In functional programming, the concept of catamorphism (from the Ancient Greek: κατά "downwards" and μορφή "form, shape") denotes the unique homomorphism from an initial algebra into some other algebra.
Catamorphisms provide generalizations of folds of lists to arbitrary algebraic data types, which can be described as initial algebras. The dual concept is that of anamorphism that generalize unfolds. A hylomorphism is the composition of an anamorphism followed by a catamorphism.