Homework 3
1 Introduction
For this homework, you will implement some SML functions using list and tuple
data structures.
1. You may reuse any functions you have already de ned for a previous
question.
2. Your solution should be a working ML program in a text le that I can
run on a console using command like use “hwk3.sml”;
3. You may add comments to your program such as (* Question 1 *).
4. Some of these functions involve recursion.
2 Questions
1. Write a function plus that adds two complex numbers, where a complex
number is written as a tuple of two integers. For example, (1; 2) is a
complex number with real part 1 and imaginary part 2.
plus ((1, 2), (3, 4)) should return (4, 6).
2. Write a function times that multiples two complex numbers. For example,
times ((1,2), (3,4)) should return (1 * 3 – 2 * 4, 1 * 4 + 2 * 3),
which is (~5, 10,).
3. Write a function until that takes two integers x and y and return a
list from x to y – 1. If x y, it should return nil. For example,
until (1, 4) should return [1,2,3].
4. Write a function append that takes an integer x and a list of integers and
return a list of pairs where the left of each pair is x and right of each pair
is a list element. For example, append (1, [1, 2, 3]) should return
[(1,1), (1,2), (1, 3)].
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5. Write a function pair that takes two lists of integers and generates a list
of pairs, where each pair is a combination of each element from each list.
For example, pair ([1,2], [3,4,5]) should return
[(1,3), (1,4), (1,5), (2,3), (2,4), (2,5)].
3 Submission
Please write your solution in a text le by the name of hwk3.sml and submit it
to the dropbox.
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