Intensional Kleene and Rice theorems for abstract program semantics

Classical results in computability theory, notably Rice's theorem, focus on the extensional content of programs, namely, partial recursive functions that programs compute. Later work investigated intensional generalisations such take into account way which are computed, thus affected by specific computing them. In this paper, we single out a novel class program semantics based abstract domains properties able to capture nonextensional aspects computations, as their asymptotic complexity or logical invariants, and allow us generalise some foundational Theorem Kleene's Second Recursion these semantics. particular, it turns for semantics, any nontrivial property is undecidable every decidable over-approximation necessarily includes an infinite set false positives covers all values semantic domain.