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;;             U. C. Berkeley            ;;
;;      EECS Computer Science Division   ;;
;;         CS3 Lecture 04 Answers        ;;
;;    (Words, Sentences, True & False)   ;;
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;; WORDS AND SENTENCES
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;;;;;;;;;;
;; Quoting
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;;; Expressions, as we've seen

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

square
;; ==> #[procedure square]

cal
;; ==> *** ERROR -- Unbound variable: cal

(+ 1 2)
;; ==> 3

(this is a sentence)
;; ==> *** ERROR -- Unbound variable: this

;;; But what if I don't want to evaluate it, 
;;; but just take it literally? The answer: quote

(quote square)
;; ==> square

(quote cal)
;; ==> cal

(quote (+ 1 2))
;; ==> (+ 1 2)

(quote (this is a sentence))
;; ==> (this is a sentence)

;;; We use an abbreviation for it: '

'square
;; ==> square

(quote cal)
;; ==> cal

'(+ 1 2)
;; ==> (+ 1 2)

'(this is a sentence)
;; ==> (this is a sentence)

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; Selectors (of words and sentences)
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(first 501)
;; ==> 5

(first 'cal)
;; ==> c

(first '(cal is number 1))
;; ==> cal

(first (first '(cal is number 1)))
;; ==> c

(last 501)
;; ==> 1

(last 'cal)
;; ==> l

(last '(cal is number 1))
;; ==> 1

(butfirst 501)
;; ==> "01"
;; This is a number, even though it's in double-quotes

(* 795 (butfirst 501))
;; ==> 795

(bf 'cal)
;; ==> al

(bf '(cal is number 1))
;; ==> (is number 1)

(butlast 501)
;; ==> 50

(bl 'cal)
;; ==> ca

(bl '(cal is number 1))
;; ==> (cal is number)

(item 3 795)
;; ==> 5

(item 2 'cal)
;; ==> a

(item 1 '(cal is number 1))
;; ==> cal

;; second
;; 
;; Return the second element of word-or-sentence
;;
(define (second word-or-sentence)
   (first (butfirst word-or-sentence)))

(second '(cal is number 1))
;; ==> is

(second '795) 
;; ==> 9

;; but-first-two
;; 
;; Return all but the first two elements of word-or-sentence
;;
(define (but-first-two word-or-sentence)
   (butfirst (butfirst word-or-sentence)))

(but-first-two '(cal is number 1))
;; ==> (number 1)

;; How do I get m from '(cal is number 1)?
==>

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; Constructors (of words and sentences)
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(word 'owha "tagoo" 'siam 01 'huh?)
;; ==> owhatagoosiam1huh?

(word 9 02 10)
;; ==> 9210

(word 9 "02" 10)
;; ==> 90210

(sentence 'cal 'is 'number 1)
;; (cal is number 1)

(se '(cal is) (word 'num 'ber) '(1))
;; (cal is number 1)

;;;;;;;;;;;;;;;;;
;; TRUE AND FALSE
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;;;;;;;;;;;;;
;; Predicates
;;;;;;;;;;;;;

(member? 'i 'team)
;; ==> #f

(before? 'aardvark 'zebra)
;; ==> #t

(< 1 2 3) 
;; ==> #t

;;;;;;;;;;;;;;;;;
;; And / Or / Not
;;;;;;;;;;;;;;;;;

(and #t #f)
;; ==> #f

(or #t #f)
;; ==> #t

(and 1 2)
;; ==> 2

(or 1 2)
;; ==> 1

(and #f #f 3)
;; ==> #f

(or #f #f 3)
;; ==> 3

(not #f)
;; ==> #t

(not #t)
;; ==> #f

(not 3)
;; ==> #f

;;; Short-circuit example

(/ 6 0)
;; ==> *** ERROR -- Division by zero

(and #t (/ 6 0))
;; ==> *** ERROR -- Division by zero

(and #f (/ 6 0))
;; ==> #f

(or #f (/ 6 0))
;; ==> *** ERROR -- Division by zero

(or #t (/ 6 0))
;; ==> #t

;;; Test if number is between 0 and 100

(define (num-between-0-and-100 num)
;; ==> (and (> number 0) (< number 100))

(num-between-0-and-100 -5)
;; ==> #f

(num-between-0-and-100 32)
;; ==> #t

(num-between-0-and-100 105)
;; ==> #f

;;; Could this be done more efficiently 
;;; (i.e., without ands and ors)?

