proof-assistant

Testing & Quality

Assist in constructing algorithm correctness proofs

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Source SKILL.md: https://github.com/a5c-ai/babysitter/blob/HEAD/library/specializations/algorithms-optimization/skills/proof-assistant/SKILL.md

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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

{
  "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

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