high order function transform example 1

cartesian_product1.hs

module Cartesian_product1 where
import Prelude hiding(product)
 
product1 [] = [[]]
product1 (xs:xss) = 
  h xs (product1 xss) where
    h [] xss = []
    h (x : xs) xss =
      map (x:) xss ++ h xs xss
      

mapa :: (b -> a) -> [a] -> [b] -> [a]
mapa g z l = foldr f z l where
    f x y = (g x) : y 
    
 
product2 [] = [[]]
product2 (xs:xss) = 
  h xs (product2 xss) where
    h [] xss = []
    h (x:xs) xss =
      mapa (x:) (h xs xss) xss
      
 
product3 [] = [[]]
product3 (xs:xss) = 
  h xs (product3 xss) where
    h [] xss = []
    h (x:xs) xss =
      foldr f (h xs xss) xss where 
          f xs yss = (x:xs):yss


-- some as cartProdN8 in Cartesian_product2

          
product4 [] = [[]]
product4 (xs:xss) = 
  h xs (product4 xss) where
   h xs yss = foldr g [] xs where
     g x zss = foldr f zss yss where 
         f xs yss = (x:xs):yss 

--- product4 have the same struct like foldr

product5 xss = 
  foldr h [[]] xss where 
    h xs yss = foldr g [] xs where 
      g x zss = foldr f zss yss where 
         f xs yss = (x:xs):yss