#lang racket

;; higherorder.rkt

;; CS 313 - higher-order functions

; compute sum of (f x) for x = lo .. hi, incrementing x by calling (next x)
(define (sumfun f next lo hi)
  (if (> lo hi)
      0
      (+ (f lo)
         (sumfun f next (next lo) hi))))

(define (square x)
  (* x x))

(define (add1 x)
  (+ x 1))

; (sumfun square add1 3 6)

; using lambda:
; (sumfun (lambda (x) (* x x))
;         (lambda (x) (+ x 1))
;        3 6)

; 'map' the function f to each element in mylist
; (equivalent to the built-in function map)
(define (mymap f mylist)
  (if (null? mylist)
      '()
      (cons (f (car mylist)) (mymap f (cdr mylist)))))

; (mymap square '(1 2 3 10))
; -> '(1 4 9 100)

; (mymap (lambda (x) (+ x 10)) '(1 2 3 10))
; -> '(11 12 13 20)