+        return self._kwargs.get('context', {})
 
 
 class ValueConstraintError(PyAsn1Error):
@@ -34,6 +63,14 @@ class SubstrateUnderrunError(PyAsn1Error):
     """
 
 
+class EndOfStreamError(SubstrateUnderrunError):
+    """ASN.1 data structure deserialization error
+
+    The `EndOfStreamError` exception indicates the condition of the input
+    stream has been closed.
+    """
+
+
 class UnsupportedSubstrateError(PyAsn1Error):
     """Unsupported substrate type to parse as ASN.1 data."""
 
diff --git a/tests/codec/__main__.py b/tests/codec/__main__.py
index 7a4cf20..dbd744a 100644
--- a/tests/codec/__main__.py
+++ b/tests/codec/__main__.py
@@ -11,7 +11,8 @@ except ImportError:
     import unittest
 
 suite = unittest.TestLoader().loadTestsFromNames(
-    ['tests.codec.ber.__main__.suite',
+    ['tests.codec.streaming.__main__.suite',
+     'tests.codec.ber.__main__.suite',
      'tests.codec.cer.__main__.suite',
      'tests.codec.der.__main__.suite',
      'tests.codec.native.__main__.suite']
diff --git a/tests/codec/ber/test_decoder.py b/tests/codec/ber/test_decoder.py
index e72e025..2430ff4 100644
--- a/tests/codec/ber/test_decoder.py
+++ b/tests/codec/ber/test_decoder.py
@@ -23,10 +23,11 @@ from pyasn1.type import namedtype
 from pyasn1.type import opentype
 from pyasn1.type import univ
 from pyasn1.type import char
+from pyasn1.codec import streaming
 from pyasn1.codec.ber import decoder
 from pyasn1.codec.ber import eoo
 from pyasn1.compat.octets import ints2octs, str2octs, null
-from pyasn1.error import PyAsn1Error, SubstrateUnderrunError, UnsupportedSubstrateError
+from pyasn1 import error
 
 
 class LargeTagDecoderTestCase(BaseTestCase):
@@ -78,7 +79,7 @@ class IntegerDecoderTestCase(BaseTestCase):
             decoder.decode(
                 ints2octs((2, 1, 12)), asn1Spec=univ.Null()
             ) == (12, null)
-        except PyAsn1Error:
+        except error.PyAsn1Error:
             pass
         else:
             assert 0, 'wrong asn1Spec worked out'
@@ -89,7 +90,7 @@ class IntegerDecoderTestCase(BaseTestCase):
     def testTagFormat(self):
         try:
             decoder.decode(ints2octs((34, 1, 12)))
-        except PyAsn1Error:
+        except error.PyAsn1Error:
             pass
         else:
             assert 0, 'wrong tagFormat worked out'
@@ -111,7 +112,7 @@ class BooleanDecoderTestCase(BaseTestCase):
     def testTagFormat(self):
         try:
             decoder.decode(ints2octs((33, 1, 1)))
-        except PyAsn1Error:
+        except error.PyAsn1Error:
             pass
         else:
             assert 0, 'wrong tagFormat worked out'
@@ -138,24 +139,22 @@ class BitStringDecoderTestCase(BaseTestCase):
             ints2octs((35, 128, 3, 2, 0, 169, 3, 2, 1, 138, 0, 0))
         ) == ((1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1), null)
 
-    # TODO: Not clear how to deal with substrateFun in stream implementation
-    # def testDefModeChunkedSubst(self):
-    #     assert decoder.decode(
-    #         ints2octs((35, 8, 3, 2, 0, 169, 3, 2, 1, 138)),
-    #         substrateFun=lambda a, b, c: (b, b[c:])
-    #     ) == (ints2octs((3, 2, 0, 169, 3, 2, 1, 138)), str2octs(''))
+    def testDefModeChunkedSubst(self):
+        assert decoder.decode(
+            ints2octs((35, 8, 3, 2, 0, 169, 3, 2, 1, 138)),
+            substrateFun=lambda a, b, c, d: streaming.read(b, c)
+        ) == (ints2octs((3, 2, 0, 169, 3, 2, 1, 138)), str2octs(''))
 
-    # TODO: Not clear how to deal with substrateFun in stream implementation
-    # def testIndefModeChunkedSubst(self):
-    #     assert decoder.decode(
-    #         ints2octs((35, 128, 3, 2, 0, 169, 3, 2, 1, 138, 0, 0)),
-    #         substrateFun=lambda a, b, c: (b, str2octs(''))
-    #     ) == (ints2octs((3, 2, 0, 169, 3, 2, 1, 138, 0, 0)), str2octs(''))
+    def testIndefModeChunkedSubst(self):
+        assert decoder.decode(
+            ints2octs((35, 128, 3, 2, 0, 169, 3, 2, 1, 138, 0, 0)),
+            substrateFun=lambda a, b, c, d: streaming.read(b, c)
+        ) == (ints2octs((3, 2, 0, 169, 3, 2, 1, 138, 0, 0)), str2octs(''))
 
     def testTypeChecking(self):
         try:
             decoder.decode(ints2octs((35, 4, 2, 2, 42, 42)))
-        except PyAsn1Error:
+        except error.PyAsn1Error:
             pass
         else:
             assert 0, 'accepted mis-encoded bit-string constructed out of an integer'
@@ -183,22 +182,20 @@ class OctetStringDecoderTestCase(BaseTestCase):
             ints2octs((36, 128, 4, 4, 81, 117, 105, 99, 4, 4, 107, 32, 98, 114, 4, 4, 111, 119, 110, 32, 4, 3, 102, 111, 120, 0, 0))
         ) == (str2octs('Quick brown fox'), null)
 
