metainfo.py

# Copyright 2018 Markus Scheidgen
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#   http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an"AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

from typing import Type, TypeVar, Union, Tuple, Iterable, List, Any, Dict, Set, \
    Callable as TypingCallable, cast
from collections.abc import Iterable as IterableABC
import sys
import inspect
import re
import json
import itertools
import numpy as np
import pint
import pint.unit
import pint.quantity
import aniso8601
from datetime import datetime
import pytz
import docstring_parser


m_package: 'Package' = None

is_bootstrapping = True
MSectionBound = TypeVar('MSectionBound', bound='MSection')
T = TypeVar('T')


# Metainfo errors

class MetainfoError(Exception):
    """ Metainfo related errors. """
    pass


class DeriveError(MetainfoError):
    """ An error occurred while computing a derived value. """
    pass


class MetainfoReferenceError(MetainfoError):
    """ An error indicating that a reference could not be resolved. """
    pass


# Metainfo quantity data types

class Enum(list):
    """ Allows to define str types with values limited to a pre-set list of possible values. """
    def __init__(self, *args):
        if len(args) == 1 and isinstance(args[0], list):
            super().__init__(args[0])

        else:
            super().__init__(args)


class MProxy():
    """ A placeholder object that acts as reference to a value that is not yet resolved.

    Attributes:
        url: The reference represented as an URL string.
    """

    def __init__(self, url: str):
        self.url = url


class DataType:
    """
    Allows to define custom data types that can be used in the meta-info.

    The metainfo supports the most types out of the box. These includes the python build-in
    primitive types (int, bool, str, float, ...), references to sections, and enums.
    However, in some occasions you need to add custom data types.

    This base class lets you customize various aspects of value treatment. This includes
    type checks and various value transformations. This allows to store values in the
    section differently from how the usermight set/get them, and it allows to have non
    serializeable values that are transformed on de-/serialization.
    """
    def set_normalize(self, section: 'MSection', quantity_def: 'Quantity', value: Any) -> Any:
        """ Transforms the given value before it is set and checks its type. """
        return value

    def get_normalize(self, section: 'MSection', quantity_def: 'Quantity', value: Any) -> Any:
        """ Transforms the given value when it is get. """
        return value

    def serialize(self, section: 'MSection', quantity_def: 'Quantity', value: Any) -> Any:
        """ Transforms the given value when making the section serializeable. """
        return value

    def deserialize(self, section: 'MSection', quantity_def: 'Quantity', value: Any) -> Any:
        """ Transforms the given value from its serializeable form. """
        return value


range_re = re.compile(r'(\d)\.\.(\d|\*)')


class _Dimension(DataType):

    def set_normalize(self, section, quantity_def: 'Quantity', value):
        if isinstance(value, int):
            return value

        if isinstance(value, str):
            if value.isidentifier():
                return value
            if re.match(range_re, value):
                return value

        if isinstance(value, Section):
            return value

        if isinstance(value, type) and hasattr(value, 'm_def'):
            return value

        raise TypeError('%s is not a valid dimension' % str(value))

    @staticmethod
    def check_dimension(section, dimension, length):
        if isinstance(dimension, int):
            return dimension == length
        if isinstance(dimension, str):
            if dimension.isidentifier():
                return dimension == getattr(section, dimension)

            m = re.match(range_re, dimension)
            start = int(m.group(1))
            end = -1 if m.group(2) == '*' else int(m.group(2))
            return start <= length and (end == -1 or length <= end)


class _Unit(DataType):
    def set_normalize(self, section, quantity_def: 'Quantity', value):
        if isinstance(value, str):
            value = units.parse_units(value)

        elif not isinstance(value, pint.unit._Unit):
            raise TypeError('Units must be given as str or pint Unit instances.')

        return value

    def serialize(self, section, quantity_def: 'Quantity', value):
        return value.__str__()

    def deserialize(self, section, quantity_def: 'Quantity', value):
        return units.parse_units(value)


units = pint.UnitRegistry()
""" The default pint unit registry that should be used to give units to quantity definitions. """


class _Callable(DataType):
    def serialize(self, section, quantity_def: 'Quantity', value):
        raise MetainfoError('Callables cannot be serialized')

    def deserialize(self, section, quantity_def: 'Quantity', value):
        raise MetainfoError('Callables cannot be serialized')


class _QuantityType(DataType):
    """ Data type for defining the type of a metainfo quantity.

