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aristotle-lean

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Aristotle Lean

Aristotle Lean

Trit: -1 (MINUS) Domain: Formal Verification / Theorem Proving Provider: Harmonic (harmonic.fun)
Trit: -1 (MINUS) 领域: 形式化验证 / 定理证明 提供方: Harmonic (harmonic.fun)

Overview

概述

Aristotle is an IMO Gold Medal level Lean4 theorem prover that fills 
sorry
holes in proofs, auto-generates counterexamples for false statements, and integrates with Mathlib and lake dependencies.
Aristotle是一款具备IMO金牌水平的Lean4定理证明器，能够填补证明中的
sorry
空缺，为错误命题自动生成反例，并且支持与Mathlib和lake依赖集成。

API Configuration

API配置

Endpoint: aristotle.harmonic.fun
Auth: Auth0-based (requires signup/login at harmonic.fun)
Endpoint: aristotle.harmonic.fun
Auth: Auth0-based (requires signup/login at harmonic.fun)

Capabilities

功能特性

  1. Sorry Hole Filling: Completes incomplete Lean4 proofs
  2. Dual Input: Accepts English descriptions or Lean4 code
  3. Counterexample Generation: Auto-generates counterexamples for false statements
  4. Project Integration: Works with project theorems, lake dependencies, Mathlib
  5. PROVIDED SOLUTION Tag: Use comment tag to mark solution regions
  1. Sorry空缺填补：补全不完整的Lean4证明
  2. 双输入支持：接受英文描述或Lean4代码
  3. 反例生成：为错误命题自动生成反例
  4. 项目集成：适配项目定理、lake依赖、Mathlib
  5. PROVIDED SOLUTION标签：可使用注释标签标记解决方案区域

Benchmarks

基准测试

BenchmarkScore
MiniF2F90%
VERINA96.8%
基准测试得分
MiniF2F90%
VERINA96.8%

Usage Pattern

使用示例

lean
-- English prompt in comment
-- "Prove that the sum of two even numbers is even"

theorem sum_even (a b : ℕ) (ha : Even a) (hb : Even b) : Even (a + b) := by
  sorry  -- Aristotle fills this
lean
-- PROVIDED SOLUTION: explicit solution marker
theorem my_theorem : P → Q := by
  -- PROVIDED SOLUTION
  sorry
lean
-- English prompt in comment
-- "Prove that the sum of two even numbers is even"

theorem sum_even (a b : ℕ) (ha : Even a) (hb : Even b) : Even (a + b) := by
  sorry  -- Aristotle fills this
lean
-- PROVIDED SOLUTION: explicit solution marker
theorem my_theorem : P → Q := by
  -- PROVIDED SOLUTION
  sorry

Integration with GF(3)

GF(3)集成

This skill participates in triadic composition:
  • Trit -1 (MINUS): Verification/validation/analysis
  • Conservation: Σ trits ≡ 0 (mod 3) across skill triplets
本技能支持三元组合成：
  • Trit -1 (MINUS): 验证/确认/分析
  • 守恒规则: 技能三元组的trits总和满足 Σ trits ≡ 0 (mod 3)

Related Skills

相关技能

  • lean4-metaprogramming (trit +1)
  • mathlib-tactics (trit 0)
  • proof-assistant (trit -1)
  • formal-verification (trit -1)
Skill Name: aristotle-lean Type: Formal Verification / Theorem Proving Trit: -1 (MINUS) GF(3): Conserved in triplet composition
  • lean4-metaprogramming (trit +1)
  • mathlib-tactics (trit 0)
  • proof-assistant (trit -1)
  • formal-verification (trit -1)
技能名称: aristotle-lean 类型: 形式化验证 / 定理证明 Trit: -1 (MINUS) GF(3): 三元组合成时满足守恒规则

Non-Backtracking Geodesic Qualification

无回溯测地资格

Condition: μ(n) ≠ 0 (Möbius squarefree)
This skill is qualified for non-backtracking geodesic traversal:
  1. Prime Path: No state revisited in skill invocation chain
  2. Möbius Filter: Composite paths (backtracking) cancel via μ-inversion
  3. GF(3) Conservation: Trit sum ≡ 0 (mod 3) across skill triplets
  4. Spectral Gap: Ramanujan bound λ₂ ≤ 2√(k-1) for k-regular expansion
Geodesic Invariant:
  ∀ path P: backtrack(P) = ∅ ⟹ μ(|P|) ≠ 0
  
Möbius Inversion:
  f(n) = Σ_{d|n} g(d) ⟹ g(n) = Σ_{d|n} μ(n/d) f(d)
条件: μ(n) ≠ 0 (莫比乌斯无平方因子)
本技能具备无回溯测地遍历资格：
  1. 素路径: 技能调用链中不会重复访问状态
  2. 莫比乌斯过滤器: 复合路径（回溯）通过μ反转抵消
  3. GF(3)守恒: 技能三元组的Trit总和满足 ≡ 0 (mod 3)
  4. 谱间隙: k正则展开满足拉马努金界 λ₂ ≤ 2√(k-1)
Geodesic Invariant:
  ∀ path P: backtrack(P) = ∅ ⟹ μ(|P|) ≠ 0
  
Möbius Inversion:
  f(n) = Σ_{d|n} g(d) ⟹ g(n) = Σ_{d|n} μ(n/d) f(d)

SDF Interleaving

SDF对接

This skill connects to Software Design for Flexibility (Hanson & Sussman, 2021):
本技能对接《Software Design for Flexibility》（Hanson & Sussman, 2021）：

Primary Chapter: 4. Pattern Matching

核心对应章节：4. 模式匹配

Concepts: unification, match, segment variables, pattern
涉及概念: 合一、匹配、段变量、模式

GF(3) Balanced Triad

GF(3)平衡三元组

aristotle-lean (−) + SDF.Ch4 (+) + [balancer] (○) = 0
Skill Trit: -1 (MINUS - verification)
aristotle-lean (−) + SDF.Ch4 (+) + [balancer] (○) = 0
技能Trit: -1 (MINUS - 验证)

Connection Pattern

对接模式

Pattern matching extracts structure. This skill recognizes and transforms patterns.
模式匹配用于提取结构，本技能可识别并转换模式。