File: lists.pl

package info (click to toggle)
swi-prolog 8.0.2+dfsg-3+deb10u1
  • links: PTS, VCS
  • area: main
  • in suites: buster
  • size: 72,036 kB
  • sloc: ansic: 349,612; perl: 306,654; java: 5,208; cpp: 4,436; sh: 3,042; ruby: 1,594; yacc: 845; makefile: 136; xml: 82; sed: 12; sql: 6
file content (734 lines) | stat: -rw-r--r-- 21,611 bytes parent folder | download | duplicates (2)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
/*  Part of SWI-Prolog

    Author:        Jan Wielemaker and Richard O'Keefe
    E-mail:        J.Wielemaker@cs.vu.nl
    WWW:           http://www.swi-prolog.org
    Copyright (c)  2002-2016, University of Amsterdam
                              VU University Amsterdam
    All rights reserved.

    Redistribution and use in source and binary forms, with or without
    modification, are permitted provided that the following conditions
    are met:

    1. Redistributions of source code must retain the above copyright
       notice, this list of conditions and the following disclaimer.

    2. Redistributions in binary form must reproduce the above copyright
       notice, this list of conditions and the following disclaimer in
       the documentation and/or other materials provided with the
       distribution.

    THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
    "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
    LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
    FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
    COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
    INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
    BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
    LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
    CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
    LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
    ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
    POSSIBILITY OF SUCH DAMAGE.
*/

:- module(lists,
        [ member/2,                     % ?X, ?List
          append/2,                     % +ListOfLists, -List
          append/3,                     % ?A, ?B, ?AB
          prefix/2,                     % ?Part, ?Whole
          select/3,                     % ?X, ?List, ?Rest
          selectchk/3,                  % ?X, ?List, ?Rest
          select/4,                     % ?X, ?XList, ?Y, ?YList
          selectchk/4,                  % ?X, ?XList, ?Y, ?YList
          nextto/3,                     % ?X, ?Y, ?List
          delete/3,                     % ?List, ?X, ?Rest
          nth0/3,                       % ?N, ?List, ?Elem
          nth1/3,                       % ?N, ?List, ?Elem
          nth0/4,                       % ?N, ?List, ?Elem, ?Rest
          nth1/4,                       % ?N, ?List, ?Elem, ?Rest
          last/2,                       % +List, -Element
          proper_length/2,              % @List, -Length
          same_length/2,                % ?List1, ?List2
          reverse/2,                    % +List, -Reversed
          permutation/2,                % ?List, ?Permutation
          flatten/2,                    % +Nested, -Flat

                                        % Ordered operations
          max_member/2,                 % -Max, +List
          min_member/2,                 % -Min, +List

                                        % Lists of numbers
          sum_list/2,                   % +List, -Sum
          max_list/2,                   % +List, -Max
          min_list/2,                   % +List, -Min
          numlist/3,                    % +Low, +High, -List

                                        % set manipulation
          is_set/1,                     % +List
          list_to_set/2,                % +List, -Set
          intersection/3,               % +List1, +List2, -Intersection
          union/3,                      % +List1, +List2, -Union
          subset/2,                     % +SubSet, +Set
          subtract/3                    % +Set, +Delete, -Remaining
        ]).
:- use_module(library(error)).
:- use_module(library(pairs)).

:- set_prolog_flag(generate_debug_info, false).

/** <module> List Manipulation

This library provides  commonly  accepted   basic  predicates  for  list
manipulation in the Prolog community. Some additional list manipulations
are built-in. See e.g., memberchk/2, length/2.

The implementation of this library  is   copied  from many places. These
include: "The Craft of Prolog", the   DEC-10  Prolog library (LISTRO.PL)
and the YAP lists library. Some   predicates  are reimplemented based on
their specification by Quintus and SICStus.

