aoa-property-invariants

Intent

Use invariant-oriented thinking to test broad behavior through properties rather than only through a short list of fixed examples.

Trigger boundary

Use this skill when:

• a rule should hold across many inputs or states
• examples alone feel too narrow
• the system has conservation, monotonicity, idempotency, or structural invariants
• safety or correctness depends on broad input coverage

Do not use this skill when:

• the behavior is mostly about presentation details or narrow snapshots
• the main problem is checking whether existing checks really cover the invariant; use aoa-invariant-coverage-audit first
• the main problem is a boundary contract rather than a stable invariant; use aoa-contract-test
• no meaningful invariant is yet understood

Inputs

• target rule or domain truth
• current examples or tests
• input space or generators
• known edge cases

Outputs

• explicit invariants
• property-oriented tests or checks
• notes on generator assumptions
• verification summary

Procedure

1. identify what must remain true across many cases
2. separate strong invariants from weak hopes or vague expectations
3. express those invariants as property-oriented tests or repeated checks
4. keep the generators or inputs bounded and reviewable
5. run the checks and report what properties now constrain behavior

Contracts

• each property should express a real invariant, not a wish
• the test should broaden coverage beyond a small handpicked set
• generator assumptions should remain understandable

Risks and anti-patterns

• writing weak properties that prove almost nothing
• confusing random data with meaningful coverage
• letting overly broad generators or harness complexity hide the protected domain truth
• using polished invariant language while the actual stable truth remains underspecified
• using property checks where a small set of concrete examples would be clearer
• using invariant language to avoid naming the actual rule or boundary that matters

Verification

• confirm the property expresses a meaningful invariant
• confirm the invariant broadens coverage beyond fixed examples
• confirm the report names which stable truth was violated or protected, not only that generated inputs failed
• confirm the result is understandable to another human or agent

Technique traceability

Manifest-backed techniques:

• AOA-T-0017 from 8Dionysus/aoa-techniques at 5c6f0496edc3c2e74590baa35627c85fe58ef765 using path techniques/evaluation/property-invariants/TECHNIQUE.md and sections: Intent, When to use, Inputs, Outputs, Core procedure, Contracts, Risks, Validation
• AOA-T-0007 from 8Dionysus/aoa-techniques at 5c6f0496edc3c2e74590baa35627c85fe58ef765 using path techniques/evaluation/signal-first-gate-promotion/TECHNIQUE.md and sections: summary, Validation

Adaptation points

Project overlays should add:

• local generator tools
• domain-specific invariants
• rules for when property-based checks are mandatory, optional, or out of scope