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Vítor Santos Costa
2015-11-18 15:06:25 +00:00
parent 7236d4a527
commit ce8a19d381
88 changed files with 7982 additions and 2083 deletions
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library/ordsets.yap
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@@ -1,26 +1,42 @@
/**
* @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
% 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!
:- 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 Ordered_Sets Ordered Sets
@ingroup library
@{
* @ingroup library
* @{
The following ordered set manipulation routines are available once
included with the `use_module(library(ordsets))` command. An
@@ -29,29 +45,22 @@ 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 list_to_ord_set(+ _List_, ? _Set_)
Holds when _Set_ is the ordered representation of the set
represented by the unordered representation _List_.
*/
/** @pred merge(+ _List1_, + _List2_, - _Merged_)
Holds when _Merged_ is the stable merge of the two given lists.
Notice that merge/3 will not remove duplicates, so merging
ordered sets will not necessarily result in an ordered set. Use
`ord_union/3` instead.
*/
/** @pred ord_add_element(+ _Set1_, + _Element_, ? _Set2_)
@@ -173,29 +182,6 @@ Holds when _Union_ is the union of the lists _Sets_.
*/
:- 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
]).
/*
:- mode
@@ -221,7 +207,7 @@ Holds when _Union_ is the union of the lists _Sets_.
*/
% list_to_ord_set(+List, ?Set)
%% @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
@@ -231,7 +217,7 @@ list_to_ord_set(List, Set) :-
sort(List, Set).
% merge(+List1, +List2, -Merged)
%% @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
@@ -250,7 +236,7 @@ merge(List1, [], List1).
% ord_disjoint(+Set1, +Set2)
%% @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.
@@ -267,7 +253,7 @@ ord_disjoint(>, Head1, Tail1, _, Tail2) :-
% ord_insert(+Set1, +Element, ?Set2)
%% @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
@@ -292,7 +278,7 @@ ord_insert(>, Head, Tail, Element, [Element,Head|Tail]).
% ord_intersect(+Set1, +Set2)
%% @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 = .
@@ -310,7 +296,7 @@ ord_intersect(L1, L2, L) :-
ord_intersection(L1, L2, L).
% ord_intersection(+Set1, +Set2, ?Intersection)
%% @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.
@@ -327,7 +313,7 @@ ord_intersection([Head1|Tail1], [Head2|Tail2], Intersection) :-
ord_intersection([Head1|Tail1], Tail2, Intersection)
).
% ord_intersection(+Set1, +Set2, ?Intersection, ?Difference)
%% @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.
@@ -408,7 +394,7 @@ ord_del_element(>, Head1, Tail1, _, [Head1|Tail1]).
% ord_symdiff(+Set1, +Set2, ?Difference)
%% @pred ord_symdiff(+Set1, +Set2, ?Difference)
% is true when Difference is the symmetric difference of Set1 and Set2.
ord_symdiff(Set1, [], Set1) :- !.
@@ -444,7 +430,7 @@ ord_union(>, Head1, Tail1, Head2, Tail2, [Head2|Union]) :-
ord_union([Head1|Tail1], Tail2, Union).
% ord_union(+Set1, +Set2, ?Union, ?Difference)
%% @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.
@@ -463,7 +449,7 @@ ord_union(>, Head1, Tail1, Head2, Tail2, [Head2|Union], [Head2|Diff]) :-
% ord_setproduct(+Set1, +Set2, ?Product)
%% @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