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 definitely_expand(Body,_) :- avl_mem_construct(Body,_).
1835 definitely_expand(exists(TEIDS,Body),P) :- P = [ID], TEIDS = [TEID], % TO DO: detect multiple ids
1836 % detect {res|#y.(y:AVL & res=Expr(y))} % test 1101
1837 Body = b(conjunct(b(Mem,pred,_),Eq),pred,_),
1838 Eq = b(equal(EqA,EqB),pred,_),
1839 avl_mem_construct(Mem,LHS), get_texpr_id(LHS,EID), get_texpr_id(TEID,EID),
1840 (get_texpr_id(EqA,ID) -> true ; get_texpr_id(EqB,ID)).
1841
1842 avl_mem_construct(member(LHS,RHS),LHS) :- RHS = b(value(V),_,_), nonvar(V), V=avl_set(_).
1843
1844 % dont_expand_this_explicit_set with default limit (20000)
1845 dont_expand_this_explicit_set(closure(P,T,B)) :- !,
1846 dont_expand_this_closure(P,T,B).
1847 dont_expand_this_explicit_set(S) :-
1848 is_infinite_or_very_large_explicit_set(S).
1849
1850 % dont_expand_this_explicit_set with extra limit argument:
1851 dont_expand_this_explicit_set(closure(P,T,B),Limit) :- !, dont_expand_this_closure(P,T,B,Limit).
1852 dont_expand_this_explicit_set(S,_) :- is_infinite_or_very_large_explicit_set(S).
1853
1854 % true if we have a closure / global_set that should not be expanded
1855 % 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))
1856 dont_expand_symbolic_explicit_set(closure(P,T,B)) :- !,
1857 dont_expand_this_closure(P,T,B).
1858 dont_expand_symbolic_explicit_set(avl_set(_)) :- !,
1859 fail. % already expanded
1860 dont_expand_symbolic_explicit_set(S) :-
1861 is_infinite_or_very_large_explicit_set(S).
1862
1863
1864 dont_expand_this_closure(P,T,B) :-
1865 get_preference(comprehension_set_symbolic_limit,Limit), % Default 20000
1866 dont_expand_this_closure(P,T,B,Limit). % % increase limit in Data valid mode?
1867
1868 dont_expand_this_closure(_P,_T,b(_,_,INFO),_Limit) :-
1869 ? member(prob_annotation(KIND),INFO),
1870 (KIND = 'SYMBOLIC' -> ! % cf is_symbolic_closure in closures
1871 ; KIND = 'FORCE' -> !, fail). % was wrapped in FORCE external_function
1872 dont_expand_this_closure(P,T,B,_Limit) :-
1873 is_interval_closure_or_integerset(closure(P,T,B),Low,Up), !,
1874 % interval closures are quite efficient for certain manipulations
1875 (number(Low), number(Up)
1876 -> dont_expand_interval(Low,Up)
1877 ; true % we have a closure with inf/minus_inf or variables as bounds; in both cases keep the closure
1878 ).
1879 dont_expand_this_closure(P,T,B,Limit) :-
1880 is_infinite_or_very_large_closure(P,T,B,Limit).
1881 %% TODO: also prevent expansion of things like ff = %x.(x:STRING & REGEX_MATCH(x,"[a-z]+")=TRUE|TRUE)
1882
1883 % do not automatically expand these intervals
1884 dont_expand_interval(Low,Up) :-
1885 Up+1-Low > 100. % another magic constant ; which value to choose ??
1886 do_expand_interval(Low,Up) :- Up+1-Low =< 100.
1887
1888 is_converted_lambda_closure(_P,_T,b(_,_,INFO)) :-
1889 ? member(prob_annotation('LAMBDA'),INFO).
1890
1891 is_symbolic_closure_or_symbolic_mode(P,T,B) :-
1892 ? (is_symbolic_closure(P,T,B) -> true
1893 ; preference(convert_comprehension_sets_into_closures,true)
1894 % by default suppose closures should be dealt with symbolically
1895 ).
1896 /*
1897 % check both LAMBDA + not RECURSIVE
1898 is_converted_non_recursive_lambda_closure(_,_,b(_,_,INFO)) :- is_conv_lambda_nonrec(INFO).
1899 is_conv_lambda_nonrec([prob_annotation(A)|T]) :- !,
1900 (A='LAMBDA' -> \+ memberchk(prob_annotation('RECURSIVE'),T)
1901 ; A\='RECURSIVE' -> is_conv_lambda_nonrec(T)).
1902 is_conv_lambda_nonrec([_|T]) :- is_conv_lambda_nonrec(T). */
1903
1904
1905
1906 % a set that is so large that expanding it would probably cause problems
1907 is_infinite_or_very_large_explicit_set(S) :-
1908 get_preference(comprehension_set_symbolic_limit,Limit), % Default 20000
1909 is_infinite_or_very_large_explicit_set(S,Limit). % increase limit in Data valid mode?
1910
1911 :- use_module(inf_arith,[infgreater/2]).
1912
1913 is_infinite_or_very_large_explicit_set(X,_) :- var(X),!,print(var_is_infinite_check(X)),nl,fail.
1914 is_infinite_or_very_large_explicit_set(closure(P,T,B),Limit) :- !,
1915 % treat closure separately here; some special rules
1916 is_infinite_or_very_large_closure(P,T,B,Limit).
1917 is_infinite_or_very_large_explicit_set(avl_set(A),Limit) :- !, % we could compute log and use avl_height_less_than
1918 quick_avl_approximate_size(A,Size), Size >= Limit.
1919 is_infinite_or_very_large_explicit_set(X,Limit) :- % closures are checked above
1920 explicit_set_cardinality(X,Card),
1921 nonvar(Card),infgreater(Card,Limit).
1922
1923
1924 is_very_large_or_symbolic_closure(P,T,B,Limit) :-
1925 ? (is_symbolic_closure(P,T,B) -> true ; is_infinite_or_very_large_closure(P,T,B,Limit)).
1926 :- use_module(bsyntaxtree,[is_a_disjunct/3]).
1927 is_infinite_or_very_large_closure(P,T,B,Limit) :-
1928 is_a_disjunct(B,D1,D2), % Assumption: there is no card_for_specific_closure code for disjuncts
1929 !,
1930 (is_infinite_or_very_large_closure(P,T,D1,Limit) -> true
1931 ; is_infinite_or_very_large_closure(P,T,D2,Limit)).
1932 is_infinite_or_very_large_closure(Par,T,Body,Limit) :-
1933 is_closure1_value_closure(Par,T,Body,VAL),!,
1934 nonvar(VAL), % it could still be large or infinite
1935 (Limit>1 -> NLimit is Limit/2 ; NLimit = Limit), % reduce limit as closure1 usually blows up
1936 is_infinite_or_very_large_explicit_set(VAL,NLimit).
1937 is_infinite_or_very_large_closure(P,T,B,Limit) :-
1938 card_for_specific_closure3(Kind,P,T,B,Card,Code),
1939 on_enumeration_warning(call(Code),
1940 (debug_println(9,cannot_expand_specific_closure_for_card(Kind,Limit)),
1941 % see test 1519 for relevance
1942 Card=inf)), % assume it is large
1943 !,
1944 nonvar(Card),infgreater(Card,Limit),
1945 perfmessages_bexpr(symbolic_closure,['Cardinality ',Card,' greater than limit ',Limit,' for '],B).
1946
1947
1948 is_infinite_or_symbolic_closure(P,T,B) :-
1949 ? (is_symbolic_closure(P,T,B) -> true ; is_infinite_closure(P,T,B)).
1950 is_infinite_closure(P,T,B) :-
1951 is_a_disjunct(B,D1,D2), % Assumption: there is no card_for_specific_closure code for disjuncts
1952 !,
1953 (is_infinite_closure(P,T,D1) -> true ; is_infinite_closure(P,T,D2)).
1954 is_infinite_closure(Par,T,Body) :-
1955 is_closure1_value_closure(Par,T,Body,VAL),!, % TO DO: also check if closure1 is large this way
1956 nonvar(VAL), % if var: it could still be infinite !! TO DO fix
1957 is_infinite_explicit_set(VAL).
1958 is_infinite_closure(Par,T,Body) :-
1959 card_for_specific_closure(closure(Par,T,Body),Card,Code),
1960 call(Code), % TO DO: catch enumeration exceptions (see is_infinite_or_very_large_closure above)
1961 Card == inf. % TODO: instantiate inf before to avoid computing huge numbers
1962
1963
1964 :- use_module(memoization,[compute_memo_hash/2, get_stored_memo_expansion/3, store_memo_expansion/3]).
1965 /* transitive closure */
1966 closure1_for_explicit_set(avl_set(A),Res) :-
1967 preferences:preference(use_closure_expansion_memoization,true),!,
1968 compute_memo_hash(closure1_for_explicit_set(A),Hash),
1969 (get_stored_memo_expansion(Hash,closure1_for_explicit_set(A),StoredResult)
1970 -> Res = StoredResult
1971 ; closure1_for_explicit_set_direct(avl_set(A),Result),
1972 store_memo_expansion(Hash,closure1_for_explicit_set(A),Result),
1973 Res = Result
1974 ).
1975 closure1_for_explicit_set(avl_set(A),Res) :- closure1_for_explicit_set_direct(avl_set(A),Res).
1976
1977 % sometimes faster, but can also be considerably slower:
1978 %:- use_module(extrasrc(avl_ugraphs),[avl_transitive_closure/2]).
1979 %closure1_for_explicit_set_direct(avl_set(A),Res) :-
1980 % avl_transitive_closure(A,TC),
1981 % construct_avl_set(TC,Res).
1982 closure1_for_explicit_set_direct(avl_set(A),Res) :-
1983 avl_domain(A,AList),
1984 iterate_closure(AList,A,A,IterationRes),
1985 construct_avl_set(IterationRes,Res).
1986
1987 /* transitive closure starting from some initial set */
1988 /* not sure if we should do this:
1989 closure1_for_explicit_set_from(avl_set(A),StartFrom,Res) :-
1990 preferences:preference(use_closure_expansion_memoization,true),
1991 compute_memo_hash(closure1_for_explicit_set(A),Hash),
1992 stored_expansion(Hash,closure1_for_explicit_set(A),StoredResult),!,
1993 domain_restriction_explicit_set(StartFrom,StoredResult,Res). */
1994 % StartFrom can be avl_set(empty)
1995 closure1_for_explicit_set_from(avl_set(A),StartFrom,Res) :-
1996 avl_domain(A,AList),
1997 filter_start_relation(AList,StartFrom,FAList),
1998 (FAList = [] -> Res=[]
1999 ; convert_to_avl(FAList,avl_set(Start)),
2000 iterate_closure(FAList,A,Start,IterationRes),
2001 construct_avl_set(IterationRes,Res)).
2002 filter_start_relation([],_,[]).
2003 filter_start_relation([(X,Y)|T],StartSet,Res) :-
2004 (element_of_custom_set(X,StartSet) -> Res = [(X,Y)|RT] ; Res=RT),
2005 filter_start_relation(T,StartSet,RT).
2006
2007 iterate_closure([],_,Res,Res).
2008 iterate_closure([(X,Y)|T],InitialRelation,Relation,Res) :-
2009 %(Key = (X,Y) -> true ; add_error_and_fail(iterate_closure,'Not a relation element: ',Key)),
2010 add_tuples(X,Y,InitialRelation,Relation,NewRelation,AddedTuples),
2011 % better: do added tuples straight away ?
2012 iterate_closure(T,InitialRelation,NewRelation,NewRelation2),
2013 iterate_closure(AddedTuples,InitialRelation,NewRelation2,Res).
2014
2015 add_tuples(X,Y,AVL,AVLClosureSoFar,Res,NewTuples) :-
2016 findall((X,Z), (avl_fetch_pair(Y,AVL,Z), %ok instead of safe_avl_member((Y,Z),AVL),; Y in AVL form, Z var
2017 %Y \= Z, % self-loops are already in initial AVLClosure, this will never add a new pair
2018 % if we use AVLClosureSoFar instead of AVL: considerably slower
2019 \+ avl_fetch((X,Z),AVLClosureSoFar)), NewTuples),
2020 add_to_avl(NewTuples,AVLClosureSoFar,Res).
2021
2022 :- use_module(bsyntaxtree,[create_negation/2]).
2023 % SUBSET_OF <:
2024 % subset_of_explicit_set: returns code to be executed if this subset check can be done in an optimized way
2025 % TO DO: add strict_subset <<: + more cases, e.g., interval & avl_set, ...
2026 % interval & interval already handled in check_subset_of_global_sets
2027 subset_of_explicit_set(AVL,Closure,Code,_WF) :- nonvar(AVL),AVL=avl_set(A),
2028 is_interval_closure_or_integerset(Closure,Low,Up),!,
2029 Code=custom_explicit_sets:check_avl_in_interval(A,Low,Up).
2030 subset_of_explicit_set(Closure,CS,Code,WF) :- nonvar(CS), is_custom_explicit_set(CS),
2031 is_interval_closure_or_integerset(Closure,Low,Up),!,
2032 Code=custom_explicit_sets:check_interval_in_custom_set(Low,Up,CS,WF).
2033 subset_of_explicit_set(AVL1,AVL2,Code,_WF) :-
2034 nonvar(AVL1),AVL1=avl_set(A1), nonvar(AVL2),AVL2=avl_set(A2),!,
2035 Code = custom_explicit_sets:check_avl_subset(A1,A2).
2036 subset_of_explicit_set(C1,AVL2,Code,_WF) :- nonvar(C1),
2037 simple_finite_set(AVL2),
2038 ? is_simple_infinite_set(C1),!, % infinite set cannot be subset of finite one
2039 Code = fail.
2040 subset_of_explicit_set(C1,C2,Code,WF) :- nonvar(C1),
2041 is_cartesian_product_closure(C1,S11,S12),!,
2042 ((S11==[] ; S12==[]) -> Code=true /* we always have a subset */
2043 ; is_definitely_not_empty(S11),
2044 is_definitely_not_empty(S12), % only use optimisation if we know S11, S12 to be non-empty
2045 nonvar(C2), is_cartesian_product_closure(C2,S21,S22),
2046 Code = (kernel_objects:check_subset_of_wf(S11,S21,WF),
2047 kernel_objects:check_subset_of_wf(S12,S22,WF) )
2048 ).
2049 subset_of_explicit_set(Set1,Set2,Code,WF) :-
2050 nonvar(Set2),is_cartesian_product_closure(Set2,S21,S22),!,
2051 % TO DO: maybe don't do this if Set1 is avl_set ??
2052 debug_println(9,'Applying C <: S21*S22 <=> C : S21 <-> S22'),
2053 Code = bsets_clp:relation_over_wf(Set1,S21,S22,WF).
2054 subset_of_explicit_set(C1,C2,Code,WF) :- nonvar(C1), nonvar(C2),
2055 ? is_powerset_closure(C1,Constructor1,Set1),
2056 ? is_powerset_closure(C2,Constructor2,Set2),
2057 subset_constructor(Constructor1,Constructor2,R),
2058 !,
2059 Code = (R=pred_true, kernel_objects:check_subset_of_wf(Set1,Set2,WF)).
2060 subset_of_explicit_set(Set1,Set2,Code,WF) :-
2061 AllowRegularClosure=false,
2062 symbolic_subset_of_explicit_set(Set1,Set2,AllowRegularClosure,Code,WF).
2063
2064 symbolic_subset_of_explicit_set(Set1,Set2,AllowRegularClosure,Code,WF) :-
2065 %print_term_summary(subset(Set1,Set2)),nl,
2066 get_subset_counter_example_closure(Set1,Set2,NewP,NewT,NewB,AllowRegularClosure,DefResult),
2067 % {x|P1} <: {x|P2} <=> {x|P1 & not(P2)}={}
2068 !, %translate:print_bexpr(NewB),nl,
2069 (DefResult==definitely_non_empty -> Code = fail
2070 ; clean_up(NewB,[],CNewB), % can be useful to apply remove_member_comprehension
2071 Code = custom_explicit_sets:is_empty_closure_wf(NewP,NewT,CNewB,WF)).
2072
2073 % get closure representing the counter examples to Set1 <: Set2: i.e. elements in Set1 and not in Set2
2074 % used for symbolic treatment of subset, not_subset and test_subset
2075 % note: in case this fails subset_test1 will expand Set1
2076 % DefiniteResultFlag may return the information that the generated closure is definitely not empty
2077 % AllowRegularClosure=false means it will only be applied for symbolic or infinite closures
2078 get_subset_counter_example_closure(Set1,Set2,NewP,NewT,NewB,AllowRegularClosure,DefiniteResultFlag) :-
2079 get_closure(Set1,P1,T1,B1),
2080 get_subset_counter_aux(P1,T1,B1,Set2,NewP,NewT,NewB,AllowRegularClosure,DefiniteResultFlag).
2081
2082 get_subset_counter_aux(P1,T1,B1,Set2,NewP,NewT,NewB,AllowRegularClosure,DefRes) :-
2083 nonvar(Set2), is_definitely_finite(Set2), !,
2084 create_couple_term(P1,T1,P1Couple), % can currently still fail for more than 2 args
2085 (is_infinite_closure(P1,T1,B1)
2086 -> DefRes=definitely_non_empty % there are definitely counter examples as Set2 is finite
2087 ; AllowRegularClosure=true -> DefRes = unknown
2088 ? ; is_symbolic_closure(P1,T1,B1) -> DefRes=unknown
2089 ),
2090 NewP=P1, NewT=T1,
2091 % {x|P1} <: {a1,...} <=> {x|P1 & x /: {a1,...}}={}
2092 get_texpr_type(P1Couple,CoupleType1),
2093 VSet2 = b(value(Set2),set(CoupleType1),[]),
2094 create_texpr(not_member(P1Couple,VSet2),pred,[],NegPred2),
2095 conjunct_predicates([B1,NegPred2],NewB).
2096 get_subset_counter_aux(P1,T1,B1,Set2,NewP,NewT,NewB,AllowRegularClosure,unknown) :-
2097 get_closure(Set2,P2,T2,B2),
2098 (AllowRegularClosure=true -> true
2099 ; is_infinite_or_symbolic_closure(P1,T1,B1) -> true
2100 % should we also allow ??
2101 % ; is_symbolic_closure(P2,T2,B2)
2102 ),
2103 % not necessary maybe as subset_test1 only expands Set1
2104 % {x|P1} <: {x|P2} <=> {x|P1 & not(P2)}={}
2105 unify_closure_predicates(P1,T1,B1, P2,T2,B2 , NewP,NewT, NewB1,NewB2),
2106 create_negation(NewB2,NegNewB2),
2107 bsyntaxtree:conjunct_predicates([NewB1,NegNewB2],NewB).
2108
2109
2110 % get_closure or infinite global set:
2111 get_closure(V,_,_,_) :- var(V),!,fail.
2112 get_closure(closure(P,T,B),P,T,B).
2113 ?get_closure(global_set(G),P,T,B) :- is_infinite_global_set(G,Type),!,
2114 ID = '_zzzz_unary',
2115 TID = b(identifier(ID),Type,[]),
2116 TSet = b(value(global_set(G)),set(Type),[]),
2117 P = [ID], T=[Type], B= b(member(TID,TSet),pred,[prob_annotation('SYMBOLIC')]).
2118
2119
2120 subset_constructor(X,X,R) :- !,R=pred_true.
2121 subset_constructor(fin1,_,R) :- !,R=pred_true.
2122 subset_constructor(fin,pow,R) :- !,R=pred_true.
2123 subset_constructor(X,Y,R) :- strict_subset_constructor(X,Y),!,R=pred_true.
2124 subset_constructor(X,Y,R) :- strict_subset_constructor(Y,X),!,R=pred_false.
2125 % pow1,fin1 ; pow,fin ; and pow1,fin only ok if type infinite
2126 strict_subset_constructor(pow1,pow).
2127 strict_subset_constructor(fin1,fin).
2128
2129 % more rules for <->, +->, ...
2130 % what if same closure: then we also know it is a subset
2131
2132 % to be completed:
2133 % code that instantiates R to subset or not_subset, may have to delay
2134 test_subset_of_explicit_set(Set1,_,_,_,_) :- var(Set1),!,fail.
2135 test_subset_of_explicit_set(avl_set(A),Closure,R,WF,Code) :-
2136 is_interval_closure_or_integerset(Closure,Low,Up),!,
2137 Code=custom_explicit_sets:test_avl_in_interval(A,Low,Up,R,WF).
2138 test_subset_of_explicit_set(_,Set2,_,_,_) :- var(Set2),!,fail.
2139 test_subset_of_explicit_set(avl_set(A1),avl_set(A2),R,_WF,Code) :-
2140 Code = (custom_explicit_sets:check_avl_subset(A1,A2) -> R=pred_true ; R=pred_false).
2141 test_subset_of_explicit_set(global_set(G),Set2,R,_WF,Code) :-
2142 is_infinite_global_set(G,_), % TODO: we could extend this to other infinite sets
2143 is_definitely_finite(Set2), !,
2144 Code =(R=pred_false).
2145 test_subset_of_explicit_set(Set1,Set2,Res,WF,Code) :-
2146 AllowRegular=false,
2147 get_subset_counter_example_closure(Set1,Set2,NewP,NewT,NewB,AllowRegular,DefResult),
2148 % {x|P1} <: {x|P2} <=> {x|P1 & not(P2)}={}
2149 !,
2150 (DefResult==definitely_non_empty -> Code = (Res=pred_false)
2151 ; Code = custom_explicit_sets:test_empty_closure_wf(NewP,NewT,NewB,Res,WF)
2152 ).
2153 % TO DO: add is_cartesian_product_closure case
2154 is_definitely_finite([]).
2155 is_definitely_finite(avl_set(_)).
2156
2157 :- use_module(kernel_equality,[test_interval_subset_wf/6]).
2158
2159 :- public test_avl_in_interval/5. % used in test_subset_of_explicit_set
2160 % see also check_avl_in_interval(A,Low,Up), check_avl_not_in_interval(A,Low,Up).
2161 test_avl_in_interval(A,Low2,Up2,Res,WF) :-
2162 avl_min(A,int(Min)), % not needed if Low2==minus_inf
2163 avl_max(A,int(Max)), % not needed if Up2==inf
2164 test_interval_subset_wf(Min,Max,Low2,Up2,Res,WF).
2165
2166 % ----------------------
2167
2168 is_definitely_not_empty(X) :- nonvar(X),
2169 (X=[_|_] -> true
2170 ; is_custom_explicit_set(X), is_non_empty_explicit_set(X)).
2171
2172 % check if defnitely not empty and provide a witness
2173 is_definitely_not_empty_with_witness(X,El) :- nonvar(X),
2174 get_witness_element(X,El).
2175 get_witness_element([H|_],H).
2176 get_witness_element(avl_set(node(H,_True,_,_,_)),H).
2177 % TO DO: add global_set(GS),...
2178
2179 check_avl_subset(A1,A2) :- avl_max(A1,Max1), avl_max(A2,Max2),
2180 Max1@>Max2,!, % then A1 cannot be subset of A2
2181 fail.
2182 check_avl_subset(A1,A2) :-
2183 avl_min(A1,Cur1), avl_min(A2,Cur2),
2184 check_avl_subset_loop(Cur1,A1,Cur2,A2).
2185 check_avl_subset_loop(Cur1,AVL1,Cur2,AVL2) :-
2186 (Cur1 @> Cur2 -> avl_next(Cur2,AVL2,NC2), check_avl_subset_loop(Cur1,AVL1,NC2,AVL2)
2187 ; Cur1=Cur2 -> (avl_next(Cur1,AVL1,NC1)
2188 -> avl_next(Cur2,AVL2,NC2),
2189 check_avl_subset_loop(NC1,AVL1,NC2,AVL2)
2190 ; true /* all objects of AVL1 inspected */)
2191 ).
2192
2193 % check A <: Low..Up
2194 check_avl_in_interval(A,Low,Up) :- % does not have to delay: if we have minus_inf & inf they will be known straightaway
2195 (Low==minus_inf -> true
2196 ; avl_min(A,Min), kernel_objects:less_than_equal(int(Low),Min)),
2197 (Up==inf -> true
2198 ; avl_max(A,Max), kernel_objects:less_than_equal(Max,int(Up))).
2199
2200 % some experiments:
2201 % 1..x <: {1,2,3,5} & x>1 & !y.(y>x & y<10 => 1..y /<: {1,2,3,5})
2202 % {ss | ss <: 0..0 & ss /= {} & ss=0..max(ss)}
2203 % {ss | ss <: 0..0 & ss /= {} & ss=min(ss)..max(ss)} // does not work yet
2204 % x..x+1 <: {0,2,3,5}
2205 % x..x+2 <: {0,2,3,5} // does not work yet
2206 % r = {x|x:1..400 & x mod 3/=0} & res={v|v:0..1300 & v..v+1 <: r}
2207 % check Low..Up <: Avl
2208
2209 check_interval_in_custom_set(Low,Up,CS,WF) :-
2210 Low \== minus_inf,
2211 Up \== inf,
2212 b_interpreter_check:check_arithmetic_operator('<=',Low,Up,LeqRes),
2213 (var(LeqRes) -> get_binary_choice_wait_flag_exp_backoff(16,check_interval_in_custom_set,WF,WF2) ; true),
2214 check_interval_in_custom_set_aux(LeqRes,Low,Up,CS,WF2).
2215
2216 :- block check_interval_in_custom_set_aux(-,?,?,?,-).
2217 check_interval_in_custom_set_aux(pred_true,Low,Up,CS,_WF2) :-
2218 element_of_custom_set_wf(int(Low),CS,WF),
2219 element_of_custom_set_wf(int(Up),CS,WF),
2220 interval_in_avl_block(Low,Up,CS,WF).
2221 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
2222
2223 :- block interval_in_avl_block(-,?,?,?), interval_in_avl_block(?,-,?,?).
2224 interval_in_avl_block(Low,Up,CS,WF) :-
2225 Low1 is Low+1, interval_in_avl_loop(Low1,Up,CS,WF).
2226 interval_in_avl_loop(Low,Up,_CS,_WF) :- Low>=Up,!. % Lower bound and upper bound already checked
2227 interval_in_avl_loop(Low,Up,CS,WF) :-
2228 element_of_custom_set_wf(int(Low),CS,WF), L1 is Low+1,
2229 interval_in_avl_loop(L1,Up,CS,WF).
2230
2231
2232 :- public not_check_avl_subset/2. % used in not_subset_of_explicit_set_aux
2233 not_check_avl_subset(A1,A2) :- \+ check_avl_subset(A1,A2).
2234
2235 not_subset_of_explicit_set(S1,S2,Code,WF) :- nonvar(S1),
2236 ? not_subset_of_explicit_set_aux(S1,S2,Code,WF).
2237 not_subset_of_explicit_set_aux(avl_set(A),Closure,Code,_WF) :-
2238 is_interval_closure_or_integerset(Closure,Low,Up),!,
2239 Code=custom_explicit_sets:check_avl_not_in_interval(A,Low,Up).
2240 not_subset_of_explicit_set_aux(avl_set(A1),AVL2,Code,_WF) :-
2241 nonvar(AVL2),AVL2=avl_set(A2),
2242 Code = custom_explicit_sets:not_check_avl_subset(A1,A2).
2243 not_subset_of_explicit_set_aux(CS,AVL,Code,_WF) :-
2244 ? is_simple_infinite_set(CS),
2245 % TO DO: provide code for interval/NAT/INT /<: AVL
2246 simple_finite_set(AVL),
2247 !,
2248 Code = true. % G cannot be subset of finite set
2249 not_subset_of_explicit_set_aux(C1,C2,Code,WF) :- is_cartesian_product_closure(C1,S11,S12),
2250 ((S11==[] ; S12==[]) -> Code=fail /* we always have a subset */
2251 ; is_definitely_not_empty(S11),
2252 is_definitely_not_empty(S12), % only use optimisation if we know S11, S12 to be non-empty
2253 nonvar(C2), is_cartesian_product_closure(C2,S21,S22),
2254 Code = (kernel_objects:not_both_subset_of(S11,S12, S21,S22, WF))
2255 ), !.
2256 not_subset_of_explicit_set_aux(C1,C2,Code,WF) :- nonvar(C2),
2257 ? is_powerset_closure(C1,Constructor1,Set1),
2258 ? is_powerset_closure(C2,Constructor2,Set2),
2259 subset_constructor(Constructor1,Constructor2,R),!,
2260 Code = (R=pred_false -> true ; kernel_objects:not_subset_of_wf(Set1,Set2,WF)).
2261 not_subset_of_explicit_set_aux(Set1,Set2,Code,WF) :-
2262 AllowRegular=false,
2263 get_subset_counter_example_closure(Set1,Set2,NewP,NewT,NewB,AllowRegular,DefResult),
2264 % {x|P1} <: {x|P2} <=> {x|P1 & not(P2)}={}
2265 !,
2266 (DefResult==definitely_non_empty -> Code = true
2267 ; Code = custom_explicit_sets:is_non_empty_closure_wf(NewP,NewT,NewB,WF)
2268 ).
2269
2270
2271 :- public check_avl_not_in_interval/3. % used in not_subset_of_explicit_set_aux
2272 :- block check_avl_not_in_interval(?,-,?). % TO DO: use non-blocking version, minus_inf, and inf set directly
2273 check_avl_not_in_interval(A,Low,Up) :- avl_min(A,int(Min)),
2274 check_avl_not_in_interval4(Low,Up,A,Min).
2275
2276 check_avl_not_in_interval4(Low,_Up,_A,Min) :- Low \== minus_inf, Min < Low,!.
2277 check_avl_not_in_interval4(_Low,Up,A,_Min) :-
2278 Up \== inf, avl_max(A,Max),
2279 kernel_objects:less_than(int(Up),Max). % Up could still be a variable
2280
2281
2282 % checks for simple infinite sets, without Cartesian Product, ... decomposition
2283 ?is_simple_infinite_set(global_set(X)) :- !, is_infinite_global_set(X,_).
2284 is_simple_infinite_set(CS) :- is_interval_closure_or_integerset(CS,Low,Up), infinite_interval(Low,Up).
2285
2286 simple_finite_set(AVL) :- nonvar(AVL), (AVL=avl_set(_) -> true ; AVL = []).
2287
2288 % IMAGE [.]
2289 image_for_id_closure(closure(Par,Types,Body),Set,Res) :-
2290 is_full_id_closure(Par,Types,Body),!,
2291 Res=Set.
2292
2293 image_for_explicit_set(closure(Par,Types,Body),Set,Res,WF) :-
2294 ? image_for_closure(Par,Types,Body,Set,Res,WF).
2295 image_for_explicit_set(avl_set(A),Set,Res,WF) :- nonvar(Set),
2296 image_for_explicit_avl_set(A,Set,Res,WF).
2297
2298
2299 image_for_closure(Par,Types,Body,Set,Res,_WF) :-
2300 is_id_closure_over(Par,Types,Body,ID_Domain,Full),!,
2301 (Full=true -> Res=Set ; kernel_objects:intersection(ID_Domain,Set,Res)).
2302 % infinite function case dealt with in image1 in bsets_clp
2303 % TO DO: other closure(); Maybe special case if Set is an interval ?
2304 image_for_closure(Par,Types,Body,Set,Res,WF) :-
2305 is_closure1_value_closure(Par,Types,Body,VAL), % TODO: also detect reflexive closure, iteration (iterate(rel,k))
2306 % compute closure1(VAL)[Set]
2307 ? bsets_clp:image_for_closure1_wf(VAL,Set,Res,WF).
2308
2309 is_closure1_value_closure(Par,Types,Body,VAL) :-
2310 is_member_closure(Par,Types,Body,couple(A,A),MemSET), nonvar(MemSET),
2311 MemSET = closure(V), % this is the closure1 B operator !
2312 nonvar(V), V=b(value(VAL),_,_).
2313
2314 image_for_explicit_avl_set(A,Set,Res,_WF) :- % Set is nonvar
2315 is_interval_closure_or_integerset(Set,From1,To1),!,
2316 % Note: if From1, To1 not yet known we will block and not revert to other image calculation code
2317 % Important e.g. for performance of San Juan (AdaptedBModelPropCheck/acs_as_env_cfg_ipart.mch)
2318 %we used to check for: ground(From1),ground(To1),
2319 interval_image_for_explicit_avl_set(From1,To1,A,Set,Res).
2320 image_for_explicit_avl_set(A,Set,Res,WF) :-
2321 \+ bsets_clp:keep_symbolic(Set), % in this case we fall back to treatment in bsets_clp (image1)
2322 expand_custom_set_to_list_gg(Set,ESet,GG,image_for_explicit_avl_set),
2323 empty_avl(Empty),
2324 (GG=guaranteed_ground -> image_explicit_ground(ESet,A,Empty,Res,WF)
2325 ; image_explicit(ESet,A,Empty,Res,WF)).
2326
2327 :- block interval_image_for_explicit_avl_set(-,?,?,?,?),
2328 interval_image_for_explicit_avl_set(?,-,?,?,?).
2329 interval_image_for_explicit_avl_set(From1,To1,_A,_Set,Res) :-
2330 number(From1), number(To1), From1>To1,!,
2331 kernel_objects:empty_set(Res).
2332 interval_image_for_explicit_avl_set(From1,To1,A,_Set,Res) :-
2333 findall(Image-true, avl_image_interval(From1,To1, A,Image),ImageList),
2334 normalised_list_to_avl(ImageList,ImageAvl),
2335 ? equal_object(ImageAvl,Res).
2336
2337
2338 %! singleton_set(+Set,-Element).
2339 singleton_set(X,_) :- var(X),!,fail.
2340 singleton_set([H|T],R) :- T==[], R=H.
2341 singleton_set(avl_set(node(Y,_,_,empty,empty)),Y). % same as is_one_element_custom_set
2342
2343 is_one_element_custom_set(avl_set(node(Y,_,_,empty,empty)),Y).
2344 is_one_element_avl(node(Y,_,_,empty,empty),Y).
2345
2346 % requires El to be ground
2347 construct_one_element_custom_set(El,avl_set(AVL)) :-
2348 empty_avl(E),avl_store(El,E,true,AVL).
2349
2350 construct_avl_set(Avl,Res) :- empty_avl(Avl) -> Res = [] ; Res = avl_set(Avl).
2351
2352 :- block image_explicit(-,?,?,?,?).
2353 image_explicit([],_,Acc,Res,WF) :- !,
2354 construct_avl_set(Acc,AVLS),
2355 ? kernel_objects:equal_object_wf(Res,AVLS,image_explicit,WF).
2356 image_explicit([D1|T],AVLRelation,In,Out,WF) :- !,
2357 ground_value_check(D1,G1),
2358 ((var(T);T==[]) % TO DO: see below, make propagation also interesting in other circumstances
2359 -> must_be_in_domain_check(G1,D1,T,AVLRelation,In,Out,WF)
2360 ; true),
2361 ? image_explicit_aux(G1,D1,AVLRelation,T,In,Out,WF).
2362 image_explicit(Set,_,_,_,_) :- add_error_and_fail(image_explicit,'Unknown set: ',Set).
2363
2364 % a version of image_explicit where the list is guaranteed to be ground
2365 image_explicit_ground([],_,Acc,Res,WF) :- !,
2366 construct_avl_set(Acc,AVLS),
2367 kernel_objects:equal_object_wf(Res,AVLS,image_explicit,WF).
2368 image_explicit_ground([D1|T],AVLRelation,In,Out,WF) :- !,
2369 image_explicit_aux_ground(D1,AVLRelation,T,In,Out,WF).
2370 image_explicit_ground(Set,_,_,_,_) :- add_error_and_fail(image_explicit_ground,'Unknown set: ',Set).
2371
2372 :- block must_be_in_domain_check(-,?,?,?,?,-,?),
2373 must_be_in_domain_check(-,?,-,?,?,?,?).
2374 % if result requires at least one more element, then D must be in domain of Relation
2375 % ensures that we get a domain for j in x = {1|->2,2|->4, 4|->8} & x[{j}]={8}
2376 % we could even propagate using inverse of AVLRelation ?!
2377 must_be_in_domain_check(GroundD,D,T,AVLRelation,In,Out,WF) :-
2378 T==[], % apart from D, there are no more elements to be added
2379 var(GroundD), % otherwise we already have a value for D
2380 delta_witness(In,Out,Witness), % obtain at least one value that D must map to
2381 !,
2382 quick_propagation_element_information(avl_set(AVLRelation),(D,Witness),WF,_). % Witness avoids pending co-routines
2383 % TO DO: we could check that *all* elements of Out have this value
2384 % 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
2385 must_be_in_domain_check(_,_D,_T,_,_In,_Out,_). % :- print(must_be(D,T,In,Out)),nl.
2386
2387 % provide, if possible, a witness element in Out not in In
2388 delta_witness(In,Out,_Witness) :- (var(In) ; var(Out)),!,fail.
2389 %delta_witness(empty,Out,Witness) :- is_definitely_not_empty_with_witness(Out,Witness).
2390 delta_witness(In,Out,Witness) :-
2391 is_custom_explicit_set(Out,delta_witness),
2392 difference_of_explicit_set(Out,avl_set(In),Diff), % could be expensive to compute !? delay ? print(delta(Diff)),nl,
2393 is_definitely_not_empty_with_witness(Diff,Witness).
