Check if a function halts for all inputs

Question

I want to write a program that checks if a function, say f halts for all values of its input. In short -

haltChecker = function (arg) => bool

e.g. in JavaScript,

bool haltChecker ( f(a) ){
    return {f halts for all values of a};
}

Solution in JS is not required, any language will do.

Thanks.

Answer 1

The halting-problem is undecidable. Tough luck.

To give a simple example, consider the Collatz conjecture (actually, this is a bad example, as it is not proven to be undecidable - but it demonstrates that the problem is hard :).

Answer 2

You could amaze your professor with this.

Answer 3

This is also know a the Halting Problem and cannot be solved in this generic form. The best you can do is to write a program which might return true if the function stops for all inputs but it also might run indefinitely.