# "MLing Sets" CSCI 305 Solution

This lab requires an independent study of the ML language. You are encouraged to use any web tutorials and resources to learn ML beyond those in the book and provided by me (i.e. you will need to find them).

Given the size of the class, I will not be able to debug your code for you

Please do not send panicked emails requesting I fix your bug for you.

Allow yourself plenty of time, and use patience, perseverance, and the internet to debug your code.

I will gladly answer clarifying questions about the goals and instructions of the Lab assignment. What this means is that if you come to my office hours or email me with questions concerning the following items or their derivatives, the provided stock answer applies. When it comes to these assignments, think of me more as your client/customer who is acquiring your product. Before coming to me with a question regarding the assignment, ask whether

you would ask a client/customer that question.

Can you take a look at this code and tell me what I'm doing wrong? No.

Can you help me debug this program? No.

Can you help me get XXX running on my computer? No.

Can you tell me why my code isn't working? No.

ML

For this lab, you will use ML. You may use any flavor of ML of your choice. I recommend the Standard New Jersey flavor for Linux and MacOS, and PolyML for Windows.

What's Already In the File

The provided code in file ml_lab.sml has the following pieces of code (in order from top to

bottom of the file):

Lines 1 - 8: -- A Header Comment Block, fill this in with appropriate information, note that your

first and last name do not have angle brackets surrounding them.

(***************************************************************

*

* CSCI 305 - ML Programming Lab

*

* <firstname <lastname

* <email-address

*

***************************************************************)

Line 10: The place where I would suggest placing your code.

(* Define your data type and functions here *)

Lines 12 - 31: Some simple funtions to print the contents of Sets, note these will not work until

you have defined the sets data type with the corresponding Set and Empty constructors.

(* Simple function to stringify the contents of a Set of characters *)

fun stringifyCharSet Empty = ""

| printCharSet (Set(y, ys)) = Char.toString(y) ^ " " ^ stringifyCharSet(ys);

(* Simple function to stringify the contents of a Set of ints *)

fun stringifyIntSet Empty = ""

| printIntSet (Set(w, ws)) = Int.toString(w) ^ " " ^ stringifyIntSet(ws);

(* Simple function to stringify the contents of a Set of strings *)

fun stringifyStringSet Empty = ""

| printStringSet (Set(z, zs)) = z ^ " " ^ stringifyStringSet(zs);

(* Simple function that prints a set of integers *)

fun print_int x = print ("{ " ^ stringifyIntSet(x) ^ "}\n");

(* Simple function that prints a set of strings *)

fun print_str x = print ("{ " ^ stringifyStringSet(x) ^ "}\n");

(* Simple function that prints a set of characters *)

fun print_chr x = print ("{ " ^ stringifyCharSet(x) ^ "}\n");

Lines 33 - 37: Some example code for the list2Set function, note this will not work until after

you define the list2Set function.

list2Set [1, 3, 2];

list2Set [#"a", #"b", #"c"];

list2Set [];

list2Set [6, 2, 2];

list2Set ["x", "y", "z", "x"];

Lines 39 - 58: The code from the lab questions, from which answers to questions 1, 5, 7, 9 and

10 will come.

(* Question 1 *)

f [3, 1, 4, 1, 5, 9]

(* Question 5 *)

val quest5 = isMember "one" (list2Set ["1", "2", "3", "4"]);

print ("\nQuestion 5: " ^ Bool.toString(quest5) ^ "\n");

(* Question 7 *)

val quest7 = list2Set ["it", "was", "the", "best", "of", "times,", "it", "was", "the",

print "\nQuestion 7: ";

print_str quest7;

print "\n";

(* Question 9 *)

print "\nQuestion 9: ";

print_str (union (list2Set ["green", "eggs", "and"]) (list2Set ["ham"]));

(* Question 10 *)

print "\nQuestion 10: ";

print_str (intersect (list2Set ["stewed", "tomatoes", "and", "macaroni"]) (list2Set ["macaroni

Other Files

Along with the source code in ml_lab.sml there are three other files:

LICENSE - A simple license for this code based on the MIT License.

README - What you are currently reading.

README.pdf - A pdf version of what you are currently reading.

