proof-assistant

协助构建算法正确性证明

SKILL.md

--- frontmatter

name: proof-assistant
description: Assist in constructing algorithm correctness proofs
allowed-tools:
  - Read
  - Write
  - Grep
  - Glob

Proof Assistant Skill

Purpose

Assist in constructing formal correctness proofs for algorithms using standard proof techniques.

Capabilities

•Proof structure templates (induction, contradiction, etc.)
•Step-by-step proof guidance
•Termination argument generation
•Proof review and validation
•Identify proof gaps

Target Processes

•correctness-proof-testing
•algorithm-implementation

Proof Techniques

Mathematical Induction

•Base case identification
•Inductive hypothesis formulation
•Inductive step construction

Proof by Contradiction

•Assumption negation
•Logical derivation
•Contradiction identification

Loop Invariant Proofs

•Invariant specification
•Three-part proof (init, maintenance, termination)

Structural Induction

•For recursive data structures
•Base case (leaf/empty)
•Inductive case (composite)

Input Schema

json

{
  "type": "object",
  "properties": {
    "algorithm": { "type": "string" },
    "code": { "type": "string" },
    "proofType": {
      "type": "string",
      "enum": ["induction", "contradiction", "invariant", "structural"]
    },
    "claim": { "type": "string" },
    "partialProof": { "type": "string" }
  },
  "required": ["algorithm", "claim"]
}

Output Schema

json

{
  "type": "object",
  "properties": {
    "success": { "type": "boolean" },
    "proof": { "type": "string" },
    "structure": { "type": "array" },
    "gaps": { "type": "array" },
    "suggestions": { "type": "array" }
  },
  "required": ["success"]
}