2394
2395
2396 :- block image_explicit_aux(-,?,?, ?,?,?,?). % we know that D1 is ground
2397 image_explicit_aux(_,D1,AVLRelation,T,In,Out,WF) :-
2398 all_images(D1,AVLRelation,NewImages), % compute AVLRelation[{D1}]
2399 add_to_avl(NewImages,In,In2),
2400 ? image_explicit(T,AVLRelation,In2,Out,WF).
2401 image_explicit_aux_ground(D1,AVLRelation,T,In,Out,WF) :-
2402 all_images(D1,AVLRelation,NewImages), % compute AVLRelation[{D1}]
2403 add_to_avl(NewImages,In,In2),
2404 image_explicit_ground(T,AVLRelation,In2,Out,WF).
2405
2406 all_images(From,AVLRelation,Images) :-
2407 findall(AY,avl_member_pair_arg1_ground(From,AY,AVLRelation),Images). % we know From ground and AY free variable
2408 % findall(AY,safe_avl_member_pair(From,AY,AVLRelation),Images). %
2409
2410 % compute relational composition ( ; ) if second arg is an AVL set
2411 % TO DO: add support for infinite closures; avoid expanding them [currently handled by symbolic composition in bsets_clp]
2412 rel_composition_for_explicit_set(Rel1,Rel2,Comp) :- nonvar(Rel2),
2413 Rel2=avl_set(A2), % TO DO: see if we can maybe convert Rel2 to AVL ?
2414 % \+ bsets_clp:keep_symbolic(Rel1), check already done in bsets
2415 expand_custom_set_to_list_gg(Rel1,Relation1,GG,rel_composition_for_explicit_set),
2416 empty_avl(In),
2417 (GG=guaranteed_ground
2418 -> rel_avl_compose2_ground(Relation1,A2,In,Comp)
2419 ; rel_avl_compose2(Relation1,A2,In,Comp)).
2420
2421 :- block rel_avl_compose2(-,?,?,?).
2422 rel_avl_compose2([],_,In,Res) :- construct_avl_set(In,A),
2423 ? equal_object(Res,A,rel_avl_compose2). % as we delay; we need to use equal_object at the end
2424 rel_avl_compose2([(X,Y)|T],A2,In,Out) :-
2425 when((ground(X),ground(Y)),
2426 (all_image_pairs_ground(X,Y,A2,ImagePairs),
2427 add_to_avl(ImagePairs,In,In2),
2428 rel_avl_compose2(T,A2,In2,Out))).
2429
2430 % a version where argument is guaranteed to be ground; no when-ground checks
2431 rel_avl_compose2_ground([],_,In,Res) :- construct_avl_set(In,A),
2432 equal_object(Res,A,rel_avl_compose2). % as we delay; we need to use equal_object at the end
2433 rel_avl_compose2_ground([(X,Y)|T],A2,In,Out) :-
2434 all_image_pairs_ground(X,Y,A2,ImagePairs),
2435 add_to_avl(ImagePairs,In,In2),
2436 rel_avl_compose2_ground(T,A2,In2,Out).
2437
2438 %all_image_pairs(From,To,AVLRelation,ImagePairs) :-
2439 % findall((From,AY),safe_avl_member_pair(To,AY,AVLRelation),ImagePairs).
2440 all_image_pairs_ground(From,To,AVLRelation,ImagePairs) :-
2441 findall((From,AY),avl_member_pair_arg1_ground(To,AY,AVLRelation),ImagePairs).
2442 % 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).
2443
2444 /* succeeds if it can compute domain by some clever way */
2445 domain_of_explicit_set_wf(global_set(GS),_R,_) :- !,
2446 add_error_and_fail(domain_of_explicit_set_wf,'Cannot compute domain of global set: ',GS).
2447 domain_of_explicit_set_wf(freetype(GS),_R,_) :- !,
2448 add_error_and_fail(domain_of_explicit_set_wf,'Cannot compute domain of freetype: ',GS).
2449 domain_of_explicit_set_wf(avl_set(A),Res,_) :- !,
2450 domain_of_avl_set(A,Res).
2451 domain_of_explicit_set_wf(C,R,WF) :- dom_for_specific_closure(C,Dom,_,WF),!,
2452 Dom=R.
2453 domain_of_explicit_set_wf(C,R,_) :-
2454 ? dom_symbolic(C,CC),!,
2455 R=CC.
2456 domain_of_explicit_set_wf(closure(P,T,B),Res,WF) :-
2457 % does not seem to be reached, as dom_symbolic now seems to cover all cases
2458 expand_custom_set_wf(closure(P,T,B),EC,domain_of_explicit_set,WF),
2459 domain_of_list_blocking(EC,R),
2460 normalised_list_to_avl_when_ground(R,Res).
2461
2462 % avl tree is a relation with an integer domain
2463 %avl_integer_domain(node((int(_From),_KeyTo),_True,_,_L,_R)).
2464
2465 % the first clause is in principle faster
2466 % but we don't gain time compared to treatment in second clause; we just avoid building up the domain list
2467 %domain_of_avl_set(A,Res) :- avl_integer_domain(A),
2468 % \+ avl_tools:avl_height_less_than(A,10), % try and detect interval if height >= 10
2469 % avl_is_pf_with_interval_domain(A,First,Last),!,
2470 % construct_interval_closure(First,Last,Res).
2471 domain_of_avl_set(A,Res) :-
2472 avl_domain(A,EC), % -> expand_custom_set(avl_set(A),EC),
2473 domain_of_sorted_list(EC,SizeRes,R), % size of list can be smaller than A if we have a relation
2474 (SizeRes=size_res(Size,int(Last)), R=[int(First)-true|_],
2475 Size>1000,
2476 Size is Last+1-First % we have an interval; quite common that we have functions with intervals as domain
2477 -> debug_println(19,constructing_interval_for_domain(First,Last)),
2478 construct_interval_closure(First,Last,Res)
2479 ; ord_list_to_avlset(R,Res,domain)
2480 ).
2481
2482 % check if an AVL tree represents a function with an interval domain
2483 %avl_is_pf_with_interval_domain(AVL,Min,Max) :-
2484 % avl_min(AVL,(int(Min),_)),avl_max(AVL,(int(Max),_)),
2485 % Size is 1+Max-Min, avl_size_possible(AVL,Size),
2486 % is_avl_partial_function(AVL),
2487 % % now check real size
2488 % avl_size(AVL,Size).
2489
2490 % check if an avl represents a set of integers:
2491 avl_integer_set(node(int(_TOP),_True,_,_L,_R)).
2492
2493 % check if an avl set is an interval:
2494 avl_is_interval(AVL,Min,Max) :-
2495 avl_integer_set(AVL),
2496 avl_min(AVL,int(Min)),avl_max(AVL,int(Max)),
2497 Size is 1+Max-Min,
2498 avl_size_possible(AVL,Size),
2499 avl_size(AVL,Size).
2500
2501
2502
2503 :- use_module(bsyntaxtree,[create_typed_id/3]).
2504 dom_symbolic(closure(Paras,Types,Pred), Res) :-
2505 expand_pair_closure(Paras,Types,Pred,[X,Y],[TX,TY],NewPred),
2506 !, % single argument which is a pair
2507 % simply call code for range ; inverting arguments
2508 bsyntaxtree:check_used_ids_in_ast(Pred),
2509 bsyntaxtree:check_used_ids_in_ast(NewPred),
2510 ran_symbolic_closure(Y,[X],TY,[TX],NewPred,Res).
2511 dom_symbolic(closure(Paras,Types,Pred), Res) :-
2512 append(Xs,[Y],Paras), Xs \= [],
2513 append(TXs,[TY],Types),
2514 % simply call code for range ; inverting arguments
2515 ran_symbolic_closure(Y,Xs,TY,TXs,Pred,Res).
2516 % TO DO: allow computation if Paras is a single argument and more than pair
2517
2518 % just computes domain: it can also be successful for lambda closures
2519 dom_for_specific_closure(closure(P,T,Pred),Domain,Functionality,WF) :-
2520 dom_for_specific_closure_aux(P,T,Pred,Domain,Functionality,WF).
2521 dom_for_specific_closure_aux(P,T,Pred,Domain,Functionality,_WF) :-
2522 is_lambda_value_domain_closure(P,T,Pred, DomainValue,Expr),
2523 (preference(find_abort_values,full) -> bsyntaxtree:always_well_defined_or_disprover_mode(Expr)
2524 ; true),
2525 % Warning: this will lead to dom(%x.(x:1..3|1/0)) = 1..3 to be true; discarding WD condition
2526 % this is not as bad as {1|->2}(0) = 3 to be silently failing though; hence only done if TRY_FIND_ABORT = full
2527 !,
2528 Domain=DomainValue,
2529 Functionality=function(total).
2530 %dom_for_specific_closure_aux([ID],[Type],Pred,Domain,Functionality,_WF) :- Functionality=relation,
2531 % Pred = b(exists(Paras,ClosurePred),pred,Info1),
2532 % % dom({res|#(paras).(.... & res= domVal|->ran)}) = {res|#(paras).(.... & res= domVal)}
2533 % closures:select_equality(ClosurePred,ID,RHSExpr,Type,Info,RestPred),
2534 % RHSExpr = couple(DomValue,_),
2535 % closures:does_not_occur_in(ID,RestPred),
2536 % Type = couple(DomT,_),
2537 % TID = b(identifier(ID),DomT,[]),
2538 % % safe_create_texpr
2539 % conjunct_predicates([RestPred,b(equal(TID,DomValue),pred,[])],NewClosurePred),
2540 % NewPred = b(exists(Paras,NewClosurePred),pred,Info1),
2541 % Domain = closure([ID],[DomT],NewPred).
2542 dom_for_specific_closure_aux(P,T,Pred,Domain,Functionality,WF) :-
2543 dom_range_for_specific_closure2(P,T,Pred, Domain,_Range,domain_only,Functionality,WF).
2544 %TO DO treat overwrite closure dom(F1<+F2) = dom(F1) \/ dom(F2)
2545
2546 dom_for_lambda_closure(closure(P,T,Pred),Domain) :-
2547 is_lambda_value_domain_closure(P,T,Pred, DomainValue,_Expr),
2548 Domain=DomainValue.
2549
2550 % TO DO: add total functions
2551 %dom_for_specific_closure2([F],[T],
2552 % b(member(b(identifier(F),T,_), b(total_function(value(A),B),set(couple(DOM,RAN)),_)), pred,_) ,
2553 % A).
2554
2555 :- block domain_of_list_blocking(-,?).
2556 % the list will be sorted according to the term ordering for (_,_); hence it will
2557 % already be sorted for the projection onto the first element
2558 % maybe the speed difference is not worth it ??
2559 domain_of_list_blocking([],[]).
2560 domain_of_list_blocking([(A,_B)|T],[A-true|DT]) :- domain_blocking_aux(T,A,DT).
2561 :- block domain_blocking_aux(-,?,?).
2562 domain_blocking_aux([],_,[]).
2563 domain_blocking_aux([(A,_B)|T],Prev,Res) :-
2564 compare(Comp,A,Prev),
2565 (Comp = '='
2566 -> domain_blocking_aux(T,Prev,Res)
2567 ; Res = [A-true|DT],
2568 (Comp = '<' -> add_error_fail(custom_explicit_sets,'Domain list not_sorted: ',(A,Prev)) ; true),
2569 domain_blocking_aux(T,A,DT) ).
2570
2571 % and now a non-blocking version:
2572 domain_of_sorted_list([],size_res(0,'$none'),[]).
2573 domain_of_sorted_list([(A,_B)|T],Size,[A-true|DT]) :- domain_aux(T,A,DT,1,Size).
2574
2575 % TO DO: count length and determine when we have an interval
2576 domain_aux([],Prev,[],Acc,size_res(Acc,Prev)).
2577 domain_aux([(A,_B)|T],Prev,Res,SizeAcc,Size) :- SA1 is SizeAcc+1,
2578 compare(Comp,A,Prev),
2579 (Comp = '='
2580 -> domain_aux(T,Prev,Res,SA1,Size)
2581 ; Res = [A-true|DT],
2582 (Comp = '<' -> add_error_fail(custom_explicit_sets,'Domain list not_sorted: ',(A,Prev)) ; true),
2583 domain_aux(T,A,DT,SA1,Size) ).
2584
2585 /* succeeds if it can compute domain by some clever way */
2586 range_of_explicit_set_wf(global_set(GS),_R,_) :- !,
2587 add_error_and_fail(range_of_explicit_set_wf,'Cannot compute domain of global set: ',GS).
2588 range_of_explicit_set_wf(freetype(GS),_R,_) :- !,
2589 add_error_and_fail(range_of_explicit_set_wf,'Cannot compute domain of freetype: ',GS).
2590 range_of_explicit_set_wf(avl_set(A),Res,_) :- !,
2591 avl_domain(A,EC), % -> expand_custom_set(avl_set(A),EC),
2592 range(EC,R),
2593 normalised_list_to_avl(R,Res).
2594 range_of_explicit_set_wf(C,R,WF) :-
2595 ran_for_specific_closure(C,Ran,WF),!,
2596 Ran=R.
2597 range_of_explicit_set_wf(C,R,_) :-
2598 ran_symbolic(C,CC),!,
2599 R=CC.
2600 range_of_explicit_set_wf(closure(P,T,B),Res,WF) :-
2601 expand_custom_set_wf(closure(P,T,B),EC,range_of_explicit_set_wf,WF),
2602 % TO DO: it would be more useful here to directly just expand the projection onto the last component of P
2603 range_blocking(EC,R),
2604 normalised_list_to_avl_when_ground(R,Res).
2605
2606 % TO DO: in future it is maybe better to add an in_range_wf kernel predicate
2607 ran_symbolic(closure(Paras,Types,Pred), Res) :-
2608 ? (is_memoization_closure(Paras,Types,Pred,_)
2609 -> !,fail % memoization closures can never be dealt with symbolically; we need expansion
2610 ; true),
2611 expand_pair_closure(Paras,Types,Pred,[Y,X],[TY,TX],NewPred),!,
2612 % following test (1541) works with this: 2 : ran({y|#(x).(y = x |-> x + 2 & x : NATURAL)})
2613 ran_symbolic_closure(Y,[X],TY,[TX],NewPred,Res). %, print('res: '),translate:print_bvalue(Res),nl.
2614 ran_symbolic(closure([Y,X],[TY,TX],Pred), Res) :-
2615 ran_symbolic_closure(Y,[X],TY,[TX],Pred,Res).
2616 % TO DO: treat closures with more arguments: we need to quantify Y1,...Yn [Y1,...,Yn,X]
2617
2618 % Replace single Identifier YX of type pair by pair (Y,X) where Y,X are (fresh) variables not occuring in Pred
2619 % example: {y| #(x).(y = x |-> x + 2 & x : NATURAL)} --> {y__1,y__2|#(x).(y__1 |-> y__2 = x |-> x + 2 & x : NATURAL)}
2620 expand_pair_closure([YX],[TYX],Pred,[Y,X],[TY,TX],NewPred) :- TYX = couple(TY,TX),
2621 % Replace single ID YX of type pair by pair (Y,X) where Y,X are (fresh) variables not occuring in Pred
2622 % example: {y| #(x).(y = x |-> x + 2 & x : NATURAL)} --> {y__1,y__2|#(x).(y__1 |-> y__2 = x |-> x + 2 & x : NATURAL)}
2623 % following test (1541) works with this: 2 : ran({y|#(x).(y = x |-> x + 2 & x : NATURAL)})
2624 gensym:gensym(YX,Y),gensym:gensym(YX,X),
2625 create_typed_id(Y,TY,YTID), create_typed_id(X,TX,XTID),
2626 Pair = b(couple(YTID,XTID),TYX,[]),
2627 bsyntaxtree:replace_id_by_expr(Pred,YX,Pair,NewPred).
2628
2629 :- use_module(bsyntaxtree,[create_exists_opt_liftable/3]).
2630 %:- use_module(bsyntaxtree,[add_texpr_info_if_new/3]).
2631 ran_symbolic_closure(Y,Xs,TY,TXs,Pred,Res) :-
2632 % create closure for {Xs | #Y.(Pred)} where Pred uses Y|->Xs
2633 rename_ran_ids(Xs,Pred,[],XIDs,Pred2),
2634 create_typed_id(Y,TY,YTID),
2635 create_exists_opt_liftable([YTID],Pred2,Exists), % Y is liftable as the source is a closure with all ids
2636 %bsyntaxtree:check_used_ids_in_ast(Exists),
2637 %bsyntaxtree:create_exists_opt([YTID],[Pred2],Exists), %or
2638 %b_interpreter_components:create_and_simplify_exists([YTID],Pred2,Exists),
2639 %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;
2640 % 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
2641 Res = closure(XIDs,TXs,Exists).
2642
2643
2644
2645 :- use_module(library(lists),[select/3]).
2646
2647 % rename lambda_results :
2648 rename_ran_ids([],Pred,_,[],Pred).
2649 rename_ran_ids([X|TX],Pred,Acc,[XID|TTX],Pred2) :-
2650 % in case X is _lambda_result_ we need to rename it as it then would not get enumerated !
2651 (X == '_lambda_result_'
2652 -> get_fresh_id('_was_lambda_result_',TX,Acc,XID),
2653 % we could remove lambda_result info field, but it will no longer match new id anyway
2654 ? rename_bt(Pred,[rename(X,XID)],Pred2),
2655 TTX=TX
2656 % TODO: maybe we should also remove the prob_annotation('LAMBDA-EQUALITY') info inside Pred for the ids and equality !?
2657 ? ; XID = X, rename_ran_ids(TX,Pred,[X|Acc],TTX,Pred2)
2658 ).
2659
2660 :- use_module(b_ast_cleanup,[get_unique_id/2]).
2661 get_fresh_id(ID,List1,List2,Res) :- nonmember(ID,List1), nonmember(ID,List2),!, Res=ID.
2662 get_fresh_id(ID,_,_,FRESHID) :- nl,print('*** VARIABLE_CLASH PREVENTED: '), print(ID),nl,
2663 get_unique_id(ID,FRESHID).
2664
2665 :- block range_blocking(-,?).
2666 range_blocking([],[]).
2667 range_blocking([(_A,B)|T],[B-true|DT]) :- range_blocking(T,DT).
2668 % and a non-blocking version:
2669 range([],[]).
2670 range([(_A,B)|T],[B-true|DT]) :- range(T,DT).
2671
2672 ran_for_specific_closure(closure(P,T,Pred),Range,WF) :-
2673 dom_range_for_specific_closure2(P,T,Pred, _Domain,Range,range_only,_Functionality,WF).
2674 %ran_for_specific_closure(closure_x(P,T,Pred,_Exp),Card,_) :- ran_for_specific_closure2(P,T,Pred,Card).
2675
2676 :- use_module(bsyntaxtree,[conjunct_predicates/2, disjunct_predicates/2, create_typed_id/3, get_texpr_type/2]).
2677 override_custom_explicit_set_wf(R,S,Res,WF) :- /* R <+ S */
2678 ? nonvar(R),override_custom_explicit_set_aux(R,S,Res,WF).
2679 override_custom_explicit_set_aux(CL,Rel2,Res,_WF) :-
2680 CL=closure(P0,T,B0),
2681 ( preference(convert_comprehension_sets_into_closures,true), % cf keep_symbolic in bsets_clp
2682 (var(Rel2) -> true
2683 ; Rel2 \= avl_set(_)) % if Rel2 is avl_set then maybe better to compute explicitly; unless infinite
2684 ; quick_size_check_larger_than(Rel2,Size2,133) ->
2685 % if we have a large AVL set anyway; then allow expansion up to a larger limit; cf machine 670_002.mch
2686 % a lot of machines use A*B*C <+ {....} to more compactly define large explicit sets
2687 (Size2=inf -> Limit = 200000
2688 ; Limit is min(200000,Size2*150)),
2689 dont_expand_this_closure(P0,T,B0,Limit)
2690 ; dont_expand_this_closure(P0,T,B0) % use default limit and checks for symbolic closure
2691 ),
2692 !,
2693 ? rename_ran_ids(P0,B0,[],P,B), % any '_lambda_result_' id is no longer guaranteed to be assigned a value in all cases
2694 NewClosure=closure(P,T,NewBody),
2695 % B <+ Rel2 ---> NewBody = P:Rel2 or (prj1(P) /: dom(Rel2) & B)
2696 % TODO better? : %x.(x:Domain|IF x:dom(SFF) THEN SFF(x) ELSE DEFAULT)?
2697 generate_typed_id_pairs(P,T,NestedPairs),
2698 get_texpr_type(NestedPairs,PairsType),
2699 RelPairsType = set(PairsType),
2700 ValS = b(value(Rel2),RelPairsType,[]),
2701 MemS = b(member(NestedPairs,ValS),pred,[]), % P:Rel2
2702 get_prj1(NestedPairs,DomExpr),
2703 get_texpr_type(DomExpr,DomType),
2704 Domain = b(domain(ValS),set(DomType),[]), % TO DO: perform some optimisations like dom(%x.(P|E)) --> {x|P}
2705 %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
2706 NotMemDomS = b(not_member(DomExpr,Domain),pred,[]), % prj1(P) /: dom(Rel2)
2707 conjunct_predicates([NotMemDomS,B],RHS),
2708 disjunct_predicates([MemS,RHS],NewBody),
2709 %print(override),nl, bsyntaxtree:check_used_ids_in_ast(NewBody),
2710 mark_closure_as_symbolic(NewClosure,Res).
2711 % TO DO: add a case where for second set we have: dont_expand_this_closure
2712 override_custom_explicit_set_aux(R,S,Res,WF) :-
2713 is_custom_explicit_set(R,override_custom_explicit_set),
2714 nonvar(S), is_custom_explicit_set(S,override_custom_explicit_set),
2715 %% hit_profiler:add_profile_hit(override(R,S),3), %%
2716 override_custom_explicit_set2(R,S,Res,WF).
2717
2718 override_custom_explicit_set2(R,S,Res,_WF) :- is_one_element_custom_set(S,(X,Y)),
2719 override_pair_explicit_set(R,X,Y,NewR),!,
2720 Res=NewR.
2721 % TO DO: if R is very large and S relatively small : iterate by calling override_pair_explicit_set
2722 override_custom_explicit_set2(R,S,Res,WF) :-
2723 expand_custom_set_wf(R,ER,override_custom_explicit_set_aux1,WF),
2724 expand_custom_set_wf(S,ES,override_custom_explicit_set_aux2,WF),
2725 override_list(ER,ES,LRes,Done),
2726 finish_restriction(Done,LRes,Res).
2727
2728 quick_size_check_larger_than(Set,Size,Limit) :-
2729 quick_custom_explicit_set_approximate_size(Set,Size),
2730 (is_inf_or_overflow_card(Size) -> true ; Size > Limit).
2731 get_prj1(b(couple(DomExpr,_),_,_),Prj1) :- !, Prj1 = DomExpr.
2732 get_prj1(BE,b(first_of_pair(BE),DT,[])) :- % some closures have a single identifier; we need to apply prj1
2733 BE = b(_E,couple(DT,_RT),_I).
2734
2735 % translate a parameter name and type list into a nested-pair value
2736 generate_typed_id_pairs([ID|IT],[Type|TT],Res) :- create_typed_id(ID,Type,TypedID),
2737 conv2(IT,TT,TypedID,Res).
2738 conv2([],[],X,X).
2739 conv2([ID|IT],[Type|TT],Acc,Res) :- create_typed_id(ID,Type,TypedID),
2740 get_texpr_type(Acc,AccType),
2741 Couple = b(couple(Acc,TypedID),couple(AccType,Type),[]),
2742 conv2(IT,TT,Couple,Res).
2743
2744 :- block override_list(-,?,?,?), override_list(?,-,?,?).
2745 override_list([],S,Res,Done) :- !, copy_to_true_list(S,Res,Done).
2746 override_list(R,[],Res,Done) :- !, copy_to_true_list(R,Res,Done).
2747 override_list([(From1,To1)|T1],[(From2,To2)|T2],Res,Done) :-
2748 (From1 @< From2
2749 -> Res = [(From1,To1)-true|TR], override_list(T1,[(From2,To2)|T2],TR,Done)
2750 ; From2 @< From1
2751 -> Res = [(From2,To2)-true|TR], override_list([(From1,To1)|T1],T2,TR,Done)
2752 ; override_list(T1,[(From2,To2)|T2],Res,Done)).
2753
2754 :- block copy_to_true_list(-,?,?).
2755 % add -true to get lists that can be converted to avl
2756 copy_to_true_list([],[],true).
2757 copy_to_true_list([H|T],[H-true|CT],Done) :- copy_to_true_list(T,CT,Done).
2758
2759 :- use_module(closures,[get_domain_range_for_closure_types/3]).
2760 % compute a closure with the functionality violations of a closure
2761 symbolic_functionality_check_closure(closure(P,T,B),closure([DID,ID1,ID2],[DomType,RanType,RanType],Body)) :-
2762 % construct {d,z_,z__| (d,z_):R & (d,z__):R & z_\= z__}
2763 generate_typed_id_pairs(P,T,NestedPairs),
2764 get_texpr_type(NestedPairs,PairsType),
2765 RelPairsType = set(PairsType),
2766 TRel = b(value(closure(P,T,B)),RelPairsType,[]),
2767 DID = '_domain', ID1 = '_zzzz_unary', ID2 = '_zzzz_binary',
2768 TDID = b(identifier(DID),DomType,[]),
2769 TID1 = b(identifier(ID1),RanType,[]),
2770 TID2 = b(identifier(ID2),RanType,[]),
2771 Mem1 = b(member( b(couple(TDID,TID1),PairsType,[]),TRel),pred,[]),
2772 Mem2 = b(member( b(couple(TDID,TID2),PairsType,[]),TRel),pred,[]),
2773 get_domain_range_for_closure_types(T,DomType,RanType),
2774 NeqRan = b(not_equal(TID1,TID2), pred, []),
2775 conjunct_predicates([Mem1,Mem2,NeqRan],Body),
2776 bsyntaxtree:check_used_ids_in_ast(Body).
2777 %bsyntaxtree:check_ast(Body).
2778
2779 % compute a closure with the injectivity violations of a closure
2780 symbolic_injectivity_check_closure(closure(P,T,B),closure([RID,ID1,ID2],[RanType,DomType,DomType],Body)) :-
2781 % construct {r,z_,z__| (z_,r):R & (z__,r):R & z_\= z__}
2782 generate_typed_id_pairs(P,T,NestedPairs),
2783 get_texpr_type(NestedPairs,PairsType),
2784 RelPairsType = set(PairsType),
2785 TRel = b(value(closure(P,T,B)),RelPairsType,[]), % what if closure body B has WD condition?
2786 RID = '_range', ID1 = '_zzzz_unary', ID2 = '_zzzz_binary',
2787 TRID = b(identifier(RID),RanType,[]),
2788 TID1 = b(identifier(ID1),DomType,[]),
2789 TID2 = b(identifier(ID2),DomType,[]),
2790 Mem1 = b(member( b(couple(TID1,TRID),PairsType,[]),TRel),pred,[]),
2791 Mem2 = b(member( b(couple(TID2,TRID),PairsType,[]),TRel),pred,[]),
2792 get_domain_range_for_closure_types(T,DomType,RanType),
2793 NeqRan = b(not_equal(TID1,TID2), pred, []),
2794 conjunct_predicates([Mem1,Mem2,NeqRan],Body),
2795 bsyntaxtree:check_used_ids_in_ast(Body).
2796 %bsyntaxtree:check_ast(Body).
2797
2798 % -------------------------
2799
2800
2801 % check whether we have a partial function
2802 is_avl_partial_function(empty) :- !.
2803 is_avl_partial_function(node((KeyFrom,_KeyTo),_True,_,L,R)) :- !,
2804 is_avl_partial_function2(L,'$$MIN$$',KeyFrom),
2805 is_avl_partial_function2(R,KeyFrom,'$$MAX$$').
2806 is_avl_partial_function(X) :- add_internal_error('Not avl_set or relation: ',is_avl_partial_function(X)),fail.
2807
2808 % we traverse the tree from top to bottom, keeping track of possible upper- and lower-bounds
2809 % if any value matches the upper or lower bound, the we do not have a partial function
2810 is_avl_partial_function2(empty,_,_).
2811 is_avl_partial_function2(node((KeyFrom,_KeyTo),_True,_,L,R),ParentFrom,ParentTo) :-
2812 KeyFrom \= ParentFrom, KeyFrom \= ParentTo,
2813 is_avl_partial_function2(L,ParentFrom,KeyFrom),
2814 is_avl_partial_function2(R,KeyFrom,ParentTo).
2815
2816 % the dual of the above, returning a counter example
2817 is_not_avl_partial_function(node((KeyFrom,_KeyTo),_True,_,L,R),DuplicateKey) :- !,
2818 (is_not_avl_partial_function2(L,'$$MIN$$',KeyFrom,DuplicateKey) -> true
2819 ; is_not_avl_partial_function2(R,KeyFrom,'$$MAX$$',DuplicateKey)).
2820 is_not_avl_partial_function2(node((KeyFrom,_KeyTo),_True,_,L,R),ParentFrom,ParentTo,DuplicateKey) :-
2821 ( KeyFrom = ParentFrom -> DuplicateKey=KeyFrom
2822 ; KeyFrom = ParentTo -> DuplicateKey=KeyFrom
2823 ; is_not_avl_partial_function2(L,ParentFrom,KeyFrom,DuplicateKey) -> true
2824 ; is_not_avl_partial_function2(R,KeyFrom,ParentTo,DuplicateKey) -> true).
2825
2826
2827 % check whether we have a function which is total over a given domain; both as AVL sets
2828 is_avl_total_function_over_domain(empty,empty) :- !.
2829 is_avl_total_function_over_domain(AVLFun,AVLDom) :-
2830 avl_domain(AVLFun,FunList),
2831 avl_domain(AVLDom,DomList),
2832 is_avl_total_fun2(FunList,DomList).
2833
2834 is_avl_total_fun2([],[]).
2835 is_avl_total_fun2([(From,_To)|FT],[From|DomT]) :- is_avl_total_fun2(FT,DomT).
2836
2837
2838 %not_is_avl_partial_function(AVLF) :- \+ is_avl_partial_function(AVLF).
2839
2840 :- use_module(kernel_equality,[membership_test_wf/4]).
2841 % check whether an AVL Relation is not over a specific domain & range
2842 is_not_avl_relation_over_domain_range(AVLRel,Domain,Range,WF) :- AVLRel \= empty,
2843 avl_min_pair(AVLRel,RFrom,RTo),
2844 membership_test_wf(Domain,RFrom,MemRes,WF),
2845 is_not_avl_rel_dom1(MemRes,RFrom,RTo,AVLRel,Domain,Range,WF).
2846
2847 :- block is_not_avl_rel_dom1(-, ?,?,?,?,?,?).
2848 is_not_avl_rel_dom1(pred_false,_,_,_,_,_,_WF).
2849 is_not_avl_rel_dom1(pred_true,RFrom,RTo,AVLRel,Domain,Range,WF) :-
2850 membership_test_wf(Range,RTo,MemRes,WF),
2851 is_not_avl_rel_dom2(MemRes,RFrom,RTo,AVLRel,Domain,Range,WF).
2852
2853 :- block is_not_avl_rel_dom2(-, ?,?,?,?,?,?).
2854 is_not_avl_rel_dom2(pred_false,_,_,_,_,_,_WF).
2855 is_not_avl_rel_dom2(pred_true,RFrom,RTo,AVLRel,Domain,Range,WF) :-
2856 avl_next((RFrom,RTo),AVLRel,(RFrom2,RTo2)),
2857 membership_test_wf(Domain,RFrom2,MemRes,WF),
2858 is_not_avl_rel_dom1(MemRes,RFrom2,RTo2,AVLRel,Domain,Range,WF).
2859
2860 % check whether an AVL Relation is not over a specific range
2861 is_not_avl_relation_over_range(AVLRel,Range,WF) :- AVLRel \= empty,
2862 avl_min_pair(AVLRel,RFrom,RTo),
2863 membership_test_wf(Range,RTo,MemRes,WF),
2864 is_not_avl_rel_ran2(MemRes,RFrom,RTo,AVLRel,Range,WF).
2865
2866 :- block is_not_avl_rel_ran2(-, ?,?,?,?,?).
2867 is_not_avl_rel_ran2(pred_false,_,_,_,_,_WF).
2868 is_not_avl_rel_ran2(pred_true,RFrom,RTo,AVLRel,Range,WF) :-
2869 avl_next((RFrom,RTo),AVLRel,(RFrom2,RTo2)),
2870 kernel_equality:membership_test_wf(Range,RTo2,MemRes,WF),
2871 is_not_avl_rel_ran2(MemRes,RFrom2,RTo2,AVLRel,Range,WF).
2872
2873 % check whether we have a relation
2874 is_avl_relation(node((_KeyFrom,_KeyTo),_True,_,_,_)).
2875
2876 % check whether a Relation has all its range elments in a certain Range (not necessarily AVL)
2877 % TO DO: if Domain is an interval: we could take avl_min and avl_max and rely on lexicographic ordering
2878 is_avl_relation_over_domain(AVL,IntervalClosure,_WF) :-
2879 is_interval_closure_or_integerset(IntervalClosure,Low,Up),!,
2880 ((avl_min(AVL,(int(ALow),_)), avl_max(AVL,(int(AUp),_)))
2881 -> cs_greater_than_equal(ALow,Low), cs_greater_than_equal(Up,AUp) %,print(ok),nl
2882 ; (AVL=empty -> true ; add_error_and_fail(is_avl_relation_over_domain,'Not a relation with integer domain: ',AVL))).
2883 is_avl_relation_over_domain(_,Domain,_) :-
2884 quick_is_definitely_maximal_set(Domain),!.
2885 %is_definitely_maximal_set(Domain),!.
2886 is_avl_relation_over_domain(AVL,Domain,WF) :- is_avl_relation_over_domain2(AVL,Domain,WF).
2887 is_avl_relation_over_domain2(empty,_,_).
2888 is_avl_relation_over_domain2(node((KeyFrom,_KeyTo),_,_,L,R), Domain,WF) :-
2889 is_avl_relation_over_domain2(L, Domain,WF),
2890 is_avl_relation_over_domain2(R, Domain,WF),
2891 kernel_objects:check_element_of_wf(KeyFrom,Domain,WF).
2892
2893 % : faster to check than is_definitely_maximal_set
2894 quick_is_definitely_maximal_set(X) :- nonvar(X),
2895 quick_is_definitely_maximal_set_aux(X).
2896 quick_is_definitely_maximal_set_aux(global_set(GS)) :-
2897 nonvar(GS),is_maximal_global_set(GS).
2898 quick_is_definitely_maximal_set_aux(avl_set(AVL)) :-
2899 quick_definitely_maximal_set_avl(AVL).
2900
2901 % check whether a Relation has all its range elments in a certain Range (not necessarily AVL)
2902
2903
2904
2905 is_avl_relation_over_range(empty,_,_) :- !.
2906 is_avl_relation_over_range(_,Range,_) :-
2907 %quick_is_definitely_maximal_set(Range),
2908 is_definitely_maximal_set(Range),
2909 !.
2910 is_avl_relation_over_range(AVL,Range,WF) :- is_avl_relation_over_range2(AVL,Range,WF).
2911
2912 is_avl_relation_over_range2(empty,_,_).
2913 is_avl_relation_over_range2(node((_KeyFrom,KeyTo),_,_,L,R), Range,WF) :-
2914 is_avl_relation_over_range(L, Range,WF),
2915 kernel_objects:check_element_of_wf(KeyTo,Range,WF),
2916 is_avl_relation_over_range2(R, Range,WF).
2917
2918 % safe version of is_avl_sequence, does not throw error when type cannot be a sequence
2919 safe_is_avl_sequence(empty) :- !.
2920 safe_is_avl_sequence(node((int(KeyFrom),_KeyTo),_True,_,L,R)) :- !,
2921 is_avl_sequence2(L,0,KeyFrom),
2922 is_avl_sequence2(R,KeyFrom,'$$MAX$$').
2923
2924 is_avl_sequence(empty) :- !.
2925 is_avl_sequence(node((int(KeyFrom),_KeyTo),_True,_,L,R)) :- !,
2926 is_avl_sequence2(L,0,KeyFrom),
2927 is_avl_sequence2(R,KeyFrom,'$$MAX$$').
2928 is_avl_sequence(X) :- add_error_and_fail(is_avl_sequence,'Not avl_set or sequence: ',X).
2929
2930 % we traverse the tree from top to bottom, keeping track of possible upper- and lower-bounds
2931 % if any value matches the upper or lower bound, the we do not have a partial function
2932 is_avl_sequence2(empty,X,Y) :-
2933 (Y=='$$MAX$$' -> true ; Y is X+1). % otherwise there is a gap in the sequence
2934 is_avl_sequence2(node((int(KeyFrom),_KeyTo),_,_,L,R),ParentFrom,ParentTo) :-
2935 KeyFrom > ParentFrom, KeyFrom \= ParentTo,
2936 is_avl_sequence2(L,ParentFrom,KeyFrom),
2937 is_avl_sequence2(R,KeyFrom,ParentTo).
