1 % (c) 2009-2025 Lehrstuhl fuer Softwaretechnik und Programmiersprachen,
2 % Heinrich Heine Universitaet Duesseldorf
3 % This software is licenced under EPL 1.0 (http://www.eclipse.org/org/documents/epl-v10.html)
4
5
6 :- module(custom_explicit_sets,[is_set_value/2,
7 is_custom_explicit_set/1, is_custom_explicit_set/2, is_custom_explicit_set_nonvar/1,
8 %equal_explicit_sets/2,
9 equal_explicit_sets_wf/3,
10 not_equal_explicit_sets_wf/3,
11 equality_explicit_sets_wf/4, same_texpr_body/2, same_closure/2,
12 is_empty_explicit_set/1, is_empty_explicit_set_wf/2, is_empty_closure_wf/4,
13 is_non_empty_explicit_set/1, is_non_empty_explicit_set_wf/2,
14 is_non_empty_closure_wf/4,
15 test_empty_explicit_set_wf/3, test_empty_closure_wf/5,
16 is_definitely_maximal_set/1,
17 explicit_set_cardinality/2, explicit_set_cardinality_wf/3,
18 explicit_set_cardinality_for_wf/2,
19 card_for_specific_custom_set/3, % only succeeds if we can compute it efficiently
20 card_for_specific_closure/4,
21 efficient_card_for_set/3, % same, but also for lists
22 quick_custom_explicit_set_approximate_size/2,
23 avl_approximate_size/2, avl_approximate_size/3,
24 is_infinite_explicit_set/1, is_infinite_closure/3,
25 is_infinite_global_set/2, is_simple_infinite_set/1,
26 dont_expand_this_explicit_set/1, dont_expand_this_explicit_set/2,
27 dont_expand_symbolic_explicit_set/1,
28 definitely_expand_this_explicit_set/1,
29 is_infinite_or_very_large_explicit_set/1,
30 is_infinite_or_very_large_explicit_set/2,
31 is_cartesian_product_closure/3,
32 expand_custom_set/2, expand_custom_set_wf/4,
33 try_expand_custom_set/2, try_expand_custom_set_with_catch/3,
34 try_expand_custom_set_wf/4,
35 expand_custom_set_to_list/2, expand_custom_set_to_list/4,
36 expand_custom_set_to_list_wf/5,
37 try_expand_custom_set_to_list_wf/5,
38 expand_custom_set_to_list_no_dups_wf/5,
39 expand_custom_set_to_list_gg/4,
40 try_expand_custom_set_to_list/4,
41 expand_interval_closure_to_avl/3,
42 expand_custom_set_to_list_now/2,
43 expand_closure_to_avl_or_list/6,
44 expand_closure_to_list/7,
45 expand_only_custom_closure_global/4, %try_expand_only_custom_closure_global/2,
46 expand_and_convert_to_avl_set/4,
47 ord_list_to_avlset_direct/3, sorted_ground_normalised_list_to_avlset/3,
48 try_expand_and_convert_to_avl/2, convert_to_avl/2,
49 should_be_converted_to_avl_from_lists/1, should_be_converted_to_avl/1,
50 try_expand_and_convert_to_avl_with_check/3,
51 try_expand_and_convert_to_avl_with_check/4,
52 try_expand_and_convert_to_avl_unless_large_wf/3,
53 %try_expand_and_convert_to_avl_unless_large_wf/3,
54 try_expand_and_convert_to_avl_if_smaller_than/3,
55 is_small_specific_custom_set/2,
56 quick_propagation_element_information/4,
57 element_of_custom_set/2, element_of_custom_set_wf/3,
58 element_of_closure/5,
59 check_element_of_function_closure/6,
60 not_element_of_custom_set_wf/3,
61 membership_custom_set/3, membership_custom_set_wf/4, membership_avl_set_wf/4,
62 quick_test_avl_membership/3,
63 lazy_check_elements_of_closure/6,
64
65 is_efficient_custom_set/1,
66 remove_minimum_element_custom_set/3,
67
68 is_maximal_global_set/1, quick_is_definitely_maximal_set/1,
69 quick_definitely_maximal_set_avl/1,
70 is_one_element_custom_set/2, singleton_set/2, construct_singleton_avl_set/2,
71 is_one_element_avl/2,
72 construct_one_element_custom_set/2,
73 avl_is_interval/3,
74
75 %closure0_for_explicit_set/2,
76 closure1_for_explicit_set/2, closure1_for_explicit_set_from/3,
77 check_in_domain_of_avlset/2, check_unique_in_domain_of_avlset/2,
78 domain_of_explicit_set_wf/3, range_of_explicit_set_wf/3,
79 is_avl_partial_function/1, is_not_avl_partial_function/2,
80 is_avl_total_function_over_domain/2,
81 quick_definitely_maximal_total_function_avl/1,
82 is_avl_relation/1,
83 is_avl_relation_over_domain/3,
84 is_avl_relation_over_range/3,
85 is_not_avl_relation_over_domain_range/4, is_not_avl_relation_over_range/3,
86 is_avl_sequence/1, safe_is_avl_sequence/1,
87 get_avl_sequence/2,
88 is_injective_avl_relation/2,
89 invert_explicit_set/2, union_of_explicit_set/3,
90 union_generalized_explicit_set/3,
91 difference_of_explicit_set_wf/4,
92 intersection_of_explicit_set_wf/4, intersection_with_interval_closure/3,
93 disjoint_intervals_with_inf/4,
94 image_for_id_closure/3, image_for_explicit_set/4,
95 rel_composition_for_explicit_set/3,
96 element_can_be_added_or_removed_to_avl/1,
97 add_element_to_explicit_set_wf/4, remove_element_from_explicit_set/3,
98 delete_element_from_explicit_set/3,
99 at_most_one_match_possible/3,
100 apply_to_avl_set/5, try_apply_to_avl_set/3,
101 min_of_explicit_set_wf/3, max_of_explicit_set_wf/3,
102 sum_or_mul_of_explicit_set/3,
103 %sum_of_range_custom_explicit_set/2, mul_of_range_custom_explicit_set/2,
104 domain_restriction_explicit_set_wf/4,
105 range_restriction_explicit_set_wf/4,
106 domain_subtraction_explicit_set_wf/4,
107 range_subtraction_explicit_set_wf/4,
108 override_pair_explicit_set/4,
109 direct_product_explicit_set/3,
110 override_custom_explicit_set_wf/4,
111 symbolic_functionality_check_closure/2, symbolic_injectivity_check_closure/2,
112
113 subset_of_explicit_set/4, not_subset_of_explicit_set/4,
114 test_subset_of_explicit_set/5,
115
116 conc_custom_explicit_set/2,
117 prefix_of_custom_explicit_set/4, suffix_of_custom_explicit_set/4,
118 concat_custom_explicit_set/4, prepend_custom_explicit_set/3,
119 append_custom_explicit_set/4,
120 tail_sequence_custom_explicit_set/5,
121 last_sequence_explicit_set/2, %first_sequence_explicit_set/2,
122 front_sequence_custom_explicit_set/3,
123 reverse_custom_explicit_set/2,
124 size_of_custom_explicit_set/3,
125
126 get_first_avl_elements/4,
127 construct_avl_from_lists/2, construct_avl_from_lists_wf/3,
128 equal_avl_tree/2,
129 check_avl_in_interval/3, check_interval_in_custom_set/4,
130 check_avl_subset/2,
131 construct_closure/4, is_closure/4, % from closures
132 construct_member_closure/5, % from closures
133
134 construct_interval_closure/3,
135 is_interval_closure/3, % checks if we have a finite interval closure Low..Up (but bounds can be variables)
136 is_interval_closure/5,
137 is_interval_closure_or_integerset/3, is_interval_closure_or_integerset/4,
138 is_interval_with_integer_bounds/3, % checks that bounds are known
139
140 is_powerset_closure/3,
141
142 dom_range_for_specific_closure/5,
143 dom_for_specific_closure/4,
144 dom_for_lambda_closure/2,
145 portray_custom_explicit_set/1,
146 closure_occurs_check/4
147 ]).
148
149 :- meta_predicate call_card_for_relations(-,-,0).
150
151 :- use_module(error_manager).
152 :- use_module(self_check).
153 :- use_module(preferences,[get_preference/2]).
154 :- use_module(library(avl)).
155 :- use_module(kernel_waitflags).
156 :- use_module(kernel_tools).
157 :- use_module(delay).
158 :- use_module(tools).
159 :- use_module(avl_tools).
160 :- use_module(library(clpfd)).
161
162 :- use_module(module_information,[module_info/2]).
163 :- module_info(group,kernel).
164 :- module_info(description,'This module provides customised operations for the custom explicit set representations of ProB (closures, avl_sets and global_sets).').
165
166 :- use_module(tools_printing,[print_term_summary/1, print_error/1]).
167 :- use_module(preferences,[preference/2]).
168 :- use_module(kernel_objects,[equal_object/2, equal_object/3]).
169 :- use_module(kernel_freetypes,[enumerate_freetype_wf/4,freetype_cardinality/2,
170 is_infinite_freetype/1, is_empty_freetype/1,
171 is_non_empty_freetype/1, test_empty_freetype/2]).
172
173 :- use_module(clpfd_interface,[try_post_constraint/1, clpfd_reify_inlist/4]).
174 :- use_module(closures).
175 :- use_module(performance_messages).
176 :- use_module(b_compiler).
177
178 :- load_files(library(system), [when(compile_time), imports([environ/2])]).
179
180 /* These meta_predicate declarations do not seem to have the right effect;
181 the predicates below return code, they do not get passed code
182 :- meta_predicate card_for_specific_custom_set(*,*,0).
183 :- meta_predicate card_for_specific_closure(*,*,0).
184 :- meta_predicate is_a_relation(*,*,*,*,*,*,0).
185 :- meta_predicate subset_of_explicit_set(*,*,0,*).
186 :- meta_predicate not_subset_of_explicit_set(*,*,0,*).
187 */
188
189 construct_avl_from_lists(S,Res) :-
190 (convert_to_avl(S,CS) -> true ; print(convert_to_avl_failed(S,CS)),nl,CS=S),
191 Res = CS.
192
193 % version with WF to see call stack in case of virtual time-outs due to expansions
194 construct_avl_from_lists_wf(S,Res,WF) :-
195 (convert_to_avl_wf(S,CS,WF) -> true ; print(convert_to_avl_wf_failed(S,CS)),nl,CS=S),
196 Res = CS.
197
198 :- use_module(tools,[safe_sort/3]).
199 :- block normalised_list_to_avl_when_ground(-,?).
200 normalised_list_to_avl_when_ground(S,R) :- % call if you are not sure that S will be ground; e.g. after closure expansion
201 ground_value_check(S,GS),
202 blocking_normalised_list_to_avl(GS,S,R).
203 :- block blocking_normalised_list_to_avl(-,?,?).
204 blocking_normalised_list_to_avl(_,S,R) :- normalised_list_to_avl(S,R).
205
206 normalised_list_to_avl(S,R) :- safe_sort(normalised_list_to_avl,S,SS),
207 ord_list_to_avlset_direct(SS,AVL,normalised_list_to_avl),
208 equal_object(AVL,R). % due to co-routine, R can now be instantiated
209
210 %set_to_avl(List,R) :- empty_avl(A), add_to_avl(List,A,AR), R=avl_set(AR).
211 add_to_avl([],R,R).
212 add_to_avl([H|T],AVL,AVLOUT) :- avl_store(H,AVL,true,AVL1),
213 add_to_avl(T,AVL1,AVLOUT).
214
215
216 % get only the first x elements of an AVL tree
217 get_first_avl_elements(empty,_,R,all) :- !,R=[].
218 get_first_avl_elements(AVL,X,FirstXEls,CutOff) :-
219 avl_min(AVL,Min), get_first_els(X,Min,AVL,FirstXEls,CutOff).
220
221 get_first_els(X,_,_AVL,R,CutOff) :- X<1,!,R=[], CutOff=not_all.
222 get_first_els(X,Cur,AVL,[Cur|T],CutOff) :-
223 (avl_next(Cur,AVL,Nxt) -> X1 is X-1,get_first_els(X1,Nxt,AVL,T,CutOff)
224 ; T=[],CutOff=all).
225
226 %expand_and_try_convert_to_avl(C,R) :- is_closure(C,_,_,_), expand_custom_set(C,EC), expand_and_convert_to_avl
227 %expand_and_convert_to_avl(C,R) :- convert_to_avl(C,R).
228
229 /* convert all list data-values (with all-sub-values) into avl-form */
230 /* assumption: the value is ground when convert_to_avl is called */
231
232 :- load_files(library(system), [when(compile_time), imports([environ/2])]).
233 :- if(environ(prob_safe_mode,true)).
234 convert_to_avl(X,R) :- \+ ground_value(X), !, add_error(convert_to_avl,'Non-ground argument: ',convert_to_avl(X,R)), R=X.
235 :- endif.
236 convert_to_avl(X,R) :- var(X), !, add_error(convert_to_avl,'Variable argument: ',convert_to_avl(X,R)), R=X.
237 ?convert_to_avl(Term,R) :- no_conversion_necessary(Term),!,
238 R=Term.
239 convert_to_avl(closure(P,T,B),R) :- !,
240 R=closure(P,T,B).
241 convert_to_avl(avl_set(A),R) :- !,(A==empty -> add_warning(convert_to_avl,'Emtpy avl_set'), R=[]
242 ; R=avl_set(A)).
243 convert_to_avl((A,B),(CA,CB)) :- !,convert_to_avl(A,CA), convert_to_avl(B,CB).
244 convert_to_avl(freetype(X),R) :- !, R=freetype(X).
245 convert_to_avl(freeval(ID,Case,Value),R) :- !, R=freeval(ID,Case,CValue),convert_to_avl(Value,CValue).
246 convert_to_avl(rec(Fields),R) :- !, convert_fields(Fields,CFields), R=rec(CFields).
247 convert_to_avl(global_set(GS),R) :- !, R=global_set(GS).
248 ?convert_to_avl([H|T],R) :- !, convert_cons_to_avl_inside_set_wf(H,T,R,no_wf_available).
249 %convert_to_avl(abort(X),_R) :- print(deprecetated_convert_to_avl(abort(X))),nl,!, fail.
250 convert_to_avl(X,R) :- add_internal_error('Unknown term: ',convert_to_avl(X,R)), R=X.
251
252 % pass WF for call stack in case of expansions TODO: complete
253 convert_to_avl_wf((A,B),(CA,CB),WF) :- !,convert_to_avl_wf(A,CA,WF), convert_to_avl_wf(B,CB,WF).
254 convert_to_avl_wf([H|T],R,WF) :- !, convert_cons_to_avl_inside_set_wf(H,T,R,WF).
255 convert_to_avl_wf(X,R,_) :- convert_to_avl(X,R).
256
257 convert_fields(Var,R) :- var(Var),!,
258 add_internal_error('Var arg: ',convert_fields(Var,R)),fail.
259 convert_fields([],[]).
260 convert_fields([field(FieldName,Value)|T],[field(FieldName,CValue)|CT]) :-
261 convert_to_avl_inside_set(Value,CValue),
262 convert_fields(T,CT).
263
264 l_convert_to_avl_wf(Var,_,WF) :- var(Var),!,
265 add_warning_wf(l_convert_to_avl_wf,'Cannot expand variable to avl: ',Var,unknown,WF),
266 fail.
267 l_convert_to_avl_wf([],[],_).
268 l_convert_to_avl_wf(avl_set(A),R,WF) :-
269 expand_custom_set_wf(avl_set(A),ES,l_convert_to_avl,WF),
270 l_convert_to_avl_wf(ES,R,WF).
271 l_convert_to_avl_wf(closure(P,T,B),R,WF) :-
272 expand_custom_set_wf(closure(P,T,B),ES,l_convert_to_avl,WF),
273 l_convert_to_avl_wf(ES,R,WF).
274 l_convert_to_avl_wf([H|T],[CH-true|CT],WF) :-
275 ? convert_to_avl_inside_set_wf(H,CH,WF), l_convert_to_avl_wf(T,CT,WF).
276
277 :- assert_must_succeed((X=(fd(1,'Name'),fd(2,'Name')),
278 custom_explicit_sets:convert_to_avl_inside_set(X,R), R==X)).
279
280 convert_to_avl_inside_set(Var,R) :- var(Var),!,
281 add_internal_error('Var arg: ',convert_to_avl_inside_set(Var,R)),fail.
282 :- if(environ(prob_safe_mode,true)).
283 convert_to_avl_inside_set(fd(A,T),R) :- var(A),!,
284 add_error(convert_to_avl,'Non-ground FD-Term: ',convert_to_avl_inside_set(fd(A,T),R)), R=fd(A,T).
285 convert_to_avl_inside_set(int(X),R) :- var(X),!,
286 add_error(convert_to_avl,'Non-ground integer: ',convert_to_avl_inside_set(int(X),R)), R=int(X).
287 convert_to_avl_inside_set(string(X),R) :- var(X),!,
288 add_error(convert_to_avl,'Non-ground string: ',convert_to_avl_inside_set(string(X),R)), R=string(X).
289 convert_to_avl_inside_set(term(X),R) :- (var(X) ; X=floating(F), var(F)), !,
290 add_error(convert_to_avl,'Non-ground term: ',convert_to_avl_inside_set(term(X),R)), R=term(X).
291 :- endif.
292 ?convert_to_avl_inside_set(Term,R) :- no_conversion_necessary(Term),!,R=Term.
293 convert_to_avl_inside_set(closure(P,T,B),R) :- !,
294 % inside a set, closures need to be expanded to check against other elements
295 expand_closure_to_avl_wf(P,T,B,R,no_wf_available).
296 %convert_to_avl_inside_set(closure_x(_P,_T,_B,E),R) :- !, convert_to_avl_inside_set(E,R).
297 convert_to_avl_inside_set(avl_set(A),R) :- !, normalise_avl_set(A,R). %AVL's inside other AVL's need to be normalised !
298 convert_to_avl_inside_set((A,B),(CA,CB)) :- !,convert_to_avl_inside_set(A,CA), convert_to_avl_inside_set(B,CB).
299 convert_to_avl_inside_set(freetype(X),R) :- !,
300 expand_custom_set(freetype(X),EC,check), convert_to_avl_inside_set(EC,R).
301 convert_to_avl_inside_set(freeval(ID,Case,Value),R) :- !,
302 R=freeval(ID,Case,CValue),convert_to_avl_inside_set(Value,CValue).
303 convert_to_avl_inside_set(rec(Fields),R) :- !, convert_fields(Fields,CFields), R=rec(CFields).
304 convert_to_avl_inside_set(global_set(GS),R) :- !,
305 % first check if GS infinite integer set: in this case do not expand; there can be no confusion with finite avl_sets
306 ? (is_infinite_global_set(GS,_) -> R = global_set(GS)
307 ; expand_only_custom_closure_global(global_set(GS),EC,check,no_wf_available), convert_to_avl_inside_set(EC,R)).
308 convert_to_avl_inside_set([H|T],R) :- !,convert_cons_to_avl_inside_set_wf(H,T,R,no_wf_available).
309 convert_to_avl_inside_set(X,R) :-
310 add_internal_error('Unknown or non-ground argument: ',convert_to_avl_inside_set(X,R)),
311 fail.
312
313 ?convert_to_avl_inside_set_wf(Term,R,_WF) :- no_conversion_necessary(Term),!,R=Term.
314 convert_to_avl_inside_set_wf(closure(P,T,B),R,WF) :- !,
315 ? expand_closure_to_avl_wf(P,T,B,R,WF). % inside a set, closures need to be expanded to check against other elements
316 convert_to_avl_inside_set_wf((A,B),(CA,CB),WF) :- !,
317 ? convert_to_avl_inside_set_wf(A,CA,WF), convert_to_avl_inside_set_wf(B,CB,WF).
318 convert_to_avl_inside_set_wf([H|T],R,WF) :- !,convert_cons_to_avl_inside_set_wf(H,T,R,WF).
319 convert_to_avl_inside_set_wf(V,CV,_WF) :- % use version without WF; TO DO: adapt fully
320 convert_to_avl_inside_set(V,CV).
321
322 % true when we have a simple value that does not need to be converted for use within an avl_set:
323 no_conversion_necessary([]).
324 no_conversion_necessary(pred_false). /* bool_false */
325 no_conversion_necessary(pred_true). /* bool_true */
326 no_conversion_necessary(fd(FD,_)) :- nonvar(FD).
327 no_conversion_necessary(int(I)) :- nonvar(I).
328 no_conversion_necessary(string(S)) :- nonvar(S).
329 ?no_conversion_necessary(term(T)) :- nonvar(T), no_conversion_nec_term(T).
330
331 no_conversion_nec_term(floating(T)) :- nonvar(T).
332 no_conversion_nec_term(T) :- atom(T).
333
334 normalise_avl_set(A,R) :- A=node(_,_,0,empty,empty), !,R=avl_set(A).
335 normalise_avl_set(A,R) :-
336 avl_to_list(A,L),
337 ord_list_to_avlset_direct(L,R,convert_to_avl_inside_set). %AVL's inside other AVL's need to be normalised !
338
339 convert_cons_to_avl_inside_set_wf(H,T,R,WF) :- T==[], !,
340 convert_to_avl_inside_set_wf(H,CH,WF),
341 R = avl_set(node(CH,true,0,empty,empty)).
342 ?convert_cons_to_avl_inside_set_wf(H,T,R,WF) :- l_convert_to_avl_wf([H|T],S,WF),
343 sort(S,SS),
344 ord_list_to_avlset_direct(SS,R,convert_to_avl_inside_set).
345
346 construct_singleton_avl_set(Val,avl_set(node(Val,true,0,empty,empty))).
347
348
349 is_set_value(X,Origin) :- var(X), !,print(is_set_value(Origin)),nl,fail.
350 is_set_value([],_) :- !.
351 is_set_value([_|_],_) :- !.
352 is_set_value(X,_) :- is_custom_explicit_set(X).
353
354 is_custom_explicit_set(X,Origin) :- var(X), !,print(var_is_custom_explicit_set(Origin)),nl,fail.
355 is_custom_explicit_set(X,_) :- is_custom_explicit_set(X).
356
357 is_custom_explicit_set(X) :- var(X), !,print(var_is_custom_explicit_set),nl,fail.
358 is_custom_explicit_set(global_set(_)).
359 is_custom_explicit_set(freetype(_)).
360 %is_custom_explicit_set(integer_global_set(_)).
361 is_custom_explicit_set(avl_set(_)).
362 is_custom_explicit_set(closure(_Parameters,_PT,_Cond)).
363
364 % use if you know the argument to be nonvar
365 is_custom_explicit_set_nonvar(global_set(_)).
366 is_custom_explicit_set_nonvar(freetype(_)).
367 is_custom_explicit_set_nonvar(avl_set(_)).
368 is_custom_explicit_set_nonvar(closure(_Parameters,_PT,_Cond)).
369
370 %:- assert_must_succeed(( custom_explicit_sets:portray_custom_explicit_set(avl_set(empty)) )). % now generates error
371 :- use_module(translate,[translate_bvalue/2]).
372 portray_custom_explicit_set(S) :- translate_bvalue(S,A), format(A,[]),nl.
373
374 /* a predicate to check equality of two custom explicit sets */
375
376 %equal_explicit_sets(A,B) :- equal_explicit_sets_wf(A,B,no_wf_available).
377
378 %equal_explicit_sets(X,Y) :- print_term_summary(equal_explicit_sets(X,Y)),fail.
379 :- block equal_explicit_sets_wf(-,?,?), equal_explicit_sets_wf(?,-,?).
380 ?equal_explicit_sets_wf(A,B,WF) :- equal_explicit_sets4(A,B,allow_expansion,WF).
381
382 equal_explicit_sets4(global_set(X),global_set(Y),_,_WF) :- !,X=Y.
383 equal_explicit_sets4(global_set(B),avl_set(A),E,WF) :- !,equal_explicit_sets4(avl_set(A),global_set(B),E,WF).
384 equal_explicit_sets4(freetype(X),freetype(Y),_,_WF) :- !,X=Y.
385 equal_explicit_sets4(avl_set(A),avl_set(B),_,_WF) :- !,
386 equal_avl_tree(A,B). % alternatively, we could normalise avl_trees and only store normalised versions
387 equal_explicit_sets4(avl_set(A),I2,_,_WF) :-
388 is_interval_closure_or_integerset(I2,L2,U2,Finite2),!, % also covers I2=global_set(...)
389 Finite2=finite, % only a finite interval can be equal to an AVL set
390 avl_equal_to_interval(A,L2,U2).
391 equal_explicit_sets4(avl_set(A),global_set(B),_,WF) :- \+ b_global_sets:b_integer_set(B), !, % integersets dealt with above
392 explicit_set_cardinality_wf(global_set(B),Card,WF),
393 is_finite_card(Card), % Card \= inf as avl_set must be finite
394 explicit_set_cardinality_wf(avl_set(A),Card,WF). /* the sets must be identical as global_set contains all values */
395 equal_explicit_sets4(avl_set(A),CPB,_,WF) :-
396 is_cartesian_product_closure(CPB,B1,B2),!,
397 decompose_avl_set_into_cartesian_product_wf(A,A1,A2,WF),
398 kernel_objects:equal_object_wf(A1,B1,equal_explicit_sets4,WF),
399 kernel_objects:equal_object_wf(A2,B2,equal_explicit_sets4,WF).
400 ?equal_explicit_sets4(closure(P,T,B),avl_set(A),E,WF) :- !, equal_explicit_sets4(avl_set(A),closure(P,T,B),E,WF).
401 equal_explicit_sets4(I1,I2,_,_WF) :- is_interval_closure_or_integerset(I1,L1,U1,Finite1),
402 is_interval_closure_or_integerset(I2,L2,U2,Finite2), !,
403 Finite1=Finite2, % either both finite or infinite
404 L1=L2, U1=U2.
405 equal_explicit_sets4(CPA,CPB,_,WF) :-
406 ? is_cartesian_product_closure(CPA,A1,A2),
407 is_cartesian_product_closure(CPB,B1,B2),!,
408 equal_cartesian_product_wf(A1,A2,B1,B2,WF).
409 % what if both subset or relations or functions ... closure: TO DO: add support
410 equal_explicit_sets4(S1,S2,_,WF) :-
411 is_not_member_value_closure_or_integerset(S1,TYPE,MS1),
412 is_not_member_value_closure_or_integerset(S2,TYPE,MS2),
413 !,
414 kernel_objects:equal_object_wf(MS1,MS2,equal_explicit_sets4,WF).
415 equal_explicit_sets4(closure(P1,T1,B1),closure(P2,T2,B2),_,_WF) :-
416 same_closure_body(P1,T1,B1,P2,T2,B2),!.
417 %equal_explicit_sets4(X,Y) :- X==Y,!.
418 equal_explicit_sets4(Set1,Set2,allow_expansion,WF) :-
419 %kernel_objects:test_finite_set_wf(Set1,F1,WF), kernel_objects:test_finite_set_wf(Set2,F2,WF), equal_expansions(F1,F2,Set1,Set2)
420 card_for_specific_custom_set(Set1,Card1,Code1), % TO DO: do not throw info away if Set2 cannot be determined
421 card_for_specific_custom_set(Set2,Card2,Code2),
422 !,
423 call(Code1), call(Code2),
424 % TO DO: if one of the two sets is infinite, then it would be enough to know that the other is not infinite for failure without expansion
425 equal_expansions(Card1,Card2,Set1,Set2,WF).
426 ?equal_explicit_sets4(Set1,Set2,allow_expansion,WF) :- equal_expansions(0,0,Set1,Set2,WF).
427
428
429 :- use_module(btypechecker, [unify_types_strict/2]).
430 % detect e.g. when one closure has seq(Type) and the other one set(integer,Type)
431 same_types([],[]).
432 same_types([H1|T1],[H2|T2]) :- unify_types_strict(H1,H2), same_types(T1,T2).
433
434 :- block equal_expansions(-,?,?,?,?).
435 equal_expansions(F1,F2,Set1,Set2,WF) :- (number(F1);number(F2)),!,
436 % NOTE: sometimes we get inf for finite but very large sets
437 F1=F2, % unify; can propagate info back to closure; e.g. prj2(BOOL,NAT) = prj2(BOOL,0..n)
438 ? equal_expansions2(F1,F2,Set1,Set2,WF).
439 equal_expansions(F1,F2,Set1,Set2,WF) :-
440 equal_expansions2(F1,F2,Set1,Set2,WF).
441
442 :- block equal_expansions2(-,?,?,?,?), equal_expansions2(?,-,?,?,?).
443 %equal_expansions(0,0,avl_set(A),closure(P,T,B)) :- check_subset ?? in both directions ?
444 %equal_expansions2(inf,inf,Set1,Set2,WF) :- WF \= no_wf_available, !, % symbolic treatment
445 equal_expansions2(F,F,Set1,Set2,WF) :-
446 % only expand if both sets have same cardinality
447 % print_term_summary(equal_expansions3(F,Set1,Set2)),nl,
448 ? equal_expansions3(F,Set1,Set2,WF).
449
450 % TO DO: check if this brings something:
451 %equal_expansions3(avl_set(A),closure(P,T,B),_WF) :- !,
452 % expand_closure_to_avl_or_list(P,T,B,E2,check), % in case E2 is avl_set; we can use equal_avl_tree
453 % ((nonvar(E2),E2=avl_set(B2))
454 % -> print(eql_avl),nl, print_term_summary(equal_avl_tree(A,B2)),nl, equal_avl_tree(A,B2)
455 % ; print(eql_non_avl),nl,equal_object(avl_set(A),E2,equal_expansions3)
456 % ).
457 %:- use_module(library(lists),[perm2/4]).
458 %equal_expansions3(F,Set1,Set2,_WF) :- number(F), F>100, % test with: {{},{TRUE},{FALSE},{TRUE,FALSE}} = /*@symbolic */ {x|x<:BOOL} or
459 % {x|x<:POW(BOOL*BOOL) & (x={} or card(x)>0)} = /*@symbolic */ {x|x<:POW(BOOL*BOOL)} 26 sec -> 14 sec
460 % case does not seem to appear very often
461 % perm2(Set1,Set2,avl_set(_),Set),
462 % is_definitely_maximal_set(Set),
463 %Set2 is maximal and has the same cardinality as F, hence Set1 must be identical to Set2
464 % !,
465 % debug_println(9,equal_to_maximal_closure(F)).
466 equal_expansions3(F,Set1,Set2,WF) :-
467 ? get_identity_as_equivalence(F,Set1,Set2,EQUIV),
468 !,% translate:print_bexpr(EQUIV),nl,
469 copy_wf_start(WF,equal_expansions,CWF),
470 b_test_boolean_expression(EQUIV,[],[],CWF),
471 copy_wf_finish(WF,CWF).
472 % Alternative could be, if difference were to be fully treated symbolically:
473 % difference_of_explicit_set_wf(Set1,Set2,R12,WF), difference_of_explicit_set_wf(Set2,Set1,R21,WF),
474 % kernel_objects:empty_set_wf(R12,WF), kernel_objects:empty_set_wf(R21,WF).
475 equal_expansions3(_,Set1,Set2,WF) :-
476 expand_custom_set_wf(Set1,E1,equal_expansions1,WF),
477 expand_custom_set_wf(Set2,E2,equal_expansions2,WF),
478 E1=E2. /* ensure that ordering and normalization is same for all representations ! */
479
480
481 :- use_module(b_ast_cleanup, [clean_up/3]).
482 get_identity_as_equivalence(F,Set1,Set2,CleanedEQUIV) :-
483 (F=inf %; is_infinite_explicit_set(Set1) ; is_infinite_explicit_set(Set2)
484 ; Set1 \= avl_set(_),Set2 \= avl_set(_), % if one of the two sets is an AVL Set: better compute the other set explicitly instead of using this symbolic treatment
485 (dont_expand_this_explicit_set(Set1,100000) ;
486 dont_expand_this_explicit_set(Set2,100000)
487 )
488 % avl_test check for test 1081; TO DO: instead of test try to expand set and if this leads to enum warning use symbolic check
489 ),
490 ? get_identity_as_equivalence_aux(Set1,Set2,EQUIV),
491 clean_up(EQUIV,[],CleanedEQUIV).
492 % can be useful to replace x : {v|P(v)} --> x:P(x) (remove_member_comprehension) and reuse predicates, see 2483
493 get_identity_as_equivalence_aux(Set1,Set2,EQUIV) :-
494 ? kernel_objects:infer_value_type(Set1,SType),
495 is_set_type(SType,Type),
496 % Construct: !x.(x:Set1 <=> x:Set2) ??
497 get_pos_infos_for_explicit_set(Set1,I1),
498 get_pos_infos_for_explicit_set(Set2,I2),
499 I12 = I1, % we could merge position_info; but two sets could be very far apart
500 TID = b(identifier('_equality_sets_'),Type,[]),
501 EQUIV = b(forall([TID],b(truth,pred,[used_ids([])]),
502 b(equivalence(
503 b(member(TID,b(value(Set1),SType,I1)),pred,I1),
504 b(member(TID,b(value(Set2),SType,I2)),pred,I2)
505 ) ,pred,I12)
506 ),pred,[used_ids([]),I12]).
507
508 :- use_module(bsyntaxtree, [get_texpr_pos/2]).
509 get_pos_infos_for_explicit_set(closure(_,_,Body),[Pos]) :- get_texpr_pos(Body,Pos),!.
510 get_pos_infos_for_explicit_set(_,[]).
511
512 :- use_module(kernel_equality,[eq_atomic/4, equality_objects/3,
513 equality_objects_wf_no_enum/4, equality_objects_with_type_wf/5]).
514 /* maybe rewrite equal_explicit_sets and not_... to use this to avoid maintaining multiple versions */
515 equality_explicit_sets_wf(global_set(X),global_set(Y),R,_WF) :- !, eq_atomic(X,Y,set,R).
516 equality_explicit_sets_wf(global_set(B),avl_set(A),R,WF) :- !,equality_explicit_sets_wf(avl_set(A),global_set(B),R,WF).
517 equality_explicit_sets_wf(freetype(X),freetype(Y),R,_) :- !, eq_atomic(X,Y,set,R).
518 equality_explicit_sets_wf(avl_set(A),avl_set(B),R,_) :- !,
519 (equal_avl_tree(A,B) -> R=pred_true ; R=pred_false). % alternatively, we could normalise avl_trees and only store normalised versions
520 equality_explicit_sets_wf(avl_set(A),I2,R,WF) :- is_interval_closure_or_integerset(I2,L2,U2),!,
521 % also covers I2=global_set(...)
522 avl_equality_to_interval(A,L2,U2,R,WF).
523 equality_explicit_sets_wf(avl_set(A),global_set(B),R,WF) :- \+ b_global_sets:b_integer_set(B), !,
524 explicit_set_cardinality_wf(global_set(B),Card,WF),
525 (is_finite_card(Card), % Card \= inf, %as avl_set must be finite
526 explicit_set_cardinality_wf(avl_set(A),Card,WF)
527 -> R=pred_true /* the sets must be identical as global_set contains all values */
528 ; R=pred_false).
529 equality_explicit_sets_wf(avl_set(A),CPB,R,WF) :-
530 is_cartesian_product_closure(CPB,B1,B2),!,
531 if(decompose_avl_set_into_cartesian_product_wf(A,A1,A2,WF), % should not produce pending co-routines
532 equality_cartesian_product_wf(A1,A2,B1,B2,R,WF),
533 R=pred_false % no cartesian product can be equal to this avl_set
534 ).
535 equality_explicit_sets_wf(closure(P,T,B),avl_set(A),R,WF) :- !,
536 equality_explicit_sets_wf(avl_set(A),closure(P,T,B),R,WF).
537 equality_explicit_sets_wf(I1,I2,R,WF) :- is_interval_closure_or_integerset(I1,L1,U1,Finite1),
538 is_interval_closure_or_integerset(I2,L2,U2,Finite2), !,
539 (Finite1=Finite2 -> equality_objects_wf_no_enum((int(L1),int(U1)),(int(L2),int(U2)),R,WF)
540 ; R = pred_false).
541 equality_explicit_sets_wf(CPA,CPB,R,WF) :-
542 is_cartesian_product_closure(CPA,A1,A2), is_cartesian_product_closure(CPB,B1,B2),!,
543 equality_cartesian_product_wf(A1,A2,B1,B2,R,WF).
544 equality_explicit_sets_wf(S1,S2,R,WF) :-
545 is_not_member_value_closure_or_integerset(S1,TYPE,MS1),
546 is_not_member_value_closure_or_integerset(S2,TYPE,MS2),!,
547 equality_objects_with_type_wf(TYPE,MS1,MS2,R,WF).
548 equality_explicit_sets_wf(closure(P,T,B),closure(P,T,B2),R,_) :-
549 same_texpr_body(B,B2),!,R=pred_true.
550 equality_explicit_sets_wf(Set1,Set2,R,WF) :-
551 Set1 \= [_|_], Set2 \= [_|_], % below we check for avl_set; i.e., useful are only closure/3, global_set/1, ...
552 ? get_identity_as_equivalence(unknown,Set1,Set2,EQUIV),!,
553 copy_wf_start(WF,equal_expansions,CWF),
554 % EQUIV is a universal quantification, usually over an infinite domain
555 b_interpreter_check:b_force_check_boolean_expression(EQUIV,[],[],CWF,R), % we know EQUIV cannot be reified
556 copy_wf_finish(WF,CWF).
557 % TO DO: add complement sets,
558
559 /* Cartesian Product Comparison */
560 :- use_module(kernel_equality,[empty_cartesian_product_wf/4]).
561 % A1*A2 = B1*B2 <=> (((A1={} or A2={}) & (B1={} or B2={})) or (A1=B1 & A2=B2))
562 equal_cartesian_product_wf(A1,A2,B1,B2,WF) :-
563 equality_cartesian_product_wf(A1,A2,B1,B2,pred_true,WF).
564 not_equal_cartesian_product_wf(A1,A2,B1,B2,WF) :-
565 equality_cartesian_product_wf(A1,A2,B1,B2,pred_false,WF).
566
567 equality_cartesian_product_wf(A1,A2,B1,B2,R,_WF) :-
568 nonvar(A1), A1=closure(P,T,BdyA1),
569 nonvar(B1), B1=closure(P,T,BdyB1),
570 nonvar(A2), A2=closure(P2,T2,BdyA2),
571 nonvar(B2), B2=closure(P2,T2,BdyB2),
572 % they have the same names; probably we are comparing identical values (e.g., in bvisual2)
573 same_texpr_body(BdyA1,BdyB1),
574 % note: we cannot simply call equality of A2 and B2 as cartesian products can be empty, see test 2072
575 same_texpr_body(BdyA2,BdyB2),
576 !,
577 R=pred_true.
578 equality_cartesian_product_wf(A1,A2,B1,B2,R,WF) :-
579 empty_cartesian_product_wf(A1,A2,EmptyA,WF),
580 equality_cart_product2(EmptyA,A1,A2,B1,B2,R,WF).
581 :- block equality_cart_product2(-, ?,?,?,?,?,?).
582 equality_cart_product2(pred_true,_,_,B1,B2,R,WF) :- empty_cartesian_product_wf(B1,B2,R,WF).
583 equality_cart_product2(pred_false,A1,A2,B1,B2,R,WF) :- equality_objects_wf_no_enum((A1,A2),(B1,B2),R,WF).
584
585 /* COMPARING AVL-SET with INTERVAL */
586
587 % check if an avl tree is equal to an interval range
588 avl_equal_to_interval(_A,L2,U2) :-
589 infinite_interval(L2,U2),!,fail. % otherwise infinite & avl_set is finite
590 % we can now assume L2, U2 are numbers (but could not yet be instantiated)
591 avl_equal_to_interval(A,L2,U2) :-
592 avl_min(A,int(L2)), avl_max(A,int(U2)),
593 Card is 1+U2-L2,
594 explicit_set_cardinality(avl_set(A),Card). % sets are equal: same size + same lower & upper bound
595
596 avl_not_equal_to_interval(A,L2,U2,WF) :- avl_equality_to_interval(A,L2,U2,pred_false,WF).
597
598 avl_equality_to_interval(_A,L2,U2,R,_WF) :-
599 infinite_interval(L2,U2),!,R=pred_false. % interval infinite & avl_set is finite
600 % we can now assume L2, U2 are numbers (but could not yet be instantiated)
601 avl_equality_to_interval(A,L2,U2,R,WF) :-
602 avl_min(A,int(AL)), avl_max(A,int(AU)),
603 Card is 1+AU-AL,
604 explicit_set_cardinality_wf(avl_set(A),ACard,WF),
605 equality_objects_wf_no_enum((int(ACard),(int(AL),int(AU))),
606 (int(Card),(int(L2),int(U2))),R,WF).
607 % sets are equal if same size + same lower & upper bound
608
609 /* COMPARING TWO CLOSURES */
610
611 % a variation of equal_explicit_sets which tries not expand and just compares two closures
612
613 same_closure(I1,I2) :-
614 is_interval_closure_or_integerset(I1,L1,U1,Finite1),
615 is_interval_closure_or_integerset(I2,L2,U2,Finite2), !,
616 Finite1=Finite2,
617 L1=L2, U1=U2.
618 same_closure(CPA,CPB) :-
619 is_cartesian_product_closure(CPA,A1,A2),
620 is_cartesian_product_closure(CPB,B1,B2),!,
621 equal_cartesian_product_wf(A1,A2,B1,B2,no_wf_available). % could be expensive
622 same_closure(S1,S2) :-
623 is_not_member_value_closure_or_integerset(S1,TYPE,MS1),
624 is_not_member_value_closure_or_integerset(S2,TYPE,MS2),
625 !,
626 kernel_objects:equal_object(MS1,MS2,same_closure). % could be expensive
627 same_closure(closure(P1,T1,B1),closure(P2,T2,B2)) :- same_closure_body_with_parameter_renaming(P1,T1,B1,P2,T2,B2).
628
629 same_closure_body(P,T1, B1, P,T2,B2) :-
630 same_types(T1,T2),
631 same_texpr_body(B1,B2).
632
633 % a version of same_closure_body which allows renaming of the parameters
634 same_closure_body_with_parameter_renaming(P1,T1, B1, P2,T2,B2) :-
635 same_types(T1,T2),
636 create_renaming(P1,P2,Renaming),
637 % TO DO: pass Renaming in AVL tree and rename on the fly
638 rename_bt(B2,Renaming,RenamedB2),
639 same_texpr_body(B1,RenamedB2).
640
641 create_renaming([],[],[]).
642 create_renaming([ID|T1],[ID|T2],TR) :- !, create_renaming(T1,T2,TR).
643 create_renaming([ID1|T1],[ID2|T2],[rename(ID2,ID1)|TR]) :-
644 create_renaming(T1,T2,TR).
645
646
647 % check if two wrapped expressions are equal (modulo associated Info, e.g. source loc info)
648 % and checking inserted values for equality (sometimes storing a closure will convert small inner closures into AVL sets)
649 same_texpr_body(E1,E2) :- empty_avl(E),same_texpr_body(E1,E,E2).
650 same_texpr_body(b(E1,Type1,_),AVL,b(E2,Type2,_)) :-
651 unify_types_strict(Type1,Type2), % check in principle redundant
652 same_texpr2(E1,AVL,E2).
653
654 :- use_module(bsyntaxtree,[safe_syntaxelement_det/5, is_set_type/2,get_texpr_ids/2,
655 get_texpr_expr/2, get_negated_operator_expr/2]).
656 same_texpr2(value(V1),AVL,RHS) :- !,same_texpr_value2(RHS,AVL,V1).
657 same_texpr2(LHS,AVL,value(V2)) :- !,same_texpr_value2(LHS,AVL,V2).
658 same_texpr2(lazy_let_expr(ID,LHS,RHS),AVL,lazy_let_expr(ID2,LHS2,RHS2)) :- !,
659 same_texpr_body(LHS,AVL,LHS2),
660 avl_store(ID,AVL,ID2,NewAVL),
661 same_texpr_body(RHS,NewAVL,RHS2).
662 same_texpr2(lazy_let_pred(ID,LHS,RHS),AVL,lazy_let_pred(ID2,LHS2,RHS2)) :- !,
663 same_texpr_body(LHS,AVL,LHS2),
664 avl_store(ID,AVL,ID2,NewAVL),
665 same_texpr_body(RHS,NewAVL,RHS2).
666 same_texpr2(lazy_lookup(ID1), AVL,lazy_lookup(ID2)) :- !, avl_fetch(ID1,AVL,ID2).
667 same_texpr2(E1,AVL,E2) :- % Should we only enable this for same_closure_body_with_parameter_renaming?
668 quantifier_construct(E1,Functor,TParas1,Body1),
669 quantifier_construct(E2,Functor,TParas2,Body2),
670 !,
671 same_quantified_expression(TParas1,Body1,AVL,TParas2,Body2).
672 same_texpr2(E1,AVL,E2) :-
673 functor(E1,F,Arity),
674 functor(E2,F,Arity),!,
675 safe_syntaxelement_det(E1,Subs1,_Names1,_List1,Constant1),
676 safe_syntaxelement_det(E2,Subs2,_Names2,_List2,Constant2),
677 Constant2==Constant1,
678 same_sub_expressions(Subs1,AVL,Subs2).
679 same_texpr2(E1,AVL,E2) :- same_texpr_with_rewrite(E1,AVL,E2),!.
680 same_texpr2(E1,AVL,E2) :- same_texpr_with_rewrite(E2,AVL,E1).
681 %same_texpr2(E1,_,E2) :-
682 % functor(E1,F1,Arity1),
683 % functor(E2,F2,Arity2), print(not_eq(F1,Arity1,F2,Arity2)),nl, print(E1),nl, print(E2),nl,nl,fail.
684 % some differences: assertion_expression/3 and function/2, ...
685
686 % some rewrite rules from ast_cleanup; but we cannot replicate all rules here
687 same_texpr_with_rewrite(negation(TE1),AVL,E2) :-
688 get_negated_operator_expr(b(E2,pred,[]),NegE2),!,
689 get_texpr_expr(TE1,E1),
690 same_texpr2(E1,AVL,NegE2).
691 same_texpr_with_rewrite(member(X1,b(value(Set1),_,_)),AVL,equal(X2,b(El2,_,_))) :-
692 singleton_set(Set1,El1), !,
693 % X : {El} <===> X = El ; required for JSON trace replay of test 1491
694 same_texpr_body(X1,X2),
695 same_texpr_value2(El2,AVL,El1).
696 same_texpr_with_rewrite(not_member(X1,b(value(Set1),_,_)),AVL,not_equal(X2,b(El2,_,_))) :-
697 singleton_set(Set1,El1), !,
698 % X /: {El} <===> X /= El ; required for JSON trace replay of test 1491
699 same_texpr_body(X1,X2),
700 same_texpr_value2(El2,AVL,El1).
701
702 % constructs with local quantified parameters:
703 quantifier_construct(comprehension_set(TParas,Body),comprehension_set,TParas,Body).
704 quantifier_construct(exists(TParas,Body),exists,TParas,Body).
705 quantifier_construct(forall(TParas,LHS,RHS),forall,TParas,Body) :-
706 Body = b(implication(LHS,RHS),pred,[]).
707 % TODO?: SIGMA, PI, UNION, INTER
708
709 :- use_module(bsyntaxtree,[split_names_and_types/3]).
710 same_quantified_expression(TParas1,Body1,AVL,TParas2,Body2) :-
711 split_names_and_types(TParas1,P1,T1),
712 split_names_and_types(TParas2,P2,T2),
713 same_types(T1,T2),
714 create_renaming(P1,P2,Renaming),
715 rename_bt(Body2,Renaming,RenamedB2), % TODO: store renaming in AVL and lookup on the fly
716 same_texpr_body(Body1,AVL,RenamedB2).
717
718 same_texpr_value2(E2,_,V2) :- var(V2),!,V2==E2.
719 same_texpr_value2(interval(Min,Max),_,avl_set(A)) :- !, % occurs in JSON trace replay for test 268
720 avl_equal_to_interval(A,Min,Max). % TODO: also compare the other way around above; only apply if Card not too large?
721 same_texpr_value2(value(V2),_,V1) :- !,
722 same_value_inside_closure(V1,V2).
723 %(same_value_inside_closure(V1,V2) -> true ; print(not_eq_vals(V1,V2)),nl,fail).
724 same_texpr_value2(comprehension_set(Paras,B2),AVL,closure(P,_,B1)) :- !,
725 get_texpr_ids(Paras,P),!,
726 same_texpr_body(B1,AVL,B2).
727 same_texpr_value2(cartesian_product(TB1,TB2),AVL,V1) :-
728 decompose_value_into_cartesian_product(V1,A1,A2), !,
729 %print(cart(A1,A2)),nl,
730 get_texpr_expr(TB1,B1),
731 same_texpr_value2(B1,AVL,A1),
732 get_texpr_expr(TB2,B2),
733 same_texpr_value2(B2,AVL,A2).
734 same_texpr_value2(StaticExpr,_,int(Nr)) :- number(Nr),
735 b_ast_cleanup:pre_compute_static_int_expression(StaticExpr,Nr),!.
736 % TO DO: maybe also check if both sides can be evaluated
737 % TO DO: move pre_compute_static_int_expression to another module
738 same_texpr_value2(E2,AVL,V1) :- rewrite_value(V1,E2,NewE1),!,
739 same_texpr2(NewE1,AVL,E2).
740 %same_texpr_value2(E1,_,E2) :-
741 % functor(E1,F1,Arity1),
742 % functor(E2,F2,Arity2), print(not_eq_val(F1,Arity1,F2,Arity2)),nl, fail,print(E1),nl, print(E2),nl,nl,fail.
743
744 decompose_value_into_cartesian_product(avl_set(A),A1,A2) :- !,
745 decompose_avl_set_into_cartesian_product_wf(A,A1,A2,no_wf_available).
746 decompose_value_into_cartesian_product(Closure,A1,A2) :- is_cartesian_product_closure(Closure,A1,A2).
747
748
749 % rewrite values back to AST nodes
750 rewrite_value(value(V),OtherVal,New) :- nonvar(V),
751 rewrite_value_aux(V,OtherVal,New).
752 %rewrite_value(function(Lambda,Argument),assertion_expression(_,_,_),assertion_expression(Cond,Msg,Expr)) :- b_ast_cleanup:rewrite_function_application(Lambda,Argument,[],assertion_expression(Cond,Msg,Expr)).
753 rewrite_value_aux(closure(P,T,B),_,Set) :-
754 is_member_closure(P,T,B,_,Set). % TO DO: ensure that ast_cleanup does not generate useless member closures ?
755 rewrite_value_aux(global_set(GS),_,AST) :-
756 rewrite_glob_set(GS,AST).
757 rewrite_value_aux(avl_set(A),interval(_,_),interval(TLow,TUp)) :-
758 avl_equal_to_interval(A,Low,Up),
759 TLow = b(integer(Low),integer,[]), TUp = b(integer(Up),integer,[]).
760 rewrite_value_aux(int(A),integer(_),integer(A)) :- number(A).
761 rewrite_value_aux(pred_true,_,boolean_true).
762 rewrite_value_aux(pred_false,_,boolean_false).
763 rewrite_value_aux(string(A),integer(_),string(A)) :- % value(string(A)) rewritten to AST node string(A)
764 atom(A).
765
766
767 rewrite_glob_set('REAL',real_set).
768 rewrite_glob_set('FLOAT',float_set).
769 rewrite_glob_set('STRING',string_set).
770 rewrite_glob_set(I,integer_set(I)) :-
771 kernel_objects:integer_global_set(I).
772
773 allow_expansion(avl_set(_),closure(P,T,B)) :-
774 is_small_specific_custom_set(closure(P,T,B),100).
775 allow_expansion(closure(P,T,B),avl_set(_)) :-
776 is_small_specific_custom_set(closure(P,T,B),100).
777
778 same_sub_expressions([],_,[]).
779 same_sub_expressions([H1|T1],AVL,[H2|T2]) :-
780 same_texpr_body(H1,AVL,H2),
781 same_sub_expressions(T1,AVL,T2).
782
783 same_value_inside_closure(V1,V2) :- var(V1),!, V1==V2.
784 same_value_inside_closure(_,V2) :- var(V2),!,fail.
785 same_value_inside_closure(rec(Fields1),rec(Fields2)) :- !,
786 % sets of records come in this form: struct(b(value(rec(FIELDS)),record(_),_))
787 same_fields_inside_closure(Fields1,Fields2).
788 same_value_inside_closure(V1,V2) :-
789 % we could attempt this only if the outer closure was large/infinite ??
790 is_custom_explicit_set(V1), is_custom_explicit_set(V2),
791 !,
792 (allow_expansion(V1,V2) -> EXP=allow_expansion ; EXP = no_expansion),
793 equal_explicit_sets4(V1,V2,EXP,no_wf_available). % usually only sets compiled differently inside closures
794 same_value_inside_closure([H1|T1],avl_set(A2)) :- !, % relevant for JSON trace replay for test 1263
795 try_convert_to_avl([H1|T1],V1), V1=avl_set(A1),
796 equal_avl_tree(A1,A2).
797 same_value_inside_closure(avl_set(A2),[H1|T1]) :- !,
798 try_convert_to_avl([H1|T1],V1), V1=avl_set(A1),
799 equal_avl_tree(A1,A2).
800 same_value_inside_closure(V1,V2) :- V1==V2.
801
802 same_fields_inside_closure(V1,V2) :- var(V1),!, V1==V2.
803 same_fields_inside_closure(_,V2) :- var(V2),!,fail.
804 same_fields_inside_closure([],[]).
805 same_fields_inside_closure([field(Name,V1)|T1],[field(Name,V2)|T2]) :-
806 same_value_inside_closure(V1,V2),
807 same_fields_inside_closure(T1,T2).
808
809 /*
810 same_texpr_body_debug(H1,H2) :-
811 (same_texpr_body(H1,H2) -> true
812 ; print('FAIL: '),nl,
813 translate:print_bexpr(H1),nl, translate:print_bexpr(H2),nl, print(H1),nl, print(H2),nl, fail). */
814
815 %test(Y2,Z2) :- empty_avl(X), avl_store(1,X,2,Y), avl_store(2,X,3,Z),
816 % avl_store(2,Y,3,Y2), avl_store(1,Z,2,Z2), equal_avl_tree(Y2,Z2).
817
818 %equal_avl_tree(A,B) :- avl_min(A,Min), avl_min(B,Min), cmp(Min,A,B).
819 %cmp(El,A,B) :-
820 % (avl_next(El,A,Nxt) -> (avl_next(El,B,Nxt), cmp(Nxt,A,B))
821 % ; \+ avl_next(El,B,Nxt) ).
