CSE 130 - Programming Assignment #3

OCaml

100 points

Must be turned in no later than 4:59:59 PM on April 30
(see submission instructions below)

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Note: See this for instructions on starting OCaml in the ACS lab machines. To download and install OCaml version on your home machines see the instructions here. Remember that this is only to enable you to play with the assignment at home: the final version turned in must work on the ACS Linux machines. Note: While you can use windows to begin working with OCaml, the code you turn in must be that required for the ACS Linux environment.

Code Documentation and General Requirements

Code for all programming assignments should be well documented. A working program with no comments will receive only partial credit. Documentation entails writing a description of each function/method, class/structure, as well as comments throughout the code to explain the program logic. Comments in OCaml/NJ are enclosed within (* *), and may be nested. It is understood that some of the exercises in this programming assignment require extremely little code and will not require extensive comments.

While few programming assignments pretend to mimic the "real" world, they may, nevertheless, contain some of the ambiguity that exists outside the classroom. If, for example, an assignment is amenable to differing interpretations, such that more than one algorithm may implement a correct solution to the assignment, it is incumbent upon the programmer to document not only the functionality of the algorithm (and more broadly his/her interpretation of the program requirements), but to articulate clearly the reasoning behind a particular choice of solution.


Assignment Overview

The overall objective of this assignment is to expose you to fold, fold, and more fold. And just when you think you've had enough, FOLD. The assignment is spread over two files misc.ml, test.ml, that you need to download. The first file contains several skeleton OCaml functions, with missing bodies, i.e. expressions, which currently contain the text raise Failure "to be written" . Your task is to replace the text in those files with the the appropriate OCaml code for each of those expressions.

Note: All the solutions can be done using the purely functional fragment of OCaml, using constructs covered in class, and most require the use of recursion. Solutions using imperative features such as references or while loops will receive no credit. Feel free to use any library functions that you want.

It is a good idea to start this assignment early as it is somewhat harder than the first assignment.


Assignment Testing and Evaluation

Your functions/programs must compile and/or run on a Linux ACS machine (e.g. ieng6.ucsd.edu , as this is where the verification of your solutions will occur. While you may develop your code on any system, ensure that your code runs as expected on an ACS machine prior to submission. You should test your code in the directories from which the zip files (see below) will be created, as this will approximate the environment used for grading the assignment.

Most of the points, except those for comments and style, will be awarded automatically, by evaluating your functions against a given test suite. The fourth file, test.ml contains a very small suite of tests which gives you a flavor of of these tests. At any stage, by typing at the UNIX shell :

ocaml test.ml | grep "130>>" > log
you will get a report on how your code stacks up against the simple tests.

The last line of the file log must contain the word "Compiled" otherwise you get a zero for the whole assignment. If for some problem, you cannot get the code to compile, leave it as is with the raise ..., with your partial solution enclosed below as a comment. There will be no exceptions to this rule. The second last line of the log file will contain your overall score, and the other lines will give you a readout for each test. You are encouraged to try to understand the code in test.ml, and subsequently devise your own tests and add them to test.ml, but you will not be graded on this.

Alternately, inside the OCaml shell, type (user input is in red):

- #use "test.ml";;
.
.
.
- : int * int = (...,...)
and it should return a pair of integers, reflecting your score and the max possible score on the sample tests. If instead an error message appears, your code will receive a zero.



Submission Instructions

1. Create the zip file for submission

Your solutions to this assignment will be stored in separate files under a directory called solution/, inside which you will place the files: misc.ml. There should be no other files in the directory.

After creating and populating the directory as described above, create a zip file called <LastName>_<FirstName>_cse130_pa3.zip by going into the directory solution and executing the UNIX shell command:

zip <LastName>_<FirstName>_cse130_pa3.zip *
You can refer to an example submission file to compare with yours. Make sure that your zipped file's structure is the same as the example.

2. Test the zip file to check for its validity

Once you've created the zip file with your solutions, you will use the validate_pa3 program to see whether your zip file's structure is well-formed to be inspected by our grading system by executing the UNIX shell command:

validate_pa3 <LastName>_<FirstName>_cse130_pa3.zip
The validate_pa3 program will output OK if your zip file is well-formed and your solution is compiled. Otherwise, it will output some error messages. Before going to step 3, make sure that your zip file passes validate_pa3 program. Otherwise you get a zero for the whole assignment. If you have any trouble with this, refer to the instructions in step 1.

3. Submit the zip file via the turnin program

Once your zip file passes the validation check by validate_pa3, you will use the turnin program to submit this file for grading by going into the directory solution/ and executing the UNIX shell command:

turnin -c cs130s -p pa3 <LastName>_<FirstName>_cse130_pa3.zip

The turnin program will provide you with a confirmation of the submission process; make sure that the size of the file indicated by turnin matches the size of your tar file. See the ACS Web page on turnin for more information on the operation of the program.


