You’re looking for bound:

T = TypeVar('T', bound=Callable)

From the docs:

a type variable may specify an upper bound using bound=<type>. This means that an actual type substituted (explicitly or implicitly) for the type variable must be a subclass of the boundary type, see PEP 484.

TypeVar(name, *args) means that the type has to be one of args, so all instances of T would just be replaceable by Callable if T = TypeVar('T', Callable) were allowed.

You should be able to see the difference here (though I didn’t actually try it, heh):

from typing import Generic, TypeVar, Callable

T = TypeVar('T', Callable, bool)

class Foo(Generic[T]):
    value: T

    def __init__(self, value: T) -> None:
        self.value = value

class Bar:
    baz = 5

    def __call__(self):
        pass

f = Foo(Bar())
print(f.value.baz)  # doesn’t typecheck because f.value is only a Callable

You can achieve your goal by passing an extra parameter bound to TypeVar, as described in PEP484:

A type variable may specify an upper bound using bound=<type>. This means that an actual type substituted (explicitly or implicitly) for the type variable must be a subtype of the boundary type. A common example is the definition of a Comparable type that works well enough to catch the most common errors:

Sample code from mentioned PEP:

from typing import TypeVar

class Comparable(metaclass=ABCMeta):
    @abstractmethod
    def __lt__(self, other: Any) -> bool: ...
    ... # __gt__ etc. as well

CT = TypeVar('CT', bound=Comparable)

def min(x: CT, y: CT) -> CT:
    if x < y:
        return x
    else:
        return y

min(1, 2) # ok, return type int
min('x', 'y') # ok, return type str

In latest version (verified with 0.521) of mypy, the scenario above is correctly handled.

When you do T = TypeVar("T", bound=Union[A, B]), you are saying T can be bound to either Union[A, B] or any subtype of Union[A, B]. It's upper-bounded to the union.

So for example, if you had a function of type def f(x: T) -> T, it would be legal to pass in values of any of the following types:

1. Union[A, B] (or a union of any subtypes of A and B such as Union[A, BChild])
2. A (or any subtype of A)
3. B (or any subtype of B)

This is how generics behave in most programming languages: they let you impose a single upper bound.

But when you do T = TypeVar("T", A, B), you are basically saying T must be either upper-bounded by A or upper-bounded by B. That is, instead of establishing a single upper-bound, you get to establish multiple!

So this means while it would be legal to pass in values of either types A or B into f, it would not be legal to pass in Union[A, B] since the union is neither upper-bounded by A nor B.

So for example, suppose you had a iterable that could contain either ints or strs.

If you want this iterable to contain any arbitrary mixture of ints or strs, you only need a single upper-bound of a Union[int, str]. For example:

from typing import TypeVar, Union, List, Iterable

mix1: List[Union[int, str]] = [1, "a", 3]
mix2: List[Union[int, str]] = [4, "x", "y"]
all_ints = [1, 2, 3]
all_strs = ["a", "b", "c"]


T1 = TypeVar('T1', bound=Union[int, str])

def concat1(x: Iterable[T1], y: Iterable[T1]) -> List[T1]:
    out: List[T1] = []
    out.extend(x)
    out.extend(y)
    return out

# Type checks
a1 = concat1(mix1, mix2)

# Also type checks (though your type checker may need a hint to deduce
# you really do want a union)
a2: List[Union[int, str]] = concat1(all_ints, all_strs)

# Also type checks
a3 = concat1(all_strs, all_strs)

In contrast, if you want to enforce that the function will accept either a list of all ints or all strs but never a mixture of either, you'll need multiple upper bounds.

T2 = TypeVar('T2', int, str)

def concat2(x: Iterable[T2], y: Iterable[T2]) -> List[T2]:
    out: List[T2] = []
    out.extend(x)
    out.extend(y)
    return out

# Does NOT type check
b1 = concat2(mix1, mix2)

# Also does NOT type check
b2 = concat2(all_ints, all_strs)

# But this type checks
b3 = concat2(all_ints, all_ints)