822
823 % The following is faster than using avl_next
824 equal_avl_tree(A,B) :-
825 % statistics(walltime,[WT1,_]),if(equal_avl_tree2(A,B),true,(statistics(walltime,[_,W]),print(wall(W)),nl)).
826 %equal_avl_tree2(A,B) :-
827 avl_min(A,Min),
828 !,
829 avl_min(B,Min),
830 avl_max(A,Max), avl_max(B,Max),
831 % maybe also check avl_height +/- factor of 1.4405 (page 460, Knuth 3) ? but it seems this would trigger only extremely rarely
832 %avl_height(A,H1), avl_height(A,H2), log(check(Min,Max,H1,H2)),
833 avl_domain(A,L), avl_domain(B,L).
834 equal_avl_tree(empty,_) :- !, format(user_error,'*** Warning: empty AVL tree in equal_avl_tree~n',[]).
835 equal_avl_tree(A,B) :- add_internal_error('Illegal AVL tree: ',equal_avl_tree(A,B)),fail.
836
837 /* a predicate to check equality of two custom explicit sets */
838
839 % TO DO: deal with second set being a variable with kernel_cardinality_attr attribute
840 :- block not_equal_explicit_sets_wf(-,?,?), not_equal_explicit_sets_wf(?,-,?).
841 not_equal_explicit_sets_wf(global_set(X),global_set(Y),_) :- !,dif(X,Y).
842 not_equal_explicit_sets_wf(global_set(B),avl_set(A),WF) :- !,
843 \+ equal_explicit_sets4(avl_set(A),global_set(B),allow_expansion,WF).
844 not_equal_explicit_sets_wf(freetype(X),freetype(Y),_) :- !,dif(X,Y).
845 not_equal_explicit_sets_wf(avl_set(A),avl_set(B),_) :- !,
846 \+ equal_avl_tree(A,B).
847 %not_equal_explicit_sets_wf(X,Y,_) :- X==Y,!,fail.
848 not_equal_explicit_sets_wf(avl_set(A),I2,WF) :- is_interval_closure_or_integerset(I2,L2,U2),!, % also covers I2=global_set(...)
849 avl_not_equal_to_interval(A,L2,U2,WF).
850 not_equal_explicit_sets_wf(avl_set(A),global_set(B),WF) :- !,
851 \+ equal_explicit_sets4(avl_set(A),global_set(B),allow_expansion,WF).
852 not_equal_explicit_sets_wf(avl_set(A),CPB,WF) :-
853 is_cartesian_product_closure(CPB,B1,B2),!,
854 if(decompose_avl_set_into_cartesian_product_wf(A,A1,A2,WF), % should not produce pending co-routines, but better safe
855 kernel_objects:not_equal_object_wf((A1,A2),(B1,B2),WF),
856 true % no cartesian product can be equal to this avl_set
857 ).
858 not_equal_explicit_sets_wf(closure(P,T,B),avl_set(A),WF) :- !,
859 not_equal_explicit_sets_wf(avl_set(A),closure(P,T,B),WF).
860 not_equal_explicit_sets_wf(I1,I2,_) :- is_interval_closure_or_integerset(I1,L1,U1,Finite1),
861 is_interval_closure_or_integerset(I2,L2,U2,Finite2), !,
862 dif((Finite1,L1,U1),(Finite2,L2,U2)). % maybe we should call not_equal_objects on integers (not on inf values)?
863 not_equal_explicit_sets_wf(CPA,CPB,WF) :-
864 ? is_cartesian_product_closure(CPA,A1,A2), is_cartesian_product_closure(CPB,B1,B2),!,
865 not_equal_cartesian_product_wf(A1,A2,B1,B2,WF).
866 not_equal_explicit_sets_wf(S1,S2,WF) :-
867 is_not_member_value_closure_or_integerset(S1,TYPE,MS1),
868 is_not_member_value_closure_or_integerset(S2,TYPE,MS2),!,
869 kernel_objects:not_equal_object_wf(MS1,MS2,WF).
870 not_equal_explicit_sets_wf(closure(P,T,B),closure(P,T,B2),_) :-
871 same_texpr_body(B,B2),!,fail.
872 % TO DO: maybe support interval & avl_set comparison
873 not_equal_explicit_sets_wf(Set1,Set2,WF) :-
874 card_for_specific_custom_set(Set1,Card1,Code1), card_for_specific_custom_set(Set2,Card2,Code2),
875 call(Code1), call(Code2),!,
876 ? not_equal_expansions(Card1,Card2,Set1,Set2,WF).
877 ?not_equal_explicit_sets_wf(Set1,Set2,WF) :- not_equal_expansions(0,0,Set1,Set2,WF).
878
879
880 :- block not_equal_expansions(-,?,?,?,?), not_equal_expansions(?,-,?,?,?).
881 not_equal_expansions(F1,F2,_,_,_) :- F1 \= F2,!. % sets guaranteed to be different
882 not_equal_expansions(F,F,Set1,Set2,WF) :-
883 ? get_identity_as_equivalence(F,Set1,Set2,EQUIV),
884 !, %write(not),nl,translate:print_bexpr(EQUIV),nl,
885 copy_wf_start(WF,equal_expansions,CWF),
886 b_not_test_boolean_expression(EQUIV,[],[],CWF),
887 ? copy_wf_finish(WF,CWF).
888 not_equal_expansions(F,F,Set1,Set2,WF) :-
889 % only expand if both sets have same cardinality
890 expand_custom_set_wf(Set1,E1,not_equal_expansions1,WF),
891 expand_custom_set_wf(Set2,E2,not_equal_expansions2,WF),
892 dif(E1,E2). /* TO DO: ensure that ordering and normalization is same for all representations ! */
893
894
895
896
897 :- use_module(b_global_sets,[b_empty_global_set/1, b_non_empty_global_set/1, b_global_set_cardinality/2]).
898 is_empty_explicit_set_wf(closure(P,T,B),WF) :- !,
899 is_empty_closure_wf(P,T,B,WF).
900 is_empty_explicit_set_wf(S,_WF) :- is_empty_explicit_set(S).
901
902 % with WF we can delay computing Card; see test 1272 / card({x|x:1..10 & x*x<i}) = 0 & i>1
903 % TO DO: ideally we could just write this: is_empty_closure_wf(P,T,B,WF) :- closure_cardinality(P,T,B,0,WF). ; but empty_set / not_exists optimisation not triggered in closure_cardinality (yet); would avoid duplicate code
904 is_empty_closure_wf(P,T,B,WF) :-
905 is_lambda_value_domain_closure(P,T,B, DomainValue,_Expr),!,
906 kernel_objects:empty_set_wf(DomainValue,WF).
907 is_empty_closure_wf(P,T,B,WF) :- is_cartesian_product_closure_aux(P,T,B,A1,A2),!,
908 very_approximate_cardinality(A1,C1,WF),
909 very_approximate_cardinality(A2,C2,WF),
910 blocking_safe_mul(C1,C2,0).
911 is_empty_closure_wf(P,T,B,_WF) :-
912 card_for_specific_closure2(P,T,B,CC,Code),
913 !,
914 call(Code),CC=0.
915 is_empty_closure_wf(P,T,Body,WF) :-
916 WF \== no_wf_available, % only do this if we have a WF store; see comments for closure_cardinality ; code relevant for test 1272; card({x|x:1..10 & x*x<i}) = 0 & i>1
917 \+ ground_bexpr(Body), % otherwise better to use not_test_exists below (e.g., Bosch v6 Codespeed benchmark)
918 b_interpreter_check:reify_closure_with_small_cardinality(P,T,Body, WF, ReifiedList),
919 !,
920 domain(ReifiedList,0,1),
921 sum(ReifiedList,'#=',0).
922 is_empty_closure_wf(P,T,B,WF) :-
923 ? get_recursive_identifier_of_closure_body(B,TRID),!,
924 def_get_texpr_id(TRID,RID),
925 gen_typed_ids(P,T,TypedParas),
926 % now add Recursive ID's value to local state:
927 b_interpreter:b_not_test_exists(TypedParas,B,[used_ids([RID])],[bind(RID,closure(P,T,B))],[],no_compile,WF).
928 is_empty_closure_wf(P,T,B,WF) :- !, % try and check that not(#(P).(B)); i.e., there is no solution for the Body B; solves tests 1542, detecting that {x|x>100 & x mod 102 = 2} = {} is false
929 gen_typed_ids(P,T,TypedParas),
930 b_interpreter:b_not_test_exists(TypedParas,B,[used_ids([])],[],[],no_compile,WF). % used_ids are empty, as all variables already compiled into values
931
932 % very_approximate_cardinality: only required to return 0 for empty set, and number or inf for non-empty set, tested in 1893
933 :- block very_approximate_cardinality(-,?,?).
934 very_approximate_cardinality(avl_set(A),C,_) :- !, (A=empty -> print(empty_avl),nl,C=0 ; C=1).
935 very_approximate_cardinality([],C,_) :- !, C=0.
936 very_approximate_cardinality([_|_],C,_) :- !, C=1.
937 very_approximate_cardinality(Set,C,WF) :- kernel_objects:cardinality_as_int_wf(Set,int(C),WF).
938 % TO DO: maybe call is_empty_closure or similar for closures
939
940 gen_typed_ids([],[],R) :- !, R=[].
941 gen_typed_ids([ID|IT],[Type|TT],[b(identifier(ID),Type,[])|TTT]) :- !,
942 % TO DO: add Info field from outer set comprehension
943 gen_typed_ids(IT,TT,TTT).
944 gen_typed_ids(I,T,TI) :- add_internal_error('Call failed: ',gen_typed_ids(I,T,TI)),fail.
945
946 % version with WF can also deal with closures via exists !
947 is_empty_explicit_set(global_set(GS)) :- !, b_empty_global_set(GS).
948 is_empty_explicit_set(freetype(ID)) :- !, is_empty_freetype(ID).
949 is_empty_explicit_set(avl_set(A)) :- !,
950 (var(A) -> add_warning(is_empty_explicit_set,'Variable avl_set')
951 ; empty_avl(A), add_warning(is_empty_explicit_set,'Empty avl_set')
952 ).
953 is_empty_explicit_set(C) :- card_for_specific_closure(C,CC,Code),!,call(Code),CC=0.
954 is_empty_explicit_set(ES) :- expand_custom_set(ES,[],is_empty_explicit_set).
955
956
957 is_non_empty_explicit_set(CS) :- is_non_empty_explicit_set_wf(CS,no_wf_available).
958
959 is_non_empty_explicit_set_wf(global_set(GS),_WF) :- !, b_non_empty_global_set(GS).
960 is_non_empty_explicit_set_wf(freetype(ID),_WF) :- !, is_non_empty_freetype(ID).
961 is_non_empty_explicit_set_wf(avl_set(A),_WF) :- !,
962 (empty_avl(A) -> print('### Warning: empty avl_set (2)'),nl,fail
963 ; true).
964 ?is_non_empty_explicit_set_wf(closure(P,T,B),WF) :- !, is_non_empty_closure_wf(P,T,B,WF).
965 %is_non_empty_explicit_set_wf(ES,_WF) :- expand_custom_set(ES,[_|_],is_non_empty_explicit_set).
966
967
968 % TO DO: this code is a bit redundant with is_empty_closure_wf
969 is_non_empty_closure_wf(P,T,B,WF) :-
970 is_lambda_value_domain_closure(P,T,B, DomainValue,_Expr),!,
971 ? kernel_objects:not_empty_set_wf(DomainValue,WF).
972 is_non_empty_closure_wf(P,T,B,WF) :- is_cartesian_product_closure_aux(P,T,B,A1,A2),!,
973 very_approximate_cardinality(A1,C1,WF),
974 very_approximate_cardinality(A2,C2,WF),
975 blocking_safe_mul(C1,C2,CC),gt0(CC).
976 is_non_empty_closure_wf(P,T,B,_WF) :-
977 card_for_specific_closure2(P,T,B,CC,Code),!,call(Code),gt0(CC).
978 % TO DO: reify_closure_with_small_cardinality
979 is_non_empty_closure_wf(P,T,B,WF) :- WF \== no_wf_available,
980 ? get_recursive_identifier_of_closure_body(B,TRID),!,
981 def_get_texpr_id(TRID,RID),
982 gen_typed_ids(P,T,TypedParas),
983 % now add Recursive ID's value to local state:
984 b_interpreter:b_test_exists(TypedParas,B,[used_ids([RID])],[bind(RID,closure(P,T,B))],[],WF).
985 is_non_empty_closure_wf(P,T,B,WF) :- WF \== no_wf_available,
986 % otherwise enumeration of test_exists will behave strangely; leading to enumeration warnings,... [TO DO: ensure we always have a WF or fix this below ?]
987 % try and check that not(#(P).(B)); i.e., there is no solution for the Body B; solves tests 1542; test 1146 also triggers this code
988 (debug_mode(off) -> true ; print(non_empty_closure_test(P)),nl, translate:print_bexpr(B),nl),
989 gen_typed_ids(P,T,TypedParas),
990 !,
991 ? b_interpreter:b_test_exists(TypedParas,B,[used_ids([])],[],[],WF). % used_ids are empty, as all variables already compiled into values
992 % some rules for set_subtraction, ... closures ?? if left part infinite and right part finite it must be infinite
993 is_non_empty_closure_wf(P,T,B,WF) :-
994 expand_custom_set_wf(closure(P,T,B),[_|_],is_non_empty_closure_wf,WF).
995
996
997 % TO DO: expand cart / reify and use for pf_test
998 test_empty_closure_wf(P,T,B,Res,WF) :-
999 is_lambda_value_domain_closure(P,T,B, DomainValue,_Expr),!,
1000 kernel_equality:empty_set_test_wf(DomainValue,Res,WF).
1001 %test_empty_closure_wf(P,T,B,WF) :- is_cartesian_product_closure_aux(P,T,B,A1,A2),!,
1002 test_empty_closure_wf(P,T,B,Res,_WF) :-
1003 card_for_specific_closure2(P,T,B,CC,Code),!,call(Code),leq0(CC,Res).
1004 test_empty_closure_wf(P,T,B,Res,WF) :-
1005 \+ is_memoization_closure(P,T,B,_MemoID),
1006 preferences:preference(use_closure_expansion_memoization,false),
1007 !,
1008 bexpr_variables(B,ClosureWaitVars),
1009 % this does not perform a few optimisations of expand_normal closure:
1010 % memoization, stored_memo_expansion, is_closure1_value_closure, is_lambda_closure
1011 % print(test_empty_closure_wf),nl, translate:print_bexpr(B),nl,
1012 when((ground(ClosureWaitVars) ; nonvar(Res)),
1013 test_empty_closure_wf2(P,T,B,Res,WF)).
1014 test_empty_closure_wf(P,T,B,Res,WF) :- % print(expand_test(P)),nl,
1015 % was expand_custom_set_wf(closure(P,T,B),ExpES,test_empty_closure_wf,WF), in turn calls expand_closure_to_list
1016 expand_normal_closure(P,T,B,ExpES,_CDone,check(test_empty_closure_wf),WF),
1017 kernel_equality:empty_set_test_wf(ExpES,Res,WF).
1018 % /*@symbolic */ {x|x:1..100000000 & x mod 22=1} = x & (x={} <=> B=TRUE)
1019
1020 test_empty_closure_wf2(P,T,B,Res,WF) :-
1021 Res == pred_true,!,
1022 is_empty_closure_wf(P,T,B,WF).
1023 test_empty_closure_wf2(P,T,B,Res,WF) :- Res == pred_false,!,
1024 is_non_empty_closure_wf(P,T,B,WF).
1025 test_empty_closure_wf2(P,T,B,Res,WF) :-
1026 (is_empty_closure_now(P,T,B,WF) % we need to force expansion here to be able to use local cut ->
1027 % expand_normal_closure would now also expand the closure;
1028 -> Res=pred_true
1029 ; Res=pred_false).
1030
1031 % check if closure now; ground everything except WFE
1032 is_empty_closure_now(P,T,B,OuterWF) :-
1033 create_inner_wait_flags(OuterWF,is_empty_closure_now,WF),
1034 debug_opt_push_wait_flag_call_stack_info(WF,
1035 external_call('Check if empty set',[closure(P,T,B)],unknown),WF2),
1036 is_empty_closure_wf(P,T,B,WF2),
1037 ground_inner_wait_flags(WF2). % does not ground WFE in case WD errors are pending
1038
1039 :- block leq0(-,?).
1040 leq0(inf,Res) :- !, Res=pred_false.
1041 leq0(inf_overflow,Res) :- !, Res=pred_false.
1042 leq0(CC,Res) :- (CC>0 -> Res=pred_false ; Res=pred_true).
1043
1044 test_empty_explicit_set_wf(V,Res,_) :- var(V),!,
1045 add_internal_error('Illegal call: ',test_empty_explicit_set(V,Res,_)),fail.
1046 test_empty_explicit_set_wf(global_set(GS),Res,_WF) :- !,
1047 (b_empty_global_set(GS) -> Res=pred_true ; Res=pred_false).
1048 test_empty_explicit_set_wf(freetype(ID),Res,_WF) :- !, test_empty_freetype(ID,Res).
1049 test_empty_explicit_set_wf(avl_set(A),Res,_WF) :- !,
1050 (var(A) -> add_warning(test_empty_explicit_set_wf,'Variable avl_set'), Res=pred_true
1051 ; empty_avl(A), add_warning(test_empty_explicit_set_wf,'Empty avl_set'), Res = pred_true
1052 ; Res=pred_false).
1053 test_empty_explicit_set_wf(closure(P,T,B),Res,WF) :- !,
1054 test_empty_closure_wf(P,T,B,Res,WF).
1055 test_empty_explicit_set_wf(ES,Res,WF) :-
1056 expand_custom_set(ES,ExpES,test_empty_explicit_set),
1057 kernel_equality:empty_set_test_wf(ExpES,Res,WF).
1058
1059 :- block gt0(-).
1060 gt0(CC) :- (CC=inf -> true ; CC=inf_overflow -> true ; CC>0).
1061
1062 % a version to compute cardinality for
1063 explicit_set_cardinality_for_wf(closure(P,T,B),Card) :-
1064 (is_symbolic_closure_or_symbolic_mode(P,T,B) ; \+ ground_bexpr(B)),
1065 !,
1066 Card = inf. % assume card is infinite for WF computation; it may be finite!
1067 %explicit_set_cardinality_for_wf(avl_set(AVL),Size) :- !, quick_avl_approximate_size(AVL,Size).
1068 explicit_set_cardinality_for_wf(CS,Card) :- card_for_specific_custom_set(CS,Card,Code),!,
1069 on_enumeration_warning(call(Code),Card=inf). % see test 1519 for relevance
1070 explicit_set_cardinality_for_wf(_,inf). % assume card is infinite for WF computation; it may be finite!
1071 % TO DO: maybe never expand closures here !? -> closure_cardinality can expand closure !!!!!!
1072 %explicit_set_cardinality_for_wf(CS,Card) :-
1073 % on_enumeration_warning(
1074 % explicit_set_cardinality(CS,Card),
1075 % (debug_println(assuming_inf_card_for_wf), % see test 1519 for relevance
1076 % Card = inf)). % assume card is infinite for WF computation; it may be finite!
1077
1078 explicit_set_cardinality(CS,Card) :-
1079 % init_wait_flags(WF,[explicit_set_cardinality]), % there are a few checks for no_wf_available below
1080 explicit_set_cardinality_wf(CS,Card,no_wf_available).
1081 % ground_wait_flags(WF).
1082
1083 explicit_set_cardinality_wf(global_set(GS),Card,_) :- !,b_global_set_cardinality(GS,Card).
1084 explicit_set_cardinality_wf(freetype(GS),Card,_WF) :- !, freetype_cardinality(GS,Card).
1085 explicit_set_cardinality_wf(avl_set(S),Card,_WF) :- !,avl_size(S,Card).
1086 ?explicit_set_cardinality_wf(closure(P,T,B),Card,WF) :- closure_cardinality(P,T,B,Card,WF).
1087
1088 closure_cardinality(P,T,B,Card,WF) :-
1089 is_lambda_value_domain_closure(P,T,B, DomainValue,_Expr),!,
1090 kernel_objects:cardinality_as_int_wf(DomainValue,int(Card),WF). % always compute it; card_for_specific_closure will only compute it if it can be done efficiently
1091 closure_cardinality(P,T,B,Card,WF) :- is_cartesian_product_closure_aux(P,T,B,A1,A2),!,
1092 kernel_objects:cardinality_as_int_wf(A1,int(C1),WF),
1093 kernel_objects:cardinality_as_int_wf(A2,int(C2),WF),
1094 blocking_safe_mul(C1,C2,Card).
1095 % TO DO: card_for_specific_closure2 calls is_lambda_value_domain_closure and is_cartesian_product_closure_aux again !
1096 closure_cardinality(P,T,B,Card,_WF) :-
1097 card_for_specific_closure2(P,T,B,CC,Code),
1098 !,
1099 call(Code),Card=CC.
1100 closure_cardinality(P,T,Body,Card,WF) :-
1101 (WF == no_wf_available -> CBody=Body
1102 ? ; b_compiler:b_compile(Body,P,[],[],CBody)
1103 ),
1104 % reify will work better if we used b_compiler:compile so that more sets can be detected as small
1105 closure_cardinality2(P,T,CBody,Card,WF).
1106 closure_cardinality2(P,T,Body,Card,WF) :-
1107 WF \== no_wf_available, % only do this if we have a WF store
1108 ? if(b_interpreter_check:reify_closure_with_small_cardinality(P,T,Body, WF, ReifiedList),
1109 true,
1110 (perfmessagecall(reify,reification_of_closure_for_card_failed(P),translate:print_bexpr(Body),Body),fail)),
1111 !,
1112 domain(ReifiedList,0,1),
1113 sum(ReifiedList,'#=',Card),
1114 % in this case we know card to be finite ! TO DO: ensure that check_finite propagates Card variable
1115 debug_println(9,reified_cardinality_sum(ReifiedList,Card)). % fd_dom(Card,Dom),print(dom(Card,Dom)),nl.
1116 % should we add a special check if Card=0 ? usually Card not instantiated at this point !
1117 %closure_cardinality(P,T,B,Card,WF) :- Card==0, %is_symbolic_closure(P,T,B),
1118 % !, is_empty_closure_wf(P,T,B,WF).
1119 closure_cardinality2(P,T,B,Card,WF) :-
1120 % TO DO: bexpr_variables(ClosureBody,ClosureWaitVars) and wait until those are bound; if Card = 0 -> empty_set; we can try to reifiy again
1121 expand_custom_set_wf(closure(P,T,B),Expansion,closure_cardinality,WF),
1122 my_length(Expansion,0,Card).
1123
1124 :- block my_length(-,?,?).
1125 my_length([],A,A).
1126 my_length([_|T],A,R) :- A1 is A+1, my_length(T,A1,R).
1127
1128 % compute domain and range for specific relations;
1129 % not the closure is total over the domain and surjective over the range
1130 % WARNING: this should never enumerate on its own, it is often called with
1131 % a cut straight after it; if some enumeration happens then only first solution
1132 % will be pursued (e.g., cond_assign_eq_obj)
1133 dom_range_for_specific_closure([],[],[],function(bijection),_WF).
1134 dom_range_for_specific_closure(closure(P,T,Pred),Domain,Range,Functionality,WF) :-
1135 dom_range_for_specific_closure2(P,T,Pred, Domain,Range,dom_and_range,Functionality,WF).
1136
1137 dom_range_for_specific_closure2(Par,Typ,Body, Domain,Range,Required,Functionality,WF) :-
1138 is_member_closure(Par,Typ,Body,TYPE,SET),
1139 dom_range_for_member_closure(SET,TYPE,Domain,Range,Required,Functionality,WF),!.
1140 dom_range_for_specific_closure2(Par,Typ,Body, DOMAIN,RANGE,_,Functionality,WF) :-
1141 is_cartesian_product_closure_aux(Par,Typ,Body,SET1,SET2),!,
1142 (singleton_set(SET2,_) % checks nonvar
1143 -> Functionality = function(total) % function if card(SET2)=1
1144 ; Functionality=relation),
1145 kernel_equality:empty_set_test_wf(SET1,EqRes1,WF),
1146 cond_assign_eq_obj_wf(EqRes1,RANGE,[],SET2,WF), % if SET1=[] then Range=[]
1147 kernel_equality:empty_set_test_wf(SET2,EqRes2,WF),
1148 cond_assign_eq_obj_wf(EqRes2,DOMAIN,[],SET1,WF). %if SET2=[] then Domain=[]
1149 dom_range_for_specific_closure2(Par,Typ,Body, DomainRange,DomainRange,_,function(bijection),_WF) :-
1150 is_id_closure_over(Par,Typ,Body,DomainRange,_).
1151
1152
1153 dom_range_for_member_closure(identity(b(value(SET1),ST1,_)),_SEQT,SET1,SET1,_,function(bijection),_) :-
1154 is_set_type(ST1,_). /* _SEQT=id(T1) */
1155 dom_range_for_member_closure(closure(V),_SEQT,Domain,Range,Required,Functionality,WF) :- % closure1 transitive closure
1156 % rx : A <-> B <=> closure1(rx) : A <-> B means we can simply remove closure1(.) wrapper
1157 V = b(value(VAL),_,_), nonvar(VAL),
1158 %write(peel_clos1_dom_range(Required)),nl, tools_printing:print_term_summary(closure(V)),nl,
1159 (VAL = closure(P,T,B)
1160 -> dom_range_for_specific_closure2(P,T,B,Domain,Range,Required,Functionality,WF)
1161 ; Functionality = relation, % we do not know if this is going to be a function
1162 (Required=domain_only -> true ; range_of_explicit_set_wf(VAL,Range,WF)),
1163 (Required=range_only -> true ; domain_of_explicit_set_wf(VAL,Domain,WF))
1164 ).
1165
1166 % not sure if we need this: memoized functions are infinite usually and range can never be computed anyway
1167 %dom_range_for_member_closure(Expr,_,Domain,Range,Func) :-
1168 % expand_memoize_stored_function_reference(Expr,ExpandedValue),
1169 % dom_range_for_specific_closure(ExpandedValue,Domain,Range,Func,no_wf_available).
1170
1171 :- block cond_assign_eq_obj_wf(-,?,?,?,?).
1172 %cond_assign_eq_obj_wf(PTF,R,A,B,_) :- var(PTF), add_error(cond_assign_eq_obj,'block declaration bug warning: ',cond_assign_eq_obj(PTF,R,A,B)),fail. % comment in to detect if affected by block declaration bug
1173 cond_assign_eq_obj_wf(pred_true,Res,A,_,WF) :- equal_object_wf(Res,A,cond_assign_eq_obj_wf_1,WF).
1174 cond_assign_eq_obj_wf(pred_false,Res,_,B,WF) :- equal_object_wf(Res,B,cond_assign_eq_obj_wf_2,WF).
1175
1176 is_cartesian_product_closure(closure(Par,Typ,Body),SET1,SET2) :-
1177 ? is_cartesian_product_closure_aux(Par,Typ,Body,SET1,SET2).
1178 is_cartesian_product_closure_aux(Par,Types,b(truth,pred,Info),SET1,SET2) :- Par=[_,_|_],!,
1179 append(LPar,[RParID],Par), append(LTypes,[RType],Types),
1180 construct_closure_if_necessary(LPar,LTypes,b(truth,pred,Info),SET1),
1181 construct_closure_if_necessary([RParID],[RType],b(truth,pred,Info),SET2).
1182 is_cartesian_product_closure_aux(Par,Types,Body,SET1,SET2) :- Par=[_,_|_],!,
1183 append(LPar,[RParID],Par), append(LTypes,[RType],Types),!,
1184 split_conjunct(Body,[RParID], RConjL, LPar, LConjL),
1185 bsyntaxtree:conjunct_predicates(RConjL,RConj), bsyntaxtree:conjunct_predicates(LConjL,LConj),
1186 construct_closure_if_necessary(LPar,LTypes,LConj,SET1),
1187 construct_closure_if_necessary([RParID],[RType],RConj,SET2).
1188 is_cartesian_product_closure_aux(Par,Typ,Body,SET1,SET2) :-
1189 SET = cartesian_product(b(value(SET1),ST1,_), b(value(SET2),ST2,_)),
1190 is_member_closure(Par,Typ,Body,couple(T1m,T2m),SET),
1191 is_set_type(ST1,T1),unify_types_strict(T1,T1m),
1192 is_set_type(ST2,T2),unify_types_strict(T2,T2m),!.
1193 %is_cartesian_product_closure_aux([ID1,ID2],[T1,T2],FBody,SET1,SET2) :- % is this not redundant wrt split ??
1194 % % a closure of the form {ID1,ID2|ID1 : SET1 & ID2 : SET2} ;
1195 % % can get generated when computing domain symbolically of lambda abstraction
1196 % FBody = b(Body,pred,_),
1197 % is_cartesian_product_body(Body,ID1,ID2,T1,T2,SET1,SET2). % ,print(cart_res(SET1,SET2)),nl.
1198
1199 % try and split conjunct into two disjoint parts (for detecting cartesian products)
1200 % on the specified variables
1201 % fails if it cannot be done
1202 split_conjunct(b(PRED,pred,Info),Vars1,C1,Vars2,C2) :-
1203 split_conjunct_aux(PRED,Info,Vars1,C1,Vars2,C2).
1204 split_conjunct_aux(truth,_Info,_Vars1,C1,_Vars2,C2) :- !,C1=[],C2=[].
1205 split_conjunct_aux(conjunct(A,B),_Info,Vars1,C1,Vars2,C2) :- !, % TO DO: use DCG
1206 split_conjunct(B,Vars1,CB1,Vars2,CB2), !, % Note: conjunct_predicates will create inner conjunct in A and atomic Expression in B
1207 split_conjunct(A,Vars1,CA1,Vars2,CA2),!,
1208 append(CA1,CB1,C1), append(CA2,CB2,C2).
1209 split_conjunct_aux(E,Info,Vars1,C1,_Vars2,C2) :- unique_id_comparison(E,ID),!,
1210 (member(ID,Vars1) -> C1=[b(E,pred,Info)], C2=[] ; C1=[], C2=[b(E,pred,Info)]).
1211
1212 unique_id_comparison(less(b(L,_,_),b(R,_,_)), ID) :- unique_id_comparison_aux(L,R,ID).
1213 unique_id_comparison(less_equal(b(L,_,_),b(R,_,_)), ID) :- unique_id_comparison_aux(L,R,ID).
1214 unique_id_comparison(greater(b(L,_,_),b(R,_,_)), ID) :- unique_id_comparison_aux(L,R,ID).
1215 unique_id_comparison(greater_equal(b(L,_,_),b(R,_,_)), ID) :- unique_id_comparison_aux(L,R,ID).
1216 unique_id_comparison(member(b(identifier(ID),_,_),b(V,_,_)), ID) :- explicit_value(V).
1217 unique_id_comparison(subset(b(identifier(ID),_,_),b(V,_,_)), ID) :- explicit_value(V).
1218 unique_id_comparison(equal(b(L,_,_),b(R,_,_)), ID) :- unique_id_comparison_aux(L,R,ID). % means we also detect something like %x.(x : INTEGER|0) as cartesian product
1219 % what about not_equal
1220
1221 unique_id_comparison_aux(identifier(ID),V,ID) :- !,explicit_value(V).
1222 unique_id_comparison_aux(V,identifier(ID),ID) :- explicit_value(V).
1223
1224 explicit_value(value(_)) :- !.
1225 explicit_value(integer(_)) :- !.
1226 explicit_value(unary_minus(TV)) :- !, explicit_tvalue(TV).
1227 explicit_value(interval(TV1,TV2)) :- !,
1228 explicit_tvalue(TV1), explicit_tvalue(TV2).
1229 %explicit_value(seq(B)) :- !, explicit_tvalue(B). % are encoded as values by b_compile
1230 %explicit_value(seq1(B)) :- !, explicit_tvalue(B).
1231 %explicit_value(iseq(B)) :- !, explicit_tvalue(B).
1232 %explicit_value(iseq1(B)) :- !, explicit_tvalue(B).
1233 %explicit_value(struct(B)) :- !, explicit_tvalue(B).
1234 %explicit_value(rec(Fields)) :- !, explicit_tfields(Fields).
1235 explicit_value(total_bijection(A,B)) :- !, explicit_tvalue(A),explicit_tvalue(B). % see test 1897 for cases below
1236 explicit_value(total_injection(A,B)) :- !, explicit_tvalue(A),explicit_tvalue(B).
1237 explicit_value(total_function(A,B)) :- !, explicit_tvalue(A),explicit_tvalue(B).
1238 explicit_value(total_surjection(A,B)) :- !, explicit_tvalue(A),explicit_tvalue(B).
1239 explicit_value(partial_function(A,B)) :- !, explicit_tvalue(A),explicit_tvalue(B).
1240 explicit_value(partial_injection(A,B)) :- !, explicit_tvalue(A),explicit_tvalue(B).
1241 explicit_value(partial_surjection(A,B)) :- !, explicit_tvalue(A),explicit_tvalue(B).
1242 explicit_value(relations(A,B)) :- !, explicit_tvalue(A),explicit_tvalue(B).
1243 explicit_value(total_relation(A,B)) :- !, explicit_tvalue(A),explicit_tvalue(B).
1244 explicit_value(surjection_relation(A,B)) :- !, explicit_tvalue(A),explicit_tvalue(B).
1245 explicit_value(total_surjection_relation(A,B)) :- !, explicit_tvalue(A),explicit_tvalue(B).
1246 explicit_value(real_set) :- !.
1247 explicit_value(string_set) :- !.
1248
1249 explicit_tvalue(b(B,_,_)) :- !, explicit_value(B).
1250
1251 %explicit_tfields(V) :- var(V),!,fail.
1252 %explicit_tfields([]).
1253 %explicit_tfields([field(N,V)|T]) :- ground(N),explicit_tvalue(V),explicit_tfields(T).
1254
1255 % conjunct_predicates([CA1,CB1],C1),
1256 % conjunct_predicates([CA2,CB2],C2).
1257
1258 /* *********
1259 is_cartesian_product_body(conjunct(A,B),ID1,ID2,_T1,_T2,SET1,SET2) :- !,
1260 member_pred_value(A,CID1,CSET1),
1261 member_pred_value(B,CID2,CSET2),
1262 (ID1=CID1,ID2=CID2,SET1=CSET1,SET2=CSET2 ; ID1=CID2,ID2=CID1,SET1=CSET2,SET2=CSET1).
1263 is_cartesian_product_body(A,ID1,ID2,T1,T2,SET1,SET2) :-
1264 member_pred_value2(A,AID,ASET),
1265 ( AID=ID1 -> SET1=ASET, construct_closure_if_necessary([ID2],[T2],b(truth,pred,[]),SET2)
1266 ; AID=ID2 -> SET2=ASET, construct_closure_if_necessary([ID1],[T1],b(truth,pred,[]),SET1)).
1267
1268 member_pred_value(b(B,pred,_), ID,VAL) :- print(member_pred_value2(B,ID,VAL)),nl,
1269 member_pred_value2(B,ID,VAL).
1270 member_pred_value2(member(b(identifier(ID),_CT1,_),b(value(VAL),_SCT1,_)), ID,VAL). %_SCT1 = set(CT1)
1271 */
1272
1273 % check if we have POW(SET1) or SET1<->SET2 (equiv. to POW(SET1*SET2))
1274 is_full_powerset_or_relations_or_struct_closure(closure(Par,Typ,Body),SUBSETS) :-
1275 %TYPE = set(T),
1276 is_member_closure(Par,Typ,Body,TYPE,SET),
1277 is_full_powset_aux(SET,TYPE,SUBSETS).
1278
1279 :- use_module(library(lists),[maplist/3, maplist/4]).
1280 is_full_powset_aux(pow_subset(b(value(SET1),set(T1),_)),set(T1),[SET1]).
1281 is_full_powset_aux(relations(S1,S2),set(couple(T1,T2)),[SET1,SET2]) :-
1282 S1 = b(value(SET1),set(T1),_), S2 = b(value(SET2),set(T2),_).
1283 is_full_powset_aux(struct(b(value(rec(FIELDS)),record(_),_)),record(_),FieldValueSets) :-
1284 maplist(get_field_val,FIELDS,FieldValueSets).
1285
1286 get_field_val(field(_,Val),Val).
1287
1288 %[field(duration,global_set('INTEGER')),field(rhythm,global_set('INTEGER')),field(slot,avl_set(...))]
1289
1290 is_powerset_closure(closure(Par,Typ,Body),PType,Subset) :-
1291 ? is_set_type(TYPE,T),
1292 is_member_closure(Par,Typ,Body,TYPE,SET),
1293 nonvar(SET),
1294 is_powset_aux(SET,PType,b(VS,set(T),_)) ,
1295 nonvar(VS), VS = value(Subset). %,print(powerset(Subset)),nl.
1296 is_powset_aux(pow_subset(A),pow,A).
1297 is_powset_aux(pow1_subset(A),pow1,A).
1298 is_powset_aux(fin_subset(A),fin,A).
1299 is_powset_aux(fin1_subset(A),fin1,A).
1300
1301 % group together closures which can be treated like cartesian products in the sense that:
1302 % Closure is empty if either Set1 or Set2 (could also be empty in other conditions though)
1303 % Closure is subset of other Closure if same Constructor and both sets are subsets
1304 /* is_cartesian_product_like_closure(Closure,Constructor,Set1,Set2) :-
1305 is_cartesian_product_closure(Closure,S11,S12),!,
1306 Constructor = cartesian_product,Set1=S11,Set2=S12.
1307 is_cartesian_product_like_closure(closure(Par,Typ,Body),Constructor,Set1,Set2) :-
1308 is_member_closure(Par,Typ,Body,TYPE,SET),
1309 is_cart_like_relation(SET,Constructor,b(value(Set1),set(_T1),_), b(value(Set1),set(_T2),_)).
1310 is_cart_like_relation(relations(A,B),relations,A,B).
1311 is_cart_like_relation(partial_function(A,B),partial_function,A,B).
1312 is_cart_like_relation(partial_injection(A,B),partial_injection,A,B). */
1313
1314 % (closure([_zzzz_unary],[set(couple(integer,string))],b(member(b(identifier(_zzzz_unary),set(couple(integer,string)),[]),b(relations(b(value(global_set(INTEGER)),set(integer),[]),b(value(global_set(STRING)),set(string),[])),set(set(couple(integer,string))),[])),pred,[])))
1315 % 1 1 Fail: custom_explicit_sets:is_powset_aux(relations(b(value(global_set('INTEGER')),set(integer),[]),b(value(global_set('STRING')),set(string),[])),couple(integer,string),_19584) ?
1316
1317 % card_for_specific_custom_set(+Set,-Cardinality,-CodeToComputeCardinality)
1318 % succeeds if card can be computed efficiently
1319 card_for_specific_custom_set(CS,C,Cd) :- var(CS),!,
1320 add_internal_error('Internal error: var ',card_for_specific_custom_set(CS,C,Cd)),fail.
1321 card_for_specific_custom_set(global_set(GS),Card,true) :- !, b_global_set_cardinality(GS,Card).
1322 card_for_specific_custom_set(freetype(Id),Card,true) :- !, freetype_cardinality(Id,Card).
1323 card_for_specific_custom_set(avl_set(S),Card,true) :- !,avl_size(S,Card).
1324 card_for_specific_custom_set(closure(P,T,B),Card,CodeToComputeCard) :-
1325 card_for_specific_closure3(_,P,T,B,Card,CodeToComputeCard).
1326
1327 card_for_specific_closure(closure(P,T,Pred),Card,CodeToComputeCard) :-
1328 card_for_specific_closure3(_ClosureKind,P,T,Pred,Card,CodeToComputeCard).
1329 card_for_specific_closure(closure(P,T,Pred),ClosureKind,Card,CodeToComputeCard) :-
1330 card_for_specific_closure3(ClosureKind,P,T,Pred,Card,CodeToComputeCard).
1331
1332 :- use_module(btypechecker,[couplise_list/2]).
1333 :- use_module(bsyntaxtree,[is_truth/1]).
1334 card_for_specific_closure2(Par,Typ,Body, Card,Code) :-
1335 card_for_specific_closure3(_ClosureKind,Par,Typ,Body, Card,Code).
1336
1337 % first argument for debugging purposes or filtering
1338 card_for_specific_closure3(special_closure,Par,Typ,Body, Card,Code) :-
1339 is_special_infinite_closure(Par,Typ,Body),!,Card=inf, Code=true.
1340 card_for_specific_closure3(truth_closure,_,Types,Body,Card,Code) :- is_truth(Body),!,
1341 % TO DO: also treat multiple parameters
1342 couplise_list(Types,Type),
1343 Code=kernel_objects:max_cardinality(Type,Card).
1344 card_for_specific_closure3(interval_closure,Par,Typ,Body, Card,Code) :-
1345 ? is_geq_leq_interval_closure(Par,Typ,Body,Low,Up), !,
1346 card_of_interval_inf(Low,Up,Card),
1347 Code=true. % should we return card_of_interval_inf as code ?
1348 % TO DO: deal with non-infinite not_member_closures, prj1, prj2, id, ...
1349 card_for_specific_closure3(lambda_closure,Par,Typ,Body, Card,Code) :-
1350 is_lambda_value_domain_closure(Par,Typ,Body, DomainValue,_Expr),!, nonvar(DomainValue),
1351 efficient_card_for_set(DomainValue,Card,Code).
1352 card_for_specific_closure3(cartesian_product,Par,Typ,Body, Card,Code) :-
1353 is_cartesian_product_closure_aux(Par,Typ,Body,A1,A2),!, nonvar(A1), nonvar(A2),
1354 efficient_card_for_set(A1,Card1,Code1),
1355 efficient_card_for_set(A2,Card2,Code2),
1356 Code = (Code1,Code2, custom_explicit_sets:blocking_safe_mul(Card1,Card2,Card)).
1357 card_for_specific_closure3(member_closure,Par,Typ,Body, Card,Code) :-
1358 is_member_closure(Par,Typ,Body,TYPE,SET),
1359 nonvar(SET),!,
1360 card_for_member_closure(SET,TYPE,Card,Code).
1361 % Note: _ExprInfo could have: contains_wd_condition,
1362 % but if lambda is well-defined we compute the correct card ; if not then card is not well-defined anyway
1363 % maybe we should check contains_wd_condition produce a warning msg ?
1364
1365 % inner values can sometimes be a list, e.g., [pred_true,pred_false] for BOOL
1366 efficient_card_for_set(VAR,_,_) :- var(VAR),!,fail.
1367 efficient_card_for_set([],Card,Code) :- !, Card=0,Code=true.
1368 efficient_card_for_set([_|T],Card,Code) :- known_length(T,1,C), !, Card = C, Code=true.
1369 efficient_card_for_set(CS,Card,Code) :- card_for_specific_custom_set(CS,Card,Code).
1370 known_length(X,_,_) :- var(X),!,fail.
1371 known_length([],A,A).
1372 known_length([_|T],A,R) :- A1 is A+1, known_length(T,A1,R).
1373 known_length(avl_set(S),Acc,Res) :- avl_size(S,Card),
1374 Res is Acc+Card.
1375 % TO DO: also support closures
1376
1377 card_for_member_closure(parallel_product(b(value(A1),ST1,_),b(value(A2),ST1,_)),_T,Card,CodeToComputeCard) :- !,
1378 nonvar(A1), nonvar(A2),
1379 efficient_card_for_set(A1,Card1,Code1),
1380 CodeToComputeCard = (Code1,Code2, custom_explicit_sets:blocking_safe_mul(Card1,Card2,Card)),
1381 % cardinality computed like for cartesian_product.
1382 efficient_card_for_set(A2,Card2,Code2).
1383 card_for_member_closure(seq(b(value(SET1),ST1,_)),_SEQT,Card,CodeToComputeCard) :- !, /* _SEQT=seq(T1) */
1384 is_set_type(ST1,_T1),
1385 CodeToComputeCard = custom_explicit_sets:seq_card(SET1,Card).
1386 card_for_member_closure(seq1(b(value(SET1),ST1,_)),_SEQT,Card,CodeToComputeCard) :- !, /* _SEQT=seq1(T1) */
1387 is_set_type(ST1,_T1),
1388 CodeToComputeCard = custom_explicit_sets:seq1_card(SET1,Card).
1389 card_for_member_closure(perm(b(value(SET1),ST1,_)),_SEQT,Card,CodeToComputeCard) :- !, /* _SEQT=perm(T1) */
1390 is_set_type(ST1,_T1),
1391 CodeToComputeCard = (kernel_objects:cardinality_as_int(SET1,int(SCard)),
1392 custom_explicit_sets:blocking_factorial(SCard,Card)).
1393 card_for_member_closure(iseq(b(value(SET1),ST1,_)),_SEQT,Card,CodeToComputeCard) :- !, /* _SEQT=iseq(T1) */
1394 is_set_type(ST1,_T1),
1395 CodeToComputeCard = (kernel_objects:cardinality_as_int(SET1,int(SCard)),
1396 kernel_card_arithmetic:blocking_nr_iseq(SCard,Card)).
1397 card_for_member_closure(iseq1(b(value(SET1),ST1,_)),_SEQT,Card,CodeToComputeCard) :- !, /* _SEQT=iseq1(T1) */
1398 is_set_type(ST1,_T1),
1399 CodeToComputeCard = (kernel_objects:cardinality_as_int(SET1,int(SCard)),
1400 kernel_card_arithmetic:blocking_nr_iseq1(SCard,Card)).
1401 card_for_member_closure(identity(b(value(SET1),ST1,_)),_SEQT,Card,CodeToComputeCard) :- !, /* _SEQT=id(T1) */
1402 is_set_type(ST1,_T1),
1403 CodeToComputeCard =
1404 kernel_objects:cardinality_as_int(SET1,int(Card)).
1405 card_for_member_closure(struct(b(RecVal,record(_FieldSetTypes),_)), record(_FieldTypes), % set of records
1406 Card,CodeToComputeCard) :-
1407 !,
1408 (RecVal=value(RECF), nonvar(RECF), RECF=rec(FIELDS) % value has been computed:
1409 -> CodeToComputeCard = custom_explicit_sets:get_field_cardinality(FIELDS,Card)
1410 ; RecVal = rec(TypedFields), % we still have a typed AST
1411 maplist(get_field_val_type,TypedFields,Exprs,Types),
1412 l_card_for_member_closure(Exprs,Types,Card, CodeToComputeCard)
1413 ).
1414 % now dealt with separately above: card_for_member_closure(cartesian_product(b(value(SET1),set(T1),_), b(value(SET2),set(T2),_)),
1415 % couple(T1,T2), Card,CodeToComputeCard) :- !,
1416 % CodeToComputeCard =
1417 % (kernel_objects:cardinality_as_int(SET1,int(SCard1)),
1418 % kernel_objects:cardinality_as_int(SET2,int(SCard2)),
1419 % custom_explicit_sets:blocking_safe_mul(SCard1,SCard2,Card) ).
1420 card_for_member_closure(POW,TYPE, Card,CodeToComputeCard) :-
1421 (POW = pow_subset(b(value(SET),TYPE,_)) ;
1422 POW = fin_subset(b(value(SET),TYPE,_))),!,
1423 CodeToComputeCard =
1424 (kernel_objects:cardinality_as_int(SET,int(SCard)),
1425 custom_explicit_sets:blocking_safe_pow2(SCard,Card)
1426 ).
1427 card_for_member_closure(POW,TYPE, Card,CodeToComputeCard) :-
1428 (POW = pow1_subset(b(value(SET),TYPE,_)) ;
1429 POW = fin1_subset(b(value(SET),TYPE,_))),!,
1430 CodeToComputeCard =
1431 (kernel_objects:cardinality_as_int(SET,int(SCard)),
1432 custom_explicit_sets:blocking_safe_pow2(SCard,C1),
1433 custom_explicit_sets:safe_dec(C1,Card)
1434 ).
1435 card_for_member_closure(RELEXPR,SType, Card,CodeToComputeCard) :-
1436 is_set_type(SType,couple(T1,T2)),
1437 is_a_relation(RELEXPR, b(value(DOM),set(T1),_),
1438 b(value(RAN),set(T2),_), DCard,RCard,Card,RELCODE),!,
1439 CodeToComputeCard =
1440 (
1441 kernel_objects:cardinality_as_int(DOM,int(DCard)),
1442 kernel_objects:cardinality_as_int(RAN,int(RCard)),
1443 custom_explicit_sets:call_card_for_relations(DCard,RCard,RELCODE)
1444 ).
1445 card_for_member_closure(BODY, integer, Card,CodeToComputeCard) :-
1446 is_interval_with_integer_bounds(BODY,Low,Up),!,
1447 CodeToComputeCard = custom_explicit_sets:card_of_interval_inf(Low,Up,Card).
1448 card_for_member_closure(value(Value), _Type, Card,CodeToComputeCard) :-
1449 % we have a closure of the type {x|x:S}; equivalent to S
1450 (nonvar(Value),
1451 Value=closure(P,T,B)
1452 -> % cardinality_as_int may expand it ! is bad if e.g. we called this code to check if a closure is infinite
1453 card_for_specific_closure2(P,T,B,Card,CodeToComputeCard) % will not expand, but fail if cannot be computed
1454 % TO DO: provide an argument: precise_or_efficient
1455 ; CodeToComputeCard = kernel_objects:cardinality_as_int(Value,int(Card))
1456 ).
1457 %card_for_member_closure(BODY, Type, Card,CodeToComputeCard) :- print(try_card(BODY,Type)),nl,fail.
1458 % TO DO: add maybe other common closures ? simple value closure
1459 % also: what if subexpressions are not of value() type ?
1460
1461 :- public call_card_for_relations/3.
1462 :- block call_card_for_relations(-,?,?), call_card_for_relations(?,-,?).
1463 call_card_for_relations(_,_,RELCODE) :- call(RELCODE).
1464
1465 get_field_val_type(field(_F1,b(Expr1,Type1,_)),Expr1,Type1).
1466
1467 l_card_for_member_closure([Expr1],[Type1],Card,CodeToComputeCard) :- !,
1468 card_for_member_closure(Expr1,Type1,Card, CodeToComputeCard).
1469 l_card_for_member_closure([Expr1|ET],[Type1|TT],Card,CodeToComputeCard) :-
1470 CodeToComputeCard = (Code1,Code2, custom_explicit_sets:blocking_safe_mul(Card1,Card2,Card)),
1471 card_for_member_closure(Expr1,Type1,Card1, Code1),
1472 l_card_for_member_closure(ET,TT,Card2,Code2).
1473
1474 :- public safe_dec/2. % used in card_for_member_closure
1475 :- block safe_dec(-,?).
1476 safe_dec(inf,R) :- !, R=inf.
1477 safe_dec(inf_overflow,R) :- !, R=inf_overflow.
1478 safe_dec(X,R) :- R is X-1.
1479
1480 :- use_module(kernel_equality,[empty_set_test/2]).
1481 :- public seq_card/2. % used in card_for_member_closure
1482 :- block seq_card(-,?).
1483 seq_card([],R) :- !,R=1.
1484 seq_card([_|_],R) :- !,R=inf.
1485 seq_card(X,Res) :- empty_set_test(X,EqRes),
1486 set_card(EqRes,1,Res).
1487
1488 :- block set_card(-,?,?).
1489 set_card(pred_true,Nr,Nr).
1490 set_card(pred_false,_,inf).
1491 % card(seq({n|n>10 & (n mod 20=3 & n mod 20 = 4) }))
1492
1493 :- public seq1_card/2. % used in card_for_member_closure
1494 :- block seq1_card(-,?).
1495 seq1_card([],R) :- !,R=0.
1496 seq1_card([_|_],R) :- !,R=inf.
1497 seq1_card(X,Res) :- empty_set_test(X,EqRes), set_card(EqRes,0,Res).
1498
1499 :- public get_field_cardinality/2. % used in card_for_member_closure
1500 get_field_cardinality([],1).
1501 get_field_cardinality([field(_Name,Value)|T],ResCard) :-
1502 kernel_objects:cardinality_as_int(Value,int(SCard1)),
1503 get_field_cardinality(T,RestCard), blocking_safe_mul(SCard1,RestCard,ResCard).
1504
1505 :- use_module(kernel_card_arithmetic).
1506
1507 :- block blocking_safe_mul(-,-,?).
1508 blocking_safe_mul(A,B,R) :-
1509 ( A==0 -> R=0
1510 ; B==0 -> R=0
1511 ; A==1 -> R=B
1512 ; B==1 -> R=A
1513 ; blocking_safe_mul2(A,B,R) ).
1514
1515 :- block blocking_safe_mul2(-,?,?), blocking_safe_mul2(?,-,?).
1516 blocking_safe_mul2(A,B,Res) :-
1517 (safe_mul(A,B,AB) -> Res=AB
1518 ; add_warning(blocking_safe_mul2,'Call failed: ',blocking_safe_mul2(A,B,Res)),
1519 % could happen for something like prj2(BOOL,NAT) = prj2(BOOL,0..n)
1520 fail).
1521
1522 :- public blocking_safe_pow2/2. % used in card_for_member_closure above
1523 :- block blocking_safe_pow2(-,?).
1524 blocking_safe_pow2(A,Res) :-
1525 (safe_pow2(A,A2) -> Res=A2
1526 ; add_warning(blocking_safe_pow2,'Call failed: ',safe_pow2(A,Res)),fail).
1527
1528
1529
1530
1531 :- assert_must_succeed((custom_explicit_sets:card_for_specific_closure2(['_zzzz_binary'],[integer],
1532 b(member(b(identifier('_zzzz_binary'),integer,[generated]),
1533 b(interval(b(value(int(1)),integer,[]),b(value(int(10)),integer,[])),set(integer),[])),pred,[]),R,C),
1534 call(C),
1535 R=10)).
1536
1537 %! is_interval_closure_or_integerset(+I,-L,-U)
1538 is_interval_closure_or_integerset(Var,_,_) :- var(Var),!,fail.
1539 is_interval_closure_or_integerset(global_set(X),Low,Up) :- !, get_integer_set_interval(X,Low,Up).
1540 is_interval_closure_or_integerset(Set,El,El) :- singleton_set(Set,ELX),
1541 nonvar(ELX), ELX=int(El),!. % new, useful??
1542 is_interval_closure_or_integerset(closure(P,T,B),Low,Up) :-
1543 ? (is_geq_leq_interval_closure(P,T,B,Low,Up) -> true ; is_interval_closure(P,T,B,Low,Up)).
1544
1545 % with an additional argument to know if the set is finite or infinite:
1546 is_interval_closure_or_integerset(Set,Low,Up,Finite) :-
1547 is_interval_closure_or_integerset(Set,Low,Up),
1548 % if we obtain Low, Up as variables then these must be finite numbers; they cannot stand for inf
1549 (infinite_interval(Low,Up) -> Finite=infinite ; Finite=finite).
