Abstract. We provide a program logic for specifying a core subset of the sequential POSIX file system, and for reasoning abstractly about client programs working with the file system.

Indexes are ubiquitous. Examples include associative arrays, dictionaries, maps and hashes used in applications such as databases, file systems and dynamic languages. Abstractly, a sequential index can be viewed as a partial function from keys to values. Values can be queried by their keys, and the index can be mutated by adding or removing mappings. Whilst appealingly simple, this abstract specification is insufficient for reasoning about indexes that are accessed concurrently.We present an abstract specification for concurrent indexes. We verify several representative concurrent client applications using our specification, demonstrating that clients can reason abstractly without having to consider specific underlying implementations. Our specification would, however, mean nothing if it were not satisfied by standard implementations of concurrent indexes. We verify that our specification is satisfied by algorithms based on linked lists, hash tables and B Link trees. The complexity of these algorithms, in particular the B Link tree algorithm, can be completely hidden from the client's view by our abstract specification.General Terms Algorithms, Concurrency, Theory, Verification.

Indexes are ubiquitous. Examples include associative arrays, dictionaries, maps and hashes used in applications such as databases, file systems and dynamic languages. Abstractly, a sequential index can be viewed as a partial function from keys to values. Values can be queried by their keys, and the index can be mutated by adding or removing mappings. Whilst appealingly simple, this abstract specification is insufficient for reasoning about indexes that are accessed concurrently.We present an abstract specification for concurrent indexes. We verify several representative concurrent client applications using our specification, demonstrating that clients can reason abstractly without having to consider specific underlying implementations. Our specification would, however, mean nothing if it were not satisfied by standard implementations of concurrent indexes. We verify that our specification is satisfied by algorithms based on linked lists, hash tables and B Link trees. The complexity of these algorithms, in particular the B Link tree algorithm, can be completely hidden from the client's view by our abstract specification.General Terms Algorithms, Concurrency, Theory, Verification.

Abstract. Local reasoning has become a well-established technique in program verification, which has been shown to be useful at many different levels of abstraction. In separation logic, we use a low-level abstraction that is close to how the machine sees the program state. In context logic, we work with high-level abstractions that are close to how the clients of modules see the program state. We apply program refinement to local reasoning, demonstrating that high-level local reasoning is sound for module implementations. We consider two approaches: one that preserves the high-level locality at the low level; and one that breaks the high-level 'fiction' of locality.

16.06.15 KB. Ok to add published verison, OA paper© 2014 The Authors.We study abstract local reasoning for concurrent libraries. There are two main approaches: provide a specification of a library by abstracting from concrete reasoning about an implementation; or provide a direct abstract library specification, justified by refining to an implementation. Both approaches have a significant gap in their reasoning, due to a mismatch between the abstract connectivity of the abstract data structures and the concrete connectivity of the concrete heap representations. We demonstrate this gap using structural separation logic (SSL) for specifying a concurrent tree library and concurrent abstract predicates (CAP) for reasoning about a concrete tree implementation. The gap between the abstract and concrete connectivity emerges as a mismatch between the SSL tree predicates and CAP heap predicates. This gap is closed by an interface function I which links the abstract and concrete connectivity. In the accompanying technical report, we generalise our SSL reasoning and results to arbitrary concurrent data libraries