A Proof Calculus for Natural Semantics Based on Greatest Fixed Point Semantics

Formal semantics of programming languages needs to model the potentially infinite state transition behavior of programs as well as the computation of their final results simultaneously. This requirement is essential in correctness proofs for compilers. We show that a greatest fixed point interpretation of natural semantics is able to model both aspects equally well. Technically, we infer this interpretation of natural semantics based on an easily omprehensible introduction to the dual definition and proof principles of induction and coinduction. Furthermore, we develop a proof calculus based on it and demonstrate its application for two typical problems.