| le(tbl) `a total order on the values of "Key.T"`
The total order "le(tbl)" must be time-invariant.
The methods have the following specifications:
The call "tbl.iterateOrdered(up)" returns an iterator, which is an object that can be used to iterate over all the key-value pairs in "tbl", ordered by key. The order is increasing if "up" is "TRUE", decreasing otherwise.
If "i" is the result of the call "tbl.iterateOrdered(up)", then the call "i.next(k, v)" sets "k" and "v" to the key and value of the next pair and returns "TRUE". If no entries remain, the call returns "FALSE" without setting "k" or "v". It is a checked runtime error to call "next" or "seek" after "next" has returned "FALSE". The client must ensure that while an iterator is in use, the parent table is not modified.
The call "i.seek(k)" skips past zero or more key-value pairs (either forward or backward) so that a subsequent call of "next" returns the first pair with key greater than or equal to "k" if "i" is in increasing order or with key less than or equal to "k" if "i" is in decreasing order.
The type "Default" is an implementation of "T" using randomized heap-ordered binary trees or ``treaps'' (see \cite{Aragon}). In this implementation, seeking forward (relative to the iterator's order) is more efficient than seeking backward. If a forward seek skips over "d" key-value pairs, the expected time for the seek is "O(log d)". The time for a backward seek is "O(log(table.size()))", no matter how far back it skips.
The call "dflt.init()" returns "dflt" after initializing it to an empty table.
The call "dflt.keyCompare(k1, k2)" returns "Key.Compare(k1, k2)". The other methods call "keyCompare" whenever they need to consult "le(tbl)". This means a subtype of "Default" can determine "le(tbl)" by overriding "keyCompare", providing "keyCompare" implements a total order.
For efficiency, sorted tables and their iterators are not monitored, so a client accessing a table from multiple threads must ensure that if two operations are active concurrently, then neither of them has side effects on the same table or iterator. The "T.put", "T.delete", and "Default.init" methods are the only ones with side effects on the table. An iterator's "next" method has side-effects on the iterator.