[cochne]

You can certainly write a program which can determine if a program would halt. It just won't be able to output a yes or no for _every_ program. In some cases it would have to output 'undecidable'. Most of the practical programs you might want to feed into this program will have an answer.

[trehalose]

If I may nitpick, it shouldn't ever output "undecidable" but rather something like "undecided" or "I give up". A program that can be trivially seen to halt if we let it run for a quadrillion years is only "undecidable" in the sense that we might get impatient and die.