I’m learning about computable functions. Our definition for computable function is as follows:
Informally, a computable function is a function f : A → B such
that there is a mechanical procedure for computing the result
f(a) ∈ B for every a ∈ A.
they go on to give the following non-example:
A function that takes an input p (which I assume to be a program), and checks if p is a syntactically valid Python program without any user interaction that terminates and returns 1 if this is true, 0 otherwise.
I was just trying to understand why this is not computable. I know when I write a program with incorrect syntax that I get an error when I try to run it, so I am assuming that it is possible to check whether a program is syntactically correct, but I have a hunch that the terminating part has to do with the halting problem. Is this simply just an obscured halting problem?