Warmup

Begin by entering this function in ML. The lines that begin with a semicolon are comment lines that

you will fill in.

fun f [] = [] (* a *)

| f (x::xs) = (x + 1) :: (f xs) (* b *)

Lab Questions 1 - 4

1. Run this function as f [3, 1, 4, 1, 5, 9] . What output do you get?

2. What does this function f do?

3. Give a comment that explains the line following (a) .

4. Give a comment that explains the line following (b) .

Sets datatype

Construct a datatype used to represent sets, called set , it should have two different types: Set

and Empty . Where Set is of type 'element * 'element set , meaning that it hold some

polymorphic type 'element and a sets of 'element .

isMember function

Write a function isMember that determines if an element e is part of the set, set . This function

will return true if e is a member of the set, set , and false otherwise.

fun isMember e set = ; (* complete this function definition *)

list2Set function

Write a function list2Set that convertes a list into a set ensuring that the properties of a well

formed set, i.e., that is has no duplicates, are maintained. You may find it useful to make use of

your isMember function in your list2Set function.

For example:

list2Set [1, 3, 2]; = Set (1, Set (3, Set (2, Empty)))

list2Set [#"a", #"b", #"c"]; = Set (#"a", Set (#"b", Set (#"c", Empty)))

list2Set []; = Empty

list2Set [6, 2, 2]; = Set (6, Set(2, Empty))

list2Set ["x", "y", "z", "x"]; = Set ("x", Set ("y", Set ("z", Empty)))

fun isSet set = ; (* complete this function definition *)

Lab Questions 5 - 8

Your answers must reflect the output of your code. No credit will be given to answers if you have

not submitted the respective correct function implementation.

1. What output do you get for the call: isMember "one" ["1", "2", "3", "4"]

2. Does your isMember function use head or tail recursion?

3. What output do you get for the call

list2Set ["it", "was", "the", "best", "of", "times,", "it", "was", "the", "worst", "of", "times"];

1. Research tail recursion . Describe, in a few short sentences, why it can be beneficial to

write tail recursing functions.

Union function

Write a function union that takes the set union of set set1 and set set2 and returns a set

representing the mathematical union of the two sets. You may use the functions you defined

previously ( list2Set and isMember ), if useful, in addition to any of the common ML functions

mentioned in class. Comment your function.

fun union set1 set2 = ; (* complete this function definition *)

Intersect function

Write a function intersect that takes the set intersection of set set1 and set set2 and returns

a set representing the mathematical intersection of the two sets. Comment your function.

fun intersect set1 set2 = ; (* Complete this function definition *)

Lab Questions 9 - 10

Your answers must reflect the output of your code for these functions. No credit will be given to

answers if you have not submitted the respective correct function implementation in ML.

1. What output do you get for the call:

union (list2Set ["green", "eggs", "and"]) (list2Set ["ham"]);

1. What output do you get for the call:

intersect (list2Set ["stewed", "tomatoes", "and", "macaroni"]) (list2Set ["macaroni",

Lab Questions 11 - 15

The following questions are for feedback and evaluation purposes. Points are awarded for any

sincere answer.

1. Name something you like about ML. Explain.

2. Name something you dislike about ML. Explain.

3. Did you enjoy this lab? Which aspects did you like and/or dislike?

4. Approximately how many hours did you spend on this lab?

5. Do you think you will use ML again? For which type(s) of project(s)?

Submission

Each student will complete and submit this assignment individually. Do not consult with others.

However, you are encouraged to use the internet to learn ML but not to research the

questions asked in this lab.

Comment your program appropriately.

Save the final version of your program as [lastname]_[firstname].ml_lab.ml Type your lab

questions in plain text as [lastname]_[firstname].ml_lab.questions.txt . Include your name in

the text file.

Submit your files to the ML Lab dropbox folder on BrightSpace. Do not archive your files but

instead use two attachments. Submit your files before the due date as late submissions will not be

accepted.

Grading

Total Assignment Points: 100, Total Grade Points: 7.5

The rubric for this assignment is as follows:

5 points each for questions 1 - 15, Total 75 points

Questions 1, 5, 7, 9, and 10 will be graded all or nothing

Questions 11 - 15, will be given full credit for reasonable answers

The remaining questions will be graded with partial credit

15 points for working code, with no errors: All or nothing

10 points for documented code

2 points per function: isMember , list2Set , union , and intersect commented with a

good description of what the function does

2 points for header

Given the size of the class, I will not be able to debug your code for you

Please do not send panicked emails requesting I fix your bug for you.

