Interval merging

Merging intervals in the bracket form

A handily simple function for a merging task:

Given N input closed intervals in bracket form:
Ii := [left(i),right(i)], i = 1,2...,N (mathematical notation).

The set union{Ii) can be written as a canonical partition by intervals Jk; i.e., union{Ii) = union(Jk), where Jk are M intervals (with M<=N, so the partition is minimum cardinal), and {Jk} are disjoint to each other (their intersections are empty).

This function returns Jk = [lower(k),upper(k)], k=1,2,...M, in the ascending sorted order.