sqlalchemy.ext.hybrid

Define attributes on ORM-mapped classes that have "hybrid" behavior. "hybrid" means the attribute has distinct behaviors defined at the class level and at the instance level. The :mod:`~sqlalchemy.ext.hybrid` extension provides a special form of method decorator and has minimal dependencies on the rest of SQLAlchemy. Its basic theory of operation can work with any descriptor-based expression system. Consider a mapping ``Interval``, representing integer ``start`` and ``end`` values. We can define higher level functions on mapped classes that produce SQL expressions at the class level, and Python expression evaluation at the instance level. Below, each function decorated with :class:`.hybrid_method` or :class:`.hybrid_property` may receive ``self`` as an instance of the class, or may receive the class directly, depending on context:: from __future__ import annotations from sqlalchemy.ext.hybrid import hybrid_method from sqlalchemy.ext.hybrid import hybrid_property from sqlalchemy.orm import DeclarativeBase from sqlalchemy.orm import Mapped from sqlalchemy.orm import mapped_column class Base(DeclarativeBase): pass class Interval(Base): __tablename__ = 'interval' id: Mapped[int] = mapped_column(primary_key=True) start: Mapped[int] end: Mapped[int] def __init__(self, start: int, end: int): self.start = start self.end = end @hybrid_property def length(self) -> int: return self.end - self.start @hybrid_method def contains(self, point: int) -> bool: return (self.start <= point) & (point <= self.end) @hybrid_method def intersects(self, other: Interval) -> bool: return self.contains(other.start) | self.contains(other.end) Above, the ``length`` property returns the difference between the ``end`` and ``start`` attributes. With an instance of ``Interval``, this subtraction occurs in Python, using normal Python descriptor mechanics:: >>> i1 = Interval(5, 10) >>> i1.length 5 When dealing with the ``Interval`` class itself, the :class:`.hybrid_property` descriptor evaluates the function body given the ``Interval`` class as the argument, which when evaluated with SQLAlchemy expression mechanics returns a new SQL expression: .. sourcecode:: pycon+sql >>> from sqlalchemy import select >>> print(select(Interval.length)) {printsql}SELECT interval."end" - interval.start AS length FROM interval{stop} >>> print(select(Interval).filter(Interval.length > 10)) {printsql}SELECT interval.id, interval.start, interval."end" FROM interval WHERE interval."end" - interval.start > :param_1 Filtering methods such as :meth:`.Select.filter_by` are supported with hybrid attributes as well: .. sourcecode:: pycon+sql >>> print(select(Interval).filter_by(length=5)) {printsql}SELECT interval.id, interval.start, interval."end" FROM interval WHERE interval."end" - interval.start = :param_1 The ``Interval`` class example also illustrates two methods, ``contains()`` and ``intersects()``, decorated with :class:`.hybrid_method`. This decorator applies the same idea to methods that :class:`.hybrid_property` applies to attributes. The methods return boolean values, and take advantage of the Python ``|`` and ``&`` bitwise operators to produce equivalent instance-level and SQL expression-level boolean behavior: .. sourcecode:: pycon+sql >>> i1.contains(6) True >>> i1.contains(15) False >>> i1.intersects(Interval(7, 18)) True >>> i1.intersects(Interval(25, 29)) False >>> print(select(Interval).filter(Interval.contains(15))) {printsql}SELECT interval.id, interval.start, interval."end" FROM interval WHERE interval.start <= :start_1 AND interval."end" > :end_1{stop} >>> ia = aliased(Interval) >>> print(select(Interval, ia).filter(Interval.intersects(ia))) {printsql}SELECT interval.id, interval.start, interval."end", interval_1.id AS interval_1_id, interval_1.start AS interval_1_start, interval_1."end" AS interval_1_end FROM interval, interval AS interval_1 WHERE interval.start <= interval_1.start AND interval."end" > interval_1.start OR interval.start <= interval_1."end" AND interval."end" > interval_1."end"{stop} .. _hybrid_distinct_expression: Defining Expression Behavior Distinct from Attribute Behavior -------------------------------------------------------------- In the previous section, our usage of the ``&`` and ``|`` bitwise operators within the ``Interval.contains`` and ``Interval.intersects`` methods was fortunate, considering our functions operated on two boolean values to return a new one. In many cases, the construction of an in-Python function and a SQLAlchemy SQL expression