;; definition of function, fun, that adds 7 to the input (define fun (lambda (x) (+ x 7)))


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1 Homework 1 Due 13 September Handout 2 CSC 131: Fall, September Reading 1. Read Mitchell, Chapter The Scheme Tutorial and the Scheme Quick Reference from the Links web page, as needed for the programming questions. 3. (Optional, but recommended J. McCarthy, Recursive functions of symbolic expressions and their computation by machine, Comm. ACM 3,4 ( You can find a link to this on the cs131 web site. The most relevant sections are 1, 2 and 4; you can also skim the other sections if you like. Problems 1. (30 points Lisp Programming For this problem, use the Scheme interpreter on the Unix machines in the computer lab. You can use the Scheme interpreter interactively by running the command scheme, which will enter the Scheme readevalprint loop. However, I recommend putting your Scheme code into a file and then running the interpreter on that file. To run the program in the file example.ss, type scheme example.ss at the command line. The interpreter will read and evaluate the expressions in the file, in order. For example, suppose example.ss contains the following: ;; definition of function, fun, that adds 7 to the input (define fun (lambda (x (+ x 7 ;; simple expression to add 3 to 5 (+ 3 5 ;; square a number (define (square x (* x x Evaluating this file produces no output, but you can now use the functions fun and square defined in the file. Petite Chez Scheme Version 6.9c Copyright (c Cadence Research Systems Loaded EOPL init file > (square 2 4 > (square (square 3 1
2 81 > (fun > (exit It evaluates the two expressions containing square, and the one using fun and then quits. It is important that the program ends with (exit so that the Scheme interpreter will exit and return you to the Unix shell. Now try the same thing by running these within Emacs using the directions given in the document Using emacs with Scheme available via the course web page. In general, you should find this to be a better experience in debugging your programs. Please remember that the dialect of LISP we use, Scheme, is similar to what is described in the book, but many of the key words are different. Use the ideas in the book, but look up precise key words in the Quick reference guide and tutorial linked to via the course web pages. (a What is the value of the following expressions? Try to work them out yourself, and verify your answers on the computer: i. (car (inky blinky pinky clyde ii. (cons inky (cdr (clyde blinky pinky iii. (car (car (cdr (inky (blinky pinky clyde iv. (cons (+ 1 2 (cdr (+ 1 2 v. (map (lambda (x (/ x 2 ( vi. (map (lambda (x (car x ((WOMBATS 3 (WALLAROOS 1 (NUMBATS 33 vii. (map (lambda (x (cdr x ((WOMBATS 3 (WALLAROOS 1 (NUMBATS 33 Write a function called listlength that returns the length of a list. Do not use the builtin length function in your solution. > (listlength (cons 1 (cons 2 (cons 3 (cons 4 nil 4 > (listlength (A B (C D 3 Write a function double that doubles every element in a list of numbers. Write this two different ways first use recursion over lists and then use map. > (double (1 2 3 (2 4 6 (b Recursive Definitions Not all recursive programs take the same amount of time to run. Consider, for instance, the following function that raises a number to a power: (define (power base exp (if (eq? exp 0 1 (* base (power base ( exp 1 There are more efficient means of exponentiation. First write a Lisp function that squares an integer, and then using this function, design a Lisp function fastexp which calculates b e for any e 0 by the rule: b 0 = 1 b e = (b (e/2 2 if e is even b e = b (b e 1 if power is odd 2
3 It is easy to blow this optimization and not save any multiplications. Show that the program you implemented is indeed faster than the original by comparing the number of multiplications that must be done for some exponent e in the first and second algorithms. (Hint it is easiest to calculate the number of multiplications if the exponent, e, is of the form 2 k for the second algorithm. Give the answer for exponents of this form and then try to give an upper bound for the others. (c Recursive list manipulation Write a function mergelist that takes two lists and joins them together into one large list by alternating elements from the original lists. If one list is longer, the extra part is appended onto the end of the merged list. The following examples demonstrate how to merge the lists together: > (mergelist (1 2 3 (A B C (1 A 2 B 3 C > (mergelist (1 2 (A B C D (1 A 2 B C D > (mergelist (1 2 3 nil (1 2 3 > (mergelist ((1 2 (3 4 (A B ((1 2 A (3 4 B (d Reverse