PEP: 695
Title: Type Parameter Syntax
Author: Eric Traut <erictr at microsoft.com>
Sponsor: Guido van Rossum <guido@python.org>
Discussions-To: https://mail.python.org/archives/list/typing-sig@python.org/thread/BB2BGYJY2YG5IWESKGTAPUQL3N27ZKVW/
Status: Final
Type: Standards Track
Topic: Typing
Created: 15-Jun-2022
Python-Version: 3.12
Post-History: `20-Jun-2022 <https://mail.python.org/archives/list/typing-sig@python.org/thread/BB2BGYJY2YG5IWESKGTAPUQL3N27ZKVW/>`__,
              `04-Dec-2022 <https://discuss.python.org/t/pep-695-type-parameter-syntax/21646>`__
Resolution: https://discuss.python.org/t/pep-695-type-parameter-syntax/21646/92

.. canonical-typing-spec:: :ref:`typing:variance-inference`,
                           :ref:`typing:type-aliases`,
                           :ref:`python:type-params`,
                           :ref:`python:type` and
                           :ref:`python:annotation-scopes`.

Abstract
========

This PEP specifies an improved syntax for specifying type parameters within
a generic class, function, or type alias. It also introduces a new statement
for declaring type aliases.


Motivation
==========

:pep:`484` introduced type variables into the language. :pep:`612` built
upon this concept by introducing parameter specifications, and
:pep:`646` added variadic type variables.

While generic types and type parameters have grown in popularity, the
syntax for specifying type parameters still feels "bolted on" to Python.
This is a source of confusion among Python developers.

There is consensus within the Python static typing community that it is time
to provide a formal syntax that is similar to other modern programming
languages that support generic types.

An analysis of 25 popular typed Python libraries revealed that type
variables (in particular, the ``typing.TypeVar`` symbol) were used in
14% of modules.


Points of Confusion
-------------------

While the use of type variables has become widespread, the manner in which
they are specified within code is the source of confusion among many
Python developers. There are a couple of factors that contribute to this
confusion.

The scoping rules for type variables are difficult to understand. Type
variables are typically allocated within the global scope, but their semantic
meaning is valid only when used within the context of a generic class,
function, or type alias. A single runtime instance of a type variable may be
reused in multiple generic contexts, and it has a different semantic meaning
in each of these contexts. This PEP proposes to eliminate this source of
confusion by declaring type parameters at a natural place within a class,
function, or type alias declaration statement.

Generic type aliases are often misused because it is not clear to developers
that a type argument must be supplied when the type alias is used. This leads
to an implied type argument of ``Any``, which is rarely the intent. This PEP
proposes to add new syntax that makes generic type alias declarations
clear.

:pep:`483` and :pep:`484` introduced the concept of "variance" for a type
variable used within a generic class. Type variables can be invariant,
covariant, or contravariant. The concept of variance is an advanced detail
of type theory that is not well understood by most Python developers, yet
they must confront this concept today when defining their first generic
class. This PEP largely eliminates the need for most developers
to understand the concept of variance when defining generic classes.

When more than one type parameter is used with a generic class or type alias,
the rules for type parameter ordering can be confusing. It is normally based on
the order in which they first appear within a class or type alias declaration
statement. However, this can be overridden in a class definition by
including a "Generic" or "Protocol" base class. For example, in the class
declaration ``class ClassA(Mapping[K, V])``, the type parameters are
ordered as ``K`` and then ``V``. However, in the class declaration
``class ClassB(Mapping[K, V], Generic[V, K])``, the type parameters are
ordered as ``V`` and then ``K``. This PEP proposes to make type parameter
ordering explicit in all cases.

The practice of sharing a type variable across multiple generic contexts
creates other problems today. Modern editors provide features like "find
all references" and "rename all references" that operate on symbols at the
semantic level. When a type parameter is shared among multiple generic
classes, functions, and type aliases, all references are semantically
equivalent.

Type variables defined within the global scope also need to be given a name
that starts with an underscore to indicate that the variable is private to
the module. Globally-defined type variables are also often given names to
indicate their variance, leading to cumbersome names like "_T_contra" and
"_KT_co". The current mechanisms for allocating type variables also requires
the developer to supply a redundant name in quotes (e.g. ``T = TypeVar("T")``).
This PEP eliminates the need for the redundant name and cumbersome
variable names.

Defining type parameters today requires importing the ``TypeVar`` and
``Generic`` symbols from the ``typing`` module. Over the past several releases
of Python, efforts have been made to eliminate the need to import ``typing``
symbols for common use cases, and the PEP furthers this goal.


Summary Examples
================

Defining a generic class prior to this PEP looks something like this.

::

    from typing import Generic, TypeVar

    _T_co = TypeVar("_T_co", covariant=True, bound=str)

    class ClassA(Generic[_T_co]):
        def method1(self) -> _T_co:
            ...


With the new syntax, it looks like this.

::

    class ClassA[T: str]:
        def method1(self) -> T:
            ...


Here is an example of a generic function today.

::

    from typing import TypeVar

    _T = TypeVar("_T")

    def func(a: _T, b: _T) -> _T:
        ...

And the new syntax.

::

    def func[T](a: T, b: T) -> T:
        ...


Here is an example of a generic type alias today.

::

    from typing import TypeAlias

    _T = TypeVar("_T")

    ListOrSet: TypeAlias = list[_T] | set[_T]


And with the new syntax.

::

    type ListOrSet[T] = list[T] | set[T]


Specification
=============

Type Parameter Declarations
---------------------------

Here is a new syntax for declaring type parameters for generic
classes, functions, and type aliases. The syntax adds support for
a comma-delimited list of type parameters in square brackets after
the name of the class, function, or type alias.

Simple (non-variadic) type variables are declared with an unadorned name.
Variadic type variables are preceded by ``*`` (see :pep:`646` for details).
Parameter specifications are preceded by ``**`` (see :pep:`612` for details).

::

    # This generic class is parameterized by a TypeVar T, a
    # TypeVarTuple Ts, and a ParamSpec P.
    class ChildClass[T, *Ts, **P]: ...

There is no need to include ``Generic`` as a base class. Its inclusion as
a base class is implied by the presence of type parameters, and it will
automatically be included in the ``__mro__`` and ``__orig_bases__`` attributes
for the class. The explicit use of a ``Generic`` base class will result in a
runtime error.

