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yap-6.3/library/ordsets.yap
Vítor Santos Costa 15404b3835 small 
- do not call goal expansion on meta-calls (that is done by undef).
- docs updates
- fix init code
2015-12-15 09:28:43 +00:00

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/**
* @file ordsets.yap
* @author : R.A.O'Keefe
* @date 22 May 1983
* @author VITOR SANTOS COSTA <vsc@VITORs-MBP.lan>
* @date 1999
* @brief
*
*
*/
% This file has been included as an YAP library by Vitor Santos Costa, 1999
:- module(ordsets, [
list_to_ord_set/2, % List -> Set
merge/3, % OrdList x OrdList -> OrdList
ord_add_element/3, % Set x Elem -> Set
ord_del_element/3, % Set x Elem -> Set
ord_disjoint/2, % Set x Set ->
ord_insert/3, % Set x Elem -> Set
ord_member/2, % Set -> Elem
ord_intersect/2, % Set x Set ->
ord_intersect/3, % Set x Set -> Set
ord_intersection/3, % Set x Set -> Set
ord_intersection/4, % Set x Set -> Set x Set
ord_seteq/2, % Set x Set ->
ord_setproduct/3, % Set x Set -> Set
ord_subset/2, % Set x Set ->
ord_subtract/3, % Set x Set -> Set
ord_symdiff/3, % Set x Set -> Set
ord_union/2, % Set^2 -> Set
ord_union/3, % Set x Set -> Set
ord_union/4, % Set x Set -> Set x Set,
ord_empty/1, % -> Set
ord_memberchk/2 % Element X Set
]).
/** @defgroup ordsets Ordered Sets
* @ingroup library
* @{
The following ordered set manipulation routines are available once
included with the `use_module(library(ordsets))` command. An
ordered set is represented by a list having unique and ordered
elements. Output arguments are guaranteed to be ordered sets, if the
relevant inputs are. This is a slightly patched version of Richard
O'Keefe's original library.
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!
*/
/** @pred ord_add_element(+ _Set1_, + _Element_, ? _Set2_)
Inserting _Element_ in _Set1_ returns _Set2_. It should give
exactly the same result as `merge(Set1, [Element], Set2)`, but a
bit faster, and certainly more clearly. The same as ord_insert/3.
*/
/** @pred ord_del_element(+ _Set1_, + _Element_, ? _Set2_)
Removing _Element_ from _Set1_ returns _Set2_.
*/
/** @pred ord_disjoint(+ _Set1_, + _Set2_)
Holds when the two ordered sets have no element in common.
*/
/** @pred ord_insert(+ _Set1_, + _Element_, ? _Set2_)
Inserting _Element_ in _Set1_ returns _Set2_. It should give
exactly the same result as `merge(Set1, [Element], Set2)`, but a
bit faster, and certainly more clearly. The same as ord_add_element/3.
*/
/** @pred ord_intersect(+ _Set1_, + _Set2_)
Holds when the two ordered sets have at least one element in common.
*/
/** @pred ord_intersection(+ _Set1_, + _Set2_, ? _Intersection_)
Holds when Intersection is the ordered representation of _Set1_
and _Set2_.
*/
/** @pred ord_intersection(+ _Set1_, + _Set2_, ? _Intersection_, ? _Diff_)
Holds when Intersection is the ordered representation of _Set1_
and _Set2_. _Diff_ is the difference between _Set2_ and _Set1_.
*/
/** @pred ord_member(+ _Element_, + _Set_)
Holds when _Element_ is a member of _Set_.
*/
/** @pred ord_seteq(+ _Set1_, + _Set2_)
Holds when the two arguments represent the same set.
*/
/** @pred ord_setproduct(+ _Set1_, + _Set2_, - _Set_)
If Set1 and Set2 are ordered sets, Product will be an ordered
set of x1-x2 pairs.
*/
/** @pred ord_subset(+ _Set1_, + _Set2_)
Holds when every element of the ordered set _Set1_ appears in the
ordered set _Set2_.
*/
/** @pred ord_subtract(+ _Set1_, + _Set2_, ? _Difference_)
Holds when _Difference_ contains all and only the elements of _Set1_
which are not also in _Set2_.
*/
/** @pred ord_symdiff(+ _Set1_, + _Set2_, ? _Difference_)
Holds when _Difference_ is the symmetric difference of _Set1_
and _Set2_.
*/
/** @pred ord_union(+ _Set1_, + _Set2_, ? _Union_)
Holds when _Union_ is the union of _Set1_ and _Set2_.
*/
/** @pred ord_union(+ _Set1_, + _Set2_, ? _Union_, ? _Diff_)
Holds when _Union_ is the union of _Set1_ and _Set2_ and
_Diff_ is the difference.
*/
/** @pred ord_union(+ _Sets_, ? _Union_)
Holds when _Union_ is the union of the lists _Sets_.
*/
/*
:- mode
list_to_ord_set(+, ?),
merge(+, +, -),
ord_disjoint(+, +),
ord_disjoint(+, +, +, +, +),
ord_insert(+, +, ?),
ord_insert(+, +, +, +, ?),
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(+, +, +, +, +, ?).
*/
%% @pred 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).
%% @ored 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).
%% @ored 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).
