upDown_1.hs

up = (1:)
down = (-1:)
done = []

states = scanl (+) 0

minMaxEnd commands = 
  let s = states commands
   in (minimum s, maximum s, last s)

example = up.up.up.down.down.up $ done

exampleStates = states example

upDown_2.hs

import Control.Applicative
import Control.Monad.Free

data Command a = Up a | Down a deriving (Eq, Show, Functor)

type Sequence = Free Command ()

up, down :: Sequence -> Sequence
up = Free . Up
down = Free . Down

done :: Sequence
done = Pure ()

go = ($done)

example1 = up . up . down . up $ done

example2 = do
  go up
  go up
  go down
  go up

-- example1 == example2

toList :: Num a => Sequence -> [a]
toList = iter f . fmap (const [])  where
  f (Up xs) = 1 : xs
  f (Down xs) = -1 : xs