    A metainfo quantity type can be one of

    - python build-in primitives: int, float, bool, str
    - numpy dtypes, e.g. f, int32
    - a section definition to define references
    - an Enum instance to use it's values as possible str values
    - a custom datatype, i.e. instance of :class:`DataType`
    - Any
    """

    def set_normalize(self, section, quantity_def, value):
        if value in [str, int, float, bool]:
            return value

        if isinstance(value, Enum):
            for enum_value in value:
                if not isinstance(enum_value, str):
                    raise TypeError('Enum value %s is not a string.' % enum_value)
            return value

        if type(value) == np.dtype:
            return value

        if isinstance(value, Section):
            return value

        if isinstance(value, DataType):
            return value

        if value == Any:
            return value

        if isinstance(value, type):
            section = getattr(value, 'm_def', None)
            if section is not None:
                return Reference(section)

        raise MetainfoError(
            'Type %s of %s is not a valid metainfo quantity type' %
            (value, quantity_def))

    def serialize(self, section, quantity_def, value):
        if value is str or value is int or value is float or value is bool:
            return dict(type_kind='python', type_data=value.__name__)

        if isinstance(value, Enum):
            return dict(type_kind='Enum', type_data=list(value))

        if type(value) == np.dtype:
            return dict(type_kind='numpy', type_data=str(value))

        if isinstance(value, Reference):
            return dict(type_kind='reference', type_data=value.target_section_def.m_path())

        if isinstance(value, DataType):
            module = value.__class__.__module__
            if module is None or module == str.__class__.__module__:
                type_data = value.__class__.__name__
            else:
                type_data = '%s.%s' % (module, value.__class__.__name__)

            return dict(type_kind='custom', type_data=type_data)

        if value == Any:
            return dict(type_kind='Any')

        raise MetainfoError(
            'Type %s of %s is not a valid metainfo quantity type' %
            (value, quantity_def))


class Reference(DataType):
    """ Datatype used for reference quantities. """

    def __init__(self, section_def: 'Section'):
        if not isinstance(section_def, Section):
            raise MetainfoError('%s is not a section definition.' % section_def)
        self.target_section_def = section_def

    def set_normalize(self, section: 'MSection', quantity_def: 'Quantity', value: Any) -> Any:
        if self.target_section_def.m_follows(Definition.m_def):
            # special case used in metainfo definitions, where we reference metainfo definitions
            # using their Python class. E.g. referencing a section definition using its
            # class instead of the object: Run vs. Run.m_def
            if isinstance(value, type):
                definition = getattr(value, 'm_def', None)
                if definition is not None and definition.m_follows(self.target_section_def):
                    return definition

        if isinstance(value, MProxy):
            return value

        if not isinstance(value, MSection):
            raise TypeError(
                'The value %s is not a section and can not be used as a reference.' % value)

        if not value.m_follows(self.target_section_def):
            raise TypeError(
                '%s is not a %s and therefore an invalid value of %s.' %
                (value, self.target_section_def, quantity_def))

        return value

    def get_normalize(self, section: 'MSection', quantity_def: 'Quantity', value: Any) -> Any:
        if isinstance(value, MProxy):
            resolved: 'MSection' = section.m_resolve(value.url)
            if resolved is None:
                raise ReferenceError('Could not resolve %s from %s.' % (value, section))
            section.m_set(quantity_def, value)
            return resolved

        return value

    def serialize(self, section: 'MSection', quantity_def: 'Quantity', value: Any) -> Any:
        return value.m_path()

    def deserialize(self, section: 'MSection', quantity_def: 'Quantity', value: Any) -> Any:
        return MProxy(value)


class _Datetime(DataType):

    def __parse(self, datetime_str: str) -> datetime:
        try:
            try:
                return aniso8601.parse_datetime(datetime_str)
            except ValueError:
                date = aniso8601.parse_date(datetime_str)
                return datetime(date.year, date.month, date.day)
        except Exception:
            raise TypeError('Invalid date literal "{0}"'.format(datetime_str))

    def set_normalize(self, section: 'MSection', quantity_def: 'Quantity', value: Any) -> Any:
        if isinstance(value, str):
            value = self.__parse(value)

        if not isinstance(value, datetime):
            raise TypeError('%s is not a datetime.' % value)

        return value

    def serialize(self, section: 'MSection', quantity_def: 'Quantity', value: Any) -> Any:
        value.replace(tzinfo=pytz.utc)
        return value.isoformat()

    def deserialize(self, section: 'MSection', quantity_def: 'Quantity', value: Any) -> Any:
        return self.__parse(value)


Dimension = _Dimension()
Unit = _Unit()
QuantityType = _QuantityType()
Callable = _Callable()
Datetime = _Datetime()


# Metainfo data storage and reflection interface

class MObjectMeta(type):

    def __new__(self, cls_name, bases, dct):
        cls = super().__new__(self, cls_name, bases, dct)

        init = getattr(cls, '__init_cls__')
        if init is not None and not is_bootstrapping:
            init()
        return cls


Content = Tuple['MSection', int, 'SubSection', 'MSection']

SectionDef = Union[str, 'Section', 'SubSection', Type[MSectionBound]]
""" Type for section definition references.

This can either be :

- the name of the section
- the section definition itself
- the definition of a sub section
- or the section definition Python class
"""


class MData:
    """ An interface for low-level metainfo data objects.

    Metainfo data objects store the data of a single section instance. This interface
    constitutes the minimal functionality for accessing and modifying section data.
    Different implementations of this interface, can realize different storage backends.

