chronomorphisms https://stackoverflow.com/questions/46525571/an-example-for-chronomorphism

chronomorphisms.txt

(This answer pilfers wholesale from [this other answer][1] its example of histomorphism on lists.)

A simple —and not very compelling— example of chronomorphism would be a "safe tail" function for run-length-encoded lists:

    tailRunLen :: [(Int,a)] -> Maybe [a]
    tailRunLen = chrono alg coalg
      where
        alg v = case v of
            Nil             -> Nothing -- empty list
            Cons _ (b :< x) -> case x of
                Nil       -> Just []   -- length 1 list
                Cons a _ -> fmap (a:) b
        coalg v = case v of
           [] -> Nil
           (i,a) : ias -> Cons a . foldr (.) id (replicate (pred i) $ Free . Cons a) $ Pure ias

The idea is that we use a futuromorphism to expand the list several items at a time 
(as many layers as the run-length for the element) and then use a histomorphism that 
lets us distinguish between the empty and 1-element list by "looking back two steps".

In action:

    λ tailRunLen [(2,'a'),(3,'b')]
    Just "abbb"
    λ tailRunLen []
    Nothing

  [1]: https://stackoverflow.com/a/24895262/1364288