Extracting Program Logics From Abstract Interpretations Defined by Logical Relations

interpretation: computing on properties readInt(x) if x>0 : x:= pred(x) x:= succ(x) writeInt(x) Q: Is output pos? A: abstractly interpret domain Int by Sign = {neg , zero, pos , any }: readSign(x) if isPos(x): x:= pred(x) x:= succ(x) writeSign(x) where succ(pos) = pos succ(zero) = pos succ(neg) = any succ(any) = any and pred(neg) = neg pred(zero) = neg pred(pos) = any pred(any) = any Calculate the static analysis: {zero 7→ pos , neg 7→ any , pos 7→ any , any 7→ any} The Question is decided only for zero — the static analysis is sound but incomplete.