1 % (c) 2009-2026 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_wf/3, 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_wf/4,
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 intersect_intervals_with_inf/6,
140
141 is_powerset_closure/3,
142
143 dom_range_for_specific_closure/5,
144 dom_for_specific_closure/4,
145 dom_for_lambda_closure/2,
146 portray_custom_explicit_set/1,
147 closure_occurs_check/4
148 ]).
149
150 :- meta_predicate call_card_for_relations(-,-,0).
151
152 :- use_module(error_manager).
153 :- use_module(self_check).
154 :- use_module(preferences,[get_preference/2]).
155 :- use_module(library(avl)).
156 :- use_module(kernel_waitflags).
157 :- use_module(kernel_tools).
158 :- use_module(delay).
159 :- use_module(tools).
160 :- use_module(avl_tools).
161 :- use_module(library(clpfd)).
162
163 :- use_module(module_information,[module_info/2]).
164 :- module_info(group,kernel).
165 :- module_info(description,'This module provides customised operations for the custom explicit set representations of ProB (closures, avl_sets and global_sets).').
166
167 :- use_module(tools_printing,[print_term_summary/1, print_error/1]).
168 :- use_module(preferences,[preference/2]).
169 :- use_module(kernel_objects,[equal_object/2, equal_object/3]).
170 :- use_module(kernel_freetypes,[enumerate_freetype_wf/4,freetype_cardinality/2,
171 is_infinite_freetype/1, is_empty_freetype/1,
172 is_non_empty_freetype/1, test_empty_freetype/2]).
173
174 :- use_module(clpfd_interface,[try_post_constraint/1, clpfd_reify_inlist/4]).
175 :- use_module(closures).
176 :- use_module(performance_messages).
177 :- use_module(b_compiler).
178 :- use_module(btypechecker,[couplise_list/2, unify_types_strict/2, merge_types/3]).
179
180 :- load_files(library(system), [when(compile_time), imports([environ/2])]).
181
182 /* These meta_predicate declarations do not seem to have the right effect;
183 the predicates below return code, they do not get passed code
184 :- meta_predicate card_for_specific_custom_set(*,*,0).
185 :- meta_predicate card_for_specific_closure(*,*,0).
186 :- meta_predicate is_a_relation(*,*,*,*,*,*,0).
187 :- meta_predicate subset_of_explicit_set(*,*,0,*).
188 :- meta_predicate not_subset_of_explicit_set(*,*,0,*).
189 */
190
191 construct_avl_from_lists(S,Res) :-
192 (convert_to_avl(S,CS) -> true ; print(convert_to_avl_failed(S,CS)),nl,CS=S),
193 Res = CS.
194
195 % version with WF to see call stack in case of virtual time-outs due to expansions
196 construct_avl_from_lists_wf(S,Res,WF) :-
197 (convert_to_avl_wf(S,CS,WF) -> true ; print(convert_to_avl_wf_failed(S,CS)),nl,CS=S),
198 Res = CS.
199
200 :- use_module(tools,[safe_sort/3]).
201 :- block normalised_list_to_avl_when_ground(-,?).
202 normalised_list_to_avl_when_ground(S,R) :- % call if you are not sure that S will be ground; e.g. after closure expansion
203 ground_value_check(S,GS),
204 blocking_normalised_list_to_avl(GS,S,R).
205 :- block blocking_normalised_list_to_avl(-,?,?).
206 blocking_normalised_list_to_avl(_,S,R) :- normalised_list_to_avl(S,R).
207
208 normalised_list_to_avl(S,R) :- safe_sort(normalised_list_to_avl,S,SS),
209 ord_list_to_avlset_direct(SS,AVL,normalised_list_to_avl),
210 equal_object(AVL,R). % due to co-routine, R can now be instantiated
211
212 %set_to_avl(List,R) :- empty_avl(A), add_to_avl(List,A,AR), R=avl_set(AR).
213 add_to_avl([],R,R).
214 add_to_avl([H|T],AVL,AVLOUT) :- avl_store(H,AVL,true,AVL1),
215 add_to_avl(T,AVL1,AVLOUT).
216
217
218 % get only the first x elements of an AVL tree
219 get_first_avl_elements(empty,_,R,all) :- !,R=[].
220 get_first_avl_elements(AVL,X,FirstXEls,CutOff) :-
221 avl_min(AVL,Min), get_first_els(X,Min,AVL,FirstXEls,CutOff).
222
223 get_first_els(X,_,_AVL,R,CutOff) :- X<1,!,R=[], CutOff=not_all.
224 get_first_els(X,Cur,AVL,[Cur|T],CutOff) :-
225 (avl_next(Cur,AVL,Nxt) -> X1 is X-1,get_first_els(X1,Nxt,AVL,T,CutOff)
226 ; T=[],CutOff=all).
227
228 %expand_and_try_convert_to_avl(C,R) :- is_closure(C,_,_,_), expand_custom_set(C,EC), expand_and_convert_to_avl
229 %expand_and_convert_to_avl(C,R) :- convert_to_avl(C,R).
230
231 /* convert all list data-values (with all-sub-values) into avl-form */
232 /* assumption: the value is ground when convert_to_avl is called */
233
234 :- load_files(library(system), [when(compile_time), imports([environ/2])]).
235 :- if(environ(prob_safe_mode,true)).
236 convert_to_avl(X,R) :- \+ ground_value(X), !, add_error(convert_to_avl,'Non-ground argument: ',convert_to_avl(X,R)), R=X.
237 :- endif.
238 convert_to_avl(X,R) :- var(X), !, add_error(convert_to_avl,'Variable argument: ',convert_to_avl(X,R)), R=X.
239 ?convert_to_avl(Term,R) :- no_conversion_necessary(Term),!,
240 R=Term.
241 convert_to_avl(closure(P,T,B),R) :- !,
242 R=closure(P,T,B).
243 convert_to_avl(avl_set(A),R) :- !,(A==empty -> add_warning(convert_to_avl,'Emtpy avl_set'), R=[]
244 ; R=avl_set(A)).
245 convert_to_avl((A,B),(CA,CB)) :- !,convert_to_avl(A,CA), convert_to_avl(B,CB).
246 convert_to_avl(freetype(X),R) :- !, R=freetype(X).
247 convert_to_avl(freeval(ID,Case,Value),R) :- !, R=freeval(ID,Case,CValue),convert_to_avl(Value,CValue).
248 convert_to_avl(rec(Fields),R) :- !, convert_fields(Fields,CFields), R=rec(CFields).
249 convert_to_avl(global_set(GS),R) :- !, R=global_set(GS).
250 convert_to_avl([H|T],R) :- !, convert_cons_to_avl_inside_set_wf(H,T,R,no_wf_available).
251 %convert_to_avl(abort(X),_R) :- print(deprecetated_convert_to_avl(abort(X))),nl,!, fail.
252 convert_to_avl(X,R) :- add_internal_error('Unknown term: ',convert_to_avl(X,R)), R=X.
253
254 % pass WF for call stack in case of expansions TODO: complete
255 convert_to_avl_wf((A,B),(CA,CB),WF) :- !,convert_to_avl_wf(A,CA,WF), convert_to_avl_wf(B,CB,WF).
256 convert_to_avl_wf([H|T],R,WF) :- !, convert_cons_to_avl_inside_set_wf(H,T,R,WF).
257 convert_to_avl_wf(X,R,_) :- convert_to_avl(X,R).
258
259 convert_fields(Var,R) :- var(Var),!,
260 add_internal_error('Var arg: ',convert_fields(Var,R)),fail.
261 convert_fields([],[]).
262 convert_fields([field(FieldName,Value)|T],[field(FieldName,CValue)|CT]) :-
263 convert_to_avl_inside_set(Value,CValue),
264 convert_fields(T,CT).
265
266 l_convert_to_avl_wf(Var,_,WF) :- var(Var),!,
267 add_warning_wf(l_convert_to_avl_wf,'Cannot expand variable to avl: ',Var,unknown,WF),
268 fail.
269 l_convert_to_avl_wf([],[],_).
270 l_convert_to_avl_wf(avl_set(A),R,WF) :-
271 expand_custom_set_wf(avl_set(A),ES,l_convert_to_avl,WF),
272 l_convert_to_avl_wf(ES,R,WF).
273 l_convert_to_avl_wf(closure(P,T,B),R,WF) :-
274 expand_custom_set_wf(closure(P,T,B),ES,l_convert_to_avl,WF),
275 l_convert_to_avl_wf(ES,R,WF).
276 l_convert_to_avl_wf([H|T],[CH-true|CT],WF) :-
277 convert_to_avl_inside_set_wf(H,CH,WF), l_convert_to_avl_wf(T,CT,WF).
278
279 :- assert_must_succeed((X=(fd(1,'Name'),fd(2,'Name')),
280 custom_explicit_sets:convert_to_avl_inside_set(X,R), R==X)).
281
282 convert_to_avl_inside_set(Var,R) :- var(Var),!,
283 add_internal_error('Var arg: ',convert_to_avl_inside_set(Var,R)),fail.
284 :- if(environ(prob_safe_mode,true)).
285 convert_to_avl_inside_set(fd(A,T),R) :- var(A),!,
286 add_error(convert_to_avl,'Non-ground FD-Term: ',convert_to_avl_inside_set(fd(A,T),R)), R=fd(A,T).
287 convert_to_avl_inside_set(int(X),R) :- var(X),!,
288 add_error(convert_to_avl,'Non-ground integer: ',convert_to_avl_inside_set(int(X),R)), R=int(X).
289 convert_to_avl_inside_set(string(X),R) :- var(X),!,
290 add_error(convert_to_avl,'Non-ground string: ',convert_to_avl_inside_set(string(X),R)), R=string(X).
291 convert_to_avl_inside_set(term(X),R) :- (var(X) ; X=floating(F), var(F)), !,
292 add_error(convert_to_avl,'Non-ground term: ',convert_to_avl_inside_set(term(X),R)), R=term(X).
293 :- endif.
294 ?convert_to_avl_inside_set(Term,R) :- no_conversion_necessary(Term),!,R=Term.
295 convert_to_avl_inside_set(closure(P,T,B),R) :- !,
296 % inside a set, closures need to be expanded to check against other elements
297 expand_closure_to_avl_wf(P,T,B,R,no_wf_available).
298 %convert_to_avl_inside_set(closure_x(_P,_T,_B,E),R) :- !, convert_to_avl_inside_set(E,R).
299 convert_to_avl_inside_set(avl_set(A),R) :- !, normalise_avl_set(A,R). %AVL's inside other AVL's need to be normalised !
300 convert_to_avl_inside_set((A,B),(CA,CB)) :- !,convert_to_avl_inside_set(A,CA), convert_to_avl_inside_set(B,CB).
301 convert_to_avl_inside_set(freetype(X),R) :- !,
302 expand_custom_set(freetype(X),EC,check), convert_to_avl_inside_set(EC,R).
303 convert_to_avl_inside_set(freeval(ID,Case,Value),R) :- !,
304 R=freeval(ID,Case,CValue),convert_to_avl_inside_set(Value,CValue).
305 convert_to_avl_inside_set(rec(Fields),R) :- !, convert_fields(Fields,CFields), R=rec(CFields).
306 convert_to_avl_inside_set(global_set(GS),R) :- !,
307 % first check if GS infinite integer set: in this case do not expand; there can be no confusion with finite avl_sets
308 (is_infinite_global_set(GS,_) -> R = global_set(GS)
309 ; expand_only_custom_closure_global(global_set(GS),EC,check,no_wf_available), convert_to_avl_inside_set(EC,R)).
310 convert_to_avl_inside_set([H|T],R) :- !,convert_cons_to_avl_inside_set_wf(H,T,R,no_wf_available).
311 convert_to_avl_inside_set(X,R) :-
312 add_internal_error('Unknown or non-ground argument: ',convert_to_avl_inside_set(X,R)),
313 fail.
314
315 ?convert_to_avl_inside_set_wf(Term,R,_WF) :- no_conversion_necessary(Term),!,R=Term.
316 convert_to_avl_inside_set_wf(closure(P,T,B),R,WF) :- !,
317 expand_closure_to_avl_wf(P,T,B,R,WF). % inside a set, closures need to be expanded to check against other elements
318 convert_to_avl_inside_set_wf((A,B),(CA,CB),WF) :- !,
319 convert_to_avl_inside_set_wf(A,CA,WF), convert_to_avl_inside_set_wf(B,CB,WF).
320 convert_to_avl_inside_set_wf([H|T],R,WF) :- !,convert_cons_to_avl_inside_set_wf(H,T,R,WF).
321 convert_to_avl_inside_set_wf(V,CV,_WF) :- % use version without WF; TO DO: adapt fully
322 convert_to_avl_inside_set(V,CV).
323
324 % true when we have a simple value that does not need to be converted for use within an avl_set:
325 no_conversion_necessary([]).
326 no_conversion_necessary(pred_false). /* bool_false */
327 no_conversion_necessary(pred_true). /* bool_true */
328 no_conversion_necessary(fd(FD,_)) :- nonvar(FD).
329 no_conversion_necessary(int(I)) :- nonvar(I).
330 no_conversion_necessary(string(S)) :- nonvar(S).
331 ?no_conversion_necessary(term(T)) :- nonvar(T), no_conversion_nec_term(T).
332
333 no_conversion_nec_term(floating(T)) :- nonvar(T).
334 no_conversion_nec_term(T) :- atom(T).
335
336 normalise_avl_set(A,R) :- A=node(_,_,0,empty,empty), !,R=avl_set(A).
337 normalise_avl_set(A,R) :-
338 avl_to_list(A,L),
339 ord_list_to_avlset_direct(L,R,convert_to_avl_inside_set). %AVL's inside other AVL's need to be normalised !
340
341 convert_cons_to_avl_inside_set_wf(H,T,R,WF) :- T==[], !,
342 convert_to_avl_inside_set_wf(H,CH,WF),
343 R = avl_set(node(CH,true,0,empty,empty)).
344 convert_cons_to_avl_inside_set_wf(H,T,R,WF) :- l_convert_to_avl_wf([H|T],S,WF),
345 sort(S,SS),
346 ord_list_to_avlset_direct(SS,R,convert_to_avl_inside_set).
347
348 construct_singleton_avl_set(Val,avl_set(node(Val,true,0,empty,empty))).
349
350
351 is_set_value(X,Origin) :- var(X), !,print(is_set_value(Origin)),nl,fail.
352 is_set_value([],_) :- !.
353 is_set_value([_|_],_) :- !.
354 is_set_value(X,_) :- is_custom_explicit_set(X).
355
356 is_custom_explicit_set(X,Origin) :- var(X), !,print(var_is_custom_explicit_set(Origin)),nl,fail.
357 is_custom_explicit_set(X,_) :- is_custom_explicit_set(X).
358
359 is_custom_explicit_set(X) :- var(X), !,print(var_is_custom_explicit_set),nl,fail.
360 is_custom_explicit_set(global_set(_)).
361 is_custom_explicit_set(freetype(_)).
362 %is_custom_explicit_set(integer_global_set(_)).
363 is_custom_explicit_set(avl_set(_)).
364 is_custom_explicit_set(closure(_Parameters,_PT,_Cond)).
365
366 % use if you know the argument to be nonvar
367 is_custom_explicit_set_nonvar(global_set(_)).
368 is_custom_explicit_set_nonvar(freetype(_)).
369 is_custom_explicit_set_nonvar(avl_set(_)).
370 is_custom_explicit_set_nonvar(closure(_Parameters,_PT,_Cond)).
371
372 %:- assert_must_succeed(( custom_explicit_sets:portray_custom_explicit_set(avl_set(empty)) )). % now generates error
373 :- use_module(translate,[translate_bvalue/2]).
374 portray_custom_explicit_set(S) :- translate_bvalue(S,A), format(A,[]),nl.
375
376 /* a predicate to check equality of two custom explicit sets */
377
378 %equal_explicit_sets(A,B) :- equal_explicit_sets_wf(A,B,no_wf_available).
379
380 %equal_explicit_sets(X,Y) :- print_term_summary(equal_explicit_sets(X,Y)),fail.
381 :- block equal_explicit_sets_wf(-,?,?), equal_explicit_sets_wf(?,-,?).
382 equal_explicit_sets_wf(A,B,WF) :- equal_explicit_sets4(A,B,allow_expansion,WF).
383
384 equal_explicit_sets4(global_set(X),global_set(Y),_,_WF) :- !,X=Y.
385 equal_explicit_sets4(global_set(B),avl_set(A),E,WF) :- !,equal_explicit_sets4(avl_set(A),global_set(B),E,WF).
386 equal_explicit_sets4(freetype(X),freetype(Y),_,_WF) :- !,X=Y.
387 equal_explicit_sets4(avl_set(A),avl_set(B),_,_WF) :- !,
388 equal_avl_tree(A,B). % alternatively, we could normalise avl_trees and only store normalised versions
389 equal_explicit_sets4(avl_set(A),I2,_,_WF) :-
390 is_interval_closure_or_integerset(I2,L2,U2,Finite2),!, % also covers I2=global_set(...)
391 Finite2=finite, % only a finite interval can be equal to an AVL set
392 avl_equal_to_interval(A,L2,U2).
393 equal_explicit_sets4(avl_set(A),global_set(B),_,WF) :- \+ b_global_sets:b_integer_set(B), !, % integersets dealt with above
394 explicit_set_cardinality_wf(global_set(B),Card,WF),
395 is_finite_card(Card), % Card \= inf as avl_set must be finite
396 explicit_set_cardinality_wf(avl_set(A),Card,WF). /* the sets must be identical as global_set contains all values */
397 equal_explicit_sets4(avl_set(A),CPB,_,WF) :-
398 is_cartesian_product_closure(CPB,B1,B2),!,
399 decompose_avl_set_into_cartesian_product_wf(A,A1,A2,WF),
400 kernel_objects:equal_object_wf(A1,B1,equal_explicit_sets4,WF),
401 kernel_objects:equal_object_wf(A2,B2,equal_explicit_sets4,WF).
402 equal_explicit_sets4(closure(P,T,B),avl_set(A),E,WF) :- !, equal_explicit_sets4(avl_set(A),closure(P,T,B),E,WF).
403 equal_explicit_sets4(I1,I2,_,_WF) :- is_interval_closure_or_integerset(I1,L1,U1,Finite1),
404 is_interval_closure_or_integerset(I2,L2,U2,Finite2), !,
405 Finite1=Finite2, % either both finite or infinite
406 L1=L2, U1=U2.
407 equal_explicit_sets4(CPA,CPB,_,WF) :-
408 ? is_cartesian_product_closure(CPA,A1,A2),
409 ? is_cartesian_product_closure(CPB,B1,B2),!,
410 equal_cartesian_product_wf(A1,A2,B1,B2,WF).
411 % what if both subset or relations or functions ... closure: TO DO: add support
412 equal_explicit_sets4(S1,S2,_,WF) :-
413 is_not_member_value_closure_or_integerset(S1,TYPE,MS1),
414 is_not_member_value_closure_or_integerset(S2,TYPE,MS2),
415 !,
416 kernel_objects:equal_object_wf(MS1,MS2,equal_explicit_sets4,WF).
417 equal_explicit_sets4(closure(P1,T1,B1),closure(P2,T2,B2),_,_WF) :-
418 same_closure_body(P1,T1,B1,P2,T2,B2),!.
419 %equal_explicit_sets4(X,Y) :- X==Y,!.
420 equal_explicit_sets4(Set1,Set2,allow_expansion,WF) :-
421 %kernel_objects:test_finite_set_wf(Set1,F1,WF), kernel_objects:test_finite_set_wf(Set2,F2,WF), equal_expansions(F1,F2,Set1,Set2)
422 card_for_specific_custom_set(Set1,Card1,Code1), % TO DO: do not throw info away if Set2 cannot be determined
423 card_for_specific_custom_set(Set2,Card2,Code2),
424 !,
425 call(Code1), call(Code2),
426 % 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
427 equal_expansions(Card1,Card2,Set1,Set2,WF).
428 equal_explicit_sets4(Set1,Set2,allow_expansion,WF) :- equal_expansions(0,0,Set1,Set2,WF).
429
430
431 % detect e.g. when one closure has seq(Type) and the other one set(integer,Type)
432 same_types([],[]).
433 same_types([H1|T1],[H2|T2]) :- unify_types_strict(H1,H2), same_types(T1,T2).
434
435 :- block equal_expansions(-,?,?,?,?).
436 equal_expansions(F1,F2,Set1,Set2,WF) :- (number(F1);number(F2)),!,
437 % NOTE: sometimes we get inf for finite but very large sets
438 F1=F2, % unify; can propagate info back to closure; e.g. prj2(BOOL,NAT) = prj2(BOOL,0..n)
439 equal_expansions2(F1,F2,Set1,Set2,WF).
440 equal_expansions(F1,F2,Set1,Set2,WF) :-
441 equal_expansions2(F1,F2,Set1,Set2,WF).
442
443 :- block equal_expansions2(-,?,?,?,?), equal_expansions2(?,-,?,?,?).
444 %equal_expansions(0,0,avl_set(A),closure(P,T,B)) :- check_subset ?? in both directions ?
445 %equal_expansions2(inf,inf,Set1,Set2,WF) :- WF \= no_wf_available, !, % symbolic treatment
446 equal_expansions2(F,F,Set1,Set2,WF) :-
447 % only expand if both sets have same cardinality
448 % print_term_summary(equal_expansions3(F,Set1,Set2)),nl,
449 equal_expansions3(F,Set1,Set2,WF).
450
451 % TO DO: check if this brings something:
452 %equal_expansions3(avl_set(A),closure(P,T,B),_WF) :- !,
453 % expand_closure_to_avl_or_list(P,T,B,E2,check), % in case E2 is avl_set; we can use equal_avl_tree
454 % ((nonvar(E2),E2=avl_set(B2))
455 % -> print(eql_avl),nl, print_term_summary(equal_avl_tree(A,B2)),nl, equal_avl_tree(A,B2)
456 % ; print(eql_non_avl),nl,equal_object(avl_set(A),E2,equal_expansions3)
457 % ).
458 %:- use_module(library(lists),[perm2/4]).
459 %equal_expansions3(F,Set1,Set2,_WF) :- number(F), F>100, % test with: {{},{TRUE},{FALSE},{TRUE,FALSE}} = /*@symbolic */ {x|x<:BOOL} or
460 % {x|x<:POW(BOOL*BOOL) & (x={} or card(x)>0)} = /*@symbolic */ {x|x<:POW(BOOL*BOOL)} 26 sec -> 14 sec
461 % case does not seem to appear very often
462 % perm2(Set1,Set2,avl_set(_),Set),
463 % is_definitely_maximal_set(Set),
464 %Set2 is maximal and has the same cardinality as F, hence Set1 must be identical to Set2
465 % !,
466 % debug_println(9,equal_to_maximal_closure(F)).
467 equal_expansions3(F,Set1,Set2,WF) :-
468 ? get_identity_as_equivalence(F,Set1,Set2,EQUIV),
469 !,% translate:print_bexpr(EQUIV),nl,
470 opt_push_wait_flag_call_stack_info(WF,b_operator_call(equal,[Set1,Set2],unknown),WF2),
471 copy_wf_start(WF2,equal_expansions,CWF),
472 b_test_boolean_expression(EQUIV,[],[],CWF),
473 copy_wf_finish(WF2,CWF).
474 % Alternative could be, if difference were to be fully treated symbolically:
475 % difference_of_explicit_set_wf(Set1,Set2,R12,WF), difference_of_explicit_set_wf(Set2,Set1,R21,WF),
476 % kernel_objects:empty_set_wf(R12,WF), kernel_objects:empty_set_wf(R21,WF).
477 equal_expansions3(_,Set1,Set2,WF) :-
478 expand_custom_set_wf(Set1,E1,equal_expansions1,WF),
479 expand_custom_set_wf(Set2,E2,equal_expansions2,WF),
480 E1=E2. /* ensure that ordering and normalization is same for all representations ! */
481
482
483 :- use_module(bsyntaxtree, [create_forall/3]).
484 :- use_module(b_ast_cleanup, [clean_up/3]).
485 get_identity_as_equivalence(F,Set1,Set2,CleanedEQUIV) :-
486 (F=inf %; is_infinite_explicit_set(Set1) ; is_infinite_explicit_set(Set2)
487 ; 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
488 (dont_expand_this_explicit_set(Set1,100000) ;
489 dont_expand_this_explicit_set(Set2,100000)
490 )
491 % 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
492 ),
493 get_identity_as_equivalence_aux(Set1,Set2,EQUIV),
494 clean_up(EQUIV,[],CleanedEQUIV).
495 % can be useful to replace x : {v|P(v)} --> x:P(x) (remove_member_comprehension) and reuse predicates, see 2483
496 get_identity_as_equivalence_aux(Set1,Set2,EQUIV) :-
497 kernel_objects:infer_value_type(Set1,S1Type),
498 kernel_objects:infer_value_type(Set2,S2Type),
499 merge_types(S1Type,S2Type,SType),
500 is_set_type(SType,Type),
501 % Construct: !x.(x:Set1 <=> x:Set2) ?? see test 2009
502 get_pos_infos_for_explicit_set(Set1,I1),
503 get_pos_infos_for_explicit_set(Set2,I2),
504 I12 = I1, % we could merge position_info; but two sets could be very far apart
505 TID = b(identifier('_equality_sets_'),Type,[]),
506 Mem1 = b(member(TID,b(value(Set1),SType,I1)),pred,I1),
507 Mem2 = b(member(TID,b(value(Set2),SType,I2)),pred,I2),
508 Body1 = b(equivalence(Mem1,Mem2),pred,I12),
509 create_forall([TID],Body1,EQUIV).
510 %translate:print_bexpr(EQUIV),nl.
511
512 :- use_module(bsyntaxtree, [get_texpr_pos/2]).
513 get_pos_infos_for_explicit_set(closure(_,_,Body),[Pos]) :- get_texpr_pos(Body,Pos),!.
514 get_pos_infos_for_explicit_set(_,[]).
515
516 :- use_module(kernel_equality,[eq_atomic/4, equality_objects/3,
517 equality_objects_wf_no_enum/4, equality_objects_with_type_wf/5]).
518 /* maybe rewrite equal_explicit_sets and not_... to use this to avoid maintaining multiple versions */
519 equality_explicit_sets_wf(global_set(X),global_set(Y),R,_WF) :- !, eq_atomic(X,Y,set,R).
520 equality_explicit_sets_wf(global_set(B),avl_set(A),R,WF) :- !,equality_explicit_sets_wf(avl_set(A),global_set(B),R,WF).
521 equality_explicit_sets_wf(freetype(X),freetype(Y),R,_) :- !, eq_atomic(X,Y,set,R).
522 equality_explicit_sets_wf(avl_set(A),avl_set(B),R,_) :- !,
523 (equal_avl_tree(A,B) -> R=pred_true ; R=pred_false). % alternatively, we could normalise avl_trees and only store normalised versions
524 equality_explicit_sets_wf(avl_set(A),I2,R,WF) :- is_interval_closure_or_integerset(I2,L2,U2),!,
525 % also covers I2=global_set(...)
526 avl_equality_to_interval(A,L2,U2,R,WF).
527 equality_explicit_sets_wf(avl_set(A),global_set(B),R,WF) :- \+ b_global_sets:b_integer_set(B), !,
528 explicit_set_cardinality_wf(global_set(B),Card,WF),
529 (is_finite_card(Card), % Card \= inf, %as avl_set must be finite
530 explicit_set_cardinality_wf(avl_set(A),Card,WF)
531 -> R=pred_true /* the sets must be identical as global_set contains all values */
532 ; R=pred_false).
533 equality_explicit_sets_wf(avl_set(A),CPB,R,WF) :-
534 is_cartesian_product_closure(CPB,B1,B2),!,
535 if(decompose_avl_set_into_cartesian_product_wf(A,A1,A2,WF), % should not produce pending co-routines
536 equality_cartesian_product_wf(A1,A2,B1,B2,R,WF),
537 R=pred_false % no cartesian product can be equal to this avl_set
538 ).
539 equality_explicit_sets_wf(closure(P,T,B),avl_set(A),R,WF) :- !,
540 equality_explicit_sets_wf(avl_set(A),closure(P,T,B),R,WF).
541 equality_explicit_sets_wf(I1,I2,R,WF) :- is_interval_closure_or_integerset(I1,L1,U1,Finite1),
542 is_interval_closure_or_integerset(I2,L2,U2,Finite2), !,
543 (Finite1=Finite2 -> equality_objects_wf_no_enum((int(L1),int(U1)),(int(L2),int(U2)),R,WF)
544 ; R = pred_false).
545 equality_explicit_sets_wf(CPA,CPB,R,WF) :-
546 is_cartesian_product_closure(CPA,A1,A2), is_cartesian_product_closure(CPB,B1,B2),!,
547 equality_cartesian_product_wf(A1,A2,B1,B2,R,WF).
548 equality_explicit_sets_wf(S1,S2,R,WF) :-
549 is_not_member_value_closure_or_integerset(S1,TYPE,MS1),
550 is_not_member_value_closure_or_integerset(S2,TYPE,MS2),!,
551 equality_objects_with_type_wf(TYPE,MS1,MS2,R,WF).
552 equality_explicit_sets_wf(closure(P,T,B),closure(P,T,B2),R,_) :-
553 same_texpr_body(B,B2),!,R=pred_true.
554 equality_explicit_sets_wf(Set1,Set2,R,WF) :-
555 Set1 \= [_|_], Set2 \= [_|_], % below we check for avl_set; i.e., useful are only closure/3, global_set/1, ...
556 ? get_identity_as_equivalence(unknown,Set1,Set2,EQUIV),!,
557 opt_push_wait_flag_call_stack_info(WF,b_operator_call(equal,[Set1,Set2],unknown),WF2),
558 copy_wf_start(WF2,equal_expansions,CWF),
559 % EQUIV is a universal quantification, usually over an infinite domain
560 b_interpreter_check:b_force_check_boolean_expression(EQUIV,[],[],CWF,R), % we know EQUIV cannot be reified
561 copy_wf_finish(WF2,CWF).
562 % TO DO: add complement sets,
563
564 /* Cartesian Product Comparison */
565 :- use_module(kernel_equality,[empty_cartesian_product_wf/4]).
566 % A1*A2 = B1*B2 <=> (((A1={} or A2={}) & (B1={} or B2={})) or (A1=B1 & A2=B2))
567 equal_cartesian_product_wf(A1,A2,B1,B2,WF) :-
568 equality_cartesian_product_wf(A1,A2,B1,B2,pred_true,WF).
569 not_equal_cartesian_product_wf(A1,A2,B1,B2,WF) :-
570 equality_cartesian_product_wf(A1,A2,B1,B2,pred_false,WF).
571
572 equality_cartesian_product_wf(A1,A2,B1,B2,R,_WF) :-
573 nonvar(A1), A1=closure(P,T,BdyA1),
574 nonvar(B1), B1=closure(P,T,BdyB1),
575 nonvar(A2), A2=closure(P2,T2,BdyA2),
576 nonvar(B2), B2=closure(P2,T2,BdyB2),
577 % they have the same names; probably we are comparing identical values (e.g., in bvisual2)
578 same_texpr_body(BdyA1,BdyB1),
579 % note: we cannot simply call equality of A2 and B2 as cartesian products can be empty, see test 2072
580 same_texpr_body(BdyA2,BdyB2),
581 !,
582 R=pred_true.
583 equality_cartesian_product_wf(A1,A2,B1,B2,R,WF) :-
584 empty_cartesian_product_wf(A1,A2,EmptyA,WF),
585 equality_cart_product2(EmptyA,A1,A2,B1,B2,R,WF).
586 :- block equality_cart_product2(-, ?,?,?,?,?,?).
587 equality_cart_product2(pred_true,_,_,B1,B2,R,WF) :- empty_cartesian_product_wf(B1,B2,R,WF).
588 equality_cart_product2(pred_false,A1,A2,B1,B2,R,WF) :- equality_objects_wf_no_enum((A1,A2),(B1,B2),R,WF).
589
590 /* COMPARING AVL-SET with INTERVAL */
591
592 % check if an avl tree is equal to an interval range
593 avl_equal_to_interval(_A,L2,U2) :-
594 infinite_interval(L2,U2),!,fail. % otherwise infinite & avl_set is finite
595 % we can now assume L2, U2 are numbers (but could not yet be instantiated)
596 avl_equal_to_interval(A,L2,U2) :-
597 avl_min(A,int(L2)), avl_max(A,int(U2)),
598 Card is 1+U2-L2,
599 explicit_set_cardinality(avl_set(A),Card). % sets are equal: same size + same lower & upper bound
600
601 avl_not_equal_to_interval(A,L2,U2,WF) :- avl_equality_to_interval(A,L2,U2,pred_false,WF).
602
603 avl_equality_to_interval(_A,L2,U2,R,_WF) :-
604 infinite_interval(L2,U2),!,R=pred_false. % interval infinite & avl_set is finite
605 % we can now assume L2, U2 are numbers (but could not yet be instantiated)
606 avl_equality_to_interval(A,L2,U2,R,WF) :-
607 avl_min(A,int(AL)), avl_max(A,int(AU)),
608 Card is 1+AU-AL,
609 explicit_set_cardinality_wf(avl_set(A),ACard,WF),
610 equality_objects_wf_no_enum((int(ACard),(int(AL),int(AU))),
611 (int(Card),(int(L2),int(U2))),R,WF).
612 % sets are equal if same size + same lower & upper bound
613
614 /* COMPARING TWO CLOSURES */
615
616 % a variation of equal_explicit_sets which tries not expand and just compares two closures
617
618 same_closure(I1,I2) :-
619 is_interval_closure_or_integerset(I1,L1,U1,Finite1),
620 is_interval_closure_or_integerset(I2,L2,U2,Finite2), !,
621 Finite1=Finite2,
622 L1=L2, U1=U2.
623 same_closure(CPA,CPB) :-
624 is_cartesian_product_closure(CPA,A1,A2),
625 is_cartesian_product_closure(CPB,B1,B2),!,
626 equal_cartesian_product_wf(A1,A2,B1,B2,no_wf_available). % could be expensive
627 same_closure(S1,S2) :-
628 is_not_member_value_closure_or_integerset(S1,TYPE,MS1),
629 is_not_member_value_closure_or_integerset(S2,TYPE,MS2),
630 !,
631 kernel_objects:equal_object(MS1,MS2,same_closure). % could be expensive
632 same_closure(closure(P1,T1,B1),closure(P2,T2,B2)) :- same_closure_body_with_parameter_renaming(P1,T1,B1,P2,T2,B2).
633
634 same_closure_body(P,T1, B1, P,T2,B2) :-
635 same_types(T1,T2),
636 same_texpr_body(B1,B2).
637
638 % a version of same_closure_body which allows renaming of the parameters
639 same_closure_body_with_parameter_renaming(P1,T1, B1, P2,T2,B2) :-
640 same_types(T1,T2),
641 create_renaming(P1,P2,Renaming),
642 % TO DO: pass Renaming in AVL tree and rename on the fly
643 rename_bt(B2,Renaming,RenamedB2),
644 same_texpr_body(B1,RenamedB2).
645
646 create_renaming([],[],[]).
647 create_renaming([ID|T1],[ID|T2],TR) :- !, create_renaming(T1,T2,TR).
648 create_renaming([ID1|T1],[ID2|T2],[rename(ID2,ID1)|TR]) :-
649 create_renaming(T1,T2,TR).
650
651
652 % check if two wrapped expressions are equal (modulo associated Info, e.g. source loc info)
653 % and checking inserted values for equality (sometimes storing a closure will convert small inner closures into AVL sets)
654 same_texpr_body(E1,E2) :- empty_avl(E),same_texpr_body(E1,E,E2).
655 same_texpr_body(b(E1,Type1,_),AVL,b(E2,Type2,_)) :-
656 unify_types_strict(Type1,Type2), % check in principle redundant
657 same_texpr2(E1,AVL,E2).
658
659 :- use_module(value_persistance,[cache_is_activated/0]).
660 :- use_module(bsyntaxtree,[safe_syntaxelement_det/5, is_set_type/2,get_texpr_ids/2,
661 get_texpr_expr/2, get_negated_operator_expr/2]).
662 same_texpr2(value(V1),AVL,RHS) :- !,same_texpr_value2(RHS,AVL,V1).
663 same_texpr2(LHS,AVL,value(V2)) :- !,same_texpr_value2(LHS,AVL,V2).
664 same_texpr2(lazy_let_expr(ID,LHS,RHS),AVL,lazy_let_expr(ID2,LHS2,RHS2)) :- !,
665 same_texpr_body(LHS,AVL,LHS2),
666 avl_store(ID,AVL,ID2,NewAVL),
667 same_texpr_body(RHS,NewAVL,RHS2).
668 same_texpr2(lazy_let_pred(ID,LHS,RHS),AVL,lazy_let_pred(ID2,LHS2,RHS2)) :- !,
669 same_texpr_body(LHS,AVL,LHS2),
670 avl_store(ID,AVL,ID2,NewAVL),
671 same_texpr_body(RHS,NewAVL,RHS2).
672 same_texpr2(lazy_lookup(ID1), AVL,lazy_lookup(ID2)) :- !, avl_fetch(ID1,AVL,ID2).
673 same_texpr2(E1,AVL,E2) :- % Should we only enable this for same_closure_body_with_parameter_renaming?
674 quantifier_construct(E1,Functor,TParas1,Body1),
675 quantifier_construct(E2,Functor,TParas2,Body2),
676 !,
677 same_quantified_expression(TParas1,Body1,AVL,TParas2,Body2).
678 same_texpr2(assertion_expression(Pred,MsgStr,EXPR),AVL,assertion_expression(Pred2,MsgStr2,EXPR2)) :- !,
679 (MsgStr==MsgStr2 -> true
680 ; cache_is_activated,
681 debug_println(19,ignoring_difference_in_assertion_msg(MsgStr,MsgStr2))),
682 % difference can happen when constant was computed in other context,
683 % e.g, when cache_is_activated with different position info (with and wo file info, see Debug_6min_zone_du_PAS)
684 % Value-wise MsgStr cannot make a difference; only makes a difference in error message when expr not WD
685 same_texpr_body(Pred,AVL,Pred2),
686 same_texpr_body(EXPR,AVL,EXPR2).
687 same_texpr2(E1,AVL,E2) :-
688 functor(E1,F,Arity),
689 functor(E2,F,Arity),!,
690 safe_syntaxelement_det(E1,Subs1,_Names1,_List1,Constant1),
691 safe_syntaxelement_det(E2,Subs2,_Names2,_List2,Constant2),
692 Constant2==Constant1,
693 same_sub_expressions(Subs1,AVL,Subs2).
694 same_texpr2(E1,AVL,E2) :- same_texpr_with_rewrite(E1,AVL,E2),!.
695 same_texpr2(E1,AVL,E2) :- same_texpr_with_rewrite(E2,AVL,E1).
696 %same_texpr2(E1,_,E2) :-
697 % functor(E1,F1,Arity1),
698 % functor(E2,F2,Arity2), print(not_eq(F1,Arity1,F2,Arity2)),nl, print(E1),nl, print(E2),nl,nl,fail.
699 % some differences: assertion_expression/3 and function/2, ...
700
701 % some rewrite rules from ast_cleanup; but we cannot replicate all rules here
702 same_texpr_with_rewrite(negation(TE1),AVL,E2) :-
703 get_negated_operator_expr(b(E2,pred,[]),NegE2),!,
704 get_texpr_expr(TE1,E1),
705 same_texpr2(E1,AVL,NegE2).
706 same_texpr_with_rewrite(member(X1,b(value(Set1),_,_)),AVL,equal(X2,b(El2,_,_))) :-
707 singleton_set(Set1,El1), !,
708 % X : {El} <===> X = El ; required for JSON trace replay of test 1491
709 same_texpr_body(X1,X2),
710 same_texpr_value2(El2,AVL,El1).
711 same_texpr_with_rewrite(not_member(X1,b(value(Set1),_,_)),AVL,not_equal(X2,b(El2,_,_))) :-
712 singleton_set(Set1,El1), !,
713 % X /: {El} <===> X /= El ; required for JSON trace replay of test 1491
714 same_texpr_body(X1,X2),
715 same_texpr_value2(El2,AVL,El1).
716
717 % constructs with local quantified parameters:
718 quantifier_construct(comprehension_set(TParas,Body),comprehension_set,TParas,Body).
719 quantifier_construct(exists(TParas,Body),exists,TParas,Body).
720 quantifier_construct(forall(TParas,LHS,RHS),forall,TParas,Body) :-
721 Body = b(implication(LHS,RHS),pred,[]).
722 % TODO?: SIGMA, PI, UNION, INTER
723
724 :- use_module(bsyntaxtree,[split_names_and_types/3]).
725 same_quantified_expression(TParas1,Body1,AVL,TParas2,Body2) :-
726 split_names_and_types(TParas1,P1,T1),
727 split_names_and_types(TParas2,P2,T2),
728 same_types(T1,T2),
729 create_renaming(P1,P2,Renaming),
730 rename_bt(Body2,Renaming,RenamedB2), % TODO: store renaming in AVL and lookup on the fly
731 same_texpr_body(Body1,AVL,RenamedB2).
732
733 same_texpr_value2(E2,_,V2) :- var(V2),!,V2==E2.
734 same_texpr_value2(interval(Min,Max),_,avl_set(A)) :- !, % occurs in JSON trace replay for test 268
735 avl_equal_to_interval(A,Min,Max). % TODO: also compare the other way around above; only apply if Card not too large?
736 same_texpr_value2(value(V2),_,V1) :- !,
737 same_value_inside_closure(V1,V2).
738 %(same_value_inside_closure(V1,V2) -> true ; print(not_eq_vals(V1,V2)),nl,fail).
739 same_texpr_value2(comprehension_set(Paras,B2),AVL,closure(P,_,B1)) :- !,
740 get_texpr_ids(Paras,P),!,
741 same_texpr_body(B1,AVL,B2).
742 same_texpr_value2(cartesian_product(TB1,TB2),AVL,V1) :-
743 decompose_value_into_cartesian_product(V1,A1,A2), !,
744 %print(cart(A1,A2)),nl,
745 get_texpr_expr(TB1,B1),
746 same_texpr_value2(B1,AVL,A1),
747 get_texpr_expr(TB2,B2),
748 same_texpr_value2(B2,AVL,A2).
749 same_texpr_value2(StaticExpr,_,int(Nr)) :- number(Nr),
750 b_ast_cleanup:pre_compute_static_int_expression(StaticExpr,Nr),!.
751 % TO DO: maybe also check if both sides can be evaluated
752 % TO DO: move pre_compute_static_int_expression to another module
753 same_texpr_value2(E2,AVL,V1) :- rewrite_value(V1,E2,NewE1),!,
754 same_texpr2(NewE1,AVL,E2).
755 %same_texpr_value2(E1,_,E2) :-
756 % functor(E1,F1,Arity1),
757 % functor(E2,F2,Arity2), print(not_eq_val(F1,Arity1,F2,Arity2)),nl, fail,print(E1),nl, print(E2),nl,nl,fail.
758
759 decompose_value_into_cartesian_product(avl_set(A),A1,A2) :- !,
760 decompose_avl_set_into_cartesian_product_wf(A,A1,A2,no_wf_available).
761 decompose_value_into_cartesian_product(Closure,A1,A2) :- is_cartesian_product_closure(Closure,A1,A2).
762
763
764 % rewrite values back to AST nodes
765 rewrite_value(value(V),OtherVal,New) :- nonvar(V),
766 rewrite_value_aux(V,OtherVal,New).
767 %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)).
768 rewrite_value_aux(closure(P,T,B),_,Set) :-
769 is_member_closure(P,T,B,_,Set). % TO DO: ensure that ast_cleanup does not generate useless member closures ?
770 rewrite_value_aux(global_set(GS),_,AST) :-
771 rewrite_glob_set(GS,AST).
772 rewrite_value_aux(avl_set(A),interval(_,_),interval(TLow,TUp)) :-
773 avl_equal_to_interval(A,Low,Up),
774 TLow = b(integer(Low),integer,[]), TUp = b(integer(Up),integer,[]).
775 rewrite_value_aux(int(A),integer(_),integer(A)) :- number(A).
776 rewrite_value_aux(pred_true,_,boolean_true).
777 rewrite_value_aux(pred_false,_,boolean_false).
778 rewrite_value_aux(string(A),integer(_),string(A)) :- % value(string(A)) rewritten to AST node string(A)
779 atom(A).
780
781
782 rewrite_glob_set('REAL',real_set).
783 rewrite_glob_set('FLOAT',float_set).
784 rewrite_glob_set('STRING',string_set).
785 rewrite_glob_set(I,integer_set(I)) :-
786 kernel_objects:integer_global_set(I).
787
788 allow_expansion(avl_set(_),closure(P,T,B)) :-
789 is_small_specific_custom_set(closure(P,T,B),100).
790 allow_expansion(closure(P,T,B),avl_set(_)) :-
791 is_small_specific_custom_set(closure(P,T,B),100).
792
793 same_sub_expressions([],_,[]).
794 same_sub_expressions([H1|T1],AVL,[H2|T2]) :-
795 same_texpr_body(H1,AVL,H2),
796 same_sub_expressions(T1,AVL,T2).
797
798 same_value_inside_closure(V1,V2) :- var(V1),!, V1==V2.
799 same_value_inside_closure(_,V2) :- var(V2),!,fail.
800 same_value_inside_closure(rec(Fields1),rec(Fields2)) :- !,
801 % sets of records come in this form: struct(b(value(rec(FIELDS)),record(_),_))
802 same_fields_inside_closure(Fields1,Fields2).
803 same_value_inside_closure(V1,V2) :-
804 % we could attempt this only if the outer closure was large/infinite ??
805 is_custom_explicit_set(V1), is_custom_explicit_set(V2),
806 !,
807 (allow_expansion(V1,V2) -> EXP=allow_expansion ; EXP = no_expansion),
808 equal_explicit_sets4(V1,V2,EXP,no_wf_available). % usually only sets compiled differently inside closures
809 same_value_inside_closure([H1|T1],avl_set(A2)) :- !, % relevant for JSON trace replay for test 1263
810 try_convert_to_avl([H1|T1],V1), V1=avl_set(A1),
811 equal_avl_tree(A1,A2).
812 same_value_inside_closure(avl_set(A2),[H1|T1]) :- !,
813 try_convert_to_avl([H1|T1],V1), V1=avl_set(A1),
814 equal_avl_tree(A1,A2).
815 same_value_inside_closure(V1,V2) :- V1==V2.
816
817 same_fields_inside_closure(V1,V2) :- var(V1),!, V1==V2.
818 same_fields_inside_closure(_,V2) :- var(V2),!,fail.
819 same_fields_inside_closure([],[]).
820 same_fields_inside_closure([field(Name,V1)|T1],[field(Name,V2)|T2]) :-
821 same_value_inside_closure(V1,V2),
822 same_fields_inside_closure(T1,T2).
823
824 /*
825 same_texpr_body_debug(H1,H2) :-
826 (same_texpr_body(H1,H2) -> true
827 ; print('FAIL: '),nl,
828 translate:print_bexpr(H1),nl, translate:print_bexpr(H2),nl, print(H1),nl, print(H2),nl, fail). */
829
830 %test(Y2,Z2) :- empty_avl(X), avl_store(1,X,2,Y), avl_store(2,X,3,Z),
831 % avl_store(2,Y,3,Y2), avl_store(1,Z,2,Z2), equal_avl_tree(Y2,Z2).
832
833 %equal_avl_tree(A,B) :- avl_min(A,Min), avl_min(B,Min), cmp(Min,A,B).
834 %cmp(El,A,B) :-
835 % (avl_next(El,A,Nxt) -> (avl_next(El,B,Nxt), cmp(Nxt,A,B))
836 % ; \+ avl_next(El,B,Nxt) ).
837
838 % The following is faster than using avl_next
839 equal_avl_tree(A,B) :-
840 % statistics(walltime,[WT1,_]),if(equal_avl_tree2(A,B),true,(statistics(walltime,[_,W]),print(wall(W)),nl)).
841 %equal_avl_tree2(A,B) :-
842 avl_min(A,Min),
843 !,
844 avl_min(B,Min),
845 avl_max(A,Max), avl_max(B,Max),
846 % maybe also check avl_height +/- factor of 1.4405 (page 460, Knuth 3) ? but it seems this would trigger only extremely rarely
847 %avl_height(A,H1), avl_height(A,H2), log(check(Min,Max,H1,H2)),
848 avl_domain(A,L), avl_domain(B,L).
849 equal_avl_tree(empty,_) :- !, format(user_error,'*** Warning: empty AVL tree in equal_avl_tree~n',[]).
850 equal_avl_tree(A,B) :- add_internal_error('Illegal AVL tree: ',equal_avl_tree(A,B)),fail.
851
852 /* a predicate to check equality of two custom explicit sets */
853
854 % TO DO: deal with second set being a variable with kernel_cardinality_attr attribute
855 :- block not_equal_explicit_sets_wf(-,?,?), not_equal_explicit_sets_wf(?,-,?).
856 not_equal_explicit_sets_wf(global_set(X),global_set(Y),_) :- !,dif(X,Y).
857 not_equal_explicit_sets_wf(global_set(B),avl_set(A),WF) :- !,
858 \+ equal_explicit_sets4(avl_set(A),global_set(B),allow_expansion,WF).
859 not_equal_explicit_sets_wf(freetype(X),freetype(Y),_) :- !,dif(X,Y).
860 not_equal_explicit_sets_wf(avl_set(A),avl_set(B),_) :- !,
861 \+ equal_avl_tree(A,B).
862 %not_equal_explicit_sets_wf(X,Y,_) :- X==Y,!,fail.
863 not_equal_explicit_sets_wf(avl_set(A),I2,WF) :- is_interval_closure_or_integerset(I2,L2,U2),!, % also covers I2=global_set(...)
864 avl_not_equal_to_interval(A,L2,U2,WF).
865 not_equal_explicit_sets_wf(avl_set(A),global_set(B),WF) :- !,
866 \+ equal_explicit_sets4(avl_set(A),global_set(B),allow_expansion,WF).
867 not_equal_explicit_sets_wf(avl_set(A),CPB,WF) :-
868 is_cartesian_product_closure(CPB,B1,B2),!,
869 if(decompose_avl_set_into_cartesian_product_wf(A,A1,A2,WF), % should not produce pending co-routines, but better safe
870 kernel_objects:not_equal_object_wf((A1,A2),(B1,B2),WF),
871 true % no cartesian product can be equal to this avl_set
872 ).
873 not_equal_explicit_sets_wf(closure(P,T,B),avl_set(A),WF) :- !,
874 not_equal_explicit_sets_wf(avl_set(A),closure(P,T,B),WF).
875 not_equal_explicit_sets_wf(I1,I2,_) :- is_interval_closure_or_integerset(I1,L1,U1,Finite1),
876 is_interval_closure_or_integerset(I2,L2,U2,Finite2), !,
877 dif((Finite1,L1,U1),(Finite2,L2,U2)). % maybe we should call not_equal_objects on integers (not on inf values)?
878 not_equal_explicit_sets_wf(CPA,CPB,WF) :-
879 is_cartesian_product_closure(CPA,A1,A2), is_cartesian_product_closure(CPB,B1,B2),!,
880 not_equal_cartesian_product_wf(A1,A2,B1,B2,WF).
881 not_equal_explicit_sets_wf(S1,S2,WF) :-
882 is_not_member_value_closure_or_integerset(S1,TYPE,MS1),
883 is_not_member_value_closure_or_integerset(S2,TYPE,MS2),!,
884 kernel_objects:not_equal_object_wf(MS1,MS2,WF).
885 not_equal_explicit_sets_wf(closure(P,T,B),closure(P,T,B2),_) :-
886 same_texpr_body(B,B2),!,fail.
887 % TO DO: maybe support interval & avl_set comparison
888 not_equal_explicit_sets_wf(Set1,Set2,WF) :-
889 card_for_specific_custom_set(Set1,Card1,Code1), card_for_specific_custom_set(Set2,Card2,Code2),
890 call(Code1), call(Code2),!,
891 not_equal_expansions(Card1,Card2,Set1,Set2,WF).
892 not_equal_explicit_sets_wf(Set1,Set2,WF) :- not_equal_expansions(0,0,Set1,Set2,WF).
893
894
895 :- block not_equal_expansions(-,?,?,?,?), not_equal_expansions(?,-,?,?,?).