::

    class ClassA[T](Generic[T]): ...  # Runtime error


A ``Protocol`` base class with type arguments may generate a runtime
error. Type checkers should generate an error in this case because
the use of type arguments is not needed, and the order of type parameters
for the class are no longer dictated by their order in the ``Protocol``
base class.

::

    class ClassA[S, T](Protocol): ... # OK

    class ClassB[S, T](Protocol[S, T]): ... # Recommended type checker error


Type parameter names within a generic class, function, or type alias must be
unique within that same class, function, or type alias. A duplicate name
generates a syntax error at compile time. This is consistent with the
requirement that parameter names within a function signature must be unique.

::

    class ClassA[T, *T]: ... # Syntax Error

    def func1[T, **T](): ... # Syntax Error


Class type parameter names are mangled if they begin with a double
underscore, to avoid complicating the name lookup mechanism for names used
within the class. However, the ``__name__`` attribute of the type parameter
will hold the non-mangled name.


Upper Bound Specification
-------------------------

For a non-variadic type parameter, an "upper bound" type can be specified
through the use of a type annotation expression. If an upper bound is
not specified, the upper bound is assumed to be ``object``.

::

    class ClassA[T: str]: ...

The specified upper bound type must use an expression form that is allowed in
type annotations. More complex expression forms should be flagged
as an error by a type checker. Quoted forward references are allowed.

The specified upper bound type must be concrete. An attempt to use a generic
type should be flagged as an error by a type checker. This is consistent with
the existing rules enforced by type checkers for a ``TypeVar`` constructor call.

::

    class ClassA[T: dict[str, int]]: ...  # OK

    class ClassB[T: "ForwardReference"]: ...  # OK

    class ClassC[V]:
        class ClassD[T: dict[str, V]]: ...  # Type checker error: generic type

    class ClassE[T: [str, int]]: ...  # Type checker error: illegal expression form


Constrained Type Specification
------------------------------

:pep:`484` introduced the concept of a "constrained type variable" which is
constrained to a set of two or more types. The new syntax supports this type
of constraint through the use of a literal tuple expression that contains
two or more types.

::

    class ClassA[AnyStr: (str, bytes)]: ...  # OK

    class ClassB[T: ("ForwardReference", bytes)]: ...  # OK

    class ClassC[T: ()]: ...  # Type checker error: two or more types required

    class ClassD[T: (str, )]: ...  # Type checker error: two or more types required

    t1 = (bytes, str)
    class ClassE[T: t1]: ...  # Type checker error: literal tuple expression required


If the specified type is not a tuple expression or the tuple expression includes
complex expression forms that are not allowed in a type annotation, a type
checker should generate an error. Quoted forward references are allowed.

::

    class ClassF[T: (3, bytes)]: ...  # Type checker error: invalid expression form


The specified constrained types must be concrete. An attempt to use a generic
type should be flagged as an error by a type checker. This is consistent with
the existing rules enforced by type checkers for a ``TypeVar`` constructor call.

::

    class ClassG[T: (list[S], str)]: ...  # Type checker error: generic type


Runtime Representation of Bounds and Constraints
------------------------------------------------

The upper bounds and constraints of ``TypeVar`` objects are accessible at
runtime through the ``__bound__`` and ``__constraints__`` attributes.
For ``TypeVar`` objects defined through the new syntax, these attributes
become lazily evaluated, as discussed under `Lazy Evaluation`_ below.


Generic Type Alias
------------------

We propose to introduce a new statement for declaring type aliases. Similar
to ``class`` and ``def`` statements, a ``type`` statement defines a scope
for type parameters.

::

    # A non-generic type alias
    type IntOrStr = int | str

    # A generic type alias
    type ListOrSet[T] = list[T] | set[T]


Type aliases can refer to themselves without the use of quotes.

::

    # A type alias that includes a forward reference
    type AnimalOrVegetable = Animal | "Vegetable"

    # A generic self-referential type alias
    type RecursiveList[T] = T | list[RecursiveList[T]]


The ``type`` keyword is a new soft keyword. It is interpreted as a keyword
only in this part of the grammar. In all other locations, it is assumed to
be an identifier name.

Type parameters declared as part of a generic type alias are valid only
when evaluating the right-hand side of the type alias.

As with ``typing.TypeAlias``, type checkers should restrict the right-hand
expression to expression forms that are allowed within type annotations.
The use of more complex expression forms (call expressions, ternary operators,
arithmetic operators, comparison operators, etc.) should be flagged as an
error.

Type alias expressions are not allowed to use traditional type variables (i.e.
those allocated with an explicit ``TypeVar`` constructor call). Type checkers
should generate an error in this case.

::

    T = TypeVar("T")
    type MyList = list[T]  # Type checker error: traditional type variable usage


We propose to deprecate the existing ``typing.TypeAlias`` introduced in
:pep:`613`. The new syntax eliminates its need entirely.


Runtime Type Alias Class
------------------------

At runtime, a ``type`` statement will generate an instance of
``typing.TypeAliasType``. This class represents the type. Its attributes
include:

* ``__name__`` is a str representing the name of the type alias
* ``__type_params__`` is a tuple of ``TypeVar``, ``TypeVarTuple``, or
  ``ParamSpec`` objects that parameterize the type alias if it is generic
* ``__value__`` is the evaluated value of the type alias

All of these attributes are read-only.

The value of the type alias is evaluated lazily (see `Lazy Evaluation`_ below).


Type Parameter Scopes
---------------------

When the new syntax is used, a new lexical scope is introduced, and this scope
includes the type parameters. Type parameters can be accessed by name
within inner scopes. As with other symbols in Python, an inner scope can
define its own symbol that overrides an outer-scope symbol of the same name.
This section provides a verbal description of the new scoping rules.
The `Scoping Behavior`_ section below specifies the behavior in terms
of a translation to near-equivalent existing Python code.

Type parameters are visible to other
type parameters declared elsewhere in the list. This allows type parameters
to use other type parameters within their definition. While there is currently
no use for this capability, it preserves the ability in the future to support
upper bound expressions or type argument defaults that depend on earlier
type parameters.

A compiler error or runtime exception is generated if the definition of an
earlier type parameter references a later type parameter even if the name is
defined in an outer scope.