    All section instances will implement this interface, usually be delegating calls to
    a standalone implementation of this interface. This allows to configure various
    data backends on section instance creation.
    """

    def __getitem__(self, key):
        raise NotImplementedError()

    def __setitem__(self, key, value):
        raise NotImplementedError()

    def m_set(self, section: 'MSection', quantity_def: 'Quantity', value: Any) -> None:
        """ Set the given value for the given quantity. """
        raise NotImplementedError()

    def m_get(self, section: 'MSection', quantity_def: 'Quantity') -> Any:
        """ Retrieve the given value for the given quantity. """
        raise NotImplementedError()

    def m_is_set(self, section: 'MSection', quantity_def: 'Quantity') -> bool:
        """ True iff this quantity was explicitely set. """
        raise NotImplementedError()

    def m_add_values(
            self, section: 'MSection', quantity_def: 'Quantity', values: Any,
            offset: int) -> None:
        """ Add (partial) values for the given quantity of higher dimensionality. """
        raise NotImplementedError()

    def m_add_sub_section(
            self, section: 'MSection', sub_section_def: 'SubSection',
            sub_section: 'MSection') -> None:
        """ Adds the given section instance as a sub section of the given sub section definition. """
        raise NotImplementedError()

    def m_get_sub_section(
            self, section: 'MSection', sub_section_def: 'SubSection',
            index: int) -> 'MSection':
        """ Retrieves a single sub section of the given sub section definition. """
        raise NotImplementedError()

    def m_get_sub_sections(
            self, section: 'MSection', sub_section_def: 'SubSection') -> Iterable['MSection']:
        """ Retrieves  all sub sections of the given sub section definition. """
        raise NotImplementedError()

    def m_sub_section_count(self, section: 'MSection', sub_section_def: 'SubSection') -> int:
        """ Returns the number of sub sections for the given sub section definition. """
        raise NotImplementedError()


class MDataDict(MData):
    """ A simple dict backed implementaton of :class:`MData`. It is used by default. """

    def __init__(self, dct: Dict[str, Any] = None):
        if dct is None:
            dct = {}

        self.dct = dct

    def __getitem__(self, key):
        return self.dct[key]

    def __setitem__(self, key, value):
        self.dct[key] = value

    def m_set(self, section: 'MSection', quantity_def: 'Quantity', value: Any) -> None:
        self.dct[quantity_def.name] = value

    def m_get(self, section: 'MSection', quantity_def: 'Quantity') -> Any:
        quantity_name = quantity_def.name
        if quantity_name not in self.dct:
            return quantity_def.default
        else:
            return self.dct[quantity_name]

    def m_is_set(self, section: 'MSection', quantity_def: 'Quantity') -> bool:
        return quantity_def.name in self.dct

    def m_add_values(
            self, section: 'MSection', quantity_def: 'Quantity', values: Any,
            offset: int) -> None:

        # TODO
        raise NotImplementedError()

    def m_add_sub_section(
            self, section: 'MSection', sub_section_def: 'SubSection',
            sub_section: 'MSection') -> None:

        sub_section_name = sub_section_def.name
        if sub_section_def.repeats:
            sub_section_lst = self.dct.get(sub_section_name, None)
            if sub_section_lst is None:
                sub_section_lst = self.dct.setdefault(sub_section_name, [])

            sub_section_lst.append(sub_section)

        else:
            self.dct[sub_section_name] = sub_section

    def m_get_sub_section(
            self, section: 'MSection', sub_section_def: 'SubSection',
            index: int) -> 'MSection':

        if sub_section_def.repeats:
            return self.dct[sub_section_def.name][index]

        else:
            return self.dct.get(sub_section_def.name, None)

    def m_get_sub_sections(
            self, section: 'MSection', sub_section_def: 'SubSection') -> Iterable['MSection']:
        return self.dct.get(sub_section_def.name, [])

    def m_sub_section_count(self, section: 'MSection', sub_section_def: 'SubSection') -> int:
        sub_section_name = sub_section_def.name
        if sub_section_name not in self.dct:
            return 0

        if not sub_section_def.repeats:
            return 1

        return len(self.dct[sub_section_name])


class MSection(metaclass=MObjectMeta):
    """Base class for all section instances on all meta-info levels.

    All `section instances` indirectly instantiate the :class:`MSection` and therefore all
    members of :class:`MSection` are available on all `section instances`. :class:`MSection`
    provides many special attributes and functions (they all start with ``m_``) that allow
    to reflect on a `section's definition` and allow to manipulate the `section instance`
    without a priori knowledge of the `section defintion`.

    It also carries all the data for each section. All sub-classes only define specific
    sections in terms of possible sub-sections and quantities. The data is managed here.

    Attributes:
        m_def: The `section definition` that this `section instance` follows as a
            :class:`Section` object.

        m_parent:
            If this section is a sub-section, this references the parent section instance.

        m_parent_sub_section:
            If this section is a sub-section, this is the :class:`SubSection` that defines
            this relationship.

        m_parent_index:
            For repeatable sections, parent keep a list of sub-sections. This is the index
            of this section in the respective parent sub-section list.

        m_data: The :class:`MData` implementations that stores the section data. It keeps
            the quantity values and sub-section. It should only be read directly
            (and never manipulated).

