When checking mypy does not give any errors, believes that everything is in order.
If after calling FUNC2 Add line:

value_b = func1 ('11 ')

The error messages immediately go:

error: "func1" Does not return a value
Error: Argument 1 to "Func1" HAS Incompatible Type "STR"; EXPECTED "INT"

Why Mypy ignores errors inside the FUNC2 method ?

Answer 1, Authority 100%

Mypy does not check the code inside the functions that no annotations (apparently, it is done so that it is possible to add annotations gradually).

Exposure from the documentation:

no errors reported For Obviously Wrong Code

There Are Several Common Reasons Why Obviously Wrong Code Is Not Flagged AS An Error.

• The Function Containing The Error Is Not Annotated. Functions That Do Not Have Any Annotations (Neiter for Any Argument Nor for the Return Type) Are Not Type-Checked, and Even The Most Blatant Type Errs (EG 2 + 'A' ) Pass Silently. The Solutions Is To Add Annotations. WHERE THAT ISNTATIONS CAN BE CHECKED USING - Check-Untyped-Defs .

That is, if the second function, specify the return - & gt returned value; None or when calling myPy Add the - check-untyped-defs flag, then the code inside the second function will start checked:

$ mypy --check-untyped-defs test.py
test.py:8: error: "Func1" Does Not Return A Value
test.py:8: Error: Argument 1 to "Func1" HAS Incompatible Type "STR"; EXPECTED "INT"
Found 2 Errors In 1 File (Checked 1 Source File)

For hardcore lovers, I can also recommend the -Strict , when it is turned on, it will give a whole 4 errors:

$ mypy --Strict test.py
test.py:6: Error: Function Is Missing A Return Type Annotation
Test.PY: 6: Note: Use "- & gt; none" If Function Does Not Return A Value
test.py:8: error: "Func1" Does Not Return A Value
test.py:8: Error: Argument 1 to "Func1" HAS Incompatible Type "STR"; EXPECTED "INT"
test.py:12: Error: Call to Untyped Function "Func2" in Typed Context
Found 4 Errors In 1 File (Checked 1 Source File)

Turning on - Strict equivalent to turning on the following flags (list is obtained by running Mypy -h ): - Warn-Unused-Configs , - Disallow-Any-Generics , - Disallow-Subclassing-Any , - DiSallow-Untyped-Calls , - -disallow-unhyped-defs , - disallow-incomplete-defs , - check-untyped-defs , - Disallow-Untyped- Decorators , - No-implicit-optional , - Warn-Redundant-Casts , - Warn-Unused-Ignores , - Warn-Return-Any , - No-implicit-reexport , - Strict-Equality .

Actually, the desired option - Check-Untyped-DEFS originally found the addition of all these flags and launching with the removal of flags one by one.