2938
2939 % for performance: it is not worthwhile to make a version that checks that
2940 % we have a sequence over a range using a single traversal
2941
2942
2943 % get avl_sequence elements as sorted list (without indices)
2944 % used by external function REPLACE
2945 get_avl_sequence(AVL,SeqList) :-
2946 get_avl_sequence_dcg(AVL,SeqList,[]).
2947
2948 get_avl_sequence_dcg(empty) --> [].
2949 get_avl_sequence_dcg(node((int(_),SeqEl),_True,_,L,R)) -->
2950 get_avl_sequence_dcg(L),
2951 [SeqEl],
2952 get_avl_sequence_dcg(R).
2953
2954
2955 % ---------------------------
2956 prefix_of_custom_explicit_set(avl_set(A),MinIndex,Result,WF) :-
2957 size_of_avl_sequence(A,Size,WF),
2958 (MinIndex > Size
2959 -> add_wd_error('index larger than size of sequence in prefix_sequence (/|\\)! ', '>'(MinIndex,Size),WF)
2960 % ; MinIndex = 0 -> Result = [] % case already treated in bsets_clp
2961 ; MinIndex = Size -> Result=avl_set(A)
2962 ; prefix_of_custom_explicit_set2(A,MinIndex,OrdList,[]),
2963 ord_list_to_avlset(OrdList,Result,prefix_of_custom_explicit_set)
2964 ).
2965 prefix_of_custom_explicit_set2(empty,_MaxIndex) --> {true}.
2966 prefix_of_custom_explicit_set2(node((int(KeyFrom),KeyTo),_True,_,L,R),MaxIndex) -->
2967 ({KeyFrom = MaxIndex}
2968 -> prefix_of_custom_explicit_set2(L,MaxIndex), [((int(KeyFrom),KeyTo)-true)]
2969 ; {KeyFrom > MaxIndex} -> prefix_of_custom_explicit_set2(L,MaxIndex)
2970 ; prefix_of_custom_explicit_set2(L,MaxIndex), [((int(KeyFrom),KeyTo)-true)],
2971 prefix_of_custom_explicit_set2(R,MaxIndex)
2972 ).
2973
2974 % size is only well-defined for sequences:
2975 size_of_custom_explicit_set(avl_set(AVL),int(Size),WF) :- size_of_avl_sequence(AVL,Size,WF).
2976 size_of_custom_explicit_set(closure(P,T,B),Res,WF) :-
2977 is_lambda_value_domain_closure(P,T,B, DomainValue,_Expr),
2978 kernel_cardinality_attr:finite_cardinality_as_int_wf(DomainValue,Res,WF).
2979 size_of_avl_sequence(AVL,Size,WF) :-
2980 preference(find_abort_values,true),
2981 \+ is_avl_sequence(AVL),!,
2982 avl_max_pair(AVL,int(Sz),_),
2983 add_wd_error('Applying size to a value which is not a sequence',b(value(avl_set(AVL)),seq(any),[]),WF),
2984 Size=Sz. % other calls to size_of_avl_sequence currently expect a value
2985 size_of_avl_sequence(AVL,Size,WF) :-
2986 % TO DO: checking minimum is 1?
2987 avl_max_pair(AVL,int(Sz),_),
2988 avl_height(AVL,H), % we cannot compute the height together with max; we need the longest path!
2989 get_min_max_card(H,MinSize,MaxSize),
2990 %avl_size(AVL,Real),format('AVL SeqSize: ~w, height: ~w, real size:~w, min: ~w, max: ~w~n',[Sz,H,Real,MinSize,MaxSize]),
2991 (Sz > MaxSize
2992 -> 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),
2993 avl_size(AVL,Size)
2994 % 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})
2995 ; Sz < MinSize
2996 -> 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),
2997 avl_size(AVL,Size)
2998 % triggered by e.g. size([0,2,2,2] |> {2})
2999 ; Size=Sz).
3000
3001 get_min_max_card(Height,MinCard,MaxCard) :-
3002 % 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
3003 MaxCard is 2^Height - 1,
3004 % 1.618034 is golden ration phi 0.5(1+sqrt(5)) , 2.236068 is sqrt(5)
3005 % proof in Knuth uses fact: N > phi^(h+2)/sqrt(5) - 2
3006 MinCard is ceiling((1.61803398875**(Height+2)) / 2.2360679775 - 2).
3007
3008 % check if a candidate size is possible given height:
3009 avl_size_possible(AVL,SizeCandidate) :-
3010 avl_height(AVL,Height), % TO DO: restrict to something like log2 of Height
3011 get_min_max_card(Height,MinCard,MaxCard),
3012 MinCard =< SizeCandidate,
3013 SizeCandidate =< MaxCard.
3014
3015
3016 suffix_of_custom_explicit_set(avl_set(A),MinIndex,Result,WF) :-
3017 size_of_avl_sequence(A,Size,WF),
3018 (MinIndex > Size
3019 -> add_wd_error('index larger than size of sequence in suffix_sequence (\\|/)! ', '>'(MinIndex,Size),WF)
3020 % ; MinIndex = 0 -> Result = avl_set(A) % case already treated in bsets_clp
3021 ; MinIndex = Size -> Result=[]
3022 ; suffix_of_custom_explicit_set2(A,MinIndex,OrdList,[]),
3023 ord_list_to_avlset(OrdList,Result,suffix_of_custom_explicit_set)
3024 ).
3025 suffix_of_custom_explicit_set2(empty,_MinIndex) --> {true}.
3026 suffix_of_custom_explicit_set2(node((int(KeyFrom),KeyTo),_True,_,L,R),MinIndex) -->
3027 ({KeyFrom =< MinIndex} -> suffix_of_custom_explicit_set2(R,MinIndex)
3028 ; {ShiftedKeyFrom is KeyFrom-MinIndex},
3029 ({KeyFrom =:= MinIndex+1}
3030 -> {true} ; suffix_of_custom_explicit_set2(L,MinIndex)),
3031 [((int(ShiftedKeyFrom),KeyTo)-true)],
3032 suffix_of_custom_explicit_set2(R,MinIndex)
3033 ).
3034
3035 shift_avl_sequence_to_ord_list(AVL,Offset,ShiftedOrdList) :-
3036 avl_to_list(AVL,List),shift_seq(List,Offset,ShiftedOrdList).
3037 % it does not seem to be worth to use avl_to_list_dcg_offset or a variation thereof
3038 % it is not really slower to do two traversals (avl_to_list and shift_seq)
3039
3040 shift_seq([],_,[]).
3041 shift_seq([(int(I),Val)-true|T],Offset,[(int(NI),Val)-true|ST]) :- NI is I+Offset,
3042 shift_seq(T,Offset,ST).
3043
3044 :- use_module(debug).
3045 concat_custom_explicit_set(avl_set(S1),Seq2,Res,WF) :- nonvar(Seq2), Seq2=avl_set(S2),
3046 size_of_avl_sequence(S1,Size1,WF),
3047 shift_avl_sequence_to_ord_list(S2,Size1,OL2),
3048 % if OL2 is small we could use avl_store like in append_custom_explicit_set
3049 %avl_to_list(S1,OL1),
3050 avl_to_list_dcg(S1,NewOrdList,OL2), % use OL2 rather than [] as tail
3051 %append(OL1,OL2,NewOrdList), % we could avoid traversing OL1 again by doing a custom avl_to_list/3 which specifies tail
3052 ord_list_to_avlset(NewOrdList,Res,concat). % , print_term_summary(res_concat(Res)).
3053
3054 % a DCG version of avl_to_list; allows to call it with something else than [] as tail
3055 avl_to_list_dcg(empty) --> [].
3056 avl_to_list_dcg(node(Key,Val,_,L,R)) -->
3057 avl_to_list_dcg(L), [(Key-Val)],
3058 avl_to_list_dcg(R).
3059
3060 /* conc: concatenation of sequence of sequences (general_concat) */
3061 conc_custom_explicit_set(avl_set(AVL),Res) :-
3062 avl_min_pair(AVL,int(ONE),First),
3063 conc2_cs(First,ONE,AVL,0,NewOrdList),
3064 ord_list_to_avlset(NewOrdList,Res,conc).
3065
3066 conc2_cs(Seq,NrSeq,AVL,Offset,OrdList) :-
3067 add_seq(Seq,Offset,OrdList,NewOffset,TailOrd),
3068 (avl_next((int(NrSeq),Seq),AVL,(int(N2),Seq2))
3069 -> conc2_cs(Seq2,N2,AVL,NewOffset,TailOrd)
3070 ; TailOrd=[]).
3071
3072 add_seq([],Offset,OrdRes,NewOffset,TailOrdRes) :- NewOffset=Offset, TailOrdRes=OrdRes.
3073 add_seq(avl_set(ASeq),Offset,OrdRes,NewOffset,TailOrd) :-
3074 avl_to_list_dcg_offset(ASeq,Offset,NrEls,OrdRes,TailOrd), NewOffset is Offset+NrEls.
3075
3076 % a version of avl_to_list for sequences which autmatically adds an offset
3077 avl_to_list_dcg_offset(empty,_,0) --> [].
3078 avl_to_list_dcg_offset(node((int(Idx),El),Val,_,L,R),Offset,NrEls) -->
3079 {NIdx is Idx+Offset},
3080 avl_to_list_dcg_offset(L,Offset,N1),
3081 [((int(NIdx),El)-Val)],
3082 avl_to_list_dcg_offset(R,Offset,N2), {NrEls is N1+N2+1}.
3083
3084 prepend_custom_explicit_set(avl_set(S1),ObjectToPrepend,Res) :-
3085 %hit_profiler:add_profile_hit(prepend_custom_explicit_set(avl_set(S1),ObjectToPrepend,Res)),
3086 element_can_be_added_or_removed_to_avl(ObjectToPrepend),
3087 shift_avl_sequence_to_ord_list(S1,1,OL1),
3088 ord_list_to_avlset([(int(1),ObjectToPrepend)-true|OL1],Res).
3089
3090 append_custom_explicit_set(avl_set(S1),ObjectToAppend,Res,WF) :-
3091 element_can_be_added_or_removed_to_avl(ObjectToAppend), % implies that ObjectToAppend is ground
3092 size_of_avl_sequence(S1,Size1,WF), NewSize is Size1+1,
3093 add_ground_element_to_explicit_set_wf(avl_set(S1),(int(NewSize),ObjectToAppend),Res,WF).
3094
3095 % compute tail of a sequence and also return first element
3096 tail_sequence_custom_explicit_set(avl_set(S1),First,Res,Span,WF) :-
3097 shift_avl_sequence_to_ord_list(S1,-1,NewOrdList),
3098 (NewOrdList = [(int(0),First)-true|TailOL] -> ord_list_to_avlset(TailOL,Res)
3099 ; add_wd_error_span('tail argument is not a sequence!', avl_set(S1),Span,WF)
3100 % add_error_fail(tail_sequence,'tail applied to ', NewOrdList))
3101 ).
3102 last_sequence_explicit_set(avl_set(AVL),Last) :-
3103 avl_max_pair(AVL,int(_Sz),Last).
3104 % 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 ?
3105 %first_sequence_explicit_set(avl_set(AVL),First) :- % not used anymore; apply_to used instead
3106 % avl_min_pair(AVL,int(_One),First).
3107
3108 % compute front and return last element at the same time
3109 front_sequence_custom_explicit_set(avl_set(AVL),Last,Res) :-
3110 avl_max_pair(AVL,int(Size),Last),
3111 direct_remove_element_from_avl(AVL, (int(Size),Last), Res). % we know Last is already in AVL-converted format
3112
3113
3114 reverse_custom_explicit_set(avl_set(AVL),Res) :-
3115 avl_to_list_dcg_offset(AVL,0,Size,List,[]),
3116 S1 is Size+1,
3117 reverse_list(List,S1,[],RevList),
3118 ord_list_to_avl(RevList,RevAVL),
3119 Res=avl_set(RevAVL).
3120
3121 reverse_list([],_,Acc,Acc).
3122 reverse_list([(int(Idx),El)-V|T],S1,Acc,Res) :-
3123 NewIdx is S1 - Idx,
3124 reverse_list(T,S1,[(int(NewIdx),El)-V|Acc],Res).
3125
3126 % check if a relation is injective ; compute range at the same time; note AVL can be empty
3127 is_injective_avl_relation(AVL,RangeRes) :-
3128 avl_domain(AVL,ElList),
3129 empty_avl(EmptyAcc),
3130 is_avl_inj_list(ElList,EmptyAcc,Range),
3131 construct_avl_set(Range,RangeRes).
3132
3133 is_avl_inj_list([],Range,Range).
3134 is_avl_inj_list([(_From,To)|T],InRange,OutRange) :-
3135 (avl_fetch(To,InRange) -> fail /* this is not an injection; a range element is repeated */
3136 ; avl_store(To,InRange,true,InRange1),
3137 is_avl_inj_list(T,InRange1,OutRange)
3138 ).
3139
3140 % Example predicates that work with code below:
3141 % card(id((1..1000)*(1..1000))~)=1000*1000
3142 % card(((1..1000)*(1..1000))~)=1000*1000
3143 invert_explicit_set(global_set(GS),_R) :- !,
3144 add_error_and_fail(invert_explicit_set,'Cannot compute inverse of global set: ',GS).
3145 invert_explicit_set(freetype(GS),_R) :- !,
3146 add_error_and_fail(invert_explicit_set,'Cannot compute inverse of freetype: ',GS).
3147 invert_explicit_set(closure([P1,P2],[T1,T2],Clo),R) :- !,
3148 % TODO: also invert closures with single argument or more arguments
3149 % e.g., {a,b,c|a=1 & b=1 &c:1..10}~ = {c,ab|ab=(1,1) & c:1..10}
3150 R = closure([P2,P1],[T2,T1],Clo).
3151 invert_explicit_set(closure([P1],[T1],Clo),R) :-
3152 is_member_closure_with_info([P1],[T1],Clo,_Type,Info,MEM),
3153 invert_member_predicate(MEM,T1,InvMEM,InvT1),!,
3154 construct_member_closure(P1,InvT1,Info,InvMEM,R).
3155 invert_explicit_set(C,AVL) :- expand_custom_set(C,EC,invert_explicit_set), %% convert to AVL ?
3156 inv_and_norm(EC,AVL).
3157
3158 invert_member_predicate(cartesian_product(A,B),couple(TA,TB),
3159 cartesian_product(B,A),couple(TB,TA)).
3160 invert_member_predicate(identity(A),TA,identity(A),TA).
3161
3162
3163 :- block inv_and_norm(-,?).
3164 inv_and_norm(EC,AVL) :- inv(EC,R,Done), norm(Done,R,AVL).
3165
3166 :- block norm(-,?,?).
3167 norm(_,R,AVL) :- normalised_list_to_avl(R,AVL).
3168
3169 :- block inv(-,?,?).
3170 inv([],[],done).
3171 inv([(A,B)|T],[(B,A)-true|DT],Done) :- inv(T,DT,Done).
3172
3173
3174
3175 % checks whether a ground value is in the domain of an AVL relation
3176 check_in_domain_of_avlset(X,AVL) :- convert_to_avl_inside_set(X,AX),!,
3177 ? (avl_fetch_pair(AX,AVL,_) -> true ; fail).
3178 check_in_domain_of_avlset(X,AVL) :-
3179 print('### could not convert arg for check_in_domain_of_avlset'),nl,
3180 print(X),nl,
3181 safe_avl_member_pair(X,_,AVL).
3182
3183 % checks whether a ground value is in the domain of an AVL relation and has only one solution
3184 check_unique_in_domain_of_avlset(X,AVL) :- convert_to_avl_inside_set(X,AX),!,
3185 ? avl_fetch_pair(AX,AVL,AY1),!,
3186 ? (avl_fetch_pair(AX,AVL,AY2), AY1 \= AY2 -> fail
3187 ; true).
3188
3189
3190 % utility to check if for a value there is at most one matching element in an AVL set
3191 % optimized for function application
3192 at_most_one_match_possible(Element,AVL,Matches) :- nonvar(Element),
3193 Element=(Index,_Rest), % Function Application; TO DO: does this cover all func. appl ?
3194 element_can_be_added_or_removed_to_avl(Index),
3195 convert_to_avl_inside_set(Index,AX), % is ground and normalised ?
3196 % TO DO: check AVL size ? Check other patterns ?
3197 findall((AX,Match),avl_tools:avl_fetch_pair(AX,AVL,Match),Matches),
3198 Matches \= [_,_|_].
3199
3200
3201
3202 apply_to_avl_set(A,X,Y,Span,WF) :-
3203 ground_value_check(X,GroundX),
3204 ? apply_to_avl_set_aux(A,X,Y,GroundX,Span,WF).
3205
3206 apply_to_avl_set_aux(A,X,Y,GroundX,Span,WF) :- nonvar(GroundX),!,
3207 ? apply_check_tuple(X,Y,A,Span,WF). % we could call apply_check_tuple_ground to avoid one ground test
3208 % We know that A is a function: we can deterministically apply if X is ground;
3209 % if Y is ground this is only the cases for injective functions
3210 apply_to_avl_set_aux(A,X,Y,GroundX,Span,WF) :-
3211 %(preference(data_validation_mode,true); % we now reduce priority of backpropagation below
3212 preference(find_abort_values,true),
3213 % do not try inverse propagation onto argument X of function application A(X) = Y
3214 !,
3215 avl_approximate_size(A,3,ApproxSizeA),
3216 apply_check_tuple_delay(X,Y,A,ApproxSizeA,Span,WF,GroundX,_,_).
3217 apply_to_avl_set_aux(A,X,Y,GroundX,Span,WF) :-
3218 ground_value_check(Y,GroundY),
3219 avl_approximate_size(A,3,ApproxSizeA), % exact size for height <= 3; approximate size above
3220 (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
3221 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
3222 %propagate_avl_element_information((X,Y),A,ApproxSizeA,WF), % could be done; but would prevent WD problems from being detected
3223 % this waitflag is used when neither X nor Y are ground;
3224 % quite often not much is gained by enumerating possible values; unless X or Y are constrained or trigger other computations
3225 % WSz is 10*ApproxSizeA, % magic value
3226 %(ApproxSizeA > 100 -> InversePrioSize = 4
3227 % ; 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
3228 % delay_get_wait_flag(GroundY,GroundX,WF1,InversePrioSize,apply_to_explicit_inverse(X,Y),WF,WF2),
3229 %(ApproxSizeA<4000 -> propagate_apply(X,Y,A,ApproxSizeA,WF,GroundX,GroundY) ; true),
3230 apply_check_tuple_delay(X,Y,A,ApproxSizeA,Span,WF,GroundX,WF1,GroundY),
3231 (preference(use_clpfd_solver,false) -> true
3232 % should we also check: preference(find_abort_values,true)?
3233 ; get_wait_flag0(WF,WF0),
3234 propagate_apply(X,Y,A,ApproxSizeA,WF,WF0,GroundX,WF1,GroundY)).
3235
3236 :- block propagate_apply(?,?,?,?,?,-,?,?,?).
3237 propagate_apply(X,Y,AVL,ApproxSizeA,WF,_,GroundX,WF1,GroundY) :-
3238 var(GroundX), var(WF1), var(GroundY),
3239 (preference(disprover_mode,true)
3240 -> XX=X % this will also instantiate X and prevent finding WD errors
3241 ; (ApproxSizeA<128 -> true
3242 ; preference(solver_strength,SS), ApproxSizeA < 128+SS*100), % up until 4000 it may make sense to constrain Y
3243 preference(data_validation_mode,false), % note: this can slow down ProB, e.g., test 1105; hence allow disabling it
3244 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
3245 propagate_value(X,XX) % only instantiate X, propagation only makes sense for propagate_avl_element_information_small, as otherwise only X will be bounded
3246 ),
3247 !,
3248 propagate_avl_element_information_direct((XX,Y),AVL,ApproxSizeA,WF).
3249 propagate_apply(_,_,_,_,_,_,_,_,_).
3250
3251 % only propagate in one direction to allow to find WD errors but also prevent pending co-routines/constraints
3252 :- block propagate_value(-,?).
3253 propagate_value(int(X),R) :- !,
3254 (
3255 %%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
3256 propagate_fd_dom(X,RX), R=int(RX), propagate_atomic_value(X,RX)
3257 ).
3258 propagate_value(fd(X,T),R) :- !,
3259 (
3260 %%integer(X) -> R=fd(X,T) ; % for SWI 8.5.10 and older, see above
3261 propagate_fd_dom(X,RX), R=fd(RX,T), propagate_atomic_value(X,RX)
3262 ).
3263 propagate_value((X1,X2),R) :- !, R=(RX1,RX2), propagate_value(X1,RX1), propagate_value(X2,RX2).
3264 propagate_value(pred_true,R) :- !, if(R=pred_true,true,debug_println(9,function_arg_outside_domain(pred_true))).
3265 propagate_value(pred_false,R) :- !, if(R=pred_false,true,debug_println(9,function_arg_outside_domain(pred_false))).
3266 propagate_value(string(X),R) :- !, R=string(RX),propagate_atomic_value(X,RX).
3267 propagate_value(X,RX) :- equal_object(X,RX). % TO DO: get rid of this: this propagates and prevents finding WD errors
3268 :- block propagate_atomic_value(-,?).
3269 propagate_atomic_value(X,Y) :-
3270 if(X=Y,true,debug_println(9,function_arg_outside_domain(X))).
3271
3272 %propagate_fd_dom(X,RX) :- integer(X),!,RX=X. % relevant for SWI 8.5.10 and older where fd_set fails for integers
3273 propagate_fd_dom(X,RX) :- fd_set(X,Dom),in_set(RX,Dom).
3274
3275
3276 /*
3277 :- block propagate_apply(-,?,?,?,?,-,-).
3278 % call propagate as soon as we know something about the function argument and we do not propgagate completely using GroundX/Y anyway
3279 propagate_apply(X,Y,AVL,Size,WF,GroundX,GroundY) :- print(prop_apply(Size,GroundX,GroundY,X,Y)),nl,
3280 (nonvar(GroundX) -> true ; nonvar(GroundY) -> true
3281 ; propagate_avl_element_information((X,Y),AVL,Size,WF)).
3282
3283 % get the waitflag when first WF set and other two not
3284 :- block delay_get_wait_flag(-,-,-,?,?,?,?).
3285 delay_get_wait_flag(_,WF1,WF2, _,_,_,_) :- (nonvar(WF1);nonvar(WF2)),!. % DO NOTHING
3286 delay_get_wait_flag(_,_,_,Prio,Info,WF,WF2) :- get_wait_flag(Prio,Info,WF,WF2).
3287 */
3288
3289 :- block apply_check_tuple_delay(?,?,?, ?,?,?, -,-,-).
3290 apply_check_tuple_delay(X,Y,AVL,_ApproxSizeA,Span,WF,GroundX,WF1,_) :-
3291 (nonvar(GroundX);nonvar(WF1)),!,
3292 ? apply_check_tuple(X,Y,AVL,Span,WF).
3293 apply_check_tuple_delay(X,Y,AVL,ApproxSizeA,Span,WF,_GroundX,_WF1,_GroundY) :-
3294 % Y is ground; try to do an inverse function lookup
3295 ? inverse_apply_ok(Y,X,AVL,ApproxSizeA,Span),
3296 !,
3297 % print(inverse_apply(Y,X,ApproxSizeA,_GroundX)),nl,
3298 inverse_get_possible_values(X,Y,AVL,Res),
3299 Res=avl_set(InvAVL), % if empty set : we fail
3300 (preference(data_validation_mode,true),
3301 avl_approximate_size(InvAVL,10,ApproxSize),
3302 ApproxSize>1
3303 -> A2 is (ApproxSize*15*ApproxSize)//ApproxSizeA, % used to be A2 is ApproxSize*100,
3304 A22 is max(A2,ApproxSize),
3305 (get_inversion_penalty(Span)
3306 -> A23 is A22 * 100 %, add_message(f,'Inversion Penalty: ',Y:A22,Span)
3307 ; A23=A22),
3308 % give lower priority for backwards propagation, upto 15 times if no reduction from backwards propagation
3309 % but also take into account how much we reduce the size by inverting
3310 % relevant for, e.g., Machines_perf_0111/Thales_All/rule_OPS_SDS_3940.mch
3311 % or rule_OPS_SDS_6496 -> 15 instead of 150 improves performance
3312 get_bounded_wait_flag(A23,element_of_avl_inverse_apply_ok(X),WF,WF2),
3313 % does not call propagate_avl_element_information(X,InvAVL,ApproxSize,WF) or avl_to_table
3314 element_of_avl_set_wf3(X,InvAVL,ApproxSize,WF2,WF) % TODO: pass GroundX
3315 %apply_check_tuple_delay(X,Y,AVL,ApproxSizeA,Span,WF,GroundX,WF1,_) % now wait on WF1 or GroundX
3316 ? ; element_of_avl_set_wf(InvAVL,X,WF)
3317 ).
3318 apply_check_tuple_delay(X,Y,AVL,ApproxSizeA,Span,WF,GroundX,WF1,_GroundY) :-
3319 apply_check_tuple_delay(X,Y,AVL,ApproxSizeA,Span,WF,GroundX,WF1,_). % now wait on WF1 or GroundX
3320
3321 % check if the function call was annotated as not suitable for backwards inverse function lookup propagation
3322 get_inversion_penalty(span_predicate(b(_Function,_,Info),_LS,_S)) :- !,
3323 get_inversion_penalty(Info).
3324 get_inversion_penalty(Info) :-
3325 member(prob_annotation('INVERSION_PENALTY'),Info).
3326
3327 inverse_get_possible_values(X,Y,AVL,Res) :-
3328 get_template(X,XX,_),
3329 copy_term(XX,XX_Copy), % avoid that findall instantiates X
3330 % TODO: copy_value_term similar to ground_value to avoid traversing avl_sets; but usually X is not a set
3331 findall(XX_Copy, safe_avl_member_default((XX_Copy,Y),AVL), PossibleValues),
3332 PossibleValues \= [], % fail straightaway
3333 sort(PossibleValues,SPV),
3334 % length(SPV,Len),print(inverse_image(Y,Len)),nl, print_term_summary(apply_check_tuple_delay(X,Y,AVL)),nl,
3335 convert_to_avl(SPV,Res).
3336
3337 % is it ok to compute inverse ? only makes sense if AVL tree not too big and quite functional
3338 inverse_apply_ok(pred_true,_,_AVL,ApproxSizeA,_) :- !, % only two values possible, probably half of AVL will be returned
3339 ApproxSizeA < 1023. % corresponds to avl_height < 10
3340 inverse_apply_ok(pred_false,_,_AVL,ApproxSizeA,_) :- !,ApproxSizeA < 1023.
3341 % TO DO: other small types, such as fd(_,_)
3342 inverse_apply_ok(_,_,_AVL,ApproxSizeA,_) :- ApproxSizeA < 255,!.
3343 inverse_apply_ok(_,X,_AVL,ApproxSizeA,Span) :- ApproxSizeA < 65535, % corresponds Height < 16
3344 (preference(data_validation_mode,true) ->
3345 (preference(solver_strength,SS), ApproxSizeA < 16383+SS -> true
3346 ; perfmessage(inverse,'Function call not inverted (increase SOLVER_STRENGTH to enable this), approximate function size: ',ApproxSizeA,Span),
3347 fail
3348 )
3349 ; true),
3350 ? quick_non_ground_check(X).
3351 %inverse_apply_ok(_,_,_,_).
3352
3353 % sometimes the ground_value_check co-routine hasn't grounded GroundX yet ! so do a quick check
3354 quick_non_ground_check(X) :- var(X),!.
3355 quick_non_ground_check([]) :- !,fail.
3356 quick_non_ground_check(avl_set(_)) :- !,fail.
3357 quick_non_ground_check(pred_true) :- !,fail.
3358 quick_non_ground_check(pred_false) :- !,fail.
3359 quick_non_ground_check(int(X)) :- !,var(X).
3360 quick_non_ground_check(string(X)) :- !,var(X).
3361 quick_non_ground_check(fd(X,T)) :- !,(var(X) ; var(T)).
3362 quick_non_ground_check((A,B)) :- !, (quick_non_ground_check(A) -> true ; quick_non_ground_check(B)).
3363 quick_non_ground_check(_). % assume it is non ground
3364
3365
3366
3367 % apply_check_tuple is allowed to enumerate: either X is ground or Y is ground
3368 apply_check_tuple(X,Y,A,Span,WF) :-
3369 ground_value(X),
3370 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)
3371 avl_apply(AX,A,XY,Span,WF),
3372 ? kernel_objects:equal_object_wf(XY,Y,apply_check_tuple,WF).
3373 :- if(environ(no_wd_checking, true)).
3374 apply_check_tuple(X,Y,A,_Span,WF) :- safe_avl_member_default_wf((X,Y),A,WF).
3375 :- else.
3376 apply_check_tuple(X,Y,A,_Span,WF) :- preferences:preference(find_abort_values,false), !,
3377 ? safe_avl_member_default_wf((X,Y),A,WF).
3378 apply_check_tuple(X,Y,A,Span,WF) :- !,
3379 if(safe_avl_member_default_wf((X,XY),A,WF), % does not detect abort errors if X unbound
3380 kernel_objects:equal_object_wf(XY,Y,apply_check_tuple_avl,WF),
3381 add_wd_error_span('function applied outside of domain (#4): ','@fun'(X,avl_set(A)),Span,WF)).
3382 :- endif.
3383
3384
3385 % ------------------------------------------
3386
3387
3388 :- use_module(b_global_sets,[b_type2_set/2]).
3389 :- use_module(bsyntaxtree,[rename_bt/3]).
3390 union_of_explicit_set(global_set(GS),_,R) :- is_maximal_global_set(GS), !,
3391 R= global_set(GS). /* global_set is already maximal */
3392 union_of_explicit_set(freetype(GS),_,R) :- !, R= freetype(GS). /* freetype is already maximal */
3393 union_of_explicit_set(closure(P,T,B),_,R) :- is_definitely_maximal_closure(P,T,B), !,
3394 R= closure(P,T,B). /* global_set is already maximal */
3395 union_of_explicit_set(_,S2,R) :- is_definitely_maximal_set(S2),!, % will also look at AVL set
3396 R=S2.
3397 union_of_explicit_set(S1,S2,R) :- nonvar(S2), S2 = [], !, R=S1.
3398 union_of_explicit_set(S1,S2,_) :- (var(S1);var(S2)),!,fail. % then we cannot compute it here
3399 union_of_explicit_set(S2,S1,R) :-
3400 is_not_member_value_closure(S1,TYPE,MS1), nonvar(MS1), is_efficient_custom_set(MS1),
3401 % also works if S2 is complement closure
3402 difference_of_explicit_set(MS1,S2,Diff),!,
3403 construct_complement_closure_if_necessary(Diff,TYPE,R).
3404 union_of_explicit_set(avl_set(A1),S2,R) :- !, union_of_avl_set(S2,A1,R).
3405 union_of_explicit_set(S1,S2,R) :-
3406 ? is_not_member_value_closure(S1,TYPE,MS1), nonvar(MS1), is_efficient_custom_set(MS1),
3407 difference_of_explicit_set(MS1,S2,Diff),!,
3408 construct_complement_closure_if_necessary(Diff,TYPE,R).
3409 union_of_explicit_set(S1,avl_set(A2),R) :- !, union_of_avl_set(S1,A2,R).
3410 union_of_explicit_set(I1,I2,R) :- is_interval_closure_or_integerset(I1,From1,To1), ground(From1), ground(To1),
3411 is_interval_closure_or_integerset(I2,From2,To2), ground(From2), ground(To2),
3412 !,
3413 (union_of_interval(From1,To1,From2,To2,FromRes,ToRes)
3414 -> construct_interval_closure(FromRes,ToRes,R)
3415 ; small_enough_for_expansion(From1,To1),small_enough_for_expansion(From2,To2) ->
3416 % do not attempt union_of_closure below
3417 expand_interval_closure_to_avl(From1,To1,R1), R1=avl_set(A1), % empty interval already dealt with above !?
3418 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(_))
3419 union_of_avl(A1,A2,ARes),R=avl_set(ARes) /* AVL not normalised */
3420 ; transform_global_sets_into_closure(I1,closure(Par,T,Body)),
3421 union_of_closure(I2,Par,T,Body,R)
3422 ).
3423 union_of_explicit_set(closure(P,T,B),C2,Res) :-
3424 union_of_closure(C2,P,T,B,Res).
3425
3426 small_enough_for_expansion(From1,To1) :- number(To1), number(From1), To1-From1<250.
3427
3428 :- use_module(bsyntaxtree,[extract_info/2, extract_info_wo_used_ids/2, extract_info/3, rename_bt/3, replace_id_by_expr/4]).
3429
3430 union_of_closure(global_set(X),P,T,B,Res) :- !, transform_global_sets_into_closure(global_set(X),C),
3431 union_of_closure(C,P,T,B,Res).
3432 union_of_closure(closure(P2,T2,B2),P,T,B,Res) :- !,
3433 % T2 should be equal to T, module seq(_) <-> set(couple(integer,_))
3434 unify_closure_predicates(P,T,B, P2,T2,B2 , NewP,NewT, NewB1,NewB2),
3435 debug:debug_println(9,union_of_two_closures(P,P2,NewP,NewT)),
3436 extract_info(B,B2,NewInfo),
3437 construct_disjunct(NewB1,NewB2,Disj),
3438 Res = closure(NewP,NewT,b(Disj,pred,NewInfo)).
3439
3440 % rename predicates of two closures so that they work on common closure parameter ids
3441 % and can then be either joined by conjunction or disjunction
3442 unify_closure_predicates(P,T,B, P2,T2,B2 , NewP,NewT, NewB1,NewB2) :-
3443 length(P,Len1), length(P2,Len2),
3444 (Len1=Len2
3445 -> generate_renaming_list(P,P2,RL),
3446 rename_bt(B2,RL,NewB2),
3447 NewP=P, NewT=T, NewB1 = B
3448 ; Len1 < Len2 -> unify_clos_lt(P,T,B, P2,T2,B2 , NewP,NewT, NewB1,NewB2)
3449 ; unify_clos_lt(P2,T2,B2, P,T,B , NewP,NewT, NewB2,NewB1) % inverted the predicate
3450 ).
3451
3452 % TO DO: generalize: currently only works for single identifier on left
3453 % but works for id(NATURAL) \/ %x.(x<0|-x) or abs = id(NATURAL) \/ %x.(x<0|-x) & abs(2)=a2 & abs(-2)=am2
3454 unify_clos_lt([ID1],[couple(_,_)],B, P2,T2,B2 , NewP,NewT, NewB1,NewB2) :-
3455 rename_lambda_result_id(P2,B2,P3,B3),
3456 create_couple_term(P3,T2,Pair),
3457 replace_id_by_expr(B,ID1,Pair,NewB1),
3458 NewP=P3, NewT=T2, NewB2=B3.
3459
3460 % _lambda_result_ id is not enumerated, hence we have to avoid inserting such ids into NewB1 as part of the pPair
3461 rename_lambda_result_id(['_lambda_result_',ID2],B2,[FRESHID,ID2],B3) :- !,get_unique_id('_RANGE_',FRESHID),
3462 rename_bt(B2,[rename('_lambda_result_',FRESHID)],B3).
3463 rename_lambda_result_id([ID1,'_lambda_result_'],B2,[ID1,FRESHID],B3) :- !,get_unique_id('_RANGE_',FRESHID),
3464 rename_bt(B2,[rename('_lambda_result_',FRESHID)],B3).
3465 rename_lambda_result_id(P2,B2,P2,B2).
3466
3467 % translate a list of atomic ids and a list of types into a couple-term
3468 create_couple_term([ID1],[T1],Res) :- !,
3469 create_texpr(identifier(ID1),T1,[],Res).
3470 create_couple_term([ID1,ID2],[T1,T2],Res) :-
3471 bsyntaxtree:create_couple(b(identifier(ID1),T1,[]),b(identifier(ID2),T2,[]),Res).
3472 % TODO: extend for more than two args
3473
3474 generate_renaming_list([],[],[]).
3475 generate_renaming_list([ID|T],[ID2|T2],RL) :-
3476 (ID==ID2 -> generate_renaming_list(T,T2,RL)
3477 ; RL = [rename(ID2,ID)|RL2],
3478 generate_renaming_list(T,T2,RL2)).
3479
3480
3481 % a more clever way of constructing a disjunct; factor out common prefixes
3482 % (A & B1) or (A1 & B2) <=> A1 & (B1 or B2)
3483 % TO DO: we should try and get the leftmost basic conjunct !
3484 /* construct_disjunct(b(conjunct(A1,A2),pred,IA), b(conjunct(B1,B2),pred,_IB), Res) :-
3485
3486 print('TRY DISJUNCT FACTOR: '), translate:print_bexpr(A1),nl,
3487 translate:print_bexpr(B1),nl,
3488 same_texpr_body(A1,B1),!,
3489 print('DISJUNCT FACTOR: '), translate:print_bexpr(A1),nl,
3490 Res = conjunct(A1,b(Disj,pred,IA)),
3491 construct_disjunct(A2,B2,Disj).
3492 */
3493 construct_disjunct(A,B,disjunct(A,B)).
3494
3495 :- use_module(btypechecker,[couplise_list/2]).
3496 % TO DO: quick_check if AVL A1 is maximal ?
