Zygohistomorphic prepromorphisms

Zygohistomorphic prepromorphisms are an intentionally overcomplicated combination of recursion-schemes concepts that started as a joke.

Used when you really need both semi-mutual recursion and history and to repeatedly apply a natural transformation as you get deeper into the functor. Zygo implements semi-mutual recursion like a zygomorphism. Para gives you access to your result à la paramorphism.

import Control.Morphism.Zygo
import Control.Morphism.Prepro
import Control.Morphism.Histo
import Control.Functor.Algebra
import Control.Functor.Extras

zygoHistoPrepro 
  :: (Unfoldable t, Foldable t) 
  => (Base t b -> b) 
  -> (forall c. Base t c -> Base t c) 
  -> (Base t (EnvT b (Stream (Base t)) a) -> a) 
  -> t
  -> a
zygoHistoPrepro f g t = gprepro (distZygoT f distHisto) g t
-- unless you want a generalized zygomorphism.