Hiding the Complexity of Concurrent Indexes

Index data structures, such as B trees and hash tables, are commonly used in database implementations. A database implementor typically works with a high-level view of indexes as mappings from keys to values. Using this high-level view, he is able to build up complex abstractions such as transactions, without needing to know exactly how indexes work ‘under the hood’. This high-level intuition breaks down when the index is accessed concurrently. If two threads share access to a key, neither can be sure whether the other has removed its value. A specification of a concurrent index must account for this sharing. Also, the algorithms that implement concurrent indexes are highly complex and subtle. Justifying the use of a high-level specification requires hiding the complexity of an implementation and is thus a major challenge. In this paper, we give an abstract specification for concurrent indexes, and prove that it is satisfied by concrete implementations. Our specification captures high-level sharing of index elements, allowing collaboration between threads. We show that a widely-used implementation based on B trees is correct with respect to our abstract specification. Finally, we demonstrate that our specification is useful by verifying several client algorithms.