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Proceedings of the ACM on Programming Languages · April 2025

QED in Context: An Observation Study of Proof Assistant Users

Jessica Shi, Cassia Torczon, Harrison Goldstein, Benjamin C. Pierce, Andrew Head

Department of Computer and Information Science, University of Pennsylvania

Thematic analysis HCI & computer science

How they used Delve

HCI and programming-languages researchers at the University of Pennsylvania used Delve for the open coding pass of a thematic analysis of roughly 43 hours of observation transcripts from 30 Rocq and Lean users, producing the codebook behind a POPL paper on what proof assistant use really looks like.

“The first author then conducted a thematic analysis [10] of the transcripts. This analysis involved an initial open coding pass using the Delve qualitative coding tool [23]. In this pass, the author reviewed transcripts for interesting patterns of usage and tagged them with codes. These codes were updated throughout analysis for consistency and completeness.”

Field
Human-computer interaction and programming languages; how experts actually work with interactive theorem provers (Rocq and Lean) in their everyday practice
Data
About 43 hours of screen-and-audio session recordings from 30 proof assistant users working in Rocq and Lean on their own everyday tasks, auto-transcribed by Zoom and then heavily revised by two authors to fix transcription errors and embed notes on participants' actions and the code they were working with
Approach
Contextual inquiry: participants were observed doing their own everyday proof work. Analysis was a thematic analysis run in two passes - an initial open coding pass in Delve tagging patterns of usage, with codes revised throughout for consistency and completeness, then a second axial pass applying the revised codebook. The whole authoring team reviewed examples and the codebook in meetings and asynchronous review; once about 75% of transcripts were coded, another author audited the analysis by spot-checking excerpts for every code, and all examples were checked back against the video recordings.
Data types
Observation

Abstract

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.

Citation

Jessica Shi, Cassia Torczon, Harrison Goldstein, Benjamin C. Pierce, Andrew Head (2025). QED in Context: An Observation Study of Proof Assistant Users. Proceedings of the ACM on Programming Languages. https://doi.org/10.1145/3720426

Resources

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