Example of using an anamorphism (with helper catamorphism)

Anamorphism.hs

{-# LANGUAGE BlockArguments,DeriveFunctor,LambdaCase,ScopedTypeVariables,NoImplicitPrelude #-}

import Control.Arrow
import Prelude hiding (replicate)

newtype Fix f = In { out :: f (Fix f) }

type FAlgebra f a = f a -> a
cata :: (Functor f) => FAlgebra f a -> Fix f -> a
cata f = out >>> fmap (cata f) >>> f

type FCoAlgebra f a = a -> f a
ana :: (Functor f) => FCoAlgebra f a -> a -> Fix f
ana f = In <<< fmap (ana f) <<< f

-- ==========

data List a f
  = Cons a f
  | Nil
  deriving Functor

replicate :: forall a. Int -> a -> Fix (List a)
replicate n a = ana go n where
  go :: FCoAlgebra (List a) Int
  go 0 = Nil
  go n = Cons a (n - 1)

main = print $ len (replicate 10 'a')  -- "10"
 where len = cata \case
         Nil -> 0
         Cons _ rest -> 1 + rest