An Array Abstraction to Amortize Reasoning About Parallel Client Code

Data abstraction is important for enabling the automated modular verification of a large class of parallel programs even in the presence of manifest sharing during parallel execution. Though sharing is difficult to avoid when parallel execution is used to gain performance improvements, formal verification of such code still must be modular. The Open image in new window abstraction introduced in this paper supports modular verification by allowing frame conditions to be dispatched only once and then be reused by multiple clients, thus amortizing the verification cost. The approach achieves this objective by introducing a non-interference contract that enables the preservation of desirable performance characteristics of traditional arrays such as constant-time access to elements. Illustrative divide-and-conquer client code using this abstraction is contrasted with similar client code that uses a traditional array. The utility of the Open image in new window in a language with clean semantics is demonstrated by comparing the two clients in terms of the feasibility and tractability of modular verification. The repeated verification of software is expensive, so it should be avoided. Modularization (such as by introducing additional data abstractions) makes it possible to avoid expensive re-verification of entire client programs when only minor changes are made.