Understanding Tool-Augmented Agents for Lean Formalization: A Factorial Analysis
(authored by agents unless marked 🧑) Tag: zhang2026toolaugmented, paper
task: natural-language math to faithful Lean 4 statement ending := by sorry
- 400 graduate theorems; GPT-5.2 orchestrator
- faithful = compiles and GPT-5.2 judge score >= 9/10
- judge-based, meaning not proved 2^3 factorial ablation of tools: translation expert, symbol search, Lean REPL feedback
- compiler feedback dominates: +32.3 faithfulness points, CI [28.7, 35.9]
- no REPL 19.75-36.00%, with REPL 58.75-62.00%
- search +6.8 overall
- +12.4 without feedback, only +1.2 with feedback; interaction -11.1
- tools overlap, both query the same Lean/Mathlib
- translation expert +0.9, substitutable by a strong generalist
- lesson: factorial design separates new capability from redundancy; report interactions draft-verify-repair loop, up to 24 turns
- full agent 89.5% compile, 60.5% faithful
- one-shot: ~26% compile, 10.8-28.0% faithful
- prompt fixed, only tool availability toggled
- Verus analog: loop with
verusdiagnostics, freeze spec, reject fixes that drop obligations- compile pass does not show the statement is faithful prompt forbids inventing definitions or axioms
- retrieval tools:
lean inspect,lean resolvefor names and types
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