::

    # The following generates no compiler error, but a type checker
    # should generate an error because an upper bound type must be concrete,
    # and ``Sequence[S]`` is generic. Future extensions to the type system may
    # eliminate this limitation.
    class ClassA[S, T: Sequence[S]]: ...

    # The following generates no compiler error, because the bound for ``S``
    # is lazily evaluated. However, type checkers should generate an error.
    class ClassB[S: Sequence[T], T]: ...


A type parameter declared as part of a generic class is valid within the
class body and inner scopes contained therein. Type parameters are also
accessible when evaluating the argument list (base classes and any keyword
arguments) that comprise the class definition. This allows base classes
to be parameterized by these type parameters. Type parameters are not
accessible outside of the class body, including class decorators.

::

    class ClassA[T](BaseClass[T], param = Foo[T]): ...  # OK

    print(T)  # Runtime error: 'T' is not defined

    @dec(Foo[T])  # Runtime error: 'T' is not defined
    class ClassA[T]: ...


A type parameter declared as part of a generic function is valid within
the function body and any scopes contained therein. It is also valid within
parameter and return type annotations. Default argument values for function
parameters are evaluated outside of this scope, so type parameters are
not accessible in default value expressions. Likewise, type parameters are not
in scope for function decorators.

::

    def func1[T](a: T) -> T: ...  # OK

    print(T)  # Runtime error: 'T' is not defined

    def func2[T](a = list[T]): ...  # Runtime error: 'T' is not defined

    @dec(list[T])  # Runtime error: 'T' is not defined
    def func3[T](): ...

A type parameter declared as part of a generic type alias is valid within
the type alias expression.

::

    type Alias1[K, V] = Mapping[K, V] | Sequence[K]


Type parameter symbols defined in outer scopes cannot be bound with
``nonlocal`` statements in inner scopes.

::

    S = 0

    def outer1[S]():
        S = 1
        T = 1

        def outer2[T]():

            def inner1():
                nonlocal S  # OK because it binds variable S from outer1
                nonlocal T  # Syntax error: nonlocal binding not allowed for type parameter

            def inner2():
                global S  # OK because it binds variable S from global scope


The lexical scope introduced by the new type parameter syntax is unlike
traditional scopes introduced by a ``def`` or ``class`` statement. A type
parameter scope acts more like a temporary "overlay" to the containing scope.
The only new symbols contained
within its symbol table are the type parameters defined using the new syntax.
References to all other symbols are treated as though they were found within
the containing scope. This allows base class lists (in class definitions) and
type annotation expressions (in function definitions) to reference symbols
defined in the containing scope.

::

    class Outer:
        class Private:
            pass

        # If the type parameter scope was like a traditional scope,
        # the base class 'Private' would not be accessible here.
        class Inner[T](Private, Sequence[T]):
            pass

        # Likewise, 'Inner' would not be available in these type annotations.
        def method1[T](self, a: Inner[T]) -> Inner[T]:
            return a


The compiler allows inner scopes to define a local symbol that overrides an
outer-scoped type parameter.

Consistent with the scoping rules defined in :pep:`484`, type checkers should
generate an error if inner-scoped generic classes, functions, or type aliases
reuse the same type parameter name as an outer scope.

::

    T = 0

    @decorator(T)  # Argument expression `T` evaluates to 0
    class ClassA[T](Sequence[T]):
        T = 1

        # All methods below should result in a type checker error
        # "type parameter 'T' already in use" because they are using the
        # type parameter 'T', which is already in use by the outer scope
        # 'ClassA'.
        def method1[T](self):
            ...

        def method2[T](self, x = T):  # Parameter 'x' gets default value of 1
            ...

        def method3[T](self, x: T):  # Parameter 'x' has type T (scoped to method3)
            ...


Symbols referenced in inner scopes are resolved using existing rules except
that type parameter scopes are also considered during name resolution.

::

    T = 0

    # T refers to the global variable
    print(T)  # Prints 0

    class Outer[T]:
        T = 1

        # T refers to the local variable scoped to class 'Outer'
        print(T)  # Prints 1

        class Inner1:
            T = 2

            # T refers to the local type variable within 'Inner1'
            print(T)  # Prints 2

            def inner_method(self):
                # T refers to the type parameter scoped to class 'Outer';
                # If 'Outer' did not use the new type parameter syntax,
                # this would instead refer to the global variable 'T'
                print(T)  # Prints 'T'

        def outer_method(self):
            T = 3

            # T refers to the local variable within 'outer_method'
            print(T)  # Prints 3

            def inner_func():
                # T refers to the variable captured from 'outer_method'
                print(T)  # Prints 3


When the new type parameter syntax is used for a generic class, assignment
expressions are not allowed within the argument list for the class definition.
Likewise, with functions that use the new type parameter syntax, assignment
expressions are not allowed within parameter or return type annotations, nor
are they allowed within the expression that defines a type alias, or within
the bounds and constraints of a ``TypeVar``. Similarly, ``yield``, ``yield from``,
and ``await`` expressions are disallowed in these contexts.

This restriction is necessary because expressions evaluated within the
new lexical scope should not introduce symbols within that scope other than
the defined type parameters, and should not affect whether the enclosing function
is a generator or coroutine.

::

    class ClassA[T]((x := Sequence[T])): ...  # Syntax error: assignment expression not allowed

    def func1[T](val: (x := int)): ...  # Syntax error: assignment expression not allowed

    def func2[T]() -> (x := Sequence[T]): ...  # Syntax error: assignment expression not allowed

    type Alias1[T] = (x := list[T])  # Syntax error: assignment expression not allowed


Accessing Type Parameters at Runtime
------------------------------------

A new attribute called ``__type_params__`` is available on generic classes,
functions, and type aliases. This attribute is a tuple of the
type parameters that parameterize the class, function, or alias.
The tuple contains ``TypeVar``, ``ParamSpec``, and ``TypeVarTuple`` instances.

Type parameters declared using the new syntax will not appear within the
dictionary returned by ``globals()`` or ``locals()``.


Variance Inference
------------------

This PEP eliminates the need for variance to be specified for type
parameters. Instead, type checkers will infer the variance of type parameters
based on their usage within a class. Type parameters are inferred to be
invariant, covariant, or contravariant depending on how they are used.

