# How can you state how abstract interpretation gets around Rice's Theorem succinctly?

At this question, abstract interpretation has a nice in-depth look. However, I'd like someone to clearly and very precisely state how abstract interpretation takes the result of Rice's Theorem over the Turing-complete programming languages/Turing machines, and uses abstract interpretation to get similar results for decidability for non-trivial program properties; or, rather, how does abstract interpretation get around Rice's Theorem/the Halting Problem?

• It's unclear what you're asking. Any abstract interpretation will be sucessful only on a subset of programs, never on all. Therefore there's no conflict with undecidability. – Mikolas Jan 18 '18 at 21:45

Abstract interpretation may only over-approximate properties of programs: the most precise abstract value of a program $P$ may be $a$, but any algorithm for computing an abstract value will in general compute some value $a'\geq a$ for $P$ (possibly $\top$ in the worst case).