foldr, foldl, map, reduce

• Rechnung beginnt am rechten Ende

  foldr :: (a -> b -> b) -> b -> [a] -> b
  foldr (-) 0 [1,2,3] = 2
  

• Rechnung beginnt am linken Ende:

  foldl :: (b -> a -> b) -> b -> [a] -> b
  foldl (-) 0 [1,2,3] = -6
  

• für assoziative Operation, beliebige Klammerung:

  reduce :: b -> (b -> b -> b) -> [b] -> b
  

• mit elementweiser Transformation (map):

  foldb :: b->(a->b)->(b->b->b)-> [a] -> b
  map   :: (a -> b) -> [a] -> [b]
  foldb n f g xs = reduce n g ( map f xs )