Interactive theorem provers, or proof assistants, are important tools across many areas of computer science and mathematics, but even experts find them challenging to use effectively. To improve their design, we need a deeper, user-centric understanding of proof assistant usage. We present the results of an observation study of proof assistant users. We use contextual inquiry methodology, observing 30 participants doing their everyday work in Rocq and Lean. We qualitatively analyze their experiences to surface four observations: that proof writers iterate on their proofs by reacting to and incorporating feedback from the proof assistant; that proof progress often involves challenging conversations with the proof assistant; that proofs are constructed in consultation with a wide array of external resources; and that proof writers are guided by design considerations that go beyond “getting to QED.” Our documentation of these themes clarifies what proof assistant usage looks like currently and identifies potential opportunities that researchers should consider when working to improve the usability of proof assistants.

In type systems with dependency tracking, programmers can assign an ordered set of levels to computations and prevent information flow from high-level computations to the low-level ones. The key notion in such systems is indistinguishability : a definition of program equivalence that takes into account the parts of the program that an observer may depend on. In this paper, we investigate the use of dependency tracking in the context of dependently-typed languages. We present the Dependent Calculus of Indistinguishability (DCOI), a system that adopts indistinguishability as the definition of equality used by the type checker. DCOI also internalizes that relation as an observer-indexed propositional equality type, so that programmers may reason about indistinguishability within the language. Our design generalizes and extends prior systems that combine dependency tracking with dependent types and is the first to support conversion and propositional equality at arbitrary observer levels. We have proven type soundness and noninterference theorems for DCOI and have developed a prototype implementation of its type checker.

Property-based testing is a mainstay of functional programming, boasting a rich literature, an enthusiastic user community, and an abundance of tools — so many, indeed, that new users may have difficulty choosing. Moreover, any given framework may support a variety of strategies for generating test inputs; even experienced users may wonder which are better in a given situation. Sadly, the PBT literature, though long on creativity, is short on rigorous comparisons to help answer such questions. We present Etna, a platform for empirical evaluation and comparison of PBT techniques. Etna incorporates a number of popular PBT frameworks and testing workloads from the literature, and its extensible architecture makes adding new ones easy, while handling the technical drudgery of performance measurement. To illustrate its benefits, we use Etna to carry out several experiments with popular PBT approaches in both Coq and Haskell, allowing users to more clearly understand best practices and tradeoffs.