(I'm the author of the paper BTW.) Regarding TLA+ and CakeML: TLA+ seems like a good idea, Leslie Lamport talks a lot of sense in most of his papers. I especially recommend "Composition: A Way to Make Proofs Harder" (https://lamport.azurewebsites.net/pubs/lamport-composition.p...). It sums up a lot of my feelings about "simplifying" a problem by adding more layers and generalizing the layers so that they have more work to do individually. I'm not sure I'm totally on board the idea of using temporal logic; my plan is to just use plain first order logic to talk about the states of a computer.

Regarding CakeML, I'm really impressed by the work they've done, and I think they more than anyone else are leading the charge on getting verification as pervasive as possible at every level (especially the low levels, where historically it has been difficult to get past the closed source barrier). That said, I think they are not doing an optimal job at being a bootstrap. They have a system that does that and so much more that if you just want a bootstrap it's way overkill. And you pay for that overkill - 14 hour compilation per target (see https://cakeml.org/regression.cgi).