;; The first three lines of this file were inserted by DrRacket. They record metadata
;; about the language level of this file in a form that our tools can easily process.
#reader(lib "htdp-beginner-reader.ss" "lang")((modname lect17-cond-semantics-stepper) (read-case-sensitive #t) (teachpacks ()) (htdp-settings #(#t constructor repeating-decimal #f #t none #f ())))
(require "student-extras.rkt")

; - review: using local variables (or not)
; - syntax/semantics of `cond`, w/o '...'
; - stepping through my-max (w/ and w/o `let`)


;; We re-write the following to use 0,1,2 or 3 local variables, via `let*`:

; downcased-initial : string -> string
; Given a *non-empty* string `w`,
; return its first character, downcased.
;
#;(define (downcased-initial w)
    (string (char-downcase (string-ref w 0)))) 


;; Step through this:
;(downcased-initial "hello")


#| Syntax,semantics of `cond`:

 A <cond-expr> is:
     (cond <qas>)

 A <qas> ("question/answers") is either:
   - ε                          (that's our notation for 'nothing at all')
   - [<expr_q> <expr_a>]
     <qas>


Semantics of `cond`:
  eval of (cond <qas>) returns:
    - if <qas> is ε, then: semantics say trigger a run-time error.
    - if <qas> is   [<expr_q> <expr_a>] <qas>, then:
        eval <expr_q>;
          If true:  return result of eval'ing <expr_a>.
          If false: return result of eval'ing (cond <qas>).

|#




;;;;;;;;;;;;;;; my-max



; my-max : list-of-number -> number 
; Return the largest number in `a-lon`.
;
(define (my-max a-lon)
  (cond [(empty? a-lon) -inf.0]
        [(cons? a-lon)  
         (let* {[max-of-rest  (my-max (rest a-lon))]}
           (if (> max-of-rest (first a-lon))
               max-of-rest
               (first a-lon)))]))

; The point of `let`:
;  - avoid repeated calculation!  
;  - name a sub-part of the overall problem.


(define (root a b c)
  (/ (+ (- b) (sqrt (- (sqr b) (* 4 a c))))
     (* 2 a)))

; vs:
(define (root2 a b c)
  (let* {[discriminant (- (sqr b) (* 4 a c))]
         [numerator    (+ (- b) (sqrt discriminant))]
         [denominator  (* 2 a)]}
    (/ numerator denominator)))

(my-max (cons 1 (cons 2 empty)))

(my-max (cons -18 (cons -17 (cons -16 (cons -15 (cons -14 (cons -13 (cons -12 (cons -11 (cons -10 (cons -9 (cons -8 (cons -7 (cons -6 (cons -5 (cons -4 (cons -3 (cons -2 (cons -1 empty)))))))))))))))))))

(my-max (cons -23 (cons -22 (cons -21 (cons -20 (cons -19 (cons -18 (cons -17 (cons -16 (cons -15 (cons -14 (cons -13 (cons -12 (cons -11 (cons -10 (cons -9 (cons -8 (cons -7 (cons -6 (cons -5 (cons -4 (cons -3 (cons -2 (cons -1 empty))))))))))))))))))))))))