3497 union_of_avl_set(avl_set(A2),A1,R) :- !, union_of_avl(A1,A2,ARes), R=avl_set(ARes). /* AVL not normalised */
3498 union_of_avl_set(I2,A1,R) :- is_interval_closure_or_integerset(I2,From2,To2), !,
3499 ground(From2), ground(To2), % we can only compute it if bounds known
3500 (avl_min(A1,int(Min)), low_border(From2,Min,FromRes), avl_max(A1,int(Max)), up_border(To2,Max,ToRes)
3501 -> /* AVL contained (almost) in Interval */
3502 construct_interval_closure(FromRes,ToRes,R)
3503 ; \+ small_interval(From2,To2) ->
3504 transform_global_sets_into_closure(I2,closure(Par,T,Body)), % we may have something like NATURAL1,...
3505 union_of_avl_set_with_closure(Par,T,Body,A1,R)
3506 ; expand_and_convert_to_avl_set(I2,A2,union_of_avl_set,'? \\/ ARG'), % can generate ARel=empty; will fail if not possible to convert
3507 union_of_avl(A1,A2,ARes), R=avl_set(ARes)
3508 ).
3509 union_of_avl_set(closure(Par,T,Body),A1,Res) :- is_infinite_or_symbolic_closure(Par,T,Body),!,
3510 % 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)
3511 union_of_avl_set_with_closure(Par,T,Body,A1,Res).
3512 union_of_avl_set(S2,A1,Res) :-
3513 S2 \= freetype(_),
3514 ground_value(S2), % could be a closure
3515 !,
3516 (try_expand_and_convert_to_avl_set(S2,A2,union)
3517 -> union_of_avl(A1,A2,ARes), Res=avl_set(ARes) /* AVL not normalised */
3518 ; S2=closure(Par,T,Body),
3519 union_of_avl_set_with_closure(Par,T,Body,A1,Res)).
3520
3521 try_expand_and_convert_to_avl_set(S2,A2,Source) :-
3522 % false: do not add enumeration warning events as errors
3523 catch_enumeration_warning_exceptions(expand_and_convert_to_avl_set(S2,A2,Source,''),fail,false,ignore(Source)).
3524
3525 % try expanding to list, but catch enumeration warnings and fail if they do occur
3526 % used by override(...)
3527 %try_expand_custom_set_to_list(CS,_,_,_) :- nonvar(CS),CS=global_set(GS),is_infinite_global_set(GS,_),
3528 % !,
3529 % fail.
3530 try_expand_custom_set_to_list(CS,_,_,_) :- nonvar(CS),
3531 (is_symbolic_closure(CS) ; is_infinite_explicit_set(CS)),
3532 !, % we could also check is_symbolic_closure
3533 fail.
3534 try_expand_custom_set_to_list(CS,List,Done,Source) :-
3535 % false: do not add enumeration warning events as errors
3536 catch_enumeration_warning_exceptions(expand_custom_set_to_list(CS,List,Done,Source),fail,false,ignore(Source)).
3537
3538
3539 small_interval(From,To) :- number(From), number(To), To-From < 10000.
3540
3541 union_of_avl_set_with_closure(Par,T,Body,A1,Res) :-
3542 Body = b(_,BodyT,_),
3543 setup_typed_ids(Par,T,TypedPar),
3544 btypechecker:couplise_list(TypedPar,TypedCPar),
3545 generate_couple_types(TypedCPar,ParExpr,ParType),
3546 debug:debug_println(9,union_of_avl_and_infinite_closure(Par,T,BodyT)),
3547 BodyAvl = b(member(ParExpr,b(value(avl_set(A1)),set(ParType),[])),pred,[]),
3548 extract_info_wo_used_ids(Body,NewInfo),
3549 Res = closure(Par,T,b(disjunct(BodyAvl,Body),pred,NewInfo)).
3550 % mark_closure_as_symbolic(closure(Par,T,b(disjunct(BodyAvl,Body),pred,NewInfo)),Res).
3551
3552 low_border(Low,AVLMin,R) :- geq_inf(AVLMin,Low),!,R=Low.
3553 low_border(Low,AVLMin,R) :- number(Low),AVLMin is Low-1,R=AVLMin. % extend lower border by one
3554 up_border(Up,AVLMax,R) :- geq_inf(Up,AVLMax),!,R=Up.
3555 up_border(Up,AVLMax,R) :- number(Up),AVLMax is Up+1,R=AVLMax. % extend upper border by one
3556
3557
3558 setup_typed_ids([],[],[]).
3559 setup_typed_ids([ID|TI],[Type|TT],[b(identifier(ID),Type,[])|BT]) :- setup_typed_ids(TI,TT,BT).
3560
3561 generate_couple_types(couple(A,B),b(couple(TA,TB),Type,[]),Type) :- !, Type = couple(TTA,TTB),
3562 generate_couple_types(A,TA,TTA),
3563 generate_couple_types(B,TB,TTB).
3564 generate_couple_types(b(X,T,I),b(X,T,I),T).
3565
3566
3567 % try to see if two intervals can be unioned into a new interval
3568 union_of_interval(F1,T1,F2,T2,FR,TR) :-
3569 geq_inf(F2,F1), geq_inf(T1,T2),!,FR=F1,TR=T1. % interval [F2,T2] contained in [F1,T1]
3570 union_of_interval(F2,T2,F1,T1,FR,TR) :- geq_inf(F2,F1), geq_inf(T1,T2),!,FR=F1,TR=T1. % see above
3571 union_of_interval(F1,T1,F2,T2,FR,TR) :- number(F2),
3572 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
3573 union_of_interval(F2,T2,F1,T1,FR,TR) :- number(F2),
3574 geq_inf(F2,F1), number(T1),T11 is T1+1,geq_inf(T11,F2), geq_inf(T2,F2),!,FR=F1,TR=T2. % see above
3575
3576 :- use_module(library(ordsets),[ord_union/3]).
3577 union_of_avl(A1,A2,ARes) :-
3578 avl_height(A2,Sz2),
3579 (Sz2 < 2 % we have something like Set := Set \/ {x}; no need to compute height of A1
3580 -> union_of_avl1(A1,99999,A2,Sz2,ARes)
3581 ; avl_height(A1,Sz1), % TODO: we could call avl_height_less_than or avl_height_compare
3582 (Sz1<Sz2 -> union_of_avl1(A2,Sz2,A1,Sz1,ARes) ; union_of_avl1(A1,Sz1,A2,Sz2,ARes))
3583 ).
3584 union_of_avl1(A1,Sz1,A2,Sz2,ARes) :- Sz2>2, Sz1 =< Sz2+3, % difference not too big; Sz2 at least a certain size
3585 !,
3586 avl_to_list(A2,List2), % get all members
3587 avl_to_list(A1,List1),
3588 ord_union(List1,List2,L12),
3589 ord_list_to_avl(L12,ARes).
3590 union_of_avl1(A1,_Sz1,A2,_Sz2,ARes) :- % this version is better when A2 is small compared to A1
3591 avl_domain(A2,List2), % get all members
3592 add_to_avl(List2,A1,ARes).
3593
3594 :- use_module(library(lists),[reverse/2]).
3595 % a custom version for union(A) where A is AVL set; avoid converting/expanding accumulators and computing avl_height
3596 % 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
3597 union_generalized_explicit_set(avl_set(SetsOfSets),Res,WF) :-
3598 expand_custom_set_to_list_wf(avl_set(SetsOfSets),ESetsOfSets,_,union_generalized_wf,WF),
3599 % length(ESetsOfSets,Len),print(union_gen(Len)),nl,
3600 (ESetsOfSets=[OneSet]
3601 -> Res=OneSet % avoid converting to list and back to Avl
3602 ; 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
3603 % note: dom({r,x|x:1..50000 & r:{x*x}}) is still 3 times faster
3604 union_of_avls(RESetsOfSets,[],Res)).
3605
3606 % take the union of a list of avl_sets
3607 union_of_avls([],Acc,Res) :- ord_list_to_avl(Acc,ARes), construct_avl_set(ARes,Res).
3608 union_of_avls([H|T],Acc,Res) :-
3609 union_of_avl_with_acc(H,Acc,NewAcc),
3610 union_of_avls(T,NewAcc,Res).
3611
3612 union_of_avl_with_acc(avl_set(H),Acc,NewAcc) :- !,
3613 avl_to_list(H,HList),
3614 ord_union(Acc,HList,NewAcc).
3615 union_of_avl_with_acc([],Acc,Res) :- !,Res=Acc.
3616 % other custom sets should normally not appear, we obtain the list as elements stored in an avl_set
3617 union_of_avl_with_acc(G,_,_) :- add_internal_error('Uncovered element: ',union_of_avl_with_acc(G,_,_)),fail.
3618
3619
3620
3621 % TO DO: there are no rules for is_not_member_value_closure for intersection below
3622 intersection_of_explicit_set_wf(global_set(GS),S2,R,_WF) :- is_maximal_global_set(GS), !, R=S2.
3623 intersection_of_explicit_set_wf(freetype(_GS),S2,R,_WF) :- !, R=S2.
3624 intersection_of_explicit_set_wf(_,S2,_,_WF) :- var(S2),!,fail. % code below may instantiate S2
3625 intersection_of_explicit_set_wf(S1,S2,R,_WF) :- is_definitely_maximal_set(S2), !, R=S1.
3626 intersection_of_explicit_set_wf(_S1,[],R,_WF) :-!, R=[].
3627 intersection_of_explicit_set_wf(avl_set(A1),I2,R,_WF) :-
3628 is_interval_closure_or_integerset(I2,From1,To1),
3629 !,
3630 intersect_avl_interval(A1,From1,To1,R).
3631 intersection_of_explicit_set_wf(I1,I2,R,_WF) :-
3632 intersection_with_interval_closure(I1,I2,R),!.
3633 intersection_of_explicit_set_wf(S1,S2,R,_WF) :-
3634 get_avl_sets(S1,S2,A1,A2),
3635 !, % if too large: better to apply normal intersection code ?
3636 % if one of the args is an interval this is already caught in kernel_objects calling intersection_with_interval_closure; see SetIntersectionBig.mch
3637 avl_domain(A1,ES), % A1 has the smaller height; important for e.g. SetIntersectionBig2.mch
3638 inter2(ES,A2,IRes),
3639 ord_list_to_avlset(IRes,R,intersection). % we have generated the elements in the right order already
3640 intersection_of_explicit_set_wf(Set1,Set2,R,WF) :-
3641 transform_global_sets_into_closure(Set1,closure(P1,T1,B1)),
3642 transform_global_sets_into_closure(Set2,closure(P2,T2,B2)),
3643 % gets called, e.g., for {x|x /: NATURAL1} /\ NATURAL1
3644 unify_closure_predicates(P1,T1,B1, P2,T2,B2 , NewP,NewT, NewB1,NewB2),
3645 debug:debug_println(9,intersection_of_two_closures(P1,P2,NewP,NewT)),
3646 conjunct_predicates([NewB1,NewB2],BI),
3647 % create a conjunction: can be much more efficient than seperately expanding;
3648 % also works well if one of the closures is infinite
3649 C = closure(NewP,NewT,BI),
3650 expand_custom_set_wf(C,R,intersection_of_explicit_set_wf,WF). % we could keep it symbolic; maybe use SYMBOLIC pref
3651 % to do: also use above for closure and AVL set with member(P,value(avl_set(A)))
3652 % we could also apply the same principle to difference_of_explicit_set
3653 % currently we enable intersection to be treated symbolically (not_symbolic_binary(intersection) commented out)
3654 % This means the above clause for intersection_of_explicit_set_wf is less useful
3655 % a special case; just for interval closures
3656 intersection_with_interval_closure(I1,I2,R) :-
3657 is_interval_closure_or_integerset(I1,From1,To1), nonvar(I2),
3658 intersection_with_interval_closure_aux(I2,From1,To1,R).
3659 intersection_with_interval_closure(avl_set(A1),I2,R) :-
3660 is_interval_closure_or_integerset(I2,From1,To1),
3661 !,
3662 intersect_avl_interval(A1,From1,To1,R).
3663
3664 % try and get AVL sets from two args; first AVL set is smaller one according to height
3665 get_avl_sets(avl_set(A1),S2,AA1,AA2) :- nonvar(S2), S2=avl_set(A2),
3666 ? (avl_height_compare(A1,A2,R), R=lt
3667 -> (AA1,AA2)=(A1,A2)
3668 ; (AA1,AA2)=(A2,A1)).
3669 %get_avl_sets(S1,S2,AA1,AA2) :- nonvar(S2),S2=avl_set(A2), get_avl_set_arg(S1,A1),
3670 % (avl_height_compare(A1,A2,R),R=gt -> (AA1,AA2)=(A2,A1) ; (AA1,AA2)=(A1,A2)).
3671
3672
3673 %intersection_with_interval_closure_aux(avl_set(A),...
3674 intersection_with_interval_closure_aux(I2,From1,To1,R) :-
3675 is_interval_closure_or_integerset(I2,From2,To2),!,
3676 intersect_intervals_with_inf(From1,To1,From2,To2,FromRes,ToRes),
3677 construct_interval_closure(FromRes,ToRes,R).
3678 % (is_interval_closure_or_integerset(R,F,T) -> print(ok(F,T)),nl ; print(ko),nl).
3679 intersection_with_interval_closure_aux(avl_set(A2),From1,To1,R) :-
3680 intersect_avl_interval(A2,From1,To1,R).
3681
3682 % intersect avl with interval
3683 % TO DO: expand interval if small (or small intersection with AVL) and use avl intersection
3684 intersect_avl_interval(_,From2,To2,_) :- (var(From2) ; var(To2)),!,fail.
3685 intersect_avl_interval(A1,From2,To2,R) :- avl_min(A1,int(Min)),
3686 geq_inf(Min,From2),
3687 geq_inf(To2,Min), avl_max(A1,int(Max)),
3688 geq_inf(To2,Max),
3689 % AVL fully contained in interval; no need to expand to list and back again
3690 !,
3691 construct_avl_set(A1,R).
3692 intersect_avl_interval(A1,From2,To2,R) :-
3693 avl_domain(A1,ES),
3694 inter_interval(ES,From2,To2,IRes),
3695 ord_list_to_avlset(IRes,R,intersect_avl_interval).
3696
3697 inter_interval([],_,_, []).
3698 inter_interval([IH|T],From2,To2, Res) :- IH = int(H),
3699 (geq_inf(To2,H) ->
3700 (geq_inf(H,From2) -> Res = [IH-true|Res2] ; Res = Res2),
3701 inter_interval(T,From2,To2,Res2)
3702 ; Res = [] % we have exceeded the upper limit of the interval
3703 ).
3704
3705 intersect_intervals_with_inf(From1,To1,From2,To2,FromRes,ToRes) :-
3706 minimum_with_inf(To1,To2,ToRes),
3707 maximum_with_inf(From1,From2,FromRes).
3708
3709 % check if two intervals are disjoint
3710 disjoint_intervals_with_inf(From1,To1,From2,To2) :-
3711 intersect_intervals_with_inf(From1,To1,From2,To2,Low,Up),
3712 number(Up), number(Low), Low > Up.
3713
3714 inter2([],_, []).
3715 inter2([H|T],A1, Res) :-
3716 (avl_fetch(H,A1) -> Res = [H-true|Res2] ; Res = Res2), inter2(T,A1,Res2).
3717
3718 ord_list_to_avlset(OL,R) :- ord_list_to_avlset(OL,R,unknown).
3719 ord_list_to_avlset(OrdList,Res,Origin) :-
3720 % assumes that we have generated the elements in the right order already
3721 (OrdList=[] -> Res=[]
3722 ; check_sorted(OrdList,Origin),
3723 ord_list_to_avl(OrdList,ARes), Res=avl_set(ARes)).
3724
3725 % a version which accepts a list of values without -true
3726 % values have to be ground and already converted for use in avl_set
3727 sorted_ground_normalised_list_to_avlset(List,Res,PP) :-
3728 add_true_to_list(List,LT),
3729 ord_list_to_avlset_direct(LT,Res,PP).
3730
3731 add_true_to_list([],[]).
3732 add_true_to_list([H|T],[H-true|TT]) :- add_true_to_list(T,TT).
3733
3734 % the same, but without checking sorted (only use if you are really sure the list is sorted)
3735 ord_list_to_avlset_direct([],[],_).
3736 ord_list_to_avlset_direct([H|T],Res,_):-
3737 (T==[] -> H=Key-Val, Res = avl_set(node(Key,Val,0,empty,empty)) % slightly faster than calling ord_list_to_avl
3738 ; ord_list_to_avl([H|T],ARes), Res = avl_set(ARes)).
3739
3740 check_sorted([],_) :- !.
3741 check_sorted([H-_|T],Origin) :- !, check_sorted2(T,H,Origin).
3742 check_sorted(X,Origin) :- add_error_and_fail(ord_list_to_avlset,'Not a list of -/2 pairs: ',Origin:X).
3743
3744 check_sorted2([],_,_) :- !.
3745 check_sorted2([H-_|T],PH,Origin) :- PH @< H,!, check_sorted2(T,H,Origin).
3746 check_sorted2(X,Prev,Origin) :-
3747 add_error_and_fail(ord_list_to_avlset,'Not a sorted list of -/2 pairs: ',Origin:(X,Prev)).
3748
3749 % ------------------
3750
3751 :- use_module(kernel_freetypes,[is_maximal_freetype/1]).
3752 is_definitely_maximal_set(S) :- nonvar(S),
3753 is_definitely_maximal_set2(S).
3754 is_definitely_maximal_set2(freetype(ID)) :- is_maximal_freetype(ID).
3755 is_definitely_maximal_set2(global_set(GS)) :- is_maximal_global_set(GS).
3756 is_definitely_maximal_set2(closure(P,T,B)) :- is_definitely_maximal_closure(P,T,B).
3757 is_definitely_maximal_set2(avl_set(S)) :- quick_definitely_maximal_set_avl(S).
3758 is_definitely_maximal_set2([H|T]) :- nonvar(H), is_definitely_maximal_list(H,T). %, nl,print(maximal(H,T)),nl,nl.
3759 %H==pred_true, T == [pred_false]. % for some reason BOOL is sometimes presented this way
3760 is_definitely_maximal_set2(empty) :- % detect unwrapped AVL sets
3761 add_internal_error('Not a set: ',is_definitely_maximal_set2(empty)),fail.
3762 is_definitely_maximal_set2(node(A,B,C,D,E)) :-
3763 add_internal_error('Not a set: ',is_definitely_maximal_set2(node(A,B,C,D,E))),fail.
3764
3765 is_definitely_maximal_list(pred_true,T) :- nonvar(T), T=[_|_]. %
3766 is_definitely_maximal_list(pred_false,T) :- nonvar(T), T=[_|_].%
3767 is_definitely_maximal_list(fd(_,Type),T) :- nonvar(T),b_global_set_cardinality(Type,Card),
3768 % check if we have the same number of elements as the type: then the set must me maximal
3769 length_at_least(T,Card).
3770 % We could try and and also treat pairs
3771
3772 length_at_least(1,_) :- !. % we have already removed 1 element; T can be nil
3773 length_at_least(N,T) :- nonvar(T), T=[_|TT], N1 is N-1, length_at_least(N1,TT).
3774
3775 is_definitely_maximal_closure(_,_,b(truth,_Pred,_)) :- !.
3776 is_definitely_maximal_closure(P,T,B) :- is_cartesian_product_closure_aux(P,T,B,S1,S2),!,
3777 is_definitely_maximal_set(S1),is_definitely_maximal_set(S2).
3778 is_definitely_maximal_closure(P,T,B) :-
3779 is_full_powerset_or_relations_or_struct_closure(closure(P,T,B),Sets),
3780 l_is_definitely_maximal_set(Sets).
3781
3782 l_is_definitely_maximal_set([]).
3783 l_is_definitely_maximal_set([H|T]) :- is_definitely_maximal_set(H), l_is_definitely_maximal_set(T).
3784
3785 % check if we have an AVL tree covering all elements of the underlying type
3786 quick_definitely_maximal_set_avl(AVL) :-
3787 AVL=node(El,_True,_,_Left,_Right),
3788 quick_definitely_maximal_set_avl_aux(El,AVL).
3789 quick_definitely_maximal_set_avl_aux(El,AVL) :-
3790 try_get_finite_max_card_from_ground_value(El,Card),
3791 % this could fail if El contains empty sets !
3792 % also: it must fail if Card is infinite (no avl_set can be maximal)
3793 (Card < 1000 -> true
3794 ; preferences:preference(solver_strength,SS), Card < 1000+SS*100
3795 ), % otherwise too expensive a check avl_size
3796 quick_avl_approximate_size(AVL,MaxSize),
3797 MaxSize >= Card, % otherwise no sense in computing avl_size, which is linear in size of AVL
3798 avl_size(AVL,Size),
3799 %(MaxSize>=Size -> print(ok(Size,all(Card))),nl ; print('**** ERROR: '), print(Size),nl,trace),
3800 Size=Card.
3801
3802 % check if we have an AVL function with domain covering all elements of the underlying type
3803 quick_definitely_maximal_total_function_avl(AVL) :-
3804 AVL=node(El,_True,_,_Left,_Right),
3805 El=(DomEl,_),
3806 quick_definitely_maximal_set_avl_aux(DomEl,AVL), % the size is exactly the size of the domain
3807 is_avl_partial_function(AVL).
3808
3809 % ----------------------
3810 % set_subtraction /
3811 difference_of_explicit_set(S1,S2,R) :-
3812 difference_of_explicit_set_wf(S1,S2,R,no_wf_available).
3813 % this is called with first argument nonvar (for set_subtraction operator):
3814 difference_of_explicit_set_wf(_S1,S2,R,_) :-
3815 is_definitely_maximal_set(S2), !, R=[].
3816 difference_of_explicit_set_wf(S1,S2,R,_) :- nonvar(S2), S2=[],!, R=S1.
3817 difference_of_explicit_set_wf(S1,S2,R,_) :-
3818 %nonvar(S1),
3819 ? is_very_large_maximal_global_set(S1,Type), !, % TO DO: also for freetype ? cartesian products,...
3820 /* we have a complement-set */
3821 complement_set(S2,Type,R).
3822 difference_of_explicit_set_wf(S1,S2,Result,_) :-
3823 is_not_member_value_closure(S1,Type,MS1),
3824 nonvar(MS1), is_custom_explicit_set(MS1,difference_of_explicit_set_wf),!,
3825 union_complement_set(MS1,S2,Type,Result).
3826 difference_of_explicit_set_wf(_,S2,_,_) :- var(S2), !, fail. % then we cannot do anything below
3827 difference_of_explicit_set_wf(S1,S2,R,WF) :-
3828 is_not_member_value_closure(S2,_Type,MS2), nonvar(MS2),
3829 intersection_of_explicit_set_wf(MS2,S1,R,WF),!.
3830 difference_of_explicit_set_wf(I1,I2,R,_) :-
3831 is_interval_closure_or_integerset(I1,From1,To1),
3832 is_interval_closure_or_integerset(I2,From2,To2),
3833 difference_interval(From1,To1,From2,To2,FromRes,ToRes),
3834 % TO DO: also treat case when difference yields two disjoint intervals
3835 % 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}
3836 !,
3837 construct_interval_closure(FromRes,ToRes,R).
3838 difference_of_explicit_set_wf(avl_set(A1),S2,R,WF) :-
3839 (S2=avl_set(A2) ;
3840 ground_value(S2), expand_and_convert_to_avl_set_unless_very_large(S2,A2,WF)),!,
3841 avl_height(A2,H2),
3842 %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,
3843 avl_height(A1,H1),
3844 ((H2<2 -> true ; H1 > H2+1) % then it is more efficient to expand A2 and remove the A2 elements from A1;
3845 % note that difference_of_explicit_set2 now also sometimes expands both:
3846 % exact threshold when it is beneficial: difference_of_explicit_set2/3
3847 % 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)
3848 % {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))
3849 % {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))
3850 -> expand_custom_set_to_sorted_list(S2,ES,_,difference_of_explicit_set1,WF),
3851 difference_of_explicit_set3(ES,A1,R)
3852 ; expand_custom_set_to_sorted_list(avl_set(A1),ES,Done,difference_of_explicit_set2,WF),
3853 difference_of_explicit_set2(ES,H1,A2,H2,R,Done)).
3854 difference_of_explicit_set_wf(S1,S2,R,WF) :-
3855 (S2=avl_set(A2) ;
3856 ground_value(S2), expand_and_convert_to_avl_set_unless_very_large(S2,A2,WF)),!,
3857 avl_height(A2,A2Height),
3858 difference_with_avl(S1,A2,A2Height,R,WF).
3859 % to do: we could detect same_texpr_body for two closures and return R=[]
3860
3861 :- use_module(avl_tools,[avl_approximate_size_from_height/2]).
3862 :- use_module(bsyntaxtree,[safe_create_texpr/4, create_texpr/4, conjunct_predicates/2, mark_bexpr_as_symbolic/2]).
3863 difference_with_avl(S1,A2,A2Height,R,_) :-
3864 is_closure_or_integer_set(S1,[ID],[T],B),
3865 % check if the first argument is infinite; then do the difference set symbolically
3866 % this could supersed the complement set construction and be generalised to other sets apart from avl_sets as A2
3867 avl_approximate_size_from_height(A2Height,A2Size),
3868 Limit is max(A2Size*10,1000000), % if A2 is more than 10% size of S1, probably better to compute difference explicitly
3869 is_very_large_or_symbolic_closure([ID],[T],B,Limit),
3870 !, % TO DO: also allow multiple identifiers
3871 create_texpr(identifier(ID),T,[],TID),
3872 create_texpr(value(avl_set(A2)),set(T),[],A2Value),
3873 create_texpr(not_member(TID,A2Value),pred,[],NotMemA2),
3874 conjunct_predicates([B,NotMemA2],NewBody),
3875 mark_bexpr_as_symbolic(NewBody,NewBodyS),
3876 R = closure([ID],[T],NewBodyS).
3877 difference_with_avl(S1,A2,A2Height,R,WF) :-
3878 (nonvar(S1),S1=avl_set(A1) -> avl_height(A1,H1) ; H1=unknown),
3879 expand_custom_set_to_sorted_list(S1,ES,Done,difference_of_explicit_set3,WF),
3880 difference_of_explicit_set2(ES,H1,A2,A2Height,R,Done).
3881
3882
3883 % construct complement of a set
3884 union_complement_set(S1,S2,Type,Result) :-
3885 ground_value_check(S2,G2),
3886 when(nonvar(G2),union_complement_set2(S1,S2,Type,Result)).
3887 union_complement_set2(S1,S2,Type,Result) :-
3888 union_of_explicit_set(S1,S2,S12),
3889 construct_complement_closure_if_necessary(S12,Type,R),
3890 kernel_objects:equal_object(R,Result,union_complement_set2).
3891
3892 % construct complement of a set
3893 complement_set(S2,Type,Result) :-
3894 ground_value_check(S2,G2),
3895 when(nonvar(G2),complement_set2(S2,Type,Result)).
3896 complement_set2(S2,Type,Result) :-
3897 is_not_member_value_closure(S2,Type,MS2),!, % complement of complement
3898 kernel_objects:equal_object(MS2,Result,complement_set2).
3899 complement_set2(S2,Type,Result) :-
3900 try_expand_and_convert_to_avl_with_check(S2,ExpandedS2,difference_complement_set),
3901 construct_complement_closure_if_necessary(ExpandedS2,Type,R),
3902 kernel_objects:equal_object(R,Result,complement_set2).
3903
3904 :- block construct_complement_closure_if_necessary(-,?,?).
3905 construct_complement_closure_if_necessary(Set,TYPE,R) :-
3906 (Set=[] -> b_type2_set(TYPE,R)
3907 ; is_not_member_value_closure(Set,TYPE,MS) -> R=MS % complement of complement
3908 ; construct_complement_closure(Set,TYPE,R)).
3909
3910 % succeeds if difference of two intervals is also an interval
3911 % SourceLow..SourceUp \ DiffLow..DiffUp
3912 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,9,11,1,8)).
3913 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,9,inf,1,8)).
3914 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,10,12,1,9)).
3915 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,11,12,1,10)).
3916 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,12,13,1,10)).
3917 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,11,inf,1,10)).
3918 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,inf,11,inf,1,10)).
3919 % :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,9,8,1,10)). % 9..8 empty not detected
3920 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,1,8,9,10)).
3921 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,1,10,11,10)). % empty
3922 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,1,inf,inf,10)).
3923 :- assert_must_succeed(custom_explicit_sets:difference_interval(3,10,1,2,3,10)).
3924 :- assert_must_succeed(custom_explicit_sets:difference_interval(3,inf,1,2,3,inf)).
3925 :- assert_must_succeed(custom_explicit_sets:difference_interval(3,10,1,3,4,10)).
3926 :- assert_must_succeed(custom_explicit_sets:difference_interval(3,10,1,9,10,10)).
3927 :- assert_must_succeed(custom_explicit_sets:difference_interval(3,10,1,10,11,10)).
3928 difference_interval(SourceLow,SourceUp,DiffLow,DiffUp,ResLow,ResUp) :-
3929 (nonvar(SourceLow),nonvar(DiffLow),nonvar(DiffUp),
3930 geq_inf(SourceLow,DiffLow)
3931 -> % DiffLow is to left of SourceLow
3932 inc(DiffUp,D1),
3933 maximum_with_inf(D1,SourceLow,ResLow),
3934 ResUp=SourceUp % also works if SourceUp is a variable
3935 ; nonvar(DiffUp),nonvar(SourceUp),nonvar(DiffLow),
3936 geq_inf(DiffUp,SourceUp)
3937 -> % DiffUp is to right of SourceUp
3938 ResLow=SourceLow, % also works if SourceLow is a variable
3939 dec(DiffLow,D1),
3940 minimum_with_inf(SourceUp,D1,ResUp)).
3941
3942 inc(N,R) :- N==inf,!,R=inf.
3943 inc(N,N1) :- N1 is N+1.
3944 dec(N,R) :- N==inf,!,R=inf.
3945 dec(N,N1) :- N1 is N-1.
3946
3947 :- use_module(library(ordsets), [ord_subtract/3]).
3948 :- block difference_of_explicit_set2(?,?,?,?,?,-).
3949 difference_of_explicit_set2(ES,A1Height,A2,A2Height,R,_) :-
3950 (number(A1Height), A1Height+4 >= A2Height -> true
3951 ; A2Height < 5
3952 ; Limit is 2**(A2Height-4),
3953 length_larger_than(ES,Limit)
3954 % TO DO: we could try and pass sizes from specific closures to this predicate
3955 ),
3956 % A1 is not much larger than A2, then it is probably faster to use ord_subtract on expanded A2
3957 % {x|x mod 2 =0 & x:1..10000} - {y|y mod 3 =0 & y : 1..200000} : still more efficient with ord_subtract
3958 !,
3959 avl_domain(A2,A2Expanded),
3960 ord_subtract(ES,A2Expanded,OrdRes),
3961 sorted_ground_normalised_list_to_avlset(OrdRes,AVL,difference_of_explicit_set2),
3962 equal_object(AVL,R).
3963 difference_of_explicit_set2(ES,_A1Height,A2,_A2Height,R,_) :-
3964 avl_min(A2,Min),
3965 diff1(ES,Min,A2,IRes),
3966 ord_list_to_avlset(IRes,AVL,difference), % we have generated the elements in the right order already
3967 equal_object(AVL,R). % due to delays in expansion the result could be instantiated
3968
3969
3970 length_larger_than([_|T],Limit) :-
3971 (Limit<1 -> true
3972 ; L1 is Limit-1, length_larger_than(T,L1)).
3973
3974 diff1([],_, _,[]).
3975 diff1([H|T],Min,A1, Res) :-
3976 (H @< Min -> Res = [H-true|Res2],diff1(T,Min,A1,Res2)
3977 ; diff2([H|T],A1,Res)).% TO DO: compute avl_max
3978
3979 diff2([],_, []).
3980 diff2([H|T],A1, Res) :-
3981 (avl_fetch(H,A1) -> Res = Res2 ; Res = [H-true|Res2]), diff2(T,A1,Res2).
3982
3983 % another version to be used when second set small in comparison to first set
3984 difference_of_explicit_set3([],A1,Res) :- construct_avl_set(A1,AVL),
3985 equal_object(AVL,Res). % due to delay in expansion, Res could now be instantiated
3986 difference_of_explicit_set3([H|T],A1,ARes) :-
3987 (avl_delete(H,A1,_True,A2) -> true ; A2=A1),
3988 difference_of_explicit_set3(T,A2,ARes).
3989
3990 % -------------------------
3991
3992 % a version of add_element_to_explicit_set where we have already done the groundness check
3993 add_ground_element_to_explicit_set_wf(avl_set(A),Element,R,WF) :- !,
3994 convert_to_avl_inside_set_wf(Element,AEl,WF),
3995 avl_store(AEl,A,true,A2),!,R=avl_set(A2).
3996 add_ground_element_to_explicit_set_wf(Set,Element,R,WF) :-
3997 add_element_to_explicit_set_wf(Set,Element,R,WF).
3998
3999 add_element_to_explicit_set_wf(global_set(GS),_,R,_) :- is_maximal_global_set(GS), !, R=global_set(GS).
4000 add_element_to_explicit_set_wf(freetype(ID),_,R,_) :- is_maximal_freetype(ID),!, R=freetype(ID).
4001 add_element_to_explicit_set_wf(avl_set(A),Element,R,WF) :-
4002 ground_value(Element), %% was element_can_be_added_or_removed_to_avl(Element),
4003 convert_to_avl_inside_set_wf(Element,AEl,WF),
4004 avl_store(AEl,A,true,A2),!,R=avl_set(A2). /* AVL not normalised */
4005 /* do we need to add support for (special) closures ??
4006 add_element_to_explicit_set_wf(Clos,Element,R,_) :- nonvar(Element),Element=int(X), nonvar(X),
4007 is_interval_closure_or_integerset(Clos,Low,Up), ground(Low), ground(Up),
4008 union_of_interval(X,X,Low,Up,FromRes,ToRes),
4009 !,
4010 construct_interval_closure(FromRes,ToRes,R).
4011 % not-member closure not dealt with here
4012 */
4013
4014 element_can_be_added_or_removed_to_avl(Element) :-
4015 ground_value(Element),
4016 does_not_contain_closure(Element).
4017 ground_element_can_be_added_or_removed_to_avl(Element) :- /* use if you know the element to be ground */
4018 does_not_contain_closure(Element).
4019
4020 % does not contain closure or infinite other sets
4021 does_not_contain_closure([]).
4022 does_not_contain_closure([H|T]) :-
4023 (simple_value(H) -> true /* TO DO: check if we could have a closure at the end ?? */
4024 ; does_not_contain_closure(H),list_does_not_contain_closure(T)).
4025 does_not_contain_closure(fd(_,_)).
4026 does_not_contain_closure(pred_true /* bool_true */).
4027 does_not_contain_closure(pred_false /* bool_false */).
4028 does_not_contain_closure(int(_)).
4029 does_not_contain_closure(string(_)).
4030 does_not_contain_closure(term(_)). % real/floating number
4031 does_not_contain_closure((X,Y)) :- does_not_contain_closure(X), does_not_contain_closure(Y).
4032 does_not_contain_closure(avl_set(_)).
4033 ?does_not_contain_closure(global_set(G)) :- \+ is_infinite_global_set(G,_).
4034 %does_not_contain_closure(freetype(_)).
4035 does_not_contain_closure(freeval(_,_,Value)) :- does_not_contain_closure(Value).
4036 does_not_contain_closure(rec(Fields)) :- does_not_contain_closure_fields(Fields).
4037
4038 does_not_contain_closure_fields([]).
4039 does_not_contain_closure_fields([field(_,Val)|T]) :- does_not_contain_closure(Val),
4040 does_not_contain_closure_fields(T).
4041
4042 list_does_not_contain_closure([]).
4043 list_does_not_contain_closure([H|T]) :-
4044 does_not_contain_closure(H),list_does_not_contain_closure(T).
4045 list_does_not_contain_closure(avl_set(_)).
4046 list_does_not_contain_closure(global_set(G)) :- \+ is_infinite_global_set(G,_).
4047
4048 simple_value(fd(_,_)).
4049 simple_value(pred_true /* bool_true */).
4050 simple_value(pred_false /* bool_false */).
4051 simple_value(int(_)).
4052 simple_value((A,B)) :- simple_value(A), simple_value(B).
4053 simple_value(string(_)).
4054
4055
4056 % a version of the above which throws error if element cannot be added
4057 % assumes element_can_be_added_or_removed_to_avl has been checked
4058 remove_element_from_explicit_set(avl_set(A),Element,R) :-
4059 element_can_be_added_or_removed_to_avl(Element), % remove check?
4060 convert_to_avl_inside_set(Element,AEl), !,
4061 direct_remove_element_from_avl(A,AEl,R).
4062 remove_element_from_explicit_set(ES,Element,R) :-
4063 add_internal_error('Cannot remove element from explicit set:',remove_element_from_explicit_set(ES,Element,R)).
4064
4065 direct_remove_element_from_avl(A,AEl,R) :-
4066 avl_delete(AEl,A,_True,A2),
4067 construct_avl_set(A2,R). /* AVL not normalised */
4068
4069 /* same as remove but element can be absent */
4070 delete_element_from_explicit_set(avl_set(A),Element,R) :-
4071 element_can_be_added_or_removed_to_avl(Element),
4072 convert_to_avl_inside_set(Element,AEl), !,
4073 (avl_delete(AEl,A,_True,A2)
4074 -> construct_avl_set(A2,R)
4075 ; R = avl_set(A)
4076 ). /* AVL not normalised */
4077
4078 is_maximal_global_set(GS) :- is_maximal_global_set(GS,_Type).