Python type checkers already include the ability to determine the variance of
type parameters for the purpose of validating variance within a generic
protocol class. This capability can be used for all classes (whether or not
they are protocols) to calculate the variance of each type parameter.

The algorithm for computing the variance of a type parameter is as follows.

For each type parameter in a generic class:

1. If the type parameter is variadic (``TypeVarTuple``) or a parameter
specification (``ParamSpec``), it is always considered invariant. No further
inference is needed.

2. If the type parameter comes from a traditional ``TypeVar`` declaration and
is not specified as ``infer_variance`` (see below), its variance is specified
by the ``TypeVar`` constructor call. No further inference is needed.

3. Create two specialized versions of the class. We'll refer to these as
``upper`` and ``lower`` specializations. In both of these specializations,
replace all type parameters other than the one being inferred by a dummy type
instance (a concrete anonymous class that is type compatible with itself and
assumed to meet the bounds or constraints of the type parameter). In
the ``upper`` specialized class, specialize the target type parameter with
an ``object`` instance. This specialization ignores the type parameter's
upper bound or constraints. In the ``lower`` specialized class, specialize
the target type parameter with itself (i.e. the corresponding type argument
is the type parameter itself).

4. Determine whether ``lower`` can be assigned to ``upper`` using normal type
compatibility rules. If so, the target type parameter is covariant. If not,
determine whether ``upper`` can be assigned to ``lower``. If so, the target
type parameter is contravariant. If neither of these combinations are
assignable, the target type parameter is invariant.

Here is an example.

::

    class ClassA[T1, T2, T3](list[T1]):
        def method1(self, a: T2) -> None:
            ...

        def method2(self) -> T3:
            ...

To determine the variance of ``T1``, we specialize ``ClassA`` as follows:

::

    upper = ClassA[object, Dummy, Dummy]
    lower = ClassA[T1, Dummy, Dummy]

We find that ``upper`` is not assignable to ``lower`` using normal type
compatibility rules defined in :pep:`484`. Likewise, ``lower`` is not assignable
to ``upper``, so we conclude that ``T1`` is invariant.

To determine the variance of ``T2``, we specialize ``ClassA`` as follows:

::

    upper = ClassA[Dummy, object, Dummy]
    lower = ClassA[Dummy, T2, Dummy]

Since ``upper`` is assignable to ``lower``, ``T2`` is contravariant.

To determine the variance of ``T3``, we specialize ``ClassA`` as follows:

::

    upper = ClassA[Dummy, Dummy, object]
    lower = ClassA[Dummy, Dummy, T3]

Since ``lower`` is assignable to ``upper``, ``T3`` is covariant.


Auto Variance For TypeVar
-------------------------

The existing ``TypeVar`` class constructor accepts keyword parameters named
``covariant`` and ``contravariant``. If both of these are ``False``, the
type variable is assumed to be invariant. We propose to add another keyword
parameter named ``infer_variance`` indicating that a type checker should use
inference to determine whether the type variable is invariant, covariant or
contravariant. A corresponding instance variable ``__infer_variance__`` can be
accessed at runtime to determine whether the variance is inferred. Type
variables that are implicitly allocated using the new syntax will always
have ``__infer_variance__`` set to ``True``.

A generic class that uses the traditional syntax may include combinations of
type variables with explicit and inferred variance.

::

    T1 = TypeVar("T1", infer_variance=True)  # Inferred variance
    T2 = TypeVar("T2")  # Invariant
    T3 = TypeVar("T3", covariant=True)  # Covariant

    # A type checker should infer the variance for T1 but use the
    # specified variance for T2 and T3.
    class ClassA(Generic[T1, T2, T3]): ...


Compatibility with Traditional TypeVars
---------------------------------------

The existing mechanism for allocating ``TypeVar``, ``TypeVarTuple``, and
``ParamSpec`` is retained for backward compatibility. However, these
"traditional" type variables should not be combined with type parameters
allocated using the new syntax. Such a combination should be flagged as
an error by type checkers. This is necessary because the type parameter
order is ambiguous.

It is OK to combine traditional type variables with new-style type parameters
if the class, function, or type alias does not use the new syntax. The
new-style type parameters must come from an outer scope in this case.

::

    K = TypeVar("K")

    class ClassA[V](dict[K, V]): ...  # Type checker error

    class ClassB[K, V](dict[K, V]): ...  # OK

    class ClassC[V]:
        # The use of K and V for "method1" is OK because it uses the
        # "traditional" generic function mechanism where type parameters
        # are implicit. In this case V comes from an outer scope (ClassC)
        # and K is introduced implicitly as a type parameter for "method1".
        def method1(self, a: V, b: K) -> V | K: ...

        # The use of M and K are not allowed for "method2". A type checker
        # should generate an error in this case because this method uses the
        # new syntax for type parameters, and all type parameters associated
        # with the method must be explicitly declared. In this case, ``K``
        # is not declared by "method2", nor is it supplied by a new-style
        # type parameter defined in an outer scope.
        def method2[M](self, a: M, b: K) -> M | K: ...


Runtime Implementation
======================

Grammar Changes
---------------

This PEP introduces a new soft keyword ``type``. It modifies the grammar
in the following ways:

1. Addition of optional type parameter clause in ``class`` and ``def`` statements.

::

    type_params: '[' t=type_param_seq  ']'

    type_param_seq: a[asdl_typeparam_seq*]=','.type_param+ [',']

    type_param:
        | a=NAME b=[type_param_bound]
        | '*' a=NAME
        | '**' a=NAME

    type_param_bound: ":" e=expression

    # Grammar definitions for class_def_raw and function_def_raw are modified
    # to reference type_params as an optional syntax element. The definitions
    # of class_def_raw and function_def_raw are simplified here for brevity.

    class_def_raw: 'class' n=NAME t=[type_params] ...

    function_def_raw: a=[ASYNC] 'def' n=NAME t=[type_params] ...


2. Addition of new ``type`` statement for defining type aliases.

::

    type_alias: "type" n=NAME t=[type_params] '=' b=expression


AST Changes
-----------

This PEP introduces a new AST node type called ``TypeAlias``.

::

    TypeAlias(expr name, typeparam* typeparams, expr value)

It also adds an AST node type that represents a type parameter.

