/* Part of SWI-Prolog Author: Jon Jagger E-mail: J.R.Jagger@shu.ac.uk Copyright (c) 1993-2011, Jon Jagger All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ :- module(oset, [ oset_is/1, oset_union/3, oset_int/3, oset_diff/3, oset_dint/2, oset_dunion/2, oset_addel/3, oset_delel/3, oset_power/2 ]). /** Ordered set manipulation This library defines set operations on sets represented as ordered lists. @author Jon Jagger @deprecated Use the de-facto library ordsets.pl */ %% oset_is(+OSet) % check that OSet in correct format (standard order) oset_is(-) :- !, fail. % var filter oset_is([]). oset_is([H|T]) :- oset_is(T, H). oset_is(-, _) :- !, fail. % var filter oset_is([], _H). oset_is([H|T], H0) :- H0 @< H, % use standard order oset_is(T, H). %% oset_union(+OSet1, +OSet2, -Union). oset_union([], Union, Union). oset_union([H1|T1], L2, Union) :- union2(L2, H1, T1, Union). union2([], H1, T1, [H1|T1]). union2([H2|T2], H1, T1, Union) :- compare(Order, H1, H2), union3(Order, H1, T1, H2, T2, Union). union3(<, H1, T1, H2, T2, [H1|Union]) :- union2(T1, H2, T2, Union). union3(=, H1, T1, _H2, T2, [H1|Union]) :- oset_union(T1, T2, Union). union3(>, H1, T1, H2, T2, [H2|Union]) :- union2(T2, H1, T1, Union). %% oset_int(+OSet1, +OSet2, -Int) % ordered set intersection oset_int([], _Int, []). oset_int([H1|T1], L2, Int) :- isect2(L2, H1, T1, Int). isect2([], _H1, _T1, []). isect2([H2|T2], H1, T1, Int) :- compare(Order, H1, H2), isect3(Order, H1, T1, H2, T2, Int). isect3(<, _H1, T1, H2, T2, Int) :- isect2(T1, H2, T2, Int). isect3(=, H1, T1, _H2, T2, [H1|Int]) :- oset_int(T1, T2, Int). isect3(>, H1, T1, _H2, T2, Int) :- isect2(T2, H1, T1, Int). %% oset_diff(+InOSet, +NotInOSet, -Diff) % ordered set difference oset_diff([], _Not, []). oset_diff([H1|T1], L2, Diff) :- diff21(L2, H1, T1, Diff). diff21([], H1, T1, [H1|T1]). diff21([H2|T2], H1, T1, Diff) :- compare(Order, H1, H2), diff3(Order, H1, T1, H2, T2, Diff). diff12([], _H2, _T2, []). diff12([H1|T1], H2, T2, Diff) :- compare(Order, H1, H2), diff3(Order, H1, T1, H2, T2, Diff). diff3(<, H1, T1, H2, T2, [H1|Diff]) :- diff12(T1, H2, T2, Diff). diff3(=, _H1, T1, _H2, T2, Diff) :- oset_diff(T1, T2, Diff). diff3(>, H1, T1, _H2, T2, Diff) :- diff21(T2, H1, T1, Diff). %% oset_dunion(+SetofSets, -DUnion) % distributed union oset_dunion([], []). oset_dunion([H|T], DUnion) :- oset_dunion(T, H, DUnion). oset_dunion([], DUnion, DUnion). oset_dunion([H|T], DUnion0, DUnion) :- oset_union(H, DUnion0, DUnion1), oset_dunion(T, DUnion1, DUnion). %% oset_dint(+SetofSets, -DInt) % distributed intersection oset_dint([], []). oset_dint([H|T], DInt) :- dint(T, H, DInt). dint([], DInt, DInt). dint([H|T], DInt0, DInt) :- oset_int(H, DInt0, DInt1), dint(T, DInt1, DInt). %! oset_power(+Set, -PSet) % % True when PSet is the powerset of Set. That is, Pset is a set of % all subsets of Set, where each subset is a proper ordered set. oset_power(S, PSet) :- reverse(S, R), pset(R, [[]], PSet0), sort(PSet0, PSet). % The powerset of a set is the powerset of a set of one smaller, % together with the set of one smaller where each subset is extended % with the new element. Note that this produces the elements of the set % in reverse order. Hence the reverse in oset_power/2. pset([], PSet, PSet). pset([H|T], PSet0, PSet) :- happ(PSet0, H, PSet1), pset(T, PSet1, PSet). happ([], _, []). happ([S|Ss], H, [[H|S],S|Rest]) :- happ(Ss, H, Rest). %% oset_addel(+Set, +El, -Add) % ordered set element addition oset_addel([], El, [El]). oset_addel([H|T], El, Add) :- compare(Order, H, El), addel(Order, H, T, El, Add). addel(<, H, T, El, [H|Add]) :- oset_addel(T, El, Add). addel(=, H, T, _El, [H|T]). addel(>, H, T, El, [El,H|T]). %% oset_delel(+Set, +El, -Del) % ordered set element deletion oset_delel([], _El, []). oset_delel([H|T], El, Del) :- compare(Order, H, El), delel(Order, H, T, El, Del). delel(<, H, T, El, [H|Del]) :- oset_delel(T, El, Del). delel(=, _H, T, _El, T). delel(>, H, T, _El, [H|T]).