A Refinement-Based Methodology for Verifying Abstract Data Type Implementations
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This thesis is about techniques for proving the functional correctness of Abstract Data Type (ADT) implementations. We provide a framework for proving the functional correctness of imperative language implementations of ADTs, using a theory of refinement. We develop a theory of refinement to reason about both declarative and imperative language implementations of ADTs. Our theory facilitates compositional reasoning about complex implementations that may use several layers of sub-ADTs. Based on our theory of refinement, we propose a methodology for proving the functional correctness of an existing imperative language implementation of an ADT. We propose a mechanizable translation from an abstract model in the Z language to an abstract implementation in VCC’s ghost language. Then we present a technique to carry out the refinement checks completely within the VCC tool. We apply our proposed methodology to prove the functional correctness of the scheduling-related functionality of FreeRTOS, a popular open-source real-time operating system. We focused on the scheduler-related functionality, found major deviations from the intended behavior, and did a machine-checked proof of the correctness of the fixed code. We also present an eﬃcient way to phrase the refinement conditions in VCC, which considerably improves VCC’s performance. We evaluated this technique on a simplified version of FreeRTOS which we constructed for this verification exercise. Using our eﬃcient approach, VCC always terminates and leads to a reduction of over 90% in the total time taken by a naive check, when evaluated on this case-study.