lean-hit-development

Add a new Higher Inductive Type by defining axioms for point and path constructors, implementing recursion principles with computation rules, and building an encode/decode scheme between π₁ and a group presentation. Follow established HIT patterns like Circle or Torus for consistency.

Encode/decode schemes establish a correspondence between the fundamental group π₁ of a space and an abstract group presentation. Encoding maps paths to group elements; decoding reconstructs paths from presentations, enabling computational manipulation of topological invariants.

Yes. Recursion principles with β-rules and computation rules are required for every HIT. They specify how functions eliminate into the type and ensure their behavior on constructors, enabling sound inductive reasoning over the space.

Define base point constructors and loop constructors as axioms. For S¹, declare a base point and one loop; for T², add two commuting loops. Wrap the result in SimpleEquiv packaging and register the piOneEquiv to make the structure accessible.

Group presentations abstract the algebraic structure of π₁ for a HIT. The encode/decode interface maps between concrete HIT paths and presentation generators, allowing topological computations to leverage group-theoretic algorithms and simplifications.

Yes. Existing Circle, Torus, and Sphere implementations provide proven patterns for axiomatization, recursion principles, and encode/decode design. Following these templates ensures consistency and reduces the risk of axiom inconsistency in new HIT declarations.