have enough differences that two separate Python expressions should be defined. The :mod:`~sqlalchemy.ext.hybrid` decorator defines a **modifier** :meth:`.hybrid_property.expression` for this purpose. As an example we'll define the radius of the interval, which requires the usage of the absolute value function:: from sqlalchemy import ColumnElement from sqlalchemy import Float from sqlalchemy import func from sqlalchemy import type_coerce class Interval(Base): # ... @hybrid_property def radius(self) -> float: return abs(self.length) / 2 @radius.inplace.expression @classmethod def _radius_expression(cls) -> ColumnElement[float]: return type_coerce(func.abs(cls.length) / 2, Float) In the above example, the :class:`.hybrid_property` first assigned to the name ``Interval.radius`` is amended by a subsequent method called ``Interval._radius_expression``, using the decorator ``@radius.inplace.expression``, which chains together two modifiers :attr:`.hybrid_property.inplace` and :attr:`.hybrid_property.expression`. The use of :attr:`.hybrid_property.inplace` indicates that the :meth:`.hybrid_property.expression` modifier should mutate the existing hybrid object at ``Interval.radius`` in place, without creating a new object. Notes on this modifier and its rationale are discussed in the next section :ref:`hybrid_pep484_naming`. The use of ``@classmethod`` is optional, and is strictly to give typing tools a hint that ``cls`` in this case is expected to be the ``Interval`` class, and not an instance of ``Interval``. .. note:: :attr:`.hybrid_property.inplace` as well as the use of ``@classmethod`` for proper typing support are available as of SQLAlchemy 2.0.4, and will not work in earlier versions. With ``Interval.radius`` now including an expression element, the SQL function ``ABS()`` is returned when accessing ``Interval.radius`` at the class level: .. sourcecode:: pycon+sql >>> from sqlalchemy import select >>> print(select(Interval).filter(Interval.radius > 5)) {printsql}SELECT interval.id, interval.start, interval."end" FROM interval WHERE abs(interval."end" - interval.start) / :abs_1 > :param_1 .. _hybrid_pep484_naming: Using ``inplace`` to create pep-484 compliant hybrid properties --------------------------------------------------------------- In the previous section, a :class:`.hybrid_property` decorator is illustrated which includes two separate method-level functions being decorated, both to produce a single object attribute referred towards as ``Interval.radius``. There are actually several different modifiers we can use for :class:`.hybrid_property` including :meth:`.hybrid_property.expression`, :meth:`.hybrid_property.setter` and :meth:`.hybrid_property.update_expression`. SQLAlchemy's :class:`.hybrid_property` decorator intends that adding on these methods may be done in the identical manner as Python's built-in ``@property`` decorator, where idiomatic use is to continue to redefine the attribute repeatedly, using the **same attribute name** each time, as in the example below that illustrates the use of :meth:`.hybrid_property.setter` and :meth:`.hybrid_property.expression` for the ``Interval.radius`` descriptor:: # correct use, however is not accepted by pep-484 tooling class Interval(Base): # ... @hybrid_property def radius(self): return abs(self.length) / 2 @radius.setter def radius(self, value): self.length = value * 2 @radius.expression def radius(cls): return type_coerce(func.abs(cls.length) / 2, Float) Above, there are three ``Interval.radius`` methods, but as each are decorated, first by the :class:`.hybrid_property` decorator and then by the ``@radius`` name itself, the end effect is that ``Interval.radius`` is a single attribute with three different functions contained within it. This style of use is taken from `Python's documented use of @property <https://docs.python.org/3/library/functions.html#property>`_. It is important to note that the way both ``@property`` as well as :class:`.hybrid_property` work, a **copy of the descriptor is made each time**. That is, each call to ``@radius.expression``, ``@radius.setter`` etc. make a new object entirely. This allows the attribute to be re-defined in subclasses without issue (see :ref:`hybrid_reuse_subclass` later in this section for how this is used). However, the above approach is not compatible with typing tools such as mypy and pyright. Python's own ``@property`` decorator does not have this limitation only because `these tools hardcode the behavior of @property <https://github.com/python/typing/discussions/1102>`_, meaning