::

    typeparam = TypeVar(identifier name, expr? bound)
        | ParamSpec(identifier name)
        | TypeVarTuple(identifier name)

Bounds and constraints are represented identically in the AST. In the implementation,
any expression that is a ``Tuple`` AST node is treated as a constraint, and any other
expression is treated as a bound.

It also modifies existing AST node types ``FunctionDef``, ``AsyncFunctionDef``
and ``ClassDef`` to include an additional optional attribute called
``typeparams`` that includes a list of type parameters associated with the
function or class.

Lazy Evaluation
---------------

This PEP introduces three new contexts where expressions may occur that represent
static types: ``TypeVar`` bounds, ``TypeVar`` constraints, and the value of type
aliases. These expressions may contain references to names
that are not yet defined. For example, type aliases may be recursive, or even mutually
recursive, and type variable bounds may refer back to the current class. If these
expressions were evaluated eagerly, users would need to enclose such expressions in
quotes to prevent runtime errors. :pep:`563` and :pep:`649` detail the problems with
this situation for type annotations.

To prevent a similar situation with the new syntax proposed in this PEP, we propose
to use lazy evaluation for these expressions, similar to the approach in :pep:`649`.
Specifically, each expression will be saved in a code object, and the code object
is evaluated only when the corresponding attribute is accessed (``TypeVar.__bound__``,
``TypeVar.__constraints__``, or ``TypeAlias.__value__``). After the value is
successfully evaluated, the value is saved and later calls will return the same value
without re-evaluating the code object.

If :pep:`649` is implemented, additional evaluation mechanisms should be added to
mirror the options that PEP provides for annotations. In the current version of the
PEP, that might include adding an ``__evaluate_bound__`` method to ``TypeVar`` taking
a ``format`` parameter with the same meaning as in PEP 649's ``__annotate__`` method
(and a similar ``__evaluate_constraints__`` method, as well as an ``__evaluate_value__``
method on ``TypeAliasType``).
However, until PEP 649 is accepted and implemented, only the default evaluation format
(PEP 649's "VALUE" format) will be supported.

As a consequence of lazy evaluation, the value observed for an attribute may
depend on the time the attribute is accessed.

::

   X = int

   class Foo[T: X, U: X]:
       t, u = T, U

   print(Foo.t.__bound__)  # prints "int"
   X = str
   print(Foo.u.__bound__)  # prints "str"

Similar examples affecting type annotations can be constructed using the
semantics of PEP 563 or PEP 649.

A naive implementation of lazy evaluation would handle class namespaces
incorrectly, because functions within a class do not normally have access to
the enclosing class namespace. The implementation will retain a reference to
the class namespace so that class-scoped names are resolved correctly.

.. _695-scoping-behavior:

Scoping Behavior
----------------

The new syntax requires a new kind of scope that behaves differently
from existing scopes in Python. Thus, the new syntax cannot be described exactly in terms of
existing Python scoping behavior. This section specifies these scopes
further by reference to existing scoping behavior: the new scopes behave
like function scopes, except for a number of minor differences listed below.

All examples include functions introduced with the pseudo-keyword ``def695``.
This keyword will not exist in the actual language; it is used to
clarify that the new scopes are for the most part like function scopes.

``def695`` scopes differ from regular function scopes in the following ways:

- If a ``def695`` scope is immediately within a class scope, or within another
  ``def695`` scope that is immediately within a class scope, then names defined
  in that class scope can be accessed within the ``def695`` scope. (Regular functions,
  by contrast, cannot access names defined within an enclosing class scope.)
- The following constructs are disallowed directly within a ``def695`` scope, though
  they may be used within other scopes nested inside a ``def695`` scope:

  - ``yield``
  - ``yield from``
  - ``await``
  - ``:=`` (walrus operator)

- The qualified name (``__qualname__``) of objects (classes and functions) defined within ``def695`` scopes
  is as if the objects were defined within the closest enclosing scope.
- Names bound within ``def695`` scopes cannot be rebound with a ``nonlocal`` statement in nested scopes.

``def695`` scopes are used for the evaluation of several new syntactic constructs proposed
in this PEP. Some are evaluated eagerly (when a type alias, function, or class is defined); others are
evaluated lazily (only when evaluation is specifically requested). In all cases, the scoping semantics are identical:

- Eagerly evaluated values:

  - The type parameters of generic type aliases
  - The type parameters and annotations of generic functions
  - The type parameters and base class expressions of generic classes
- Lazily evaluated values:

  - The value of generic type aliases
  - The bounds of type variables
  - The constraints of type variables

In the below translations, names that start with two underscores are internal to the implementation
and not visible to actual Python code. We use the following intrinsic functions, which in the real
implementation are defined directly in the interpreter:

- ``__make_typealias(*, name, type_params=(), evaluate_value)``: Creates a new ``typing.TypeAlias`` object with the given
  name, type parameters, and lazily evaluated value. The value is not evaluated until the ``__value__`` attribute
  is accessed.
- ``__make_typevar_with_bound(*, name, evaluate_bound)``: Creates a new ``typing.TypeVar`` object with the given
  name and lazily evaluated bound. The bound is not evaluated until the ``__bound__`` attribute is accessed.
- ``__make_typevar_with_constraints(*, name, evaluate_constraints)``: Creates a new ``typing.TypeVar`` object with the given
  name and lazily evaluated constraints. The constraints are not evaluated until the ``__constraints__`` attribute
  is accessed.

Non-generic type aliases are translated as follows::

   type Alias = int

Equivalent to::

   def695 __evaluate_Alias():
       return int

   Alias = __make_typealias(name='Alias', evaluate_value=__evaluate_Alias)

Generic type aliases::

   type Alias[T: int] = list[T]

Equivalent to::

   def695 __generic_parameters_of_Alias():
       def695 __evaluate_T_bound():
           return int
       T = __make_typevar_with_bound(name='T', evaluate_bound=__evaluate_T_bound)

       def695 __evaluate_Alias():
           return list[T]
       return __make_typealias(name='Alias', type_params=(T,), evaluate_value=__evaluate_Alias)

   Alias = __generic_parameters_of_Alias()

Generic functions::

   def f[T](x: T) -> T:
       return x

Equivalent to::

   def695 __generic_parameters_of_f():
       T = typing.TypeVar(name='T')

       def f(x: T) -> T:
           return x
       f.__type_params__ = (T,)
       return f

   f = __generic_parameters_of_f()

A fuller example of generic functions, illustrating the scoping behavior of defaults, decorators, and bounds.
Note that this example does not use ``ParamSpec`` correctly, so it should be rejected by a static type checker.
It is however valid at runtime, and it us used here to illustrate the runtime semantics.