    """

    m_def: 'Section' = None

    def __init__(self, m_def: 'Section' = None, m_data: MData = None, **kwargs):

        self.m_def: 'Section' = m_def
        self.m_parent: 'MSection' = None
        self.m_parent_sub_section: 'SubSection' = None
        self.m_parent_index = -1

        # get missing m_def from class
        cls = self.__class__
        if self.m_def is None:
            self.m_def = cls.m_def

        # check m_def
        if cls.m_def is not None:
            if self.m_def != cls.m_def:
                MetainfoError('Section class and section definition must match.')

            if self.m_def.extends_base_section:
                MetainfoError('Section extends another section and cannot be instantiated.')

        else:
            if not is_bootstrapping:
                MetainfoError('Section has not m_def.')

        # get annotations from kwargs
        self.m_annotations: Dict[str, Any] = {}
        rest = {}
        for key, value in kwargs.items():
            if key.startswith('a_'):
                self.m_annotations[key[2:]] = value
            else:
                rest[key] = value

        # initialize data
        self.m_data = m_data
        if self.m_data is None:
            self.m_data = MDataDict()

        # set remaining kwargs
        if is_bootstrapping:
            self.m_data.dct.update(**rest)  # type: ignore
        else:
            self.m_update(**rest)

    @classmethod
    def __init_cls__(cls):
        # ensure that the m_def is defined
        m_def = cls.m_def
        if m_def is None:
            m_def = Section()
            setattr(cls, 'm_def', m_def)

        # transfer name m_def
        m_def.name = cls.__name__
        m_def.section_cls = cls

        # add base sections
        extended_base_section = None
        if m_def.extends_base_section:
            base_sections_count = len(cls.__bases__)
            if base_sections_count == 0:
                raise MetainfoError(
                    'Section %s extend the base section, but has no base section.' % m_def)

            if base_sections_count > 1:
                raise MetainfoError(
                    'Section %s extend the base section, but has more than one base section' % m_def)

            base_section_cls = cls.__bases__[0]
            extended_base_section = base_section = getattr(base_section_cls, 'm_def', None)
            if base_section is None:
                raise MetainfoError(
                    'The base section of %s is not a section class.' % m_def)

            for name, attr in cls.__dict__.items():
                if isinstance(attr, Property):
                    setattr(base_section_cls, name, attr)

            section_to_add_properties_to = base_section
        else:
            for base_cls in cls.__bases__:
                if base_cls != MSection:
                    base_section = getattr(base_cls, 'm_def')
                    if base_section is None:
                        raise TypeError(
                            'Section defining classes must have MSection or a decendant as '
                            'base classes.')

                    base_sections = list(m_def.m_get(Section.base_sections))
                    base_sections.append(base_section)
                    m_def.m_set(Section.base_sections, base_sections)

            section_to_add_properties_to = m_def

        constraints: Set[str] = set()
        event_handlers: Set[Callable] = set(m_def.event_handlers)
        for name, attr in cls.__dict__.items():
            # transfer names and descriptions for properties
            if isinstance(attr, Property):
                attr.name = name
                if attr.description is not None:
                    attr.description = inspect.cleandoc(attr.description).strip()
                    attr.__doc__ = attr.description

                if isinstance(attr, Quantity):
                    section_to_add_properties_to.m_add_sub_section(Section.quantities, attr)
                elif isinstance(attr, SubSection):
                    section_to_add_properties_to.m_add_sub_section(Section.sub_sections, attr)
                else:
                    raise NotImplementedError('Unknown property kind.')

            if inspect.isfunction(attr):
                method_name = attr.__name__

                # transfer constraints
                if method_name.startswith('c_'):
                    constraint = method_name[2:]
                    constraints.add(constraint)

                # register event_handlers from event_handler methods
                if method_name.startswith('on_set') or method_name.startswith('on_add_sub_section'):
                    if attr not in event_handlers:
                        event_handlers.add(attr)

        # add handler and constraints from base sections
        for base_section in m_def.all_base_sections:
            for constraint in base_section.constraints:
                constraints.add(constraint)
            for event_handler in base_section.event_handlers:
                event_handlers.add(event_handler)

        m_def.constraints = list(constraints)
        m_def.event_handlers = list(event_handlers)

        # add section cls' section to the module's package
        module_name = cls.__module__
        pkg = Package.from_module(module_name)
        pkg.m_add_sub_section(Package.section_definitions, cls.m_def)

        # apply_google_docstrings
        # Parses the google doc string of the given class and properly updates the
        # definition descriptions.