-    # TODO: Not clear how to deal with substrateFun in stream implementation
-    # def testDefModeChunkedSubst(self):
-    #     assert decoder.decode(
-    #         ints2octs(
-    #             (36, 23, 4, 4, 81, 117, 105, 99, 4, 4, 107, 32, 98, 114, 4, 4, 111, 119, 110, 32, 4, 3, 102, 111, 120)),
-    #         substrateFun=lambda a, b, c: (b, b[c:])
-    #     ) == (ints2octs((4, 4, 81, 117, 105, 99, 4, 4, 107, 32, 98, 114, 4, 4, 111, 119, 110, 32, 4, 3, 102, 111, 120)), str2octs(''))
+    def testDefModeChunkedSubst(self):
+        assert decoder.decode(
+            ints2octs(
+                (36, 23, 4, 4, 81, 117, 105, 99, 4, 4, 107, 32, 98, 114, 4, 4, 111, 119, 110, 32, 4, 3, 102, 111, 120)),
+            substrateFun=lambda a, b, c, d: streaming.read(b, c)
+        ) == (ints2octs((4, 4, 81, 117, 105, 99, 4, 4, 107, 32, 98, 114, 4, 4, 111, 119, 110, 32, 4, 3, 102, 111, 120)), str2octs(''))
 
-    # TODO: Not clear how to deal with substrateFun in stream implementation
-    # def testIndefModeChunkedSubst(self):
-    #     assert decoder.decode(
-    #         ints2octs((36, 128, 4, 4, 81, 117, 105, 99, 4, 4, 107, 32, 98, 114, 4, 4, 111, 119, 110, 32, 4, 3, 102, 111,
-    #                    120, 0, 0)),
-    #         substrateFun=lambda a, b, c: (b, str2octs(''))
-    #     ) == (ints2octs(
-    #         (4, 4, 81, 117, 105, 99, 4, 4, 107, 32, 98, 114, 4, 4, 111, 119, 110, 32, 4, 3, 102, 111, 120, 0, 0)), str2octs(''))
+    def testIndefModeChunkedSubst(self):
+        assert decoder.decode(
+            ints2octs((36, 128, 4, 4, 81, 117, 105, 99, 4, 4, 107, 32, 98, 114, 4, 4, 111, 119, 110, 32, 4, 3, 102, 111,
+                       120, 0, 0)),
+            substrateFun=lambda a, b, c, d: streaming.read(b, c)
+        ) == (ints2octs(
+            (4, 4, 81, 117, 105, 99, 4, 4, 107, 32, 98, 114, 4, 4, 111, 119, 110, 32, 4, 3, 102, 111, 120, 0, 0)), str2octs(''))
 
 
 class ExpTaggedOctetStringDecoderTestCase(BaseTestCase):
@@ -246,22 +243,20 @@ class ExpTaggedOctetStringDecoderTestCase(BaseTestCase):
         assert self.o.tagSet == o.tagSet
         assert self.o.isSameTypeWith(o)
 
-    # TODO: Not clear how to deal with substrateFun in stream implementation
-    # def testDefModeSubst(self):
-    #     assert decoder.decode(
-    #         ints2octs((101, 17, 4, 15, 81, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 32, 102, 111, 120)),
-    #         substrateFun=lambda a, b, c: (b, b[c:])
-    #     ) == (ints2octs((4, 15, 81, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 32, 102, 111, 120)), str2octs(''))
+    def testDefModeSubst(self):
+        assert decoder.decode(
+            ints2octs((101, 17, 4, 15, 81, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 32, 102, 111, 120)),
+            substrateFun=lambda a, b, c, d: streaming.read(b, c)
+        ) == (ints2octs((4, 15, 81, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 32, 102, 111, 120)), str2octs(''))
 
-    # TODO: Not clear how to deal with substrateFun in stream implementation
-    # def testIndefModeSubst(self):
-    #     assert decoder.decode(
-    #         ints2octs((
-    #                   101, 128, 36, 128, 4, 15, 81, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 32, 102, 111, 120, 0,
-    #                   0, 0, 0)),
-    #         substrateFun=lambda a, b, c: (b, str2octs(''))
-    #     ) == (ints2octs(
-    #         (36, 128, 4, 15, 81, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 32, 102, 111, 120, 0, 0, 0, 0)), str2octs(''))
+    def testIndefModeSubst(self):
+        assert decoder.decode(
+            ints2octs((
+                      101, 128, 36, 128, 4, 15, 81, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 32, 102, 111, 120, 0,
+                      0, 0, 0)),
+            substrateFun=lambda a, b, c, d: streaming.read(b, c)
+        ) == (ints2octs(
+            (36, 128, 4, 15, 81, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 32, 102, 111, 120, 0, 0, 0, 0)), str2octs(''))
 
