Quotients of Bounded Natural Functors

The functorial structure of type constructors is the foundation for many definition and proof principles in higher-order logic (HOL). For example, inductive coinductive datatypes can be built modularly from bounded natural functors (BNFs), a class well-behaved constructors. Composition, fixpoints, and, under certain conditions, subtypes are known to preserve BNF structure. In this article, we tackle preservation question quotients, last important principle introducing new types HOL. We identify sufficient conditions which quotient inherits its underlying type. Surprisingly, lifting obvious manner fails some problem that also affects quotients polynomial used Lean assistant. provide strictly more general scheme supports such problematic quotients. extend Isabelle/HOL assistant with command automates registration as BNF, reducing burden on user full set axioms our inheritance conditions. demonstrate command's usefulness through several case studies.