Data Abstraction and Information Hiding

This paper describes an approach for verifying programs in the presence of data abstraction and information hiding, which are key features of modern programming languages with objects and modules. The paper draws on our experience building and using an automatic program checker, and focuses on the property of modular soundness: that is, the property that the separate verifications of the individual modules of a program suffice to ensure the correctness of the composite program. We found this desirable property surprisingly difficult to achieve. A key feature of our methodology for modular soundness is a new specification construct: the abstraction dependency, which reveals which concrete variables appear in the representation of a given abstract variable, without revealing the abstraction function itself. This paper discusses in detail two varieties of abstraction dependencies: static and dynamic. The paper also presents a new technical definition of modular soundness as a monotonicity property of verifiability with respect to scope and uses this technical definition to formally prove the modular soundness of a programming discipline for static dependencies.