4079 is_maximal_global_set(GS,_) :- var(GS),!,fail.
4080 is_maximal_global_set('INTEGER',Type) :- !, Type=integer.
4081 is_maximal_global_set('REAL',Type) :- !, Type=real.
4082 is_maximal_global_set('FLOAT',_) :- !, fail.
4083 is_maximal_global_set('STRING',Type) :- !, Type=string.
4084 is_maximal_global_set(GS,global(GS)) :-
4085 \+ kernel_objects:integer_global_set(GS).
4086
4087 % To do: maybe get rid of all complement set code; add in_difference_set as symbolic binary operator
4088 %is_very_large_maximal_global_set(X,_) :- print(very(X)),nl,fail.
4089 is_very_large_maximal_global_set(closure(P,T,B),Type) :- is_definitely_maximal_closure(P,T,B),
4090 couplise_list(T,Type).
4091 is_very_large_maximal_global_set(global_set('INTEGER'),integer).
4092 is_very_large_maximal_global_set(global_set('STRING'),string).
4093 is_very_large_maximal_global_set(global_set('REAL'),string).
4094 is_very_large_maximal_global_set(freetype(ID),freetype(ID)) :- is_infinite_freetype(ID).
4095
4096
4097
4098 remove_minimum_element_custom_set(avl_set(S),X,RES) :- !,
4099 avl_del_min(S,X,_True,Res0),
4100 (empty_avl(Res0) -> RES=[] ; RES = avl_set(Res0)).
4101 %remove_minimum_element_custom_set(closure(P,T,B),X,RES) :-
4102 % is_interval_closure_or_integerset(Clos,Low,Up),!,
4103 % X = Low, TO DO: construct new interval closure
4104 remove_minimum_element_custom_set(CS,X,RES) :-
4105 expand_custom_set_to_list(CS,ECS,Done,remove_minimum_element_custom_set),
4106 remove_minimum_element_custom_set2(ECS,X,RES,Done).
4107
4108 :- block remove_minimum_element_custom_set2(?,?,?,-).
4109 % wait until Done: otherwise the Tail of the list could be instantiated by somebody else; interfering with expand_custom_set_to_list
4110 remove_minimum_element_custom_set2([H|T],X,RES,_) :- equal_object((H,T),(X,RES)).
4111
4112
4113 min_of_explicit_set_wf(avl_set(S),Min,_) :- !, avl_min(S,Min).
4114 min_of_explicit_set_wf(Clos,Min,WF) :-
4115 is_interval_closure_or_integerset(Clos,Low,Up),
4116 (Low == minus_inf
4117 -> add_wd_error('minimum of unbounded infinite set not defined:',Clos,WF)
4118 ; cs_greater_than_equal(Up,Low),
4119 Min=int(Low)).
4120
4121 cs_greater_than_equal(X,Y) :-
4122 ((X==inf;Y==minus_inf) -> true ; kernel_objects:less_than_equal_direct(Y,X)).
4123
4124
4125 max_of_explicit_set_wf(avl_set(S),Max,_) :- !,avl_max(S,Max).
4126 max_of_explicit_set_wf(Clos,Max,WF) :-
4127 is_interval_closure_or_integerset(Clos,Low,Up),
4128 (Up==inf
4129 -> add_wd_error('maximum of unbounded infinite set not defined:',Clos,WF)
4130 ; cs_greater_than_equal(Up,Low),
4131 Max=int(Up)).
4132
4133 % ------------- SIGMA/PI --------------
4134
4135 % compute sum or product of an integer set:
4136 sum_or_mul_of_explicit_set(avl_set(S),SUMorMUL,Result) :-
4137 avl_domain(S,Dom),
4138 (SUMorMUL=sum -> simple_sum_list(Dom,0,R) ; simple_mul_list(Dom,1,R)),
4139 Result = int(R).
4140 sum_or_mul_of_explicit_set(CS,SUMorMUL,Result) :- SUMorMUL == sum,
4141 is_interval_closure(CS,Low,Up),
4142 sum_interval(Low,Up,Result),
4143 sum_interval_clpfd_prop(Low,Up,Result).
4144
4145 :- block sum_interval(-,?,?), sum_interval(?,-,?).
4146 sum_interval(Low,Up,_) :- (\+ number(Low) ; \+ number(Up)),!,
4147 add_error(sum_interval,'Cannot compute sum of interval: ',Low:Up),fail.
4148 sum_interval(Low,Up,Result) :- Low>Up,!, Result=int(0).
4149 sum_interval(Low,Up,Result) :-
4150 R is ((1+Up-Low)*(Low+Up)) // 2, % generalisation of Gauss formula k*(k+1)//2
4151 Result = int(R).
4152
4153 sum_interval_clpfd_prop(Low,Up,Result) :-
4154 preferences:preference(use_clpfd_solver,true), Result=int(R),
4155 var(R), % we haven't computed the result yet; the bounds are not known; set up constraint propagation rules
4156 !,
4157 try_post_constraint((Low #>= 0) #=> (R #> 0)), % we could provide better bounds here for negative numbers
4158 try_post_constraint(((Low #=< Up) #\/ (R #\= 0)) #=> (R #= ((1+Up-Low)*(Low+Up))//2)),
4159 try_post_constraint((Low #> Up) #=> (R #= 0)).
4160 % not working yet: x = SIGMA(i).(i:-3..n|i) & x=0 & n< -1
4161 sum_interval_clpfd_prop(_,_,_).
4162
4163 simple_sum_list([],A,A).
4164 simple_sum_list([int(H)|T],Acc,R) :- NA is Acc+H, simple_sum_list(T,NA,R).
4165 simple_mul_list([],A,A).
4166 simple_mul_list([int(H)|T],Acc,R) :- NA is Acc*H, simple_mul_list(T,NA,R).
4167
4168
4169 /*
4170 direct_product_symbolic(S,R,Res) :- % NOT YET FINISHED
4171 nonvar(S), S=closure(PS,[T1,TS2],RS),
4172 nonvar(R), R=closure(PR,[T1,TR1],RR),
4173 is_lambda_value_domain_closure(PS,TS,RS, SDomainValue,SExpr),
4174 is_lambda_value_domain_closure(PR,TR,RR, RDomainValue,RExpr),
4175 construct_closure(['zzz','_lambda_result_'],[T1,couple(TR1,TR2)],
4176 member(zzz,SDomainValue) , member(zzz,RDomainValue), eq(lambda,pair(SExpr,RExpr))).
4177 */
4178
4179 % we assume that try_expand_and_convert_to_avl_unless_very_large already called on arguments
4180 direct_product_explicit_set(S,R,Res) :-
4181 nonvar(R), %is_custom_explicit_set(R,direct_product),
4182 nonvar(S), %is_custom_explicit_set(S,direct_product),
4183 direct_product_explicit_set_aux(S,R,Res).
4184 %direct_product_explicit_set_aux(S,R,Res) :- (S = closure(_,_,_) ; R = closure(_,_,_)),
4185 % print_term_summary(direct_product_explicit_set_aux(S,R,Res)),nl,
4186 % % TO DO: generate closure
4187 % fail.
4188 direct_product_explicit_set_aux(avl_set(AS),avl_set(AR),Res) :-
4189 % the expansion guarantees that we have the lists ES and ER then in sorted order
4190 avl_domain(AS,ES), % -> expand_custom_set(avl_set(AS),ES),
4191 avl_domain(AR,ER), % -> expand_custom_set(avl_set(AR),ER),
4192 direct_product3(ES,ER,DPList),
4193 ord_list_to_avlset(DPList,DPAVL,direct_product), % is it really ordered ? findall must also return things ordered!
4194 equal_object(DPAVL,Res,direct_product_explicit_set).
4195
4196 direct_product3([],_Rel2,[]).
4197 direct_product3([(From,To1)|T1],Rel2,Res) :-
4198 get_next_mapped_to_eq(T1,From,TTo,Tail1), ToList1 = [To1|TTo],
4199 get_next_mapped_to(Rel2,From,ToList2,Tail2),
4200 calc_direct_product(ToList1,From,ToList2,Res,Rest),
4201 (Tail2=[] -> Rest=[] ; direct_product3(Tail1,Tail2,Rest)).
4202
4203 % get all elements which map to From, supposing that the list is sorted & we have already had a match
4204 get_next_mapped_to_eq([],_,[],[]).
4205 get_next_mapped_to_eq([(From2,To2)|T],From,Result,Tail) :-
4206 (From=From2 -> Result = [To2|RR], get_next_mapped_to_eq(T,From,RR,Tail)
4207 ; Result = [], Tail = [(From2,To2)|T]
4208 ).
4209
4210 % get all elements which map to From, supposing the list is sorted
4211 get_next_mapped_to([],_,[],[]).
4212 get_next_mapped_to([(From2,To2)|T],From,Result,Tail) :-
4213 (From=From2 -> Result = [To2|RR], get_next_mapped_to_eq(T,From,RR,Tail)
4214 ; From2 @> From -> Result = [], Tail = [(From2,To2)|T]
4215 ; get_next_mapped_to(T,From,Result,Tail)
4216 ).
4217
4218 calc_direct_product([],_From,_,Tail,Tail).
4219 calc_direct_product([To1|T1],From,To2List,Result,Tail) :-
4220 findall((From,(To1,To2))-true,member(To2,To2List),Result,ResResult),
4221 calc_direct_product(T1,From,To2List,ResResult,Tail).
4222
4223 % TO DO: maybe also add a special rule for infinite R such as event_b_identity ?
4224 domain_restriction_explicit_set_wf(S,R,Res,WF) :- /* S <| R */
4225 nonvar(R),
4226 (nonvar(S),is_one_element_custom_set(S,El),R \= closure(_,_,_) ->
4227 domain_restrict_singleton_element(El,R,Res)
4228 ; restriction_explicit_set_wf(S,R,Res,domain,pred_true,WF)).
4229 domain_subtraction_explicit_set_wf(S,R,Res,WF) :- /* S <<| R */
4230 (nonvar(S),is_one_element_custom_set(S,El), nonvar(R), R=avl_set(AVL) ->
4231 avl_domain_subtraction_singleton(AVL,El,ARes),
4232 construct_avl_set(ARes,Res) % TO DO: use this also when S is small and R large
4233 ; restriction_explicit_set_wf(S,R,Res,domain,pred_false,WF)).
4234 range_restriction_explicit_set_wf(R,S,Res,WF) :- /* R |> S */
4235 restriction_explicit_set_wf(S,R,Res,range,pred_true,WF).
4236 range_subtraction_explicit_set_wf(R,S,Res,WF) :- /* R |>> S */
4237 restriction_explicit_set_wf(S,R,Res,range,pred_false,WF).
4238
4239
4240 domain_restrict_singleton_element(El,R,Res) :- /* {El} <| R ; TO DO maybe apply this technique for "small" sets as well */
4241 nonvar(R), is_custom_explicit_set(R,domain_restrict_singleton_element),
4242 expand_and_convert_to_avl_set(R,AR,domain_restrict_singleton_element,''), % can generate ARel=empty; will fail if not possible to convert
4243 findall((El,Z)-true, avl_fetch_pair(El,AR,Z), RTuples),
4244 ord_list_to_avlset(RTuples,Res,domain_restrict_singleton_element).
4245
4246 restriction_explicit_set_wf(Set,Rel,Res,_RanOrDom,AddWhen,WF) :- Set==[],!,
4247 (AddWhen=pred_false
4248 -> equal_object_wf(Rel,Res,restriction_explicit_set_wf,WF) % {} <<| Rel = Rel |>> {} = Rel
4249 ; kernel_objects:empty_set_wf(Res,WF)
4250 ).
4251 restriction_explicit_set_wf(Set,Rel,Res,_RanOrDom,AddWhen,WF) :- is_definitely_maximal_set(Set),!,
4252 (AddWhen=pred_true
4253 -> equal_object_wf(Rel,Res,restriction_explicit_set_wf,WF) % TYPE <| Rel = Rel |> TYPE = Rel
4254 ; kernel_objects:empty_set_wf(Res,WF)
4255 ).
4256 restriction_explicit_set_wf(_,Rel,_,_,_,_) :- var(Rel),!,fail.
4257 restriction_explicit_set_wf(Set,closure(Paras,Types,Body),Res,RanOrDom,AddWhen,WF) :-
4258 % perform symbolic treatment by adding restriction predicate to Body
4259 !,
4260 (RanOrDom=domain
4261 -> get_domain_id_or_expr(Paras,Types,TID,TT)
4262 ; get_range_id_or_expr(Paras,Types,TID,TT)
4263 ),
4264 TSet=b(value(Set),set(TT),[]),
4265 (AddWhen = pred_true
4266 -> PRED = member(TID,TSet)
4267 ; PRED = not_member(TID,TSet) ),
4268 conjunct_predicates([b(PRED,pred,[]),Body],NewBody),
4269 % translate:print_bexpr(NewBody),nl,
4270 try_expand_and_convert_to_avl_with_catch_wf(closure(Paras,Types,NewBody),Res,restriction_explicit_set_wf,WF).
4271 restriction_explicit_set_wf(Set,Rel,Res,RanOrDom,AddWhen,WF) :-
4272 is_custom_explicit_set(Rel,restriction_explicit_set_wf),
4273 expand_and_convert_to_avl_set(Rel,ARel,restriction_explicit_set_wf,''), % can generate ARel=empty; will fail if not possible to convert
4274 avl_domain(ARel,ERel), % -> expand_custom_set(avl_set(ARel),ERel),
4275 %try_expand_and_convert_to_avl_unless_large_wf(Set,ES,WF),
4276 (nonvar(Set),Set=avl_set(AVLS)
4277 -> restrict2_avl(ERel,AVLS,DRes,RanOrDom,AddWhen,Done)
4278 ; restrict2(ERel,Set,DRes,RanOrDom,AddWhen,Done,WF)
4279 ),
4280 finish_restriction(Done,DRes,Res).
4281
4282 % extract domain expression for domain restriction/subtraction predicate:
4283 get_domain_id_or_expr([DR],[couple(TD,TR)], PRJ1, TD) :- !, % special case: just one parameter in closure
4284 TID = b(identifier(DR),couple(TD,TR),[]),
4285 PRJ1 = b(first_of_pair(TID),TD,[]).
4286 get_domain_id_or_expr([D1|Paras],[TD1|Types],Expr,Type) :-
4287 get_dom_couple_aux(Paras,Types, b(identifier(D1),TD1,[]), TD1, Expr,Type).
4288
4289 get_dom_couple_aux([_RangeID],[_], AccExpr, AccType, Expr, Type) :- !, Expr=AccExpr, Type=AccType.
4290 get_dom_couple_aux([D2|TParas],[TD2|Types], AccExpr, AccType, Expr, Type) :-
4291 TID2 = b(identifier(D2),TD2,[]),
4292 NewAccType = couple(AccType,TD2),
4293 NewAcc = b(couple(AccExpr,TID2),NewAccType,[]),
4294 get_dom_couple_aux(TParas,Types,NewAcc,NewAccType,Expr,Type).
4295
4296 :- use_module(library(lists),[last/2]).
4297 % extract range expression for range restriction/subtraction predicate:
4298 get_range_id_or_expr( [DR],[CType], PRJ2, TR) :- !, % special case: just one parameter in closure
4299 CType = couple(TD,TR),
4300 TID = b(identifier(DR),CType,[]),
4301 PRJ2 = b(second_of_pair(TID),TD,[]).
4302 get_range_id_or_expr( [_|Paras],[_|Types], b(identifier(R),TR,[]), TR) :-
4303 last(Paras,R), last(Types,TR).
4304
4305 :- block finish_restriction(-,?,?).
4306 finish_restriction(_,DRes,Res) :-
4307 ord_list_to_avlset(DRes,Restriction,restriction),
4308 ? equal_object(Restriction,Res,finish_restriction). % as we may block below: we need to use equal_object
4309
4310 restrict2([],_,[],_,_,done,_WF).
4311 restrict2([(From,To)|T],S,Res,RanOrDom,AddWhen,Done,WF) :-
4312 (RanOrDom==domain -> El=From ; El=To),
4313 kernel_equality:membership_test_wf(S,El,MemRes,WF), % TO DO: WF Version !!
4314 /* this only makes sense once we have the full result as argument:
4315 (nonvar(MemRes) -> true % it is already decided
4316 ; AddWhen=pred_true -> kernel_equality:membership_test_wf(Res,(From,To),MemRes,WF)
4317 ; kernel_equality:membership_test_wf(Res,(From,To),InResult,WF), bool_pred:negate(InResult,MemRes)
4318 ), */
4319 ? restrict3(MemRes,From,To,T,S,Res,RanOrDom,AddWhen,Done,WF).
4320 :- block restrict3(-, ?,?, ?,?,?, ?,?,?,?).
4321 restrict3(MemRes, From,To, T,S,Res, RanOrDom,AddWhen,Done,WF) :-
4322 (AddWhen=MemRes -> Res = [(From,To)-true|TRes]
4323 ; Res=TRes),
4324 ? restrict2(T,S,TRes,RanOrDom,AddWhen,Done,WF).
4325
4326 % optimised version when second set is also an AVL tree: less blocking,...
4327 restrict2_avl([],_,[],_,_,done).
4328 restrict2_avl([(From,To)|T],AVLS,Res,RanOrDom,AddWhen,Done) :-
4329 fetch(RanOrDom,From,To,AVLS,MemRes),
4330 (AddWhen=MemRes -> Res = [(From,To)-true|TRes]
4331 ; Res=TRes),
4332 restrict2_avl(T,AVLS,TRes,RanOrDom,AddWhen,Done).
4333
4334 fetch(domain,El,_,AVLS,MemRes) :- (avl_fetch(El,AVLS) -> MemRes=pred_true ; MemRes = pred_false).
4335 fetch(range,_,El,AVLS,MemRes) :- (avl_fetch(El,AVLS) -> MemRes=pred_true ; MemRes = pred_false).
4336
4337 % override R(X) := Y
4338 override_pair_explicit_set(avl_set(S),X,Y,avl_set(NewAVL)) :- element_can_be_added_or_removed_to_avl(X),
4339 element_can_be_added_or_removed_to_avl(Y),
4340 convert_to_avl_inside_set(X,AX),
4341 convert_to_avl_inside_set(Y,AY),
4342 avl_domain_subtraction_singleton(S,AX,AVL2),
4343 avl_store((AX,AY), AVL2, true, NewAVL).
4344
4345 avl_domain_subtraction_singleton(AVL,AX,NewAVL) :-
4346 avl_delete_pair(AX,AVL,_True,AVL2),
4347 !, % recurse, in case we have multiple entries
4348 % this recursion could be avoided if we know AVL to be a function
4349 avl_domain_subtraction_singleton(AVL2,AX,NewAVL).
4350 avl_domain_subtraction_singleton(AVL,_,AVL).
4351
4352 % try and decompose an AVL set into a cartesian product
4353 % AVL = Set1 * Set2
4354 % much faster e.g. for let xx = ((1..10)*(3..1000)\/ {0}*(3..1000)) and then xx = AA*BB
4355 % should not produce pending co-routines
4356 decompose_avl_set_into_cartesian_product_wf(AVL,DomainSet,RangeSet,WF) :-
4357 avl_domain(AVL,Expansion),
4358 decompose_cart(Expansion,'$none',DomainList,[],RangeList),
4359 construct_avl_from_lists_wf(DomainList,DomainSet,WF),
4360 construct_avl_from_lists_wf(RangeList,RangeSet,WF).
4361
4362 decompose_cart([],_,[],[],_).
4363 decompose_cart([(A,B)|T],Prev,Domain,Range,FullRange) :-
4364 (A=Prev
4365 -> Range = [B|TRange],
4366 decompose_cart(T,Prev,Domain,TRange,FullRange)
4367 ; Domain = [A|TDom], Range=[],
4368 FullRange = [B|TRange],
4369 decompose_cart(T,A,TDom,TRange,FullRange)
4370 ).
4371
4372 /* --------- */
4373 /* EXPANSION */
4374 /* --------- */
4375
4376 :- use_module(b_global_sets,[all_elements_of_type_wf/3, all_elements_of_type_rand_wf/3]).
4377 :- use_module(kernel_freetypes,[expand_freetype/3]).
4378
4379 expand_custom_set(X,R) :- expand_custom_set_wf(X,R,expand_custom_set,no_wf_available).
4380 expand_custom_set(X,R,Src) :- expand_custom_set_wf(X,R,Src,no_wf_available).
4381 expand_custom_set_wf(X,R,Source,WF) :- var(X), !,
4382 add_error_and_fail(expand_custom_set_wf, 'Variable as argument: ',expand_custom_set_wf(X,R,Source,WF)).
4383 expand_custom_set_wf(global_set(GS),ExpandedSet,_,WF) :- !,
4384 all_elements_of_type_wf(GS,ExpandedSet,WF). % they are generated in order
4385 expand_custom_set_wf(freetype(GS),ValueList,_,WF) :- !,
4386 expand_freetype(GS,ValueList,WF).
4387 expand_custom_set_wf(avl_set(AVL),ExpandedSet,_,_) :- !,
4388 avl_domain(AVL,ExpandedSet).
4389 expand_custom_set_wf(closure(Parameters,PTypes,Cond),Res,Source,WF) :- !,
4390 ? expand_closure_to_list(Parameters,PTypes,Cond,Res,_Done,Source,WF).
4391 %wait_try_expand_custom_set(Res1,Res). % could be in AVL form; no longer the case !
4392 expand_custom_set_wf(Set,_,Source,_) :-
4393 add_error_and_fail(expand_custom_set(Source),'Cannot expand custom set: ',Set).
4394
4395
4396
4397 %try_expand_only_custom_closure_global(X,Y) :-
4398 % (var(X) -> X=Y ; expand_only_custom_closure_global(X,Y,check)).
4399
4400 expand_only_custom_closure_global(X,R,C,_WF) :- var(X), !,
4401 add_error_and_fail(expand_only_custom_closure_global, 'Variable as argument: ',expand_only_custom_closure_global(X,R,C)).
4402 expand_only_custom_closure_global(global_set(GS),ExpandedSet,_,WF) :- !,all_elements_of_type_wf(GS,ExpandedSet,WF).
4403 expand_only_custom_closure_global(freetype(GS),ExpandedSet,_,_WF) :- !,ExpandedSet=freetype(GS).
4404 expand_only_custom_closure_global(avl_set(AVL),ExpandedSet,_,_WF) :- !, ExpandedSet=avl_set(AVL).
4405 expand_only_custom_closure_global(closure(Parameters,PTypes,Cond),Res,CheckTimeOuts,WF) :- !,
4406 (Res==[] -> is_empty_explicit_set(closure(Parameters,PTypes,Cond)) % TO DO: think about other special cases
4407 ; expand_closure_to_avl_or_list(Parameters,PTypes,Cond,Res,CheckTimeOuts,WF)).
4408 expand_only_custom_closure_global(Set,Set,_CheckTimeOuts,_WF).
4409 %:- add_error_and_fail(expand_only_custom_closure_global,'Cannot expand custom set: ',Set).
4410
4411
4412 try_expand_custom_set_with_catch(CS,Expansion,PP) :-
4413 on_enumeration_warning(try_expand_custom_set_wf(CS,Expansion,PP,no_wf_available),
4414 Expansion=CS).
4415
4416 try_expand_custom_set(CS,Expansion) :-
4417 try_expand_custom_set_wf(CS,Expansion,try_expand_custom_set,no_wf_available).
4418
4419
4420 try_expand_custom_set_wf(CS,Res,_,_) :- var(CS),!,Res=CS.
4421 try_expand_custom_set_wf([],Res,_,_) :- !, Res=[].
4422 try_expand_custom_set_wf([H|T],Res,_,_) :- !, Res=[H|T].
4423 try_expand_custom_set_wf(CS,Res,Src,WF) :-
4424 expand_custom_set_wf(CS,Res,Src,WF). % will generate error message for illegal sets
4425
4426
4427 :- assert_must_succeed((expand_custom_set_to_list(closure(['_zzzz_unit_tests'],
4428 [couple(integer,integer)],
4429 b(member(b(identifier('_zzzz_unit_tests'),couple(integer,integer),[generated]),
4430 b(value([(int(1),int(22))]),set(couple(integer,integer)),[])),pred,[])),R),R==[(int(1),int(22))])).
4431
4432 expand_custom_set_to_list(CS,List) :- expand_custom_set_to_list(CS,List,_Done,unknown).
4433
4434 % a version of expansion which returns guaranteed_ground if the List is guaranteed to be ground
4435 expand_custom_set_to_list_gg(CS,List,GuaranteedGround,_PP) :-
4436 nonvar(CS), CS=avl_set(AVL), var(List),
4437 !,
4438 GuaranteedGround = guaranteed_ground,
4439 avl_domain(AVL,List).
4440 expand_custom_set_to_list_gg(CS,List,not_guaranteed_ground,PP) :-
4441 expand_custom_set_to_list(CS,List,_Done,PP).
4442
4443 % a version where the expansion should happen straightaway and should not block:
4444 expand_custom_set_to_list_now(CS,List) :- expand_custom_set_to_list(CS,List,Done,unknown),
4445 (Done==true -> true ; print_error(expand_custom_set_to_list_not_done(CS,List))).
4446
4447 :- block expand_custom_set_to_sorted_list(-,-,?,?,?).
4448 % sorts the resulting list if needed
4449 % due to random enumeration
4450 expand_custom_set_to_sorted_list(From,To,Done,Source,WF) :-
4451 expand_custom_set_to_list(From,UnsortedTo,Done,Source),
4452 (get_preference(randomise_enumeration_order,true)
4453 -> sort_when_done(Done,UnsortedTo,To,WF) ; UnsortedTo = To).
4454
4455 :- block sort_when_done(-,?,?,?).
4456 sort_when_done(_,Unsorted,Res,WF) :- sort(Unsorted,Sorted),
4457 equal_object_wf(Sorted,Res,sort_when_done,WF).
4458
4459 expand_custom_set_to_list(From,To,Done,Source) :-
4460 expand_custom_set_to_list_wf(From,To,Done,Source,no_wf_available).
4461
4462 :- use_module(kernel_objects,[equal_object_wf/4]).
4463
4464 % try expand custom set to list; on enumeration warning set Done to enumeration_warning
4465 try_expand_custom_set_to_list_wf(From,To,Done,Source,WF) :-
4466 on_enumeration_warning(expand_custom_set_to_list_wf(From,To,Done,Source,WF),
4467 (Done=enumeration_warning)).
4468
4469 expand_custom_set_to_list_wf(From,To,Done,Source,WF) :-
4470 expand_custom_set_to_list_k_wf(From,To,Done,_Kind,Source,WF).
4471
4472 % a variation of expand_custom_set_to_list which also checks that there are no duplicates in the list
4473 expand_custom_set_to_list_no_dups_wf(From,To,Done,Source,WF) :-
4474 expand_custom_set_to_list_k_wf(From,To,Done,Kind,Source,WF),
4475 check_dups(Kind,To,WF).
4476
4477 :- block check_dups(-,?,?).
4478 check_dups(unsorted_list,List,WF) :- !,
4479 kernel_objects:check_no_duplicates_in_list(List,[],WF).
4480 check_dups(_,_,_).
4481
4482 % warn if duplicates in list; to do: use in prob_safe mode
4483 %:- block warn_dups(-,?,?,?).
4484 %warn_dups(unsorted_list,List,Src,WF) :- !,
4485 % kernel_objects:warn_if_duplicates_in_list(List,Src,WF).
4486 %warn_dups(_,_,_,_).
4487
4488
4489
4490 :- block expand_custom_set_to_list_k_wf(-,-,?,?,?,?).
4491 % ensures that the output is a pure list; the list skeleton should not be instantiated by anybody else
4492 expand_custom_set_to_list_k_wf(From,To,Done,Kind,Source,WF) :-
4493 (var(From) ->
4494 (is_list_skeleton(To)
4495 ? -> equal_object_wf(To,From,Source,WF), Done=true, Kind=unsorted_list
4496 ? ; expand_custom_set_to_list2(To,From,Done,Kind,Source,WF))
4497 ; var(To),is_list_skeleton(From)
4498 -> To=From, Done=true, Kind=unsorted_list % equal_object_wf will also to a Prolog unification
4499 ? ; expand_custom_set_to_list2(From,To,Done,Kind,Source,WF)).
4500
4501 expand_custom_set_to_list2([],ExpandedSet,Done,Kind,_Source,WF) :- !,
4502 ? equal_object_wf([],ExpandedSet,expand_custom_set_to_list2,WF),Done=true,Kind=empty_set.
4503 expand_custom_set_to_list2([H|T],ExpandedSet,Done,Kind,Source,WF) :- !, Kind=unsorted_list,
4504 ? equal_object_wf([H|ET],ExpandedSet,expand_custom_set_to_list2,WF),
4505 ? expand_custom_set_to_list3(T,ET,Done,Source,WF).
4506 expand_custom_set_to_list2(global_set(GS),ExpandedSet,Done,Kind,_Source,WF) :- !,
4507 all_elements_of_type_rand_wf(GS,R,WF),
4508 check_list(R,expand_custom_set_to_list2),
4509 equal_object_wf(R,ExpandedSet,expand_custom_set_to_list2,WF),Done=true,Kind=sorted_list.
4510 expand_custom_set_to_list2(avl_set(AVL),ExpandedSet,Done,Kind,_Source,WF) :- !,
4511 avl_domain(AVL,R),
4512 ? equal_object_wf(R,ExpandedSet,expand_custom_set_to_list2,WF), Done=true,Kind=sorted_list.
4513 expand_custom_set_to_list2(closure(Parameters,PTypes,Cond),ExpandedSet,Done,Kind,Source,WF) :- !,
4514 expand_closure_to_list(Parameters,PTypes,Cond,ExpandedSet,Done,Source,WF),
4515 Kind=sorted_list.
4516 %assign_expand_result(CDone,Res,ExpandedSet,Done).
4517 expand_custom_set_to_list2(freetype(ID),ExpandedSet,Done,Kind,_Source,WF) :- !,
4518 expand_freetype(ID,R,WF),
4519 equal_object_wf(R,ExpandedSet,expand_custom_set_to_list2,WF),
4520 Done=true,Kind=sorted_list.
4521 % missing avl_set wrapper:
4522 expand_custom_set_to_list2(node(A,B,C,D,E),ExpandedSet,Done,Kind,Source,WF) :- !,
4523 add_internal_error('Illegal argument: ',expand_custom_set_to_list2(node(A,B,C,D,E),ExpandedSet,Done,Source)),
4524 expand_custom_set_to_list2(avl_set(node(A,B,C,D,E)),ExpandedSet,Done,Kind,Source,WF).
4525 expand_custom_set_to_list2(E,ES,Done,Kind,Source,WF) :-
4526 add_internal_error('Illegal argument: ',expand_custom_set_to_list2(E,ES,Done,Kind,Source,WF)),fail.
4527
4528 :- block expand_custom_set_to_list3(-,-,?,?,?). % we are no longer sure which was From and which is To
4529 expand_custom_set_to_list3(From,To,Done,Source,WF) :-
4530 ? (var(From) -> expand_custom_set_to_list2(To,From,Done,_,Source,WF) ;
4531 ? expand_custom_set_to_list2(From,To,Done,_,Source,WF)).
4532
4533
4534 is_list_skeleton(X) :- var(X),!,fail.
4535 is_list_skeleton([]).
4536 is_list_skeleton([_|T]) :- is_list_skeleton(T).
4537
4538 % true if it is more efficient to keep this, rather than expand into list
4539 is_efficient_custom_set(avl_set(_)).
4540 is_efficient_custom_set(closure(P,T,B)) :-
4541 (is_interval_closure(closure(P,T,B),_,_) -> true ; is_infinite_or_symbolic_closure(P,T,B)).
4542 ?is_efficient_custom_set(global_set(X)) :- is_infinite_global_set(X,_).
4543 is_efficient_custom_set(freetype(_)).
4544
4545 % tries to expand & convert to avl_set; fails if not possible: NOTE: also generates empty AVL
4546 expand_and_convert_to_avl_set(R,AER,Origin,Source) :-
4547 try_expand_and_convert_to_avl(R,ER,Origin,Source),
4548 nonvar(ER),(ER==[] -> AER=empty ; ER=avl_set(AER)).
4549
4550
4551 expand_and_convert_to_avl_set_unless_very_large(R,AER,WF) :-
4552 try_expand_and_convert_to_avl_unless_very_large_wf(R,ER,WF),
4553 nonvar(ER),(ER==[] -> AER=empty ; ER=avl_set(AER)).
4554
4555
4556 % similar to unless_large version, but will only expand if it is guaranteed to be small
4557
4558 try_expand_and_convert_to_avl_if_smaller_than(freetype(GS),Res,_) :- !, Res = freetype(GS).
4559 try_expand_and_convert_to_avl_if_smaller_than([H|T],Res,_) :- !, try_expand_and_convert_to_avl([H|T],Res).
4560 try_expand_and_convert_to_avl_if_smaller_than(avl_set(A),Res,_) :- !, Res=avl_set(A).
4561 try_expand_and_convert_to_avl_if_smaller_than(CS,Res,Limit) :-
4562 (is_small_specific_custom_set(CS,Limit)
4563 -> try_expand_and_convert_to_avl(CS,Res,try_expand_and_convert_to_avl_if_smaller_than,'')
4564 ; Res = CS % TO DO: maybe look at cardinality of types and determine max. cardinality
4565 ).
4566 is_small_specific_custom_set(CS,Limit) :- card_for_specific_custom_set(CS,Card,Code),
4567 call(Code), is_finite_card(Card), Card<Limit.
4568 get_card_for_specific_custom_set(CS,Card) :-
4569 card_for_specific_custom_set(CS,Card,Code),
4570 call(Code), ground(Card).
4571
4572 try_expand_and_convert_to_avl_unless_very_large_wf(CS,Res,WF) :-
4573 try_expand_and_convert_to_avl_unless_large_wf(CS,Res,10000,WF).
4574
4575 try_expand_and_convert_to_avl_unless_large_wf(CS,Res,WF) :-
4576 try_expand_and_convert_to_avl_unless_large_wf(CS,Res,2000,WF).
4577
4578 try_expand_and_convert_to_avl_unless_large_wf(CS,Res,_,_WF) :- var(CS), !, CS=Res.
4579 try_expand_and_convert_to_avl_unless_large_wf(global_set(GS),Res,_,_WF) :- !, Res = global_set(GS).
4580 try_expand_and_convert_to_avl_unless_large_wf(freetype(GS),Res,_,_WF) :- !, Res = freetype(GS).
4581 %try_expand_and_convert_to_avl_unless_large_wf(CS,Res,_WF) :- is_interval_closure(CS,Low,Up),!,
4582 % ((ground(Low),ground(Up),Size is 1+Up-Low, Size<2000)
4583 %% -> try_expand_and_convert_to_avl(CS,Res)
4584 % ; Res = CS
4585 % ).
4586 try_expand_and_convert_to_avl_unless_large_wf(closure(P,T,B),Res,Limit,_WF) :-
4587 is_very_large_or_symbolic_closure(P,T,B,Limit),!, % is explicitly marked as SYMBOLIC
4588 Res=closure(P,T,B).
4589 try_expand_and_convert_to_avl_unless_large_wf(CS,Res,_Limit,WF) :-
4590 % TO DO: check if maybe we cannot determine card explicitly, but have a large lower-bound
4591 try_expand_and_convert_to_avl_wf(CS,Res,try_expand_and_convert_to_avl_unless_large,'',WF).
4592
4593
4594
4595 % calls try_expand_and_convert_to_avl and returns original value if enumeration warning occured
4596 try_expand_and_convert_to_avl_with_catch_wf(CS,Res,Origin,WF) :-
4597 on_enumeration_warning(try_expand_and_convert_to_avl_wf(CS,Res,Origin,'',WF),
4598 Res=CS).
4599
4600 /* tries to generate an avl-structure, if possible */
4601 try_expand_and_convert_to_avl(CS,Res) :-
4602 try_expand_and_convert_to_avl_wf(CS,Res,try_expand_and_convert_to_avl,'',no_wf_available).
4603
4604 try_expand_and_convert_to_avl(CS,Res,Origin,Source) :-
4605 try_expand_and_convert_to_avl_wf(CS,Res,Origin,Source,no_wf_available).
4606
4607 try_expand_and_convert_to_avl_wf(CS,Res,_,_,_WF) :- var(CS), !, CS=Res.
4608 try_expand_and_convert_to_avl_wf(avl_set(A),R,_,_,_WF) :- !, R=avl_set(A).
4609 try_expand_and_convert_to_avl_wf([],R,_,_,_WF) :- !, R=[].
4610 try_expand_and_convert_to_avl_wf([H|T],R,_,_,WF) :- !, try_convert_to_avl_wf([H|T],R,WF).
4611 try_expand_and_convert_to_avl_wf(closure(P,T,B),Res,Origin,_Source,WF) :- !,
4612 debug_opt_push_wait_flag_call_stack_info(WF,
4613 external_call('TRY EXPANDING',[closure(P,T,B)],unknown),WF2),
4614 expand_only_custom_closure_global(closure(P,T,B),Expansion,check(Origin),WF2),
4615 try_convert_to_avl_wf(Expansion,Res,WF).