1550
1551
1552 get_integer_set_interval('NAT',0,MAXINT) :- (preferences:preference(maxint,MAXINT)->true).
1553 get_integer_set_interval('NAT1',1,MAXINT) :- (preferences:preference(maxint,MAXINT)->true).
1554 get_integer_set_interval('INT',MININT,MAXINT) :-
1555 ((preferences:preference(maxint,MAXINT),preferences:preference(minint,MININT))->true).
1556 get_integer_set_interval('NATURAL',0,inf).
1557 get_integer_set_interval('NATURAL1',1,inf).
1558 get_integer_set_interval('INTEGER',minus_inf,inf).
1559 % TO DO: add minus_inf to kernel_objects !
1560
1561 :- block geq_inf(-,?), geq_inf(?,-).
1562 geq_inf(inf,_) :- !.
1563 geq_inf(minus_inf,B) :- !, B=minus_inf.
1564 geq_inf(_,minus_inf) :- !.
1565 geq_inf(A,inf) :- !, A=inf.
1566 geq_inf(inf_overflow,_) :- !.
1567 geq_inf(A,inf_overflow) :- !, A=inf_overflow.
1568 geq_inf(A,B) :- A >= B.
1569
1570 :- block minimum_with_inf(-,-,?).
1571 % in the first three cases we can determine outcome without knowing both args
1572 minimum_with_inf(A,B,R) :- (A==minus_inf ; B==minus_inf),!,R=minus_inf.
1573 minimum_with_inf(A,B,R) :- A==inf,!,R=B.
1574 minimum_with_inf(A,B,R) :- B==inf,!,R=A.
1575 minimum_with_inf(A,B,R) :- minimum_with_inf1(A,B,R), geq_inf(A,R), geq_inf(B,R).
1576 :- block minimum_with_inf1(-,?,?), minimum_with_inf1(?,-,?).
1577 minimum_with_inf1(minus_inf,_,R) :- !, R=minus_inf.
1578 minimum_with_inf1(_,minus_inf,R) :- !, R=minus_inf.
1579 minimum_with_inf1(inf,B,R) :- !, R=B.
1580 minimum_with_inf1(A,inf,R) :- !, R=A.
1581 minimum_with_inf1(inf_overflow,B,R) :- !, R=B.
1582 minimum_with_inf1(A,inf_overflow,R) :- !, R=A.
1583 minimum_with_inf1(A,B,R) :- (A<B -> R=A ; R=B).
1584
1585 :- block maximum_with_inf(-,-,?).
1586 % in the first three cases we can determine outcome without knowing both args
1587 maximum_with_inf(A,B,R) :- (A==inf ; B==inf),!,R=inf.
1588 maximum_with_inf(A,B,R) :- A==minus_inf,!,R=B.
1589 maximum_with_inf(A,B,R) :- B==minus_inf,!,R=A.
1590 maximum_with_inf(A,B,R) :- maximum_with_inf1(A,B,R), geq_inf(R,A), geq_inf(R,B).
1591 :- block maximum_with_inf1(-,?,?), maximum_with_inf1(?,-,?).
1592 maximum_with_inf1(inf,_,R) :- !, R=inf.
1593 maximum_with_inf1(_,inf,R) :- !, R=inf.
1594 maximum_with_inf1(minus_inf,B,R) :- !, R=B.
1595 maximum_with_inf1(A,minus_inf,R) :- !, R=A.
1596 maximum_with_inf1(inf_overflow,_,R) :- !, R=inf_overflow.
1597 maximum_with_inf1(_,inf_overflow,R) :- !, R=inf_overflow.
1598 maximum_with_inf1(A,B,R) :- (A>B -> R=A ; R=B).
1599
1600 /* utilities for detecting interval closures */
1601 construct_interval_closure(Low,Up,Res) :- (Low==inf;Up==minus_inf),!,Res=[].
1602 construct_interval_closure(Low,Up,Res) :- number(Low),number(Up), Low>Up,!,Res=[].
1603 construct_interval_closure(Low,Up,Res) :- Up==inf,!,
1604 ( Low==0 -> Res = global_set('NATURAL')
1605 ; Low==1 -> Res = global_set('NATURAL1')
1606 ; Low==minus_inf -> Res = global_set('INTEGER')
1607 ; Low==inf -> Res = []
1608 ; construct_greater_equal_closure(Low,Res)
1609 ).
1610 construct_interval_closure(Low,Up,Res) :- Low==minus_inf,!,
1611 construct_less_equal_closure(Up,Res).
1612 construct_interval_closure(Low,Up,Res) :- Low==Up,!,
1613 (number(Low) -> construct_one_element_custom_set(int(Low),Res)
1614 ; Res = [int(Low)]).
1615 construct_interval_closure(Low,Up,Res) :-
1616 construct_interval_set(Low,Up,Set),
1617 construct_member_closure('_zzzz_unary',integer,[],Set,Res).
1618
1619 transform_global_sets_into_closure(closure(P,T,B),closure(P,T,B)).
1620 transform_global_sets_into_closure(global_set(X),Res) :-
1621 transform_global_set_into_closure_aux(X,Res).
1622 transform_global_set_into_closure_aux('NATURAL',Res) :-
1623 construct_greater_equal_closure(0,Res).
1624 transform_global_set_into_closure_aux('NATURAL1',Res) :-
1625 construct_greater_equal_closure(1,Res).
1626 % TO DO: add INTEGER
1627
1628
1629
1630 is_geq_leq_interval_closure([Par],[integer],b(Body,pred,Span),Low,Up) :-
1631 (var(Par)
1632 -> add_internal_error('Non-ground closure: ',closure([Par],[integer],b(Body,pred,Span))),fail
1633 ? ; get_geq_leq_bounds(Body,Par,Low,Up)).
1634
1635 infinite_interval(Low,Up) :- (Low==minus_inf -> true ; Up==inf).
1636
1637 :- assert_must_succeed((card_of_interval_inf(1,10,10))).
1638 :- assert_must_succeed((card_of_interval_inf(1,inf,R),R==inf)).
1639 :- assert_must_succeed((card_of_interval_inf(minus_inf,0,R),R==inf)).
1640 :- assert_must_succeed((card_of_interval_inf(2,2,R), R==1)).
1641 :- assert_must_succeed((card_of_interval_inf(12,2,R), R==0)).
1642 :- assert_must_succeed((card_of_interval_inf(2,B,10), B==11)).
1643 :- assert_must_succeed((card_of_interval_inf(A,12,10), A==3)).
1644 :- assert_must_succeed((card_of_interval_inf(A,12,0), A=222)).
1645 :- assert_must_succeed((card_of_interval_inf(12,B,0), B=11)).
1646 :- assert_must_fail((card_of_interval_inf(A,12,0), A=12)).
1647 % compute cardinality of interval; allow bounds to be inf and minus_inf (but if so, they must be bound straightaway)
1648 card_of_interval_inf(A,B,Card) :-
1649 ? at_least_two_vars(A,B,Card), % initially this will usually be true, if only one variable we can compute result
1650 preferences:preference(use_clpfd_solver,true),
1651 !,
1652 clpfd_interface:post_constraint(Card #= max(0,1+B-A),custom_explicit_sets:block_card_of_interval_inf(A,B,Card)).
1653 card_of_interval_inf(A,B,Card) :- block_card_of_interval_inf(A,B,Card).
1654
1655 ?at_least_two_vars(A,B,C) :- var(A),!,(var(B) -> not_infinite_bound(C) ; number(B),var(C)).
1656 at_least_two_vars(A,B,C) :- number(A), var(B),var(C).
1657 not_infinite_bound(A) :- (var(A) ; number(A)). % inf can only appear immediately, not for variables
1658
1659 :- block block_card_of_interval_inf(-,?,-),block_card_of_interval_inf(?,-,-).
1660 block_card_of_interval_inf(A,_,Card) :- A==minus_inf,!, Card=inf.
1661 block_card_of_interval_inf(_,B,Card) :- B==inf,!, Card=inf.
1662 block_card_of_interval_inf(From,To,Card) :- number(From),number(To),!,
1663 (From>To -> Card=0 ; Card is (To-From)+1).
1664 block_card_of_interval_inf(A,B,C) :- number(C),!, number_card_of_interval_inf_aux(C,A,B).
1665 block_card_of_interval_inf(A,B,C) :- C==inf,!,
1666 % probably this should systematically fail; if A and B are not inf/minus_inf now they will never be
1667 print(infinite_interval_requested(A,B,C)),nl,
1668 when((nonvar(A),nonvar(B)), block_card_of_interval_inf(A,B,C)).
1669 block_card_of_interval_inf(A,B,C) :- add_internal_error('Illegal call: ',card_of_interval_inf(A,B,C)).
1670 :- use_module(inf_arith,[block_inf_greater/2]).
1671 number_card_of_interval_inf_aux(0,A,B) :- !, % empty interval
1672 % if A and B are variables then they will not become inf later ??
1673 % inf can only be set directly for sets such as {x|x>4} or NATURAL1
1674 (((var(A);number(A)),(var(B);number(B)))
1675 % hence we can use ordinary comparison (with CLPFD) here
1676 -> kernel_objects:less_than_direct(B,A)
1677 % TO DO: we could do this even if both A and B are variables !! ex : {n,m|n..m = {} & m..100={} & 103..n={}}
1678 ; block_inf_greater(A,B)).
1679 %number_card_of_interval_inf_aux(Card,From,B) :- number(From),!, B is (From+Card)-1.
1680 %number_card_of_interval_inf_aux(Card,A,To) :- number(To),!, A is 1+To-Card.
1681 number_card_of_interval_inf_aux(Card,A,B) :-
1682 Card>0, C1 is Card-1,
1683 kernel_objects:int_minus(int(B),int(A),int(C1)).
1684
1685
1686 get_geq_leq_bounds(conjunct(b(LEFT,pred,_),b(RIGHT,pred,_)), Par,Low,Up) :-
1687 ? get_geq_leq_bounds(LEFT,Par,From1,To1),
1688 ? get_geq_leq_bounds(RIGHT,Par,From2,To2),
1689 intersect_intervals_with_inf(From1,To1,From2,To2,Low,Up).
1690 get_geq_leq_bounds(member(b(identifier(Par),integer,_),
1691 b(Value,set(integer),_)),Par,Low,Up) :-
1692 get_value_bounds(Value,Low,Up).
1693 ?get_geq_leq_bounds(greater_equal(b(A,_,_),b(B,_,_)),Par,Low,Up) :- get_bounds2(greater_equal,A,B,Par,Low,Up).
1694 ?get_geq_leq_bounds( less_equal(b(A,_,_),b(B,_,_)),Par,Low,Up) :- get_bounds2(less_equal,A,B,Par,Low,Up).
1695 ?get_geq_leq_bounds( greater(b(A,_,_),b(B,_,_)),Par,Low,Up) :- get_bounds2(greater,A,B,Par,Low,Up).
1696 ?get_geq_leq_bounds( less(b(A,_,_),b(B,_,_)),Par,Low,Up) :- get_bounds2(less,A,B,Par,Low,Up).
1697
1698 get_value_bounds(value(GS),Low,Up) :- is_interval_closure_or_integerset(GS,Low,Up). % recursive call
1699 % nonvar(GS), GS=global_set(ISET), get_integer_set_interval(ISET,Low,Up).
1700 get_value_bounds(interval(b(TLow,_,_),b(TUp,_,_)),Low,Up) :-
1701 integer_value(TLow,Low),
1702 integer_value(TUp,Up).
1703
1704 get_bounds2(greater_equal,identifier(Par),V,Par,X,inf) :- integer_value(V,X).
1705 get_bounds2(greater_equal,V,identifier(Par),Par,minus_inf,X) :- integer_value(V,X).
1706 get_bounds2(less_equal,identifier(Par),V,Par,minus_inf,X) :- integer_value(V,X).
1707 get_bounds2(less_equal,V,identifier(Par),Par,X,inf) :- integer_value(V,X).
1708 get_bounds2(greater,identifier(Par),V,Par,X1,inf) :- integer_value(V,X), kernel_objects:int_plus(int(X),int(1),int(X1)). %, X1 is X+1.
1709 get_bounds2(greater,V,identifier(Par),Par,minus_inf,X1) :- integer_value(V,X), kernel_objects:int_minus(int(X),int(1),int(X1)). %X1 is X-1.
1710 get_bounds2(less,V,identifier(Par),Par,X1,inf) :- integer_value(V,X), kernel_objects:int_plus(int(X),int(1),int(X1)). %X1 is X+1.
1711 get_bounds2(less,identifier(Par),V,Par,minus_inf,X1) :- integer_value(V,X),
1712 kernel_objects:int_minus(int(X),int(1),int(X1)). %X1 is X-1.
1713 % to do: add negation thereof ??
1714
1715 integer_value(V,_) :- var(V),!, print(var_integer_value(V)),nl,fail.
1716 integer_value(integer(X),R) :- !, R=X.
1717 integer_value(unary_minus(b(X,_,_)),R) :- !, integer_value(X,RM),
1718 number(RM), % if RM is not a number we could setup CLPFD constraint ?!
1719 R is -(RM).
1720 integer_value(minus(b(X,_,_),b(Y,_,_)),R) :- !, % some AST compilation rules generate X-1, X+1 ...
1721 integer_value(X,RMX),
1722 integer_value(Y,RMY),
1723 kernel_objects:int_minus(int(RMX),int(RMY),int(R)).
1724 integer_value(plus(b(X,_,_),b(Y,_,_)),R) :- !, % some AST compilation rules generate X-1, X+1 ...
1725 integer_value(X,RMX),
1726 integer_value(Y,RMY),
1727 kernel_objects:int_plus(int(RMX),int(RMY),int(R)).
1728 integer_value(value(V),R) :- !, V=int(R).
1729
1730 is_interval_closure(closure(Par,[integer],Pred),Low,Up) :-
1731 is_interval_closure_aux(Par,Pred,Low,Up).
1732 is_interval_closure(Par,[integer],Pred,Low,Up) :-
1733 is_interval_closure_aux(Par,Pred,Low,Up).
1734 is_interval_closure_aux(Par,Pred,Low,Up) :-
1735 is_member_closure(Par,[integer],Pred,integer,Set),
1736 is_interval_with_integer_bounds(Set,Low,Up).
1737 %is_interval_closure(closure_x(Par,[integer],Pred,_),Low,Up) :-
1738 % is_interval_closure(closure(Par,[integer],Pred),Low,Up).
1739
1740 is_interval_closure_body(Body,ID,Low,Up) :-
1741 is_member_closure([ID],[integer],Body,integer,Set),!,
1742 is_interval_with_integer_bounds(Set,Low,Up).
1743 is_interval_closure_body(Body,ID,Low,Up) :-
1744 ? is_geq_leq_interval_closure([ID],[integer],Body,Low,Up),
1745 number(Low), number(Up).
1746
1747 :- use_module(bsyntaxtree,[get_texpr_info/2,get_texpr_id/2]).
1748 % do a single check if we have interval, member or not-member closure, avoiding redundant checking
1749 % TO DO: move this and related predicates to closures module ?
1750 is_special_closure(_Ids,_Types,Pred,Result) :-
1751 get_texpr_info(Pred,Info),memberchk(prob_annotation(recursive(RId)),Info),!,
1752 Result = recursive_special_closure(RId).
1753 is_special_closure(Ids,Types,Pred,Result) :-
1754 ? is_memoization_closure(Ids,Types,Pred,MemoID),!,
1755 Result = memoization_closure(MemoID).
1756 is_special_closure([ID],[TYPE],b(PRED,_,_), Result) :-
1757 ( closures:is_member_closure_aux(PRED, ID,TYPE,SET) ->
1758 ( (TYPE=integer, is_interval_with_integer_bounds(SET,Low,Up)) ->
1759 Result = interval(Low,Up)
1760 ; Result = member_closure(ID,TYPE,SET))
1761 ; closures:is_not_member_closure_aux(PRED,ID,TYPE,SET) ->
1762 Result = not_member_closure(ID,TYPE,SET)
1763 ? ; (TYPE=integer,get_geq_leq_bounds(PRED,ID,Low,Up),number(Low), number(Up)) ->
1764 Result = interval(Low,Up)
1765 ).
1766
1767
1768 construct_interval_set(Low,Up,Res) :-
1769 Res = interval(b(value(int(Low)),integer,[]),
1770 b(value(int(Up)), integer,[])).
1771 is_interval_with_integer_bounds(X,L,U) :- var(X),!,
1772 add_internal_error('var arg: ',is_interval_with_integer_bounds(X,L,U)),fail.
1773 is_interval_with_integer_bounds(interval(b(TLOW,integer,_),b(TUP, integer,_)),Low,Up) :-
1774 integer_value(TLOW,Low), integer_value(TUP,Up).
1775
1776
1777 is_a_relation(relations(Domain,Range),Domain,Range,DCard,RCard,Card,Code) :- %% '<->'
1778 Code = (kernel_card_arithmetic:safe_mul(DCard,RCard,Exp), kernel_card_arithmetic:safe_pow2(Exp,Card)).
1779 is_a_relation(partial_function(Domain,Range),Domain,Range,DCard,RCard,Card,Code) :- %% '+->'
1780 Code = (kernel_card_arithmetic:safe_add_card(RCard,1,R1),kernel_card_arithmetic:safe_pown(R1,DCard,Card)).
1781 is_a_relation(total_function(Domain,Range),Domain,Range,DCard,RCard,Card,Code) :- %% '-->'
1782 Code = (kernel_card_arithmetic:safe_pown(RCard,DCard,Card)).
1783 is_a_relation(partial_bijection(Domain,Range),Domain,Range,DCard,RCard,Card,Code) :- %% '>+>>'
1784 Code = (kernel_card_arithmetic:partial_bijection_card(DCard,RCard,Card)).
1785 is_a_relation(total_bijection(Domain,Range),Domain,Range,DCard,RCard,Card,Code) :- %% '>->>'
1786 Code = (kernel_card_arithmetic:total_bijection_card(DCard,RCard,Card)).
1787 is_a_relation(total_injection(Domain,Range),Domain,Range,DCard,RCard,Card,Code) :- %% '>->'
1788 Code = (kernel_card_arithmetic:blocking_factorial_k(RCard,DCard,Card)).
1789 is_a_relation(partial_injection(Domain,Range),Domain,Range,DCard,RCard,Card,Code) :- %% '>+>'
1790 Code = (kernel_card_arithmetic:partial_injection_card(DCard,RCard,Card)).
1791 is_a_relation(total_surjection(Domain,Range),Domain,Range,DCard,RCard,Card,Code) :- %% '-->>'
1792 Code = (kernel_card_arithmetic:total_surjection_card(DCard,RCard,Card)).
1793 is_a_relation(partial_surjection(Domain,Range),Domain,Range,DCard,RCard,Card,Code) :- %% '+->>'
1794 Code = (kernel_card_arithmetic:partial_surjection_card(DCard,RCard,Card)).
1795 is_a_relation(total_relation(Domain,Range),Domain,Range,DCard,RCard,Card,Code) :- %% '<<->'
1796 Code = (kernel_card_arithmetic:total_relation_card(DCard,RCard,Card)).
1797 is_a_relation(surjection_relation(Domain,Range),Domain,Range,DCard,RCard,Card,Code) :- %% '<->>'
1798 % just swap args: card(A<->>B) = card(B<<->A)
1799 Code = (kernel_card_arithmetic:total_relation_card(RCard,DCard,Card)).
1800 % TO DO: total_surjection_relation <<->>
1801
1802
1803
1804 :- use_module(b_global_sets,[infinite_global_set/1]).
1805
1806 :- block is_infinite_global_set(-,?).
1807 is_infinite_global_set('NATURAL',integer).
1808 is_infinite_global_set('NATURAL1',integer).
1809 is_infinite_global_set('INTEGER',integer).
1810 is_infinite_global_set('FLOAT',real).
1811 is_infinite_global_set('REAL',real).
1812 is_infinite_global_set('STRING',string).
1813 is_infinite_global_set(G,global(G)) :- infinite_global_set(G).
1814
1815 %is_finite_integer_global_set('NAT').
1816 %is_finite_integer_global_set('NAT1').
1817 %is_finite_integer_global_set('INT').
1818
1819 % detects (certain) infinite explict sets
1820 is_infinite_explicit_set(X) :- var(X),!, add_internal_error(is_infinite_explicit_set,var(X)),fail.
1821 ?is_infinite_explicit_set(global_set(X)) :- is_infinite_global_set(X,_).
1822 is_infinite_explicit_set(freetype(X)) :- is_infinite_freetype(X).
1823 is_infinite_explicit_set(closure(Par,T,Body)) :- is_infinite_closure(Par,T,Body).
1824
1825 % detect some closure that we should definitely expand; even in SYMBOLIC mode or for ABSTRACT_CONSTANTS
1826 definitely_expand_this_explicit_set(Var) :- var(Var),!,fail.
1827 definitely_expand_this_explicit_set(closure(P,T,B)) :-
1828 (B = b(Body,_,_), definitely_expand(Body,P) -> true
1829 ; is_interval_closure(P,T,B,Low,Up), do_expand_interval(Low,Up)).
1830 % some lambda functions have small domain, but are very complicated to compute (test 1078, 1376)
1831 % hence the following is not sufficient:
1832 % ;is_small_specific_custom_set(closure(P,T,B),100), print(exp(T)),nl,translate:print_bexpr(B),nl,fail).
1833
1834 :- use_module(bsyntaxtree,[occurs_in_expr/2]).
1835 definitely_expand(Body,_) :- avl_mem_construct(Body,_).
1836 definitely_expand(exists(ExistsTIDs,Body),P) :- P = [ID],
1837 % detect AVL projection expressions like {res|#y.(y:AVL & res=Expr(y))} % test 1101
1838 Body = b(conjunct(b(Mem,pred,_),Eq),pred,_),
1839 Eq = b(equal(EqA,EqB),pred,_),
1840 avl_mem_construct(Mem,LHS),
1841 tlhs_uses_exists(LHS,ExistsTIDs,[]),
1842 ( get_texpr_id(EqA,ID) -> \+ occurs_in_expr(ID,EqB)
1843 ; get_texpr_id(EqB,ID) -> \+ occurs_in_expr(ID,EqA) ). % we assign to set compr. ID
1844 % example where ID occurs in other expression: {v|#w.(w : (1 .. 10) & v = (v + w) - 2)}; test 2516
1845
1846 tlhs_uses_exists(b(E,_,_)) --> lhs_uses_exists(E).
1847 ?lhs_uses_exists(identifier(EID),In,Out) :-!, select(TEID,In,Out),
1848 get_texpr_id(TEID,EID),!. % TODO: we could allow using an identifier twice
1849 lhs_uses_exists(value(V)) --> {nonvar(V), simple_value(V), ground_value(V)}.
1850 lhs_uses_exists(couple(A,B)) --> tlhs_uses_exists(A), tlhs_uses_exists(B).
1851 lhs_uses_exists(boolean_true) --> [].
1852 lhs_uses_exists(boolean_false) --> [].
1853 lhs_uses_exists(empty_set) --> [].
1854 lhs_uses_exists(empty_sequence) --> [].
1855 lhs_uses_exists(integer(_)) --> [].
1856 lhs_uses_exists(real(_)) --> [].
1857 lhs_uses_exists(string(_)) --> [].
1858
1859 avl_mem_construct(member(LHS,RHS),LHS) :- RHS = b(value(V),_,_), nonvar(V),
1860 (V=avl_set(_) -> true
1861 ; is_interval_closure_or_integerset(V,L,U), integer(L), integer(U), U-L < 1000
1862 ).
1863
1864 % dont_expand_this_explicit_set with default limit (20000)
1865 dont_expand_this_explicit_set(closure(P,T,B)) :- !,
1866 dont_expand_this_closure(P,T,B).
1867 dont_expand_this_explicit_set(S) :-
1868 is_infinite_or_very_large_explicit_set(S).
1869
1870 % dont_expand_this_explicit_set with extra limit argument:
1871 dont_expand_this_explicit_set(closure(P,T,B),Limit) :- !, dont_expand_this_closure(P,T,B,Limit).
1872 dont_expand_this_explicit_set(S,_) :- is_infinite_or_very_large_explicit_set(S).
1873
1874 % true if we have a closure / global_set that should not be expanded
1875 % TO DO: we could detect finite (is_lambda_value_domain_closure) closures which contain infinite elements such as %p.(p : BOOL|%t.(t : NATURAL|t .. t + 7))
1876 dont_expand_symbolic_explicit_set(closure(P,T,B)) :- !,
1877 dont_expand_this_closure(P,T,B).
1878 dont_expand_symbolic_explicit_set(avl_set(_)) :- !,
1879 fail. % already expanded
1880 dont_expand_symbolic_explicit_set(S) :-
1881 is_infinite_or_very_large_explicit_set(S).
1882
1883
1884 dont_expand_this_closure(P,T,B) :-
1885 get_preference(comprehension_set_symbolic_limit,Limit), % Default 20000
1886 dont_expand_this_closure(P,T,B,Limit). % % increase limit in Data valid mode?
1887
1888 dont_expand_this_closure(_P,_T,b(_,_,INFO),_Limit) :-
1889 ? member(prob_annotation(KIND),INFO),
1890 (KIND = 'SYMBOLIC' -> ! % cf is_symbolic_closure in closures
1891 ; KIND = 'FORCE' -> !, fail). % was wrapped in FORCE external_function
1892 dont_expand_this_closure(P,T,B,_Limit) :-
1893 is_interval_closure_or_integerset(closure(P,T,B),Low,Up), !,
1894 % interval closures are quite efficient for certain manipulations
1895 (number(Low), number(Up)
1896 -> dont_expand_interval(Low,Up)
1897 ; true % we have a closure with inf/minus_inf or variables as bounds; in both cases keep the closure
1898 ).
1899 dont_expand_this_closure(P,T,B,Limit) :-
1900 is_infinite_or_very_large_closure(P,T,B,Limit).
1901 %% TODO: also prevent expansion of things like ff = %x.(x:STRING & REGEX_MATCH(x,"[a-z]+")=TRUE|TRUE)
1902
1903 % do not automatically expand these intervals
1904 dont_expand_interval(Low,Up) :-
1905 Up+1-Low > 100. % another magic constant ; which value to choose ??
1906 do_expand_interval(Low,Up) :- Up+1-Low =< 100.
1907
1908 is_converted_lambda_closure(_P,_T,b(_,_,INFO)) :-
1909 ? member(prob_annotation('LAMBDA'),INFO).
1910
1911 is_symbolic_closure_or_symbolic_mode(P,T,B) :-
1912 ? (is_symbolic_closure(P,T,B) -> true
1913 ; preference(convert_comprehension_sets_into_closures,true)
1914 % by default suppose closures should be dealt with symbolically
1915 ).
1916 /*
1917 % check both LAMBDA + not RECURSIVE
1918 is_converted_non_recursive_lambda_closure(_,_,b(_,_,INFO)) :- is_conv_lambda_nonrec(INFO).
1919 is_conv_lambda_nonrec([prob_annotation(A)|T]) :- !,
1920 (A='LAMBDA' -> \+ memberchk(prob_annotation('RECURSIVE'),T)
1921 ; A\='RECURSIVE' -> is_conv_lambda_nonrec(T)).
1922 is_conv_lambda_nonrec([_|T]) :- is_conv_lambda_nonrec(T). */
1923
1924
1925
1926 % a set that is so large that expanding it would probably cause problems
1927 is_infinite_or_very_large_explicit_set(S) :-
1928 get_preference(comprehension_set_symbolic_limit,Limit), % Default 20000
1929 is_infinite_or_very_large_explicit_set(S,Limit). % increase limit in Data valid mode?
1930
1931 :- use_module(inf_arith,[infgreater/2]).
1932
1933 is_infinite_or_very_large_explicit_set(X,_) :- var(X),!,print(var_is_infinite_check(X)),nl,fail.
1934 is_infinite_or_very_large_explicit_set(closure(P,T,B),Limit) :- !,
1935 % treat closure separately here; some special rules
1936 is_infinite_or_very_large_closure(P,T,B,Limit).
1937 is_infinite_or_very_large_explicit_set(avl_set(A),Limit) :- !, % we could compute log and use avl_height_less_than
1938 quick_avl_approximate_size(A,Size), Size >= Limit.
1939 is_infinite_or_very_large_explicit_set(X,Limit) :- % closures are checked above
1940 explicit_set_cardinality(X,Card),
1941 nonvar(Card),infgreater(Card,Limit).
1942
1943
1944 is_very_large_or_symbolic_closure(P,T,B,Limit) :-
1945 ? (is_symbolic_closure(P,T,B) -> true ; is_infinite_or_very_large_closure(P,T,B,Limit)).
1946 :- use_module(bsyntaxtree,[is_a_disjunct/3]).
1947 is_infinite_or_very_large_closure(P,T,B,Limit) :-
1948 is_a_disjunct(B,D1,D2), % Assumption: there is no card_for_specific_closure code for disjuncts
1949 !,
1950 (is_infinite_or_very_large_closure(P,T,D1,Limit) -> true
1951 ; is_infinite_or_very_large_closure(P,T,D2,Limit)).
1952 is_infinite_or_very_large_closure(Par,T,Body,Limit) :-
1953 is_closure1_value_closure(Par,T,Body,VAL),!,
1954 nonvar(VAL), % it could still be large or infinite
1955 (Limit>1 -> NLimit is Limit/2 ; NLimit = Limit), % reduce limit as closure1 usually blows up
1956 is_infinite_or_very_large_explicit_set(VAL,NLimit).
1957 is_infinite_or_very_large_closure(P,T,B,Limit) :-
1958 card_for_specific_closure3(Kind,P,T,B,Card,Code),
1959 on_enumeration_warning(call(Code),
1960 (debug_println(9,cannot_expand_specific_closure_for_card(Kind,Limit)),
1961 % see test 1519 for relevance
1962 Card=inf)), % assume it is large
1963 !,
1964 nonvar(Card),infgreater(Card,Limit),
1965 perfmessages_bexpr(symbolic_closure,['Cardinality ',Card,' greater than limit ',Limit,' for '],B).
1966
1967
1968 is_infinite_or_symbolic_closure(P,T,B) :-
1969 ? (is_symbolic_closure(P,T,B) -> true ; is_infinite_closure(P,T,B)).
1970 is_infinite_closure(P,T,B) :-
1971 is_a_disjunct(B,D1,D2), % Assumption: there is no card_for_specific_closure code for disjuncts
1972 !,
1973 (is_infinite_closure(P,T,D1) -> true ; is_infinite_closure(P,T,D2)).
1974 is_infinite_closure(Par,T,Body) :-
1975 is_closure1_value_closure(Par,T,Body,VAL),!, % TO DO: also check if closure1 is large this way
1976 nonvar(VAL), % if var: it could still be infinite !! TO DO fix
1977 is_infinite_explicit_set(VAL).
1978 is_infinite_closure(Par,T,Body) :-
1979 card_for_specific_closure(closure(Par,T,Body),Card,Code),
1980 call(Code), % TO DO: catch enumeration exceptions (see is_infinite_or_very_large_closure above)
1981 Card == inf. % TODO: instantiate inf before to avoid computing huge numbers
1982
1983
1984 :- use_module(memoization,[compute_memo_hash/2, get_stored_memo_expansion/3, store_memo_expansion/3]).
1985 /* transitive closure */
1986 closure1_for_explicit_set(avl_set(A),Res) :-
1987 preferences:preference(use_closure_expansion_memoization,true),!,
1988 compute_memo_hash(closure1_for_explicit_set(A),Hash),
1989 (get_stored_memo_expansion(Hash,closure1_for_explicit_set(A),StoredResult)
1990 -> Res = StoredResult
1991 ; closure1_for_explicit_set_direct(avl_set(A),Result),
1992 store_memo_expansion(Hash,closure1_for_explicit_set(A),Result),
1993 Res = Result
1994 ).
1995 closure1_for_explicit_set(avl_set(A),Res) :- closure1_for_explicit_set_direct(avl_set(A),Res).
1996
1997 % sometimes faster, but can also be considerably slower:
1998 %:- use_module(extrasrc(avl_ugraphs),[avl_transitive_closure/2]).
1999 %closure1_for_explicit_set_direct(avl_set(A),Res) :-
2000 % avl_transitive_closure(A,TC),
2001 % construct_avl_set(TC,Res).
2002 closure1_for_explicit_set_direct(avl_set(A),Res) :-
2003 avl_domain(A,AList),
2004 iterate_closure(AList,A,A,IterationRes),
2005 construct_avl_set(IterationRes,Res).
2006
2007 /* transitive closure starting from some initial set */
2008 /* not sure if we should do this:
2009 closure1_for_explicit_set_from(avl_set(A),StartFrom,Res) :-
2010 preferences:preference(use_closure_expansion_memoization,true),
2011 compute_memo_hash(closure1_for_explicit_set(A),Hash),
2012 stored_expansion(Hash,closure1_for_explicit_set(A),StoredResult),!,
2013 domain_restriction_explicit_set(StartFrom,StoredResult,Res). */
2014 % StartFrom can be avl_set(empty)
2015 closure1_for_explicit_set_from(avl_set(A),StartFrom,Res) :-
2016 avl_domain(A,AList),
2017 filter_start_relation(AList,StartFrom,FAList),
2018 (FAList = [] -> Res=[]
2019 ; convert_to_avl(FAList,avl_set(Start)),
2020 iterate_closure(FAList,A,Start,IterationRes),
2021 construct_avl_set(IterationRes,Res)).
2022 filter_start_relation([],_,[]).
2023 filter_start_relation([(X,Y)|T],StartSet,Res) :-
2024 (element_of_custom_set(X,StartSet) -> Res = [(X,Y)|RT] ; Res=RT),
2025 filter_start_relation(T,StartSet,RT).
2026
2027 iterate_closure([],_,Res,Res).
2028 iterate_closure([(X,Y)|T],InitialRelation,Relation,Res) :-
2029 %(Key = (X,Y) -> true ; add_error_and_fail(iterate_closure,'Not a relation element: ',Key)),
2030 add_tuples(X,Y,InitialRelation,Relation,NewRelation,AddedTuples),
2031 % better: do added tuples straight away ?
2032 iterate_closure(T,InitialRelation,NewRelation,NewRelation2),
2033 iterate_closure(AddedTuples,InitialRelation,NewRelation2,Res).
2034
2035 add_tuples(X,Y,AVL,AVLClosureSoFar,Res,NewTuples) :-
2036 findall((X,Z), (avl_fetch_pair(Y,AVL,Z), %ok instead of safe_avl_member((Y,Z),AVL),; Y in AVL form, Z var
2037 %Y \= Z, % self-loops are already in initial AVLClosure, this will never add a new pair
2038 % if we use AVLClosureSoFar instead of AVL: considerably slower
2039 \+ avl_fetch((X,Z),AVLClosureSoFar)), NewTuples),
2040 add_to_avl(NewTuples,AVLClosureSoFar,Res).
2041
2042 :- use_module(bsyntaxtree,[create_negation/2]).
2043 % SUBSET_OF <:
2044 % subset_of_explicit_set: returns code to be executed if this subset check can be done in an optimized way
2045 % TO DO: add strict_subset <<: + more cases, e.g., interval & avl_set, ...
2046 % interval & interval already handled in check_subset_of_global_sets
2047 subset_of_explicit_set(AVL,Closure,Code,_WF) :- nonvar(AVL),AVL=avl_set(A),
2048 is_interval_closure_or_integerset(Closure,Low,Up),!,
2049 Code=custom_explicit_sets:check_avl_in_interval(A,Low,Up).
2050 subset_of_explicit_set(Closure,CS,Code,WF) :- nonvar(CS), is_custom_explicit_set(CS),
2051 is_interval_closure_or_integerset(Closure,Low,Up),!,
2052 Code=custom_explicit_sets:check_interval_in_custom_set(Low,Up,CS,WF).
2053 subset_of_explicit_set(AVL1,AVL2,Code,_WF) :-
2054 nonvar(AVL1),AVL1=avl_set(A1), nonvar(AVL2),AVL2=avl_set(A2),!,
2055 Code = custom_explicit_sets:check_avl_subset(A1,A2).
2056 subset_of_explicit_set(C1,AVL2,Code,_WF) :- nonvar(C1),
2057 simple_finite_set(AVL2),
2058 ? is_simple_infinite_set(C1),!, % infinite set cannot be subset of finite one
2059 Code = fail.
2060 subset_of_explicit_set(C1,C2,Code,WF) :- nonvar(C1),
2061 is_cartesian_product_closure(C1,S11,S12),!,
2062 ((S11==[] ; S12==[]) -> Code=true /* we always have a subset */
2063 ; is_definitely_not_empty(S11),
2064 is_definitely_not_empty(S12), % only use optimisation if we know S11, S12 to be non-empty
2065 nonvar(C2), is_cartesian_product_closure(C2,S21,S22),
2066 Code = (kernel_objects:check_subset_of_wf(S11,S21,WF),
2067 kernel_objects:check_subset_of_wf(S12,S22,WF) )
2068 ).
2069 subset_of_explicit_set(Set1,Set2,Code,WF) :-
2070 nonvar(Set2),is_cartesian_product_closure(Set2,S21,S22),!,
2071 % TO DO: maybe don't do this if Set1 is avl_set ??
2072 debug_println(9,'Applying C <: S21*S22 <=> C : S21 <-> S22'),
2073 Code = bsets_clp:relation_over_wf(Set1,S21,S22,WF).
2074 subset_of_explicit_set(C1,C2,Code,WF) :- nonvar(C1), nonvar(C2),
2075 ? is_powerset_closure(C1,Constructor1,Set1),
2076 ? is_powerset_closure(C2,Constructor2,Set2),
2077 subset_constructor(Constructor1,Constructor2,R),
2078 !,
2079 Code = (R=pred_true, kernel_objects:check_subset_of_wf(Set1,Set2,WF)).
2080 subset_of_explicit_set(Set1,Set2,Code,WF) :-
2081 AllowRegularClosure=false,
2082 symbolic_subset_of_explicit_set(Set1,Set2,AllowRegularClosure,Code,WF).
2083
2084 symbolic_subset_of_explicit_set(Set1,Set2,AllowRegularClosure,Code,WF) :-
2085 %print_term_summary(subset(Set1,Set2)),nl,
2086 get_subset_counter_example_closure(Set1,Set2,NewP,NewT,NewB,AllowRegularClosure,DefResult),
2087 % {x|P1} <: {x|P2} <=> {x|P1 & not(P2)}={}
2088 !, %translate:print_bexpr(NewB),nl,
2089 (DefResult==definitely_non_empty -> Code = fail
2090 ; clean_up(NewB,[],CNewB), % can be useful to apply remove_member_comprehension
2091 Code = custom_explicit_sets:is_empty_closure_wf(NewP,NewT,CNewB,WF)).
2092
2093 % get closure representing the counter examples to Set1 <: Set2: i.e. elements in Set1 and not in Set2
2094 % used for symbolic treatment of subset, not_subset and test_subset
2095 % note: in case this fails subset_test1 will expand Set1
2096 % DefiniteResultFlag may return the information that the generated closure is definitely not empty
2097 % AllowRegularClosure=false means it will only be applied for symbolic or infinite closures
2098 get_subset_counter_example_closure(Set1,Set2,NewP,NewT,NewB,AllowRegularClosure,DefiniteResultFlag) :-
2099 get_closure(Set1,P1,T1,B1),
2100 get_subset_counter_aux(P1,T1,B1,Set2,NewP,NewT,NewB,AllowRegularClosure,DefiniteResultFlag).
2101
2102 get_subset_counter_aux(P1,T1,B1,Set2,NewP,NewT,NewB,AllowRegularClosure,DefRes) :-
2103 nonvar(Set2), is_definitely_finite(Set2), !,
2104 create_couple_term(P1,T1,P1Couple), % can currently still fail for more than 2 args
2105 (is_infinite_closure(P1,T1,B1)
2106 -> DefRes=definitely_non_empty % there are definitely counter examples as Set2 is finite
2107 ; AllowRegularClosure=true -> DefRes = unknown
2108 ? ; is_symbolic_closure(P1,T1,B1) -> DefRes=unknown
2109 ),
2110 NewP=P1, NewT=T1,
2111 % {x|P1} <: {a1,...} <=> {x|P1 & x /: {a1,...}}={}
2112 get_texpr_type(P1Couple,CoupleType1),
2113 VSet2 = b(value(Set2),set(CoupleType1),[]),
2114 create_texpr(not_member(P1Couple,VSet2),pred,[],NegPred2),
2115 conjunct_predicates([B1,NegPred2],NewB).
2116 get_subset_counter_aux(P1,T1,B1,Set2,NewP,NewT,NewB,AllowRegularClosure,unknown) :-
2117 get_closure(Set2,P2,T2,B2),
2118 (AllowRegularClosure=true -> true
2119 ; is_infinite_or_symbolic_closure(P1,T1,B1) -> true
2120 % should we also allow ??
2121 % ; is_symbolic_closure(P2,T2,B2)
2122 ),
2123 % not necessary maybe as subset_test1 only expands Set1
2124 % {x|P1} <: {x|P2} <=> {x|P1 & not(P2)}={}
2125 unify_closure_predicates(P1,T1,B1, P2,T2,B2 , NewP,NewT, NewB1,NewB2),
2126 create_negation(NewB2,NegNewB2),
2127 bsyntaxtree:conjunct_predicates([NewB1,NegNewB2],NewB).
2128
2129
2130 % get_closure or infinite global set:
2131 get_closure(V,_,_,_) :- var(V),!,fail.
2132 get_closure(closure(P,T,B),P,T,B).
2133 ?get_closure(global_set(G),P,T,B) :- is_infinite_global_set(G,Type),!,
2134 ID = '_zzzz_unary',
2135 TID = b(identifier(ID),Type,[]),
2136 TSet = b(value(global_set(G)),set(Type),[]),
2137 P = [ID], T=[Type], B= b(member(TID,TSet),pred,[prob_annotation('SYMBOLIC')]).
2138
2139
2140 subset_constructor(X,X,R) :- !,R=pred_true.
2141 subset_constructor(fin1,_,R) :- !,R=pred_true.
2142 subset_constructor(fin,pow,R) :- !,R=pred_true.
2143 subset_constructor(X,Y,R) :- strict_subset_constructor(X,Y),!,R=pred_true.
2144 subset_constructor(X,Y,R) :- strict_subset_constructor(Y,X),!,R=pred_false.
2145 % pow1,fin1 ; pow,fin ; and pow1,fin only ok if type infinite
2146 strict_subset_constructor(pow1,pow).
2147 strict_subset_constructor(fin1,fin).
2148
2149 % more rules for <->, +->, ...
2150 % what if same closure: then we also know it is a subset
2151
2152 % to be completed:
2153 % code that instantiates R to subset or not_subset, may have to delay
2154 test_subset_of_explicit_set(Set1,_,_,_,_) :- var(Set1),!,fail.
2155 test_subset_of_explicit_set(avl_set(A),Closure,R,WF,Code) :-
2156 is_interval_closure_or_integerset(Closure,Low,Up),!,
2157 Code=custom_explicit_sets:test_avl_in_interval(A,Low,Up,R,WF).
2158 test_subset_of_explicit_set(_,Set2,_,_,_) :- var(Set2),!,fail.
2159 test_subset_of_explicit_set(avl_set(A1),avl_set(A2),R,_WF,Code) :-
2160 Code = (custom_explicit_sets:check_avl_subset(A1,A2) -> R=pred_true ; R=pred_false).
2161 test_subset_of_explicit_set(global_set(G),Set2,R,_WF,Code) :-
2162 ? is_infinite_global_set(G,_), % TODO: we could extend this to other infinite sets
2163 is_definitely_finite(Set2), !,
2164 Code =(R=pred_false).
2165 test_subset_of_explicit_set(Set1,Set2,Res,WF,Code) :-
2166 AllowRegular=false,
2167 get_subset_counter_example_closure(Set1,Set2,NewP,NewT,NewB,AllowRegular,DefResult),
2168 % {x|P1} <: {x|P2} <=> {x|P1 & not(P2)}={}
2169 !,
2170 (DefResult==definitely_non_empty -> Code = (Res=pred_false)
2171 ; Code = custom_explicit_sets:test_empty_closure_wf(NewP,NewT,NewB,Res,WF)
2172 ).
2173 % TO DO: add is_cartesian_product_closure case
2174 is_definitely_finite([]).
2175 is_definitely_finite(avl_set(_)).
2176
2177 :- use_module(kernel_equality,[test_interval_subset_wf/6]).
2178
2179 :- public test_avl_in_interval/5. % used in test_subset_of_explicit_set
2180 % see also check_avl_in_interval(A,Low,Up), check_avl_not_in_interval(A,Low,Up).
2181 test_avl_in_interval(A,Low2,Up2,Res,WF) :-
2182 avl_min(A,int(Min)), % not needed if Low2==minus_inf
2183 avl_max(A,int(Max)), % not needed if Up2==inf
2184 test_interval_subset_wf(Min,Max,Low2,Up2,Res,WF).
2185
2186 % ----------------------
2187
2188 is_definitely_not_empty(X) :- nonvar(X),
2189 (X=[_|_] -> true
2190 ; is_custom_explicit_set(X), is_non_empty_explicit_set(X)).
2191
2192 % check if defnitely not empty and provide a witness
2193 is_definitely_not_empty_with_witness(X,El) :- nonvar(X),
2194 get_witness_element(X,El).
2195 get_witness_element([H|_],H).
2196 get_witness_element(avl_set(node(H,_True,_,_,_)),H).
2197 % TO DO: add global_set(GS),...
2198
2199 check_avl_subset(A1,A2) :- avl_max(A1,Max1), avl_max(A2,Max2),
2200 Max1@>Max2,!, % then A1 cannot be subset of A2
2201 fail.
2202 check_avl_subset(A1,A2) :-
2203 avl_min(A1,Cur1), avl_min(A2,Cur2),
2204 check_avl_subset_loop(Cur1,A1,Cur2,A2).
2205 check_avl_subset_loop(Cur1,AVL1,Cur2,AVL2) :-
2206 (Cur1 @> Cur2 -> avl_next(Cur2,AVL2,NC2), check_avl_subset_loop(Cur1,AVL1,NC2,AVL2)
2207 ; Cur1=Cur2 -> (avl_next(Cur1,AVL1,NC1)
2208 -> avl_next(Cur2,AVL2,NC2),
2209 check_avl_subset_loop(NC1,AVL1,NC2,AVL2)
2210 ; true /* all objects of AVL1 inspected */)
2211 ).
2212
2213 % check A <: Low..Up
2214 check_avl_in_interval(A,Low,Up) :- % does not have to delay: if we have minus_inf & inf they will be known straightaway
2215 (Low==minus_inf -> true
2216 ; avl_min(A,Min), kernel_objects:less_than_equal(int(Low),Min)),
2217 (Up==inf -> true
2218 ; avl_max(A,Max), kernel_objects:less_than_equal(Max,int(Up))).
2219
2220 % some experiments:
2221 % 1..x <: {1,2,3,5} & x>1 & !y.(y>x & y<10 => 1..y /<: {1,2,3,5})
2222 % {ss | ss <: 0..0 & ss /= {} & ss=0..max(ss)}
2223 % {ss | ss <: 0..0 & ss /= {} & ss=min(ss)..max(ss)} // does not work yet
2224 % x..x+1 <: {0,2,3,5}
2225 % x..x+2 <: {0,2,3,5} // does not work yet
2226 % r = {x|x:1..400 & x mod 3/=0} & res={v|v:0..1300 & v..v+1 <: r}
2227 % check Low..Up <: Avl
2228
2229 check_interval_in_custom_set(Low,Up,CS,WF) :-
2230 Low \== minus_inf,
2231 Up \== inf,
2232 b_interpreter_check:check_arithmetic_operator('<=',Low,Up,LeqRes),
2233 (var(LeqRes) -> get_binary_choice_wait_flag_exp_backoff(16,check_interval_in_custom_set,WF,WF2) ; true),
2234 check_interval_in_custom_set_aux(LeqRes,Low,Up,CS,WF2).
2235
2236 :- block check_interval_in_custom_set_aux(-,?,?,?,-).
2237 check_interval_in_custom_set_aux(pred_true,Low,Up,CS,_WF2) :-
2238 element_of_custom_set_wf(int(Low),CS,WF),
2239 element_of_custom_set_wf(int(Up),CS,WF),
2240 interval_in_avl_block(Low,Up,CS,WF).
2241 check_interval_in_custom_set_aux(pred_false,_Low,_Up,_CS,_WF2). % Interval is empty; but infinitely many solutions for Low and Up exist in principle
2242
2243 :- block interval_in_avl_block(-,?,?,?), interval_in_avl_block(?,-,?,?).
2244 interval_in_avl_block(Low,Up,CS,WF) :-
2245 Low1 is Low+1, interval_in_avl_loop(Low1,Up,CS,WF).
2246 interval_in_avl_loop(Low,Up,_CS,_WF) :- Low>=Up,!. % Lower bound and upper bound already checked
2247 interval_in_avl_loop(Low,Up,CS,WF) :-
2248 element_of_custom_set_wf(int(Low),CS,WF), L1 is Low+1,
2249 interval_in_avl_loop(L1,Up,CS,WF).
2250
2251
2252 :- public not_check_avl_subset/2. % used in not_subset_of_explicit_set_aux
2253 not_check_avl_subset(A1,A2) :- \+ check_avl_subset(A1,A2).
2254
2255 not_subset_of_explicit_set(S1,S2,Code,WF) :- nonvar(S1),
2256 ? not_subset_of_explicit_set_aux(S1,S2,Code,WF).
2257 not_subset_of_explicit_set_aux(avl_set(A),Closure,Code,_WF) :-
2258 is_interval_closure_or_integerset(Closure,Low,Up),!,
2259 Code=custom_explicit_sets:check_avl_not_in_interval(A,Low,Up).
2260 not_subset_of_explicit_set_aux(avl_set(A1),AVL2,Code,_WF) :-
2261 nonvar(AVL2),AVL2=avl_set(A2),
2262 Code = custom_explicit_sets:not_check_avl_subset(A1,A2).
2263 not_subset_of_explicit_set_aux(CS,AVL,Code,_WF) :-
2264 ? is_simple_infinite_set(CS),
2265 % TO DO: provide code for interval/NAT/INT /<: AVL
2266 simple_finite_set(AVL),
2267 !,
2268 Code = true. % G cannot be subset of finite set
2269 not_subset_of_explicit_set_aux(C1,C2,Code,WF) :- is_cartesian_product_closure(C1,S11,S12),
2270 ((S11==[] ; S12==[]) -> Code=fail /* we always have a subset */
2271 ; is_definitely_not_empty(S11),
2272 is_definitely_not_empty(S12), % only use optimisation if we know S11, S12 to be non-empty
2273 nonvar(C2), is_cartesian_product_closure(C2,S21,S22),
2274 Code = (kernel_objects:not_both_subset_of(S11,S12, S21,S22, WF))
2275 ), !.
2276 not_subset_of_explicit_set_aux(C1,C2,Code,WF) :- nonvar(C2),
2277 ? is_powerset_closure(C1,Constructor1,Set1),
2278 ? is_powerset_closure(C2,Constructor2,Set2),
2279 subset_constructor(Constructor1,Constructor2,R),!,
2280 Code = (R=pred_false -> true ; kernel_objects:not_subset_of_wf(Set1,Set2,WF)).
2281 not_subset_of_explicit_set_aux(Set1,Set2,Code,WF) :-
2282 AllowRegular=false,
2283 get_subset_counter_example_closure(Set1,Set2,NewP,NewT,NewB,AllowRegular,DefResult),
2284 % {x|P1} <: {x|P2} <=> {x|P1 & not(P2)}={}
2285 !,
2286 (DefResult==definitely_non_empty -> Code = true
2287 ; Code = custom_explicit_sets:is_non_empty_closure_wf(NewP,NewT,NewB,WF)
2288 ).
2289
2290
2291 :- public check_avl_not_in_interval/3. % used in not_subset_of_explicit_set_aux
2292 :- block check_avl_not_in_interval(?,-,?). % TO DO: use non-blocking version, minus_inf, and inf set directly
2293 check_avl_not_in_interval(A,Low,Up) :- avl_min(A,int(Min)),
2294 check_avl_not_in_interval4(Low,Up,A,Min).
2295
2296 check_avl_not_in_interval4(Low,_Up,_A,Min) :- Low \== minus_inf, Min < Low,!.
2297 check_avl_not_in_interval4(_Low,Up,A,_Min) :-
2298 Up \== inf, avl_max(A,Max),
2299 kernel_objects:less_than(int(Up),Max). % Up could still be a variable
2300
2301
2302 % checks for simple infinite sets, without Cartesian Product, ... decomposition
2303 ?is_simple_infinite_set(global_set(X)) :- !, is_infinite_global_set(X,_).
2304 is_simple_infinite_set(CS) :- is_interval_closure_or_integerset(CS,Low,Up), infinite_interval(Low,Up).
2305
2306 simple_finite_set(AVL) :- nonvar(AVL), (AVL=avl_set(_) -> true ; AVL = []).
2307
2308 % IMAGE [.]
2309 image_for_id_closure(closure(Par,Types,Body),Set,Res) :-
2310 is_full_id_closure(Par,Types,Body),!,
2311 Res=Set.
2312
2313 image_for_explicit_set(closure(Par,Types,Body),Set,Res,WF) :-
2314 ? image_for_closure(Par,Types,Body,Set,Res,WF).
2315 image_for_explicit_set(avl_set(A),Set,Res,WF) :- nonvar(Set),
2316 image_for_explicit_avl_set(A,Set,Res,WF).
2317
2318
2319 image_for_closure(Par,Types,Body,Set,Res,_WF) :-
2320 is_id_closure_over(Par,Types,Body,ID_Domain,Full),!,
2321 (Full=true -> Res=Set ; kernel_objects:intersection(ID_Domain,Set,Res)).
2322 % infinite function case dealt with in image1 in bsets_clp
2323 % TO DO: other closure(); Maybe special case if Set is an interval ?
2324 image_for_closure(Par,Types,Body,Set,Res,WF) :-
2325 is_closure1_value_closure(Par,Types,Body,VAL), % TODO: also detect reflexive closure, iteration (iterate(rel,k))
2326 % compute closure1(VAL)[Set]
2327 ? bsets_clp:image_for_closure1_wf(VAL,Set,Res,WF).
2328
2329 is_closure1_value_closure(Par,Types,Body,VAL) :-
2330 is_member_closure(Par,Types,Body,couple(A,A),MemSET), nonvar(MemSET),
2331 MemSET = closure(V), % this is the closure1 B operator !
2332 nonvar(V), V=b(value(VAL),_,_).
