Repair formal proofs for a verified garbage collector
Codex edited files and ran builds to repair CertiGC proofs; it handled local repair well, but humans had to check that its invariants preserved the specification.
Done withCodex
- What they did
- Codex had repository access, edited Rocq proof files, ran targeted make builds, and used a rocq-mcp server to inspect proof states. It repaired the VST proofs first, then the graph-isomorphism theorem. It proposed the recorded-backward-edge invariant, and the author reviewed it. He required discussion before any Definition changed and refused new VST preconditions without evidence.
- How it went
- The branch compiled and merged upstream as PR 30. The main theorem was accepted April 29, and a later audit removed a stale no-backward-edge premise. It was a single case, not a controlled study.
- Worth knowing
- Expect heavy supervision: about 59 active Codex hours, 415 human prompts and 13,305 tool calls over ten days, with no measured speedup.
Try it yourself with Codex
In my [Coq/Lean/Isabelle] project at [folder], the proof [file or lemma] is broken after [change you made]. Edit the files, run the build, and repair the proof with the smallest local changes. Do not weaken or change any specification or invariant without asking me first, and finish with a list of every statement you altered so I can review it.
Source: arxiv.org · Undated
Five of these in your inbox every morning
The best things people got an AI agent to do, each with the prompt to try it.
More like this
Turn tickets into merged pull requests
Pulls tasks from GitHub Issues or Linear, then runs Claude Code or Codex in isolated Kubernetes pods to carry each one through to a PR.
Recommend a hotel from client notes using Codex
A travel advisor had Codex use client notes to recommend a Belmond hotel in Italy, checking live booking engines and generating a detailed Word doc.
Diagnose a killed process on a server
Codex CLI over SSH found the OOM killer in kernel logs on a 2 GB droplet with no swap and listed fixes by risk without changing anything.
Find a Linux vulnerability hidden for 23 years
An account of Claude Code uncovering a long-standing vulnerability in Linux.
Verify SPICE simulations against a real oscilloscope
MCP servers for an oscilloscope and SPICE simulator let Claude Code compare simulated circuits with real hardware measurements, closing the loop.
Open recent protein-ligand structures in PDB
A researcher had Comet find the three latest GSK3B protein-ligand complexes in the PDB and open each in Ligand Interaction view.