Untangling Mechanized Proofs
Name
3426425.3426940.pdf
Size
1.65 MB
Format
Adobe PDF
Checksum (MD5)
9686609bf5f10a587d0f5388b180a880
Author(s)
Pit-Claudel, Cl?ment
Date Issued
November 16, 2020
Publisher
ACM|Proceedings of the 13th ACM SIGPLAN International Conference on Software Language Engineering
Citation
Pit-Claudel, Cl?ment. 2020. "Untangling Mechanized Proofs."
Version
Final published version
Abstract
Proof assistants like Coq, Lean, or HOL4 rely heavily on stateful meta-programs called scripts to assemble proofs. Unlike pen-and-paper proofs, proof scripts only describe the steps to take (induct on x, apply a theorem, …), not the states that these steps lead to; as a result, plain proof scripts are essentially incomprehensible without the assistance of an interactive user interface able to run the script and show the corresponding proof states.
Until now, the standard process to communicate a proof without forcing readers to execute its script was to manually copy-paste intermediate proof states into the script, as source code comments — a tedious and error-prone exercise. Additional prose (such as for a book or tutorial) was likewise embedded in comments, preserving executability at the cost of a mediocre text-editing experience.
This paper describes a new approach to the development and dissemination of literate proof scripts, with a focus on the Coq proof assistant. Specifically, we describe two contributions: a compiler that interleaves Coq’s output with the original proof script to produce interactive webpages that are complete, self-contained presentations of Coq proofs; and a new literate programming toolkit that allows authors to switch seamlessly between prose- and code-oriented views of the same sources, by translating back and forth between reStructuredText documents and literate Coq source files. In combination, these tools offer a new way to write, communicate, and preserve proofs, combining the flexibility of procedural proof scripts and the intelligibility of declarative proofs.
Description
SLE ’20, November 16–17, 2020, Virtual, USA
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1145/3426425.3426940