Problem #1: Warm-Up (misc.ml)

(a) 10 points

Fill in the skeleton given for sqsum , which uses List.fold_left to get an OCaml function sqsum : int list -> int that takes a list of integers [x1;...;xn]) and returns the integer: x1^2 + ... + xn^2 . Your task is to fill in the appropriate values for (1) the folding function f and (2) the base case base. Once you have implemented the function, you should get the following behavior at the OCaml prompt:

# sqsum [];;
- : int = 0
# sqsum [1;2;3;4] ;;
- : int = 30
# sqsum [-1;-2;-3;-4] ;;
- : int = 30

(b) 20 points

Fill in the skeleton given for pipe, which uses List.fold_left to get an OCaml function pipe : ('a -> 'a) list -> ('a -> 'a) . The function pipe takes a list of functions [f1;...;fn]) and returns a function f such that for any x, the application f x returns the result fn(...(f2(f1 x))). Again, your task is to fill in the appropriate values for (1) the folding function f and (2) the base case base. Once you have implemented the function, you should get the following behavior at the OCaml prompt:

# pipe [] 3;;
- : int = 3
# pipe [(fun x-> 2*x);(fun x -> x + 3)] 3 ;;
- : int = 9
# pipe [(fun x -> x + 3);(fun x-> 2*x)] 3;;
- : int = 12

(c) 15 points

Fill in the skeleton given for sepConcat, which uses List.fold_left to get an OCaml function sepConcat : string -> string list -> -> string. The function sepConcat is a curried function which takes as input a string sep to be used as a separator, and a list of strings [s1;...;sn]. If there are 0 strings in the list, then sepConcat should return "". If there is 1 string in the list, then sepConcat should return s1. Otherwise, sepConcat should return the concatination s1 sep s2 sep s3 ... sep sn. You should only modify the parts of the skeleton consisting of failwith "to be implemented". You will need to define the function f, and give values for base and l. Once you have filled in these parts, you should get the following behavior at the OCaml prompt:

# sepConcat ", " ["foo";"bar";"baz"];;
- : string = "foo, bar, baz"
# sepConcat "---" [];;
- : string = ""
# sepConcat "" ["a";"b";"c";"d";"e"];;
- : string = "abcde"
# sepConcat "X" ["hello"];;
- : string = "hello"

(d) 5 points

Implement the curried OCaml function stringOfList : ('a -> string) -> 'a list -> string. The first input is a function f: 'a -> string which will be called by stringOfList to convert each element of the list to a string. The second input is a list l: 'a list, which we will think of as having the elemtns l1, l2, ..., ln. Your stringOfList function should return a string representation of the list l as a concatenation of the following: "[" (f l1) "; " (f l2) "; " (f l3) "; " ... "; " (f ln) "]". This function can be implemented on one line without using any recursion by calling List.map and sepConcat with appropriate inputes. Once you have completed this function, you should get the following behavior at the OCaml prompt:

# stringOfList string_of_int [1;2;3;4;5;6];;
- : string = "[1; 2; 3; 4; 5; 6]"
# stringOfList (fun x -> x) ["foo"];;
- : string = "[foo]"
# stringOfList (stringOfList string_of_int) [[1;2;3];[4;5];[6];[]];;
- : string = "[[1; 2; 3]; [4; 5]; [6]; []]"


Problem #2: Big Numbers (misc.ml)

As you may have noticed, the OCaml type int only contains values upto a certain size. For example, entering 9999999999 results in the message int constant too large . You will now implement functions to manipulate large numbers represented as lists of integers.

(a) 5 + 5 + 5 points

Write a curried function clone : 'a -> int -> 'a list which first takes as input x and then takes as input an integer n. The result is a list of length n, where each element is x. If n is 0 or negative, clone should return the empty list. Once you have implemented the function, you should get the following behavior at the OCaml prompt:

# clone 3 5;;
- : int list = [3; 3; 3; 3; 3]
# clone "foo" 2;;
- : string list = ["foo"; "foo"]
# clone clone (-3);;
- : ('_a -> int -> '_a list) list = []

Use the function clone to write a curried function padZero : int list -> int list -> int list * int list which takes two lists: [x1,...,xn] [y1,...,ym] and adds zeros in front to make the lists equal. Once you have implemented the function, you should get the following behavior at the OCaml prompt:

# padZero [9;9] [1;0;0;2];;
- : int list * int list = ([0;0;9;9],[1;0;0;2])
# padZero [1;0;0;2] [9;9];;
- : int list * int list = ([1;0;0;2],[0;0;9;9])

Now write a function removeZero : int list -> int list , that takes a list and removes a prefix of trailing zeros. Once you have implemented the function, you should get the following behavior at the OCaml prompt:

# removeZero [0;0;0;1;0;0;2];;
- : int list = [1;0;0;2]
# removeZero [9;9];;
- : int list = [9;9]
# removeZero [0;0;0;0];;
- : int list = []

(b) 15 points

Suppose we use the list [d1;d2;d3;...;dn], where each di is in the range [0..9], to represent the (positive) integer d1d2d3...dn. For example, the list [9;9;9;9;9;9;9;9;9;9] represents the integer 9999999999. Fill out the implementation for bigAdd : int list -> int list -> int list , so that it takes two integer lists, where each integer is in the range [0..9] and returns the list corresponding to the addition of the two big integers. Again, you have to fill in the implementation to supply the appropriate values to f, base, args . Once you have implemented the function, you should get the following behavior at the OCaml prompt:

# bigAdd [9;9] [1;0;0;2];;
- : int list = [1;1;0;1]
# bigAdd [9;9;9;9] [9;9;9];;
- : int list = [1;0;9;9;8]

(c) 10 + 10 points

Next you will write functions to multiply two big integers. First write a function mulByDigit : int -> int list -> int list which takes an integer digit and a big integer, and returns the big integer list which is the result of multiplying the big integer with the digit. Once you have implemented the function, you should get the following behavior at the OCaml prompt:

# mulByDigit 9 [9;9;9;9];;
- : int list = [8;9;9;9;1]

Now, using the function mulByDigit, fill in the implementation of bigMul : int list -> int list -> int list . Again, you have to fill in implementations for f , base , args only. Once you are done, you should get the following behavior at the prompt:

# bigMul [9;9;9;9] [9;9;9;9];;
- : int list = [9;9;9;8;0;0;0;1]
# bigMul [9;9;9;9;9] [9;9;9;9;9];;
- : int list = [9;9;9;9;8;0;0;0;0;1]