(define (num-between-0-and-100-efficient num)
;; ==>  (< 0 num 100)

;;;;;
;; IF
;;;;;
  
(/ 6 3)
;; ==> 2

(/ 6 0)
;; ==> *** ERROR -- Division by zero 

(define (safe-divide num1 num2)
  (if (= 0 num2)
      'infinity
      (/ num1 num2)))

(safe-divide 6 0)
;; ==> infinity

(safe-divide 6 3)
;; ==> 2

;;; Why is if a special form? 
;;; What would happen in safe-divide if it wasn't?

;;; ==> It would evaluate (/ num1 num2) regardless of whether
;;; it was going to be the branch and crash when num2 was zero.
;;; What's wrong with this? 
;;; What does the following return and what should it return?

(safe-divide 0 0) ;; This should return ==> undefined
;; ==> infinity

;;; Let's add a second test for num1 = 0

(define (safe-divide-fixed num1 num2)
  (if (zero? num2)
      (if (zero? num1)
          'undefined
          'infinity)
      (/ num1 num2)))

(safe-divide-fixed 0 0)
;; ==> undefined

;;; If is composable
;;; 
;;; Look at the two examples below. They perform the same
;;; computation. Note the use of if in the second example.

(define (grade-sentence name pass-or-fail)
  (if (equal? pass-or-fail 'pass)
      (se 'Hi name '(you have passed the course))
      (se 'Hi name '(you have miserably failed the course))))

(define (grade-sentence name pass-or-fail)
  (se 'Hi name '(you have)
      (if (equal? pass-or-fail 'pass) 'passed '(miserably failed))
      '(the course)))

(grade-sentence '(dr einstein) 'pass)
;; ==> (hi dr einstein you have passed the course)

(grade-sentence 'bart 'fail)
;; ==> (hi bart you have miserably failed the course)

;;;;;;;
;; COND
;;;;;;;

;; Want to write answer, which when given a sentence
;; responds as follows:
;;
;; : (answer '(are you a computer))
;; (yes i am a computer)
;;
;; : (answer '(am i smart))
;; (yes you are smart)
;; 
;; Otherwise
;; 
;; : (answer '(this is a random sentence))
;; (i do not understand)

(define (answer sent)
  (cond ((and (equal? (first sent) 'are)
              (equal? (second sent) 'you))
         (se '(yes i am) (but-first-two sent)))
        ((and (equal? (first sent) 'am)
              (equal? (second sent) 'i))
         (se '(yes you are) (but-first-two sent)))
        (else
         '(i do not understand))))

(answer '(are you a macintosh))
;; ==> (yes i am a macintosh)

(answer '(am i in bear territory))
;; ==> (yes you are in bear territory)

;;; Now let's break it!

(answer '( are you going with me to the movies? ))
;; ==> (yes i am going with me to the movies?)

;; Let's now modify answer so that it reads
;; : (are subjects description)
;; (yes subjects are description)
;;
;; e.g. 
;; : (answer '(are people here)) 
;; (yes people are here)

(define (answer sent)
  (cond ((equal? (se (first sent) (second sent)) '(are you))
         (se '(yes i am) (but-first-two sent)))
        ((equal? (first sent) 'are)
         (se 'yes (second sent) 'are (but-first-two sent)))
        ((equal? (first sent) 'am)
         (se '(yes you are) (but-first-two sent)))
        (else
         '(i do not understand))))

(answer '(are we the best class ever))
;; ==> (yes you are the best class ever)

(answer '(are cats the cutest animals))
;; ==> (yes cats are the cutest animals)

;; Now let's break it!
;; (You should think of other ways to break it!)

(answer '(are dogs and cats friendly))
;; ==> (yes dogs are and cats friendly)