/**
* 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.
*
* Examples:
* ?- 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.
*
* Restrictions
* 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.
*
* Trademarks
* Jekejeke is a registered trademark of XLOG Technologies GmbH.
*/
:- package(library(jekpro/frequent/advanced)).
:- module(ordsets, []).
/**
* ord_contains(E, O):
* The predicate succeeds when the set O contains the element E.
*/
% ord_contains(+Elem, +OrdSet)
:- public ord_contains/2.
ord_contains(X, [Y|_]) :-
X @< Y, !, fail.
ord_contains(X, [Y|_]) :-
X == Y, !.
ord_contains(X, [_|Y]) :-
ord_contains(X, Y).
/**
* ord_difference(O1, O2, O3):
* The predicate succeeds when O3 unifies with the difference of O1 by O2.
*/
% ord_difference(+OrdSet, +OrdSet, -OrdSet)
:- public ord_difference/3.
ord_difference([X|Y], [Z|T], [X|R]) :-
X @< Z, !,
ord_difference(Y, [Z|T], R).
ord_difference([X|Y], [Z|T], R) :-
X == Z, !,
ord_difference(Y, T, R).
ord_difference([X|Y], [_|T], R) :-
ord_difference([X|Y], T, R).
ord_difference([], _, []) :- !.
ord_difference(X, [], X).
/**
* ord_intersection(O1, O2, O3):
* The predicate succeeds when O3 unifies with the intersection of O1 and O2.
*/
% ord_intersection(+OrdSet, +OrdSet, -OrdSet)
:- public ord_intersection/3.
ord_intersection([X|Y], [Z|T], R) :-
X @< Z, !,
ord_intersection(Y, [Z|T], R).
ord_intersection([X|Y], [Z|T], [X|R]) :-
X == Z, !,
ord_intersection(Y, T, R).
ord_intersection([X|Y], [_|T], R) :-
ord_intersection([X|Y], T, R).
ord_intersection([], _, []) :- !.
ord_intersection(_, [], []).
/**
* ord_union(O1, O2, O3):
* The predicate succeeds when O3 unifies with the union of O1 and O2.
*/
% ord_union(+OrdSet, +OrdSet, -OrdSet)
:- public ord_union/3.
ord_union([X|Y], [Z|T], [X|R]) :-
X @< Z, !,
ord_union(Y, [Z|T], R).
ord_union([X|Y], [Z|T], [X|R]) :-
X == Z, !,
ord_union(Y, T, R).
ord_union([X|Y], [Z|T], [Z|R]) :-
ord_union([X|Y], T, R).
ord_union([], X, X) :- !.
ord_union(X, [], X).
/**
* ord_subset(O1, O2):
* The predicate succeeds when O1 is a subset of O2.
*/
% ord_subset(+OrdSet, +OrdSet)
:- public ord_subset/2.
ord_subset([X|_], [Z|_]) :-
X @< Z, !, fail.
ord_subset([X|Y], [Z|T]) :-
X == Z, !,
ord_subset(Y, T).
ord_subset([X|Y], [_|T]) :-
ord_subset([X|Y], T).
ord_subset([], _).