Computer Science 538
Lecture Notes for 4-3-00
Lecture by Professor Fischer
Notes by Michael Waddell

Using the OPTION property in SML
-------------------------------

Syntax:
Datatype 'a option = none/some of 'a;

Usage:
Val Zilch = none;
Val Mucho = some(10E9);

However, the structure is what counts, not the keywords.  Thus, the following
is also legal:

Datatype 'a present = absent / here of 'a;

This datatype gives us an easy way to specify when data is unavailable.
It also allows us to build recursive data types very simply:

Example: Binary tree

Datatype Bintree = Null / Leaf / Node of Bintree*Bintree;

Usage:

Node(Leaf,Null)

       ___
      |___|
   ___/
  |___|

Node(Leaf,Leaf)
       ___
      |___|
   ___/   \___
  |___|   |___|

Leaf
       ___
      |___|

Null
        ?

Here's a useful function:

Fun size(Null)=0
 |  size(Leaf)=1
 |  size(Node(L,R))=size(L)+size(R)+1;

How do we attach a datafield to each node of a b-tree?

Syntax:
Datatype 'a bintree = Null | Leaf of 'a | node of 'a bintree*'a bintree;

Usage:

Node(Leaf(1),Leaf(7))
       ___
      |___|
   ___/   \___
  |_1_|   |_7_|

What if we wanted data in the internal nodes too?

Syntax:
Datatype 'a bintree = Null | Leaf of 'a | node of 'a*'a bintree*'a bintree;

Usage:

Node(5,Leaf(1),Leaf(7))
       ___
      |_5_|
   ___/   \___
  |_1_|   |_7_|

What if I want to allow values to be null sometimes?

Answer: Use OPTION!

Syntax:
Datatype 'a bintree = Null | Leaf of 'a option
                           | node of 'a option*'a bintree*'a bintree;

Usage:

Node(Some(5),Leaf(Some(1)),Leaf(Some(7)))
       ___
      |_5_|
   ___/   \___
  |_1_|   |_7_|

Let's look at the frontier of the tree (the leaves read left->right.)

Fun Frontier(Null)=[]
 |  Frontier(Leaf(V))=[V]
 |  Frontier(Node(T1,T2))=Frontier(T1)@Frontier(T2);

Note: @ is the infix append operator.