This assignment is to implement 2-3 Trees in Omega using Omega';s type system to enforce the invariants of 2-3 trees.

See the following set of slides about 2-3 Trees I found on the web as an introduction.

2-3 Trees have the follwoing invariants (taken from wikipedia with some of my own improvements).

1. Every non-leaf is a 2-node or a 3-node. A 2-node contains one data item and has two children. A 3-node contains two data items and has 3 children.
2. All leaves are at the same level (the bottom level). This means the distance from a leaf to the root is the same for all leaf nodes.
3. All data is kept in sorted order.
4. Leaf node will contain 1 or 2 data fields.

Here is a picture of a 2-3 tree.

As homework do the following

1. Define an Omega generalized algebraic datatype to encode 2-3-Trees.
2. Use type indexes to encode as many of the invariants as you can. (You may leave out the sorted order invariant if you desire, but even this one is possible).
3. Write an insert function that inserts an element and maintains the index invaraints, thus maintaining the balance invariant of the tree.

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