Hoare logic for Java in Isabelle/HOL

Abstract

SUMMARYThis article presents a Hoare-style calculus for a substantial subset of Java Card, which we call Java ight . In particular, the language includes side-effecting expressions, mutual recursion, dynamic method binding, full exception handling, and static class initialization.The Hoare logic of partial correctness is proved not only sound (w.r.t. our operational semantics of Java ight , described in detail elsewhere) but even complete. It is the first logic for an object-oriented language that is provably complete. The completeness proof uses a refinement of the Most General Formula approach. The proof of soundness gives new insights into the role of type safety. Further by-products of this work are a new general methodology for handling side-effecting expressions and their results, the discovery of the strongest possible rule of consequence, and a flexible Call rule for mutual recursion. We also give a small but non-trivial application example.All definitions and proofs have been done formally with the interactive theorem prover Isabelle/HOL. This guarantees not only rigorous definitions, but also gives maximal confidence in the results obtained.

EAM: Expansive Access Modifiers in OOP

“…The Java formalization [6] was mature enough to let us add and analyze access modifiers [1] but it didn't consider drawbacks mentioned in our work and didn't offer any solutions for them.…”

A program logic for resources

“…Most closely related to our work on the metatheoretical side are Nipkow's implementation of Hoare logic [25], the Java-light logic by von Oheimb [36], Kleymann's thesis [21], and Hofmann's [26] work on completeness of program logics. The formalized logic by Nipkow in [25] concerns a while language with parameterless functions, with proofs of soundness and completeness.…”

“…The program logic for Java-light by von Oheimb [36] is encoded in Isabelle and proven sound and complete. It covers more object-orientated features, but it works on a higher level than our logic for a bytecode language and does not address resources.…”

An observationally complete program logic for imperative higher-order functions

“…Names have been used in Hoare logic since an early work by Kowaltowski [67], and are found in the work by von Oheimb [68], Leavens and Baker [69] and Abadi and Leino [70], for treating parameter passing and return values. These works do not treat higher-order procedures and data types, which are uniformly captured in the present logic along with parameters and return values through the use of names.…”