        # This allows to document quantities and sub-sections with 'Args:' in the section
        # class. It will remove the 'Args' section from the section definition and will
        # set the respective pieces to the quantity and sub-section descriptions.
        docstring = cls.__doc__
        if docstring is not None:
            parsed_docstring = docstring_parser.parse(docstring)
            short = parsed_docstring.short_description
            dsc = parsed_docstring.long_description

            if short and dsc:
                description = '%s %s' % (short.strip(), dsc.strip())
            elif short:
                description = short.strip()
            elif dsc:
                description = dsc.strip()
            else:
                description = None

            if m_def.description is None:
                m_def.description = description

            for param in parsed_docstring.params:
                prop = m_def.all_properties.get(param.arg_name)
                if prop is not None:
                    if prop.description is None:
                        prop.description = param.description

        # validate
        def validate(definition):
            errors = definition.m_all_validate()
            if len(errors) > 0:
                raise MetainfoError(
                    '%s. The section definition %s violates %d more constraints' %
                    (str(errors[0]).strip('.'), definition, len(errors) - 1))

        if extended_base_section is not None:
            validate(extended_base_section)
        validate(m_def)

    def __check_np(self, quantity_def: 'Quantity', value: np.ndarray) -> np.ndarray:
        # TODO this feels expensive, first check, then possible convert very often?
        # if quantity_ref.type != value.dtype:
        #     raise MetainfoError(
        #         'Quantity dtype %s and value dtype %s do not match.' %
        #         (quantity_ref.type, value.dtype))

        return value

    def __set_normalize(self, quantity_def: 'Quantity', value: Any) -> Any:

        if isinstance(quantity_def.type, DataType):
            return quantity_def.type.set_normalize(self, quantity_def, value)

        elif isinstance(quantity_def.type, Section):
            if isinstance(value, MProxy):
                return value

            if not isinstance(value, MSection):
                raise TypeError(
                    'The value %s for reference quantity %s is not a section instance.' %
                    (value, quantity_def))

            if not value.m_follows(quantity_def.type):
                raise TypeError(
                    'The value %s for quantity %s does not follow %s' %
                    (value, quantity_def, quantity_def.type))

        elif isinstance(quantity_def.type, Enum):
            if value not in quantity_def.type:
                raise TypeError(
                    'The value %s is not an enum value for quantity %s.' %
                    (value, quantity_def))

        elif quantity_def.type == Any:
            pass

        else:
            if type(value) != quantity_def.type:
                raise TypeError(
                    'The value %s with type %s for quantity %s is not of type %s' %
                    (value, type(value), quantity_def, quantity_def.type))

        return value

    def __resolve_synonym(self, quantity_def: 'Quantity') -> 'Quantity':
        if quantity_def.synonym_for is not None:
            return self.m_def.all_quantities[quantity_def.synonym_for]
        return quantity_def

    def __to_np(self, quantity_def: 'Quantity', value):
        if isinstance(value, pint.quantity._Quantity):
            if quantity_def.unit is None:
                raise MetainfoError(
                    'The quantity %s has not a unit, but value %s has.' %
                    (quantity_def, value))
            value = value.to(quantity_def.unit).magnitude

        if len(quantity_def.shape) > 0 and type(value) != np.ndarray:
            try:
                value = np.asarray(value)
            except TypeError:
                raise TypeError(
                    'Could not convert value %s of %s to a numpy array' %
                    (value, quantity_def))
        elif type(value) != quantity_def.type.type:
            try:
                value = quantity_def.type.type(value)
            except TypeError:
                raise TypeError(
                    'Could not convert value %s of %s to a numpy scalar' %
                    (value, quantity_def))

        return self.__check_np(quantity_def, value)

    def m_set(self, quantity_def: 'Quantity', value: Any) -> None:
        """ Set the given value for the given quantity. """
        quantity_def = self.__resolve_synonym(quantity_def)

        if quantity_def.derived is not None:
            raise MetainfoError('The quantity %s is derived and cannot be set.' % quantity_def)

        if type(quantity_def.type) == np.dtype:
            value = self.__to_np(quantity_def, value)

        else:
            dimensions = len(quantity_def.shape)
            if dimensions == 0:
                value = self.__set_normalize(quantity_def, value)

            elif dimensions == 1:
                if type(value) == str or not isinstance(value, IterableABC):
                    raise TypeError(
                        'The shape of %s requires an iterable value, but %s is not iterable.' %
                        (quantity_def, value))

                value = list(self.__set_normalize(quantity_def, item) for item in value)

            else:
                raise MetainfoError(
                    'Only numpy arrays and dtypes can be used for higher dimensional '
                    'quantities.')

        self.m_data.m_set(self, quantity_def, value)

        for handler in self.m_def.event_handlers:
            if handler.__name__.startswith('on_set'):
                handler(self, quantity_def, value)

    def m_get(self, quantity_def: 'Quantity') -> Any:
        """ Retrieve the given value for the given quantity. """
        quantity_def = self.__resolve_synonym(quantity_def)
        if quantity_def.derived is not None:
            try:
                return quantity_def.derived(self)
            except Exception as e:
                raise DeriveError('Could not derive value for %s: %s' % (quantity_def, str(e)))

        value = self.m_data.m_get(self, quantity_def)

        if isinstance(quantity_def.type, DataType) and quantity_def.type.get_normalize != DataType.get_normalize:
            dimensions = len(quantity_def.shape)
            if dimensions == 0:
                value = quantity_def.type.get_normalize(self, quantity_def, value)

            elif dimensions == 1:
                value = list(
                    quantity_def.type.get_normalize(self, quantity_def, item)
                    for item in value)

            else:
                raise MetainfoError(
                    'Only numpy arrays and dtypes can be used for higher dimensional '
                    'quantities.')

