# Assignment 8 Writing basic OCaml functions

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CPSC 326: Homework Assignment 8
The goal of this assignment is to gain practice writing basic OCaml functions. Note that you are free to use
whatever IDE and machine you prefer for this assignment. However, to complete the assignment, you will
Overview:
1. Use the GitHub Classroom link (posted in Piazza) to copy the starter code into your own repository.
Clone the repository in the directory where you will be working on the assignment (e.g., onto ada
2. Write the functions described below in hw8.ml.
3. Write multiple tests for each function to ensure correctness within the hw8_tests.ml file.
4. Submit your two program files. Be sure to add, commit, and push all assignment files to your
GitHub repo. You can verify that your work has been submitted via the GitHub page for your repo.
Instructions: Implement the following functions from scratch in hw8.ml (i.e., without just calling functions provided by OCaml). In addition you must:
• only use the OCaml constructs we’ve discussed so far in class or as provided in the function description (if you go beyond what we’ve done, you’ll receive no points for the question);
• only use if-then-else constructs for conditionals (i.e., you cannot use pattern matching and
guards);
• follow the general style guide provided by OCaml (https://ocaml.org/learn/tutorials/guidelines.
html)
date, and a brief description; and
• create sufficient test cases for your functions to ensure they work correctly.
The following functions must be implemented as stated above. If you have questions on how any of the
following are supposed to work, please ask either during class or on piazza:
1. Implement a function my_min x y that evaluates to the minimum of the values x and y. For example,
my_min 2 3, my_min 4 2, and my_min 2 2 should each evaluate to 2. You cannot use any other
2. Implement a function my_median x y z that evaluates to the middle value of x, y, and z. For
example, my_median 1 2 3, my_median 3 1 2, and my_median 2 3 2 should each evaluate to 2.
In addition, my_median 2 2 2 and my_median 2 1 2 should each also evaluate to 2. You cannot
use any other functions in your implementation.
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3. Implement a function my_triangle_area base height that computes the triangle height given a
base and a height value (as floats). You cannot use any other functions in your implementation.
4. Implement a function my_circle_area radius that computes the area of a circle given the radius
(as a float). Note that to raise a float value to a power you can use the exponentiation operator **,
e.g., v ** 3.0 would cube the value v. You cannot use any other functions in your implementation.
5. Implement a function my_midpoint (x1,y1) (x2,y2) to compute the midpoint between two points.
Assume the points are given as floats. For example my_midpoint (1.,1.) (3.,5.) would evaluate
to (2.,3.). Note this function uses 2-tuples of floats to represent points. You cannot use any other
6. Implement a function my_manhattan_distance (x1,y1) (x2,y2) to compute the “Manhattan”
(i.e., “taxicab”) distance between two points (defined as the absolute distance travelled in the x-axis
plus the absolute distance travelled in the y-axis, as if you are walking city blocks to get from location
1 to location 2). Assume the points are given as floats. For example my_manhattan_distance
(1.,1.) (3.,4.) and my_manhattan_distance (3.,1.) (1.,4.) would both evaluate to 5..
To compute an absolute float value, you can use the OCaml abs_float function. You cannot use
any other functions in your implementation.
7. Implement a function my_euclidean_distance (x1,y1) (x2,y2) to compute the “Euclidean” distance (i.e., the straight-line distance from location 1 to location 2) between two points. For example,
my_euclidean_distance (1.,1.) (4.,5.) should evaluate to 5.. To take the square root, you
can use the OCaml sqrt function. You cannot use any other functions in your implementation.
8. Implement a function my_range_sum v1 v2 that returns the sum of values starting at v1 and ending
at v2. For example, my_range_sum 2 2 is 2, my_range_sum 2 3 is 5 (i.e., 2 + 3), my_range_sum
2 4 is 9 (i.e., 2 + 3 + 4), and my_range_sum 2 1 is 0. You must write this as a recursive function.
You cannot use any other functions in your implementation.
9. Implement a function my_gcd x y that returns the greatest common divisor of two integers x and
y. You must use the recursive division-based version of Euclid’s Algorithm. You can use the OCaml
infix function mod in your function. You cannot use any other functions in your implementation.
