[deltaoneseven]

It's talking about idealistic foundations. The idea that software being a theoretical language with a well defined domain and codomain can be written with zero bugs and zero testing to catch those bugs. Zero bug code is written utilizing the tools of math, such as axioms, theorems, and logic to derive zero bug code without the need to utilize engineering principles. (I'm exaggerating a bit with the word "zero", "nearly zero" is more accurate, but too wordy)

In practice we try to eliminate bugs in software engineering by doing testing as if software was some material with unknown properties. This method is easy to understand but ultimately has it's weaknesses as tests only prove a program works for a single test. This is the "foundation" most engineers are use to.

As I stated previously, the "foundation" these book refer to are an idealism involving proving an entire program to be bug free without running it or testing it. Hence this is the reason why it's so foreign to you. You're likely use to software from a testing perspective.

Vestiges of this "foundation" have leaked into the common practice of software engineering. It's called type checking. In type checking your computer uses a similar method to guarantee your program has zero type bugs. It doesn't run any type testing, it literally just proves that your program is type safe and correct.

[strangeattractr]

Thank you for this comment, you shed some light on something I considered too opaque to dig into and made it clear why this would be useful.

[layer8]

> as if software was some material with unknown properties

That‘s a great way to put it!