        elif type(quantity_def.type) == np.dtype:
            if quantity_def.unit is not None:
                value = value * quantity_def.unit

        return value

    def m_is_set(self, quantity_def: 'Quantity') -> bool:
        """ True if the given quantity is set. """
        quantity_def = self.__resolve_synonym(quantity_def)
        if quantity_def.derived is not None:
            return True

        return self.m_data.m_is_set(self, quantity_def)

    def m_add_values(self, quantity_def: 'Quantity', values: Any, offset: int) -> None:
        """ Add (partial) values for the given quantity of higher dimensionality. """
        self.m_data.m_add_values(self, quantity_def, values, offset)

    def m_add_sub_section(self, sub_section_def: 'SubSection', sub_section: 'MSection') -> None:
        """ Adds the given section instance as a sub section of the given sub section definition. """

        parent_index = -1
        if sub_section_def.repeats:
            parent_index = self.m_sub_section_count(sub_section_def)
        sub_section.m_parent = self
        sub_section.m_parent_sub_section = sub_section_def
        sub_section.m_parent_index = parent_index

        self.m_data.m_add_sub_section(self, sub_section_def, sub_section)

        for handler in self.m_def.event_handlers:
            if handler.__name__.startswith('on_add_sub_section'):
                handler(self, sub_section_def, sub_section)

    def m_get_sub_section(self, sub_section_def: 'SubSection', index: int) -> 'MSection':
        """ Retrieves a single sub section of the given sub section definition. """
        return self.m_data.m_get_sub_section(self, sub_section_def, index)

    def m_get_sub_sections(self, sub_section_def: 'SubSection') -> Iterable['MSection']:
        """ Retrieves  all sub sections of the given sub section definition. """
        return self.m_data.m_get_sub_sections(self, sub_section_def)

    def m_sub_section_count(self, sub_section_def: 'SubSection') -> int:
        """ Returns the number of sub sections for the given sub section definition. """
        return self.m_data.m_sub_section_count(self, sub_section_def)

    def m_create(
            self, section_cls: Type[MSectionBound], sub_section_def: 'SubSection' = None,
            **kwargs) -> MSectionBound:
        """ Creates a section instance and adds it to this section provided there is a
        corresponding sub section.

        Args:
            section_cls: The section class for the sub-secton to create
            sub_section_def: If there are multiple sub-sections for the given class,
                this must be used to explicitely state the sub-section definition.
        """

        section_def = section_cls.m_def
        sub_section_defs = self.m_def.all_sub_sections_by_section.get(section_def, [])
        n_sub_section_defs = len(sub_section_defs)
        if n_sub_section_defs == 0:
            raise TypeError('There is no sub section to hold a %s in %s.' % (section_def, self.m_def))

        if n_sub_section_defs > 1 and sub_section_def is None:
            raise MetainfoError(
                'There are multiple sub section to hold a %s in %s, '
                'but no sub-section was explicitely given.' % (section_def, self.m_def))

        if sub_section_def is not None and sub_section_def not in sub_section_defs:
            raise MetainfoError(
                'The given sub-section class %s does not match the given sub-section '
                'definition %s.' % (section_cls, sub_section_def))

        if sub_section_def is None:
            sub_section_def = sub_section_defs[0]

        sub_section = section_cls(**kwargs)
        self.m_add_sub_section(sub_section_def, sub_section)

        return cast(MSectionBound, sub_section)

    def m_update(self, safe: bool = True, **kwargs):
        """ Updates all quantities and sub-sections with the given arguments. """
        if safe:
            for name, value in kwargs.items():
                prop = self.m_def.all_properties.get(name, None)
                if prop is None:
                    raise KeyError('%s is not an attribute of this section %s' % (name, self))

                if isinstance(prop, SubSection):
                    if prop.repeats:
                        if isinstance(value, List):
                            for item in value:
                                self.m_add_sub_section(prop, item)
                        else:
                            raise TypeError('Sub section %s repeats, but no list was given' % prop.name)
                    else:
                        self.m_add_sub_section(prop, item)

                else:
                    self.m_set(prop, value)

        else:
            self.m_data.m_data.dct.update(**kwargs)  # type: ignore

    def m_as(self, section_cls: Type[MSectionBound]) -> MSectionBound:
        """ 'Casts' this section to the given extending sections. """
        return cast(MSectionBound, self)

    def m_follows(self, definition: 'Section') -> bool:
        """ Determines if this section's definition is or is derived from the given definition. """
        return self.m_def == definition or definition in self.m_def.all_base_sections

    def m_to_dict(self, with_meta: bool = False) -> Dict[str, Any]:
        """Returns the data of this section as a json serializeable dictionary. """

        def items() -> Iterable[Tuple[str, Any]]:
            # metadata
            if with_meta:
                yield 'm_def', self.m_def.name
                if self.m_parent_index != -1:
                    yield 'm_parent_index', self.m_parent_index
                if self.m_parent_sub_section is not None:
                    yield 'm_parent_sub_section', self.m_parent_sub_section.name

