Jan Burse, created Jun 25. 2019
* This module provides ordered sets. The ordered sets are
* represented by lists [x1, .., xn]. The lists must be ordered
* and duplicate free. If this precondition is violated the
* behaviour of the predicates is undefined.
* ?- ord_union([2,3,4],[1,2,4,5],X).
* X = [1,2,3,4,5]
* ?- ord_union([1,2,4,5],[2,3,4],X).
* X = [1,2,3,4,5]
* The realization uses a membership check based on (==)/2 and
* lexical ordering based on (@<)/2. As a result the predicates
* are safe to be used with non-ground terms. On the other hand,
* since this comparison is not arithmetical, 1 and 1.0 are for
* example considered different.
* An unordered set can be converted into an ordered set by
* using the ISO predicate sort/2. Also there is no need for
* predicate permutation/2 here, since equality of ordered sets
* can be tested via the ISO predicate ==/2, provided the elements
* are sufficiently normalized.
* Warranty & Liability
* To the extent permitted by applicable law and unless explicitly
* otherwise agreed upon, XLOG Technologies GmbH makes no warranties
* regarding the provided information. XLOG Technologies GmbH assumes
* no liability that any problems might be solved with the information
* provided by XLOG Technologies GmbH.
* Rights & License
* All industrial property rights regarding the information - copyright
* and patent rights in particular - are the sole property of XLOG
* Technologies GmbH. If the company was not the originator of some
* excerpts, XLOG Technologies GmbH has at least obtained the right to
* reproduce, change and translate the information.
* Reproduction is restricted to the whole unaltered document. Reproduction
* of the information is only allowed for non-commercial uses. Selling,
* giving away or letting of the execution of the library is prohibited.
* The library can be distributed as part of your applications and libraries
* for execution provided this comment remains unchanged.
* Only to be distributed with programs that add significant and primary
* functionality to the library. Not to be distributed with additional
* software intended to replace any components of the library.
* Jekejeke is a registered trademark of XLOG Technologies GmbH.
* ord_contains(E, O):
* The predicate succeeds when the set O contains the element E.
% ord_contains(+Elem, +OrdSet)
* ord_difference(O1, O2, O3):
* The predicate succeeds when O3 unifies with the difference of O1 by O2.
% ord_difference(+OrdSet, +OrdSet, -OrdSet)
* ord_intersection(O1, O2, O3):
* The predicate succeeds when O3 unifies with the intersection of O1 and O2.
% ord_intersection(+OrdSet, +OrdSet, -OrdSet)
* ord_union(O1, O2, O3):
* The predicate succeeds when O3 unifies with the union of O1 and O2.
% ord_union(+OrdSet, +OrdSet, -OrdSet)
* ord_subset(O1, O2):
* The predicate succeeds when O1 is a subset of O2.
% ord_subset(+OrdSet, +OrdSet)