@compat Virtually every Prolog system has library(lists), but the set
        of provided predicates is diverse.  There is a fair agreement
        on the semantics of most of these predicates, although error
        handling may vary.
*/

%!  member(?Elem, ?List)
%
%   True if Elem is a  member   of  List.  The SWI-Prolog definition
%   differs from the classical one.  Our definition avoids unpacking
%   each list element twice and  provides   determinism  on the last
%   element.  E.g. this is deterministic:
%
%       ==
%           member(X, [One]).
%       ==
%
%   @author Gertjan van Noord

member(El, [H|T]) :-
    member_(T, El, H).

member_(_, El, El).
member_([H|T], El, _) :-
    member_(T, El, H).

%!  append(?List1, ?List2, ?List1AndList2)
%
%   List1AndList2 is the concatenation of List1 and List2

append([], L, L).
append([H|T], L, [H|R]) :-
    append(T, L, R).

%!  append(+ListOfLists, ?List)
%
%   Concatenate a list of lists.  Is  true   if  ListOfLists  is a list of
%   lists, and List is the concatenation of these lists.
%
%   @param  ListOfLists must be a list of _possibly_ partial lists

append(ListOfLists, List) :-
    must_be(list, ListOfLists),
    append_(ListOfLists, List).

append_([], []).
append_([L|Ls], As) :-
    append(L, Ws, As),
    append_(Ls, Ws).


%!  prefix(?Part, ?Whole)
%
%   True iff Part is a leading substring of Whole.  This is the same
%   as append(Part, _, Whole).

prefix([], _).
prefix([E|T0], [E|T]) :-
    prefix(T0, T).


%!  select(?Elem, ?List1, ?List2)
%
%   Is true when List1,  with  Elem   removed,  results  in  List2. This
%   implementation is determinsitic if the  last   element  of List1 has
%   been selected.

select(X, [Head|Tail], Rest) :-
    select3_(Tail, Head, X, Rest).

select3_(Tail, Head, Head, Tail).
select3_([Head2|Tail], Head, X, [Head|Rest]) :-
    select3_(Tail, Head2, X, Rest).


%!  selectchk(+Elem, +List, -Rest) is semidet.
%
%   Semi-deterministic removal of first element in List that unifies
%   with Elem.

selectchk(Elem, List, Rest) :-
    select(Elem, List, Rest0),
    !,
    Rest = Rest0.


%!  select(?X, ?XList, ?Y, ?YList) is nondet.
%
%   Select from two lists at the  same   positon.  True  if XList is
%   unifiable with YList apart a single element at the same position
%   that is unified with X in XList and   with Y in YList. A typical
%   use for this predicate is to _replace_   an element, as shown in
%   the example below. All possible   substitutions are performed on
%   backtracking.
%
%     ==
%     ?- select(b, [a,b,c,b], 2, X).
%     X = [a, 2, c, b] ;
%     X = [a, b, c, 2] ;
%     false.
%     ==
%
%   @see selectchk/4 provides a semidet version.

select(X, XList, Y, YList) :-
    select4_(XList, X, Y, YList).

select4_([X|List], X, Y, [Y|List]).
select4_([X0|XList], X, Y, [X0|YList]) :-
    select4_(XList, X, Y, YList).

%!  selectchk(?X, ?XList, ?Y, ?YList) is semidet.
%
%   Semi-deterministic version of select/4.

selectchk(X, XList, Y, YList) :-
    select(X, XList, Y, YList),
    !.

%!  nextto(?X, ?Y, ?List)
%
%   True if Y directly follows X in List.

nextto(X, Y, [X,Y|_]).
nextto(X, Y, [_|Zs]) :-
    nextto(X, Y, Zs).

%!  delete(+List1, @Elem, -List2) is det.
%
%   Delete matching elements from a list. True  when List2 is a list
%   with all elements from List1 except   for  those that unify with
%   Elem. Matching Elem with elements of List1  is uses =|\+ Elem \=
%   H|=, which implies that Elem is not changed.
%
%   @deprecated There are too many ways in which one might want to
%               delete elements from a list to justify the name.
%               Think of matching (= vs. ==), delete first/all,
%               be deterministic or not.
%   @see select/3, subtract/3.

delete([], _, []).
delete([Elem|Tail], Del, Result) :-
    (   \+ Elem \= Del
    ->  delete(Tail, Del, Result)
    ;   Result = [Elem|Rest],
        delete(Tail, Del, Rest)
    ).


/*  nth0/3, nth1/3 are improved versions from
    Martin Jansche <martin@pc03.idf.uni-heidelberg.de>
*/

%!  nth0(?Index, ?List, ?Elem)
%
%   True when Elem is the Index'th  element of List. Counting starts
%   at 0.
%
%   @error  type_error(integer, Index) if Index is not an integer or
%           unbound.
%   @see nth1/3.

nth0(Index, List, Elem) :-
    (   integer(Index)
    ->  nth0_det(Index, List, Elem)         % take nth deterministically
    ;   var(Index)
    ->  List = [H|T],
        nth_gen(T, Elem, H, 0, Index)       % match
    ;   must_be(integer, Index)
    ).

nth0_det(0, [Elem|_], Elem) :- !.
nth0_det(1, [_,Elem|_], Elem) :- !.
nth0_det(2, [_,_,Elem|_], Elem) :- !.
nth0_det(3, [_,_,_,Elem|_], Elem) :- !.
nth0_det(4, [_,_,_,_,Elem|_], Elem) :- !.
nth0_det(5, [_,_,_,_,_,Elem|_], Elem) :- !.
nth0_det(N, [_,_,_,_,_,_   |Tail], Elem) :-
    M is N - 6,
    M >= 0,
    nth0_det(M, Tail, Elem).

nth_gen(_, Elem, Elem, Base, Base).
nth_gen([H|Tail], Elem, _, N, Base) :-
    succ(N, M),
    nth_gen(Tail, Elem, H, M, Base).


%!  nth1(?Index, ?List, ?Elem)
%
%   Is true when Elem is  the   Index'th  element  of List. Counting
%   starts at 1.
%
%   @see nth0/3.

nth1(Index, List, Elem) :-
    (   integer(Index)
    ->  Index0 is Index - 1,
        nth0_det(Index0, List, Elem)        % take nth deterministically
    ;   var(Index)
    ->  List = [H|T],
        nth_gen(T, Elem, H, 1, Index)       % match
    ;   must_be(integer, Index)
    ).

%!  nth0(?N, ?List, ?Elem, ?Rest) is det.
%
%   Select/insert element at index.  True  when   Elem  is  the N'th
%   (0-based) element of List and Rest is   the  remainder (as in by
%   select/3) of List.  For example:
%
%     ==
%     ?- nth0(I, [a,b,c], E, R).
%     I = 0, E = a, R = [b, c] ;
%     I = 1, E = b, R = [a, c] ;
%     I = 2, E = c, R = [a, b] ;
%     false.
%     ==
%
%     ==
%     ?- nth0(1, L, a1, [a,b]).
%     L = [a, a1, b].
%     ==

nth0(V, In, Element, Rest) :-
    var(V),
    !,
    generate_nth(0, V, In, Element, Rest).
nth0(V, In, Element, Rest) :-
    must_be(nonneg, V),
    find_nth0(V, In, Element, Rest).

%!  nth1(?N, ?List, ?Elem, ?Rest) is det.
%
%   As nth0/4, but counting starts at 1.

nth1(V, In, Element, Rest) :-
    var(V),
    !,
    generate_nth(1, V, In, Element, Rest).
nth1(V, In, Element, Rest) :-
    must_be(positive_integer, V),
    succ(V0, V),
    find_nth0(V0, In, Element, Rest).

generate_nth(I, I, [Head|Rest], Head, Rest).
generate_nth(I, IN, [H|List], El, [H|Rest]) :-
    I1 is I+1,
    generate_nth(I1, IN, List, El, Rest).

find_nth0(0, [Head|Rest], Head, Rest) :- !.
find_nth0(N, [Head|Rest0], Elem, [Head|Rest]) :-
    M is N-1,
    find_nth0(M, Rest0, Elem, Rest).


%!  last(?List, ?Last)
%
%   Succeeds when Last  is  the  last   element  of  List.  This
%   predicate is =semidet= if List is a  list and =multi= if List is
%   a partial list.
%
%   @compat There is no de-facto standard for the argument order of
%           last/2.  Be careful when porting code or use
%           append(_, [Last], List) as a portable alternative.

last([X|Xs], Last) :-
    last_(Xs, X, Last).

last_([], Last, Last).
last_([X|Xs], _, Last) :-
    last_(Xs, X, Last).


%!  proper_length(@List, -Length) is semidet.
%
%   True when Length is the number of   elements  in the proper list
%   List.  This is equivalent to
%
%     ==
%     proper_length(List, Length) :-
%           is_list(List),
%           length(List, Length).
%     ==

proper_length(List, Length) :-
    '$skip_list'(Length0, List, Tail),
    Tail == [],
    Length = Length0.


%!  same_length(?List1, ?List2)
%
%   Is true when List1 and List2 are   lists with the same number of
%   elements. The predicate is deterministic if  at least one of the
%   arguments is a proper list.  It   is  non-deterministic  if both
%   arguments are partial lists.
%
%   @see length/2

same_length([], []).
same_length([_|T1], [_|T2]) :-
    same_length(T1, T2).


%!  reverse(?List1, ?List2)
%
%   Is true when the elements of List2 are in reverse order compared to
%   List1.

reverse(Xs, Ys) :-
    reverse(Xs, [], Ys, Ys).

reverse([], Ys, Ys, []).
reverse([X|Xs], Rs, Ys, [_|Bound]) :-
    reverse(Xs, [X|Rs], Ys, Bound).


%!  permutation(?Xs, ?Ys) is nondet.
%
%   True when Xs is a permutation of Ys. This can solve for Ys given
%   Xs or Xs given Ys, or  even   enumerate  Xs and Ys together. The
%   predicate  permutation/2  is  primarily   intended  to  generate
%   permutations. Note that a list of  length N has N! permutations,
%   and  unbounded  permutation  generation   becomes  prohibitively
%   expensive, even for rather short lists (10! = 3,628,800).
%
%   If both Xs and Ys are provided  and both lists have equal length
%   the order is |Xs|^2. Simply testing  whether Xs is a permutation
%   of Ys can be  achieved  in   order  log(|Xs|)  using  msort/2 as
%   illustrated below with the =semidet= predicate is_permutation/2:
%
%     ==
%     is_permutation(Xs, Ys) :-
%       msort(Xs, Sorted),
%       msort(Ys, Sorted).
%     ==
%
%   The example below illustrates that Xs   and Ys being proper lists
%   is not a sufficient condition to use the above replacement.
%
%     ==
%     ?- permutation([1,2], [X,Y]).
%     X = 1, Y = 2 ;
%     X = 2, Y = 1 ;
%     false.
%     ==
%
%   @error  type_error(list, Arg) if either argument is not a proper
%           or partial list.

permutation(Xs, Ys) :-
    '$skip_list'(Xlen, Xs, XTail),
    '$skip_list'(Ylen, Ys, YTail),
    (   XTail == [], YTail == []            % both proper lists
    ->  Xlen == Ylen
    ;   var(XTail), YTail == []             % partial, proper
    ->  length(Xs, Ylen)
    ;   XTail == [], var(YTail)             % proper, partial
    ->  length(Ys, Xlen)
    ;   var(XTail), var(YTail)              % partial, partial
    ->  length(Xs, Len),
        length(Ys, Len)
    ;   must_be(list, Xs),                  % either is not a list
        must_be(list, Ys)
    ),
    perm(Xs, Ys).

perm([], []).
perm(List, [First|Perm]) :-
    select(First, List, Rest),
    perm(Rest, Perm).

%!  flatten(+NestedList, -FlatList) is det.
%
%   Is true if FlatList is a  non-nested version of NestedList. Note
%   that empty lists are removed. In   standard Prolog, this implies
%   that the atom '[]' is removed  too.   In  SWI7, `[]` is distinct
%   from '[]'.
%
%   Ending up needing flatten/2 often   indicates, like append/3 for
%   appending two lists, a bad design. Efficient code that generates
%   lists from generated small  lists   must  use  difference lists,
%   often possible through grammar rules for optimal readability.
%
%   @see append/2

flatten(List, FlatList) :-
    flatten(List, [], FlatList0),
    !,
    FlatList = FlatList0.

flatten(Var, Tl, [Var|Tl]) :-
    var(Var),
    !.
flatten([], Tl, Tl) :- !.
flatten([Hd|Tl], Tail, List) :-
    !,
    flatten(Hd, FlatHeadTail, List),
    flatten(Tl, Tail, FlatHeadTail).
flatten(NonList, Tl, [NonList|Tl]).


                 /*******************************
                 *       ORDER OPERATIONS       *
                 *******************************/

%!  max_member(-Max, +List) is semidet.
%
%   True when Max is the largest  member   in  the standard order of
%   terms.  Fails if List is empty.
%
%   @see compare/3
%   @see max_list/2 for the maximum of a list of numbers.

max_member(Max, [H|T]) :-
    max_member_(T, H, Max).

max_member_([], Max, Max).
max_member_([H|T], Max0, Max) :-
    (   H @=< Max0
    ->  max_member_(T, Max0, Max)
    ;   max_member_(T, H, Max)
    ).


%!  min_member(-Min, +List) is semidet.
%
%   True when Min is the smallest member   in  the standard order of
%   terms. Fails if List is empty.
%
%   @see compare/3
%   @see min_list/2 for the minimum of a list of numbers.

min_member(Min, [H|T]) :-
    min_member_(T, H, Min).

min_member_([], Min, Min).
min_member_([H|T], Min0, Min) :-
    (   H @>= Min0
    ->  min_member_(T, Min0, Min)
    ;   min_member_(T, H, Min)
    ).


                 /*******************************
                 *       LISTS OF NUMBERS       *
                 *******************************/

%!  sum_list(+List, -Sum) is det.
%
%   Sum is the result of adding all numbers in List.

sum_list(Xs, Sum) :-
    sum_list(Xs, 0, Sum).

sum_list([], Sum, Sum).
sum_list([X|Xs], Sum0, Sum) :-
    Sum1 is Sum0 + X,
    sum_list(Xs, Sum1, Sum).

%!  max_list(+List:list(number), -Max:number) is semidet.
%
%   True if Max is the largest number in List.  Fails if List is
%   empty.
%
%   @see max_member/2.

max_list([H|T], Max) :-
    max_list(T, H, Max).

max_list([], Max, Max).
max_list([H|T], Max0, Max) :-
    Max1 is max(H, Max0),
    max_list(T, Max1, Max).


%!  min_list(+List:list(number), -Min:number) is semidet.
%
%   True if Min is the smallest  number   in  List. Fails if List is
%   empty.
%
%   @see min_member/2.

min_list([H|T], Min) :-
    min_list(T, H, Min).

min_list([], Min, Min).
min_list([H|T], Min0, Min) :-
    Min1 is min(H, Min0),
    min_list(T, Min1, Min).


%!  numlist(+Low, +High, -List) is semidet.
%
%   List is a list [Low, Low+1, ... High].  Fails if High < Low.
%
%   @error type_error(integer, Low)
%   @error type_error(integer, High)

numlist(L, U, Ns) :-
    must_be(integer, L),
    must_be(integer, U),
    L =< U,
    numlist_(L, U, Ns).

numlist_(U, U, List) :-
    !,
    List = [U].
numlist_(L, U, [L|Ns]) :-
    L2 is L+1,
    numlist_(L2, U, Ns).


                /********************************
                *       SET MANIPULATION        *
                *********************************/

%!  is_set(@Set) is semidet.
%
%   True if Set is a proper  list without duplicates. Equivalence is
%   based on ==/2. The  implementation   uses  sort/2, which implies
%   that the complexity is N*log(N) and   the  predicate may cause a
%   resource-error. There are no other error conditions.

is_set(Set) :-
    '$skip_list'(Len, Set, Tail),
    Tail == [],                             % Proper list
    sort(Set, Sorted),
    length(Sorted, Len).


