7COM1023 Programming Paradigms

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1 7COM Programming Paradigms Practical Answers Expressions We will commence by typing in some expressions to familiarise ourselves with the environment.. Type in the following and evaluate them by pressing return: a) b). c) / d) / e) f). Answers a) > b) >. c) > / d) > / e) > "" "" f) >.. Type in the following expressions and evaluate. Do you get what you expect? a) (+ 4) b) (sqr ) c) (- 9 7) d) (- 7) e) (+ (* ) 4) f) (* (- 4) (+ )) g) (sqr (* 4))

2 Answers a) > (+ 4) 7 b) > (sqr ) c) > (- 9 7) d) > (- 7) -7 e) > (+ (* ) 4) 4 f) > (* (- 4) (+ )) 8 g) > (sqr (* 4)) 44 Write each of the above expressions in standard mathematical notation. a) + 4 b) c) 9 7 d) 7 e) ( * ) + 4 f) ( 4) * ( + ) g) *4

3 . Change each of the following into Lisp expressions and evaluate: a) + b) c) 7-4 d) ( + 4) ( ) e) 4 f) ( * 4) + ((-4)*) g) + *7 Answers a) > (+ ) b) > (sqr ) c) > (- 7 4) d) > (- (+ 4) (- )) e) > (- (sqr ) (sqr 4)) 9 f) > (+ (* 4) (* (- 4) )) g) > (+ (* 7))

4 4. Explore the following lisp functions that each work on numerical arguments: +, -, +, -, gcd, lcm, expt, sqrt, rational, rationalize, numerator, denominator, random. + and functions as above. + and - require further investigation. gcd denotes the greatest common divisor (the largest number to divide into the given numbers) > (gcd 9 ) > (gcd 9 ) > (gcd 9 8 4) lcm denotes the lowest common multiple (the smallest number in each of the sets of multiples generated by te given numbers) > (lcm ) > (lcm 4) > (lcm 4 ) > (lcm 4) 4 > (lcm 9 ) 9 > (lcm ) expt denotes the exponential function a x where a and x are two required input values. > (expt ) > (expt ) > (expt 4) Note that (expt ) gives the same result as (sqr ). sqrt denotes the square root of a value. We have met this function already. rational this function is not defined. Did it denote something in Scheme? Is there an alternative for DrRacket? > (rational (sqrt )) rational: this function is not defined > (rational? (sqrt )) The last result is interesting since the square root of is not a rational number. What could be happening here?

5 rationalize is also not defined. Example: > (rationalize (sqrt )) rationalize: this function is not defined Did it denote something in Scheme? Is there an alternative for DrRacket? Fractions consist of a numerator divided by a denominator. > (numerator /7) > (denominator /7) 7 > (numerator /4) > (denominator /4) 7 The random function generates a random number between and the number that you input. > (random ) > (random ) > (random ) > (random ) > (random ) > (random ) > (random ) > (random ) > (random ) > (random ) > (random ) > (random ) > (random ) > (random ) > (random ) > (random ) > (random ) > (random )

6 . Use ( define <id> <expression> ) to define three constants one, two and three as,, respectively. Evaluate and inspect the results to confirm that they hold the values that you expect. Use these to carry out some simple arithmetic such as (+ one three),. What happens if you now define three to be 4 and then evaluate (+ one three)? Answers. > (define one ) > (define two ) > (define three ) > one > two > three > (+ one three) 4 > (define three 4) three: this name was defined previously and cannot be re-defined > (+ one three) 4. The constant pi is defined already in Lisp. What is it s value? > pi #i

7 7. What do the following achieve? a) (string-append monday tuesday ) b) (substring monday ) c) (string? monday ) d) (string? ) e) (sqrt ) f) (sqrt -) g) (number? 7) h) (number? seven ) i) (equal ) j) (equal one ) Answers. a) > (string-append "monday" "tuesday") "mondaytuesday" b) > (substring "monday" ) "mon" c) > (string? "monday") d) > (string? ) false e) > (sqrt ) f) > (sqrt -) +i g) > (number? 7) h) > (number? "seven") false i) > (equal? ) false j) > (equal? one ) 8. Define a variable called radius and set the variable equal to. Write an expression that will calculate the area of the circle (define radius ) > (* pi (sqr radius)) #i

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