#lang racket
(require rackunit)

; -----------------------------------------------------------------------
; Racket functions are bound to names in the same way as any other value!
; In this expression, + is a free variable:
; 
; (lambda (x y)
;   (+ (* x x) (* y y)))))
;
; You can verify that + is free for yourself by evaluating:

(define capture-+             ; receives a function as an argument,
  (lambda (+)                 ; ** binds it to + **,
    (lambda (x y)
      (+ (* x x) (* y y)))))  ; and uses + here.

(define sum-of-squares (capture-+ *))          ; pass in *

;(check-equal? (sum-of-squares 3 4) 25)        ; 9 + 16 = 25, right?

; -----------------------------------------------------------------------
; Try these in the REPL.  Dr. Racket provides strong support for software
; engineering by not letting us do this sort of mental gymnastics in our
; programs.

; (if (zero? 0) 1 foo)     ; foo cannot be reached

; (and #f foo)             ; foo cannot be reached

; (
;   (lambda (x)            ; this function ignores its argument...
;     (lambda (z) z))
;   (lambda (x) foo)       ; ... so foo cannot be reached
; )

; See:
;
; (((lambda (x) (lambda (z) z))
;   (lambda (x) foo))
;  'x)