; binding of variables in lambda expressions

; what is the result of evaluating (foo 2) in each case

; Case 1
(define y 1) ;; y is bound in the global scope

; foo is bound in the global scope, x is local, y is free
(define foo (lambda (x) (+ x y))) 

(foo 2)

; Case 2
(define y 2) ;; change the binding of y
(foo 2) ;; re-evaluate foo

; Case 3
(define y 3) ;; change the binding of y again
(foo 2) ;; re-evaluate foo

; Case 4
(let ((y 4)) (foo y)) ;; let creates local bindings only.
(foo 2)

; Case 5
(define foo 
  (let ((y 4)) ;; y is now bound locally inside of foo
    (lambda (x) (+ x y))))

(foo 2)

;; in scheme, we often write "helper" functions that do some of the
;; work of a main function. Rather than populating the global namespace
;; with these helper functions, we can lexically nest them inside the
;; scope of the main function. For example, instead of
;; defining tfact as a global name to be called by the
;; function fact, we can used a NAMED LET and nest it inside
;; the definition of fact:

(define tfact
  (lambda (n m)
    (if (= n 0) m
        (tfact (- n 1) (* n m)))))

(define fact
  (lambda (n) (tfact n 1)))
    
;; using a named let
(define fact
   (lambda (n)
       (let tfact ((n n) (m 1)) ;; tfact is local to fact
	    (if (= n 0) m
                (tfact (- n 1) (* n m))))))

(fact 10)