pereira@sri-unix.UUCP (08/15/83)
% File : ORDSET.PL
% Author : R.A.O'Keefe
% Updated: 22 May 1983
% Purpose: Ordered set manipulation utilities
% In this module, sets are represented by ordered lists with no
% duplicates. Thus {c,r,a,f,t} would be [a,c,f,r,t]. The ordering
% is defined by the @< family of term comparison predicates, which
% is the ordering used by sort/2 and setof/3.
% The benefit of the ordered representation is that the elementary
% set operations can be done in time proportional to the Sum of the
% argument sizes rather than their Product. Some of the unordered
% set routines, such as member/2, length/2,, select/3 can be used
% unchanged. The main difficulty with the ordered representation is
% remembering to use it!
:- public
list_to_ord_set/2, % List -> Set
merge/3, % OrdList x OrdList -> OrdList
ord_disjoint/2, % Set x Set ->
ord_intersect/2, % Set x Set ->
ord_intersect/3, % Set x Set -> Set
ord_seteq/2, % Set x Set ->
ord_subset/2, % Set x Set ->
ord_subtract/3, % Set x Set -> Set
ord_symdiff/3, % Set x Set -> Set
ord_union/3. % Set x Set -> Set
:- mode
list_to_ord_set(+, ?),
merge(+, +, -),
ord_disjoint(+, +),
ord_disjoint(+, +, +, +, +),
ord_intersect(+, +),
ord_intersect(+, +, +, +, +),
ord_intersect(+, +, ?),
ord_intersect(+, +, +, +, +, ?),
ord_seteq(+, +),
ord_subset(+, +),
ord_subset(+, +, +, +, +),
ord_subtract(+, +, ?),
ord_subtract(+, +, +, +, +, ?),
ord_symdiff(+, +, ?),
ord_symdiff(+, +, +, +, +, ?),
ord_union(+, +, ?),
ord_union(+, +, +, +, +, ?).
% list_to_ord_set(+List, ?Set)
% is true when Set is the ordered representation of the set represented
% by the unordered representation List. The only reason for giving it
% a name at all is that you may not have realised that sort/2 could be
% used this way.
list_to_ord_set(List, Set) :-
sort(List, Set).
% merge(+List1, +List2, -Merged)
% is true when Merged is the stable merge of the two given lists.
% If the two lists are not ordered, the merge doesn't mean a great
% deal. Merging is perfectly well defined when the inputs contain
% duplicates, and all copies of an element are preserved in the
% output, e.g. merge("122357", "34568", "12233455678"). Study this
% routine carefully, as it is the basis for all the rest.
merge([Head1|Tail1], [Head2|Tail2], [Head2|Merged]) :-
Head1 @> Head2, !,
merge([Head1|Tail1], Tail2, Merged).
merge([Head1|Tail1], List2, [Head1|Merged]) :-
List2 \== [], !,
merge(Tail1, List2, Merged).
merge([], List2, List2) :- !.
merge(List1, [], List1).
% ord_disjoint(+Set1, +Set2)
% is true when the two ordered sets have no element in common. If the
% arguments are not ordered, I have no idea what happens.
ord_disjoint([], _) :- !.
ord_disjoint(_, []) :- !.
ord_disjoint([Head1|Tail1], [Head2|Tail2]) :-
compare(Order, Head1, Head2),
ord_disjoint(Order, Head1, Tail1, Head2, Tail2).
ord_disjoint(<, _, Tail1, Head2, Tail2) :-
ord_disjoint(Tail1, [Head2|Tail2]).
ord_disjoint(>, Head1, Tail1, _, Tail2) :-
ord_disjoint([Head1|Tail1], Tail2).
% ord_intersect(+Set1, +Set2)
% is true when the two ordered sets have at least one element in common.
% Note that the test is == rather than = .
ord_intersect([Head1|Tail1], [Head2|Tail2]) :-
compare(Order, Head1, Head2),
ord_intersect(Order, Head1, Tail1, Head2, Tail2).
ord_intersect(=, _, _, _, _).
ord_intersect(<, _, Tail1, Head2, Tail2) :-
ord_intersect(Tail1, [Head2|Tail2]).
ord_intersect(>, Head1, Tail1, _, Tail2) :-
ord_intersect([Head1|Tail1], Tail2).
