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CISC 360 Assignment 1
September 18, 2020
Reminder: All work submitted must be your own. You may (and should) ask for help from the
instructor, TAs or on Piazza.
Most of the questions on this assignment are about writing code, but a few questions are about
stepping. Please write your answers within the comments indicated in the file a1.hs (search for
Q3.1 and Q3.2).
Start early: Even if some questions look easy to you, Haskell is a very different language and
you may need more time than you think.
Late policy: Assignments submitted up to 24 hours late (that is, by 11:59 pm the following
day) will be accepted with a 15% penalty.
0 IMPORTANT: Your file must compile
Your file must load (:load in GHCi) successfully, or we will automatically subtract 30% from your
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.
1 Add your student ID
The file a1.hs will not compile until you add your student ID number by writing it after the =:
-- Your student ID:
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.
2 Writing and testing small Haskell functions
2.1 between
This function takes three integers m, n and p, and should return True if m ≤ n ≤ p, and return
False otherwise.
Fill in the definition of between by replacing the word undefined with appropriate Haskell
code, and, if necessary, deleting the = (for example, if you decide to define between using guards).
a1, Jana Dunfield, CISC 360, Fall 2020 1 2020/9/18
§1 Add your student ID
We have already written five test cases for between, called test between1, 2, etc. These are
combined into test between, which is True only if all five tests pass.
2.2 carry
The carry function takes two integers, and should return 1 if both integers are odd, and 0 otherwise
(if both are even, or if one of them is even and the other is odd). (The name comes from the fact
that its result is the “carry bit” produced by adding the least significant bits of the two integers.)
3 Stepping questions
3.1 First expression
These questions ask you to step two small expressions. For example, the first stepping question asks
you to do the three steps needed to get the result. Replace the parts. (If you want to check
the last line, you can find it by entering the expression into GHCi.)
(\x -> x * (3 + x)) 2
=> _______________________ _________________________
=> _______________________ _________________________
=> __ by arithmetic
3.2 Second expression
The other expression is somewhat larger, and uses a function double, which is defined in the
Hint: The first step does not apply the function double. Haskell sees the expression
(\a -> \b -> a (a 3)) double 0
as the expression
(\a -> \b -> a (a 3)) double
applied to the argument 0.
The expression
(\a -> \b -> a (a 3)) double
is the function (\a -> \b -> a (a 3)) applied to the argument double. That is where the first
step happens.
Hint: The correct solution steps 6 times (as indicated by the structure of blanks).
a1, Jana Dunfield, CISC 360, Fall 2020 2 2020/9/18
§4 tower
4 tower
In this question, you need to write a function tower. Your function should be recursive—its definition
will call itself—and should not use lists.
The idea is that tower is specified by the following equation:
The only remaining problem is that you may want to think of the Π product as looping from k
to n, but Haskell does not have loops, so you have to use recursion instead. This will be discussed
more in lecture, but the example of diag from the lecture notes may be helpful: diag n computes
the sum of integers from 0 up to n, but does not use a loop. Instead, it calls itself recursively on
n − 1. You can think of it as counting down from n to 0.
The file a1.hs includes a few tests for tower.
5 Base conversion
The functions you’ll write for this question return Haskell strings, which are lists of characters. We
have not discussed lists in any detail; however, for this problem, you should only need to know the
a1, Jana Dunfield, CISC 360, Fall 2020 3 2020/9/18
§5 Base conversion
• To return a string containing a single character 0, write
You could also write "0".
• To concatenate (append) two strings, use the built-in function ++. For example:
[’1’, ’2’, 3’] ++ [’4’]
returns "1234", which is the same thing as [’1’, ’2’, ’3’, ’4’].
5.1 toBinary
Read the specification in the comment immediately above toBinary.
Fill in the definition of toBinary by replacing the word undefined with appropriate Haskell
code, and, if necessary, deleting the = (for example, if you decide to define toBinary using guards).
5.2 toNary
Read the specification in the comment immediately above toNary.
We have already written part of the definition, to check for an invalid base—toNary only needs
to handle bases between 2 and 10. If you pass a valid base to toNary, you will get an error (“Nonexhaustive
patterns in function toNary”) when Haskell “falls off the end” of the definition. You can
fix this by adding an additional guard to toNary.
You should handle all bases between 2 and 10 with the same code. Don’t “hard-code” each
base; you should have no more than two guards (the given one, and one additional guard), and
should not do something like
... = if base == 2 then ...
else if base == 3 then ...
else if base == 4 then ...
a1, Jana Dunfield, CISC 360, Fall 2020 4 2020/9/18

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