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For small modules, SPARK with this book from the limited feedback I have:

https://www.amazon.com/Building-High-Integrity-Applications-...

Verification of larger programs is hard for a lot of reasons. Easiest method is to do Design-by-Contract in a memory-safe language. Anything easy to specify in contracts goes there where stuff easier to test for is done that way. If your language doesn't support it, you can do it with asserts, conditionals in functions, or constructors/destructors in OOP.

http://www.eiffel.com/developers/design_by_contract_in_detai...

Then, you hit the app with tests generated from the contracts and fuzz testing that both run while the contract conditions have runtime checks in the code. That means a failure will take you right to the precondition, invariant, or post condition that is broken.

For analyzing distributed stuff, TLA+ is your best bet with an accessible tutorial for a subset available here:

https://learntla.com/introduction/




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