Introduction to First-Class Functions

• In order to appreciate the utility of first-class functions, we need to properly understand what “functional programming” is first.

  1. No mutation
  2. Functions can be used as values (first-class functions)
  3. Style encourages recursion
  4. Style is closer to mathematical functions
  5. Programming idioms use laziness (lazy evaluation?)

• First-class functions are functions that can be used wherever we can use values.

  • They can be used as parts of data structures (e.g. lists and tuples).
  • They can be passed as an argument to another function.
  • They can also be returned as a result from another function.

<aside> 🆙 A function that takes a first-class function as an argument is known as a higher-order function. Higher-order functions are very useful in storing code that will be reused (with different first-class functions as arguments).

</aside>

• Afterwards, we’ll touch on the idea of function closures as well.
  • Function closures are nested functions that can use bindings from outside the function definition/scope.
  • Closures are usually nested functions that use bindings from its enclosing function.
  • It’s important to note that there is a distinct conceptual difference between first-class functions and closures (although the two are confused for each other).

Functions as Arguments

• Functions can be passed as arguments to other functions.

  fun f (g...) = ... g (...) ...
  fun h1 ... = ...
  fun h2 ... =
  	... f (h1,...) ... f (h2,...) ...
  

• In what situations do we use functions as arguments?

  • When we have multiple functions which share similar structures, we can factor out the structure and replicate the functionality of the original functions through the use of a higher-order function.

  • In the words of Dr. Grossman:

    ”Replace N similar functions with calls to 1 function where you pass in N different (short) functions as arguments”

  • In the example above, the “similar” functions are the “lame” functions, the common function is n_times, and the short functions used as arguments are incr, double, and tl.