this syntax is not available to SQLAlchemy under :pep:`484` compliance. In order to produce a reasonable syntax while remaining typing compliant, the :attr:`.hybrid_property.inplace` decorator allows the same decorator to be re-used with different method names, while still producing a single decorator under one name:: # correct use which is also accepted by pep-484 tooling class Interval(Base): # ... @hybrid_property def radius(self) -> float: return abs(self.length) / 2 @radius.inplace.setter def _radius_setter(self, value: float) -> None: # for example only self.length = value * 2 @radius.inplace.expression @classmethod def _radius_expression(cls) -> ColumnElement[float]: return type_coerce(func.abs(cls.length) / 2, Float) Using :attr:`.hybrid_property.inplace` further qualifies the use of the decorator that a new copy should not be made, thereby maintaining the ``Interval.radius`` name while allowing additional methods ``Interval._radius_setter`` and ``Interval._radius_expression`` to be differently named. .. versionadded:: 2.0.4 Added :attr:`.hybrid_property.inplace` to allow less verbose construction of composite :class:`.hybrid_property` objects while not having to use repeated method names. Additionally allowed the use of ``@classmethod`` within :attr:`.hybrid_property.expression`, :attr:`.hybrid_property.update_expression`, and :attr:`.hybrid_property.comparator` to allow typing tools to identify ``cls`` as a class and not an instance in the method signature. Defining Setters ---------------- The :meth:`.hybrid_property.setter` modifier allows the construction of a custom setter method, that can modify values on the object:: class Interval(Base): # ... @hybrid_property def length(self) -> int: return self.end - self.start @length.inplace.setter def _length_setter(self, value: int) -> None: self.end = self.start + value The ``length(self, value)`` method is now called upon set:: >>> i1 = Interval(5, 10) >>> i1.length 5 >>> i1.length = 12 >>> i1.end 17 .. _hybrid_bulk_update: Allowing Bulk ORM Update ------------------------ A hybrid can define a custom "UPDATE" handler for when using ORM-enabled updates, allowing the hybrid to be used in the SET clause of the update. Normally, when using a hybrid with :func:`_sql.update`, the SQL expression is used as the column that's the target of the SET. If our ``Interval`` class had a hybrid ``start_point`` that linked to ``Interval.start``, this could be substituted directly:: from sqlalchemy import update stmt = update(Interval).values({Interval.start_point: 10}) However, when using a composite hybrid like ``Interval.length``, this hybrid represents more than one column. We can set up a handler that will accommodate a value passed in the VALUES expression which can affect this, using the :meth:`.hybrid_property.update_expression` decorator. A handler that works similarly to our setter would be:: from typing import List, Tuple, Any class Interval(Base): # ... @hybrid_property def length(self) -> int: return self.end - self.start @length.inplace.setter def _length_setter(self, value: int) -> None: self.end = self.start + value @length.inplace.update_expression def _length_update_expression(cls, value: Any) -> List[Tuple[Any, Any]]: return [ (cls.end, cls.start + value) ] Above, if we use ``Interval.length`` in an UPDATE expression, we get a hybrid SET expression: .. sourcecode:: pycon+sql >>> from sqlalchemy import update >>> print(update(Interval).values({Interval.length: 25})) {printsql}UPDATE interval SET "end"=(interval.start + :start_1) This SET expression is accommodated by the ORM automatically. .. seealso:: :ref:`orm_expression_update_delete` - includes background on ORM-enabled UPDATE statements Working with Relationships -------------------------- There's no essential difference when creating hybrids that work with related objects as opposed to column-based data. The need for distinct expressions tends to be greater. The two variants we'll illustrate are the "join-dependent" hybrid, and the "correlated subquery" hybrid. Join-Dependent Relationship Hybrid ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Consider the following declarative mapping which relates a ``User`` to a ``SavingsAccount``:: from __future__ import annotations from decimal import Decimal from typing import cast from typing import List from typing import Optional from sqlalchemy import ForeignKey from sqlalchemy import Numeric from sqlalchemy import String from sqlalchemy import SQLColumnExpression