 
 class NullDecoderTestCase(BaseTestCase):
@@ -271,7 +266,7 @@ class NullDecoderTestCase(BaseTestCase):
     def testTagFormat(self):
         try:
             decoder.decode(ints2octs((37, 0)))
-        except PyAsn1Error:
+        except error.PyAsn1Error:
             pass
         else:
             assert 0, 'wrong tagFormat worked out'
@@ -340,7 +335,7 @@ class ObjectIdentifierDecoderTestCase(BaseTestCase):
             decoder.decode(
                 ints2octs((6, 5, 85, 4, 128, 129, 0))
             )
-        except PyAsn1Error:
+        except error.PyAsn1Error:
             pass
         else:
             assert 0, 'Leading 0x80 tolerated'
@@ -350,7 +345,7 @@ class ObjectIdentifierDecoderTestCase(BaseTestCase):
             decoder.decode(
                 ints2octs((6, 7, 1, 0x80, 0x80, 0x80, 0x80, 0x80, 0x7F))
             )
-        except PyAsn1Error:
+        except error.PyAsn1Error:
             pass
         else:
             assert 0, 'Leading 0x80 tolerated'
@@ -360,7 +355,7 @@ class ObjectIdentifierDecoderTestCase(BaseTestCase):
             decoder.decode(
                 ints2octs((6, 2, 0x80, 1))
             )
-        except PyAsn1Error:
+        except error.PyAsn1Error:
             pass
         else:
             assert 0, 'Leading 0x80 tolerated'
@@ -370,7 +365,7 @@ class ObjectIdentifierDecoderTestCase(BaseTestCase):
             decoder.decode(
                 ints2octs((6, 2, 0x80, 0x7F))
             )
-        except PyAsn1Error:
+        except error.PyAsn1Error:
             pass
         else:
             assert 0, 'Leading 0x80 tolerated'
@@ -378,7 +373,7 @@ class ObjectIdentifierDecoderTestCase(BaseTestCase):
     def testTagFormat(self):
         try:
             decoder.decode(ints2octs((38, 1, 239)))
-        except PyAsn1Error:
+        except error.PyAsn1Error:
             pass
         else:
             assert 0, 'wrong tagFormat worked out'
@@ -386,7 +381,7 @@ class ObjectIdentifierDecoderTestCase(BaseTestCase):
     def testZeroLength(self):
         try:
             decoder.decode(ints2octs((6, 0, 0)))
-        except PyAsn1Error:
+        except error.PyAsn1Error:
             pass
         else:
             assert 0, 'zero length tolerated'
@@ -394,7 +389,7 @@ class ObjectIdentifierDecoderTestCase(BaseTestCase):
     def testIndefiniteLength(self):
         try:
             decoder.decode(ints2octs((6, 128, 0)))
-        except PyAsn1Error:
+        except error.PyAsn1Error:
             pass
         else:
             assert 0, 'indefinite length tolerated'
@@ -402,7 +397,7 @@ class ObjectIdentifierDecoderTestCase(BaseTestCase):
     def testReservedLength(self):
         try:
             decoder.decode(ints2octs((6, 255, 0)))
-        except PyAsn1Error:
+        except error.PyAsn1Error:
             pass
         else:
             assert 0, 'reserved length tolerated'
@@ -479,7 +474,7 @@ class RealDecoderTestCase(BaseTestCase):
     def testTagFormat(self):
         try:
             decoder.decode(ints2octs((41, 0)))
-        except PyAsn1Error:
+        except error.PyAsn1Error:
             pass
         else:
             assert 0, 'wrong tagFormat worked out'
@@ -487,7 +482,7 @@ class RealDecoderTestCase(BaseTestCase):
     def testShortEncoding(self):
         try:
             decoder.decode(ints2octs((9, 1, 131)))
-        except PyAsn1Error:
+        except error.PyAsn1Error:
             pass
         else:
             assert 0, 'accepted too-short real'
@@ -684,27 +679,25 @@ class SequenceDecoderTestCase(BaseTestCase):
             ints2octs((48, 128, 5, 0, 36, 128, 4, 4, 113, 117, 105, 99, 4, 4, 107, 32, 98, 114, 4, 3, 111, 119, 110, 0, 0, 2, 1, 1, 0, 0))
         ) == (self.s, null)
 
-    # TODO: Not clear how to deal with substrateFun in stream implementation
-    # def testWithOptionalAndDefaultedDefModeSubst(self):
-    #     assert decoder.decode(
-    #         ints2octs((48, 18, 5, 0, 4, 11, 113, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 2, 1, 1)),
-    #         substrateFun=lambda a, b, c: (b, b[c:])
-    #     ) == (ints2octs((5, 0, 4, 11, 113, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 2, 1, 1)), str2octs(''))
-
-    # TODO: Not clear how to deal with substrateFun in stream implementation
-    # def testWithOptionalAndDefaultedIndefModeSubst(self):
-    #     assert decoder.decode(
-    #         ints2octs((48, 128, 5, 0, 36, 128, 4, 11, 113, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 0, 0, 2, 1, 1, 0, 0)),
-    #         substrateFun=lambda a, b, c: (b, str2octs(''))
-    #     ) == (ints2octs(
-    #         (5, 0, 36, 128, 4, 11, 113, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 0, 0, 2, 1, 1, 0, 0)), str2octs(''))
+    def testWithOptionalAndDefaultedDefModeSubst(self):
+        assert decoder.decode(
+            ints2octs((48, 18, 5, 0, 4, 11, 113, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 2, 1, 1)),
+            substrateFun=lambda a, b, c, d: streaming.read(b, c)
+        ) == (ints2octs((5, 0, 4, 11, 113, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 2, 1, 1)), str2octs(''))
+
+    def testWithOptionalAndDefaultedIndefModeSubst(self):
+        assert decoder.decode(
+            ints2octs((48, 128, 5, 0, 36, 128, 4, 11, 113, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 0, 0, 2, 1, 1, 0, 0)),
+            substrateFun=lambda a, b, c, d: streaming.read(b, c)
+        ) == (ints2octs(
+            (5, 0, 36, 128, 4, 11, 113, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 0, 0, 2, 1, 1, 0, 0)), str2octs(''))
 
