We introduce Lurk, a new LISP-based programming language for zk-SNARKs. Traditional approaches to programming over zero-knowledge proofs require compiling the desired computation into a flat circuit, imposing serious constraints on the size and complexity of computations that can be achieved in practice. Lurk programs are instead provided as data to the universal Lurk interpreter circuit, allowing the resulting language to be Turing-complete without compromising the size of the resulting proof artifacts. Our work describes the design and theory behind Lurk, along with detailing how its implementation of content addressing can be used to sidestep many of the usual concerns of programming zero-knowledge proofs.

Current static verification techniques do not provide good support for incrementality, making it difficult for developers to focus on specifying and verifying the properties and components that are most important. Dynamic verification approaches support incrementality, but cannot provide static guarantees. To bridge this gap, prior work proposed gradual verification, which supports incrementality by allowing every assertion to be complete, partial, or omitted, and provides sound verification that smoothly scales from dynamic to static checking. The prior approach to gradual verification, however, was limited to programs without recursive data structures. This paper extends gradual verification to programs that manipulate recursive, mutable data structures on the heap. We address several technical challenges, such as semantically connecting iso- and equi-recursive interpretations of abstract predicates, and supporting gradual verification of heap ownership. This work thus lays the foundation for future tools that work on realistic programs and support verification within an engineering process in which cost-benefit trade-offs can be made.