358 lines
11 KiB
Prolog
358 lines
11 KiB
Prolog
% This file has been included as an YAP library by Vitor Santos Costa, 1999
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% File : ORDSET.PL
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% Author : R.A.O'Keefe
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% Updated: 22 May 1983
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% Purpose: Ordered set manipulation utilities
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% In this module, sets are represented by ordered lists with no
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% duplicates. Thus {c,r,a,f,t} would be [a,c,f,r,t]. The ordering
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% is defined by the @< family of term comparison predicates, which
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% is the ordering used by sort/2 and setof/3.
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% The benefit of the ordered representation is that the elementary
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% set operations can be done in time proportional to the Sum of the
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% argument sizes rather than their Product. Some of the unordered
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% set routines, such as member/2, length/2, select/3 can be used
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% unchanged. The main difficulty with the ordered representation is
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% remembering to use it!
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:- module(ordsets, [
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list_to_ord_set/2, % List -> Set
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merge/3, % OrdList x OrdList -> OrdList
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ord_add_element/3, % Set x Elem -> Set
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ord_del_element/3, % Set x Elem -> Set
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ord_disjoint/2, % Set x Set ->
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ord_insert/3, % Set x Elem -> Set
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ord_member/2, % Set -> Elem
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ord_intersect/2, % Set x Set ->
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ord_intersect/3, % Set x Set -> Set
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ord_intersection/3, % Set x Set -> Set
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ord_intersection/4, % Set x Set -> Set x Set
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ord_seteq/2, % Set x Set ->
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ord_setproduct/3, % Set x Set -> Set
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ord_subset/2, % Set x Set ->
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ord_subtract/3, % Set x Set -> Set
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ord_symdiff/3, % Set x Set -> Set
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ord_union/2, % Set^2 -> Set
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ord_union/3, % Set x Set -> Set
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ord_union/4, % Set x Set -> Set x Set,
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ord_empty/1, % -> Set
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ord_memberchk/2 % Element X Set
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]).
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/*
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:- mode
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list_to_ord_set(+, ?),
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merge(+, +, -),
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ord_disjoint(+, +),
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ord_disjoint(+, +, +, +, +),
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ord_insert(+, +, ?),
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ord_insert(+, +, +, +, ?),
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ord_intersect(+, +),
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ord_intersect(+, +, +, +, +),
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ord_intersect(+, +, ?),
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ord_intersect(+, +, +, +, +, ?),
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ord_seteq(+, +),
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ord_subset(+, +),
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ord_subset(+, +, +, +, +),
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ord_subtract(+, +, ?),
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ord_subtract(+, +, +, +, +, ?),
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ord_symdiff(+, +, ?),
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ord_symdiff(+, +, +, +, +, ?),
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ord_union(+, +, ?),
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ord_union(+, +, +, +, +, ?).
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*/
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% list_to_ord_set(+List, ?Set)
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% is true when Set is the ordered representation of the set represented
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% by the unordered representation List. The only reason for giving it
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% a name at all is that you may not have realised that sort/2 could be
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% used this way.
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list_to_ord_set(List, Set) :-
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sort(List, Set).
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% merge(+List1, +List2, -Merged)
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% is true when Merged is the stable merge of the two given lists.
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% If the two lists are not ordered, the merge doesn't mean a great
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% deal. Merging is perfectly well defined when the inputs contain
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% duplicates, and all copies of an element are preserved in the
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% output, e.g. merge("122357", "34568", "12233455678"). Study this
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% routine carefully, as it is the basis for all the rest.
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merge([Head1|Tail1], [Head2|Tail2], [Head2|Merged]) :-
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Head1 @> Head2, !,
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merge([Head1|Tail1], Tail2, Merged).
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merge([Head1|Tail1], List2, [Head1|Merged]) :-
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List2 \== [], !,
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merge(Tail1, List2, Merged).
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merge([], List2, List2) :- !.
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merge(List1, [], List1).
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% ord_disjoint(+Set1, +Set2)
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% is true when the two ordered sets have no element in common. If the
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% arguments are not ordered, I have no idea what happens.
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ord_disjoint([], _) :- !.
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ord_disjoint(_, []) :- !.
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ord_disjoint([Head1|Tail1], [Head2|Tail2]) :-
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compare(Order, Head1, Head2),
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ord_disjoint(Order, Head1, Tail1, Head2, Tail2).
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ord_disjoint(<, _, Tail1, Head2, Tail2) :-
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ord_disjoint(Tail1, [Head2|Tail2]).
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ord_disjoint(>, Head1, Tail1, _, Tail2) :-
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ord_disjoint([Head1|Tail1], Tail2).
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% ord_insert(+Set1, +Element, ?Set2)
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% ord_add_element(+Set1, +Element, ?Set2)
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% is the equivalent of add_element for ordered sets. It should give
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% exactly the same result as merge(Set1, [Element], Set2), but a bit
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% faster, and certainly more clearly.
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ord_add_element([], Element, [Element]).
