Earlier quoted context omitted.
Programming is a branch of engineering. Very little programming is done by proof; It's done by experimentation, debugger, and tests are human-reasoned and hopefully cover all codepaths and critical junctures (for every x > 0, you test x=1, x=0, x=-1). Proof is of critical importance - It's how you find those junctures, for example, how you optimize, how you design and how you reason about runtime, etc. But programmin…
Reminds me of the famous Knuth quote: > Beware of bugs in the above code; I have only proved it correct, not tried it. Deep thinking and mathematical proofs are tremendously useful when thinking about a well-defined and scoped problem at a more or less fixed level of abstraction. The problem with software engineering is that in practice all abstractions are leaky, and so you inevitably find yourself dealing with issu…
That's a great point. We utilize best practices, like automated tests, to narrow the gap between pure experimentation and mathematical proof. Proofs in most code would be difficult to impossible because most of use libraries that use other libraries, etc., so we just do the best we can given the time and monetary constraints that we have.