Usefulness of generic representative abstractions in mathlib

Identify the circumstances in which abstracting representative-selection constructions along the type axis is more useful than misleading, and determine the additional use cases that would justify introducing such an abstraction in mathlib.

Background

The paper examines whether constructions for selecting representatives of connected components should be generalized from the specific ConnectedComponent type to arbitrary quotient types. Although the generic abstraction is technically possible, it was rejected in the discussed development because of concerns about misuse in other contexts.

The authors nevertheless hypothesize that type-axis abstraction may be worthwhile. They state that its appropriate formulation and placement depend on identifying further use cases and recognizing when the abstraction clarifies rather than misleads. Those use cases and circumstances are not known.

References

We hypothesize that an abstraction along the type axis is still worthwhile. However, including it would require identifying the circumstances in which this notion is more useful than misleading.

— Tutte's theorem as an educational formalization project  (2504.18146 - Otte, 25 Apr 2025) in Section 3.2.2, subsection “Example: Abstraction of representatives”