     def testTagFormat(self):
         try:
             decoder.decode(
                 ints2octs((16, 18, 5, 0, 4, 11, 113, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 2, 1, 1))
             )
-        except PyAsn1Error:
+        except error.PyAsn1Error:
             pass
         else:
             assert 0, 'wrong tagFormat worked out'
@@ -886,7 +879,7 @@ class SequenceDecoderWithUntaggedOpenTypesTestCase(BaseTestCase):
                 decodeOpenTypes=True
             )
 
-        except PyAsn1Error:
+        except error.PyAsn1Error:
             pass
 
         else:
@@ -1025,7 +1018,7 @@ class SequenceDecoderWithUnaggedSetOfOpenTypesTestCase(BaseTestCase):
                 decodeOpenTypes=True
             )
 
-        except PyAsn1Error:
+        except error.PyAsn1Error:
             pass
 
         else:
@@ -1172,27 +1165,25 @@ class SetDecoderTestCase(BaseTestCase):
             ints2octs((49, 128, 5, 0, 36, 128, 4, 4, 113, 117, 105, 99, 4, 4, 107, 32, 98, 114, 4, 3, 111, 119, 110, 0, 0, 2, 1, 1, 0, 0))
         ) == (self.s, null)
 
-    # TODO: Not clear how to deal with substrateFun in stream implementation
-    # def testWithOptionalAndDefaultedDefModeSubst(self):
-    #     assert decoder.decode(
-    #         ints2octs((49, 18, 5, 0, 4, 11, 113, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 2, 1, 1)),
-    #         substrateFun=lambda a, b, c: (b, b[c:])
-    #     ) == (ints2octs((5, 0, 4, 11, 113, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 2, 1, 1)), str2octs(''))
-
-    # TODO: Not clear how to deal with substrateFun in stream implementation
-    # def testWithOptionalAndDefaultedIndefModeSubst(self):
-    #     assert decoder.decode(
-    #         ints2octs((49, 128, 5, 0, 36, 128, 4, 11, 113, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 0, 0, 2, 1, 1, 0, 0)),
-    #         substrateFun=lambda a, b, c: (b, str2octs(''))
-    #     ) == (ints2octs(
-    #         (5, 0, 36, 128, 4, 11, 113, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 0, 0, 2, 1, 1, 0, 0)), str2octs(''))
+    def testWithOptionalAndDefaultedDefModeSubst(self):
+        assert decoder.decode(
+            ints2octs((49, 18, 5, 0, 4, 11, 113, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 2, 1, 1)),
+            substrateFun=lambda a, b, c, d: streaming.read(b, c)
+        ) == (ints2octs((5, 0, 4, 11, 113, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 2, 1, 1)), str2octs(''))
+
+    def testWithOptionalAndDefaultedIndefModeSubst(self):
+        assert decoder.decode(
+            ints2octs((49, 128, 5, 0, 36, 128, 4, 11, 113, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 0, 0, 2, 1, 1, 0, 0)),
+            substrateFun=lambda a, b, c, d: streaming.read(b, c)
+        ) == (ints2octs(
+            (5, 0, 36, 128, 4, 11, 113, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 0, 0, 2, 1, 1, 0, 0)), str2octs(''))
 
     def testTagFormat(self):
         try:
             decoder.decode(
                 ints2octs((16, 18, 5, 0, 4, 11, 113, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 2, 1, 1))
             )
-        except PyAsn1Error:
+        except error.PyAsn1Error:
             pass
         else:
             assert 0, 'wrong tagFormat worked out'
@@ -1505,28 +1496,26 @@ class AnyDecoderTestCase(BaseTestCase):
         s = univ.Any('\004\003fox').subtype(implicitTag=tag.Tag(tag.tagClassContext, tag.tagFormatSimple, 4))
         assert decoder.decode(ints2octs((164, 128, 4, 3, 102, 111, 120, 0, 0)), asn1Spec=s) == (s, null)
 
-    # TODO: Not clear how to deal with substrateFun in stream implementation
-    # def testByUntaggedSubst(self):
-    #     assert decoder.decode(
-    #         ints2octs((4, 3, 102, 111, 120)),
-    #         asn1Spec=self.s,
-    #         substrateFun=lambda a, b, c: (b, b[c:])
-    #     ) == (ints2octs((4, 3, 102, 111, 120)), str2octs(''))
+    def testByUntaggedSubst(self):
+        assert decoder.decode(
+            ints2octs((4, 3, 102, 111, 120)),
+            asn1Spec=self.s,
+            substrateFun=lambda a, b, c, d: streaming.read(b, c)
+        ) == (ints2octs((4, 3, 102, 111, 120)), str2octs(''))
 
