Catamorphism Generation and Fusion Using Coq

Catamorphisms are a class of higher-order functions that recursively traverse an inductive data structure to produce a value. An important result related to catamorphisms is the fusion theorem, which gives sufficient conditions to rewrite compositions of catamorphisms. We use the Coq proof assistant to automatically define a catamorphism and a fusion theorem according to an arbitrary inductive type definition. Catamorphisms are then used to define functional specifications and the fusion theorem is applied to derive efficient programs that match those specifications.