;; Be sure to set the Language Level to Beginner
;; Run this file using "Step", not "Execute".


;; sum:  lon -> num
;; Sums the numbers in a lon.

(define (sum a-lon)
  (cond
    [(empty? a-lon) 0]
    [(cons? a-lon) (+ (first a-lon) (sum (rest a-lon)))]))

"sum tests:"
(define myLON (cons 10 (cons 15 empty)))

;; this line is so you can see the stepper evaluate the function:
(sum myLON)


"Hand evaluation check: "
;; Note the inclusion of which Law of Scheme is at work.

(=
 
;; initial function invocation 
(sum myLON)

;; substitute in for placeholder - Law of Scheme for Placeholders:
(sum (cons 10 (cons 15 empty)))

;; substitute definition of function for function call -- Law of Scheme for functions:
(cond
 ((empty? (cons 10 (cons 15 empty))) 0)
 ((cons?  (cons 10 (cons 15 empty))) (+ (first(cons 10 (cons 15 empty))) (sum (rest (cons 10 (cons 15 empty)))))))

;; The stepper puts a few extra steps in here to show that it is evaluating the first statement in the cond.
;; These steps that may be omitted.

;; Evaluate conditional expression first -- Law of Scheme for cond:
(cond
 (false 0)
 ((cons?  (cons 10 (cons 15 empty))) (+ (first(cons 10 (cons 15 empty))) (sum (rest (cons 10 (cons 15 empty)))))))

;; If false, go to next conditional expression -- Law of Scheme for cond:
(cond
  ((cons?  (cons 10 (cons 15 empty))) (+ (first(cons 10 (cons 15 empty))) (sum (rest (cons 10 (cons 15 empty)))))))

;;  Evaluate conditional expression first -- Law of Scheme for cond:
(cond
  (true (+ (first(cons 10 (cons 15 empty))) (sum (rest (cons 10 (cons 15 empty)))))))

;; Subsitute return value of function (cond here)-- Law of Scheme for functions:
(+ (first(cons 10 (cons 15 empty))) (sum (rest (cons 10 (cons 15 empty)))))

;; Evaluate inner expressions first - Law of Scheme for functions:
(+ 10 (sum (rest (cons 10 (cons 15 empty)))))

;; Evaluate inner expressions first - Law of Scheme for functions:
(+ 10 (sum (cons 15 empty)))

;; Substitute definition of function for function call -- Law of Scheme for functions:
(+ 10 (cond
  ((empty? (cons 15 empty)) 0)
  ((cons? (cons 15 empty)) (+ (first (cons 15 empty)) (sum (rest (cons 15 empty)))))))

;; Stepper steps left out again.

;; Evaluate conditional expression first -- Law of Scheme for cond:
(+ 10 (cond
  (false 0)
  ((cons? (cons 15 empty)) (+ (first (cons 15 empty)) (sum (rest (cons 15 empty)))))))

;; If false, go to next conditional expression -- Law of Scheme for cond:
(+ 10 (cond
  ((cons? (cons 15 empty)) (+ (first (cons 15 empty)) (sum (rest (cons 15 empty)))))))

;; Evaluate conditional expression first -- Law of Scheme for cond:
(+ 10 (cond
  (true (+ (first (cons 15 empty)) (sum (rest (cons 15 empty)))))))

;; Subsitute return value of function (cond here)-- Law of Scheme for functions:
(+ 10 (+ (first (cons 15 empty)) (sum (rest (cons 15 empty)))))

;; Evaluate inner expressions first - Law of Scheme for functions:
(+ 10 (+ 15 (sum (rest (cons 15 empty)))))

;; Evaluate inner expressions first - Law of Scheme for functions:
(+ 10 (+ 15 (sum empty)))

;; Substitute definition of function for function call -- Law of Scheme for functions:
(+ 10 (+ 15 (cond
   ((empty? empty) 0)
   ((cons? empty) (+ (first empty) (sum (rest empty)))))))

;; Evaluate conditional expression first -- Law of Scheme for cond:
(+ 10 (+ 15 (cond
  (true 0)
  ((cons? empty) (+ (first empty) (sum (rest empty)))))))

;; Subsitute return value of function (cond here)-- Law of Scheme for functions:
(+ 10 (+ 15 0))

;; Evaluate inner expressions first - Law of Scheme for functions:

(+ 10 15)

;; Apply function -- Law of Scheme for functions-- one more time to get the answer -- finally!  whew!
25

)

;; BE NICE TO YOUR GRADER:  UNDERLINE THE EXPRESSION THAT IS GOING TO BE EVALUATED NEXT (Just as the stepper does).  --- Your graders thank you!