Aka merge-insertion sort.
This is a fairly inefficient sort in terms of speed and memory consumption. The main advantage is that is uses very few comparisons. For situations where each comparison is extremely expensive (e.g., you have to make a network request, query a database, or ask for human input) this may be useful.
Because this algorithm is only useful when comparisons are expensive, the API requires you to explicitly provide a comparison function.
Suppose you have a list of items and want to sort them by repeatedly comparing pairs of elements.
Keep track of the human-provided comparisons in a Vec<(T, T), Ordering>
Sort the list with a comparison function based on the known orderings. Anywhere we do not have the required ordering, choose arbitrarily. Store the first pair.
Ask the human user to order that first unknown ordering.
Repeat. Eventually you will have all of the required orderings to fully sort the items.