from sqlalchemy.ext.hybrid import hybrid_property from sqlalchemy.orm import DeclarativeBase from sqlalchemy.orm import Mapped from sqlalchemy.orm import mapped_column from sqlalchemy.orm import relationship class Base(DeclarativeBase): pass class SavingsAccount(Base): __tablename__ = 'account' id: Mapped[int] = mapped_column(primary_key=True) user_id: Mapped[int] = mapped_column(ForeignKey('user.id')) balance: Mapped[Decimal] = mapped_column(Numeric(15, 5)) owner: Mapped[User] = relationship(back_populates="accounts") class User(Base): __tablename__ = 'user' id: Mapped[int] = mapped_column(primary_key=True) name: Mapped[str] = mapped_column(String(100)) accounts: Mapped[List[SavingsAccount]] = relationship( back_populates="owner", lazy="selectin" ) @hybrid_property def balance(self) -> Optional[Decimal]: if self.accounts: return self.accounts[0].balance else: return None @balance.inplace.setter def _balance_setter(self, value: Optional[Decimal]) -> None: assert value is not None if not self.accounts: account = SavingsAccount(owner=self) else: account = self.accounts[0] account.balance = value @balance.inplace.expression @classmethod def _balance_expression(cls) -> SQLColumnExpression[Optional[Decimal]]: return cast("SQLColumnExpression[Optional[Decimal]]", SavingsAccount.balance) The above hybrid property ``balance`` works with the first ``SavingsAccount`` entry in the list of accounts for this user. The in-Python getter/setter methods can treat ``accounts`` as a Python list available on ``self``. .. tip:: The ``User.balance`` getter in the above example accesses the ``self.acccounts`` collection, which will normally be loaded via the :func:`.selectinload` loader strategy configured on the ``User.balance`` :func:`_orm.relationship`. The default loader strategy when not otherwise stated on :func:`_orm.relationship` is :func:`.lazyload`, which emits SQL on demand. When using asyncio, on-demand loaders such as :func:`.lazyload` are not supported, so care should be taken to ensure the ``self.accounts`` collection is accessible to this hybrid accessor when using asyncio. At the expression level, it's expected that the ``User`` class will be used in an appropriate context such that an appropriate join to ``SavingsAccount`` will be present: .. sourcecode:: pycon+sql >>> from sqlalchemy import select >>> print(select(User, User.balance). ... join(User.accounts).filter(User.balance > 5000)) {printsql}SELECT "user".id AS user_id, "user".name AS user_name, account.balance AS account_balance FROM "user" JOIN account ON "user".id = account.user_id WHERE account.balance > :balance_1 Note however, that while the instance level accessors need to worry about whether ``self.accounts`` is even present, this issue expresses itself differently at the SQL expression level, where we basically would use an outer join: .. sourcecode:: pycon+sql >>> from sqlalchemy import select >>> from sqlalchemy import or_ >>> print (select(User, User.balance).outerjoin(User.accounts). ... filter(or_(User.balance < 5000, User.balance == None))) {printsql}SELECT "user".id AS user_id, "user".name AS user_name, account.balance AS account_balance FROM "user" LEFT OUTER JOIN account ON "user".id = account.user_id WHERE account.balance < :balance_1 OR account.balance IS NULL Correlated Subquery Relationship Hybrid ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ We can, of course, forego being dependent on the enclosing query's usage of joins in favor of the correlated subquery, which can portably be packed into a single column expression. A correlated subquery is more portable, but often performs more poorly at the SQL level. Using the same technique illustrated at :ref:`mapper_column_property_sql_expressions`, we can adjust our ``SavingsAccount`` example to aggregate the balances for *all* accounts, and use a correlated subquery for the column expression:: from __future__ import annotations from decimal import Decimal from typing import List from sqlalchemy import ForeignKey from sqlalchemy import func from sqlalchemy import Numeric from sqlalchemy import select from sqlalchemy import SQLColumnExpression from sqlalchemy import String from sqlalchemy.ext.hybrid import hybrid_property from sqlalchemy.orm import DeclarativeBase from sqlalchemy.orm import Mapped from sqlalchemy.orm import mapped_column from sqlalchemy.orm import relationship class Base(DeclarativeBase): pass class SavingsAccount(Base): __tablename__ = 'account' id: Mapped[int] = mapped_column(primary_key=True) user_id: Mapped[int] = mapped_column(ForeignKey('user.id')) balance: Mapped[Decimal] = mapped_column(Numeric(15, 5)) owner: Mapped[User] = relationship(back_populates="accounts") class User(Base): __tablename__ = 'user' id: Mapped[int] = mapped_column(primary_key=True) name: Mapped[str] = mapped_column(String(100)) accounts: Mapped[List[SavingsAccount]] = relationship( back_populates="owner", lazy="selectin" ) @hybrid_property def balance(self) -> Decimal: return sum((acc.balance for acc in self.accounts), start=Decimal("0")) @balance.inplace.expression @classmethod def _balance_expression(cls) -> SQLColumnExpression[Decimal]: return ( select(func.sum(SavingsAccount.balance)) .where(SavingsAccount.user_id == cls.id) .label("total_balance") ) The above recipe will give us the ``balance`` column which renders a correlated SELECT: .. sourcecode:: pycon+sql >>> from sqlalchemy import select >>> print(select(User).filter(User.balance > 400)) {printsql}SELECT "user".id, "user".name FROM "user" WHERE ( SELECT sum(account.balance) AS sum_1 FROM account WHERE account.user_id = "user".id ) > :param_1 .. _hybrid_custom_comparators: Building Custom Comparators --------------------------- The hybrid property also includes a helper that allows construction of custom comparators. A comparator object allows one to customize the behavior of each SQLAlchemy expression operator individually. They are useful when creating custom types that have some highly idiosyncratic behavior on the SQL side. .. note:: The :meth:`.hybrid_property.comparator` decorator introduced in this section **replaces** the use of the :meth:`.hybrid_property.expression` decorator. They cannot be used together. The example class below allows case-insensitive comparisons on the attribute named ``word_insensitive``:: from __future__ import annotations from typing import Any from sqlalchemy import ColumnElement from sqlalchemy import func from sqlalchemy.ext.hybrid import Comparator from sqlalchemy.ext.hybrid import hybrid_property from sqlalchemy.orm import DeclarativeBase from sqlalchemy.orm import Mapped from sqlalchemy.orm import mapped_column class Base(DeclarativeBase): pass class CaseInsensitiveComparator(Comparator[str]): def __eq__(self, other: Any) -> ColumnElement[bool]: # type: ignore[override] # noqa: E501 return func.lower(self.__clause_element__()) == func.lower(other) class SearchWord(Base): __tablename__ = 'searchword' id: Mapped[int] = mapped_column(primary_key=True) word: Mapped[str] @hybrid_property def word_insensitive(self) -> str: return self.word.lower() @word_insensitive.inplace.comparator @classmethod def _word_insensitive_comparator(cls) -> CaseInsensitiveComparator: return CaseInsensitiveComparator(cls.word) Above, SQL expressions against ``word_insensitive`` will apply the ``LOWER()`` SQL function to both sides: .. sourcecode:: pycon+sql >>> from sqlalchemy import select >>> print(select(SearchWord).filter_by(word_insensitive="Trucks")) {printsql}SELECT searchword.id, searchword.word FROM searchword WHERE lower(searchword.word) = lower(:lower_1) The ``CaseInsensitiveComparator`` above implements part of the :class:`.ColumnOperators` interface. A "coercion" operation like lowercasing can be applied to all comparison operations (i.e. ``eq``, ``lt``, ``gt``, etc.) using :meth:`.Operators.operate`:: class CaseInsensitiveComparator(Comparator): def operate(self, op, other, **kwargs): return op( func.lower(self.__clause_element__()), func.lower(other), **kwargs, ) .. _hybrid_reuse_subclass: Reusing Hybrid Properties across Subclasses ------------------------------------------- A hybrid can be referred to from a superclass, to allow modifying methods like :meth:`.hybrid_property.getter`, :meth:`.hybrid_property.setter` to be used to redefine those methods on a subclass. This is similar to how the standard Python ``@property`` object works:: class FirstNameOnly(Base): # ... first_name: Mapped[str] @hybrid_property def name(self) -> str: return self.first_name @name.inplace.setter def _name_setter(self, value: str) -> None: self.first_name = value class FirstNameLastName(FirstNameOnly): # ... last_name: Mapped[str] # 'inplace' is not used here; calling getter creates a copy # of FirstNameOnly.name that is local to FirstNameLastName @FirstNameOnly.name.getter def name(self) -> str: return self.first_name + ' ' + self.last_name @name.inplace.setter def _name_setter(self, value: str) -> None: self.first_name, self.last_name = value.split(' ', 1) Above, the ``FirstNameLastName`` class refers to the hybrid from ``FirstNameOnly.name`` to repurpose its getter and setter for the subclass. When overriding :meth:`.hybrid_property.expression` and :meth:`.hybrid_property.comparator` alone as the first reference to the superclass, these names conflict with the same-named accessors on the class- level :class:`.QueryableAttribute` object returned at the class level. To override these methods when referring directly to the parent class descriptor, add the special qualifier :attr:`.hybrid_property.overrides`, which will de- reference the instrumented attribute back to the hybrid object:: class FirstNameLastName(FirstNameOnly): # ... last_name: Mapped[str] @FirstNameOnly.name.overrides.expression @classmethod def name(cls): return func.concat(cls.first_name, ' ', cls.last_name) Hybrid Value Objects -------------------- Note in our previous example, if we were to compare the ``word_insensitive`` attribute of a ``SearchWord`` instance to a plain Python string, the plain Python string would not be coerced to lower case - the ``CaseInsensitiveComparator`` we built, being returned by ``@word_insensitive.comparator``, only applies to the SQL side. A more comprehensive form of the custom comparator is to construct a *Hybrid Value Object*. This technique applies the target value or expression to a value object which is then returned by the accessor in all cases. The value object allows control of all operations upon the value as well as how compared values are treated, both on the SQL expression side as well as the Python value side. Replacing the previous ``CaseInsensitiveComparator`` class with a new ``CaseInsensitiveWord`` class:: class CaseInsensitiveWord(Comparator): "Hybrid value representing a lower case representation of a word." def __init__(self, word): if isinstance(word, basestring): self.word = word.lower() elif isinstance(word, CaseInsensitiveWord): self.word = word.word else: self.word = func.lower(word) def operate(self, op, other, **kwargs): if not isinstance(other, CaseInsensitiveWord): other = CaseInsensitiveWord(other) return op(self.word, other.word, **kwargs) def __clause_element__(self): return self.word def __str__(self): return self.word key = 'word' "Label to apply to Query tuple results" Above, the ``CaseInsensitiveWord`` object represents ``self.word``, which may be a SQL function, or may be a Python native. By overriding ``operate()`` and ``__clause_element__()`` to work in terms of ``self.word``, all comparison operations will work against the "converted" form of ``word``, whether it be SQL side or Python side. Our ``SearchWord`` class can now deliver the ``CaseInsensitiveWord`` object unconditionally from a single hybrid call:: class SearchWord(Base): __tablename__ = 'searchword' id: Mapped[int] = mapped_column(primary_key=True) word: Mapped[str] @hybrid_property def word_insensitive(self) -> CaseInsensitiveWord: return CaseInsensitiveWord(self.word) The ``word_insensitive`` attribute now has case-insensitive comparison behavior universally, including SQL expression vs. Python expression (note the Python value is converted to lower case on the Python side here): .. sourcecode:: pycon+sql >>> print(select(SearchWord).filter_by(word_insensitive="Trucks")) {printsql}SELECT searchword.id AS searchword_id, searchword.word AS searchword_word FROM searchword WHERE lower(searchword.word) = :lower_1 SQL expression versus SQL expression: .. sourcecode:: pycon+sql >>> from sqlalchemy.orm import aliased >>> sw1 = aliased(SearchWord) >>> sw2 = aliased(SearchWord) >>> print( ... select(sw1.word_insensitive, sw2.word_insensitive).filter( ... sw1.word_insensitive > sw2.word_insensitive ... ) ... ) {printsql}SELECT lower(searchword_1.word) AS lower_1, lower(searchword_2.word) AS lower_2 FROM searchword AS searchword_1, searchword AS searchword_2 WHERE lower(searchword_1.word) > lower(searchword_2.word) Python only expression:: >>> ws1 = SearchWord(word="SomeWord") >>> ws1.word_insensitive == "sOmEwOrD" True >>> ws1.word_insensitive == "XOmEwOrX" False >>> print(ws1.word_insensitive) someword The Hybrid Value pattern is very useful for any kind of value that may have multiple representations, such as timestamps, time deltas, units of measurement, currencies and encrypted passwords. .. seealso:: `Hybrids and Value Agnostic Types <https://techspot.zzzeek.org/2011/10/21/hybrids-and-value-agnostic-types/>`_ - on the techspot.zzzeek.org blog `Value Agnostic Types, Part II <https://techspot.zzzeek.org/2011/10/29/value-agnostic-types-part-ii/>`_ - on the techspot.zzzeek.org blog