2333
2334 image_for_explicit_avl_set(A,Set,Res,_WF) :- % Set is nonvar
2335 is_interval_closure_or_integerset(Set,From1,To1),!,
2336 % Note: if From1, To1 not yet known we will block and not revert to other image calculation code
2337 % Important e.g. for performance of San Juan (AdaptedBModelPropCheck/acs_as_env_cfg_ipart.mch)
2338 %we used to check for: ground(From1),ground(To1),
2339 interval_image_for_explicit_avl_set(From1,To1,A,Set,Res).
2340 image_for_explicit_avl_set(A,Set,Res,WF) :-
2341 \+ bsets_clp:keep_symbolic(Set), % in this case we fall back to treatment in bsets_clp (image1)
2342 expand_custom_set_to_list_gg(Set,ESet,GG,image_for_explicit_avl_set),
2343 empty_avl(Empty),
2344 (GG=guaranteed_ground -> image_explicit_ground(ESet,A,Empty,Res,WF)
2345 ; image_explicit(ESet,A,Empty,Res,WF)).
2346
2347 :- block interval_image_for_explicit_avl_set(-,?,?,?,?),
2348 interval_image_for_explicit_avl_set(?,-,?,?,?).
2349 interval_image_for_explicit_avl_set(From1,To1,_A,_Set,Res) :-
2350 number(From1), number(To1), From1>To1,!,
2351 kernel_objects:empty_set(Res).
2352 interval_image_for_explicit_avl_set(From1,To1,A,_Set,Res) :-
2353 findall(Image-true, avl_image_interval(From1,To1, A,Image),ImageList),
2354 normalised_list_to_avl(ImageList,ImageAvl),
2355 ? equal_object(ImageAvl,Res).
2356
2357
2358 %! singleton_set(+Set,-Element).
2359 singleton_set(X,_) :- var(X),!,fail.
2360 singleton_set([H|T],R) :- T==[], R=H.
2361 singleton_set(avl_set(node(Y,_,_,empty,empty)),Y). % same as is_one_element_custom_set
2362
2363 is_one_element_custom_set(avl_set(node(Y,_,_,empty,empty)),Y).
2364 is_one_element_avl(node(Y,_,_,empty,empty),Y).
2365
2366 % requires El to be ground
2367 construct_one_element_custom_set(El,avl_set(AVL)) :-
2368 empty_avl(E),avl_store(El,E,true,AVL).
2369
2370 construct_avl_set(Avl,Res) :- empty_avl(Avl) -> Res = [] ; Res = avl_set(Avl).
2371
2372 :- block image_explicit(-,?,?,?,?).
2373 image_explicit([],_,Acc,Res,WF) :- !,
2374 construct_avl_set(Acc,AVLS),
2375 ? kernel_objects:equal_object_wf(Res,AVLS,image_explicit,WF).
2376 image_explicit([D1|T],AVLRelation,In,Out,WF) :- !,
2377 ground_value_check(D1,G1),
2378 ((var(T);T==[]) % TO DO: see below, make propagation also interesting in other circumstances
2379 -> must_be_in_domain_check(G1,D1,T,AVLRelation,In,Out,WF)
2380 ; true),
2381 ? image_explicit_aux(G1,D1,AVLRelation,T,In,Out,WF).
2382 image_explicit(Set,_,_,_,_) :- add_error_and_fail(image_explicit,'Unknown set: ',Set).
2383
2384 % a version of image_explicit where the list is guaranteed to be ground
2385 image_explicit_ground([],_,Acc,Res,WF) :- !,
2386 construct_avl_set(Acc,AVLS),
2387 kernel_objects:equal_object_wf(Res,AVLS,image_explicit,WF).
2388 image_explicit_ground([D1|T],AVLRelation,In,Out,WF) :- !,
2389 image_explicit_aux_ground(D1,AVLRelation,T,In,Out,WF).
2390 image_explicit_ground(Set,_,_,_,_) :- add_error_and_fail(image_explicit_ground,'Unknown set: ',Set).
2391
2392 :- block must_be_in_domain_check(-,?,?,?,?,-,?),
2393 must_be_in_domain_check(-,?,-,?,?,?,?).
2394 % if result requires at least one more element, then D must be in domain of Relation
2395 % ensures that we get a domain for j in x = {1|->2,2|->4, 4|->8} & x[{j}]={8}
2396 % we could even propagate using inverse of AVLRelation ?!
2397 must_be_in_domain_check(GroundD,D,T,AVLRelation,In,Out,WF) :-
2398 T==[], % apart from D, there are no more elements to be added
2399 var(GroundD), % otherwise we already have a value for D
2400 delta_witness(In,Out,Witness), % obtain at least one value that D must map to
2401 !,
2402 quick_propagation_element_information(avl_set(AVLRelation),(D,Witness),WF,_). % Witness avoids pending co-routines
2403 % TO DO: we could check that *all* elements of Out have this value
2404 % TO DO: below we could check that In is a subset of Out; e.g., for x = %i.(i:1..10|i+i) & x[{5,j,k}]={16,11}; we could also check that Out is subset of range of relation
2405 must_be_in_domain_check(_,_D,_T,_,_In,_Out,_). % :- print(must_be(D,T,In,Out)),nl.
2406
2407 % provide, if possible, a witness element in Out not in In
2408 delta_witness(In,Out,_Witness) :- (var(In) ; var(Out)),!,fail.
2409 %delta_witness(empty,Out,Witness) :- is_definitely_not_empty_with_witness(Out,Witness).
2410 delta_witness(In,Out,Witness) :-
2411 is_custom_explicit_set(Out,delta_witness),
2412 difference_of_explicit_set(Out,avl_set(In),Diff), % could be expensive to compute !? delay ? print(delta(Diff)),nl,
2413 is_definitely_not_empty_with_witness(Diff,Witness).
2414
2415
2416 :- block image_explicit_aux(-,?,?, ?,?,?,?). % we know that D1 is ground
2417 image_explicit_aux(_,D1,AVLRelation,T,In,Out,WF) :-
2418 all_images(D1,AVLRelation,NewImages), % compute AVLRelation[{D1}]
2419 add_to_avl(NewImages,In,In2),
2420 ? image_explicit(T,AVLRelation,In2,Out,WF).
2421 image_explicit_aux_ground(D1,AVLRelation,T,In,Out,WF) :-
2422 all_images(D1,AVLRelation,NewImages), % compute AVLRelation[{D1}]
2423 add_to_avl(NewImages,In,In2),
2424 image_explicit_ground(T,AVLRelation,In2,Out,WF).
2425
2426 all_images(From,AVLRelation,Images) :-
2427 findall(AY,avl_member_pair_arg1_ground(From,AY,AVLRelation),Images). % we know From ground and AY free variable
2428 % findall(AY,safe_avl_member_pair(From,AY,AVLRelation),Images). %
2429
2430 % compute relational composition ( ; ) if second arg is an AVL set
2431 % TO DO: add support for infinite closures; avoid expanding them [currently handled by symbolic composition in bsets_clp]
2432 rel_composition_for_explicit_set(Rel1,Rel2,Comp) :- nonvar(Rel2),
2433 Rel2=avl_set(A2), % TO DO: see if we can maybe convert Rel2 to AVL ?
2434 % \+ bsets_clp:keep_symbolic(Rel1), check already done in bsets
2435 expand_custom_set_to_list_gg(Rel1,Relation1,GG,rel_composition_for_explicit_set),
2436 empty_avl(In),
2437 (GG=guaranteed_ground
2438 -> rel_avl_compose2_ground(Relation1,A2,In,Comp)
2439 ; rel_avl_compose2(Relation1,A2,In,Comp)).
2440
2441 :- block rel_avl_compose2(-,?,?,?).
2442 rel_avl_compose2([],_,In,Res) :- construct_avl_set(In,A),
2443 ? equal_object(Res,A,rel_avl_compose2). % as we delay; we need to use equal_object at the end
2444 rel_avl_compose2([(X,Y)|T],A2,In,Out) :-
2445 when((ground(X),ground(Y)),
2446 (all_image_pairs_ground(X,Y,A2,ImagePairs),
2447 add_to_avl(ImagePairs,In,In2),
2448 rel_avl_compose2(T,A2,In2,Out))).
2449
2450 % a version where argument is guaranteed to be ground; no when-ground checks
2451 rel_avl_compose2_ground([],_,In,Res) :- construct_avl_set(In,A),
2452 equal_object(Res,A,rel_avl_compose2). % as we delay; we need to use equal_object at the end
2453 rel_avl_compose2_ground([(X,Y)|T],A2,In,Out) :-
2454 all_image_pairs_ground(X,Y,A2,ImagePairs),
2455 add_to_avl(ImagePairs,In,In2),
2456 rel_avl_compose2_ground(T,A2,In2,Out).
2457
2458 %all_image_pairs(From,To,AVLRelation,ImagePairs) :-
2459 % findall((From,AY),safe_avl_member_pair(To,AY,AVLRelation),ImagePairs).
2460 all_image_pairs_ground(From,To,AVLRelation,ImagePairs) :-
2461 findall((From,AY),avl_member_pair_arg1_ground(To,AY,AVLRelation),ImagePairs).
2462 % To: already in AVL format; AY is variable -> we could use avl_fetch_pair directly : findall((From,AY),avl_fetch_pair(To,AVLRelation,AY),ImagePairs).
2463
2464 /* succeeds if it can compute domain by some clever way */
2465 domain_of_explicit_set_wf(global_set(GS),_R,_) :- !,
2466 add_error_and_fail(domain_of_explicit_set_wf,'Cannot compute domain of global set: ',GS).
2467 domain_of_explicit_set_wf(freetype(GS),_R,_) :- !,
2468 add_error_and_fail(domain_of_explicit_set_wf,'Cannot compute domain of freetype: ',GS).
2469 domain_of_explicit_set_wf(avl_set(A),Res,_) :- !,
2470 domain_of_avl_set(A,Res).
2471 domain_of_explicit_set_wf(C,R,WF) :- dom_for_specific_closure(C,Dom,_,WF),!,
2472 Dom=R.
2473 domain_of_explicit_set_wf(C,R,_) :-
2474 ? dom_symbolic(C,CC),!,
2475 R=CC.
2476 domain_of_explicit_set_wf(closure(P,T,B),Res,WF) :-
2477 % does not seem to be reached, as dom_symbolic now seems to cover all cases
2478 expand_custom_set_wf(closure(P,T,B),EC,domain_of_explicit_set,WF),
2479 domain_of_list_blocking(EC,R),
2480 normalised_list_to_avl_when_ground(R,Res).
2481
2482 % avl tree is a relation with an integer domain
2483 %avl_integer_domain(node((int(_From),_KeyTo),_True,_,_L,_R)).
2484
2485 % the first clause is in principle faster
2486 % but we don't gain time compared to treatment in second clause; we just avoid building up the domain list
2487 %domain_of_avl_set(A,Res) :- avl_integer_domain(A),
2488 % \+ avl_tools:avl_height_less_than(A,10), % try and detect interval if height >= 10
2489 % avl_is_pf_with_interval_domain(A,First,Last),!,
2490 % construct_interval_closure(First,Last,Res).
2491 domain_of_avl_set(A,Res) :-
2492 avl_domain(A,EC), % -> expand_custom_set(avl_set(A),EC),
2493 domain_of_sorted_list(EC,SizeRes,R), % size of list can be smaller than A if we have a relation
2494 (SizeRes=size_res(Size,int(Last)), R=[int(First)-true|_],
2495 Size>1000,
2496 Size is Last+1-First % we have an interval; quite common that we have functions with intervals as domain
2497 -> debug_println(19,constructing_interval_for_domain(First,Last)),
2498 construct_interval_closure(First,Last,Res)
2499 ; ord_list_to_avlset(R,Res,domain)
2500 ).
2501
2502 % check if an AVL tree represents a function with an interval domain
2503 %avl_is_pf_with_interval_domain(AVL,Min,Max) :-
2504 % avl_min(AVL,(int(Min),_)),avl_max(AVL,(int(Max),_)),
2505 % Size is 1+Max-Min, avl_size_possible(AVL,Size),
2506 % is_avl_partial_function(AVL),
2507 % % now check real size
2508 % avl_size(AVL,Size).
2509
2510 % check if an avl represents a set of integers:
2511 avl_integer_set(node(int(_TOP),_True,_,_L,_R)).
2512
2513 % check if an avl set is an interval:
2514 avl_is_interval(AVL,Min,Max) :-
2515 avl_integer_set(AVL),
2516 avl_min(AVL,int(Min)),avl_max(AVL,int(Max)),
2517 Size is 1+Max-Min,
2518 avl_size_possible(AVL,Size),
2519 avl_size(AVL,Size).
2520
2521
2522
2523 :- use_module(bsyntaxtree,[create_typed_id/3]).
2524 dom_symbolic(closure(Paras,Types,Pred), Res) :-
2525 expand_pair_closure(Paras,Types,Pred,[X,Y],[TX,TY],NewPred),
2526 !, % single argument which is a pair
2527 % simply call code for range ; inverting arguments
2528 bsyntaxtree:check_used_ids_in_ast(Pred),
2529 bsyntaxtree:check_used_ids_in_ast(NewPred),
2530 ran_symbolic_closure(Y,[X],TY,[TX],NewPred,Res).
2531 dom_symbolic(closure(Paras,Types,Pred), Res) :-
2532 append(Xs,[Y],Paras), Xs \= [],
2533 append(TXs,[TY],Types),
2534 % simply call code for range ; inverting arguments
2535 ran_symbolic_closure(Y,Xs,TY,TXs,Pred,Res).
2536 % TO DO: allow computation if Paras is a single argument and more than pair
2537
2538 % just computes domain: it can also be successful for lambda closures
2539 dom_for_specific_closure(closure(P,T,Pred),Domain,Functionality,WF) :-
2540 dom_for_specific_closure_aux(P,T,Pred,Domain,Functionality,WF).
2541 dom_for_specific_closure_aux(P,T,Pred,Domain,Functionality,_WF) :-
2542 is_lambda_value_domain_closure(P,T,Pred, DomainValue,Expr),
2543 (preference(find_abort_values,full) -> bsyntaxtree:always_well_defined_or_disprover_mode(Expr)
2544 ; true),
2545 % Warning: this will lead to dom(%x.(x:1..3|1/0)) = 1..3 to be true; discarding WD condition
2546 % this is not as bad as {1|->2}(0) = 3 to be silently failing though; hence only done if TRY_FIND_ABORT = full
2547 !,
2548 Domain=DomainValue,
2549 Functionality=function(total).
2550 %dom_for_specific_closure_aux([ID],[Type],Pred,Domain,Functionality,_WF) :- Functionality=relation,
2551 % Pred = b(exists(Paras,ClosurePred),pred,Info1),
2552 % % dom({res|#(paras).(.... & res= domVal|->ran)}) = {res|#(paras).(.... & res= domVal)}
2553 % closures:select_equality(ClosurePred,ID,RHSExpr,Type,Info,RestPred),
2554 % RHSExpr = couple(DomValue,_),
2555 % closures:does_not_occur_in(ID,RestPred),
2556 % Type = couple(DomT,_),
2557 % TID = b(identifier(ID),DomT,[]),
2558 % % safe_create_texpr
2559 % conjunct_predicates([RestPred,b(equal(TID,DomValue),pred,[])],NewClosurePred),
2560 % NewPred = b(exists(Paras,NewClosurePred),pred,Info1),
2561 % Domain = closure([ID],[DomT],NewPred).
2562 dom_for_specific_closure_aux(P,T,Pred,Domain,Functionality,WF) :-
2563 dom_range_for_specific_closure2(P,T,Pred, Domain,_Range,domain_only,Functionality,WF).
2564 %TO DO treat overwrite closure dom(F1<+F2) = dom(F1) \/ dom(F2)
2565
2566 dom_for_lambda_closure(closure(P,T,Pred),Domain) :-
2567 is_lambda_value_domain_closure(P,T,Pred, DomainValue,_Expr),
2568 Domain=DomainValue.
2569
2570 % TO DO: add total functions
2571 %dom_for_specific_closure2([F],[T],
2572 % b(member(b(identifier(F),T,_), b(total_function(value(A),B),set(couple(DOM,RAN)),_)), pred,_) ,
2573 % A).
2574
2575 :- block domain_of_list_blocking(-,?).
2576 % the list will be sorted according to the term ordering for (_,_); hence it will
2577 % already be sorted for the projection onto the first element
2578 % maybe the speed difference is not worth it ??
2579 domain_of_list_blocking([],[]).
2580 domain_of_list_blocking([(A,_B)|T],[A-true|DT]) :- domain_blocking_aux(T,A,DT).
2581 :- block domain_blocking_aux(-,?,?).
2582 domain_blocking_aux([],_,[]).
2583 domain_blocking_aux([(A,_B)|T],Prev,Res) :-
2584 compare(Comp,A,Prev),
2585 (Comp = '='
2586 -> domain_blocking_aux(T,Prev,Res)
2587 ; Res = [A-true|DT],
2588 (Comp = '<' -> add_error_fail(custom_explicit_sets,'Domain list not_sorted: ',(A,Prev)) ; true),
2589 domain_blocking_aux(T,A,DT) ).
2590
2591 % and now a non-blocking version:
2592 domain_of_sorted_list([],size_res(0,'$none'),[]).
2593 domain_of_sorted_list([(A,_B)|T],Size,[A-true|DT]) :- domain_aux(T,A,DT,1,Size).
2594
2595 % TO DO: count length and determine when we have an interval
2596 domain_aux([],Prev,[],Acc,size_res(Acc,Prev)).
2597 domain_aux([(A,_B)|T],Prev,Res,SizeAcc,Size) :- SA1 is SizeAcc+1,
2598 compare(Comp,A,Prev),
2599 (Comp = '='
2600 -> domain_aux(T,Prev,Res,SA1,Size)
2601 ; Res = [A-true|DT],
2602 (Comp = '<' -> add_error_fail(custom_explicit_sets,'Domain list not_sorted: ',(A,Prev)) ; true),
2603 domain_aux(T,A,DT,SA1,Size) ).
2604
2605 /* succeeds if it can compute domain by some clever way */
2606 range_of_explicit_set_wf(global_set(GS),_R,_) :- !,
2607 add_error_and_fail(range_of_explicit_set_wf,'Cannot compute domain of global set: ',GS).
2608 range_of_explicit_set_wf(freetype(GS),_R,_) :- !,
2609 add_error_and_fail(range_of_explicit_set_wf,'Cannot compute domain of freetype: ',GS).
2610 range_of_explicit_set_wf(avl_set(A),Res,_) :- !,
2611 avl_domain(A,EC), % -> expand_custom_set(avl_set(A),EC),
2612 range(EC,R),
2613 normalised_list_to_avl(R,Res).
2614 range_of_explicit_set_wf(C,R,WF) :-
2615 ran_for_specific_closure(C,Ran,WF),!,
2616 Ran=R.
2617 range_of_explicit_set_wf(C,R,_) :-
2618 ran_symbolic(C,CC),!,
2619 R=CC.
2620 range_of_explicit_set_wf(closure(P,T,B),Res,WF) :-
2621 expand_custom_set_wf(closure(P,T,B),EC,range_of_explicit_set_wf,WF),
2622 % TO DO: it would be more useful here to directly just expand the projection onto the last component of P
2623 range_blocking(EC,R),
2624 normalised_list_to_avl_when_ground(R,Res).
2625
2626 % TO DO: in future it is maybe better to add an in_range_wf kernel predicate
2627 ran_symbolic(closure(Paras,Types,Pred), Res) :-
2628 ? (is_memoization_closure(Paras,Types,Pred,_)
2629 -> !,fail % memoization closures can never be dealt with symbolically; we need expansion
2630 ; true),
2631 expand_pair_closure(Paras,Types,Pred,[Y,X],[TY,TX],NewPred),!,
2632 % following test (1541) works with this: 2 : ran({y|#(x).(y = x |-> x + 2 & x : NATURAL)})
2633 ran_symbolic_closure(Y,[X],TY,[TX],NewPred,Res). %, print('res: '),translate:print_bvalue(Res),nl.
2634 ran_symbolic(closure([Y,X],[TY,TX],Pred), Res) :-
2635 ran_symbolic_closure(Y,[X],TY,[TX],Pred,Res).
2636 % TO DO: treat closures with more arguments: we need to quantify Y1,...Yn [Y1,...,Yn,X]
2637
2638 % Replace single Identifier YX of type pair by pair (Y,X) where Y,X are (fresh) variables not occuring in Pred
2639 % example: {y| #(x).(y = x |-> x + 2 & x : NATURAL)} --> {y__1,y__2|#(x).(y__1 |-> y__2 = x |-> x + 2 & x : NATURAL)}
2640 expand_pair_closure([YX],[TYX],Pred,[Y,X],[TY,TX],NewPred) :- TYX = couple(TY,TX),
2641 % Replace single ID YX of type pair by pair (Y,X) where Y,X are (fresh) variables not occuring in Pred
2642 % example: {y| #(x).(y = x |-> x + 2 & x : NATURAL)} --> {y__1,y__2|#(x).(y__1 |-> y__2 = x |-> x + 2 & x : NATURAL)}
2643 % following test (1541) works with this: 2 : ran({y|#(x).(y = x |-> x + 2 & x : NATURAL)})
2644 gensym:gensym(YX,Y),gensym:gensym(YX,X),
2645 create_typed_id(Y,TY,YTID), create_typed_id(X,TX,XTID),
2646 Pair = b(couple(YTID,XTID),TYX,[]),
2647 bsyntaxtree:replace_id_by_expr(Pred,YX,Pair,NewPred).
2648
2649 :- use_module(bsyntaxtree,[create_exists_opt_liftable/3]).
2650 %:- use_module(bsyntaxtree,[add_texpr_info_if_new/3]).
2651 ran_symbolic_closure(Y,Xs,TY,TXs,Pred,Res) :-
2652 % create closure for {Xs | #Y.(Pred)} where Pred uses Y|->Xs
2653 rename_ran_ids(Xs,Pred,[],XIDs,Pred2),
2654 create_typed_id(Y,TY,YTID),
2655 create_exists_opt_liftable([YTID],Pred2,Exists), % Y is liftable as the source is a closure with all ids
2656 %bsyntaxtree:check_used_ids_in_ast(Exists),
2657 %bsyntaxtree:create_exists_opt([YTID],[Pred2],Exists), %or
2658 %b_interpreter_components:create_and_simplify_exists([YTID],Pred2,Exists),
2659 %bsyntaxtree:add_texpr_info_if_new(Exists,allow_to_lift_exists,Exists2), % leads to pending co-routines in self_checks for bsets for apply_to;
2660 % Reason: the tests ground only det WF; without lifting the exists is fully evaluated (and its waitflags with prio 2 and higher grounded) as the wait arguments are ground; with lifting only the det WF is grounded leading to pending coroutines
2661 Res = closure(XIDs,TXs,Exists).
2662
2663
2664
2665 :- use_module(library(lists),[select/3]).
2666
2667 % rename lambda_results :
2668 rename_ran_ids([],Pred,_,[],Pred).
2669 rename_ran_ids([X|TX],Pred,Acc,[XID|TTX],Pred2) :-
2670 % in case X is _lambda_result_ we need to rename it as it then would not get enumerated !
2671 (X == '_lambda_result_'
2672 -> get_fresh_id('_was_lambda_result_',TX,Acc,XID),
2673 % we could remove lambda_result info field, but it will no longer match new id anyway
2674 ? rename_bt(Pred,[rename(X,XID)],Pred2),
2675 TTX=TX
2676 % TODO: maybe we should also remove the prob_annotation('LAMBDA-EQUALITY') info inside Pred for the ids and equality !?
2677 ? ; XID = X, rename_ran_ids(TX,Pred,[X|Acc],TTX,Pred2)
2678 ).
2679
2680 :- use_module(b_ast_cleanup,[get_unique_id/2]).
2681 get_fresh_id(ID,List1,List2,Res) :- nonmember(ID,List1), nonmember(ID,List2),!, Res=ID.
2682 get_fresh_id(ID,_,_,FRESHID) :- nl,print('*** VARIABLE_CLASH PREVENTED: '), print(ID),nl,
2683 get_unique_id(ID,FRESHID).
2684
2685 :- block range_blocking(-,?).
2686 range_blocking([],[]).
2687 range_blocking([(_A,B)|T],[B-true|DT]) :- range_blocking(T,DT).
2688 % and a non-blocking version:
2689 range([],[]).
2690 range([(_A,B)|T],[B-true|DT]) :- range(T,DT).
2691
2692 ran_for_specific_closure(closure(P,T,Pred),Range,WF) :-
2693 dom_range_for_specific_closure2(P,T,Pred, _Domain,Range,range_only,_Functionality,WF).
2694 %ran_for_specific_closure(closure_x(P,T,Pred,_Exp),Card,_) :- ran_for_specific_closure2(P,T,Pred,Card).
2695
2696 :- use_module(bsyntaxtree,[conjunct_predicates/2, disjunct_predicates/2, create_typed_id/3, get_texpr_type/2]).
2697 override_custom_explicit_set_wf(R,S,Res,WF) :- /* R <+ S */
2698 ? nonvar(R),override_custom_explicit_set_aux(R,S,Res,WF).
2699 override_custom_explicit_set_aux(CL,Rel2,Res,_WF) :-
2700 CL=closure(P0,T,B0),
2701 ( preference(convert_comprehension_sets_into_closures,true), % cf keep_symbolic in bsets_clp
2702 (var(Rel2) -> true
2703 ; Rel2 \= avl_set(_)) % if Rel2 is avl_set then maybe better to compute explicitly; unless infinite
2704 ; quick_size_check_larger_than(Rel2,Size2,133) ->
2705 % if we have a large AVL set anyway; then allow expansion up to a larger limit; cf machine 670_002.mch
2706 % a lot of machines use A*B*C <+ {....} to more compactly define large explicit sets
2707 (Size2=inf -> Limit = 200000
2708 ; Limit is min(200000,Size2*150)),
2709 dont_expand_this_closure(P0,T,B0,Limit)
2710 ; dont_expand_this_closure(P0,T,B0) % use default limit and checks for symbolic closure
2711 ),
2712 !,
2713 ? rename_ran_ids(P0,B0,[],P,B), % any '_lambda_result_' id is no longer guaranteed to be assigned a value in all cases
2714 NewClosure=closure(P,T,NewBody),
2715 % B <+ Rel2 ---> NewBody = P:Rel2 or (prj1(P) /: dom(Rel2) & B)
2716 % TODO better? : %x.(x:Domain|IF x:dom(SFF) THEN SFF(x) ELSE DEFAULT)?
2717 generate_typed_id_pairs(P,T,NestedPairs),
2718 get_texpr_type(NestedPairs,PairsType),
2719 RelPairsType = set(PairsType),
2720 ValS = b(value(Rel2),RelPairsType,[]),
2721 MemS = b(member(NestedPairs,ValS),pred,[]), % P:Rel2
2722 get_prj1(NestedPairs,DomExpr),
2723 get_texpr_type(DomExpr,DomType),
2724 Domain = b(domain(ValS),set(DomType),[]), % TO DO: perform some optimisations like dom(%x.(P|E)) --> {x|P}
2725 %bsets_clp:domain_wf(Rel2,DomainOfRel2,WF), Domain = b(value(DomainOfRel2),DomType,[]), % this DOES NOT work for 1619, 1706 where override is used for infinite functions
2726 NotMemDomS = b(not_member(DomExpr,Domain),pred,[]), % prj1(P) /: dom(Rel2)
2727 conjunct_predicates([NotMemDomS,B],RHS),
2728 disjunct_predicates([MemS,RHS],NewBody),
2729 %print(override),nl, bsyntaxtree:check_used_ids_in_ast(NewBody),
2730 mark_closure_as_symbolic(NewClosure,Res).
2731 % TO DO: add a case where for second set we have: dont_expand_this_closure
2732 override_custom_explicit_set_aux(R,S,Res,WF) :-
2733 is_custom_explicit_set(R,override_custom_explicit_set),
2734 nonvar(S), is_custom_explicit_set(S,override_custom_explicit_set),
2735 %% hit_profiler:add_profile_hit(override(R,S),3), %%
2736 override_custom_explicit_set2(R,S,Res,WF).
2737
2738 override_custom_explicit_set2(R,S,Res,_WF) :- is_one_element_custom_set(S,(X,Y)),
2739 override_pair_explicit_set(R,X,Y,NewR),!,
2740 Res=NewR.
2741 % TO DO: if R is very large and S relatively small : iterate by calling override_pair_explicit_set
2742 override_custom_explicit_set2(R,S,Res,WF) :-
2743 expand_custom_set_wf(R,ER,override_custom_explicit_set_aux1,WF),
2744 expand_custom_set_wf(S,ES,override_custom_explicit_set_aux2,WF),
2745 override_list(ER,ES,LRes,Done),
2746 finish_restriction(Done,LRes,Res).
2747
2748 quick_size_check_larger_than(Set,Size,Limit) :-
2749 quick_custom_explicit_set_approximate_size(Set,Size),
2750 (is_inf_or_overflow_card(Size) -> true ; Size > Limit).
2751 get_prj1(b(couple(DomExpr,_),_,_),Prj1) :- !, Prj1 = DomExpr.
2752 get_prj1(BE,b(first_of_pair(BE),DT,[])) :- % some closures have a single identifier; we need to apply prj1
2753 BE = b(_E,couple(DT,_RT),_I).
2754
2755 % translate a parameter name and type list into a nested-pair value
2756 generate_typed_id_pairs([ID|IT],[Type|TT],Res) :- create_typed_id(ID,Type,TypedID),
2757 conv2(IT,TT,TypedID,Res).
2758 conv2([],[],X,X).
2759 conv2([ID|IT],[Type|TT],Acc,Res) :- create_typed_id(ID,Type,TypedID),
2760 get_texpr_type(Acc,AccType),
2761 Couple = b(couple(Acc,TypedID),couple(AccType,Type),[]),
2762 conv2(IT,TT,Couple,Res).
2763
2764 :- block override_list(-,?,?,?), override_list(?,-,?,?).
2765 override_list([],S,Res,Done) :- !, copy_to_true_list(S,Res,Done).
2766 override_list(R,[],Res,Done) :- !, copy_to_true_list(R,Res,Done).
2767 override_list([(From1,To1)|T1],[(From2,To2)|T2],Res,Done) :-
2768 (From1 @< From2
2769 -> Res = [(From1,To1)-true|TR], override_list(T1,[(From2,To2)|T2],TR,Done)
2770 ; From2 @< From1
2771 -> Res = [(From2,To2)-true|TR], override_list([(From1,To1)|T1],T2,TR,Done)
2772 ; override_list(T1,[(From2,To2)|T2],Res,Done)).
2773
2774 :- block copy_to_true_list(-,?,?).
2775 % add -true to get lists that can be converted to avl
2776 copy_to_true_list([],[],true).
2777 copy_to_true_list([H|T],[H-true|CT],Done) :- copy_to_true_list(T,CT,Done).
2778
2779 :- use_module(closures,[get_domain_range_for_closure_types/3]).
2780 % compute a closure with the functionality violations of a closure
2781 symbolic_functionality_check_closure(closure(P,T,B),closure([DID,ID1,ID2],[DomType,RanType,RanType],Body)) :-
2782 % construct {d,z_,z__| (d,z_):R & (d,z__):R & z_\= z__}
2783 generate_typed_id_pairs(P,T,NestedPairs),
2784 get_texpr_type(NestedPairs,PairsType),
2785 RelPairsType = set(PairsType),
2786 TRel = b(value(closure(P,T,B)),RelPairsType,[]),
2787 DID = '_domain', ID1 = '_zzzz_unary', ID2 = '_zzzz_binary',
2788 TDID = b(identifier(DID),DomType,[]),
2789 TID1 = b(identifier(ID1),RanType,[]),
2790 TID2 = b(identifier(ID2),RanType,[]),
2791 Mem1 = b(member( b(couple(TDID,TID1),PairsType,[]),TRel),pred,[]),
2792 Mem2 = b(member( b(couple(TDID,TID2),PairsType,[]),TRel),pred,[]),
2793 get_domain_range_for_closure_types(T,DomType,RanType),
2794 NeqRan = b(not_equal(TID1,TID2), pred, []),
2795 conjunct_predicates([Mem1,Mem2,NeqRan],Body),
2796 bsyntaxtree:check_used_ids_in_ast(Body).
2797 %bsyntaxtree:check_ast(Body).
2798
2799 % compute a closure with the injectivity violations of a closure
2800 symbolic_injectivity_check_closure(closure(P,T,B),closure([RID,ID1,ID2],[RanType,DomType,DomType],Body)) :-
2801 % construct {r,z_,z__| (z_,r):R & (z__,r):R & z_\= z__}
2802 generate_typed_id_pairs(P,T,NestedPairs),
2803 get_texpr_type(NestedPairs,PairsType),
2804 RelPairsType = set(PairsType),
2805 TRel = b(value(closure(P,T,B)),RelPairsType,[]), % what if closure body B has WD condition?
2806 RID = '_range', ID1 = '_zzzz_unary', ID2 = '_zzzz_binary',
2807 TRID = b(identifier(RID),RanType,[]),
2808 TID1 = b(identifier(ID1),DomType,[]),
2809 TID2 = b(identifier(ID2),DomType,[]),
2810 Mem1 = b(member( b(couple(TID1,TRID),PairsType,[]),TRel),pred,[]),
2811 Mem2 = b(member( b(couple(TID2,TRID),PairsType,[]),TRel),pred,[]),
2812 get_domain_range_for_closure_types(T,DomType,RanType),
2813 NeqRan = b(not_equal(TID1,TID2), pred, []),
2814 conjunct_predicates([Mem1,Mem2,NeqRan],Body),
2815 bsyntaxtree:check_used_ids_in_ast(Body).
2816 %bsyntaxtree:check_ast(Body).
2817
2818 % -------------------------
2819
2820
2821 % check whether we have a partial function
2822 is_avl_partial_function(empty) :- !.
2823 is_avl_partial_function(node((KeyFrom,_KeyTo),_True,_,L,R)) :- !,
2824 is_avl_partial_function2(L,'$$MIN$$',KeyFrom),
2825 is_avl_partial_function2(R,KeyFrom,'$$MAX$$').
2826 is_avl_partial_function(X) :- add_internal_error('Not avl_set or relation: ',is_avl_partial_function(X)),fail.
2827
2828 % we traverse the tree from top to bottom, keeping track of possible upper- and lower-bounds
2829 % if any value matches the upper or lower bound, the we do not have a partial function
2830 is_avl_partial_function2(empty,_,_).
2831 is_avl_partial_function2(node((KeyFrom,_KeyTo),_True,_,L,R),ParentFrom,ParentTo) :-
2832 KeyFrom \= ParentFrom, KeyFrom \= ParentTo,
2833 is_avl_partial_function2(L,ParentFrom,KeyFrom),
2834 is_avl_partial_function2(R,KeyFrom,ParentTo).
2835
2836 % the dual of the above, returning a counter example
2837 is_not_avl_partial_function(node((KeyFrom,_KeyTo),_True,_,L,R),DuplicateKey) :- !,
2838 (is_not_avl_partial_function2(L,'$$MIN$$',KeyFrom,DuplicateKey) -> true
2839 ; is_not_avl_partial_function2(R,KeyFrom,'$$MAX$$',DuplicateKey)).
2840 is_not_avl_partial_function2(node((KeyFrom,_KeyTo),_True,_,L,R),ParentFrom,ParentTo,DuplicateKey) :-
2841 ( KeyFrom = ParentFrom -> DuplicateKey=KeyFrom
2842 ; KeyFrom = ParentTo -> DuplicateKey=KeyFrom
2843 ; is_not_avl_partial_function2(L,ParentFrom,KeyFrom,DuplicateKey) -> true
2844 ; is_not_avl_partial_function2(R,KeyFrom,ParentTo,DuplicateKey) -> true).
2845
2846
2847 % check whether we have a function which is total over a given domain; both as AVL sets
2848 is_avl_total_function_over_domain(empty,empty) :- !.
2849 is_avl_total_function_over_domain(AVLFun,AVLDom) :-
2850 avl_domain(AVLFun,FunList),
2851 avl_domain(AVLDom,DomList),
2852 is_avl_total_fun2(FunList,DomList).
2853
2854 is_avl_total_fun2([],[]).
2855 is_avl_total_fun2([(From,_To)|FT],[From|DomT]) :- is_avl_total_fun2(FT,DomT).
2856
2857
2858 %not_is_avl_partial_function(AVLF) :- \+ is_avl_partial_function(AVLF).
2859
2860 :- use_module(kernel_equality,[membership_test_wf/4]).
2861 % check whether an AVL Relation is not over a specific domain & range
2862 is_not_avl_relation_over_domain_range(AVLRel,Domain,Range,WF) :- AVLRel \= empty,
2863 avl_min_pair(AVLRel,RFrom,RTo),
2864 membership_test_wf(Domain,RFrom,MemRes,WF),
2865 is_not_avl_rel_dom1(MemRes,RFrom,RTo,AVLRel,Domain,Range,WF).
2866
2867 :- block is_not_avl_rel_dom1(-, ?,?,?,?,?,?).
2868 is_not_avl_rel_dom1(pred_false,_,_,_,_,_,_WF).
2869 is_not_avl_rel_dom1(pred_true,RFrom,RTo,AVLRel,Domain,Range,WF) :-
2870 membership_test_wf(Range,RTo,MemRes,WF),
2871 is_not_avl_rel_dom2(MemRes,RFrom,RTo,AVLRel,Domain,Range,WF).
2872
2873 :- block is_not_avl_rel_dom2(-, ?,?,?,?,?,?).
2874 is_not_avl_rel_dom2(pred_false,_,_,_,_,_,_WF).
2875 is_not_avl_rel_dom2(pred_true,RFrom,RTo,AVLRel,Domain,Range,WF) :-
2876 avl_next((RFrom,RTo),AVLRel,(RFrom2,RTo2)),
2877 membership_test_wf(Domain,RFrom2,MemRes,WF),
2878 is_not_avl_rel_dom1(MemRes,RFrom2,RTo2,AVLRel,Domain,Range,WF).
2879
2880 % check whether an AVL Relation is not over a specific range
2881 is_not_avl_relation_over_range(AVLRel,Range,WF) :- AVLRel \= empty,
2882 avl_min_pair(AVLRel,RFrom,RTo),
2883 membership_test_wf(Range,RTo,MemRes,WF),
2884 is_not_avl_rel_ran2(MemRes,RFrom,RTo,AVLRel,Range,WF).
2885
2886 :- block is_not_avl_rel_ran2(-, ?,?,?,?,?).
2887 is_not_avl_rel_ran2(pred_false,_,_,_,_,_WF).
2888 is_not_avl_rel_ran2(pred_true,RFrom,RTo,AVLRel,Range,WF) :-
2889 avl_next((RFrom,RTo),AVLRel,(RFrom2,RTo2)),
2890 kernel_equality:membership_test_wf(Range,RTo2,MemRes,WF),
2891 is_not_avl_rel_ran2(MemRes,RFrom2,RTo2,AVLRel,Range,WF).
2892
2893 % check whether we have a relation
2894 is_avl_relation(node((_KeyFrom,_KeyTo),_True,_,_,_)).
2895
2896 % check whether a Relation has all its range elments in a certain Range (not necessarily AVL)
2897 % TO DO: if Domain is an interval: we could take avl_min and avl_max and rely on lexicographic ordering
2898 is_avl_relation_over_domain(AVL,IntervalClosure,_WF) :-
2899 is_interval_closure_or_integerset(IntervalClosure,Low,Up),!,
2900 ((avl_min(AVL,(int(ALow),_)), avl_max(AVL,(int(AUp),_)))
2901 -> cs_greater_than_equal(ALow,Low), cs_greater_than_equal(Up,AUp) %,print(ok),nl
2902 ; (AVL=empty -> true ; add_error_and_fail(is_avl_relation_over_domain,'Not a relation with integer domain: ',AVL))).
2903 is_avl_relation_over_domain(_,Domain,_) :-
2904 quick_is_definitely_maximal_set(Domain),!.
2905 %is_definitely_maximal_set(Domain),!.
2906 is_avl_relation_over_domain(AVL,Domain,WF) :- is_avl_relation_over_domain2(AVL,Domain,WF).
2907 is_avl_relation_over_domain2(empty,_,_).
2908 is_avl_relation_over_domain2(node((KeyFrom,_KeyTo),_,_,L,R), Domain,WF) :-
2909 is_avl_relation_over_domain2(L, Domain,WF),
2910 is_avl_relation_over_domain2(R, Domain,WF),
2911 kernel_objects:check_element_of_wf(KeyFrom,Domain,WF).
2912
2913 % : faster to check than is_definitely_maximal_set
2914 quick_is_definitely_maximal_set(X) :- nonvar(X),
2915 quick_is_definitely_maximal_set_aux(X).
2916 quick_is_definitely_maximal_set_aux(global_set(GS)) :-
2917 nonvar(GS),is_maximal_global_set(GS).
2918 quick_is_definitely_maximal_set_aux(avl_set(AVL)) :-
2919 quick_definitely_maximal_set_avl(AVL).
2920
2921 % check whether a Relation has all its range elments in a certain Range (not necessarily AVL)
2922
2923
2924
2925 is_avl_relation_over_range(empty,_,_) :- !.
2926 is_avl_relation_over_range(_,Range,_) :-
2927 %quick_is_definitely_maximal_set(Range),
2928 is_definitely_maximal_set(Range),
2929 !.
2930 is_avl_relation_over_range(AVL,Range,WF) :- is_avl_relation_over_range2(AVL,Range,WF).
2931
2932 is_avl_relation_over_range2(empty,_,_).
2933 is_avl_relation_over_range2(node((_KeyFrom,KeyTo),_,_,L,R), Range,WF) :-
2934 is_avl_relation_over_range(L, Range,WF),
2935 kernel_objects:check_element_of_wf(KeyTo,Range,WF),
2936 is_avl_relation_over_range2(R, Range,WF).
2937
2938 % safe version of is_avl_sequence, does not throw error when type cannot be a sequence
2939 safe_is_avl_sequence(empty) :- !.
2940 safe_is_avl_sequence(node((int(KeyFrom),_KeyTo),_True,_,L,R)) :- !,
2941 is_avl_sequence2(L,0,KeyFrom),
2942 is_avl_sequence2(R,KeyFrom,'$$MAX$$').
2943
2944 is_avl_sequence(empty) :- !.
2945 is_avl_sequence(node((int(KeyFrom),_KeyTo),_True,_,L,R)) :- !,
2946 is_avl_sequence2(L,0,KeyFrom),
2947 is_avl_sequence2(R,KeyFrom,'$$MAX$$').
2948 is_avl_sequence(X) :- add_error_and_fail(is_avl_sequence,'Not avl_set or sequence: ',X).
2949
2950 % we traverse the tree from top to bottom, keeping track of possible upper- and lower-bounds
2951 % if any value matches the upper or lower bound, the we do not have a partial function
2952 is_avl_sequence2(empty,X,Y) :-
2953 (Y=='$$MAX$$' -> true ; Y is X+1). % otherwise there is a gap in the sequence
2954 is_avl_sequence2(node((int(KeyFrom),_KeyTo),_,_,L,R),ParentFrom,ParentTo) :-
2955 KeyFrom > ParentFrom, KeyFrom \= ParentTo,
2956 is_avl_sequence2(L,ParentFrom,KeyFrom),
2957 is_avl_sequence2(R,KeyFrom,ParentTo).
2958
2959 % for performance: it is not worthwhile to make a version that checks that
2960 % we have a sequence over a range using a single traversal
2961
2962
2963 % get avl_sequence elements as sorted list (without indices)
2964 % used by external function REPLACE
2965 get_avl_sequence(AVL,SeqList) :-
2966 get_avl_sequence_dcg(AVL,SeqList,[]).
2967
2968 get_avl_sequence_dcg(empty) --> [].
2969 get_avl_sequence_dcg(node((int(_),SeqEl),_True,_,L,R)) -->
2970 get_avl_sequence_dcg(L),
2971 [SeqEl],
2972 get_avl_sequence_dcg(R).
2973
2974
2975 % ---------------------------
2976 prefix_of_custom_explicit_set(avl_set(A),MinIndex,Result,WF) :-
2977 size_of_avl_sequence(A,Size,WF),
2978 (MinIndex > Size
2979 -> add_wd_error('index larger than size of sequence in prefix_sequence (/|\\)! ', '>'(MinIndex,Size),WF)
2980 % ; MinIndex = 0 -> Result = [] % case already treated in bsets_clp
2981 ; MinIndex = Size -> Result=avl_set(A)
2982 ; prefix_of_custom_explicit_set2(A,MinIndex,OrdList,[]),
2983 ord_list_to_avlset(OrdList,Result,prefix_of_custom_explicit_set)
2984 ).
2985 prefix_of_custom_explicit_set2(empty,_MaxIndex) --> {true}.
2986 prefix_of_custom_explicit_set2(node((int(KeyFrom),KeyTo),_True,_,L,R),MaxIndex) -->
2987 ({KeyFrom = MaxIndex}
2988 -> prefix_of_custom_explicit_set2(L,MaxIndex), [((int(KeyFrom),KeyTo)-true)]
2989 ; {KeyFrom > MaxIndex} -> prefix_of_custom_explicit_set2(L,MaxIndex)
2990 ; prefix_of_custom_explicit_set2(L,MaxIndex), [((int(KeyFrom),KeyTo)-true)],
2991 prefix_of_custom_explicit_set2(R,MaxIndex)
2992 ).
2993
2994 % size is only well-defined for sequences:
2995 size_of_custom_explicit_set(avl_set(AVL),int(Size),WF) :- size_of_avl_sequence(AVL,Size,WF).
2996 size_of_custom_explicit_set(closure(P,T,B),Res,WF) :-
2997 is_lambda_value_domain_closure(P,T,B, DomainValue,_Expr),
2998 kernel_cardinality_attr:finite_cardinality_as_int_wf(DomainValue,Res,WF).
2999 size_of_avl_sequence(AVL,Size,WF) :-
3000 preference(find_abort_values,true),
3001 \+ is_avl_sequence(AVL),!,
3002 avl_max_pair(AVL,int(Sz),_),
3003 add_wd_error('Applying size to a value which is not a sequence',b(value(avl_set(AVL)),seq(any),[]),WF),
3004 Size=Sz. % other calls to size_of_avl_sequence currently expect a value
3005 size_of_avl_sequence(AVL,Size,WF) :-
3006 % TO DO: checking minimum is 1?
3007 avl_max_pair(AVL,int(Sz),_),
3008 avl_height(AVL,H), % we cannot compute the height together with max; we need the longest path!
3009 get_min_max_card(H,MinSize,MaxSize),
3010 %avl_size(AVL,Real),format('AVL SeqSize: ~w, height: ~w, real size:~w, min: ~w, max: ~w~n',[Sz,H,Real,MinSize,MaxSize]),
3011 (Sz > MaxSize
3012 -> add_wd_error('Applying size to a value which is not a sequence (maximum index too large)',b(value(avl_set(AVL)),seq(any),[]),WF),
3013 avl_size(AVL,Size)
3014 % triggered by e.g. size({0|->1,0|->2,1|->3}) or size({0|->1,1|->2,3|->3,1|->22,1|->23,1|->24,1|->25,1|->26})
3015 ; Sz < MinSize
3016 -> add_wd_error('Applying size to a value which is not a sequence (maximum index too small)',b(value(avl_set(AVL)),seq(any),[]),WF),
3017 avl_size(AVL,Size)
3018 % triggered by e.g. size([0,2,2,2] |> {2})
3019 ; Size=Sz).
3020
3021 get_min_max_card(Height,MinCard,MaxCard) :-
3022 % page 460, Knuth 3: The height of a balanced tree with N internal nodes always lies between lg(N+1) and 1.4405 lg(N+2) - 0.3277
3023 MaxCard is 2^Height - 1,
3024 % 1.618034 is golden ration phi 0.5(1+sqrt(5)) , 2.236068 is sqrt(5)
3025 % proof in Knuth uses fact: N > phi^(h+2)/sqrt(5) - 2
3026 MinCard is ceiling((1.61803398875**(Height+2)) / 2.2360679775 - 2).
3027
3028 % check if a candidate size is possible given height:
3029 avl_size_possible(AVL,SizeCandidate) :-
3030 avl_height(AVL,Height), % TO DO: restrict to something like log2 of Height
3031 get_min_max_card(Height,MinCard,MaxCard),
3032 MinCard =< SizeCandidate,
3033 SizeCandidate =< MaxCard.
3034
3035
3036 suffix_of_custom_explicit_set(avl_set(A),MinIndex,Result,WF) :-
3037 size_of_avl_sequence(A,Size,WF),
3038 (MinIndex > Size
3039 -> add_wd_error('index larger than size of sequence in suffix_sequence (\\|/)! ', '>'(MinIndex,Size),WF)
3040 % ; MinIndex = 0 -> Result = avl_set(A) % case already treated in bsets_clp
3041 ; MinIndex = Size -> Result=[]
3042 ; suffix_of_custom_explicit_set2(A,MinIndex,OrdList,[]),
3043 ord_list_to_avlset(OrdList,Result,suffix_of_custom_explicit_set)
3044 ).
3045 suffix_of_custom_explicit_set2(empty,_MinIndex) --> {true}.
3046 suffix_of_custom_explicit_set2(node((int(KeyFrom),KeyTo),_True,_,L,R),MinIndex) -->
3047 ({KeyFrom =< MinIndex} -> suffix_of_custom_explicit_set2(R,MinIndex)
3048 ; {ShiftedKeyFrom is KeyFrom-MinIndex},
3049 ({KeyFrom =:= MinIndex+1}
3050 -> {true} ; suffix_of_custom_explicit_set2(L,MinIndex)),
3051 [((int(ShiftedKeyFrom),KeyTo)-true)],
3052 suffix_of_custom_explicit_set2(R,MinIndex)
3053 ).
3054
3055 shift_avl_sequence_to_ord_list(AVL,Offset,ShiftedOrdList) :-
3056 avl_to_list(AVL,List),shift_seq(List,Offset,ShiftedOrdList).
3057 % it does not seem to be worth to use avl_to_list_dcg_offset or a variation thereof
3058 % it is not really slower to do two traversals (avl_to_list and shift_seq)
3059
3060 shift_seq([],_,[]).
3061 shift_seq([(int(I),Val)-true|T],Offset,[(int(NI),Val)-true|ST]) :- NI is I+Offset,
3062 shift_seq(T,Offset,ST).
3063
3064 :- use_module(debug).
3065 concat_custom_explicit_set(avl_set(S1),Seq2,Res,WF) :- nonvar(Seq2), Seq2=avl_set(S2),
3066 size_of_avl_sequence(S1,Size1,WF),
3067 shift_avl_sequence_to_ord_list(S2,Size1,OL2),
3068 % if OL2 is small we could use avl_store like in append_custom_explicit_set
3069 %avl_to_list(S1,OL1),
3070 avl_to_list_dcg(S1,NewOrdList,OL2), % use OL2 rather than [] as tail
3071 %append(OL1,OL2,NewOrdList), % we could avoid traversing OL1 again by doing a custom avl_to_list/3 which specifies tail
3072 ord_list_to_avlset(NewOrdList,Res,concat). % , print_term_summary(res_concat(Res)).
3073
3074 % a DCG version of avl_to_list; allows to call it with something else than [] as tail
3075 avl_to_list_dcg(empty) --> [].
3076 avl_to_list_dcg(node(Key,Val,_,L,R)) -->
3077 avl_to_list_dcg(L), [(Key-Val)],
3078 avl_to_list_dcg(R).
3079
3080 /* conc: concatenation of sequence of sequences (general_concat) */
3081 conc_custom_explicit_set(avl_set(AVL),Res) :-
3082 avl_min_pair(AVL,int(ONE),First),
3083 conc2_cs(First,ONE,AVL,0,NewOrdList),
3084 ord_list_to_avlset(NewOrdList,Res,conc).
3085
3086 conc2_cs(Seq,NrSeq,AVL,Offset,OrdList) :-
3087 add_seq(Seq,Offset,OrdList,NewOffset,TailOrd),
3088 (avl_next((int(NrSeq),Seq),AVL,(int(N2),Seq2))
3089 -> conc2_cs(Seq2,N2,AVL,NewOffset,TailOrd)
3090 ; TailOrd=[]).
3091
3092 add_seq([],Offset,OrdRes,NewOffset,TailOrdRes) :- NewOffset=Offset, TailOrdRes=OrdRes.
3093 add_seq(avl_set(ASeq),Offset,OrdRes,NewOffset,TailOrd) :-
3094 avl_to_list_dcg_offset(ASeq,Offset,NrEls,OrdRes,TailOrd), NewOffset is Offset+NrEls.
3095
3096 % a version of avl_to_list for sequences which autmatically adds an offset
3097 avl_to_list_dcg_offset(empty,_,0) --> [].
3098 avl_to_list_dcg_offset(node((int(Idx),El),Val,_,L,R),Offset,NrEls) -->
3099 {NIdx is Idx+Offset},
3100 avl_to_list_dcg_offset(L,Offset,N1),
3101 [((int(NIdx),El)-Val)],
3102 avl_to_list_dcg_offset(R,Offset,N2), {NrEls is N1+N2+1}.
3103
3104 prepend_custom_explicit_set(avl_set(S1),ObjectToPrepend,Res) :-
3105 %hit_profiler:add_profile_hit(prepend_custom_explicit_set(avl_set(S1),ObjectToPrepend,Res)),
3106 element_can_be_added_or_removed_to_avl(ObjectToPrepend),
3107 shift_avl_sequence_to_ord_list(S1,1,OL1),
3108 ord_list_to_avlset([(int(1),ObjectToPrepend)-true|OL1],Res).
3109
3110 append_custom_explicit_set(avl_set(S1),ObjectToAppend,Res,WF) :-
3111 element_can_be_added_or_removed_to_avl(ObjectToAppend), % implies that ObjectToAppend is ground
3112 size_of_avl_sequence(S1,Size1,WF), NewSize is Size1+1,
3113 add_ground_element_to_explicit_set_wf(avl_set(S1),(int(NewSize),ObjectToAppend),Res,WF).
3114
3115 % compute tail of a sequence and also return first element
3116 tail_sequence_custom_explicit_set(avl_set(S1),First,Res,Span,WF) :-
3117 shift_avl_sequence_to_ord_list(S1,-1,NewOrdList),
3118 (NewOrdList = [(int(0),First)-true|TailOL] -> ord_list_to_avlset(TailOL,Res)
3119 ; add_wd_error_span('tail argument is not a sequence!', avl_set(S1),Span,WF)
3120 % add_error_fail(tail_sequence,'tail applied to ', NewOrdList))
3121 ).
