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5.2.6 Function Types

function types are understood in the restrictive sense, specifying:

• The argument syntax that the function must be called with. This is information about what argument counts are acceptable, and which keyword arguments are recognized. In Python, warnings about argument syntax are a consequence of function type checking.
• The types of the argument values that the caller must pass. If the compiler can prove that some argument to a call is of a type disallowed by the called function’s type, then it will give a compile-time type warning. In addition to being used for compile-time type checking, these type assertions are also used as output type assertions in code generation. For example, if foo is declared to have a fixnum argument, then the 1+ in (foo (1+ x)) is compiled with knowledge that the result must be a fixnum.
• The types the values that will be bound to argument variables in the function’s definition. Declaring a function’s type with ftype implicitly declares the types of the arguments in the definition. Python checks for consistency between the definition and the ftype declaration. Because of precise type checking, an error will be signaled when a function is called with an argument of the wrong type.
• The type of return value(s) that the caller can expect. This information is a useful input to type inference. For example, if a function is declared to return a fixnum, then when a call to that function appears in an expression, the expression will be compiled with knowledge that the call will return a fixnum.
• The type of return value(s) that the definition must return. The result type in an ftype declaration is treated like an implicit the wrapped around the body of the definition. If the definition returns a value of the wrong type, an error will be signaled. If the compiler can prove that the function returns the wrong type, then it will give a compile-time warning.

This is consistent with the new interpretation of function types and the ftype declaration in the proposed X3J13 cleanup “function-type-argument-type-semantics”. Note also, that if you don’t explicitly declare the type of a function using a global ftype declaration, then Python will compute a function type from the definition, providing a degree of inter-routine type inference, see function-type-inference.