            # quantities
            for name, quantity in self.m_def.all_quantities.items():
                if quantity.virtual or not self.m_is_set(quantity):
                    continue

                if self.m_is_set(quantity) and quantity.derived is None:
                    serialize: TypingCallable[[Any], Any] = str
                    if isinstance(quantity.type, DataType):

                        def data_type_serialize(value):
                            return quantity.type.serialize(self, quantity, value)

                        serialize = data_type_serialize

                    elif quantity.type in [str, int, float, bool]:
                        serialize = quantity.type

                    elif type(quantity.type) == np.dtype:
                        pass

                    elif isinstance(quantity.type, Enum):
                        pass

                    elif quantity.type == Any:
                        def _serialize(value: Any):
                            if type(value) not in [str, int, float, bool, list, type(None)]:
                                raise MetainfoError(
                                    'Only python primitives are allowed for Any typed non '
                                    'virtual quantities: %s of quantity %s in section %s' %
                                    (value, quantity, self))

                            return value

                        serialize = _serialize

                    else:
                        raise MetainfoError(
                            'Do not know how to serialize data with type %s for quantity %s' %
                            (quantity.type, quantity))

                    value = cast(MDataDict, self.m_data).dct[name]

                    if type(quantity.type) == np.dtype:
                        serializable_value = value.tolist()

                    else:
                        if len(quantity.shape) == 0:
                            serializable_value = serialize(value)
                        elif len(quantity.shape) == 1:
                            serializable_value = [serialize(i) for i in value]
                        else:
                            raise NotImplementedError('Higher shapes (%s) not supported: %s' % (quantity.shape, quantity))

                    yield name, serializable_value

            # sub sections
            for name, sub_section_def in self.m_def.all_sub_sections.items():
                if sub_section_def.repeats:
                    if self.m_sub_section_count(sub_section_def) > 0:
                        yield name, [
                            item.m_to_dict()
                            for item in self.m_get_sub_sections(sub_section_def)]
                else:
                    sub_section = self.m_get_sub_section(sub_section_def, -1)
                    if sub_section is not None:
                        yield name, sub_section.m_to_dict()

        return {key: value for key, value in items()}

    @classmethod
    def m_from_dict(cls: Type[MSectionBound], dct: Dict[str, Any]) -> MSectionBound:
        """ Creates a section from the given serializable data dictionary.

        This is the 'opposite' of :func:`m_to_dict`. It takes a deserialised dict, e.g
        loaded from JSON, and turns it into a proper section, i.e. instance of the given
        section class.
        """

        section_def = cls.m_def

        # remove m_def, m_parent_index, m_parent_sub_section metadata,
        # they set themselves automatically
        dct.pop('m_def', None)
        dct.pop('m_parent_index', None)
        dct.pop('m_parent_sub_section', None)

        section = cls()

        for name, sub_section_def in section_def.all_sub_sections.items():
            if name in dct:
                sub_section_value = dct.pop(name)
                if sub_section_def.repeats:
                    for sub_section_dct in sub_section_value:
                        sub_section = sub_section_def.sub_section.section_cls.m_from_dict(sub_section_dct)
                        section.m_add_sub_section(sub_section_def, sub_section)

                else:
                    sub_section = sub_section_def.sub_section.section_cls.m_from_dict(sub_section_value)
                    section.m_add_sub_section(sub_section_def, sub_section)

        for name, quantity_def in section_def.all_quantities.items():
            if name in dct:
                quantity_value = dct[name]

                if type(quantity_def.type) == np.dtype:
                    quantity_value = np.asarray(quantity_value)

                if isinstance(quantity_def.type, DataType):
                    dimensions = len(quantity_def.shape)
                    if dimensions == 0:
                        quantity_value = quantity_def.type.deserialize(
                            section, quantity_def, quantity_value)
                    elif dimensions == 1:
                        quantity_value = list(
                            quantity_def.type.deserialize(section, quantity_def, item)
                            for item in quantity_value)
                    else:
                        raise MetainfoError(
                            'Only numpy quantities can have more than 1 dimension.')

                section.m_data.dct[name] = quantity_value  # type: ignore

        return section

    def m_to_json(self, **kwargs):
        """ Returns the data of this section as a json string. """
        return json.dumps(self.m_to_dict(), **kwargs)

    def m_all_contents(self) -> Iterable[Content]:
        """ Returns an iterable over all sub and sub subs sections. """
        for content in self.m_contents():
            for sub_content in content[0].m_all_contents():
                yield sub_content

            yield content

    def m_contents(self) -> Iterable[Content]:
        """ Returns an iterable over all direct subs sections. """
        for sub_section_def in self.m_def.all_sub_sections.values():
            if sub_section_def.repeats:
                index = 0
                for sub_section in self.m_get_sub_sections(sub_section_def):
                    yield sub_section, index, sub_section_def, self
                    index += 1

            else:
                sub_section = self.m_get_sub_section(sub_section_def, -1)
                yield sub_section, -1, sub_section_def, self