3122 last_sequence_explicit_set(avl_set(AVL),Last) :-
3123 avl_max_pair(AVL,int(_Sz),Last).
3124 % TO DO: we could compute height of the path to max H, then check that Sz is in 2**(H-1)+1 .. 2**(H+1)-1 ?
3125 %first_sequence_explicit_set(avl_set(AVL),First) :- % not used anymore; apply_to used instead
3126 % avl_min_pair(AVL,int(_One),First).
3127
3128 % compute front and return last element at the same time
3129 front_sequence_custom_explicit_set(avl_set(AVL),Last,Res) :-
3130 avl_max_pair(AVL,int(Size),Last),
3131 direct_remove_element_from_avl(AVL, (int(Size),Last), Res). % we know Last is already in AVL-converted format
3132
3133
3134 reverse_custom_explicit_set(avl_set(AVL),Res) :-
3135 avl_to_list_dcg_offset(AVL,0,Size,List,[]),
3136 S1 is Size+1,
3137 reverse_list(List,S1,[],RevList),
3138 ord_list_to_avl(RevList,RevAVL),
3139 Res=avl_set(RevAVL).
3140
3141 reverse_list([],_,Acc,Acc).
3142 reverse_list([(int(Idx),El)-V|T],S1,Acc,Res) :-
3143 NewIdx is S1 - Idx,
3144 reverse_list(T,S1,[(int(NewIdx),El)-V|Acc],Res).
3145
3146 % check if a relation is injective ; compute range at the same time; note AVL can be empty
3147 is_injective_avl_relation(AVL,RangeRes) :-
3148 avl_domain(AVL,ElList),
3149 empty_avl(EmptyAcc),
3150 is_avl_inj_list(ElList,EmptyAcc,Range),
3151 construct_avl_set(Range,RangeRes).
3152
3153 is_avl_inj_list([],Range,Range).
3154 is_avl_inj_list([(_From,To)|T],InRange,OutRange) :-
3155 (avl_fetch(To,InRange) -> fail /* this is not an injection; a range element is repeated */
3156 ; avl_store(To,InRange,true,InRange1),
3157 is_avl_inj_list(T,InRange1,OutRange)
3158 ).
3159
3160 % Example predicates that work with code below:
3161 % card(id((1..1000)*(1..1000))~)=1000*1000
3162 % card(((1..1000)*(1..1000))~)=1000*1000
3163 invert_explicit_set(global_set(GS),_R) :- !,
3164 add_error_and_fail(invert_explicit_set,'Cannot compute inverse of global set: ',GS).
3165 invert_explicit_set(freetype(GS),_R) :- !,
3166 add_error_and_fail(invert_explicit_set,'Cannot compute inverse of freetype: ',GS).
3167 invert_explicit_set(closure([P1,P2],[T1,T2],Clo),R) :- !,
3168 % TODO: also invert closures with single argument or more arguments
3169 % e.g., {a,b,c|a=1 & b=1 &c:1..10}~ = {c,ab|ab=(1,1) & c:1..10}
3170 R = closure([P2,P1],[T2,T1],Clo).
3171 invert_explicit_set(closure([P1],[T1],Clo),R) :-
3172 is_member_closure_with_info([P1],[T1],Clo,_Type,Info,MEM),
3173 invert_member_predicate(MEM,T1,InvMEM,InvT1),!,
3174 construct_member_closure(P1,InvT1,Info,InvMEM,R).
3175 invert_explicit_set(C,AVL) :- expand_custom_set(C,EC,invert_explicit_set), %% convert to AVL ?
3176 inv_and_norm(EC,AVL).
3177
3178 invert_member_predicate(cartesian_product(A,B),couple(TA,TB),
3179 cartesian_product(B,A),couple(TB,TA)).
3180 invert_member_predicate(identity(A),TA,identity(A),TA).
3181
3182
3183 :- block inv_and_norm(-,?).
3184 inv_and_norm(EC,AVL) :- inv(EC,R,Done), norm(Done,R,AVL).
3185
3186 :- block norm(-,?,?).
3187 norm(_,R,AVL) :- normalised_list_to_avl(R,AVL).
3188
3189 :- block inv(-,?,?).
3190 inv([],[],done).
3191 inv([(A,B)|T],[(B,A)-true|DT],Done) :- inv(T,DT,Done).
3192
3193
3194
3195 % checks whether a ground value is in the domain of an AVL relation
3196 check_in_domain_of_avlset(X,AVL) :- convert_to_avl_inside_set(X,AX),!,
3197 ? (avl_fetch_pair(AX,AVL,_) -> true ; fail).
3198 check_in_domain_of_avlset(X,AVL) :-
3199 print('### could not convert arg for check_in_domain_of_avlset'),nl,
3200 print(X),nl,
3201 safe_avl_member_pair(X,_,AVL).
3202
3203 % checks whether a ground value is in the domain of an AVL relation and has only one solution
3204 check_unique_in_domain_of_avlset(X,AVL) :- convert_to_avl_inside_set(X,AX),!,
3205 ? avl_fetch_pair(AX,AVL,AY1),!,
3206 ? (avl_fetch_pair(AX,AVL,AY2), AY1 \= AY2 -> fail
3207 ; true).
3208
3209
3210 % utility to check if for a value there is at most one matching element in an AVL set
3211 % optimized for function application
3212 at_most_one_match_possible(Element,AVL,Matches) :- nonvar(Element),
3213 Element=(Index,_Rest), % Function Application; TO DO: does this cover all func. appl ?
3214 element_can_be_added_or_removed_to_avl(Index),
3215 convert_to_avl_inside_set(Index,AX), % is ground and normalised ?
3216 % TO DO: check AVL size ? Check other patterns ?
3217 findall((AX,Match),avl_tools:avl_fetch_pair(AX,AVL,Match),Matches),
3218 Matches \= [_,_|_].
3219
3220
3221
3222 apply_to_avl_set(A,X,Y,Span,WF) :-
3223 ground_value_check(X,GroundX),
3224 ? apply_to_avl_set_aux(A,X,Y,GroundX,Span,WF).
3225
3226 apply_to_avl_set_aux(A,X,Y,GroundX,Span,WF) :- nonvar(GroundX),!,
3227 ? apply_check_tuple(X,Y,A,Span,WF). % we could call apply_check_tuple_ground to avoid one ground test
3228 % We know that A is a function: we can deterministically apply if X is ground;
3229 % if Y is ground this is only the cases for injective functions
3230 apply_to_avl_set_aux(A,X,Y,GroundX,Span,WF) :-
3231 %(preference(data_validation_mode,true); % we now reduce priority of backpropagation below
3232 preference(find_abort_values,true),
3233 % do not try inverse propagation onto argument X of function application A(X) = Y
3234 !,
3235 avl_approximate_size(A,3,ApproxSizeA),
3236 apply_check_tuple_delay(X,Y,A,ApproxSizeA,Span,WF,GroundX,_,_).
3237 apply_to_avl_set_aux(A,X,Y,GroundX,Span,WF) :-
3238 ground_value_check(Y,GroundY),
3239 avl_approximate_size(A,3,ApproxSizeA), % exact size for height <= 3; approximate size above
3240 (ApproxSizeA < 4 -> SPrio=ApproxSizeA ; SPrio is ApproxSizeA * 10), % magic number; ideally we want X or Y to be known beforehand; if none are known we may miss WD errors and may enumerate useless intermediate variables
3241 get_bounded_wait_flag(SPrio,apply_to_explicit(X,Y),WF,WF1), % this only makes sense if X is a domain variable to be enumerated
3242 %propagate_avl_element_information((X,Y),A,ApproxSizeA,WF), % could be done; but would prevent WD problems from being detected
3243 % this waitflag is used when neither X nor Y are ground;
3244 % quite often not much is gained by enumerating possible values; unless X or Y are constrained or trigger other computations
3245 % WSz is 10*ApproxSizeA, % magic value
3246 %(ApproxSizeA > 100 -> InversePrioSize = 4
3247 % ; avl_range_size_and_propagate_element_info(A,X,Y,RSize), InversePrioSize is ApproxSizeA // RSize), % we could probably compute the exact worst case with the same complexity
3248 % delay_get_wait_flag(GroundY,GroundX,WF1,InversePrioSize,apply_to_explicit_inverse(X,Y),WF,WF2),
3249 %(ApproxSizeA<4000 -> propagate_apply(X,Y,A,ApproxSizeA,WF,GroundX,GroundY) ; true),
3250 apply_check_tuple_delay(X,Y,A,ApproxSizeA,Span,WF,GroundX,WF1,GroundY),
3251 (preference(use_clpfd_solver,false) -> true
3252 % should we also check: preference(find_abort_values,true)?
3253 ; get_wait_flag0(WF,WF0),
3254 propagate_apply(X,Y,A,ApproxSizeA,WF,WF0,GroundX,WF1,GroundY)).
3255
3256 :- block propagate_apply(?,?,?,?,?,-,?,?,?).
3257 propagate_apply(X,Y,AVL,ApproxSizeA,WF,_,GroundX,WF1,GroundY) :-
3258 var(GroundX), var(WF1), var(GroundY),
3259 (preference(disprover_mode,true)
3260 -> XX=X % this will also instantiate X and prevent finding WD errors
3261 ; (ApproxSizeA<128 -> true
3262 ; preference(solver_strength,SS), ApproxSizeA < 128+SS*100), % up until 4000 it may make sense to constrain Y
3263 preference(data_validation_mode,false), % note: this can slow down ProB, e.g., test 1105; hence allow disabling it
3264 preference(find_abort_values,false), % TO DO: v = %x.(x:1..20|x+x) & {y,z|y<4 & z=v(y) & (y:{-1,2})} =res: no WD ERROR found
3265 propagate_value(X,XX) % only instantiate X, propagation only makes sense for propagate_avl_element_information_small, as otherwise only X will be bounded
3266 ),
3267 !,
3268 propagate_avl_element_information_direct((XX,Y),AVL,ApproxSizeA,WF).
3269 propagate_apply(_,_,_,_,_,_,_,_,_).
3270
3271 % only propagate in one direction to allow to find WD errors but also prevent pending co-routines/constraints
3272 :- block propagate_value(-,?).
3273 propagate_value(int(X),R) :- !,
3274 (
3275 %%integer(X) -> R=int(X) ; % relevant for SWI 8.5.10 and older where fd_set fails for integers, see test 788; should be fixed in next release
3276 propagate_fd_dom(X,RX), R=int(RX), propagate_atomic_value(X,RX)
3277 ).
3278 propagate_value(fd(X,T),R) :- !,
3279 (
3280 %%integer(X) -> R=fd(X,T) ; % for SWI 8.5.10 and older, see above
3281 propagate_fd_dom(X,RX), R=fd(RX,T), propagate_atomic_value(X,RX)
3282 ).
3283 propagate_value((X1,X2),R) :- !, R=(RX1,RX2), propagate_value(X1,RX1), propagate_value(X2,RX2).
3284 propagate_value(pred_true,R) :- !, if(R=pred_true,true,debug_println(9,function_arg_outside_domain(pred_true))).
3285 propagate_value(pred_false,R) :- !, if(R=pred_false,true,debug_println(9,function_arg_outside_domain(pred_false))).
3286 propagate_value(string(X),R) :- !, R=string(RX),propagate_atomic_value(X,RX).
3287 propagate_value(X,RX) :- equal_object(X,RX). % TO DO: get rid of this: this propagates and prevents finding WD errors
3288 :- block propagate_atomic_value(-,?).
3289 propagate_atomic_value(X,Y) :-
3290 if(X=Y,true,debug_println(9,function_arg_outside_domain(X))).
3291
3292 %propagate_fd_dom(X,RX) :- integer(X),!,RX=X. % relevant for SWI 8.5.10 and older where fd_set fails for integers
3293 propagate_fd_dom(X,RX) :- fd_set(X,Dom),in_set(RX,Dom).
3294
3295
3296 /*
3297 :- block propagate_apply(-,?,?,?,?,-,-).
3298 % call propagate as soon as we know something about the function argument and we do not propgagate completely using GroundX/Y anyway
3299 propagate_apply(X,Y,AVL,Size,WF,GroundX,GroundY) :- print(prop_apply(Size,GroundX,GroundY,X,Y)),nl,
3300 (nonvar(GroundX) -> true ; nonvar(GroundY) -> true
3301 ; propagate_avl_element_information((X,Y),AVL,Size,WF)).
3302
3303 % get the waitflag when first WF set and other two not
3304 :- block delay_get_wait_flag(-,-,-,?,?,?,?).
3305 delay_get_wait_flag(_,WF1,WF2, _,_,_,_) :- (nonvar(WF1);nonvar(WF2)),!. % DO NOTHING
3306 delay_get_wait_flag(_,_,_,Prio,Info,WF,WF2) :- get_wait_flag(Prio,Info,WF,WF2).
3307 */
3308
3309 :- block apply_check_tuple_delay(?,?,?, ?,?,?, -,-,-).
3310 apply_check_tuple_delay(X,Y,AVL,_ApproxSizeA,Span,WF,GroundX,WF1,_) :-
3311 (nonvar(GroundX);nonvar(WF1)),!,
3312 ? apply_check_tuple(X,Y,AVL,Span,WF).
3313 apply_check_tuple_delay(X,Y,AVL,ApproxSizeA,Span,WF,_GroundX,_WF1,_GroundY) :-
3314 % Y is ground; try to do an inverse function lookup
3315 ? inverse_apply_ok(Y,X,AVL,ApproxSizeA,Span),
3316 !,
3317 % print(inverse_apply(Y,X,ApproxSizeA,_GroundX)),nl,
3318 inverse_get_possible_values(X,Y,AVL,Res),
3319 Res=avl_set(InvAVL), % if empty set : we fail
3320 (preference(data_validation_mode,true),
3321 avl_approximate_size(InvAVL,10,ApproxSize),
3322 ApproxSize>1
3323 -> A2 is (ApproxSize*15*ApproxSize)//ApproxSizeA, % used to be A2 is ApproxSize*100,
3324 A22 is max(A2,ApproxSize),
3325 (get_inversion_penalty(Span)
3326 -> A23 is A22 * 100 %, add_message(f,'Inversion Penalty: ',Y:A22,Span)
3327 ; A23=A22),
3328 % give lower priority for backwards propagation, upto 15 times if no reduction from backwards propagation
3329 % but also take into account how much we reduce the size by inverting
3330 % relevant for, e.g., Machines_perf_0111/Thales_All/rule_OPS_SDS_3940.mch
3331 % or rule_OPS_SDS_6496 -> 15 instead of 150 improves performance
3332 get_bounded_wait_flag(A23,element_of_avl_inverse_apply_ok(X),WF,WF2),
3333 % does not call propagate_avl_element_information(X,InvAVL,ApproxSize,WF) or avl_to_table
3334 element_of_avl_set_wf3(X,InvAVL,ApproxSize,WF2,WF) % TODO: pass GroundX
3335 %apply_check_tuple_delay(X,Y,AVL,ApproxSizeA,Span,WF,GroundX,WF1,_) % now wait on WF1 or GroundX
3336 ? ; element_of_avl_set_wf(InvAVL,X,WF)
3337 ).
3338 apply_check_tuple_delay(X,Y,AVL,ApproxSizeA,Span,WF,GroundX,WF1,_GroundY) :-
3339 apply_check_tuple_delay(X,Y,AVL,ApproxSizeA,Span,WF,GroundX,WF1,_). % now wait on WF1 or GroundX
3340
3341 % check if the function call was annotated as not suitable for backwards inverse function lookup propagation
3342 get_inversion_penalty(span_predicate(b(_Function,_,Info),_LS,_S)) :- !,
3343 get_inversion_penalty(Info).
3344 get_inversion_penalty(Info) :-
3345 member(prob_annotation('INVERSION_PENALTY'),Info).
3346
3347 inverse_get_possible_values(X,Y,AVL,Res) :-
3348 get_template(X,XX,_),
3349 copy_term(XX,XX_Copy), % avoid that findall instantiates X
3350 % TODO: copy_value_term similar to ground_value to avoid traversing avl_sets; but usually X is not a set
3351 findall(XX_Copy, safe_avl_member_default((XX_Copy,Y),AVL), PossibleValues),
3352 PossibleValues \= [], % fail straightaway
3353 sort(PossibleValues,SPV),
3354 % length(SPV,Len),print(inverse_image(Y,Len)),nl, print_term_summary(apply_check_tuple_delay(X,Y,AVL)),nl,
3355 convert_to_avl(SPV,Res).
3356
3357 % is it ok to compute inverse ? only makes sense if AVL tree not too big and quite functional
3358 inverse_apply_ok(pred_true,_,_AVL,ApproxSizeA,_) :- !, % only two values possible, probably half of AVL will be returned
3359 ApproxSizeA < 1023. % corresponds to avl_height < 10
3360 inverse_apply_ok(pred_false,_,_AVL,ApproxSizeA,_) :- !,ApproxSizeA < 1023.
3361 % TO DO: other small types, such as fd(_,_)
3362 inverse_apply_ok(_,_,_AVL,ApproxSizeA,_) :- ApproxSizeA < 255,!.
3363 inverse_apply_ok(_,X,_AVL,ApproxSizeA,Span) :- ApproxSizeA < 65535, % corresponds Height < 16
3364 (preference(data_validation_mode,true) ->
3365 (preference(solver_strength,SS), ApproxSizeA < 16383+SS -> true
3366 ; perfmessage(inverse,'Function call not inverted (increase SOLVER_STRENGTH to enable this), approximate function size: ',ApproxSizeA,Span),
3367 fail
3368 )
3369 ; true),
3370 ? quick_non_ground_check(X).
3371 %inverse_apply_ok(_,_,_,_).
3372
3373 % sometimes the ground_value_check co-routine hasn't grounded GroundX yet ! so do a quick check
3374 quick_non_ground_check(X) :- var(X),!.
3375 quick_non_ground_check([]) :- !,fail.
3376 quick_non_ground_check(avl_set(_)) :- !,fail.
3377 quick_non_ground_check(pred_true) :- !,fail.
3378 quick_non_ground_check(pred_false) :- !,fail.
3379 quick_non_ground_check(int(X)) :- !,var(X).
3380 quick_non_ground_check(string(X)) :- !,var(X).
3381 quick_non_ground_check(fd(X,T)) :- !,(var(X) ; var(T)).
3382 quick_non_ground_check((A,B)) :- !, (quick_non_ground_check(A) -> true ; quick_non_ground_check(B)).
3383 quick_non_ground_check(_). % assume it is non ground
3384
3385
3386
3387 % apply_check_tuple is allowed to enumerate: either X is ground or Y is ground
3388 apply_check_tuple(X,Y,A,Span,WF) :-
3389 ground_value(X),
3390 convert_to_avl_inside_set_wf(X,AX,WF),!, % we can do optimized lookup + checking in one go (but avl_apply only does partial check)
3391 avl_apply(AX,A,XY,Span,WF),
3392 ? kernel_objects:equal_object_wf(XY,Y,apply_check_tuple,WF).
3393 :- if(environ(no_wd_checking, true)).
3394 apply_check_tuple(X,Y,A,_Span,WF) :- safe_avl_member_default_wf((X,Y),A,WF).
3395 :- else.
3396 apply_check_tuple(X,Y,A,_Span,WF) :- preferences:preference(find_abort_values,false), !,
3397 ? safe_avl_member_default_wf((X,Y),A,WF).
3398 apply_check_tuple(X,Y,A,Span,WF) :- !,
3399 if(safe_avl_member_default_wf((X,XY),A,WF), % does not detect abort errors if X unbound
3400 kernel_objects:equal_object_wf(XY,Y,apply_check_tuple_avl,WF),
3401 add_wd_error_span('function applied outside of domain (#4): ','@fun'(X,avl_set(A)),Span,WF)).
3402 :- endif.
3403
3404
3405 % ------------------------------------------
3406
3407
3408 :- use_module(b_global_sets,[b_type2_set/2]).
3409 :- use_module(bsyntaxtree,[rename_bt/3]).
3410 union_of_explicit_set(global_set(GS),_,R) :- is_maximal_global_set(GS), !,
3411 R= global_set(GS). /* global_set is already maximal */
3412 union_of_explicit_set(freetype(GS),_,R) :- !, R= freetype(GS). /* freetype is already maximal */
3413 union_of_explicit_set(closure(P,T,B),_,R) :- is_definitely_maximal_closure(P,T,B), !,
3414 R= closure(P,T,B). /* global_set is already maximal */
3415 union_of_explicit_set(_,S2,R) :- is_definitely_maximal_set(S2),!, % will also look at AVL set
3416 R=S2.
3417 union_of_explicit_set(S1,S2,R) :- nonvar(S2), S2 = [], !, R=S1.
3418 union_of_explicit_set(S1,S2,_) :- (var(S1);var(S2)),!,fail. % then we cannot compute it here
3419 union_of_explicit_set(S2,S1,R) :-
3420 is_not_member_value_closure(S1,TYPE,MS1), nonvar(MS1), is_efficient_custom_set(MS1),
3421 % also works if S2 is complement closure
3422 difference_of_explicit_set(MS1,S2,Diff),!,
3423 construct_complement_closure_if_necessary(Diff,TYPE,R).
3424 union_of_explicit_set(avl_set(A1),S2,R) :- !, union_of_avl_set(S2,A1,R).
3425 union_of_explicit_set(S1,S2,R) :-
3426 ? is_not_member_value_closure(S1,TYPE,MS1), nonvar(MS1), is_efficient_custom_set(MS1),
3427 difference_of_explicit_set(MS1,S2,Diff),!,
3428 construct_complement_closure_if_necessary(Diff,TYPE,R).
3429 union_of_explicit_set(S1,avl_set(A2),R) :- !, union_of_avl_set(S1,A2,R).
3430 union_of_explicit_set(I1,I2,R) :- is_interval_closure_or_integerset(I1,From1,To1), ground(From1), ground(To1),
3431 is_interval_closure_or_integerset(I2,From2,To2), ground(From2), ground(To2),
3432 !,
3433 (union_of_interval(From1,To1,From2,To2,FromRes,ToRes)
3434 -> construct_interval_closure(FromRes,ToRes,R)
3435 ; small_enough_for_expansion(From1,To1),small_enough_for_expansion(From2,To2) ->
3436 % do not attempt union_of_closure below
3437 expand_interval_closure_to_avl(From1,To1,R1), R1=avl_set(A1), % empty interval already dealt with above !?
3438 expand_interval_closure_to_avl(From2,To2,R2), R2=avl_set(A2), % Note: unification after call as expand_interval calls equal_object (which gets confused by partially instantiated avl_set(_))
3439 union_of_avl(A1,A2,ARes),R=avl_set(ARes) /* AVL not normalised */
3440 ; transform_global_sets_into_closure(I1,closure(Par,T,Body)),
3441 union_of_closure(I2,Par,T,Body,R)
3442 ).
3443 union_of_explicit_set(closure(P,T,B),C2,Res) :-
3444 union_of_closure(C2,P,T,B,Res).
3445
3446 small_enough_for_expansion(From1,To1) :- number(To1), number(From1), To1-From1<250.
3447
3448 :- use_module(bsyntaxtree,[extract_info/2, extract_info_wo_used_ids/2, extract_info/3, rename_bt/3, replace_id_by_expr/4]).
3449
3450 union_of_closure(global_set(X),P,T,B,Res) :- !, transform_global_sets_into_closure(global_set(X),C),
3451 union_of_closure(C,P,T,B,Res).
3452 union_of_closure(closure(P2,T2,B2),P,T,B,Res) :- !,
3453 % T2 should be equal to T, module seq(_) <-> set(couple(integer,_))
3454 unify_closure_predicates(P,T,B, P2,T2,B2 , NewP,NewT, NewB1,NewB2),
3455 debug:debug_println(9,union_of_two_closures(P,P2,NewP,NewT)),
3456 extract_info(B,B2,NewInfo),
3457 construct_disjunct(NewB1,NewB2,Disj),
3458 Res = closure(NewP,NewT,b(Disj,pred,NewInfo)).
3459
3460 % rename predicates of two closures so that they work on common closure parameter ids
3461 % and can then be either joined by conjunction or disjunction
3462 unify_closure_predicates(P,T,B, P2,T2,B2 , NewP,NewT, NewB1,NewB2) :-
3463 length(P,Len1), length(P2,Len2),
3464 (Len1=Len2
3465 -> generate_renaming_list(P,P2,RL),
3466 rename_bt(B2,RL,NewB2),
3467 NewP=P, NewT=T, NewB1 = B
3468 ; Len1 < Len2 -> unify_clos_lt(P,T,B, P2,T2,B2 , NewP,NewT, NewB1,NewB2)
3469 ; unify_clos_lt(P2,T2,B2, P,T,B , NewP,NewT, NewB2,NewB1) % inverted the predicate
3470 ).
3471
3472 % TO DO: generalize: currently only works for single identifier on left
3473 % but works for id(NATURAL) \/ %x.(x<0|-x) or abs = id(NATURAL) \/ %x.(x<0|-x) & abs(2)=a2 & abs(-2)=am2
3474 unify_clos_lt([ID1],[couple(_,_)],B, P2,T2,B2 , NewP,NewT, NewB1,NewB2) :-
3475 rename_lambda_result_id(P2,B2,P3,B3),
3476 create_couple_term(P3,T2,Pair),
3477 replace_id_by_expr(B,ID1,Pair,NewB1),
3478 NewP=P3, NewT=T2, NewB2=B3.
3479
3480 % _lambda_result_ id is not enumerated, hence we have to avoid inserting such ids into NewB1 as part of the pPair
3481 rename_lambda_result_id(['_lambda_result_',ID2],B2,[FRESHID,ID2],B3) :- !,get_unique_id('_RANGE_',FRESHID),
3482 rename_bt(B2,[rename('_lambda_result_',FRESHID)],B3).
3483 rename_lambda_result_id([ID1,'_lambda_result_'],B2,[ID1,FRESHID],B3) :- !,get_unique_id('_RANGE_',FRESHID),
3484 rename_bt(B2,[rename('_lambda_result_',FRESHID)],B3).
3485 rename_lambda_result_id(P2,B2,P2,B2).
3486
3487 % translate a list of atomic ids and a list of types into a couple-term
3488 create_couple_term([ID1],[T1],Res) :- !,
3489 create_texpr(identifier(ID1),T1,[],Res).
3490 create_couple_term([ID1,ID2],[T1,T2],Res) :-
3491 bsyntaxtree:create_couple(b(identifier(ID1),T1,[]),b(identifier(ID2),T2,[]),Res).
3492 % TODO: extend for more than two args
3493
3494 generate_renaming_list([],[],[]).
3495 generate_renaming_list([ID|T],[ID2|T2],RL) :-
3496 (ID==ID2 -> generate_renaming_list(T,T2,RL)
3497 ; RL = [rename(ID2,ID)|RL2],
3498 generate_renaming_list(T,T2,RL2)).
3499
3500
3501 % a more clever way of constructing a disjunct; factor out common prefixes
3502 % (A & B1) or (A1 & B2) <=> A1 & (B1 or B2)
3503 % TO DO: we should try and get the leftmost basic conjunct !
3504 /* construct_disjunct(b(conjunct(A1,A2),pred,IA), b(conjunct(B1,B2),pred,_IB), Res) :-
3505
3506 print('TRY DISJUNCT FACTOR: '), translate:print_bexpr(A1),nl,
3507 translate:print_bexpr(B1),nl,
3508 same_texpr_body(A1,B1),!,
3509 print('DISJUNCT FACTOR: '), translate:print_bexpr(A1),nl,
3510 Res = conjunct(A1,b(Disj,pred,IA)),
3511 construct_disjunct(A2,B2,Disj).
3512 */
3513 construct_disjunct(A,B,disjunct(A,B)).
3514
3515 :- use_module(btypechecker,[couplise_list/2]).
3516 % TO DO: quick_check if AVL A1 is maximal ?
3517 union_of_avl_set(avl_set(A2),A1,R) :- !, union_of_avl(A1,A2,ARes), R=avl_set(ARes). /* AVL not normalised */
3518 union_of_avl_set(I2,A1,R) :- is_interval_closure_or_integerset(I2,From2,To2), !,
3519 ground(From2), ground(To2), % we can only compute it if bounds known
3520 (avl_min(A1,int(Min)), low_border(From2,Min,FromRes), avl_max(A1,int(Max)), up_border(To2,Max,ToRes)
3521 -> /* AVL contained (almost) in Interval */
3522 construct_interval_closure(FromRes,ToRes,R)
3523 ; \+ small_interval(From2,To2) ->
3524 transform_global_sets_into_closure(I2,closure(Par,T,Body)), % we may have something like NATURAL1,...
3525 union_of_avl_set_with_closure(Par,T,Body,A1,R)
3526 ; expand_and_convert_to_avl_set(I2,A2,union_of_avl_set,'? \\/ ARG'), % can generate ARel=empty; will fail if not possible to convert
3527 union_of_avl(A1,A2,ARes), R=avl_set(ARes)
3528 ).
3529 union_of_avl_set(closure(Par,T,Body),A1,Res) :- is_infinite_or_symbolic_closure(Par,T,Body),!,
3530 % TO DO: what if we are in SYMBOLIC mode and the type of T is infinite; maybe we should also keep the union symbolic ?? (cf Ticket/Georghe1)
3531 union_of_avl_set_with_closure(Par,T,Body,A1,Res).
3532 union_of_avl_set(S2,A1,Res) :-
3533 S2 \= freetype(_),
3534 ground_value(S2), % could be a closure
3535 !,
3536 (try_expand_and_convert_to_avl_set(S2,A2,union)
3537 -> union_of_avl(A1,A2,ARes), Res=avl_set(ARes) /* AVL not normalised */
3538 ; S2=closure(Par,T,Body),
3539 union_of_avl_set_with_closure(Par,T,Body,A1,Res)).
3540
3541 try_expand_and_convert_to_avl_set(S2,A2,Source) :-
3542 % false: do not add enumeration warning events as errors
3543 catch_enumeration_warning_exceptions(expand_and_convert_to_avl_set(S2,A2,Source,''),fail,false,ignore(Source)).
3544
3545 % try expanding to list, but catch enumeration warnings and fail if they do occur
3546 % used by override(...)
3547 %try_expand_custom_set_to_list(CS,_,_,_) :- nonvar(CS),CS=global_set(GS),is_infinite_global_set(GS,_),
3548 % !,
3549 % fail.
3550 try_expand_custom_set_to_list(CS,_,_,_) :- nonvar(CS),
3551 (is_symbolic_closure(CS) ; is_infinite_explicit_set(CS)),
3552 !, % we could also check is_symbolic_closure
3553 fail.
3554 try_expand_custom_set_to_list(CS,List,Done,Source) :-
3555 % false: do not add enumeration warning events as errors
3556 catch_enumeration_warning_exceptions(expand_custom_set_to_list(CS,List,Done,Source),fail,false,ignore(Source)).
3557
3558
3559 small_interval(From,To) :- number(From), number(To), To-From < 10000.
3560
3561 union_of_avl_set_with_closure(Par,T,Body,A1,Res) :-
3562 Body = b(_,BodyT,_),
3563 setup_typed_ids(Par,T,TypedPar),
3564 btypechecker:couplise_list(TypedPar,TypedCPar),
3565 generate_couple_types(TypedCPar,ParExpr,ParType),
3566 debug:debug_println(9,union_of_avl_and_infinite_closure(Par,T,BodyT)),
3567 BodyAvl = b(member(ParExpr,b(value(avl_set(A1)),set(ParType),[])),pred,[]),
3568 extract_info_wo_used_ids(Body,NewInfo),
3569 Res = closure(Par,T,b(disjunct(BodyAvl,Body),pred,NewInfo)).
3570 % mark_closure_as_symbolic(closure(Par,T,b(disjunct(BodyAvl,Body),pred,NewInfo)),Res).
3571
3572 low_border(Low,AVLMin,R) :- geq_inf(AVLMin,Low),!,R=Low.
3573 low_border(Low,AVLMin,R) :- number(Low),AVLMin is Low-1,R=AVLMin. % extend lower border by one
3574 up_border(Up,AVLMax,R) :- geq_inf(Up,AVLMax),!,R=Up.
3575 up_border(Up,AVLMax,R) :- number(Up),AVLMax is Up+1,R=AVLMax. % extend upper border by one
3576
3577
3578 setup_typed_ids([],[],[]).
3579 setup_typed_ids([ID|TI],[Type|TT],[b(identifier(ID),Type,[])|BT]) :- setup_typed_ids(TI,TT,BT).
3580
3581 generate_couple_types(couple(A,B),b(couple(TA,TB),Type,[]),Type) :- !, Type = couple(TTA,TTB),
3582 generate_couple_types(A,TA,TTA),
3583 generate_couple_types(B,TB,TTB).
3584 generate_couple_types(b(X,T,I),b(X,T,I),T).
3585
3586
3587 % try to see if two intervals can be unioned into a new interval
3588 union_of_interval(F1,T1,F2,T2,FR,TR) :-
3589 geq_inf(F2,F1), geq_inf(T1,T2),!,FR=F1,TR=T1. % interval [F2,T2] contained in [F1,T1]
3590 union_of_interval(F2,T2,F1,T1,FR,TR) :- geq_inf(F2,F1), geq_inf(T1,T2),!,FR=F1,TR=T1. % see above
3591 union_of_interval(F1,T1,F2,T2,FR,TR) :- number(F2),
3592 geq_inf(F2,F1), number(T1),T11 is T1+1,geq_inf(T11,F2), geq_inf(T2,F2),!,FR=F1,TR=T2. % intervals can be joined
3593 union_of_interval(F2,T2,F1,T1,FR,TR) :- number(F2),
3594 geq_inf(F2,F1), number(T1),T11 is T1+1,geq_inf(T11,F2), geq_inf(T2,F2),!,FR=F1,TR=T2. % see above
3595
3596 :- use_module(library(ordsets),[ord_union/3]).
3597 union_of_avl(A1,A2,ARes) :-
3598 avl_height(A2,Sz2),
3599 (Sz2 < 2 % we have something like Set := Set \/ {x}; no need to compute height of A1
3600 -> union_of_avl1(A1,99999,A2,Sz2,ARes)
3601 ; avl_height(A1,Sz1), % TODO: we could call avl_height_less_than or avl_height_compare
3602 (Sz1<Sz2 -> union_of_avl1(A2,Sz2,A1,Sz1,ARes) ; union_of_avl1(A1,Sz1,A2,Sz2,ARes))
3603 ).
3604 union_of_avl1(A1,Sz1,A2,Sz2,ARes) :- Sz2>2, Sz1 =< Sz2+3, % difference not too big; Sz2 at least a certain size
3605 !,
3606 avl_to_list(A2,List2), % get all members
3607 avl_to_list(A1,List1),
3608 ord_union(List1,List2,L12),
3609 ord_list_to_avl(L12,ARes).
3610 union_of_avl1(A1,_Sz1,A2,_Sz2,ARes) :- % this version is better when A2 is small compared to A1
3611 avl_domain(A2,List2), % get all members
3612 add_to_avl(List2,A1,ARes).
3613
3614 :- use_module(library(lists),[reverse/2]).
3615 % a custom version for union(A) where A is AVL set; avoid converting/expanding accumulators and computing avl_height
3616 % runtime of e.g., UNION(x).(x:1000..1514|0..x) 0.65 sec or UNION(n).(n:10000..10010|UNION(x).(x:n..n+1000|n..x)) 4.8 sec is considerably smaller with this version
3617 union_generalized_explicit_set(avl_set(SetsOfSets),Res,WF) :-
3618 expand_custom_set_to_list_wf(avl_set(SetsOfSets),ESetsOfSets,_,union_generalized_wf,WF),
3619 % length(ESetsOfSets,Len),print(union_gen(Len)),nl,
3620 (ESetsOfSets=[OneSet]
3621 -> Res=OneSet % avoid converting to list and back to Avl
3622 ; reverse(ESetsOfSets,RESetsOfSets), % be sure to insert larger values first, so that ord_union has less work to do below; useful if you have many small singleton sets, for example union(ran(%x.(x : 1 .. 10000|{x * x}))) 2.37 secs --> 0.15 secs
3623 % note: dom({r,x|x:1..50000 & r:{x*x}}) is still 3 times faster
3624 union_of_avls(RESetsOfSets,[],Res)).
3625
3626 % take the union of a list of avl_sets
3627 union_of_avls([],Acc,Res) :- ord_list_to_avl(Acc,ARes), construct_avl_set(ARes,Res).
3628 union_of_avls([H|T],Acc,Res) :-
3629 union_of_avl_with_acc(H,Acc,NewAcc),
3630 union_of_avls(T,NewAcc,Res).
3631
3632 union_of_avl_with_acc(avl_set(H),Acc,NewAcc) :- !,
3633 avl_to_list(H,HList),
3634 ord_union(Acc,HList,NewAcc).
3635 union_of_avl_with_acc([],Acc,Res) :- !,Res=Acc.
3636 % other custom sets should normally not appear, we obtain the list as elements stored in an avl_set
3637 union_of_avl_with_acc(G,_,_) :- add_internal_error('Uncovered element: ',union_of_avl_with_acc(G,_,_)),fail.
3638
3639
3640
3641 % TO DO: there are no rules for is_not_member_value_closure for intersection below
3642 intersection_of_explicit_set_wf(global_set(GS),S2,R,_WF) :- is_maximal_global_set(GS), !, R=S2.
3643 intersection_of_explicit_set_wf(freetype(_GS),S2,R,_WF) :- !, R=S2.
3644 intersection_of_explicit_set_wf(_,S2,_,_WF) :- var(S2),!,fail. % code below may instantiate S2
3645 intersection_of_explicit_set_wf(S1,S2,R,_WF) :- is_definitely_maximal_set(S2), !, R=S1.
3646 intersection_of_explicit_set_wf(_S1,[],R,_WF) :-!, R=[].
3647 intersection_of_explicit_set_wf(avl_set(A1),I2,R,_WF) :-
3648 is_interval_closure_or_integerset(I2,From1,To1),
3649 !,
3650 intersect_avl_interval(A1,From1,To1,R).
3651 intersection_of_explicit_set_wf(I1,I2,R,_WF) :-
3652 intersection_with_interval_closure(I1,I2,R),!.
3653 intersection_of_explicit_set_wf(S1,S2,R,_WF) :-
3654 get_avl_sets(S1,S2,A1,A2),
3655 !, % if too large: better to apply normal intersection code ?
3656 % if one of the args is an interval this is already caught in kernel_objects calling intersection_with_interval_closure; see SetIntersectionBig.mch
3657 avl_domain(A1,ES), % A1 has the smaller height; important for e.g. SetIntersectionBig2.mch
3658 inter2(ES,A2,IRes),
3659 ord_list_to_avlset(IRes,R,intersection). % we have generated the elements in the right order already
3660 intersection_of_explicit_set_wf(Set1,Set2,R,WF) :-
3661 transform_global_sets_into_closure(Set1,closure(P1,T1,B1)),
3662 transform_global_sets_into_closure(Set2,closure(P2,T2,B2)),
3663 % gets called, e.g., for {x|x /: NATURAL1} /\ NATURAL1
3664 unify_closure_predicates(P1,T1,B1, P2,T2,B2 , NewP,NewT, NewB1,NewB2),
3665 debug:debug_println(9,intersection_of_two_closures(P1,P2,NewP,NewT)),
3666 conjunct_predicates([NewB1,NewB2],BI),
3667 % create a conjunction: can be much more efficient than seperately expanding;
3668 % also works well if one of the closures is infinite
3669 C = closure(NewP,NewT,BI),
3670 expand_custom_set_wf(C,R,intersection_of_explicit_set_wf,WF). % we could keep it symbolic; maybe use SYMBOLIC pref
3671 % to do: also use above for closure and AVL set with member(P,value(avl_set(A)))
3672 % we could also apply the same principle to difference_of_explicit_set
3673 % currently we enable intersection to be treated symbolically (not_symbolic_binary(intersection) commented out)
3674 % This means the above clause for intersection_of_explicit_set_wf is less useful
3675 % a special case; just for interval closures
3676 intersection_with_interval_closure(I1,I2,R) :-
3677 is_interval_closure_or_integerset(I1,From1,To1), nonvar(I2),
3678 intersection_with_interval_closure_aux(I2,From1,To1,R).
3679 intersection_with_interval_closure(avl_set(A1),I2,R) :-
3680 is_interval_closure_or_integerset(I2,From1,To1),
3681 !,
3682 intersect_avl_interval(A1,From1,To1,R).
3683
3684 % try and get AVL sets from two args; first AVL set is smaller one according to height
3685 get_avl_sets(avl_set(A1),S2,AA1,AA2) :- nonvar(S2), S2=avl_set(A2),
3686 ? (avl_height_compare(A1,A2,R), R=lt
3687 -> (AA1,AA2)=(A1,A2)
3688 ; (AA1,AA2)=(A2,A1)).
3689 %get_avl_sets(S1,S2,AA1,AA2) :- nonvar(S2),S2=avl_set(A2), get_avl_set_arg(S1,A1),
3690 % (avl_height_compare(A1,A2,R),R=gt -> (AA1,AA2)=(A2,A1) ; (AA1,AA2)=(A1,A2)).
3691
3692
3693 %intersection_with_interval_closure_aux(avl_set(A),...
3694 intersection_with_interval_closure_aux(I2,From1,To1,R) :-
3695 is_interval_closure_or_integerset(I2,From2,To2),!,
3696 intersect_intervals_with_inf(From1,To1,From2,To2,FromRes,ToRes),
3697 construct_interval_closure(FromRes,ToRes,R).
3698 % (is_interval_closure_or_integerset(R,F,T) -> print(ok(F,T)),nl ; print(ko),nl).
3699 intersection_with_interval_closure_aux(avl_set(A2),From1,To1,R) :-
3700 intersect_avl_interval(A2,From1,To1,R).
3701
3702 % intersect avl with interval
3703 % TO DO: expand interval if small (or small intersection with AVL) and use avl intersection
3704 intersect_avl_interval(_,From2,To2,_) :- (var(From2) ; var(To2)),!,fail.
3705 intersect_avl_interval(A1,From2,To2,R) :- avl_min(A1,int(Min)),
3706 geq_inf(Min,From2),
3707 geq_inf(To2,Min), avl_max(A1,int(Max)),
3708 geq_inf(To2,Max),
3709 % AVL fully contained in interval; no need to expand to list and back again
3710 !,
3711 construct_avl_set(A1,R).
3712 intersect_avl_interval(A1,From2,To2,R) :-
3713 avl_domain(A1,ES),
3714 inter_interval(ES,From2,To2,IRes),
3715 ord_list_to_avlset(IRes,R,intersect_avl_interval).
3716
3717 inter_interval([],_,_, []).
3718 inter_interval([IH|T],From2,To2, Res) :- IH = int(H),
3719 (geq_inf(To2,H) ->
3720 (geq_inf(H,From2) -> Res = [IH-true|Res2] ; Res = Res2),
3721 inter_interval(T,From2,To2,Res2)
3722 ; Res = [] % we have exceeded the upper limit of the interval
3723 ).
3724
3725 intersect_intervals_with_inf(From1,To1,From2,To2,FromRes,ToRes) :-
3726 minimum_with_inf(To1,To2,ToRes),
3727 maximum_with_inf(From1,From2,FromRes).
3728
3729 % check if two intervals are disjoint
3730 disjoint_intervals_with_inf(From1,To1,From2,To2) :-
3731 intersect_intervals_with_inf(From1,To1,From2,To2,Low,Up),
3732 number(Up), number(Low), Low > Up.
3733
3734 inter2([],_, []).
3735 inter2([H|T],A1, Res) :-
3736 (avl_fetch(H,A1) -> Res = [H-true|Res2] ; Res = Res2), inter2(T,A1,Res2).
3737
3738 ord_list_to_avlset(OL,R) :- ord_list_to_avlset(OL,R,unknown).
3739 ord_list_to_avlset(OrdList,Res,Origin) :-
3740 % assumes that we have generated the elements in the right order already
3741 (OrdList=[] -> Res=[]
3742 ; check_sorted(OrdList,Origin),
3743 ord_list_to_avl(OrdList,ARes), Res=avl_set(ARes)).
3744
3745 % a version which accepts a list of values without -true
3746 % values have to be ground and already converted for use in avl_set
3747 sorted_ground_normalised_list_to_avlset(List,Res,PP) :-
3748 add_true_to_list(List,LT),
3749 ord_list_to_avlset_direct(LT,Res,PP).
3750
3751 add_true_to_list([],[]).
3752 add_true_to_list([H|T],[H-true|TT]) :- add_true_to_list(T,TT).
3753
3754 % the same, but without checking sorted (only use if you are really sure the list is sorted)
3755 ord_list_to_avlset_direct([],[],_).
3756 ord_list_to_avlset_direct([H|T],Res,_):-
3757 (T==[] -> H=Key-Val, Res = avl_set(node(Key,Val,0,empty,empty)) % slightly faster than calling ord_list_to_avl
3758 ; ord_list_to_avl([H|T],ARes), Res = avl_set(ARes)).
3759
3760 check_sorted([],_) :- !.
3761 check_sorted([H-_|T],Origin) :- !, check_sorted2(T,H,Origin).
3762 check_sorted(X,Origin) :- add_error_and_fail(ord_list_to_avlset,'Not a list of -/2 pairs: ',Origin:X).
3763
3764 check_sorted2([],_,_) :- !.
3765 check_sorted2([H-_|T],PH,Origin) :- PH @< H,!, check_sorted2(T,H,Origin).
3766 check_sorted2(X,Prev,Origin) :-
3767 add_error_and_fail(ord_list_to_avlset,'Not a sorted list of -/2 pairs: ',Origin:(X,Prev)).
3768
3769 % ------------------
3770
3771 :- use_module(kernel_freetypes,[is_maximal_freetype/1]).
3772 is_definitely_maximal_set(S) :- nonvar(S),
3773 is_definitely_maximal_set2(S).
3774 is_definitely_maximal_set2(freetype(ID)) :- is_maximal_freetype(ID).
3775 is_definitely_maximal_set2(global_set(GS)) :- is_maximal_global_set(GS).
3776 is_definitely_maximal_set2(closure(P,T,B)) :- is_definitely_maximal_closure(P,T,B).
3777 is_definitely_maximal_set2(avl_set(S)) :- quick_definitely_maximal_set_avl(S).
3778 is_definitely_maximal_set2([H|T]) :- nonvar(H), is_definitely_maximal_list(H,T). %, nl,print(maximal(H,T)),nl,nl.
3779 %H==pred_true, T == [pred_false]. % for some reason BOOL is sometimes presented this way
3780 is_definitely_maximal_set2(empty) :- % detect unwrapped AVL sets
3781 add_internal_error('Not a set: ',is_definitely_maximal_set2(empty)),fail.
3782 is_definitely_maximal_set2(node(A,B,C,D,E)) :-
3783 add_internal_error('Not a set: ',is_definitely_maximal_set2(node(A,B,C,D,E))),fail.
3784
3785 is_definitely_maximal_list(pred_true,T) :- nonvar(T), T=[_|_]. %
3786 is_definitely_maximal_list(pred_false,T) :- nonvar(T), T=[_|_].%
3787 is_definitely_maximal_list(fd(_,Type),T) :- nonvar(T),b_global_set_cardinality(Type,Card),
3788 % check if we have the same number of elements as the type: then the set must me maximal
3789 length_at_least(T,Card).
3790 % We could try and and also treat pairs
3791
3792 length_at_least(1,_) :- !. % we have already removed 1 element; T can be nil
3793 length_at_least(N,T) :- nonvar(T), T=[_|TT], N1 is N-1, length_at_least(N1,TT).
3794
3795 is_definitely_maximal_closure(_,_,b(truth,_Pred,_)) :- !.
3796 is_definitely_maximal_closure(P,T,B) :- is_cartesian_product_closure_aux(P,T,B,S1,S2),!,
3797 is_definitely_maximal_set(S1),is_definitely_maximal_set(S2).
3798 is_definitely_maximal_closure(P,T,B) :-
3799 is_full_powerset_or_relations_or_struct_closure(closure(P,T,B),Sets),
3800 l_is_definitely_maximal_set(Sets).
3801
3802 l_is_definitely_maximal_set([]).
3803 l_is_definitely_maximal_set([H|T]) :- is_definitely_maximal_set(H), l_is_definitely_maximal_set(T).
3804
3805 % check if we have an AVL tree covering all elements of the underlying type
3806 quick_definitely_maximal_set_avl(AVL) :-
3807 AVL=node(El,_True,_,_Left,_Right),
3808 quick_definitely_maximal_set_avl_aux(El,AVL).
3809 quick_definitely_maximal_set_avl_aux(El,AVL) :-
3810 try_get_finite_max_card_from_ground_value(El,Card),
3811 % this could fail if El contains empty sets !
3812 % also: it must fail if Card is infinite (no avl_set can be maximal)
3813 (Card < 1000 -> true
3814 ; preferences:preference(solver_strength,SS), Card < 1000+SS*100
3815 ), % otherwise too expensive a check avl_size
3816 quick_avl_approximate_size(AVL,MaxSize),
3817 MaxSize >= Card, % otherwise no sense in computing avl_size, which is linear in size of AVL
3818 avl_size(AVL,Size),
3819 %(MaxSize>=Size -> print(ok(Size,all(Card))),nl ; print('**** ERROR: '), print(Size),nl,trace),
3820 Size=Card.
3821
3822 % check if we have an AVL function with domain covering all elements of the underlying type
3823 quick_definitely_maximal_total_function_avl(AVL) :-
3824 AVL=node(El,_True,_,_Left,_Right),
3825 El=(DomEl,_),
3826 quick_definitely_maximal_set_avl_aux(DomEl,AVL), % the size is exactly the size of the domain
3827 is_avl_partial_function(AVL).
3828
3829 % ----------------------
3830 % set_subtraction /
3831 difference_of_explicit_set(S1,S2,R) :-
3832 difference_of_explicit_set_wf(S1,S2,R,no_wf_available).
3833 % this is called with first argument nonvar (for set_subtraction operator):
3834 difference_of_explicit_set_wf(_S1,S2,R,_) :-
3835 is_definitely_maximal_set(S2), !, R=[].
3836 difference_of_explicit_set_wf(S1,S2,R,_) :- nonvar(S2), S2=[],!, R=S1.
3837 difference_of_explicit_set_wf(S1,S2,R,_) :-
3838 %nonvar(S1),
3839 ? is_very_large_maximal_global_set(S1,Type), !, % TO DO: also for freetype ? cartesian products,...
3840 /* we have a complement-set */
3841 complement_set(S2,Type,R).
3842 difference_of_explicit_set_wf(S1,S2,Result,_) :-
3843 is_not_member_value_closure(S1,Type,MS1),
3844 nonvar(MS1), is_custom_explicit_set(MS1,difference_of_explicit_set_wf),!,
3845 union_complement_set(MS1,S2,Type,Result).
3846 difference_of_explicit_set_wf(_,S2,_,_) :- var(S2), !, fail. % then we cannot do anything below
3847 difference_of_explicit_set_wf(S1,S2,R,WF) :-
3848 is_not_member_value_closure(S2,_Type,MS2), nonvar(MS2),
3849 intersection_of_explicit_set_wf(MS2,S1,R,WF),!.
3850 difference_of_explicit_set_wf(I1,I2,R,_) :-
3851 is_interval_closure_or_integerset(I1,From1,To1),
3852 is_interval_closure_or_integerset(I2,From2,To2),
3853 difference_interval(From1,To1,From2,To2,FromRes,ToRes),
3854 % TO DO: also treat case when difference yields two disjoint intervals
3855 % i.e., do not fail and forget info about interval bounds in case we cannot compute difference as a an interval, e.g., INT - {0}
3856 !,
3857 construct_interval_closure(FromRes,ToRes,R).
3858 difference_of_explicit_set_wf(avl_set(A1),S2,R,WF) :-
3859 (S2=avl_set(A2) ;
3860 ground_value(S2), expand_and_convert_to_avl_set_unless_very_large(S2,A2,WF)),!,
3861 avl_height(A2,H2),
3862 %avl_min(A1,Min1),avl_max(A1,Max1), avl_min(A2,Min2),avl_max(A2,Max2), avl_height(A1,H1),nl,print(diff(avl(H1,Min1,Max1),avl(H2,Min2,Max2))),nl,
3863 avl_height(A1,H1),
3864 ((H2<2 -> true ; H1 > H2+1) % then it is more efficient to expand A2 and remove the A2 elements from A1;
3865 % note that difference_of_explicit_set2 now also sometimes expands both:
3866 % exact threshold when it is beneficial: difference_of_explicit_set2/3
3867 % for {x|x:1..200000 & x mod 2 = 0} - {y|y:2500..29010 & y mod 2 = 0} -> 150 ms vs 80 ms avl(17,int(2),int(200000)),avl(14,int(2500),int(29010)
3868 % {x|x:1..200000 & x mod 2 = 0} - {y|y:2500..59010 & y mod 2 = 0} -> 180 ms vs 80 ms avl(17,int(2),int(200000)),avl(15,int(2500),int(59010))
3869 % {x|x:1..200000 & x mod 2 = 0} - {y|y:500..159010 & y mod 2 = 0} -> 180 ms vs 250 ms avl(17,int(2),int(200000)),avl(17,int(500),int(159010))
3870 -> expand_custom_set_to_sorted_list(S2,ES,_,difference_of_explicit_set1,WF),
3871 difference_of_explicit_set3(ES,A1,R)
3872 ; expand_custom_set_to_sorted_list(avl_set(A1),ES,Done,difference_of_explicit_set2,WF),
3873 difference_of_explicit_set2(ES,H1,A2,H2,R,Done)).
3874 difference_of_explicit_set_wf(S1,S2,R,WF) :-
3875 (S2=avl_set(A2) ;
3876 ground_value(S2), expand_and_convert_to_avl_set_unless_very_large(S2,A2,WF)),!,
3877 avl_height(A2,A2Height),
3878 difference_with_avl(S1,A2,A2Height,R,WF).
3879 % to do: we could detect same_texpr_body for two closures and return R=[]
3880
3881 :- use_module(avl_tools,[avl_approximate_size_from_height/2]).
3882 :- use_module(bsyntaxtree,[safe_create_texpr/4, create_texpr/4, conjunct_predicates/2, mark_bexpr_as_symbolic/2]).
