IdeaWell

Project ideas from Hacker News discussions.

Are We Stuck with Lean?

Original Article

Hacker News Discussion

📝 Discussion Summary (Click to expand)

Theme 1 – Ultra‑small, auditable kernel

“Metamath's Python verifier - its trusted kernel - is just 700 lines of Python short” – 7373737373

Theme 2 – Logic isn’t baked in; many foundations are interchangeable

“In Metamath the axioms are not built‑in… you can use intuitionistic logic, New Foundations, HOL, or design your own” – dwheeler

Theme 3 – Users favour familiar tools and resist forcing a single prover on everyone

“I find it really strange that people who don't use Lean don't just get on and use the alternatives rather than trying to get everyone who is using Lean to use something else.” – seanhunter

🚀 Project Ideas

Generating project ideas…

Metaverify

Summary

  • A lightweight universal proof verifier CLI that can ingest proof scripts from Metamath, Lean, Coq, and Isabelle and validate them against the respective kernels in seconds.
  • Provides a fast, trust‑worthy kernel check for any formalized theorem, lowering the barrier to independent verification.

Details

Key Value
Target Audience Researchers, graduate students, and proof assistants maintainers who need reliable, independent validation of formal proofs.
Core Feature Multi‑backend verification engine with plug‑in adapters and a unified JSON schema for proof artifacts.
Tech Stack Rust (for performance), Python bindings, WASM front‑end for web UI, Docker for isolation.
Difficulty Medium
Monetization Revenue-ready: SaaS API tiered subscription (free tier 10k verifications/month, paid $0.001 per additional verification).

Notes

  • HN commenters emphasized the importance of small, auditable kernels and fast verification; Metaverify directly addresses those by exposing a unified validator.
  • The project can host a public benchmarking API, encouraging community contributions and ensuring trust in disparate proof systems.
  • Potential to integrate with LLM‑generated proofs, allowing automatic verification without human intervention.

ProofViz

Summary

  • An interactive web platform that visualizes proof dependency graphs and highlights unverified steps, bug counts, and coverage metrics for any formal proof.
  • Enables mathematicians to audit and explore proof objects intuitively, reducing reliance on opaque verification logs.

Details

Key Value
Target Audience Mathematicians, educators, and proof assistants developers seeking better tooling for proof transparency.
Core Feature Real‑time graph visualization of theorem dependencies, automated bug‑detection overlays, and exportable audit reports.
Tech Stack TypeScript/React, D3.js for graph rendering, Node.js backend, PostgreSQL for storing proof metadata.
Difficulty Low
Monetization Revenue-ready: Freemium model with premium analytics (team collaboration, API access) at $15/user/month.

Notes

  • Frequent HN discussions about “no hand‑waving” and verification speed; ProofViz makes verification outcomes visible and explorable.
  • The visualized bug‑count metric mentioned in the discussion can be directly displayed, appealing to the community's desire for transparency.
  • Could integrate with existing proof repositories (e.g., set.mm, Lean’s mathlib) to auto‑import and display audits.

BridgeProof

Summary

  • A cross‑system proof translation tool that converts verified statements and proofs between major proof assistants (Lean ↔ Metamath ↔ Coq) while preserving logical validity.
  • Offers a safety net for teams migrating legacy formalizations to newer frameworks without rewriting from scratch.

Details

Key Value
Target Audience Formalization teams, academic institutions, and open‑source math libraries looking to switch or synchronize proof bases.
Core Feature Automated mapping of syntax and semantics across proof assistants, with built‑in validation of the translated output.
Tech Stack Python (for high‑level orchestration), MLIR for intermediate representation, Z3 SMT solver for consistency checks.
Difficulty High
Monetization Revenue-ready: Consulting licensing for enterprise migration services (starting at $5,000/project).

Notes

  • The discussion highlighted friction around adopting different foundations (ZFC vs DTT) and the need to “port” large codebases; BridgeProof directly solves this.
  • By providing confidence that translated proofs remain sound, the tool aligns with the community’s emphasis on rigorous verification and reduces migration risk.
  • Could be marketed as a SaaS migration platform with automated test suites for migrated proofs, opening recurring revenue streams.

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