CSE 130 - Programming Assignment #3

Ocaml

100 points

Must be turned in no later than 11:59:59 PM on 02/09/2008
(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 3.10.03 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.

Integrity of Scholarship

University rules on integrity of scholarship will be strictly enforced. By completing this assignment, you implicitly agree to abide by the UCSD Policy on Integrity of Scholarship described beginning on page 68 of the Academic Regulations section (PDF) of the 2007-2008 General Catalog, in particular, "all academic work will be done by the student to whom it is assigned, without unauthorized aid of any kind."

You are expected to do your own work on this assignment; there are no group projects in this course. You may (and are encouraged to) engage in general discussions with your classmates regarding the assignment, but specific details of a solution, including the solution itself, must always be your own work. Incidents that violate the University's rules on integrity of scholarship will be taken seriously: In addition to receiving a zero (0) on the assignment, students may also face other penalties, up to and including, expulsion from the University. Should you have any doubt about the moral and/or ethical implications of an activity associated with the completion of this assignment, please see the instructors.


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 some advanced features of Ocaml such as higher-order functions, abstract datatypes and modules, as well as to fully understand the notion of scoping, binding, environments and closures, by implementing a mini-ML interpreter. Again, no individual function requires more than 10-15 lines, so if you're answer is longer, you can be sure that you need to rethink your solution. The assignment is spread over two files misc.ml, test.ml, that you need to download. The first four files contain 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 pa3_solution/, inside which you will place the file: 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>_pa3.zip by going into the directory solution and executing the UNIX shell command:

zip <LastName>_<FirstName>__pa3.zip *

2. Submit the zip file via the turnin program

Once you've created the zip file with your solutions, 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 cs130w -p pa3 <LastName>_<FirstName>_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 fold 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 fold to get an Ocaml function sqsum: ('a -> 'a) list -> ('a -> 'a) . The function pipe takes a list of functions takes a list of integers [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


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 points

Use the function clone to write a 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 a pair of 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, b, 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 list * int -> int list which takes a tuple of a big integer and an (integer) digit, 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 * int list . Again, you have to fill in implementations for f , base , args only. Once you are done, you should get the following behaviour 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]

Problem #3: Regular Expressions (misc.ml)

The function exact_match: string -> string -> bool takes as input a regular expression string, and returns a function, which takes a string, and returns true iff the string matches the regular expression exactly. Consider the behavior of is_uint which is equal to exact_match "[0-9]+". It returns true for exactly those strings that correspond to a non-empty sequence of digits, i.e. for those strings that correspond to unsigned integers.

(a) 5 points

Next fill in the skeleton using a regular expression describing integers, to get a Ocaml function is_int : string -> bool, such that is_int s returns true iff s corresponds to an integer. An integer is defined as a sequence of at least one decimal digits preceded by an optional minus sign. A regular expression for such integers is "^-?[0-9]+$". For more information on Ocaml regular expressions, see here. Once you have implemented the function, you should get the following behavior at the Ocaml prompt:

# is_int "-12" ;;
- : bool = true
# is_int "ucsd" ;;
- : bool = false

(b) 10 points

Now fill in the regular expression template to get an Ocaml function is_sentence: string -> bool that takes a string s and returns true if s is a sentence and false otherwise. A sentence is defined as a sequence of words separated by spaces. A word is a sequence of letters. The first word in a sentence must be capitalized and the sentence must end with a period. No other punctuation is allowed. Once you have implemented the function, you should get the following behavior at the Ocaml prompt:

# is_sentence "Ocaml is fun." ;;
- : bool = true
# is_sentence "Mugatu." ;;
- : bool = true
# is_sentence "this is the end" ;;
- : bool = false
# is_sentence "29" ;;
- : bool = false

(c) 10 points

Now fill in the regular expression templates sign, num and expo to get an Ocaml function is_float: string -> bool that takes a string s and returns true if s is a string corresponding to a floating point number and false otherwise. A floating point number is defined as an optional sign which is an + or -, followed by a num which is a decimal point with a non-empty sequence of digits on at least one side, followed by an optional exponent which is an E or e followed by an optional sign followed by an integer. Once you have implemented the function, you should get the following behavior at the Ocaml prompt:

# is_float "1.0" ;;
- : bool = true
# is_float "-1." ;;
- : bool = true
# is_float "-.8" ;;
- : bool = true
# is_float "2.e-10" ;;
- : bool = true
# is_float "-3.14E10" ;;
- : bool = true
# is_float "." ;;
- : bool = false
# is_float "e12" ;;
- : bool = false
# is_float "12" ;;
- : bool = false
# is_float "-" ;;
- : bool = false