896 not_equal_expansions(F1,F2,_,_,_) :- F1 \= F2,!. % sets guaranteed to be different
897 not_equal_expansions(F,F,Set1,Set2,WF) :-
898 get_identity_as_equivalence(F,Set1,Set2,EQUIV),
899 !, %write(not),nl,translate:print_bexpr(EQUIV),nl,
900 opt_push_wait_flag_call_stack_info(WF,b_operator_call(equal,[Set1,Set2],unknown),WF2),
901 copy_wf_start(WF2,equal_expansions,CWF),
902 b_not_test_boolean_expression(EQUIV,[],[],CWF),
903 copy_wf_finish(WF2,CWF).
904 not_equal_expansions(F,F,Set1,Set2,WF) :-
905 % only expand if both sets have same cardinality
906 expand_custom_set_wf(Set1,E1,not_equal_expansions1,WF),
907 expand_custom_set_wf(Set2,E2,not_equal_expansions2,WF),
908 dif(E1,E2). /* TO DO: ensure that ordering and normalization is same for all representations ! */
909
910
911
912
913 :- use_module(b_global_sets,[b_empty_global_set/1, b_non_empty_global_set/1, b_global_set_cardinality/2]).
914 is_empty_explicit_set_wf(closure(P,T,B),WF) :- !,
915 is_empty_closure_wf(P,T,B,WF).
916 is_empty_explicit_set_wf(S,_WF) :- is_empty_explicit_set(S).
917
918 % with WF we can delay computing Card; see test 1272 / card({x|x:1..10 & x*x<i}) = 0 & i>1
919 % 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
920 is_empty_closure_wf(P,T,B,WF) :-
921 is_lambda_value_domain_closure(P,T,B, DomainValue,_Expr),!,
922 kernel_objects:empty_set_wf(DomainValue,WF).
923 is_empty_closure_wf(P,T,B,WF) :- is_cartesian_product_closure_aux(P,T,B,A1,A2),!,
924 very_approximate_cardinality(A1,C1,WF),
925 very_approximate_cardinality(A2,C2,WF),
926 blocking_safe_mul(C1,C2,0).
927 is_empty_closure_wf(P,T,B,_WF) :-
928 card_for_specific_closure2(P,T,B,CC,Code),
929 !,
930 call(Code),CC=0.
931 is_empty_closure_wf(P,T,Body,WF) :-
932 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
933 \+ ground_bexpr(Body), % otherwise better to use not_test_exists below (e.g., Bosch v6 Codespeed benchmark)
934 b_interpreter_check:reify_closure_with_small_cardinality(P,T,Body, WF, ReifiedList),
935 !,
936 domain(ReifiedList,0,1),
937 sum(ReifiedList,'#=',0).
938 is_empty_closure_wf(P,T,B,WF) :-
939 get_recursive_identifier_of_closure_body(B,TRID),!,
940 def_get_texpr_id(TRID,RID),
941 gen_typed_ids(P,T,TypedParas),
942 % now add Recursive ID's value to local state:
943 b_interpreter:b_not_test_exists(TypedParas,B,[used_ids([RID])],[bind(RID,closure(P,T,B))],[],no_compile,WF).
944 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
945 gen_typed_ids(P,T,TypedParas),
946 b_interpreter:b_not_test_exists(TypedParas,B,[used_ids([])],[],[],no_compile,WF). % used_ids are empty, as all variables already compiled into values
947
948 % very_approximate_cardinality: only required to return 0 for empty set, and number or inf for non-empty set, tested in 1893
949 :- block very_approximate_cardinality(-,?,?).
950 very_approximate_cardinality(avl_set(A),C,_) :- !, (A=empty -> print(empty_avl),nl,C=0 ; C=1).
951 very_approximate_cardinality([],C,_) :- !, C=0.
952 very_approximate_cardinality([_|_],C,_) :- !, C=1.
953 very_approximate_cardinality(Set,C,WF) :- kernel_objects:cardinality_as_int_wf(Set,int(C),WF).
954 % TO DO: maybe call is_empty_closure or similar for closures
955
956 gen_typed_ids([],[],R) :- !, R=[].
957 gen_typed_ids([ID|IT],[Type|TT],[b(identifier(ID),Type,[])|TTT]) :- !,
958 % TO DO: add Info field from outer set comprehension
959 gen_typed_ids(IT,TT,TTT).
960 gen_typed_ids(I,T,TI) :- add_internal_error('Call failed: ',gen_typed_ids(I,T,TI)),fail.
961
962 % version with WF can also deal with closures via exists !
963 is_empty_explicit_set(global_set(GS)) :- !, b_empty_global_set(GS).
964 is_empty_explicit_set(freetype(ID)) :- !, is_empty_freetype(ID).
965 is_empty_explicit_set(avl_set(A)) :- !,
966 (var(A) -> add_warning(is_empty_explicit_set,'Variable avl_set')
967 ; empty_avl(A), add_warning(is_empty_explicit_set,'Empty avl_set')
968 ).
969 is_empty_explicit_set(C) :- card_for_specific_closure(C,CC,Code),!,call(Code),CC=0.
970 is_empty_explicit_set(ES) :- expand_custom_set(ES,[],is_empty_explicit_set).
971
972
973 is_non_empty_explicit_set(CS) :- is_non_empty_explicit_set_wf(CS,no_wf_available).
974
975 is_non_empty_explicit_set_wf(global_set(GS),_WF) :- !, b_non_empty_global_set(GS).
976 is_non_empty_explicit_set_wf(freetype(ID),_WF) :- !, is_non_empty_freetype(ID).
977 is_non_empty_explicit_set_wf(avl_set(A),_WF) :- !,
978 (empty_avl(A) -> print('### Warning: empty avl_set (2)'),nl,fail
979 ; true).
980 is_non_empty_explicit_set_wf(closure(P,T,B),WF) :- !, is_non_empty_closure_wf(P,T,B,WF).
981 %is_non_empty_explicit_set_wf(ES,_WF) :- expand_custom_set(ES,[_|_],is_non_empty_explicit_set).
982
983
984 % TO DO: this code is a bit redundant with is_empty_closure_wf
985 is_non_empty_closure_wf(P,T,B,WF) :-
986 is_lambda_value_domain_closure(P,T,B, DomainValue,_Expr),!,
987 kernel_objects:not_empty_set_wf(DomainValue,WF).
988 is_non_empty_closure_wf(P,T,B,WF) :- is_cartesian_product_closure_aux(P,T,B,A1,A2),!,
989 very_approximate_cardinality(A1,C1,WF),
990 very_approximate_cardinality(A2,C2,WF),
991 blocking_safe_mul(C1,C2,CC),gt0(CC).
992 is_non_empty_closure_wf(P,T,B,_WF) :-
993 card_for_specific_closure2(P,T,B,CC,Code),!,call(Code),gt0(CC).
994 % TO DO: reify_closure_with_small_cardinality
995 is_non_empty_closure_wf(P,T,B,WF) :- WF \== no_wf_available,
996 get_recursive_identifier_of_closure_body(B,TRID),!,
997 def_get_texpr_id(TRID,RID),
998 gen_typed_ids(P,T,TypedParas),
999 % now add Recursive ID's value to local state:
1000 b_interpreter:b_test_exists(TypedParas,B,[used_ids([RID])],[bind(RID,closure(P,T,B))],[],WF).
1001 is_non_empty_closure_wf(P,T,B,WF) :- WF \== no_wf_available,
1002 % otherwise enumeration of test_exists will behave strangely; leading to enumeration warnings,... [TO DO: ensure we always have a WF or fix this below ?]
1003 % 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
1004 (debug_mode(off) -> true ; print(non_empty_closure_test(P)),nl, translate:print_bexpr(B),nl),
1005 gen_typed_ids(P,T,TypedParas),
1006 !,
1007 b_interpreter:b_test_exists(TypedParas,B,[used_ids([])],[],[],WF). % used_ids are empty, as all variables already compiled into values
1008 % some rules for set_subtraction, ... closures ?? if left part infinite and right part finite it must be infinite
1009 is_non_empty_closure_wf(P,T,B,WF) :-
1010 expand_custom_set_wf(closure(P,T,B),[_|_],is_non_empty_closure_wf,WF).
1011
1012
1013 % TO DO: expand cart / reify and use for pf_test
1014 test_empty_closure_wf(P,T,B,Res,WF) :-
1015 is_lambda_value_domain_closure(P,T,B, DomainValue,_Expr),!,
1016 kernel_equality:empty_set_test_wf(DomainValue,Res,WF).
1017 %test_empty_closure_wf(P,T,B,WF) :- is_cartesian_product_closure_aux(P,T,B,A1,A2),!,
1018 test_empty_closure_wf(P,T,B,Res,_WF) :-
1019 card_for_specific_closure2(P,T,B,CC,Code),!,call(Code),leq0(CC,Res).
1020 test_empty_closure_wf(P,T,B,Res,WF) :-
1021 \+ is_memoization_closure(P,T,B,_MemoID),
1022 preferences:preference(use_closure_expansion_memoization,false),
1023 !,
1024 bexpr_variables(B,ClosureWaitVars),
1025 % this does not perform a few optimisations of expand_normal closure:
1026 % memoization, stored_memo_expansion, is_closure1_value_closure, is_lambda_closure
1027 % print(test_empty_closure_wf),nl, translate:print_bexpr(B),nl,
1028 when((ground(ClosureWaitVars) ; nonvar(Res)),
1029 test_empty_closure_wf2(P,T,B,Res,WF)).
1030 test_empty_closure_wf(P,T,B,Res,WF) :- % print(expand_test(P)),nl,
1031 % was expand_custom_set_wf(closure(P,T,B),ExpES,test_empty_closure_wf,WF), in turn calls expand_closure_to_list
1032 expand_normal_closure(P,T,B,ExpES,_CDone,check(test_empty_closure_wf),WF),
1033 kernel_equality:empty_set_test_wf(ExpES,Res,WF).
1034 % /*@symbolic */ {x|x:1..100000000 & x mod 22=1} = x & (x={} <=> B=TRUE)
1035
1036 test_empty_closure_wf2(P,T,B,Res,WF) :-
1037 Res == pred_true,!,
1038 is_empty_closure_wf(P,T,B,WF).
1039 test_empty_closure_wf2(P,T,B,Res,WF) :- Res == pred_false,!,
1040 is_non_empty_closure_wf(P,T,B,WF).
1041 test_empty_closure_wf2(P,T,B,Res,WF) :-
1042 (is_empty_closure_now(P,T,B,WF) % we need to force expansion here to be able to use local cut ->
1043 % expand_normal_closure would now also expand the closure;
1044 -> Res=pred_true
1045 ; Res=pred_false).
1046
1047 % check if closure now; ground everything except WFE
1048 is_empty_closure_now(P,T,B,OuterWF) :-
1049 create_inner_wait_flags(OuterWF,is_empty_closure_now,WF),
1050 debug_opt_push_wait_flag_call_stack_info(WF,
1051 external_call('Check if empty set',[closure(P,T,B)],unknown),WF2),
1052 is_empty_closure_wf(P,T,B,WF2),
1053 ground_inner_wait_flags(WF2). % does not ground WFE in case WD errors are pending
1054
1055 :- block leq0(-,?).
1056 leq0(inf,Res) :- !, Res=pred_false.
1057 leq0(inf_overflow,Res) :- !, Res=pred_false.
1058 leq0(CC,Res) :- (CC>0 -> Res=pred_false ; Res=pred_true).
1059
1060 test_empty_explicit_set_wf(V,Res,_) :- var(V),!,
1061 add_internal_error('Illegal call: ',test_empty_explicit_set(V,Res,_)),fail.
1062 test_empty_explicit_set_wf(global_set(GS),Res,_WF) :- !,
1063 (b_empty_global_set(GS) -> Res=pred_true ; Res=pred_false).
1064 test_empty_explicit_set_wf(freetype(ID),Res,_WF) :- !, test_empty_freetype(ID,Res).
1065 test_empty_explicit_set_wf(avl_set(A),Res,_WF) :- !,
1066 (var(A) -> add_warning(test_empty_explicit_set_wf,'Variable avl_set'), Res=pred_true
1067 ; empty_avl(A), add_warning(test_empty_explicit_set_wf,'Empty avl_set'), Res = pred_true
1068 ; Res=pred_false).
1069 test_empty_explicit_set_wf(closure(P,T,B),Res,WF) :- !,
1070 test_empty_closure_wf(P,T,B,Res,WF).
1071 test_empty_explicit_set_wf(ES,Res,WF) :-
1072 expand_custom_set(ES,ExpES,test_empty_explicit_set),
1073 kernel_equality:empty_set_test_wf(ExpES,Res,WF).
1074
1075 :- block gt0(-).
1076 gt0(CC) :- (CC=inf -> true ; CC=inf_overflow -> true ; CC>0).
1077
1078 % a version to compute cardinality for
1079 explicit_set_cardinality_for_wf(closure(P,T,B),Card) :-
1080 (is_symbolic_closure_or_symbolic_mode(P,T,B) ; \+ ground_bexpr(B)),
1081 !,
1082 Card = inf. % assume card is infinite for WF computation; it may be finite!
1083 %explicit_set_cardinality_for_wf(avl_set(AVL),Size) :- !, quick_avl_approximate_size(AVL,Size).
1084 explicit_set_cardinality_for_wf(CS,Card) :- card_for_specific_custom_set(CS,Card,Code),!,
1085 on_enumeration_warning(call(Code),Card=inf). % see test 1519 for relevance
1086 explicit_set_cardinality_for_wf(_,inf). % assume card is infinite for WF computation; it may be finite!
1087 % TO DO: maybe never expand closures here !? -> closure_cardinality can expand closure !!!!!!
1088 %explicit_set_cardinality_for_wf(CS,Card) :-
1089 % on_enumeration_warning(
1090 % explicit_set_cardinality(CS,Card),
1091 % (debug_println(assuming_inf_card_for_wf), % see test 1519 for relevance
1092 % Card = inf)). % assume card is infinite for WF computation; it may be finite!
1093
1094 explicit_set_cardinality(CS,Card) :-
1095 % init_wait_flags(WF,[explicit_set_cardinality]), % there are a few checks for no_wf_available below
1096 explicit_set_cardinality_wf(CS,Card,no_wf_available).
1097 % ground_wait_flags(WF).
1098
1099 explicit_set_cardinality_wf(global_set(GS),Card,_) :- !,b_global_set_cardinality(GS,Card).
1100 explicit_set_cardinality_wf(freetype(GS),Card,_WF) :- !, freetype_cardinality(GS,Card).
1101 explicit_set_cardinality_wf(avl_set(S),Card,_WF) :- !,avl_size(S,Card).
1102 explicit_set_cardinality_wf(closure(P,T,B),Card,WF) :- closure_cardinality(P,T,B,Card,WF).
1103
1104 closure_cardinality(P,T,B,Card,WF) :-
1105 is_lambda_value_domain_closure(P,T,B, DomainValue,_Expr),!,
1106 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
1107 closure_cardinality(P,T,B,Card,WF) :- is_cartesian_product_closure_aux(P,T,B,A1,A2),!,
1108 kernel_objects:cardinality_as_int_wf(A1,int(C1),WF),
1109 kernel_objects:cardinality_as_int_wf(A2,int(C2),WF),
1110 blocking_safe_mul(C1,C2,Card).
1111 % TO DO: card_for_specific_closure2 calls is_lambda_value_domain_closure and is_cartesian_product_closure_aux again !
1112 closure_cardinality(P,T,B,Card,_WF) :-
1113 card_for_specific_closure2(P,T,B,CC,Code),
1114 !,
1115 call(Code),Card=CC.
1116 closure_cardinality(P,T,Body,Card,WF) :-
1117 (WF == no_wf_available -> CBody=Body
1118 ; b_compiler:b_compile(Body,P,[],[],CBody)
1119 ),
1120 % reify will work better if we used b_compiler:compile so that more sets can be detected as small
1121 closure_cardinality2(P,T,CBody,Card,WF).
1122 closure_cardinality2(P,T,Body,Card,WF) :-
1123 WF \== no_wf_available, % only do this if we have a WF store
1124 if(b_interpreter_check:reify_closure_with_small_cardinality(P,T,Body, WF, ReifiedList),
1125 true,
1126 (perfmessagecall(reify,reification_of_closure_for_card_failed(P),translate:print_bexpr(Body),Body),fail)),
1127 !,
1128 domain(ReifiedList,0,1),
1129 sum(ReifiedList,'#=',Card),
1130 % in this case we know card to be finite ! TO DO: ensure that check_finite propagates Card variable
1131 debug_println(9,reified_cardinality_sum(ReifiedList,Card)). % fd_dom(Card,Dom),print(dom(Card,Dom)),nl.
1132 % should we add a special check if Card=0 ? usually Card not instantiated at this point !
1133 %closure_cardinality(P,T,B,Card,WF) :- Card==0, %is_symbolic_closure(P,T,B),
1134 % !, is_empty_closure_wf(P,T,B,WF).
1135 closure_cardinality2(P,T,B,Card,WF) :-
1136 % TO DO: bexpr_variables(ClosureBody,ClosureWaitVars) and wait until those are bound; if Card = 0 -> empty_set; we can try to reifiy again
1137 expand_custom_set_wf(closure(P,T,B),Expansion,closure_cardinality,WF),
1138 my_length(Expansion,0,Card).
1139
1140 :- block my_length(-,?,?).
1141 my_length([],A,A).
1142 my_length([_|T],A,R) :- A1 is A+1, my_length(T,A1,R).
1143
1144 % compute domain and range for specific relations;
1145 % not the closure is total over the domain and surjective over the range
1146 % WARNING: this should never enumerate on its own, it is often called with
1147 % a cut straight after it; if some enumeration happens then only first solution
1148 % will be pursued (e.g., cond_assign_eq_obj)
1149 dom_range_for_specific_closure([],[],[],function(bijection),_WF).
1150 dom_range_for_specific_closure(closure(P,T,Pred),Domain,Range,Functionality,WF) :-
1151 dom_range_for_specific_closure2(P,T,Pred, Domain,Range,dom_and_range,Functionality,WF).
1152
1153 dom_range_for_specific_closure2(Par,Typ,Body, Domain,Range,Required,Functionality,WF) :-
1154 is_member_closure(Par,Typ,Body,_TYPE,SET),
1155 dom_range_for_member_closure(SET,Domain,Range,Required,Functionality,WF),!.
1156 dom_range_for_specific_closure2(Par,Typ,Body, DOMAIN,RANGE,_,Functionality,WF) :-
1157 is_cartesian_product_closure_aux(Par,Typ,Body,SET1,SET2),!,
1158 (singleton_set(SET2,_) % checks nonvar
1159 -> Functionality = function(total) % function if card(SET2)=1
1160 ; Functionality=relation),
1161 kernel_equality:empty_set_test_wf(SET1,EqRes1,WF),
1162 cond_assign_eq_obj_wf(EqRes1,RANGE,[],SET2,WF), % if SET1=[] then Range=[]
1163 kernel_equality:empty_set_test_wf(SET2,EqRes2,WF),
1164 cond_assign_eq_obj_wf(EqRes2,DOMAIN,[],SET1,WF). %if SET2=[] then Domain=[]
1165 dom_range_for_specific_closure2(Par,Typ,Body, DomainRange,DomainRange,_,function(bijection),_WF) :-
1166 is_id_closure_over(Par,Typ,Body,DomainRange,_).
1167
1168
1169 dom_range_for_member_closure(identity(b(value(SET1),ST1,_)),SET1,SET1,_,function(bijection),_) :-
1170 is_set_type(ST1,_). /* _SEQT=id(T1) */
1171 dom_range_for_member_closure(closure(V),Domain,Range,Required,Functionality,WF) :- % closure1 transitive closure
1172 % rx : A <-> B <=> closure1(rx) : A <-> B means we can simply remove closure1(.) wrapper
1173 V = b(value(VAL),_,_), nonvar(VAL),
1174 %write(peel_clos1_dom_range(Required)),nl, tools_printing:print_term_summary(closure(V)),nl,
1175 (VAL = closure(P,T,B)
1176 -> dom_range_for_specific_closure2(P,T,B,Domain,Range,Required,Functionality,WF)
1177 ; Functionality = relation, % we do not know if this is going to be a function
1178 (Required=domain_only -> true ; range_of_explicit_set_or_simple_value_wf(VAL,Range,WF)),
1179 (Required=range_only -> true ; domain_of_explicit_set_or_simple_value_wf(VAL,Domain,WF))
1180 ).
1181 dom_range_for_member_closure(Expr,Domain,Range,Required,Functionality,WF) :-
1182 is_comprehension_set_or_closure(Expr,P,T,Pred),
1183 (Required=domain_only
1184 -> Range = term(undefined), dom_for_specific_closure_aux(P,T,Pred, Domain,Functionality,WF)
1185 ; dom_range_for_specific_closure2(P,T,Pred, Domain,Range,Required,Functionality,WF)).
1186
1187
1188 domain_of_explicit_set_or_simple_value_wf([],Domain,_WF) :- !, Domain=[].
1189 domain_of_explicit_set_or_simple_value_wf([H|T],Domain,WF) :- !, T==[], % see test 2102
1190 H = (DomEl,_), equal_object_wf(Domain,[DomEl],domain_of_explicit_set_or_simple_value_wf,WF).
1191 domain_of_explicit_set_or_simple_value_wf(VAL,Domain,WF) :- domain_of_explicit_set_wf(VAL,Domain,WF).
1192
1193 range_of_explicit_set_or_simple_value_wf([],Range,_WF) :- !, Range=[].
1194 range_of_explicit_set_or_simple_value_wf([H|T],Range,WF) :- !, T==[],
1195 H = (_,RanEl), equal_object_wf(Range,[RanEl],range_of_explicit_set_or_simple_value_wf,WF).
1196 range_of_explicit_set_or_simple_value_wf(VAL,Range,WF) :- range_of_explicit_set_wf(VAL,Range,WF).
1197
1198
1199 is_comprehension_set_or_closure(comprehension_set(TP,Pred),P,T,Pred) :- split_names_and_types(TP,P,T).
1200 is_comprehension_set_or_closure(value(V),P,T,Pred) :- nonvar(V), V = closure(P,T,Pred).
1201
1202 % not sure if we need this: memoized functions are infinite usually and range can never be computed anyway
1203 %dom_range_for_member_closure(Expr,Domain,Range,Func) :-
1204 % expand_memoize_stored_function_reference(Expr,ExpandedValue),
1205 % dom_range_for_specific_closure(ExpandedValue,Domain,Range,Func,no_wf_available).
1206
1207 :- block cond_assign_eq_obj_wf(-,?,?,?,?).
1208 %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
1209 cond_assign_eq_obj_wf(pred_true,Res,A,_,WF) :- equal_object_wf(Res,A,cond_assign_eq_obj_wf_1,WF).
1210 cond_assign_eq_obj_wf(pred_false,Res,_,B,WF) :- equal_object_wf(Res,B,cond_assign_eq_obj_wf_2,WF).
1211
1212 is_cartesian_product_closure(closure(Par,Typ,Body),SET1,SET2) :-
1213 ? is_cartesian_product_closure_aux(Par,Typ,Body,SET1,SET2).
1214 is_cartesian_product_closure_aux(Par,Types,b(truth,pred,Info),SET1,SET2) :- Par=[_,_|_],!,
1215 append(LPar,[RParID],Par), append(LTypes,[RType],Types),
1216 construct_closure_if_necessary(LPar,LTypes,b(truth,pred,Info),SET1),
1217 construct_closure_if_necessary([RParID],[RType],b(truth,pred,Info),SET2).
1218 is_cartesian_product_closure_aux(Par,Types,Body,SET1,SET2) :- Par=[_,_|_],!,
1219 append(LPar,[RParID],Par), append(LTypes,[RType],Types),!,
1220 split_conjunct(Body,[RParID], RConjL, LPar, LConjL),
1221 bsyntaxtree:conjunct_predicates(RConjL,RConj), bsyntaxtree:conjunct_predicates(LConjL,LConj),
1222 construct_closure_if_necessary(LPar,LTypes,LConj,SET1),
1223 construct_closure_if_necessary([RParID],[RType],RConj,SET2).
1224 is_cartesian_product_closure_aux(Par,Typ,Body,SET1,SET2) :-
1225 SET = cartesian_product(b(value(SET1),ST1,_), b(value(SET2),ST2,_)),
1226 is_member_closure(Par,Typ,Body,couple(T1m,T2m),SET),
1227 is_set_type(ST1,T1),unify_types_strict(T1,T1m),
1228 is_set_type(ST2,T2),unify_types_strict(T2,T2m),!.
1229 %is_cartesian_product_closure_aux([ID1,ID2],[T1,T2],FBody,SET1,SET2) :- % is this not redundant wrt split ??
1230 % % a closure of the form {ID1,ID2|ID1 : SET1 & ID2 : SET2} ;
1231 % % can get generated when computing domain symbolically of lambda abstraction
1232 % FBody = b(Body,pred,_),
1233 % is_cartesian_product_body(Body,ID1,ID2,T1,T2,SET1,SET2). % ,print(cart_res(SET1,SET2)),nl.
1234
1235 % try and split conjunct into two disjoint parts (for detecting cartesian products)
1236 % on the specified variables
1237 % fails if it cannot be done
1238 split_conjunct(b(PRED,pred,Info),Vars1,C1,Vars2,C2) :-
1239 split_conjunct_aux(PRED,Info,Vars1,C1,Vars2,C2).
1240 split_conjunct_aux(truth,_Info,_Vars1,C1,_Vars2,C2) :- !,C1=[],C2=[].
1241 split_conjunct_aux(conjunct(A,B),_Info,Vars1,C1,Vars2,C2) :- !, % TO DO: use DCG
1242 split_conjunct(B,Vars1,CB1,Vars2,CB2), !, % Note: conjunct_predicates will create inner conjunct in A and atomic Expression in B
1243 split_conjunct(A,Vars1,CA1,Vars2,CA2),!,
1244 append(CA1,CB1,C1), append(CA2,CB2,C2).
1245 split_conjunct_aux(E,Info,Vars1,C1,_Vars2,C2) :- unique_id_comparison(E,ID),!,
1246 (member(ID,Vars1) -> C1=[b(E,pred,Info)], C2=[] ; C1=[], C2=[b(E,pred,Info)]).
1247
1248 unique_id_comparison(less(b(L,_,_),b(R,_,_)), ID) :- unique_id_comparison_aux(L,R,ID).
1249 unique_id_comparison(less_equal(b(L,_,_),b(R,_,_)), ID) :- unique_id_comparison_aux(L,R,ID).
1250 unique_id_comparison(greater(b(L,_,_),b(R,_,_)), ID) :- unique_id_comparison_aux(L,R,ID).
1251 unique_id_comparison(greater_equal(b(L,_,_),b(R,_,_)), ID) :- unique_id_comparison_aux(L,R,ID).
1252 unique_id_comparison(member(b(identifier(ID),_,_),b(V,_,_)), ID) :- explicit_value(V).
1253 unique_id_comparison(subset(b(identifier(ID),_,_),b(V,_,_)), ID) :- explicit_value(V).
1254 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
1255 % what about not_equal
1256
1257 unique_id_comparison_aux(identifier(ID),V,ID) :- !,explicit_value(V).
1258 unique_id_comparison_aux(V,identifier(ID),ID) :- explicit_value(V).
1259
1260 explicit_value(value(_)) :- !.
1261 explicit_value(integer(_)) :- !.
1262 explicit_value(unary_minus(TV)) :- !, explicit_tvalue(TV).
1263 explicit_value(interval(TV1,TV2)) :- !,
1264 explicit_tvalue(TV1), explicit_tvalue(TV2).
1265 explicit_value(seq(B)) :- !, explicit_tvalue(B). % usually encoded as values by b_compile
1266 explicit_value(seq1(B)) :- !, explicit_tvalue(B).
1267 explicit_value(iseq(B)) :- !, explicit_tvalue(B).
1268 explicit_value(iseq1(B)) :- !, explicit_tvalue(B).
1269 explicit_value(struct(B)) :- !, explicit_tvalue(B).
1270 explicit_value(rec(Fields)) :- !,
1271 explicit_tfields(Fields). % triggered in test 2274, 2358, 1983, 2388, 2275, 2484
1272 explicit_value(fin_subset(A)) :- !, explicit_tvalue(A).
1273 explicit_value(fin1_subset(A)) :- !, explicit_tvalue(A).
1274 explicit_value(pow_subset(A)) :- !, explicit_tvalue(A).
1275 explicit_value(pow1_subset(A)) :- !, explicit_tvalue(A).
1276 explicit_value(cartesian_product(A,B)) :- !, explicit_tvalue(A),explicit_tvalue(B).
1277 explicit_value(total_bijection(A,B)) :- !, explicit_tvalue(A),explicit_tvalue(B). % see test 1897 for cases below
1278 explicit_value(total_injection(A,B)) :- !, explicit_tvalue(A),explicit_tvalue(B).
1279 explicit_value(total_function(A,B)) :- !, explicit_tvalue(A),explicit_tvalue(B).
1280 explicit_value(total_surjection(A,B)) :- !, explicit_tvalue(A),explicit_tvalue(B).
1281 explicit_value(partial_function(A,B)) :- !, explicit_tvalue(A),explicit_tvalue(B).
1282 explicit_value(partial_injection(A,B)) :- !, explicit_tvalue(A),explicit_tvalue(B).
1283 explicit_value(partial_surjection(A,B)) :- !, explicit_tvalue(A),explicit_tvalue(B).
1284 explicit_value(relations(A,B)) :- !, explicit_tvalue(A),explicit_tvalue(B).
1285 explicit_value(total_relation(A,B)) :- !, explicit_tvalue(A),explicit_tvalue(B).
1286 explicit_value(surjection_relation(A,B)) :- !, explicit_tvalue(A),explicit_tvalue(B).
1287 explicit_value(total_surjection_relation(A,B)) :- !, explicit_tvalue(A),explicit_tvalue(B).
1288 explicit_value(real_set) :- !.
1289 explicit_value(string_set) :- !.
1290
1291 explicit_tvalue(b(B,_,_)) :- !, explicit_value(B).
1292
1293 explicit_tfields(V) :- var(V),!,fail.
1294 explicit_tfields([]).
1295 explicit_tfields([field(N,V)|T]) :- ground(N),explicit_tvalue(V),explicit_tfields(T).
1296
1297 % conjunct_predicates([CA1,CB1],C1),
1298 % conjunct_predicates([CA2,CB2],C2).
1299
1300 /* *********
1301 is_cartesian_product_body(conjunct(A,B),ID1,ID2,_T1,_T2,SET1,SET2) :- !,
1302 member_pred_value(A,CID1,CSET1),
1303 member_pred_value(B,CID2,CSET2),
1304 (ID1=CID1,ID2=CID2,SET1=CSET1,SET2=CSET2 ; ID1=CID2,ID2=CID1,SET1=CSET2,SET2=CSET1).
1305 is_cartesian_product_body(A,ID1,ID2,T1,T2,SET1,SET2) :-
1306 member_pred_value2(A,AID,ASET),
1307 ( AID=ID1 -> SET1=ASET, construct_closure_if_necessary([ID2],[T2],b(truth,pred,[]),SET2)
1308 ; AID=ID2 -> SET2=ASET, construct_closure_if_necessary([ID1],[T1],b(truth,pred,[]),SET1)).
1309
1310 member_pred_value(b(B,pred,_), ID,VAL) :- print(member_pred_value2(B,ID,VAL)),nl,
1311 member_pred_value2(B,ID,VAL).
1312 member_pred_value2(member(b(identifier(ID),_CT1,_),b(value(VAL),_SCT1,_)), ID,VAL). %_SCT1 = set(CT1)
1313 */
1314
1315 % check if we have POW(SET1) or SET1<->SET2 (equiv. to POW(SET1*SET2))
1316 is_full_powerset_or_relations_or_struct_closure(closure(Par,Typ,Body),SUBSETS) :-
1317 %TYPE = set(T),
1318 is_member_closure(Par,Typ,Body,TYPE,SET),
1319 is_full_powset_aux(SET,TYPE,SUBSETS).
1320
1321 :- use_module(library(lists),[maplist/3, maplist/4]).
1322 is_full_powset_aux(pow_subset(b(value(SET1),set(T1),_)),set(T1),[SET1]).
1323 is_full_powset_aux(relations(S1,S2),set(couple(T1,T2)),[SET1,SET2]) :-
1324 S1 = b(value(SET1),set(T1),_), S2 = b(value(SET2),set(T2),_).
1325 is_full_powset_aux(struct(b(value(rec(FIELDS)),record(_),_)),record(_),FieldValueSets) :-
1326 maplist(get_field_val,FIELDS,FieldValueSets).
1327
1328 get_field_val(field(_,Val),Val).
1329
1330 %[field(duration,global_set('INTEGER')),field(rhythm,global_set('INTEGER')),field(slot,avl_set(...))]
1331
1332 is_powerset_closure(closure(Par,Typ,Body),PType,Subset) :-
1333 is_member_closure(Par,Typ,Body,TYPE,SET),
1334 is_set_type(TYPE,T),
1335 nonvar(SET),
1336 is_powset_aux(SET,PType,b(VS,set(T),_)), % should never be seq(.) type
1337 nonvar(VS), VS = value(Subset). %,print(powerset(Subset)),nl.
1338 is_powset_aux(pow_subset(A),pow,A).
1339 is_powset_aux(pow1_subset(A),pow1,A).
1340 is_powset_aux(fin_subset(A),fin,A).
1341 is_powset_aux(fin1_subset(A),fin1,A).
1342
1343 % group together closures which can be treated like cartesian products in the sense that:
1344 % Closure is empty if either Set1 or Set2 (could also be empty in other conditions though)
1345 % Closure is subset of other Closure if same Constructor and both sets are subsets
1346 /* is_cartesian_product_like_closure(Closure,Constructor,Set1,Set2) :-
1347 is_cartesian_product_closure(Closure,S11,S12),!,
1348 Constructor = cartesian_product,Set1=S11,Set2=S12.
1349 is_cartesian_product_like_closure(closure(Par,Typ,Body),Constructor,Set1,Set2) :-
1350 is_member_closure(Par,Typ,Body,TYPE,SET),
1351 is_cart_like_relation(SET,Constructor,b(value(Set1),set(_T1),_), b(value(Set1),set(_T2),_)).
1352 is_cart_like_relation(relations(A,B),relations,A,B).
1353 is_cart_like_relation(partial_function(A,B),partial_function,A,B).
1354 is_cart_like_relation(partial_injection(A,B),partial_injection,A,B). */
1355
1356 % (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,[])))
1357 % 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) ?
1358
1359 % card_for_specific_custom_set(+Set,-Cardinality,-CodeToComputeCardinality)
1360 % succeeds if card can be computed efficiently
1361 card_for_specific_custom_set(CS,C,Cd) :- var(CS),!,
1362 add_internal_error('Internal error: var ',card_for_specific_custom_set(CS,C,Cd)),fail.
1363 card_for_specific_custom_set(global_set(GS),Card,true) :- !, b_global_set_cardinality(GS,Card).
1364 card_for_specific_custom_set(freetype(Id),Card,true) :- !, freetype_cardinality(Id,Card).
1365 card_for_specific_custom_set(avl_set(S),Card,true) :- !,avl_size(S,Card).
1366 card_for_specific_custom_set(closure(P,T,B),Card,CodeToComputeCard) :-
1367 card_for_specific_closure3(_,P,T,B,Card,CodeToComputeCard).
1368
1369 card_for_specific_closure(closure(P,T,Pred),Card,CodeToComputeCard) :-
1370 card_for_specific_closure3(_ClosureKind,P,T,Pred,Card,CodeToComputeCard).
1371 card_for_specific_closure(closure(P,T,Pred),ClosureKind,Card,CodeToComputeCard) :-
1372 card_for_specific_closure3(ClosureKind,P,T,Pred,Card,CodeToComputeCard).
1373
1374 :- use_module(bsyntaxtree,[is_truth/1]).
1375 card_for_specific_closure2(Par,Typ,Body, Card,Code) :-
1376 card_for_specific_closure3(_ClosureKind,Par,Typ,Body, Card,Code).
1377
1378 :- use_module(kernel_reals,[is_real_interval_closure_with_known_card/4]).
1379 % first argument for debugging purposes or filtering
1380 card_for_specific_closure3(special_closure,Par,Typ,Body, Card,Code) :-
1381 is_special_infinite_closure(Par,Typ,Body),!,Card=inf, Code=true.
1382 card_for_specific_closure3(truth_closure,_,Types,Body,Card,Code) :- is_truth(Body),!,
1383 % TO DO: also treat multiple parameters
1384 couplise_list(Types,Type),
1385 Code=kernel_objects:max_cardinality(Type,Card).
1386 card_for_specific_closure3(interval_closure,Par,Typ,Body, Card,Code) :-
1387 is_geq_leq_interval_closure(Par,Typ,Body,Low,Up), !,
1388 card_of_interval_inf(Low,Up,Card),
1389 Code=true. % should we return card_of_interval_inf as code ?
1390 card_for_specific_closure3(real_interval_closure,Par,Typ,Body, Card,Code) :-
1391 is_real_interval_closure_with_known_card(Par,Typ,Body,CC), !,
1392 Card=CC, Code=true.
1393 % TO DO: deal with non-infinite not_member_closures, prj1, prj2, id, ...
1394 card_for_specific_closure3(lambda_closure,Par,Typ,Body, Card,Code) :-
1395 is_lambda_value_domain_closure(Par,Typ,Body, DomainValue,_Expr),!, nonvar(DomainValue),
1396 efficient_card_for_set(DomainValue,Card,Code).
1397 card_for_specific_closure3(cartesian_product,Par,Typ,Body, Card,Code) :-
1398 is_cartesian_product_closure_aux(Par,Typ,Body,A1,A2),!, nonvar(A1), nonvar(A2),
1399 efficient_card_for_set(A1,Card1,Code1),
1400 efficient_card_for_set(A2,Card2,Code2),
1401 Code = (Code1,Code2, custom_explicit_sets:blocking_safe_mul(Card1,Card2,Card)).
1402 card_for_specific_closure3(member_closure,Par,Typ,Body, Card,Code) :-
1403 is_member_closure(Par,Typ,Body,TYPE,SET),
1404 nonvar(SET),!,
1405 card_for_member_closure(SET,TYPE,Card,Code).
1406 % Note: _ExprInfo could have: contains_wd_condition,
1407 % but if lambda is well-defined we compute the correct card ; if not then card is not well-defined anyway
1408 % maybe we should check contains_wd_condition produce a warning msg ?
1409
1410 % inner values can sometimes be a list, e.g., [pred_true,pred_false] for BOOL
1411 efficient_card_for_set(VAR,_,_) :- var(VAR),!,fail.
1412 efficient_card_for_set([],Card,Code) :- !, Card=0,Code=true.
1413 efficient_card_for_set([_|T],Card,Code) :- known_length(T,1,C), !, Card = C, Code=true.
1414 efficient_card_for_set(CS,Card,Code) :- card_for_specific_custom_set(CS,Card,Code).
1415 known_length(X,_,_) :- var(X),!,fail.
1416 known_length([],A,A).
1417 known_length([_|T],A,R) :- A1 is A+1, known_length(T,A1,R).
1418 known_length(avl_set(S),Acc,Res) :- avl_size(S,Card),
1419 Res is Acc+Card.
1420 % TO DO: also support closures
1421
1422 card_for_member_closure(parallel_product(b(value(A1),ST1,_),b(value(A2),ST1,_)),_T,Card,CodeToComputeCard) :- !,
1423 nonvar(A1), nonvar(A2),
1424 efficient_card_for_set(A1,Card1,Code1),
1425 CodeToComputeCard = (Code1,Code2, custom_explicit_sets:blocking_safe_mul(Card1,Card2,Card)),
1426 % cardinality computed like for cartesian_product.
1427 efficient_card_for_set(A2,Card2,Code2).
1428 card_for_member_closure(seq(b(Value,ST1,_)),_SEQT,Card,CodeToComputeCard) :- !, /* _SEQT=seq(T1) */
1429 is_set_type(ST1,_T1),
1430 get_cart_product_of_values(Value,ListOfSets), % accept a value or cartesian product of values
1431 CodeToComputeCard = custom_explicit_sets:seq_card_of_cart_product(ListOfSets,1,Card). % Card is 1 or inf
1432 card_for_member_closure(seq1(b(Value,ST1,_)),_SEQT,Card,CodeToComputeCard) :- !, /* _SEQT=seq1(T1) */
1433 is_set_type(ST1,_T1),
1434 get_cart_product_of_values(Value,ListOfSets), % accept a value or cartesian product of values
1435 CodeToComputeCard = custom_explicit_sets:seq_card_of_cart_product(ListOfSets,0,Card). % Card is 0 or inf
1436 card_for_member_closure(perm(b(value(SET1),ST1,_)),_SEQT,Card,CodeToComputeCard) :- !, /* _SEQT=perm(T1) */
1437 is_set_type(ST1,_T1),
1438 CodeToComputeCard = (kernel_objects:cardinality_as_int(SET1,int(SCard)),
1439 custom_explicit_sets:blocking_factorial(SCard,Card)).
1440 card_for_member_closure(iseq(b(value(SET1),ST1,_)),_SEQT,Card,CodeToComputeCard) :- !, /* _SEQT=iseq(T1) */
1441 is_set_type(ST1,_T1),
1442 CodeToComputeCard = (kernel_objects:cardinality_as_int(SET1,int(SCard)),
1443 kernel_card_arithmetic:blocking_nr_iseq(SCard,Card)).
1444 card_for_member_closure(iseq1(b(value(SET1),ST1,_)),_SEQT,Card,CodeToComputeCard) :- !, /* _SEQT=iseq1(T1) */
1445 is_set_type(ST1,_T1),
1446 CodeToComputeCard = (kernel_objects:cardinality_as_int(SET1,int(SCard)),
1447 kernel_card_arithmetic:blocking_nr_iseq1(SCard,Card)).
1448 card_for_member_closure(identity(b(value(SET1),ST1,_)),_SEQT,Card,CodeToComputeCard) :- !, /* _SEQT=id(T1) */
1449 is_set_type(ST1,_T1),
1450 CodeToComputeCard =
1451 kernel_objects:cardinality_as_int(SET1,int(Card)).
1452 card_for_member_closure(struct(b(RecVal,record(_FieldSetTypes),_)), record(_FieldTypes), % set of records
1453 Card,CodeToComputeCard) :-
1454 !,
1455 (RecVal=value(RECF), nonvar(RECF), RECF=rec(FIELDS) % value has been computed:
1456 -> CodeToComputeCard = custom_explicit_sets:get_field_cardinality(FIELDS,Card)
1457 ; RecVal = rec(TypedFields), % we still have a typed AST
1458 maplist(get_field_val_type,TypedFields,Exprs,Types),
1459 l_card_for_member_closure(Exprs,Types,Card, CodeToComputeCard)
1460 ).
1461 card_for_member_closure(value(Value), _Type, Card,CodeToComputeCard) :- !,
1462 % we have a closure of the type {x|x:S}; equivalent to S
1463 (nonvar(Value),
1464 Value=closure(P,T,B)
1465 -> % cardinality_as_int may expand it ! is bad if e.g. we called this code to check if a closure is infinite
1466 card_for_specific_closure2(P,T,B,Card,CodeToComputeCard) % will not expand, but fail if cannot be computed
1467 % TO DO: provide an argument: precise_or_efficient
1468 ; CodeToComputeCard = kernel_objects:cardinality_as_int(Value,int(Card))
1469 ).
1470 card_for_member_closure(comprehension_set(TP,B), _Type, Card,CodeToComputeCard) :- !, % see test 2571
1471 split_names_and_types(TP,P,T), % what if Body reads variables; b_compile should have removed them??
1472 card_for_specific_closure3(_ClosureKind,P,T,B,Card,CodeToComputeCard).
1473 % now dealt with separately above: card_for_member_closure(cartesian_product(b(value(SET1),set(T1),_), b(value(SET2),set(T2),_)),
1474 % couple(T1,T2), Card,CodeToComputeCard) :- !,
1475 % CodeToComputeCard =
1476 % (kernel_objects:cardinality_as_int(SET1,int(SCard1)),
1477 % kernel_objects:cardinality_as_int(SET2,int(SCard2)),
1478 % custom_explicit_sets:blocking_safe_mul(SCard1,SCard2,Card) ).
1479 card_for_member_closure(POW,TYPE, Card,CodeToComputeCard) :-
1480 (POW = pow_subset(b(value(SET),TYPE,_)) ;
1481 POW = fin_subset(b(value(SET),TYPE,_))),!,
1482 CodeToComputeCard =
1483 (kernel_objects:cardinality_as_int(SET,int(SCard)),
1484 custom_explicit_sets:blocking_safe_pow2(SCard,Card)
1485 ).
1486 card_for_member_closure(POW,TYPE, Card,CodeToComputeCard) :-
1487 (POW = pow1_subset(b(value(SET),TYPE,_)) ;
1488 POW = fin1_subset(b(value(SET),TYPE,_))),!,
1489 CodeToComputeCard =
1490 (kernel_objects:cardinality_as_int(SET,int(SCard)),
1491 custom_explicit_sets:blocking_safe_pow2(SCard,C1),
1492 custom_explicit_sets:safe_dec(C1,Card)
1493 ).
1494 card_for_member_closure(RELEXPR,SType, Card,CodeToComputeCard) :-
1495 is_set_type(SType,couple(T1,T2)),
1496 is_a_relation(RELEXPR, b(value(DOM),set(T1),_),
1497 b(value(RAN),set(T2),_), DCard,RCard,Card,RELCODE),!,
1498 CodeToComputeCard =
1499 (
1500 kernel_objects:cardinality_as_int(DOM,int(DCard)),
1501 kernel_objects:cardinality_as_int(RAN,int(RCard)),
1502 custom_explicit_sets:call_card_for_relations(DCard,RCard,RELCODE)
1503 ).
1504 card_for_member_closure(BODY, integer, Card,CodeToComputeCard) :-
1505 is_interval_with_integer_bounds(BODY,Low,Up),!,
1506 CodeToComputeCard = custom_explicit_sets:card_of_interval_inf(Low,Up,Card).
1507 %card_for_member_closure(BODY, Type, Card,CodeToComputeCard) :- print(try_card(BODY,Type)),nl,fail.
1508 % TO DO: add maybe other common closures ? simple value closure
1509 % also: what if subexpressions are not of value() type ?
1510
1511 :- public call_card_for_relations/3.
1512 :- block call_card_for_relations(-,?,?), call_card_for_relations(?,-,?).
1513 call_card_for_relations(_,_,RELCODE) :- call(RELCODE).
1514
1515 get_field_val_type(field(_F1,b(Expr1,Type1,_)),Expr1,Type1).
1516
1517 l_card_for_member_closure([Expr1],[Type1],Card,CodeToComputeCard) :- !,
1518 card_for_member_closure(Expr1,Type1,Card, CodeToComputeCard).
1519 l_card_for_member_closure([Expr1|ET],[Type1|TT],Card,CodeToComputeCard) :-
1520 CodeToComputeCard = (Code1,Code2, custom_explicit_sets:blocking_safe_mul(Card1,Card2,Card)),
1521 card_for_member_closure(Expr1,Type1,Card1, Code1),
1522 l_card_for_member_closure(ET,TT,Card2,Code2).
1523
1524 :- public safe_dec/2. % used in card_for_member_closure
1525 :- block safe_dec(-,?).
1526 safe_dec(inf,R) :- !, R=inf.
1527 safe_dec(inf_overflow,R) :- !, R=inf_overflow.
1528 safe_dec(X,R) :- R is X-1.
1529
1530 :- use_module(kernel_equality,[empty_set_test/2]).
1531 :- public seq_card/3. % used in card_for_member_closure
1532 :- block seq_card(-,?,?).
1533 seq_card([],EmptyVal,R) :- !,R=EmptyVal.
1534 seq_card([_|_],_,R) :- !,R=inf.
1535 seq_card(X,EmptyVal,Res) :- empty_set_test(X,EqRes),
1536 set_card_or_inf(EqRes,EmptyVal,Res).
1537
1538 :- block set_card_or_inf(-,?,?).
1539 set_card_or_inf(pred_true,Nr,Nr).
1540 set_card_or_inf(pred_false,_,inf).
1541 % card(seq({n|n>10 & (n mod 20=3 & n mod 20 = 4) }))
1542
1543 % for list [S1,S2,...,Sn] of sets we compute
1544 % cardinality of seq(1)( S1 ** S2 ... ** Sn) to be either 0/1 (if one set is empty) or inf (if all sets are non-empty)
1545 :- public seq_card_of_cart_product/3. % used in card_for_member_closure
1546 seq_card_of_cart_product([Set],EmptyCard,Res) :- !,
1547 seq_card(Set,EmptyCard,Res).
1548 seq_card_of_cart_product([Set1|T],EmptyCard,Res) :-
1549 seq_card(Set1,EmptyCard,Res1),
1550 (Res1==EmptyCard -> Res=Res1
1551 ; combine_card(Res1,Res2,Res),
1552 seq_card_of_cart_product([Set1|T],EmptyCard,Res2)
1553 ).
1554
1555 % combine cardinalities of either 0/1 and inf
1556 :- block combine_card(-,-,?).
1557 combine_card(X,Y,R) :- X==inf,!,R=Y.
1558 combine_card(X,Y,R) :- Y==inf,!,R=X.
1559 combine_card(X,_,R) :- integer(X),!,R=X.
1560 combine_card(_,R,R).
1561
1562 get_cart_product_of_values(Value,ListOfSetValues) :- get_cart_product_of_values(Value,ListOfSetValues,[]). %write(get_cart(ListOfSetValues)),nl,nl.
1563 % check if something is a value or a cartesian product of values
1564 % the result will be used for emptyness check and should NOT be used to compute the cardinality
1565 get_cart_product_of_values(value(SET)) --> !, [SET].
1566 get_cart_product_of_values(cartesian_product(A,B)) --> !,
1567 tcart_product_of_values(A), tcart_product_of_values(B).
1568 get_cart_product_of_values(pow_subset(_)) --> !, [ [] ]. % create some non-empty set; POW({}) is not empty
1569 get_cart_product_of_values(fin_subset(_)) --> !, [ [] ]. % ditto
1570 get_cart_product_of_values(seq(_)) --> !, [ [] ]. % ditto
1571 get_cart_product_of_values(iseq(_)) --> !,[ [] ]. % ditto
1572 get_cart_product_of_values(pow1_subset(A)) --> !, tcart_product_of_values(A). % POW1(S)={} <=> S={}
1573 get_cart_product_of_values(fin1_subset(A)) --> !, tcart_product_of_values(A). % FIN1(S)={} <=> S={}
1574 get_cart_product_of_values(seq1(A)) --> !, tcart_product_of_values(A). % seq1(S)={} <=> S={}
1575 get_cart_product_of_values(iseq1(A)) --> !, tcart_product_of_values(A). % iseq1(S)={} <=> S={}
1576 %get_cart_product_of_values(X) --> {functor(X,F,N), write(uncov_get_cart(F,N)),nl,fail}.
1577 % TODO: records,relations,...
1578
1579 tcart_product_of_values(b(E,_,_)) --> get_cart_product_of_values(E).
1580
1581
1582
1583 :- public get_field_cardinality/2. % used in card_for_member_closure
1584 get_field_cardinality([],1).
1585 get_field_cardinality([field(_Name,Value)|T],ResCard) :-
1586 kernel_objects:cardinality_as_int(Value,int(SCard1)),
1587 get_field_cardinality(T,RestCard), blocking_safe_mul(SCard1,RestCard,ResCard).
1588
1589 :- use_module(kernel_card_arithmetic).
1590
1591 :- block blocking_safe_mul(-,-,?).
1592 blocking_safe_mul(A,B,R) :-
1593 ( A==0 -> R=0
1594 ; B==0 -> R=0
1595 ; A==1 -> R=B
1596 ; B==1 -> R=A
1597 ; blocking_safe_mul2(A,B,R) ).
1598
1599 :- block blocking_safe_mul2(-,?,?), blocking_safe_mul2(?,-,?).
1600 blocking_safe_mul2(A,B,Res) :-
1601 (safe_mul(A,B,AB) -> Res=AB
1602 ; add_warning(blocking_safe_mul2,'Call failed: ',blocking_safe_mul2(A,B,Res)),
1603 % could happen for something like prj2(BOOL,NAT) = prj2(BOOL,0..n)
1604 fail).
1605
1606 :- public blocking_safe_pow2/2. % used in card_for_member_closure above
1607 :- block blocking_safe_pow2(-,?).
1608 blocking_safe_pow2(A,Res) :-
1609 (safe_pow2(A,A2) -> Res=A2
1610 ; add_warning(blocking_safe_pow2,'Call failed: ',safe_pow2(A,Res)),fail).
1611
1612
1613
1614
1615 :- assert_must_succeed((custom_explicit_sets:card_for_specific_closure2(['_zzzz_binary'],[integer],
1616 b(member(b(identifier('_zzzz_binary'),integer,[generated]),
1617 b(interval(b(value(int(1)),integer,[]),b(value(int(10)),integer,[])),set(integer),[])),pred,[]),R,C),
1618 call(C),
1619 R=10)).
1620
1621 %! is_interval_closure_or_integerset(+I,-L,-U)
1622 is_interval_closure_or_integerset(Var,_,_) :- var(Var),!,fail.
1623 is_interval_closure_or_integerset(global_set(X),Low,Up) :- !, get_integer_set_interval(X,Low,Up).
1624 is_interval_closure_or_integerset(Set,El,El) :- singleton_set(Set,ELX),
1625 nonvar(ELX), ELX=int(El),!. % new, useful??
1626 is_interval_closure_or_integerset(closure(P,T,B),Low,Up) :-
1627 (is_geq_leq_interval_closure(P,T,B,Low,Up) -> true ; is_interval_closure(P,T,B,Low,Up)).
1628
1629 % with an additional argument to know if the set is finite or infinite:
1630 is_interval_closure_or_integerset(Set,Low,Up,Finite) :-
1631 is_interval_closure_or_integerset(Set,Low,Up),
1632 % if we obtain Low, Up as variables then these must be finite numbers; they cannot stand for inf
1633 (infinite_interval(Low,Up) -> Finite=infinite ; Finite=finite).
1634
1635 % a version that also accepts real intervals
1636 :- use_module(kernel_reals,[is_interval_closure_or_realset/3]).
1637 is_interval_closure_or_numberset(Set,Low,Up) :- is_interval_closure_or_integerset(Set,L,U),!, Low=L,Up=U.
1638 is_interval_closure_or_numberset(Set,Low,Up) :- is_interval_closure_or_realset(Set,Low,Up).
1639
1640 get_integer_set_interval('NAT',0,MAXINT) :- (preferences:preference(maxint,MAXINT)->true).
1641 get_integer_set_interval('NAT1',1,MAXINT) :- (preferences:preference(maxint,MAXINT)->true).
1642 get_integer_set_interval('INT',MININT,MAXINT) :-
1643 ((preferences:preference(maxint,MAXINT),preferences:preference(minint,MININT))->true).
1644 get_integer_set_interval('NATURAL',0,inf).
1645 get_integer_set_interval('NATURAL1',1,inf).
1646 get_integer_set_interval('INTEGER',minus_inf,inf).
1647 % TO DO: add minus_inf to kernel_objects !
1648
1649 :- block geq_inf(-,?), geq_inf(?,-).
1650 geq_inf(inf,_) :- !.
1651 geq_inf(minus_inf,B) :- !, B=minus_inf.
1652 geq_inf(_,minus_inf) :- !.
1653 geq_inf(A,inf) :- !, A=inf.
1654 geq_inf(inf_overflow,_) :- !.
1655 geq_inf(A,inf_overflow) :- !, A=inf_overflow.
1656 geq_inf(A,B) :- A >= B.
1657
1658 :- block minimum_with_inf(-,-,?).
1659 % in the first three cases we can determine outcome without knowing both args
1660 minimum_with_inf(A,B,R) :- (A==minus_inf ; B==minus_inf),!,R=minus_inf.
1661 minimum_with_inf(A,B,R) :- A==inf,!,R=B.
1662 minimum_with_inf(A,B,R) :- B==inf,!,R=A.
1663 minimum_with_inf(A,B,R) :- minimum_with_inf1(A,B,R), geq_inf(A,R), geq_inf(B,R).
1664 :- block minimum_with_inf1(-,?,?), minimum_with_inf1(?,-,?).
1665 minimum_with_inf1(minus_inf,_,R) :- !, R=minus_inf.
1666 minimum_with_inf1(_,minus_inf,R) :- !, R=minus_inf.
1667 minimum_with_inf1(inf,B,R) :- !, R=B.
1668 minimum_with_inf1(A,inf,R) :- !, R=A.
1669 minimum_with_inf1(inf_overflow,B,R) :- !, R=B.
1670 minimum_with_inf1(A,inf_overflow,R) :- !, R=A.
1671 minimum_with_inf1(A,B,R) :- (A<B -> R=A ; R=B).
1672
1673 :- block maximum_with_inf(-,-,?).
1674 % in the first three cases we can determine outcome without knowing both args
1675 maximum_with_inf(A,B,R) :- (A==inf ; B==inf),!,R=inf.
1676 maximum_with_inf(A,B,R) :- A==minus_inf,!,R=B.
1677 maximum_with_inf(A,B,R) :- B==minus_inf,!,R=A.
1678 maximum_with_inf(A,B,R) :- maximum_with_inf1(A,B,R), geq_inf(R,A), geq_inf(R,B).
1679 :- block maximum_with_inf1(-,?,?), maximum_with_inf1(?,-,?).
1680 maximum_with_inf1(inf,_,R) :- !, R=inf.
1681 maximum_with_inf1(_,inf,R) :- !, R=inf.
1682 maximum_with_inf1(minus_inf,B,R) :- !, R=B.
1683 maximum_with_inf1(A,minus_inf,R) :- !, R=A.
1684 maximum_with_inf1(inf_overflow,_,R) :- !, R=inf_overflow.
1685 maximum_with_inf1(_,inf_overflow,R) :- !, R=inf_overflow.
1686 maximum_with_inf1(A,B,R) :- (A>B -> R=A ; R=B).
1687
1688 /* utilities for detecting interval closures */
1689 construct_interval_closure(Low,Up,Res) :- (Low==inf;Up==minus_inf),!,Res=[].
1690 construct_interval_closure(Low,Up,Res) :- number(Low),number(Up), Low>Up,!,Res=[].
1691 construct_interval_closure(Low,Up,Res) :- Up==inf,!,
1692 ( Low==0 -> Res = global_set('NATURAL')
1693 ; Low==1 -> Res = global_set('NATURAL1')
1694 ; Low==minus_inf -> Res = global_set('INTEGER')
1695 ; Low==inf -> Res = []
1696 ; construct_greater_equal_closure(Low,Res)
1697 ).
1698 construct_interval_closure(Low,Up,Res) :- Low==minus_inf,!,
1699 construct_less_equal_closure(Up,Res).
1700 construct_interval_closure(Low,Up,Res) :- Low==Up,!,
1701 (number(Low) -> construct_one_element_custom_set(int(Low),Res)
1702 ; Res = [int(Low)]).
1703 construct_interval_closure(Low,Up,Res) :-
1704 construct_interval_set(Low,Up,Set),
1705 construct_member_closure('_zzzz_unary',integer,[],Set,Res).
1706
1707 transform_global_sets_into_closure(closure(P,T,B),closure(P,T,B)).
1708 transform_global_sets_into_closure(global_set(X),Res) :-
1709 transform_global_set_into_closure_aux(X,Res).
1710 transform_global_set_into_closure_aux('NATURAL',Res) :-
1711 construct_greater_equal_closure(0,Res).
1712 transform_global_set_into_closure_aux('NATURAL1',Res) :-
1713 construct_greater_equal_closure(1,Res).
1714 % TO DO: add INTEGER
1715
1716
1717
1718 is_geq_leq_interval_closure([Par],[integer],b(Body,pred,Span),Low,Up) :-
1719 (var(Par)
1720 -> add_internal_error('Non-ground closure: ',closure([Par],[integer],b(Body,pred,Span))),fail
1721 ; get_geq_leq_bounds(Body,Par,Low,Up)).
1722
1723 infinite_interval(Low,Up) :- (Low==minus_inf -> true ; Up==inf).
1724
1725 :- assert_must_succeed((card_of_interval_inf(1,10,10))).
1726 :- assert_must_succeed((card_of_interval_inf(1,inf,R),R==inf)).
1727 :- assert_must_succeed((card_of_interval_inf(_,inf,R),R==inf)).
1728 :- assert_must_succeed((card_of_interval_inf(minus_inf,0,R),R==inf)).
1729 :- assert_must_succeed((card_of_interval_inf(minus_inf,_,R),R==inf)).
1730 :- assert_must_succeed((card_of_interval_inf(minus_inf,inf,R),R==inf)).
1731 :- assert_must_succeed((card_of_interval_inf(2,2,R), R==1)).
1732 :- assert_must_succeed((card_of_interval_inf(12,2,R), R==0)).
1733 :- assert_must_succeed((card_of_interval_inf(2,B,10), B==11)).
1734 :- assert_must_succeed((card_of_interval_inf(A,12,10), A==3)).
1735 :- assert_must_succeed((card_of_interval_inf(A,12,0), A=222)).
1736 :- assert_must_succeed((card_of_interval_inf(12,B,0), B=11)).
1737 :- assert_must_fail((card_of_interval_inf(A,12,0), A=12)).
1738 % compute cardinality of interval; allow bounds to be inf and minus_inf (but if so, they must be bound straightaway)
1739 card_of_interval_inf(A,B,Card) :-
1740 at_least_two_vars(A,B,Card), % initially this will usually be true, if only one variable we can compute result
1741 preferences:preference(use_clpfd_solver,true),
1742 !,
1743 clpfd_interface:post_constraint(Card #= max(0,1+B-A),custom_explicit_sets:block_card_of_interval_inf(A,B,Card)).
1744 card_of_interval_inf(A,B,Card) :- A==minus_inf,!,
1745 (B==minus_inf -> add_internal_error('Illegal call: ',card_of_interval_inf(A,B,Card)) ; true),
1746 Card=inf.
1747 card_of_interval_inf(A,B,Card) :- B==inf,!,
1748 (A==inf -> add_internal_error('Illegal call: ',card_of_interval_inf(A,B,Card)) ; true),
1749 Card=inf.
1750 card_of_interval_inf(A,B,Card) :- block_card_of_interval_inf(A,B,Card).
1751
1752 at_least_two_vars(A,B,C) :- var(A),!,(var(B) -> not_infinite_bound(C) ; number(B),var(C)).
1753 at_least_two_vars(A,B,C) :- number(A), var(B),var(C).
1754 not_infinite_bound(A) :- (var(A) ; number(A)). % inf can only appear immediately, not for variables
1755
1756 :- block block_card_of_interval_inf(-,?,-),block_card_of_interval_inf(?,-,-).
1757 block_card_of_interval_inf(A,_,Card) :- A==minus_inf,!, Card=inf.
1758 block_card_of_interval_inf(_,B,Card) :- B==inf,!, Card=inf.
1759 block_card_of_interval_inf(From,To,Card) :- number(From),number(To),!,
1760 (From>To -> Card=0 ; Card is (To-From)+1).
1761 block_card_of_interval_inf(A,B,C) :- number(C),!, number_card_of_interval_inf_aux(C,A,B).
1762 block_card_of_interval_inf(A,B,C) :- C==inf,!,
1763 % probably this should systematically fail; if A and B are not inf/minus_inf now they will never be
1764 print(infinite_interval_requested(A,B,C)),nl,
1765 when((nonvar(A),nonvar(B)), block_card_of_interval_inf(A,B,C)).
1766 block_card_of_interval_inf(A,B,C) :- add_internal_error('Illegal call: ',card_of_interval_inf(A,B,C)).
1767 :- use_module(inf_arith,[block_inf_greater/2]).
1768 number_card_of_interval_inf_aux(0,A,B) :- !, % empty interval
1769 % if A and B are variables then they will not become inf later ??
1770 % inf can only be set directly for sets such as {x|x>4} or NATURAL1
1771 (((var(A);number(A)),(var(B);number(B)))
1772 % hence we can use ordinary comparison (with CLPFD) here
1773 -> kernel_objects:less_than_direct(B,A)
1774 % TO DO: we could do this even if both A and B are variables !! ex : {n,m|n..m = {} & m..100={} & 103..n={}}
1775 ; block_inf_greater(A,B)).
1776 %number_card_of_interval_inf_aux(Card,From,B) :- number(From),!, B is (From+Card)-1.
1777 %number_card_of_interval_inf_aux(Card,A,To) :- number(To),!, A is 1+To-Card.
1778 number_card_of_interval_inf_aux(Card,A,B) :-
1779 Card>0, C1 is Card-1,
1780 kernel_objects:int_minus(int(B),int(A),int(C1)).
1781
1782
1783 get_geq_leq_bounds(conjunct(b(LEFT,pred,_),b(RIGHT,pred,_)), Par,Low,Up) :-
1784 get_geq_leq_bounds(LEFT,Par,From1,To1),
1785 get_geq_leq_bounds(RIGHT,Par,From2,To2),
1786 intersect_intervals_with_inf(From1,To1,From2,To2,Low,Up).
1787 get_geq_leq_bounds(member(b(identifier(Par),integer,_),
1788 b(Value,set(integer),_)),Par,Low,Up) :-
1789 get_value_bounds(Value,Low,Up).
1790 get_geq_leq_bounds(greater_equal(b(A,_,_),b(B,_,_)),Par,Low,Up) :- get_bounds2(greater_equal,A,B,Par,Low,Up).
1791 get_geq_leq_bounds( less_equal(b(A,_,_),b(B,_,_)),Par,Low,Up) :- get_bounds2(less_equal,A,B,Par,Low,Up).
1792 get_geq_leq_bounds( greater(b(A,_,_),b(B,_,_)),Par,Low,Up) :- get_bounds2(greater,A,B,Par,Low,Up).
1793 get_geq_leq_bounds( less(b(A,_,_),b(B,_,_)),Par,Low,Up) :- get_bounds2(less,A,B,Par,Low,Up).
1794
1795 get_value_bounds(value(GS),Low,Up) :- is_interval_closure_or_integerset(GS,Low,Up). % recursive call
1796 % nonvar(GS), GS=global_set(ISET), get_integer_set_interval(ISET,Low,Up).
1797 get_value_bounds(interval(b(TLow,_,_),b(TUp,_,_)),Low,Up) :-
1798 integer_value(TLow,Low),
1799 integer_value(TUp,Up).
1800
1801 get_bounds2(greater_equal,identifier(Par),V,Par,X,inf) :- integer_value(V,X).
1802 get_bounds2(greater_equal,V,identifier(Par),Par,minus_inf,X) :- integer_value(V,X).
1803 get_bounds2(less_equal,identifier(Par),V,Par,minus_inf,X) :- integer_value(V,X).
1804 get_bounds2(less_equal,V,identifier(Par),Par,X,inf) :- integer_value(V,X).
1805 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.
1806 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.
1807 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.
1808 get_bounds2(less,identifier(Par),V,Par,minus_inf,X1) :- integer_value(V,X),
1809 kernel_objects:int_minus(int(X),int(1),int(X1)). %X1 is X-1.
1810 % to do: add negation thereof ??
1811
1812 integer_value(V,_) :- var(V),!, print(var_integer_value(V)),nl,fail.
1813 integer_value(integer(X),R) :- !, R=X.
1814 integer_value(unary_minus(b(X,_,_)),R) :- !, integer_value(X,RM),
1815 number(RM), % if RM is not a number we could setup CLPFD constraint ?!
1816 R is -(RM).
1817 integer_value(minus(b(X,_,_),b(Y,_,_)),R) :- !, % some AST compilation rules generate X-1, X+1 ...
1818 integer_value(X,RMX),
1819 integer_value(Y,RMY),
1820 kernel_objects:int_minus(int(RMX),int(RMY),int(R)).
1821 integer_value(plus(b(X,_,_),b(Y,_,_)),R) :- !, % some AST compilation rules generate X-1, X+1 ...
1822 integer_value(X,RMX),
1823 integer_value(Y,RMY),
1824 kernel_objects:int_plus(int(RMX),int(RMY),int(R)).
1825 integer_value(value(V),R) :- V=int(R).
1826
1827 is_interval_closure(closure(Par,[integer],Pred),Low,Up) :-
1828 is_interval_closure_aux(Par,Pred,Low,Up).
1829 is_interval_closure(Par,[integer],Pred,Low,Up) :-
1830 is_interval_closure_aux(Par,Pred,Low,Up).
1831 is_interval_closure_aux(Par,Pred,Low,Up) :-
1832 is_member_closure(Par,[integer],Pred,integer,Set),
1833 is_interval_with_integer_bounds(Set,Low,Up).
1834 %is_interval_closure(closure_x(Par,[integer],Pred,_),Low,Up) :-
1835 % is_interval_closure(closure(Par,[integer],Pred),Low,Up).
1836
1837 is_interval_closure_body(Body,ID,Low,Up) :-
1838 is_member_closure([ID],[integer],Body,integer,Set),!,
1839 is_interval_with_integer_bounds(Set,Low,Up).
1840 is_interval_closure_body(Body,ID,Low,Up) :-
1841 is_geq_leq_interval_closure([ID],[integer],Body,Low,Up),
1842 number(Low), number(Up).
1843
1844 :- use_module(bsyntaxtree,[get_texpr_info/2,get_texpr_id/2]).
1845 % do a single check if we have interval, member or not-member closure, avoiding redundant checking
1846 % TO DO: move this and related predicates to closures module ?
1847 is_special_closure(_Ids,_Types,Pred,Result) :-
1848 get_texpr_info(Pred,Info),memberchk(prob_annotation(recursive(RId)),Info),!,
1849 Result = recursive_special_closure(RId).
1850 is_special_closure(Ids,Types,Pred,Result) :-
1851 is_memoization_closure(Ids,Types,Pred,MemoID),!,
1852 Result = memoization_closure(MemoID).
1853 is_special_closure([ID],[TYPE],b(PRED,_,_), Result) :-
1854 ( closures:is_member_closure_aux(PRED, [ID],[TYPE],_,SET) ->
1855 ( (TYPE=integer, is_interval_with_integer_bounds(SET,Low,Up)) ->
1856 Result = interval(Low,Up)
1857 ; Result = member_closure(ID,TYPE,SET))
1858 ; closures:is_not_member_closure_aux(PRED,ID,TYPE,SET) ->
1859 Result = not_member_closure(ID,TYPE,SET)
1860 ; (TYPE=integer,get_geq_leq_bounds(PRED,ID,Low,Up),number(Low), number(Up)) ->
1861 Result = interval(Low,Up)
1862 ).
1863
1864
1865 construct_interval_set(Low,Up,Res) :-
1866 Res = interval(b(value(int(Low)),integer,[]),
1867 b(value(int(Up)), integer,[])).
1868 is_interval_with_integer_bounds(X,L,U) :- var(X),!,
1869 add_internal_error('var arg: ',is_interval_with_integer_bounds(X,L,U)),fail.
1870 is_interval_with_integer_bounds(interval(b(TLOW,integer,_),b(TUP, integer,_)),Low,Up) :-
1871 integer_value(TLOW,Low), integer_value(TUP,Up).
1872
1873
1874 is_a_relation(relations(Domain,Range),Domain,Range,DCard,RCard,Card,Code) :- %% '<->'
1875 Code = (kernel_card_arithmetic:safe_mul(DCard,RCard,Exp), kernel_card_arithmetic:safe_pow2(Exp,Card)).
1876 is_a_relation(partial_function(Domain,Range),Domain,Range,DCard,RCard,Card,Code) :- %% '+->'
1877 Code = (kernel_card_arithmetic:safe_add_card(RCard,1,R1),kernel_card_arithmetic:safe_pown(R1,DCard,Card)).
1878 is_a_relation(total_function(Domain,Range),Domain,Range,DCard,RCard,Card,Code) :- %% '-->'
1879 Code = (kernel_card_arithmetic:safe_pown(RCard,DCard,Card)).
1880 is_a_relation(partial_bijection(Domain,Range),Domain,Range,DCard,RCard,Card,Code) :- %% '>+>>'
1881 Code = (kernel_card_arithmetic:partial_bijection_card(DCard,RCard,Card)).
1882 is_a_relation(total_bijection(Domain,Range),Domain,Range,DCard,RCard,Card,Code) :- %% '>->>'
1883 Code = (kernel_card_arithmetic:total_bijection_card(DCard,RCard,Card)).
1884 is_a_relation(total_injection(Domain,Range),Domain,Range,DCard,RCard,Card,Code) :- %% '>->'
1885 Code = (kernel_card_arithmetic:blocking_factorial_k(RCard,DCard,Card)).
1886 is_a_relation(partial_injection(Domain,Range),Domain,Range,DCard,RCard,Card,Code) :- %% '>+>'
1887 Code = (kernel_card_arithmetic:partial_injection_card(DCard,RCard,Card)).
1888 is_a_relation(total_surjection(Domain,Range),Domain,Range,DCard,RCard,Card,Code) :- %% '-->>'
1889 Code = (kernel_card_arithmetic:total_surjection_card(DCard,RCard,Card)).
1890 is_a_relation(partial_surjection(Domain,Range),Domain,Range,DCard,RCard,Card,Code) :- %% '+->>'
1891 Code = (kernel_card_arithmetic:partial_surjection_card(DCard,RCard,Card)).
1892 is_a_relation(total_relation(Domain,Range),Domain,Range,DCard,RCard,Card,Code) :- %% '<<->'
1893 Code = (kernel_card_arithmetic:total_relation_card(DCard,RCard,Card)).
1894 is_a_relation(surjection_relation(Domain,Range),Domain,Range,DCard,RCard,Card,Code) :- %% '<->>'
1895 % just swap args: card(A<->>B) = card(B<<->A)
1896 Code = (kernel_card_arithmetic:total_relation_card(RCard,DCard,Card)).
1897 % TO DO: total_surjection_relation <<->>
1898
1899
1900
1901 :- use_module(b_global_sets,[infinite_global_set/1]).
1902
1903 :- block is_infinite_global_set(-,?).
1904 is_infinite_global_set('NATURAL',integer).
1905 is_infinite_global_set('NATURAL1',integer).
1906 is_infinite_global_set('INTEGER',integer).
1907 is_infinite_global_set('FLOAT',real).
1908 is_infinite_global_set('REAL',real).
1909 is_infinite_global_set('STRING',string).
1910 is_infinite_global_set(G,global(G)) :- infinite_global_set(G).
1911
1912 %is_finite_integer_global_set('NAT').
1913 %is_finite_integer_global_set('NAT1').
1914 %is_finite_integer_global_set('INT').
1915
1916 % detects (certain) infinite explict sets
1917 is_infinite_explicit_set(X) :- var(X),!, add_internal_error(is_infinite_explicit_set,var(X)),fail.
1918 ?is_infinite_explicit_set(global_set(X)) :- is_infinite_global_set(X,_).
1919 is_infinite_explicit_set(freetype(X)) :- is_infinite_freetype(X).
1920 is_infinite_explicit_set(closure(Par,T,Body)) :- is_infinite_closure(Par,T,Body).
1921
1922 % detect some closure that we should definitely expand; even in SYMBOLIC mode or for ABSTRACT_CONSTANTS
1923 definitely_expand_this_explicit_set(Var) :- var(Var),!,fail.
1924 definitely_expand_this_explicit_set(closure(P,T,B)) :-
1925 (B = b(Body,_,_), definitely_expand(Body,P) -> true
1926 ; is_interval_closure(P,T,B,Low,Up), do_expand_interval(Low,Up)).
1927 % some lambda functions have small domain, but are very complicated to compute (test 1078, 1376)
1928 % hence the following is not sufficient:
1929 % ;is_small_specific_custom_set(closure(P,T,B),100), print(exp(T)),nl,translate:print_bexpr(B),nl,fail).
1930
1931 :- use_module(bsyntaxtree,[occurs_in_expr/2]).
1932 definitely_expand(Body,_) :- avl_mem_construct(Body,_).
1933 definitely_expand(exists(ExistsTIDs,Body),P) :- P = [ID],
1934 % detect AVL projection expressions like {res|#y.(y:AVL & res=Expr(y))} % test 1101
1935 Body = b(conjunct(b(Mem,pred,_),Eq),pred,_),
1936 Eq = b(equal(EqA,EqB),pred,_),
1937 avl_mem_construct(Mem,LHS),
1938 tlhs_uses_exists(LHS,ExistsTIDs,[]),
1939 ( get_texpr_id(EqA,ID) -> \+ occurs_in_expr(ID,EqB)
1940 ; get_texpr_id(EqB,ID) -> \+ occurs_in_expr(ID,EqA) ). % we assign to set compr. ID
1941 % example where ID occurs in other expression: {v|#w.(w : (1 .. 10) & v = (v + w) - 2)}; test 2516
1942
1943 tlhs_uses_exists(b(E,_,_)) --> lhs_uses_exists(E).
1944 lhs_uses_exists(identifier(EID),In,Out) :-!, select(TEID,In,Out),
1945 get_texpr_id(TEID,EID),!. % TODO: we could allow using an identifier twice
1946 lhs_uses_exists(value(V)) --> {nonvar(V), simple_value(V), ground_value(V)}.
1947 lhs_uses_exists(couple(A,B)) --> tlhs_uses_exists(A), tlhs_uses_exists(B).
1948 lhs_uses_exists(boolean_true) --> [].
1949 lhs_uses_exists(boolean_false) --> [].
1950 lhs_uses_exists(empty_set) --> [].
1951 lhs_uses_exists(empty_sequence) --> [].
1952 lhs_uses_exists(integer(_)) --> [].
1953 lhs_uses_exists(real(_)) --> [].
1954 lhs_uses_exists(string(_)) --> [].
1955
1956 avl_mem_construct(member(LHS,RHS),LHS) :- RHS = b(value(V),_,_), nonvar(V),
1957 (V=avl_set(_) -> true
1958 ; is_interval_closure_or_integerset(V,L,U), integer(L), integer(U), U-L < 1000
1959 ).
1960
1961 % dont_expand_this_explicit_set with default limit (20000)
1962 dont_expand_this_explicit_set(closure(P,T,B)) :- !,
1963 dont_expand_this_closure(P,T,B).
1964 dont_expand_this_explicit_set(S) :-
1965 is_infinite_or_very_large_explicit_set(S).
1966
1967 % dont_expand_this_explicit_set with extra limit argument:
1968 dont_expand_this_explicit_set(closure(P,T,B),Limit) :- !, dont_expand_this_closure(P,T,B,Limit).
1969 dont_expand_this_explicit_set(S,_) :- is_infinite_or_very_large_explicit_set(S).
1970
1971 % true if we have a closure / global_set that should not be expanded
1972 % 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))
1973 dont_expand_symbolic_explicit_set(closure(P,T,B)) :- !,
1974 dont_expand_this_closure(P,T,B).
1975 dont_expand_symbolic_explicit_set(avl_set(_)) :- !,
1976 fail. % already expanded
1977 dont_expand_symbolic_explicit_set(S) :-
1978 is_infinite_or_very_large_explicit_set(S).
1979
1980
1981 dont_expand_this_closure(P,T,B) :-
1982 get_preference(comprehension_set_symbolic_limit,Limit), % Default 20000
1983 dont_expand_this_closure(P,T,B,Limit). % % increase limit in Data valid mode?
1984
1985 dont_expand_this_closure(_P,_T,b(_,_,INFO),_Limit) :-
1986 ? member(prob_annotation(KIND),INFO),
1987 (KIND = 'SYMBOLIC' -> ! % cf is_symbolic_closure in closures
1988 ; KIND = 'FORCE' -> !, fail). % was wrapped in FORCE external_function
1989 dont_expand_this_closure(P,T,B,_Limit) :-
1990 is_interval_closure_or_numberset(closure(P,T,B),Low,Up), !,
1991 % interval closures are quite efficient for certain manipulations
1992 (integer(Low), integer(Up)
1993 -> dont_expand_interval(Low,Up)
1994 % ; float(Low), float(Up) -> Low < Up % probably very many values between; requires new 4.10 solver to detect emptyness TODO
1995 ; true % we have a closure with inf/minus_inf or variables as bounds or floats; in all cases keep the closure
1996 ).
1997 dont_expand_this_closure(P,T,B,Limit) :-
1998 is_infinite_or_very_large_closure(P,T,B,Limit).
1999 %% TODO: also prevent expansion of things like ff = %x.(x:STRING & REGEX_MATCH(x,"[a-z]+")=TRUE|TRUE)
2000
2001 % do not automatically expand these integer intervals
2002 dont_expand_interval(Low,Up) :-
2003 Up+1-Low > 100. % another magic constant ; which value to choose ??
2004 % do expand these integer intervals:
2005 do_expand_interval(Low,Up) :- Up+1-Low =< 100.
2006
2007 is_converted_lambda_closure(_P,_T,b(_,_,INFO)) :-
2008 member(prob_annotation('LAMBDA'),INFO).
2009
2010 is_symbolic_closure_or_symbolic_mode(P,T,B) :-
2011 (is_symbolic_closure(P,T,B) -> true
2012 ; preference(convert_comprehension_sets_into_closures,true)
2013 % by default suppose closures should be dealt with symbolically
2014 ).
2015 /*
2016 % check both LAMBDA + not RECURSIVE
2017 is_converted_non_recursive_lambda_closure(_,_,b(_,_,INFO)) :- is_conv_lambda_nonrec(INFO).
2018 is_conv_lambda_nonrec([prob_annotation(A)|T]) :- !,
2019 (A='LAMBDA' -> \+ memberchk(prob_annotation('RECURSIVE'),T)
2020 ; A\='RECURSIVE' -> is_conv_lambda_nonrec(T)).
2021 is_conv_lambda_nonrec([_|T]) :- is_conv_lambda_nonrec(T). */
2022
2023
2024
2025 % a set that is so large that expanding it would probably cause problems
2026 is_infinite_or_very_large_explicit_set(S) :-
2027 get_preference(comprehension_set_symbolic_limit,Limit), % Default 20000
2028 is_infinite_or_very_large_explicit_set(S,Limit). % increase limit in Data valid mode?
2029
2030 :- use_module(inf_arith,[infgreater/2]).
2031
2032 is_infinite_or_very_large_explicit_set(X,_) :- var(X),!,print(var_is_infinite_check(X)),nl,fail.
2033 is_infinite_or_very_large_explicit_set(closure(P,T,B),Limit) :- !,
2034 % treat closure separately here; some special rules
2035 is_infinite_or_very_large_closure(P,T,B,Limit).
2036 is_infinite_or_very_large_explicit_set(avl_set(A),Limit) :- !, % we could compute log and use avl_height_less_than
2037 quick_avl_approximate_size(A,Size), Size >= Limit.
2038 is_infinite_or_very_large_explicit_set(X,Limit) :- % closures are checked above
2039 explicit_set_cardinality(X,Card),
2040 nonvar(Card),infgreater(Card,Limit).
2041
2042
2043 is_very_large_or_symbolic_closure(P,T,B,Limit) :-
2044 (is_symbolic_closure(P,T,B) -> true ; is_infinite_or_very_large_closure(P,T,B,Limit)).
2045 :- use_module(bsyntaxtree,[is_a_disjunct/3]).
2046 is_infinite_or_very_large_closure(P,T,B,Limit) :-
2047 is_a_disjunct(B,D1,D2), % Assumption: there is no card_for_specific_closure code for disjuncts
2048 !,
2049 (is_infinite_or_very_large_closure(P,T,D1,Limit) -> true
2050 ; is_infinite_or_very_large_closure(P,T,D2,Limit)).
2051 is_infinite_or_very_large_closure(Par,T,Body,Limit) :-
2052 is_closure1_value_closure(Par,T,Body,VAL),!,
2053 nonvar(VAL), % it could still be large or infinite
2054 (Limit>1 -> NLimit is Limit/2 ; NLimit = Limit), % reduce limit as closure1 usually blows up
2055 is_infinite_or_very_large_explicit_set(VAL,NLimit).
2056 is_infinite_or_very_large_closure(P,T,B,Limit) :-
2057 card_for_specific_closure3(Kind,P,T,B,Card,Code),
2058 on_enumeration_warning(call(Code),
2059 (debug_println(9,cannot_expand_specific_closure_for_card(Kind,Limit)),
2060 % see test 1519 for relevance
2061 Card=inf)), % assume it is large
2062 !,
2063 nonvar(Card),infgreater(Card,Limit),
2064 perfmessages_bexpr(symbolic_closure,['Cardinality ',Card,' greater than limit ',Limit,' for '],B).
2065
2066
2067 is_infinite_or_symbolic_closure(P,T,B) :-
2068 (is_symbolic_closure(P,T,B) -> true ; is_infinite_closure(P,T,B)).
2069 is_infinite_closure(P,T,B) :-
2070 is_a_disjunct(B,D1,D2), % Assumption: there is no card_for_specific_closure code for disjuncts
2071 !,
2072 (is_infinite_closure(P,T,D1) -> true ; is_infinite_closure(P,T,D2)).
2073
2074 is_infinite_closure(Par,Types,Body) :-
2075 is_member_closure(Par,Types,Body,Type,MemSET), !,
2076 nonvar(MemSET),
2077 is_infinite_member_closure_body(MemSET,Type).
2078 is_infinite_closure(Par,T,Body) :-
2079 card_for_specific_closure(closure(Par,T,Body),Card,Code),
2080 call(Code), % TO DO: catch enumeration exceptions (see is_infinite_or_very_large_closure above)
2081 Card == inf. % TODO: instantiate inf before to avoid computing huge numbers
2082
2083 is_infinite_member_closure_body(closure(b(VALExpr,_,_)),couple(A,A)) :-
2084 is_infinite_member_closure_body(VALExpr,couple(A,A)).
2085 % if VALExpr is a var value: it could still be infinite !! TO DO fix
2086 % % TO DO: also check closure1 is infinite
2087 is_infinite_member_closure_body(value(VAL),_) :- nonvar(VAL),
2088 is_infinite_explicit_set(VAL).
2089 is_infinite_member_closure_body(comprehension_set(Par,Body),_) :-
2090 split_names_and_types(Par,P,T),
2091 is_infinite_closure(P,T,Body).
2092 % TODO: call unary_member_closure_for_finite(SET,Check,SET1), with Check=finite
2093 is_infinite_member_closure_body(Body,TYPE) :-
2094 card_for_member_closure(Body,TYPE,Card,Code),
2095 call(Code), % TO DO: catch enumeration exceptions (see is_infinite_or_very_large_closure above)
2096 Card == inf. % TODO: instantiate inf before to avoid computing huge numbers
2097
2098
2099 :- use_module(memoization,[compute_memo_hash/2, get_stored_memo_expansion/3, store_memo_expansion/3]).
2100 /* transitive closure */
2101 closure1_for_explicit_set(avl_set(A),Res) :-
2102 preferences:preference(use_closure_expansion_memoization,true),!,
2103 compute_memo_hash(closure1_for_explicit_set(A),Hash),
2104 (get_stored_memo_expansion(Hash,closure1_for_explicit_set(A),StoredResult)
2105 -> Res = StoredResult
2106 ; closure1_for_explicit_set_direct(avl_set(A),Result),
2107 store_memo_expansion(Hash,closure1_for_explicit_set(A),Result),
2108 Res = Result
2109 ).
2110 closure1_for_explicit_set(avl_set(A),Res) :- closure1_for_explicit_set_direct(avl_set(A),Res).
2111
2112 % sometimes faster, but can also be considerably slower:
2113 %:- use_module(extrasrc(avl_ugraphs),[avl_transitive_closure/2]).
2114 %closure1_for_explicit_set_direct(avl_set(A),Res) :-
2115 % avl_transitive_closure(A,TC),
2116 % construct_avl_set(TC,Res).
2117 closure1_for_explicit_set_direct(avl_set(A),Res) :-
2118 perfmessage_bexpr(closure1,'Computing transitive closure1 of: ',b(value(avl_set(A)),any,[])),
2119 avl_domain(A,AList),
2120 iterate_closure(AList,A,A,IterationRes),
2121 construct_avl_set(IterationRes,Res).
2122
2123 /* transitive closure starting from some initial set */
2124 /* not sure if we should do this:
2125 closure1_for_explicit_set_from(avl_set(A),StartFrom,Res) :-
2126 preferences:preference(use_closure_expansion_memoization,true),
2127 compute_memo_hash(closure1_for_explicit_set(A),Hash),
2128 stored_expansion(Hash,closure1_for_explicit_set(A),StoredResult),!,
2129 domain_restriction_explicit_set(StartFrom,StoredResult,Res). */
2130 % StartFrom can be avl_set(empty)
2131 closure1_for_explicit_set_from(avl_set(A),StartFrom,Res) :-
2132 avl_domain(A,AList),
2133 filter_start_relation(AList,StartFrom,FAList),
2134 (FAList = [] -> Res=[]
2135 ; convert_to_avl(FAList,avl_set(Start)),
2136 iterate_closure(FAList,A,Start,IterationRes),
2137 construct_avl_set(IterationRes,Res)).
2138 filter_start_relation([],_,[]).
2139 filter_start_relation([(X,Y)|T],StartSet,Res) :-
2140 (element_of_custom_set(X,StartSet) -> Res = [(X,Y)|RT] ; Res=RT),
2141 filter_start_relation(T,StartSet,RT).
2142
2143 iterate_closure([],_,Res,Res).
2144 iterate_closure([(X,Y)|T],InitialRelation,Relation,Res) :-
2145 %(Key = (X,Y) -> true ; add_error_and_fail(iterate_closure,'Not a relation element: ',Key)),
2146 add_tuples(X,Y,InitialRelation,Relation,NewRelation,AddedTuples),
2147 % better: do added tuples straight away ?
2148 iterate_closure(T,InitialRelation,NewRelation,NewRelation2),
2149 iterate_closure(AddedTuples,InitialRelation,NewRelation2,Res).
2150
2151 add_tuples(X,Y,AVL,AVLClosureSoFar,Res,NewTuples) :-
2152 findall((X,Z), (avl_fetch_pair(Y,AVL,Z), %ok instead of safe_avl_member((Y,Z),AVL),; Y in AVL form, Z var
2153 %Y \= Z, % self-loops are already in initial AVLClosure, this will never add a new pair
2154 % if we use AVLClosureSoFar instead of AVL: considerably slower
2155 \+ avl_fetch((X,Z),AVLClosureSoFar)), NewTuples),
2156 add_to_avl(NewTuples,AVLClosureSoFar,Res).
2157
2158 :- use_module(bsyntaxtree,[create_negation/2]).
2159 % SUBSET_OF <:
2160 % subset_of_explicit_set: returns code to be executed if this subset check can be done in an optimized way
2161 % TO DO: add strict_subset <<: + more cases, e.g., interval & avl_set, ...
2162 % interval & interval already handled in check_subset_of_global_sets
2163 subset_of_explicit_set(AVL,Closure,Code,_WF) :- nonvar(AVL),AVL=avl_set(A),
2164 is_interval_closure_or_integerset(Closure,Low,Up),!,
2165 Code=custom_explicit_sets:check_avl_in_interval(A,Low,Up).
2166 subset_of_explicit_set(Closure,CS,Code,WF) :- nonvar(CS), is_custom_explicit_set(CS),
2167 is_interval_closure_or_integerset(Closure,Low,Up),!,
2168 Code=custom_explicit_sets:check_interval_in_custom_set(Low,Up,CS,WF).
2169 subset_of_explicit_set(AVL1,AVL2,Code,_WF) :-
2170 nonvar(AVL1),AVL1=avl_set(A1), nonvar(AVL2),AVL2=avl_set(A2),!,
2171 Code = custom_explicit_sets:check_avl_subset(A1,A2).
2172 subset_of_explicit_set(C1,AVL2,Code,_WF) :- nonvar(C1),
2173 simple_finite_set(AVL2),
2174 is_simple_infinite_set(C1),!, % infinite set cannot be subset of finite one
2175 Code = fail.
2176 subset_of_explicit_set(C1,C2,Code,WF) :- nonvar(C1),
2177 is_cartesian_product_closure(C1,S11,S12),!,
2178 ((S11==[] ; S12==[]) -> Code=true /* we always have a subset */
2179 ; is_definitely_not_empty(S11),
2180 is_definitely_not_empty(S12), % only use optimisation if we know S11, S12 to be non-empty
2181 nonvar(C2), is_cartesian_product_closure(C2,S21,S22),
2182 Code = (kernel_objects:check_subset_of_wf(S11,S21,WF),
2183 kernel_objects:check_subset_of_wf(S12,S22,WF) )
2184 ).
2185 subset_of_explicit_set(Set1,Set2,Code,WF) :-
2186 nonvar(Set2),is_cartesian_product_closure(Set2,S21,S22),!,
2187 % TO DO: maybe don't do this if Set1 is avl_set ??
2188 debug_println(9,'Applying C <: S21*S22 <=> C : S21 <-> S22'),
2189 Code = bsets_clp:relation_over_wf(Set1,S21,S22,WF).
2190 subset_of_explicit_set(C1,C2,Code,WF) :- nonvar(C1), nonvar(C2),
2191 is_powerset_closure(C1,Constructor1,Set1),
2192 is_powerset_closure(C2,Constructor2,Set2),
2193 subset_constructor(Constructor1,Constructor2,R),
2194 !,
2195 Code = (R=pred_true, kernel_objects:check_subset_of_wf(Set1,Set2,WF)).
2196 subset_of_explicit_set(Set1,Set2,Code,WF) :-
2197 AllowRegularClosure=false,
2198 symbolic_subset_of_explicit_set(Set1,Set2,AllowRegularClosure,Code,WF).
2199
2200 symbolic_subset_of_explicit_set(Set1,Set2,AllowRegularClosure,Code,WF) :-
2201 %print_term_summary(subset(Set1,Set2)),nl,
2202 get_subset_counter_example_closure(Set1,Set2,NewP,NewT,NewB,AllowRegularClosure,DefResult),
2203 % {x|P1} <: {x|P2} <=> {x|P1 & not(P2)}={}
2204 !, %translate:print_bexpr(NewB),nl,
2205 (DefResult==definitely_non_empty -> Code = fail
2206 ; clean_up(NewB,[],CNewB), % can be useful to apply remove_member_comprehension
2207 Code = custom_explicit_sets:is_empty_closure_wf(NewP,NewT,CNewB,WF)).
2208
2209 % get closure representing the counter examples to Set1 <: Set2: i.e. elements in Set1 and not in Set2
2210 % used for symbolic treatment of subset, not_subset and test_subset
2211 % note: in case this fails subset_test1 will expand Set1
2212 % DefiniteResultFlag may return the information that the generated closure is definitely not empty
2213 % AllowRegularClosure=false means it will only be applied for symbolic or infinite closures
2214 get_subset_counter_example_closure(Set1,Set2,NewP,NewT,NewB,AllowRegularClosure,DefiniteResultFlag) :-
2215 get_closure(Set1,P1,T1,B1),
2216 get_subset_counter_aux(P1,T1,B1,Set2,NewP,NewT,NewB,AllowRegularClosure,DefiniteResultFlag).
2217
2218 get_subset_counter_aux(P1,T1,B1,Set2,NewP,NewT,NewB,AllowRegularClosure,DefRes) :-
2219 nonvar(Set2), is_definitely_finite(Set2), !,
2220 create_couple_term(P1,T1,P1Couple), % can currently still fail for more than 2 args
2221 (is_infinite_closure(P1,T1,B1)
2222 -> DefRes=definitely_non_empty % there are definitely counter examples as Set2 is finite
2223 ; AllowRegularClosure=true -> DefRes = unknown
2224 ; is_symbolic_closure(P1,T1,B1) -> DefRes=unknown
2225 ),
2226 NewP=P1, NewT=T1,
2227 % {x|P1} <: {a1,...} <=> {x|P1 & x /: {a1,...}}={}
2228 get_texpr_type(P1Couple,CoupleType1),
2229 VSet2 = b(value(Set2),set(CoupleType1),[]),
2230 create_texpr(not_member(P1Couple,VSet2),pred,[],NegPred2),
2231 conjunct_predicates([B1,NegPred2],NewB).
2232 get_subset_counter_aux(P1,T1,B1,Set2,NewP,NewT,NewB,AllowRegularClosure,unknown) :-
2233 get_closure(Set2,P2,T2,B2),
2234 (AllowRegularClosure=true -> true
2235 ; is_infinite_or_symbolic_closure(P1,T1,B1) -> true
2236 % should we also allow ??
2237 % ; is_symbolic_closure(P2,T2,B2)
2238 ),
2239 % not necessary maybe as subset_test1 only expands Set1
2240 % {x|P1} <: {x|P2} <=> {x|P1 & not(P2)}={}
2241 unify_closure_predicates(P1,T1,B1, P2,T2,B2 , NewP,NewT, NewB1,NewB2),
2242 create_negation(NewB2,NegNewB2),
2243 bsyntaxtree:conjunct_predicates([NewB1,NegNewB2],NewB).
2244
2245
2246 % get_closure or infinite global set:
2247 get_closure(V,_,_,_) :- var(V),!,fail.
2248 get_closure(closure(P,T,B),P,T,B).
2249 ?get_closure(global_set(G),P,T,B) :- is_infinite_global_set(G,Type),!,
2250 ID = '_zzzz_unary',
2251 TID = b(identifier(ID),Type,[]),
2252 TSet = b(value(global_set(G)),set(Type),[]),
2253 P = [ID], T=[Type], B= b(member(TID,TSet),pred,[prob_annotation('SYMBOLIC')]).
2254
2255
2256 subset_constructor(X,X,R) :- !,R=pred_true.
2257 subset_constructor(fin1,_,R) :- !,R=pred_true.
2258 subset_constructor(fin,pow,R) :- !,R=pred_true.
2259 subset_constructor(X,Y,R) :- strict_subset_constructor(X,Y),!,R=pred_true.
2260 subset_constructor(X,Y,R) :- strict_subset_constructor(Y,X),!,R=pred_false.
2261 % pow1,fin1 ; pow,fin ; and pow1,fin only ok if type infinite
2262 strict_subset_constructor(pow1,pow).
2263 strict_subset_constructor(fin1,fin).
2264
2265 % more rules for <->, +->, ...
2266 % what if same closure: then we also know it is a subset
2267
2268 % to be completed:
2269 % code that instantiates R to subset or not_subset, may have to delay
2270 test_subset_of_explicit_set(Set1,_,_,_,_) :- var(Set1),!,fail.
2271 test_subset_of_explicit_set(avl_set(A),Closure,R,WF,Code) :-
2272 is_interval_closure_or_integerset(Closure,Low,Up),!,
2273 Code=custom_explicit_sets:test_avl_in_interval(A,Low,Up,R,WF).
2274 test_subset_of_explicit_set(_,Set2,_,_,_) :- var(Set2),!,fail.
2275 test_subset_of_explicit_set(avl_set(A1),avl_set(A2),R,_WF,Code) :-
2276 Code = (custom_explicit_sets:check_avl_subset(A1,A2) -> R=pred_true ; R=pred_false).
2277 test_subset_of_explicit_set(global_set(G),Set2,R,_WF,Code) :-
2278 is_infinite_global_set(G,_), % TODO: we could extend this to other infinite sets
2279 is_definitely_finite(Set2), !,
2280 Code =(R=pred_false).
2281 test_subset_of_explicit_set(Set1,Set2,Res,WF,Code) :-
2282 AllowRegular=false,
2283 get_subset_counter_example_closure(Set1,Set2,NewP,NewT,NewB,AllowRegular,DefResult),
2284 % {x|P1} <: {x|P2} <=> {x|P1 & not(P2)}={}
2285 !,
2286 (DefResult==definitely_non_empty -> Code = (Res=pred_false)
2287 ; Code = custom_explicit_sets:test_empty_closure_wf(NewP,NewT,NewB,Res,WF)
2288 ).
2289 % TO DO: add is_cartesian_product_closure case
2290 is_definitely_finite([]).
2291 is_definitely_finite(avl_set(_)).
2292
2293 :- use_module(kernel_equality,[test_interval_subset_wf/6]).
2294
2295 :- public test_avl_in_interval/5. % used in test_subset_of_explicit_set
2296 % see also check_avl_in_interval(A,Low,Up), check_avl_not_in_interval(A,Low,Up).
2297 test_avl_in_interval(A,Low2,Up2,Res,WF) :-
2298 avl_min(A,int(Min)), % not needed if Low2==minus_inf
2299 avl_max(A,int(Max)), % not needed if Up2==inf
2300 test_interval_subset_wf(Min,Max,Low2,Up2,Res,WF).
2301
2302 % ----------------------
2303
2304 is_definitely_not_empty(X) :- nonvar(X),
2305 (X=[_|_] -> true
2306 ; is_custom_explicit_set(X), is_non_empty_explicit_set(X)).
2307
2308 % check if defnitely not empty and provide a witness
2309 is_definitely_not_empty_with_witness(X,El) :- nonvar(X),
2310 get_witness_element(X,El).
2311 get_witness_element([H|_],H).
2312 get_witness_element(avl_set(node(H,_True,_,_,_)),H).
2313 % TO DO: add global_set(GS),...
2314
2315 check_avl_subset(A1,A2) :- avl_max(A1,Max1), avl_max(A2,Max2),
2316 Max1@>Max2,!, % then A1 cannot be subset of A2
2317 fail.
2318 check_avl_subset(A1,A2) :-
2319 avl_min(A1,Cur1), avl_min(A2,Cur2),
2320 check_avl_subset_loop(Cur1,A1,Cur2,A2).
2321 check_avl_subset_loop(Cur1,AVL1,Cur2,AVL2) :-
2322 (Cur1 @> Cur2 -> avl_next(Cur2,AVL2,NC2), check_avl_subset_loop(Cur1,AVL1,NC2,AVL2)
2323 ; Cur1=Cur2 -> (avl_next(Cur1,AVL1,NC1)
2324 -> avl_next(Cur2,AVL2,NC2),
2325 check_avl_subset_loop(NC1,AVL1,NC2,AVL2)
2326 ; true /* all objects of AVL1 inspected */)
2327 ).
2328
2329 % check A <: Low..Up
2330 check_avl_in_interval(A,Low,Up) :- % does not have to delay: if we have minus_inf & inf they will be known straightaway
2331 (Low==minus_inf -> true
2332 ; avl_min(A,Min), kernel_objects:less_than_equal(int(Low),Min)),
2333 (Up==inf -> true
2334 ; avl_max(A,Max), kernel_objects:less_than_equal(Max,int(Up))).
2335
2336 % some experiments:
2337 % 1..x <: {1,2,3,5} & x>1 & !y.(y>x & y<10 => 1..y /<: {1,2,3,5})
2338 % {ss | ss <: 0..0 & ss /= {} & ss=0..max(ss)}
2339 % {ss | ss <: 0..0 & ss /= {} & ss=min(ss)..max(ss)} // does not work yet
2340 % x..x+1 <: {0,2,3,5}
2341 % x..x+2 <: {0,2,3,5} // does not work yet
2342 % r = {x|x:1..400 & x mod 3/=0} & res={v|v:0..1300 & v..v+1 <: r}
2343 % check Low..Up <: Avl
2344
2345 check_interval_in_custom_set(Low,Up,CS,WF) :-
2346 Low \== minus_inf,
2347 Up \== inf,
2348 b_interpreter_check:check_arithmetic_operator('<=',Low,Up,LeqRes),
2349 (var(LeqRes) -> get_binary_choice_wait_flag_exp_backoff(16,check_interval_in_custom_set,WF,WF2) ; true),
2350 ? check_interval_in_custom_set_aux(LeqRes,Low,Up,CS,WF2).
2351
2352 :- block check_interval_in_custom_set_aux(-,?,?,?,-).
2353 check_interval_in_custom_set_aux(pred_true,Low,Up,CS,_WF2) :-
2354 ? element_of_custom_set_wf(int(Low),CS,WF),
2355 ? element_of_custom_set_wf(int(Up),CS,WF),
2356 interval_in_avl_block(Low,Up,CS,WF).
2357 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
2358
2359 :- block interval_in_avl_block(-,?,?,?), interval_in_avl_block(?,-,?,?).
2360 interval_in_avl_block(Low,Up,CS,WF) :-
2361 Low1 is Low+1, interval_in_avl_loop(Low1,Up,CS,WF).
2362 interval_in_avl_loop(Low,Up,_CS,_WF) :- Low>=Up,!. % Lower bound and upper bound already checked
2363 interval_in_avl_loop(Low,Up,CS,WF) :-
2364 element_of_custom_set_wf(int(Low),CS,WF), L1 is Low+1,
2365 interval_in_avl_loop(L1,Up,CS,WF).
2366
2367
2368 :- public not_check_avl_subset/2. % used in not_subset_of_explicit_set_aux
2369 not_check_avl_subset(A1,A2) :- \+ check_avl_subset(A1,A2).
2370
2371 not_subset_of_explicit_set(S1,S2,Code,WF) :- nonvar(S1),
2372 ? not_subset_of_explicit_set_aux(S1,S2,Code,WF).
2373 not_subset_of_explicit_set_aux(avl_set(A),Closure,Code,_WF) :-
2374 is_interval_closure_or_integerset(Closure,Low,Up),!,
2375 Code=custom_explicit_sets:check_avl_not_in_interval(A,Low,Up).
2376 not_subset_of_explicit_set_aux(avl_set(A1),AVL2,Code,_WF) :-
2377 nonvar(AVL2),AVL2=avl_set(A2),
2378 Code = custom_explicit_sets:not_check_avl_subset(A1,A2).
2379 not_subset_of_explicit_set_aux(CS,AVL,Code,_WF) :-
2380 is_simple_infinite_set(CS),
2381 % TO DO: provide code for interval/NAT/INT /<: AVL
2382 simple_finite_set(AVL),
2383 !,
2384 Code = true. % G cannot be subset of finite set
2385 not_subset_of_explicit_set_aux(C1,C2,Code,WF) :- is_cartesian_product_closure(C1,S11,S12),
2386 ((S11==[] ; S12==[]) -> Code=fail /* we always have a subset */
2387 ; is_definitely_not_empty(S11),
2388 is_definitely_not_empty(S12), % only use optimisation if we know S11, S12 to be non-empty
2389 nonvar(C2), is_cartesian_product_closure(C2,S21,S22),
2390 Code = (kernel_objects:not_both_subset_of(S11,S12, S21,S22, WF))
2391 ), !.
2392 not_subset_of_explicit_set_aux(C1,C2,Code,WF) :- nonvar(C2),
2393 is_powerset_closure(C1,Constructor1,Set1),
2394 is_powerset_closure(C2,Constructor2,Set2),
2395 subset_constructor(Constructor1,Constructor2,R),!,
2396 Code = (R=pred_false -> true ; kernel_objects:not_subset_of_wf(Set1,Set2,WF)).
2397 not_subset_of_explicit_set_aux(Set1,Set2,Code,WF) :-
2398 AllowRegular=false,
2399 get_subset_counter_example_closure(Set1,Set2,NewP,NewT,NewB,AllowRegular,DefResult),
2400 % {x|P1} <: {x|P2} <=> {x|P1 & not(P2)}={}
2401 !,
2402 (DefResult==definitely_non_empty -> Code = true
2403 ; Code = custom_explicit_sets:is_non_empty_closure_wf(NewP,NewT,NewB,WF)
2404 ).
2405
2406
2407 :- public check_avl_not_in_interval/3. % used in not_subset_of_explicit_set_aux
2408 :- block check_avl_not_in_interval(?,-,?). % TO DO: use non-blocking version, minus_inf, and inf set directly
2409 check_avl_not_in_interval(A,Low,Up) :- avl_min(A,int(Min)),
2410 check_avl_not_in_interval4(Low,Up,A,Min).
2411
2412 check_avl_not_in_interval4(Low,_Up,_A,Min) :- Low \== minus_inf, Min < Low,!.
2413 check_avl_not_in_interval4(_Low,Up,A,_Min) :-
2414 Up \== inf, avl_max(A,Max),
2415 kernel_objects:less_than(int(Up),Max). % Up could still be a variable
2416
2417
2418 % checks for simple infinite sets, without Cartesian Product, ... decomposition
2419 is_simple_infinite_set(global_set(X)) :- !, is_infinite_global_set(X,_).
2420 is_simple_infinite_set(CS) :- is_interval_closure_or_integerset(CS,Low,Up), infinite_interval(Low,Up).
2421
2422 simple_finite_set(AVL) :- nonvar(AVL), (AVL=avl_set(_) -> true ; AVL = []).
2423
2424 % IMAGE [.]
2425 image_for_id_closure(closure(Par,Types,Body),Set,Res) :-
2426 is_full_id_closure(Par,Types,Body),!,
2427 Res=Set.
2428
2429 image_for_explicit_set(closure(Par,Types,Body),Set,Res,WF) :-
2430 image_for_closure(Par,Types,Body,Set,Res,WF).
2431 image_for_explicit_set(avl_set(A),Set,Res,WF) :- nonvar(Set),
2432 image_for_explicit_avl_set(A,Set,Res,WF).
2433
2434
2435 image_for_closure(Par,Types,Body,Set,Res,_WF) :-
2436 is_id_closure_over(Par,Types,Body,ID_Domain,Full),!,
2437 (Full=true -> Res=Set ; kernel_objects:intersection(ID_Domain,Set,Res)).
2438 % infinite function case dealt with in image1 in bsets_clp
2439 % TO DO: other closure(); Maybe special case if Set is an interval ?
2440 image_for_closure(Par,Types,Body,Set,Res,WF) :-
2441 is_closure1_value_closure(Par,Types,Body,VAL), % TODO: also detect reflexive closure, iteration (iterate(rel,k))
2442 % compute closure1(VAL)[Set]
2443 bsets_clp:image_for_closure1_wf(VAL,Set,Res,WF).
2444
2445 is_closure1_value_closure(Par,Types,Body,VAL) :-
2446 is_member_closure(Par,Types,Body,couple(A,A),MemSET), nonvar(MemSET),
2447 MemSET = closure(V), % this is the closure1 B operator !
2448 nonvar(V), V=b(value(VAL),_,_).
2449
2450 image_for_explicit_avl_set(A,Set,Res,_WF) :- % Set is nonvar
2451 is_interval_closure_or_integerset(Set,From1,To1),!,
2452 % Note: if From1, To1 not yet known we will block and not revert to other image calculation code
2453 % Important e.g. for performance of San Juan (AdaptedBModelPropCheck/acs_as_env_cfg_ipart.mch)
2454 %we used to check for: ground(From1),ground(To1),
2455 interval_image_for_explicit_avl_set(From1,To1,A,Set,Res).
2456 image_for_explicit_avl_set(A,Set,Res,WF) :-
2457 \+ bsets_clp:keep_symbolic(Set), % in this case we fall back to treatment in bsets_clp (image1)
2458 expand_custom_set_to_list_gg(Set,ESet,GG,image_for_explicit_avl_set),
2459 empty_avl(Empty),
2460 (GG=guaranteed_ground -> image_explicit_ground(ESet,A,Empty,Res,WF)
2461 ; image_explicit(ESet,A,Empty,Res,WF)).
2462
2463 :- block interval_image_for_explicit_avl_set(-,?,?,?,?),
2464 interval_image_for_explicit_avl_set(?,-,?,?,?).
2465 interval_image_for_explicit_avl_set(From1,To1,_A,_Set,Res) :-
2466 number(From1), number(To1), From1>To1,!,
2467 kernel_objects:empty_set(Res).
2468 interval_image_for_explicit_avl_set(From1,To1,A,_Set,Res) :-
2469 findall(Image-true, avl_image_interval(From1,To1, A,Image),ImageList),
2470 normalised_list_to_avl(ImageList,ImageAvl),
2471 ? equal_object(ImageAvl,Res).
2472
2473
2474 %! singleton_set(+Set,-Element).
2475 singleton_set(X,_) :- var(X),!,fail.
2476 singleton_set([H|T],R) :- T==[], R=H.
2477 singleton_set(avl_set(node(Y,_,_,empty,empty)),Y). % same as is_one_element_custom_set
2478
2479 is_one_element_custom_set(avl_set(node(Y,_,_,empty,empty)),Y).
2480 is_one_element_avl(node(Y,_,_,empty,empty),Y).
2481
2482 % requires El to be ground
2483 construct_one_element_custom_set(El,avl_set(AVL)) :-
2484 empty_avl(E),avl_store(El,E,true,AVL).
2485
2486 construct_avl_set(Avl,Res) :- empty_avl(Avl) -> Res = [] ; Res = avl_set(Avl).
2487
2488 :- block image_explicit(-,?,?,?,?).
2489 image_explicit([],_,Acc,Res,WF) :- !,
2490 construct_avl_set(Acc,AVLS),
2491 ? kernel_objects:equal_object_wf(Res,AVLS,image_explicit,WF).
2492 image_explicit([D1|T],AVLRelation,In,Out,WF) :- !,
2493 ground_value_check(D1,G1),
2494 ((var(T);T==[]) % TO DO: see below, make propagation also interesting in other circumstances
2495 -> must_be_in_domain_check(G1,D1,T,AVLRelation,In,Out,WF)
2496 ; true),
2497 image_explicit_aux(G1,D1,AVLRelation,T,In,Out,WF).
2498 image_explicit(Set,_,_,_,_) :- add_error_and_fail(image_explicit,'Unknown set: ',Set).
2499
2500 % a version of image_explicit where the list is guaranteed to be ground
2501 image_explicit_ground([],_,Acc,Res,WF) :- !,
2502 construct_avl_set(Acc,AVLS),
2503 kernel_objects:equal_object_wf(Res,AVLS,image_explicit,WF).
2504 image_explicit_ground([D1|T],AVLRelation,In,Out,WF) :- !,
2505 image_explicit_aux_ground(D1,AVLRelation,T,In,Out,WF).
2506 image_explicit_ground(Set,_,_,_,_) :- add_error_and_fail(image_explicit_ground,'Unknown set: ',Set).
2507
2508 :- block must_be_in_domain_check(-,?,?,?,?,-,?),
2509 must_be_in_domain_check(-,?,-,?,?,?,?).
2510 % if result requires at least one more element, then D must be in domain of Relation
2511 % ensures that we get a domain for j in x = {1|->2,2|->4, 4|->8} & x[{j}]={8}
2512 % we could even propagate using inverse of AVLRelation ?!
2513 must_be_in_domain_check(GroundD,D,T,AVLRelation,In,Out,WF) :-
2514 T==[], % apart from D, there are no more elements to be added
2515 var(GroundD), % otherwise we already have a value for D
2516 delta_witness(In,Out,Witness), % obtain at least one value that D must map to
2517 !,
2518 quick_propagation_element_information(avl_set(AVLRelation),(D,Witness),WF,_). % Witness avoids pending co-routines
2519 % TO DO: we could check that *all* elements of Out have this value
2520 % 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
2521 must_be_in_domain_check(_,_D,_T,_,_In,_Out,_). % :- print(must_be(D,T,In,Out)),nl.
2522
2523 % provide, if possible, a witness element in Out not in In
2524 delta_witness(In,Out,_Witness) :- (var(In) ; var(Out)),!,fail.
2525 %delta_witness(empty,Out,Witness) :- is_definitely_not_empty_with_witness(Out,Witness).
2526 delta_witness(In,Out,Witness) :-
2527 is_custom_explicit_set(Out,delta_witness),
2528 difference_of_explicit_set(Out,avl_set(In),Diff), % could be expensive to compute !? delay ? print(delta(Diff)),nl,
2529 is_definitely_not_empty_with_witness(Diff,Witness).
2530
2531
2532 :- block image_explicit_aux(-,?,?, ?,?,?,?). % we know that D1 is ground
2533 image_explicit_aux(_,D1,AVLRelation,T,In,Out,WF) :-
2534 all_images(D1,AVLRelation,NewImages), % compute AVLRelation[{D1}]
2535 add_to_avl(NewImages,In,In2),
2536 ? image_explicit(T,AVLRelation,In2,Out,WF).
2537 image_explicit_aux_ground(D1,AVLRelation,T,In,Out,WF) :-
2538 all_images(D1,AVLRelation,NewImages), % compute AVLRelation[{D1}]
2539 add_to_avl(NewImages,In,In2),
2540 image_explicit_ground(T,AVLRelation,In2,Out,WF).
2541
2542 all_images(From,AVLRelation,Images) :-
2543 findall(AY,avl_member_pair_arg1_ground(From,AY,AVLRelation),Images).
2544 % we know that From is ground and AY free variable
2545
2546
2547 % compute relational composition ( ; ) if second arg is an AVL set
2548 % TO DO: add support for infinite closures; avoid expanding them [currently handled by symbolic composition in bsets_clp]
2549 rel_composition_for_explicit_set(Rel1,Rel2,Comp) :- nonvar(Rel2),
2550 Rel2=avl_set(A2), % TO DO: see if we can maybe convert Rel2 to AVL ?
2551 % \+ bsets_clp:keep_symbolic(Rel1), check already done in bsets
2552 expand_custom_set_to_list_gg(Rel1,Relation1,GG,rel_composition_for_explicit_set),
2553 empty_avl(In),
2554 (GG=guaranteed_ground
2555 -> rel_avl_compose2_ground(Relation1,A2,In,Comp)
2556 ; rel_avl_compose2(Relation1,A2,In,Comp)).
2557
2558 :- block rel_avl_compose2(-,?,?,?).
2559 rel_avl_compose2([],_,In,Res) :- construct_avl_set(In,A),
2560 equal_object(Res,A,rel_avl_compose2). % as we delay; we need to use equal_object at the end
2561 rel_avl_compose2([(X,Y)|T],A2,In,Out) :-
2562 when((ground(X),ground(Y)),
2563 (all_image_pairs_ground(X,Y,A2,ImagePairs),
2564 add_to_avl(ImagePairs,In,In2),
2565 rel_avl_compose2(T,A2,In2,Out))).
2566
2567 % a version where argument is guaranteed to be ground; no when-ground checks
2568 rel_avl_compose2_ground([],_,In,Res) :- construct_avl_set(In,A),
2569 equal_object(Res,A,rel_avl_compose2). % as we delay; we need to use equal_object at the end
2570 rel_avl_compose2_ground([(X,Y)|T],A2,In,Out) :-
2571 all_image_pairs_ground(X,Y,A2,ImagePairs),
2572 add_to_avl(ImagePairs,In,In2),
2573 rel_avl_compose2_ground(T,A2,In2,Out).
2574
2575 all_image_pairs_ground(From,To,AVLRelation,ImagePairs) :-
2576 findall((From,AY),avl_member_pair_arg1_ground(To,AY,AVLRelation),ImagePairs).
2577 % 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).
2578
2579 /* succeeds if it can compute domain by some clever way */
2580 domain_of_explicit_set_wf(global_set(GS),_R,_) :- !,
2581 add_error_and_fail(domain_of_explicit_set_wf,'Cannot compute domain of global set: ',GS).
2582 domain_of_explicit_set_wf(freetype(GS),_R,_) :- !,
2583 add_error_and_fail(domain_of_explicit_set_wf,'Cannot compute domain of freetype: ',GS).
2584 domain_of_explicit_set_wf(avl_set(A),Res,_) :- !,
2585 domain_of_avl_set(A,Res).
2586 domain_of_explicit_set_wf(C,R,WF) :- dom_for_specific_closure(C,Dom,_,WF),!,
2587 Dom=R.
2588 domain_of_explicit_set_wf(C,R,_) :-
2589 dom_symbolic(C,CC),!,
2590 R=CC.
2591 domain_of_explicit_set_wf(closure(P,T,B),Res,WF) :-
2592 % does not seem to be reached, as dom_symbolic now seems to cover all cases
2593 expand_custom_set_wf(closure(P,T,B),EC,domain_of_explicit_set,WF),
2594 domain_of_list_blocking(EC,R),
2595 normalised_list_to_avl_when_ground(R,Res).
2596
2597 % avl tree is a relation with an integer domain
2598 %avl_integer_domain(node((int(_From),_KeyTo),_True,_,_L,_R)).
2599
2600 % the first clause is in principle faster
2601 % but we don't gain time compared to treatment in second clause; we just avoid building up the domain list
2602 %domain_of_avl_set(A,Res) :- avl_integer_domain(A),
2603 % \+ avl_tools:avl_height_less_than(A,10), % try and detect interval if height >= 10
2604 % avl_is_pf_with_interval_domain(A,First,Last),!,
2605 % construct_interval_closure(First,Last,Res).
2606 domain_of_avl_set(A,Res) :-
2607 avl_domain(A,EC), % -> expand_custom_set(avl_set(A),EC),
2608 domain_of_sorted_list(EC,SizeRes,R), % size of list can be smaller than A if we have a relation
2609 (SizeRes=size_res(Size,int(Last)), R=[int(First)-true|_],
2610 Size>1000,
2611 Size is Last+1-First % we have an interval; quite common that we have functions with intervals as domain
2612 -> debug_println(19,constructing_interval_for_domain(First,Last)),
2613 construct_interval_closure(First,Last,Res)
2614 ; ord_list_to_avlset(R,Res,domain)
2615 ).
2616
2617 % check if an AVL tree represents a function with an interval domain
2618 %avl_is_pf_with_interval_domain(AVL,Min,Max) :-
2619 % avl_min(AVL,(int(Min),_)),avl_max(AVL,(int(Max),_)),
2620 % Size is 1+Max-Min, avl_size_possible(AVL,Size),
2621 % is_avl_partial_function(AVL),
2622 % % now check real size
2623 % avl_size(AVL,Size).
2624
2625 % check if an avl represents a set of integers:
2626 avl_integer_set(node(int(_TOP),_True,_,_L,_R)).
2627
2628 % check if an avl set is an interval:
2629 avl_is_interval(AVL,Min,Max) :-
2630 avl_integer_set(AVL),
2631 avl_min(AVL,int(Min)),avl_max(AVL,int(Max)),
2632 Size is 1+Max-Min,
2633 avl_size_possible(AVL,Size),
2634 avl_size(AVL,Size).
2635
2636
2637
2638 :- use_module(bsyntaxtree,[create_typed_id/3]).
2639 dom_symbolic(closure(Paras,Types,Pred), Res) :-
2640 expand_pair_closure(Paras,Types,Pred,[X,Y],[TX,TY],NewPred),
2641 !, % single argument which is a pair
2642 % simply call code for range ; inverting arguments
2643 bsyntaxtree:check_used_ids_in_ast(Pred),
2644 bsyntaxtree:check_used_ids_in_ast(NewPred),
2645 ran_symbolic_closure(Y,[X],TY,[TX],NewPred,Res).
2646 dom_symbolic(closure(Paras,Types,Pred), Res) :-
2647 append(Xs,[Y],Paras), Xs \= [],
2648 append(TXs,[TY],Types),
2649 % simply call code for range ; inverting arguments
2650 ran_symbolic_closure(Y,Xs,TY,TXs,Pred,Res).
2651 % TO DO: allow computation if Paras is a single argument and more than pair
2652
2653 % just computes domain: it can also be successful for lambda closures
2654 dom_for_specific_closure(closure(P,T,Pred),Domain,Functionality,WF) :-
2655 dom_for_specific_closure_aux(P,T,Pred,Domain,Functionality,WF).
2656 dom_for_specific_closure_aux(P,T,Pred,Domain,Functionality,_WF) :-
2657 is_lambda_value_domain_closure(P,T,Pred, DomainValue,Expr),
2658 (preference(find_abort_values,full) -> bsyntaxtree:always_well_defined_or_disprover_mode(Expr)
2659 ; true),
2660 % Warning: this will lead to dom(%x.(x:1..3|1/0)) = 1..3 to be true; discarding WD condition
2661 % this is not as bad as {1|->2}(0) = 3 to be silently failing though; hence only done if TRY_FIND_ABORT = full
2662 !,
2663 Domain=DomainValue,
2664 Functionality=function(total).
2665 %dom_for_specific_closure_aux([ID],[Type],Pred,Domain,Functionality,_WF) :- Functionality=relation,
2666 % Pred = b(exists(Paras,ClosurePred),pred,Info1),
2667 % % dom({res|#(paras).(.... & res= domVal|->ran)}) = {res|#(paras).(.... & res= domVal)}
2668 % closures:select_equality(ClosurePred,ID,RHSExpr,Type,Info,RestPred),
2669 % RHSExpr = couple(DomValue,_),
2670 % closures:does_not_occur_in(ID,RestPred),
2671 % Type = couple(DomT,_),
2672 % TID = b(identifier(ID),DomT,[]),
2673 % % safe_create_texpr
2674 % conjunct_predicates([RestPred,b(equal(TID,DomValue),pred,[])],NewClosurePred),
2675 % NewPred = b(exists(Paras,NewClosurePred),pred,Info1),
2676 % Domain = closure([ID],[DomT],NewPred).
2677 dom_for_specific_closure_aux(P,T,Pred,Domain,Functionality,WF) :-
2678 dom_range_for_specific_closure2(P,T,Pred, Domain,_Range,domain_only,Functionality,WF).
2679 dom_for_specific_closure_aux(P,T,Pred,Domain,Functionality,WF) :-
2680 % see test 2571, also triggered in tests 1970, 2102 for reflexive closure, 1878
2681 Functionality = relation, % TODO: check if DomainA,B disjoint -> Functionality is function(.) if FuncA,FuncB are functions, see invariant rho_c ∈ REAL +-> REAL in f_m1 of Abrial hybrid flight; also do similar treatment for range
2682 is_a_disjunct(Pred,PredA,PredB),
2683 % example from test 2571: f = {x,y| x|->y : %xx.(xx>0|xx) or (x <= 0 & y=1)} & f: INTEGER --> INTEGER
2684 dom_for_specific_closure_aux(P,T,PredA,DomainA,_FuncA,WF),
2685 dom_for_specific_closure_aux(P,T,PredB,DomainB,_FuncB,WF),
2686 kernel_objects:union_wf(DomainA,DomainB,Domain,WF).
2687
2688
2689
2690 %TO DO treat overwrite closure dom(F1<+F2) = dom(F1) \/ dom(F2)
2691
2692 dom_for_lambda_closure(closure(P,T,Pred),Domain) :-
2693 is_lambda_value_domain_closure(P,T,Pred, DomainValue,_Expr),
2694 Domain=DomainValue.
2695
2696 % TO DO: add total functions
2697 %dom_for_specific_closure2([F],[T],
2698 % b(member(b(identifier(F),T,_), b(total_function(value(A),B),set(couple(DOM,RAN)),_)), pred,_) ,
2699 % A).
2700
2701 :- block domain_of_list_blocking(-,?).
2702 % the list will be sorted according to the term ordering for (_,_); hence it will
2703 % already be sorted for the projection onto the first element
2704 % maybe the speed difference is not worth it ??
2705 domain_of_list_blocking([],[]).
2706 domain_of_list_blocking([(A,_B)|T],[A-true|DT]) :- domain_blocking_aux(T,A,DT).
2707 :- block domain_blocking_aux(-,?,?).
2708 domain_blocking_aux([],_,[]).
2709 domain_blocking_aux([(A,_B)|T],Prev,Res) :-
2710 compare(Comp,A,Prev),
2711 (Comp = '='
2712 -> domain_blocking_aux(T,Prev,Res)
2713 ; Res = [A-true|DT],
2714 (Comp = '<' -> add_error_fail(custom_explicit_sets,'Domain list not_sorted: ',(A,Prev)) ; true),
2715 domain_blocking_aux(T,A,DT) ).
2716
2717 % and now a non-blocking version:
2718 domain_of_sorted_list([],size_res(0,'$none'),[]).
2719 domain_of_sorted_list([(A,_B)|T],Size,[A-true|DT]) :- domain_aux(T,A,DT,1,Size).
2720
2721 % TO DO: count length and determine when we have an interval
2722 domain_aux([],Prev,[],Acc,size_res(Acc,Prev)).
2723 domain_aux([(A,_B)|T],Prev,Res,SizeAcc,Size) :- SA1 is SizeAcc+1,
2724 compare(Comp,A,Prev),
2725 (Comp = '='
2726 -> domain_aux(T,Prev,Res,SA1,Size)
2727 ; Res = [A-true|DT],
2728 (Comp = '<' -> add_error_fail(custom_explicit_sets,'Domain list not_sorted: ',(A,Prev)) ; true),
2729 domain_aux(T,A,DT,SA1,Size) ).
2730
2731 /* succeeds if it can compute domain by some clever way */
2732 range_of_explicit_set_wf(global_set(GS),_R,_) :- !,
2733 add_error_and_fail(range_of_explicit_set_wf,'Cannot compute domain of global set: ',GS).
2734 range_of_explicit_set_wf(freetype(GS),_R,_) :- !,
2735 add_error_and_fail(range_of_explicit_set_wf,'Cannot compute domain of freetype: ',GS).
2736 range_of_explicit_set_wf(avl_set(A),Res,_) :- !,
2737 avl_domain(A,EC), % -> expand_custom_set(avl_set(A),EC),
2738 range(EC,R),
2739 normalised_list_to_avl(R,Res).
2740 range_of_explicit_set_wf(C,R,WF) :-
2741 ran_for_specific_closure(C,Ran,WF),!,
2742 Ran=R.
2743 range_of_explicit_set_wf(C,R,_) :-
2744 ran_symbolic(C,CC),!,
2745 R=CC.
2746 range_of_explicit_set_wf(closure(P,T,B),Res,WF) :-
2747 expand_custom_set_wf(closure(P,T,B),EC,range_of_explicit_set_wf,WF),
2748 % TO DO: it would be more useful here to directly just expand the projection onto the last component of P
2749 range_blocking(EC,R),
2750 normalised_list_to_avl_when_ground(R,Res).
2751
2752 % TO DO: in future it is maybe better to add an in_range_wf kernel predicate
2753 ran_symbolic(closure(Paras,Types,Pred), Res) :-
2754 (is_memoization_closure(Paras,Types,Pred,_)
2755 -> !,fail % memoization closures can never be dealt with symbolically; we need expansion
2756 ; true),
2757 expand_pair_closure(Paras,Types,Pred,[Y,X],[TY,TX],NewPred),!,
2758 % following test (1541) works with this: 2 : ran({y|#(x).(y = x |-> x + 2 & x : NATURAL)})
2759 ran_symbolic_closure(Y,[X],TY,[TX],NewPred,Res). %, print('res: '),translate:print_bvalue(Res),nl.
2760 ran_symbolic(closure([Y,X],[TY,TX],Pred), Res) :-
2761 ran_symbolic_closure(Y,[X],TY,[TX],Pred,Res).
2762 % TO DO: treat closures with more arguments: we need to quantify Y1,...Yn [Y1,...,Yn,X]
2763
2764 % Replace single Identifier YX of type pair by pair (Y,X) where Y,X are (fresh) variables not occuring in Pred
2765 % example: {y| #(x).(y = x |-> x + 2 & x : NATURAL)} --> {y__1,y__2|#(x).(y__1 |-> y__2 = x |-> x + 2 & x : NATURAL)}
2766 expand_pair_closure([YX],[TYX],Pred,[Y,X],[TY,TX],NewPred) :- TYX = couple(TY,TX),
2767 % Replace single ID YX of type pair by pair (Y,X) where Y,X are (fresh) variables not occuring in Pred
2768 % example: {y| #(x).(y = x |-> x + 2 & x : NATURAL)} --> {y__1,y__2|#(x).(y__1 |-> y__2 = x |-> x + 2 & x : NATURAL)}
2769 % following test (1541) works with this: 2 : ran({y|#(x).(y = x |-> x + 2 & x : NATURAL)})
2770 gensym:gensym(YX,Y),gensym:gensym(YX,X),
2771 create_typed_id(Y,TY,YTID), create_typed_id(X,TX,XTID),
2772 Pair = b(couple(YTID,XTID),TYX,[]),
2773 bsyntaxtree:replace_id_by_expr(Pred,YX,Pair,NewPred).
2774
2775 :- use_module(bsyntaxtree,[create_exists_opt_liftable/3]).
2776 %:- use_module(bsyntaxtree,[add_texpr_info_if_new/3]).
2777 ran_symbolic_closure(Y,Xs,TY,TXs,Pred,Res) :-
2778 % create closure for {Xs | #Y.(Pred)} where Pred uses Y|->Xs
2779 rename_ran_ids(Xs,Pred,[],XIDs,Pred2),
2780 create_typed_id(Y,TY,YTID),
2781 create_exists_opt_liftable([YTID],Pred2,Exists), % Y is liftable as the source is a closure with all ids
2782 %bsyntaxtree:check_used_ids_in_ast(Exists),
2783 %bsyntaxtree:create_exists_opt([YTID],[Pred2],Exists), %or
2784 %b_interpreter_components:create_and_simplify_exists([YTID],Pred2,Exists),
2785 %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;
2786 % 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
2787 Res = closure(XIDs,TXs,Exists).
2788
2789
2790
2791 :- use_module(library(lists),[select/3]).
2792
2793 % rename lambda_results :
2794 rename_ran_ids([],Pred,_,[],Pred).
2795 rename_ran_ids([X|TX],Pred,Acc,[XID|TTX],Pred2) :-
2796 % in case X is _lambda_result_ we need to rename it as it then would not get enumerated !
2797 (X == '_lambda_result_'
2798 -> get_fresh_id('_was_lambda_result_',TX,Acc,XID),
2799 % we could remove lambda_result info field, but it will no longer match new id anyway
2800 rename_bt(Pred,[rename(X,XID)],Pred2),
2801 TTX=TX
2802 % TODO: maybe we should also remove the prob_annotation('LAMBDA-EQUALITY') info inside Pred for the ids and equality !?
2803 ; XID = X, rename_ran_ids(TX,Pred,[X|Acc],TTX,Pred2)
2804 ).
2805
2806 :- use_module(b_ast_cleanup,[get_unique_id/2]).
2807 get_fresh_id(ID,List1,List2,Res) :- nonmember(ID,List1), nonmember(ID,List2),!, Res=ID.
2808 get_fresh_id(ID,_,_,FRESHID) :- nl,print('*** VARIABLE_CLASH PREVENTED: '), print(ID),nl,
2809 get_unique_id(ID,FRESHID).
2810
2811 :- block range_blocking(-,?).
2812 range_blocking([],[]).
2813 range_blocking([(_A,B)|T],[B-true|DT]) :- range_blocking(T,DT).
2814 % and a non-blocking version:
2815 range([],[]).
2816 range([(_A,B)|T],[B-true|DT]) :- range(T,DT).
2817
2818 ran_for_specific_closure(closure(P,T,Pred),Range,WF) :-
2819 dom_range_for_specific_closure2(P,T,Pred, _Domain,Range,range_only,_Functionality,WF).
2820 %ran_for_specific_closure(closure_x(P,T,Pred,_Exp),Card,_) :- ran_for_specific_closure2(P,T,Pred,Card).
2821
2822 :- use_module(bsyntaxtree,[conjunct_predicates/2, disjunct_predicates/2, create_typed_id/3, get_texpr_type/2]).
2823 override_custom_explicit_set_wf(R,S,Res,WF) :- /* R <+ S */
2824 nonvar(R),override_custom_explicit_set_aux(R,S,Res,WF).
2825 override_custom_explicit_set_aux(CL,Rel2,Res,_WF) :-
2826 CL=closure(P0,T,B0),
2827 ( preference(convert_comprehension_sets_into_closures,true), % cf keep_symbolic in bsets_clp
2828 (var(Rel2) -> true
2829 ; Rel2 \= avl_set(_)) % if Rel2 is avl_set then maybe better to compute explicitly; unless infinite
2830 ; quick_size_check_larger_than(Rel2,Size2,133) ->
2831 % if we have a large AVL set; then allow expansion up to a larger limit; cf machine 670_002.mch
2832 % a lot of machines use A*B*C <+ {....} to more compactly define large explicit sets
2833 (Size2=inf -> Limit = 200000
2834 ; Limit is min(200000,Size2*150)),
2835 dont_expand_this_closure(P0,T,B0,Limit)
2836 ; dont_expand_this_closure(P0,T,B0) % use default limit and checks for symbolic closure
2837 ),
2838 !,
2839 rename_ran_ids(P0,B0,[],P,B), % any '_lambda_result_' id is no longer guaranteed to be assigned a value in all cases
2840 NewClosure=closure(P,T,NewBody),
2841 % B <+ Rel2 ---> NewBody = P:Rel2 or (prj1(P) /: dom(Rel2) & B)
2842 % TODO better? : %x.(x:Domain|IF x:dom(SFF) THEN SFF(x) ELSE DEFAULT)?
2843 generate_typed_id_pairs(P,T,NestedPairs),
2844 get_texpr_type(NestedPairs,PairsType),
2845 RelPairsType = set(PairsType),
2846 ValS = b(value(Rel2),RelPairsType,[]),
2847 MemS = b(member(NestedPairs,ValS),pred,[]), % P:Rel2
2848 get_prj1(NestedPairs,DomExpr),
2849 get_texpr_type(DomExpr,DomType),
2850 Domain = b(domain(ValS),set(DomType),[]), % TO DO: perform some optimisations like dom(%x.(P|E)) --> {x|P}
2851 %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
2852 NotMemDomS = b(not_member(DomExpr,Domain),pred,[]), % prj1(P) /: dom(Rel2)
2853 conjunct_predicates([NotMemDomS,B],RHS),
2854 disjunct_predicates([MemS,RHS],NewBody),
2855 %print(override),nl, bsyntaxtree:check_used_ids_in_ast(NewBody),
2856 mark_closure_as_symbolic(NewClosure,Res).
2857 % TO DO: add a case where for second set we have: dont_expand_this_closure
2858 override_custom_explicit_set_aux(R,S,Res,WF) :-
2859 is_custom_explicit_set(R,override_custom_explicit_set),
2860 nonvar(S), is_custom_explicit_set(S,override_custom_explicit_set),
2861 %% hit_profiler:add_profile_hit(override(R,S),3), %%
2862 override_custom_explicit_set2(R,S,Res,WF).
2863
2864 override_custom_explicit_set2(R,S,Res,_WF) :- is_one_element_custom_set(S,(X,Y)),
2865 override_pair_explicit_set(R,X,Y,NewR),!, % override pair only succeeds for avl_set
2866 Res=NewR.
2867 % TO DO: if R is very large and S relatively small : iterate by calling override_pair_explicit_set
2868 override_custom_explicit_set2(R,S,Res,WF) :-
2869 \+ dont_expand_this_explicit_set(S), % see test 2564
2870 expand_custom_set_wf(R,ER,override_custom_explicit_set_aux1,WF),
2871 expand_custom_set_wf(S,ES,override_custom_explicit_set_aux2,WF),
2872 override_list(ER,ES,LRes,Done),
2873 finish_restriction(Done,LRes,Res).
2874
2875 quick_size_check_larger_than(Set,Size,Limit) :-
2876 quick_custom_explicit_set_approximate_size(Set,Size),
2877 (is_inf_or_overflow_card(Size) -> true ; Size > Limit).
2878 get_prj1(b(couple(DomExpr,_),_,_),Prj1) :- !, Prj1 = DomExpr.
2879 get_prj1(BE,b(first_of_pair(BE),DT,[])) :- % some closures have a single identifier; we need to apply prj1
2880 BE = b(_E,couple(DT,_RT),_I).
2881
2882 % translate a parameter name and type list into a nested-pair value
2883 generate_typed_id_pairs([ID|IT],[Type|TT],Res) :- create_typed_id(ID,Type,TypedID),
2884 conv2(IT,TT,TypedID,Res).
2885 conv2([],[],X,X).
2886 conv2([ID|IT],[Type|TT],Acc,Res) :- create_typed_id(ID,Type,TypedID),
2887 get_texpr_type(Acc,AccType),
2888 Couple = b(couple(Acc,TypedID),couple(AccType,Type),[]),
2889 conv2(IT,TT,Couple,Res).
2890
2891 :- block override_list(-,?,?,?), override_list(?,-,?,?).
2892 override_list([],S,Res,Done) :- !, copy_to_true_list(S,Res,Done).
2893 override_list(R,[],Res,Done) :- !, copy_to_true_list(R,Res,Done).
2894 override_list([(From1,To1)|T1],[(From2,To2)|T2],Res,Done) :-
2895 (From1 @< From2
2896 -> Res = [(From1,To1)-true|TR], override_list(T1,[(From2,To2)|T2],TR,Done)
2897 ; From2 @< From1
2898 -> Res = [(From2,To2)-true|TR], override_list([(From1,To1)|T1],T2,TR,Done)
2899 ; override_list(T1,[(From2,To2)|T2],Res,Done)).
2900
2901 :- block copy_to_true_list(-,?,?).
2902 % add -true to get lists that can be converted to avl
2903 copy_to_true_list([],[],true).
2904 copy_to_true_list([H|T],[H-true|CT],Done) :- copy_to_true_list(T,CT,Done).
2905
2906 %:- use_module(extrasrc(b_expression_sharing),[cse_optimize_predicate/2]).
2907 :- use_module(closures,[get_domain_range_for_closure_types/3]).
2908 % compute a closure with the functionality violations of a closure
2909 symbolic_functionality_check_closure(closure(P,T,B),closure([DID,ID1,ID2],[DomType,RanType,RanType],Body)) :-
2910 % construct {d,z_,z__| (d,z_):R & (d,z__):R & z_\= z__}
2911 generate_typed_id_pairs(P,T,NestedPairs),
2912 get_texpr_type(NestedPairs,PairsType),
2913 RelPairsType = set(PairsType),
2914 TRel = b(value(closure(P,T,B)),RelPairsType,[]),
2915 DID = '_domain', ID1 = '_zzzz_unary', ID2 = '_zzzz_binary',
2916 TDID = b(identifier(DID),DomType,[]),
2917 TID1 = b(identifier(ID1),RanType,[]),
2918 TID2 = b(identifier(ID2),RanType,[]),
2919 construct_pair_membership(TDID,TID1,PairsType,TRel,Mem1),
2920 construct_pair_membership(TDID,TID2,PairsType,TRel,Mem2),
2921 get_domain_range_for_closure_types(T,DomType,RanType),
2922 NeqRan = b(not_equal(TID1,TID2), pred, []),
2923 conjunct_predicates([Mem1,Mem2,NeqRan],Body),
2924 %TODO: cse_optimize_predicate(UnOptBody,Body),
2925 bsyntaxtree:check_used_ids_in_ast(Body).
2926 %bsyntaxtree:check_ast(Body).
2927
2928 :- use_module(bsyntaxtree,[replace_ids_by_exprs/4]).
2929 % assumes TID1 and TID2 are distinct identifiers
2930 construct_pair_membership(TID1,TID2,_PairsType,b(Rel,_,_),MemPred) :-
2931 is_comprehension_set_or_closure(Rel,P,_T,Pred0),
2932 P = [ID1,ID2],
2933 !, % TID1|->TID2 : {x,y|P(x,y)} ==> P(TID1,TID2); see also remove_member_comprehension ast_cleanup rule
2934 replace_ids_by_exprs(Pred0,[ID1,ID2],[TID1,TID2],MemPred), % simultaneous replacement, in case of clashes !
2935 debug_println(9,inlined_pair_membership(ID1,ID2)).
2936 construct_pair_membership(TID1,TID2,PairsType,TRel,MemPred) :-
2937 MemPred = b(member( b(couple(TID1,TID2),PairsType,[]),TRel),pred,[]).
2938
2939
2940
2941 % compute a closure with the injectivity violations of a closure
2942 symbolic_injectivity_check_closure(closure(P,T,B),closure([RID,ID1,ID2],[RanType,DomType,DomType],Body)) :-
2943 % construct {r,z_,z__| (z_,r):R & (z__,r):R & z_\= z__}
2944 generate_typed_id_pairs(P,T,NestedPairs),
2945 get_texpr_type(NestedPairs,PairsType),
2946 RelPairsType = set(PairsType),
2947 TRel = b(value(closure(P,T,B)),RelPairsType,[]), % what if closure body B has WD condition?
2948 RID = '_range', ID1 = '_zzzz_unary', ID2 = '_zzzz_binary',
2949 TRID = b(identifier(RID),RanType,[]),
2950 TID1 = b(identifier(ID1),DomType,[]),
2951 TID2 = b(identifier(ID2),DomType,[]),
2952 construct_pair_membership(TID1,TRID,PairsType,TRel,Mem1),
2953 construct_pair_membership(TID2,TRID,PairsType,TRel,Mem2),
2954 get_domain_range_for_closure_types(T,DomType,RanType),
2955 NeqRan = b(not_equal(TID1,TID2), pred, []),
2956 conjunct_predicates([Mem1,Mem2,NeqRan],Body),
2957 bsyntaxtree:check_used_ids_in_ast(Body).
2958 %bsyntaxtree:check_ast(Body).
2959
2960 % -------------------------
2961
2962
2963 % check whether we have a partial function
2964 is_avl_partial_function(empty) :- !.
2965 is_avl_partial_function(node((KeyFrom,_KeyTo),_True,_,L,R)) :- !,
2966 is_avl_partial_function2(L,'$$MIN$$',KeyFrom),
2967 is_avl_partial_function2(R,KeyFrom,'$$MAX$$').
2968 is_avl_partial_function(X) :- add_internal_error('Not avl_set or relation: ',is_avl_partial_function(X)),fail.
2969
2970 % we traverse the tree from top to bottom, keeping track of possible upper- and lower-bounds
2971 % if any value matches the upper or lower bound, the we do not have a partial function
2972 is_avl_partial_function2(empty,_,_).
2973 is_avl_partial_function2(node((KeyFrom,_KeyTo),_True,_,L,R),ParentFrom,ParentTo) :-
2974 KeyFrom \= ParentFrom, KeyFrom \= ParentTo,
2975 is_avl_partial_function2(L,ParentFrom,KeyFrom),
2976 is_avl_partial_function2(R,KeyFrom,ParentTo).
2977
2978 % the dual of the above, returning a counter example
2979 is_not_avl_partial_function(node((KeyFrom,_KeyTo),_True,_,L,R),DuplicateKey) :- !,
2980 (is_not_avl_partial_function2(L,'$$MIN$$',KeyFrom,DuplicateKey) -> true
2981 ; is_not_avl_partial_function2(R,KeyFrom,'$$MAX$$',DuplicateKey)).
2982 is_not_avl_partial_function2(node((KeyFrom,_KeyTo),_True,_,L,R),ParentFrom,ParentTo,DuplicateKey) :-
2983 ( KeyFrom = ParentFrom -> DuplicateKey=KeyFrom
2984 ; KeyFrom = ParentTo -> DuplicateKey=KeyFrom
2985 ; is_not_avl_partial_function2(L,ParentFrom,KeyFrom,DuplicateKey) -> true
2986 ; is_not_avl_partial_function2(R,KeyFrom,ParentTo,DuplicateKey) -> true).
2987
2988
2989 % check whether we have a function which is total over a given domain; both as AVL sets
2990 is_avl_total_function_over_domain(empty,empty) :- !.
2991 is_avl_total_function_over_domain(AVLFun,AVLDom) :-
2992 avl_domain(AVLFun,FunList),
2993 avl_domain(AVLDom,DomList),
2994 is_avl_total_fun2(FunList,DomList).
2995
2996 is_avl_total_fun2([],[]).
2997 is_avl_total_fun2([(From,_To)|FT],[From|DomT]) :- is_avl_total_fun2(FT,DomT).
2998
2999
3000 %not_is_avl_partial_function(AVLF) :- \+ is_avl_partial_function(AVLF).
3001
3002 :- use_module(kernel_equality,[membership_test_wf/4]).
3003 % check whether an AVL Relation is not over a specific domain & range
3004 is_not_avl_relation_over_domain_range(AVLRel,Domain,Range,WF) :- AVLRel \= empty,
3005 avl_min_pair(AVLRel,RFrom,RTo),
3006 membership_test_wf(Domain,RFrom,MemRes,WF),
3007 is_not_avl_rel_dom1(MemRes,RFrom,RTo,AVLRel,Domain,Range,WF).
3008
3009 :- block is_not_avl_rel_dom1(-, ?,?,?,?,?,?).
3010 is_not_avl_rel_dom1(pred_false,_,_,_,_,_,_WF).
3011 is_not_avl_rel_dom1(pred_true,RFrom,RTo,AVLRel,Domain,Range,WF) :-
3012 membership_test_wf(Range,RTo,MemRes,WF),
3013 is_not_avl_rel_dom2(MemRes,RFrom,RTo,AVLRel,Domain,Range,WF).
3014
3015 :- block is_not_avl_rel_dom2(-, ?,?,?,?,?,?).
3016 is_not_avl_rel_dom2(pred_false,_,_,_,_,_,_WF).
3017 is_not_avl_rel_dom2(pred_true,RFrom,RTo,AVLRel,Domain,Range,WF) :-
3018 avl_next((RFrom,RTo),AVLRel,(RFrom2,RTo2)),
3019 membership_test_wf(Domain,RFrom2,MemRes,WF),
3020 is_not_avl_rel_dom1(MemRes,RFrom2,RTo2,AVLRel,Domain,Range,WF).
3021
3022 % check whether an AVL Relation is not over a specific range
3023 is_not_avl_relation_over_range(AVLRel,Range,WF) :- AVLRel \= empty,
3024 avl_min_pair(AVLRel,RFrom,RTo),
3025 membership_test_wf(Range,RTo,MemRes,WF),
3026 is_not_avl_rel_ran2(MemRes,RFrom,RTo,AVLRel,Range,WF).
3027
3028 :- block is_not_avl_rel_ran2(-, ?,?,?,?,?).
3029 is_not_avl_rel_ran2(pred_false,_,_,_,_,_WF).
3030 is_not_avl_rel_ran2(pred_true,RFrom,RTo,AVLRel,Range,WF) :-
3031 avl_next((RFrom,RTo),AVLRel,(RFrom2,RTo2)),
3032 kernel_equality:membership_test_wf(Range,RTo2,MemRes,WF),
3033 is_not_avl_rel_ran2(MemRes,RFrom2,RTo2,AVLRel,Range,WF).
3034
3035 % check whether we have a relation
3036 is_avl_relation(node((_KeyFrom,_KeyTo),_True,_,_,_)).
3037
3038 % check whether a Relation has all its range elments in a certain Range (not necessarily AVL)
3039 % TO DO: if Domain is an interval: we could take avl_min and avl_max and rely on lexicographic ordering
3040 is_avl_relation_over_domain(AVL,IntervalClosure,_WF) :-
3041 is_interval_closure_or_integerset(IntervalClosure,Low,Up),!,
3042 ((avl_min(AVL,(int(ALow),_)), avl_max(AVL,(int(AUp),_)))
3043 -> cs_greater_than_equal(ALow,Low), cs_greater_than_equal(Up,AUp) %,print(ok),nl
3044 ; (AVL=empty -> true ; add_error_and_fail(is_avl_relation_over_domain,'Not a relation with integer domain: ',AVL))).
3045 is_avl_relation_over_domain(_,Domain,_) :-
3046 quick_is_definitely_maximal_set(Domain),!.
3047 %is_definitely_maximal_set(Domain),!.
3048 ?is_avl_relation_over_domain(AVL,Domain,WF) :- is_avl_relation_over_domain2(AVL,Domain,WF).
3049 is_avl_relation_over_domain2(empty,_,_).
3050 is_avl_relation_over_domain2(node((KeyFrom,_KeyTo),_,_,L,R), Domain,WF) :-
3051 ? is_avl_relation_over_domain2(L, Domain,WF),
3052 ? is_avl_relation_over_domain2(R, Domain,WF),
3053 ? kernel_objects:check_element_of_wf(KeyFrom,Domain,WF).
3054
3055 % : faster to check than is_definitely_maximal_set
3056 quick_is_definitely_maximal_set(X) :- nonvar(X),
3057 quick_is_definitely_maximal_set_aux(X).
3058 quick_is_definitely_maximal_set_aux(global_set(GS)) :-
3059 nonvar(GS),is_maximal_global_set(GS).
3060 quick_is_definitely_maximal_set_aux(avl_set(AVL)) :-
3061 quick_definitely_maximal_set_avl(AVL).
3062
3063 % check whether a Relation has all its range elments in a certain Range (not necessarily AVL)
3064
3065
3066
3067 is_avl_relation_over_range(empty,_,_) :- !.
3068 is_avl_relation_over_range(_,Range,_) :-
3069 %quick_is_definitely_maximal_set(Range),
3070 is_definitely_maximal_set(Range),
3071 !.
3072 ?is_avl_relation_over_range(AVL,Range,WF) :- is_avl_relation_over_range2(AVL,Range,WF).
3073
3074 is_avl_relation_over_range2(empty,_,_).
3075 is_avl_relation_over_range2(node((_KeyFrom,KeyTo),_,_,L,R), Range,WF) :-
3076 ? is_avl_relation_over_range(L, Range,WF),
3077 ? kernel_objects:check_element_of_wf(KeyTo,Range,WF),
3078 ? is_avl_relation_over_range2(R, Range,WF).
3079
3080 % safe version of is_avl_sequence, does not throw error when type cannot be a sequence
3081 safe_is_avl_sequence(empty) :- !.
3082 safe_is_avl_sequence(node((int(KeyFrom),_KeyTo),_True,_,L,R)) :- !,
3083 is_avl_sequence2(L,0,KeyFrom),
3084 is_avl_sequence2(R,KeyFrom,'$$MAX$$').
3085
3086 is_avl_sequence(empty) :- !.
3087 is_avl_sequence(node((int(KeyFrom),_KeyTo),_True,_,L,R)) :- !,
3088 is_avl_sequence2(L,0,KeyFrom),
3089 is_avl_sequence2(R,KeyFrom,'$$MAX$$').
3090 is_avl_sequence(X) :- add_error_and_fail(is_avl_sequence,'Not avl_set or sequence: ',X).
3091
3092 % we traverse the tree from top to bottom, keeping track of possible upper- and lower-bounds
3093 % if any value matches the upper or lower bound, then we do not have a partial function
3094 is_avl_sequence2(empty,X,Y) :-
3095 (Y=='$$MAX$$' -> true ; Y is X+1). % otherwise there is a gap in the sequence
3096 is_avl_sequence2(node((int(KeyFrom),_KeyTo),_,_,L,R),ParentFrom,ParentTo) :-
3097 KeyFrom > ParentFrom, KeyFrom \= ParentTo,
3098 is_avl_sequence2(L,ParentFrom,KeyFrom),
3099 is_avl_sequence2(R,KeyFrom,ParentTo).
3100
3101 % for performance: it is not worthwhile to make a version that checks that
3102 % we have a sequence over a range using a single traversal
3103
3104
3105 % get avl_sequence elements as sorted list (without indices)
3106 % used by external function REPLACE
3107 get_avl_sequence(AVL,SeqList) :-
3108 get_avl_sequence_dcg(AVL,SeqList,[]).
3109
3110 get_avl_sequence_dcg(empty) --> [].
3111 get_avl_sequence_dcg(node((int(_),SeqEl),_True,_,L,R)) -->
3112 get_avl_sequence_dcg(L),
3113 [SeqEl],
3114 get_avl_sequence_dcg(R).
3115
3116
3117 % ---------------------------
3118 prefix_of_custom_explicit_set(avl_set(A),MinIndex,Result,WF) :-
3119 size_of_avl_sequence(A,Size,WF),
3120 (MinIndex > Size
3121 -> add_wd_error('index larger than size of sequence in prefix_sequence (/|\\)! ', '>'(MinIndex,Size),WF)
3122 % ; MinIndex = 0 -> Result = [] % case already treated in bsets_clp
3123 ; MinIndex = Size -> Result=avl_set(A)
3124 ; prefix_of_custom_explicit_set2(A,MinIndex,OrdList,[]),
3125 ord_list_to_avlset(OrdList,Result,prefix_of_custom_explicit_set)
3126 ).
3127 prefix_of_custom_explicit_set2(empty,_MaxIndex) --> {true}.
3128 prefix_of_custom_explicit_set2(node((int(KeyFrom),KeyTo),_True,_,L,R),MaxIndex) -->
3129 ({KeyFrom = MaxIndex}
3130 -> prefix_of_custom_explicit_set2(L,MaxIndex), [((int(KeyFrom),KeyTo)-true)]
3131 ; {KeyFrom > MaxIndex} -> prefix_of_custom_explicit_set2(L,MaxIndex)
3132 ; prefix_of_custom_explicit_set2(L,MaxIndex), [((int(KeyFrom),KeyTo)-true)],
3133 prefix_of_custom_explicit_set2(R,MaxIndex)
3134 ).
3135
3136 % size is only well-defined for sequences:
3137 size_of_custom_explicit_set(avl_set(AVL),int(Size),WF) :- size_of_avl_sequence(AVL,Size,WF).
3138 size_of_custom_explicit_set(closure(P,T,B),Res,WF) :-
3139 is_lambda_value_domain_closure(P,T,B, DomainValue,_Expr),
3140 kernel_cardinality_attr:finite_cardinality_as_int_wf(DomainValue,Res,WF).
3141
3142 size_of_avl_sequence(AVL,Size,WF) :-
3143 avl_min_pair(AVL,int(One),_), One =\= 1,
3144 !,
3145 avl_size(AVL,Sz),
3146 add_wd_error('Applying size to a value which is not a sequence (minimum index is not 1)',b(value(avl_set(AVL)),seq(any),[]),WF),
3147 Size=Sz. % other calls to size_of_avl_sequence currently expect a value
3148 size_of_avl_sequence(AVL,Size,WF) :-
3149 \+ preference(find_abort_values,false),
3150 \+ is_avl_sequence(AVL),
3151 !,
3152 avl_size(AVL,Sz),
3153 add_wd_error('Applying size to a value which is not a sequence',b(value(avl_set(AVL)),seq(any),[]),WF),
3154 Size=Sz. % other calls to size_of_avl_sequence currently expect a value
3155 size_of_avl_sequence(AVL,Size,WF) :-
3156 avl_max_pair(AVL,int(Sz),_),
3157 avl_height(AVL,H), % we cannot compute the height together with max; we need the longest path!
3158 get_min_max_card(H,MinSize,MaxSize),
3159 %avl_size(AVL,Real),format('AVL SeqSize: ~w, height: ~w, real size:~w, min: ~w, max: ~w~n',[Sz,H,Real,MinSize,MaxSize]),
3160 (Sz > MaxSize
3161 -> 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),
3162 avl_size(AVL,Size)
3163 % 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})
3164 ; Sz < MinSize
3165 -> 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),
3166 avl_size(AVL,Size)
3167 % triggered by e.g. size([0,2,2,2] |> {2})
3168 ; Size=Sz).
3169
3170 get_min_max_card(Height,MinCard,MaxCard) :-
3171 % 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
3172 MaxCard is 2^Height - 1,
3173 % 1.618034 is golden ration phi 0.5(1+sqrt(5)) , 2.236068 is sqrt(5)
3174 % proof in Knuth uses fact: N > phi^(h+2)/sqrt(5) - 2
3175 MinCard is ceiling((1.61803398875**(Height+2)) / 2.2360679775 - 2).
3176
3177 % check if a candidate size is possible given height:
3178 avl_size_possible(AVL,SizeCandidate) :-
3179 avl_height(AVL,Height), % TO DO: restrict to something like log2 of Height
3180 get_min_max_card(Height,MinCard,MaxCard),
3181 MinCard =< SizeCandidate,
3182 SizeCandidate =< MaxCard.
3183
3184
3185 suffix_of_custom_explicit_set(avl_set(A),MinIndex,Result,WF) :-
3186 size_of_avl_sequence(A,Size,WF),
3187 (MinIndex > Size
3188 -> add_wd_error('index larger than size of sequence in suffix_sequence (\\|/)! ', '>'(MinIndex,Size),WF)
3189 % ; MinIndex = 0 -> Result = avl_set(A) % case already treated in bsets_clp
3190 ; MinIndex = Size -> Result=[]
3191 ; suffix_of_custom_explicit_set2(A,MinIndex,OrdList,[]),
3192 ord_list_to_avlset(OrdList,Result,suffix_of_custom_explicit_set)
3193 ).
3194 suffix_of_custom_explicit_set2(empty,_MinIndex) --> {true}.
3195 suffix_of_custom_explicit_set2(node((int(KeyFrom),KeyTo),_True,_,L,R),MinIndex) -->
3196 ({KeyFrom =< MinIndex} -> suffix_of_custom_explicit_set2(R,MinIndex)
3197 ; {ShiftedKeyFrom is KeyFrom-MinIndex},
3198 ({KeyFrom =:= MinIndex+1}
3199 -> {true} ; suffix_of_custom_explicit_set2(L,MinIndex)),
3200 [((int(ShiftedKeyFrom),KeyTo)-true)],
3201 suffix_of_custom_explicit_set2(R,MinIndex)
3202 ).
3203
3204 shift_avl_sequence_to_ord_list(AVL,Offset,ShiftedOrdList) :-
3205 avl_to_list(AVL,List),shift_seq(List,Offset,ShiftedOrdList).
3206 % it does not seem to be worth to use avl_to_list_dcg_offset or a variation thereof
3207 % it is not really slower to do two traversals (avl_to_list and shift_seq)
3208
3209 shift_seq([],_,[]).
3210 shift_seq([(int(I),Val)-true|T],Offset,[(int(NI),Val)-true|ST]) :- NI is I+Offset,
3211 shift_seq(T,Offset,ST).
3212
3213 :- use_module(debug).
3214 concat_custom_explicit_set(avl_set(S1),Seq2,Res,WF) :- nonvar(Seq2), Seq2=avl_set(S2),
3215 size_of_avl_sequence(S1,Size1,WF),
3216 shift_avl_sequence_to_ord_list(S2,Size1,OL2),
3217 % if OL2 is small we could use avl_store like in append_custom_explicit_set
3218 %avl_to_list(S1,OL1),
3219 avl_to_list_dcg(S1,NewOrdList,OL2), % use OL2 rather than [] as tail
3220 %append(OL1,OL2,NewOrdList), % we could avoid traversing OL1 again by doing a custom avl_to_list/3 which specifies tail
3221 ord_list_to_avlset(NewOrdList,Res,concat). % , print_term_summary(res_concat(Res)).
3222
3223 % a DCG version of avl_to_list; allows to call it with something else than [] as tail
3224 avl_to_list_dcg(empty) --> [].
3225 avl_to_list_dcg(node(Key,Val,_,L,R)) -->
3226 avl_to_list_dcg(L), [(Key-Val)],
3227 avl_to_list_dcg(R).
3228
3229 /* conc: concatenation of sequence of sequences (general_concat) */
3230 conc_custom_explicit_set(avl_set(AVL),Res) :-
3231 avl_min_pair(AVL,int(ONE),First),
3232 conc2_cs(First,ONE,AVL,0,NewOrdList),
3233 ord_list_to_avlset(NewOrdList,Res,conc).
3234
3235 conc2_cs(Seq,NrSeq,AVL,Offset,OrdList) :-
3236 add_seq(Seq,Offset,OrdList,NewOffset,TailOrd),
3237 (avl_next((int(NrSeq),Seq),AVL,(int(N2),Seq2))
3238 -> conc2_cs(Seq2,N2,AVL,NewOffset,TailOrd)
3239 ; TailOrd=[]).
3240
3241 add_seq([],Offset,OrdRes,NewOffset,TailOrdRes) :- NewOffset=Offset, TailOrdRes=OrdRes.
3242 add_seq(avl_set(ASeq),Offset,OrdRes,NewOffset,TailOrd) :-
3243 avl_to_list_dcg_offset(ASeq,Offset,NrEls,OrdRes,TailOrd), NewOffset is Offset+NrEls.
3244
3245 % a version of avl_to_list for sequences which autmatically adds an offset
3246 avl_to_list_dcg_offset(empty,_,0) --> [].
3247 avl_to_list_dcg_offset(node((int(Idx),El),Val,_,L,R),Offset,NrEls) -->
3248 {NIdx is Idx+Offset},
3249 avl_to_list_dcg_offset(L,Offset,N1),
3250 [((int(NIdx),El)-Val)],
3251 avl_to_list_dcg_offset(R,Offset,N2), {NrEls is N1+N2+1}.
3252
3253 prepend_custom_explicit_set(avl_set(S1),ObjectToPrepend,Res) :-
3254 %hit_profiler:add_profile_hit(prepend_custom_explicit_set(avl_set(S1),ObjectToPrepend,Res)),
3255 element_can_be_added_or_removed_to_avl(ObjectToPrepend),
3256 shift_avl_sequence_to_ord_list(S1,1,OL1),
3257 ord_list_to_avlset([(int(1),ObjectToPrepend)-true|OL1],Res).
3258
3259 append_custom_explicit_set(avl_set(S1),ObjectToAppend,Res,WF) :-
3260 element_can_be_added_or_removed_to_avl(ObjectToAppend), % implies that ObjectToAppend is ground
3261 size_of_avl_sequence(S1,Size1,WF), NewSize is Size1+1,
3262 add_ground_element_to_explicit_set_wf(avl_set(S1),(int(NewSize),ObjectToAppend),Res,WF).
3263
3264 % compute tail of a sequence and also return first element
3265 tail_sequence_custom_explicit_set(avl_set(S1),First,Res,Span,WF) :-
3266 shift_avl_sequence_to_ord_list(S1,-1,NewOrdList),
3267 (NewOrdList = [(int(0),First)-true|TailOL] -> ord_list_to_avlset(TailOL,Res)
3268 ; add_wd_error_span('tail argument is not a sequence!', avl_set(S1),Span,WF)
3269 % add_error_fail(tail_sequence,'tail applied to ', NewOrdList))
3270 ).
3271 last_sequence_explicit_set(avl_set(AVL),Last) :-
3272 avl_max_pair(AVL,int(_Sz),Last).
3273 % 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 ?
3274 %first_sequence_explicit_set(avl_set(AVL),First) :- % not used anymore; apply_to used instead
3275 % avl_min_pair(AVL,int(_One),First).
3276
3277 % compute front and return last element at the same time
3278 front_sequence_custom_explicit_set(avl_set(AVL),Last,Res) :-
3279 avl_max_pair(AVL,int(Size),Last),
3280 direct_remove_element_from_avl(AVL, (int(Size),Last), Res). % we know Last is already in AVL-converted format
3281
3282
3283 reverse_custom_explicit_set(avl_set(AVL),Res) :-
3284 avl_to_list_dcg_offset(AVL,0,Size,List,[]),
3285 S1 is Size+1,
3286 reverse_list(List,S1,[],RevList),
3287 ord_list_to_avl(RevList,RevAVL),
3288 Res=avl_set(RevAVL).
3289
3290 reverse_list([],_,Acc,Acc).
3291 reverse_list([(int(Idx),El)-V|T],S1,Acc,Res) :-
3292 NewIdx is S1 - Idx,
3293 reverse_list(T,S1,[(int(NewIdx),El)-V|Acc],Res).
3294
3295 % check if a relation is injective ; compute range at the same time; note AVL can be empty
3296 is_injective_avl_relation(AVL,RangeRes) :-
3297 avl_domain(AVL,ElList),
3298 empty_avl(EmptyAcc),
3299 is_avl_inj_list(ElList,EmptyAcc,Range),
3300 construct_avl_set(Range,RangeRes).
3301
3302 is_avl_inj_list([],Range,Range).
3303 is_avl_inj_list([(_From,To)|T],InRange,OutRange) :-
3304 (avl_fetch(To,InRange) -> fail /* this is not an injection; a range element is repeated */
3305 ; avl_store(To,InRange,true,InRange1),
3306 is_avl_inj_list(T,InRange1,OutRange)
3307 ).
3308
3309 % Example predicates that work with code below:
3310 % card(id((1..1000)*(1..1000))~)=1000*1000
3311 % card(((1..1000)*(1..1000))~)=1000*1000
3312 invert_explicit_set(global_set(GS),_R) :- !,
3313 add_error_and_fail(invert_explicit_set,'Cannot compute inverse of global set: ',GS).
3314 invert_explicit_set(freetype(GS),_R) :- !,
3315 add_error_and_fail(invert_explicit_set,'Cannot compute inverse of freetype: ',GS).
3316 invert_explicit_set(closure([P1,P2],[T1,T2],Clo),R) :- !,
3317 % TODO: also invert closures with single argument or more arguments
3318 % e.g., {a,b,c|a=1 & b=1 &c:1..10}~ = {c,ab|ab=(1,1) & c:1..10}
3319 R = closure([P2,P1],[T2,T1],Clo).
3320 invert_explicit_set(closure([P1],[T1],Clo),R) :-
3321 is_member_closure_with_info([P1],[T1],Clo,_Type,Info,MEM),
3322 invert_member_predicate(MEM,T1,InvMEM,InvT1),!,
3323 construct_member_closure(P1,InvT1,Info,InvMEM,R).
3324 invert_explicit_set(C,AVL) :- expand_custom_set(C,EC,invert_explicit_set), %% convert to AVL ?
3325 inv_and_norm(EC,AVL).
3326
3327 invert_member_predicate(cartesian_product(A,B),couple(TA,TB),
3328 cartesian_product(B,A),couple(TB,TA)).
3329 invert_member_predicate(identity(A),TA,identity(A),TA).
3330
3331
3332 :- block inv_and_norm(-,?).
3333 inv_and_norm(EC,AVL) :- inv(EC,R,Done), norm(Done,R,AVL).
3334
3335 :- block norm(-,?,?).
3336 norm(_,R,AVL) :- normalised_list_to_avl(R,AVL).
3337
3338 :- block inv(-,?,?).
3339 inv([],[],done).
3340 inv([(A,B)|T],[(B,A)-true|DT],Done) :- inv(T,DT,Done).
3341
3342
3343
3344 % checks whether a ground value is in the domain of an AVL relation
3345 check_in_domain_of_avlset_wf(X,AVL,_WF) :-
3346 convert_to_avl_inside_set(X,AX),!,
3347 ? (avl_fetch_pair(AX,AVL,_) -> true ; fail).
3348 check_in_domain_of_avlset_wf(X,AVL,WF) :-
3349 print('### could not convert arg for check_in_domain_of_avlset'),nl,
3350 print(X),nl,
3351 safe_flex_avl_member_default_wf((X,_),AVL,WF).
3352
3353 % checks whether a ground value is in the domain of an AVL relation and has only one solution
3354 check_unique_in_domain_of_avlset(X,AVL) :- convert_to_avl_inside_set(X,AX),!,
3355 avl_fetch_pair(AX,AVL,AY1),!,
3356 (avl_fetch_pair(AX,AVL,AY2), AY1 \= AY2 -> fail
3357 ; true).
3358
3359
3360 % utility to check if for a value there is at most one matching element in an AVL set
3361 % optimized for function application
3362 at_most_one_match_possible(Element,AVL,Matches) :- nonvar(Element),
3363 Element=(Index,_Rest), % Function Application; TO DO: does this cover all func. appl ?
3364 element_can_be_added_or_removed_to_avl(Index),
3365 convert_to_avl_inside_set(Index,AX), % is ground and normalised ?
3366 % TO DO: check AVL size ? Check other patterns ?
3367 findall((AX,Match),avl_tools:avl_fetch_pair(AX,AVL,Match),Matches),
3368 Matches \= [_,_|_].
3369
3370
3371
3372 apply_to_avl_set(A,X,Y,Span,WF) :-
3373 ground_value_check(X,GroundX),
3374 ? apply_to_avl_set_aux(A,X,Y,GroundX,Span,WF).
3375
3376 apply_to_avl_set_aux(A,X,Y,GroundX,Span,WF) :- nonvar(GroundX),!,
3377 apply_check_tuple(X,Y,A,Span,WF). % we could call apply_check_tuple_ground to avoid one ground test
3378 % We know that A is a function: we can deterministically apply if X is ground;
3379 % if Y is ground this is only the cases for injective functions
3380 apply_to_avl_set_aux(A,X,Y,GroundX,Span,WF) :-
3381 %(preference(data_validation_mode,true); % we now reduce priority of backpropagation below
3382 \+ preference(find_abort_values,false),
3383 % do not try inverse propagation onto argument X of function application A(X) = Y
3384 !,
3385 avl_approximate_size(A,3,ApproxSizeA),
3386 apply_check_tuple_delay(X,Y,A,ApproxSizeA,Span,WF,GroundX,_,_).
3387 apply_to_avl_set_aux(A,X,Y,GroundX,Span,WF) :-
3388 ground_value_check(Y,GroundY),
3389 avl_approximate_size(A,3,ApproxSizeA), % exact size for height <= 3; approximate size above
3390 (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
3391 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
3392 %propagate_avl_element_information((X,Y),A,ApproxSizeA,WF), % could be done; but would prevent WD problems from being detected
3393 % this waitflag is used when neither X nor Y are ground;
3394 % quite often not much is gained by enumerating possible values; unless X or Y are constrained or trigger other computations
3395 % WSz is 10*ApproxSizeA, % magic value
3396 %(ApproxSizeA > 100 -> InversePrioSize = 4
3397 % ; 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
3398 % delay_get_wait_flag(GroundY,GroundX,WF1,InversePrioSize,apply_to_explicit_inverse(X,Y),WF,WF2),
3399 %(ApproxSizeA<4000 -> propagate_apply(X,Y,A,ApproxSizeA,WF,GroundX,GroundY) ; true),
3400 ? apply_check_tuple_delay(X,Y,A,ApproxSizeA,Span,WF,GroundX,WF1,GroundY),
3401 (preference(use_clpfd_solver,false) -> true
3402 % should we also check: preference(find_abort_values,true)?
3403 ; get_wait_flag0(WF,WF0),
3404 propagate_apply(X,Y,A,ApproxSizeA,WF,WF0,GroundX,WF1,GroundY)).
3405
3406 :- block propagate_apply(?,?,?,?,?,-,?,?,?).
3407 propagate_apply(X,Y,AVL,ApproxSizeA,WF,_,GroundX,WF1,GroundY) :-
3408 var(GroundX), var(WF1), var(GroundY),
3409 (preference(disprover_mode,true)
3410 -> XX=X % this will also instantiate X and prevent finding WD errors
3411 ; (ApproxSizeA<128 -> true
3412 ; preference(solver_strength,SS), ApproxSizeA < 128+SS*100), % up until 4000 it may make sense to constrain Y
3413 preference(data_validation_mode,false), % note: this can slow down ProB, e.g., test 1105; hence allow disabling it
3414 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
3415 propagate_value(X,XX) % only instantiate X, propagation only makes sense for propagate_avl_element_information_small, as otherwise only X will be bounded
3416 ),
3417 !,
3418 propagate_avl_element_information_direct((XX,Y),AVL,ApproxSizeA,WF).
3419 propagate_apply(_,_,_,_,_,_,_,_,_).
3420
3421 % only propagate in one direction to allow to find WD errors but also prevent pending co-routines/constraints
3422 :- block propagate_value(-,?).
3423 propagate_value(int(X),R) :- !,
3424 (
3425 %%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
3426 propagate_fd_dom(X,RX), R=int(RX), propagate_atomic_value(X,RX)
3427 ).
3428 propagate_value(fd(X,T),R) :- !,
3429 (
3430 %%integer(X) -> R=fd(X,T) ; % for SWI 8.5.10 and older, see above
3431 propagate_fd_dom(X,RX), R=fd(RX,T), propagate_atomic_value(X,RX)
3432 ).
3433 propagate_value((X1,X2),R) :- !, R=(RX1,RX2), propagate_value(X1,RX1), propagate_value(X2,RX2).
3434 propagate_value(pred_true,R) :- !, if(R=pred_true,true,debug_println(9,function_arg_outside_domain(pred_true))).
3435 propagate_value(pred_false,R) :- !, if(R=pred_false,true,debug_println(9,function_arg_outside_domain(pred_false))).
3436 propagate_value(string(X),R) :- !, R=string(RX),propagate_atomic_value(X,RX).
3437 propagate_value(X,RX) :- equal_object(X,RX). % TO DO: get rid of this: this propagates and prevents finding WD errors
3438 :- block propagate_atomic_value(-,?).
3439 propagate_atomic_value(X,Y) :-
3440 if(X=Y,true,debug_println(9,function_arg_outside_domain(X))).
3441
3442 %propagate_fd_dom(X,RX) :- integer(X),!,RX=X. % relevant for SWI 8.5.10 and older where fd_set fails for integers
3443 propagate_fd_dom(X,RX) :- fd_set(X,Dom),in_set(RX,Dom).
3444
3445
3446 /*
3447 :- block propagate_apply(-,?,?,?,?,-,-).
3448 % call propagate as soon as we know something about the function argument and we do not propgagate completely using GroundX/Y anyway
3449 propagate_apply(X,Y,AVL,Size,WF,GroundX,GroundY) :- print(prop_apply(Size,GroundX,GroundY,X,Y)),nl,
3450 (nonvar(GroundX) -> true ; nonvar(GroundY) -> true
3451 ; propagate_avl_element_information((X,Y),AVL,Size,WF)).
3452
3453 % get the waitflag when first WF set and other two not
3454 :- block delay_get_wait_flag(-,-,-,?,?,?,?).
3455 delay_get_wait_flag(_,WF1,WF2, _,_,_,_) :- (nonvar(WF1);nonvar(WF2)),!. % DO NOTHING
3456 delay_get_wait_flag(_,_,_,Prio,Info,WF,WF2) :- get_wait_flag(Prio,Info,WF,WF2).
3457 */
3458
3459 :- block apply_check_tuple_delay(?,?,?, ?,?,?, -,-,-).
3460 apply_check_tuple_delay(X,Y,AVL,_ApproxSizeA,Span,WF,GroundX,WF1,_) :-
3461 (nonvar(GroundX);nonvar(WF1)),!,
3462 apply_check_tuple(X,Y,AVL,Span,WF).
3463 apply_check_tuple_delay(X,Y,AVL,ApproxSizeA,Span,WF,_GroundX,_WF1,_GroundY) :-
3464 % Y is ground; try to do an inverse function lookup
3465 inverse_apply_ok(Y,X,AVL,ApproxSizeA,Span),
3466 !,
3467 % print(inverse_apply(Y,X,ApproxSizeA,_GroundX)),nl,
3468 inverse_get_possible_values(X,Y,AVL,Res),
3469 Res=avl_set(InvAVL), % if empty set : we fail
3470 (preference(data_validation_mode,true),
3471 avl_approximate_size(InvAVL,10,ApproxSize),
3472 ApproxSize>1
3473 -> A2 is (ApproxSize*15*ApproxSize)//ApproxSizeA, % used to be A2 is ApproxSize*100,
3474 A22 is max(A2,ApproxSize),
3475 (get_inversion_penalty(Span)
3476 -> A23 is A22 * 100 %, add_message(f,'Inversion Penalty: ',Y:A22,Span)
3477 ; A23=A22),
3478 % give lower priority for backwards propagation, upto 15 times if no reduction from backwards propagation
3479 % but also take into account how much we reduce the size by inverting
3480 % relevant for, e.g., Machines_perf_0111/Thales_All/rule_OPS_SDS_3940.mch
3481 % or rule_OPS_SDS_6496 -> 15 instead of 150 improves performance
3482 get_bounded_wait_flag(A23,element_of_avl_inverse_apply_ok(X),WF,WF2),
3483 % does not call propagate_avl_element_information(X,InvAVL,ApproxSize,WF) or avl_to_table
3484 element_of_avl_set_wf3(X,InvAVL,ApproxSize,WF2,WF) % TODO: pass GroundX
3485 %apply_check_tuple_delay(X,Y,AVL,ApproxSizeA,Span,WF,GroundX,WF1,_) % now wait on WF1 or GroundX
3486 ? ; element_of_avl_set_wf(InvAVL,X,WF)
3487 ).
3488 apply_check_tuple_delay(X,Y,AVL,ApproxSizeA,Span,WF,GroundX,WF1,_GroundY) :-
3489 apply_check_tuple_delay(X,Y,AVL,ApproxSizeA,Span,WF,GroundX,WF1,_). % now wait on WF1 or GroundX
3490
3491 % check if the function call was annotated as not suitable for backwards inverse function lookup propagation
3492 get_inversion_penalty(span_predicate(b(_Function,_,Info),_LS,_S)) :- !,
3493 get_inversion_penalty(Info).
3494 get_inversion_penalty(Info) :-
3495 member(prob_annotation('INVERSION_PENALTY'),Info).
3496
3497 inverse_get_possible_values(X,Y,AVL,Res) :-
3498 get_template(X,XX,_),
3499 copy_term(XX,XX_Copy), % avoid that findall instantiates X
3500 % TODO: copy_value_term similar to ground_value to avoid traversing avl_sets; but usually X is not a set
3501 findall(XX_Copy, safe_avl_member_default((XX_Copy,Y),AVL), PossibleValues),
3502 PossibleValues \= [], % fail straightaway
3503 sort(PossibleValues,SPV),
3504 % length(SPV,Len),print(inverse_image(Y,Len)),nl, print_term_summary(apply_check_tuple_delay(X,Y,AVL)),nl,
3505 convert_to_avl(SPV,Res).
3506
3507 % is it ok to compute inverse ? only makes sense if AVL tree not too big and quite functional
3508 inverse_apply_ok(pred_true,_,_AVL,ApproxSizeA,_) :- !, % only two values possible, probably half of AVL will be returned
3509 ApproxSizeA < 1023. % corresponds to avl_height < 10
3510 inverse_apply_ok(pred_false,_,_AVL,ApproxSizeA,_) :- !,ApproxSizeA < 1023.
3511 % TO DO: other small types, such as fd(_,_)
3512 inverse_apply_ok(_,_,_AVL,ApproxSizeA,_) :- ApproxSizeA < 255,!.
3513 inverse_apply_ok(_,X,_AVL,ApproxSizeA,Span) :- ApproxSizeA < 65535, % corresponds Height < 16
3514 (preference(data_validation_mode,true) ->
3515 (preference(solver_strength,SS), ApproxSizeA < 16383+SS -> true
3516 ; perfmessage(inverse,'Function call not inverted (increase SOLVER_STRENGTH to enable this), approximate function size: ',ApproxSizeA,Span),
3517 fail
3518 )
3519 ; true),
3520 quick_non_ground_check(X).
3521 %inverse_apply_ok(_,_,_,_).
3522
3523 % sometimes the ground_value_check co-routine hasn't grounded GroundX yet ! so do a quick check
3524 quick_non_ground_check(X) :- var(X),!.
3525 quick_non_ground_check([]) :- !,fail.
3526 quick_non_ground_check(avl_set(_)) :- !,fail.
3527 quick_non_ground_check(pred_true) :- !,fail.
3528 quick_non_ground_check(pred_false) :- !,fail.
3529 quick_non_ground_check(int(X)) :- !,var(X).
3530 quick_non_ground_check(string(X)) :- !,var(X).
3531 quick_non_ground_check(fd(X,T)) :- !,(var(X) ; var(T)).
3532 quick_non_ground_check((A,B)) :- !, (quick_non_ground_check(A) -> true ; quick_non_ground_check(B)).
3533 quick_non_ground_check(_). % assume it is non ground
3534
3535
3536
3537 % apply_check_tuple is allowed to enumerate: either X is ground or Y is ground
3538 apply_check_tuple(X,Y,A,Span,WF) :-
3539 ground_value(X),
3540 convert_to_avl_inside_set_wf(X,AX,WF),!, % we can do optimized lookup + checking in one go
3541 % (but avl_apply only does partial check)
3542 avl_apply(AX,A,XY,Span,WF),
3543 kernel_objects:equal_object_wf(XY,Y,apply_check_tuple,WF).
3544 :- if(environ(no_wd_checking, true)).
3545 apply_check_tuple(X,Y,A,_Span,WF) :- safe_avl_member_default_wf((X,Y),A,WF).
3546 :- else.
3547 apply_check_tuple(X,Y,A,_Span,WF) :- preferences:preference(find_abort_values,false), !,
3548 safe_flex_avl_member_default_wf((X,Y),A,WF). % will do a ground check again for X in flexible_decompose_index
3549 apply_check_tuple(X,Y,A,Span,WF) :- !,
3550 if(safe_flex_avl_member_default_wf((X,XY),A,WF), % does not detect abort errors if X unbound
3551 kernel_objects:equal_object_wf(XY,Y,apply_check_tuple_avl,WF),
3552 add_wd_error_span('function applied outside of domain (#4): ','@fun'(X,avl_set(A)),Span,WF)).
3553 :- endif.
3554
3555
3556 % ------------------------------------------
3557
3558
3559 :- use_module(b_global_sets,[b_type2_set/2]).
3560 :- use_module(bsyntaxtree,[rename_bt/3]).
3561 union_of_explicit_set(global_set(GS),_,R) :- is_maximal_global_set(GS), !,
3562 R= global_set(GS). /* global_set is already maximal */
3563 union_of_explicit_set(freetype(GS),_,R) :- !, R= freetype(GS). /* freetype is already maximal */
3564 union_of_explicit_set(closure(P,T,B),_,R) :- is_definitely_maximal_closure(P,T,B), !,
3565 R= closure(P,T,B). /* global_set is already maximal */
3566 union_of_explicit_set(_,S2,R) :- is_definitely_maximal_set(S2),!, % will also look at AVL set
3567 R=S2.
3568 union_of_explicit_set(S1,S2,R) :- nonvar(S2), S2 = [], !, R=S1.
3569 union_of_explicit_set(S1,S2,_) :- (var(S1);var(S2)),!,fail. % then we cannot compute it here
3570 union_of_explicit_set(S2,S1,R) :-
3571 is_not_member_value_closure(S1,TYPE,MS1), nonvar(MS1), is_efficient_custom_set(MS1),
3572 % also works if S2 is complement closure
3573 difference_of_explicit_set(MS1,S2,Diff),!,
3574 construct_complement_closure_if_necessary(Diff,TYPE,R).
3575 union_of_explicit_set(avl_set(A1),S2,R) :- !, union_of_avl_set(S2,A1,R).
3576 union_of_explicit_set(S1,S2,R) :-
3577 is_not_member_value_closure(S1,TYPE,MS1), nonvar(MS1), is_efficient_custom_set(MS1),
3578 difference_of_explicit_set(MS1,S2,Diff),!,
3579 construct_complement_closure_if_necessary(Diff,TYPE,R).
3580 union_of_explicit_set(S1,avl_set(A2),R) :- !, union_of_avl_set(S1,A2,R).
3581 union_of_explicit_set(I1,I2,R) :- is_interval_closure_or_integerset(I1,From1,To1), ground(From1), ground(To1),
3582 is_interval_closure_or_integerset(I2,From2,To2), ground(From2), ground(To2),
3583 !,
3584 (union_of_interval(From1,To1,From2,To2,FromRes,ToRes)
3585 -> construct_interval_closure(FromRes,ToRes,R)
3586 ; small_enough_for_expansion(From1,To1),small_enough_for_expansion(From2,To2) ->
3587 % do not attempt union_of_closure below
3588 expand_interval_closure_to_avl(From1,To1,R1), R1=avl_set(A1), % empty interval already dealt with above !?
3589 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(_))
3590 union_of_avl(A1,A2,ARes),R=avl_set(ARes) /* AVL not normalised */
3591 ; transform_global_sets_into_closure(I1,closure(Par,T,Body)),
3592 union_of_closure(I2,Par,T,Body,R)
3593 ).
3594 union_of_explicit_set(closure(P,T,B),C2,Res) :-
3595 union_of_closure(C2,P,T,B,Res).
3596
3597 small_enough_for_expansion(From1,To1) :- number(To1), number(From1), To1-From1<250.
3598
3599 :- use_module(bsyntaxtree,[extract_info/2, extract_info_wo_used_ids/2, extract_info/3, rename_bt/3, replace_id_by_expr/4]).
3600
3601 union_of_closure(global_set(X),P,T,B,Res) :- !, transform_global_sets_into_closure(global_set(X),C),
3602 union_of_closure(C,P,T,B,Res).
3603 union_of_closure(closure(P2,T2,B2),P,T,B,Res) :- !,
3604 % T2 should be equal to T, module seq(_) <-> set(couple(integer,_))
3605 unify_closure_predicates(P,T,B, P2,T2,B2 , NewP,NewT, NewB1,NewB2),
3606 debug:debug_println(9,union_of_two_closures(P,P2,NewP,NewT)),
3607 extract_info(B,B2,NewInfo),
3608 construct_disjunct(NewB1,NewB2,Disj),
3609 Res = closure(NewP,NewT,b(Disj,pred,NewInfo)).
3610
3611 % rename predicates of two closures so that they work on common closure parameter ids
3612 % and can then be either joined by conjunction or disjunction
3613 unify_closure_predicates(P,T,B, P2,T2,B2 , NewP,NewT, NewB1,NewB2) :-
3614 length(P,Len1), length(P2,Len2),
3615 (Len1=Len2
3616 -> generate_renaming_list(P,P2,RL),
3617 rename_bt(B2,RL,NewB2),
3618 NewP=P, NewT=T, NewB1 = B
3619 ; Len1 < Len2 -> unify_clos_lt(P,T,B, P2,T2,B2 , NewP,NewT, NewB1,NewB2)
3620 ; unify_clos_lt(P2,T2,B2, P,T,B , NewP,NewT, NewB2,NewB1) % inverted the predicate
3621 ).
3622
3623 % TO DO: generalize: currently only works for single identifier on left
3624 % but works for id(NATURAL) \/ %x.(x<0|-x) or abs = id(NATURAL) \/ %x.(x<0|-x) & abs(2)=a2 & abs(-2)=am2
3625 unify_clos_lt([ID1],[couple(_,_)],B, P2,T2,B2 , NewP,NewT, NewB1,NewB2) :-
3626 rename_lambda_result_id(P2,B2,P3,B3),
3627 create_couple_term(P3,T2,Pair),
3628 replace_id_by_expr(B,ID1,Pair,NewB1),
3629 NewP=P3, NewT=T2, NewB2=B3.
3630
3631 % _lambda_result_ id is not enumerated, hence we have to avoid inserting such ids into NewB1 as part of the pPair
3632 rename_lambda_result_id(['_lambda_result_',ID2],B2,[FRESHID,ID2],B3) :- !,get_unique_id('_RANGE_',FRESHID),
3633 rename_bt(B2,[rename('_lambda_result_',FRESHID)],B3).
3634 rename_lambda_result_id([ID1,'_lambda_result_'],B2,[ID1,FRESHID],B3) :- !,get_unique_id('_RANGE_',FRESHID),
3635 rename_bt(B2,[rename('_lambda_result_',FRESHID)],B3).
3636 rename_lambda_result_id(P2,B2,P2,B2).
3637
3638 % translate a list of atomic ids and a list of types into a couple-term
3639 create_couple_term([ID1],[T1],Res) :- !,
3640 create_texpr(identifier(ID1),T1,[],Res).
3641 create_couple_term([ID1,ID2],[T1,T2],Res) :-
3642 bsyntaxtree:create_couple(b(identifier(ID1),T1,[]),b(identifier(ID2),T2,[]),Res).
3643 % TODO: extend for more than two args
3644
3645 generate_renaming_list([],[],[]).
3646 generate_renaming_list([ID|T],[ID2|T2],RL) :-
3647 (ID==ID2 -> generate_renaming_list(T,T2,RL)
3648 ; RL = [rename(ID2,ID)|RL2],
3649 generate_renaming_list(T,T2,RL2)).
3650
3651
3652 % a more clever way of constructing a disjunct; factor out common prefixes
3653 % (A & B1) or (A1 & B2) <=> A1 & (B1 or B2)
3654 % TO DO: we should try and get the leftmost basic conjunct !
3655 /* construct_disjunct(b(conjunct(A1,A2),pred,IA), b(conjunct(B1,B2),pred,_IB), Res) :-
3656
3657 print('TRY DISJUNCT FACTOR: '), translate:print_bexpr(A1),nl,
3658 translate:print_bexpr(B1),nl,
3659 same_texpr_body(A1,B1),!,
3660 print('DISJUNCT FACTOR: '), translate:print_bexpr(A1),nl,
3661 Res = conjunct(A1,b(Disj,pred,IA)),
3662 construct_disjunct(A2,B2,Disj).
3663 */
3664 construct_disjunct(A,B,disjunct(A,B)).
3665
3666 % TO DO: quick_check if AVL A1 is maximal ?
3667 union_of_avl_set(avl_set(A2),A1,R) :- !, union_of_avl(A1,A2,ARes), R=avl_set(ARes). /* AVL not normalised */
3668 union_of_avl_set(I2,A1,R) :- is_interval_closure_or_integerset(I2,From2,To2), !,
3669 ground(From2), ground(To2), % we can only compute it if bounds known
3670 (avl_min(A1,int(Min)), low_border(From2,Min,FromRes), avl_max(A1,int(Max)), up_border(To2,Max,ToRes)
3671 -> /* AVL contained (almost) in Interval */
3672 construct_interval_closure(FromRes,ToRes,R)
3673 ; \+ small_interval(From2,To2) ->
3674 transform_global_sets_into_closure(I2,closure(Par,T,Body)), % we may have something like NATURAL1,...
3675 union_of_avl_set_with_closure(Par,T,Body,A1,R)
3676 ; expand_and_convert_to_avl_set(I2,A2,union_of_avl_set,'? \\/ ARG'), % can generate ARel=empty; will fail if not possible to convert
3677 union_of_avl(A1,A2,ARes), R=avl_set(ARes)
3678 ).
3679 union_of_avl_set(closure(Par,T,Body),A1,Res) :- is_infinite_or_symbolic_closure(Par,T,Body),!,
3680 % 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)
3681 union_of_avl_set_with_closure(Par,T,Body,A1,Res).
3682 union_of_avl_set(S2,A1,Res) :-
3683 S2 \= freetype(_),
3684 ground_value(S2), % could be a closure
3685 !,
3686 (try_expand_and_convert_to_avl_set(S2,A2,union)
3687 -> union_of_avl(A1,A2,ARes), Res=avl_set(ARes) /* AVL not normalised */
3688 ; S2=closure(Par,T,Body),
3689 union_of_avl_set_with_closure(Par,T,Body,A1,Res)).
3690
3691 try_expand_and_convert_to_avl_set(S2,A2,Source) :-
3692 % false: do not add enumeration warning events as errors
3693 catch_enumeration_warning_exceptions(expand_and_convert_to_avl_set(S2,A2,Source,''),fail,false,ignore(Source)).
3694
3695 % try expanding to list, but catch enumeration warnings and fail if they do occur
3696 % used by override(...)
3697 %try_expand_custom_set_to_list(CS,_,_,_) :- nonvar(CS),CS=global_set(GS),is_infinite_global_set(GS,_),
3698 % !,
3699 % fail.
3700 try_expand_custom_set_to_list(CS,_,_,_) :- nonvar(CS),
3701 (is_symbolic_closure(CS) ; is_infinite_explicit_set(CS)),
3702 !, % we could also check is_symbolic_closure
3703 fail.
3704 try_expand_custom_set_to_list(CS,List,Done,Source) :-
3705 % false: do not add enumeration warning events as errors
3706 catch_enumeration_warning_exceptions(expand_custom_set_to_list(CS,List,Done,Source),fail,false,ignore(Source)).
3707
3708
3709 small_interval(From,To) :- number(From), number(To), To-From < 10000.
3710
3711 union_of_avl_set_with_closure(Par,T,Body,A1,Res) :-
3712 Body = b(_,BodyT,_),
3713 setup_typed_ids(Par,T,TypedPar),
3714 couplise_list(TypedPar,TypedCPar),
3715 generate_couple_types(TypedCPar,ParExpr,ParType),
3716 debug:debug_println(9,union_of_avl_and_infinite_closure(Par,T,BodyT)),
3717 BodyAvl = b(member(ParExpr,b(value(avl_set(A1)),set(ParType),[])),pred,[]),
3718 extract_info_wo_used_ids(Body,NewInfo),
3719 Res = closure(Par,T,b(disjunct(BodyAvl,Body),pred,NewInfo)).
3720 % mark_closure_as_symbolic(closure(Par,T,b(disjunct(BodyAvl,Body),pred,NewInfo)),Res).
3721
3722 low_border(Low,AVLMin,R) :- geq_inf(AVLMin,Low),!,R=Low.
3723 low_border(Low,AVLMin,R) :- number(Low),AVLMin is Low-1,R=AVLMin. % extend lower border by one
3724 up_border(Up,AVLMax,R) :- geq_inf(Up,AVLMax),!,R=Up.
3725 up_border(Up,AVLMax,R) :- number(Up),AVLMax is Up+1,R=AVLMax. % extend upper border by one
3726
3727
3728 setup_typed_ids([],[],[]).
3729 setup_typed_ids([ID|TI],[Type|TT],[b(identifier(ID),Type,[])|BT]) :- setup_typed_ids(TI,TT,BT).
3730
3731 generate_couple_types(couple(A,B),b(couple(TA,TB),Type,[]),Type) :- !, Type = couple(TTA,TTB),
3732 generate_couple_types(A,TA,TTA),
3733 generate_couple_types(B,TB,TTB).
3734 generate_couple_types(b(X,T,I),b(X,T,I),T).
3735
3736
3737 % try to see if two intervals can be unioned into a new interval
3738 union_of_interval(F1,T1,F2,T2,FR,TR) :-
3739 geq_inf(F2,F1), geq_inf(T1,T2),!,FR=F1,TR=T1. % interval [F2,T2] contained in [F1,T1]
3740 union_of_interval(F2,T2,F1,T1,FR,TR) :- geq_inf(F2,F1), geq_inf(T1,T2),!,FR=F1,TR=T1. % see above
3741 union_of_interval(F1,T1,F2,T2,FR,TR) :- number(F2),
3742 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
3743 union_of_interval(F2,T2,F1,T1,FR,TR) :- number(F2),
3744 geq_inf(F2,F1), number(T1),T11 is T1+1,geq_inf(T11,F2), geq_inf(T2,F2),!,FR=F1,TR=T2. % see above
3745
3746 :- use_module(library(ordsets),[ord_union/3]).
3747 union_of_avl(A1,A2,ARes) :-
3748 avl_height(A2,Sz2),
3749 (Sz2 < 2 % we have something like Set := Set \/ {x}; no need to compute height of A1
3750 -> union_of_avl1(A1,99999,A2,Sz2,ARes)
3751 ; avl_height(A1,Sz1), % TODO: we could call avl_height_less_than or avl_height_compare
3752 (Sz1<Sz2 -> union_of_avl1(A2,Sz2,A1,Sz1,ARes) ; union_of_avl1(A1,Sz1,A2,Sz2,ARes))
3753 ).
3754 union_of_avl1(A1,Sz1,A2,Sz2,ARes) :- Sz2>2, Sz1 =< Sz2+3, % difference not too big; Sz2 at least a certain size
3755 !,
3756 avl_to_list(A2,List2), % get all members
3757 avl_to_list(A1,List1),
3758 ord_union(List1,List2,L12),
3759 ord_list_to_avl(L12,ARes).
3760 union_of_avl1(A1,_Sz1,A2,_Sz2,ARes) :- % this version is better when A2 is small compared to A1
3761 avl_domain(A2,List2), % get all members
3762 add_to_avl(List2,A1,ARes).
3763
3764 :- use_module(library(lists),[reverse/2]).
3765 % a custom version for union(A) where A is AVL set; avoid converting/expanding accumulators and computing avl_height
3766 % 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
3767 union_generalized_explicit_set(avl_set(SetsOfSets),Res,WF) :-
3768 expand_custom_set_to_list_wf(avl_set(SetsOfSets),ESetsOfSets,_,union_generalized_wf,WF),
3769 % length(ESetsOfSets,Len),print(union_gen(Len)),nl,
3770 (ESetsOfSets=[OneSet]
3771 -> Res=OneSet % avoid converting to list and back to Avl
3772 ; 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
3773 % note: dom({r,x|x:1..50000 & r:{x*x}}) is still 3 times faster
3774 union_of_avls(RESetsOfSets,[],Res)).
3775
3776 % take the union of a list of avl_sets
3777 union_of_avls([],Acc,Res) :- ord_list_to_avl(Acc,ARes), construct_avl_set(ARes,Res).
3778 union_of_avls([H|T],Acc,Res) :-
3779 union_of_avl_with_acc(H,Acc,NewAcc),
3780 union_of_avls(T,NewAcc,Res).
3781
3782 union_of_avl_with_acc(avl_set(H),Acc,NewAcc) :- !,
3783 avl_to_list(H,HList),
3784 ord_union(Acc,HList,NewAcc).
3785 union_of_avl_with_acc([],Acc,Res) :- !,Res=Acc.
3786 % other custom sets should normally not appear, we obtain the list as elements stored in an avl_set
3787 union_of_avl_with_acc(G,_,_) :- add_internal_error('Uncovered element: ',union_of_avl_with_acc(G,_,_)),fail.
3788
3789
3790
3791 % TO DO: there are no rules for is_not_member_value_closure for intersection below
3792 intersection_of_explicit_set_wf(global_set(GS),S2,R,_WF) :- is_maximal_global_set(GS), !, R=S2.
3793 intersection_of_explicit_set_wf(freetype(_GS),S2,R,_WF) :- !, R=S2.
3794 intersection_of_explicit_set_wf(_,S2,_,_WF) :- var(S2),!,fail. % code below may instantiate S2
3795 intersection_of_explicit_set_wf(S1,S2,R,_WF) :- is_definitely_maximal_set(S2), !, R=S1.
3796 intersection_of_explicit_set_wf(_S1,[],R,_WF) :-!, R=[].
3797 intersection_of_explicit_set_wf(avl_set(A1),I2,R,_WF) :-
3798 is_interval_closure_or_integerset(I2,From1,To1),
3799 !,
3800 intersect_avl_interval(A1,From1,To1,R).
3801 intersection_of_explicit_set_wf(I1,I2,R,_WF) :-
3802 ? intersection_with_interval_closure(I1,I2,R),!.
3803 intersection_of_explicit_set_wf(S1,S2,R,_WF) :-
3804 get_avl_sets(S1,S2,A1,A2),
3805 !, % if too large: better to apply normal intersection code ?
3806 % if one of the args is an interval this is already caught in kernel_objects calling intersection_with_interval_closure; see SetIntersectionBig.mch
3807 avl_domain(A1,ES), % A1 has the smaller height; important for e.g. SetIntersectionBig2.mch
3808 inter2(ES,A2,IRes),
3809 ord_list_to_avlset(IRes,R,intersection). % we have generated the elements in the right order already
3810 intersection_of_explicit_set_wf(Set1,Set2,R,WF) :-
3811 transform_global_sets_into_closure(Set1,closure(P1,T1,B1)),
3812 transform_global_sets_into_closure(Set2,closure(P2,T2,B2)),
3813 % gets called, e.g., for {x|x /: NATURAL1} /\ NATURAL1
3814 unify_closure_predicates(P1,T1,B1, P2,T2,B2 , NewP,NewT, NewB1,NewB2),
3815 debug:debug_println(9,intersection_of_two_closures(P1,P2,NewP,NewT)),
3816 conjunct_predicates([NewB1,NewB2],BI),
3817 % create a conjunction: can be much more efficient than seperately expanding;
3818 % also works well if one of the closures is infinite
3819 C = closure(NewP,NewT,BI),
3820 expand_custom_set_wf(C,R,intersection_of_explicit_set_wf,WF). % we could keep it symbolic; maybe use SYMBOLIC pref
3821 % to do: also use above for closure and AVL set with member(P,value(avl_set(A)))
3822 % we could also apply the same principle to difference_of_explicit_set
3823 % currently we enable intersection to be treated symbolically (not_symbolic_binary(intersection) commented out)
3824 % This means the above clause for intersection_of_explicit_set_wf is less useful
3825 % a special case; just for interval closures
3826 intersection_with_interval_closure(I1,I2,R) :-
3827 is_interval_closure_or_integerset(I1,From1,To1), nonvar(I2),
3828 intersection_with_interval_closure_aux(I2,From1,To1,R).
3829 intersection_with_interval_closure(avl_set(A1),I2,R) :-
3830 is_interval_closure_or_integerset(I2,From1,To1),
3831 !,
3832 intersect_avl_interval(A1,From1,To1,R).
3833
3834 % try and get AVL sets from two args; first AVL set is smaller one according to height
3835 get_avl_sets(avl_set(A1),S2,AA1,AA2) :- nonvar(S2), S2=avl_set(A2),
3836 ? (avl_height_compare(A1,A2,R), R=lt
3837 -> (AA1,AA2)=(A1,A2)
3838 ; (AA1,AA2)=(A2,A1)).
3839 %get_avl_sets(S1,S2,AA1,AA2) :- nonvar(S2),S2=avl_set(A2), get_avl_set_arg(S1,A1),
3840 % (avl_height_compare(A1,A2,R),R=gt -> (AA1,AA2)=(A2,A1) ; (AA1,AA2)=(A1,A2)).
3841
3842
3843 %intersection_with_interval_closure_aux(avl_set(A),...
3844 intersection_with_interval_closure_aux(I2,From1,To1,R) :-
3845 is_interval_closure_or_integerset(I2,From2,To2),!,
3846 intersect_intervals_with_inf(From1,To1,From2,To2,FromRes,ToRes),
3847 construct_interval_closure(FromRes,ToRes,R).
3848 % (is_interval_closure_or_integerset(R,F,T) -> print(ok(F,T)),nl ; print(ko),nl).
3849 intersection_with_interval_closure_aux(avl_set(A2),From1,To1,R) :-
3850 intersect_avl_interval(A2,From1,To1,R).
3851
3852 % intersect avl with interval
3853 % TO DO: expand interval if small (or small intersection with AVL) and use avl intersection
3854 intersect_avl_interval(_,From2,To2,_) :- (var(From2) ; var(To2)),!,fail.
3855 intersect_avl_interval(A1,From2,To2,R) :- avl_min(A1,int(Min)),
3856 geq_inf(Min,From2),
3857 geq_inf(To2,Min), avl_max(A1,int(Max)),
3858 geq_inf(To2,Max),
3859 % AVL fully contained in interval; no need to expand to list and back again
3860 !,
3861 construct_avl_set(A1,R).
3862 intersect_avl_interval(A1,From2,To2,R) :-
3863 avl_domain(A1,ES),
3864 inter_interval(ES,From2,To2,IRes),
3865 ord_list_to_avlset(IRes,R,intersect_avl_interval).
3866
3867 inter_interval([],_,_, []).
3868 inter_interval([IH|T],From2,To2, Res) :- IH = int(H),
3869 (geq_inf(To2,H) ->
3870 (geq_inf(H,From2) -> Res = [IH-true|Res2] ; Res = Res2),
3871 inter_interval(T,From2,To2,Res2)
3872 ; Res = [] % we have exceeded the upper limit of the interval
3873 ).
3874
3875 % also works with real/float intervals:
3876 intersect_intervals_with_inf(From1,To1,From2,To2,FromRes,ToRes) :-
3877 minimum_with_inf(To1,To2,ToRes),
3878 maximum_with_inf(From1,From2,FromRes).
3879
3880 % check if two intervals are disjoint
3881 disjoint_intervals_with_inf(From1,To1,From2,To2) :-
3882 intersect_intervals_with_inf(From1,To1,From2,To2,Low,Up),
3883 number(Up), number(Low), Low > Up.
3884
3885 inter2([],_, []).
3886 inter2([H|T],A1, Res) :-
3887 (avl_fetch(H,A1) -> Res = [H-true|Res2] ; Res = Res2), inter2(T,A1,Res2).
3888
3889 ord_list_to_avlset(OL,R) :- ord_list_to_avlset(OL,R,unknown).
3890 ord_list_to_avlset(OrdList,Res,Origin) :-
3891 % assumes that we have generated the elements in the right order already
3892 (OrdList=[] -> Res=[]
3893 ; check_sorted(OrdList,Origin),
3894 ord_list_to_avl(OrdList,ARes), Res=avl_set(ARes)).
3895
3896 % a version which accepts a list of values without -true
3897 % values have to be ground and already converted for use in avl_set
3898 sorted_ground_normalised_list_to_avlset(List,Res,PP) :-
3899 add_true_to_list(List,LT),
3900 ord_list_to_avlset_direct(LT,Res,PP).
3901
3902 add_true_to_list([],[]).
3903 add_true_to_list([H|T],[H-true|TT]) :- add_true_to_list(T,TT).
3904
3905 % the same, but without checking sorted (only use if you are really sure the list is sorted)
3906 ord_list_to_avlset_direct([],[],_).
3907 ord_list_to_avlset_direct([H|T],Res,_):-
3908 (T==[] -> H=Key-Val, Res = avl_set(node(Key,Val,0,empty,empty)) % slightly faster than calling ord_list_to_avl
3909 ; ord_list_to_avl([H|T],ARes), Res = avl_set(ARes)).
3910
3911 check_sorted([],_) :- !.
3912 check_sorted([H-_|T],Origin) :- !, check_sorted2(T,H,Origin).
3913 check_sorted(X,Origin) :- add_error_and_fail(ord_list_to_avlset,'Not a list of -/2 pairs: ',Origin:X).
3914
3915 check_sorted2([],_,_) :- !.
3916 check_sorted2([H-_|T],PH,Origin) :- PH @< H,!, check_sorted2(T,H,Origin).
3917 check_sorted2(X,Prev,Origin) :-
3918 add_error_and_fail(ord_list_to_avlset,'Not a sorted list of -/2 pairs: ',Origin:(X,Prev)).
3919
3920 % ------------------
3921
3922 :- use_module(kernel_freetypes,[is_maximal_freetype/1]).
3923 is_definitely_maximal_set(S) :- nonvar(S),
3924 is_definitely_maximal_set2(S).
3925 is_definitely_maximal_set2(freetype(ID)) :- is_maximal_freetype(ID).
3926 is_definitely_maximal_set2(global_set(GS)) :- is_maximal_global_set(GS).
3927 is_definitely_maximal_set2(closure(P,T,B)) :- is_definitely_maximal_closure(P,T,B).
3928 is_definitely_maximal_set2(avl_set(S)) :- quick_definitely_maximal_set_avl(S).
3929 is_definitely_maximal_set2([H|T]) :- nonvar(H), is_definitely_maximal_list(H,T). %, nl,print(maximal(H,T)),nl,nl.
3930 %H==pred_true, T == [pred_false]. % for some reason BOOL is sometimes presented this way
3931 is_definitely_maximal_set2(empty) :- % detect unwrapped AVL sets
3932 add_internal_error('Not a set: ',is_definitely_maximal_set2(empty)),fail.
3933 is_definitely_maximal_set2(node(A,B,C,D,E)) :-
3934 add_internal_error('Not a set: ',is_definitely_maximal_set2(node(A,B,C,D,E))),fail.
3935
3936 is_definitely_maximal_list(pred_true,T) :- nonvar(T), T=[_|_]. %
3937 is_definitely_maximal_list(pred_false,T) :- nonvar(T), T=[_|_].%
3938 is_definitely_maximal_list(fd(_,Type),T) :- nonvar(T),b_global_set_cardinality(Type,Card),
3939 % check if we have the same number of elements as the type: then the set must me maximal
3940 length_at_least(T,Card).
3941 % We could try and and also treat pairs
3942
3943 length_at_least(1,_) :- !. % we have already removed 1 element; T can be nil
3944 length_at_least(N,T) :- nonvar(T), T=[_|TT], N1 is N-1, length_at_least(N1,TT).
3945
3946 is_definitely_maximal_closure(_,_,b(truth,_Pred,_)) :- !.
3947 is_definitely_maximal_closure(P,T,B) :- is_cartesian_product_closure_aux(P,T,B,S1,S2),!,
3948 is_definitely_maximal_set(S1),is_definitely_maximal_set(S2).
3949 is_definitely_maximal_closure(P,T,B) :-
3950 is_full_powerset_or_relations_or_struct_closure(closure(P,T,B),Sets),
3951 l_is_definitely_maximal_set(Sets).
3952
3953 l_is_definitely_maximal_set([]).
3954 l_is_definitely_maximal_set([H|T]) :- is_definitely_maximal_set(H), l_is_definitely_maximal_set(T).
3955
3956 % check if we have an AVL tree covering all elements of the underlying type
3957 quick_definitely_maximal_set_avl(AVL) :-
3958 AVL=node(El,_True,_,_Left,_Right),
3959 quick_definitely_maximal_set_avl_aux(El,AVL).
3960 quick_definitely_maximal_set_avl_aux(El,AVL) :-
3961 try_get_finite_max_card_from_ground_value(El,Card),
3962 % this could fail if El contains empty sets !
3963 % also: it must fail if Card is infinite (no avl_set can be maximal)
3964 (Card < 1000 -> true
3965 ; preferences:preference(solver_strength,SS), Card < 1000+SS*100
3966 ), % otherwise too expensive a check avl_size
3967 quick_avl_approximate_size(AVL,MaxSize),
3968 MaxSize >= Card, % otherwise no sense in computing avl_size, which is linear in size of AVL
3969 avl_size(AVL,Size),
3970 %(MaxSize>=Size -> print(ok(Size,all(Card))),nl ; print('**** ERROR: '), print(Size),nl,trace),
3971 Size=Card.
3972
3973 % check if we have an AVL function with domain covering all elements of the underlying type
3974 quick_definitely_maximal_total_function_avl(AVL) :-
3975 AVL=node(El,_True,_,_Left,_Right),
3976 El=(DomEl,_),
3977 quick_definitely_maximal_set_avl_aux(DomEl,AVL), % the size is exactly the size of the domain
3978 is_avl_partial_function(AVL).
3979
3980 % ----------------------
3981 % set_subtraction /
3982 difference_of_explicit_set(S1,S2,R) :-
3983 difference_of_explicit_set_wf(S1,S2,R,no_wf_available).
3984 % this is called with first argument nonvar (for set_subtraction operator):
3985 difference_of_explicit_set_wf(_S1,S2,R,_) :-
3986 is_definitely_maximal_set(S2), !, R=[].
3987 difference_of_explicit_set_wf(S1,S2,R,_) :- nonvar(S2), S2=[],!, R=S1.
3988 difference_of_explicit_set_wf(S1,S2,R,_) :-
3989 %nonvar(S1),
3990 is_very_large_maximal_global_set(S1,Type), !, % TO DO: also for freetype ? cartesian products,...
3991 /* we have a complement-set */
3992 complement_set(S2,Type,R).
3993 difference_of_explicit_set_wf(S1,S2,Result,_) :-
3994 is_not_member_value_closure(S1,Type,MS1),
3995 nonvar(MS1), is_custom_explicit_set(MS1,difference_of_explicit_set_wf),!,
3996 union_complement_set(MS1,S2,Type,Result).
3997 difference_of_explicit_set_wf(_,S2,_,_) :- var(S2), !, fail. % then we cannot do anything below
3998 difference_of_explicit_set_wf(S1,S2,R,WF) :-
3999 is_not_member_value_closure(S2,_Type,MS2), nonvar(MS2),
4000 intersection_of_explicit_set_wf(MS2,S1,R,WF),!.
4001 difference_of_explicit_set_wf(I1,I2,R,_) :-
4002 is_interval_closure_or_integerset(I1,From1,To1),
4003 is_interval_closure_or_integerset(I2,From2,To2),
4004 difference_interval(From1,To1,From2,To2,FromRes,ToRes),
4005 % TO DO: also treat case when difference yields two disjoint intervals
4006 % 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}
4007 !,
4008 construct_interval_closure(FromRes,ToRes,R).
4009 difference_of_explicit_set_wf(avl_set(A1),S2,R,WF) :-
4010 (S2=avl_set(A2) ;
4011 ground_value(S2), expand_and_convert_to_avl_set_unless_very_large(S2,A2,WF)),!,
4012 avl_height(A2,H2),
4013 %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,
4014 avl_height(A1,H1),
4015 ((H2<2 -> true ; H1 > H2+1) % then it is more efficient to expand A2 and remove the A2 elements from A1;
4016 % note that difference_of_explicit_set2 now also sometimes expands both:
4017 % exact threshold when it is beneficial: difference_of_explicit_set2/3
4018 % 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)
4019 % {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))
4020 % {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))
4021 -> expand_custom_set_to_sorted_list(S2,ES,_,difference_of_explicit_set1,WF),
4022 difference_of_explicit_set3(ES,A1,R)
4023 ; expand_custom_set_to_sorted_list(avl_set(A1),ES,Done,difference_of_explicit_set2,WF),
4024 difference_of_explicit_set2(ES,H1,A2,H2,R,Done)).
4025 difference_of_explicit_set_wf(S1,S2,R,WF) :-
4026 (S2=avl_set(A2) ;
4027 ground_value(S2), expand_and_convert_to_avl_set_unless_very_large(S2,A2,WF)),!,
4028 avl_height(A2,A2Height),
4029 difference_with_avl(S1,A2,A2Height,R,WF).
4030 % to do: we could detect same_texpr_body for two closures and return R=[]
4031
4032 :- use_module(avl_tools,[avl_approximate_size_from_height/2]).
4033 :- use_module(bsyntaxtree,[safe_create_texpr/4, create_texpr/4, conjunct_predicates/2, mark_bexpr_as_symbolic/2]).
4034 difference_with_avl(S1,A2,A2Height,R,_) :-
4035 is_closure_or_integer_set(S1,[ID],[T],B),
4036 % check if the first argument is infinite; then do the difference set symbolically
4037 % this could supersed the complement set construction and be generalised to other sets apart from avl_sets as A2
4038 avl_approximate_size_from_height(A2Height,A2Size),
4039 Limit is max(A2Size*10,1000000), % if A2 is more than 10% size of S1, probably better to compute difference explicitly
4040 is_very_large_or_symbolic_closure([ID],[T],B,Limit),
4041 !, % TO DO: also allow multiple identifiers
4042 create_texpr(identifier(ID),T,[],TID),
4043 create_texpr(value(avl_set(A2)),set(T),[],A2Value),
4044 create_texpr(not_member(TID,A2Value),pred,[],NotMemA2),
4045 conjunct_predicates([B,NotMemA2],NewBody),
4046 mark_bexpr_as_symbolic(NewBody,NewBodyS),
4047 R = closure([ID],[T],NewBodyS).
4048 difference_with_avl(S1,A2,A2Height,R,WF) :-
4049 (nonvar(S1),S1=avl_set(A1) -> avl_height(A1,H1) ; H1=unknown),
4050 expand_custom_set_to_sorted_list(S1,ES,Done,difference_of_explicit_set3,WF),
4051 difference_of_explicit_set2(ES,H1,A2,A2Height,R,Done).
4052
4053
4054 % construct complement of a set
4055 union_complement_set(S1,S2,Type,Result) :-
4056 ground_value_check(S2,G2),
4057 when(nonvar(G2),union_complement_set2(S1,S2,Type,Result)).
4058 union_complement_set2(S1,S2,Type,Result) :-
4059 union_of_explicit_set(S1,S2,S12),
4060 construct_complement_closure_if_necessary(S12,Type,R),
4061 kernel_objects:equal_object(R,Result,union_complement_set2).
4062
4063 % construct complement of a set
4064 complement_set(S2,Type,Result) :-
4065 ground_value_check(S2,G2),
4066 when(nonvar(G2),complement_set2(S2,Type,Result)).
4067 complement_set2(S2,Type,Result) :-
4068 is_not_member_value_closure(S2,Type,MS2),!, % complement of complement
4069 kernel_objects:equal_object(MS2,Result,complement_set2).
4070 complement_set2(S2,Type,Result) :-
4071 try_expand_and_convert_to_avl_with_check(S2,ExpandedS2,difference_complement_set),
4072 construct_complement_closure_if_necessary(ExpandedS2,Type,R),
4073 kernel_objects:equal_object(R,Result,complement_set2).
4074
4075 :- block construct_complement_closure_if_necessary(-,?,?).
4076 construct_complement_closure_if_necessary(Set,TYPE,R) :-
4077 (Set=[] -> b_type2_set(TYPE,R)
4078 ; is_not_member_value_closure(Set,TYPE,MS) -> R=MS % complement of complement
4079 ; construct_complement_closure(Set,TYPE,R)).
4080
4081 % succeeds if difference of two intervals is also an interval
4082 % SourceLow..SourceUp \ DiffLow..DiffUp
4083 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,9,11,1,8)).
4084 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,9,inf,1,8)).
4085 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,10,12,1,9)).
4086 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,11,12,1,10)).
4087 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,12,13,1,10)).
4088 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,11,inf,1,10)).
4089 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,inf,11,inf,1,10)).
4090 % :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,9,8,1,10)). % 9..8 empty not detected
4091 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,1,8,9,10)).
4092 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,1,10,11,10)). % empty
4093 :- assert_must_succeed(custom_explicit_sets:difference_interval(1,10,1,inf,inf,10)).
4094 :- assert_must_succeed(custom_explicit_sets:difference_interval(3,10,1,2,3,10)).
4095 :- assert_must_succeed(custom_explicit_sets:difference_interval(3,inf,1,2,3,inf)).
4096 :- assert_must_succeed(custom_explicit_sets:difference_interval(3,10,1,3,4,10)).
4097 :- assert_must_succeed(custom_explicit_sets:difference_interval(3,10,1,9,10,10)).
4098 :- assert_must_succeed(custom_explicit_sets:difference_interval(3,10,1,10,11,10)).
4099 difference_interval(SourceLow,SourceUp,DiffLow,DiffUp,ResLow,ResUp) :-
4100 (nonvar(SourceLow),nonvar(DiffLow),nonvar(DiffUp),
4101 geq_inf(SourceLow,DiffLow)
4102 -> % DiffLow is to left of SourceLow
4103 inc(DiffUp,D1),
4104 maximum_with_inf(D1,SourceLow,ResLow),
4105 ResUp=SourceUp % also works if SourceUp is a variable
4106 ; nonvar(DiffUp),nonvar(SourceUp),nonvar(DiffLow),
4107 geq_inf(DiffUp,SourceUp)
4108 -> % DiffUp is to right of SourceUp
4109 ResLow=SourceLow, % also works if SourceLow is a variable
4110 dec(DiffLow,D1),
4111 minimum_with_inf(SourceUp,D1,ResUp)).
4112
4113 inc(N,R) :- N==inf,!,R=inf.
4114 inc(N,N1) :- N1 is N+1.
4115 dec(N,R) :- N==inf,!,R=inf.
4116 dec(N,N1) :- N1 is N-1.
4117
4118 :- use_module(library(ordsets), [ord_subtract/3]).
4119 :- block difference_of_explicit_set2(?,?,?,?,?,-).
4120 difference_of_explicit_set2(ES,A1Height,A2,A2Height,R,_) :-
4121 (number(A1Height), A1Height+4 >= A2Height -> true
4122 ; A2Height < 5
4123 ; Limit is 2**(A2Height-4),
4124 length_larger_than(ES,Limit)
4125 % TO DO: we could try and pass sizes from specific closures to this predicate
4126 ),
4127 % A1 is not much larger than A2, then it is probably faster to use ord_subtract on expanded A2
4128 % {x|x mod 2 =0 & x:1..10000} - {y|y mod 3 =0 & y : 1..200000} : still more efficient with ord_subtract
4129 !,
4130 avl_domain(A2,A2Expanded),
4131 ord_subtract(ES,A2Expanded,OrdRes),
4132 sorted_ground_normalised_list_to_avlset(OrdRes,AVL,difference_of_explicit_set2),
4133 equal_object(AVL,R).
4134 difference_of_explicit_set2(ES,_A1Height,A2,_A2Height,R,_) :-
4135 avl_min(A2,Min),
4136 diff1(ES,Min,A2,IRes),
4137 ord_list_to_avlset(IRes,AVL,difference), % we have generated the elements in the right order already
4138 equal_object(AVL,R). % due to delays in expansion the result could be instantiated
4139
4140
4141 length_larger_than([_|T],Limit) :-
4142 (Limit<1 -> true
4143 ; L1 is Limit-1, length_larger_than(T,L1)).
4144
4145 diff1([],_, _,[]).
4146 diff1([H|T],Min,A1, Res) :-
4147 (H @< Min -> Res = [H-true|Res2],diff1(T,Min,A1,Res2)
4148 ; diff2([H|T],A1,Res)).% TO DO: compute avl_max
4149
4150 diff2([],_, []).
4151 diff2([H|T],A1, Res) :-
4152 (avl_fetch(H,A1) -> Res = Res2 ; Res = [H-true|Res2]), diff2(T,A1,Res2).
4153
4154 % another version to be used when second set small in comparison to first set
4155 difference_of_explicit_set3([],A1,Res) :- construct_avl_set(A1,AVL),
4156 equal_object(AVL,Res). % due to delay in expansion, Res could now be instantiated
4157 difference_of_explicit_set3([H|T],A1,ARes) :-
4158 (avl_delete(H,A1,_True,A2) -> true ; A2=A1),
4159 difference_of_explicit_set3(T,A2,ARes).
4160
4161 % -------------------------
4162
4163 % a version of add_element_to_explicit_set where we have already done the groundness check
4164 add_ground_element_to_explicit_set_wf(avl_set(A),Element,R,WF) :- !,
4165 convert_to_avl_inside_set_wf(Element,AEl,WF),
4166 avl_store(AEl,A,true,A2),!,R=avl_set(A2).
4167 add_ground_element_to_explicit_set_wf(Set,Element,R,WF) :-
4168 add_element_to_explicit_set_wf(Set,Element,R,WF).
4169
4170 add_element_to_explicit_set_wf(global_set(GS),_,R,_) :- is_maximal_global_set(GS), !, R=global_set(GS).
4171 add_element_to_explicit_set_wf(freetype(ID),_,R,_) :- is_maximal_freetype(ID),!, R=freetype(ID).
4172 add_element_to_explicit_set_wf(avl_set(A),Element,R,WF) :-
4173 ground_value(Element), %% was element_can_be_added_or_removed_to_avl(Element),
4174 convert_to_avl_inside_set_wf(Element,AEl,WF),
4175 avl_store(AEl,A,true,A2),!,R=avl_set(A2). /* AVL not normalised */
4176 /* do we need to add support for (special) closures ??
4177 add_element_to_explicit_set_wf(Clos,Element,R,_) :- nonvar(Element),Element=int(X), nonvar(X),
4178 is_interval_closure_or_integerset(Clos,Low,Up), ground(Low), ground(Up),
4179 union_of_interval(X,X,Low,Up,FromRes,ToRes),
4180 !,
4181 construct_interval_closure(FromRes,ToRes,R).
4182 % not-member closure not dealt with here
4183 */
4184
4185 element_can_be_added_or_removed_to_avl(Element) :-
4186 ground_value(Element),
4187 does_not_contain_closure(Element).
4188 ground_element_can_be_added_or_removed_to_avl(Element) :- /* use if you know the element to be ground */
4189 does_not_contain_closure(Element).
4190
4191 % does not contain closure or infinite other sets
4192 does_not_contain_closure([]).
4193 does_not_contain_closure([H|T]) :-
4194 (simple_value(H) -> true /* TO DO: check if we could have a closure at the end ?? */
4195 ; does_not_contain_closure(H),list_does_not_contain_closure(T)).
4196 does_not_contain_closure(fd(_,_)).
4197 does_not_contain_closure(pred_true /* bool_true */).
4198 does_not_contain_closure(pred_false /* bool_false */).
4199 does_not_contain_closure(int(_)).
4200 does_not_contain_closure(string(_)).
4201 does_not_contain_closure(term(_)). % real/floating number
4202 does_not_contain_closure((X,Y)) :- does_not_contain_closure(X), does_not_contain_closure(Y).
4203 does_not_contain_closure(avl_set(_)).
4204 does_not_contain_closure(global_set(G)) :- \+ is_infinite_global_set(G,_).
4205 %does_not_contain_closure(freetype(_)).
4206 does_not_contain_closure(freeval(_,_,Value)) :- does_not_contain_closure(Value).
4207 does_not_contain_closure(rec(Fields)) :- does_not_contain_closure_fields(Fields).
4208
4209 does_not_contain_closure_fields([]).
4210 does_not_contain_closure_fields([field(_,Val)|T]) :- does_not_contain_closure(Val),
4211 does_not_contain_closure_fields(T).
4212
4213 list_does_not_contain_closure([]).
4214 list_does_not_contain_closure([H|T]) :-
4215 does_not_contain_closure(H),list_does_not_contain_closure(T).
4216 list_does_not_contain_closure(avl_set(_)).
4217 list_does_not_contain_closure(global_set(G)) :- \+ is_infinite_global_set(G,_).
4218
4219 simple_value(fd(_,_)).
4220 simple_value(pred_true /* bool_true */).
4221 simple_value(pred_false /* bool_false */).
4222 simple_value(int(_)).
4223 simple_value((A,B)) :- simple_value(A), simple_value(B).
4224 simple_value(string(_)).
4225
4226
4227 % a version of the above which throws error if element cannot be added
4228 % assumes element_can_be_added_or_removed_to_avl has been checked
4229 remove_element_from_explicit_set(avl_set(A),Element,R) :-
4230 element_can_be_added_or_removed_to_avl(Element), % remove check?
4231 convert_to_avl_inside_set(Element,AEl), !,
4232 direct_remove_element_from_avl(A,AEl,R).
4233 remove_element_from_explicit_set(ES,Element,R) :-
4234 add_internal_error('Cannot remove element from explicit set:',remove_element_from_explicit_set(ES,Element,R)).
4235
4236 direct_remove_element_from_avl(A,AEl,R) :-
4237 avl_delete(AEl,A,_True,A2),
4238 construct_avl_set(A2,R). /* AVL not normalised */
4239
4240 /* same as remove but element can be absent */
4241 delete_element_from_explicit_set(avl_set(A),Element,R) :-
4242 element_can_be_added_or_removed_to_avl(Element),
4243 convert_to_avl_inside_set(Element,AEl), !,
4244 (avl_delete(AEl,A,_True,A2)
4245 -> construct_avl_set(A2,R)
4246 ; R = avl_set(A)
4247 ). /* AVL not normalised */
4248
4249 is_maximal_global_set(GS) :- is_maximal_global_set(GS,_Type).
4250 is_maximal_global_set(GS,_) :- var(GS),!,fail.
4251 is_maximal_global_set('INTEGER',Type) :- !, Type=integer.
4252 is_maximal_global_set('REAL',Type) :- !, Type=real.
4253 is_maximal_global_set('FLOAT',_) :- !, fail.
4254 is_maximal_global_set('STRING',Type) :- !, Type=string.
4255 is_maximal_global_set(GS,global(GS)) :-
4256 \+ kernel_objects:integer_global_set(GS).
4257
4258 % To do: maybe get rid of all complement set code; add in_difference_set as symbolic binary operator
4259 %is_very_large_maximal_global_set(X,_) :- print(very(X)),nl,fail.
4260 is_very_large_maximal_global_set(closure(P,T,B),Type) :- is_definitely_maximal_closure(P,T,B),
4261 couplise_list(T,Type).
4262 is_very_large_maximal_global_set(global_set('INTEGER'),integer).
4263 is_very_large_maximal_global_set(global_set('STRING'),string).
4264 is_very_large_maximal_global_set(global_set('REAL'),string).
4265 is_very_large_maximal_global_set(freetype(ID),freetype(ID)) :- is_infinite_freetype(ID).
4266
4267
4268
4269 remove_minimum_element_custom_set(avl_set(S),X,RES) :- !,
4270 avl_del_min(S,X,_True,Res0),
4271 (empty_avl(Res0) -> RES=[] ; RES = avl_set(Res0)).
4272 %remove_minimum_element_custom_set(closure(P,T,B),X,RES) :-
4273 % is_interval_closure_or_integerset(Clos,Low,Up),!,
4274 % X = Low, TO DO: construct new interval closure
4275 remove_minimum_element_custom_set(CS,X,RES) :-
4276 expand_custom_set_to_list(CS,ECS,Done,remove_minimum_element_custom_set),
4277 remove_minimum_element_custom_set2(ECS,X,RES,Done).
4278
4279 :- block remove_minimum_element_custom_set2(?,?,?,-).
4280 % wait until Done: otherwise the Tail of the list could be instantiated by somebody else; interfering with expand_custom_set_to_list
4281 remove_minimum_element_custom_set2([H|T],X,RES,_) :- equal_object((H,T),(X,RES)).
4282
4283
4284 min_of_explicit_set_wf(avl_set(S),Min,_) :- !, avl_min(S,Min).
4285 min_of_explicit_set_wf(Clos,Min,WF) :-
4286 is_interval_closure_or_integerset(Clos,Low,Up),
4287 (Low == minus_inf
4288 -> add_wd_error('minimum of unbounded infinite set not defined:',Clos,WF)
4289 ; cs_greater_than_equal(Up,Low),
4290 Min=int(Low)).
4291
4292 cs_greater_than_equal(X,Y) :-
4293 ((X==inf;Y==minus_inf) -> true ; kernel_objects:less_than_equal_direct(Y,X)).
4294
4295
4296 max_of_explicit_set_wf(avl_set(S),Max,_) :- !,avl_max(S,Max).
4297 max_of_explicit_set_wf(Clos,Max,WF) :-
4298 is_interval_closure_or_integerset(Clos,Low,Up),
4299 (Up==inf
4300 -> add_wd_error('maximum of unbounded infinite set not defined:',Clos,WF)
4301 ; cs_greater_than_equal(Up,Low),
4302 Max=int(Up)).
4303
4304 % ------------- SIGMA/PI --------------
4305
4306 % compute sum or product of an integer set:
4307 sum_or_mul_of_explicit_set(avl_set(S),SUMorMUL,Result) :-
4308 avl_domain(S,Dom),
4309 (SUMorMUL=sum -> simple_sum_list(Dom,0,R) ; simple_mul_list(Dom,1,R)),
4310 Result = int(R).
4311 sum_or_mul_of_explicit_set(CS,SUMorMUL,Result) :- SUMorMUL == sum,
4312 is_interval_closure(CS,Low,Up),
4313 sum_interval(Low,Up,Result),
4314 sum_interval_clpfd_prop(Low,Up,Result).
4315
4316 :- block sum_interval(-,?,?), sum_interval(?,-,?).
4317 sum_interval(Low,Up,_) :- (\+ number(Low) ; \+ number(Up)),!,
4318 add_error(sum_interval,'Cannot compute sum of interval: ',Low:Up),fail.
4319 sum_interval(Low,Up,Result) :- Low>Up,!, Result=int(0).
4320 sum_interval(Low,Up,Result) :-
4321 R is ((1+Up-Low)*(Low+Up)) // 2, % generalisation of Gauss formula k*(k+1)//2
4322 Result = int(R).
4323
4324 sum_interval_clpfd_prop(Low,Up,Result) :-
4325 preferences:preference(use_clpfd_solver,true), Result=int(R),
4326 var(R), % we haven't computed the result yet; the bounds are not known; set up constraint propagation rules
4327 !,
4328 try_post_constraint((Low #>= 0) #=> (R #> 0)), % we could provide better bounds here for negative numbers
4329 try_post_constraint(((Low #=< Up) #\/ (R #\= 0)) #=> (R #= ((1+Up-Low)*(Low+Up))//2)),
4330 try_post_constraint((Low #> Up) #=> (R #= 0)).
4331 % not working yet: x = SIGMA(i).(i:-3..n|i) & x=0 & n< -1
4332 sum_interval_clpfd_prop(_,_,_).
4333
4334 simple_sum_list([],A,A).
4335 simple_sum_list([int(H)|T],Acc,R) :- NA is Acc+H, simple_sum_list(T,NA,R).
4336 simple_mul_list([],A,A).
4337 simple_mul_list([int(H)|T],Acc,R) :- NA is Acc*H, simple_mul_list(T,NA,R).
4338
4339
4340 /*
4341 direct_product_symbolic(S,R,Res) :- % NOT YET FINISHED
4342 nonvar(S), S=closure(PS,[T1,TS2],RS),
4343 nonvar(R), R=closure(PR,[T1,TR1],RR),
4344 is_lambda_value_domain_closure(PS,TS,RS, SDomainValue,SExpr),
4345 is_lambda_value_domain_closure(PR,TR,RR, RDomainValue,RExpr),
4346 construct_closure(['zzz','_lambda_result_'],[T1,couple(TR1,TR2)],
4347 member(zzz,SDomainValue) , member(zzz,RDomainValue), eq(lambda,pair(SExpr,RExpr))).
4348 */
4349
4350 % we assume that try_expand_and_convert_to_avl_unless_very_large already called on arguments
4351 direct_product_explicit_set(S,R,Res) :-
4352 nonvar(R), %is_custom_explicit_set(R,direct_product),
4353 nonvar(S), %is_custom_explicit_set(S,direct_product),
4354 direct_product_explicit_set_aux(S,R,Res).
4355 %direct_product_explicit_set_aux(S,R,Res) :- (S = closure(_,_,_) ; R = closure(_,_,_)),
4356 % print_term_summary(direct_product_explicit_set_aux(S,R,Res)),nl,
4357 % % TO DO: generate closure
4358 % fail.
4359 direct_product_explicit_set_aux(avl_set(AS),avl_set(AR),Res) :-
4360 % the expansion guarantees that we have the lists ES and ER then in sorted order
4361 avl_domain(AS,ES), % -> expand_custom_set(avl_set(AS),ES),
4362 avl_domain(AR,ER), % -> expand_custom_set(avl_set(AR),ER),
4363 direct_product3(ES,ER,DPList),
4364 ord_list_to_avlset(DPList,DPAVL,direct_product), % is it really ordered ? findall must also return things ordered!
4365 equal_object(DPAVL,Res,direct_product_explicit_set).
4366
4367 direct_product3([],_Rel2,[]).
4368 direct_product3([(From,To1)|T1],Rel2,Res) :-
4369 get_next_mapped_to_eq(T1,From,TTo,Tail1), ToList1 = [To1|TTo],
4370 get_next_mapped_to(Rel2,From,ToList2,Tail2),
4371 calc_direct_product(ToList1,From,ToList2,Res,Rest),
4372 (Tail2=[] -> Rest=[] ; direct_product3(Tail1,Tail2,Rest)).
4373
4374 % get all elements which map to From, supposing that the list is sorted & we have already had a match
4375 get_next_mapped_to_eq([],_,[],[]).
4376 get_next_mapped_to_eq([(From2,To2)|T],From,Result,Tail) :-
4377 (From=From2 -> Result = [To2|RR], get_next_mapped_to_eq(T,From,RR,Tail)
4378 ; Result = [], Tail = [(From2,To2)|T]
4379 ).
4380
4381 % get all elements which map to From, supposing the list is sorted
4382 get_next_mapped_to([],_,[],[]).
4383 get_next_mapped_to([(From2,To2)|T],From,Result,Tail) :-
4384 (From=From2 -> Result = [To2|RR], get_next_mapped_to_eq(T,From,RR,Tail)
4385 ; From2 @> From -> Result = [], Tail = [(From2,To2)|T]
4386 ; get_next_mapped_to(T,From,Result,Tail)
4387 ).
4388
4389 calc_direct_product([],_From,_,Tail,Tail).
4390 calc_direct_product([To1|T1],From,To2List,Result,Tail) :-
4391 findall((From,(To1,To2))-true,member(To2,To2List),Result,ResResult),
4392 calc_direct_product(T1,From,To2List,ResResult,Tail).
4393
4394 % TO DO: maybe also add a special rule for infinite R such as event_b_identity ?
4395 domain_restriction_explicit_set_wf(S,R,Res,WF) :- /* S <| R */
4396 nonvar(R),
4397 (nonvar(S),is_one_element_custom_set(S,El),R \= closure(_,_,_) ->
4398 domain_restrict_singleton_element(El,R,Res)
4399 ; restriction_explicit_set_wf(S,R,Res,domain,pred_true,WF)).
4400 domain_subtraction_explicit_set_wf(S,R,Res,WF) :- /* S <<| R */
4401 (nonvar(S),is_one_element_custom_set(S,El), nonvar(R), R=avl_set(AVL) ->
4402 avl_domain_subtraction_singleton(AVL,El,ARes),
4403 construct_avl_set(ARes,Res) % TO DO: use this also when S is small and R large
4404 ; restriction_explicit_set_wf(S,R,Res,domain,pred_false,WF)).
4405 range_restriction_explicit_set_wf(R,S,Res,WF) :- /* R |> S */
4406 restriction_explicit_set_wf(S,R,Res,range,pred_true,WF).
4407 range_subtraction_explicit_set_wf(R,S,Res,WF) :- /* R |>> S */
4408 restriction_explicit_set_wf(S,R,Res,range,pred_false,WF).
4409
4410
4411 domain_restrict_singleton_element(El,R,Res) :- /* {El} <| R ; TO DO maybe apply this technique for "small" sets as well */
4412 nonvar(R), is_custom_explicit_set(R,domain_restrict_singleton_element),
4413 expand_and_convert_to_avl_set(R,AR,domain_restrict_singleton_element,''), % can generate ARel=empty; will fail if not possible to convert
4414 findall((El,Z)-true, avl_fetch_pair(El,AR,Z), RTuples),
4415 ord_list_to_avlset(RTuples,Res,domain_restrict_singleton_element).
4416
4417 restriction_explicit_set_wf(Set,Rel,Res,_RanOrDom,AddWhen,WF) :- Set==[],!,
4418 (AddWhen=pred_false
4419 -> equal_object_wf(Rel,Res,restriction_explicit_set_wf,WF) % {} <<| Rel = Rel |>> {} = Rel
4420 ; kernel_objects:empty_set_wf(Res,WF)
4421 ).
4422 restriction_explicit_set_wf(Set,Rel,Res,_RanOrDom,AddWhen,WF) :- is_definitely_maximal_set(Set),!,
4423 (AddWhen=pred_true
4424 -> equal_object_wf(Rel,Res,restriction_explicit_set_wf,WF) % TYPE <| Rel = Rel |> TYPE = Rel
4425 ; kernel_objects:empty_set_wf(Res,WF)
4426 ).
4427 restriction_explicit_set_wf(_,Rel,_,_,_,_) :- var(Rel),!,fail.
4428 restriction_explicit_set_wf(Set,closure(Paras,Types,Body),Res,RanOrDom,AddWhen,WF) :-
4429 % perform symbolic treatment by adding restriction predicate to Body
4430 !,
4431 (RanOrDom=domain
4432 -> get_domain_id_or_expr(Paras,Types,TID,TT)
4433 ; get_range_id_or_expr(Paras,Types,TID,TT)
4434 ),
4435 TSet=b(value(Set),set(TT),[]),
4436 (AddWhen = pred_true
4437 -> PRED = member(TID,TSet)
4438 ; PRED = not_member(TID,TSet) ),
4439 conjunct_predicates([b(PRED,pred,[]),Body],NewBody),
4440 % translate:print_bexpr(NewBody),nl,
4441 try_expand_and_convert_to_avl_with_catch_wf(closure(Paras,Types,NewBody),Res,restriction_explicit_set_wf,WF).
4442 restriction_explicit_set_wf(Set,Rel,Res,RanOrDom,AddWhen,WF) :-
4443 is_custom_explicit_set(Rel,restriction_explicit_set_wf),
4444 expand_and_convert_to_avl_set(Rel,ARel,restriction_explicit_set_wf,''), % can generate ARel=empty; will fail if not possible to convert
4445 avl_domain(ARel,ERel), % -> expand_custom_set(avl_set(ARel),ERel),
4446 %try_expand_and_convert_to_avl_unless_large_wf(Set,ES,WF),
4447 (nonvar(Set),Set=avl_set(AVLS)
4448 -> restrict2_avl(ERel,AVLS,DRes,RanOrDom,AddWhen,Done)
4449 ; restrict2(ERel,Set,DRes,RanOrDom,AddWhen,Done,WF)
4450 ),
4451 finish_restriction(Done,DRes,Res).
4452
4453 % extract domain expression for domain restriction/subtraction predicate:
4454 get_domain_id_or_expr([DR],[couple(TD,TR)], PRJ1, TD) :- !, % special case: just one parameter in closure
4455 TID = b(identifier(DR),couple(TD,TR),[]),
4456 PRJ1 = b(first_of_pair(TID),TD,[]).
4457 get_domain_id_or_expr([D1|Paras],[TD1|Types],Expr,Type) :-
4458 get_dom_couple_aux(Paras,Types, b(identifier(D1),TD1,[]), TD1, Expr,Type).
4459
4460 get_dom_couple_aux([_RangeID],[_], AccExpr, AccType, Expr, Type) :- !, Expr=AccExpr, Type=AccType.
4461 get_dom_couple_aux([D2|TParas],[TD2|Types], AccExpr, AccType, Expr, Type) :-
4462 TID2 = b(identifier(D2),TD2,[]),
4463 NewAccType = couple(AccType,TD2),
4464 NewAcc = b(couple(AccExpr,TID2),NewAccType,[]),
4465 get_dom_couple_aux(TParas,Types,NewAcc,NewAccType,Expr,Type).
4466
4467 :- use_module(library(lists),[last/2]).
4468 % extract range expression for range restriction/subtraction predicate:
4469 get_range_id_or_expr( [DR],[CType], PRJ2, TR) :- !, % special case: just one parameter in closure
4470 CType = couple(TD,TR),
4471 TID = b(identifier(DR),CType,[]),
4472 PRJ2 = b(second_of_pair(TID),TD,[]).
4473 get_range_id_or_expr( [_|Paras],[_|Types], b(identifier(R),TR,[]), TR) :-
4474 last(Paras,R), last(Types,TR).
4475
4476 :- block finish_restriction(-,?,?).
4477 finish_restriction(_,DRes,Res) :-
4478 ord_list_to_avlset(DRes,Restriction,restriction),
4479 equal_object(Restriction,Res,finish_restriction). % as we may block below: we need to use equal_object
4480
4481 restrict2([],_,[],_,_,done,_WF).
4482 restrict2([(From,To)|T],S,Res,RanOrDom,AddWhen,Done,WF) :-
4483 (RanOrDom==domain -> El=From ; El=To),
4484 kernel_equality:membership_test_wf(S,El,MemRes,WF), % TO DO: WF Version !!
4485 /* this only makes sense once we have the full result as argument:
4486 (nonvar(MemRes) -> true % it is already decided
4487 ; AddWhen=pred_true -> kernel_equality:membership_test_wf(Res,(From,To),MemRes,WF)
4488 ; kernel_equality:membership_test_wf(Res,(From,To),InResult,WF), bool_pred:negate(InResult,MemRes)
4489 ), */
4490 restrict3(MemRes,From,To,T,S,Res,RanOrDom,AddWhen,Done,WF).
4491 :- block restrict3(-, ?,?, ?,?,?, ?,?,?,?).
4492 restrict3(MemRes, From,To, T,S,Res, RanOrDom,AddWhen,Done,WF) :-
4493 (AddWhen=MemRes -> Res = [(From,To)-true|TRes]
4494 ; Res=TRes),
4495 restrict2(T,S,TRes,RanOrDom,AddWhen,Done,WF).
4496
4497 % optimised version when second set is also an AVL tree: less blocking,...
4498 restrict2_avl([],_,[],_,_,done).
4499 restrict2_avl([(From,To)|T],AVLS,Res,RanOrDom,AddWhen,Done) :-
4500 fetch(RanOrDom,From,To,AVLS,MemRes),
4501 (AddWhen=MemRes -> Res = [(From,To)-true|TRes]
4502 ; Res=TRes),
4503 restrict2_avl(T,AVLS,TRes,RanOrDom,AddWhen,Done).
4504
4505 fetch(domain,El,_,AVLS,MemRes) :- (avl_fetch(El,AVLS) -> MemRes=pred_true ; MemRes = pred_false).
4506 fetch(range,_,El,AVLS,MemRes) :- (avl_fetch(El,AVLS) -> MemRes=pred_true ; MemRes = pred_false).
4507
4508 % override R(X) := Y
4509 override_pair_explicit_set(avl_set(S),X,Y,avl_set(NewAVL)) :- element_can_be_added_or_removed_to_avl(X),
4510 element_can_be_added_or_removed_to_avl(Y),
4511 convert_to_avl_inside_set(X,AX),
4512 convert_to_avl_inside_set(Y,AY),
4513 avl_domain_subtraction_singleton(S,AX,AVL2),
4514 avl_store((AX,AY), AVL2, true, NewAVL).
4515
4516 avl_domain_subtraction_singleton(AVL,AX,NewAVL) :-
4517 avl_delete_pair(AX,AVL,_True,AVL2),
4518 !, % recurse, in case we have multiple entries
4519 % this recursion could be avoided if we know AVL to be a function
4520 avl_domain_subtraction_singleton(AVL2,AX,NewAVL).
4521 avl_domain_subtraction_singleton(AVL,_,AVL).
4522
4523 % try and decompose an AVL set into a cartesian product
4524 % AVL = Set1 * Set2
4525 % much faster e.g. for let xx = ((1..10)*(3..1000)\/ {0}*(3..1000)) and then xx = AA*BB
4526 % should not produce pending co-routines
4527 decompose_avl_set_into_cartesian_product_wf(AVL,DomainSet,RangeSet,WF) :-
4528 avl_domain(AVL,Expansion),
4529 decompose_cart(Expansion,'$none',DomainList,[],RangeList),
4530 construct_avl_from_lists_wf(DomainList,DomainSet,WF),
4531 construct_avl_from_lists_wf(RangeList,RangeSet,WF).
4532
4533 decompose_cart([],_,[],[],_).
4534 decompose_cart([(A,B)|T],Prev,Domain,Range,FullRange) :-
4535 (A=Prev
4536 -> Range = [B|TRange],
4537 decompose_cart(T,Prev,Domain,TRange,FullRange)
4538 ; Domain = [A|TDom], Range=[],
4539 FullRange = [B|TRange],
4540 decompose_cart(T,A,TDom,TRange,FullRange)
4541 ).
4542
4543 /* --------- */
4544 /* EXPANSION */
4545 /* --------- */
4546
4547 :- use_module(b_global_sets,[all_elements_of_type_wf/3, all_elements_of_type_rand_wf/3]).
4548 :- use_module(kernel_freetypes,[expand_freetype/3]).
4549
4550 expand_custom_set(X,R) :- expand_custom_set_wf(X,R,expand_custom_set,no_wf_available).
4551 expand_custom_set(X,R,Src) :- expand_custom_set_wf(X,R,Src,no_wf_available).
4552 expand_custom_set_wf(X,R,Source,WF) :- var(X), !,
4553 add_error_and_fail(expand_custom_set_wf, 'Variable as argument: ',expand_custom_set_wf(X,R,Source,WF)).
4554 expand_custom_set_wf(global_set(GS),ExpandedSet,_,WF) :- !,
4555 all_elements_of_type_wf(GS,ExpandedSet,WF). % they are generated in order
4556 expand_custom_set_wf(freetype(GS),ValueList,_,WF) :- !,
4557 expand_freetype(GS,ValueList,WF).
4558 expand_custom_set_wf(avl_set(AVL),ExpandedSet,_,_) :- !,
4559 avl_domain(AVL,ExpandedSet).
4560 expand_custom_set_wf(closure(Parameters,PTypes,Cond),Res,Source,WF) :- !,
4561 expand_closure_to_list(Parameters,PTypes,Cond,Res,_Done,Source,WF).
4562 %wait_try_expand_custom_set(Res1,Res). % could be in AVL form; no longer the case !
4563 expand_custom_set_wf(Set,_,Source,_) :-
4564 add_error_and_fail(expand_custom_set(Source),'Cannot expand custom set: ',Set).
4565
4566
4567
4568 %try_expand_only_custom_closure_global(X,Y) :-
4569 % (var(X) -> X=Y ; expand_only_custom_closure_global(X,Y,check)).
4570
4571 expand_only_custom_closure_global(X,R,C,_WF) :- var(X), !,
4572 add_error_and_fail(expand_only_custom_closure_global, 'Variable as argument: ',expand_only_custom_closure_global(X,R,C)).
4573 expand_only_custom_closure_global(global_set(GS),ExpandedSet,_,WF) :- !,all_elements_of_type_wf(GS,ExpandedSet,WF).
4574 expand_only_custom_closure_global(freetype(GS),ExpandedSet,_,_WF) :- !,ExpandedSet=freetype(GS).
4575 expand_only_custom_closure_global(avl_set(AVL),ExpandedSet,_,_WF) :- !, ExpandedSet=avl_set(AVL).
4576 expand_only_custom_closure_global(closure(Parameters,PTypes,Cond),Res,CheckTimeOuts,WF) :- !,
4577 (Res==[] -> is_empty_explicit_set(closure(Parameters,PTypes,Cond)) % TO DO: think about other special cases
4578 ; expand_closure_to_avl_or_list(Parameters,PTypes,Cond,Res,CheckTimeOuts,WF)).
4579 expand_only_custom_closure_global(Set,Set,_CheckTimeOuts,_WF).
4580 %:- add_error_and_fail(expand_only_custom_closure_global,'Cannot expand custom set: ',Set).
4581
4582
4583 try_expand_custom_set_with_catch(CS,Expansion,PP) :-
4584 on_enumeration_warning(try_expand_custom_set_wf(CS,Expansion,PP,no_wf_available),
4585 Expansion=CS).
4586
4587 try_expand_custom_set(CS,Expansion) :-
4588 try_expand_custom_set_wf(CS,Expansion,try_expand_custom_set,no_wf_available).
4589
4590
4591 try_expand_custom_set_wf(CS,Res,_,_) :- var(CS),!,Res=CS.
4592 try_expand_custom_set_wf([],Res,_,_) :- !, Res=[].
4593 try_expand_custom_set_wf([H|T],Res,_,_) :- !, Res=[H|T].
4594 try_expand_custom_set_wf(CS,Res,Src,WF) :-
4595 expand_custom_set_wf(CS,Res,Src,WF). % will generate error message for illegal sets
4596
4597
4598 :- assert_must_succeed((expand_custom_set_to_list(closure(['_zzzz_unit_tests'],
4599 [couple(integer,integer)],
4600 b(member(b(identifier('_zzzz_unit_tests'),couple(integer,integer),[generated]),
4601 b(value([(int(1),int(22))]),set(couple(integer,integer)),[])),pred,[])),R),R==[(int(1),int(22))])).
4602
4603 expand_custom_set_to_list(CS,List) :- expand_custom_set_to_list(CS,List,_Done,unknown).
4604
4605 % a version of expansion which returns guaranteed_ground if the List is guaranteed to be ground
4606 expand_custom_set_to_list_gg(CS,List,GuaranteedGround,_PP) :-
4607 nonvar(CS), CS=avl_set(AVL), var(List),
4608 !,
4609 GuaranteedGround = guaranteed_ground,
4610 avl_domain(AVL,List).
4611 expand_custom_set_to_list_gg(CS,List,not_guaranteed_ground,PP) :-
4612 expand_custom_set_to_list(CS,List,_Done,PP).
4613
4614 % a version where the expansion should happen straightaway and should not block:
4615 expand_custom_set_to_list_now(CS,List) :- expand_custom_set_to_list(CS,List,Done,unknown),
4616 (Done==true -> true ; print_error(expand_custom_set_to_list_not_done(CS,List))).
4617
4618 :- block expand_custom_set_to_sorted_list(-,-,?,?,?).
4619 % sorts the resulting list if needed
4620 % due to random enumeration
4621 expand_custom_set_to_sorted_list(From,To,Done,Source,WF) :-
4622 expand_custom_set_to_list(From,UnsortedTo,Done,Source),
4623 (get_preference(randomise_enumeration_order,true)
4624 -> sort_when_done(Done,UnsortedTo,To,WF) ; UnsortedTo = To).
4625
4626 :- block sort_when_done(-,?,?,?).
4627 sort_when_done(_,Unsorted,Res,WF) :- sort(Unsorted,Sorted),
4628 equal_object_wf(Sorted,Res,sort_when_done,WF).
4629
4630 expand_custom_set_to_list(From,To,Done,Source) :-
4631 expand_custom_set_to_list_wf(From,To,Done,Source,no_wf_available).
4632
4633 :- use_module(kernel_objects,[equal_object_wf/4]).
4634
4635 % try expand custom set to list; on enumeration warning set Done to enumeration_warning
4636 try_expand_custom_set_to_list_wf(From,To,Done,Source,WF) :-
4637 on_enumeration_warning(expand_custom_set_to_list_wf(From,To,Done,Source,WF),
4638 (Done=enumeration_warning)).
4639
4640 expand_custom_set_to_list_wf(From,To,Done,Source,WF) :-
4641 expand_custom_set_to_list_k_wf(From,To,Done,_Kind,Source,WF).
4642
4643 % a variation of expand_custom_set_to_list which also checks that there are no duplicates in the list
4644 expand_custom_set_to_list_no_dups_wf(From,To,Done,Source,WF) :-
4645 expand_custom_set_to_list_k_wf(From,To,Done,Kind,Source,WF),
4646 check_dups(Kind,To,WF).
4647
4648 :- block check_dups(-,?,?).
4649 check_dups(unsorted_list,List,WF) :- !,
4650 kernel_objects:check_no_duplicates_in_list(List,[],WF).
4651 check_dups(_,_,_).
4652
4653 % warn if duplicates in list; to do: use in prob_safe mode
4654 %:- block warn_dups(-,?,?,?).
4655 %warn_dups(unsorted_list,List,Src,WF) :- !,
4656 % kernel_objects:warn_if_duplicates_in_list(List,Src,WF).
4657 %warn_dups(_,_,_,_).
4658
4659
4660
4661 :- block expand_custom_set_to_list_k_wf(-,-,?,?,?,?).
4662 % ensures that the output is a pure list; the list skeleton should not be instantiated by anybody else
4663 expand_custom_set_to_list_k_wf(From,To,Done,Kind,Source,WF) :-
4664 (var(From) ->
4665 (is_list_skeleton(To)
4666 ? -> equal_object_wf(To,From,Source,WF), Done=true, Kind=unsorted_list
4667 ; expand_custom_set_to_list2(To,From,Done,Kind,Source,WF))
4668 ; var(To),is_list_skeleton(From)
4669 -> To=From, Done=true, Kind=unsorted_list % equal_object_wf will also to a Prolog unification
4670 ? ; expand_custom_set_to_list2(From,To,Done,Kind,Source,WF)).
4671
4672 expand_custom_set_to_list2([],ExpandedSet,Done,Kind,_Source,WF) :- !,
4673 ? equal_object_wf([],ExpandedSet,expand_custom_set_to_list2,WF),Done=true,Kind=empty_set.
4674 expand_custom_set_to_list2([H|T],ExpandedSet,Done,Kind,Source,WF) :- !, Kind=unsorted_list,
4675 ? equal_object_wf([H|ET],ExpandedSet,expand_custom_set_to_list2,WF),
4676 ? expand_custom_set_to_list3(T,ET,Done,Source,WF).
4677 expand_custom_set_to_list2(global_set(GS),ExpandedSet,Done,Kind,_Source,WF) :- !,
4678 all_elements_of_type_rand_wf(GS,R,WF),
4679 check_list(R,expand_custom_set_to_list2),
4680 equal_object_wf(R,ExpandedSet,expand_custom_set_to_list2,WF),Done=true,Kind=sorted_list.
4681 expand_custom_set_to_list2(avl_set(AVL),ExpandedSet,Done,Kind,_Source,WF) :- !,
4682 avl_domain(AVL,R),
4683 ? equal_object_wf(R,ExpandedSet,expand_custom_set_to_list2,WF), Done=true,Kind=sorted_list.
4684 expand_custom_set_to_list2(closure(Parameters,PTypes,Cond),ExpandedSet,Done,Kind,Source,WF) :- !,
4685 ? expand_closure_to_list(Parameters,PTypes,Cond,ExpandedSet,Done,Source,WF),
4686 Kind=sorted_list.
4687 %assign_expand_result(CDone,Res,ExpandedSet,Done).
4688 expand_custom_set_to_list2(freetype(ID),ExpandedSet,Done,Kind,_Source,WF) :- !,
4689 expand_freetype(ID,R,WF),
4690 equal_object_wf(R,ExpandedSet,expand_custom_set_to_list2,WF),
4691 Done=true,Kind=sorted_list.
4692 % missing avl_set wrapper:
4693 expand_custom_set_to_list2(node(A,B,C,D,E),ExpandedSet,Done,Kind,Source,WF) :- !,
4694 add_internal_error('Illegal argument: ',expand_custom_set_to_list2(node(A,B,C,D,E),ExpandedSet,Done,Source)),
4695 expand_custom_set_to_list2(avl_set(node(A,B,C,D,E)),ExpandedSet,Done,Kind,Source,WF).
4696 expand_custom_set_to_list2(E,ES,Done,Kind,Source,WF) :-
4697 add_internal_error('Illegal argument: ',expand_custom_set_to_list2(E,ES,Done,Kind,Source,WF)),fail.
4698
4699 :- block expand_custom_set_to_list3(-,-,?,?,?). % we are no longer sure which was From and which is To
4700 expand_custom_set_to_list3(From,To,Done,Source,WF) :-
4701 ? (var(From) -> expand_custom_set_to_list2(To,From,Done,_,Source,WF) ;
4702 ? expand_custom_set_to_list2(From,To,Done,_,Source,WF)).
4703
4704
4705 is_list_skeleton(X) :- var(X),!,fail.
4706 is_list_skeleton([]).
4707 is_list_skeleton([_|T]) :- is_list_skeleton(T).
4708
4709 % true if it is more efficient to keep this, rather than expand into list
4710 is_efficient_custom_set(avl_set(_)).
4711 is_efficient_custom_set(closure(P,T,B)) :-
4712 (is_interval_closure(closure(P,T,B),_,_) -> true ; is_infinite_or_symbolic_closure(P,T,B)).
4713 is_efficient_custom_set(global_set(X)) :- is_infinite_global_set(X,_).
4714 is_efficient_custom_set(freetype(_)).
4715
4716 % tries to expand & convert to avl_set; fails if not possible: NOTE: also generates empty AVL
4717 expand_and_convert_to_avl_set(R,AER,Origin,Source) :-
4718 try_expand_and_convert_to_avl(R,ER,Origin,Source),
4719 nonvar(ER),(ER==[] -> AER=empty ; ER=avl_set(AER)).
4720
4721
4722 expand_and_convert_to_avl_set_unless_very_large(R,AER,WF) :-
4723 try_expand_and_convert_to_avl_unless_very_large_wf(R,ER,WF),
4724 nonvar(ER),(ER==[] -> AER=empty ; ER=avl_set(AER)).
4725
4726
4727 % similar to unless_large version, but will only expand if it is guaranteed to be small
4728
4729 try_expand_and_convert_to_avl_if_smaller_than(freetype(GS),Res,_) :- !, Res = freetype(GS).
4730 try_expand_and_convert_to_avl_if_smaller_than([H|T],Res,_) :- !, try_expand_and_convert_to_avl([H|T],Res).
4731 try_expand_and_convert_to_avl_if_smaller_than(avl_set(A),Res,_) :- !, Res=avl_set(A).
4732 try_expand_and_convert_to_avl_if_smaller_than(CS,Res,Limit) :-
4733 (is_small_specific_custom_set(CS,Limit)
4734 -> try_expand_and_convert_to_avl(CS,Res,try_expand_and_convert_to_avl_if_smaller_than,'')
4735 ; Res = CS % TO DO: maybe look at cardinality of types and determine max. cardinality
4736 ).
4737 is_small_specific_custom_set(CS,Limit) :- card_for_specific_custom_set(CS,Card,Code),
4738 call(Code), is_finite_card(Card), Card<Limit.
4739 get_card_for_specific_custom_set(CS,Card) :-
4740 card_for_specific_custom_set(CS,Card,Code),
4741 call(Code), ground(Card).
4742
4743 try_expand_and_convert_to_avl_unless_very_large_wf(CS,Res,WF) :-
4744 try_expand_and_convert_to_avl_unless_large_wf(CS,Res,10000,WF).
4745
4746 try_expand_and_convert_to_avl_unless_large_wf(CS,Res,WF) :-
4747 try_expand_and_convert_to_avl_unless_large_wf(CS,Res,2000,WF).
4748
4749 try_expand_and_convert_to_avl_unless_large_wf(CS,Res,_,_WF) :- var(CS), !, CS=Res.
4750 try_expand_and_convert_to_avl_unless_large_wf(global_set(GS),Res,_,_WF) :- !, Res = global_set(GS).
4751 try_expand_and_convert_to_avl_unless_large_wf(freetype(GS),Res,_,_WF) :- !, Res = freetype(GS).
4752 %try_expand_and_convert_to_avl_unless_large_wf(CS,Res,_WF) :- is_interval_closure(CS,Low,Up),!,
4753 % ((ground(Low),ground(Up),Size is 1+Up-Low, Size<2000)
4754 %% -> try_expand_and_convert_to_avl(CS,Res)
4755 % ; Res = CS
4756 % ).
4757 try_expand_and_convert_to_avl_unless_large_wf(closure(P,T,B),Res,Limit,_WF) :-
4758 is_very_large_or_symbolic_closure(P,T,B,Limit),!, % is explicitly marked as SYMBOLIC
4759 Res=closure(P,T,B).
4760 try_expand_and_convert_to_avl_unless_large_wf(CS,Res,_Limit,WF) :-
4761 % TO DO: check if maybe we cannot determine card explicitly, but have a large lower-bound
4762 try_expand_and_convert_to_avl_wf(CS,Res,try_expand_and_convert_to_avl_unless_large,'',WF).
4763
4764
4765
4766 % calls try_expand_and_convert_to_avl and returns original value if enumeration warning occured
4767 try_expand_and_convert_to_avl_with_catch_wf(CS,Res,Origin,WF) :-
4768 on_enumeration_warning(try_expand_and_convert_to_avl_wf(CS,Res,Origin,'',WF),
4769 Res=CS).
4770
4771 /* tries to generate an avl-structure, if possible */
4772 try_expand_and_convert_to_avl(CS,Res) :-
4773 try_expand_and_convert_to_avl_wf(CS,Res,try_expand_and_convert_to_avl,'',no_wf_available).
4774
4775 try_expand_and_convert_to_avl(CS,Res,Origin,Source) :-
4776 try_expand_and_convert_to_avl_wf(CS,Res,Origin,Source,no_wf_available).
4777
4778 try_expand_and_convert_to_avl_wf(CS,Res,_,_,_WF) :- var(CS), !, CS=Res.
4779 try_expand_and_convert_to_avl_wf(avl_set(A),R,_,_,_WF) :- !, R=avl_set(A).
4780 try_expand_and_convert_to_avl_wf([],R,_,_,_WF) :- !, R=[].
4781 try_expand_and_convert_to_avl_wf([H|T],R,_,_,WF) :- !, try_convert_to_avl_wf([H|T],R,WF).
4782 try_expand_and_convert_to_avl_wf(closure(P,T,B),Res,Origin,_Source,WF) :- !,
4783 debug_opt_push_wait_flag_call_stack_info(WF,
4784 external_call('TRY EXPANDING',[closure(P,T,B)],unknown),WF2),
4785 expand_only_custom_closure_global(closure(P,T,B),Expansion,check(Origin),WF2),
4786 try_convert_to_avl_wf(Expansion,Res,WF).
4787 try_expand_and_convert_to_avl_wf(CS,Res,Origin,_Source,WF) :-
4788 (\+ is_custom_explicit_set(CS,try_expand_and_convert_to_avl_wf)
4789 -> Expansion = CS
4790 ; expand_only_custom_closure_global(CS,Expansion,check(Origin),WF)
4791 ),
4792 try_convert_to_avl_wf(Expansion,Res,WF).
4793
4794 try_convert_to_avl(Expansion,Res) :-
4795 (should_be_converted_to_avl_from_lists(Expansion) -> construct_avl_from_lists(Expansion,Res) ; Res=Expansion).
4796 try_convert_to_avl_wf(Expansion,Res,WF) :-
4797 (should_be_converted_to_avl_from_lists(Expansion) -> construct_avl_from_lists_wf(Expansion,Res,WF) ; Res=Expansion).
4798
4799 should_be_converted_to_avl_from_lists(Value) :- var(Value),!,fail.
4800 should_be_converted_to_avl_from_lists(Value) :-
4801 \+ is_custom_explicit_set(Value,should_be_converted_to_avl_from_lists), % already avl_set, global_set or closure
4802 \+ do_not_convert_aux(Value),
4803 ground_value(Value).
4804
4805 do_not_convert_aux(V) :- var(V),!.
4806 do_not_convert_aux((A,B)) :- !,
4807 (do_not_convert_aux(A) -> true ; do_not_convert_aux(B)).
4808 do_not_convert_aux([H|T]) :- !, % do not convert a set containing a symbolic closure
4809 (var(T) -> true ; do_not_convert_aux(H)).
4810 do_not_convert_aux(rec(Fields)) :- !,
4811 (var(Fields) -> true
4812 ? ; member(field(_,V),Fields), do_not_convert_aux(V) -> true).
4813 do_not_convert_aux(H) :-
4814 is_symbolic_closure(H).
4815
4816 should_be_converted_to_avl(Value) :- %preference(use_avl_trees_for_sets,true),
4817 ground_value(Value).
4818
4819 try_expand_and_convert_to_avl_with_check(CS,Res,Origin) :-
4820 try_expand_and_convert_to_avl_with_check(CS,Res,do_not_keep_intervals,Origin).
4821
4822 try_expand_and_convert_to_avl_with_check(CS,Res,_,_Origin) :- var(CS),!, Res = CS.
4823 try_expand_and_convert_to_avl_with_check([],Res,_,_Origin) :- !, Res=[].
4824 try_expand_and_convert_to_avl_with_check(avl_set(A),Res,_,_Origin) :- !, Res=avl_set(A).
4825 try_expand_and_convert_to_avl_with_check([H|T],Res,_,Origin) :- !, try_expand_and_convert_to_avl([H|T],Res,Origin,'').
4826 %try_expand_and_convert_to_avl_with_check(CS,Res,_Origin) :-
4827 % \+ is_custom_explicit_set(CS,try_expand_and_convert_to_avl),!, Res = CS.
4828 try_expand_and_convert_to_avl_with_check(CS,Res,KeepIntervals,_Origin) :-
4829 is_interval_closure(CS,Low,Up),
4830 (var(Low) -> true ; var(Up) -> true % better keep this symbolic as we may be able to do constraint propagation
4831 ; KeepIntervals=keep_intervals(Size) -> Up-Low >= Size
4832 ),
4833 !, % TO DO: see if we should do this check in try_expand_and_convert_to_avl above instead
4834 Res=CS.
4835 try_expand_and_convert_to_avl_with_check(CS,Res,_,Origin) :-
4836 get_card_for_specific_custom_set(CS,Size), % TO DO: avoid checking for special closures twice (below in try_expand_and_convert_to_avl ?)
4837 !,
4838 try_expconv_to_avl_with_size(Size,CS,Res,Origin).
4839 try_expand_and_convert_to_avl_with_check(CS,Res,_,Origin) :-
4840 try_expand_and_convert_to_avl(CS,Res,Origin,'').
4841
4842 try_expconv_to_avl_with_size(inf,CS,Res,Origin) :- !,
4843 debug_format(9,'### Not expanding infinite set~n### ORIGIN: ~w~n',[Origin]),
4844 Res=CS.
4845 try_expconv_to_avl_with_size(inf_overflow,CS,Res,Origin) :- !,
4846 debug_format(9,'### Not expanding very large set~n### ORIGIN: ~w~n',[Origin]),
4847 Res=CS.
4848 try_expconv_to_avl_with_size(Size,CS,Res,Origin) :- Size>=10000000, !,
4849 /* will probably never terminate */
4850 debug_format(9,'### Not expanding very large set with cardinality ~w~n### ORIGIN: ~w~n',[Size,Origin]),
4851 Res=CS.
4852 try_expconv_to_avl_with_size(Size,CS,Res,Origin) :- Size>=50000, !,
4853 print('### WARNING: expanding very large comprehension set, size = '), print(Size),nl,
4854 print('### ORIGIN: '), print(Origin),nl,
4855 try_expand_and_convert_to_avl(CS,Res,Origin,'').
4856 try_expconv_to_avl_with_size(_Size,CS,Res,Origin) :-
4857 try_expand_and_convert_to_avl(CS,Res,Origin,'').
4858
4859 /* underlying assumption for var case: if G is a global set: we get back the
4860 global_set tag immediately: no need to use when to wait;
4861 better: ensure that b_compute_expression always returns a nonvar term */
4862
4863
4864 :- assert_must_succeed((custom_explicit_sets:try_expand_custom_set(closure([xx],[integer],b(falsity,pred,[])),R),R = [])).
4865 :- assert_must_succeed((custom_explicit_sets:test_closure(X),custom_explicit_sets:expand_custom_set(X,EX),
4866 EX = [(fd(1,'Name'),_),(fd(3,'Name'),_)])).
4867
4868 test_closure(X) :- X = closure(['_zzzz_binary'],[couple(global('Name'),set(global('Name')))],
4869 b(member(b(identifier('_zzzz_binary'),couple(global('Name'),set(global('Name'))),[generated]),
4870 b(cartesian_product(b(value([fd(1,'Name'),fd(3,'Name')]),set(global('Name')),[]),
4871 b(value([[fd(2,'Name'),fd(3,'Name')]]),set(set(global('Name'))),[])),
4872 set(couple(global('Name'),set(global('Name')))),[])),pred,[])).
4873
4874
4875 /* --------- */
4876 /* ELEMENT_OF */
4877 /* --------- */
4878
4879
4880 /* A function that instantiates last argument when membership test can be decided */
4881
4882 membership_custom_set(CS,X,R) :- print(warning_deprecated_non_wf_version(CS,X,R)),nl,
4883 membership_custom_set_wf(CS,X,R,_WF).
4884
4885 ?membership_custom_set_wf(avl_set(A),X,R,WF) :- !, membership_avl_set_wf(A,X,R,WF).
4886 membership_custom_set_wf(freetype(_GS),_X,R,_WF) :- !, R=pred_true. % should be covered by clause above
4887 membership_custom_set_wf(CS,X,R,WF) :- R==pred_true,!, element_of_custom_set_wf(X,CS,WF).
4888 membership_custom_set_wf(CS,X,R,WF) :- R==pred_false,!, not_element_of_custom_set_wf(X,CS,WF).
4889 membership_custom_set_wf(CS,_X,R,_WF) :-
4890 is_definitely_maximal_set(CS),!,
4891 R=pred_true.
4892 membership_custom_set_wf(closure(Par,Types,Body),X,R,WF) :- !,
4893 ? closure_membership_wf(X,Par,Types,Body,R,WF).
4894 %membership_custom_set_wf(CS,X,R,WF) :- is_one_element_custom_set(CS,Y),!, % only succeeds for AVL
4895 % kernel_equality:equality_objects_wf_no_enumr(X,Y,R,WF).
4896 membership_custom_set_wf(global_set(GS),X,R,WF) :- !,
4897 membership_global_set(GS,X,R,WF).
4898 membership_custom_set_wf(CS,X,R,WF) :-
4899 add_internal_error('Illegal custom set: ',membership_custom_set_wf(CS,X,R,WF)),fail.
4900
4901 membership_avl_set_wf(A,X,R,WF) :- R==pred_true,!, element_of_avl_set_wf(A,X,WF).
4902 membership_avl_set_wf(A,X,R,WF) :- R==pred_false,!, not_element_of_custom_set_wf(X,avl_set(A),WF).
4903 membership_avl_set_wf(A,X,R,WF) :- is_one_element_avl(A,Y),!,
4904 ? kernel_equality:equality_objects_wf_no_enum(X,Y,R,WF).
4905 membership_avl_set_wf(A,_X,R,_WF) :-
4906 quick_definitely_maximal_set_avl(A),!,
4907 R=pred_true.
4908 membership_avl_set_wf(A,X,R,WF) :- reify_avl_membership(A,X,R,FullReification),
4909 (FullReification==true
4910 -> true %print_term_summary(full_reification(A,X,R)),nl,nl %% did slow down e.g. Bosch Deadlock v9, seems no longer the case
4911 ? ; when((ground(X);nonvar(R)),membership_avl_set_wf2(A,X,R,WF))).
4912
4913 ?membership_avl_set_wf2(A,X,R,WF) :- R==pred_true,!, element_of_avl_set_wf(A,X,WF).
4914 membership_avl_set_wf2(A,X,R,WF) :- R==pred_false,!, not_element_of_custom_set_wf(X,avl_set(A),WF).
4915 membership_avl_set_wf2(AVL,X,R,_WF) :-
4916 ground_element_can_be_added_or_removed_to_avl(X), !,
4917 ? (safe_avl_member(X,AVL) %safe_avl_member_ground(X,AVL)
4918 -> R=pred_true ; R=pred_false).
4919 membership_avl_set_wf2(AVL,X,Res,WF) :- % X is ground but cannot be added
4920 ? (Res \== pred_false, element_of_avl_set_wf(AVL,X,WF), Res=pred_true
4921 ;
4922 Res \== pred_true, not_element_of_custom_set_wf(X,avl_set(AVL),WF), Res=pred_false).
4923
4924 membership_global_set(GS,_X,R,_WF) :- is_maximal_global_set(GS),!,
4925 R=pred_true.
4926 membership_global_set(GS,X,R,WF) :- ground(X),!,
4927 (element_of_global_set_wf(X,GS,WF) -> R=pred_true ; R=pred_false).
4928 membership_global_set(GS,X,R,_WF) :- get_integer_set_interval(GS,Low,Up),!,
4929 membership_interval(X,Low,Up,R).
4930 membership_global_set(GS,X,R,WF) :- % this case should probably never apply
4931 (GS=='FLOAT' -> true % currently it actually is also treated like REAL
4932 ; print(uncovered_membership(GS,X,R,WF)),nl),
4933 when(ground(X), (element_of_global_set_wf(X,GS,WF) -> R=pred_true ; R=pred_false)).
4934
4935 membership_interval(X,Low,Up,Res) :- nonvar(Up),Up=inf,!,X=int(IX),
4936 b_interpreter_check:check_arithmetic_operator('<=',Low,IX,Res).
4937 membership_interval(X,Low,Up,Res) :- kernel_equality:in_nat_range_test(X,int(Low),int(Up),Res).
4938
4939 :- use_module(bool_pred).
4940 closure_membership_wf(X,[ZZZZ],[integer],CondClosure,Res,_WF) :-
4941 is_interval_closure_body(CondClosure,ZZZZ,LOW,UP),!,
4942 kernel_equality:in_nat_range_test(X,int(LOW),int(UP),Res).
4943 % TO DO: deal with open intervals 0..inf ...
4944 closure_membership_wf(X,Par,Types,Body,Res,WF) :-
4945 is_member_closure(Par,Types,Body,_Type,VAL),
4946 (VAL=value(_) ; VAL = cartesian_product(b(value(A),_,_),b(value(B),_,_))),!,
4947 (VAL=value(Set)
4948 ? -> kernel_objects:membership_test_wf(Set,X,Res,WF)
4949 ; kernel_equality:cartesian_pair_test_wf(X,A,B,Res,WF)).
4950 closure_membership_wf(X,Par,Typ,Body,Res,WF) :-
4951 is_not_member_closure(Par,Typ,Body,_Type,value(Set)),!,
4952 bool_pred:negate(ResXSet,Res), % was kernel_equality:inv_mem_obj(ResXSet,Res),
4953 kernel_objects:membership_test_wf(Set,X,ResXSet,WF).
4954 % TO DO: if closure = POW closure -> translate into subset_test pow_subset
4955 % TO DO: support a few other closures related to symbolic unary/binary operators: closure1, POW(..), ... ?
4956 % TO DO: expand if set is small
4957 closure_membership_wf(X,Par,Types,Body,Res,WF) :- ground_value(X),!,
4958 closure_membership_ground_wf(X,closure(Par,Types,Body),Res,WF).
4959 closure_membership_wf(X,Par,Types,Body,Res,WF) :-
4960 CS = closure(Par,Types,Body),
4961 is_small_specific_custom_set(CS,100),
4962 try_expand_and_convert_to_avl_wf(CS,Expanded,closure_membership_wf,'',WF),
4963 nonvar(Expanded), Expanded=avl_set(_),
4964 !,
4965 membership_custom_set_wf(Expanded,X,Res,WF).
4966 closure_membership_wf(X,Par,Types,Body,Res,WF) :-
4967 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
4968 get_texpr_info(Body,BodyInfo),
4969 \+ 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)
4970 % TO DO: add recursive parameter below in set_up_typed_localstate2; + in which other circumstances do we need to set up recursion identifier !
4971 % Try reifiyng the body
4972 NegationContext=positive,
4973 copy_wf_start(WF,closure_membership_wf,CWF),
4974 b_interpreter:set_up_typed_localstate2(Par,Types,BodyInfo,ParValues,TypedVals,[],State,NegationContext),
4975 %couplise_list(Types,XType),
4976 convert_list_into_pairs(ParValues,SingleParValue),
4977 kernel_objects:equal_object(X,SingleParValue,closure_membership_wf),
4978 b_interpreter_check:b_check_boolean_expression(Body,[],State,CWF,PredRes),
4979 !,
4980 (debug_mode(on) -> print('REIFICATION of closure: '), translate:print_bexpr(Body),nl, print(pred_res(X,PredRes)),nl ; true),
4981 b_enumerate:b_tighter_enumerate_all_values(TypedVals,WF), % not necessary ?? as X should get enumerated
4982 Res=PredRes,
4983 copy_wf_finish(WF,CWF).
4984 closure_membership_wf(X,Par,Types,Body,Res,WF) :-
4985 when( (ground(X);nonvar(Res)), %%
4986 % 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
4987 closure_membership_ground_wf(X,closure(Par,Types,Body),Res,WF)).
4988
4989 closure_membership_ground_wf(X,CS,Res,WF) :- nonvar(Res),!,
4990 % this optimization is checked in test 1452
4991 (Res==pred_true -> element_of_custom_set_wf(X,CS,WF) ; not_element_of_custom_set_wf(X,CS,WF)).
4992 closure_membership_ground_wf(X,CS,Res,WF) :-
4993 % to ensure that we leave no choice point behind we have to force full evaluation of element/not_element calls:
4994 % hence we do not call element_of_custom_set_wf or not_element_of_custom_set_wf below !!
4995 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;
4996 % used to be important for test 1146, but this is no longer the case
4997 %term_variables(CS,Vars),print(closure_membership_ground_wf_aux(LWF,vars(Vars),CS)),nl,
4998 ground_value_check(CS,CSGr),
4999 %when((nonvar(LWF),(nonvar(CSGr);nonvar(Res))),closure_membership_ground_wf_aux(X,CS,Res)).
5000 block_closure_membership_ground_wf_aux(X,CS,Res,CSGr,LWF,WF). % Note: wrong block in commit 332cb17487017d819e9140427b1017a3045b3685 caused problem for test 1162
5001
5002 :- block block_closure_membership_ground_wf_aux(?,?,?,?,-,?),
5003 block_closure_membership_ground_wf_aux(?,?,-,-,?,?).
5004 block_closure_membership_ground_wf_aux(X,CS,Res, _,_,WF) :-
5005 ? closure_membership_ground_wf_aux(X,CS,Res,WF).
5006
5007 % X & CS are ground or Res is known
5008 closure_membership_ground_wf_aux(X,CS,Res,WF) :- Res==pred_true,!,
5009 element_of_custom_set_wf(X,CS,WF).
5010 closure_membership_ground_wf_aux(X,CS,Res,WF) :- Res==pred_false,!,
5011 not_element_of_custom_set_wf(X,CS,WF).
5012 closure_membership_ground_wf_aux(X,CS,Res,_WF) :-
5013 % we know that X is a ground value and CS is ground: we can determine completely whether X is element of CS or not
5014 ? if(element_of_custom_set(X,CS),Res=pred_true, Res=pred_false).
5015 /* used to be: (Res \== pred_false, element_of_custom_set(X,CS), Res=pred_true
5016 ; Res \== pred_true, not_element_of_custom_set(X,CS), Res=pred_false)).
5017 */
5018
5019
5020
5021 :- use_module(kernel_objects,[element_of_global_set/2,element_of_global_set_wf/3]).
5022 element_of_custom_set_wf(X,CS,WF) :-
5023 ? element_of_custom_set_wf2(CS,X,WF). %, print(check_ok(X)),nl.
5024
5025 element_of_custom_set_wf2(node(A,B,C,D,E),X,WF) :-
5026 add_internal_error('Unwrapped avl_set: ',element_of_custom_set_wf2(node(A,B,C,D,E),X,WF)),fail.
5027 element_of_custom_set_wf2(global_set(GS),X,WF) :- element_of_global_set_wf(X,GS,WF).
5028 element_of_custom_set_wf2(freetype(ID),X,WF) :-
5029 (is_maximal_freetype(ID) -> true
5030 ; add_internal_error('Uncovered case: ',element_of_custom_set_wf2(freetype(ID),X,WF))
5031 ). % we assume freetypes to be maximal !
5032 ?element_of_custom_set_wf2(avl_set(AVL),X,WF) :- element_of_avl_set_wf(AVL,X,WF).
5033 element_of_custom_set_wf2(closure(Parameters,PT,Cond),X,WF) :-
5034 ? element_of_closure(X,Parameters,PT,Cond,WF).
5035
5036 element_of_avl_set_wf(node(Y,_,_,empty,empty),X,WF) :- !,
5037 ? kernel_objects:equal_object_wf(X,Y,element_of_custom_set_wf2,WF).
5038 ?element_of_avl_set_wf(AVL,X,_WF) :- ground_value(X),!, safe_avl_member(X,AVL). %safe_avl_member_ground(X,AVL).
5039 element_of_avl_set_wf(AVL,X,WF) :-
5040 avl_approximate_size(AVL,10,ApproxSize),
5041 ? element_of_avl_set_wf(AVL,ApproxSize,X,WF).
5042
5043 :- use_module(clpfd_tables).
5044
5045 element_of_avl_set_wf(AVL,ApproxSize,X,WF) :-
5046 % first check if worthwhile to attempt table treatment
5047 % after fixing table/2 bug runtimes have slowed down and test 1753 became much slower
5048 % for test 1753 a threshold of < 63 would be ideal; but test 1716 requires size 91
5049 % TODO: re-evaluate when SICStus 4.8 available
5050 preferences:preference(use_clpfd_solver,true),
5051 preferences:preference(solver_strength,SS),
5052 ApproxSize < 100+SS,
5053 (var(X) -> true
5054 ; X = (X1,_X2) -> (ground_value(X1) -> ApproxSize < 10+SS ; true)
5055 ; X=rec(_) -> true
5056 %; X=int(_) -> true ; X=fd(_,_) -> true % for scalar values we already use in_fd_value_list_wf via avl_fd_value_check
5057 ),
5058 can_translate_avl_to_table(AVL,SkeletonType,WF),
5059 !,
5060 ? check_element_of_avl_with_table(X,SkeletonType,AVL,WF).
5061 element_of_avl_set_wf(AVL,ApproxSize,X,WF) :-
5062 ? propagate_avl_element_information(X,AVL,ApproxSize,WF), %translate:translate_bvalue(avl_set(AVL),SS),
5063 get_bounded_wait_flag(ApproxSize,element_of_avl(X),WF,WF1),
5064 ? element_of_avl_set_wf3(X,AVL,ApproxSize,WF1,WF).
5065
5066
5067 % compute an approximate size (small sets are computed exactly)
5068 avl_approximate_size(AVL,Size) :- avl_approximate_size(AVL,10,Size).
5069
5070 avl_approximate_size(AVL,HeightBound,Size) :- var(AVL),!,
5071 add_internal_error('AVL Set is variable: ', avl_approximate_size(AVL,HeightBound,Size)),
5072 Size=1000000.
5073 avl_approximate_size(AVL,HeightBound,Size) :- % when the AVL gets too large; not so important that we have a precise estimation anyway
5074 % so: save some time and just compute height
5075 avl_height(AVL,Height),
5076 (Height>HeightBound
5077 -> Size is floor(2**Height-1)
5078 ; avl_size(AVL,Size)).
5079
5080 :- block element_of_avl_set_wf3(-,?,?,-,?).
5081 element_of_avl_set_wf3(X,AVL,_ApproxSize,_WF1,_WF) :- var(X), !,
5082 ? safe_avl_member(X,AVL).
5083 % TO DO: if randomise_enumeration_order is true then choose elements in random order
5084 element_of_avl_set_wf3((X,Y),AVL,ApproxSize,WF1,WF) :- !,
5085 ground_value_check(X,GrX), % as soon as X is ground we can efficiently find possible values for Y
5086 % TODO: it could be that X is also a pair or a record with first field known;
5087 % see flexible_decompose_index and safe_flex_avl_member_default_wf
5088 ? block_couple_element_of_avl_set_grX_wf1(X,Y,AVL,ApproxSize,GrX,WF1,WF).
5089 element_of_avl_set_wf3(X,AVL,_ApproxSize,WF1,_WF) :-
5090 ground_value_check(X,GrX),
5091 ? safe_avl_member_block(X,AVL,GrX,WF1).
5092
5093 :- block safe_avl_member_block(?,?,-,-).
5094 safe_avl_member_block(X,AVL,_,_) :-
5095 ? safe_avl_member(X,AVL).
5096
5097 % ---------------------------------------------------
5098
5099
5100 :- block block_couple_element_of_avl_set_grX_wf1(?, - ,?,?,-,-,?).
5101 block_couple_element_of_avl_set_grX_wf1(X,Y,AVL,ApproxSize,GrX,WF1,WF) :-
5102 var(GrX), var(WF1),
5103 !,
5104 % we know the result Y but not yet fully the input value X
5105 (ApproxSize < 129 % TO DO: improve this; unify with inverse_apply_ok(Y,X,AVL,ApproxSize) ?
5106 -> ground_value_check(Y,GrY) % wait until Y is fully known
5107 ; (preference(solver_strength,SS), ApproxSize < 129+SS)
5108 -> ground_value_check(Y,GrY)
5109 % TO DO: we could look at avl_min and avl_max and estimate spread of range keys
5110 ; cond_perfmessage([data_validation_mode/false],no_inverse_avl_lookup(ApproxSize,Y)) % do not bind GrY; we wait until GrX or WF1 is bound
5111 ),
5112 block_couple_element_of_avl_set_grX_grY_wf1(X,Y,AVL,ApproxSize,GrX,GrY,WF1,WF).
5113 block_couple_element_of_avl_set_grX_wf1(X,Y,AVL,_ApproxSize,GrX,WF1,WF) :-
5114 ? couple_element_of_avl_set(X,Y,AVL,GrX,WF1,WF).
5115
5116 :- block block_couple_element_of_avl_set_grX_grY_wf1(?,?,?,?, -,-,-,?).
5117 block_couple_element_of_avl_set_grX_grY_wf1(X,Y,AVL,_ApproxSize, GrX,_GrY,WF1,WF) :-
5118 var(GrX), var(WF1), % i.e., Y is known
5119 % we know the result Y but not yet fully the input value X
5120 %inverse_apply_ok(Y,X,AVL,ApproxSize),
5121 !,
5122 inverse_get_possible_values(X,Y,AVL,Res),
5123 Res = avl_set(InvAVL),
5124 element_of_avl_set_wf(InvAVL,X,WF).
5125 block_couple_element_of_avl_set_grX_grY_wf1(X,Y,AVL,_ApproxSize,GrX,_GrY,WF1,WF) :-
5126 ? couple_element_of_avl_set(X,Y,AVL,GrX,WF1,WF).
5127
5128
5129 % special treatment for relations: if the first component is known: then we can check how many images there are
5130 couple_element_of_avl_set(X,Y,AVL,GrX,WF1,WF) :-
5131 nonvar(WF1), var(GrX), %\+ground(X),
5132 !,
5133 ? safe_flex_avl_member_default_wf((X,Y),AVL,WF).
5134 couple_element_of_avl_set(X,Y,AVLRelation,_GrX,_,WF) :- % X must be ground
5135 get_template(Y,TY,_ToUnifyAfter), % was copy_term(Y,CY) but could cause issues with closures with variables
5136 copy_term(TY,CY), % avoid that we instantiate Y and trigger co-routines
5137 findall(CY,avl_member_pair_arg1_ground(X,CY,AVLRelation),Images),
5138 Images \= [],
5139 construct_avl_from_lists_wf(Images,AVL,WF),
5140 ? element_of_custom_set_wf2(AVL,Y,WF). % will set up waitflag if necessary
5141
5142 % a version of safe_avl_member_default_wf which tries to flexibly find a usable index into the AVL first
5143 % it checks if a value can be decomposed into a ground index and the rest of a value
5144 % it also works for records indexing on first field
5145 % see tests 2351, 2353, 1966;
5146 safe_flex_avl_member_default_wf(Element,AVL,WF) :-
5147 \+ avl_height_less_than(AVL,4), % AVL tree large enough for indexing; check not necessary?; see test 2287
5148 flexible_decompose_index(Element,Key,Rest1,Path),!, % TODO: if fails: perfmessage
5149 % see Machine_Nov25/RVF428_MSTE_FOLIO.mch where this optimisation is very useful
5150 avl_fetch_with_flexible_index(Key, Path, AVL ,Rest2),
5151 kernel_objects:equal_object_wf(Rest1,Rest2,avl_fetch_with_flexible_index,WF).
5152 safe_flex_avl_member_default_wf(Element,AVL,WF) :-
5153 ? safe_avl_member_default_wf(Element,AVL,WF).
5154
5155 % set Res -> pred_true or pred_false if membership can be decided early
5156 % interval closures already dealt with by closure_membership
5157 % maximal sets are also already dealt with by membership_custom_set
5158 reify_avl_membership(AVL,Element,Res,FullReification) :-
5159 is_avl_simple_set(AVL,Type),
5160 preferences:preference(use_clpfd_solver,true), % to do: require maybe only for integer type !?
5161 \+ ground_value(Element),
5162 !,
5163 reify_avl_mem2(Type,Element,AVL,Res,FullReification).
5164 reify_avl_membership(_,_,_,false).
5165
5166
5167 is_avl_simple_set(node(El,_True,_,_,_),Type) :- simple_type(El,Type).
5168 simple_type(int(_),integer).
5169 simple_type(fd(_,GS),global(GS)).
5170
5171
5172 reify_avl_mem2(integer,int(El),AVL,Res,FullReification) :-
5173 avl_min(AVL,int(Min)), avl_max(AVL,int(Max)),
5174 (reify_integer_avl_mem(AVL,Min,Max) % reify if AVL small enough
5175 -> avl_domain(AVL,R),project_avl_domain_on_fd(R,FDList),
5176 clpfd_reify_inlist(El,FDList,FDRes,Posted),
5177 propagate_fd_membership(FDRes,Res,inlist(El,FDList)),
5178 FullReification=Posted
5179 ; clpfd_interface:try_post_constraint((El in Min..Max) #<=> FDRes),
5180 propagate_not_membership(FDRes,Res,int(El,Min,Max)),
5181 FullReification=false
5182 ).
5183 % this could also be enabled with CLPFD = FALSE ?? no overflows are possible
5184 reify_avl_mem2(global(GS),fd(El,GS),AVL,Res,FullReification) :-
5185 avl_domain(AVL,R),project_avl_domain_on_fd(R,FDList),
5186 b_global_sets:b_get_fd_type_bounds(GS,Low,Up),
5187 (is_full_fdlist(FDList,Low,Up)
5188 -> Res=pred_true, % all the values are in the list; it must be a member
5189 % normally this should also be detected by clpfd_reify_inlist, unless no constraint was set up for El
5190 % 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
5191 FullReification=true
5192 ; clpfd_reify_inlist(El,FDList,FDRes,Posted),
5193 propagate_fd_membership(FDRes,Res,inlist(El,FDList)),
5194 FullReification=Posted
5195 ).
5196 %reify_avl_mem2(global(GS),fd(El,GS),AVL,Res) :-
5197 % avl_min(AVL,fd(Min,GS)), avl_max(AVL,fd(Max,GS)),
5198 % clpfd_interface:try_post_constraint((El in Min..Max) #<=> FDRes),
5199 % propagate_not_membership(FDRes,Res,fd(El,GS,Min,Max)).
5200
5201 % assumes list is sorted
5202 is_full_fdlist(List,Low,Up) :- integer(Up), is_full_fdlist2(List,Low,Up).
5203 is_full_fdlist2([],Low,Up) :- Low>Up.
5204 is_full_fdlist2([Low|T],Low,Up) :- L1 is Low+1, is_full_fdlist2(T,L1,Up).
5205
5206 % check if avl small enough to call clpfd_reify_inlist
5207 reify_integer_avl_mem(_AVL,Min,Max) :- MaxSizeM1 is Max-Min, MaxSizeM1 =< 20,!.
5208 reify_integer_avl_mem(AVL,_Min,_Max) :- avl_height_less_than_with_solver_strength(AVL,5).
5209
5210
5211
5212 project_avl_domain_on_fd([],[]).
5213 project_avl_domain_on_fd([H|T],[PH|PT]) :- project_avl_domain(H,PH), project_avl_domain_on_fd(T,PT).
5214 project_avl_domain(int(X),X).
5215 project_avl_domain(fd(X,_),X).
5216
5217
5218 :- block propagate_fd_membership(-,-,?).
5219 % if we make it propagate_fd_membership(-,-?) Bosch examples becomes much slower ?
5220 % Indeed: membership_custom_set will already force membership or non-membership !
5221 %propagate_fd_membership(X,M,Info) :- var(X),!, print(propagate_fd(X,M,Info)),nl, (M=pred_true ->X=1 ; X=0).
5222 propagate_fd_membership(1,pred_true,_Info).
5223 propagate_fd_membership(0,pred_false,_Info).
5224
5225 :- block propagate_not_membership(-,?,?).
5226 propagate_not_membership(1,_,_). % there could be elements in the interval which are not in the set
5227 propagate_not_membership(0,Res,_Info) :-
5228 Res=pred_false.
5229
5230 % -----------------
5231
5232 % fails if not possible to quickly compute approximate size
5233 quick_custom_explicit_set_approximate_size(V,_) :- var(V),!,fail.
5234 quick_custom_explicit_set_approximate_size(avl_set(AVL),Size) :- !,
5235 quick_avl_approximate_size(AVL,Size).
5236 quick_custom_explicit_set_approximate_size(CS,Size) :-
5237 card_for_specific_custom_set(CS,Size,Code),
5238 on_enumeration_warning(call(Code),fail),
5239 atomic(Size). % inf or number; sometimes card_for_specific_custom_set can return a variable
5240
5241 :- use_module(clpfd_lists,[try_get_fd_value_list/4, get_fd_value/3, in_fd_value_list_wf/4]).
5242 % a membership propagation, but only done if it can be done quickly
5243
5244
5245 % quick_propagation_element_information(Set, Element, WF, PossiblyCompiledSet)
5246 % use last element for next iteration if you call quick_propagation_element_information in a loop
5247 :- block quick_propagation_element_information(-,?,?,?).
5248 quick_propagation_element_information(Set,_El,_,R) :-
5249 preferences:preference(use_clpfd_solver,false),
5250 !, R=Set.
5251 quick_propagation_element_information(avl_set(AVL),Element,WF,NewSet) :- !,
5252 quick_avl_approximate_size(AVL,Size),
5253 NewSet=avl_set_with_size(AVL,Size),
5254 propagate_avl_element_information_direct(Element,AVL,Size,WF).
5255 quick_propagation_element_information(avl_set_with_size(AVL,Size),Element,WF,NewSet) :- !,
5256 NewSet = avl_set_with_size(AVL,Size),
5257 propagate_avl_element_information_direct(Element,AVL,Size,WF).
5258 quick_propagation_element_information(closure(P,T,B),Element,WF,NewSet) :- !,
5259 NewSet = closure(P,T,B),
5260 element_of_closure(Element,P,T,B,WF).
5261 quick_propagation_element_information(fd_value_list(FDList,GroundList,Type),El,WF,NewSet) :- !,
5262 NewSet = fd_value_list(FDList,GroundList,Type),
5263 get_fd_value(Type,El,ElFD),
5264 in_fd_value_list_wf(GroundList,ElFD,FDList,WF).
5265 quick_propagation_element_information(Set,El,WF,NewSet) :-
5266 try_get_fd_value_list(Set,Type,FDList,GroundList),!,
5267 FDList \= [], % if list is empty membership fails
5268 NewSet = fd_value_list(FDList,GroundList,Type),
5269 % clpfd_inlist requires list of integers as second argument
5270 get_fd_value(Type,El,ElFD),
5271 % We could apply filter_non_matching_elements here
5272 in_fd_value_list_wf(GroundList,ElFD,FDList,WF).
5273 quick_propagation_element_information(Set,_,_,Set).
5274
5275 % -----------------
5276
5277 % infer information about an element of an AVL set
5278 propagate_avl_element_information(Element,AVL,Size,WF) :-
5279 (preferences:preference(use_clpfd_solver,true)
5280 ? -> propagate_avl_element_information_direct(Element,AVL,Size,WF)
5281 ; true).
5282
5283 propagate_avl_element_information_direct(Element,AVL,Size,WF) :-
5284 (Size<100 -> %30 which magic constant to use here; use larger value in SMT mode ?
5285 ? propagate_avl_element_information_small(Element,AVL,WF)
5286 ; is_avl_fd_index_set(AVL,Type) ->
5287 propagate_avl_element_information_large(Type,Element,AVL),
5288 (Size < 4000, nonvar(Element), Element = (_,_) % another magic constant
5289 -> Prio is Size // 60,
5290 get_wait_flag(Prio,propagate_avl_element_information(Element),WF,LWF),
5291 propagate_avl_el_large_block(Element,AVL,WF,LWF) % will do precise propagation
5292 ; true)
5293 ; true).
5294 % TO DO: we could call in_nat_range_wf; this way it would also work in non-CLPFD mode
5295
5296 :- block propagate_avl_el_large_block(?,?,?,-).
5297 propagate_avl_el_large_block((A,B),_,_,_) :-
5298 (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
5299 !.
5300 propagate_avl_el_large_block(Element,AVL,WF,_LWF) :-
5301 % TO DO: maybe look if we should not use clpfd_list, but only upper & lower bound
5302 propagate_avl_element_information_small(Element,AVL,WF). % will do precise propagation.
5303
5304 :- use_module(clpfd_lists,[avl_fd_value_check/4]).
5305 :- use_module(clpfd_interface,[catch_and_ignore_clpfd_overflow/2]).
5306 propagate_avl_element_information_small(Element,AVL,WF) :-
5307 ? catch_and_ignore_clpfd_overflow(propagate_avl_element_information_small, % relevant test e.g. 1708 (with used_ids_defined_by_equality)
5308 avl_fd_value_check(AVL,Element,WF,_FullyChecked)).
5309
5310 propagate_avl_element_information_large(Type,El,AVL) :-
5311 avl_min(AVL,Min), avl_max(AVL,Max),
5312 % if Size small enough and smaller than Max-Min we call clpfd_inlist on domain
5313 % Note: overflows should be caught below; we could check that Min/Max are within CLPFD range
5314 couple_prj1_in_range(Type,El,Min,Max).
5315
5316 couple_prj1_in_range(integer,int(El),int(Min),int(Max)) :- clpfd_interface:clpfd_inrange(El,Min,Max).
5317 couple_prj1_in_range(global(GS),fd(El,GS),fd(Min,GS),fd(Max,GS)) :- clpfd_interface:clpfd_inrange(El,Min,Max).
5318 couple_prj1_in_range(couple_prj1(T),(El,_),(Min,_),(Max,_)) :- couple_prj1_in_range(T,El,Min,Max).
5319 couple_prj1_in_range(rec_first_field(Name,T),rec([field(Name,El)|TF]),
5320 rec([field(Name,Min)|TMin]),rec([field(Name,Max)|_])) :-
5321 (var(TF)
5322 -> copy_field_names(TMin,TF) % if Fields not yet instantiated: copy over all fields
5323 ; true),
5324 couple_prj1_in_range(T,El,Min,Max).
5325
5326 copy_field_names([],[]).
5327 copy_field_names([field(N,_)|T],[field(N,_)|CT]) :- copy_field_names(T,CT).
5328
5329 % check if the first component of the AVL elements of a type such that we can propagate FD information
5330 is_avl_fd_index_set(node(El,_True,_,_,_),Type) :-
5331 simple_index_type(El,Type).
5332 simple_index_type((El,_),couple_prj1(T)) :- simple_index_type(El,T).
5333 simple_index_type(int(_),integer).
5334 simple_index_type(fd(_,GS),global(GS)).
5335 simple_index_type(rec(Fields),rec_first_field(Name,T)) :- nonvar(Fields),
5336 Fields = [field(Name,El)|_],
5337 simple_index_type(El,T).
5338 %simple_index_type((int(_),_),couple_integer).
5339 %simple_index_type(((int(_),_),_),couple_couple_integer).
5340 %simple_index_type((fd(_,GS),_),couple_global(GS)).
5341
5342
5343 /* avoid instantiating non-normalised with normalised values leading to failure */
5344 :- assert_must_succeed((X=(fd(1,'Name'),fd(2,'Name')), A=node(X,true,0,empty,empty),
5345 custom_explicit_sets:safe_avl_member(X,A) )).
5346
5347 ?safe_avl_member(X,AVL) :- var(X), !, my_avl_member(X,AVL).
5348 %safe_avl_member(Value,AVL) :- decompose_index(Value,Key,RestVal), avl_fetch_indexed(Value,Key,RestVal,AVL).
5349 %safe_avl_member(X,AVL) :- ground_value(X), convert_to_avl_inside_set(X,AX), !, avl_fetch(AX,AVL).
5350 ?safe_avl_member(X,AVL) :- safe_flex_avl_member_default_wf(X,AVL,no_wf_available).
5351
5352
5353 % a version of safe_avl_member where the first argument is guaranteed to be ground
5354 % somehow using this seems to slow-down evaluation for vesg_Dec12; Caching ??
5355 %safe_avl_member_ground(X,AVL) :-
5356 % convert_to_avl_inside_set(X,AX), !, avl_fetch(AX,AVL).
5357 %safe_avl_member_ground((X,Y),AVL) :- !, avl_member_pair_arg1_ground(X,Y,AVL).
5358 %safe_avl_member_ground(X,AVL) :- safe_avl_member_default_wf(X,AVL,no_wf_available).
5359
5360
5361 % can be used to try and lookup a function value without creating WD errors, ...
5362 % used in b_compiler to compile function applications
5363 try_apply_to_avl_set_wf(X,Y,AVL,WF) :- ground_value(X),
5364 avl_member_pair_arg1_ground_wf(X,Y,AVL,WF).
5365
5366 % we know X is ground; typically Y is a free variable and it is used within a findall:
5367 avl_member_pair_arg1_ground(X,Y,AVL) :-
5368 ? avl_member_pair_arg1_ground_wf(X,Y,AVL,no_wf_available).
5369
5370 avl_member_pair_arg1_ground_wf(X,Y,AVL,WF) :- convert_to_avl_inside_set(X,AX), !,
5371 get_template(Y,RY,ToUnifyAfter),
5372 ? avl_fetch_pair(AX,AVL,RY), % see flexible_decompose_index, safe_flex_avl_member_default_wf
5373 unify_after_wf(ToUnifyAfter,WF).
5374 avl_member_pair_arg1_ground_wf(X,Y,AVL,_WF) :-
5375 safe_avl_member_default((X,Y),AVL).
5376
5377 safe_avl_member_default(X,AVL) :-
5378 ? safe_avl_member_default_wf(X,AVL,no_wf_available).
5379 safe_avl_member_default_wf(X,AVL,WF) :- % statistics(runtime,_),
5380 get_template(X,Template,ToUnifyAfter),
5381 ? my_avl_member(Template,AVL),
5382 % statistics(runtime,[_,T2]), print(avl_member(Template,T2)),nl,
5383 ? unify_after_wf(ToUnifyAfter,WF). % kernel_objects:equal_object(Template,X)).
5384
5385 unify_after_wf([],_).
5386 ?unify_after_wf([A/B|T],WF) :- kernel_objects:equal_object_wf(A,B,unify_after,WF),
5387 unify_after_wf(T,WF).
5388
5389
5390
5391 get_template(A,R,ToUnifyAfter) :-
5392 (var(A) -> ToUnifyAfter=[A/R]
5393 ; get_template2(A,R,ToUnifyAfter) -> true
5394 ; add_internal_error('Could_not_get_template: ',get_template(A,R,_))).
5395
5396 get_template2((A,B),(TA,TB),ToUnifyAfter) :- get_template(A,TA,ToUnifyAfter1), get_template(B,TB,ToUnifyAfter2),
5397 append(ToUnifyAfter1,ToUnifyAfter2,ToUnifyAfter). % TO DO: use DifferenceLists / DCG
5398 get_template2(int(X),int(X),[]).
5399 get_template2(fd(A,B),fd(A,B),[]).
5400 get_template2([],[],[]).
5401 get_template2(pred_false /* bool_false */,pred_false /* bool_false */,[]).
5402 get_template2(pred_true /* bool_true */,pred_true /* bool_true */,[]).
5403 get_template2([H|T],R,ToUnifyAfter) :-
5404 (ground_value(H),ground_value(T)
5405 -> convert_to_avl_inside_set([H|T],R),ToUnifyAfter=[]
5406 ; ToUnifyAfter=[[H|T]/R]).
5407 % ; R=avl_set(A), ToUnifyAfter=[[H|T]/avl_set(A)]).
5408 get_template2(closure(P,T,B),R,[]) :- ground_value(closure(P,T,B)),
5409 expand_closure_to_avl_wf(P,T,B,R,no_wf_available),!.
5410 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 ?
5411 %get_template2(closure_x(_,_,_),_AVL_OR_EMPTY).
5412 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 ??
5413 get_template2(string(X),string(X),[]).
5414 get_template2(term(X),term(X),[]).
5415 get_template2(freetype(X),R,[]) :- convert_to_avl_inside_set(freetype(X),R).
5416 get_template2(rec(Fields),rec(TFields),ToUnifyAfter) :- get_fields_template(Fields,TFields,ToUnifyAfter).
5417 get_template2(freeval(ID,Case,Value),freeval(ID,Case,TValue),ToUnifyAfter) :- get_template(Value,TValue,ToUnifyAfter).
5418 get_template2(global_set(GS),R,[]) :- convert_to_avl_inside_set(global_set(GS),R).
5419
5420
5421 get_fields_template(A,R,[rec(A)/rec(R)]) :- var(A),!.
5422 get_fields_template([],[],ToUnifyAfter) :- !, ToUnifyAfter=[].
5423 get_fields_template([field(Name,Val)|T],[field(Name,TVal)|TT],ToUnifyAfter) :- nonvar(Name),!,
5424 get_template(Val,TVal,ToUnifyAfter1),
5425 get_fields_template(T,TT,ToUnifyAfter2), append(ToUnifyAfter1,ToUnifyAfter2,ToUnifyAfter).
5426 get_fields_template(A,R,[rec(A)/rec(R)]).
5427
5428
5429 % succeed if we can decide membership of an avl_set on the spot
5430 quick_test_avl_membership(AVL,X,Res) :-
5431 element_can_be_added_or_removed_to_avl(X),
5432 convert_to_avl_inside_set(X,AX),
5433 (avl_fetch(AX,AVL) -> Res=pred_true ; Res=pred_false).
5434
5435 % ---------------------
5436
5437 % a dispatch predicate
5438 my_avl_member(Key,AVL) :-
5439 (preferences:preference(randomise_enumeration_order,true)
5440 ? -> random_avl_member(Key,AVL) ; avl_member_opt(Key,AVL)).
5441 :- use_module(library(random),[random/3]).
5442 random_avl_member(Key,AVL) :- avl_height(AVL,Height), H1 is Height+1, random_avl_member(Key,H1,AVL).
5443 % 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)
5444 random_avl_member(Key, H, node(K,_,_,L,R)) :-
5445 random(1,H,1), !, H1 is H-1,
5446 (Key=K ; random_avl_member(Key,H1,L) ; random_avl_member(Key,H1,R)).
5447 random_avl_member(Key, H, node(K,_,_,L,R)) :- random(1,3,1), !, H1 is H-1,
5448 (random_avl_member(Key,H1,L) ; random_avl_member(Key,H1,R) ; Key=K).
5449 random_avl_member(Key, H, node(K,_,_,L,R)) :- H1 is H-1,
5450 (random_avl_member(Key,H1,R) ; random_avl_member(Key,H1,L) ; Key=K).
5451
5452 % a variation of avl_member from library(avl) which tries to avoid leaving choice points behind
5453 avl_member_opt(Key, node(K,_,_,L,R)) :-
5454 ( avl_member_opt(Key, L)
5455 ; R=empty -> Key = K % avoid trailing choice_point
5456 ? ; (Key=K ; avl_member_opt(Key, R))
5457 ).
5458
5459 % ---------------------
5460
5461 :- use_module(kernel_objects,[check_element_of_wf/3,not_element_of_wf/3]).
5462 :- use_module(memoization,[element_of_memoization_closure/6]).
5463 element_of_special_closure(interval(LOW,UP),X,WF,_,_,_) :- !,
5464 %hit_profiler:add_profile_hit(in_nat_range(X,LOW,UP,CondClosure)),
5465 kernel_objects:in_nat_range_wf(X,int(LOW),int(UP),WF).
5466 element_of_special_closure(member_closure(_ID,_Type,VAL),X,WF,_,_,_) :-
5467 (VAL=value(_) ; VAL = cartesian_product(b(value(A),_,_),b(value(B),_,_))),!,
5468 %hit_profiler:add_profile_hit(in_member_closure(X,Par,Typ,Body)),
5469 ? (VAL=value(Set) -> check_element_of_wf(X,Set,WF)
5470 ; X=(XA,XB),
5471 kernel_objects:check_element_of_wf(XA,A,WF),
5472 kernel_objects:check_element_of_wf(XB,B,WF)).
5473 element_of_special_closure(not_member_closure(_ID,_Type,value(Set)),X,WF,_,_,_) :- !,
5474 %hit_profiler:add_profile_hit(in_not_member_closure(X,Par,Typ,Set)),
5475 not_element_of_wf(X,Set,WF).
5476 % we used to have to add enumerator, as not_element_of does not instantiate; e.g. relevant when doing X :: GS - {y}
5477 % This is no longer required
5478 % see test 6 (../prob_examples/public_examples/B/FeatureChecks/NotMemberCheck.mch)
5479 element_of_special_closure(recursive_special_closure(RId),X,WF,Parameters,PT,CondClosure) :- !,
5480 add_recursive_parameter(Parameters,PT,X,RId,CondClosure,NewParameters,NewPT,Value,WF),
5481 element_of_normal_closure(Value,NewParameters,NewPT,CondClosure,WF).
5482 element_of_special_closure(memoization_closure(MemoID),X,WF,P,T,B) :- !,
5483 element_of_memoization_closure(MemoID,X,WF,P,T,B).
5484 element_of_special_closure(_,X,WF,Parameters,PT,CondClosure) :-
5485 % none of the special cases above apply after all
5486 element_of_normal_closure(X,Parameters,PT,CondClosure,WF).
5487
5488 :- block element_of_closure(?,-,?,?,?), element_of_closure(?,?,?,-,?).