4616 try_expand_and_convert_to_avl_wf(CS,Res,Origin,_Source,WF) :-
4617 (\+ is_custom_explicit_set(CS,try_expand_and_convert_to_avl_wf)
4618 -> Expansion = CS
4619 ; expand_only_custom_closure_global(CS,Expansion,check(Origin),WF)
4620 ),
4621 try_convert_to_avl_wf(Expansion,Res,WF).
4622
4623 try_convert_to_avl(Expansion,Res) :-
4624 (should_be_converted_to_avl_from_lists(Expansion) -> construct_avl_from_lists(Expansion,Res) ; Res=Expansion).
4625 try_convert_to_avl_wf(Expansion,Res,WF) :-
4626 (should_be_converted_to_avl_from_lists(Expansion) -> construct_avl_from_lists_wf(Expansion,Res,WF) ; Res=Expansion).
4627
4628 should_be_converted_to_avl_from_lists(Value) :- var(Value),!,fail.
4629 should_be_converted_to_avl_from_lists(Value) :-
4630 \+ is_custom_explicit_set(Value,should_be_converted_to_avl_from_lists), % already avl_set, global_set or closure
4631 ? \+ do_not_convert_aux(Value),
4632 ground_value(Value).
4633
4634 do_not_convert_aux(V) :- var(V),!.
4635 do_not_convert_aux((A,B)) :- !,
4636 ? (do_not_convert_aux(A) -> true ; do_not_convert_aux(B)).
4637 do_not_convert_aux([H|T]) :- !, % do not convert a set containing a symbolic closure
4638 ? (var(T) -> true ; do_not_convert_aux(H)).
4639 do_not_convert_aux(rec(Fields)) :- !,
4640 (var(Fields) -> true
4641 ? ; member(field(_,V),Fields), do_not_convert_aux(V) -> true).
4642 do_not_convert_aux(H) :-
4643 ? is_symbolic_closure(H).
4644
4645 should_be_converted_to_avl(Value) :- %preference(use_avl_trees_for_sets,true),
4646 ground_value(Value).
4647
4648 try_expand_and_convert_to_avl_with_check(CS,Res,Origin) :-
4649 try_expand_and_convert_to_avl_with_check(CS,Res,do_not_keep_intervals,Origin).
4650
4651 try_expand_and_convert_to_avl_with_check(CS,Res,_,_Origin) :- var(CS),!, Res = CS.
4652 try_expand_and_convert_to_avl_with_check([],Res,_,_Origin) :- !, Res=[].
4653 try_expand_and_convert_to_avl_with_check(avl_set(A),Res,_,_Origin) :- !, Res=avl_set(A).
4654 try_expand_and_convert_to_avl_with_check([H|T],Res,_,Origin) :- !, try_expand_and_convert_to_avl([H|T],Res,Origin,'').
4655 %try_expand_and_convert_to_avl_with_check(CS,Res,_Origin) :-
4656 % \+ is_custom_explicit_set(CS,try_expand_and_convert_to_avl),!, Res = CS.
4657 try_expand_and_convert_to_avl_with_check(CS,Res,KeepIntervals,_Origin) :-
4658 is_interval_closure(CS,Low,Up),
4659 (var(Low) -> true ; var(Up) -> true % better keep this symbolic as we may be able to do constraint propagation
4660 ; KeepIntervals=keep_intervals(Size) -> Up-Low >= Size
4661 ),
4662 !, % TO DO: see if we should do this check in try_expand_and_convert_to_avl above instead
4663 Res=CS.
4664 try_expand_and_convert_to_avl_with_check(CS,Res,_,Origin) :-
4665 get_card_for_specific_custom_set(CS,Size), % TO DO: avoid checking for special closures twice (below in try_expand_and_convert_to_avl ?)
4666 !,
4667 try_expconv_to_avl_with_size(Size,CS,Res,Origin).
4668 try_expand_and_convert_to_avl_with_check(CS,Res,_,Origin) :-
4669 try_expand_and_convert_to_avl(CS,Res,Origin,'').
4670
4671 try_expconv_to_avl_with_size(inf,CS,Res,Origin) :- !,
4672 debug_format(9,'### Not expanding infinite set~n### ORIGIN: ~w~n',[Origin]),
4673 Res=CS.
4674 try_expconv_to_avl_with_size(inf_overflow,CS,Res,Origin) :- !,
4675 debug_format(9,'### Not expanding very large set~n### ORIGIN: ~w~n',[Origin]),
4676 Res=CS.
4677 try_expconv_to_avl_with_size(Size,CS,Res,Origin) :- Size>=10000000, !,
4678 /* will probably never terminate */
4679 debug_format(9,'### Not expanding very large set with cardinality ~w~n### ORIGIN: ~w~n',[Size,Origin]),
4680 Res=CS.
4681 try_expconv_to_avl_with_size(Size,CS,Res,Origin) :- Size>=50000, !,
4682 print('### WARNING: expanding very large comprehension set, size = '), print(Size),nl,
4683 print('### ORIGIN: '), print(Origin),nl,
4684 try_expand_and_convert_to_avl(CS,Res,Origin,'').
4685 try_expconv_to_avl_with_size(_Size,CS,Res,Origin) :-
4686 try_expand_and_convert_to_avl(CS,Res,Origin,'').
4687
4688 /* underlying assumption for var case: if G is a global set: we get back the
4689 global_set tag immediately: no need to use when to wait;
4690 better: ensure that b_compute_expression always returns a nonvar term */
4691
4692
4693 :- assert_must_succeed((custom_explicit_sets:try_expand_custom_set(closure([xx],[integer],b(falsity,pred,[])),R),R = [])).
4694 :- assert_must_succeed((custom_explicit_sets:test_closure(X),custom_explicit_sets:expand_custom_set(X,EX),
4695 EX = [(fd(1,'Name'),_),(fd(3,'Name'),_)])).
4696
4697 test_closure(X) :- X = closure(['_zzzz_binary'],[couple(global('Name'),set(global('Name')))],
4698 b(member(b(identifier('_zzzz_binary'),couple(global('Name'),set(global('Name'))),[generated]),
4699 b(cartesian_product(b(value([fd(1,'Name'),fd(3,'Name')]),set(global('Name')),[]),
4700 b(value([[fd(2,'Name'),fd(3,'Name')]]),set(set(global('Name'))),[])),
4701 set(couple(global('Name'),set(global('Name')))),[])),pred,[])).
4702
4703
4704 /* --------- */
4705 /* ELEMENT_OF */
4706 /* --------- */
4707
4708
4709 /* A function that instantiates last argument when membership test can be decided */
4710
4711 membership_custom_set(CS,X,R) :- print(warning_deprecated_non_wf_version(CS,X,R)),nl,
4712 membership_custom_set_wf(CS,X,R,_WF).
4713
4714 ?membership_custom_set_wf(avl_set(A),X,R,WF) :- !, membership_avl_set_wf(A,X,R,WF).
4715 membership_custom_set_wf(freetype(_GS),_X,R,_WF) :- !, R=pred_true. % should be covered by clause above
4716 membership_custom_set_wf(CS,X,R,WF) :- R==pred_true,!, element_of_custom_set_wf(X,CS,WF).
4717 membership_custom_set_wf(CS,X,R,WF) :- R==pred_false,!, not_element_of_custom_set_wf(X,CS,WF).
4718 membership_custom_set_wf(CS,_X,R,_WF) :-
4719 is_definitely_maximal_set(CS),!,
4720 R=pred_true.
4721 membership_custom_set_wf(closure(Par,Types,Body),X,R,WF) :- !,
4722 ? closure_membership_wf(X,Par,Types,Body,R,WF).
4723 %membership_custom_set_wf(CS,X,R,WF) :- is_one_element_custom_set(CS,Y),!, % only succeeds for AVL
4724 % kernel_equality:equality_objects_wf_no_enumr(X,Y,R,WF).
4725 membership_custom_set_wf(global_set(GS),X,R,WF) :- !,
4726 membership_global_set(GS,X,R,WF).
4727 membership_custom_set_wf(CS,X,R,WF) :-
4728 add_internal_error('Illegal custom set: ',membership_custom_set_wf(CS,X,R,WF)),fail.
4729
4730 membership_avl_set_wf(A,X,R,WF) :- R==pred_true,!, element_of_avl_set_wf(A,X,WF).
4731 membership_avl_set_wf(A,X,R,WF) :- R==pred_false,!, not_element_of_custom_set_wf(X,avl_set(A),WF).
4732 membership_avl_set_wf(A,X,R,WF) :- is_one_element_avl(A,Y),!,
4733 ? kernel_equality:equality_objects_wf_no_enum(X,Y,R,WF).
4734 membership_avl_set_wf(A,_X,R,_WF) :-
4735 quick_definitely_maximal_set_avl(A),!,
4736 R=pred_true.
4737 membership_avl_set_wf(A,X,R,WF) :- reify_avl_membership(A,X,R,FullReification),
4738 (FullReification==true
4739 -> true %print_term_summary(full_reification(A,X,R)),nl,nl %% did slow down e.g. Bosch Deadlock v9, seems no longer the case
4740 ? ; when((ground(X);nonvar(R)),membership_avl_set_wf2(A,X,R,WF))).
4741
4742 ?membership_avl_set_wf2(A,X,R,WF) :- R==pred_true,!, element_of_avl_set_wf(A,X,WF).
4743 membership_avl_set_wf2(A,X,R,WF) :- R==pred_false,!, not_element_of_custom_set_wf(X,avl_set(A),WF).
4744 membership_avl_set_wf2(AVL,X,R,_WF) :-
4745 ground_element_can_be_added_or_removed_to_avl(X), !,
4746 (safe_avl_member(X,AVL) %safe_avl_member_ground(X,AVL)
4747 -> R=pred_true ; R=pred_false).
4748 membership_avl_set_wf2(AVL,X,Res,WF) :- % X is ground but cannot be added
4749 (Res \== pred_false, element_of_avl_set_wf(AVL,X,WF), Res=pred_true
4750 ;
4751 Res \== pred_true, not_element_of_custom_set_wf(X,avl_set(AVL),WF), Res=pred_false).
4752
4753 membership_global_set(GS,_X,R,_WF) :- is_maximal_global_set(GS),!,
4754 R=pred_true.
4755 membership_global_set(GS,X,R,WF) :- ground(X),!,
4756 (element_of_global_set_wf(X,GS,WF) -> R=pred_true ; R=pred_false).
4757 membership_global_set(GS,X,R,_WF) :- get_integer_set_interval(GS,Low,Up),!,
4758 membership_interval(X,Low,Up,R).
4759 membership_global_set(GS,X,R,WF) :- % this case should probably never apply
4760 (GS=='FLOAT' -> true % currently it actually is also treated like REAL
4761 ; print(uncovered_membership(GS,X,R,WF)),nl),
4762 when(ground(X), (element_of_global_set_wf(X,GS,WF) -> R=pred_true ; R=pred_false)).
4763
4764 membership_interval(X,Low,Up,Res) :- nonvar(Up),Up=inf,!,X=int(IX),
4765 b_interpreter_check:check_arithmetic_operator('<=',Low,IX,Res).
4766 membership_interval(X,Low,Up,Res) :- kernel_equality:in_nat_range_test(X,int(Low),int(Up),Res).
4767
4768 :- use_module(bool_pred).
4769 closure_membership_wf(X,[ZZZZ],[integer],CondClosure,Res,_WF) :-
4770 is_interval_closure_body(CondClosure,ZZZZ,LOW,UP),!,
4771 kernel_equality:in_nat_range_test(X,int(LOW),int(UP),Res).
4772 % TO DO: deal with open intervals 0..inf ...
4773 closure_membership_wf(X,Par,Types,Body,Res,WF) :-
4774 is_member_closure(Par,Types,Body,_Type,VAL),
4775 (VAL=value(_) ; VAL = cartesian_product(b(value(A),_,_),b(value(B),_,_))),!,
4776 (VAL=value(Set)
4777 -> kernel_objects:membership_test_wf(Set,X,Res,WF)
4778 ? ; kernel_equality:cartesian_pair_test_wf(X,A,B,Res,WF)).
4779 closure_membership_wf(X,Par,Typ,Body,Res,WF) :-
4780 is_not_member_closure(Par,Typ,Body,_Type,value(Set)),!,
4781 bool_pred:negate(ResXSet,Res), % was kernel_equality:inv_mem_obj(ResXSet,Res),
4782 kernel_objects:membership_test_wf(Set,X,ResXSet,WF).
4783 % TO DO: if closure = POW closure -> translate into subset_test pow_subset
4784 % TO DO: support a few other closures related to symbolic unary/binary operators: closure1, POW(..), ... ?
4785 % TO DO: expand if set is small
4786 closure_membership_wf(X,Par,Types,Body,Res,WF) :- ground_value(X),!,
4787 closure_membership_ground_wf(X,closure(Par,Types,Body),Res,WF).
4788 closure_membership_wf(X,Par,Types,Body,Res,WF) :-
4789 CS = closure(Par,Types,Body),
4790 is_small_specific_custom_set(CS,100),
4791 try_expand_and_convert_to_avl_wf(CS,Expanded,closure_membership_wf,'',WF),
4792 nonvar(Expanded), Expanded=avl_set(_),
4793 !,
4794 membership_custom_set_wf(Expanded,X,Res,WF).
4795 closure_membership_wf(X,Par,Types,Body,Res,WF) :-
4796 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
4797 get_texpr_info(Body,BodyInfo),
4798 \+ 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)
4799 % TO DO: add recursive parameter below in set_up_typed_localstate2; + in which other circumstances do we need to set up recursion identifier !
4800 % Try reifiyng the body
4801 NegationContext=positive,
4802 copy_wf_start(WF,closure_membership_wf,CWF),
4803 b_interpreter:set_up_typed_localstate2(Par,Types,BodyInfo,ParValues,TypedVals,[],State,NegationContext),
4804 %couplise_list(Types,XType),
4805 convert_list_into_pairs(ParValues,SingleParValue),
4806 kernel_objects:equal_object(X,SingleParValue,closure_membership_wf),
4807 b_interpreter_check:b_check_boolean_expression(Body,[],State,CWF,PredRes),
4808 !,
4809 (debug_mode(on) -> print('REIFICATION of closure: '), translate:print_bexpr(Body),nl, print(pred_res(X,PredRes)),nl ; true),
4810 b_enumerate:b_tighter_enumerate_all_values(TypedVals,WF), % not necessary ?? as X should get enumerated
4811 Res=PredRes,
4812 copy_wf_finish(WF,CWF).
4813 closure_membership_wf(X,Par,Types,Body,Res,WF) :-
4814 when( (ground(X);nonvar(Res)), %%
4815 % 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
4816 closure_membership_ground_wf(X,closure(Par,Types,Body),Res,WF)).
4817
4818 closure_membership_ground_wf(X,CS,Res,WF) :- nonvar(Res),!,
4819 % this optimization is checked in test 1452
4820 (Res==pred_true -> element_of_custom_set_wf(X,CS,WF) ; not_element_of_custom_set_wf(X,CS,WF)).
4821 closure_membership_ground_wf(X,CS,Res,WF) :-
4822 % to ensure that we leave no choice point behind we have to force full evaluation of element/not_element calls:
4823 % hence we do not call element_of_custom_set_wf or not_element_of_custom_set_wf below !!
4824 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;
4825 % used to be important for test 1146, but this is no longer the case
4826 %term_variables(CS,Vars),print(closure_membership_ground_wf_aux(LWF,vars(Vars),CS)),nl,
4827 ground_value_check(CS,CSGr),
4828 %when((nonvar(LWF),(nonvar(CSGr);nonvar(Res))),closure_membership_ground_wf_aux(X,CS,Res)).
4829 block_closure_membership_ground_wf_aux(X,CS,Res,CSGr,LWF,WF). % Note: wrong block in commit 332cb17487017d819e9140427b1017a3045b3685 caused problem for test 1162
4830
4831 :- block block_closure_membership_ground_wf_aux(?,?,?,?,-,?),
4832 block_closure_membership_ground_wf_aux(?,?,-,-,?,?).
4833 block_closure_membership_ground_wf_aux(X,CS,Res, _,_,WF) :-
4834 ? closure_membership_ground_wf_aux(X,CS,Res,WF).
4835
4836 % X & CS are ground or Res is known
4837 closure_membership_ground_wf_aux(X,CS,Res,WF) :- Res==pred_true,!,
4838 element_of_custom_set_wf(X,CS,WF).
4839 closure_membership_ground_wf_aux(X,CS,Res,WF) :- Res==pred_false,!,
4840 not_element_of_custom_set_wf(X,CS,WF).
4841 closure_membership_ground_wf_aux(X,CS,Res,_WF) :-
4842 % we know that X is a ground value and CS is ground: we can determine completely whether X is element of CS or not
4843 ? if(element_of_custom_set(X,CS),Res=pred_true, Res=pred_false).
4844 /* used to be: (Res \== pred_false, element_of_custom_set(X,CS), Res=pred_true
4845 ; Res \== pred_true, not_element_of_custom_set(X,CS), Res=pred_false)).
4846 */
4847
4848
4849
4850 :- use_module(kernel_objects,[element_of_global_set/2,element_of_global_set_wf/3]).
4851 element_of_custom_set_wf(X,CS,WF) :-
4852 ? element_of_custom_set_wf2(CS,X,WF). %, print(check_ok(X)),nl.
4853
4854 element_of_custom_set_wf2(node(A,B,C,D,E),X,WF) :-
4855 add_internal_error('Unwrapped avl_set: ',element_of_custom_set_wf2(node(A,B,C,D,E),X,WF)),fail.
4856 element_of_custom_set_wf2(global_set(GS),X,WF) :- element_of_global_set_wf(X,GS,WF).
4857 element_of_custom_set_wf2(freetype(ID),X,WF) :-
4858 (is_maximal_freetype(ID) -> true
4859 ; add_internal_error('Uncovered case: ',element_of_custom_set_wf2(freetype(ID),X,WF))
4860 ). % we assume freetypes to be maximal !
4861 ?element_of_custom_set_wf2(avl_set(AVL),X,WF) :- element_of_avl_set_wf(AVL,X,WF).
4862 element_of_custom_set_wf2(closure(Parameters,PT,Cond),X,WF) :-
4863 ? element_of_closure(X,Parameters,PT,Cond,WF).
4864
4865 element_of_avl_set_wf(node(Y,_,_,empty,empty),X,WF) :- !,
4866 ? kernel_objects:equal_object_wf(X,Y,element_of_custom_set_wf2,WF).
4867 element_of_avl_set_wf(AVL,X,_WF) :- ground_value(X),!, safe_avl_member(X,AVL). %safe_avl_member_ground(X,AVL).
4868 element_of_avl_set_wf(AVL,X,WF) :-
4869 avl_approximate_size(AVL,10,ApproxSize),
4870 ? element_of_avl_set_wf(AVL,ApproxSize,X,WF).
4871
4872 :- use_module(clpfd_tables).
4873
4874 element_of_avl_set_wf(AVL,ApproxSize,X,WF) :-
4875 % first check if worthwhile to attempt table treatment
4876 % after fixing table/2 bug runtimes have slowed down and test 1753 became much slower
4877 % for test 1753 a threshold of < 63 would be ideal; but test 1716 requires size 91
4878 % TODO: re-evaluate when SICStus 4.8 available
4879 preferences:preference(use_clpfd_solver,true),
4880 preferences:preference(solver_strength,SS),
4881 ApproxSize < 100+SS,
4882 (var(X) -> true
4883 ; X = (X1,_X2) -> (ground_value(X1) -> ApproxSize < 10+SS ; true)
4884 ; X=rec(_) -> true
4885 %; X=int(_) -> true ; X=fd(_,_) -> true % for scalar values we already use in_fd_value_list_wf via avl_fd_value_check
4886 ),
4887 can_translate_avl_to_table(AVL,SkeletonType),
4888 !,
4889 ? check_element_of_avl_with_table(X,SkeletonType,AVL,WF).
4890 element_of_avl_set_wf(AVL,ApproxSize,X,WF) :-
4891 ? propagate_avl_element_information(X,AVL,ApproxSize,WF), %translate:translate_bvalue(avl_set(AVL),SS),
4892 get_bounded_wait_flag(ApproxSize,element_of_avl(X),WF,WF1),
4893 ? element_of_avl_set_wf3(X,AVL,ApproxSize,WF1,WF).
4894
4895
4896 % compute an approximate size (small sets are computed exactly)
4897 avl_approximate_size(AVL,Size) :- avl_approximate_size(AVL,10,Size).
4898
4899 avl_approximate_size(AVL,HeightBound,Size) :- var(AVL),!,
4900 add_internal_error('AVL Set is variable: ', avl_approximate_size(AVL,HeightBound,Size)),
4901 Size=1000000.
4902 avl_approximate_size(AVL,HeightBound,Size) :- % when the AVL gets too large; not so important that we have a precise estimation anyway
4903 % so: save some time and just compute height
4904 avl_height(AVL,Height),
4905 (Height>HeightBound
4906 -> Size is floor(2**Height-1)
4907 ; avl_size(AVL,Size)).
4908
4909 :- block element_of_avl_set_wf3(-,?,?,-,?).
4910 ?element_of_avl_set_wf3(X,AVL,_ApproxSize,_WF1,_WF) :- var(X), !, safe_avl_member(X,AVL).
4911 % TO DO: if randomise_enumeration_order is true then choose elements in random order
4912 :- if(environ(prob_data_validation_mode,xxxtrue)). % currently disabled due to bug related to 14082013/435_002.mch TO DO: investigate
4913 element_of_avl_set_wf3((X,Y),AVL,ApproxSize,WF1,WF) :- !,
4914 %% ((var(WF1), \+ ground(X)) -> print(avl_relation_check(X,Y)),nl, %%
4915 %% copy_term((X,Y),Copy), findall(Copy,safe_avl_member(Copy,AVL),Cs), print(Cs),nl, Cs \=[] %% check that at least one element exists
4916 %% ; true),
4917 couple_element_of_avl_set_wf(X,Y,AVL,ApproxSize,WF1,WF).
4918 :- else.
4919 element_of_avl_set_wf3((X,Y),AVL,ApproxSize,WF1,WF) :- !,
4920 ground_value_check(X,GrX),
4921 ? block_couple_element_of_avl_set_grX_wf1(X,Y,AVL,ApproxSize,GrX,WF1,WF).
4922 %when((nonvar(WF1) ; ground(X)), couple_element_of_avl_set(X,Y,AVL,GrX,WF1,WF)).
4923 :- endif.
4924 element_of_avl_set_wf3(X,AVL,_ApproxSize,WF1,_WF) :-
4925 ground_value_check(X,GrX),
4926 safe_avl_member_block(X,AVL,GrX,WF1).
4927
4928 :- block safe_avl_member_block(?,?,-,-).
4929 safe_avl_member_block(X,AVL,_,_) :-
4930 ? safe_avl_member(X,AVL).
4931
4932 :- if(environ(prob_data_validation_mode,true)).
4933 :- public couple_element_of_avl_set_wf/6. % used in conditional if above
4934 :- block couple_element_of_avl_set_wf(-,?,?,?,-,?).
4935 couple_element_of_avl_set_wf(X,Y,AVL,ApproxSize,WF1,WF) :-
4936 ground_value_check(X,GrX),
4937 ((nonvar(WF1);nonvar(GrX)) -> couple_element_of_avl_set(X,Y,AVL,GrX,WF1,WF)
4938 %; true -> when((nonvar(WF1) ; ground(X)), couple_element_of_avl_set(X,Y,AVL,WF1,WF))
4939 ; nonvar(X),X=(X1,X2),ground(X1) -> triple_element_of_avl_set(X1,X2,Y,AVL,WF)
4940 ; nonvar(X),X=(X1,X2) ->
4941 avl_member_blocking((X,Y),AVL),
4942 (ground(Y),ground(X1) -> safe_avl_member_pair_wf(X,Y,AVL,WF)
4943 ; when(ground(X1),(\+ ground(X2) -> triple_element_of_avl_set(X1,X2,Y,AVL,WF) ; true % avl_member_blocking will have done its work
4944 )),
4945 block_couple_element_of_avl_set(X,Y,AVL,WF1,WF)
4946 )
4947 ; %when((nonvar(WF1) ; ground(X)), couple_element_of_avl_set(X,Y,AVL,WF1,WF))
4948 block_couple_element_of_avl_set_grX_wf1(X,Y,AVL,ApproxSize,GrX,WF1,WF)
4949 /* ; (simple_avl_type(AVL)
4950 -> avl_member_blocking((X,Y),AVL) % TO DO: don't call couple_element_of_avl_set ! avoid double traversal !!
4951 ; true),
4952 block_couple_element_of_avl_set_grX_wf1(X,Y,AVL,GrX,WF1,WF) */
4953 ).
4954
4955 :- block block_couple_element_of_avl_set(?,?,?,-,?).
4956 block_couple_element_of_avl_set(X,Y,_AVL,_WF1,_WF) :- ground(X),ground(Y),!.
4957 block_couple_element_of_avl_set(X,Y,AVL,_WF1,WF) :- safe_avl_member_pair_wf(X,Y,AVL,WF).
4958
4959 triple_element_of_avl_set(X1,X2,Y,AVLRelation,WF) :- % X1 must be ground
4960 copy_term((X2,Y),(CX2,CY)),
4961 findall((CX2,CY),safe_avl_member_pair((X1,CX2),CY,AVLRelation),Images),
4962 % we pass no WF to safe_avl_member_pair; we need to fully evaluate all unifications due to findall
4963 Images \= [],
4964 construct_avl_from_lists_wf(Images,AVL,WF),
4965 element_of_custom_set_wf2(AVL,(X2,Y),WF). % will set up waitflag if necessary
4966 :- endif.
4967
4968 % ---------------------------------------------------
4969
4970 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))).
4971
4972 %simple_avl_type(node(K,_,_,_,_)) :- simple_value(K). % we can index directly on AVL, without having to normalise inner values
4973 % in particular, we can apply avl_member_blocking
4974
4975 :- 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) )).
4976 :- 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) )).
4977 :- 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) )).
4978 :- assert_must_fail(( custom_explicit_sets:test_avl_set(A), custom_explicit_sets:avl_member_blocking(((X,_Y),_Z),A), X=int(5) )).
4979 % a blocking version of avl_member; will not instantiate the element; just prune
4980
4981 avl_member_blocking(Key, AVL) :- AVL=node(K,_,_,L,R),
4982 %avl_height(AVL,Height),
4983 avl_member_blocking4(Key,K,L,R).
4984
4985 avl_member_blocking4(Key,Kavl,L,R) :- L=empty,R=empty,!,
4986 Key=Kavl. % we could do equal_object
4987 avl_member_blocking4(Key,Kavl,L,R) :-
4988 match_possible(Key,Kavl,MatchPossible), % check if in principle a match could occur
4989 (Kavl=(_,_) ->
4990 (avl_min(R,Knext) -> true ; dif(O,>), Knext=no_match,
4991 force_comp(MatchPossible,O,'<')),
4992 (avl_max(L,Kprev) -> true ; dif(O,<), Kprev=no_match,
4993 force_comp(MatchPossible,O,'>'))
4994 ; Knext = no_match, Kprev = no_match
4995 ),
4996 (nonvar(O) -> true
4997 /* ; (MatchPossible==pred_false, avl_height(L,Height), Height < 8,
4998 copy_term(Key,CKey), \+ safe_avl_member(CKey,L), \+ safe_avl_member(CKey,R))
4999 -> print(cannot_match(Key)),nl,fail */
5000 ; compare_blocking(O, Key, Kavl, Kprev,Knext)),
5001 avl_member_blocking_aux(O, Key, Kavl, L, R).
5002
5003 %force_comp(V,_,_) :- var(V),!.
5004 :- block force_comp(-,?,?).
5005 force_comp(pred_true,_,_).
5006 force_comp(pred_false,R,R).
5007
5008 :- block avl_member_blocking_aux(-,?,?,?,?).
5009 avl_member_blocking_aux(<, Key, _K, AVL, _) :- avl_member_blocking(Key, AVL).
5010 avl_member_blocking_aux(=, Key, Key, _L, _R). % we could use equal_object
5011 avl_member_blocking_aux(>, Key, _K, _, AVL) :- avl_member_blocking(Key, AVL).
5012
5013 % a blocking version of compare
5014 compare_blocking(Res,A,Kavl, Kprev, Knext) :- block_compare(A,Kavl,Res, Kprev, Knext).
5015
5016 :- block block_compare(-,?,?,?,?), block_compare(?,-,?,?,?).
5017 block_compare((A,B),Kavl,Res, Kprev, Knext) :- !,
5018 (Kavl=(RA,RB) ->
5019 match_key(Kprev,RA,PA,PB),
5020 match_key(Knext,RA,NA,NB),
5021 block_compare(A,RA,ACRes,PA,NA),
5022 block_compare_aux(ACRes,B,RB,Res,PB,NB)
5023 ; add_internal_error('Illegal type: ',block_compare((A,B),Kavl,Res, Kprev, Knext)),fail).
5024 % TO DO: same for records; but currently not used anyway
5025 block_compare(int(A),int(B),Res,_,_) :- !, block_compare_atomic(A,B,Res).
5026 block_compare(pred_false,B,Res,_,_) :- !, block_compare_atomic(pred_false,B,Res).
5027 block_compare(pred_true,B,Res,_,_) :- !, block_compare_atomic(pred_true,B,Res).
5028 block_compare(string(A),string(B),Res,_,_) :- !, block_compare_atomic(A,B,Res).
5029 block_compare(fd(A,T),fd(B,T),Res,_,_) :- !, block_compare_atomic(A,B,Res).
5030 block_compare(avl_set(A),Kavl,Res,_,_) :- !,
5031 convert_to_avl_inside_set(avl_set(A),ConvertedA),compare(Res,ConvertedA,Kavl).
5032 block_compare([],[],Res,_,_) :- !, Res = '='.
5033 block_compare([],_,Res,_,_) :- !, Res = '<'.
5034 block_compare(A,Kavl,Res,_,_) :-
5035 % does deal with various representations of sets !! closure/global_set/...
5036 when(ground(A),
5037 (convert_to_avl_inside_set(A,ConvertedA),compare(Res,ConvertedA,Kavl))).
5038
5039 match_key((KeyA,KeyB),Key,ResA,ResB) :- !, ResA=KeyA,
5040 (Key==KeyA -> ResB=KeyB ; ResB = no_match).
5041 match_key(_,_,no_match,no_match).
5042
5043 :- block block_compare_atomic(-,?,?), block_compare_atomic(?,-,?).
5044 block_compare_atomic(A,B,Res) :- compare(Res,A,B).
5045
5046 :- block block_compare_aux(-,?,?,?, ?,?).
5047 block_compare_aux(ACRes,B,D,Res, Kprev,Knext) :-
5048 (ACRes='<' -> Res = '<'
5049 ; ACRes = '>' -> Res = '>'
5050 ; Kprev=no_match, Knext=no_match ->
5051 Res = '=' % we cannot match neither previous nor next key: force match
5052 ; block_compare(B,D,Res,Kprev,Knext)). % TO DO: check with prev & next value: if no match possible force Res='='
5053
5054 % check if a match is possible between two terms
5055 :- block match_possible(-,?,?), match_possible(?,-,?).
5056 match_possible([],[],Possible) :- !, Possible=pred_true.
5057 match_possible([],avl_set(_),Possible) :- !, Possible=pred_false.
5058 match_possible(avl_set(_),[],Possible) :- !, Possible=pred_false.
5059 match_possible(int(A),int(B),Possible) :- !, match_possible_atomic(A,B,Possible).
5060 match_possible(fd(A,T),fd(B,T),Possible) :- !, match_possible_atomic(A,B,Possible).
5061 match_possible(string(A),string(B),Possible) :- !, match_possible_atomic(A,B,Possible).
5062 match_possible((A1,A2),(B1,B2),Possible) :- !, match_possible(A1,B1,P1),
5063 match_possible(A2,B2,P2), kernel_equality:conjoin_test(P1,P2,Possible,_WF). %% WF <--- TO DO
5064 match_possible(_,_,pred_true).
5065
5066 :- block match_possible_atomic(-,?,?), match_possible_atomic(?,-,?).
5067 match_possible_atomic(A,B,Res) :- (A==B -> Res=pred_true ; Res=pred_false).
5068
5069 % --------------------------------------------
5070
5071 :- block block_couple_element_of_avl_set_grX_wf1(?, - ,?,?,-,-,?).
5072 block_couple_element_of_avl_set_grX_wf1(X,Y,AVL,ApproxSize,GrX,WF1,WF) :-
5073 var(GrX), var(WF1),
5074 !,
5075 % we know the result Y but not yet fully the input value X
5076 (ApproxSize < 129 % TO DO: improve this; unify with inverse_apply_ok(Y,X,AVL,ApproxSize) ?
5077 -> ground_value_check(Y,GrY) % wait until Y is fully known
5078 ; (preference(solver_strength,SS), ApproxSize < 129+SS)
5079 -> ground_value_check(Y,GrY)
5080 % TO DO: we could look at avl_min and avl_max and estimate spread of range keys
5081 ; cond_perfmessage([data_validation_mode/false],no_inverse_avl_lookup(ApproxSize,Y)) % do not bind GrY; we wait until GrX or WF1 is bound
5082 ),
5083 block_couple_element_of_avl_set_grX_grY_wf1(X,Y,AVL,ApproxSize,GrX,GrY,WF1,WF).
5084 block_couple_element_of_avl_set_grX_wf1(X,Y,AVL,_ApproxSize,GrX,WF1,WF) :-
5085 ? couple_element_of_avl_set(X,Y,AVL,GrX,WF1,WF).
5086
5087 :- block block_couple_element_of_avl_set_grX_grY_wf1(?,?,?,?, -,-,-,?).
5088 block_couple_element_of_avl_set_grX_grY_wf1(X,Y,AVL,_ApproxSize, GrX,_GrY,WF1,WF) :-
5089 var(GrX), var(WF1), % i.e., Y is known
5090 % we know the result Y but not yet fully the input value X
5091 %inverse_apply_ok(Y,X,AVL,ApproxSize),
5092 !,
5093 inverse_get_possible_values(X,Y,AVL,Res),
5094 Res = avl_set(InvAVL),
5095 element_of_avl_set_wf(InvAVL,X,WF).
5096 %couple_element_of_avl_set(X,Y,AVL,GrX,1,WF).
5097 block_couple_element_of_avl_set_grX_grY_wf1(X,Y,AVL,_ApproxSize,GrX,_GrY,WF1,WF) :-
5098 ? couple_element_of_avl_set(X,Y,AVL,GrX,WF1,WF).
5099
5100
5101 % special treatment for relations: if the first component is known: then we can check how many images there are
5102 couple_element_of_avl_set(X,Y,AVL,GrX,WF1,WF) :-
5103 nonvar(WF1), var(GrX), %\+ground(X),
5104 !,
5105 ? safe_avl_member_default_wf((X,Y),AVL,WF).
5106 couple_element_of_avl_set(X,Y,AVLRelation,_GrX,_,WF) :- % X must be ground
5107 get_template(Y,TY,_ToUnifyAfter), % was copy_term(Y,CY) but could cause issues with closures with variables
5108 copy_term(TY,CY), % avoid that we instantiate Y and trigger co-routines
5109 findall(CY,avl_member_pair_arg1_ground(X,CY,AVLRelation),Images), % should we use Y instead of CY
5110 Images \= [],
5111 construct_avl_from_lists_wf(Images,AVL,WF),
5112 ? element_of_custom_set_wf2(AVL,Y,WF). % will set up waitflag if necessary
5113
5114
5115 % set Res -> pred_true or pred_false if membership can be decided early
5116 % interval closures already dealt with by closure_membership
5117 % maximal sets are also already dealt with by membership_custom_set
5118 reify_avl_membership(AVL,Element,Res,FullReification) :-
5119 is_avl_simple_set(AVL,Type),
5120 preferences:preference(use_clpfd_solver,true), % to do: require maybe only for integer type !?
5121 \+ ground_value(Element),
5122 !,
5123 reify_avl_mem2(Type,Element,AVL,Res,FullReification).
5124 reify_avl_membership(_,_,_,false).
5125
5126
5127 is_avl_simple_set(node(El,_True,_,_,_),Type) :- simple_type(El,Type).
5128 simple_type(int(_),integer).
5129 simple_type(fd(_,GS),global(GS)).
5130
5131
5132 reify_avl_mem2(integer,int(El),AVL,Res,FullReification) :-
5133 avl_min(AVL,int(Min)), avl_max(AVL,int(Max)),
5134 (reify_integer_avl_mem(AVL,Min,Max) % reify if AVL small enough
5135 -> avl_domain(AVL,R),project_avl_domain_on_fd(R,FDList),
5136 clpfd_reify_inlist(El,FDList,FDRes,Posted),
5137 propagate_fd_membership(FDRes,Res,inlist(El,FDList)),
5138 FullReification=Posted
5139 ; clpfd_interface:try_post_constraint((El in Min..Max) #<=> FDRes),
5140 propagate_not_membership(FDRes,Res,int(El,Min,Max)),
5141 FullReification=false
5142 ).
