What is "catamorphism"

n. (context computer science English) a generalization of the folds on lists known from functional programming to arbitrary abstract data types that can be described as initial algebras

In category theory, the concept of catamorphism (from Greek: κατά = downwards or according to; μορφή = form or shape) denotes the unique homomorphism from an initial algebra into some other algebra.

In functional programming, 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.