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

Some parts of programs can be proved. For example, the C# compiler that statically verify and guarantee type safety, if the the compilation succeeds. But I suspect the core of your question is to prove that a program performs correctly. Many (I do not dare say most) algorithms can be proved to be correct, but a whole program probably cannot be proved statically due to the following:

• Verification requires all possible branches (calls, ifs and interupts) to be traversed, which in advanced program code has super-cubic time complexity (hence it will never complete within reasonable time).
• Some programming techniques, either through making components or using reflection, makes it impossible to statically predict execution of code (i.e. you don't know how another programmer will use your library, and the compiler has a hard time predict how reflection in a consumer will invoke functionality.

And those are just some...