Lambda the Ultimate

For those who do not think that "catamorphism" sounds scary, Generic Accumulations paper presents a new flavor of fold: fold with accumulators (afold).

You might be acquainted with its cousin - pfold, or fold with parameters. Both come from the family of comonadic fold.

A homepage of Alberto Pardo contains more information on them.

PS: if you are new to fold or bananas/lenses, LtU papers page has a couple of introductory links.