[willtim]

> Ah ha, but you see, you can perform transformations on tagless-final terms that are not strict catamorphisms ... so matching two levels deep is possible.

No this is not correct. Oleg provides a solution to double negation by creating a catamorphism that folds to a function. It's still a catamorphism. And folding to a function is not something the average Java programmer is likely to understand easily.

[siraben]

Right, so it's not that it's not possible but rather it's somewhat awkward to express non-compositional folds in the final approach. I'm not currently aware of a mechanical way to do the translation.

[willtim]

Yes, I'm claiming the restriction will be too much for many people, assuming we are trying to create a new language here. However, expressing a solution as a catamorphism is a good thing to do and helps reasoning. It's a form of structured programming (recursion is the "goto" of functional programming!).