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ord_add_element([Head|Tail], Element, Set) :-
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compare(Order, Head, Element),
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ord_insert(Order, Head, Tail, Element, Set).
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ord_insert([], Element, [Element]).
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ord_insert([Head|Tail], Element, Set) :-
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compare(Order, Head, Element),
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ord_insert(Order, Head, Tail, Element, Set).
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ord_insert(<, Head, Tail, Element, [Head|Set]) :-
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ord_insert(Tail, Element, Set).
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ord_insert(=, Head, Tail, _, [Head|Tail]).
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ord_insert(>, Head, Tail, Element, [Element,Head|Tail]).
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% ord_intersect(+Set1, +Set2)
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% is true when the two ordered sets have at least one element in common.
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% Note that the test is == rather than = .
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ord_intersect([Head1|Tail1], [Head2|Tail2]) :-
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compare(Order, Head1, Head2),
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ord_intersect(Order, Head1, Tail1, Head2, Tail2).
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ord_intersect(=, _, _, _, _).
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ord_intersect(<, _, Tail1, Head2, Tail2) :-
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ord_intersect(Tail1, [Head2|Tail2]).
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ord_intersect(>, Head1, Tail1, _, Tail2) :-
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ord_intersect([Head1|Tail1], Tail2).
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ord_intersect(L1, L2, L) :-
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ord_intersection(L1, L2, L).
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% ord_intersection(+Set1, +Set2, ?Intersection)
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% is true when Intersection is the ordered representation of Set1
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% and Set2, provided that Set1 and Set2 are ordered sets.
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ord_intersection([], _, []) :- !.
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ord_intersection([_|_], [], []) :- !.
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ord_intersection([Head1|Tail1], [Head2|Tail2], Intersection) :-
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( Head1 == Head2 ->
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Intersection = [Head1|Tail],
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ord_intersection(Tail1, Tail2, Tail)
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;
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Head1 @< Head2 ->
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ord_intersection(Tail1, [Head2|Tail2], Intersection)
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;
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ord_intersection([Head1|Tail1], Tail2, Intersection)
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).
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% ord_intersection(+Set1, +Set2, ?Intersection, ?Difference)
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% is true when Intersection is the ordered representation of Set1
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% and Set2, provided that Set1 and Set2 are ordered sets.
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ord_intersection([], L, [], L) :- !.
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ord_intersection([_|_], [], [], []) :- !.
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ord_intersection([Head1|Tail1], [Head2|Tail2], Intersection, Difference) :-
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( Head1 == Head2 ->
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Intersection = [Head1|Tail],
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ord_intersection(Tail1, Tail2, Tail, Difference)
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;
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Head1 @< Head2 ->
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ord_intersection(Tail1, [Head2|Tail2], Intersection, Difference)
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;
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Difference = [Head2|HDifference],
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ord_intersection([Head1|Tail1], Tail2, Intersection, HDifference)
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).
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% ord_seteq(+Set1, +Set2)
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% is true when the two arguments represent the same set. Since they
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% are assumed to be ordered representations, they must be identical.
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ord_seteq(Set1, Set2) :-
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Set1 == Set2.
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% ord_subset(+Set1, +Set2)
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% is true when every element of the ordered set Set1 appears in the
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% ordered set Set2.
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ord_subset([], _) :- !.
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ord_subset([Head1|Tail1], [Head2|Tail2]) :-
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compare(Order, Head1, Head2),
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ord_subset(Order, Head1, Tail1, Head2, Tail2).
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ord_subset(=, _, Tail1, _, Tail2) :-
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ord_subset(Tail1, Tail2).
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ord_subset(>, Head1, Tail1, _, Tail2) :-
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ord_subset([Head1|Tail1], Tail2).
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% ord_subtract(+Set1, +Set2, ?Difference)
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% is true when Difference contains all and only the elements of Set1
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% which are not also in Set2.
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ord_subtract(Set1, [], Set1) :- !.
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ord_subtract([], _, []) :- !.
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ord_subtract([Head1|Tail1], [Head2|Tail2], Difference) :-
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compare(Order, Head1, Head2),
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ord_subtract(Order, Head1, Tail1, Head2, Tail2, Difference).
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ord_subtract(=, _, Tail1, _, Tail2, Difference) :-
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ord_subtract(Tail1, Tail2, Difference).
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ord_subtract(<, Head1, Tail1, Head2, Tail2, [Head1|Difference]) :-
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ord_subtract(Tail1, [Head2|Tail2], Difference).
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ord_subtract(>, Head1, Tail1, _, Tail2, Difference) :-
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ord_subtract([Head1|Tail1], Tail2, Difference).
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% ord_del_element(+Set1, Element, ?Rest)
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% is true when Rest contains the elements of Set1
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% except for Set1
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ord_del_element([], _, []).
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ord_del_element([Head1|Tail1], Head2, Rest) :-
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compare(Order, Head1, Head2),
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ord_del_element(Order, Head1, Tail1, Head2, Rest).
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ord_del_element(=, _, Tail1, _, Tail1).
