Efficient generalized folds

Fold operators capture a common recursion pattern over algebraic datatypes. A fold essentially replaces constructors by functions. However, if the datatype is parameterized, the corresponding fold operates on polymorphic functions which severely limits its applicability. In order to overcome this limitation R. Bird and R. Paterson (Bird and Paterson, 1999b) have proposed so-called generalized folds. We show how to define a variation of these folds by induction on the structure of datatype definitions. Unfortunately, for some datatypes generalized folds are less efficient than one would expect. We identify the source of inefficiency and explain how to remedy this shortcoming. While conceptually simple, our approach places high demands on the type system: it requires polymorphic recursion, rank-2 types, and a strong form of type constructor polymorphism. (orig.)SIGLEAvailable from TIB Hannover: RR 6944(99-8) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman