1/* Part of SWI-Prolog 2 3 Author: Jan Wielemaker 4 E-mail: J.Wielemaker@vu.nl 5 WWW: http://www.swi-prolog.org 6 Copyright (c) 2001-2014, University of Amsterdam 7 VU University Amsterdam 8 All rights reserved. 9 10 Redistribution and use in source and binary forms, with or without 11 modification, are permitted provided that the following conditions 12 are met: 13 14 1. Redistributions of source code must retain the above copyright 15 notice, this list of conditions and the following disclaimer. 16 17 2. Redistributions in binary form must reproduce the above copyright 18 notice, this list of conditions and the following disclaimer in 19 the documentation and/or other materials provided with the 20 distribution. 21 22 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 23 "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 24 LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS 25 FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 26 COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, 27 INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, 28 BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; 29 LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER 30 CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 31 LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN 32 ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 33 POSSIBILITY OF SUCH DAMAGE. 34*/ 35 36:- module(ordsets, 37 [ is_ordset/1, % @Term 38 list_to_ord_set/2, % +List, -OrdSet 39 ord_add_element/3, % +Set, +Element, -NewSet 40 ord_del_element/3, % +Set, +Element, -NewSet 41 ord_selectchk/3, % +Item, ?Set1, ?Set2 42 ord_intersect/2, % +Set1, +Set2 (test non-empty) 43 ord_intersect/3, % +Set1, +Set2, -Intersection 44 ord_intersection/3, % +Set1, +Set2, -Intersection 45 ord_intersection/4, % +Set1, +Set2, -Intersection, -Diff 46 ord_disjoint/2, % +Set1, +Set2 47 ord_subtract/3, % +Set, +Delete, -Remaining 48 ord_union/2, % +SetOfOrdSets, -Set 49 ord_union/3, % +Set1, +Set2, -Union 50 ord_union/4, % +Set1, +Set2, -Union, -New 51 ord_subset/2, % +Sub, +Super (test Sub is in Super) 52 % Non-Quintus extensions 53 ord_empty/1, % ?Set 54 ord_memberchk/2, % +Element, +Set, 55 ord_symdiff/3, % +Set1, +Set2, ?Diff 56 % SICSTus extensions 57 ord_seteq/2, % +Set1, +Set2 58 ord_intersection/2 % +PowerSet, -Intersection 59 ]). 60:- use_module(library(oset)). 61:- set_prolog_flag(generate_debug_info, false). 62 63/** <module> Ordered set manipulation 64 65Ordered sets are lists with unique elements sorted to the standard order 66of terms (see sort/2). Exploiting ordering, many of the set operations 67can be expressed in order N rather than N^2 when dealing with unordered 68sets that may contain duplicates. The library(ordsets) is available in a 69number of Prolog implementations. Our predicates are designed to be 70compatible with common practice in the Prolog community. The 71implementation is incomplete and relies partly on library(oset), an 72older ordered set library distributed with SWI-Prolog. New applications 73are advised to use library(ordsets). 74 75Some of these predicates match directly to corresponding list 76operations. It is advised to use the versions from this library to make 77clear you are operating on ordered sets. An exception is member/2. See 78ord_memberchk/2. 79 80The ordsets library is based on the standard order of terms. This 81implies it can handle all Prolog terms, including variables. Note 82however, that the ordering is not stable if a term inside the set is 83further instantiated. Also note that variable ordering changes if 84variables in the set are unified with each other or a variable in the 85set is unified with a variable that is `older' than the newest variable 86in the set. In practice, this implies that it is allowed to use 87member(X, OrdSet) on an ordered set that holds variables only if X is a 88fresh variable. In other cases one should cease using it as an ordset 89because the order it relies on may have been changed. 90*/ 91 92%! is_ordset(@Term) is semidet. 93% 94% True if Term is an ordered set. All predicates in this library 95% expect ordered sets as input arguments. Failing to fullfil this 96% assumption results in undefined behaviour. Typically, ordered 97% sets are created by predicates from this library, sort/2 or 98% setof/3. 99 100is_ordset(Term) :- 101 is_list(Term), 102 is_ordset2(Term). 103 104is_ordset2([]). 105is_ordset2([H|T]) :- 106 is_ordset3(T, H). 107 108is_ordset3([], _). 109is_ordset3([H2|T], H) :- 110 H2 @> H, 111 is_ordset3(T, H2). 112 113 114%! ord_empty(?List) is semidet. 115% 116% True when List is the empty ordered set. Simply unifies list 117% with the empty list. Not part of Quintus. 118 119ord_empty([]). 120 121 122%! ord_seteq(+Set1, +Set2) is semidet. 123% 124% True if Set1 and Set2 have the same elements. As both are 125% canonical sorted lists, this is the same as ==/2. 126% 127% @compat sicstus 128 129ord_seteq(Set1, Set2) :- 130 Set1 == Set2. 131 132 133%! list_to_ord_set(+List, -OrdSet) is det. 134% 135% Transform a list into an ordered set. This is the same as 136% sorting the list. 137 138list_to_ord_set(List, Set) :- 139 sort(List, Set). 140 141 142%! ord_intersect(+Set1, +Set2) is semidet. 143% 144% True if both ordered sets have a non-empty intersection. 145 146ord_intersect([H1|T1], L2) :- 147 ord_intersect_(L2, H1, T1). 148 149ord_intersect_([H2|T2], H1, T1) :- 150 compare(Order, H1, H2), 151 ord_intersect__(Order, H1, T1, H2, T2). 152 153ord_intersect__(<, _H1, T1, H2, T2) :- 154 ord_intersect_(T1, H2, T2). 155ord_intersect__(=, _H1, _T1, _H2, _T2). 156ord_intersect__(>, H1, T1, _H2, T2) :- 157 ord_intersect_(T2, H1, T1). 158 159 160%! ord_disjoint(+Set1, +Set2) is semidet. 161% 162% True if Set1 and Set2 have no common elements. This is the 163% negation of ord_intersect/2. 164 165ord_disjoint(Set1, Set2) :- 166 \+ ord_intersect(Set1, Set2). 167 168 169%! ord_intersect(+Set1, +Set2, -Intersection) 170% 171% Intersection holds the common elements of Set1 and Set2. 172% 173% @deprecated Use ord_intersection/3 174 175ord_intersect(Set1, Set2, Intersection) :- 176 oset_int(Set1, Set2, Intersection). 177 178 179%! ord_intersection(+PowerSet, -Intersection) 180% 181% Intersection of a powerset. True when Intersection is an ordered 182% set holding all elements common to all sets in PowerSet. 183% 184% @compat sicstus 185 186ord_intersection(PowerSet, Intersection) :- 187 key_by_length(PowerSet, Pairs), 188 keysort(Pairs, [_-S|Sorted]), 189 l_int(Sorted, S, Intersection). 190 191key_by_length([], []). 192key_by_length([H|T0], [L-H|T]) :- 193 length(H, L), 194 key_by_length(T0, T). 195 196l_int([], S, S). 197l_int([_-H|T], S0, S) :- 198 ord_intersection(S0, H, S1), 199 l_int(T, S1, S). 200 201 202%! ord_intersection(+Set1, +Set2, -Intersection) is det. 203% 204% Intersection holds the common elements of Set1 and Set2. 205 206ord_intersection(Set1, Set2, Intersection) :- 207 oset_int(Set1, Set2, Intersection). 208 209 210%! ord_intersection(+Set1, +Set2, ?Intersection, ?Difference) is det. 211% 212% Intersection and difference between two ordered sets. 213% Intersection is the intersection between Set1 and Set2, while 214% Difference is defined by ord_subtract(Set2, Set1, Difference). 215% 216% @see ord_intersection/3 and ord_subtract/3. 217 218ord_intersection([], L, [], L) :- !. 219ord_intersection([_|_], [], [], []) :- !. 220ord_intersection([H1|T1], [H2|T2], Intersection, Difference) :- 221 compare(Diff, H1, H2), 222 ord_intersection2(Diff, H1, T1, H2, T2, Intersection, Difference). 223 224ord_intersection2(=, H1, T1, _H2, T2, [H1|T], Difference) :- 225 ord_intersection(T1, T2, T, Difference). 226ord_intersection2(<, _, T1, H2, T2, Intersection, Difference) :- 227 ord_intersection(T1, [H2|T2], Intersection, Difference). 228ord_intersection2(>, H1, T1, H2, T2, Intersection, [H2|HDiff]) :- 229 ord_intersection([H1|T1], T2, Intersection, HDiff). 230 231 232%! ord_add_element(+Set1, +Element, ?Set2) is det. 233% 234% Insert an element into the set. This is the same as 235% ord_union(Set1, [Element], Set2). 236 237ord_add_element(Set1, Element, Set2) :- 238 oset_addel(Set1, Element, Set2). 239 240 241%! ord_del_element(+Set, +Element, -NewSet) is det. 242% 243% Delete an element from an ordered set. This is the same as 244% ord_subtract(Set, [Element], NewSet). 245 246ord_del_element(Set, Element, NewSet) :- 247 oset_delel(Set, Element, NewSet). 248 249 250%! ord_selectchk(+Item, ?Set1, ?Set2) is semidet. 251% 252% Selectchk/3, specialised for ordered sets. Is true when 253% select(Item, Set1, Set2) and Set1, Set2 are both sorted lists 254% without duplicates. This implementation is only expected to work 255% for Item ground and either Set1 or Set2 ground. The "chk" suffix 256% is meant to remind you of memberchk/2, which also expects its 257% first argument to be ground. ord_selectchk(X, S, T) => 258% ord_memberchk(X, S) & \+ ord_memberchk(X, T). 259% 260% @author Richard O'Keefe 261 262ord_selectchk(Item, [X|Set1], [X|Set2]) :- 263 X @< Item, 264 !, 265 ord_selectchk(Item, Set1, Set2). 266ord_selectchk(Item, [Item|Set1], Set1) :- 267 ( Set1 == [] 268 -> true 269 ; Set1 = [Y|_] 270 -> Item @< Y 271 ). 272 273 274%! ord_memberchk(+Element, +OrdSet) is semidet. 275% 276% True if Element is a member of OrdSet, compared using ==. Note 277% that _enumerating_ elements of an ordered set can be done using 278% member/2. 279% 280% Some Prolog implementations also provide ord_member/2, with the 281% same semantics as ord_memberchk/2. We believe that having a 282% semidet ord_member/2 is unacceptably inconsistent with the *_chk 283% convention. Portable code should use ord_memberchk/2 or 284% member/2. 285% 286% @author Richard O'Keefe 287 288ord_memberchk(Item, [X1,X2,X3,X4|Xs]) :- 289 !, 290 compare(R4, Item, X4), 291 ( R4 = (>) -> ord_memberchk(Item, Xs) 292 ; R4 = (<) -> 293 compare(R2, Item, X2), 294 ( R2 = (>) -> Item == X3 295 ; R2 = (<) -> Item == X1 296 ;/* R2 = (=), Item == X2 */ true 297 ) 298 ;/* R4 = (=) */ true 299 ). 300ord_memberchk(Item, [X1,X2|Xs]) :- 301 !, 302 compare(R2, Item, X2), 303 ( R2 = (>) -> ord_memberchk(Item, Xs) 304 ; R2 = (<) -> Item == X1 305 ;/* R2 = (=) */ true 306 ). 307ord_memberchk(Item, [X1]) :- 308 Item == X1. 309 310 311%! ord_subset(+Sub, +Super) is semidet. 312% 313% Is true if all elements of Sub are in Super 314 315ord_subset([], _). 