Write a function rev that takes one argument. If the argument is an atom it remains unchanged. Otherwise, the function returns the elements of the list in reverse order: > (rev nil nil > (rev A A > (rev (A (B C D (D (B C A > (rev ((A B (C D ((C D (A B (Yes, I know that Scheme already includes a predefined function reverse that does exactly this. I want you to write your own without using the builtin function! (e Mapping functions Write a function censorword that takes a word as an argument and returns either the word or XXXX if the word is a bad word: > (censorword lisp lisp > (censorword midterm XXXX Recall the function ismember? that we defined in class. Using that function definition, (member word (extension algorithms graphics AI midterm evaluates to#t if word is in the given list of bad words, i.e., the list (extension algorithms graphics AI midterm is the list of bad words. Use this function to write a censor function that replaces all the bad words in a sentence: 3
4 > (censor (I NEED AN EXTENSION BECAUSE I HAD AN AI MIDTERM (I NEED AN XXXX BECAUSE I HAD AN XXXX XXXX > (censor (I LIKE PROGRAMMING LANGUAGES MORE THAN GRAPHICS OR ALGORITHMS (I LIKE PROGRAMMING LANGUAGES MORE THAN XXXX OR XXXX (f Working with Structured Data Write a function averages to compute the average homework grade for each student in a data structure defined as follows: ;; Define a variable holding the data: > (define grades ((Shezad ( (Nurjahan ( (Jilan ( > (averages grades ((Shezad (Nurjahan 94.0 (Jilan 85.0 You may wish to write a helper function that takes one student entry and processes it (ie, (studentavg (Shezad ( returns (Shezad We will now sort the averages using one additional Lisp primitive: sort. Before doing that, we need a way to compare student averages. Write a method comparestudents that takes two student average lists and returns true if the first has a lower average and nil otherwise: > (comparestudents (Shezad (Nurjahan 94.0 #t > (comparestudents (Shezad 94.0 (Nurjahan #f To tie it all together, you should now be able to write: (sort (averages grades comparestudents to obtain ((Shezad (Jilan 85.0 (Nurjahan 94.0 (g Deep Reverse Now, write a function deeprev that performs a deep reverse, meaning that, unlike rev, it reverses any sublists of a list: > (deeprev A A > (deeprev null ( > (deeprev (A (B C D (D (C B A > (deeprev (1 2 ((3 4 5 ((5 ( In other words, deeprev reverses the elements of a list, and also deepreverses every element. I have defined deeprev on atoms as I did with rev. You may want to use rev in your solution. Make one file containing the function definitions for the above questions, as well as expressions to demonstrate that the functions work properly. Your code should be documented (comment lines start with ;; and include your name. 4
5 2. (10 points Lisp Programming The following code is a slight rewrite of code that appears in Mitchell, Chapter 3 (page 31. ;; substitute exp1 for all occurrences of var in exp2 (define (subst exp1 var exp2 (cond ((null? exp2 ( ((not (list? exp2 (if (eq? var exp2 exp1 exp2 (else (cons (subst exp1 var (car exp2 (subst exp1 var (cdr exp2 (define (substandeval exp1 var exp2 (eval (subst exp1 var exp2 The subst function replaces all occurences of atom var with exp1 in exp2. The function substandeval performs such a substitution and then evaluates the resulting list. For example, (substandeval * + ( evaluates to 60. Your job is to write a function multisubstandeval that performs multiple substitutions on a list before evaluating it. For example, (multisubstandeval ((x 10 (y 10 (* + (* y ( 12 x evaluates to 12. First write a function multisubst that performs the substitutions and verify that it is constructing a valid expression to evaluate. The expression (multisubst ((x 10 (y 10 (* + (* y ( 12 x evaluates to the list (+ 10 ( You may use the above subst function as part of your solution. Writing multisubstandeval is straightforward once you have done that. Here is some additional sample input: > (multisubstandeval ((x 10 (y 10 (* y ( 12 x 20 > (multisubstandeval ((x 10 (y 20 (+ * (* y (+ y (* y y x > (multisubstandeval ((x y (y 20 (+ * (* y (+ y (* y y x > (multisubstandeval ((y 20 (* cons (* y (* y (* y nil ( Substitutions should be performed from left to right in the list. For example, the substitutions ((x y (y 20 will change any x in a term to y, and then replace every y with 20. Thus, 5
6 (multisubst ((x y (y 20 (* x x evaluates to (* 20 20, and (multisubstandeval ((x y (y 20 (* x x returns (10 points Cons Cell Representations Mitchell, Problem (20 points Conditional Expressions in Lisp Mitchell, Problem 3.2 6
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