3883 difference_with_avl(S1,A2,A2Height,R,_) :-
3884 is_closure_or_integer_set(S1,[ID],[T],B),
3885 % check if the first argument is infinite; then do the difference set symbolically
3886 % this could supersed the complement set construction and be generalised to other sets apart from avl_sets as A2
3887 avl_approximate_size_from_height(A2Height,A2Size),
3888 Limit is max(A2Size*10,1000000), % if A2 is more than 10% size of S1, probably better to compute difference explicitly
3889 is_very_large_or_symbolic_closure([ID],[T],B,Limit),
3890 !, % TO DO: also allow multiple identifiers
3891 create_texpr(identifier(ID),T,[],TID),
3892 create_texpr(value(avl_set(A2)),set(T),[],A2Value),
3893 create_texpr(not_member(TID,A2Value),pred,[],NotMemA2),
3894 conjunct_predicates([B,NotMemA2],NewBody),
3895 mark_bexpr_as_symbolic(NewBody,NewBodyS),
3896 R = closure([ID],[T],NewBodyS).
3897 difference_with_avl(S1,A2,A2Height,R,WF) :-
3898 (nonvar(S1),S1=avl_set(A1) -> avl_height(A1,H1) ; H1=unknown),
3899 expand_custom_set_to_sorted_list(S1,ES,Done,difference_of_explicit_set3,WF),
3900 difference_of_explicit_set2(ES,H1,A2,A2Height,R,Done).
3901
3902
3903 % construct complement of a set
3904 union_complement_set(S1,S2,Type,Result) :-
3905 ground_value_check(S2,G2),
3906 when(nonvar(G2),union_complement_set2(S1,S2,Type,Result)).
3907 union_complement_set2(S1,S2,Type,Result) :-
3908 union_of_explicit_set(S1,S2,S12),
3909 construct_complement_closure_if_necessary(S12,Type,R),
3910 kernel_objects:equal_object(R,Result,union_complement_set2).
3911
3912 % construct complement of a set
3913 complement_set(S2,Type,Result) :-
3914 ground_value_check(S2,G2),
3915 when(nonvar(G2),complement_set2(S2,Type,Result)).
3916 complement_set2(S2,Type,Result) :-
3917 is_not_member_value_closure(S2,Type,MS2),!, % complement of complement
3918 kernel_objects:equal_object(MS2,Result,complement_set2).
3919 complement_set2(S2,Type,Result) :-
3920 try_expand_and_convert_to_avl_with_check(S2,ExpandedS2,difference_complement_set),
3921 construct_complement_closure_if_necessary(ExpandedS2,Type,R),
3922 kernel_objects:equal_object(R,Result,complement_set2).
3923
3924 :- block construct_complement_closure_if_necessary(-,?,?).
3925 construct_complement_closure_if_necessary(Set,TYPE,R) :-
3926 (Set=[] -> b_type2_set(TYPE,R)
3927 ; is_not_member_value_closure(Set,TYPE,MS) -> R=MS % complement of complement
3928 ; construct_complement_closure(Set,TYPE,R)).
3929
3930 % succeeds if difference of two intervals is also an interval
3931 % SourceLow..SourceUp \ DiffLow..DiffUp
3932 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,9,11,1,8)).
3933 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,9,inf,1,8)).
3934 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,10,12,1,9)).
3935 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,11,12,1,10)).
3936 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,12,13,1,10)).
3937 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,11,inf,1,10)).
3938 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,inf,11,inf,1,10)).
3939 % :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,9,8,1,10)). % 9..8 empty not detected
3940 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,1,8,9,10)).
3941 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,1,10,11,10)). % empty
3942 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,1,inf,inf,10)).
3943 :- assert_must_succeed(custom_explicit_sets:difference_interval(3,10,1,2,3,10)).
3944 :- assert_must_succeed(custom_explicit_sets:difference_interval(3,inf,1,2,3,inf)).
3945 :- assert_must_succeed(custom_explicit_sets:difference_interval(3,10,1,3,4,10)).
3946 :- assert_must_succeed(custom_explicit_sets:difference_interval(3,10,1,9,10,10)).
3947 :- assert_must_succeed(custom_explicit_sets:difference_interval(3,10,1,10,11,10)).
3948 difference_interval(SourceLow,SourceUp,DiffLow,DiffUp,ResLow,ResUp) :-
3949 (nonvar(SourceLow),nonvar(DiffLow),nonvar(DiffUp),
3950 geq_inf(SourceLow,DiffLow)
3951 -> % DiffLow is to left of SourceLow
3952 inc(DiffUp,D1),
3953 maximum_with_inf(D1,SourceLow,ResLow),
3954 ResUp=SourceUp % also works if SourceUp is a variable
3955 ; nonvar(DiffUp),nonvar(SourceUp),nonvar(DiffLow),
3956 geq_inf(DiffUp,SourceUp)
3957 -> % DiffUp is to right of SourceUp
3958 ResLow=SourceLow, % also works if SourceLow is a variable
3959 dec(DiffLow,D1),
3960 minimum_with_inf(SourceUp,D1,ResUp)).
3961
3962 inc(N,R) :- N==inf,!,R=inf.
3963 inc(N,N1) :- N1 is N+1.
3964 dec(N,R) :- N==inf,!,R=inf.
3965 dec(N,N1) :- N1 is N-1.
3966
3967 :- use_module(library(ordsets), [ord_subtract/3]).
3968 :- block difference_of_explicit_set2(?,?,?,?,?,-).
3969 difference_of_explicit_set2(ES,A1Height,A2,A2Height,R,_) :-
3970 (number(A1Height), A1Height+4 >= A2Height -> true
3971 ; A2Height < 5
3972 ; Limit is 2**(A2Height-4),
3973 length_larger_than(ES,Limit)
3974 % TO DO: we could try and pass sizes from specific closures to this predicate
3975 ),
3976 % A1 is not much larger than A2, then it is probably faster to use ord_subtract on expanded A2
3977 % {x|x mod 2 =0 & x:1..10000} - {y|y mod 3 =0 & y : 1..200000} : still more efficient with ord_subtract
3978 !,
3979 avl_domain(A2,A2Expanded),
3980 ord_subtract(ES,A2Expanded,OrdRes),
3981 sorted_ground_normalised_list_to_avlset(OrdRes,AVL,difference_of_explicit_set2),
3982 equal_object(AVL,R).
3983 difference_of_explicit_set2(ES,_A1Height,A2,_A2Height,R,_) :-
3984 avl_min(A2,Min),
3985 diff1(ES,Min,A2,IRes),
3986 ord_list_to_avlset(IRes,AVL,difference), % we have generated the elements in the right order already
3987 equal_object(AVL,R). % due to delays in expansion the result could be instantiated
3988
3989
3990 length_larger_than([_|T],Limit) :-
3991 (Limit<1 -> true
3992 ; L1 is Limit-1, length_larger_than(T,L1)).
3993
3994 diff1([],_, _,[]).
3995 diff1([H|T],Min,A1, Res) :-
3996 (H @< Min -> Res = [H-true|Res2],diff1(T,Min,A1,Res2)
3997 ; diff2([H|T],A1,Res)).% TO DO: compute avl_max
3998
3999 diff2([],_, []).
4000 diff2([H|T],A1, Res) :-
4001 (avl_fetch(H,A1) -> Res = Res2 ; Res = [H-true|Res2]), diff2(T,A1,Res2).
4002
4003 % another version to be used when second set small in comparison to first set
4004 difference_of_explicit_set3([],A1,Res) :- construct_avl_set(A1,AVL),
4005 equal_object(AVL,Res). % due to delay in expansion, Res could now be instantiated
4006 difference_of_explicit_set3([H|T],A1,ARes) :-
4007 (avl_delete(H,A1,_True,A2) -> true ; A2=A1),
4008 difference_of_explicit_set3(T,A2,ARes).
4009
4010 % -------------------------
4011
4012 % a version of add_element_to_explicit_set where we have already done the groundness check
4013 add_ground_element_to_explicit_set_wf(avl_set(A),Element,R,WF) :- !,
4014 convert_to_avl_inside_set_wf(Element,AEl,WF),
4015 avl_store(AEl,A,true,A2),!,R=avl_set(A2).
4016 add_ground_element_to_explicit_set_wf(Set,Element,R,WF) :-
4017 add_element_to_explicit_set_wf(Set,Element,R,WF).
4018
4019 add_element_to_explicit_set_wf(global_set(GS),_,R,_) :- is_maximal_global_set(GS), !, R=global_set(GS).
4020 add_element_to_explicit_set_wf(freetype(ID),_,R,_) :- is_maximal_freetype(ID),!, R=freetype(ID).
4021 add_element_to_explicit_set_wf(avl_set(A),Element,R,WF) :-
4022 ground_value(Element), %% was element_can_be_added_or_removed_to_avl(Element),
4023 convert_to_avl_inside_set_wf(Element,AEl,WF),
4024 avl_store(AEl,A,true,A2),!,R=avl_set(A2). /* AVL not normalised */
4025 /* do we need to add support for (special) closures ??
4026 add_element_to_explicit_set_wf(Clos,Element,R,_) :- nonvar(Element),Element=int(X), nonvar(X),
4027 is_interval_closure_or_integerset(Clos,Low,Up), ground(Low), ground(Up),
4028 union_of_interval(X,X,Low,Up,FromRes,ToRes),
4029 !,
4030 construct_interval_closure(FromRes,ToRes,R).
4031 % not-member closure not dealt with here
4032 */
4033
4034 element_can_be_added_or_removed_to_avl(Element) :-
4035 ground_value(Element),
4036 does_not_contain_closure(Element).
4037 ground_element_can_be_added_or_removed_to_avl(Element) :- /* use if you know the element to be ground */
4038 does_not_contain_closure(Element).
4039
4040 % does not contain closure or infinite other sets
4041 does_not_contain_closure([]).
4042 does_not_contain_closure([H|T]) :-
4043 (simple_value(H) -> true /* TO DO: check if we could have a closure at the end ?? */
4044 ; does_not_contain_closure(H),list_does_not_contain_closure(T)).
4045 does_not_contain_closure(fd(_,_)).
4046 does_not_contain_closure(pred_true /* bool_true */).
4047 does_not_contain_closure(pred_false /* bool_false */).
4048 does_not_contain_closure(int(_)).
4049 does_not_contain_closure(string(_)).
4050 does_not_contain_closure(term(_)). % real/floating number
4051 does_not_contain_closure((X,Y)) :- does_not_contain_closure(X), does_not_contain_closure(Y).
4052 does_not_contain_closure(avl_set(_)).
4053 ?does_not_contain_closure(global_set(G)) :- \+ is_infinite_global_set(G,_).
4054 %does_not_contain_closure(freetype(_)).
4055 does_not_contain_closure(freeval(_,_,Value)) :- does_not_contain_closure(Value).
4056 does_not_contain_closure(rec(Fields)) :- does_not_contain_closure_fields(Fields).
4057
4058 does_not_contain_closure_fields([]).
4059 does_not_contain_closure_fields([field(_,Val)|T]) :- does_not_contain_closure(Val),
4060 does_not_contain_closure_fields(T).
4061
4062 list_does_not_contain_closure([]).
4063 list_does_not_contain_closure([H|T]) :-
4064 does_not_contain_closure(H),list_does_not_contain_closure(T).
4065 list_does_not_contain_closure(avl_set(_)).
4066 list_does_not_contain_closure(global_set(G)) :- \+ is_infinite_global_set(G,_).
4067
4068 simple_value(fd(_,_)).
4069 simple_value(pred_true /* bool_true */).
4070 simple_value(pred_false /* bool_false */).
4071 simple_value(int(_)).
4072 simple_value((A,B)) :- simple_value(A), simple_value(B).
4073 simple_value(string(_)).
4074
4075
4076 % a version of the above which throws error if element cannot be added
4077 % assumes element_can_be_added_or_removed_to_avl has been checked
4078 remove_element_from_explicit_set(avl_set(A),Element,R) :-
4079 element_can_be_added_or_removed_to_avl(Element), % remove check?
4080 convert_to_avl_inside_set(Element,AEl), !,
4081 direct_remove_element_from_avl(A,AEl,R).
4082 remove_element_from_explicit_set(ES,Element,R) :-
4083 add_internal_error('Cannot remove element from explicit set:',remove_element_from_explicit_set(ES,Element,R)).
4084
4085 direct_remove_element_from_avl(A,AEl,R) :-
4086 avl_delete(AEl,A,_True,A2),
4087 construct_avl_set(A2,R). /* AVL not normalised */
4088
4089 /* same as remove but element can be absent */
4090 delete_element_from_explicit_set(avl_set(A),Element,R) :-
4091 element_can_be_added_or_removed_to_avl(Element),
4092 convert_to_avl_inside_set(Element,AEl), !,
4093 (avl_delete(AEl,A,_True,A2)
4094 -> construct_avl_set(A2,R)
4095 ; R = avl_set(A)
4096 ). /* AVL not normalised */
4097
4098 is_maximal_global_set(GS) :- is_maximal_global_set(GS,_Type).
4099 is_maximal_global_set(GS,_) :- var(GS),!,fail.
4100 is_maximal_global_set('INTEGER',Type) :- !, Type=integer.
4101 is_maximal_global_set('REAL',Type) :- !, Type=real.
4102 is_maximal_global_set('FLOAT',_) :- !, fail.
4103 is_maximal_global_set('STRING',Type) :- !, Type=string.
4104 is_maximal_global_set(GS,global(GS)) :-
4105 \+ kernel_objects:integer_global_set(GS).
4106
4107 % To do: maybe get rid of all complement set code; add in_difference_set as symbolic binary operator
4108 %is_very_large_maximal_global_set(X,_) :- print(very(X)),nl,fail.
4109 is_very_large_maximal_global_set(closure(P,T,B),Type) :- is_definitely_maximal_closure(P,T,B),
4110 couplise_list(T,Type).
4111 is_very_large_maximal_global_set(global_set('INTEGER'),integer).
4112 is_very_large_maximal_global_set(global_set('STRING'),string).
4113 is_very_large_maximal_global_set(global_set('REAL'),string).
4114 is_very_large_maximal_global_set(freetype(ID),freetype(ID)) :- is_infinite_freetype(ID).
4115
4116
4117
4118 remove_minimum_element_custom_set(avl_set(S),X,RES) :- !,
4119 avl_del_min(S,X,_True,Res0),
4120 (empty_avl(Res0) -> RES=[] ; RES = avl_set(Res0)).
4121 %remove_minimum_element_custom_set(closure(P,T,B),X,RES) :-
4122 % is_interval_closure_or_integerset(Clos,Low,Up),!,
4123 % X = Low, TO DO: construct new interval closure
4124 remove_minimum_element_custom_set(CS,X,RES) :-
4125 expand_custom_set_to_list(CS,ECS,Done,remove_minimum_element_custom_set),
4126 remove_minimum_element_custom_set2(ECS,X,RES,Done).
4127
4128 :- block remove_minimum_element_custom_set2(?,?,?,-).
4129 % wait until Done: otherwise the Tail of the list could be instantiated by somebody else; interfering with expand_custom_set_to_list
4130 remove_minimum_element_custom_set2([H|T],X,RES,_) :- equal_object((H,T),(X,RES)).
4131
4132
4133 min_of_explicit_set_wf(avl_set(S),Min,_) :- !, avl_min(S,Min).
4134 min_of_explicit_set_wf(Clos,Min,WF) :-
4135 is_interval_closure_or_integerset(Clos,Low,Up),
4136 (Low == minus_inf
4137 -> add_wd_error('minimum of unbounded infinite set not defined:',Clos,WF)
4138 ; cs_greater_than_equal(Up,Low),
4139 Min=int(Low)).
4140
4141 cs_greater_than_equal(X,Y) :-
4142 ((X==inf;Y==minus_inf) -> true ; kernel_objects:less_than_equal_direct(Y,X)).
4143
4144
4145 max_of_explicit_set_wf(avl_set(S),Max,_) :- !,avl_max(S,Max).
4146 max_of_explicit_set_wf(Clos,Max,WF) :-
4147 is_interval_closure_or_integerset(Clos,Low,Up),
4148 (Up==inf
4149 -> add_wd_error('maximum of unbounded infinite set not defined:',Clos,WF)
4150 ; cs_greater_than_equal(Up,Low),
4151 Max=int(Up)).
4152
4153 % ------------- SIGMA/PI --------------
4154
4155 % compute sum or product of an integer set:
4156 sum_or_mul_of_explicit_set(avl_set(S),SUMorMUL,Result) :-
4157 avl_domain(S,Dom),
4158 (SUMorMUL=sum -> simple_sum_list(Dom,0,R) ; simple_mul_list(Dom,1,R)),
4159 Result = int(R).
4160 sum_or_mul_of_explicit_set(CS,SUMorMUL,Result) :- SUMorMUL == sum,
4161 is_interval_closure(CS,Low,Up),
4162 sum_interval(Low,Up,Result),
4163 sum_interval_clpfd_prop(Low,Up,Result).
4164
4165 :- block sum_interval(-,?,?), sum_interval(?,-,?).
4166 sum_interval(Low,Up,_) :- (\+ number(Low) ; \+ number(Up)),!,
4167 add_error(sum_interval,'Cannot compute sum of interval: ',Low:Up),fail.
4168 sum_interval(Low,Up,Result) :- Low>Up,!, Result=int(0).
4169 sum_interval(Low,Up,Result) :-
4170 R is ((1+Up-Low)*(Low+Up)) // 2, % generalisation of Gauss formula k*(k+1)//2
4171 Result = int(R).
4172
4173 sum_interval_clpfd_prop(Low,Up,Result) :-
4174 preferences:preference(use_clpfd_solver,true), Result=int(R),
4175 var(R), % we haven't computed the result yet; the bounds are not known; set up constraint propagation rules
4176 !,
4177 try_post_constraint((Low #>= 0) #=> (R #> 0)), % we could provide better bounds here for negative numbers
4178 try_post_constraint(((Low #=< Up) #\/ (R #\= 0)) #=> (R #= ((1+Up-Low)*(Low+Up))//2)),
4179 try_post_constraint((Low #> Up) #=> (R #= 0)).
4180 % not working yet: x = SIGMA(i).(i:-3..n|i) & x=0 & n< -1
4181 sum_interval_clpfd_prop(_,_,_).
4182
4183 simple_sum_list([],A,A).
4184 simple_sum_list([int(H)|T],Acc,R) :- NA is Acc+H, simple_sum_list(T,NA,R).
4185 simple_mul_list([],A,A).
4186 simple_mul_list([int(H)|T],Acc,R) :- NA is Acc*H, simple_mul_list(T,NA,R).
4187
4188
4189 /*
4190 direct_product_symbolic(S,R,Res) :- % NOT YET FINISHED
4191 nonvar(S), S=closure(PS,[T1,TS2],RS),
4192 nonvar(R), R=closure(PR,[T1,TR1],RR),
4193 is_lambda_value_domain_closure(PS,TS,RS, SDomainValue,SExpr),
4194 is_lambda_value_domain_closure(PR,TR,RR, RDomainValue,RExpr),
4195 construct_closure(['zzz','_lambda_result_'],[T1,couple(TR1,TR2)],
4196 member(zzz,SDomainValue) , member(zzz,RDomainValue), eq(lambda,pair(SExpr,RExpr))).
4197 */
4198
4199 % we assume that try_expand_and_convert_to_avl_unless_very_large already called on arguments
4200 direct_product_explicit_set(S,R,Res) :-
4201 nonvar(R), %is_custom_explicit_set(R,direct_product),
4202 nonvar(S), %is_custom_explicit_set(S,direct_product),
4203 direct_product_explicit_set_aux(S,R,Res).
4204 %direct_product_explicit_set_aux(S,R,Res) :- (S = closure(_,_,_) ; R = closure(_,_,_)),
4205 % print_term_summary(direct_product_explicit_set_aux(S,R,Res)),nl,
4206 % % TO DO: generate closure
4207 % fail.
4208 direct_product_explicit_set_aux(avl_set(AS),avl_set(AR),Res) :-
4209 % the expansion guarantees that we have the lists ES and ER then in sorted order
4210 avl_domain(AS,ES), % -> expand_custom_set(avl_set(AS),ES),
4211 avl_domain(AR,ER), % -> expand_custom_set(avl_set(AR),ER),
4212 direct_product3(ES,ER,DPList),
4213 ord_list_to_avlset(DPList,DPAVL,direct_product), % is it really ordered ? findall must also return things ordered!
4214 equal_object(DPAVL,Res,direct_product_explicit_set).
4215
4216 direct_product3([],_Rel2,[]).
4217 direct_product3([(From,To1)|T1],Rel2,Res) :-
4218 get_next_mapped_to_eq(T1,From,TTo,Tail1), ToList1 = [To1|TTo],
4219 get_next_mapped_to(Rel2,From,ToList2,Tail2),
4220 calc_direct_product(ToList1,From,ToList2,Res,Rest),
4221 (Tail2=[] -> Rest=[] ; direct_product3(Tail1,Tail2,Rest)).
4222
4223 % get all elements which map to From, supposing that the list is sorted & we have already had a match
4224 get_next_mapped_to_eq([],_,[],[]).
4225 get_next_mapped_to_eq([(From2,To2)|T],From,Result,Tail) :-
4226 (From=From2 -> Result = [To2|RR], get_next_mapped_to_eq(T,From,RR,Tail)
4227 ; Result = [], Tail = [(From2,To2)|T]
4228 ).
4229
4230 % get all elements which map to From, supposing the list is sorted
4231 get_next_mapped_to([],_,[],[]).
4232 get_next_mapped_to([(From2,To2)|T],From,Result,Tail) :-
4233 (From=From2 -> Result = [To2|RR], get_next_mapped_to_eq(T,From,RR,Tail)
4234 ; From2 @> From -> Result = [], Tail = [(From2,To2)|T]
4235 ; get_next_mapped_to(T,From,Result,Tail)
4236 ).
4237
4238 calc_direct_product([],_From,_,Tail,Tail).
4239 calc_direct_product([To1|T1],From,To2List,Result,Tail) :-
4240 findall((From,(To1,To2))-true,member(To2,To2List),Result,ResResult),
4241 calc_direct_product(T1,From,To2List,ResResult,Tail).
4242
4243 % TO DO: maybe also add a special rule for infinite R such as event_b_identity ?
4244 domain_restriction_explicit_set_wf(S,R,Res,WF) :- /* S <| R */
4245 nonvar(R),
4246 (nonvar(S),is_one_element_custom_set(S,El),R \= closure(_,_,_) ->
4247 domain_restrict_singleton_element(El,R,Res)
4248 ; restriction_explicit_set_wf(S,R,Res,domain,pred_true,WF)).
4249 domain_subtraction_explicit_set_wf(S,R,Res,WF) :- /* S <<| R */
4250 (nonvar(S),is_one_element_custom_set(S,El), nonvar(R), R=avl_set(AVL) ->
4251 avl_domain_subtraction_singleton(AVL,El,ARes),
4252 construct_avl_set(ARes,Res) % TO DO: use this also when S is small and R large
4253 ; restriction_explicit_set_wf(S,R,Res,domain,pred_false,WF)).
4254 range_restriction_explicit_set_wf(R,S,Res,WF) :- /* R |> S */
4255 restriction_explicit_set_wf(S,R,Res,range,pred_true,WF).
4256 range_subtraction_explicit_set_wf(R,S,Res,WF) :- /* R |>> S */
4257 restriction_explicit_set_wf(S,R,Res,range,pred_false,WF).
4258
4259
4260 domain_restrict_singleton_element(El,R,Res) :- /* {El} <| R ; TO DO maybe apply this technique for "small" sets as well */
4261 nonvar(R), is_custom_explicit_set(R,domain_restrict_singleton_element),
4262 expand_and_convert_to_avl_set(R,AR,domain_restrict_singleton_element,''), % can generate ARel=empty; will fail if not possible to convert
4263 findall((El,Z)-true, avl_fetch_pair(El,AR,Z), RTuples),
4264 ord_list_to_avlset(RTuples,Res,domain_restrict_singleton_element).
4265
4266 restriction_explicit_set_wf(Set,Rel,Res,_RanOrDom,AddWhen,WF) :- Set==[],!,
4267 (AddWhen=pred_false
4268 -> equal_object_wf(Rel,Res,restriction_explicit_set_wf,WF) % {} <<| Rel = Rel |>> {} = Rel
4269 ; kernel_objects:empty_set_wf(Res,WF)
4270 ).
4271 restriction_explicit_set_wf(Set,Rel,Res,_RanOrDom,AddWhen,WF) :- is_definitely_maximal_set(Set),!,
4272 (AddWhen=pred_true
4273 -> equal_object_wf(Rel,Res,restriction_explicit_set_wf,WF) % TYPE <| Rel = Rel |> TYPE = Rel
4274 ; kernel_objects:empty_set_wf(Res,WF)
4275 ).
4276 restriction_explicit_set_wf(_,Rel,_,_,_,_) :- var(Rel),!,fail.
4277 restriction_explicit_set_wf(Set,closure(Paras,Types,Body),Res,RanOrDom,AddWhen,WF) :-
4278 % perform symbolic treatment by adding restriction predicate to Body
4279 !,
4280 (RanOrDom=domain
4281 -> get_domain_id_or_expr(Paras,Types,TID,TT)
4282 ; get_range_id_or_expr(Paras,Types,TID,TT)
4283 ),
4284 TSet=b(value(Set),set(TT),[]),
4285 (AddWhen = pred_true
4286 -> PRED = member(TID,TSet)
4287 ; PRED = not_member(TID,TSet) ),
4288 conjunct_predicates([b(PRED,pred,[]),Body],NewBody),
4289 % translate:print_bexpr(NewBody),nl,
4290 try_expand_and_convert_to_avl_with_catch_wf(closure(Paras,Types,NewBody),Res,restriction_explicit_set_wf,WF).
4291 restriction_explicit_set_wf(Set,Rel,Res,RanOrDom,AddWhen,WF) :-
4292 is_custom_explicit_set(Rel,restriction_explicit_set_wf),
4293 expand_and_convert_to_avl_set(Rel,ARel,restriction_explicit_set_wf,''), % can generate ARel=empty; will fail if not possible to convert
4294 avl_domain(ARel,ERel), % -> expand_custom_set(avl_set(ARel),ERel),
4295 %try_expand_and_convert_to_avl_unless_large_wf(Set,ES,WF),
4296 (nonvar(Set),Set=avl_set(AVLS)
4297 -> restrict2_avl(ERel,AVLS,DRes,RanOrDom,AddWhen,Done)
4298 ; restrict2(ERel,Set,DRes,RanOrDom,AddWhen,Done,WF)
4299 ),
4300 finish_restriction(Done,DRes,Res).
4301
4302 % extract domain expression for domain restriction/subtraction predicate:
4303 get_domain_id_or_expr([DR],[couple(TD,TR)], PRJ1, TD) :- !, % special case: just one parameter in closure
4304 TID = b(identifier(DR),couple(TD,TR),[]),
4305 PRJ1 = b(first_of_pair(TID),TD,[]).
4306 get_domain_id_or_expr([D1|Paras],[TD1|Types],Expr,Type) :-
4307 get_dom_couple_aux(Paras,Types, b(identifier(D1),TD1,[]), TD1, Expr,Type).
4308
4309 get_dom_couple_aux([_RangeID],[_], AccExpr, AccType, Expr, Type) :- !, Expr=AccExpr, Type=AccType.
4310 get_dom_couple_aux([D2|TParas],[TD2|Types], AccExpr, AccType, Expr, Type) :-
4311 TID2 = b(identifier(D2),TD2,[]),
4312 NewAccType = couple(AccType,TD2),
4313 NewAcc = b(couple(AccExpr,TID2),NewAccType,[]),
4314 get_dom_couple_aux(TParas,Types,NewAcc,NewAccType,Expr,Type).
4315
4316 :- use_module(library(lists),[last/2]).
4317 % extract range expression for range restriction/subtraction predicate:
4318 get_range_id_or_expr( [DR],[CType], PRJ2, TR) :- !, % special case: just one parameter in closure
4319 CType = couple(TD,TR),
4320 TID = b(identifier(DR),CType,[]),
4321 PRJ2 = b(second_of_pair(TID),TD,[]).
4322 get_range_id_or_expr( [_|Paras],[_|Types], b(identifier(R),TR,[]), TR) :-
4323 last(Paras,R), last(Types,TR).
4324
4325 :- block finish_restriction(-,?,?).
4326 finish_restriction(_,DRes,Res) :-
4327 ord_list_to_avlset(DRes,Restriction,restriction),
4328 ? equal_object(Restriction,Res,finish_restriction). % as we may block below: we need to use equal_object
4329
4330 restrict2([],_,[],_,_,done,_WF).
4331 restrict2([(From,To)|T],S,Res,RanOrDom,AddWhen,Done,WF) :-
4332 (RanOrDom==domain -> El=From ; El=To),
4333 kernel_equality:membership_test_wf(S,El,MemRes,WF), % TO DO: WF Version !!
4334 /* this only makes sense once we have the full result as argument:
4335 (nonvar(MemRes) -> true % it is already decided
4336 ; AddWhen=pred_true -> kernel_equality:membership_test_wf(Res,(From,To),MemRes,WF)
4337 ; kernel_equality:membership_test_wf(Res,(From,To),InResult,WF), bool_pred:negate(InResult,MemRes)
4338 ), */
4339 ? restrict3(MemRes,From,To,T,S,Res,RanOrDom,AddWhen,Done,WF).
4340 :- block restrict3(-, ?,?, ?,?,?, ?,?,?,?).
4341 restrict3(MemRes, From,To, T,S,Res, RanOrDom,AddWhen,Done,WF) :-
4342 (AddWhen=MemRes -> Res = [(From,To)-true|TRes]
4343 ; Res=TRes),
4344 ? restrict2(T,S,TRes,RanOrDom,AddWhen,Done,WF).
4345
4346 % optimised version when second set is also an AVL tree: less blocking,...
4347 restrict2_avl([],_,[],_,_,done).
4348 restrict2_avl([(From,To)|T],AVLS,Res,RanOrDom,AddWhen,Done) :-
4349 fetch(RanOrDom,From,To,AVLS,MemRes),
4350 (AddWhen=MemRes -> Res = [(From,To)-true|TRes]
4351 ; Res=TRes),
4352 restrict2_avl(T,AVLS,TRes,RanOrDom,AddWhen,Done).
4353
4354 fetch(domain,El,_,AVLS,MemRes) :- (avl_fetch(El,AVLS) -> MemRes=pred_true ; MemRes = pred_false).
4355 fetch(range,_,El,AVLS,MemRes) :- (avl_fetch(El,AVLS) -> MemRes=pred_true ; MemRes = pred_false).
4356
4357 % override R(X) := Y
4358 override_pair_explicit_set(avl_set(S),X,Y,avl_set(NewAVL)) :- element_can_be_added_or_removed_to_avl(X),
4359 element_can_be_added_or_removed_to_avl(Y),
4360 convert_to_avl_inside_set(X,AX),
4361 convert_to_avl_inside_set(Y,AY),
4362 avl_domain_subtraction_singleton(S,AX,AVL2),
4363 avl_store((AX,AY), AVL2, true, NewAVL).
4364
4365 avl_domain_subtraction_singleton(AVL,AX,NewAVL) :-
4366 avl_delete_pair(AX,AVL,_True,AVL2),
4367 !, % recurse, in case we have multiple entries
4368 % this recursion could be avoided if we know AVL to be a function
4369 avl_domain_subtraction_singleton(AVL2,AX,NewAVL).
4370 avl_domain_subtraction_singleton(AVL,_,AVL).
4371
4372 % try and decompose an AVL set into a cartesian product
4373 % AVL = Set1 * Set2
4374 % much faster e.g. for let xx = ((1..10)*(3..1000)\/ {0}*(3..1000)) and then xx = AA*BB
4375 % should not produce pending co-routines
4376 decompose_avl_set_into_cartesian_product_wf(AVL,DomainSet,RangeSet,WF) :-
4377 avl_domain(AVL,Expansion),
4378 decompose_cart(Expansion,'$none',DomainList,[],RangeList),
4379 construct_avl_from_lists_wf(DomainList,DomainSet,WF),
4380 construct_avl_from_lists_wf(RangeList,RangeSet,WF).
4381
4382 decompose_cart([],_,[],[],_).
4383 decompose_cart([(A,B)|T],Prev,Domain,Range,FullRange) :-
4384 (A=Prev
4385 -> Range = [B|TRange],
4386 decompose_cart(T,Prev,Domain,TRange,FullRange)
4387 ; Domain = [A|TDom], Range=[],
4388 FullRange = [B|TRange],
4389 decompose_cart(T,A,TDom,TRange,FullRange)
4390 ).
4391
4392 /* --------- */
4393 /* EXPANSION */
4394 /* --------- */
4395
4396 :- use_module(b_global_sets,[all_elements_of_type_wf/3, all_elements_of_type_rand_wf/3]).
4397 :- use_module(kernel_freetypes,[expand_freetype/3]).
4398
4399 expand_custom_set(X,R) :- expand_custom_set_wf(X,R,expand_custom_set,no_wf_available).
4400 expand_custom_set(X,R,Src) :- expand_custom_set_wf(X,R,Src,no_wf_available).
4401 expand_custom_set_wf(X,R,Source,WF) :- var(X), !,
4402 add_error_and_fail(expand_custom_set_wf, 'Variable as argument: ',expand_custom_set_wf(X,R,Source,WF)).
4403 expand_custom_set_wf(global_set(GS),ExpandedSet,_,WF) :- !,
4404 all_elements_of_type_wf(GS,ExpandedSet,WF). % they are generated in order
4405 expand_custom_set_wf(freetype(GS),ValueList,_,WF) :- !,
4406 expand_freetype(GS,ValueList,WF).
4407 expand_custom_set_wf(avl_set(AVL),ExpandedSet,_,_) :- !,
4408 avl_domain(AVL,ExpandedSet).
4409 expand_custom_set_wf(closure(Parameters,PTypes,Cond),Res,Source,WF) :- !,
4410 ? expand_closure_to_list(Parameters,PTypes,Cond,Res,_Done,Source,WF).
4411 %wait_try_expand_custom_set(Res1,Res). % could be in AVL form; no longer the case !
4412 expand_custom_set_wf(Set,_,Source,_) :-
4413 add_error_and_fail(expand_custom_set(Source),'Cannot expand custom set: ',Set).
4414
4415
4416
4417 %try_expand_only_custom_closure_global(X,Y) :-
4418 % (var(X) -> X=Y ; expand_only_custom_closure_global(X,Y,check)).
4419
4420 expand_only_custom_closure_global(X,R,C,_WF) :- var(X), !,
4421 add_error_and_fail(expand_only_custom_closure_global, 'Variable as argument: ',expand_only_custom_closure_global(X,R,C)).
4422 expand_only_custom_closure_global(global_set(GS),ExpandedSet,_,WF) :- !,all_elements_of_type_wf(GS,ExpandedSet,WF).
4423 expand_only_custom_closure_global(freetype(GS),ExpandedSet,_,_WF) :- !,ExpandedSet=freetype(GS).
4424 expand_only_custom_closure_global(avl_set(AVL),ExpandedSet,_,_WF) :- !, ExpandedSet=avl_set(AVL).
4425 expand_only_custom_closure_global(closure(Parameters,PTypes,Cond),Res,CheckTimeOuts,WF) :- !,
4426 (Res==[] -> is_empty_explicit_set(closure(Parameters,PTypes,Cond)) % TO DO: think about other special cases
4427 ; expand_closure_to_avl_or_list(Parameters,PTypes,Cond,Res,CheckTimeOuts,WF)).
4428 expand_only_custom_closure_global(Set,Set,_CheckTimeOuts,_WF).
4429 %:- add_error_and_fail(expand_only_custom_closure_global,'Cannot expand custom set: ',Set).
4430
4431
4432 try_expand_custom_set_with_catch(CS,Expansion,PP) :-
4433 on_enumeration_warning(try_expand_custom_set_wf(CS,Expansion,PP,no_wf_available),
4434 Expansion=CS).
4435
4436 try_expand_custom_set(CS,Expansion) :-
4437 try_expand_custom_set_wf(CS,Expansion,try_expand_custom_set,no_wf_available).
4438
4439
4440 try_expand_custom_set_wf(CS,Res,_,_) :- var(CS),!,Res=CS.
4441 try_expand_custom_set_wf([],Res,_,_) :- !, Res=[].
4442 try_expand_custom_set_wf([H|T],Res,_,_) :- !, Res=[H|T].
4443 try_expand_custom_set_wf(CS,Res,Src,WF) :-
4444 expand_custom_set_wf(CS,Res,Src,WF). % will generate error message for illegal sets
4445
4446
4447 :- assert_must_succeed((expand_custom_set_to_list(closure(['_zzzz_unit_tests'],
4448 [couple(integer,integer)],
4449 b(member(b(identifier('_zzzz_unit_tests'),couple(integer,integer),[generated]),
4450 b(value([(int(1),int(22))]),set(couple(integer,integer)),[])),pred,[])),R),R==[(int(1),int(22))])).
4451
4452 expand_custom_set_to_list(CS,List) :- expand_custom_set_to_list(CS,List,_Done,unknown).
4453
4454 % a version of expansion which returns guaranteed_ground if the List is guaranteed to be ground
4455 expand_custom_set_to_list_gg(CS,List,GuaranteedGround,_PP) :-
4456 nonvar(CS), CS=avl_set(AVL), var(List),
4457 !,
4458 GuaranteedGround = guaranteed_ground,
4459 avl_domain(AVL,List).
4460 expand_custom_set_to_list_gg(CS,List,not_guaranteed_ground,PP) :-
4461 expand_custom_set_to_list(CS,List,_Done,PP).
4462
4463 % a version where the expansion should happen straightaway and should not block:
4464 expand_custom_set_to_list_now(CS,List) :- expand_custom_set_to_list(CS,List,Done,unknown),
4465 (Done==true -> true ; print_error(expand_custom_set_to_list_not_done(CS,List))).
4466
4467 :- block expand_custom_set_to_sorted_list(-,-,?,?,?).
4468 % sorts the resulting list if needed
4469 % due to random enumeration
4470 expand_custom_set_to_sorted_list(From,To,Done,Source,WF) :-
4471 expand_custom_set_to_list(From,UnsortedTo,Done,Source),
4472 (get_preference(randomise_enumeration_order,true)
4473 -> sort_when_done(Done,UnsortedTo,To,WF) ; UnsortedTo = To).
4474
4475 :- block sort_when_done(-,?,?,?).
4476 sort_when_done(_,Unsorted,Res,WF) :- sort(Unsorted,Sorted),
4477 equal_object_wf(Sorted,Res,sort_when_done,WF).
4478
4479 expand_custom_set_to_list(From,To,Done,Source) :-
4480 expand_custom_set_to_list_wf(From,To,Done,Source,no_wf_available).
4481
4482 :- use_module(kernel_objects,[equal_object_wf/4]).
4483
4484 % try expand custom set to list; on enumeration warning set Done to enumeration_warning
4485 try_expand_custom_set_to_list_wf(From,To,Done,Source,WF) :-
4486 on_enumeration_warning(expand_custom_set_to_list_wf(From,To,Done,Source,WF),
4487 (Done=enumeration_warning)).
4488
4489 expand_custom_set_to_list_wf(From,To,Done,Source,WF) :-
4490 expand_custom_set_to_list_k_wf(From,To,Done,_Kind,Source,WF).
4491
4492 % a variation of expand_custom_set_to_list which also checks that there are no duplicates in the list
4493 expand_custom_set_to_list_no_dups_wf(From,To,Done,Source,WF) :-
4494 expand_custom_set_to_list_k_wf(From,To,Done,Kind,Source,WF),
4495 check_dups(Kind,To,WF).
4496
4497 :- block check_dups(-,?,?).
4498 check_dups(unsorted_list,List,WF) :- !,
4499 kernel_objects:check_no_duplicates_in_list(List,[],WF).
4500 check_dups(_,_,_).
4501
4502 % warn if duplicates in list; to do: use in prob_safe mode
4503 %:- block warn_dups(-,?,?,?).
4504 %warn_dups(unsorted_list,List,Src,WF) :- !,
4505 % kernel_objects:warn_if_duplicates_in_list(List,Src,WF).
4506 %warn_dups(_,_,_,_).
4507
4508
4509
4510 :- block expand_custom_set_to_list_k_wf(-,-,?,?,?,?).
4511 % ensures that the output is a pure list; the list skeleton should not be instantiated by anybody else
4512 expand_custom_set_to_list_k_wf(From,To,Done,Kind,Source,WF) :-
4513 (var(From) ->
4514 (is_list_skeleton(To)
4515 ? -> equal_object_wf(To,From,Source,WF), Done=true, Kind=unsorted_list
4516 ? ; expand_custom_set_to_list2(To,From,Done,Kind,Source,WF))
4517 ; var(To),is_list_skeleton(From)
4518 -> To=From, Done=true, Kind=unsorted_list % equal_object_wf will also to a Prolog unification
4519 ? ; expand_custom_set_to_list2(From,To,Done,Kind,Source,WF)).
4520
4521 expand_custom_set_to_list2([],ExpandedSet,Done,Kind,_Source,WF) :- !,
4522 ? equal_object_wf([],ExpandedSet,expand_custom_set_to_list2,WF),Done=true,Kind=empty_set.
4523 expand_custom_set_to_list2([H|T],ExpandedSet,Done,Kind,Source,WF) :- !, Kind=unsorted_list,
4524 ? equal_object_wf([H|ET],ExpandedSet,expand_custom_set_to_list2,WF),
4525 ? expand_custom_set_to_list3(T,ET,Done,Source,WF).
4526 expand_custom_set_to_list2(global_set(GS),ExpandedSet,Done,Kind,_Source,WF) :- !,
4527 all_elements_of_type_rand_wf(GS,R,WF),
4528 check_list(R,expand_custom_set_to_list2),
4529 equal_object_wf(R,ExpandedSet,expand_custom_set_to_list2,WF),Done=true,Kind=sorted_list.
4530 expand_custom_set_to_list2(avl_set(AVL),ExpandedSet,Done,Kind,_Source,WF) :- !,
4531 avl_domain(AVL,R),
4532 ? equal_object_wf(R,ExpandedSet,expand_custom_set_to_list2,WF), Done=true,Kind=sorted_list.
4533 expand_custom_set_to_list2(closure(Parameters,PTypes,Cond),ExpandedSet,Done,Kind,Source,WF) :- !,
4534 expand_closure_to_list(Parameters,PTypes,Cond,ExpandedSet,Done,Source,WF),
4535 Kind=sorted_list.
4536 %assign_expand_result(CDone,Res,ExpandedSet,Done).
4537 expand_custom_set_to_list2(freetype(ID),ExpandedSet,Done,Kind,_Source,WF) :- !,
4538 expand_freetype(ID,R,WF),
4539 equal_object_wf(R,ExpandedSet,expand_custom_set_to_list2,WF),
4540 Done=true,Kind=sorted_list.
4541 % missing avl_set wrapper:
4542 expand_custom_set_to_list2(node(A,B,C,D,E),ExpandedSet,Done,Kind,Source,WF) :- !,
4543 add_internal_error('Illegal argument: ',expand_custom_set_to_list2(node(A,B,C,D,E),ExpandedSet,Done,Source)),
4544 expand_custom_set_to_list2(avl_set(node(A,B,C,D,E)),ExpandedSet,Done,Kind,Source,WF).
4545 expand_custom_set_to_list2(E,ES,Done,Kind,Source,WF) :-
4546 add_internal_error('Illegal argument: ',expand_custom_set_to_list2(E,ES,Done,Kind,Source,WF)),fail.
4547
4548 :- block expand_custom_set_to_list3(-,-,?,?,?). % we are no longer sure which was From and which is To
4549 expand_custom_set_to_list3(From,To,Done,Source,WF) :-
4550 ? (var(From) -> expand_custom_set_to_list2(To,From,Done,_,Source,WF) ;
4551 ? expand_custom_set_to_list2(From,To,Done,_,Source,WF)).
4552
4553
4554 is_list_skeleton(X) :- var(X),!,fail.
4555 is_list_skeleton([]).
4556 is_list_skeleton([_|T]) :- is_list_skeleton(T).
4557
4558 % true if it is more efficient to keep this, rather than expand into list
4559 is_efficient_custom_set(avl_set(_)).
4560 is_efficient_custom_set(closure(P,T,B)) :-
4561 (is_interval_closure(closure(P,T,B),_,_) -> true ; is_infinite_or_symbolic_closure(P,T,B)).
4562 ?is_efficient_custom_set(global_set(X)) :- is_infinite_global_set(X,_).
4563 is_efficient_custom_set(freetype(_)).
4564
4565 % tries to expand & convert to avl_set; fails if not possible: NOTE: also generates empty AVL
4566 expand_and_convert_to_avl_set(R,AER,Origin,Source) :-
4567 try_expand_and_convert_to_avl(R,ER,Origin,Source),
4568 nonvar(ER),(ER==[] -> AER=empty ; ER=avl_set(AER)).
4569
4570
4571 expand_and_convert_to_avl_set_unless_very_large(R,AER,WF) :-
4572 try_expand_and_convert_to_avl_unless_very_large_wf(R,ER,WF),
4573 nonvar(ER),(ER==[] -> AER=empty ; ER=avl_set(AER)).
4574
4575
4576 % similar to unless_large version, but will only expand if it is guaranteed to be small
4577
4578 try_expand_and_convert_to_avl_if_smaller_than(freetype(GS),Res,_) :- !, Res = freetype(GS).
4579 try_expand_and_convert_to_avl_if_smaller_than([H|T],Res,_) :- !, try_expand_and_convert_to_avl([H|T],Res).
4580 try_expand_and_convert_to_avl_if_smaller_than(avl_set(A),Res,_) :- !, Res=avl_set(A).
4581 try_expand_and_convert_to_avl_if_smaller_than(CS,Res,Limit) :-
4582 (is_small_specific_custom_set(CS,Limit)
4583 -> try_expand_and_convert_to_avl(CS,Res,try_expand_and_convert_to_avl_if_smaller_than,'')
4584 ; Res = CS % TO DO: maybe look at cardinality of types and determine max. cardinality
4585 ).
4586 is_small_specific_custom_set(CS,Limit) :- card_for_specific_custom_set(CS,Card,Code),
4587 call(Code), is_finite_card(Card), Card<Limit.
4588 get_card_for_specific_custom_set(CS,Card) :-
4589 card_for_specific_custom_set(CS,Card,Code),
4590 call(Code), ground(Card).
4591
4592 try_expand_and_convert_to_avl_unless_very_large_wf(CS,Res,WF) :-
4593 try_expand_and_convert_to_avl_unless_large_wf(CS,Res,10000,WF).
4594
4595 try_expand_and_convert_to_avl_unless_large_wf(CS,Res,WF) :-
4596 try_expand_and_convert_to_avl_unless_large_wf(CS,Res,2000,WF).
4597
4598 try_expand_and_convert_to_avl_unless_large_wf(CS,Res,_,_WF) :- var(CS), !, CS=Res.
4599 try_expand_and_convert_to_avl_unless_large_wf(global_set(GS),Res,_,_WF) :- !, Res = global_set(GS).
4600 try_expand_and_convert_to_avl_unless_large_wf(freetype(GS),Res,_,_WF) :- !, Res = freetype(GS).
4601 %try_expand_and_convert_to_avl_unless_large_wf(CS,Res,_WF) :- is_interval_closure(CS,Low,Up),!,
4602 % ((ground(Low),ground(Up),Size is 1+Up-Low, Size<2000)
4603 %% -> try_expand_and_convert_to_avl(CS,Res)
4604 % ; Res = CS
4605 % ).
4606 try_expand_and_convert_to_avl_unless_large_wf(closure(P,T,B),Res,Limit,_WF) :-
4607 is_very_large_or_symbolic_closure(P,T,B,Limit),!, % is explicitly marked as SYMBOLIC
4608 Res=closure(P,T,B).
4609 try_expand_and_convert_to_avl_unless_large_wf(CS,Res,_Limit,WF) :-
4610 % TO DO: check if maybe we cannot determine card explicitly, but have a large lower-bound
4611 try_expand_and_convert_to_avl_wf(CS,Res,try_expand_and_convert_to_avl_unless_large,'',WF).
4612
4613
4614
4615 % calls try_expand_and_convert_to_avl and returns original value if enumeration warning occured
4616 try_expand_and_convert_to_avl_with_catch_wf(CS,Res,Origin,WF) :-
4617 on_enumeration_warning(try_expand_and_convert_to_avl_wf(CS,Res,Origin,'',WF),
4618 Res=CS).
4619
4620 /* tries to generate an avl-structure, if possible */
4621 try_expand_and_convert_to_avl(CS,Res) :-
4622 try_expand_and_convert_to_avl_wf(CS,Res,try_expand_and_convert_to_avl,'',no_wf_available).
4623
4624 try_expand_and_convert_to_avl(CS,Res,Origin,Source) :-
4625 try_expand_and_convert_to_avl_wf(CS,Res,Origin,Source,no_wf_available).
4626
4627 try_expand_and_convert_to_avl_wf(CS,Res,_,_,_WF) :- var(CS), !, CS=Res.
4628 try_expand_and_convert_to_avl_wf(avl_set(A),R,_,_,_WF) :- !, R=avl_set(A).
4629 try_expand_and_convert_to_avl_wf([],R,_,_,_WF) :- !, R=[].
4630 try_expand_and_convert_to_avl_wf([H|T],R,_,_,WF) :- !, try_convert_to_avl_wf([H|T],R,WF).
4631 try_expand_and_convert_to_avl_wf(closure(P,T,B),Res,Origin,_Source,WF) :- !,
4632 debug_opt_push_wait_flag_call_stack_info(WF,
4633 external_call('TRY EXPANDING',[closure(P,T,B)],unknown),WF2),
4634 expand_only_custom_closure_global(closure(P,T,B),Expansion,check(Origin),WF2),
4635 try_convert_to_avl_wf(Expansion,Res,WF).
4636 try_expand_and_convert_to_avl_wf(CS,Res,Origin,_Source,WF) :-
4637 (\+ is_custom_explicit_set(CS,try_expand_and_convert_to_avl_wf)
4638 -> Expansion = CS
4639 ; expand_only_custom_closure_global(CS,Expansion,check(Origin),WF)
4640 ),
4641 try_convert_to_avl_wf(Expansion,Res,WF).
4642
4643 try_convert_to_avl(Expansion,Res) :-
4644 (should_be_converted_to_avl_from_lists(Expansion) -> construct_avl_from_lists(Expansion,Res) ; Res=Expansion).
4645 try_convert_to_avl_wf(Expansion,Res,WF) :-
4646 (should_be_converted_to_avl_from_lists(Expansion) -> construct_avl_from_lists_wf(Expansion,Res,WF) ; Res=Expansion).
4647
4648 should_be_converted_to_avl_from_lists(Value) :- var(Value),!,fail.
4649 should_be_converted_to_avl_from_lists(Value) :-
4650 \+ is_custom_explicit_set(Value,should_be_converted_to_avl_from_lists), % already avl_set, global_set or closure
4651 ? \+ do_not_convert_aux(Value),
4652 ground_value(Value).
4653
4654 do_not_convert_aux(V) :- var(V),!.
4655 do_not_convert_aux((A,B)) :- !,
4656 ? (do_not_convert_aux(A) -> true ; do_not_convert_aux(B)).
4657 do_not_convert_aux([H|T]) :- !, % do not convert a set containing a symbolic closure
4658 ? (var(T) -> true ; do_not_convert_aux(H)).
4659 do_not_convert_aux(rec(Fields)) :- !,
4660 (var(Fields) -> true
4661 ? ; member(field(_,V),Fields), do_not_convert_aux(V) -> true).
4662 do_not_convert_aux(H) :-
4663 ? is_symbolic_closure(H).
4664
4665 should_be_converted_to_avl(Value) :- %preference(use_avl_trees_for_sets,true),
4666 ground_value(Value).
4667
4668 try_expand_and_convert_to_avl_with_check(CS,Res,Origin) :-
4669 try_expand_and_convert_to_avl_with_check(CS,Res,do_not_keep_intervals,Origin).
4670
4671 try_expand_and_convert_to_avl_with_check(CS,Res,_,_Origin) :- var(CS),!, Res = CS.
4672 try_expand_and_convert_to_avl_with_check([],Res,_,_Origin) :- !, Res=[].
4673 try_expand_and_convert_to_avl_with_check(avl_set(A),Res,_,_Origin) :- !, Res=avl_set(A).
4674 try_expand_and_convert_to_avl_with_check([H|T],Res,_,Origin) :- !, try_expand_and_convert_to_avl([H|T],Res,Origin,'').
4675 %try_expand_and_convert_to_avl_with_check(CS,Res,_Origin) :-
4676 % \+ is_custom_explicit_set(CS,try_expand_and_convert_to_avl),!, Res = CS.
4677 try_expand_and_convert_to_avl_with_check(CS,Res,KeepIntervals,_Origin) :-
4678 is_interval_closure(CS,Low,Up),
4679 (var(Low) -> true ; var(Up) -> true % better keep this symbolic as we may be able to do constraint propagation
4680 ; KeepIntervals=keep_intervals(Size) -> Up-Low >= Size
4681 ),
4682 !, % TO DO: see if we should do this check in try_expand_and_convert_to_avl above instead
4683 Res=CS.
4684 try_expand_and_convert_to_avl_with_check(CS,Res,_,Origin) :-
4685 get_card_for_specific_custom_set(CS,Size), % TO DO: avoid checking for special closures twice (below in try_expand_and_convert_to_avl ?)
4686 !,
4687 try_expconv_to_avl_with_size(Size,CS,Res,Origin).
4688 try_expand_and_convert_to_avl_with_check(CS,Res,_,Origin) :-
4689 try_expand_and_convert_to_avl(CS,Res,Origin,'').
4690
4691 try_expconv_to_avl_with_size(inf,CS,Res,Origin) :- !,
4692 debug_format(9,'### Not expanding infinite set~n### ORIGIN: ~w~n',[Origin]),
4693 Res=CS.
4694 try_expconv_to_avl_with_size(inf_overflow,CS,Res,Origin) :- !,
4695 debug_format(9,'### Not expanding very large set~n### ORIGIN: ~w~n',[Origin]),
4696 Res=CS.
4697 try_expconv_to_avl_with_size(Size,CS,Res,Origin) :- Size>=10000000, !,
4698 /* will probably never terminate */
4699 debug_format(9,'### Not expanding very large set with cardinality ~w~n### ORIGIN: ~w~n',[Size,Origin]),
4700 Res=CS.
4701 try_expconv_to_avl_with_size(Size,CS,Res,Origin) :- Size>=50000, !,
4702 print('### WARNING: expanding very large comprehension set, size = '), print(Size),nl,
4703 print('### ORIGIN: '), print(Origin),nl,
4704 try_expand_and_convert_to_avl(CS,Res,Origin,'').
4705 try_expconv_to_avl_with_size(_Size,CS,Res,Origin) :-
4706 try_expand_and_convert_to_avl(CS,Res,Origin,'').
