• Assignment
• Turn In

Starting Poly ML

Home:

1. •Download Poly/ML 

2. Unzip and run the Setup

3. •Open by something similar to:

Start | Programs | Poly ML |
Run | Poly ML

IUS:

student apps (on Desktop) | network Shortcuts | Shortcut to PolyML.exe | Select ML_dbase.pmd  

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•

Programming

IMMEDIATE WINDOW - Poly ML opens in immediate execution mode as in the window at right. ML instructions can be entered directly and are executed immediately. 

EDIT WINDOW - The immediate execution window doesn't support editing. To enter and edit functions do any of the following:

• use Notepad or other text editor
• open a source file in ML using: 
  • File | New

The Source1 window at right is used for entering and editing the ML functions.

EXECUTING - ML execution is done in the immediate window. Either:

• Enter ML instructions directly into immediate window, enter:

  1+4;
      val it = 5 : int

• Copy ML instructions from text editor, etc. by ML menu commands into immediate window:

   Edit | Paste 

The top window at right shows the result of pasting the reverse function from the Source1 window to the immediate window.

Debugging - Function entry and exit and certain parameters can be traced during execution, useful. Just copy and paste the following:

PolyML.Compiler.debug := true;
open PolyML.Debug;
trace true; 

Assignment

Write, test with the given expressions and print the following functions.

1. GCD returns the greatest common divisor of two integers. Write the recursive function that implements Euclid's algorithm:
   
       int GCD(int x, int y) {
           if (y==0) return x;
           else        return GCD(y, x % y);
      }
   
   The ML modulus operator is mod: 15 mod 4 is 3.
   
           gcd (9,18);
               val it = 9 : int
           gcd(16,25);
               val it = 1 : int
           gcd(27,81);
               val it = 27 : int
           gcd(36,81);
               val it = 9 : int
    
2. Biggest returns the largest number in a list.

biggest [1,~3,6,4,~2];
    val it = 6 : int
biggest [5];
    val it = 5 : int



3. Positive returns a list consisting of the positive numbers in a list.

positive [1,2,3,4,~3,5];
    val it = [1, 2, 3, 4, 5] : int list
positive [~1,~2];
    val it = [] : int list




4. Intersect returns the intersection of two lists. Hint: Use member.

        fun member (a,L) =
            if null L then false
            else if a = hd L then true
                   else member(a, tl L);

intersect ([1,2,3,4], [3,4,5,6]);
    val it = [3, 4] : int list
intersect ([1,2,3,4], [5,6,7,8]);
    val it = [] : int list



5. Insert returns an ordered list with an element inserted.

insert (4, [1,2,3,5]);
    val it = [1, 2, 3, 4, 5] : int list
insert (4, []);
    val it = [4] : int list
insert (1, [2,3,4]);
    val it = [1, 2, 3, 4] : int list



6. Sort a list. Hint: Use insert.

sort [5,4,3,2,1];
    val it = [1, 2, 3, 4, 5] : int list
sort [];
    val it = [] : int list
sort [4,2,5,1,3];
    val it = [1, 2, 3, 4, 5] : int list

Turn In

1. Cover sheet with your name, date, and Homework 1.
2. Print out of function definitions .
3. Print interactions for Assignments 1-6 containing the evaluation results of all the functions using the given test examples.

Hints

Just for comparison, below is a Java version of the insertion sort.

static LinkedList insert(Integer a, LinkedList L) {   if (L.size() == 0) L.add(a);   else if (a.intValue() > ((Integer) L.getFirst()).intValue()) {             Integer first = (Integer) L.removeFirst();             insert(a, L).addFirst(first);         }         else L.addFirst(a);   return L; } static LinkedList sort(LinkedList L) {   if (L.size() == 0) return L;   Integer first = (Integer) L.removeFirst();   return insert(first, sort(L)); }