316ord_subset([H1|T1], [H2|T2]) :- 317 compare(Order, H1, H2), 318 ord_subset_(Order, H1, T1, T2). 319 320ord_subset_(>, H1, T1, [H2|T2]) :- 321 compare(Order, H1, H2), 322 ord_subset_(Order, H1, T1, T2). 323ord_subset_(=, _, T1, T2) :- 324 ord_subset(T1, T2). 325 326 327%! ord_subtract(+InOSet, +NotInOSet, -Diff) is det. 328% 329% Diff is the set holding all elements of InOSet that are not in 330% NotInOSet. 331 332ord_subtract(InOSet, NotInOSet, Diff) :- 333 oset_diff(InOSet, NotInOSet, Diff). 334 335 336%! ord_union(+SetOfSets, -Union) is det. 337% 338% True if Union is the union of all elements in the superset 339% SetOfSets. Each member of SetOfSets must be an ordered set, the 340% sets need not be ordered in any way. 341% 342% @author Copied from YAP, probably originally by Richard O'Keefe. 343 344ord_union([], []). 345ord_union([Set|Sets], Union) :- 346 length([Set|Sets], NumberOfSets), 347 ord_union_all(NumberOfSets, [Set|Sets], Union, []). 348 349ord_union_all(N, Sets0, Union, Sets) :- 350 ( N =:= 1 351 -> Sets0 = [Union|Sets] 352 ; N =:= 2 353 -> Sets0 = [Set1,Set2|Sets], 354 ord_union(Set1,Set2,Union) 355 ; A is N>>1, 356 Z is N-A, 357 ord_union_all(A, Sets0, X, Sets1), 358 ord_union_all(Z, Sets1, Y, Sets), 359 ord_union(X, Y, Union) 360 ). 361 362 363%! ord_union(+Set1, +Set2, ?Union) is det. 364% 365% Union is the union of Set1 and Set2 366 367ord_union(Set1, Set2, Union) :- 368 oset_union(Set1, Set2, Union). 369 370 371%! ord_union(+Set1, +Set2, -Union, -New) is det. 372% 373% True iff ord_union(Set1, Set2, Union) and 374% ord_subtract(Set2, Set1, New). 375 376ord_union([], Set2, Set2, Set2). 377ord_union([H|T], Set2, Union, New) :- 378 ord_union_1(Set2, H, T, Union, New). 379 380ord_union_1([], H, T, [H|T], []). 381ord_union_1([H2|T2], H, T, Union, New) :- 382 compare(Order, H, H2), 383 ord_union(Order, H, T, H2, T2, Union, New). 384 385ord_union(<, H, T, H2, T2, [H|Union], New) :- 386 ord_union_2(T, H2, T2, Union, New). 387ord_union(>, H, T, H2, T2, [H2|Union], [H2|New]) :- 388 ord_union_1(T2, H, T, Union, New). 389ord_union(=, H, T, _, T2, [H|Union], New) :- 390 ord_union(T, T2, Union, New). 391 392ord_union_2([], H2, T2, [H2|T2], [H2|T2]). 393ord_union_2([H|T], H2, T2, Union, New) :- 394 compare(Order, H, H2), 395 ord_union(Order, H, T, H2, T2, Union, New). 396 397 398%! ord_symdiff(+Set1, +Set2, ?Difference) is det. 399% 400% Is true when Difference is the symmetric difference of Set1 and 401% Set2. I.e., Difference contains all elements that are not in the 402% intersection of Set1 and Set2. The semantics is the same as the 403% sequence below (but the actual implementation requires only a 404% single scan). 405% 406% == 407% ord_union(Set1, Set2, Union), 408% ord_intersection(Set1, Set2, Intersection), 409% ord_subtract(Union, Intersection, Difference). 410% == 411% 412% For example: 413% 414% == 415% ?- ord_symdiff([1,2], [2,3], X). 416% X = [1,3]. 417% == 418 419ord_symdiff([], Set2, Set2). 420ord_symdiff([H1|T1], Set2, Difference) :- 421 ord_symdiff(Set2, H1, T1, Difference). 422 423ord_symdiff([], H1, T1, [H1|T1]). 424ord_symdiff([H2|T2], H1, T1, Difference) :- 425 compare(Order, H1, H2), 426 ord_symdiff(Order, H1, T1, H2, T2, Difference). 427 428ord_symdiff(<, H1, Set1, H2, T2, [H1|Difference]) :- 429 ord_symdiff(Set1, H2, T2, Difference). 430ord_symdiff(=, _, T1, _, T2, Difference) :- 431 ord_symdiff(T1, T2, Difference). 432ord_symdiff(>, H1, T1, H2, Set2, [H2|Difference]) :- 433 ord_symdiff(Set2, H1, T1, Difference).