-    # TODO: Not clear how to deal with substrateFun in stream implementation
-    # def testTaggedExSubst(self):
-    #     assert decoder.decode(
-    #         ints2octs((164, 5, 4, 3, 102, 111, 120)),
-    #         asn1Spec=self.s,
-    #         substrateFun=lambda a, b, c: (b, b[c:])
-    #     ) == (ints2octs((164, 5, 4, 3, 102, 111, 120)), str2octs(''))
+    def testTaggedExSubst(self):
+        assert decoder.decode(
+            ints2octs((164, 5, 4, 3, 102, 111, 120)),
+            asn1Spec=self.s,
+            substrateFun=lambda a, b, c, d: streaming.read(b, c)
+        ) == (ints2octs((164, 5, 4, 3, 102, 111, 120)), str2octs(''))
 
 
 class EndOfOctetsTestCase(BaseTestCase):
     def testUnexpectedEoo(self):
         try:
             decoder.decode(ints2octs((0, 0)))
-        except PyAsn1Error:
+        except error.PyAsn1Error:
             pass
         else:
             assert 0, 'end-of-contents octets accepted at top level'
@@ -1539,7 +1528,7 @@ class EndOfOctetsTestCase(BaseTestCase):
     def testDefiniteNoEoo(self):
         try:
             decoder.decode(ints2octs((0x23, 0x02, 0x00, 0x00)))
-        except PyAsn1Error:
+        except error.PyAsn1Error:
             pass
         else:
             assert 0, 'end-of-contents octets accepted inside definite-length encoding'
@@ -1551,7 +1540,7 @@ class EndOfOctetsTestCase(BaseTestCase):
     def testNoLongFormEoo(self):
         try:
             decoder.decode(ints2octs((0x23, 0x80, 0x00, 0x81, 0x00)))
-        except PyAsn1Error:
+        except error.PyAsn1Error:
             pass
         else:
             assert 0, 'end-of-contents octets accepted with invalid long-form length'
@@ -1559,7 +1548,7 @@ class EndOfOctetsTestCase(BaseTestCase):
     def testNoConstructedEoo(self):
         try:
             decoder.decode(ints2octs((0x23, 0x80, 0x20, 0x00)))
-        except PyAsn1Error:
+        except error.PyAsn1Error:
             pass
         else:
             assert 0, 'end-of-contents octets accepted with invalid constructed encoding'
@@ -1567,7 +1556,7 @@ class EndOfOctetsTestCase(BaseTestCase):
     def testNoEooData(self):
         try:
             decoder.decode(ints2octs((0x23, 0x80, 0x00, 0x01, 0x00)))
-        except PyAsn1Error:
+        except error.PyAsn1Error:
             pass
         else:
             assert 0, 'end-of-contents octets accepted with unexpected data'
@@ -1590,41 +1579,50 @@ class NonStringDecoderTestCase(BaseTestCase):
         self.substrate = ints2octs([48, 18, 5, 0, 4, 11, 113, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110, 2, 1, 1])
 
     def testOctetString(self):
-        s = list(decoder.decodeStream(univ.OctetString(self.substrate), asn1Spec=self.s))
+        s = list(decoder.StreamingDecoder(
+            univ.OctetString(self.substrate), asn1Spec=self.s))
         assert [self.s] == s
 
     def testAny(self):
-        s = list(decoder.decodeStream(univ.Any(self.substrate), asn1Spec=self.s))
+        s = list(decoder.StreamingDecoder(
+            univ.Any(self.substrate), asn1Spec=self.s))
         assert [self.s] == s
 
 
 class ErrorOnDecodingTestCase(BaseTestCase):
 
     def testErrorCondition(self):
-        decode = decoder.Decoder(decoder.tagMap, decoder.typeMap)
-        substrate = b'abc'
-        stream = decoder._asSeekableStream(substrate)
+        decode = decoder.SingleItemDecoder(decoder.TAG_MAP, decoder.TYPE_MAP)
+        substrate = ints2octs((00, 1, 2))
+        stream = streaming.asSeekableStream(substrate)
 
         try:
-            asn1Object = decode(stream)
+            asn1Object = next(decode(stream))
 
-        except PyAsn1Error:
+        except error.PyAsn1Error:
             exc = sys.exc_info()[1]
-            assert isinstance(exc, PyAsn1Error), (
+            assert isinstance(exc, error.PyAsn1Error), (
                 'Unexpected exception raised %r' % (exc,))
 
         else:
             assert False, 'Unexpected decoder result %r' % (asn1Object,)
 
     def testRawDump(self):
-        decode = decoder.Decoder(decoder.tagMap, decoder.typeMap)
         substrate = ints2octs((31, 8, 2, 1, 1, 131, 3, 2, 1, 12))
-        stream = decoder._asSeekableStream(substrate, )
+        stream = streaming.asSeekableStream(substrate)
+
+        class StateMachine(decoder.SingleItemDecoder):
+            defaultErrorState = decoder.stDumpRawValue
 
-        decode.defaultErrorState = decoder.stDumpRawValue
+        class StreamingDecoder(decoder.StreamingDecoder):
+            SINGLE_ITEM_DECODER = StateMachine
 
