It would also be interesting to extend this language to the one that also has partial conditions satisfied, e.g.: - We have a set S of tuples (a,b,c) sorted by (a,b) - We would like to sort S by (a,b,c) - Therefore we only need to only sort subsets (a,b,cx)

By the way, permutation sort would be reducing the sorting algorithm to a problem of search in the configuration space of N variables. Speaking generally, you may reduce any problem to a search problem; so this doesn't only work for sorting.