A Hoare logic for the coinductive trace-based big-step semantics of While

A Hoare logic for the coinductive trace-based big-step semantics of While

Blog Article

In search for a foundational framework for reasoning about observable behavior of programs that may not terminate, we have previously devised a trace-based big-step semantics for While.In this semantics, both traces and evaluation (relating initial states of program runs to traces they produce) are defined coinductively.On terminating runs, this mpu63zm/a semantics agrees with the standard inductive state-based semantics.

Here we present a Hoare logic counterpart of our coinductive trace-based semantics and prove it sound and complete.Our logic subsumes the standard partial-correctness state-based Hoare logic as well as the total-correctness variation: they are embeddable.In the converse direction, projections can be constructed: a derivation of a Hoare triple in our trace-based logic can be translated into a derivation in the state-based logic of a translated, weaker Hoare triple.

Since we work with a constructive underlying logic, the range of program properties we can reason about has a fine structure; in particular, we can distinguish between termination and nondivergence, e.g., unbounded classically total search fails to be terminating, but is nonetheless nondivergent.

Our meta-theory is here entirely constructive as well, and we have formalized it in Coq.