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CISC 360 Assignment 2
due Tuesday, 2023–10–17 at 11:59pm, via onQ
Jana Dunfield
October 3, 2023
Reminder: All work submitted must be your own, or, if you are working with one other student,
your teammate’s.
Late policy: Assignments submitted up to 24 hours late (that is, by 11:59 pm the following
day) will be accepted without penalty. Assignments submitted more than 24 hours late will not
be accepted, except with an accommodation or a consideration granted according to policy.
0 Document your code
Some of this assignment is a “fill-in-the-blanks” assignment, so you will not need to document
much. However, if you need to write a helper function, you need to write a comment that explains
what the function does.
0 Strive for simplicity
You should try to find a simple solution. You do not have to find the simplest solution to get
full marks, but you should not have an excessively complicated solution. Marks may be deducted if
your solution is too complicated. If you are worried about whether your solution is too complicated,
contact the instructor.
0 Be careful with library functions
Haskell has a rather large built-in library. This assignment is not about how to find library functions,
but about how to use some of the core features of Haskell. You will not receive many marks if you
just call a library function that solves the whole problem. The point is to solve the problem yourself.
If you are not sure whether you are calling a library function that solves the whole problem,
contact the instructor. Note that if we suggest a library function, you may certainly use it.
(The only way I know to avoid this issue is to craft problems that are complicated and arbitrary,
such that no library function can possibly solve them. I don’t like solving complicated and arbitrary
problems, and you probably don’t either.)
0 IMPORTANT: Your file must compile
Your file must load (:load in GHCi) successfully, or we will subtract 30% from your mark.
If you are halfway through a problem and run out of time, comment out the code that is
causing :load to fail by surrounding it with {- . . . -}, and write a comment describing what you
were trying to do. We can often give (partial) marks for evidence of progress towards a solution,
but we need the file to load and compile.
a2, Jana Dunfield, CISC 360, F. 2023 1 2023/10/3
0 If you choose to work in a group of 2
You must use version control (such as GitHub, GitLab, Bitbucket, etc.). This is primarily to help
you maintain an equitable distribution of work, because commit logs provide (rough) information
about the members’ level of contribution.
Your repository must be private—otherwise, anyone who has your GitHub (etc.) username can
copy your code, which would violate academic integrity. However, upon request from the course
staff, you must give us access to your repository. (You do not need to give us access unless we ask.)
We only need one submission of the assignment. However, each of you must submit a brief
statement (.txt preferred; .pdf or .docx are acceptable).
1. Give your names and student ID numbers.
2. Estimate the number of hours you spent on the assignment.
3. Briefly describe your contribution, and your teammate’s contribution. (Coding, trying to
understand the assignment, testing, etc.)
This is meant to ensure that both group members reflect on their relative contributions.
If you do not submit a statement, you will not receive an assignment mark. This is meant to
ensure that each group member is at least involved enough to submit a statement.
Each member must submit a statement.
0 Add your student ID
Begin by renaming the file to a2-studentid.hs. For example, if your student ID number were
87654321, you should rename the file to a1-87654321.hs.
The .hs file will not compile until you add your student ID number by writing it after the =:
-- Rename this file to include your student ID: a2-studentid.hs
-- Also, add your student ID number after the "=":
student_id :: Integer
student_id =
You do not need to write your name. When we download your submission, onQ includes your
name in the filename.
If you are working in a group of 2, uncomment the “second student id” line and add the
second student’s ID number there.
1 ‘rewrite’
Haskell has a built-in function ord, with the type
ord :: Char -> Int
When applied to a Char, the ord function returns the ASCII code corresponding to that Char.
For example, ord ’A’ returns 65.
a2, Jana Dunfield, CISC 360, F. 2023 2 2023/10/3
Your task is to implement a function named rewrite. Given a String, rewrite returns a copy
of that String with all “important” Chars duplicated.
However, your employer keeps changing their mind about what is important, so the first argument to the function rewrite is a function that tells you whether a given character is important.
For example, if the first argument passed to rewrite is
divisible_by 2
then every character whose ASCII code is evenly divisible by 2 is “important” and should be duplicated. (The function divisible_by is already defined in a2.hs.)
If the first argument passed to rewrite is
(\x -> (x == ’ ’))
then every space character (and only space characters) will be considered important.
Some examples:
rewrite (divisible_by 2) "" should evaluate to ""
rewrite (\x -> x == ’ ’) "it’s a deed" should evaluate to "it’s a deed"
rewrite (divisible_by 2) "CombinatorFest" should evaluate to "CombbinnattorrFFestt"
a2, Jana Dunfield, CISC 360, F. 2023 3 2023/10/3
2 Comparing lists
2a. Fill in the definition of listCompare, which takes two lists of Ints, and should return a list of
Bools such that:
• if the kth element of the first list is less than the kth element of the second list, the kth element
of the result should be True;
• if the kth element of the first list is greater than or equal to the kth element of the second list,
the kth element of the result should be False;
• if the first and second lists are of different lengths, the result should be “padded” with False,
so that the result list is as long as the longer input.
