Narya: A proof assistant for higher-dimensional type theory (GitHub)

Narya is eventually intended to be a proof assistant implementing Multi-Modal, Multi-Directional, Higher/Parametric/Displayed Observational Type Theory, but a formal type theory combining all those adjectives has not yet been specified. At the moment, Narya implements a normalization-by-evaluation algorithm and typechecker for an observational-style theory with Id/Bridge types satisfying parametricity, of variable arity and internality. There is a parser with user-definable mixfix notations, and user-definable record types, inductive datatypes and type families, and coinductive codatatypes, with functions definable by matching and comatching case trees.