5143 % this could also be enabled with CLPFD = FALSE ?? no overflows are possible
5144 reify_avl_mem2(global(GS),fd(El,GS),AVL,Res,FullReification) :-
5145 avl_domain(AVL,R),project_avl_domain_on_fd(R,FDList),
5146 b_global_sets:b_get_fd_type_bounds(GS,Low,Up),
5147 (is_full_fdlist(FDList,Low,Up)
5148 -> Res=pred_true, % all the values are in the list; it must be a member
5149 % normally this should also be detected by clpfd_reify_inlist, unless no constraint was set up for El
5150 % 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
5151 FullReification=true
5152 ; clpfd_reify_inlist(El,FDList,FDRes,Posted),
5153 propagate_fd_membership(FDRes,Res,inlist(El,FDList)),
5154 FullReification=Posted
5155 ).
5156 %reify_avl_mem2(global(GS),fd(El,GS),AVL,Res) :-
5157 % avl_min(AVL,fd(Min,GS)), avl_max(AVL,fd(Max,GS)),
5158 % clpfd_interface:try_post_constraint((El in Min..Max) #<=> FDRes),
5159 % propagate_not_membership(FDRes,Res,fd(El,GS,Min,Max)).
5160
5161 % assumes list is sorted
5162 is_full_fdlist(List,Low,Up) :- integer(Up), is_full_fdlist2(List,Low,Up).
5163 is_full_fdlist2([],Low,Up) :- Low>Up.
5164 is_full_fdlist2([Low|T],Low,Up) :- L1 is Low+1, is_full_fdlist2(T,L1,Up).
5165
5166 % check if avl small enough to call clpfd_reify_inlist
5167 reify_integer_avl_mem(_AVL,Min,Max) :- MaxSizeM1 is Max-Min, MaxSizeM1 =< 20,!.
5168 reify_integer_avl_mem(AVL,_Min,_Max) :- avl_height_less_than_with_solver_strength(AVL,5).
5169
5170
5171
5172 project_avl_domain_on_fd([],[]).
5173 project_avl_domain_on_fd([H|T],[PH|PT]) :- project_avl_domain(H,PH), project_avl_domain_on_fd(T,PT).
5174 project_avl_domain(int(X),X).
5175 project_avl_domain(fd(X,_),X).
5176
5177
5178 :- block propagate_fd_membership(-,-,?).
5179 % if we make it propagate_fd_membership(-,-?) Bosch examples becomes much slower ?
5180 % Indeed: membership_custom_set will already force membership or non-membership !
5181 %propagate_fd_membership(X,M,Info) :- var(X),!, print(propagate_fd(X,M,Info)),nl, (M=pred_true ->X=1 ; X=0).
5182 propagate_fd_membership(1,pred_true,_Info).
5183 propagate_fd_membership(0,pred_false,_Info).
5184
5185 :- block propagate_not_membership(-,?,?).
5186 propagate_not_membership(1,_,_). % there could be elements in the interval which are not in the set
5187 propagate_not_membership(0,Res,_Info) :-
5188 Res=pred_false.
5189
5190 % -----------------
5191
5192 % fails if not possible to quickly compute approximate size
5193 quick_custom_explicit_set_approximate_size(V,_) :- var(V),!,fail.
5194 quick_custom_explicit_set_approximate_size(avl_set(AVL),Size) :- !,
5195 quick_avl_approximate_size(AVL,Size).
5196 quick_custom_explicit_set_approximate_size(CS,Size) :-
5197 card_for_specific_custom_set(CS,Size,Code),
5198 on_enumeration_warning(call(Code),fail),
5199 atomic(Size). % inf or number; sometimes card_for_specific_custom_set can return a variable
5200
5201 :- use_module(clpfd_lists,[try_get_fd_value_list/4, get_fd_value/3, in_fd_value_list_wf/4]).
5202 % a membership propagation, but only done if it can be done quickly
5203
5204
5205 % quick_propagation_element_information(Set, Element, WF, PossiblyCompiledSet)
5206 % use last element for next iteration if you call quick_propagation_element_information in a loop
5207 :- block quick_propagation_element_information(-,?,?,?).
5208 quick_propagation_element_information(Set,_El,_,R) :-
5209 preferences:preference(use_clpfd_solver,false),
5210 !, R=Set.
5211 quick_propagation_element_information(avl_set(AVL),Element,WF,NewSet) :- !,
5212 quick_avl_approximate_size(AVL,Size),
5213 NewSet=avl_set_with_size(AVL,Size),
5214 propagate_avl_element_information_direct(Element,AVL,Size,WF).
5215 quick_propagation_element_information(avl_set_with_size(AVL,Size),Element,WF,NewSet) :- !,
5216 NewSet = avl_set_with_size(AVL,Size),
5217 propagate_avl_element_information_direct(Element,AVL,Size,WF).
5218 quick_propagation_element_information(closure(P,T,B),Element,WF,NewSet) :- !,
5219 NewSet = closure(P,T,B),
5220 ? element_of_closure(Element,P,T,B,WF).
5221 quick_propagation_element_information(fd_value_list(FDList,GroundList,Type),El,WF,NewSet) :- !,
5222 NewSet = fd_value_list(FDList,GroundList,Type),
5223 get_fd_value(Type,El,ElFD),
5224 in_fd_value_list_wf(GroundList,ElFD,FDList,WF).
5225 quick_propagation_element_information(Set,El,WF,NewSet) :-
5226 ? try_get_fd_value_list(Set,Type,FDList,GroundList),!,
5227 FDList \= [], % if list is empty membership fails
5228 NewSet = fd_value_list(FDList,GroundList,Type),
5229 % clpfd_inlist requires list of integers as second argument
5230 ? get_fd_value(Type,El,ElFD),
5231 % We could apply filter_non_matching_elements here
5232 in_fd_value_list_wf(GroundList,ElFD,FDList,WF).
5233 quick_propagation_element_information(Set,_,_,Set).
5234
5235 % -----------------
5236
5237 % infer information about an element of an AVL set
5238 propagate_avl_element_information(Element,AVL,Size,WF) :-
5239 (preferences:preference(use_clpfd_solver,true)
5240 ? -> propagate_avl_element_information_direct(Element,AVL,Size,WF)
5241 ; true).
5242
5243 propagate_avl_element_information_direct(Element,AVL,Size,WF) :-
5244 (Size<100 -> %30 which magic constant to use here; use larger value in SMT mode ?
5245 ? propagate_avl_element_information_small(Element,AVL,WF)
5246 ; is_avl_fd_index_set(AVL,Type) ->
5247 propagate_avl_element_information_large(Type,Element,AVL),
5248 (Size < 4000, nonvar(Element), Element = (_,_) % another magic constant
5249 -> Prio is Size // 60,
5250 get_wait_flag(Prio,propagate_avl_element_information(Element),WF,LWF),
5251 propagate_avl_el_large_block(Element,AVL,WF,LWF) % will do precise propagation
5252 ; true)
5253 ; true).
5254 % TO DO: we could call in_nat_range_wf; this way it would also work in non-CLPFD mode
5255
5256 :- block propagate_avl_el_large_block(?,?,?,-).
5257 propagate_avl_el_large_block((A,B),_,_,_) :-
5258 (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
5259 !.
5260 propagate_avl_el_large_block(Element,AVL,WF,_LWF) :-
5261 % TO DO: maybe look if we should not use clpfd_list, but only upper & lower bound
5262 ? propagate_avl_element_information_small(Element,AVL,WF). % will do precise propagation.
5263
5264 :- use_module(clpfd_lists,[avl_fd_value_check/4]).
5265 :- use_module(clpfd_interface,[catch_and_ignore_clpfd_overflow/2]).
5266 propagate_avl_element_information_small(Element,AVL,WF) :-
5267 ? catch_and_ignore_clpfd_overflow(propagate_avl_element_information_small, % relevant test e.g. 1708 (with used_ids_defined_by_equality)
5268 avl_fd_value_check(AVL,Element,WF,_FullyChecked)).
5269
5270 propagate_avl_element_information_large(Type,El,AVL) :-
5271 avl_min(AVL,Min), avl_max(AVL,Max),
5272 % if Size small enough and smaller than Max-Min we call clpfd_inlist on domain
5273 % Note: overflows should be caught below; we could check that Min/Max are within CLPFD range
5274 couple_prj1_in_range(Type,El,Min,Max).
5275
5276 couple_prj1_in_range(integer,int(El),int(Min),int(Max)) :- clpfd_interface:clpfd_inrange(El,Min,Max).
5277 couple_prj1_in_range(global(GS),fd(El,GS),fd(Min,GS),fd(Max,GS)) :- clpfd_interface:clpfd_inrange(El,Min,Max).
5278 couple_prj1_in_range(couple_prj1(T),(El,_),(Min,_),(Max,_)) :- couple_prj1_in_range(T,El,Min,Max).
5279 couple_prj1_in_range(rec_first_field(Name,T),rec([field(Name,El)|TF]),
5280 rec([field(Name,Min)|TMin]),rec([field(Name,Max)|_])) :-
5281 (var(TF)
5282 -> copy_field_names(TMin,TF) % if Fields not yet instantiated: copy over all fields
5283 ; true),
5284 couple_prj1_in_range(T,El,Min,Max).
5285
5286 copy_field_names([],[]).
5287 copy_field_names([field(N,_)|T],[field(N,_)|CT]) :- copy_field_names(T,CT).
5288
5289 % check if the first component of the AVL elements of a type such that we can propagate FD information
5290 is_avl_fd_index_set(node(El,_True,_,_,_),Type) :-
5291 simple_index_type(El,Type).
5292 simple_index_type((El,_),couple_prj1(T)) :- simple_index_type(El,T).
5293 simple_index_type(int(_),integer).
5294 simple_index_type(fd(_,GS),global(GS)).
5295 simple_index_type(rec(Fields),rec_first_field(Name,T)) :- nonvar(Fields),
5296 Fields = [field(Name,El)|_],
5297 simple_index_type(El,T).
5298 %simple_index_type((int(_),_),couple_integer).
5299 %simple_index_type(((int(_),_),_),couple_couple_integer).
5300 %simple_index_type((fd(_,GS),_),couple_global(GS)).
5301
5302
5303 /* avoid instantiating non-normalised with normalised values leading to failure */
5304 :- assert_must_succeed((X=(fd(1,'Name'),fd(2,'Name')), A=node(X,true,0,empty,empty),
5305 custom_explicit_sets:safe_avl_member(X,A) )).
5306
5307 ?safe_avl_member(X,AVL) :- var(X), !, my_avl_member(X,AVL).
5308 %safe_avl_member((X,Y),AVL) :- !, safe_avl_member_pair(X,Y,AVL).
5309 safe_avl_member(Value,AVL) :- decompose_index(Value,Key,RestVal), !,
5310 ? avl_fetch_indexed(Value,Key,RestVal,AVL).
5311 safe_avl_member(X,AVL) :- ground_value(X), convert_to_avl_inside_set(X,AX), !, avl_fetch(AX,AVL).
5312 ?safe_avl_member(X,AVL) :- safe_avl_member_default_wf(X,AVL,no_wf_available).
5313
5314
5315 % this is a generalisation of safe_avl_member_pair
5316 % check if a value can be decomposed into an index and the rest of a value and the key is ground
5317 % it also works for records indexing on first field
5318 avl_fetch_indexed(Value,Key,RestVal,AVL) :-
5319 ground_value_or_field(Key),
5320 convert_value_or_field(Key,NormKey),
5321 !,
5322 (ground_value_or_field(RestVal),
5323 convert_to_avl_inside_set(Value,NormValue)
5324 -> avl_fetch(NormValue,AVL)
5325 ? ; avl_fetch_with_index(NormKey,AVL,RestValLookup),
5326 ? kernel_objects:equal_object(RestValLookup,RestVal,avl_fetch_indexed)
5327 ).
5328 avl_fetch_indexed(Value,_,_,AVL) :-
5329 ? safe_avl_member_default_wf(Value,AVL,no_wf_available).
5330
5331 convert_value_or_field(field(Name,Val),field(Name,NVal)) :- !,
5332 convert_to_avl_inside_set(Val,NVal).
5333 convert_value_or_field(Key,NormKey) :-
5334 convert_to_avl_inside_set(Key,NormKey).
5335
5336 % a version of safe_avl_member where the first argument is guaranteed to be ground
5337 % somehow using this seems to slow-down evaluation for vesg_Dec12; Caching ??
5338 %safe_avl_member_ground(X,AVL) :-
5339 % convert_to_avl_inside_set(X,AX), !, avl_fetch(AX,AVL).
5340 %safe_avl_member_ground((X,Y),AVL) :- !, avl_member_pair_arg1_ground(X,Y,AVL).
5341 %safe_avl_member_ground(X,AVL) :- safe_avl_member_default_wf(X,AVL,no_wf_available).
5342
5343
5344 safe_avl_member_pair(X,Y,AVL) :- safe_avl_member_pair_wf(X,Y,AVL,no_wf_available).
5345
5346 safe_avl_member_pair_wf(X,Y,AVL,_WF) :- ground_value(X),!,
5347 ( ground_value(Y),
5348 convert_to_avl_inside_set((X,Y),AX)
5349 -> avl_fetch(AX,AVL)
5350 ; avl_member_pair_arg1_ground(X,Y,AVL)). % TODO: pass WF
5351 safe_avl_member_pair_wf(X,Y,AVL,WF) :- safe_avl_member_default_wf((X,Y),AVL,WF).
5352
5353 % can be used to try and lookup a function value without creating WD errors, ...
5354 % used in b_compiler to compile function applications
5355 try_apply_to_avl_set(X,Y,AVL) :- ground_value(X),
5356 ? avl_member_pair_arg1_ground(X,Y,AVL).
5357
5358 %safe_avl_member_pair_ground(X,Y,AVL) :- convert_to_avl_inside_set((X,Y),AX),!, avl_fetch(AX,AVL).
5359 %safe_avl_member_pair_ground(X,Y,AVL) :- avl_member_pair_arg1_ground(X,Y,AVL).
5360
5361 avl_member_pair_arg1_ground(X,Y,AVL) :- convert_to_avl_inside_set(X,AX), !,
5362 get_template(Y,RY,ToUnifyAfter),
5363 ? avl_fetch_pair(AX,AVL,RY),
5364 unify_after_wf(ToUnifyAfter,no_wf_available). %kernel_objects:equal_object(RY,Y).
5365 avl_member_pair_arg1_ground(X,Y,AVL) :-
5366 safe_avl_member_default((X,Y),AVL).
5367
5368 ?safe_avl_member_default(X,AVL) :- safe_avl_member_default_wf(X,AVL,no_wf_available).
5369 %safe_avl_member_default(PP,X,AVL) :-
5370 % debug:timer_call(safe_avl_member_default(PP),custom_explicit_sets:safe_avl_member_default1(X,AVL)).
5371 safe_avl_member_default_wf(X,AVL,WF) :- %statistics(runtime,_),
5372 get_template(X,Template,ToUnifyAfter),
5373 ? my_avl_member(Template,AVL),
5374 % statistics(runtime,[_,T2]), print(avl_member(Template,T2)),nl,
5375 ? unify_after_wf(ToUnifyAfter,WF). % kernel_objects:equal_object(Template,X)).
5376
5377 unify_after_wf([],_).
5378 ?unify_after_wf([A/B|T],WF) :- kernel_objects:equal_object_wf(A,B,unify_after,WF),
5379 ? unify_after_wf(T,WF).
5380
5381
5382
5383 get_template(A,R,ToUnifyAfter) :-
5384 (var(A) -> ToUnifyAfter=[A/R]
5385 ; get_template2(A,R,ToUnifyAfter) -> true
5386 ; add_internal_error('Could_not_get_template: ',get_template(A,R,_))).
5387
5388 get_template2((A,B),(TA,TB),ToUnifyAfter) :- get_template(A,TA,ToUnifyAfter1), get_template(B,TB,ToUnifyAfter2),
5389 append(ToUnifyAfter1,ToUnifyAfter2,ToUnifyAfter). % TO DO: use DifferenceLists / DCG
5390 get_template2(int(X),int(X),[]).
5391 get_template2(fd(A,B),fd(A,B),[]).
5392 get_template2([],[],[]).
5393 get_template2(pred_false /* bool_false */,pred_false /* bool_false */,[]).
5394 get_template2(pred_true /* bool_true */,pred_true /* bool_true */,[]).
5395 get_template2([H|T],R,ToUnifyAfter) :-
5396 (ground_value(H),ground_value(T)
5397 -> convert_to_avl_inside_set([H|T],R),ToUnifyAfter=[]
5398 ; ToUnifyAfter=[[H|T]/R]).
5399 % ; R=avl_set(A), ToUnifyAfter=[[H|T]/avl_set(A)]).
5400 get_template2(closure(P,T,B),R,[]) :- ground_value(closure(P,T,B)),
5401 expand_closure_to_avl_wf(P,T,B,R,no_wf_available),!.
5402 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 ?
5403 %get_template2(closure_x(_,_,_),_AVL_OR_EMPTY).
5404 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 ??
5405 get_template2(string(X),string(X),[]).
5406 get_template2(term(X),term(X),[]).
5407 get_template2(freetype(X),R,[]) :- convert_to_avl_inside_set(freetype(X),R).
5408 get_template2(rec(Fields),rec(TFields),ToUnifyAfter) :- get_fields_template(Fields,TFields,ToUnifyAfter).
5409 get_template2(freeval(ID,Case,Value),freeval(ID,Case,TValue),ToUnifyAfter) :- get_template(Value,TValue,ToUnifyAfter).
5410 get_template2(global_set(GS),R,[]) :- convert_to_avl_inside_set(global_set(GS),R).
5411
5412
5413 get_fields_template(A,R,[rec(A)/rec(R)]) :- var(A),!.
5414 get_fields_template([],[],ToUnifyAfter) :- !, ToUnifyAfter=[].
5415 get_fields_template([field(Name,Val)|T],[field(Name,TVal)|TT],ToUnifyAfter) :- nonvar(Name),!,
5416 get_template(Val,TVal,ToUnifyAfter1),
5417 get_fields_template(T,TT,ToUnifyAfter2), append(ToUnifyAfter1,ToUnifyAfter2,ToUnifyAfter).
5418 get_fields_template(A,R,[rec(A)/rec(R)]).
5419
5420
5421 % succeed if we can decide membership of an avl_set on the spot
5422 quick_test_avl_membership(AVL,X,Res) :-
5423 element_can_be_added_or_removed_to_avl(X),
5424 convert_to_avl_inside_set(X,AX),
5425 (avl_fetch(AX,AVL) -> Res=pred_true ; Res=pred_false).
5426
5427 % ---------------------
5428
5429 % a dispatch predicate
5430 my_avl_member(Key,AVL) :-
5431 (preferences:preference(randomise_enumeration_order,true)
5432 ? -> random_avl_member(Key,AVL) ; avl_member_opt(Key,AVL)).
5433 :- use_module(library(random),[random/3]).
5434 ?random_avl_member(Key,AVL) :- avl_height(AVL,Height), H1 is Height+1, random_avl_member(Key,H1,AVL).
5435 % 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)
5436 random_avl_member(Key, H, node(K,_,_,L,R)) :-
5437 random(1,H,1), !, H1 is H-1,
5438 (Key=K ; random_avl_member(Key,H1,L) ; random_avl_member(Key,H1,R)).
5439 random_avl_member(Key, H, node(K,_,_,L,R)) :- random(1,3,1), !, H1 is H-1,
5440 ? (random_avl_member(Key,H1,L) ; random_avl_member(Key,H1,R) ; Key=K).
5441 random_avl_member(Key, H, node(K,_,_,L,R)) :- H1 is H-1,
5442 ? (random_avl_member(Key,H1,R) ; random_avl_member(Key,H1,L) ; Key=K).
5443
5444 % a variation of avl_member from library(avl) which tries to avoid leaving choice points behind
5445 avl_member_opt(Key, node(K,_,_,L,R)) :-
5446 ? ( avl_member_opt(Key, L)
5447 ; R=empty -> Key = K % avoid trailing choice_point
5448 ? ; (Key=K ; avl_member_opt(Key, R))
5449 ).
5450
5451 % ---------------------
5452
5453 :- use_module(kernel_objects,[check_element_of_wf/3,not_element_of_wf/3]).
5454 :- use_module(memoization,[element_of_memoization_closure/6]).
5455 element_of_special_closure(interval(LOW,UP),X,WF,_,_,_) :- !,
5456 %hit_profiler:add_profile_hit(in_nat_range(X,LOW,UP,CondClosure)),
5457 kernel_objects:in_nat_range_wf(X,int(LOW),int(UP),WF).
5458 element_of_special_closure(member_closure(_ID,_Type,VAL),X,WF,_,_,_) :-
5459 (VAL=value(_) ; VAL = cartesian_product(b(value(A),_,_),b(value(B),_,_))),!,
5460 %hit_profiler:add_profile_hit(in_member_closure(X,Par,Typ,Body)),
5461 (VAL=value(Set) -> check_element_of_wf(X,Set,WF)
5462 ; X=(XA,XB),
5463 ? kernel_objects:check_element_of_wf(XA,A,WF),
5464 kernel_objects:check_element_of_wf(XB,B,WF)).
5465 element_of_special_closure(not_member_closure(_ID,_Type,value(Set)),X,WF,_,_,_) :- !,
5466 %hit_profiler:add_profile_hit(in_not_member_closure(X,Par,Typ,Set)),
5467 not_element_of_wf(X,Set,WF).
5468 % we used to have to add enumerator, as not_element_of does not instantiate; e.g. relevant when doing X :: GS - {y}
5469 % This is no longer required
5470 % see test 6 (../prob_examples/public_examples/B/FeatureChecks/NotMemberCheck.mch)
5471 element_of_special_closure(recursive_special_closure(RId),X,WF,Parameters,PT,CondClosure) :- !,
5472 add_recursive_parameter(Parameters,PT,X,RId,CondClosure,NewParameters,NewPT,Value,WF),
5473 ? element_of_normal_closure(Value,NewParameters,NewPT,CondClosure,WF).
5474 element_of_special_closure(memoization_closure(MemoID),X,WF,P,T,B) :- !,
5475 element_of_memoization_closure(MemoID,X,WF,P,T,B).
5476 element_of_special_closure(_,X,WF,Parameters,PT,CondClosure) :-
5477 % none of the special cases above apply after all
5478 ? element_of_normal_closure(X,Parameters,PT,CondClosure,WF).
5479
5480 :- block element_of_closure(?,-,?,?,?), element_of_closure(?,?,?,-,?).
5481 % element_of_closure(X,Para,T,Body,_WF): check if X is a member of closure(Para,T,Body)
5482 element_of_closure(X,Parameters,PT,CondClosure,WF) :-
5483 is_special_closure(Parameters,PT,CondClosure, SpecialClosure),!,
5484 %print_term_summary(element_of_special_closure(SpecialClosure,X,WF,Parameters,PT,CondClosure)), trace_in_debug_mode,
5485 ? element_of_special_closure(SpecialClosure,X,WF,Parameters,PT,CondClosure).
5486 element_of_closure(X,Parameters,PT,CondClosure,WF) :-
5487 %print_term_summary(element_of_normal_closure(X,Parameters,PT,CondClosure,WF)), trace_in_debug_mode,
5488 ? element_of_normal_closure(X,Parameters,PT,CondClosure,WF).
5489 element_of_normal_closure(X,Parameters,PT,CondClosure,WF) :-
5490 %hit_profiler:add_profile_hit(element_of_closure(X,Parameters,PT,CondClosure)),
5491 same_length(Parameters,ParValues),
5492 convert_list_into_pairs(ParValues,X),
5493 ? b_test_closure_wo_enum(Parameters,PT,CondClosure,ParValues,WF).
5494
5495 :- use_module(store,[set_up_localstate/4]).
5496 :- block b_test_closure_wo_enum(?,?,-,?,?).
5497 b_test_closure_wo_enum(Parameters,ParameterTypes,ClosurePred,ParValues,WF) :-
5498 % same_length(Parameters,ParValues), % not necessary
5499 set_up_localstate(Parameters,ParValues,[],LocalState),
5500 ? b_enumerate:b_type_values_in_store(Parameters,ParameterTypes,LocalState),
5501 copy_wf_start(WF,b_test_closure_wo_enum(Parameters),InnerWF),
5502 % avoid that WF0 actions triggered before we have had a chance to traverse the expression
5503 ? b_test_boolean_expression(ClosurePred,LocalState,[],InnerWF),
5504 ? copy_wf_finish(WF,InnerWF).
5505
5506 % recursive identifier to list of parameters with body as value
5507 % NewValue is the Value that should be checked for membership in the adapted closure; it has one argument more
5508 add_recursive_parameter(Parameters,Types,Value,TId,CondClosure,NewParameters,NewTypes,NewValue,WF) :-
5509 TId = b(identifier(RId),SetType,_), % unification replaces: get_texpr_id(TId,RId), get_texpr_type(TId,SetType),
5510 append(Parameters,[RId],NewParameters),
5511 append(Types,[SetType],NewTypes),
5512 %tools_printing:print_term_summary(recursion(Value)),nl,
5513 % TO DO check some variant decreases
5514 (kernel_waitflags:pending_abort_error(WF)
5515 -> NewValue = (_,_) % prevent further expansion of recursion, in case WD error in recursive function
5516 % TO DO: detect whether WD error occurs within recursive function,
5517 % 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
5518 ,debug_println(19,stopping_recursion_due_to_wd_error)
5519 ; NewValue = (Value,closure(Parameters,Types,CondClosure))
5520 ).
5521
5522
5523 % same as above, but without a waitflag
5524 ?element_of_custom_set(X,CS) :- element_of_custom_set2(CS,X).
5525
5526 element_of_custom_set2(global_set(GS),X) :- !,element_of_global_set(X,GS).
5527 element_of_custom_set2(freetype(ID),_) :- is_maximal_freetype(ID),!. % freetypes are always maximal at the moment
5528 element_of_custom_set2(avl_set(AVL),X) :- !,
5529 safe_avl_member(X,AVL).
5530 element_of_custom_set2(CS,X) :- init_wait_flags(WF,[element_of_custom_set2]),
5531 element_of_custom_set_wf2(CS,X,WF),
5532 ? ground_wait_flags(WF).
5533
5534 % ---------------
5535
5536 % function application for closure
5537
5538 % same as check_element_of_wf but does not wait on Y:
5539 % should also work for relation ??
5540
5541 check_element_of_function_closure(X,Y,Parameters,PT,CondClosure,WF) :-
5542 is_special_closure(Parameters,PT,CondClosure, SpecialClosure),!, % this covers recursive closures
5543 ? element_of_special_closure(SpecialClosure,(X,Y),WF,Parameters,PT,CondClosure).
5544 check_element_of_function_closure(X,Y, P,T,ClosureBody, WF) :-
5545 % affects test 1312, unless we add s:seq(0..9) before calling num
5546 % a special rule which tries and avoid enumerating solutions to arguments of function application
5547 % usually a function application will either be given all arguments or maybe be used in inverse
5548 ? is_converted_lambda_closure(P,T,ClosureBody), %is_converted_non_recursive_lambda_closure(P,T,ClosureBody),
5549 % TO DO: also make this work for recursive closures by adding recursive args (see e.g. test 1302)
5550 is_lambda_closure(P,T,ClosureBody, OtherIDs, OtherTypes, DomainPred, EXPR),
5551 (debug:debug_level_active_for(4) ->
5552 print('Apply Fun : '), translate:print_bexpr(DomainPred), print(' | '), translate:print_bexpr(EXPR),nl,
5553 get_texpr_info(ClosureBody,I), print(info(I,WF)),nl,
5554 print_term_summary((X,Y)),nl %,trace
5555 ; true),
5556 !,
5557 % alternative: annotate X,Y as inner variable ?
5558 get_texpr_info(ClosureBody,BInfo),
5559 ? b_interpreter:set_up_typed_localstate2(OtherIDs,OtherTypes,BInfo,ParValues,_TypedVals,[],LocalState,positive),
5560 convert_list_into_pairs(ParValues,SingleParValue),
5561 kernel_objects:equal_object_wf(X,SingleParValue,check_element_of_function_closure,WF),
5562 (is_truth(DomainPred) -> true
5563 ; init_wait_flags(InnerWF,[check_element_of_function_closure]),
5564 %copy_wf01e_wait_flags(WF,InnerWF), % we could delay copying WF0 until after test_boolean_expression of DomainPred ?
5565 b_test_boolean_expression(DomainPred,LocalState,[],InnerWF),
5566 ? 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
5567 ground_value_check(X,GrX),
5568 (nonvar(GrX) -> copy_waitflag_store(InnerWF,WF) % block would trigger already
5569 ; ground_value_check(Y,GrY),
5570 (nonvar(GrY) -> copy_waitflag_store(InnerWF,WF) % block would trigger already
5571 ; get_last_wait_flag(check_element_of_function_closure(OtherIDs),WF,LastWF),
5572 block_copy_waitflag_store(InnerWF,WF,GrX,GrY,LastWF)
5573 )
5574 )
5575 ),
5576 ? b_interpreter:b_compute_expression(EXPR,LocalState,[],Y,WF).
5577 check_element_of_function_closure(X,Y, P,T,ClosureBody, WF) :-
5578 ? element_of_normal_closure((X,Y),P,T,ClosureBody,WF).
5579 % we could memoize on X here if /*@symbolic-memo */ pragma used and closure has special ID associated with it
5580
5581 :- block block_copy_waitflag_store(?,?,-,-,-).
5582 block_copy_waitflag_store(InnerWF,WF,_GrX,_GrY,_LWF) :-
5583 % copy waitflags from InnerWF store to WF
5584 copy_waitflag_store(InnerWF,WF).
5585
5586 /* -------------- */
5587 /* NOT_ELEMENT_OF */
5588 /* -------------- */
5589
5590 :- use_module(kernel_objects,[not_element_of_global_set/2]).
5591
5592 not_element_of_custom_set_wf(X,CS,WF) :-
5593 ? not_element_of_custom_set_wf2(CS,X,WF).
5594
5595 not_element_of_custom_set_wf2(global_set(GS),X,_WF) :- not_element_of_global_set(X,GS).
5596 not_element_of_custom_set_wf2(freetype(_),_,_) :- !,fail. % TO DO: what if we have List(1..3) ? can that occur ??
5597 not_element_of_custom_set_wf2(avl_set(node(Y,_,_,empty,empty)),X,WF) :- !,
5598 % X /: {Y} <=> X /= Y
5599 ? kernel_objects:not_equal_object_wf(X,Y,WF). % improve if X is ground
5600 not_element_of_custom_set_wf2(avl_set(AVL),X,_WF) :- !,
5601 ground_value_check(X,GrX),
5602 ? propagate_avl_not_element_information(X,GrX,AVL),
5603 not_element_of_avl_set_block(GrX,X,AVL).
5604 not_element_of_custom_set_wf2(closure(Parameters,PT,Cond),X,WF) :-
5605 closure_not_member(X,Parameters,PT,Cond,WF).
5606
5607 :- block not_element_of_avl_set_block(-,?,?).
5608 not_element_of_avl_set_block(_,X,AVL) :-
5609 convert_to_avl_inside_set(X,CX),
5610 \+ avl_fetch(CX,AVL). %% IMPROVE ??
5611
5612 propagate_avl_not_element_information(_,GrEl,_) :- nonvar(GrEl),!.
5613 propagate_avl_not_element_information(Element,_,AVL) :- preferences:preference(use_clpfd_solver,true),
5614 is_avl_simple_set(AVL,Type), % integer or global(GS) \+ground(Element) ,
5615 ((Type=integer -> avl_height_less_than_with_solver_strength(AVL,6) % 16-31 elements - was: avl_size<20
5616 ; true)
5617 -> !,
5618 ? propagate_avl_not_element_information3(Type,Element,AVL) % uses clpfd_not_inlist
5619 ; Type=integer, avl_height_less_than_with_solver_strength(AVL,15),
5620 avl_is_interval(AVL,Min,Max)
5621 -> !,
5622 kernel_objects:not_in_nat_range(Element,int(Min),int(Max)) % WF not used anyway in _wf version
5623 ).
5624 propagate_avl_not_element_information(_Element,_,AVL) :-
5625 quick_definitely_maximal_set_avl(AVL),
5626 !, % we require something not to be an element of the full set; impossible
5627 fail.
5628 % to do: check if all but one element is in set
5629 propagate_avl_not_element_information(_,_,_).
5630
5631 avl_height_less_than_with_solver_strength(AVL,Limit) :- preference(solver_strength,SS),
5632 RealLimit is Limit + SS/100,
5633 avl_height_less_than(AVL,RealLimit).
5634
5635 % try and compute a small finite cardinality for a ground value; fail if not possible
5636 try_get_finite_max_card_from_ground_value(pred_true,2).
5637 try_get_finite_max_card_from_ground_value(pred_false,2).
5638 try_get_finite_max_card_from_ground_value(fd(_,Type),Card) :-
5639 b_global_sets:b_fd_card(Type,Card), integer(Card).
5640 try_get_finite_max_card_from_ground_value((A,B),Card) :-
5641 try_get_finite_max_card_from_ground_value(A,CA),
5642 try_get_finite_max_card_from_ground_value(B,CB),
5643 Card is CA*CB,
5644 Card < 20000.
5645 try_get_finite_max_card_from_ground_value(rec(Fields),Card) :-
5646 try_get_finite_max_card_from_fields(Fields,Card).
5647 try_get_finite_max_card_from_ground_value(freeval(FreetypeId,_CaseId,_EArgs),Card) :-
5648 freetype_cardinality(FreetypeId,Card), number(Card), Card < 20000.
5649 try_get_finite_max_card_from_ground_value(avl_set(node(El,_True,_,_,_)),Card) :-
5650 try_get_finite_max_card_from_ground_value(El,CEl),
5651 CEl < 16,
5652 safe_pow2(CEl,Card).
5653 % int(_), term(floating(_)), string(_) are all infinite
5654
5655 try_get_finite_max_card_from_fields([],1).
5656 try_get_finite_max_card_from_fields([field(_,A)|TF],Card) :-
5657 try_get_finite_max_card_from_ground_value(A,CA),
5658 try_get_finite_max_card_from_fields(TF,CB),
5659 Card is CA*CB,
5660 Card < 20000.
5661
5662 :- use_module(b_global_sets,[get_global_type_value/3]).
5663 propagate_avl_not_element_information3(integer,int(El),AVL) :-
5664 avl_domain(AVL,R),project_avl_domain_on_fd(R,FDList),
5665 clpfd_interface:clpfd_not_inlist(El,FDList).
5666 propagate_avl_not_element_information3(global(GS),FD,AVL) :-
5667 get_global_type_value(FD,GS,El), % sets up the FD constraint if var; maybe we can detect inconsistency straightaway below
5668 avl_domain(AVL,R),project_avl_domain_on_fd(R,FDList), % maybe we can compute directly the complement ?
5669 ? clpfd_interface:clpfd_not_inlist(El,FDList).
5670
5671
5672 :- block closure_not_member(?,-,?,?,?).
5673 %, closure_not_member(-,?,?,?,?). /* El is unlikely to be instantiated by not_element_of test , but test 6 requires commenting out block declaration */
5674
5675 closure_not_member(X,Parameters,Types,Body,WF) :-
5676 is_special_closure(Parameters,Types,Body,SpecialClosure),!,
5677 not_element_of_special_closure(SpecialClosure,X,WF,Parameters,Types,Body).
5678 closure_not_member(El,Parameters,PT,Cond,WF) :-
5679 normal_closure_not_member(El,Parameters,PT,Cond,WF).
5680
5681 :- use_module(memoization,[not_element_of_memoization_closure/6]).
5682 not_element_of_special_closure(interval(LOW,UP),X,_WF,_Parameters,_Types,_Body) :-
5683 !,kernel_objects:not_in_nat_range(X,int(LOW),int(UP)).
5684 not_element_of_special_closure(member_closure(_ID,_Type,VAL),X,WF,_Parameters,_Types,_Body) :-
5685 ( VAL = value(_)
5686 ; VAL = cartesian_product(b(value(A),_,_),b(value(B),_,_))),!,
5687 %hit_profiler:add_profile_hit(member(X,Par,Typ,Body)),
5688 ( VAL=value(Set) -> kernel_objects:not_element_of_wf(X,Set,WF)
5689 ; kernel_objects:not_is_cartesian_pair(X,A,B,WF)).
5690 not_element_of_special_closure(not_member_closure(_ID,_Type,value(Set)),X,WF,_Parameters,_Types,_Body) :-
5691 !,kernel_objects:check_element_of_wf(X,Set,WF).
5692 not_element_of_special_closure(memoization_closure(MemoID),X,WF,P,T,B) :- !,
5693 not_element_of_memoization_closure(MemoID,X,WF,P,T,B).
5694 not_element_of_special_closure(recursive_special_closure(RId),X,WF,Parameters,Types,Body) :-
5695 !,
5696 add_recursive_parameter(Parameters,Types,X,RId,Body,NewParameters,NewPT,Value,WF),
5697 normal_closure_not_member(Value,NewParameters,NewPT,Body,WF).
5698
5699 not_element_of_special_closure(SC,_X,_WF,Parameters,Types,Body) :-
5700 SC \= interval(_,_),
5701 SC \= not_member_closure(_,_,_),
5702 is_definitely_maximal_closure(Parameters,Types,Body),
5703 !,
5704 fail.
