Diagrammatic notations for interactive theorem proving

Diagrams are ubiquitous in the development and presentation of proofs, yet surprisingly uncommon in computerized mathematics. Instead, authors and developers rely almost exclusively on line-oriented notations (textual abbreviations and symbols). How might we enrich interactive theorem provers with on-the-fly visual aids that are just as usable? We answer this question by identifying a key challenge: designing declarative languages for composable diagram templates, that provide good-looking implementations of common patterns, and allow for rapid prototyping of diagrams that remain stable across transformations and proof steps.