-        asn1Object = decode(stream)
-        rest = stream.read()
+        class OneShotDecoder(decoder.Decoder):
+            STREAMING_DECODER = StreamingDecoder
+
+        d = OneShotDecoder()
+
+        asn1Object, rest = d(stream)
 
         assert isinstance(asn1Object, univ.Any), (
             'Unexpected raw dump type %r' % (asn1Object,))
@@ -1643,7 +1641,7 @@ class BinaryFileTestCase(BaseTestCase):
                 out.write(ints2octs((2, 1, 12)))
 
             with open(path, "rb") as source:
-                values = list(decoder.decodeStream(source))
+                values = list(decoder.StreamingDecoder(source))
 
             assert values == [12]
         finally:
@@ -1656,9 +1654,10 @@ class BinaryFileTestCase(BaseTestCase):
                 out.write(ints2octs((2, 1, 12, 35, 128, 3, 2, 0, 169, 3, 2, 1, 138, 0, 0)))
 
             with open(path, "rb") as source:
-                values = list(decoder.decodeStream(source))
+                values = list(decoder.StreamingDecoder(source))
 
             assert values == [12, (1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1)]
+
         finally:
             os.remove(path)
 
@@ -1669,8 +1668,11 @@ class BinaryFileTestCase(BaseTestCase):
                 out.write(ints2octs((2, 1, 12, 35, 128, 3, 2, 0, 169, 3, 2, 1, 138, 0, 0, 7)))
 
             with open(path, "rb") as source:
-                with self.assertRaises(SubstrateUnderrunError):
-                    _ = list(decoder.decodeStream(source))
+                list(decoder.StreamingDecoder(source))
+
+        except error.EndOfStreamError:
+            pass
+
         finally:
             os.remove(path)
 
@@ -1679,7 +1681,7 @@ class BytesIOTestCase(BaseTestCase):
     def testRead(self):
         source = ints2octs((2, 1, 12, 35, 128, 3, 2, 0, 169, 3, 2, 1, 138, 0, 0))
         stream = io.BytesIO(source)
-        values = list(decoder.decodeStream(stream))
+        values = list(decoder.StreamingDecoder(stream))
         assert values == [12, (1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1)]
 
 
@@ -1687,8 +1689,114 @@ class UnicodeTestCase(BaseTestCase):
     def testFail(self):
         # This ensures that unicode objects in Python 2 & str objects in Python 3.7 cannot be parsed.
         source = ints2octs((2, 1, 12, 35, 128, 3, 2, 0, 169, 3, 2, 1, 138, 0, 0)).decode("latin-1")
-        with self.assertRaises(UnsupportedSubstrateError):
-            _ = next(decoder.decodeStream(source))
+        try:
+            next(decoder.StreamingDecoder(source))
+
+        except error.UnsupportedSubstrateError:
+            pass
+
+        else:
+            assert False, 'Tolerated parsing broken unicode strings'
+
+
+class RestartableDecoderTestCase(BaseTestCase):
+
+    class NonBlockingStream(io.BytesIO):
+        block = False
+
+        def read(self, size=-1):
+            self.block = not self.block
+            if self.block:
+                return  # this is what non-blocking streams sometimes do
+
+            return io.BytesIO.read(self, size)
+
+    def setUp(self):
+        BaseTestCase.setUp(self)
+
+        self.s = univ.SequenceOf(componentType=univ.OctetString())
+        self.s.setComponentByPosition(0, univ.OctetString('quick brown'))
+        source = ints2octs(
+            (48, 26,
+             4, 11, 113, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110,
+             4, 11, 113, 117, 105, 99, 107, 32, 98, 114, 111, 119, 110))
+        self.stream = self.NonBlockingStream(source)
+
+    def testPartialReadingFromNonBlockingStream(self):
+        iterator = iter(decoder.StreamingDecoder(self.stream, asn1Spec=self.s))
+
+        res = next(iterator)
+
+        assert isinstance(res, error.SubstrateUnderrunError)
+        assert 'asn1Object' not in res.context
+
+        res = next(iterator)
+
+        assert isinstance(res, error.SubstrateUnderrunError)
+        assert 'asn1Object' not in res.context
+
+        res = next(iterator)
+
+        assert isinstance(res, error.SubstrateUnderrunError)
+        assert 'asn1Object' in res.context
+        assert isinstance(res.context['asn1Object'], univ.SequenceOf)
+        assert res.context['asn1Object'].isValue
+        assert len(res.context['asn1Object']) == 0
+
+        res = next(iterator)
+
+        assert isinstance(res, error.SubstrateUnderrunError)
+        assert 'asn1Object' in res.context
+        assert isinstance(res.context['asn1Object'], univ.SequenceOf)
+        assert res.context['asn1Object'].isValue
+        assert len(res.context['asn1Object']) == 0
+
+        res = next(iterator)
+
+        assert isinstance(res, error.SubstrateUnderrunError)
+        assert 'asn1Object' in res.context
+        assert isinstance(res.context['asn1Object'], univ.SequenceOf)
+        assert res.context['asn1Object'].isValue
+        assert len(res.context['asn1Object']) == 0
+
+        res = next(iterator)
+
+        assert isinstance(res, error.SubstrateUnderrunError)
+        assert 'asn1Object' in res.context
+        assert isinstance(res.context['asn1Object'], univ.SequenceOf)
+        assert res.context['asn1Object'].isValue
+        assert len(res.context['asn1Object']) == 1
+
+        res = next(iterator)
+
+        assert isinstance(res, error.SubstrateUnderrunError)
+        assert 'asn1Object' in res.context
+        assert isinstance(res.context['asn1Object'], univ.SequenceOf)
+        assert res.context['asn1Object'].isValue
+        assert len(res.context['asn1Object']) == 1
+
+        res = next(iterator)
+
+        assert isinstance(res, error.SubstrateUnderrunError)
+        assert 'asn1Object' in res.context
+        assert isinstance(res.context['asn1Object'], univ.SequenceOf)
+        assert res.context['asn1Object'].isValue
+        assert len(res.context['asn1Object']) == 1
+
+        res = next(iterator)
+
+        assert isinstance(res, univ.SequenceOf)
+        assert res.isValue
+        assert len(res) == 2
+
+        try:
+            next(iterator)
+
+        except StopIteration:
+            pass
+
+        else:
+            assert False, 'End of stream not raised'
 
