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;;             U. C. Berkeley            ;;
;;      EECS Computer Science Division   ;;
;;  CS3 Lecture 14 (Lambdas) Answers     ;;
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;; Square
;;;;;;;;;

(define (square x)
  (* x x))
;; ==> square

;; Now let's redefine square using lambdas...

(define square 
  (lambda (x) (* x x)))
;; ==> square

(        square         3 ) ;; ==>  9
( (lambda (x) (* x x))  3 ) ;; ==>  9

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;; Lambda with multiple or no args
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(lambda () 'cal) 
;; ==> #[procedure #x18F0794]

((lambda () 'cal))
;; ==> cal

((lambda (a b) (+ a b)) 4 5)
;; ==> 9

;;;;;;;;;;;;;;;;;;;;;;
;; The truth about let
;;;;;;;;;;;;;;;;;;;;;;

(let ((a 4)
        (b 5))
    (+ a b))
;; ==> 9

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;; Functionals - squaring
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(every         square       '(1 2 3 4)) ;; ==> (1 4 9 16)
(every (lambda (x) (* x x)) '(1 2 3 4)) ;; ==> (1 4 9 16)

;;;;;;;;;;;;;;;;
;; add-1-to-sent
;;;;;;;;;;;;;;;;

;; The long way

(define (add-1-to-sent S)
  (every add-1 S))

(define (add-1 num)
  (+ num 1))

(add-1-to-sent '(1 2 3)) ;; ==> (2 3 4)

;; The short way

(define (add-1-to-sent S)
  (every (lambda (num) (+ num 1)) S))
  
(add-1-to-sent '(1 2 3)) ;; ==> (2 3 4)

;;;;;;;;;;;;;;;;
;; add-n-to-sent
;;;;;;;;;;;;;;;;

;; add-n-to-sent
;;
;; Example: (add-n-to-sent 5 '(1 2 3)) ==> (6 7 8)

(define (add-n-to-sent n S)
   (every add-n S))

;; First dead-end attempt

(define (add-n num)
  (+ num n))

(add-n-to-sent 5 '(1 2 3))
;; ==> *** ERROR IN add-n -- Unbound variable: n

;; Why is this wrong? 
;; ==> n is not known within add-n,
;; ==> only within add-n-to-sent

;; Second dead-end attempt

(define (add-n num n)
  (+ num n))

(add-n-to-sent 5 '(1 2 3))
;; ==> *** ERROR -- Wrong number of arguments passed to procedure

;; Why is this wrong?
;; ==> add-n can only have one argument!

;; Third (and final) attempt

(define (add-n-to-sent n S)
  (every (lambda (num) (+ num n)) S))

(add-n-to-sent 5 '(1 2 3)) ;; ==> (6 7 8)

;; Is lambda just convenient or is it necessary? 
;; ==> necessary, as far as you know

;;;;;;;;;;;;;;;;
;; add-1-to-odds
;;;;;;;;;;;;;;;;

;; Example:
;;
;; (add-1-to-odds '(1 out of 3 likes u 2 and u b 40))
;; ==> (2 out of 4 likes u 2 and u b 40)

(define (add-1-to-odds S)
  (every 
    (lambda (w)
      (if (and (number? w) 
               (odd? w))
          (+ 1 w)
          w))
    S))
  
(add-1-to-odds '(1 out of 3 likes u 2 and u b 40))
;; ==> (2 out of 4 likes u 2 and u b 40)

;; Is lambda just convenient or is it necessary? 
;; ==> just convenient

;;;;;;;;;;;;
;; all-letter-twister?
;;;;;;;;;;;;

;; Example:
;;
;; (all-letter-twister? 'r '(rubber bumper baby buggy)) ==> #f
;; (all-letter-twister? 's '(six sheiks sixth sheeps sick)) ==> #t

(define (all-letter-twister? letter S)
  (all? (lambda (word)
          (equal? (first word) letter))
        S))

(all-letter-twister? 'r '(rubber bumper baby buggy))
;; ==> #f
(all-letter-twister? 's '(six sheiks sixth sheeps sick))
;; ==> #t


;; Is lambda just convenient or is it necessary? 
;; ==> necessary, as far as you know