We present Parallely, a programming language and a system for verification of approximations in parallel message-passing programs. Parallely's language can express various software and hardware level approximations that reduce the computation and communication overheads at the cost of result accuracy.

Parallely's safety analysis can prove the absence of deadlocks in approximate computations and its type system can ensure that approximate values do not interfere with precise values. Parallely's quantitative accuracy analysis can reason about the frequency and magnitude of error. To support such analyses, Parallely presents an approximation-aware version of canonical sequentialization, a recently proposed verification technique that generates sequential programs that capture the semantics of well-structured parallel programs (i.e., ones that satisfy a symmetric nondeterminism property). To the best of our knowledge, Parallely is the first system designed to analyze parallel approximate programs.

We demonstrate the effectiveness of Parallely on eight benchmark applications from the domains of graph analytics, image processing, and numerical analysis. We also encode and study five approximation mechanisms from literature. Our implementation of Parallely automatically and efficiently proves type safety, reliability, and accuracy properties of the approximate benchmarks.