    def m_path(self, quantity_def: 'Quantity' = None) -> str:
        """ Returns the path of this section or the given quantity within the section hierarchy. """
        if self.m_parent is None:
            return '/'

        if self.m_parent_index == -1:
            segment = self.m_parent_sub_section.name
        else:
            segment = '%s/%d' % (self.m_parent_sub_section.name, self.m_parent_index)

        if quantity_def is not None:
            segment = '%s/%s' % (segment, quantity_def.name)

        return '%s/%s' % (self.m_parent.m_path().rstrip('/'), segment)

    def m_root(self, cls: Type[MSectionBound] = None) -> MSectionBound:
        """ Returns the first parent of the parent section that has no parent; the root. """
        if self.m_parent is None:
            return cast(MSectionBound, self)
        else:
            return self.m_parent.m_root(cls)

    def m_resolve(self, path: str, cls: Type[MSectionBound] = None) -> MSectionBound:
        """ Resolves the given path using this section as context. """

        if path.startswith('/'):
            context: 'MSection' = self.m_root()
        else:
            context = self

        path_stack = path.strip('/').split('/')
        path_stack.reverse()
        while len(path_stack) > 1:
            prop_name = path_stack.pop()
            prop_def = context.m_def.all_properties.get(prop_name, None)

            if prop_def is None:
                raise ReferenceError(
                    'Could not resolve %s, property %s does not exist in %s' %
                    (path, prop_name, context.m_def))

            if isinstance(prop_def, SubSection):
                if prop_def.repeats:
                    try:
                        index = int(path_stack.pop())
                    except ValueError:
                        raise ReferenceError(
                            'Could not resolve %s, %s repeats but there is no index in the path' %
                            (path, prop_name))

                    try:
                        context = context.m_get_sub_section(prop_def, index)
                    except Exception:
                        raise ReferenceError(
                            'Could not resolve %s, there is no sub section for %s at %d' %
                            (path, prop_name, index))

                else:
                    context = context.m_get_sub_section(prop_def, -1)
                    if context is None:
                        raise ReferenceError(
                            'Could not resolve %s, there is no sub section for %s' %
                            (path, prop_name))

            elif isinstance(prop_def, Quantity):
                if len(path_stack) > 0:
                    raise ReferenceError(
                        'Could not resolve %s, %s is not a sub section' % (path, prop_name))

                return context.m_get(prop_def)

        return cast(MSectionBound, context)

    def __validate_shape(self, quantity_def: 'Quantity', value):
        if quantity_def == Quantity.default:
            return True

        quantity_shape = quantity_def.shape

        if type(value) == np.ndarray:
            value_shape = value.shape
        if isinstance(value, list) and not isinstance(value, Enum):
            value_shape = [len(value)]
        else:
            value_shape = []

        if len(value_shape) != len(quantity_shape):
            return False

        for i in range(0, len(value_shape)):
            if not _Dimension.check_dimension(self, quantity_shape[i], value_shape[i]):
                return False

        return True

    def m_validate(self):
        """ Evaluates all constraints and shapes of this section and returns a list of errors. """
        errors: List[str] = []
        for constraint_name in self.m_def.constraints:
            constraint = getattr(self, 'c_%s' % constraint_name, None)
            if constraint is None:
                raise MetainfoError(
                    'Could not find implementation for contraint %s of section %s.' %
                    (constraint_name, self.m_def))

            try:
                constraint()
            except AssertionError as e:
                error_str = str(e).strip()
                if error_str == '':
                    error_str = 'Constraint %s violated.' % constraint_name
                errors.append(error_str)

        for quantity in self.m_def.all_quantities.values():
            if self.m_is_set(quantity):
                if not self.__validate_shape(quantity, self.m_get(quantity)):
                    errors.append(
                        'The shape of quantity %s does not match its value.' % quantity)

        return errors

    def m_all_validate(self):
        """ Evaluates all constraints in the whole section hierarchy, incl. this section. """
        errors: List[str] = []
        for section, _, _, _ in itertools.chain([(self, None, None, None)], self.m_all_contents()):
            for error in section.m_validate():
                errors.append(error)

        return errors

    def __repr__(self):
        m_section_name = self.m_def.name
        # name_quantity_def = self.m_def.all_quantities.get('name', None)
        # if name_quantity_def is not None:
        #     name = self.m_get(name_quantity_def)
        try:
            name = self.m_data['name']
        except KeyError:
            name = '<noname>'

        return '%s:%s' % (name, m_section_name)


class MCategory(metaclass=MObjectMeta):

    m_def: 'Category' = None

    @classmethod
    def __init_cls__(cls):
        # ensure that the m_def is defined
        m_def = cls.m_def
        if m_def is None:
            m_def = Category()
            setattr(cls, 'm_def', m_def)

        # transfer name and description to m_def
        m_def.name = cls.__name__
        if cls.__doc__ is not None:
            m_def.description = inspect.cleandoc(cls.__doc__).strip()

        # add section cls' section to the module's package
        module_name = cls.__module__
        pkg = Package.from_module(module_name)
        pkg.m_add_sub_section(Package.category_definitions, cls.m_def)