Invariant Analyzer Skill

Purpose

Identify and verify loop invariants to help construct correctness proofs for algorithms.

Capabilities

• Automatic loop invariant inference
• Invariant verification against code
• Precondition/postcondition extraction
• Generate formal proof structure
• Identify missing invariants

Target Processes

• correctness-proof-testing
• algorithm-implementation

Invariant Analysis Framework

Loop Invariant Properties

1. Initialization: True before first iteration
2. Maintenance: If true before iteration, true after
3. Termination: Provides useful property at end

Common Invariant Patterns

• Range invariants: "for all i in [0, k), property P(i) holds"
• Accumulator invariants: "sum equals sum of a[0..k-1]"
• Pointer invariants: "left < right and all elements < left are processed"
• State invariants: "data structure maintains property X"

Input Schema

{
  "type": "object",
  "properties": {
    "code": { "type": "string" },
    "language": { "type": "string" },
    "loopIndex": { "type": "integer" },
    "expectedInvariant": { "type": "string" }
  },
  "required": ["code"]
}

Output Schema

{
  "type": "object",
  "properties": {
    "success": { "type": "boolean" },
    "invariants": { "type": "array" },
    "preconditions": { "type": "array" },
    "postconditions": { "type": "array" },
    "proofOutline": { "type": "string" }
  },
  "required": ["success"]
}