Allow yourself plenty of time, and use patience, perseverance, and the internet to debug your code.

I will gladly answer clarifying questions about the goals and instructions of the Lab assignment. What this means is that if you come to my office hours or email me with questions concerning the following items or their derivatives, the provided stock answer applies. When it comes to these assignments, think of me more as your client/customer who is acquiring your product. Before coming to me with a question regarding the assignment, ask whether

you would ask a client/customer that question.

Can you take a look at this code and tell me what I'm doing wrong? No.

Can you help me debug this program? No.

Can you help me get XXX running on my computer? No.

Can you tell me why my code isn't working? No.

ML

For this lab, you will use ML. You may use any flavor of ML of your choice. I recommend the Standard New Jersey flavor for Linux and MacOS, and PolyML for Windows.

What's Already In the File

The provided code in file ml_lab.sml has the following pieces of code (in order from top to

bottom of the file):

Lines 1 - 8: -- A Header Comment Block, fill this in with appropriate information, note that your

first and last name do not have angle brackets surrounding them.

(***************************************************************

*

* CSCI 305 - ML Programming Lab

*

* <firstname <lastname

* <email-address

*

***************************************************************)

Line 10: The place where I would suggest placing your code.

(* Define your data type and functions here *)

Lines 12 - 31: Some simple funtions to print the contents of Sets, note these will not work until

you have defined the sets data type with the corresponding Set and Empty constructors.

(* Simple function to stringify the contents of a Set of characters *)

fun stringifyCharSet Empty = ""

| printCharSet (Set(y, ys)) = Char.toString(y) ^ " " ^ stringifyCharSet(ys);

(* Simple function to stringify the contents of a Set of ints *)

fun stringifyIntSet Empty = ""

| printIntSet (Set(w, ws)) = Int.toString(w) ^ " " ^ stringifyIntSet(ws);

(* Simple function to stringify the contents of a Set of strings *)

fun stringifyStringSet Empty = ""

| printStringSet (Set(z, zs)) = z ^ " " ^ stringifyStringSet(zs);

(* Simple function that prints a set of integers *)

fun print_int x = print ("{ " ^ stringifyIntSet(x) ^ "}\n");

(* Simple function that prints a set of strings *)

fun print_str x = print ("{ " ^ stringifyStringSet(x) ^ "}\n");

(* Simple function that prints a set of characters *)

fun print_chr x = print ("{ " ^ stringifyCharSet(x) ^ "}\n");

Lines 33 - 37: Some example code for the list2Set function, note this will not work until after

you define the list2Set function.

list2Set [1, 3, 2];

list2Set [#"a", #"b", #"c"];

list2Set [];

list2Set [6, 2, 2];

list2Set ["x", "y", "z", "x"];

Lines 39 - 58: The code from the lab questions, from which answers to questions 1, 5, 7, 9 and

10 will come.

(* Question 1 *)

f [3, 1, 4, 1, 5, 9]

(* Question 5 *)

val quest5 = isMember "one" (list2Set ["1", "2", "3", "4"]);

print ("\nQuestion 5: " ^ Bool.toString(quest5) ^ "\n");

(* Question 7 *)

val quest7 = list2Set ["it", "was", "the", "best", "of", "times,", "it", "was", "the",

print "\nQuestion 7: ";

print_str quest7;

print "\n";

(* Question 9 *)

print "\nQuestion 9: ";

print_str (union (list2Set ["green", "eggs", "and"]) (list2Set ["ham"]));

(* Question 10 *)

print "\nQuestion 10: ";

print_str (intersect (list2Set ["stewed", "tomatoes", "and", "macaroni"]) (list2Set ["macaroni

Other Files

Along with the source code in ml_lab.sml there are three other files:

LICENSE - A simple license for this code based on the MIT License.

README - What you are currently reading.

README.pdf - A pdf version of what you are currently reading.