4707
4708 /* underlying assumption for var case: if G is a global set: we get back the
4709 global_set tag immediately: no need to use when to wait;
4710 better: ensure that b_compute_expression always returns a nonvar term */
4711
4712
4713 :- assert_must_succeed((custom_explicit_sets:try_expand_custom_set(closure([xx],[integer],b(falsity,pred,[])),R),R = [])).
4714 :- assert_must_succeed((custom_explicit_sets:test_closure(X),custom_explicit_sets:expand_custom_set(X,EX),
4715 EX = [(fd(1,'Name'),_),(fd(3,'Name'),_)])).
4716
4717 test_closure(X) :- X = closure(['_zzzz_binary'],[couple(global('Name'),set(global('Name')))],
4718 b(member(b(identifier('_zzzz_binary'),couple(global('Name'),set(global('Name'))),[generated]),
4719 b(cartesian_product(b(value([fd(1,'Name'),fd(3,'Name')]),set(global('Name')),[]),
4720 b(value([[fd(2,'Name'),fd(3,'Name')]]),set(set(global('Name'))),[])),
4721 set(couple(global('Name'),set(global('Name')))),[])),pred,[])).
4722
4723
4724 /* --------- */
4725 /* ELEMENT_OF */
4726 /* --------- */
4727
4728
4729 /* A function that instantiates last argument when membership test can be decided */
4730
4731 membership_custom_set(CS,X,R) :- print(warning_deprecated_non_wf_version(CS,X,R)),nl,
4732 membership_custom_set_wf(CS,X,R,_WF).
4733
4734 ?membership_custom_set_wf(avl_set(A),X,R,WF) :- !, membership_avl_set_wf(A,X,R,WF).
4735 membership_custom_set_wf(freetype(_GS),_X,R,_WF) :- !, R=pred_true. % should be covered by clause above
4736 membership_custom_set_wf(CS,X,R,WF) :- R==pred_true,!, element_of_custom_set_wf(X,CS,WF).
4737 membership_custom_set_wf(CS,X,R,WF) :- R==pred_false,!, not_element_of_custom_set_wf(X,CS,WF).
4738 membership_custom_set_wf(CS,_X,R,_WF) :-
4739 is_definitely_maximal_set(CS),!,
4740 R=pred_true.
4741 membership_custom_set_wf(closure(Par,Types,Body),X,R,WF) :- !,
4742 ? closure_membership_wf(X,Par,Types,Body,R,WF).
4743 %membership_custom_set_wf(CS,X,R,WF) :- is_one_element_custom_set(CS,Y),!, % only succeeds for AVL
4744 % kernel_equality:equality_objects_wf_no_enumr(X,Y,R,WF).
4745 membership_custom_set_wf(global_set(GS),X,R,WF) :- !,
4746 membership_global_set(GS,X,R,WF).
4747 membership_custom_set_wf(CS,X,R,WF) :-
4748 add_internal_error('Illegal custom set: ',membership_custom_set_wf(CS,X,R,WF)),fail.
4749
4750 membership_avl_set_wf(A,X,R,WF) :- R==pred_true,!, element_of_avl_set_wf(A,X,WF).
4751 membership_avl_set_wf(A,X,R,WF) :- R==pred_false,!, not_element_of_custom_set_wf(X,avl_set(A),WF).
4752 membership_avl_set_wf(A,X,R,WF) :- is_one_element_avl(A,Y),!,
4753 ? kernel_equality:equality_objects_wf_no_enum(X,Y,R,WF).
4754 membership_avl_set_wf(A,_X,R,_WF) :-
4755 quick_definitely_maximal_set_avl(A),!,
4756 R=pred_true.
4757 membership_avl_set_wf(A,X,R,WF) :- reify_avl_membership(A,X,R,FullReification),
4758 (FullReification==true
4759 -> true %print_term_summary(full_reification(A,X,R)),nl,nl %% did slow down e.g. Bosch Deadlock v9, seems no longer the case
4760 ? ; when((ground(X);nonvar(R)),membership_avl_set_wf2(A,X,R,WF))).
4761
4762 ?membership_avl_set_wf2(A,X,R,WF) :- R==pred_true,!, element_of_avl_set_wf(A,X,WF).
4763 membership_avl_set_wf2(A,X,R,WF) :- R==pred_false,!, not_element_of_custom_set_wf(X,avl_set(A),WF).
4764 membership_avl_set_wf2(AVL,X,R,_WF) :-
4765 ground_element_can_be_added_or_removed_to_avl(X), !,
4766 (safe_avl_member(X,AVL) %safe_avl_member_ground(X,AVL)
4767 -> R=pred_true ; R=pred_false).
4768 membership_avl_set_wf2(AVL,X,Res,WF) :- % X is ground but cannot be added
4769 (Res \== pred_false, element_of_avl_set_wf(AVL,X,WF), Res=pred_true
4770 ;
4771 Res \== pred_true, not_element_of_custom_set_wf(X,avl_set(AVL),WF), Res=pred_false).
4772
4773 membership_global_set(GS,_X,R,_WF) :- is_maximal_global_set(GS),!,
4774 R=pred_true.
4775 membership_global_set(GS,X,R,WF) :- ground(X),!,
4776 (element_of_global_set_wf(X,GS,WF) -> R=pred_true ; R=pred_false).
4777 membership_global_set(GS,X,R,_WF) :- get_integer_set_interval(GS,Low,Up),!,
4778 membership_interval(X,Low,Up,R).
4779 membership_global_set(GS,X,R,WF) :- % this case should probably never apply
4780 (GS=='FLOAT' -> true % currently it actually is also treated like REAL
4781 ; print(uncovered_membership(GS,X,R,WF)),nl),
4782 when(ground(X), (element_of_global_set_wf(X,GS,WF) -> R=pred_true ; R=pred_false)).
4783
4784 membership_interval(X,Low,Up,Res) :- nonvar(Up),Up=inf,!,X=int(IX),
4785 b_interpreter_check:check_arithmetic_operator('<=',Low,IX,Res).
4786 membership_interval(X,Low,Up,Res) :- kernel_equality:in_nat_range_test(X,int(Low),int(Up),Res).
4787
4788 :- use_module(bool_pred).
4789 closure_membership_wf(X,[ZZZZ],[integer],CondClosure,Res,_WF) :-
4790 is_interval_closure_body(CondClosure,ZZZZ,LOW,UP),!,
4791 kernel_equality:in_nat_range_test(X,int(LOW),int(UP),Res).
4792 % TO DO: deal with open intervals 0..inf ...
4793 closure_membership_wf(X,Par,Types,Body,Res,WF) :-
4794 is_member_closure(Par,Types,Body,_Type,VAL),
4795 (VAL=value(_) ; VAL = cartesian_product(b(value(A),_,_),b(value(B),_,_))),!,
4796 (VAL=value(Set)
4797 -> kernel_objects:membership_test_wf(Set,X,Res,WF)
4798 ? ; kernel_equality:cartesian_pair_test_wf(X,A,B,Res,WF)).
4799 closure_membership_wf(X,Par,Typ,Body,Res,WF) :-
4800 is_not_member_closure(Par,Typ,Body,_Type,value(Set)),!,
4801 bool_pred:negate(ResXSet,Res), % was kernel_equality:inv_mem_obj(ResXSet,Res),
4802 kernel_objects:membership_test_wf(Set,X,ResXSet,WF).
4803 % TO DO: if closure = POW closure -> translate into subset_test pow_subset
4804 % TO DO: support a few other closures related to symbolic unary/binary operators: closure1, POW(..), ... ?
4805 % TO DO: expand if set is small
4806 closure_membership_wf(X,Par,Types,Body,Res,WF) :- ground_value(X),!,
4807 closure_membership_ground_wf(X,closure(Par,Types,Body),Res,WF).
4808 closure_membership_wf(X,Par,Types,Body,Res,WF) :-
4809 CS = closure(Par,Types,Body),
4810 is_small_specific_custom_set(CS,100),
4811 try_expand_and_convert_to_avl_wf(CS,Expanded,closure_membership_wf,'',WF),
4812 nonvar(Expanded), Expanded=avl_set(_),
4813 !,
4814 membership_custom_set_wf(Expanded,X,Res,WF).
4815 closure_membership_wf(X,Par,Types,Body,Res,WF) :-
4816 Body \= b(member(_,_),_,_), % otherwise we may have an infinite loop; b_check_boolean_expression will generate a closure which will call closure_membership_wf again; TO DO: refine to allow certain memberships to go through
4817 get_texpr_info(Body,BodyInfo),
4818 \+ member(prob_annotation(recursive(_RID)),BodyInfo), % otherwise we can get errors as recursive identifier _RID needs to be added to local state ! (test 1151 fails otherwise)
4819 % TO DO: add recursive parameter below in set_up_typed_localstate2; + in which other circumstances do we need to set up recursion identifier !
4820 % Try reifiyng the body
4821 NegationContext=positive,
4822 copy_wf_start(WF,closure_membership_wf,CWF),
4823 b_interpreter:set_up_typed_localstate2(Par,Types,BodyInfo,ParValues,TypedVals,[],State,NegationContext),
4824 %couplise_list(Types,XType),
4825 convert_list_into_pairs(ParValues,SingleParValue),
4826 kernel_objects:equal_object(X,SingleParValue,closure_membership_wf),
4827 b_interpreter_check:b_check_boolean_expression(Body,[],State,CWF,PredRes),
4828 !,
4829 (debug_mode(on) -> print('REIFICATION of closure: '), translate:print_bexpr(Body),nl, print(pred_res(X,PredRes)),nl ; true),
4830 b_enumerate:b_tighter_enumerate_all_values(TypedVals,WF), % not necessary ?? as X should get enumerated
4831 Res=PredRes,
4832 copy_wf_finish(WF,CWF).
4833 closure_membership_wf(X,Par,Types,Body,Res,WF) :-
4834 when( (ground(X);nonvar(Res)), %%
4835 % used to be ground(X), % with (ground(X);nonvar(Res)), test 292 failed {x,t|t : BOOL & (x : POW(1024 .. 1025) & bool(x : POW(NATURAL1)) = t)} = {{} |-> TRUE,{1024} |-> TRUE,{1024,1025} |-> TRUE,{1025} |-> TRUE} and test 1088 failed
4836 closure_membership_ground_wf(X,closure(Par,Types,Body),Res,WF)).
4837
4838 closure_membership_ground_wf(X,CS,Res,WF) :- nonvar(Res),!,
4839 % this optimization is checked in test 1452
4840 (Res==pred_true -> element_of_custom_set_wf(X,CS,WF) ; not_element_of_custom_set_wf(X,CS,WF)).
4841 closure_membership_ground_wf(X,CS,Res,WF) :-
4842 % to ensure that we leave no choice point behind we have to force full evaluation of element/not_element calls:
4843 % hence we do not call element_of_custom_set_wf or not_element_of_custom_set_wf below !!
4844 kernel_waitflags:get_idle_wait_flag(closure_membership_ground_wf,WF,LWF), % enable other triggered co-routines to fire first; some maybe much more efficient to deal with than closure expansion;
4845 % used to be important for test 1146, but this is no longer the case
4846 %term_variables(CS,Vars),print(closure_membership_ground_wf_aux(LWF,vars(Vars),CS)),nl,
4847 ground_value_check(CS,CSGr),
4848 %when((nonvar(LWF),(nonvar(CSGr);nonvar(Res))),closure_membership_ground_wf_aux(X,CS,Res)).
4849 block_closure_membership_ground_wf_aux(X,CS,Res,CSGr,LWF,WF). % Note: wrong block in commit 332cb17487017d819e9140427b1017a3045b3685 caused problem for test 1162
4850
4851 :- block block_closure_membership_ground_wf_aux(?,?,?,?,-,?),
4852 block_closure_membership_ground_wf_aux(?,?,-,-,?,?).
4853 block_closure_membership_ground_wf_aux(X,CS,Res, _,_,WF) :-
4854 ? closure_membership_ground_wf_aux(X,CS,Res,WF).
4855
4856 % X & CS are ground or Res is known
4857 closure_membership_ground_wf_aux(X,CS,Res,WF) :- Res==pred_true,!,
4858 element_of_custom_set_wf(X,CS,WF).
4859 closure_membership_ground_wf_aux(X,CS,Res,WF) :- Res==pred_false,!,
4860 not_element_of_custom_set_wf(X,CS,WF).
4861 closure_membership_ground_wf_aux(X,CS,Res,_WF) :-
4862 % we know that X is a ground value and CS is ground: we can determine completely whether X is element of CS or not
4863 ? if(element_of_custom_set(X,CS),Res=pred_true, Res=pred_false).
4864 /* used to be: (Res \== pred_false, element_of_custom_set(X,CS), Res=pred_true
4865 ; Res \== pred_true, not_element_of_custom_set(X,CS), Res=pred_false)).
4866 */
4867
4868
4869
4870 :- use_module(kernel_objects,[element_of_global_set/2,element_of_global_set_wf/3]).
4871 element_of_custom_set_wf(X,CS,WF) :-
4872 ? element_of_custom_set_wf2(CS,X,WF). %, print(check_ok(X)),nl.
4873
4874 element_of_custom_set_wf2(node(A,B,C,D,E),X,WF) :-
4875 add_internal_error('Unwrapped avl_set: ',element_of_custom_set_wf2(node(A,B,C,D,E),X,WF)),fail.
4876 element_of_custom_set_wf2(global_set(GS),X,WF) :- element_of_global_set_wf(X,GS,WF).
4877 element_of_custom_set_wf2(freetype(ID),X,WF) :-
4878 (is_maximal_freetype(ID) -> true
4879 ; add_internal_error('Uncovered case: ',element_of_custom_set_wf2(freetype(ID),X,WF))
4880 ). % we assume freetypes to be maximal !
4881 ?element_of_custom_set_wf2(avl_set(AVL),X,WF) :- element_of_avl_set_wf(AVL,X,WF).
4882 element_of_custom_set_wf2(closure(Parameters,PT,Cond),X,WF) :-
4883 ? element_of_closure(X,Parameters,PT,Cond,WF).
4884
4885 element_of_avl_set_wf(node(Y,_,_,empty,empty),X,WF) :- !,
4886 ? kernel_objects:equal_object_wf(X,Y,element_of_custom_set_wf2,WF).
4887 element_of_avl_set_wf(AVL,X,_WF) :- ground_value(X),!, safe_avl_member(X,AVL). %safe_avl_member_ground(X,AVL).
4888 element_of_avl_set_wf(AVL,X,WF) :-
4889 avl_approximate_size(AVL,10,ApproxSize),
4890 ? element_of_avl_set_wf(AVL,ApproxSize,X,WF).
4891
4892 :- use_module(clpfd_tables).
4893
4894 element_of_avl_set_wf(AVL,ApproxSize,X,WF) :-
4895 % first check if worthwhile to attempt table treatment
4896 % after fixing table/2 bug runtimes have slowed down and test 1753 became much slower
4897 % for test 1753 a threshold of < 63 would be ideal; but test 1716 requires size 91
4898 % TODO: re-evaluate when SICStus 4.8 available
4899 preferences:preference(use_clpfd_solver,true),
4900 preferences:preference(solver_strength,SS),
4901 ApproxSize < 100+SS,
4902 (var(X) -> true
4903 ; X = (X1,_X2) -> (ground_value(X1) -> ApproxSize < 10+SS ; true)
4904 ; X=rec(_) -> true
4905 %; X=int(_) -> true ; X=fd(_,_) -> true % for scalar values we already use in_fd_value_list_wf via avl_fd_value_check
4906 ),
4907 can_translate_avl_to_table(AVL,SkeletonType),
4908 !,
4909 ? check_element_of_avl_with_table(X,SkeletonType,AVL,WF).
4910 element_of_avl_set_wf(AVL,ApproxSize,X,WF) :-
4911 ? propagate_avl_element_information(X,AVL,ApproxSize,WF), %translate:translate_bvalue(avl_set(AVL),SS),
4912 get_bounded_wait_flag(ApproxSize,element_of_avl(X),WF,WF1),
4913 ? element_of_avl_set_wf3(X,AVL,ApproxSize,WF1,WF).
4914
4915
4916 % compute an approximate size (small sets are computed exactly)
4917 avl_approximate_size(AVL,Size) :- avl_approximate_size(AVL,10,Size).
4918
4919 avl_approximate_size(AVL,HeightBound,Size) :- var(AVL),!,
4920 add_internal_error('AVL Set is variable: ', avl_approximate_size(AVL,HeightBound,Size)),
4921 Size=1000000.
4922 avl_approximate_size(AVL,HeightBound,Size) :- % when the AVL gets too large; not so important that we have a precise estimation anyway
4923 % so: save some time and just compute height
4924 avl_height(AVL,Height),
4925 (Height>HeightBound
4926 -> Size is floor(2**Height-1)
4927 ; avl_size(AVL,Size)).
4928
4929 :- block element_of_avl_set_wf3(-,?,?,-,?).
4930 ?element_of_avl_set_wf3(X,AVL,_ApproxSize,_WF1,_WF) :- var(X), !, safe_avl_member(X,AVL).
4931 % TO DO: if randomise_enumeration_order is true then choose elements in random order
4932 :- if(environ(prob_data_validation_mode,xxxtrue)). % currently disabled due to bug related to 14082013/435_002.mch TO DO: investigate
4933 element_of_avl_set_wf3((X,Y),AVL,ApproxSize,WF1,WF) :- !,
4934 %% ((var(WF1), \+ ground(X)) -> print(avl_relation_check(X,Y)),nl, %%
4935 %% copy_term((X,Y),Copy), findall(Copy,safe_avl_member(Copy,AVL),Cs), print(Cs),nl, Cs \=[] %% check that at least one element exists
4936 %% ; true),
4937 couple_element_of_avl_set_wf(X,Y,AVL,ApproxSize,WF1,WF).
4938 :- else.
4939 element_of_avl_set_wf3((X,Y),AVL,ApproxSize,WF1,WF) :- !,
4940 ground_value_check(X,GrX),
4941 ? block_couple_element_of_avl_set_grX_wf1(X,Y,AVL,ApproxSize,GrX,WF1,WF).
4942 %when((nonvar(WF1) ; ground(X)), couple_element_of_avl_set(X,Y,AVL,GrX,WF1,WF)).
4943 :- endif.
4944 element_of_avl_set_wf3(X,AVL,_ApproxSize,WF1,_WF) :-
4945 ground_value_check(X,GrX),
4946 safe_avl_member_block(X,AVL,GrX,WF1).
4947
4948 :- block safe_avl_member_block(?,?,-,-).
4949 safe_avl_member_block(X,AVL,_,_) :-
4950 ? safe_avl_member(X,AVL).
4951
4952 :- if(environ(prob_data_validation_mode,true)).
4953 :- public couple_element_of_avl_set_wf/6. % used in conditional if above
4954 :- block couple_element_of_avl_set_wf(-,?,?,?,-,?).
4955 couple_element_of_avl_set_wf(X,Y,AVL,ApproxSize,WF1,WF) :-
4956 ground_value_check(X,GrX),
4957 ((nonvar(WF1);nonvar(GrX)) -> couple_element_of_avl_set(X,Y,AVL,GrX,WF1,WF)
4958 %; true -> when((nonvar(WF1) ; ground(X)), couple_element_of_avl_set(X,Y,AVL,WF1,WF))
4959 ; nonvar(X),X=(X1,X2),ground(X1) -> triple_element_of_avl_set(X1,X2,Y,AVL,WF)
4960 ; nonvar(X),X=(X1,X2) ->
4961 avl_member_blocking((X,Y),AVL),
4962 (ground(Y),ground(X1) -> safe_avl_member_pair_wf(X,Y,AVL,WF)
4963 ; when(ground(X1),(\+ ground(X2) -> triple_element_of_avl_set(X1,X2,Y,AVL,WF) ; true % avl_member_blocking will have done its work
4964 )),
4965 block_couple_element_of_avl_set(X,Y,AVL,WF1,WF)
4966 )
4967 ; %when((nonvar(WF1) ; ground(X)), couple_element_of_avl_set(X,Y,AVL,WF1,WF))
4968 block_couple_element_of_avl_set_grX_wf1(X,Y,AVL,ApproxSize,GrX,WF1,WF)
4969 /* ; (simple_avl_type(AVL)
4970 -> avl_member_blocking((X,Y),AVL) % TO DO: don't call couple_element_of_avl_set ! avoid double traversal !!
4971 ; true),
4972 block_couple_element_of_avl_set_grX_wf1(X,Y,AVL,GrX,WF1,WF) */
4973 ).
4974
4975 :- block block_couple_element_of_avl_set(?,?,?,-,?).
4976 block_couple_element_of_avl_set(X,Y,_AVL,_WF1,_WF) :- ground(X),ground(Y),!.
4977 block_couple_element_of_avl_set(X,Y,AVL,_WF1,WF) :- safe_avl_member_pair_wf(X,Y,AVL,WF).
4978
4979 triple_element_of_avl_set(X1,X2,Y,AVLRelation,WF) :- % X1 must be ground
4980 copy_term((X2,Y),(CX2,CY)),
4981 findall((CX2,CY),safe_avl_member_pair((X1,CX2),CY,AVLRelation),Images),
4982 % we pass no WF to safe_avl_member_pair; we need to fully evaluate all unifications due to findall
4983 Images \= [],
4984 construct_avl_from_lists_wf(Images,AVL,WF),
4985 element_of_custom_set_wf2(AVL,(X2,Y),WF). % will set up waitflag if necessary
4986 :- endif.
4987
4988 % ---------------------------------------------------
4989
4990 test_avl_set(node(((int(2),int(3)),int(6)),true,0,node(((int(1),int(2)),int(2)),true,0,empty,empty),node(((int(3),int(4)),int(12)),true,0,empty,empty))).
4991
4992 %simple_avl_type(node(K,_,_,_,_)) :- simple_value(K). % we can index directly on AVL, without having to normalise inner values
4993 % in particular, we can apply avl_member_blocking
4994
4995 :- assert_must_succeed(( custom_explicit_sets:test_avl_set(A), custom_explicit_sets:avl_member_blocking(((X,Y),Z),A), X=int(2), Y==int(3),Z==int(6) )).
4996 :- assert_must_succeed(( custom_explicit_sets:test_avl_set(A), custom_explicit_sets:avl_member_blocking(((X,Y),Z),A), X=int(3), Y==int(4),Z==int(12) )).
4997 :- assert_must_succeed(( custom_explicit_sets:test_avl_set(A), custom_explicit_sets:avl_member_blocking(((X,Y),Z),A), X=int(1), Y==int(2),Z==int(2) )).
4998 :- assert_must_fail(( custom_explicit_sets:test_avl_set(A), custom_explicit_sets:avl_member_blocking(((X,_Y),_Z),A), X=int(5) )).
4999 % a blocking version of avl_member; will not instantiate the element; just prune
5000
5001 avl_member_blocking(Key, AVL) :- AVL=node(K,_,_,L,R),
5002 %avl_height(AVL,Height),
5003 avl_member_blocking4(Key,K,L,R).
5004
5005 avl_member_blocking4(Key,Kavl,L,R) :- L=empty,R=empty,!,
5006 Key=Kavl. % we could do equal_object
5007 avl_member_blocking4(Key,Kavl,L,R) :-
5008 match_possible(Key,Kavl,MatchPossible), % check if in principle a match could occur
5009 (Kavl=(_,_) ->
5010 (avl_min(R,Knext) -> true ; dif(O,>), Knext=no_match,
5011 force_comp(MatchPossible,O,'<')),
5012 (avl_max(L,Kprev) -> true ; dif(O,<), Kprev=no_match,
5013 force_comp(MatchPossible,O,'>'))
5014 ; Knext = no_match, Kprev = no_match
5015 ),
5016 (nonvar(O) -> true
5017 /* ; (MatchPossible==pred_false, avl_height(L,Height), Height < 8,
5018 copy_term(Key,CKey), \+ safe_avl_member(CKey,L), \+ safe_avl_member(CKey,R))
5019 -> print(cannot_match(Key)),nl,fail */
5020 ; compare_blocking(O, Key, Kavl, Kprev,Knext)),
5021 avl_member_blocking_aux(O, Key, Kavl, L, R).
5022
5023 %force_comp(V,_,_) :- var(V),!.
5024 :- block force_comp(-,?,?).
5025 force_comp(pred_true,_,_).
5026 force_comp(pred_false,R,R).
5027
5028 :- block avl_member_blocking_aux(-,?,?,?,?).
5029 avl_member_blocking_aux(<, Key, _K, AVL, _) :- avl_member_blocking(Key, AVL).
5030 avl_member_blocking_aux(=, Key, Key, _L, _R). % we could use equal_object
5031 avl_member_blocking_aux(>, Key, _K, _, AVL) :- avl_member_blocking(Key, AVL).
5032
5033 % a blocking version of compare
5034 compare_blocking(Res,A,Kavl, Kprev, Knext) :- block_compare(A,Kavl,Res, Kprev, Knext).
5035
5036 :- block block_compare(-,?,?,?,?), block_compare(?,-,?,?,?).
5037 block_compare((A,B),Kavl,Res, Kprev, Knext) :- !,
5038 (Kavl=(RA,RB) ->
5039 match_key(Kprev,RA,PA,PB),
5040 match_key(Knext,RA,NA,NB),
5041 block_compare(A,RA,ACRes,PA,NA),
5042 block_compare_aux(ACRes,B,RB,Res,PB,NB)
5043 ; add_internal_error('Illegal type: ',block_compare((A,B),Kavl,Res, Kprev, Knext)),fail).
5044 % TO DO: same for records; but currently not used anyway
5045 block_compare(int(A),int(B),Res,_,_) :- !, block_compare_atomic(A,B,Res).
5046 block_compare(pred_false,B,Res,_,_) :- !, block_compare_atomic(pred_false,B,Res).
5047 block_compare(pred_true,B,Res,_,_) :- !, block_compare_atomic(pred_true,B,Res).
5048 block_compare(string(A),string(B),Res,_,_) :- !, block_compare_atomic(A,B,Res).
5049 block_compare(fd(A,T),fd(B,T),Res,_,_) :- !, block_compare_atomic(A,B,Res).
5050 block_compare(avl_set(A),Kavl,Res,_,_) :- !,
5051 convert_to_avl_inside_set(avl_set(A),ConvertedA),compare(Res,ConvertedA,Kavl).
5052 block_compare([],[],Res,_,_) :- !, Res = '='.
5053 block_compare([],_,Res,_,_) :- !, Res = '<'.
5054 block_compare(A,Kavl,Res,_,_) :-
5055 % does deal with various representations of sets !! closure/global_set/...
5056 when(ground(A),
5057 (convert_to_avl_inside_set(A,ConvertedA),compare(Res,ConvertedA,Kavl))).
5058
5059 match_key((KeyA,KeyB),Key,ResA,ResB) :- !, ResA=KeyA,
5060 (Key==KeyA -> ResB=KeyB ; ResB = no_match).
5061 match_key(_,_,no_match,no_match).
5062
5063 :- block block_compare_atomic(-,?,?), block_compare_atomic(?,-,?).
5064 block_compare_atomic(A,B,Res) :- compare(Res,A,B).
5065
5066 :- block block_compare_aux(-,?,?,?, ?,?).
5067 block_compare_aux(ACRes,B,D,Res, Kprev,Knext) :-
5068 (ACRes='<' -> Res = '<'
5069 ; ACRes = '>' -> Res = '>'
5070 ; Kprev=no_match, Knext=no_match ->
5071 Res = '=' % we cannot match neither previous nor next key: force match
5072 ; block_compare(B,D,Res,Kprev,Knext)). % TO DO: check with prev & next value: if no match possible force Res='='
5073
5074 % check if a match is possible between two terms
5075 :- block match_possible(-,?,?), match_possible(?,-,?).
5076 match_possible([],[],Possible) :- !, Possible=pred_true.
5077 match_possible([],avl_set(_),Possible) :- !, Possible=pred_false.
5078 match_possible(avl_set(_),[],Possible) :- !, Possible=pred_false.
5079 match_possible(int(A),int(B),Possible) :- !, match_possible_atomic(A,B,Possible).
5080 match_possible(fd(A,T),fd(B,T),Possible) :- !, match_possible_atomic(A,B,Possible).
5081 match_possible(string(A),string(B),Possible) :- !, match_possible_atomic(A,B,Possible).
5082 match_possible((A1,A2),(B1,B2),Possible) :- !, match_possible(A1,B1,P1),
5083 match_possible(A2,B2,P2), kernel_equality:conjoin_test(P1,P2,Possible,_WF). %% WF <--- TO DO
5084 match_possible(_,_,pred_true).
5085
5086 :- block match_possible_atomic(-,?,?), match_possible_atomic(?,-,?).
5087 match_possible_atomic(A,B,Res) :- (A==B -> Res=pred_true ; Res=pred_false).
5088
5089 % --------------------------------------------
5090
5091 :- block block_couple_element_of_avl_set_grX_wf1(?, - ,?,?,-,-,?).
5092 block_couple_element_of_avl_set_grX_wf1(X,Y,AVL,ApproxSize,GrX,WF1,WF) :-
5093 var(GrX), var(WF1),
5094 !,
5095 % we know the result Y but not yet fully the input value X
5096 (ApproxSize < 129 % TO DO: improve this; unify with inverse_apply_ok(Y,X,AVL,ApproxSize) ?
5097 -> ground_value_check(Y,GrY) % wait until Y is fully known
5098 ; (preference(solver_strength,SS), ApproxSize < 129+SS)
5099 -> ground_value_check(Y,GrY)
5100 % TO DO: we could look at avl_min and avl_max and estimate spread of range keys
5101 ; cond_perfmessage([data_validation_mode/false],no_inverse_avl_lookup(ApproxSize,Y)) % do not bind GrY; we wait until GrX or WF1 is bound
5102 ),
5103 block_couple_element_of_avl_set_grX_grY_wf1(X,Y,AVL,ApproxSize,GrX,GrY,WF1,WF).
5104 block_couple_element_of_avl_set_grX_wf1(X,Y,AVL,_ApproxSize,GrX,WF1,WF) :-
5105 ? couple_element_of_avl_set(X,Y,AVL,GrX,WF1,WF).
5106
5107 :- block block_couple_element_of_avl_set_grX_grY_wf1(?,?,?,?, -,-,-,?).
5108 block_couple_element_of_avl_set_grX_grY_wf1(X,Y,AVL,_ApproxSize, GrX,_GrY,WF1,WF) :-
5109 var(GrX), var(WF1), % i.e., Y is known
5110 % we know the result Y but not yet fully the input value X
5111 %inverse_apply_ok(Y,X,AVL,ApproxSize),
5112 !,
5113 inverse_get_possible_values(X,Y,AVL,Res),
5114 Res = avl_set(InvAVL),
5115 element_of_avl_set_wf(InvAVL,X,WF).
5116 %couple_element_of_avl_set(X,Y,AVL,GrX,1,WF).
5117 block_couple_element_of_avl_set_grX_grY_wf1(X,Y,AVL,_ApproxSize,GrX,_GrY,WF1,WF) :-
5118 ? couple_element_of_avl_set(X,Y,AVL,GrX,WF1,WF).
5119
5120
5121 % special treatment for relations: if the first component is known: then we can check how many images there are
5122 couple_element_of_avl_set(X,Y,AVL,GrX,WF1,WF) :-
5123 nonvar(WF1), var(GrX), %\+ground(X),
5124 !,
5125 ? safe_avl_member_default_wf((X,Y),AVL,WF).
5126 couple_element_of_avl_set(X,Y,AVLRelation,_GrX,_,WF) :- % X must be ground
5127 get_template(Y,TY,_ToUnifyAfter), % was copy_term(Y,CY) but could cause issues with closures with variables
5128 copy_term(TY,CY), % avoid that we instantiate Y and trigger co-routines
5129 findall(CY,avl_member_pair_arg1_ground(X,CY,AVLRelation),Images), % should we use Y instead of CY
5130 Images \= [],
5131 construct_avl_from_lists_wf(Images,AVL,WF),
5132 ? element_of_custom_set_wf2(AVL,Y,WF). % will set up waitflag if necessary
5133
5134
5135 % set Res -> pred_true or pred_false if membership can be decided early
5136 % interval closures already dealt with by closure_membership
5137 % maximal sets are also already dealt with by membership_custom_set
5138 reify_avl_membership(AVL,Element,Res,FullReification) :-
5139 is_avl_simple_set(AVL,Type),
5140 preferences:preference(use_clpfd_solver,true), % to do: require maybe only for integer type !?
5141 \+ ground_value(Element),
5142 !,
5143 reify_avl_mem2(Type,Element,AVL,Res,FullReification).
5144 reify_avl_membership(_,_,_,false).
5145
5146
5147 is_avl_simple_set(node(El,_True,_,_,_),Type) :- simple_type(El,Type).
5148 simple_type(int(_),integer).
5149 simple_type(fd(_,GS),global(GS)).
5150
5151
5152 reify_avl_mem2(integer,int(El),AVL,Res,FullReification) :-
5153 avl_min(AVL,int(Min)), avl_max(AVL,int(Max)),
5154 (reify_integer_avl_mem(AVL,Min,Max) % reify if AVL small enough
5155 -> avl_domain(AVL,R),project_avl_domain_on_fd(R,FDList),
5156 clpfd_reify_inlist(El,FDList,FDRes,Posted),
5157 propagate_fd_membership(FDRes,Res,inlist(El,FDList)),
5158 FullReification=Posted
5159 ; clpfd_interface:try_post_constraint((El in Min..Max) #<=> FDRes),
5160 propagate_not_membership(FDRes,Res,int(El,Min,Max)),
5161 FullReification=false
5162 ).
5163 % this could also be enabled with CLPFD = FALSE ?? no overflows are possible
5164 reify_avl_mem2(global(GS),fd(El,GS),AVL,Res,FullReification) :-
5165 avl_domain(AVL,R),project_avl_domain_on_fd(R,FDList),
5166 b_global_sets:b_get_fd_type_bounds(GS,Low,Up),
5167 (is_full_fdlist(FDList,Low,Up)
5168 -> Res=pred_true, % all the values are in the list; it must be a member
5169 % normally this should also be detected by clpfd_reify_inlist, unless no constraint was set up for El
5170 % it seems to have an effect for test 426: probcli examples/EventBPrologPackages/SSF/Bepi_Soton/M1_mch.eventb -cbc all -strict -p CLPFD TRUE -p SMT TRUE -strict -p STRICT_RAISE_WARNINGS TRUE
5171 FullReification=true
5172 ; clpfd_reify_inlist(El,FDList,FDRes,Posted),
5173 propagate_fd_membership(FDRes,Res,inlist(El,FDList)),
5174 FullReification=Posted
5175 ).
5176 %reify_avl_mem2(global(GS),fd(El,GS),AVL,Res) :-
5177 % avl_min(AVL,fd(Min,GS)), avl_max(AVL,fd(Max,GS)),
5178 % clpfd_interface:try_post_constraint((El in Min..Max) #<=> FDRes),
5179 % propagate_not_membership(FDRes,Res,fd(El,GS,Min,Max)).
5180
5181 % assumes list is sorted
5182 is_full_fdlist(List,Low,Up) :- integer(Up), is_full_fdlist2(List,Low,Up).
5183 is_full_fdlist2([],Low,Up) :- Low>Up.
5184 is_full_fdlist2([Low|T],Low,Up) :- L1 is Low+1, is_full_fdlist2(T,L1,Up).
5185
5186 % check if avl small enough to call clpfd_reify_inlist
5187 reify_integer_avl_mem(_AVL,Min,Max) :- MaxSizeM1 is Max-Min, MaxSizeM1 =< 20,!.
5188 reify_integer_avl_mem(AVL,_Min,_Max) :- avl_height_less_than_with_solver_strength(AVL,5).
5189
5190
5191
5192 project_avl_domain_on_fd([],[]).
5193 project_avl_domain_on_fd([H|T],[PH|PT]) :- project_avl_domain(H,PH), project_avl_domain_on_fd(T,PT).
5194 project_avl_domain(int(X),X).
5195 project_avl_domain(fd(X,_),X).
5196
5197
5198 :- block propagate_fd_membership(-,-,?).
5199 % if we make it propagate_fd_membership(-,-?) Bosch examples becomes much slower ?
5200 % Indeed: membership_custom_set will already force membership or non-membership !
5201 %propagate_fd_membership(X,M,Info) :- var(X),!, print(propagate_fd(X,M,Info)),nl, (M=pred_true ->X=1 ; X=0).
5202 propagate_fd_membership(1,pred_true,_Info).
5203 propagate_fd_membership(0,pred_false,_Info).
5204
5205 :- block propagate_not_membership(-,?,?).
5206 propagate_not_membership(1,_,_). % there could be elements in the interval which are not in the set
5207 propagate_not_membership(0,Res,_Info) :-
5208 Res=pred_false.
5209
5210 % -----------------
5211
5212 % fails if not possible to quickly compute approximate size
5213 quick_custom_explicit_set_approximate_size(V,_) :- var(V),!,fail.
5214 quick_custom_explicit_set_approximate_size(avl_set(AVL),Size) :- !,
5215 quick_avl_approximate_size(AVL,Size).
5216 quick_custom_explicit_set_approximate_size(CS,Size) :-
5217 card_for_specific_custom_set(CS,Size,Code),
5218 on_enumeration_warning(call(Code),fail),
5219 atomic(Size). % inf or number; sometimes card_for_specific_custom_set can return a variable
5220
5221 :- use_module(clpfd_lists,[try_get_fd_value_list/4, get_fd_value/3, in_fd_value_list_wf/4]).
5222 % a membership propagation, but only done if it can be done quickly
5223
5224
5225 % quick_propagation_element_information(Set, Element, WF, PossiblyCompiledSet)
5226 % use last element for next iteration if you call quick_propagation_element_information in a loop
5227 :- block quick_propagation_element_information(-,?,?,?).
5228 quick_propagation_element_information(Set,_El,_,R) :-
5229 preferences:preference(use_clpfd_solver,false),
5230 !, R=Set.
5231 quick_propagation_element_information(avl_set(AVL),Element,WF,NewSet) :- !,
5232 quick_avl_approximate_size(AVL,Size),
5233 NewSet=avl_set_with_size(AVL,Size),
5234 propagate_avl_element_information_direct(Element,AVL,Size,WF).
5235 quick_propagation_element_information(avl_set_with_size(AVL,Size),Element,WF,NewSet) :- !,
5236 NewSet = avl_set_with_size(AVL,Size),
5237 propagate_avl_element_information_direct(Element,AVL,Size,WF).
5238 quick_propagation_element_information(closure(P,T,B),Element,WF,NewSet) :- !,
5239 NewSet = closure(P,T,B),
5240 ? element_of_closure(Element,P,T,B,WF).
5241 quick_propagation_element_information(fd_value_list(FDList,GroundList,Type),El,WF,NewSet) :- !,
5242 NewSet = fd_value_list(FDList,GroundList,Type),
5243 get_fd_value(Type,El,ElFD),
5244 in_fd_value_list_wf(GroundList,ElFD,FDList,WF).
5245 quick_propagation_element_information(Set,El,WF,NewSet) :-
5246 ? try_get_fd_value_list(Set,Type,FDList,GroundList),!,
5247 FDList \= [], % if list is empty membership fails
5248 NewSet = fd_value_list(FDList,GroundList,Type),
5249 % clpfd_inlist requires list of integers as second argument
5250 ? get_fd_value(Type,El,ElFD),
5251 % We could apply filter_non_matching_elements here
5252 in_fd_value_list_wf(GroundList,ElFD,FDList,WF).
5253 quick_propagation_element_information(Set,_,_,Set).
5254
5255 % -----------------
5256
5257 % infer information about an element of an AVL set
5258 propagate_avl_element_information(Element,AVL,Size,WF) :-
5259 (preferences:preference(use_clpfd_solver,true)
5260 ? -> propagate_avl_element_information_direct(Element,AVL,Size,WF)
5261 ; true).
5262
5263 propagate_avl_element_information_direct(Element,AVL,Size,WF) :-
5264 (Size<100 -> %30 which magic constant to use here; use larger value in SMT mode ?
5265 ? propagate_avl_element_information_small(Element,AVL,WF)
5266 ; is_avl_fd_index_set(AVL,Type) ->
5267 propagate_avl_element_information_large(Type,Element,AVL),
5268 (Size < 4000, nonvar(Element), Element = (_,_) % another magic constant
5269 -> Prio is Size // 60,
5270 get_wait_flag(Prio,propagate_avl_element_information(Element),WF,LWF),
5271 propagate_avl_el_large_block(Element,AVL,WF,LWF) % will do precise propagation
5272 ; true)
5273 ; true).
5274 % TO DO: we could call in_nat_range_wf; this way it would also work in non-CLPFD mode
5275
5276 :- block propagate_avl_el_large_block(?,?,?,-).
5277 propagate_avl_el_large_block((A,B),_,_,_) :-
5278 (ground(A); ground_value(B)), % in first: case we will apply AVL set ; in second case probably no benefit as propagate_avl_element_information_large already propagated first element
5279 !.
5280 propagate_avl_el_large_block(Element,AVL,WF,_LWF) :-
5281 % TO DO: maybe look if we should not use clpfd_list, but only upper & lower bound
5282 ? propagate_avl_element_information_small(Element,AVL,WF). % will do precise propagation.
5283
5284 :- use_module(clpfd_lists,[avl_fd_value_check/4]).
5285 :- use_module(clpfd_interface,[catch_and_ignore_clpfd_overflow/2]).
5286 propagate_avl_element_information_small(Element,AVL,WF) :-
5287 ? catch_and_ignore_clpfd_overflow(propagate_avl_element_information_small, % relevant test e.g. 1708 (with used_ids_defined_by_equality)
5288 avl_fd_value_check(AVL,Element,WF,_FullyChecked)).
5289
5290 propagate_avl_element_information_large(Type,El,AVL) :-
5291 avl_min(AVL,Min), avl_max(AVL,Max),
5292 % if Size small enough and smaller than Max-Min we call clpfd_inlist on domain
5293 % Note: overflows should be caught below; we could check that Min/Max are within CLPFD range
5294 couple_prj1_in_range(Type,El,Min,Max).
5295
5296 couple_prj1_in_range(integer,int(El),int(Min),int(Max)) :- clpfd_interface:clpfd_inrange(El,Min,Max).
5297 couple_prj1_in_range(global(GS),fd(El,GS),fd(Min,GS),fd(Max,GS)) :- clpfd_interface:clpfd_inrange(El,Min,Max).
5298 couple_prj1_in_range(couple_prj1(T),(El,_),(Min,_),(Max,_)) :- couple_prj1_in_range(T,El,Min,Max).
5299 couple_prj1_in_range(rec_first_field(Name,T),rec([field(Name,El)|TF]),
5300 rec([field(Name,Min)|TMin]),rec([field(Name,Max)|_])) :-
5301 (var(TF)
5302 -> copy_field_names(TMin,TF) % if Fields not yet instantiated: copy over all fields
5303 ; true),
5304 couple_prj1_in_range(T,El,Min,Max).
5305
5306 copy_field_names([],[]).
5307 copy_field_names([field(N,_)|T],[field(N,_)|CT]) :- copy_field_names(T,CT).
5308
5309 % check if the first component of the AVL elements of a type such that we can propagate FD information
5310 is_avl_fd_index_set(node(El,_True,_,_,_),Type) :-
5311 simple_index_type(El,Type).
5312 simple_index_type((El,_),couple_prj1(T)) :- simple_index_type(El,T).
5313 simple_index_type(int(_),integer).
5314 simple_index_type(fd(_,GS),global(GS)).
5315 simple_index_type(rec(Fields),rec_first_field(Name,T)) :- nonvar(Fields),
5316 Fields = [field(Name,El)|_],
5317 simple_index_type(El,T).
5318 %simple_index_type((int(_),_),couple_integer).
5319 %simple_index_type(((int(_),_),_),couple_couple_integer).
5320 %simple_index_type((fd(_,GS),_),couple_global(GS)).
5321
5322
5323 /* avoid instantiating non-normalised with normalised values leading to failure */
5324 :- assert_must_succeed((X=(fd(1,'Name'),fd(2,'Name')), A=node(X,true,0,empty,empty),
5325 custom_explicit_sets:safe_avl_member(X,A) )).
5326
5327 ?safe_avl_member(X,AVL) :- var(X), !, my_avl_member(X,AVL).
5328 %safe_avl_member((X,Y),AVL) :- !, safe_avl_member_pair(X,Y,AVL).
5329 safe_avl_member(Value,AVL) :- decompose_index(Value,Key,RestVal), !,
5330 ? avl_fetch_indexed(Value,Key,RestVal,AVL).
5331 safe_avl_member(X,AVL) :- ground_value(X), convert_to_avl_inside_set(X,AX), !, avl_fetch(AX,AVL).
5332 ?safe_avl_member(X,AVL) :- safe_avl_member_default_wf(X,AVL,no_wf_available).
5333
5334
5335 % this is a generalisation of safe_avl_member_pair
5336 % check if a value can be decomposed into an index and the rest of a value and the key is ground
5337 % it also works for records indexing on first field
5338 avl_fetch_indexed(Value,Key,RestVal,AVL) :-
5339 ground_value_or_field(Key),
5340 convert_value_or_field(Key,NormKey),
5341 !,
5342 (ground_value_or_field(RestVal),
5343 convert_to_avl_inside_set(Value,NormValue)
5344 -> avl_fetch(NormValue,AVL)
5345 ? ; avl_fetch_with_index(NormKey,AVL,RestValLookup),
5346 ? kernel_objects:equal_object(RestValLookup,RestVal,avl_fetch_indexed)
5347 ).
5348 avl_fetch_indexed(Value,_,_,AVL) :-
5349 ? safe_avl_member_default_wf(Value,AVL,no_wf_available).
5350
5351 convert_value_or_field(field(Name,Val),field(Name,NVal)) :- !,
5352 convert_to_avl_inside_set(Val,NVal).
5353 convert_value_or_field(Key,NormKey) :-
5354 convert_to_avl_inside_set(Key,NormKey).
5355
5356 % a version of safe_avl_member where the first argument is guaranteed to be ground
5357 % somehow using this seems to slow-down evaluation for vesg_Dec12; Caching ??
5358 %safe_avl_member_ground(X,AVL) :-
5359 % convert_to_avl_inside_set(X,AX), !, avl_fetch(AX,AVL).
5360 %safe_avl_member_ground((X,Y),AVL) :- !, avl_member_pair_arg1_ground(X,Y,AVL).
5361 %safe_avl_member_ground(X,AVL) :- safe_avl_member_default_wf(X,AVL,no_wf_available).
5362
5363
5364 safe_avl_member_pair(X,Y,AVL) :- safe_avl_member_pair_wf(X,Y,AVL,no_wf_available).
5365
5366 safe_avl_member_pair_wf(X,Y,AVL,_WF) :- ground_value(X),!,
5367 ( ground_value(Y),
5368 convert_to_avl_inside_set((X,Y),AX)
5369 -> avl_fetch(AX,AVL)
5370 ; avl_member_pair_arg1_ground(X,Y,AVL)). % TODO: pass WF
5371 safe_avl_member_pair_wf(X,Y,AVL,WF) :- safe_avl_member_default_wf((X,Y),AVL,WF).
5372
5373 % can be used to try and lookup a function value without creating WD errors, ...
5374 % used in b_compiler to compile function applications
5375 try_apply_to_avl_set(X,Y,AVL) :- ground_value(X),
5376 ? avl_member_pair_arg1_ground(X,Y,AVL).
5377
5378 %safe_avl_member_pair_ground(X,Y,AVL) :- convert_to_avl_inside_set((X,Y),AX),!, avl_fetch(AX,AVL).
5379 %safe_avl_member_pair_ground(X,Y,AVL) :- avl_member_pair_arg1_ground(X,Y,AVL).
5380
5381 avl_member_pair_arg1_ground(X,Y,AVL) :- convert_to_avl_inside_set(X,AX), !,
5382 get_template(Y,RY,ToUnifyAfter),
5383 ? avl_fetch_pair(AX,AVL,RY),
5384 unify_after_wf(ToUnifyAfter,no_wf_available). %kernel_objects:equal_object(RY,Y).
5385 avl_member_pair_arg1_ground(X,Y,AVL) :-
5386 safe_avl_member_default((X,Y),AVL).
5387
5388 ?safe_avl_member_default(X,AVL) :- safe_avl_member_default_wf(X,AVL,no_wf_available).
5389 %safe_avl_member_default(PP,X,AVL) :-
5390 % debug:timer_call(safe_avl_member_default(PP),custom_explicit_sets:safe_avl_member_default1(X,AVL)).
5391 safe_avl_member_default_wf(X,AVL,WF) :- %statistics(runtime,_),
5392 get_template(X,Template,ToUnifyAfter),
5393 ? my_avl_member(Template,AVL),
5394 % statistics(runtime,[_,T2]), print(avl_member(Template,T2)),nl,
5395 ? unify_after_wf(ToUnifyAfter,WF). % kernel_objects:equal_object(Template,X)).
5396
5397 unify_after_wf([],_).
5398 ?unify_after_wf([A/B|T],WF) :- kernel_objects:equal_object_wf(A,B,unify_after,WF),
5399 ? unify_after_wf(T,WF).
5400
5401
5402
5403 get_template(A,R,ToUnifyAfter) :-
5404 (var(A) -> ToUnifyAfter=[A/R]
5405 ; get_template2(A,R,ToUnifyAfter) -> true
5406 ; add_internal_error('Could_not_get_template: ',get_template(A,R,_))).
5407
5408 get_template2((A,B),(TA,TB),ToUnifyAfter) :- get_template(A,TA,ToUnifyAfter1), get_template(B,TB,ToUnifyAfter2),
5409 append(ToUnifyAfter1,ToUnifyAfter2,ToUnifyAfter). % TO DO: use DifferenceLists / DCG
5410 get_template2(int(X),int(X),[]).
5411 get_template2(fd(A,B),fd(A,B),[]).
5412 get_template2([],[],[]).
5413 get_template2(pred_false /* bool_false */,pred_false /* bool_false */,[]).
5414 get_template2(pred_true /* bool_true */,pred_true /* bool_true */,[]).
5415 get_template2([H|T],R,ToUnifyAfter) :-
5416 (ground_value(H),ground_value(T)
5417 -> convert_to_avl_inside_set([H|T],R),ToUnifyAfter=[]
5418 ; ToUnifyAfter=[[H|T]/R]).
5419 % ; R=avl_set(A), ToUnifyAfter=[[H|T]/avl_set(A)]).
5420 get_template2(closure(P,T,B),R,[]) :- ground_value(closure(P,T,B)),
5421 expand_closure_to_avl_wf(P,T,B,R,no_wf_available),!.
5422 get_template2(closure(P,T,B),AVL_OR_EMPTY_OR_GS,[closure(P,T,B)/AVL_OR_EMPTY_OR_GS]). % closure could be empty or an infinite global set ?
5423 %get_template2(closure_x(_,_,_),_AVL_OR_EMPTY).
5424 get_template2(avl_set(A),avl_set(NA),[]) :- convert_to_avl_inside_set(avl_set(A),avl_set(NA)). % do we need to normalise here ??
5425 get_template2(string(X),string(X),[]).
5426 get_template2(term(X),term(X),[]).
5427 get_template2(freetype(X),R,[]) :- convert_to_avl_inside_set(freetype(X),R).
5428 get_template2(rec(Fields),rec(TFields),ToUnifyAfter) :- get_fields_template(Fields,TFields,ToUnifyAfter).
5429 get_template2(freeval(ID,Case,Value),freeval(ID,Case,TValue),ToUnifyAfter) :- get_template(Value,TValue,ToUnifyAfter).
5430 get_template2(global_set(GS),R,[]) :- convert_to_avl_inside_set(global_set(GS),R).
5431
5432
5433 get_fields_template(A,R,[rec(A)/rec(R)]) :- var(A),!.
5434 get_fields_template([],[],ToUnifyAfter) :- !, ToUnifyAfter=[].
5435 get_fields_template([field(Name,Val)|T],[field(Name,TVal)|TT],ToUnifyAfter) :- nonvar(Name),!,
5436 get_template(Val,TVal,ToUnifyAfter1),
5437 get_fields_template(T,TT,ToUnifyAfter2), append(ToUnifyAfter1,ToUnifyAfter2,ToUnifyAfter).
5438 get_fields_template(A,R,[rec(A)/rec(R)]).
5439
5440
5441 % succeed if we can decide membership of an avl_set on the spot
5442 quick_test_avl_membership(AVL,X,Res) :-
5443 element_can_be_added_or_removed_to_avl(X),
5444 convert_to_avl_inside_set(X,AX),
5445 (avl_fetch(AX,AVL) -> Res=pred_true ; Res=pred_false).
5446
5447 % ---------------------
5448
5449 % a dispatch predicate
5450 my_avl_member(Key,AVL) :-
5451 (preferences:preference(randomise_enumeration_order,true)
5452 ? -> random_avl_member(Key,AVL) ; avl_member_opt(Key,AVL)).
5453 :- use_module(library(random),[random/3]).
5454 ?random_avl_member(Key,AVL) :- avl_height(AVL,Height), H1 is Height+1, random_avl_member(Key,H1,AVL).
5455 % TO DO: make more intelligent; this is not really a very uniform way of randomly enumerating an AVL set (e.g., Key never occurs between L and R)
5456 random_avl_member(Key, H, node(K,_,_,L,R)) :-
5457 random(1,H,1), !, H1 is H-1,
5458 ? (Key=K ; random_avl_member(Key,H1,L) ; random_avl_member(Key,H1,R)).
5459 random_avl_member(Key, H, node(K,_,_,L,R)) :- random(1,3,1), !, H1 is H-1,
5460 ? (random_avl_member(Key,H1,L) ; random_avl_member(Key,H1,R) ; Key=K).
5461 random_avl_member(Key, H, node(K,_,_,L,R)) :- H1 is H-1,
5462 ? (random_avl_member(Key,H1,R) ; random_avl_member(Key,H1,L) ; Key=K).
5463
5464 % a variation of avl_member from library(avl) which tries to avoid leaving choice points behind
5465 avl_member_opt(Key, node(K,_,_,L,R)) :-
5466 ? ( avl_member_opt(Key, L)
5467 ; R=empty -> Key = K % avoid trailing choice_point
5468 ? ; (Key=K ; avl_member_opt(Key, R))
5469 ).
5470
5471 % ---------------------
5472
5473 :- use_module(kernel_objects,[check_element_of_wf/3,not_element_of_wf/3]).
5474 :- use_module(memoization,[element_of_memoization_closure/6]).
5475 element_of_special_closure(interval(LOW,UP),X,WF,_,_,_) :- !,
5476 %hit_profiler:add_profile_hit(in_nat_range(X,LOW,UP,CondClosure)),
5477 kernel_objects:in_nat_range_wf(X,int(LOW),int(UP),WF).
