Back in 2009, OKLabs/NICTA announced the first formally verified microkernel, seL4 (a member of the L4 family). Alas, it was proprietary software. Today, that's no longer the case: seL4 has been released under the GPLv2 (only, no "or later versions clause" unfortunately). An anonymous reader writes OSnews is reporting that the formally verified sel4 microkernel is now open source: "General Dynamics C4 Systems and NICTA are pleased to announce the open sourcing of seL4, the world's first operating-system kernel with an end-to-end proof of implementation correctness and security enforcement. It is still the world's most highly assured OS." Source is over at Github. It supports ARM and x86 (including the popular Beaglebone ARM board). If you have an x86 with the VT-x and Extended Page Table extensions you can even run Linux atop seL4 (and the seL4 website is served by Linux on seL4).