Warmup

Begin by entering this function in ML. The lines that begin with a semicolon are comment lines that

you will fill in.

fun f [] = [] (* a *)

| f (x::xs) = (x + 1) :: (f xs) (* b *)

Lab Questions 1 - 4

1. Run this function as f [3, 1, 4, 1, 5, 9] . What output do you get?

2. What does this function f do?

3. Give a comment that explains the line following (a) .

4. Give a comment that explains the line following (b) .

Sets datatype

Construct a datatype used to represent sets, called set , it should have two different types: Set

and Empty . Where Set is of type 'element * 'element set , meaning that it hold some

polymorphic type 'element and a sets of 'element .

isMember function

Write a function isMember that determines if an element e is part of the set, set . This function

will return true if e is a member of the set, set , and false otherwise.

fun isMember e set = ; (* complete this function definition *)

list2Set function

Write a function list2Set that convertes a list into a set ensuring that the properties of a well

formed set, i.e., that is has no duplicates, are maintained. You may find it useful to make use of

your isMember function in your list2Set function.

For example:

list2Set [1, 3, 2]; = Set (1, Set (3, Set (2, Empty)))

list2Set [#"a", #"b", #"c"]; = Set (#"a", Set (#"b", Set (#"c", Empty)))

list2Set []; = Empty

list2Set [6, 2, 2]; = Set (6, Set(2, Empty))

list2Set ["x", "y", "z", "x"]; = Set ("x", Set ("y", Set ("z", Empty)))

fun isSet set = ; (* complete this function definition *)

Lab Questions 5 - 8

Your answers must reflect the output of your code. No credit will be given to answers if you have

not submitted the respective correct function implementation.

1. What output do you get for the call: isMember "one" ["1", "2", "3", "4"]

2. Does your isMember function use head or tail recursion?

3. What output do you get for the call

list2Set ["it", "was", "the", "best", "of", "times,", "it", "was", "the", "worst", "of", "times"];

1. Research tail recursion . Describe, in a few short sentences, why it can be beneficial to

write tail recursing functions.

Union function

Write a function union that takes the set union of set set1 and set set2 and returns a set

representing the mathematical union of the two sets. You may use the functions you defined

previously ( list2Set and isMember ), if useful, in addition to any of the common ML functions

mentioned in class. Comment your function.

fun union set1 set2 = ; (* complete this function definition *)

Intersect function

Write a function intersect that takes the set intersection of set set1 and set set2 and returns

a set representing the mathematical intersection of the two sets. Comment your function.

fun intersect set1 set2 = ; (* Complete this function definition *)

Lab Questions 9 - 10

Your answers must reflect the output of your code for these functions. No credit will be given to

answers if you have not submitted the respective correct function implementation in ML.

1. What output do you get for the call:

union (list2Set ["green", "eggs", "and"]) (list2Set ["ham"]);

1. What output do you get for the call:

intersect (list2Set ["stewed", "tomatoes", "and", "macaroni"]) (list2Set ["macaroni",

Lab Questions 11 - 15

The following questions are for feedback and evaluation purposes. Points are awarded for any

sincere answer.

1. Name something you like about ML. Explain.

2. Name something you dislike about ML. Explain.

3. Did you enjoy this lab? Which aspects did you like and/or dislike?

4. Approximately how many hours did you spend on this lab?

5. Do you think you will use ML again? For which type(s) of project(s)?

Submission

Each student will complete and submit this assignment individually. Do not consult with others.

However, you are encouraged to use the internet to learn ML but not to research the

questions asked in this lab.

Comment your program appropriately.

Save the final version of your program as [lastname]_[firstname].ml_lab.ml Type your lab

questions in plain text as [lastname]_[firstname].ml_lab.questions.txt . Include your name in

the text file.

Submit your files to the ML Lab dropbox folder on BrightSpace. Do not archive your files but

instead use two attachments. Submit your files before the due date as late submissions will not be

accepted.

Grading

Total Assignment Points: 100, Total Grade Points: 7.5

The rubric for this assignment is as follows:

5 points each for questions 1 - 15, Total 75 points

Questions 1, 5, 7, 9, and 10 will be graded all or nothing

Questions 11 - 15, will be given full credit for reasonable answers

The remaining questions will be graded with partial credit

15 points for working code, with no errors: All or nothing

10 points for documented code

2 points per function: isMember , list2Set , union , and intersect commented with a

good description of what the function does

2 points for header

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