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.

"""
The NOMAD meta-info allows to define physics data quantities. These definitions are
necessary for all computer representations of respective data (e.g. in Python,
search engines, data-bases, and files).

This modules provides various Python interfaces for

- defining meta-info data
- to create and manipulate data that follows these definitions
- to (de-)serialize meta-info data in JSON (i.e. represent data in JSON formatted files)

Here is a simple example that demonstrates the definition of System related quantities:

.. code-block:: python

    class System(MSection):
        \"\"\"
        A system section includes all quantities that describe a single a simulated
        system (a.k.a. geometry).
        \"\"\"

        n_atoms = Quantity(
            type=int, description='''
            A Defines the number of atoms in the system.
            ''')

        atom_labels = Quantity(type=Enum(ase.data.chemical_symbols), shape['n_atoms'])
        atom_positions = Quantity(type=float, shape=['n_atoms', 3], unit=Units.m)
        simulation_cell = Quantity(type=float, shape=[3, 3], unit=Units.m)
        pbc = Quantity(type=bool, shape=[3])

    class Run(MSection):
        systems = SubSection(sub_section=System, repeats=True)

Here, we define a `section` called ``System``. The section mechanism allows to organize
related data into, well, sections. Sections form containment hierarchies. Here
containment is a parent-child (whole-part) relationship. In this example many ``Systems``,
are part of one ``Run``. Each ``System`` can contain values for the defined quantities:
``n_atoms``, ``atom_labels``, ``atom_positions``, ``simulation_cell``, and ``pbc``.
Quantities allow to state type, shape, and physics unit to specify possible quantity
values.

Here is an example, were we use the above definition to create, read, and manipulate
data that follows these definitions:

.. code-bock:: python

    run = Run()
    system = run.m_create(System)
    system.n_atoms = 3
    system.atom_labels = ['H', 'H', 'O']

    print(system.atom_labels)
    print(run.m_to_json(ident=2))

This last statement, will produce the following JSON:

.. code-block:: JSON

    {
        "m_def" = "Run",
        "System": [
            {
                "m_def" = "System",
                "m_parent_index" = 0,
                "n_atoms" = 3,
                "atom_labels" = [
                    "H",
                    "H",
                    "O"
                ]
            }
        ]
    }

This is the JSON representation, a serialized version of the Python representation in
the example above.

Sections can be extended with new quantities outside the original section definition.
This provides the key mechanism to extend commonly defined parts with (code) specific
quantities:

.. code-block:: Python

    class Method(nomad.metainfo.common.Method):
        x_vasp_incar_ALGO=Quantity(
            type=Enum(['Normal', 'VeryFast', ...]),
            links=['https://cms.mpi.univie.ac.at/wiki/index.php/ALGO'])
        \"\"\"
        A convenient option to specify the electronic minimisation algorithm (as of VASP.4.5)
        and/or to select the type of GW calculations.
        \"\"\"


All meta-info definitions and classes for meta-info data objects (i.e. section instances)
inherit from :class:` MSection`. This base-class provides common functions and properties
for all meta-info data objects. Names of these common parts are prefixed with ``m_``
to distinguish them from user defined quantities. This also constitute's the `reflection`
interface (in addition to Python's build in ``getattr``, ``setattr``) that allows to
create and manipulate meta-info data, without prior program time knowledge of the underlying
definitions.

.. autoclass:: MSection

The following classes can be used to define and structure meta-info data:

- sections are defined by sub-classes :class:`MSection` and using :class:`Section` to
  populate the classattribute `m_def`
- quantities are defined by assigning classattributes of a section with :class:`Quantity`
  instances
- references (from one section to another) can be defined with quantities that use
  section definitions as type
- dimensions can use defined by simply using quantity names in shapes
- categories (former `abstract type definitions`) can be given in quantity definitions
  to assign quantities to additional specialization-generalization hierarchies

See the reference of classes :class:`Section` and :class:`Quantities` for details.