5478 element_of_special_closure(member_closure(_ID,_Type,VAL),X,WF,_,_,_) :-
5479 (VAL=value(_) ; VAL = cartesian_product(b(value(A),_,_),b(value(B),_,_))),!,
5480 %hit_profiler:add_profile_hit(in_member_closure(X,Par,Typ,Body)),
5481 (VAL=value(Set) -> check_element_of_wf(X,Set,WF)
5482 ; X=(XA,XB),
5483 ? kernel_objects:check_element_of_wf(XA,A,WF),
5484 kernel_objects:check_element_of_wf(XB,B,WF)).
5485 element_of_special_closure(not_member_closure(_ID,_Type,value(Set)),X,WF,_,_,_) :- !,
5486 %hit_profiler:add_profile_hit(in_not_member_closure(X,Par,Typ,Set)),
5487 not_element_of_wf(X,Set,WF).
5488 % we used to have to add enumerator, as not_element_of does not instantiate; e.g. relevant when doing X :: GS - {y}
5489 % This is no longer required
5490 % see test 6 (../prob_examples/public_examples/B/FeatureChecks/NotMemberCheck.mch)
5491 element_of_special_closure(recursive_special_closure(RId),X,WF,Parameters,PT,CondClosure) :- !,
5492 add_recursive_parameter(Parameters,PT,X,RId,CondClosure,NewParameters,NewPT,Value,WF),
5493 ? element_of_normal_closure(Value,NewParameters,NewPT,CondClosure,WF).
5494 element_of_special_closure(memoization_closure(MemoID),X,WF,P,T,B) :- !,
5495 element_of_memoization_closure(MemoID,X,WF,P,T,B).
5496 element_of_special_closure(_,X,WF,Parameters,PT,CondClosure) :-
5497 % none of the special cases above apply after all
5498 ? element_of_normal_closure(X,Parameters,PT,CondClosure,WF).
5499
5500 :- block element_of_closure(?,-,?,?,?), element_of_closure(?,?,?,-,?).
5501 % element_of_closure(X,Para,T,Body,_WF): check if X is a member of closure(Para,T,Body)
5502 element_of_closure(X,Parameters,PT,CondClosure,WF) :-
5503 is_special_closure(Parameters,PT,CondClosure, SpecialClosure),!,
5504 %print_term_summary(element_of_special_closure(SpecialClosure,X,WF,Parameters,PT,CondClosure)), trace_in_debug_mode,
5505 ? element_of_special_closure(SpecialClosure,X,WF,Parameters,PT,CondClosure).
5506 element_of_closure(X,Parameters,PT,CondClosure,WF) :-
5507 %print_term_summary(element_of_normal_closure(X,Parameters,PT,CondClosure,WF)), trace_in_debug_mode,
5508 ? element_of_normal_closure(X,Parameters,PT,CondClosure,WF).
5509 element_of_normal_closure(X,Parameters,PT,CondClosure,WF) :-
5510 %hit_profiler:add_profile_hit(element_of_closure(X,Parameters,PT,CondClosure)),
5511 same_length(Parameters,ParValues),
5512 convert_list_into_pairs(ParValues,X),
5513 ? b_test_closure_wo_enum(Parameters,PT,CondClosure,ParValues,WF).
5514
5515 :- use_module(store,[set_up_localstate/4]).
5516 :- block b_test_closure_wo_enum(?,?,-,?,?).
5517 b_test_closure_wo_enum(Parameters,ParameterTypes,ClosurePred,ParValues,WF) :-
5518 % same_length(Parameters,ParValues), % not necessary
5519 set_up_localstate(Parameters,ParValues,[],LocalState),
5520 ? b_enumerate:b_type_values_in_store(Parameters,ParameterTypes,LocalState),
5521 copy_wf_start(WF,b_test_closure_wo_enum(Parameters),InnerWF),
5522 % avoid that WF0 actions triggered before we have had a chance to traverse the expression
5523 ? b_test_boolean_expression(ClosurePred,LocalState,[],InnerWF),
5524 ? copy_wf_finish(WF,InnerWF).
5525
5526 % recursive identifier to list of parameters with body as value
5527 % NewValue is the Value that should be checked for membership in the adapted closure; it has one argument more
5528 add_recursive_parameter(Parameters,Types,Value,TId,CondClosure,NewParameters,NewTypes,NewValue,WF) :-
5529 TId = b(identifier(RId),SetType,_), % unification replaces: get_texpr_id(TId,RId), get_texpr_type(TId,SetType),
5530 append(Parameters,[RId],NewParameters),
5531 append(Types,[SetType],NewTypes),
5532 %tools_printing:print_term_summary(recursion(Value)),nl,
5533 % TO DO check some variant decreases
5534 (kernel_waitflags:pending_abort_error(WF)
5535 -> NewValue = (_,_) % prevent further expansion of recursion, in case WD error in recursive function
5536 % TO DO: detect whether WD error occurs within recursive function,
5537 % indeed, the expansion of the recursive function could be unrelated to WD error and be important to detect inconsistency which prevents WD error: e.g., 1/x=res & recfun(x) \= 0
5538 ,debug_println(19,stopping_recursion_due_to_wd_error)
5539 ; NewValue = (Value,closure(Parameters,Types,CondClosure))
5540 ).
5541
5542
5543 % same as above, but without a waitflag
5544 ?element_of_custom_set(X,CS) :- element_of_custom_set2(CS,X).
5545
5546 element_of_custom_set2(global_set(GS),X) :- !,element_of_global_set(X,GS).
5547 element_of_custom_set2(freetype(ID),_) :- is_maximal_freetype(ID),!. % freetypes are always maximal at the moment
5548 element_of_custom_set2(avl_set(AVL),X) :- !,
5549 safe_avl_member(X,AVL).
5550 element_of_custom_set2(CS,X) :- init_wait_flags(WF,[element_of_custom_set2]),
5551 element_of_custom_set_wf2(CS,X,WF),
5552 ? ground_wait_flags(WF).
5553
5554 % ---------------
5555
5556 % function application for closure
5557
5558 % same as check_element_of_wf but does not wait on Y:
5559 % should also work for relation ??
5560
5561 check_element_of_function_closure(X,Y,Parameters,PT,CondClosure,WF) :-
5562 is_special_closure(Parameters,PT,CondClosure, SpecialClosure),!, % this covers recursive closures
5563 ? element_of_special_closure(SpecialClosure,(X,Y),WF,Parameters,PT,CondClosure).
5564 check_element_of_function_closure(X,Y, P,T,ClosureBody, WF) :-
5565 % affects test 1312, unless we add s:seq(0..9) before calling num
5566 % a special rule which tries and avoid enumerating solutions to arguments of function application
5567 % usually a function application will either be given all arguments or maybe be used in inverse
5568 ? is_converted_lambda_closure(P,T,ClosureBody), %is_converted_non_recursive_lambda_closure(P,T,ClosureBody),
5569 % TO DO: also make this work for recursive closures by adding recursive args (see e.g. test 1302)
5570 is_lambda_closure(P,T,ClosureBody, OtherIDs, OtherTypes, DomainPred, EXPR),
5571 (debug:debug_level_active_for(4) ->
5572 print('Apply Fun : '), translate:print_bexpr(DomainPred), print(' | '), translate:print_bexpr(EXPR),nl,
5573 get_texpr_info(ClosureBody,I), print(info(I,WF)),nl,
5574 print_term_summary((X,Y)),nl %,trace
5575 ; true),
5576 !,
5577 % alternative: annotate X,Y as inner variable ?
5578 get_texpr_info(ClosureBody,BInfo),
5579 ? b_interpreter:set_up_typed_localstate2(OtherIDs,OtherTypes,BInfo,ParValues,_TypedVals,[],LocalState,positive),
5580 convert_list_into_pairs(ParValues,SingleParValue),
5581 kernel_objects:equal_object_wf(X,SingleParValue,check_element_of_function_closure,WF),
5582 (is_truth(DomainPred) -> true
5583 ; init_wait_flags(InnerWF,[check_element_of_function_closure]),
5584 %copy_wf01e_wait_flags(WF,InnerWF), % we could delay copying WF0 until after test_boolean_expression of DomainPred ?
5585 b_test_boolean_expression(DomainPred,LocalState,[],InnerWF),
5586 ? get_wait_flag0(WF,WF0), get_wait_flag0(InnerWF,WF0), % was: ground_wait_flag0(InnerWF), but this can result in inner WF0 being set when outer is not yet set; see test 1948
5587 ground_value_check(X,GrX),
5588 (nonvar(GrX) -> copy_waitflag_store(InnerWF,WF) % block would trigger already
5589 ; ground_value_check(Y,GrY),
5590 (nonvar(GrY) -> copy_waitflag_store(InnerWF,WF) % block would trigger already
5591 ; get_last_wait_flag(check_element_of_function_closure(OtherIDs),WF,LastWF),
5592 block_copy_waitflag_store(InnerWF,WF,GrX,GrY,LastWF)
5593 )
5594 )
5595 ),
5596 ? b_interpreter:b_compute_expression(EXPR,LocalState,[],Y,WF).
5597 check_element_of_function_closure(X,Y, P,T,ClosureBody, WF) :-
5598 ? element_of_normal_closure((X,Y),P,T,ClosureBody,WF).
5599 % we could memoize on X here if /*@symbolic-memo */ pragma used and closure has special ID associated with it
5600
5601 :- block block_copy_waitflag_store(?,?,-,-,-).
5602 block_copy_waitflag_store(InnerWF,WF,_GrX,_GrY,_LWF) :-
5603 % copy waitflags from InnerWF store to WF
5604 copy_waitflag_store(InnerWF,WF).
5605
5606 /* -------------- */
5607 /* NOT_ELEMENT_OF */
5608 /* -------------- */
5609
5610 :- use_module(kernel_objects,[not_element_of_global_set/2]).
5611
5612 not_element_of_custom_set_wf(X,CS,WF) :-
5613 ? not_element_of_custom_set_wf2(CS,X,WF).
5614
5615 not_element_of_custom_set_wf2(global_set(GS),X,_WF) :- not_element_of_global_set(X,GS).
5616 not_element_of_custom_set_wf2(freetype(_),_,_) :- !,fail. % TO DO: what if we have List(1..3) ? can that occur ??
5617 not_element_of_custom_set_wf2(avl_set(node(Y,_,_,empty,empty)),X,WF) :- !,
5618 % X /: {Y} <=> X /= Y
5619 ? kernel_objects:not_equal_object_wf(X,Y,WF). % improve if X is ground
5620 not_element_of_custom_set_wf2(avl_set(AVL),X,_WF) :- !,
5621 ground_value_check(X,GrX),
5622 ? propagate_avl_not_element_information(X,GrX,AVL),
5623 not_element_of_avl_set_block(GrX,X,AVL).
5624 not_element_of_custom_set_wf2(closure(Parameters,PT,Cond),X,WF) :-
5625 closure_not_member(X,Parameters,PT,Cond,WF).
5626
5627 :- block not_element_of_avl_set_block(-,?,?).
5628 not_element_of_avl_set_block(_,X,AVL) :-
5629 convert_to_avl_inside_set(X,CX),
5630 \+ avl_fetch(CX,AVL). %% IMPROVE ??
5631
5632 propagate_avl_not_element_information(_,GrEl,_) :- nonvar(GrEl),!.
5633 propagate_avl_not_element_information(Element,_,AVL) :- preferences:preference(use_clpfd_solver,true),
5634 is_avl_simple_set(AVL,Type), % integer or global(GS) \+ground(Element) ,
5635 ((Type=integer -> avl_height_less_than_with_solver_strength(AVL,6) % 16-31 elements - was: avl_size<20
5636 ; true)
5637 -> !,
5638 ? propagate_avl_not_element_information3(Type,Element,AVL) % uses clpfd_not_inlist
5639 ; Type=integer, avl_height_less_than_with_solver_strength(AVL,15),
5640 avl_is_interval(AVL,Min,Max)
5641 -> !,
5642 kernel_objects:not_in_nat_range(Element,int(Min),int(Max)) % WF not used anyway in _wf version
5643 ).
5644 propagate_avl_not_element_information(_Element,_,AVL) :-
5645 quick_definitely_maximal_set_avl(AVL),
5646 !, % we require something not to be an element of the full set; impossible
5647 fail.
5648 % to do: check if all but one element is in set
5649 propagate_avl_not_element_information(_,_,_).
5650
5651 avl_height_less_than_with_solver_strength(AVL,Limit) :- preference(solver_strength,SS),
5652 RealLimit is Limit + SS/100,
5653 avl_height_less_than(AVL,RealLimit).
5654
5655 % try and compute a small finite cardinality for a ground value; fail if not possible
5656 try_get_finite_max_card_from_ground_value(pred_true,2).
5657 try_get_finite_max_card_from_ground_value(pred_false,2).
5658 try_get_finite_max_card_from_ground_value(fd(_,Type),Card) :-
5659 b_global_sets:b_fd_card(Type,Card), integer(Card).
5660 try_get_finite_max_card_from_ground_value((A,B),Card) :-
5661 try_get_finite_max_card_from_ground_value(A,CA),
5662 try_get_finite_max_card_from_ground_value(B,CB),
5663 Card is CA*CB,
5664 Card < 20000.
5665 try_get_finite_max_card_from_ground_value(rec(Fields),Card) :-
5666 try_get_finite_max_card_from_fields(Fields,Card).
5667 try_get_finite_max_card_from_ground_value(freeval(FreetypeId,_CaseId,_EArgs),Card) :-
5668 freetype_cardinality(FreetypeId,Card), number(Card), Card < 20000.
5669 try_get_finite_max_card_from_ground_value(avl_set(node(El,_True,_,_,_)),Card) :-
5670 try_get_finite_max_card_from_ground_value(El,CEl),
5671 CEl < 16,
5672 safe_pow2(CEl,Card).
5673 % int(_), term(floating(_)), string(_) are all infinite
5674
5675 try_get_finite_max_card_from_fields([],1).
5676 try_get_finite_max_card_from_fields([field(_,A)|TF],Card) :-
5677 try_get_finite_max_card_from_ground_value(A,CA),
5678 try_get_finite_max_card_from_fields(TF,CB),
5679 Card is CA*CB,
5680 Card < 20000.
5681
5682 :- use_module(b_global_sets,[get_global_type_value/3]).
5683 propagate_avl_not_element_information3(integer,int(El),AVL) :-
5684 avl_domain(AVL,R),project_avl_domain_on_fd(R,FDList),
5685 clpfd_interface:clpfd_not_inlist(El,FDList).
5686 propagate_avl_not_element_information3(global(GS),FD,AVL) :-
5687 get_global_type_value(FD,GS,El), % sets up the FD constraint if var; maybe we can detect inconsistency straightaway below
5688 avl_domain(AVL,R),project_avl_domain_on_fd(R,FDList), % maybe we can compute directly the complement ?
5689 ? clpfd_interface:clpfd_not_inlist(El,FDList).
5690
5691
5692 :- block closure_not_member(?,-,?,?,?).
5693 %, closure_not_member(-,?,?,?,?). /* El is unlikely to be instantiated by not_element_of test , but test 6 requires commenting out block declaration */
5694
5695 closure_not_member(X,Parameters,Types,Body,WF) :-
5696 is_special_closure(Parameters,Types,Body,SpecialClosure),!,
5697 not_element_of_special_closure(SpecialClosure,X,WF,Parameters,Types,Body).
5698 closure_not_member(El,Parameters,PT,Cond,WF) :-
5699 normal_closure_not_member(El,Parameters,PT,Cond,WF).
5700
5701 :- use_module(memoization,[not_element_of_memoization_closure/6]).
5702 not_element_of_special_closure(interval(LOW,UP),X,_WF,_Parameters,_Types,_Body) :-
5703 !,kernel_objects:not_in_nat_range(X,int(LOW),int(UP)).
5704 not_element_of_special_closure(member_closure(_ID,_Type,VAL),X,WF,_Parameters,_Types,_Body) :-
5705 ( VAL = value(_)
5706 ; VAL = cartesian_product(b(value(A),_,_),b(value(B),_,_))),!,
5707 %hit_profiler:add_profile_hit(member(X,Par,Typ,Body)),
5708 ( VAL=value(Set) -> kernel_objects:not_element_of_wf(X,Set,WF)
5709 ; kernel_objects:not_is_cartesian_pair(X,A,B,WF)).
5710 not_element_of_special_closure(not_member_closure(_ID,_Type,value(Set)),X,WF,_Parameters,_Types,_Body) :-
5711 !,kernel_objects:check_element_of_wf(X,Set,WF).
5712 not_element_of_special_closure(memoization_closure(MemoID),X,WF,P,T,B) :- !,
5713 not_element_of_memoization_closure(MemoID,X,WF,P,T,B).
5714 not_element_of_special_closure(recursive_special_closure(RId),X,WF,Parameters,Types,Body) :-
5715 !,
5716 add_recursive_parameter(Parameters,Types,X,RId,Body,NewParameters,NewPT,Value,WF),
5717 normal_closure_not_member(Value,NewParameters,NewPT,Body,WF).
5718
5719 not_element_of_special_closure(SC,_X,_WF,Parameters,Types,Body) :-
5720 SC \= interval(_,_),
5721 SC \= not_member_closure(_,_,_),
5722 is_definitely_maximal_closure(Parameters,Types,Body),
5723 !,
5724 fail.
5725 not_element_of_special_closure(_,X,WF,Parameters,Types,Body) :-
5726 % falling back to normal test
5727 normal_closure_not_member(X,Parameters,Types,Body,WF).
5728
5729 :- use_module(library(lists),[same_length/2]).
5730
5731 normal_closure_not_member(El,Parameters,PT,Cond,WF) :-
5732 %hit_profiler:add_profile_hit(closure_not_member(El,Parameters,PT,Cond,WF)),
5733 same_length(Parameters,ParValues),
5734 convert_list_into_pairs(ParValues,El),
5735 b_not_test_closure_wf(Parameters,PT,Cond,ParValues,WF).
5736
5737
5738
5739
5740 /* -------------------------- */
5741 /* VARIOUS CLOSURE PREDICATES */
5742 /* -------------------------- */
5743
5744
5745 :- use_module(tools,[convert_list_into_pairs/2]).
5746 :- use_module(b_interpreter,[b_test_boolean_expression/4, b_not_test_boolean_expression/4]).
5747 :- use_module(b_enumerate).
5748
5749 :- assert_pre(custom_explicit_sets:expand_closure_to_list(_,_,ClosureBody,_Result,_Done,_,_WF),
5750 (nonvar(ClosureBody),
5751 bsyntaxtree:check_if_typed_predicate(ClosureBody))).
5752 :- assert_post(custom_explicit_sets:expand_closure_to_list(_,_,_,Result,_Done,_,_WF),
5753 b_interpreter:value_type(Result)).
5754
5755 :- block expand_interval_closure_to_avl(-,?,?), expand_interval_closure_to_avl(?,-,?).
5756 expand_interval_closure_to_avl(Low,Up,Result) :-
5757 Delta is Up-Low,
5758 (Delta>9999 -> perfmessage(expanding_interval(Low,Up)) ; true),
5759 construct_interval_ord_list(Low,Up,OL),
5760 ord_list_to_avlset_direct(OL,ARes,expand_interval),
5761 ? equal_object(ARes,Result,expand_interval_closure_to_avl).
5762 construct_interval_ord_list(Low,Up,Res) :-
5763 (Low>Up -> Res = []
5764 ; Res = [int(Low)-true|T], L1 is Low+1, construct_interval_ord_list(L1,Up,T)
5765 ).
5766
5767 :- block expand_interval_closure_to_list(-,?,?,?), expand_interval_closure_to_list(?,-,?,?).
5768 expand_interval_closure_to_list(Low,Up,Result,Done) :-
5769 construct_interval_list(Low,Up,OL),
5770 ? equal_object(OL,Result,expand_interval_closure_to_list),
5771 Done=true.
5772 construct_interval_list(Low,Up,Res) :-
5773 (Low>Up -> Res = []
5774 ; Res = [int(Low)|T], L1 is Low+1, construct_interval_list(L1,Up,T)
5775 ).
5776
5777 expand_closure_to_list([X],[integer],Body,Result,Done,_,_) :-
5778 ? is_interval_closure_body(Body,X,Low,Up),!,
5779 expand_interval_closure_to_list(Low,Up,Result,Done).
5780 expand_closure_to_list(Par,Types,Body,Result,Done,Source,WF) :-
5781 ? expand_normal_closure(Par,Types,Body,CResult,CDone,expand_closure_to_list(Source),WF),
5782 expand_if_avl(CResult,Result,CDone,Done,Source),
5783 lazy_check_elements_of_closure(Result,CDone, Par,Types,Body,WF).
5784
5785 % Note: does slow down test 1306 (91ms mc time becomes 918 ms)
5786 % as long as a closure has not been fully expanded, lazily check elements
5787 % that are instantiated from the outside satisfy the closure predicate
5788 % Note: this can also instantiate unknown values used inside the closure body
5789 lazy_check_elements_of_closure(Result,CDone, Par,Types,Body,WF) :-
5790 (WF==no_wf_available -> true
5791 ; lazy_check_elements6(Result,CDone, Par,Types,Body,WF),
5792 propagate_closure_body_value_set(Par,Types,Body,Result,CDone,WF)
5793 ).
5794 % TODO: check if closure is a non-ground projection-member closure and check elements
5795 :- block lazy_check_elements6(-,-, ?,?,?,?).
5796 lazy_check_elements6(_Result,CDone, _Par,_Types,_Body,_WF) :- nonvar(CDone),!.
5797 lazy_check_elements6([H|T],CDone, Par,Types,Body,WF) :- !,
5798 ? element_of_closure(H,Par,Types,Body,WF),
5799 ? lazy_check_elements6(T,CDone, Par,Types,Body,WF).
5800 lazy_check_elements6(avl_set(A),_CDone, Par,Types,Body,WF) :- !,
5801 avl_max(A,X),
5802 element_of_closure(X,Par,Types,Body,WF).
5803 % TO DO: also check avl_min or even all elements ?
5804 lazy_check_elements6(_,_,_,_,_,_).
5805
5806 :- use_module(probsrc(bsyntaxtree),[create_typed_ids/3]).
5807 % lazy check elements from non-var closure body against a result
5808 % for example if we have {x| TRUE |-> x : Value } = Result and Value is not-ground,
5809 % we can check that for all elements TRUE|->x of Value the corresponding x is in Result, see test 2466
5810 % slows down test 1987
5811 :- block propagate_closure_body_value_set(?,?,?,-,-,?).
5812 % we delay until the result is known, possibly in SMT mode it could be useful to propagate earlier
5813 propagate_closure_body_value_set(ParIDs,Types,Body,Result,CDone,WF) :-
5814 var(CDone), % the closure has not yet been fully expanded
5815 % check if this closure can profit from set membership propagation:
5816 b_interpreter:is_for_all_set_membership_predicate2(Body,ParIDs,ParIDs,UnmatchedIDs,Set,_Pattern,_ParValues,_),
5817 UnmatchedIDs=[],
5818 Set = b(value(_Value),_,_), % check that the set is a value; it must be non-ground, otherwise CDone would be true
5819 create_couple_term(ParIDs,Types,CoupleTerm),
5820 SetTerm=b(value(Result),any,[]),
5821 safe_create_texpr(member(CoupleTerm,SetTerm),pred,[],RHS),
5822 create_typed_ids(ParIDs,Types,TIDs),
5823 !,
5824 propagate_closure_body_for_all(TIDs,Body,RHS,Result,CDone,WF).
5825 propagate_closure_body_value_set(_,_,_,_,_,_WF).
5826
5827 :- block propagate_closure_body_for_all(?,?,?,-,-,?).
5828 propagate_closure_body_for_all(TIDs,Body,RHS,_,CDone,WF) :- var(CDone),!,
5829 add_debug_message(closure,'Propagating from closure body to result: ',Body,Body),
5830 Infos=[],
5831 b_interpreter:b_for_all(TIDs,Infos,Body,RHS,[],[],WF).
5832 propagate_closure_body_for_all(_,_,_,_Result,_CDone,_WF). % propagation not required; closure expanded, cf test 1987
5833
5834 %check_valid_avl(AVL,Origin) :-
5835 % (nonvar(AVL) -> true
5836 % ; add_internal_error('Var avl_set: ', check_valid_avl(AVL,Origin)),fail).
5837
5838 :- block expand_if_avl(?,?,-,?,?).
5839 expand_if_avl(avl_set(S),Result,_,Done,Source) :- !, % we could transmit a flag to expand_normal_closure so that transform_result_into_set does not expand to avl
5840 ? expand_custom_set_to_list2(avl_set(S),Result,Done,_,expand_if_avl(Source),no_wf_available).
5841 expand_if_avl(Res,Result,_,Done,Source) :- check_list(Res,expand_if_avl(Source)),
5842 ? equal_object(Res,Result), Done=true.
5843
5844 check_list(Res,_) :- nonvar(Res), is_list(Res),!.
5845 check_list(Res,Src) :- add_error(Src,'Could not expand to list: ',Res).
5846 is_list([]). is_list([_|_]).
5847
5848 expand_closure_to_avl_or_list([X],[integer],Body,Result,_CheckTimeouts,_WF) :-
5849 ? is_interval_closure_body(Body,X,Low,Up),!,
5850 expand_interval_closure_to_avl(Low,Up,Result).
5851 %expand_closure_to_avl_or_list(P,T,Body,Result,_WF) :- is_member_closure(P,T,Body,TS,Set),
5852 % print(expand_member_closure(P,T,Body,TS,Set)),nl,fail.
5853 expand_closure_to_avl_or_list(Par,Types,Body,Result,CheckTimeouts,WF) :-
5854 expand_normal_closure(Par,Types,Body,CResult,_Done,CheckTimeouts,WF),
5855 kernel_objects:equal_object(Result,CResult,expand_closure_to_avl_or_list). % may convert to AVL, should we wait for _Done?
5856
5857
5858 % use WF just for call stack messages; we should not delay creating result
5859 expand_closure_to_avl_wf([X],[integer],Body,Result,_WF) :-
5860 is_interval_closure_body(Body,X,Low,Up),!,
5861 expand_interval_closure_to_avl(Low,Up,Result). % we could pass WF
5862 expand_closure_to_avl_wf(Par,Types,Body,Result,WF) :-
5863 ? expand_normal_closure(Par,Types,Body,S,Done,check(expand_closure_to_avl),WF),
5864 (ground_value(S) % ground value is sufficient to proceed; we do not need to check Done
5865 -> convert_to_avl_inside_set(S,R),equal_object(R,Result,expand_closure_to_avl)
5866 ; print(cannot_convert_closure_value_to_avl(closure(Par,Types),done(Done))),nl,
5867 translate:print_bexpr(Body),nl,trace,
5868 fail).
5869
5870
5871 % possible values for CheckTimeouts: check, check_no_inf, no_check, ...
5872 % Note: we no longer check is_infinite_explicit_set(closure(Parameters,ParameterTypes,ClosureBody))
5873 % and no longer raise add_closure_warning(Source,Parameters,ParameterTypes,ClosureBody,'### WARNING: expanding infinite comprehension set: ')
5874 % and no longer use preference warn_when_expanding_infinite_closures
5875 % this is relevant for e.g., test 1291
5876 expand_normal_closure(Parameters,ParameterTypes,ClosureBody,Result,Done,CheckTimeouts,WF) :-
5877 ? expand_normal_closure_memo(CheckTimeouts,Parameters,ParameterTypes,ClosureBody,Result,Done,WF).
5878
5879 :- public add_closure_warning_wf/6.
5880 add_closure_warning_wf(Source,Parameters,_ParameterTypes,_ClosureBody,_MSG,_WF) :-
5881 preference(provide_trace_information,false),preference(strict_raise_warnings,false),!,
5882 format('### TIME-OUT raised during closure expansion (~w,~w).~n### set TRACE_INFO preference to TRUE for more details.~n',[Parameters,Source]).
5883 add_closure_warning_wf(Source,Parameters,ParameterTypes,ClosureBody,MSG,WF) :-
5884 (debug_mode(on) -> Limit = 2500, AvlLim=10 ; Limit = 500, AvlLim=5),
5885 preferences:temporary_set_preference(expand_avl_upto,AvlLim,CHNG),
5886 call_cleanup(translate:translate_bvalue_with_limit(closure(Parameters,ParameterTypes,ClosureBody),Limit,CT),
5887 preferences:reset_temporary_preference(expand_avl_upto,CHNG)),
5888 bsyntaxtree:get_texpr_info(ClosureBody,Infos),
5889 add_warning_wf(Source,MSG,CT,Infos,WF), debug_print(19,'! infos: '), debug_println(Infos). %,trace.
5890
5891
5892 :- use_module(memoization,[is_memoization_closure/4,get_complete_memoization_expansion/6]).
5893
5894 % a version of closure expansion which memoizes its results; stored_expansion needs to be cleared when new machine loaded
5895 expand_normal_closure_memo(CHECK,Parameters,ParameterTypes,ClosureBody,FullResult,Done,WF) :-
5896 ? is_memoization_closure(Parameters,ParameterTypes,ClosureBody,MemoID),
5897 !, Span=ClosureBody,
5898 % MemoID can be a variable
5899 (var(MemoID) -> perfmessage(CHECK,'Getting full value of a memoized function',ClosureBody) ; true),
5900 get_complete_memoization_expansion(MemoID,FullResult,Done,Span,expand_normal_closure_memo(CHECK),WF).
5901 expand_normal_closure_memo(CHECK,Parameters,ParameterTypes,ClosureBody,FullResult,Done,WF) :-
5902 preferences:preference(use_closure_expansion_memoization,false),!,
5903 ? expand_normal_closure2(CHECK,Parameters,ParameterTypes,ClosureBody,FullResult,Done,WF).
5904 expand_normal_closure_memo(CHECK,Parameters,ParameterTypes,ClosureBody,FullResult,Done,WF) :-
5905 % maybe we should only memo when ClosureWaitVars are ground ?
5906 MemoLookupTerm = closure(Parameters,ParameterTypes,ClosureBody),
5907 compute_memo_hash(MemoLookupTerm,Hash),
5908 % idea: maybe store expansion only on second hit ?
5909 (get_stored_memo_expansion(Hash,MemoLookupTerm,StoredResult)
5910 -> %print_term_summary(reusing_expansion(Hash,Parameters,ParameterTypes,ClosureBody,StoredResult)),nl,
5911 UPV=StoredResult, %state_packing:unpack_value(StoredResult,UPV),
5912 FullResult = UPV, Done=true
5913 ; %statistics(runtime,[T1,_]), %%
5914 expand_normal_closure2(CHECK,Parameters,ParameterTypes,ClosureBody,FullResult,Done,WF),
5915 %statistics(runtime,[T2,_]), Time is T2-T1, store_memo_computation_time(Hash,Time),
5916 (Done==true/* ,T2-T1>0*/
5917 -> PackedValue=FullResult, %state_packing:pack_value(FullResult,PackedValue),
5918 store_memo_expansion(Hash,MemoLookupTerm,PackedValue)
5919 ; true)
5920 ).
5921
5922
5923 expand_normal_closure2(_CHECK,Parameters,ParameterTypes,ClosureBody,FullResult,Done,WF) :-
5924 % TO DO: add more symbolic member closures who have expression computation code
5925 is_closure1_value_closure(Parameters,ParameterTypes,ClosureBody,VAL),!,
5926 ? bsets_clp:relational_trans_closure_wf(VAL,FullResult,WF),
5927 ground_value_check(FullResult,FRGr),
5928 when(nonvar(FRGr),Done=true).
5929 expand_normal_closure2(CHECK,Parameters,ParameterTypes,ClosureBody,FullResult,Done,WF) :-
5930 % special treatment for lambda closures: Advantage: we don't have to wait for variables in EXPR body of closure
5931 % Disadvantage: EXPR only gets evaluated after a solution has been found for args: can mean repeated computations !
5932 % (cf pas_as_env_inv_cv_sui, negated version of !(cv_i).(cv_i : t_cv_pas => closure(%cv_o2.((...|>> {cv_i} : t_cv_pas <-> t_cv_pas) ASSERTION
5933 % Advantage: it can solve constraints such as f = %x.(x:1..10|x+y) & f(5)=1005 (finding y without enumeration); see test 1168
5934 \+ preferences:preference(use_smt_mode,false),
5935 is_lambda_closure(Parameters,ParameterTypes,ClosureBody, OtherIDs,OtherTypes, DomainPred, EXPR),
5936 \+ ground_bexpr(EXPR), % if EXPR is ground, there is nothing to be gained by special treatment here
5937 WF \= no_wf_available, % otherwise we may have to enumerate EXPR result leading to choice points, e.g. in phase 0
5938 !,
5939 bexpr_variables(DomainPred,ClosureWaitVars),
5940 (CHECK=no_check -> TIMEOUTCODE = true ;
5941 TIMEOUTCODE = add_closure_warning_wf(CHECK,Parameters,ParameterTypes,ClosureBody,
5942 'TIME-OUT occurred while ProB was expanding: ',WF)),
5943 (CHECK=check_no_inf -> VIRTUALTIMEOUTCODE=true ; VIRTUALTIMEOUTCODE=TIMEOUTCODE),
5944 delay_setof_check_wf( ParTuple,
5945 (custom_explicit_sets:b_test_closure(OtherIDs,OtherTypes,DomainPred,OtherValues,all_solutions,WF),
5946 convert_list_into_pairs(OtherValues,ParTuple)
5947 % TO DO: compile EXPR when we start expanding the closure: to avoid repeated re-computation of expressions for every instance
5948 ),
5949 Result, ClosureWaitVars, __Done,
5950 TIMEOUTCODE,VIRTUALTIMEOUTCODE,WF,DomainPred),
5951 (WF = no_wf_available
5952 -> init_wait_flags(WF1,[expansion_context(lambda_function_result,Parameters)])
5953 ; WF1=WF
5954 ),
5955 evaluate_result_expr(Result,EXPR,OtherIDs,EvResult,EvDone,WF1),
5956 when(nonvar(EvDone),(
5957 (WF = no_wf_available -> ground_wait_flags(WF1) ; true),
5958 kernel_objects:equal_object_wf(EvResult,FullResult,expand_normal_closure2,WF),
5959 Done=true)).
5960 expand_normal_closure2(no_check,Parameters,ParameterTypes,ClosureBody,Result,Done,WF) :- !,
5961 expand_normal_closure_direct(Parameters,ParameterTypes,ClosureBody,Result,Done,WF).
5962 expand_normal_closure2(CHECK,Parameters,ParameterTypes,ClosureBody,Result,Done,WF) :-
5963 bexpr_variables(ClosureBody,ClosureWaitVars),
5964 TIMEOUTCODE = add_closure_warning_wf(CHECK,Parameters,ParameterTypes,ClosureBody,
5965 'TIME-OUT occurred while ProB was expanding: ',WF),
5966 (CHECK=check_no_inf -> VIRTUALTIMEOUTCODE=true ; VIRTUALTIMEOUTCODE=TIMEOUTCODE),
5967 % Note: delay_setof_check_wf will throw enumeration warning for virtual timeouts, after VIRTUALTIMEOUTCODE
5968 delay_setof_check_wf( ParTuple,
5969 custom_explicit_sets:test_closure_and_convert(Parameters,ParameterTypes,ClosureBody, ParTuple,WF),
5970 Result, ClosureWaitVars, Done, TIMEOUTCODE, VIRTUALTIMEOUTCODE,WF,ClosureBody).
5971
5972 expand_normal_closure_direct(Parameters,ParameterTypes,ClosureBody,Result,Done,WF) :-
5973 bexpr_variables(ClosureBody,ClosureWaitVars),
5974 Span = ClosureBody,
5975 delay_setof_wf( ParTuple,
5976 % TO DO: refresh waitflag in outer WF store to let pending code run to completion and avoid spurious WD errors ?
5977 custom_explicit_sets:test_closure_and_convert(Parameters,ParameterTypes,ClosureBody, ParTuple,WF),
5978 Result, ClosureWaitVars, Done,WF, Span).
5979
5980
5981
5982 :- block evaluate_result_expr(-,?,?,?,?,?).
5983 evaluate_result_expr(avl_set(AVL),EXPR,OtherIDs,Res,Done,WF) :-
5984 avl_domain(AVL,R),
5985 evaluate_result_expr(R,EXPR,OtherIDs,Res,Done,WF).
5986 evaluate_result_expr([],_EXPR,_OtherIDs,[],Done,_WF) :-
5987 %ground_wait_flags(WF),
5988 Done=true.
5989 evaluate_result_expr([ParTuple|T],EXPR,OtherIDs,[FullTuple|ET],Done,WF) :-
5990 % same_length(OtherIDs,ParValues), % not necessary
5991 set_up_localstate(OtherIDs,ParValues,[],LocalState),
5992 convert_list_into_pairs(ParValues,ParTuple), % bind values in ParTuple to LocalState
5993 b_interpreter:b_compute_expression(EXPR,LocalState,[],EXPRVALUE,WF),
5994 append(ParValues,[EXPRVALUE],FullValues),
5995 convert_list_into_pairs(FullValues,FullTuple),
5996 evaluate_result_expr(T,EXPR,OtherIDs,ET,Done,WF).
5997
5998 :- use_module(bsyntaxtree,[split_names_and_types/3]).
5999 :- use_module(probsrc(bsyntaxtree), [def_get_texpr_id/2]).
6000 %:- use_module(library(lists),[prefix_length/3, suffix_length/3]).
6001 % test a closure and convert into pairs; assume we want all solutions
6002 test_closure_and_convert(Parameters,ParameterTypes,ClosureBody, ParTuple, WF) :-
6003 ? is_recursive_closure(Parameters,ParameterTypes,ClosureBody),
6004 ? get_recursive_identifier_of_closure_body(ClosureBody,TRID),!,
6005 def_get_texpr_id(TRID,RID), get_texpr_type(TRID,RType),
6006 %print(test_recursion(RID)),nl, translate:nested_print_bexpr(ClosureBody),nl,
6007 RecVal = closure(Parameters,ParameterTypes,ClosureBody), % Recursive Value added to parameters
6008 same_length(Parameters,ParValues),
6009 reset_closure_solution_counter(Parameters),
6010 ? b_test_closure([RID|Parameters],[RType|ParameterTypes],ClosureBody,[RecVal|ParValues],all_solutions,WF),
6011 convert_sol_list_into_pairs(ParValues,Parameters,ParTuple). % convert tuple without recursive value to ParTuple
6012 test_closure_and_convert(Parameters,ParameterTypes,b(exists(EParAndTypes,ClosureBody),pred,OuterInfo), ParTuple, WF) :-
6013 % Motivation: enumerating Parameters can be quite inefficient
6014 % if for example we have something like {x|#y.(y:SmallSet & x=f(y))}
6015 % Problem: the existential quantifier will be delayed until the Parameters are instantiated !
6016 % relevant test: 1162
6017 % Note: this is duplicating to some extent the code in b_test_exists_wo_expansion
6018 % However, here we can also apply lambda_closure optimisation in b_test_closure below, this is
6019 % relevant for private_examples/2023/.../rule_FICHIER_MRGATKSAATPAR_RVF219_MRGA_DE.mch
6020 ? exists_should_be_lifted(Parameters,ParameterTypes,OuterInfo,ClosureBody),
6021 split_names_and_types(EParAndTypes,EPar,ETypes),
6022 !,
6023 % print(' Lifting existential quantifier (i.e., enumerating paras with closure paras): '), print(EPar),nl,
6024 % print(outer_paras(Parameters)),nl,
6025 % append Parameters at end; in case we have a lambda function
6026 append(EPar,Parameters,FullPar), length(Parameters,NrParas),
6027 append(ETypes,ParameterTypes,FullTypes),
6028 length(EPar,NrExistsParas),
6029 length(IrrelevantParas,NrExistsParas), length(Suffix,NrParas),
6030 append(IrrelevantParas,Suffix,FullParList),
6031 copy_identifier_infos(OuterInfo,ClosureBody,ClosureBody2),
6032 reset_closure_solution_counter(Parameters),
6033 % bsyntaxtree:check_used_ids_in_ast(ClosureBody2),
6034 ? b_test_closure(FullPar,FullTypes,ClosureBody2, FullParList,all_solutions,WF),
6035 convert_sol_list_into_pairs(Suffix,Parameters,ParTuple).
6036 test_closure_and_convert(Parameters,ParameterTypes,ClosureBody, ParTuple, WF) :-
6037 reset_closure_solution_counter(Parameters),
6038 % print(test),nl, translate:nested_print_bexpr(ClosureBody),nl,
6039 length(Parameters,Len), length(ParValues,Len),
6040 %(annotate_exists(Parameters,ParameterTypes,ClosureBody,Body2) -> true ; Body2=ClosureBody),
6041 ? b_test_closure(Parameters,ParameterTypes,ClosureBody,ParValues,all_solutions,WF),
6042 convert_sol_list_into_pairs(ParValues,Parameters,ParTuple). % ,print(solution(ParTuple)),nl,nl.
6043
6044 % Lifting existential quantifier was previously done here, but was duplicating code in b_test_exists_wo_expansion
6045 % we now simply generate the allow_to_lift_exists annotation here and let b_test_exists_wo_expansion do its job
6046 %annotate_exists(Parameters,ParameterTypes,
6047 % b(exists(EParAndTypes,ClosureBody),pred,OuterInfo),
6048 % b(exists(EParAndTypes,ClosureBody),pred,[allow_to_lift_exists|OuterInfo])) :-
6049 % exists_should_be_lifted(Parameters,ParameterTypes,OuterInfo,ClosureBody).
6050
6051 % check if a top-level exists with body ExistsClosureBody should be lifted
6052 % within a closure with paras Parameters of type ParameterTypes:
6053 exists_should_be_lifted(Parameters,ParameterTypes,OuterInfo,ExistsClosureBody) :-
6054 (Parameters == ['_was_lambda_result_'] % here we are quite sure that we gain by this optimisation
6055 ? ; member(allow_to_lift_exists,OuterInfo) % parameters were originally from a set comprehension,
6056 % see test 306: in this case existential quantifier is lifted in b_interpreter anyway;
6057 % Note we counter the rewrite ran({x1,...xn|P}) ---> {xn| #(x1,...).(P)} and similarly for dom({...})
6058 ; ExistsClosureBody = b(member(_,_),_,_) % we have a simple projection closure
6059 % TO DO: maybe support other ones as well
6060 ? ; basic_type_list_cardinality(ParameterTypes,Card),
6061 (Card=inf -> true ; Card>10000)
6062 % if here are only a few parameter values: do not lift existential quantified variables
6063 ).
6064
6065 % we need to copy important infos about the outer Parameters to ClosureBody
6066 copy_identifier_infos(Info,b(InnerPred,T,II),b(InnerPred,T,II2)) :-
6067 findall(I,identifier_info(I,Info),ToCopy),
6068 append(ToCopy,II,II2).
6069 identifier_info(I,Info) :- I=prob_annotation('DO_NOT_ENUMERATE'(ID)),
6070 ? member(I,Info), ID \= '$$NONE$$'.
6071
6072 convert_sol_list_into_pairs(ParaValues,Parameters,ParTuple) :-
6073 convert_list_into_pairs(ParaValues,ParTuple),
6074 update_closure_solution_counter(Parameters,ParTuple).
6075
6076 :- if(environ(prob_debug_flag,true)).
6077 :- dynamic closure_solution_counter/3.
6078 % debugging long expansions of comprehension_set / closures
6079 reset_closure_solution_counter(Parameters) :- retractall(closure_solution_counter(Parameters,_,_)).
6080
6081 update_closure_solution_counter(Parameters,ParTuple) :-
6082 retract(closure_solution_counter(Parameters,OldCount,OldTime)),!,
6083 statistics(walltime,[W2,_]), Delta is W2-OldTime,
6084 NewCount is OldCount+1,
6085 ((Delta > 5000 ; NewCount mod 1000 =:= 0)
6086 -> format('--> Solution ~w for expansion of closure ~w (delta ~w ms): ',[NewCount,Parameters,Delta]),
6087 translate:print_bvalue(ParTuple),nl,
6088 assert(closure_solution_counter(Parameters,NewCount,W2))
6089 ; assert(closure_solution_counter(Parameters,NewCount,OldTime))
6090 ).
6091 update_closure_solution_counter(Parameters,_ParTuple) :-
6092 statistics(walltime,[W2,_]),
6093 assert(closure_solution_counter(Parameters,1,W2)).
6094 :- else.
6095 reset_closure_solution_counter(_).
6096 update_closure_solution_counter(_,_).
6097 :- endif.
6098
6099
6100
6101 % compute cardinality of a list of basic types
6102 basic_type_list_cardinality([],1).
6103 basic_type_list_cardinality([BasicType|T],Res) :-
6104 ? basic_type_list_cardinality(T,TCard),
6105 (TCard=inf -> Res=inf
6106 ? ; kernel_objects:max_cardinality(BasicType,Card),
6107 safe_mul(Card,TCard,Res)
6108 ).
6109
6110 % for lambda closures we can set up a second waitflag for the expression and only ground it when body enumeration finished
6111 % idea is to avoid perturbation of constraint solving of main closure predicate by lambda expression, see test 1737
6112 % something like %(x,y).(x:1..200 & y:1..100 & y+x<259 & y*x>10|(y+x*x+y) mod 100) is faster
6113 % this is slower : %(x,y).(x:1..200 & y:1..100 |(y+x*x+y))
6114 % currently this slows down test 1336
6115 :- block b_test_closure(?,?,-,?,?,?).
6116 b_test_closure(Parameters,ParameterTypes,ClosureBody, FullParValues, NegationContext, OuterWF) :-
6117 (preference(data_validation_mode,true)
6118 -> true % avoids ineraction between domain and range expression enumeration; see
6119 % private_examples/ClearSy/2019_May/perf_3264/rule_186.mch or
6120 % computation of 631 ic___DMI_MRGATKSAAT___Parametre_Identifiant_indices_function in rule_FICHIER_MRGATKSAATPAR_RVF219_MRGA_DE.mch
6121 % however, as b_optimize below does *not* evaluate nested set comprehensions, there can be a slowdown:
6122 % the nested set comprehension gets re-evaluated for every soluiton of the lambda parameters !
6123 % this was the case of private_examples/ClearSy/2019_Nov/rule_Regle_31C_0005/rule.mch before using SORT
6124 ; \+ preferences:preference(use_smt_mode,false)), % TO DO: enable in normal mode when performance of 1336 fixed
6125 % print(test_closure(Parameters,FullParValues)),nl,
6126 is_lambda_closure(Parameters,ParameterTypes,ClosureBody, OtherIDs,OtherTypes, DomainPred, EXPR),
6127 % TO DO: detect not only equalities at end, but any equality which is irrelevant for the rest
6128 % nl,print(lambda_closure(OtherIDs)),nl, translate:print_bexpr(EXPR),nl,
6129 append(ParValues,[LambdaResult],FullParValues),
6130 !,
6131 get_texpr_info(ClosureBody,BInfo),
6132 b_interpreter:set_up_typed_localstate2(OtherIDs,OtherTypes,BInfo,ParValues,TypedVals,[],LocalState,NegationContext),
6133 simplify_span(ClosureBody,BSpan), % sometimes BInfo no longer contains a position info, but first_sub_expr does
6134 init_quantifier_wait_flag(OuterWF,comprehension_set(NegationContext),OtherIDs,ParValues,BSpan,WF),
6135 b_test_boolean_expression(DomainPred,LocalState,[],WF),
6136 %print('PRED: '),translate:print_bexpr(ClosureBody),nl,
6137 b_tighter_enumerate_values_in_ctxt(TypedVals,DomainPred,WF), % also does: project_away_useless_enumeration_values
6138 init_quantifier_wait_flag(OuterWF,comprehension_set(NegationContext),OtherIDs,ParValues,BSpan,WF2),
6139 ? b_compiler:b_optimize(EXPR,[],LocalState,[],CEXPR,WF), % already pre-compile lookup, without constraint processing; is not sufficient for test 1336
6140 ? ground_wait_flags(WF), % TODO: also call ground inner WF in context
6141 ? b_interpreter:b_compute_expression(CEXPR,LocalState,[],LambdaResult,WF2),
6142 ground_inner_wait_flags_in_context(NegationContext,WF2).
6143 b_test_closure(Parameters,ParameterTypes,ClosureBody,ParValues,NegationContext, OuterWF) :-
6144 % tools:print_bt_message(b_test_closure_testing_closure(Parameters,ParValues)), %%
6145 get_texpr_info(ClosureBody,BInfo),
6146 ? b_interpreter:set_up_typed_localstate2(Parameters,ParameterTypes,BInfo,
6147 ParValues,TypedVals,[],LocalState,NegationContext),
6148 % print_message(b_interpreter:b_test_boolean_expression(ClosureBody,LocalState,[],WF)),
6149 simplify_span(ClosureBody,BSpan), % sometimes BInfo no longer contains a position info, but first_sub_expr does
6150 init_quantifier_wait_flag(OuterWF,comprehension_set(NegationContext),Parameters,ParValues,BSpan,WF),
6151 %external_functions:observe_parameters(Parameters,LocalState), %%
6152 ? b_test_boolean_expression(ClosureBody,LocalState,[],WF),
6153 % tools:print_bt_message(tested_bool_expr), translate:print_bexpr(ClosureBody),nl,
6154 b_enumerate:b_tighter_enumerate_values_in_ctxt(TypedVals,ClosureBody,WF), % also detects useless enumeration ids
6155 ? ground_inner_wait_flags_in_context(NegationContext,WF).
6156
6157
6158
6159 :- block b_not_test_closure_wf(?,?,?,-,?).
6160 b_not_test_closure_wf(Parameters,ParameterTypes,Closure,ParValues,WF) :-
6161 % same_length(Parameters,ParValues), % not necessary
6162 set_up_localstate(Parameters,ParValues,[],LocalState),
6163 b_enumerate:b_type_values_in_store(Parameters,ParameterTypes,LocalState),
6164 b_not_test_boolean_expression(Closure,LocalState,[],WF),
6165 get_last_wait_flag(b_not_test_closure_wf(Parameters),WF,WF2),
6166 get_texpr_info(Closure,Infos),
6167 b_not_test_closure_enum(Parameters,ParameterTypes,Infos,LocalState,WF,WF2).
6168
6169 :- block b_not_test_closure_enum(-,?,?,?,?,?).
6170 b_not_test_closure_enum(Parameters,ParameterTypes,Infos,LocalState,WF,WF2) :-
6171 b_enumerate:b_extract_typedvalc(Parameters,ParameterTypes,Infos,LocalState,TypedVals),
6172 (var(WF2) -> ground_typedvals_check(TypedVals,GrVals) ; true),
6173 b_not_test_closure_enum_aux(GrVals,WF2,TypedVals,WF).
6174
6175 :- block b_not_test_closure_enum_aux(-,-,?,?).
6176 b_not_test_closure_enum_aux(_,_,TypedVals,WF) :-
6177 b_enumerate:b_tighter_enumerate_all_values(TypedVals,WF).
6178 % , print(finished_enum(Parameters)),nl.
6179
6180
6181 :- use_module(library(terms)).
6182 % check whether a VARIABLE occurs inside a closure
6183 closure_occurs_check(VARIABLE,_Par,_ParTypes,ClosureBody) :- expression_contains_setvar(ClosureBody,VARIABLE).
6184 % /* occurs check; x = closure1(x) ; for other closures this cannot happen ???!!! TO DO: Check */
6185 % custom_explicit_sets:is_closure1_value_closure(Par,ParTypes,ClosureBody,Val),
6186 % contains_var(VARIABLE,Val).
6187
6188 expression_contains_setvar(b(E,_,_),Variable) :- !,
6189 expression_contains_setvar_aux(E,Variable).
6190 expression_contains_setvar(E,V) :- add_internal_error('Illegal Expression: ', expression_contains_setvar(E,V)),
6191 contains_var(V,E).
6192
6193 expression_contains_setvar_aux(value(Val),Variable) :- !,value_contains_setvar(Val,Variable).
6194 % a few very common cases for performance; currently this predicate is often called for recursive functions
6195 expression_contains_setvar_aux(identifier(_),_) :- !,fail.
6196 expression_contains_setvar_aux(equal(A,B),Variable) :- !,
6197 (expression_contains_setvar(A,Variable) -> true ; expression_contains_setvar(B,Variable)).
6198 expression_contains_setvar_aux(conjunct(A,B),Variable) :- !,
6199 (expression_contains_setvar(A,Variable) -> true ; expression_contains_setvar(B,Variable)).
6200 expression_contains_setvar_aux(function(A,B),Variable) :- !,
6201 (expression_contains_setvar(A,Variable) -> true ; expression_contains_setvar(B,Variable)).
6202 expression_contains_setvar_aux(union(A,B),Variable) :- !,
6203 (expression_contains_setvar(A,Variable) -> true ; expression_contains_setvar(B,Variable)).
6204 expression_contains_setvar_aux(couple(A,B),Variable) :- !,
6205 (expression_contains_setvar(A,Variable) -> true ; expression_contains_setvar(B,Variable)).
6206 % the rest via safe_syntaxelement:
6207 expression_contains_setvar_aux(Expr,V) :-
6208 safe_syntaxelement_det(Expr,Subs,_Names,_,_),!,
6209 ? member(Sub,Subs), expression_contains_setvar(Sub,V),!.
6210 expression_contains_setvar_aux(E,V) :- add_internal_error('Illegal Expression: ', expression_contains_setvar_aux(E,V)),
6211 contains_var(V,E).
6212
6213 value_contains_setvar(Val,V) :- var(Val),!,Val==V.
6214 value_contains_setvar(avl_set(_),_V) :- !, fail. % assume avl_set always properly grounded; avoid looking inside
6215 value_contains_setvar(closure(_,_,Body),V) :- !,
6216 expression_contains_setvar(Body,V).
6217 value_contains_setvar(int(_),_) :- !,fail. % we check for set variables
6218 value_contains_setvar(global_set(_),_) :- !,fail. % we check for set variables
6219 value_contains_setvar(freetype(_),_) :- !,fail. % we check for set variables
6220 value_contains_setvar(freeval(_ID,_Case,Val),V) :- !, value_contains_setvar(Val,V).
6221 value_contains_setvar(string(_),_) :- !,fail. % we check for set variables
6222 value_contains_setvar(fd(_,_),_) :- !,fail. % we check for set variables
6223 value_contains_setvar((A,B),V) :- !, (value_contains_setvar(A,V) ; value_contains_setvar(B,V)).
6224 value_contains_setvar([A|B],V) :- !, (value_contains_setvar(A,V) ; value_contains_setvar(B,V)).
6225 value_contains_setvar(Val,V) :-
6226 contains_var(V,Val).
6227
6228 % ------------------