%% @ored ord_insert(+Set1, +Element, ?Set2)
% ord_add_element(+Set1, +Element, ?Set2)
% is the equivalent of add_element for ordered sets. It should give
% exactly the same result as merge(Set1, [Element], Set2), but a bit
% faster, and certainly more clearly.
ord_add_element([], Element, [Element]).
ord_add_element([Head|Tail], Element, Set) :-
compare(Order, Head, Element),
ord_insert(Order, Head, Tail, Element, Set).
ord_insert([], Element, [Element]).
ord_insert([Head|Tail], Element, Set) :-
compare(Order, Head, Element),
ord_insert(Order, Head, Tail, Element, Set).
ord_insert(<, Head, Tail, Element, [Head|Set]) :-
ord_insert(Tail, Element, Set).
ord_insert(=, Head, Tail, _, [Head|Tail]).
ord_insert(>, Head, Tail, Element, [Element,Head|Tail]).
%% @pred 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(L1, L2, L) :-
ord_intersection(L1, L2, L).
%% @pred ord_intersection(+Set1, +Set2, ?Intersection)
% is true when Intersection is the ordered representation of Set1
% and Set2, provided that Set1 and Set2 are ordered sets.
ord_intersection([], _, []) :- !.
ord_intersection([_|_], [], []) :- !.
ord_intersection([Head1|Tail1], [Head2|Tail2], Intersection) :-
( Head1 == Head2 ->
Intersection = [Head1|Tail],
ord_intersection(Tail1, Tail2, Tail)
;
Head1 @< Head2 ->
ord_intersection(Tail1, [Head2|Tail2], Intersection)
;
ord_intersection([Head1|Tail1], Tail2, Intersection)
).
%% @pred ord_intersection(+Set1, +Set2, ?Intersection, ?Difference)
% is true when Intersection is the ordered representation of Set1
% and Set2, provided that Set1 and Set2 are ordered sets.
ord_intersection([], L, [], L) :- !.
ord_intersection([_|_], [], [], []) :- !.
ord_intersection([Head1|Tail1], [Head2|Tail2], Intersection, Difference) :-
( Head1 == Head2 ->
Intersection = [Head1|Tail],
ord_intersection(Tail1, Tail2, Tail, Difference)
;
Head1 @< Head2 ->
ord_intersection(Tail1, [Head2|Tail2], Intersection, Difference)
;
Difference = [Head2|HDifference],
ord_intersection([Head1|Tail1], Tail2, Intersection, HDifference)
).
% 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_del_element(+Set1, Element, ?Rest)
% is true when Rest contains the elements of Set1
% except for Set1
ord_del_element([], _, []).
ord_del_element([Head1|Tail1], Head2, Rest) :-
compare(Order, Head1, Head2),
ord_del_element(Order, Head1, Tail1, Head2, Rest).
ord_del_element(=, _, Tail1, _, Tail1).
ord_del_element(<, Head1, Tail1, Head2, [Head1|Difference]) :-
ord_del_element(Tail1, Head2, Difference).
ord_del_element(>, Head1, Tail1, _, [Head1|Tail1]).
%% @pred 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([S|Set1], [], [S|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).
%% @pred ord_union(+Set1, +Set2, ?Union, ?Difference)
% is true when Union is the union of Set1 and Set2 and Difference is the
% difference between Set2 and Set1.
ord_union(Set1, [], Set1, []) :- !.
ord_union([], Set2, Set2, Set2) :- !.
ord_union([Head1|Tail1], [Head2|Tail2], Union, Diff) :-
compare(Order, Head1, Head2),
ord_union(Order, Head1, Tail1, Head2, Tail2, Union, Diff).
ord_union(=, Head, Tail1, _, Tail2, [Head|Union], Diff) :-
ord_union(Tail1, Tail2, Union, Diff).
ord_union(<, Head1, Tail1, Head2, Tail2, [Head1|Union], Diff) :-
ord_union(Tail1, [Head2|Tail2], Union, Diff).
ord_union(>, Head1, Tail1, Head2, Tail2, [Head2|Union], [Head2|Diff]) :-
ord_union([Head1|Tail1], Tail2, Union, Diff).
%% @pred ord_setproduct(+Set1, +Set2, ?Product)
% is in fact identical to setproduct(Set1, Set2, Product).
% If Set1 and Set2 are ordered sets, Product will be an ordered
% set of x1-x2 pairs. Note that we cannot solve for Set1 and
% Set2, because there are infinitely many solutions when
% Product is empty, and may be a large number in other cases.
ord_setproduct([], _, []).
ord_setproduct([H|T], L, Product) :-
ord_setproduct(L, H, Product, Rest),
ord_setproduct(T, L, Rest).
ord_setproduct([], _, L, L).
ord_setproduct([H|T], X, [X-H|TX], TL) :-
ord_setproduct(T, X, TX, TL).
ord_member(El,[H|T]):-
compare(Op,El,H),
ord_member(Op,El,T).
ord_member(=,_,_).
ord_member(>,El,[H|T]) :-
compare(Op,El,H),
ord_member(Op,El,T).
ord_union([], []).
ord_union([Set|Sets], Union) :-
length([Set|Sets], NumberOfSets),
ord_union_all(NumberOfSets, [Set|Sets], Union, []).
ord_union_all(N,Sets0,Union,Sets) :-
( N=:=1 -> Sets0=[Union|Sets]
; N=:=2 -> Sets0=[Set1,Set2|Sets],
ord_union(Set1,Set2,Union)
; A is N>>1,
Z is N-A,
ord_union_all(A, Sets0, X, Sets1),
ord_union_all(Z, Sets1, Y, Sets),
ord_union(X, Y, Union)
).
ord_empty([]).
ord_memberchk(Element, [E|_]) :- E == Element, !.
ord_memberchk(Element, [_|Set]) :-
ord_memberchk(Element, Set).
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