How close are we to a world where every paper on programming languages is accompanied by an electronic appendix with machinechecked proofs? We propose an initial set of benchmarks for measuring progress in this area. Based on the metatheory of System F , a typed lambda-calculus with second-order polymorphism, subtyping, and records, these benchmarks embody many aspects of programming languages that are challenging to formalize: variable binding at both the term and type levels, syntactic forms with variable numbers of components (including binders), and proofs demanding complex induction principles. We hope that these benchmarks will help clarify the current state of the art, provide a basis for comparing competing technologies, and motivate further research.

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Conventional computer engineering relies on test-and-debug development processes, with the behavior of common interfaces described (at best) with prose specification documents. But prose specifications cannot be used in test-and-debug development in any automated way, and prose is a poor medium for expressing complex (and loose) specifications. The TCP/IP protocols and Sockets API are a good example of this: they play a vital role in modern communication and computation, and interoperability between implementations is essential. But what exactly they are is surprisingly obscure: their original development focused on “rough consensus and running code,” augmented by prose RFC specifications that do not precisely define what it means for an implementation to be correct. Ultimately, the actual standard is the de facto one of the common implementations, including, for example, the 15 000 to 20 000 lines of the BSD implementation—optimized and multithreaded C code, time dependent, with asynchronous event handlers, intertwined with the operating system, and security critical. This article reports on work done in the Netsem project to develop lightweight mathematically rigorous techniques that can be applied to such systems: to specify their behavior precisely (but loosely enough to permit the required implementation variation) and to test whether these specifications and the implementations correspond with specifications that are executable as test oracles . We developed post hoc specifications of TCP, UDP, and the Sockets API, both of the service that they provide to applications (in terms of TCP bidirectional stream connections) and of the internal operation of the protocol (in terms of TCP segments and UDP datagrams), together with a testable abstraction function relating the two. These specifications are rigorous, detailed, readable, with broad coverage, and rather accurate. Working within a general-purpose proof assistant (HOL4), we developed language idioms (within higher-order logic) in which to write the specifications: operational semantics with nondeterminism, time, system calls, monadic relational programming, and so forth. We followed an experimental semantics approach, validating the specifications against several thousand traces captured from three implementations (FreeBSD, Linux, and WinXP). Many differences between these were identified, as were a number of bugs. Validation was done using a special-purpose symbolic model checker programmed above HOL4. Having demonstrated that our logic-based engineering techniques suffice for handling real-world protocols, we argue that similar techniques could be applied to future critical software infrastructure at design time, leading to cleaner designs and (via specification-based testing) more robust and predictable implementations. In cases where specification looseness can be controlled, this should be possible with lightweight techniques, without the need for a general-purpose proof assistant, at relatively little cost.

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