Related-Input Invariant Oracle

These examples and illustrative results are independently authored teaching materials, not measured model results.

Use case

A normalizer sorts without dropping records; teaching IDs are b,a,c. A single two-record example misses order dependence/loss, so add contract-supported relational predicates.

Mechanism

Hand-check a,b,c and declare idempotence, permutation invariance and multiset preservation. Test originals, permutations and larger boundaries. Treat duplicate IDs under contract rather than a set hiding lost duplicates. Save minimized failure/transformation while retaining exact anchors. Do not invent unsupported properties.

Bad example

Check only[a,b], or idempotence alone, calling constant-empty output correct.

Good example

Keep b,a,c→a,b,c as an independent fixture. Check permutation equality, second normalization stability and multiset preservation. Include duplicate counts under contract and ensure constant-empty cannot pass combined assertions.

Why the change matters

Relations cover input transformations, while correct anchors/preservation prevent degenerate passes. They test behavioral connections rather than one output label.

Observable expectation

Teaching b,a,c normalizes to a,b,c and remains unchanged afterward. Dropping c violates preservation; constant-empty is idempotent but fails the anchor/multiset. Order-dependent behavior violates permutation invariance. These are expectations, not measured runs.

Limits

Use only contractual relations; deduplication or input-order preservation changes them. Properties do not prove all-input correctness and generators can miss boundaries. Minimization must preserve failure meaning.