Here's an elementary litmus test that anyone slightly experienced with type systems will know.
How do you type the omega combinator in Python?
lambda x: x(x)
What about the application of the omega combinator to itself?
(lambda x: x(x))(lambda x: x(x))
How do you type the Y combinator in Python?
lambda f: (lambda x: f(x(x)))(lambda x: f(x(x)))
Depending on the choice of the type system you can either answer: this cannot be assigned a type in which case your type system is too weak to express many real-world programs, or it does have a type but then your type system is so sophisticated that people using this language (just for writing BUILD rules) won't be able to understand type errors in this type system. I have yet to find a middle ground.
In case you claim this is impractical functional programming, bear in mind you can write the same thing using classes in object-oriented programming.
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Okay let's not even talk about these weird-looking "combinators" even though they have a rich history. Consider this function:
lambda x: {'this': x, 'next': x + 1}
What is its type? Again the answer depends on plenty of choices that need to be made by the type system designer. Do you force dictionaries to have a single type for values? If so, many users used to Python will reject your system for being too inflexible. If not, will you now introduce row polymorphism in your type system? Will you now introduce depth subtyping and width subtyping in your type system? (For example if a function only needs field 'x' in a dictionary but the caller passes a dictionary with both fields 'x' and 'y' should not result in an error; that's why you need subtyping.) Now let's consider the lowly plus operator. In real Python the plus operator can work on integers, floats, strings, sets, etc. Let's say your type inference algorithm uses the RHS to find that x must be an integer. But that's wrong; it could still be a float. Can you now write a type for that expression? Hint: it involves record types, intersection types, type variables and other things that would not be comprehensible.