5705 not_element_of_special_closure(_,X,WF,Parameters,Types,Body) :-
5706 % falling back to normal test
5707 normal_closure_not_member(X,Parameters,Types,Body,WF).
5708
5709 :- use_module(library(lists),[same_length/2]).
5710
5711 normal_closure_not_member(El,Parameters,PT,Cond,WF) :-
5712 %hit_profiler:add_profile_hit(closure_not_member(El,Parameters,PT,Cond,WF)),
5713 same_length(Parameters,ParValues),
5714 convert_list_into_pairs(ParValues,El),
5715 b_not_test_closure_wf(Parameters,PT,Cond,ParValues,WF).
5716
5717
5718
5719
5720 /* -------------------------- */
5721 /* VARIOUS CLOSURE PREDICATES */
5722 /* -------------------------- */
5723
5724
5725 :- use_module(tools,[convert_list_into_pairs/2]).
5726 :- use_module(b_interpreter,[b_test_boolean_expression/4, b_not_test_boolean_expression/4]).
5727 :- use_module(b_enumerate).
5728
5729 :- assert_pre(custom_explicit_sets:expand_closure_to_list(_,_,ClosureBody,_Result,_Done,_,_WF),
5730 (nonvar(ClosureBody),
5731 bsyntaxtree:check_if_typed_predicate(ClosureBody))).
5732 :- assert_post(custom_explicit_sets:expand_closure_to_list(_,_,_,Result,_Done,_,_WF),
5733 b_interpreter:value_type(Result)).
5734
5735 :- block expand_interval_closure_to_avl(-,?,?), expand_interval_closure_to_avl(?,-,?).
5736 expand_interval_closure_to_avl(Low,Up,Result) :-
5737 Delta is Up-Low,
5738 (Delta>9999 -> perfmessage(expanding_interval(Low,Up)) ; true),
5739 construct_interval_ord_list(Low,Up,OL),
5740 ord_list_to_avlset_direct(OL,ARes,expand_interval),
5741 ? equal_object(ARes,Result,expand_interval_closure_to_avl).
5742 construct_interval_ord_list(Low,Up,Res) :-
5743 (Low>Up -> Res = []
5744 ; Res = [int(Low)-true|T], L1 is Low+1, construct_interval_ord_list(L1,Up,T)
5745 ).
5746
5747 :- block expand_interval_closure_to_list(-,?,?,?), expand_interval_closure_to_list(?,-,?,?).
5748 expand_interval_closure_to_list(Low,Up,Result,Done) :-
5749 construct_interval_list(Low,Up,OL),
5750 ? equal_object(OL,Result,expand_interval_closure_to_list),
5751 Done=true.
5752 construct_interval_list(Low,Up,Res) :-
5753 (Low>Up -> Res = []
5754 ; Res = [int(Low)|T], L1 is Low+1, construct_interval_list(L1,Up,T)
5755 ).
5756
5757 expand_closure_to_list([X],[integer],Body,Result,Done,_,_) :-
5758 ? is_interval_closure_body(Body,X,Low,Up),!,
5759 expand_interval_closure_to_list(Low,Up,Result,Done).
5760 expand_closure_to_list(Par,Types,Body,Result,Done,Source,WF) :-
5761 ? expand_normal_closure(Par,Types,Body,CResult,CDone,expand_closure_to_list(Source),WF),
5762 expand_if_avl(CResult,Result,CDone,Done,Source),
5763 lazy_check_elements_of_closure(Result,CDone, Par,Types,Body,WF).
5764
5765 % Note: does slow down test 1306 (91ms mc time becomes 918 ms)
5766 % as long as a closure has not been fully expanded, lazily check elements
5767 % that are instantiated from the outside satisfy the closure predicate
5768 % Note: this can also instantiate unknown values used inside the closure body
5769 lazy_check_elements_of_closure(Result,CDone, Par,Types,Body,WF) :-
5770 (WF==no_wf_available -> true
5771 ; lazy_check_elements6(Result,CDone, Par,Types,Body,WF),
5772 propagate_closure_body_value_set(Par,Types,Body,Result,CDone,WF)
5773 ).
5774 % TODO: check if closure is a non-ground projection-member closure and check elements
5775 :- block lazy_check_elements6(-,-, ?,?,?,?).
5776 lazy_check_elements6(_Result,CDone, _Par,_Types,_Body,_WF) :- nonvar(CDone),!.
5777 lazy_check_elements6([H|T],CDone, Par,Types,Body,WF) :- !,
5778 ? element_of_closure(H,Par,Types,Body,WF),
5779 ? lazy_check_elements6(T,CDone, Par,Types,Body,WF).
5780 lazy_check_elements6(avl_set(A),_CDone, Par,Types,Body,WF) :- !,
5781 avl_max(A,X),
5782 element_of_closure(X,Par,Types,Body,WF).
5783 % TO DO: also check avl_min or even all elements ?
5784 lazy_check_elements6(_,_,_,_,_,_).
5785
5786 :- use_module(probsrc(bsyntaxtree),[create_typed_ids/3]).
5787 % lazy check elements from non-var closure body against a result
5788 % for example if we have {x| TRUE |-> x : Value } = Result and Value is not-ground,
5789 % we can check that for all elements TRUE|->x of Value the corresponding x is in Result, see test 2466
5790 % slows down test 1987
5791 :- block propagate_closure_body_value_set(?,?,?,-,-,?).
5792 % we delay until the result is known, possibly in SMT mode it could be useful to propagate earlier
5793 propagate_closure_body_value_set(ParIDs,Types,Body,Result,CDone,WF) :-
5794 var(CDone), % the closure has not yet been fully expanded
5795 % check if this closure can profit from set membership propagation:
5796 b_interpreter:is_for_all_set_membership_predicate2(Body,ParIDs,ParIDs,UnmatchedIDs,Set,_Pattern,_ParValues,_),
5797 UnmatchedIDs=[],
5798 Set = b(value(_Value),_,_), % check that the set is a value; it must be non-ground, otherwise CDone would be true
5799 create_couple_term(ParIDs,Types,CoupleTerm),
5800 SetTerm=b(value(Result),any,[]),
5801 safe_create_texpr(member(CoupleTerm,SetTerm),pred,[],RHS),
5802 create_typed_ids(ParIDs,Types,TIDs),
5803 !,
5804 propagate_closure_body_for_all(TIDs,Body,RHS,Result,CDone,WF).
5805 propagate_closure_body_value_set(_,_,_,_,_,_WF).
5806
5807 :- block propagate_closure_body_for_all(?,?,?,-,-,?).
5808 propagate_closure_body_for_all(TIDs,Body,RHS,_,CDone,WF) :- var(CDone),!,
5809 add_debug_message(closure,'Propagating from closure body to result: ',Body,Body),
5810 Infos=[],
5811 b_interpreter:b_for_all(TIDs,Infos,Body,RHS,[],[],WF).
5812 propagate_closure_body_for_all(_,_,_,_Result,_CDone,_WF). % propagation not required; closure expanded, cf test 1987
5813
5814 %check_valid_avl(AVL,Origin) :-
5815 % (nonvar(AVL) -> true
5816 % ; add_internal_error('Var avl_set: ', check_valid_avl(AVL,Origin)),fail).
5817
5818 :- block expand_if_avl(?,?,-,?,?).
5819 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
5820 ? expand_custom_set_to_list2(avl_set(S),Result,Done,_,expand_if_avl(Source),no_wf_available).
5821 expand_if_avl(Res,Result,_,Done,Source) :- check_list(Res,expand_if_avl(Source)),
5822 ? equal_object(Res,Result), Done=true.
5823
5824 check_list(Res,_) :- nonvar(Res), is_list(Res),!.
5825 check_list(Res,Src) :- add_error(Src,'Could not expand to list: ',Res).
5826 is_list([]). is_list([_|_]).
5827
5828 expand_closure_to_avl_or_list([X],[integer],Body,Result,_CheckTimeouts,_WF) :-
5829 ? is_interval_closure_body(Body,X,Low,Up),!,
5830 expand_interval_closure_to_avl(Low,Up,Result).
5831 %expand_closure_to_avl_or_list(P,T,Body,Result,_WF) :- is_member_closure(P,T,Body,TS,Set),
5832 % print(expand_member_closure(P,T,Body,TS,Set)),nl,fail.
5833 expand_closure_to_avl_or_list(Par,Types,Body,Result,CheckTimeouts,WF) :-
5834 expand_normal_closure(Par,Types,Body,CResult,_Done,CheckTimeouts,WF),
5835 kernel_objects:equal_object(Result,CResult,expand_closure_to_avl_or_list). % may convert to AVL, should we wait for _Done?
5836
5837
5838 % use WF just for call stack messages; we should not delay creating result
5839 expand_closure_to_avl_wf([X],[integer],Body,Result,_WF) :-
5840 is_interval_closure_body(Body,X,Low,Up),!,
5841 expand_interval_closure_to_avl(Low,Up,Result). % we could pass WF
5842 expand_closure_to_avl_wf(Par,Types,Body,Result,WF) :-
5843 ? expand_normal_closure(Par,Types,Body,S,Done,check(expand_closure_to_avl),WF),
5844 (ground_value(S) % ground value is sufficient to proceed; we do not need to check Done
5845 -> convert_to_avl_inside_set(S,R),equal_object(R,Result,expand_closure_to_avl)
5846 ; print(cannot_convert_closure_value_to_avl(closure(Par,Types),done(Done))),nl,
5847 translate:print_bexpr(Body),nl,trace,
5848 fail).
5849
5850
5851 % possible values for CheckTimeouts: check, check_no_inf, no_check, ...
5852 % Note: we no longer check is_infinite_explicit_set(closure(Parameters,ParameterTypes,ClosureBody))
5853 % and no longer raise add_closure_warning(Source,Parameters,ParameterTypes,ClosureBody,'### WARNING: expanding infinite comprehension set: ')
5854 % and no longer use preference warn_when_expanding_infinite_closures
5855 % this is relevant for e.g., test 1291
5856 expand_normal_closure(Parameters,ParameterTypes,ClosureBody,Result,Done,CheckTimeouts,WF) :-
5857 ? expand_normal_closure_memo(CheckTimeouts,Parameters,ParameterTypes,ClosureBody,Result,Done,WF).
5858
5859 :- public add_closure_warning_wf/6.
5860 add_closure_warning_wf(Source,Parameters,_ParameterTypes,_ClosureBody,_MSG,_WF) :-
5861 preference(provide_trace_information,false),preference(strict_raise_warnings,false),!,
5862 format('### TIME-OUT raised during closure expansion (~w,~w).~n### set TRACE_INFO preference to TRUE for more details.~n',[Parameters,Source]).
5863 add_closure_warning_wf(Source,Parameters,ParameterTypes,ClosureBody,MSG,WF) :-
5864 (debug_mode(on) -> Limit = 2500, AvlLim=10 ; Limit = 500, AvlLim=5),
5865 preferences:temporary_set_preference(expand_avl_upto,AvlLim,CHNG),
5866 call_cleanup(translate:translate_bvalue_with_limit(closure(Parameters,ParameterTypes,ClosureBody),Limit,CT),
5867 preferences:reset_temporary_preference(expand_avl_upto,CHNG)),
5868 bsyntaxtree:get_texpr_info(ClosureBody,Infos),
5869 add_warning_wf(Source,MSG,CT,Infos,WF), debug_print(19,'! infos: '), debug_println(Infos). %,trace.
5870
5871
5872 :- use_module(memoization,[is_memoization_closure/4,get_complete_memoization_expansion/6]).
5873
5874 % a version of closure expansion which memoizes its results; stored_expansion needs to be cleared when new machine loaded
5875 expand_normal_closure_memo(CHECK,Parameters,ParameterTypes,ClosureBody,FullResult,Done,WF) :-
5876 ? is_memoization_closure(Parameters,ParameterTypes,ClosureBody,MemoID),
5877 !, Span=ClosureBody,
5878 % MemoID can be a variable
5879 (var(MemoID) -> perfmessage(CHECK,'Getting full value of a memoized function',ClosureBody) ; true),
5880 get_complete_memoization_expansion(MemoID,FullResult,Done,Span,expand_normal_closure_memo(CHECK),WF).
5881 expand_normal_closure_memo(CHECK,Parameters,ParameterTypes,ClosureBody,FullResult,Done,WF) :-
5882 preferences:preference(use_closure_expansion_memoization,false),!,
5883 ? expand_normal_closure2(CHECK,Parameters,ParameterTypes,ClosureBody,FullResult,Done,WF).
5884 expand_normal_closure_memo(CHECK,Parameters,ParameterTypes,ClosureBody,FullResult,Done,WF) :-
5885 % maybe we should only memo when ClosureWaitVars are ground ?
5886 MemoLookupTerm = closure(Parameters,ParameterTypes,ClosureBody),
5887 compute_memo_hash(MemoLookupTerm,Hash),
5888 % idea: maybe store expansion only on second hit ?
5889 (get_stored_memo_expansion(Hash,MemoLookupTerm,StoredResult)
5890 -> %print_term_summary(reusing_expansion(Hash,Parameters,ParameterTypes,ClosureBody,StoredResult)),nl,
5891 UPV=StoredResult, %state_packing:unpack_value(StoredResult,UPV),
5892 FullResult = UPV, Done=true
5893 ; %statistics(runtime,[T1,_]), %%
5894 expand_normal_closure2(CHECK,Parameters,ParameterTypes,ClosureBody,FullResult,Done,WF),
5895 %statistics(runtime,[T2,_]), Time is T2-T1, store_memo_computation_time(Hash,Time),
5896 (Done==true/* ,T2-T1>0*/
5897 -> PackedValue=FullResult, %state_packing:pack_value(FullResult,PackedValue),
5898 store_memo_expansion(Hash,MemoLookupTerm,PackedValue)
5899 ; true)
5900 ).
5901
5902
5903 expand_normal_closure2(_CHECK,Parameters,ParameterTypes,ClosureBody,FullResult,Done,WF) :-
5904 % TO DO: add more symbolic member closures who have expression computation code
5905 is_closure1_value_closure(Parameters,ParameterTypes,ClosureBody,VAL),!,
5906 ? bsets_clp:relational_trans_closure_wf(VAL,FullResult,WF),
5907 ground_value_check(FullResult,FRGr),
5908 when(nonvar(FRGr),Done=true).
5909 expand_normal_closure2(CHECK,Parameters,ParameterTypes,ClosureBody,FullResult,Done,WF) :-
5910 % special treatment for lambda closures: Advantage: we don't have to wait for variables in EXPR body of closure
5911 % Disadvantage: EXPR only gets evaluated after a solution has been found for args: can mean repeated computations !
5912 % (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
5913 % Advantage: it can solve constraints such as f = %x.(x:1..10|x+y) & f(5)=1005 (finding y without enumeration); see test 1168
5914 \+ preferences:preference(use_smt_mode,false),
5915 is_lambda_closure(Parameters,ParameterTypes,ClosureBody, OtherIDs,OtherTypes, DomainPred, EXPR),
5916 \+ ground_bexpr(EXPR), % if EXPR is ground, there is nothing to be gained by special treatment here
5917 WF \= no_wf_available, % otherwise we may have to enumerate EXPR result leading to choice points, e.g. in phase 0
5918 !,
5919 bexpr_variables(DomainPred,ClosureWaitVars),
5920 (CHECK=no_check -> TIMEOUTCODE = true ;
5921 TIMEOUTCODE = add_closure_warning_wf(CHECK,Parameters,ParameterTypes,ClosureBody,
5922 'TIME-OUT occurred while ProB was expanding: ',WF)),
5923 (CHECK=check_no_inf -> VIRTUALTIMEOUTCODE=true ; VIRTUALTIMEOUTCODE=TIMEOUTCODE),
5924 delay_setof_check_wf( ParTuple,
5925 (custom_explicit_sets:b_test_closure(OtherIDs,OtherTypes,DomainPred,OtherValues,all_solutions,WF),
5926 convert_list_into_pairs(OtherValues,ParTuple)
5927 % TO DO: compile EXPR when we start expanding the closure: to avoid repeated re-computation of expressions for every instance
5928 ),
5929 Result, ClosureWaitVars, __Done,
5930 TIMEOUTCODE,VIRTUALTIMEOUTCODE,WF,DomainPred),
5931 (WF = no_wf_available
5932 -> init_wait_flags(WF1,[expansion_context(lambda_function_result,Parameters)])
5933 ; WF1=WF
5934 ),
5935 evaluate_result_expr(Result,EXPR,OtherIDs,EvResult,EvDone,WF1),
5936 when(nonvar(EvDone),(
5937 (WF = no_wf_available -> ground_wait_flags(WF1) ; true),
5938 kernel_objects:equal_object_wf(EvResult,FullResult,expand_normal_closure2,WF),
5939 Done=true)).
5940 expand_normal_closure2(no_check,Parameters,ParameterTypes,ClosureBody,Result,Done,WF) :- !,
5941 expand_normal_closure_direct(Parameters,ParameterTypes,ClosureBody,Result,Done,WF).
5942 expand_normal_closure2(CHECK,Parameters,ParameterTypes,ClosureBody,Result,Done,WF) :-
5943 bexpr_variables(ClosureBody,ClosureWaitVars),
5944 TIMEOUTCODE = add_closure_warning_wf(CHECK,Parameters,ParameterTypes,ClosureBody,
5945 'TIME-OUT occurred while ProB was expanding: ',WF),
5946 (CHECK=check_no_inf -> VIRTUALTIMEOUTCODE=true ; VIRTUALTIMEOUTCODE=TIMEOUTCODE),
5947 % Note: delay_setof_check_wf will throw enumeration warning for virtual timeouts, after VIRTUALTIMEOUTCODE
5948 delay_setof_check_wf( ParTuple,
5949 custom_explicit_sets:test_closure_and_convert(Parameters,ParameterTypes,ClosureBody, ParTuple,WF),
5950 Result, ClosureWaitVars, Done, TIMEOUTCODE, VIRTUALTIMEOUTCODE,WF,ClosureBody).
5951
5952 expand_normal_closure_direct(Parameters,ParameterTypes,ClosureBody,Result,Done,WF) :-
5953 bexpr_variables(ClosureBody,ClosureWaitVars),
5954 Span = ClosureBody,
5955 delay_setof_wf( ParTuple,
5956 % TO DO: refresh waitflag in outer WF store to let pending code run to completion and avoid spurious WD errors ?
5957 custom_explicit_sets:test_closure_and_convert(Parameters,ParameterTypes,ClosureBody, ParTuple,WF),
5958 Result, ClosureWaitVars, Done,WF, Span).
5959
5960
5961
5962 :- block evaluate_result_expr(-,?,?,?,?,?).
5963 evaluate_result_expr(avl_set(AVL),EXPR,OtherIDs,Res,Done,WF) :-
5964 avl_domain(AVL,R),
5965 evaluate_result_expr(R,EXPR,OtherIDs,Res,Done,WF).
5966 evaluate_result_expr([],_EXPR,_OtherIDs,[],Done,_WF) :-
5967 %ground_wait_flags(WF),
5968 Done=true.
5969 evaluate_result_expr([ParTuple|T],EXPR,OtherIDs,[FullTuple|ET],Done,WF) :-
5970 % same_length(OtherIDs,ParValues), % not necessary
5971 set_up_localstate(OtherIDs,ParValues,[],LocalState),
5972 convert_list_into_pairs(ParValues,ParTuple), % bind values in ParTuple to LocalState
5973 b_interpreter:b_compute_expression(EXPR,LocalState,[],EXPRVALUE,WF),
5974 append(ParValues,[EXPRVALUE],FullValues),
5975 convert_list_into_pairs(FullValues,FullTuple),
5976 evaluate_result_expr(T,EXPR,OtherIDs,ET,Done,WF).
5977
5978 :- use_module(bsyntaxtree,[split_names_and_types/3]).
5979 :- use_module(probsrc(bsyntaxtree), [def_get_texpr_id/2]).
5980 %:- use_module(library(lists),[prefix_length/3, suffix_length/3]).
5981 % test a closure and convert into pairs; assume we want all solutions
5982 test_closure_and_convert(Parameters,ParameterTypes,ClosureBody, ParTuple, WF) :-
5983 ? is_recursive_closure(Parameters,ParameterTypes,ClosureBody),
5984 ? get_recursive_identifier_of_closure_body(ClosureBody,TRID),!,
5985 def_get_texpr_id(TRID,RID), get_texpr_type(TRID,RType),
5986 %print(test_recursion(RID)),nl, translate:nested_print_bexpr(ClosureBody),nl,
5987 RecVal = closure(Parameters,ParameterTypes,ClosureBody), % Recursive Value added to parameters
5988 same_length(Parameters,ParValues),
5989 reset_closure_solution_counter(Parameters),
5990 ? b_test_closure([RID|Parameters],[RType|ParameterTypes],ClosureBody,[RecVal|ParValues],all_solutions,WF),
5991 convert_sol_list_into_pairs(ParValues,Parameters,ParTuple). % convert tuple without recursive value to ParTuple
5992 test_closure_and_convert(Parameters,ParameterTypes,b(exists(EParAndTypes,ClosureBody),pred,OuterInfo), ParTuple, WF) :-
5993 % Motivation: enumerating Parameters can be quite inefficient
5994 % if for example we have something like {x|#y.(y:SmallSet & x=f(y))}
5995 % Problem: the existential quantifier will be delayed until the Parameters are instantiated !
5996 % relevant test: 1162
5997 % Note: this is duplicating to some extent the code in b_test_exists_wo_expansion
5998 % However, here we can also apply lambda_closure optimisation in b_test_closure below, this is
5999 % relevant for private_examples/2023/.../rule_FICHIER_MRGATKSAATPAR_RVF219_MRGA_DE.mch
6000 ? exists_should_be_lifted(Parameters,ParameterTypes,OuterInfo,ClosureBody),
6001 split_names_and_types(EParAndTypes,EPar,ETypes),
6002 !,
6003 % print(' Lifting existential quantifier (i.e., enumerating paras with closure paras): '), print(EPar),nl,
6004 % print(outer_paras(Parameters)),nl,
6005 % append Parameters at end; in case we have a lambda function
6006 append(EPar,Parameters,FullPar), length(Parameters,NrParas),
6007 append(ETypes,ParameterTypes,FullTypes),
6008 length(EPar,NrExistsParas),
6009 length(IrrelevantParas,NrExistsParas), length(Suffix,NrParas),
6010 append(IrrelevantParas,Suffix,FullParList),
6011 copy_identifier_infos(OuterInfo,ClosureBody,ClosureBody2),
6012 reset_closure_solution_counter(Parameters),
6013 % bsyntaxtree:check_used_ids_in_ast(ClosureBody2),
6014 ? b_test_closure(FullPar,FullTypes,ClosureBody2, FullParList,all_solutions,WF),
6015 convert_sol_list_into_pairs(Suffix,Parameters,ParTuple).
6016 test_closure_and_convert(Parameters,ParameterTypes,ClosureBody, ParTuple, WF) :-
6017 reset_closure_solution_counter(Parameters),
6018 % print(test),nl, translate:nested_print_bexpr(ClosureBody),nl,
6019 length(Parameters,Len), length(ParValues,Len),
6020 %(annotate_exists(Parameters,ParameterTypes,ClosureBody,Body2) -> true ; Body2=ClosureBody),
6021 ? b_test_closure(Parameters,ParameterTypes,ClosureBody,ParValues,all_solutions,WF),
6022 convert_sol_list_into_pairs(ParValues,Parameters,ParTuple). % ,print(solution(ParTuple)),nl,nl.
6023
6024 % Lifting existential quantifier was previously done here, but was duplicating code in b_test_exists_wo_expansion
6025 % we now simply generate the allow_to_lift_exists annotation here and let b_test_exists_wo_expansion do its job
6026 %annotate_exists(Parameters,ParameterTypes,
6027 % b(exists(EParAndTypes,ClosureBody),pred,OuterInfo),
6028 % b(exists(EParAndTypes,ClosureBody),pred,[allow_to_lift_exists|OuterInfo])) :-
6029 % exists_should_be_lifted(Parameters,ParameterTypes,OuterInfo,ClosureBody).
6030
6031 % check if a top-level exists with body ExistsClosureBody should be lifted
6032 % within a closure with paras Parameters of type ParameterTypes:
6033 exists_should_be_lifted(Parameters,ParameterTypes,OuterInfo,ExistsClosureBody) :-
6034 (Parameters == ['_was_lambda_result_'] % here we are quite sure that we gain by this optimisation
6035 ? ; member(allow_to_lift_exists,OuterInfo) % parameters were originally from a set comprehension,
6036 % see test 306: in this case existential quantifier is lifted in b_interpreter anyway;
6037 % Note we counter the rewrite ran({x1,...xn|P}) ---> {xn| #(x1,...).(P)} and similarly for dom({...})
6038 ; ExistsClosureBody = b(member(_,_),_,_) % we have a simple projection closure
6039 % TO DO: maybe support other ones as well
6040 ? ; basic_type_list_cardinality(ParameterTypes,Card),
6041 (Card=inf -> true ; Card>10000)
6042 % if here are only a few parameter values: do not lift existential quantified variables
6043 ).
6044
6045 % we need to copy important infos about the outer Parameters to ClosureBody
6046 copy_identifier_infos(Info,b(InnerPred,T,II),b(InnerPred,T,II2)) :-
6047 findall(I,identifier_info(I,Info),ToCopy),
6048 append(ToCopy,II,II2).
6049 identifier_info(I,Info) :- I=prob_annotation('DO_NOT_ENUMERATE'(ID)),
6050 ? member(I,Info), ID \= '$$NONE$$'.
6051
6052 convert_sol_list_into_pairs(ParaValues,Parameters,ParTuple) :-
6053 convert_list_into_pairs(ParaValues,ParTuple),
6054 update_closure_solution_counter(Parameters,ParTuple).
6055
6056 :- if(environ(prob_debug_flag,true)).
6057 :- dynamic closure_solution_counter/3.
6058 % debugging long expansions of comprehension_set / closures
6059 reset_closure_solution_counter(Parameters) :- retractall(closure_solution_counter(Parameters,_,_)).
6060
6061 update_closure_solution_counter(Parameters,ParTuple) :-
6062 retract(closure_solution_counter(Parameters,OldCount,OldTime)),!,
6063 statistics(walltime,[W2,_]), Delta is W2-OldTime,
6064 NewCount is OldCount+1,
6065 ((Delta > 5000 ; NewCount mod 1000 =:= 0)
6066 -> format('--> Solution ~w for expansion of closure ~w (delta ~w ms): ',[NewCount,Parameters,Delta]),
6067 translate:print_bvalue(ParTuple),nl,
6068 assert(closure_solution_counter(Parameters,NewCount,W2))
6069 ; assert(closure_solution_counter(Parameters,NewCount,OldTime))
6070 ).
6071 update_closure_solution_counter(Parameters,_ParTuple) :-
6072 statistics(walltime,[W2,_]),
6073 assert(closure_solution_counter(Parameters,1,W2)).
6074 :- else.
6075 reset_closure_solution_counter(_).
6076 update_closure_solution_counter(_,_).
6077 :- endif.
6078
6079
6080
6081 % compute cardinality of a list of basic types
6082 basic_type_list_cardinality([],1).
6083 basic_type_list_cardinality([BasicType|T],Res) :-
6084 ? basic_type_list_cardinality(T,TCard),
6085 (TCard=inf -> Res=inf
6086 ? ; kernel_objects:max_cardinality(BasicType,Card),
6087 safe_mul(Card,TCard,Res)
6088 ).
6089
6090 % for lambda closures we can set up a second waitflag for the expression and only ground it when body enumeration finished
6091 % idea is to avoid perturbation of constraint solving of main closure predicate by lambda expression, see test 1737
6092 % something like %(x,y).(x:1..200 & y:1..100 & y+x<259 & y*x>10|(y+x*x+y) mod 100) is faster
6093 % this is slower : %(x,y).(x:1..200 & y:1..100 |(y+x*x+y))
6094 % currently this slows down test 1336
6095 :- block b_test_closure(?,?,-,?,?,?).
6096 b_test_closure(Parameters,ParameterTypes,ClosureBody, FullParValues, NegationContext, OuterWF) :-
6097 (preference(data_validation_mode,true)
6098 -> true % avoids ineraction between domain and range expression enumeration; see
6099 % private_examples/ClearSy/2019_May/perf_3264/rule_186.mch or
6100 % computation of 631 ic___DMI_MRGATKSAAT___Parametre_Identifiant_indices_function in rule_FICHIER_MRGATKSAATPAR_RVF219_MRGA_DE.mch
6101 % however, as b_optimize below does *not* evaluate nested set comprehensions, there can be a slowdown:
6102 % the nested set comprehension gets re-evaluated for every soluiton of the lambda parameters !
6103 % this was the case of private_examples/ClearSy/2019_Nov/rule_Regle_31C_0005/rule.mch before using SORT
6104 ; \+ preferences:preference(use_smt_mode,false)), % TO DO: enable in normal mode when performance of 1336 fixed
6105 % print(test_closure(Parameters,FullParValues)),nl,
6106 is_lambda_closure(Parameters,ParameterTypes,ClosureBody, OtherIDs,OtherTypes, DomainPred, EXPR),
6107 % TO DO: detect not only equalities at end, but any equality which is irrelevant for the rest
6108 % nl,print(lambda_closure(OtherIDs)),nl, translate:print_bexpr(EXPR),nl,
6109 append(ParValues,[LambdaResult],FullParValues),
6110 !,
6111 get_texpr_info(ClosureBody,BInfo),
6112 b_interpreter:set_up_typed_localstate2(OtherIDs,OtherTypes,BInfo,ParValues,TypedVals,[],LocalState,NegationContext),
6113 simplify_span(ClosureBody,BSpan), % sometimes BInfo no longer contains a position info, but first_sub_expr does
6114 init_quantifier_wait_flag(OuterWF,comprehension_set(NegationContext),OtherIDs,ParValues,BSpan,WF),
6115 b_test_boolean_expression(DomainPred,LocalState,[],WF),
6116 %print('PRED: '),translate:print_bexpr(ClosureBody),nl,
6117 b_tighter_enumerate_values_in_ctxt(TypedVals,DomainPred,WF), % also does: project_away_useless_enumeration_values
6118 init_quantifier_wait_flag(OuterWF,comprehension_set(NegationContext),OtherIDs,ParValues,BSpan,WF2),
6119 ? b_compiler:b_optimize(EXPR,[],LocalState,[],CEXPR,WF), % already pre-compile lookup, without constraint processing; is not sufficient for test 1336
6120 ? ground_wait_flags(WF), % TODO: also call ground inner WF in context
6121 ? b_interpreter:b_compute_expression(CEXPR,LocalState,[],LambdaResult,WF2),
6122 ground_inner_wait_flags_in_context(NegationContext,WF2).
6123 b_test_closure(Parameters,ParameterTypes,ClosureBody,ParValues,NegationContext, OuterWF) :-
6124 % tools:print_bt_message(b_test_closure_testing_closure(Parameters,ParValues)), %%
6125 get_texpr_info(ClosureBody,BInfo),
6126 ? b_interpreter:set_up_typed_localstate2(Parameters,ParameterTypes,BInfo,
6127 ParValues,TypedVals,[],LocalState,NegationContext),
6128 % print_message(b_interpreter:b_test_boolean_expression(ClosureBody,LocalState,[],WF)),
6129 simplify_span(ClosureBody,BSpan), % sometimes BInfo no longer contains a position info, but first_sub_expr does
6130 init_quantifier_wait_flag(OuterWF,comprehension_set(NegationContext),Parameters,ParValues,BSpan,WF),
6131 %external_functions:observe_parameters(Parameters,LocalState), %%
6132 ? b_test_boolean_expression(ClosureBody,LocalState,[],WF),
6133 % tools:print_bt_message(tested_bool_expr), translate:print_bexpr(ClosureBody),nl,
6134 b_enumerate:b_tighter_enumerate_values_in_ctxt(TypedVals,ClosureBody,WF), % also detects useless enumeration ids
6135 ? ground_inner_wait_flags_in_context(NegationContext,WF).
6136
6137
6138
6139 :- block b_not_test_closure_wf(?,?,?,-,?).
6140 b_not_test_closure_wf(Parameters,ParameterTypes,Closure,ParValues,WF) :-
6141 % same_length(Parameters,ParValues), % not necessary
6142 set_up_localstate(Parameters,ParValues,[],LocalState),
6143 b_enumerate:b_type_values_in_store(Parameters,ParameterTypes,LocalState),
6144 b_not_test_boolean_expression(Closure,LocalState,[],WF),
6145 get_last_wait_flag(b_not_test_closure_wf(Parameters),WF,WF2),
6146 get_texpr_info(Closure,Infos),
6147 b_not_test_closure_enum(Parameters,ParameterTypes,Infos,LocalState,WF,WF2).
6148
6149 :- block b_not_test_closure_enum(-,?,?,?,?,?).
6150 b_not_test_closure_enum(Parameters,ParameterTypes,Infos,LocalState,WF,WF2) :-
6151 b_enumerate:b_extract_typedvalc(Parameters,ParameterTypes,Infos,LocalState,TypedVals),
6152 (var(WF2) -> ground_typedvals_check(TypedVals,GrVals) ; true),
6153 b_not_test_closure_enum_aux(GrVals,WF2,TypedVals,WF).
6154
6155 :- block b_not_test_closure_enum_aux(-,-,?,?).
6156 b_not_test_closure_enum_aux(_,_,TypedVals,WF) :-
6157 b_enumerate:b_tighter_enumerate_all_values(TypedVals,WF).
6158 % , print(finished_enum(Parameters)),nl.
6159
6160
6161 :- use_module(library(terms)).
6162 % check whether a VARIABLE occurs inside a closure
6163 closure_occurs_check(VARIABLE,_Par,_ParTypes,ClosureBody) :- expression_contains_setvar(ClosureBody,VARIABLE).
6164 % /* occurs check; x = closure1(x) ; for other closures this cannot happen ???!!! TO DO: Check */
6165 % custom_explicit_sets:is_closure1_value_closure(Par,ParTypes,ClosureBody,Val),
6166 % contains_var(VARIABLE,Val).
6167
6168 expression_contains_setvar(b(E,_,_),Variable) :- !,
6169 expression_contains_setvar_aux(E,Variable).
6170 expression_contains_setvar(E,V) :- add_internal_error('Illegal Expression: ', expression_contains_setvar(E,V)),
6171 contains_var(V,E).
6172
6173 expression_contains_setvar_aux(value(Val),Variable) :- !,value_contains_setvar(Val,Variable).
6174 % a few very common cases for performance; currently this predicate is often called for recursive functions
6175 expression_contains_setvar_aux(identifier(_),_) :- !,fail.
6176 expression_contains_setvar_aux(equal(A,B),Variable) :- !,
6177 (expression_contains_setvar(A,Variable) -> true ; expression_contains_setvar(B,Variable)).
6178 expression_contains_setvar_aux(conjunct(A,B),Variable) :- !,
6179 (expression_contains_setvar(A,Variable) -> true ; expression_contains_setvar(B,Variable)).
6180 expression_contains_setvar_aux(function(A,B),Variable) :- !,
6181 (expression_contains_setvar(A,Variable) -> true ; expression_contains_setvar(B,Variable)).
6182 expression_contains_setvar_aux(union(A,B),Variable) :- !,
6183 (expression_contains_setvar(A,Variable) -> true ; expression_contains_setvar(B,Variable)).
6184 expression_contains_setvar_aux(couple(A,B),Variable) :- !,
6185 (expression_contains_setvar(A,Variable) -> true ; expression_contains_setvar(B,Variable)).
6186 % the rest via safe_syntaxelement:
6187 expression_contains_setvar_aux(Expr,V) :-
6188 safe_syntaxelement_det(Expr,Subs,_Names,_,_),!,
6189 ? member(Sub,Subs), expression_contains_setvar(Sub,V),!.
6190 expression_contains_setvar_aux(E,V) :- add_internal_error('Illegal Expression: ', expression_contains_setvar_aux(E,V)),
6191 contains_var(V,E).
6192
6193 value_contains_setvar(Val,V) :- var(Val),!,Val==V.
6194 value_contains_setvar(avl_set(_),_V) :- !, fail. % assume avl_set always properly grounded; avoid looking inside
6195 value_contains_setvar(closure(_,_,Body),V) :- !,
6196 expression_contains_setvar(Body,V).
6197 value_contains_setvar(int(_),_) :- !,fail. % we check for set variables
6198 value_contains_setvar(global_set(_),_) :- !,fail. % we check for set variables
6199 value_contains_setvar(freetype(_),_) :- !,fail. % we check for set variables
6200 value_contains_setvar(freeval(_ID,_Case,Val),V) :- !, value_contains_setvar(Val,V).
6201 value_contains_setvar(string(_),_) :- !,fail. % we check for set variables
6202 value_contains_setvar(fd(_,_),_) :- !,fail. % we check for set variables
6203 value_contains_setvar((A,B),V) :- !, (value_contains_setvar(A,V) ; value_contains_setvar(B,V)).
6204 value_contains_setvar([A|B],V) :- !, (value_contains_setvar(A,V) ; value_contains_setvar(B,V)).
6205 value_contains_setvar(Val,V) :-
6206 contains_var(V,Val).
6207
6208 % ------------------