In layman's terms, it is impossible to determine certain properties of an arbitrary program written in a Turing-complete language. Properties like "will this pr

In layman's terms, it is impossible to determine certain properties of an arbitrary program written in a Turing-complete language. Properties like "will this program finish within a reasonable amount of time?" or "does program X do the same thing as program Y?" For a non-turing-complete language, it may be possible to test such properties. It's crucial to understand that this distinction is not one of how practical it is to determine properties; once you open the door to Turing-completeness, all ability to reason about a program effectively flies out the window. You might be able to come up with rules-of-thumb that determine an interesting property of a program in a Turing-complete language some of the time, but there will always exist programs for which your rules-of-thumb are insufficient.