Programming assignment 2: Scheme Programming

CMPSC 461: Programming Language Concepts

Programming assignment 2: Scheme Programming

1. (3 points) Write a higher-order function dncall that takes three parameters: n, f, x; it returns x when n = 0, returns f(f(x)) when
n = 1, returns f(f(f(f(x)))) when n = 2, etc. That is, it returns the
result of calling f on x, for 2n times. For instance, invoking dncall
with n = 2, the add-one function, and x = 2 should return 6.
2. (3 points) Write a Scheme keep-if function. It takes two arguments.
The first is a boolean function f, and the second is a list l. The
keep-if function returns a new list with all elements x in l such that
f(x) = #t being kept, while those elements x such that f(x) = #f
being removed.
For example,
(keep-if (lambda (x) (> x 3)) ’(10 1 7 2))
should return the list (10 7), since both 10 and 7 are greater than 3.
Define the keep-if function by using case analysis and recursion.
3. (3 points) The least function takes a list of numbers, and returns its
least element. For example, (least ’(7 3 6 2)) should return 2. Write
the least function in Scheme in two steps:
(a) Write a least helper function; it takes a number k and a list of
numbers, x, as parameters, and returns the number which is
smallest among k and numbers in x. For example, (least helper
5 ’(4 5 6)) should return 4.
(b) Write the least function based on least helper.
4. (5 points) Write a Scheme function to-words that takes an integer
between -99 and 99, inclusive, as a parameter and returns a list of
words corresponding to the integers reading in English. Make your
function as short as possible; i.e., don’t write a COND statement with
200 tests. Example calls to your function are given below:
1
(to-words 13) ; should return (thirteen)
(to-words 42) ; should return (forty two)
(to-words -55) ; should return (negative fifty five)
Note, in order to simplify things, we are not expecting dashes in the
output (i.e., 42 is output as forty two not forty-two). Also, if the
input number is outside of the range of [-99,99], your program should
output ’error. Hint: You may want to use the built-in integer division
functions quotient and remainder.
5. (10 points) In this question, we are going to develop a Scheme program
that calculates relevant word counts. The input is two lists, the first is
a list of words to be counted and the second is a list of irrelevant words;
the output should be counts for those relevant words that appear in
the first input list. For example, if the first input list is
’(time is long but life is short)
and the list of irrelevant words is
’(but)
Then the output should be
’((short 1) (is 2) (life 1) (long 1) (time 1))
Note that you are not asked to sort the words in the output. Therefore,
the output is correct as long as the counts are correct.
Do the following steps to implement the program. In our discussion,
we call a word with a count a word-count pair, for example, (short
1) and (is 2) are word-count pairs. We call a list of word-count pairs
a word-count list.
(a) (2 points) Write a function filterWords that takes a list of words
and a list of irrelevant words and returns an output list with
irrelevant words filtered out. E.g., if the first input list is
’(time is long but life is short)
2
and the list of irrelevant words is
’(but)
Then the output should be
’(time is long life is short)
You can use the “member?” function we discussed in class, if you
find it helpful.
(b) (2 points) Write a function iniWordCountList that takes a list
of words and creates a word-count list. The resulting word-count
list should have the word count 1 for every word. Use the map
function we discussed in class to implement iniWordCountList.
For instance,
(iniWordCountList ’(time is long life is short))
should generate
((time 1) (is 1) (long 1) (life 1) (is 1) (short 1))
(c) (2 points) Write a function mergeWordCounts. It takes two inputs. The first is a word-count pair and the second is a wordcount list. This function generates a new word-count list. If the
input word-count pair has a corresponding pair in the word-count
list with the same word, then the counts should be merged; otherwise, the output word-count list should have the input word-count
list with the word-count pair at the end of the list. For instance,
(mergeWordCounts ’(is 1) ’((time 1) (is 1)))
should generate
((time 1) (is 2))
As another example
(mergeWordCounts ’(life 1) ’((time 1) (is 2)))
3
should generate
((time 1) (is 2) (life 1))
(d) (2 points) Write a function mergeByWord, which takes a wordcount list and produces a new word-count list; the output wordcount list should have one word-count pair for each word that
appears in the input list and the count should be the sum of all
counts for that word in the input list. For instance, if the input
list is
((time 1) (is 1) (long 1) (but 1) (life 1) (is 1) (short 1))
then the output should be
((short 1) (is 2) (life 1) (but 1) (long 1) (time 1))
Write mergeByWord based on the reduce function we discussed in
class and mergeWordCounts. The reduce function is not built-in
in Scheme; you can type it in yourself:
(define (reduce f l v)
(if (null? l) v
(f (car l) (reduce f (cdr l) v))))
(e) (2 points) Finally, write a relevantWordCount function that takes
in a list of words and a list of relevant words, and outputs the
right word-count list. Write this function based on filterWords,
iniWordCountList, and mergeByWord.
Notes For programming assignments, examples are given only for the purpose of clarification. By no means that our tests will solely be based on those
examples. It’s your responsibility to thoroughly test your code by designing
your own test cases.
Chapter 6 of the Scheme standard
http://www.schemers.org/Documents/Standards/R5RS/HTML/ contains a
list of standard procedures provided by Scheme (for example, the remainder and the square root functions). You may find them helpful during your
programming.
4
Submission format: Put all your code into one DrRacket file and submit
your file through Canvas. Please clearly mark your answers using comments
so that we can tell the correspondence between your code and questions.
Please ensure that your file starts with a comment that includes your name
and your Penn State network user id.
5