CMPT 383 Comparative Programming Languages
Homework 1
This homework is due by 11:59pm PT on Wednesday Jan 26, 2022. No late submission is accepted. Please save your Haskell code in a single file called h1 firstname lastname.hs (h in lower case, firstname and lastname replaced with your first and last name) and submit it to Canvas.
Requirements of this homework:
• Write type signatures for all functions using the :: operator. • Do not use the if-then-else expression in any function.
1. (20 points) Given an Int n (n ≥ 1) and an Int m (m ≥ 0), write a function called seqMultiple that returns a list of n boolean values, where the i-th value (0 ≤ i < n) indicates whether i + 1 is a multiple of m. Note that you might want to use the built-in mod function: mod x y returns the remainder when x is divided by y.
Sample input and output:
ghci> seqMultiple 5 3
[False,False,True,False,False]
ghci> seqMultiple 5 2
[False,True,False,True,False]
2. (20 points) Given an Int n (n ≥ 0), write a recursive function called fib that computes the n-th Fibonacci number. The n-th Fibonacci number is defined as:
Sample input and output:
ghci> fib 10
ghci> fib 20
fib(n)= 1,
f ib(n − 1) + f ib(n − 2),
n = 0 n=1 otherwise
3. (20 points) Given a list L, write a recursive function called listReverse that reverses the list L. Sample input and output:
ghci> listReverse [1, 2, 3]
ghci> listReverse “abc”
4. (20 points) Given two lists of Int’s, write a recursive function called listAdd that computes their sum. Specifically, the sum of two lists [x0,…,xn] and [y0,…,ym] is a list [z0,…,zk] where k = max{m,n} and
xi + yi, for 0 ≤ i ≤ min{m, n} zi = xi or yi (whichever exists), for min{m, n} < i ≤ k
Sample input and output:
ghci> listAdd [1, 2] [3, 4]
ghci> listAdd [1, 2, 3] [4, 5]
ghci> listAdd [1, 2] [3, 4, 5]
5. (20 points) Given a list L of values and a value V , write a recursive function called inList that checks if V occurs in the list L.
Sample input and output:
ghci> inList [1, 2, 3] 2
ghci> inList “abc” ‘b’