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"]
}