 
 class CompressedFilesTestCase(BaseTestCase):
@@ -1699,9 +1807,10 @@ class CompressedFilesTestCase(BaseTestCase):
                 out.write(ints2octs((2, 1, 12, 35, 128, 3, 2, 0, 169, 3, 2, 1, 138, 0, 0)))
 
             with gzip.open(path, "rb") as source:
-                values = list(decoder.decodeStream(source))
+                values = list(decoder.StreamingDecoder(source))
 
             assert values == [12, (1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1)]
+
         finally:
             os.remove(path)
 
@@ -1715,7 +1824,7 @@ class CompressedFilesTestCase(BaseTestCase):
 
             with zipfile.ZipFile(path, "r") as myzip:
                 with myzip.open("data", "r") as source:
-                    values = list(decoder.decodeStream(source))
+                    values = list(decoder.StreamingDecoder(source))
                     assert values == [12, (1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1)]
         finally:
             os.remove(path)
@@ -1729,63 +1838,12 @@ class CompressedFilesTestCase(BaseTestCase):
 
             with zipfile.ZipFile(path, "r") as myzip:
                 with myzip.open("data", "r") as source:
-                    values = list(decoder.decodeStream(source))
+                    values = list(decoder.StreamingDecoder(source))
                     assert values == [12, (1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1)] * 1000
         finally:
             os.remove(path)
 
 
-class CachingStreamWrapperTestCase(BaseTestCase):
-    def setUp(self):
-        self.shortText = b"abcdefghij"
-        self.longText = self.shortText * (io.DEFAULT_BUFFER_SIZE * 5)
-        self.shortStream = io.BytesIO(self.shortText)
-        self.longStream = io.BytesIO(self.longText)
-
-    def testReadJustFromCache(self):
-        wrapper = decoder._CachingStreamWrapper(self.shortStream)
-        wrapper.read(6)
-        wrapper.seek(3)
-        assert wrapper.read(1) == b"d"
-        assert wrapper.read(1) == b"e"
-        assert wrapper.tell() == 5
-
-    def testReadFromCacheAndStream(self):
-        wrapper = decoder._CachingStreamWrapper(self.shortStream)
-        wrapper.read(6)
-        wrapper.seek(3)
-        assert wrapper.read(4) == b"defg"
-        assert wrapper.tell() == 7
-
-    def testReadJustFromStream(self):
-        wrapper = decoder._CachingStreamWrapper(self.shortStream)
-        assert wrapper.read(6) == b"abcdef"
-        assert wrapper.tell() == 6
-
-    def testPeek(self):
-        wrapper = decoder._CachingStreamWrapper(self.longStream)
-        read_bytes = wrapper.peek(io.DEFAULT_BUFFER_SIZE + 73)
-        assert len(read_bytes) == io.DEFAULT_BUFFER_SIZE + 73
-        assert read_bytes.startswith(b"abcdefg")
-        assert wrapper.tell() == 0
-        assert wrapper.read(4) == b"abcd"
-
-    def testMarkedPositionResets(self):
-        wrapper = decoder._CachingStreamWrapper(self.longStream)
-        wrapper.read(10)
-        wrapper._markedPosition = wrapper.tell()
-        assert wrapper._markedPosition == 10
-
-        # Reach the maximum capacity of cache
-        wrapper.read(io.DEFAULT_BUFFER_SIZE)
-        assert wrapper.tell() == 10 + io.DEFAULT_BUFFER_SIZE
-
-        # The following should clear the cache
-        wrapper._markedPosition = wrapper.tell()
-        assert wrapper._markedPosition == 0
-        assert len(wrapper._cache.getvalue()) == 0
-
-
 suite = unittest.TestLoader().loadTestsFromModule(sys.modules[__name__])
 
 if __name__ == '__main__':
diff --git a/tests/codec/ber/test_encoder.py b/tests/codec/ber/test_encoder.py
index df82e7b..b880285 100644
--- a/tests/codec/ber/test_encoder.py
+++ b/tests/codec/ber/test_encoder.py
@@ -382,19 +382,19 @@ class RealEncoderTestCase(BaseTestCase):
 
