How write a function that returns a list of 'n' functions based on an input

Question

I'm looking to create a function that returns a list of 'n' functions each of which increments the input by 1, 2, 3... n respectively.

I use DrRacket to try this out. A sample of expected outcome :

> (map (lambda (f) (f 20)) (func-list 5))
(21 22 23 24 25)

I'm able to write this down in a static-way :

> (define (func-list num)
> (list (lambda (x) (+ x 1)) (lambda (x) (+ x 2)) (lambda (x) (+ x 3)) (lambda (x) (+ x 4)) (lambda (x) (+ x 5)))

[Edit]

Also that a few restrictions are placed on implementation :

1. Only 'cons' and arithmetic operations can be used
2. The func-list should take as input only one parameter ('n' being the number of functions to be returned in this case)

It would be great if somebody can help me out. Thanks in advance.

Answer 1

Instead of explicitly writing out the list, a better approach would be to recursively construct it for an arbitrary n, as follows:

(define (func-list n)
  (define (func-lst a n)
    (if (> a n)
        empty
        (cons (lambda (x) (+ x a))
              (func-lst (add1 a) n))))
  (func-lst 1 n))

For example:

> (map (lambda (f) (f 20)) (func-list 0))
'()
> (map (lambda (f) (f 20)) (func-list 5))
'(21 22 23 24 25)