Description
Reading Assignment. Read the following sections in the textbook:
• Sections 8.1-8.2: Data Types and Type Systems
• Sectoin 11.1: Computations without State
Programming Homework. The goal of this assignment is to get started using OCaml. Note
that you can download and run OCaml on your own computer (available at https://ocaml.org).
OCaml is also available for use on the shared ada server and on the department’s virtual machine.
Your job is to implement the following functions from scratch in a file hw7.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);
• follow the general style guide provided by OCaml (https://ocaml.org/learn/tutorials/
guidelines.html)
• appropriately comment your code throughout including a file header with your name, file
name, the date, and a brief description; and
• create sufficient test cases for your functions to ensure they work correctly.
The following ten 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.
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.
3. Implement a function my_triangle_area base height that computes the triangle height
given a base and a height value (as floats).
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. would cube the value v.
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.
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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.
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.
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.
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.
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)
return false;
else if (x == 1)
return true;
else
return even(x – 1);
}
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For testing, we’ll use our own “poor man’s” unit testing approach (instead of a unit testing framework
like OUnit). In particular, your program should be structured as follows:
(*
Name: …
File: hw7.ml
Date: Spring 2021
Desc: …
*)
(* Question 1: *)
let my_min x y z =
…
;;
(* Question 2:*)
let my_median x y z =
…
;;
…
(* Testing *)
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”;;
…
To check that your program “passes” the tests, from the command line simply run:
$ ocaml hw7.ml
Homework Submission. All homework must be submitted through GitHub Classroom. A link
for each assignment will be posted on Piazza when the homework is assigned. Be sure all of your
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code is pushed by the due date (which you can double check for your repository using the GitHub
website). Each programming assignment is worth 35 points. The points are allocated based on
the following.
• Correct and Complete (25 points). Your code must correctly and completely do the
requested tasks using the requested techniques. Note that for most assignments you will be
provided a partial set of test cases to help you determine a minimal level of correctness. If
your program fails any of the provided test cases you will only receive partial credit. Note
that passing the given test cases does not mean your work is complete nor correct. Your
assignment will also be graded with additional test cases (not provided to you) that will help
the graders determine the extent of your solution and your final score. Note that for C++
code, correctness also implies properly handling the creation and deletion of dynamic memory
(i.e., the absence of memory leaks).
• Evidence and Quality of Testing (5 points). As part of your homework assignments
you must develop additional test cases beyond those given to you to ensure your program is
correct and complete. These test cases must be turned in with your assignment. You will be
graded on the scope and quality of the additional test cases you provide.
• Formatting and Comments (5 points). Your code must be formatted consistently and
appropriately for the language used. For C++, you must follow the provided style guide (see
the course webpage).You must also comment your code and test cases, which at a minimum
must include a file heading (see examples provided), function comments, and meaningfully
selected variable, class, and function names. See the assignment for style guides in other
languages.
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