::

   @decorator
   def f[T: int, U: (int, str), *Ts, **P](
       x: T = SOME_CONSTANT,
       y: U,
       *args: *Ts,
       **kwargs: P.kwargs,
   ) -> T:
       return x

Equivalent to::

   __default_of_x = SOME_CONSTANT  # evaluated outside the def695 scope
   def695 __generic_parameters_of_f():
       def695 __evaluate_T_bound():
           return int
       T = __make_typevar_with_bound(name='T', evaluate_bound=__evaluate_T_bound)

       def695 __evaluate_U_constraints():
           return (int, str)
       U = __make_typevar_with_constraints(name='U', evaluate_constraints=__evaluate_U_constraints)

       Ts = typing.TypeVarTuple("Ts")
       P = typing.ParamSpec("P")

       def f(x: T = __default_of_x, y: U, *args: *Ts, **kwargs: P.kwargs) -> T:
           return x
       f.__type_params__ = (T, U, Ts, P)
       return f

   f = decorator(__generic_parameters_of_f())

Generic classes::

   class C[T](Base):
       def __init__(self, x: T):
           self.x = x

Equivalent to::

   def695 __generic_parameters_of_C():
       T = typing.TypeVar('T')
       class C(Base):
           __type_params__ = (T,)
           def __init__(self, x: T):
               self.x = x
      return C

   C = __generic_parameters_of_C()

The biggest divergence from existing behavior for ``def695`` scopes
is the behavior within class scopes. This divergence is necessary
so that generics defined within classes behave in an intuitive way::

   class C:
       class Nested: ...
       def generic_method[T](self, x: T, y: Nested) -> T: ...

Equivalent to::

   class C:
       class Nested: ...

       def695 __generic_parameters_of_generic_method():
           T = typing.TypeVar('T')

           def generic_method(self, x: T, y: Nested) -> T: ...
           return generic_method

       generic_method = __generic_parameters_of_generic_method()

In this example, the annotations for ``x`` and ``y`` are evaluated within
a ``def695`` scope, because they need access to the type parameter ``T``
for the generic method. However, they also need access to the ``Nested``
name defined within the class namespace. If ``def695`` scopes behaved
like regular function scopes, ``Nested`` would not be visible within the
function scope. Therefore, ``def695`` scopes that are immediately within
class scopes have access to that class scope, as described above.


Library Changes
---------------

Several classes in the ``typing`` module that are currently implemented in
Python must be partially implemented in C. This includes ``TypeVar``,
``TypeVarTuple``, ``ParamSpec``, and ``Generic``, and the new class
``TypeAliasType`` (described above). The implementation may delegate to the
Python version of ``typing.py`` for some behaviors that interact heavily with
the rest of the module. The
documented behaviors of these classes should not change.


Reference Implementation
========================

This proposal is prototyped in
`CPython PR #103764 <https://github.com/python/cpython/pull/103764>`_.

The Pyright type checker supports the behavior described in this PEP.


Rejected Ideas
==============

Prefix Clause
-------------
We explored various syntactic options for specifying type parameters that
preceded ``def`` and ``class`` statements. One such variant we considered
used a ``using`` clause as follows:

::

    using S, T
    class ClassA: ...

This option was rejected because the scoping rules for the type parameters
were less clear. Also, this syntax did not interact well with class and
function decorators, which are common in Python. Only one other popular
programming language, C++, uses this approach.

We likewise considered prefix forms that looked like decorators (e.g.,
``@using(S, T)``). This idea was rejected because such forms would be confused
with regular decorators, and they would not compose well with existing
decorators. Furthermore, decorators are logically executed after the statement
they are decorating, so it would be confusing for them to introduce symbols
(type parameters) that are visible within the "decorated" statement, which is
logically executed before the decorator itself.


Angle Brackets
--------------
Many languages that support generics make use of angle brackets. (Refer to
the table at the end of Appendix A for a summary.) We explored the use of
angle brackets for type parameter declarations in Python, but we ultimately
rejected it for two reasons. First, angle brackets are not considered
"paired" by the Python scanner, so end-of-line characters between a ``<``
and ``>`` token are retained. That means any line breaks within a list of
type parameters would require the use of unsightly and cumbersome ``\`` escape
sequences. Second, Python has already established the use of square brackets
for explicit specialization of a generic type (e.g., ``list[int]``). We
concluded that it would be inconsistent and confusing to use angle brackets
for generic declarations but square brackets for explicit specialization. All
other languages that we surveyed were consistent in this regard.


Bounds Syntax
-------------
We explored various syntactic options for specifying the bounds and constraints
for a type variable. We considered, but ultimately rejected, the use
of a ``<:`` token like in Scala, the use of an ``extends`` or ``with``
keyword like in various other languages, and the use of a function call
syntax similar to today's ``typing.TypeVar`` constructor. The simple colon
syntax is consistent with many other programming languages (see Appendix A),
and it was heavily preferred by a cross section of Python developers who
were surveyed.


Explicit Variance
-----------------
We considered adding syntax for specifying whether a type parameter is intended
to be invariant, covariant, or contravariant. The ``typing.TypeVar`` mechanism
in Python requires this. A few other languages including Scala and C#
also require developers to specify the variance. We rejected this idea because
variance can generally be inferred, and most modern programming languages
do infer variance based on usage. Variance is an advanced topic that
many developers find confusing, so we want to eliminate the need to
understand this concept for most Python developers.


Name Mangling
-------------
When considering implementation options, we considered a "name mangling"
approach where each type parameter was given a unique "mangled" name by the
compiler. This mangled name would be based on the qualified name of the
generic class, function or type alias it was associated with. This approach
was rejected because qualified names are not necessarily unique, which means
the mangled name would need to be based on some other randomized value.
Furthermore, this approach is not compatible with techniques used for
evaluating quoted (forward referenced) type annotations.


