Why can't programs be proven?

Question

Why can\'t a computer program be proven just as a mathematical statement can? A mathematical proof is built up on other proofs, which are built up from yet more proofs and

Answer 1

First, why are you saying "programs CAN'T be proven"?

What do you mean by "programs" anyway?

If by programs you're meaning algorithms don't you know Kruskal's? Dijkstra's? MST? Prim's? Binary Search? Mergesort? DP? All those things have mathematical models that describe their behaviors.

DESCRIBE. Math doesn't explain the why of things it simply draws a picture of the how. I can't prove to you that the Sun will rise tomorrow on the East but I can show the data where it has been doing that thing on the past.

You said: "If you write a computer program, how is it that you can take previous proven works and use them to show the truth of your program? You can't since none exist"

Wait? You CAN'T? http://en.wikipedia.org/wiki/Algorithm#Algorithmic_analysis

I can't show you "truth" I a program as much as I can't show you "truth" on language. Both are representations of our empirical understanding of the world. Not on "truth". Putting all gibberish aside I can demonstrate to you mathematically that a mergesort algorith will sort the elements on a list with O(nlogn) performance, that a Dijkstra will find the shortest path on a weighted graph, or that Euclid's algorithm will find you the greatest common divisor between two numbers. The "truth in my program" in that last case maybe that I'll find you the greatest common divisor between two numbers, don't you think?

With a recurrence equation I can delineate to you how your Fibonacci program works.

Now, is computer programming an art? I sure think it is. As much as mathematics.