Examples:
listCompare [0, 2, 4] [3, 2, 0] should be [True, False, False ]
^^^^ ^^^^^ ^^^^^
0 < 3 2 >= 2 4 >= 0
listCompare [5, 4, 3, 2] [2, 9] should be [False, True, False, False]
^^^^^^^^^^^^ ^^^^^^ ^^^^^ ^^^^ ^^^^^ ^^^^^
length 4 length 2 5 >= 2 4 < 9 2nd list 2nd list
has no 3rd has no 4th
element element
(resulting list has length 4)
2b. The function listCompare only works with integer lists. Fill in the definition of genCompare,
which takes three arguments.
1. The first argument is a comparison function cmp, of type a -> a -> Bool, which takes two
a’s and returns True if the first argument should be considered less than the second argument,
and False otherwise.
2. The second and third arguments are lists, where each list’s elements have type a.
2c. The following code uses a library function, zipWith, that behaves almost the same as listCompare.
In a comment, briefly explain why almostListCompare does not fully implement the specification
of listCompare.
almostListCompare = zipWith (<)
a2, Jana Dunfield, CISC 360, F. 2023 4 2023/10/3
3 Identity
Here is a mysterious data declaration:
data Song = Harmony Song Song
| Atom String
deriving (Show, Eq)
Hint (?): You can think of a Song as a tree having branches named Harmony, and leaves named
Atom, where the leaves contain strings.
By being sung, a Song changes according to the following “rules”:
1. If the song is a Harmony whose left child is a Harmony whose left child is Atom x where the
first character of x is ’k’, the song becomes the right child of the left child of the root.
Viewed as trees:
_ _
/ Harmony \
| / \ |
| Harmony right |
sing | / \ | = motif
| Atom motif |
| | |
\_ x _/ (only if x begins with ’k’)
2. I’m not going to try to explain this; it’s easier to look at the trees:
_ _
/ Harmony \
| / \ |
| Harmony s3 | Harmony
| / \ | / \
sing | Harmony s2 | = Harmony Harmony
| / \ | / \ / \
| Atom s1 | s1 s3 s2 s3
| | |
| y |
\_ _/ (only if y begins with ’s’)
3. If we see a Harmony that does not match the first two rules, sing should recurse on both
children:
_ _
/ Harmony \
sing | / \ | = Harmony newleft newright
| left right |
\_ _/ (only if rules 1 and 2 can’t be applied)
a2, Jana Dunfield, CISC 360, F. 2023 5 2023/10/3
where newleft is the result of calling sing on left, and newright is the result of calling
sing on right.
If the song does not match any of the above “rules”, it remains unchanged. So, for example,
sing (Atom "X") should return Atom "X". Also:
sing (Harmony (Harmony (Atom "s") (Atom "y")) (Atom "z"))
should return (Harmony (Harmony (Atom "s") (Atom "y")) (Atom "z")):
• The shape of the argument matches the first rule, but "s" does not begin with ’k’.
• The shape of the argument does not match the second rule: it needs three Harmony constructors leaning to the left, but there are only two in (Harmony (Harmony (Atom "s") (Atom
"y")) (Atom "z")).
• The shape of the argument does match the third rule. However, sing (Harmony (Atom "s")
(Atom "y")) should return (Harmony (Atom "s") (Atom "y")), and sing (Atom "z") should
return (Atom "z"), so Harmony newleft newright should be (Harmony (Harmony (Atom
"s") (Atom "y")) (Atom "z")).
3a. Implement the function song according to the three “rules” above.
A “fall-through” clause, matching any song other, has already been written for you. Haskell
does pattern matching in order, so you should add your clauses before that one.
3b. Write a function repeat sing that takes a song, and calls sing repeatedly until a “fixed point”
is reached. That is, if sing returns the same song it is given, repeat sing should return that song;
otherwise, repeat sing should call itself again with the changed song.
3c (BONUS). You can get full marks on the assignment without doing this bonus part; you might
get a total assignment grade over 100% by doing this bonus question; but this bonus question is
worth no more than 5% of the marks for the assignment.
This question might not even have an answer, so don’t attempt it unless you really want
to.
Write a song that is finite, yet “diverges”: calling repeat sing never returns, because sing
never returns the same argument.
(We can build an infinite song like this:
infinite_song = Harmony infinite_song infinite_song
The song you write for this question should be finite, with no recursion or self-reference.)
Hint: Your instructor has (obnoxiously) hidden possible clues to this question throughout the
assignment.
a2, Jana Dunfield, CISC 360, F. 2023 6 2023/10/3

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