[shalabhc]

> We know it's doable, because all such tool would do is to automate the thing we do when looking at code - running pieces of it in our head.

Yes exactly. Except it would be much faster, more precise and with more coverage than what we get with mental execution. It still wont give you total coverage, but it would be able to show where it doesn't have coverage.

> In a way, it's just a different interface for doing the same thing you might be doing with unit tests - except it would be transient, and free to exercise any internal code in your program, not just poke at public module interfaces.

Yes. One additional aspect would be the ability to run with partial information. Eg. if a function needs three arguments, you need all three to run a test. However in abstract interpretation, you could just specify one argument and still trace the execution to some degree.