10. Implement mutually recursive versions of even and odd functions my_even x and my_odd x. Your
functions should implement the following:
bool even(int x) {
if (x < 0)
return false;
else if (x == 0)
return true;
else
return odd(x – 1);
}
bool odd(int x) {
if (x < 0)
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return false;
else if (x == 1)
return true;
else
return even(x – 1);
}
For the following functions, you can use the list length, head, and tail functions, list creation (e.g.,
[List.hd xs]), the cons and append operators, the failwith function as needed, and “normal” OCaml
constructs (like let-in, comparison and arithmetic operators, etc.). However, no other helper functions or
list operations are allowed.
11. Write a function my_rev that takes a list and returns the reverse order of the list. Example: my_rev
[1; 2; 3] should return [3; 2; 1].
12. Write a function my_last that takes a list and returns the last element of the list. Example: my_last
[1; 2; 3] should return 3. Calling my_last on an empty list should result in a failure (“Empty
List”).
13. Write a function my_init that takes a list and returns a new list containing all of the elements of
the input list except for the last element. Example: my_init [1; 2; 3] should return [1; 2].
Calling my_init on an empty list should result in a failure (“Empty List”).
14. Write a function my_mem that takes a value and a list and returns true if the value is in the list, and
false otherwise. Examples: my_mem 3 [1; 2; 3; 4] should return true whereas my_mem 3 [1; 2;
4; 5] should return false.
15. Write a function my_replace that takes a pair of values and a list and returns a new list such that
each occurrence of the first value of the pair in the list is replaced with the second value. Example:
my_replace (2,8) [1; 2; 3; 2] should return [1; 8; 3; 8].
16. Write a function my_replace_all that takes a list of pairs and a list of values and returns a
new list where each occurrence of the first value in a pair is replaced by the second value in the
pair. The replacement should occur in order of pairs. Examples: my_replace_all [(‘a’,’b’);
(‘c’,’d’)] [‘a’; ‘b’; ‘c’; ‘d’] should give [‘b’; ‘b’; ‘d’; ‘d’]” and my_replace_all
[(1,2); (2,3)] [1; 2; 3; 4] should give [3; 3; 3; 4]. You can call my_replace from within
my_replace_all.
17. Write a function my_elem_sum that takes a value and a list, and returns the sum of the given values
in the list. Examples: my_elem_sum 10 [15; 10; 25] should return 10, my_elem_sum 3 [3; 2;
3; 2; 3; 4; 3] should give 12 and my_elem_sum 3 [] should give 0.
18. Write a function my_rem_dups that takes a list of values, and returns a copy of the original list with
duplicate values removed. Examples: my_rem_dups [‘a’; ‘b’; ‘a’; ‘c’; ‘b’; ‘a’] should
return [‘c’; ‘b’; ‘a’] and my_rem_dups [10; 11; 13; 11; 12] should return [10; 13; 11;
12]. Note you can call my_mem within your my_rem_dups function.
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19. Write a function my_list_min that returns the smallest of a given list of values. Example: my_list_min
[7; 1; 9; 12; 10] should return 1. The function should report failure (“Empty List”) when called
on an empty list. Be careful with respect to efficiency, i.e., your implementation must be O(n) for
an n-element list.
Testing. For testing, we’ll use our own “poor man’s” unit testing approach (instead of a unit testing
framework like OUnit). For each function, you will need to write multiple tests to ensure the function
works correctly. In particular, your hw8_test.ml program should be structured as follows.
(*
Name: <your-name-here>
File: hw8_tests.ml
Date: Spring 2023
Desc: HW8 function unit tests
*)
open Hw8
let msg = “— Running HW8 Tests — “;;
print_endline msg;;
(* For equality assertions *)
let assert_equal v1 v2 msg =
let cond = v1 = v2 in
assert (if not cond then print_endline (“TEST FAILED: ” ^ msg) ; cond)
;;
(* Question 1: my_min tests *)
assert_equal 1 (my_min 1 2) “1 = my_min 1 2”;;
assert_equal 1 (my_min 2 1) “1 = my_min 2 1”;;
assert_equal 1 (my_min 1 1) “1 = my_min 1 1”;;
(* Question 2: my_median tests *)
assert_equal 2 (my_median 1 2 3) “2 = my_median 1 2 3”;;
assert_equal 2 (my_median 3 2 1) “2 = my_median 3 2 1”;;

To check that your program “passes” the tests, from the command line you will first need to compile your
program:
ocamlopt -o hw8_tests hw8.ml hw8_tests.ml
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You can then run the executable:
./hw8_tests
If your tests succeed you should not get any additional output (other than the “Running HW8 Tests”
message.