a5c-ai 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"]
}