Higher order functions

Higher order functions

1. caracteristics

   • :: (a -> a) -> a -> a
     • Before, we didn't need parentheses because -> is naturally right-associative.
       • buy here they're mandatory
     • ndicate that the first parameter is a function that takes something and returns that same thing
     • The second parameter is something of that type also and the return value is also of the same type
   • In the body
     • applyTwice f x = f (f x) rocktopus
       • use the parameter f as a function, applying x to it by separating them with a space and then applying the result to f again

2. Haskell functions can take functions as parameters and return functions as return values

   • If the function requires us to pass it a function that takes only one paramete
     • we can just partially apply a function to the point where it takes only one parameter and then pass it.

3. a single higher order function can be used in very versatile ways.

   • Imperative programming usually uses stuff like for loops, while loops, setting something to a variable, checking its state

4. Maps and filters

   • map takes a function and a list and applies that function to every element in the list
     • producing a new list
       • map :: (a -> b) -> [a] -> [b] map _ [] = [] map f (x:xs) = f x : map f xs
   • is similar with a list comprehension
     • but using map is much more readable
   • filter is a function that takes a predicate
     • that is a function that tells whether something is true or not
       • and return a list and then returns the list of elements that satisfy the predicate
         • ilter :: (a -> Bool) -> [a] -> [a] filter _ [] = [] filter p (x:xs) | p x = x : filter p xs | otherwise = filter p xs

5. Lambdas

   • are anonymous functions that are used because we need some functions only once
     • the purpose is passing it to a higher-order function
   • To make a lambda, we write a \
     • then we write the parameters, separated by spaces
       • After put a -> and then the function body.