% ord_intersect(+Set1, +Set2, ?Intersection)
% is true when Intersection is the ordered representation of Set1
% and Set2, provided that Set1 and Set2 are ordered sets.
ord_intersect(_, [], []) :- !.
ord_intersect([], _, []) :- !.
ord_intersect([Head1|Tail1], [Head2|Tail2], Intersection) :-
compare(Order, Head1, Head2),
ord_intersect(Order, Head1, Tail1, Head2, Tail2, Intersection).
ord_intersect(=, Head, Tail1, _, Tail2, [Head|Intersection]) :-
ord_intersect(Tail1, Tail2, Intersection).
ord_intersect(<, _, Tail1, Head2, Tail2, Intersection) :-
ord_intersect(Tail1, [Head2|Tail2], Intersection).
ord_intersect(>, Head1, Tail1, _, Tail2, Intersection) :-
ord_intersect([Head1|Tail1], Tail2, Intersection).
% ord_seteq(+Set1, +Set2)
% is true when the two arguments represent the same set. Since they
% are assumed to be ordered representations, they must be identical.
ord_seteq(Set1, Set2) :-
Set1 == Set2.
% ord_subset(+Set1, +Set2)
% is true when every element of the ordered set Set1 appears in the
% ordered set Set2.
ord_subset([], _) :- !.
ord_subset([Head1|Tail1], [Head2|Tail2]) :-
compare(Order, Head1, Head2),
ord_subset(Order, Head1, Tail1, Head2, Tail2).
ord_subset(=, _, Tail1, _, Tail2) :-
ord_subset(Tail1, Tail2).
ord_subset(>, Head1, Tail1, _, Tail2) :-
ord_subset([Head1|Tail1], Tail2).
% ord_subtract(+Set1, +Set2, ?Difference)
% is true when Difference contains all and only the elements of Set1
% which are not also in Set2.
ord_subtract(Set1, [], Set1) :- !.
ord_subtract([], _, []) :- !.
ord_subtract([Head1|Tail1], [Head2|Tail2], Difference) :-
compare(Order, Head1, Head2),
ord_subtract(Order, Head1, Tail1, Head2, Tail2, Difference).
ord_subtract(=, _, Tail1, _, Tail2, Difference) :-
ord_subtract(Tail1, Tail2, Difference).
ord_subtract(<, Head1, Tail1, Head2, Tail2, [Head1|Difference]) :-
ord_subtract(Tail1, [Head2|Tail2], Difference).
ord_subtract(>, Head1, Tail1, _, Tail2, Difference) :-
ord_subtract([Head1|Tail1], Tail2, Difference).
% ord_symdiff(+Set1, +Set2, ?Difference)
% is true when Difference is the symmetric difference of Set1 and Set2.
ord_symdiff(Set1, [], Set1) :- !.
ord_symdiff([], Set2, Set2) :- !.
ord_symdiff([Head1|Tail1], [Head2|Tail2], Difference) :-
compare(Order, Head1, Head2),
ord_symdiff(Order, Head1, Tail1, Head2, Tail2, Difference).
ord_symdiff(=, _, Tail1, _, Tail2, Difference) :-
ord_symdiff(Tail1, Tail2, Difference).
ord_symdiff(<, Head1, Tail1, Head2, Tail2, [Head1|Difference]) :-
ord_symdiff(Tail1, [Head2|Tail2], Difference).
ord_symdiff(>, Head1, Tail1, Head2, Tail2, [Head2|Difference]) :-
ord_symdiff([Head1|Tail1], Tail2, Difference).
% ord_union(+Set1, +Set2, ?Union)
% is true when Union is the union of Set1 and Set2. Note that when
% something occurs in both sets, we want to retain only one copy.
ord_union(Set1, [], Set1) :- !.
ord_union([], Set2, Set2) :- !.
ord_union([Head1|Tail1], [Head2|Tail2], Union) :-
compare(Order, Head1, Head2),
ord_union(Order, Head1, Tail1, Head2, Tail2, Union).
ord_union(=, Head, Tail1, _, Tail2, [Head|Union]) :-
ord_union(Tail1, Tail2, Union).
ord_union(<, Head1, Tail1, Head2, Tail2, [Head1|Union]) :-
ord_union(Tail1, [Head2|Tail2], Union).
ord_union(>, Head1, Tail1, Head2, Tail2, [Head2|Union]) :-
ord_union([Head1|Tail1], Tail2, Union).