Appendix A: Survey of Type Parameter Syntax
===========================================

Support for generic types is found in many programming languages. In this
section, we provide a survey of the options used by other popular programming
languages. This is relevant because familiarity with other languages will
make it easier for Python developers to understand this concept. We provide
additional details here (for example, default type argument support) that
may be useful when considering future extensions to the Python type system.


C++
---

C++ uses angle brackets in combination with keywords ``template`` and
``typename`` to declare type parameters. It uses angle brackets for
specialization.

C++20 introduced the notion of generalized constraints, which can act
like protocols in Python. A collection of constraints can be defined in
a named entity called a ``concept``.

Variance is not explicitly specified, but constraints can enforce variance.

A default type argument can be specified using the ``=`` operator.

.. code-block:: c++

    // Generic class
    template <typename T>
    class ClassA
    {
        // Constraints are supported through compile-time assertions.
        static_assert(std::is_base_of<BaseClass, T>::value);

    public:
        Container<T> t;
    };

    // Generic function with default type argument
    template <typename S = int>
    S func1(ClassA<S> a, S b) {};

    // C++20 introduced a more generalized notion of "constraints"
    // and "concepts", which are named constraints.

    // A sample concept
    template<typename T>
    concept Hashable = requires(T a)
    {
        { std::hash<T>{}(a) } -> std::convertible_to<std::size_t>;
    };

    // Use of a concept in a template
    template<Hashable T>
    void func2(T value) {}

    // Alternative use of concept
    template<typename T> requires Hashable<T>
    void func3(T value) {}

    // Alternative use of concept
    template<typename T>
    void func3(T value) requires Hashable<T> {}


Java
----

Java uses angle brackets to declare type parameters and for specialization.
By default, type parameters are invariant.
The ``extends`` keyword is used to specify an upper bound. The ``super`` keyword
is used to specify a contravariant bound.

Java uses use-site variance. The compiler places limits on which methods and
members can be accessed based on the use of a generic type. Variance is
not specified explicitly.

Java provides no way to specify a default type argument.

.. code-block:: java

    // Generic class
    public class ClassA<T> {
        public Container<T> t;

        // Generic method
        public <S extends Number> void method1(S value) { }

        // Use site variance
        public void method1(ClassA<? super Integer> value) { }
    }


C#
--

C# uses angle brackets to declare type parameters and for specialization.
The ``where`` keyword and a colon is used to specify the bound for a type
parameter.

C# uses declaration-site variance using the keywords ``in`` and ``out`` for
contravariance and covariance, respectively. By default, type parameters are
invariant.

C# provides no way to specify a default type argument.

.. code-block:: c#

    // Generic class with bounds on type parameters
    public class ClassA<S, T>
        where T : SomeClass1
        where S : SomeClass2
    {
        // Generic method
        public void MyMethod<U>(U value) where U : SomeClass3 { }
    }

    // Contravariant and covariant type parameters
    public class ClassB<in S, out T>
    {
        public T MyMethod(S value) { }
    }



TypeScript
----------

TypeScript uses angle brackets to declare type parameters and for
specialization. The ``extends`` keyword is used to specify a bound. It can be
combined with other type operators such as ``keyof``.

TypeScript uses declaration-site variance. Variance is inferred from
usage, not specified explicitly. TypeScript 4.7 introduced the ability
to specify variance using ``in`` and ``out`` keywords. This was added to handle
extremely complex types where inference of variance was expensive.

A default type argument can be specified using the ``=`` operator.

TypeScript supports the ``type`` keyword to declare a type alias, and this
syntax supports generics.

.. code-block:: typescript

    // Generic interface
    interface InterfaceA<S, T extends SomeInterface1> {
        val1: S;
        val2: T;

        method1<U extends SomeInterface2>(val: U): S
    }

    // Generic function
    function func1<T, K extends keyof T>(ojb: T, key: K) { }

    // Contravariant and covariant type parameters (TypeScript 4.7)
    interface InterfaceB<in S, out T> { }

    // Type parameter with default
    interface InterfaceC<T = SomeInterface3> { }

    // Generic type alias
    type MyType<T extends SomeInterface4> = Array<T>


Scala
-----

In Scala, square brackets are used to declare type parameters. Square
brackets are also used for specialization. The ``<:`` and ``>:`` operators
are used to specify upper and lower bounds, respectively.

Scala uses use-site variance but also allows declaration-site variance
specification. It uses a ``+`` or ``-`` prefix operator for covariance and
contravariance, respectively.

Scala provides no way to specify a default type argument.

It does support higher-kinded types (type parameters that accept type
type parameters).

.. code-block:: scala


    // Generic class; type parameter has upper bound
    class ClassA[A <: SomeClass1]
    {
        // Generic method; type parameter has lower bound
        def method1[B >: A](val: B) ...
    }

    // Use of an upper and lower bound with the same type parameter
    class ClassB[A >: SomeClass1 <: SomeClass2] { }

    // Contravariant and covariant type parameters
    class ClassC[+A, -B] { }

    // Higher-kinded type
    trait Collection[T[_]]
    {
        def method1[A](a: A): T[A]
        def method2[B](b: T[B]): B
    }

    // Generic type alias
    type MyType[T <: Int] = Container[T]


Swift
-----

Swift uses angle brackets to declare type parameters and for specialization.
The upper bound of a type parameter is specified using a colon.

Swift doesn't support generic variance; all type parameters are invariant.

Swift provides no way to specify a default type argument.

.. code-block:: swift

    // Generic class
    class ClassA<T> {
        // Generic method
        func method1<X>(val: T) -> X { }
    }

    // Type parameter with upper bound constraint
    class ClassB<T: SomeClass1> {}

    // Generic type alias
    typealias MyType<A> = Container<A>


Rust
----

Rust uses angle brackets to declare type parameters and for specialization.
The upper bound of a type parameter is specified using a colon. Alternatively
a ``where`` clause can specify various constraints.

Rust does not have traditional object oriented inheritance or variance.
Subtyping in Rust is very restricted and occurs only due to variance with
respect to lifetimes.

A default type argument can be specified using the ``=`` operator.

