What you are talking about is the "trusted computing base". Prove every part of the basesystem your running on, this of course is a HUGE task, but there are people thinking and working on this.

You might injoy this darpa project: http://www.crash-safe.org/papers

The propose there own hardware, OS, languages and compilers. The Hardware Design is by Tom Knight, one of the guys who designed the lisp machine.

Its quite an intressting read.