Revisiting Catamorphisms over Datatypes with Embedded Functions

We revisit the work of Paterson and of Meijer & Hutton, which describes how to construct catamorphisms for recur-sive datatype deenitions that embed contravariant occurrences of the type being deened. Their construction requires , for each catamorphism, the deenition of an anamor-phism that has an inverse-like relationship to that cata-morphism. We present an alternative construction, which replaces the stringent requirement that an inverse anamor-phism be deened for each catamorphism with a more lenient restriction. The resulting construction has a more eecient implementation than that of Paterson, Meijer, and Hutton and the relevant restriction can be enforced by a Hindley-Milner type inference algorithm. We provide numerous examples illustrating our method.