Why not just use Lean?

· math · Source ↗

TLDR

  • Likely Isabelle’s creator argues Lean’s dominance erases 60 years of proof assistant history and makes the technical case for Isabelle over dependent-typed systems.

Key Takeaways

  • AUTOMATH (1968) already contained most formalization ingredients; Jutting proved Dedekind completeness of the reals in 1977, decades before Lean existed.
  • The LCF approach (ML abstract data types, dynamic proof checking, no proof objects) is architecturally distinct from propositions-as-types and predates it by 50 years.
  • Lean’s community dominance came from abandoning Rocq’s constructive-proof obsession and from Tom Hales + Kevin Buzzard building a library and teaching culture around it, not from technical superiority.
  • Isabelle’s sledgehammer tactic has no peer; AI-generated proofs (including Claude-assisted ones) clean up well against it and remain human-readable.
  • Dependent types force undecidable type-checking; the intensional-equality workaround (where T(N+1) and T(1+N) are distinct types) creates real proof burdens that Isabelle avoids entirely.

Hacker News Comment Review

  • The most substantive pushback challenges a core technical claim: commenters assert Lean already implements proof-object elimination equivalent to the LCF optimization, making the “RAMmageddon” waste argument factually contested.
  • The Python parallel recurred across comments: once a tool reaches critical mass with evangelists like Terence Tao, technical shortcomings stop mattering; Lean may already be past escape velocity.
  • The Lean-vs-Mathlib distinction drew real discussion: Lean the language makes pragmatic tradeoffs, but Mathlib’s deliberate adoption of classical logic (law of excluded middle) is where the mathematical power actually comes from.

Notable Comments

  • @nrds: Directly refutes the proof-object waste claim, arguing Lean implements the same kernel optimization as LCF and does not retain large proof terms.
  • @ianhorn: Notes that Lean’s VS Code extension solved the IDE-coupling problem that made Coq/Rocq inaccessible for 15 years, a tooling advantage the post underweights.

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