Higher order functions

Higher order functions

1. Curried functions

   • functions that accepted several parameters
     • space = operator
       • has the highest precedence
   • max 4 5 = (max 4) 5
   • -> (a -> a)
     • a function that takes an a and returns an a

2. Functions that:

   • take functions as parameters
     • applyTwice :: (a -> a) -> a -> a applyTwice f x = f (f x)
       • the first parameter is a function that takes something and returns that same thing
     • map
       • takes
         • function
           • &&
             • List
               • map :: (a -> b) -> [a] -> [b]
       • applies the function to every element in the list
         • producing a new list.
         • map _ [] = []
           • map f (x:xs) = f x : map f xs
     • filter
       • takes
         • predicate
           • &&
             • List
           • filter :: (a -> Bool) -> [a] -> [a]
       • returns the list of elements that satisfy the predicate
         • filter _ [] = []
           • filter p (x:xs)
             • | p x = x : filter p xs
               • | otherwise = filter p xs
   • return functions as return values

3. Lambdas

   • anonymous functions
     • expressions too
   • need a function only once?
   • \

4. Folders

   • reduce the list to some single value.
     • takes
       • binary function
         • takes 2 parameters
       • starting value
       • list
   • fold1
     • folds the list up from the left side
   • foldr
     • folds the list up from the right side

5. function application

   • $
   • lowest precedence
   • right-associative.

6. Function composition

   • (f o g) (x)
     • (f (g(x))
   • two functions produces a new function
     • when called with a parameter,
       • is like calling g with the parameter and then calling the f with that result.
   • .