.. autoclass:: Section
.. autoclass:: Quantity
"""

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
from pint.unit import _Unit
from pint import UnitRegistry
import aniso8601
from datetime import datetime
import pytz


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. """


# 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. """

    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


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(r'(\d)\.\.(\d|\*)', 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))


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, _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 = 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 in [str, int, float, 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,
    or include different rigorosity of type and shape checks.

    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`. """

    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 metainfo objects instantiate classes that inherit from ``MSection``. Each
    section or quantity definition is an ``MSection``, each actual (meta-)data carrying
    section is an ``MSection``. This class consitutes the reflection interface of the
    meta-info, since it allows to manipulate sections (and therefore all meta-info data)
    without having to know the specific sub-class.

    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.

    The reflection insterface for reading and manipulating quantity values consists of
    Pythons build in ``getattr``, ``setattr``, and ``del``, as well as member functions
    :func:`m_add_value`, and :func:`m_add_values`.

    Sub-sections and parent sections can be read and manipulated with :data:`m_parent`,
    :func:`m_sub_section`, :func:`m_create`.

    .. code-block:: python

        system = run.m_create(System)
        assert system.m_parent == run
        assert run.m_sub_section(System, system.m_parent_index) == system

    Attributes:
        m_def: The section definition that defines this sections, its possible
            sub-sections and quantities.
        m_parent: The parent section instance that this section is a sub-section of.
        m_parent_sub_section: The sub section definition that holds this section in the parent.
        m_parent_index: For repeatable sections, parent keep a list of sub-sections for
            each section definition. This is the index of this section in the respective
            parent sub-section list.
        m_data: The dictionary that holds all data of this section. It keeps the quantity
            values and sub-section. It should only be read directly (and never manipulated)
            if you are know what you are doing. You should always use the reflection interface
            if possible.
    """

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

        # add base sections
        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]
            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)

    def __check_np(self, quantity_ref: 'Quantity', value: np.ndarray) -> np.ndarray:
        # TODO
        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 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:
            if 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))

            value = self.__check_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.')

        return value

    def m_is_set(self, quantity_def: 'Quantity') -> bool:
        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], **kwargs) -> MSectionBound:
        """ Creates a section instance and adds it to this section provided there is a
        corresponding sub section.
        """

        section_def = section_cls.m_def
        sub_section_def = self.m_def.all_sub_sections_by_section.get(section_def, None)
        if sub_section_def is None:
            raise TypeError('There is no sub section to hold a %s in %s.' % (section_def, self.m_def))

        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:
                    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 = getattr(self, 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:
        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 m_validate(self):
        """ Evaluates all constraints 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)

        return errors

    def m_all_validate(self):
        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)


# Metainfo M3 (i.e. definitions of definitions)

class Definition(MSection):

    __all_definitions: Dict[Type[MSection], List[MSection]] = {}

    name: 'Quantity' = None
    description: 'Quantity' = None
    links: 'Quantity' = None
    categories: 'Quantity' = None

    def __init__(self, *args, **kwargs):
        self.all_categories: Set[Category] = set()

        super().__init__(*args, **kwargs)

        for cls in self.__class__.mro() + [self.__class__]:
            definitions = Definition.__all_definitions.setdefault(cls, [])
            definitions.append(self)

    @classmethod
    def all_definitions(cls: Type[MSectionBound]) -> Iterable[MSectionBound]:
        """ Returns all definitions of this definition class. """
        return cast(Iterable[MSectionBound], Definition.__all_definitions.get(cls, []))

    def on_set(self, quantity_def, value):
        if quantity_def == Definition.categories:
            for category in value:
                category.definitions.add(self)
                self.all_categories.add(category)
                for base_category in category.all_categories:
                    self.all_categories.add(base_category)


class Property(Definition):
    pass


class Quantity(Property):
    """Used to define quantities that store a certain piece of (meta-)data.

    Quantities are the basic building block with meta-info data. The Quantity class is
    used to define quantities within sections. A quantity definition
    is a (physics) quantity with name, type, shape, and potentially a unit.

    In Python terms, quantities are descriptors. Descriptors define how to get, set, and
    delete values for a object attribute. Meta-info descriptors ensure that
    type and shape fit the set values.
    """

    type: 'Quantity' = None
    shape: 'Quantity' = None