5489 % element_of_closure(X,Para,T,Body,_WF): check if X is a member of closure(Para,T,Body)
5490 element_of_closure(X,Parameters,PT,CondClosure,WF) :-
5491 is_special_closure(Parameters,PT,CondClosure, SpecialClosure),!,
5492 %print_term_summary(element_of_special_closure(SpecialClosure,X,WF,Parameters,PT,CondClosure)), trace_in_debug_mode,
5493 ? element_of_special_closure(SpecialClosure,X,WF,Parameters,PT,CondClosure).
5494 element_of_closure(X,Parameters,PT,CondClosure,WF) :-
5495 %print_term_summary(element_of_normal_closure(X,Parameters,PT,CondClosure,WF)), trace_in_debug_mode,
5496 ? element_of_normal_closure(X,Parameters,PT,CondClosure,WF).
5497 element_of_normal_closure(X,Parameters,PT,CondClosure,WF) :-
5498 %hit_profiler:add_profile_hit(element_of_closure(X,Parameters,PT,CondClosure)),
5499 same_length(Parameters,ParValues),
5500 convert_list_into_pairs(ParValues,X),
5501 ? b_test_closure_wo_enum(Parameters,PT,CondClosure,ParValues,WF).
5502
5503 :- use_module(store,[set_up_localstate/4]).
5504 :- block b_test_closure_wo_enum(?,?,-,?,?).
5505 b_test_closure_wo_enum(Parameters,ParameterTypes,ClosurePred,ParValues,WF) :-
5506 % same_length(Parameters,ParValues), % not necessary
5507 set_up_localstate(Parameters,ParValues,[],LocalState),
5508 b_enumerate:b_type_values_in_store(Parameters,ParameterTypes,LocalState),
5509 copy_wf_start(WF,b_test_closure_wo_enum(Parameters),InnerWF),
5510 % avoid that WF0 actions triggered before we have had a chance to traverse the expression
5511 b_test_boolean_expression(ClosurePred,LocalState,[],InnerWF),
5512 ? copy_wf_finish(WF,InnerWF).
5513
5514 % recursive identifier to list of parameters with body as value
5515 % NewValue is the Value that should be checked for membership in the adapted closure; it has one argument more
5516 add_recursive_parameter(Parameters,Types,Value,TId,CondClosure,NewParameters,NewTypes,NewValue,WF) :-
5517 TId = b(identifier(RId),SetType,_), % unification replaces: get_texpr_id(TId,RId), get_texpr_type(TId,SetType),
5518 append(Parameters,[RId],NewParameters),
5519 append(Types,[SetType],NewTypes),
5520 %tools_printing:print_term_summary(recursion(Value)),nl,
5521 % TO DO check some variant decreases
5522 (kernel_waitflags:pending_abort_error(WF)
5523 -> NewValue = (_,_) % prevent further expansion of recursion, in case WD error in recursive function
5524 % TO DO: detect whether WD error occurs within recursive function,
5525 % 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
5526 ,debug_println(19,stopping_recursion_due_to_wd_error)
5527 ; NewValue = (Value,closure(Parameters,Types,CondClosure))
5528 ).
5529
5530
5531 % same as above, but without a waitflag
5532 ?element_of_custom_set(X,CS) :- element_of_custom_set2(CS,X).
5533
5534 element_of_custom_set2(global_set(GS),X) :- !,element_of_global_set(X,GS).
5535 element_of_custom_set2(freetype(ID),_) :- is_maximal_freetype(ID),!. % freetypes are always maximal at the moment
5536 element_of_custom_set2(avl_set(AVL),X) :- !,
5537 safe_avl_member(X,AVL).
5538 element_of_custom_set2(CS,X) :- init_wait_flags(WF,[element_of_custom_set2]),
5539 element_of_custom_set_wf2(CS,X,WF),
5540 ? ground_wait_flags(WF).
5541
5542 % ---------------
5543
5544 % function application for closure
5545
5546 % same as check_element_of_wf but does not wait on Y:
5547 % should also work for relation ??
5548
5549 check_element_of_function_closure(X,Y,Parameters,PT,CondClosure,WF) :-
5550 is_special_closure(Parameters,PT,CondClosure, SpecialClosure),!, % this covers recursive closures
5551 element_of_special_closure(SpecialClosure,(X,Y),WF,Parameters,PT,CondClosure).
5552 check_element_of_function_closure(X,Y, P,T,ClosureBody, WF) :-
5553 % affects test 1312, unless we add s:seq(0..9) before calling num
5554 % a special rule which tries and avoid enumerating solutions to arguments of function application
5555 % usually a function application will either be given all arguments or maybe be used in inverse
5556 is_converted_lambda_closure(P,T,ClosureBody), %is_converted_non_recursive_lambda_closure(P,T,ClosureBody),
5557 % TO DO: also make this work for recursive closures by adding recursive args (see e.g. test 1302)
5558 is_lambda_closure(P,T,ClosureBody, OtherIDs, OtherTypes, DomainPred, EXPR),
5559 (debug:debug_level_active_for(4) ->
5560 print('Apply Fun : '), translate:print_bexpr(DomainPred), print(' | '), translate:print_bexpr(EXPR),nl,
5561 get_texpr_info(ClosureBody,I), print(info(I,WF)),nl,
5562 print_term_summary((X,Y)),nl %,trace
5563 ; true),
5564 !,
5565 % alternative: annotate X,Y as inner variable ?
5566 get_texpr_info(ClosureBody,BInfo),
5567 b_interpreter:set_up_typed_localstate2(OtherIDs,OtherTypes,BInfo,ParValues,_TypedVals,[],LocalState,positive),
5568 convert_list_into_pairs(ParValues,SingleParValue),
5569 kernel_objects:equal_object_wf(X,SingleParValue,check_element_of_function_closure,WF),
5570 (is_truth(DomainPred) -> true
5571 ; init_wait_flags(InnerWF,[check_element_of_function_closure]),
5572 %copy_wf01e_wait_flags(WF,InnerWF), % we could delay copying WF0 until after test_boolean_expression of DomainPred ?
5573 b_test_boolean_expression(DomainPred,LocalState,[],InnerWF),
5574 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
5575 ground_value_check(X,GrX),
5576 (nonvar(GrX) -> copy_waitflag_store(InnerWF,WF) % block would trigger already
5577 ; ground_value_check(Y,GrY),
5578 (nonvar(GrY) -> copy_waitflag_store(InnerWF,WF) % block would trigger already
5579 ; get_last_wait_flag(check_element_of_function_closure(OtherIDs),WF,LastWF),
5580 block_copy_waitflag_store(InnerWF,WF,GrX,GrY,LastWF)
5581 )
5582 )
5583 ),
5584 b_interpreter:b_compute_expression(EXPR,LocalState,[],Y,WF).
5585 check_element_of_function_closure(X,Y, P,T,ClosureBody, WF) :-
5586 element_of_normal_closure((X,Y),P,T,ClosureBody,WF).
5587 % we could memoize on X here if /*@symbolic-memo */ pragma used and closure has special ID associated with it
5588
5589 :- block block_copy_waitflag_store(?,?,-,-,-).
5590 block_copy_waitflag_store(InnerWF,WF,_GrX,_GrY,_LWF) :-
5591 % copy waitflags from InnerWF store to WF
5592 copy_waitflag_store(InnerWF,WF).
5593
5594 /* -------------- */
5595 /* NOT_ELEMENT_OF */
5596 /* -------------- */
5597
5598 :- use_module(kernel_objects,[not_element_of_global_set/2]).
5599
5600 not_element_of_custom_set_wf(X,CS,WF) :-
5601 not_element_of_custom_set_wf2(CS,X,WF).
5602
5603 not_element_of_custom_set_wf2(global_set(GS),X,_WF) :- not_element_of_global_set(X,GS).
5604 not_element_of_custom_set_wf2(freetype(_),_,_) :- !,fail. % TO DO: what if we have List(1..3) ? can that occur ??
5605 not_element_of_custom_set_wf2(avl_set(node(Y,_,_,empty,empty)),X,WF) :- !,
5606 % X /: {Y} <=> X /= Y
5607 kernel_objects:not_equal_object_wf(X,Y,WF). % improve if X is ground
5608 not_element_of_custom_set_wf2(avl_set(AVL),X,_WF) :- !,
5609 ground_value_check(X,GrX),
5610 propagate_avl_not_element_information(X,GrX,AVL),
5611 not_element_of_avl_set_block(GrX,X,AVL).
5612 not_element_of_custom_set_wf2(closure(Parameters,PT,Cond),X,WF) :-
5613 closure_not_member(X,Parameters,PT,Cond,WF).
5614
5615 :- block not_element_of_avl_set_block(-,?,?).
5616 not_element_of_avl_set_block(_,X,AVL) :-
5617 convert_to_avl_inside_set(X,CX),
5618 \+ avl_fetch(CX,AVL). %% IMPROVE ??
5619
5620 propagate_avl_not_element_information(_,GrEl,_) :- nonvar(GrEl),!.
5621 propagate_avl_not_element_information(Element,_,AVL) :- preferences:preference(use_clpfd_solver,true),
5622 is_avl_simple_set(AVL,Type), % integer or global(GS) \+ground(Element) ,
5623 ((Type=integer -> avl_height_less_than_with_solver_strength(AVL,6) % 16-31 elements - was: avl_size<20
5624 ; true)
5625 -> !,
5626 propagate_avl_not_element_information3(Type,Element,AVL) % uses clpfd_not_inlist
5627 ; Type=integer, avl_height_less_than_with_solver_strength(AVL,15),
5628 avl_is_interval(AVL,Min,Max)
5629 -> !,
5630 kernel_objects:not_in_nat_range(Element,int(Min),int(Max)) % WF not used anyway in _wf version
5631 ).
5632 propagate_avl_not_element_information(_Element,_,AVL) :-
5633 quick_definitely_maximal_set_avl(AVL),
5634 !, % we require something not to be an element of the full set; impossible
5635 fail.
5636 % to do: check if all but one element is in set
5637 propagate_avl_not_element_information(_,_,_).
5638
5639 avl_height_less_than_with_solver_strength(AVL,Limit) :- preference(solver_strength,SS),
5640 RealLimit is Limit + SS/100,
5641 avl_height_less_than(AVL,RealLimit).
5642
5643 % try and compute a small finite cardinality for a ground value; fail if not possible
5644 try_get_finite_max_card_from_ground_value(pred_true,2).
5645 try_get_finite_max_card_from_ground_value(pred_false,2).
5646 try_get_finite_max_card_from_ground_value(fd(_,Type),Card) :-
5647 b_global_sets:b_fd_card(Type,Card), integer(Card).
5648 try_get_finite_max_card_from_ground_value((A,B),Card) :-
5649 try_get_finite_max_card_from_ground_value(A,CA),
5650 try_get_finite_max_card_from_ground_value(B,CB),
5651 Card is CA*CB,
5652 Card < 20000.
5653 try_get_finite_max_card_from_ground_value(rec(Fields),Card) :-
5654 try_get_finite_max_card_from_fields(Fields,Card).
5655 try_get_finite_max_card_from_ground_value(freeval(FreetypeId,_CaseId,_EArgs),Card) :-
5656 freetype_cardinality(FreetypeId,Card), number(Card), Card < 20000.
5657 try_get_finite_max_card_from_ground_value(avl_set(node(El,_True,_,_,_)),Card) :-
5658 try_get_finite_max_card_from_ground_value(El,CEl),
5659 CEl < 16,
5660 safe_pow2(CEl,Card).
5661 % int(_), term(floating(_)), string(_) are all infinite
5662
5663 try_get_finite_max_card_from_fields([],1).
5664 try_get_finite_max_card_from_fields([field(_,A)|TF],Card) :-
5665 try_get_finite_max_card_from_ground_value(A,CA),
5666 try_get_finite_max_card_from_fields(TF,CB),
5667 Card is CA*CB,
5668 Card < 20000.
5669
5670 :- use_module(b_global_sets,[get_global_type_value/3]).
5671 propagate_avl_not_element_information3(integer,int(El),AVL) :-
5672 avl_domain(AVL,R),project_avl_domain_on_fd(R,FDList),
5673 clpfd_interface:clpfd_not_inlist(El,FDList).
5674 propagate_avl_not_element_information3(global(GS),FD,AVL) :-
5675 get_global_type_value(FD,GS,El), % sets up the FD constraint if var; maybe we can detect inconsistency straightaway below
5676 avl_domain(AVL,R),project_avl_domain_on_fd(R,FDList), % maybe we can compute directly the complement ?
5677 clpfd_interface:clpfd_not_inlist(El,FDList).
5678
5679
5680 :- block closure_not_member(?,-,?,?,?).
5681 %, closure_not_member(-,?,?,?,?). /* El is unlikely to be instantiated by not_element_of test , but test 6 requires commenting out block declaration */
5682
5683 closure_not_member(X,Parameters,Types,Body,WF) :-
5684 is_special_closure(Parameters,Types,Body,SpecialClosure),!,
5685 not_element_of_special_closure(SpecialClosure,X,WF,Parameters,Types,Body).
5686 closure_not_member(El,Parameters,PT,Cond,WF) :-
5687 normal_closure_not_member(El,Parameters,PT,Cond,WF).
5688
5689 :- use_module(memoization,[not_element_of_memoization_closure/6]).
5690 not_element_of_special_closure(interval(LOW,UP),X,_WF,_Parameters,_Types,_Body) :-
5691 !,kernel_objects:not_in_nat_range(X,int(LOW),int(UP)).
5692 not_element_of_special_closure(member_closure(_ID,_Type,VAL),X,WF,_Parameters,_Types,_Body) :-
5693 ( VAL = value(_)
5694 ; VAL = cartesian_product(b(value(A),_,_),b(value(B),_,_))),!,
5695 %hit_profiler:add_profile_hit(member(X,Par,Typ,Body)),
5696 ( VAL=value(Set) -> kernel_objects:not_element_of_wf(X,Set,WF)
5697 ; kernel_objects:not_is_cartesian_pair(X,A,B,WF)).
5698 not_element_of_special_closure(not_member_closure(_ID,_Type,value(Set)),X,WF,_Parameters,_Types,_Body) :-
5699 !,kernel_objects:check_element_of_wf(X,Set,WF).
5700 not_element_of_special_closure(memoization_closure(MemoID),X,WF,P,T,B) :- !,
5701 not_element_of_memoization_closure(MemoID,X,WF,P,T,B).
5702 not_element_of_special_closure(recursive_special_closure(RId),X,WF,Parameters,Types,Body) :-
5703 !,
5704 add_recursive_parameter(Parameters,Types,X,RId,Body,NewParameters,NewPT,Value,WF),
5705 normal_closure_not_member(Value,NewParameters,NewPT,Body,WF).
5706
5707 not_element_of_special_closure(SC,_X,_WF,Parameters,Types,Body) :-
5708 SC \= interval(_,_),
5709 SC \= not_member_closure(_,_,_),
5710 is_definitely_maximal_closure(Parameters,Types,Body),
5711 !,
5712 fail.
5713 not_element_of_special_closure(_,X,WF,Parameters,Types,Body) :-
5714 % falling back to normal test
5715 normal_closure_not_member(X,Parameters,Types,Body,WF).
5716
5717 :- use_module(library(lists),[same_length/2]).
5718
5719 normal_closure_not_member(El,Parameters,PT,Cond,WF) :-
5720 %hit_profiler:add_profile_hit(closure_not_member(El,Parameters,PT,Cond,WF)),
5721 same_length(Parameters,ParValues),
5722 convert_list_into_pairs(ParValues,El),
5723 b_not_test_closure_wf(Parameters,PT,Cond,ParValues,WF).
5724
5725
5726
5727
5728 /* -------------------------- */
5729 /* VARIOUS CLOSURE PREDICATES */
5730 /* -------------------------- */
5731
5732
5733 :- use_module(tools,[convert_list_into_pairs/2]).
5734 :- use_module(b_interpreter,[b_test_boolean_expression/4, b_not_test_boolean_expression/4]).
5735 :- use_module(b_enumerate).
5736
5737 :- assert_pre(custom_explicit_sets:expand_closure_to_list(_,_,ClosureBody,_Result,_Done,_,_WF),
5738 (nonvar(ClosureBody),
5739 bsyntaxtree:check_if_typed_predicate(ClosureBody))).
5740 :- assert_post(custom_explicit_sets:expand_closure_to_list(_,_,_,Result,_Done,_,_WF),
5741 b_interpreter:value_type(Result)).
5742
5743 :- block expand_interval_closure_to_avl(-,?,?), expand_interval_closure_to_avl(?,-,?).
5744 expand_interval_closure_to_avl(Low,Up,Result) :-
5745 Delta is Up-Low,
5746 (Delta>9999 -> perfmessage(expanding_interval(Low,Up)) ; true),
5747 construct_interval_ord_list(Low,Up,OL),
5748 ord_list_to_avlset_direct(OL,ARes,expand_interval),
5749 equal_object(ARes,Result,expand_interval_closure_to_avl).
5750 construct_interval_ord_list(Low,Up,Res) :-
5751 (Low>Up -> Res = []
5752 ; Res = [int(Low)-true|T], L1 is Low+1, construct_interval_ord_list(L1,Up,T)
5753 ).
5754
5755 :- block expand_interval_closure_to_list(-,?,?,?), expand_interval_closure_to_list(?,-,?,?).
5756 expand_interval_closure_to_list(Low,Up,Result,Done) :-
5757 construct_interval_list(Low,Up,OL),
5758 equal_object(OL,Result,expand_interval_closure_to_list),
5759 Done=true.
5760 construct_interval_list(Low,Up,Res) :-
5761 (Low>Up -> Res = []
5762 ; Res = [int(Low)|T], L1 is Low+1, construct_interval_list(L1,Up,T)
5763 ).
5764
5765 expand_closure_to_list([X],[integer],Body,Result,Done,_,_) :-
5766 is_interval_closure_body(Body,X,Low,Up),!,
5767 expand_interval_closure_to_list(Low,Up,Result,Done).
5768 expand_closure_to_list(Par,Types,Body,Result,Done,Source,WF) :-
5769 expand_normal_closure(Par,Types,Body,CResult,CDone,expand_closure_to_list(Source),WF),
5770 ? expand_if_avl(CResult,Result,CDone,Done,Source),
5771 lazy_check_elements_of_closure(Result,CDone, Par,Types,Body,WF).
5772
5773 % Note: does slow down test 1306 (91ms mc time becomes 918 ms)
5774 % as long as a closure has not been fully expanded, lazily check elements
5775 % that are instantiated from the outside satisfy the closure predicate
5776 % Note: this can also instantiate unknown values used inside the closure body
5777 lazy_check_elements_of_closure(Result,CDone, Par,Types,Body,WF) :-
5778 (WF==no_wf_available -> true
5779 ? ; lazy_check_elements6(Result,CDone, Par,Types,Body,WF),
5780 propagate_closure_body_value_set(Par,Types,Body,Result,CDone,WF)
5781 ).
5782 % TODO: check if closure is a non-ground projection-member closure and check elements
5783 :- block lazy_check_elements6(-,-, ?,?,?,?).
5784 lazy_check_elements6(_Result,CDone, _Par,_Types,_Body,_WF) :- nonvar(CDone),!.
5785 lazy_check_elements6([H|T],CDone, Par,Types,Body,WF) :- !,
5786 ? element_of_closure(H,Par,Types,Body,WF),
5787 lazy_check_elements6(T,CDone, Par,Types,Body,WF).
5788 lazy_check_elements6(avl_set(A),_CDone, Par,Types,Body,WF) :- !,
5789 avl_max(A,X),
5790 element_of_closure(X,Par,Types,Body,WF).
5791 % TO DO: also check avl_min or even all elements ?
5792 lazy_check_elements6(_,_,_,_,_,_).
5793
5794 :- use_module(probsrc(bsyntaxtree),[create_typed_ids/3]).
5795 % lazy check elements from non-var closure body against a result
5796 % for example if we have {x| TRUE |-> x : Value } = Result and Value is not-ground,
5797 % we can check that for all elements TRUE|->x of Value the corresponding x is in Result, see test 2466
5798 % slows down test 1987
5799 :- block propagate_closure_body_value_set(?,?,?,-,-,?).
5800 % we delay until the result is known, possibly in SMT mode it could be useful to propagate earlier
5801 propagate_closure_body_value_set(ParIDs,Types,Body,Result,CDone,WF) :-
5802 var(CDone), % the closure has not yet been fully expanded
5803 % check if this closure can profit from set membership propagation:
5804 b_interpreter:is_for_all_set_membership_predicate2(Body,ParIDs,ParIDs,UnmatchedIDs,Set,_Pattern,_ParValues,_),
5805 UnmatchedIDs=[],
5806 Set = b(value(_Value),_,_), % check that the set is a value; it must be non-ground, otherwise CDone would be true
5807 create_couple_term(ParIDs,Types,CoupleTerm),
5808 SetTerm=b(value(Result),any,[]),
5809 safe_create_texpr(member(CoupleTerm,SetTerm),pred,[],RHS),
5810 create_typed_ids(ParIDs,Types,TIDs),
5811 !,
5812 propagate_closure_body_for_all(TIDs,Body,RHS,Result,CDone,WF).
5813 propagate_closure_body_value_set(_,_,_,_,_,_WF).
5814
5815 :- block propagate_closure_body_for_all(?,?,?,-,-,?).
5816 propagate_closure_body_for_all(TIDs,Body,RHS,_,CDone,WF) :- var(CDone),!,
5817 add_debug_message(closure,'Propagating from closure body to result: ',Body,Body),
5818 Infos=[],
5819 b_interpreter:b_for_all(TIDs,Infos,Body,RHS,[],[],WF).
5820 propagate_closure_body_for_all(_,_,_,_Result,_CDone,_WF). % propagation not required; closure expanded, cf test 1987
5821
5822 %check_valid_avl(AVL,Origin) :-
5823 % (nonvar(AVL) -> true
5824 % ; add_internal_error('Var avl_set: ', check_valid_avl(AVL,Origin)),fail).
5825
5826 :- block expand_if_avl(?,?,-,?,?).
5827 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
5828 ? expand_custom_set_to_list2(avl_set(S),Result,Done,_,expand_if_avl(Source),no_wf_available).
5829 expand_if_avl(Res,Result,_,Done,Source) :- check_list(Res,expand_if_avl(Source)),
5830 equal_object(Res,Result), Done=true.
5831
5832 check_list(Res,_) :- nonvar(Res), is_list(Res),!.
5833 check_list(Res,Src) :- add_error(Src,'Could not expand to list: ',Res).
5834 is_list([]). is_list([_|_]).
5835
5836 expand_closure_to_avl_or_list([X],[integer],Body,Result,_CheckTimeouts,_WF) :-
5837 is_interval_closure_body(Body,X,Low,Up),!,
5838 expand_interval_closure_to_avl(Low,Up,Result).
5839 %expand_closure_to_avl_or_list(P,T,Body,Result,_WF) :- is_member_closure(P,T,Body,TS,Set),
5840 % print(expand_member_closure(P,T,Body,TS,Set)),nl,fail.
5841 expand_closure_to_avl_or_list(Par,Types,Body,Result,CheckTimeouts,WF) :-
5842 expand_normal_closure(Par,Types,Body,CResult,_Done,CheckTimeouts,WF),
5843 kernel_objects:equal_object(Result,CResult,expand_closure_to_avl_or_list). % may convert to AVL, should we wait for _Done?
5844
5845
5846 % use WF just for call stack messages; we should not delay creating result
5847 expand_closure_to_avl_wf([X],[integer],Body,Result,_WF) :-
5848 is_interval_closure_body(Body,X,Low,Up),!,
5849 expand_interval_closure_to_avl(Low,Up,Result). % we could pass WF
5850 expand_closure_to_avl_wf(Par,Types,Body,Result,WF) :-
5851 expand_normal_closure(Par,Types,Body,S,Done,check(expand_closure_to_avl),WF),
5852 (ground_value(S) % ground value is sufficient to proceed; we do not need to check Done
5853 -> convert_to_avl_inside_set(S,R),equal_object(R,Result,expand_closure_to_avl)
5854 ; print(cannot_convert_closure_value_to_avl(closure(Par,Types),done(Done))),nl,
5855 translate:print_bexpr(Body),nl,trace,
5856 fail).
5857
5858
5859 % possible values for CheckTimeouts: check, check_no_inf, no_check, ...
5860 % Note: we no longer check is_infinite_explicit_set(closure(Parameters,ParameterTypes,ClosureBody))
5861 % and no longer raise add_closure_warning(Source,Parameters,ParameterTypes,ClosureBody,'### WARNING: expanding infinite comprehension set: ')
5862 % and no longer use preference warn_when_expanding_infinite_closures
5863 % this is relevant for e.g., test 1291
5864 expand_normal_closure(Parameters,ParameterTypes,ClosureBody,Result,Done,CheckTimeouts,WF) :-
5865 expand_normal_closure_memo(CheckTimeouts,Parameters,ParameterTypes,ClosureBody,Result,Done,WF).
5866
5867 :- public add_closure_warning_wf/6.
5868 add_closure_warning_wf(Source,Parameters,_ParameterTypes,_ClosureBody,_MSG,_WF) :-
5869 preference(provide_trace_information,false),preference(strict_raise_warnings,false),!,
5870 format('### TIME-OUT raised during closure expansion (~w,~w).~n### set TRACE_INFO preference to TRUE for more details.~n',[Parameters,Source]).
5871 add_closure_warning_wf(Source,Parameters,ParameterTypes,ClosureBody,MSG,WF) :-
5872 (debug_mode(on) -> Limit = 2500, AvlLim=10 ; Limit = 500, AvlLim=5),
5873 preferences:temporary_set_preference(expand_avl_upto,AvlLim,CHNG),
5874 call_cleanup(translate:translate_bvalue_with_limit(closure(Parameters,ParameterTypes,ClosureBody),Limit,CT),
5875 preferences:reset_temporary_preference(expand_avl_upto,CHNG)),
5876 bsyntaxtree:get_texpr_info(ClosureBody,Infos),
5877 add_warning_wf(Source,MSG,CT,Infos,WF), debug_print(19,'! infos: '), debug_println(Infos). %,trace.
5878
5879
5880 :- use_module(memoization,[is_memoization_closure/4,get_complete_memoization_expansion/6]).
5881
5882 % a version of closure expansion which memoizes its results; stored_expansion needs to be cleared when new machine loaded
5883 expand_normal_closure_memo(CHECK,Parameters,ParameterTypes,ClosureBody,FullResult,Done,WF) :-
5884 is_memoization_closure(Parameters,ParameterTypes,ClosureBody,MemoID),
5885 !, Span=ClosureBody,
5886 % MemoID can be a variable
5887 (var(MemoID) -> perfmessage(CHECK,'Getting full value of a memoized function',ClosureBody) ; true),
5888 get_complete_memoization_expansion(MemoID,FullResult,Done,Span,expand_normal_closure_memo(CHECK),WF).
5889 expand_normal_closure_memo(CHECK,Parameters,ParameterTypes,ClosureBody,FullResult,Done,WF) :-
5890 preferences:preference(use_closure_expansion_memoization,false),!,
5891 expand_normal_closure1(CHECK,Parameters,ParameterTypes,ClosureBody,FullResult,Done,WF).
5892 expand_normal_closure_memo(CHECK,Parameters,ParameterTypes,ClosureBody,FullResult,Done,WF) :-
5893 % maybe we should only memo when ClosureWaitVars are ground ?
5894 MemoLookupTerm = closure(Parameters,ParameterTypes,ClosureBody),
5895 compute_memo_hash(MemoLookupTerm,Hash),
5896 % idea: maybe store expansion only on second hit ?
5897 (get_stored_memo_expansion(Hash,MemoLookupTerm,StoredResult)
5898 -> %print_term_summary(reusing_expansion(Hash,Parameters,ParameterTypes,ClosureBody,StoredResult)),nl,
5899 UPV=StoredResult, %state_packing:unpack_value(StoredResult,UPV),
5900 FullResult = UPV, Done=true
5901 ; %statistics(runtime,[T1,_]), %%
5902 expand_normal_closure1(CHECK,Parameters,ParameterTypes,ClosureBody,FullResult,Done,WF),
5903 %statistics(runtime,[T2,_]), Time is T2-T1, store_memo_computation_time(Hash,Time),
5904 (Done==true/* ,T2-T1>0*/
5905 -> PackedValue=FullResult, %state_packing:pack_value(FullResult,PackedValue),
5906 store_memo_expansion(Hash,MemoLookupTerm,PackedValue)
5907 ; true)
5908 ).
5909
5910 expand_normal_closure1(CHECK,Parameters,ParameterTypes,ClosureBody,FullResult,Done,WF) :-
5911 preference(provide_trace_information,false),!,
5912 expand_normal_closure2(CHECK,Parameters,ParameterTypes,ClosureBody,FullResult,Done,WF).
5913 expand_normal_closure1(CHECK,Parameters,ParameterTypes,ClosureBody,FullResult,Done,WF) :-
5914 get_texpr_info(ClosureBody,Info),
5915 push_wait_flag_call_stack_info(WF,
5916 quantifier_call(comprehension_set(all_solutions),Parameters,[],Info),WF2),
5917 expand_normal_closure2(CHECK,Parameters,ParameterTypes,ClosureBody,FullResult,Done,WF2).
5918
5919
5920 expand_normal_closure2(_CHECK,Parameters,ParameterTypes,ClosureBody,FullResult,Done,WF) :-
5921 % TO DO: add more symbolic member closures who have expression computation code
5922 is_closure1_value_closure(Parameters,ParameterTypes,ClosureBody,VAL),!,
5923 bsets_clp:relational_trans_closure_wf(VAL,FullResult,WF),
5924 ground_value_check(FullResult,FRGr),
5925 when(nonvar(FRGr),Done=true).
5926 expand_normal_closure2(CHECK,Parameters,ParameterTypes,ClosureBody,FullResult,Done,WF) :-
5927 % special treatment for lambda closures: Advantage: we don't have to wait for variables in EXPR body of closure
5928 % Disadvantage: EXPR only gets evaluated after a solution has been found for args: can mean repeated computations !
5929 % (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
5930 % Advantage: it can solve constraints such as f = %x.(x:1..10|x+y) & f(5)=1005 (finding y without enumeration); see test 1168
5931 \+ preferences:preference(use_smt_mode,false),
5932 is_lambda_closure(Parameters,ParameterTypes,ClosureBody, OtherIDs,OtherTypes, DomainPred, EXPR),
5933 \+ ground_bexpr(EXPR), % if EXPR is ground, there is nothing to be gained by special treatment here
5934 WF \= no_wf_available, % otherwise we may have to enumerate EXPR result leading to choice points, e.g. in phase 0
5935 !,
5936 bexpr_variables(DomainPred,ClosureWaitVars),
5937 (CHECK=no_check -> TIMEOUTCODE = true ;
5938 TIMEOUTCODE = add_closure_warning_wf(CHECK,Parameters,ParameterTypes,ClosureBody,
5939 'TIME-OUT occurred while ProB was expanding: ',WF)),
5940 (CHECK=check_no_inf -> VIRTUALTIMEOUTCODE=true ; VIRTUALTIMEOUTCODE=TIMEOUTCODE),
5941 delay_setof_check_wf( ParTuple,
5942 (custom_explicit_sets:b_test_closure(OtherIDs,OtherTypes,DomainPred,OtherValues,all_solutions,WF),
5943 convert_list_into_pairs(OtherValues,ParTuple)
5944 % TO DO: compile EXPR when we start expanding the closure: to avoid repeated re-computation of expressions for every instance
5945 ),
5946 Result, ClosureWaitVars, __Done,
5947 TIMEOUTCODE,VIRTUALTIMEOUTCODE,WF,DomainPred),
5948 (WF = no_wf_available
5949 -> init_wait_flags(WF1,[expansion_context(lambda_function_result,Parameters)])
5950 ; WF1=WF
5951 ),
5952 evaluate_result_expr(Result,EXPR,OtherIDs,EvResult,EvDone,WF1),
5953 when(nonvar(EvDone),(
5954 (WF = no_wf_available -> ground_wait_flags(WF1) ; true),
5955 kernel_objects:equal_object_wf(EvResult,FullResult,expand_normal_closure2,WF),
5956 Done=true)).
5957 expand_normal_closure2(no_check,Parameters,ParameterTypes,ClosureBody,Result,Done,WF) :- !,
5958 expand_normal_closure_direct(Parameters,ParameterTypes,ClosureBody,Result,Done,WF).
5959 expand_normal_closure2(CHECK,Parameters,ParameterTypes,ClosureBody,Result,Done,WF) :-
5960 bexpr_variables(ClosureBody,ClosureWaitVars),
5961 TIMEOUTCODE = add_closure_warning_wf(CHECK,Parameters,ParameterTypes,ClosureBody,
5962 'TIME-OUT occurred while ProB was expanding: ',WF),
5963 (CHECK=check_no_inf -> VIRTUALTIMEOUTCODE=true ; VIRTUALTIMEOUTCODE=TIMEOUTCODE),
5964 % Note: delay_setof_check_wf will throw enumeration warning for virtual timeouts, after VIRTUALTIMEOUTCODE
5965 delay_setof_check_wf( ParTuple,
5966 custom_explicit_sets:test_closure_and_convert(Parameters,ParameterTypes,ClosureBody, ParTuple,WF),
5967 Result, ClosureWaitVars, Done, TIMEOUTCODE, VIRTUALTIMEOUTCODE,WF,ClosureBody).
5968
5969 expand_normal_closure_direct(Parameters,ParameterTypes,ClosureBody,Result,Done,WF) :-
5970 bexpr_variables(ClosureBody,ClosureWaitVars),
5971 Span = ClosureBody,
5972 delay_setof_wf( ParTuple,
5973 % TO DO: refresh waitflag in outer WF store to let pending code run to completion and avoid spurious WD errors ?
5974 custom_explicit_sets:test_closure_and_convert(Parameters,ParameterTypes,ClosureBody, ParTuple,WF),
5975 Result, ClosureWaitVars, Done,WF, Span).
5976
5977
5978
5979 :- block evaluate_result_expr(-,?,?,?,?,?).
5980 evaluate_result_expr(avl_set(AVL),EXPR,OtherIDs,Res,Done,WF) :-
5981 avl_domain(AVL,R),
5982 evaluate_result_expr(R,EXPR,OtherIDs,Res,Done,WF).
5983 evaluate_result_expr([],_EXPR,_OtherIDs,[],Done,_WF) :-
5984 %ground_wait_flags(WF),
5985 Done=true.
5986 evaluate_result_expr([ParTuple|T],EXPR,OtherIDs,[FullTuple|ET],Done,WF) :-
5987 % same_length(OtherIDs,ParValues), % not necessary
5988 set_up_localstate(OtherIDs,ParValues,[],LocalState),
5989 convert_list_into_pairs(ParValues,ParTuple), % bind values in ParTuple to LocalState
5990 b_interpreter:b_compute_expression(EXPR,LocalState,[],EXPRVALUE,WF),
5991 append(ParValues,[EXPRVALUE],FullValues),
5992 convert_list_into_pairs(FullValues,FullTuple),
5993 evaluate_result_expr(T,EXPR,OtherIDs,ET,Done,WF).
5994
5995 :- use_module(bsyntaxtree,[split_names_and_types/3]).
5996 :- use_module(probsrc(bsyntaxtree), [def_get_texpr_id/2]).
5997 %:- use_module(library(lists),[prefix_length/3, suffix_length/3]).
5998 % test a closure and convert into pairs; assume we want all solutions
5999 test_closure_and_convert(Parameters,ParameterTypes,ClosureBody, ParTuple, WF) :-
6000 is_recursive_closure(Parameters,ParameterTypes,ClosureBody),
6001 get_recursive_identifier_of_closure_body(ClosureBody,TRID),!,
6002 def_get_texpr_id(TRID,RID), get_texpr_type(TRID,RType),
6003 %print(test_recursion(RID)),nl, translate:nested_print_bexpr(ClosureBody),nl,
6004 RecVal = closure(Parameters,ParameterTypes,ClosureBody), % Recursive Value added to parameters
6005 same_length(Parameters,ParValues),
6006 reset_closure_solution_counter(Parameters),
6007 b_test_closure([RID|Parameters],[RType|ParameterTypes],ClosureBody,[RecVal|ParValues],all_solutions,WF),
6008 convert_sol_list_into_pairs(ParValues,Parameters,ParTuple). % convert tuple without recursive value to ParTuple
6009 test_closure_and_convert(Parameters,ParameterTypes,b(exists(EParAndTypes,ClosureBody),pred,OuterInfo), ParTuple, WF) :-
6010 % Motivation: enumerating Parameters can be quite inefficient
6011 % if for example we have something like {x|#y.(y:SmallSet & x=f(y))}
6012 % Problem: the existential quantifier will be delayed until the Parameters are instantiated !
6013 % relevant test: 1162
6014 % Note: this is duplicating to some extent the code in b_test_exists_wo_expansion
6015 % However, here we can also apply lambda_closure optimisation in b_test_closure below, this is
6016 % relevant for private_examples/2023/.../rule_FICHIER_MRGATKSAATPAR_RVF219_MRGA_DE.mch
6017 ? exists_should_be_lifted(Parameters,ParameterTypes,OuterInfo,ClosureBody),
6018 split_names_and_types(EParAndTypes,EPar,ETypes),
6019 !,
6020 % print(' Lifting existential quantifier (i.e., enumerating paras with closure paras): '), print(EPar),nl,
6021 % print(outer_paras(Parameters)),nl,
6022 % append Parameters at end; in case we have a lambda function
6023 append(EPar,Parameters,FullPar), length(Parameters,NrParas),
6024 append(ETypes,ParameterTypes,FullTypes),
6025 length(EPar,NrExistsParas),
6026 length(IrrelevantParas,NrExistsParas), length(Suffix,NrParas),
6027 append(IrrelevantParas,Suffix,FullParList),
6028 copy_identifier_infos(OuterInfo,ClosureBody,ClosureBody2),
6029 reset_closure_solution_counter(Parameters),
6030 % bsyntaxtree:check_used_ids_in_ast(ClosureBody2),
6031 ? b_test_closure(FullPar,FullTypes,ClosureBody2, FullParList,all_solutions,WF),
6032 convert_sol_list_into_pairs(Suffix,Parameters,ParTuple).
6033 test_closure_and_convert(Parameters,ParameterTypes,ClosureBody, ParTuple, WF) :-
6034 reset_closure_solution_counter(Parameters),
6035 % print(test),nl, translate:nested_print_bexpr(ClosureBody),nl,
6036 length(Parameters,Len), length(ParValues,Len),
6037 %(annotate_exists(Parameters,ParameterTypes,ClosureBody,Body2) -> true ; Body2=ClosureBody),
6038 ? b_test_closure(Parameters,ParameterTypes,ClosureBody,ParValues,all_solutions,WF),
6039 convert_sol_list_into_pairs(ParValues,Parameters,ParTuple). % ,print(solution(ParTuple)),nl,nl.
6040
6041 % Lifting existential quantifier was previously done here, but was duplicating code in b_test_exists_wo_expansion
6042 % we now simply generate the allow_to_lift_exists annotation here and let b_test_exists_wo_expansion do its job
6043 %annotate_exists(Parameters,ParameterTypes,
6044 % b(exists(EParAndTypes,ClosureBody),pred,OuterInfo),
6045 % b(exists(EParAndTypes,ClosureBody),pred,[allow_to_lift_exists|OuterInfo])) :-
6046 % exists_should_be_lifted(Parameters,ParameterTypes,OuterInfo,ClosureBody).
6047
6048 % check if a top-level exists with body ExistsClosureBody should be lifted
6049 % within a closure with paras Parameters of type ParameterTypes:
6050 exists_should_be_lifted(Parameters,ParameterTypes,OuterInfo,ExistsClosureBody) :-
6051 (Parameters == ['_was_lambda_result_'] % here we are quite sure that we gain by this optimisation
6052 ? ; member(allow_to_lift_exists,OuterInfo) % parameters were originally from a set comprehension,
6053 % see test 306: in this case existential quantifier is lifted in b_interpreter anyway;
6054 % Note we counter the rewrite ran({x1,...xn|P}) ---> {xn| #(x1,...).(P)} and similarly for dom({...})
6055 ; ExistsClosureBody = b(member(_,_),_,_) % we have a simple projection closure
6056 % TO DO: maybe support other ones as well
6057 ; basic_type_list_cardinality(ParameterTypes,Card),
6058 (Card=inf -> true ; Card=inf_overflow -> true ; Card>10000) % geq_inf(Card,10001)
6059 % if here are only a few parameter values: do not lift existential quantified variables
6060 ).
6061
6062 % we need to copy important infos about the outer Parameters to ClosureBody
6063 copy_identifier_infos(Info,b(InnerPred,T,II),b(InnerPred,T,II2)) :-
6064 findall(I,identifier_info(I,Info),ToCopy),
6065 append(ToCopy,II,II2).
6066 identifier_info(I,Info) :- I=prob_annotation('DO_NOT_ENUMERATE'(ID)),
6067 member(I,Info), ID \= '$$NONE$$'.
6068
6069 convert_sol_list_into_pairs(ParaValues,Parameters,ParTuple) :-
6070 convert_list_into_pairs(ParaValues,ParTuple),
6071 update_closure_solution_counter(Parameters,ParTuple).
6072
6073 :- if(environ(prob_debug_flag,true)).
6074 :- dynamic closure_solution_counter/3.
6075 % debugging long expansions of comprehension_set / closures
6076 reset_closure_solution_counter(Parameters) :- retractall(closure_solution_counter(Parameters,_,_)).
6077
6078 update_closure_solution_counter(Parameters,ParTuple) :-
6079 retract(closure_solution_counter(Parameters,OldCount,OldTime)),!,
6080 statistics(walltime,[W2,_]), Delta is W2-OldTime,
6081 NewCount is OldCount+1,
6082 ((Delta > 5000 ; NewCount mod 1000 =:= 0)
6083 -> format('--> Solution ~w for expansion of closure ~w (delta ~w ms): ',[NewCount,Parameters,Delta]),
6084 translate:print_bvalue(ParTuple),nl,
6085 assert(closure_solution_counter(Parameters,NewCount,W2))
6086 ; assert(closure_solution_counter(Parameters,NewCount,OldTime))
6087 ).
6088 update_closure_solution_counter(Parameters,_ParTuple) :-
6089 statistics(walltime,[W2,_]),
6090 assert(closure_solution_counter(Parameters,1,W2)).
6091 :- else.
6092 reset_closure_solution_counter(_).
6093 update_closure_solution_counter(_,_).
6094 :- endif.
6095
6096
6097
6098 % compute cardinality of a list of basic types
6099 basic_type_list_cardinality([],1).
6100 basic_type_list_cardinality([BasicType|T],Res) :-
6101 basic_type_list_cardinality(T,TCard),
6102 (TCard=inf -> Res=inf
6103 ; kernel_objects:max_cardinality(BasicType,Card),
6104 safe_mul(Card,TCard,Res)
6105 ).
6106
6107 % for lambda closures we can set up a second waitflag for the expression and only ground it when body enumeration finished
6108 % idea is to avoid perturbation of constraint solving of main closure predicate by lambda expression, see test 1737
6109 % something like %(x,y).(x:1..200 & y:1..100 & y+x<259 & y*x>10|(y+x*x+y) mod 100) is faster
6110 % this is slower : %(x,y).(x:1..200 & y:1..100 |(y+x*x+y))
6111 % currently this slows down test 1336
6112 :- block b_test_closure(?,?,-,?,?,?).
6113 b_test_closure(Parameters,ParameterTypes,ClosureBody, FullParValues, NegationContext, OuterWF) :-
6114 (preference(data_validation_mode,true)
6115 -> true % avoids ineraction between domain and range expression enumeration; see
6116 % private_examples/ClearSy/2019_May/perf_3264/rule_186.mch or
6117 % computation of 631 ic___DMI_MRGATKSAAT___Parametre_Identifiant_indices_function in rule_FICHIER_MRGATKSAATPAR_RVF219_MRGA_DE.mch
6118 % however, as b_optimize below does *not* evaluate nested set comprehensions, there can be a slowdown:
6119 % the nested set comprehension gets re-evaluated for every soluiton of the lambda parameters !
6120 % this was the case of private_examples/ClearSy/2019_Nov/rule_Regle_31C_0005/rule.mch before using SORT
6121 ; \+ preferences:preference(use_smt_mode,false)), % TO DO: enable in normal mode when performance of 1336 fixed
6122 % print(test_closure(Parameters,FullParValues)),nl,
6123 is_lambda_closure(Parameters,ParameterTypes,ClosureBody, OtherIDs,OtherTypes, DomainPred, EXPR),
6124 % TO DO: detect not only equalities at end, but any equality which is irrelevant for the rest
6125 % nl,print(lambda_closure(OtherIDs)),nl, translate:print_bexpr(EXPR),nl,
6126 append(ParValues,[LambdaResult],FullParValues),
6127 !,
6128 get_texpr_info(ClosureBody,BInfo),
6129 b_interpreter:set_up_typed_localstate2(OtherIDs,OtherTypes,BInfo,ParValues,TypedVals,[],LocalState,NegationContext),
6130 simplify_span(ClosureBody,BSpan), % sometimes BInfo no longer contains a position info, but first_sub_expr does
6131 init_quantifier_wait_flag(OuterWF,comprehension_set(NegationContext),OtherIDs,ParValues,BSpan,WF),
6132 b_test_boolean_expression(DomainPred,LocalState,[],WF),
6133 %print('PRED: '),translate:print_bexpr(ClosureBody),nl,
6134 b_tighter_enumerate_values_in_ctxt(TypedVals,DomainPred,WF), % also does: project_away_useless_enumeration_values
6135 init_quantifier_wait_flag(OuterWF,comprehension_set(NegationContext),OtherIDs,ParValues,BSpan,WF2),
6136 b_compiler:b_optimize(EXPR,[],LocalState,[],CEXPR,WF), % already pre-compile lookup, without constraint processing; is not sufficient for test 1336
6137 ground_wait_flags(WF), % TODO: also call ground inner WF in context
6138 b_interpreter:b_compute_expression(CEXPR,LocalState,[],LambdaResult,WF2),
6139 ground_inner_wait_flags_in_context(NegationContext,WF2).
6140 b_test_closure(Parameters,ParameterTypes,ClosureBody,ParValues,NegationContext, OuterWF) :-
6141 % tools:print_bt_message(b_test_closure_testing_closure(Parameters,ParValues)), %%
6142 get_texpr_info(ClosureBody,BInfo),
6143 b_interpreter:set_up_typed_localstate2(Parameters,ParameterTypes,BInfo,
6144 ParValues,TypedVals,[],LocalState,NegationContext),
6145 % print_message(b_interpreter:b_test_boolean_expression(ClosureBody,LocalState,[],WF)),
6146 simplify_span(ClosureBody,BSpan), % sometimes BInfo no longer contains a position info, but first_sub_expr does
6147 init_quantifier_wait_flag(OuterWF,comprehension_set(NegationContext),Parameters,ParValues,BSpan,WF),
6148 %external_functions:observe_parameters(Parameters,LocalState), %%
6149 b_test_boolean_expression(ClosureBody,LocalState,[],WF),
6150 % tools:print_bt_message(tested_bool_expr), translate:print_bexpr(ClosureBody),nl,
6151 b_enumerate:b_tighter_enumerate_values_in_ctxt(TypedVals,ClosureBody,WF), % also detects useless enumeration ids
6152 ? ground_inner_wait_flags_in_context(NegationContext,WF).
6153
6154
6155
6156 :- block b_not_test_closure_wf(?,?,?,-,?).
6157 b_not_test_closure_wf(Parameters,ParameterTypes,Closure,ParValues,WF) :-
6158 % same_length(Parameters,ParValues), % not necessary
6159 set_up_localstate(Parameters,ParValues,[],LocalState),
6160 b_enumerate:b_type_values_in_store(Parameters,ParameterTypes,LocalState),
6161 b_not_test_boolean_expression(Closure,LocalState,[],WF),
6162 get_last_wait_flag(b_not_test_closure_wf(Parameters),WF,WF2),
6163 get_texpr_info(Closure,Infos),
6164 b_not_test_closure_enum(Parameters,ParameterTypes,Infos,LocalState,WF,WF2).
6165
6166 :- block b_not_test_closure_enum(-,?,?,?,?,?).
6167 b_not_test_closure_enum(Parameters,ParameterTypes,Infos,LocalState,WF,WF2) :-
6168 b_enumerate:b_extract_typedvalc(Parameters,ParameterTypes,Infos,LocalState,TypedVals),
6169 (var(WF2) -> ground_typedvals_check(TypedVals,GrVals) ; true),
6170 b_not_test_closure_enum_aux(GrVals,WF2,TypedVals,WF).
6171
6172 :- block b_not_test_closure_enum_aux(-,-,?,?).
6173 b_not_test_closure_enum_aux(_,_,TypedVals,WF) :-
6174 b_enumerate:b_tighter_enumerate_all_values(TypedVals,WF).
6175 % , print(finished_enum(Parameters)),nl.
6176
6177
6178 :- use_module(library(terms)).
6179 % check whether a VARIABLE occurs inside a closure
6180 closure_occurs_check(VARIABLE,_Par,_ParTypes,ClosureBody) :- expression_contains_setvar(ClosureBody,VARIABLE).
6181 % /* occurs check; x = closure1(x) ; for other closures this cannot happen ???!!! TO DO: Check */
6182 % custom_explicit_sets:is_closure1_value_closure(Par,ParTypes,ClosureBody,Val),
6183 % contains_var(VARIABLE,Val).
6184
6185 expression_contains_setvar(b(E,_,_),Variable) :- !,
6186 expression_contains_setvar_aux(E,Variable).
6187 expression_contains_setvar(E,V) :- add_internal_error('Illegal Expression: ', expression_contains_setvar(E,V)),
6188 contains_var(V,E).
6189
6190 expression_contains_setvar_aux(value(Val),Variable) :- !,value_contains_setvar(Val,Variable).
6191 % a few very common cases for performance; currently this predicate is often called for recursive functions
6192 expression_contains_setvar_aux(identifier(_),_) :- !,fail.
6193 expression_contains_setvar_aux(equal(A,B),Variable) :- !,
6194 (expression_contains_setvar(A,Variable) -> true ; expression_contains_setvar(B,Variable)).
6195 expression_contains_setvar_aux(conjunct(A,B),Variable) :- !,
6196 (expression_contains_setvar(A,Variable) -> true ; expression_contains_setvar(B,Variable)).
6197 expression_contains_setvar_aux(function(A,B),Variable) :- !,
6198 (expression_contains_setvar(A,Variable) -> true ; expression_contains_setvar(B,Variable)).
6199 expression_contains_setvar_aux(union(A,B),Variable) :- !,
6200 (expression_contains_setvar(A,Variable) -> true ; expression_contains_setvar(B,Variable)).
6201 expression_contains_setvar_aux(couple(A,B),Variable) :- !,
6202 (expression_contains_setvar(A,Variable) -> true ; expression_contains_setvar(B,Variable)).
6203 % the rest via safe_syntaxelement:
6204 expression_contains_setvar_aux(Expr,V) :-
6205 safe_syntaxelement_det(Expr,Subs,_Names,_,_),!,
6206 ? member(Sub,Subs), expression_contains_setvar(Sub,V),!.
6207 expression_contains_setvar_aux(E,V) :- add_internal_error('Illegal Expression: ', expression_contains_setvar_aux(E,V)),
6208 contains_var(V,E).
6209
6210 value_contains_setvar(Val,V) :- var(Val),!,Val==V.
6211 value_contains_setvar(avl_set(_),_V) :- !, fail. % assume avl_set always properly grounded; avoid looking inside
6212 value_contains_setvar(closure(_,_,Body),V) :- !,
6213 expression_contains_setvar(Body,V).
6214 value_contains_setvar(int(_),_) :- !,fail. % we check for set variables
6215 value_contains_setvar(global_set(_),_) :- !,fail. % we check for set variables
6216 value_contains_setvar(freetype(_),_) :- !,fail. % we check for set variables
6217 value_contains_setvar(freeval(_ID,_Case,Val),V) :- !, value_contains_setvar(Val,V).
6218 value_contains_setvar(string(_),_) :- !,fail. % we check for set variables
6219 value_contains_setvar(fd(_,_),_) :- !,fail. % we check for set variables
6220 value_contains_setvar((A,B),V) :- !, (value_contains_setvar(A,V) ; value_contains_setvar(B,V)).
6221 value_contains_setvar([A|B],V) :- !, (value_contains_setvar(A,V) ; value_contains_setvar(B,V)).
6222 value_contains_setvar(Val,V) :-
6223 contains_var(V,Val).
6224
6225 % ------------------