     def testBin3(self):
         # change binEncBase in the RealEncoder instance => for all further Real
-        binEncBase, encoder.typeMap[univ.Real.typeId].binEncBase = encoder.typeMap[univ.Real.typeId].binEncBase, 16
+        binEncBase, encoder.TYPE_MAP[univ.Real.typeId].binEncBase = encoder.TYPE_MAP[univ.Real.typeId].binEncBase, 16
         assert encoder.encode(
             univ.Real((0.00390625, 2, 0))  # check encbase = 16
         ) == ints2octs((9, 3, 160, 254, 1))
-        encoder.typeMap[univ.Real.typeId].binEncBase = binEncBase
+        encoder.TYPE_MAP[univ.Real.typeId].binEncBase = binEncBase
 
     def testBin4(self):
         # choose binEncBase automatically for all further Real (testBin[4-7])
-        binEncBase, encoder.typeMap[univ.Real.typeId].binEncBase = encoder.typeMap[univ.Real.typeId].binEncBase, None
+        binEncBase, encoder.TYPE_MAP[univ.Real.typeId].binEncBase = encoder.TYPE_MAP[univ.Real.typeId].binEncBase, None
         assert encoder.encode(
             univ.Real((1, 2, 0))  # check exponent = 0
         ) == ints2octs((9, 3, 128, 0, 1))
-        encoder.typeMap[univ.Real.typeId].binEncBase = binEncBase
+        encoder.TYPE_MAP[univ.Real.typeId].binEncBase = binEncBase
 
     def testBin5(self):
         assert encoder.encode(
diff --git a/tests/codec/cer/test_decoder.py b/tests/codec/cer/test_decoder.py
index bb5ce93..d628061 100644
--- a/tests/codec/cer/test_decoder.py
+++ b/tests/codec/cer/test_decoder.py
@@ -41,6 +41,7 @@ class BooleanDecoderTestCase(BaseTestCase):
         except PyAsn1Error:
             pass
 
+
 class BitStringDecoderTestCase(BaseTestCase):
     def testShortMode(self):
         assert decoder.decode(
diff --git a/tests/codec/cer/test_encoder.py b/tests/codec/cer/test_encoder.py
index e155571..ce26387 100644
--- a/tests/codec/cer/test_encoder.py
+++ b/tests/codec/cer/test_encoder.py
@@ -84,7 +84,6 @@ class GeneralizedTimeEncoderTestCase(BaseTestCase):
         else:
             assert 0, 'Missing timezone tolerated'
 
-
     def testDecimalCommaPoint(self):
         try:
             assert encoder.encode(
diff --git a/tests/codec/test_streaming.py b/tests/codec/test_streaming.py
new file mode 100644
index 0000000..c608b11
--- /dev/null
+++ b/tests/codec/test_streaming.py
@@ -0,0 +1,75 @@
+#
+# This file is part of pyasn1 software.
+#
+# Copyright (c) 2005-2019, Ilya Etingof <etingof@gmail.com>
+# License: http://snmplabs.com/pyasn1/license.html
+#
+import io
+import sys
+
+try:
+    import unittest2 as unittest
+
+except ImportError:
+    import unittest
+
+from tests.base import BaseTestCase
+
+from pyasn1.codec import streaming
+
+
+class CachingStreamWrapperTestCase(BaseTestCase):
+    def setUp(self):
+        self.shortText = b"abcdefghij"
+        self.longText = self.shortText * (io.DEFAULT_BUFFER_SIZE * 5)
+        self.shortStream = io.BytesIO(self.shortText)
+        self.longStream = io.BytesIO(self.longText)
+
+    def testReadJustFromCache(self):
+        wrapper = streaming.CachingStreamWrapper(self.shortStream)
+        wrapper.read(6)
+        wrapper.seek(3)
+        assert wrapper.read(1) == b"d"
+        assert wrapper.read(1) == b"e"
+        assert wrapper.tell() == 5
+
+    def testReadFromCacheAndStream(self):
+        wrapper = streaming.CachingStreamWrapper(self.shortStream)
+        wrapper.read(6)
+        wrapper.seek(3)
+        assert wrapper.read(4) == b"defg"
+        assert wrapper.tell() == 7
+
+    def testReadJustFromStream(self):
+        wrapper = streaming.CachingStreamWrapper(self.shortStream)
+        assert wrapper.read(6) == b"abcdef"
+        assert wrapper.tell() == 6
+
+    def testPeek(self):
+        wrapper = streaming.CachingStreamWrapper(self.longStream)
+        read_bytes = wrapper.peek(io.DEFAULT_BUFFER_SIZE + 73)
+        assert len(read_bytes) == io.DEFAULT_BUFFER_SIZE + 73
+        assert read_bytes.startswith(b"abcdefg")
+        assert wrapper.tell() == 0
+        assert wrapper.read(4) == b"abcd"
+
+    def testMarkedPositionResets(self):
+        wrapper = streaming.CachingStreamWrapper(self.longStream)
+        wrapper.read(10)
+        wrapper.markedPosition = wrapper.tell()
+        assert wrapper.markedPosition == 10
+
+        # Reach the maximum capacity of cache
+        wrapper.read(io.DEFAULT_BUFFER_SIZE)
+        assert wrapper.tell() == 10 + io.DEFAULT_BUFFER_SIZE
+
+        # The following should clear the cache
+        wrapper.markedPosition = wrapper.tell()
+        assert wrapper.markedPosition == 0
+        assert len(wrapper._cache.getvalue()) == 0
+
+
+suite = unittest.TestLoader().loadTestsFromModule(sys.modules[__name__])
+
+if __name__ == '__main__':
+    unittest.TextTestRunner(verbosity=2).run(suite)