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ord_del_element(<, Head1, Tail1, Head2, [Head1|Difference]) :-
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ord_del_element(Tail1, Head2, Difference).
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ord_del_element(>, Head1, Tail1, _, [Head1|Tail1]).
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% ord_symdiff(+Set1, +Set2, ?Difference)
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% is true when Difference is the symmetric difference of Set1 and Set2.
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ord_symdiff(Set1, [], Set1) :- !.
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ord_symdiff([], Set2, Set2) :- !.
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ord_symdiff([Head1|Tail1], [Head2|Tail2], Difference) :-
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compare(Order, Head1, Head2),
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ord_symdiff(Order, Head1, Tail1, Head2, Tail2, Difference).
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ord_symdiff(=, _, Tail1, _, Tail2, Difference) :-
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ord_symdiff(Tail1, Tail2, Difference).
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ord_symdiff(<, Head1, Tail1, Head2, Tail2, [Head1|Difference]) :-
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ord_symdiff(Tail1, [Head2|Tail2], Difference).
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ord_symdiff(>, Head1, Tail1, Head2, Tail2, [Head2|Difference]) :-
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ord_symdiff([Head1|Tail1], Tail2, Difference).
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% ord_union(+Set1, +Set2, ?Union)
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% is true when Union is the union of Set1 and Set2. Note that when
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% something occurs in both sets, we want to retain only one copy.
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ord_union([S|Set1], [], [S|Set1]).
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ord_union([], Set2, Set2).
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ord_union([Head1|Tail1], [Head2|Tail2], Union) :-
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compare(Order, Head1, Head2),
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ord_union(Order, Head1, Tail1, Head2, Tail2, Union).
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ord_union(=, Head, Tail1, _, Tail2, [Head|Union]) :-
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ord_union(Tail1, Tail2, Union).
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ord_union(<, Head1, Tail1, Head2, Tail2, [Head1|Union]) :-
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ord_union(Tail1, [Head2|Tail2], Union).
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ord_union(>, Head1, Tail1, Head2, Tail2, [Head2|Union]) :-
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ord_union([Head1|Tail1], Tail2, Union).
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% ord_union(+Set1, +Set2, ?Union, ?Difference)
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% is true when Union is the union of Set1 and Set2 and Difference is the
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% difference between Set2 and Set1.
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ord_union(Set1, [], Set1, []) :- !.
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ord_union([], Set2, Set2, Set2) :- !.
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ord_union([Head1|Tail1], [Head2|Tail2], Union, Diff) :-
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compare(Order, Head1, Head2),
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ord_union(Order, Head1, Tail1, Head2, Tail2, Union, Diff).
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ord_union(=, Head, Tail1, _, Tail2, [Head|Union], Diff) :-
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ord_union(Tail1, Tail2, Union, Diff).
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ord_union(<, Head1, Tail1, Head2, Tail2, [Head1|Union], Diff) :-
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ord_union(Tail1, [Head2|Tail2], Union, Diff).
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ord_union(>, Head1, Tail1, Head2, Tail2, [Head2|Union], [Head2|Diff]) :-
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ord_union([Head1|Tail1], Tail2, Union, Diff).
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% ord_setproduct(+Set1, +Set2, ?Product)
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% is in fact identical to setproduct(Set1, Set2, Product).
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% If Set1 and Set2 are ordered sets, Product will be an ordered
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% set of x1-x2 pairs. Note that we cannot solve for Set1 and
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% Set2, because there are infinitely many solutions when
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% Product is empty, and may be a large number in other cases.
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ord_setproduct([], _, []).
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ord_setproduct([H|T], L, Product) :-
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ord_setproduct(L, H, Product, Rest),
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ord_setproduct(T, L, Rest).
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ord_setproduct([], _, L, L).
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ord_setproduct([H|T], X, [X-H|TX], TL) :-
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ord_setproduct(T, X, TX, TL).
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ord_member(El,[H|T]):-
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compare(Op,El,H),
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ord_member(Op,El,T).
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ord_member(=,_,_).
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ord_member(>,El,[H|T]) :-
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compare(Op,El,H),
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ord_member(Op,El,T).
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ord_union([], []).
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ord_union([Set|Sets], Union) :-
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length([Set|Sets], NumberOfSets),
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ord_union_all(NumberOfSets, [Set|Sets], Union, []).
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ord_union_all(N,Sets0,Union,Sets) :-
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( N=:=1 -> Sets0=[Union|Sets]
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; N=:=2 -> Sets0=[Set1,Set2|Sets],
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ord_union(Set1,Set2,Union)
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; A is N>>1,
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Z is N-A,
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ord_union_all(A, Sets0, X, Sets1),
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ord_union_all(Z, Sets1, Y, Sets),
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ord_union(X, Y, Union)
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).
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ord_empty([]).
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ord_memberchk(Element, [E|_]) :- E == Element, !.
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ord_memberchk(Element, [_|Set]) :-
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ord_memberchk(Element, Set).
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