%!  list_to_set(+List, ?Set) is det.
%
%   True when Set has the same elements   as List in the same order.
%   The left-most copy of duplicate elements   is retained. List may
%   contain  variables.  Elements  _E1_  and   _E2_  are  considered
%   duplicates iff _E1_  ==  _E2_  holds.   The  complexity  of  the
%   implementation is N*log(N).
%
%   @see    sort/2 can be used to create an ordered set.  Many
%           set operations on ordered sets are order N rather than
%           order N**2.  The list_to_set/2 predicate is more
%           expensive than sort/2 because it involves, two sorts
%           and a linear scan.
%   @compat Up to version 6.3.11, list_to_set/2 had complexity
%           N**2 and equality was tested using =/2.
%   @error  List is type-checked.

list_to_set(List, Set) :-
    must_be(list, List),
    number_list(List, 1, Numbered),
    sort(1, @=<, Numbered, ONum),
    remove_dup_keys(ONum, NumSet),
    sort(2, @=<, NumSet, ONumSet),
    pairs_keys(ONumSet, Set).

number_list([], _, []).
number_list([H|T0], N, [H-N|T]) :-
    N1 is N+1,
    number_list(T0, N1, T).

remove_dup_keys([], []).
remove_dup_keys([H|T0], [H|T]) :-
    H = V-_,
    remove_same_key(T0, V, T1),
    remove_dup_keys(T1, T).

remove_same_key([V1-_|T0], V, T) :-
    V1 == V,
    !,
    remove_same_key(T0, V, T).
remove_same_key(L, _, L).


%!  intersection(+Set1, +Set2, -Set3) is det.
%
%   True if Set3 unifies with the  intersection   of  Set1 and Set2. The
%   complexity of this predicate is |Set1|*|Set2|. A _set_ is defined to
%   be an unordered list  without   duplicates.  Elements are considered
%   duplicates if they can be unified.
%
%   @see ord_intersection/3.

intersection([], _, []) :- !.
intersection([X|T], L, Intersect) :-
    memberchk(X, L),
    !,
    Intersect = [X|R],
    intersection(T, L, R).
intersection([_|T], L, R) :-
    intersection(T, L, R).


%!  union(+Set1, +Set2, -Set3) is det.
%
%   True if Set3 unifies with the union of  the lists Set1 and Set2. The
%   complexity of this predicate is |Set1|*|Set2|. A _set_ is defined to
%   be an unordered list  without   duplicates.  Elements are considered
%   duplicates if they can be unified.
%
%   @see ord_union/3

union([], L, L) :- !.
union([H|T], L, R) :-
    memberchk(H, L),
    !,
    union(T, L, R).
union([H|T], L, [H|R]) :-
    union(T, L, R).


%!  subset(+SubSet, +Set) is semidet.
%
%   True if all elements of SubSet  belong   to  Set as well. Membership
%   test is based on memberchk/2. The   complexity  is |SubSet|*|Set|. A
%   _set_ is defined  to  be  an   unordered  list  without  duplicates.
%   Elements are considered duplicates if they can be unified.
%
%   @see ord_subset/2.

subset([], _) :- !.
subset([E|R], Set) :-
    memberchk(E, Set),
    subset(R, Set).


%!  subtract(+Set, +Delete, -Result) is det.
%
%   Delete all elements  in  Delete  from   Set.  Deletion  is  based on
%   unification using memberchk/2. The complexity   is |Delete|*|Set|. A
%   _set_ is defined  to  be  an   unordered  list  without  duplicates.
%   Elements are considered duplicates if they can be unified.
%
%   @see ord_subtract/3.

subtract([], _, []) :- !.
subtract([E|T], D, R) :-
    memberchk(E, D),
    !,
    subtract(T, D, R).
subtract([H|T], D, [H|R]) :-
    subtract(T, D, R).