.. code-block:: rust

    // Generic class
    struct StructA<T> { // T's lifetime is inferred as covariant
        x: T
    }

    fn f<'a>(
        mut short_lifetime: StructA<&'a i32>,
        mut long_lifetime: StructA<&'static i32>,
    ) {
        long_lifetime = short_lifetime;
        // error: StructA<&'a i32> is not a subtype of StructA<&'static i32>
        short_lifetime = long_lifetime;
        // valid: StructA<&'static i32> is a subtype of StructA<&'a i32>
    }

    // Type parameter with bound
    struct StructB<T: SomeTrait> {}

    // Type parameter with additional constraints
    struct StructC<T>
    where
        T: Iterator,
        T::Item: Copy
    {}

    // Generic function
    fn func1<T>(val: &[T]) -> T { }

    // Generic type alias
    type MyType<T> = StructC<T>;


Kotlin
------

Kotlin uses angle brackets to declare type parameters and for specialization.
By default, type parameters are invariant. The upper bound of a type is
specified using a colon.
Alternatively, a ``where`` clause can specify various constraints.

Kotlin supports declaration-site variance where variance of type parameters is
explicitly declared using ``in`` and ``out`` keywords. It also supports use-site
variance which limits which methods and members can be used.

Kotlin provides no way to specify a default type argument.

.. code-block:: kotlin

    // Generic class
    class ClassA<T>

    // Type parameter with upper bound
    class ClassB<T : SomeClass1>

    // Contravariant and covariant type parameters
    class ClassC<in S, out T>

    // Generic function
    fun <T> func1(): T {

        // Use site variance
        val covariantA: ClassA<out Number>
        val contravariantA: ClassA<in Number>
    }

    // Generic type alias
    typealias TypeAliasFoo<T> = ClassA<T>


Julia
-----

Julia uses curly braces to declare type parameters and for specialization.
The ``<:`` operator can be used within a ``where`` clause to declare
upper and lower bounds on a type.

.. code-block:: julia

    # Generic struct; type parameter with upper and lower bounds
    # Valid for T in (Int64, Signed, Integer, Real, Number)
    struct Container{Int <: T <: Number}
        x::T
    end

    # Generic function
    function func1(v::Container{T}) where T <: Real end

    # Alternate forms of generic function
    function func2(v::Container{T} where T <: Real) end
    function func3(v::Container{<: Real}) end

    # Tuple types are covariant
    # Valid for func4((2//3, 3.5))
    function func4(t::Tuple{Real,Real}) end

Dart
----

Dart uses angle brackets to declare type parameters and for specialization.
The upper bound of a type is specified using the ``extends`` keyword.
By default, type parameters are covariant.

Dart supports declaration-site variance, where variance of type parameters is
explicitly declared using ``in``, ``out`` and ``inout`` keywords.
It does not support use-site variance.

Dart provides no way to specify a default type argument.

.. code-block:: dart

    // Generic class
    class ClassA<T> { }

    // Type parameter with upper bound
    class ClassB<T extends SomeClass1> { }

    // Contravariant and covariant type parameters
    class ClassC<in S, out T> { }

    // Generic function
    T func1<T>() { }

    // Generic type alias
    typedef TypeDefFoo<T> = ClassA<T>;

Go
--

Go uses square brackets to declare type parameters and for specialization.
The upper bound of a type is specified after the name of the parameter, and
must always be specified. The keyword ``any`` is used for an unbound type parameter.

Go doesn't support variance; all type parameters are invariant.

Go provides no way to specify a default type argument.

Go does not support generic type aliases.

.. code-block:: go

    // Generic type without a bound
    type TypeA[T any] struct {
        t T
    }

    // Type parameter with upper bound
    type TypeB[T SomeType1] struct { }

    // Generic function
    func func1[T any]() { }


Summary
-------

+------------+----------+---------+--------+----------+-----------+-----------+
|            | Decl     | Upper   | Lower  | Default  | Variance  | Variance  |
|            | Syntax   | Bound   | Bound  | Value    | Site      |           |
+============+==========+=========+========+==========+===========+===========+
| C++        | template | n/a     | n/a    | =        | n/a       | n/a       |
|            | <>       |         |        |          |           |           |
+------------+----------+---------+--------+----------+-----------+-----------+
| Java       | <>       | extends |        |          | use       | super,    |
|            |          |         |        |          |           | extends   |
+------------+----------+---------+--------+----------+-----------+-----------+
| C#         | <>       | where   |        |          | decl      | in, out   |
+------------+----------+---------+--------+----------+-----------+-----------+
| TypeScript | <>       | extends |        | =        | decl      | inferred, |
|            |          |         |        |          |           | in, out   |
+------------+----------+---------+--------+----------+-----------+-----------+
| Scala      | []       | T <: X  | T >: X |          | use, decl | +, -      |
+------------+----------+---------+--------+----------+-----------+-----------+
| Swift      | <>       | T: X    |        |          | n/a       | n/a       |
+------------+----------+---------+--------+----------+-----------+-----------+
| Rust       | <>       | T: X,   |        | =        | n/a       | n/a       |
|            |          | where   |        |          |           |           |
+------------+----------+---------+--------+----------+-----------+-----------+
| Kotlin     | <>       | T: X,   |        |          | use, decl | in, out   |
|            |          | where   |        |          |           |           |
+------------+----------+---------+--------+----------+-----------+-----------+
| Julia      | {}       | T <: X  | X <: T |          | n/a       | n/a       |
+------------+----------+---------+--------+----------+-----------+-----------+
| Dart       | <>       | extends |        |          | decl      | in, out,  |
|            |          |         |        |          |           | inout     |
+------------+----------+---------+--------+----------+-----------+-----------+
| Go         | []       | T X     |        |          | n/a       | n/a       |
+------------+----------+---------+--------+----------+-----------+-----------+
| Python     | []       | T: X    |        |          | decl      | inferred  |
| (proposed) |          |         |        |          |           |           |
+------------+----------+---------+--------+----------+-----------+-----------+


Acknowledgements
================

Thanks to Sebastian Rittau for kick-starting the discussions that led to this
proposal, to Jukka Lehtosalo for proposing the syntax for type alias
statements and to Jelle Zijlstra, Daniel Moisset, and Guido van Rossum
for their valuable feedback and suggested improvements to the specification
and implementation.


Copyright
=========

This document is placed in the public domain or under the CC0-1.0-Universal
license, whichever is more permissive.
