Problem Set 1 An introduction to SML

Due: Tuesday, September 10th, 4:00 PM

Instructions: you will do this problem set by modifying the source file ps1.sml and submitting the program that results. The program that you submit must compile. Programs that do not compile will receive an automatic zero. If you are having trouble getting your assigment to compile, please visit consulting hours. If you run out of time, it is better to comment out the parts that do not compile and hand in a file that compiles, rather than handing in a more complete file that does not compile.

Note: for functions that are not implemented, you should see something of the form "raise Fail "Not implemented."". You should remove this text and replace it with the body of the function.

There are four separate parts to this assignment.

Update 9/5

The GCD definition has been updated to include the following rules:
GCD(0, m) = m
GCD(m, n) = GCD(n, m)

You may also assume that all inputs to GCD are valid (greater than or equal to zero).

Update 9/4 The conversions for problem 3d are defined as follows:

1 liter = 1.0566882  quarts
1 quart = 0.94635295 liters
1 quart = 4.00000000 cups

Part 1: Posting to the newsgroup

Post a test message to cornell.test with the subject "CS312 Test".
DO NOT post test messages to the course newsgroup or you may be penalized.

Part 2: Improving Style

The following functions are all technically correct, but very difficult to read. Fix the indentation, use let to avoid unnecessary expressions, or whatever else you feel is needed to fix any violations of the style guide.

1. (* This function takes in two parameters, a string representing the base word that needs to have dashes appended to it, and an integer representing the number of dashes to append to the base string. The function recursively calls itself, appending a dash to the base each time until the count variable is less than 0, at which point it appends a final star. The final result is the string produced by appending an appropriate number of dashes and a star to the base string. *)
   fun foo (mommy, rudolf) =
   if (mommy <= 0) then rudolf^"*"
   else foo(mommy-1, rudolf^"-")
   


2. fun partB (x:(bool*bool)) =
   if #1(x) then if #2(x) then true else false else true
   


3. fun fib (x) =
   case x
   of 0 =>
   1 | 1 => 1 |
   _ =>
   fib(x-1) + fib(x-2)
   


4. fun printFibs(x) =
   print ("The Fibonacci number at position " ^ Int.toString x ^ " is "
   ^ Int.toString(fib(x)) ^ ".\n" ^ Int.toString(fib(x))
   ^ " is my favorite number. Is " ^ Int.toString(fib(x))
   ^ " your favorite number too?\n")
   

Part 3: Value and Function Declarations

Write val and fun declarations as follows:

1. Assign a tuple with the names of all the people on course staff to the variable reallyCoolPeople.
   


2. Bind the last letter on the "Installing Course Software" page to the variable lastLetter of type char.
   


3. Bind your name, age and whether you intend to be a CS major to a record, personal of type {name:string, age:int, cs:bool}.
   


4. Write the function cookingConversions which takes a string (either "CUPS", "QUARTS", or "LITERS") representing the units to convert from, a real representing the number of units, and another string (either "CUPS", "QUARTS", or "LITERS"), representing the units to convert to. Assume that only those three strings will be passed into the function (that is, you do not have to check for bad inputs). The function should return the number of units in the converted measure.
   


5. Declare a function gcd with the type int * int -> int for computing the Greatest Common Divisor based on the following equations: (from Paulson and Brandon)
   GCD(0, m) = m
   GCD(2m, 2n) = 2 x GCD(m, n)
   GCD(2m, 2n + 1) = GCD(m, 2n + 1)
   GCD(2m + 1, 2n + 1) = GCD(n - m, 2m + 1) m < n
   GCD(m, m) = m
   GCD(m, n) = GCD(n, m)
   

Part 4: Using the Basis Library

The basis library is one of the most helpful resources you have on your quest to learn SML. For this part of the assignment, you should browse The Standard ML Basis Library and then write short (one line) functions using the functions in the basis library.

1. Write a function, isFifthCharUpper, that takes a string as input and returns true if the 5th character is Upper Case. It returns false if the string is less than 5 characters long.
   


2. Write a function, extractIntAndFraction, that takes a real and returns a tuple of an int and a real, where the int is the integer part of the number and the real is the fraction part of the number.
   


3. Write a function, currentTimeString, that gets the current time and returns a string representing the local time in the format: " DayOfWeek Month Day HH:MM:SS Year ". For example, this example would be valid: "Fri Sep 13 20:00:00 2002"