How to write a procedure?

How do you write a procedure that outputs a function? (Racket)

• How do you write a procedure that outputs a function? (Racket) Would the procedure output a lambda?

• Answer:

  Do you mean: how do I use higher-order functions in order to yield another function? If this is so, take a look at this: (lambda (f) (lambda (x) (f x))) What this does is: 1: create an anonymous closure initialized with "f" as a parameter 2: within the scope of the first body, create a closure with "x" as a parameter 3: apply f to x (f being the closure on top of x) What this means is that (before (f x) is evaluated), f is declared as a function with x as its argument. Applying f to x is what this whole expression returns: in this case, nothing much since we haven't assigned any value except closures. Using this as a start point, consider what happens when a closure returns another closure: the inner closure gets evaluated AFTER the outter closure has passed its value around in its body. It's called delayed evaluation and permits one to pass procedures as values so that the inner procedure can expand later. Here's a concrete example of how benefic this can be. Let's define cons, car and cdr using only higher-order functions (closures): (define (cons kar kdr) (lambda (kons) (kons kar kdr))) (define (car kons) (kons (lambda (kar kdr) kar))) (define (cdr kons) (kons (lambda (kar kdr) kdr))) To understand this, pass the definitions around but remember that (define (foo bar) ...) means (define foo (lambda (bar) ...))...