1 % (c) 2009-2024 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 :- module(b_ast_cleanup, [clean_up/3, clean_up_pred/3,
6 clean_up_pred_or_expr/3,
7 clean_up_pred_or_expr_with_path/4, % provide initial path, used for eventb context infos
8 clean_up_l_wo_optimizations/4,
9 clean_up_l_with_optimizations/4,
10 check_used_ids_info/4, recompute_used_ids_info/2,
11 definitely_not_empty_and_finite/1, definitely_infinite/1, % TO DO: move to another module
12 get_unique_id/2,
13 predicate_level_optimizations/2,
14 perform_do_not_enumerate_analysis/5,
15 has_top_level_wd_condition/1]).
16
17 :- use_module(module_information,[module_info/2]).
18 :- module_info(group,typechecker).
19 :- module_info(description,'This module implements transformations/simplifications on the AST.').
20
21 :- set_prolog_flag(double_quotes, codes). % relevant for detecting prob-ignore, test 2151 on SWI
22
23 :- use_module(tools, [safe_atom_chars/3,exact_member/2,foldl/4,filter/4]).
24 :- use_module(tools_lists, [length_less/2]).
25 :- use_module(error_manager).
26 :- use_module(debug).
27 :- use_module(self_check).
28 :- use_module(bsyntaxtree).
29 :- use_module(translate,[print_bexpr/1, translate_span/2, get_definition_context_from_span/2]).
30 :- use_module(btypechecker, [unify_types_strict/2]).
31 :- use_module(preferences,[get_preference/2]).
32 :- use_module(custom_explicit_sets,[convert_to_avl/2]).
33 :- use_module(prob_rewrite_rules(b_ast_cleanup_rewrite_rules),[rewrite_rule_with_rename/7]).
34 :- use_module(b_enumeration_order_analysis, [find_do_not_enumerate_variables/4]).
35 :- use_module(performance_messages,[perfmessage/2]).
36 :- use_module(b_operation_guards,[get_operation_propositional_guards/6]).
37
38 :- use_module(library(lists)).
39 :- use_module(library(ordsets)).
40 :- use_module(library(system), [environ/2]).
41
42 % entry point for cleaning up predicates; ensures that global, predicate-level optimizations also applied
43 clean_up_pred(Expr,NonGroundExceptions,CleanedUpExpr) :-
44 clean_up(Expr,NonGroundExceptions,CExpr),
45 (get_texpr_type(CExpr,pred)
46 -> predicate_level_optimizations(CExpr,CleanedUpExpr)
47 ; add_internal_error('Not predicate: ',clean_up_pred(Expr,NonGroundExceptions,CleanedUpExpr)),
48 CleanedUpExpr = CExpr).
49
50 % Warning: arguments swapped with clean_up for maplist !
51 clean_up_pred_or_expr(NonGroundExceptions,Expr,CleanedUpExpr) :-
52 clean_up_pred_or_expr_with_path(NonGroundExceptions,Expr,CleanedUpExpr,[]).
53 clean_up_pred_or_expr_with_path(NonGroundExceptions,Expr,CleanedUpExpr,Path) :-
54 clean_up_init(NonGroundExceptions,Expr,Expr1),
55 clean_up_aux(Expr1,NonGroundExceptions,CExpr,Path),
56 (get_texpr_type(CExpr,pred)
57 -> predicate_level_optimizations(CExpr,CleanedUpExpr,Path)
58 ; CleanedUpExpr = CExpr).
59
60 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
61
62 % clean up some code afterwards
63 clean_up(Expr,NonGroundExceptions,CExpr) :- % clean-up with init
64 clean_up_init(NonGroundExceptions,Expr,Expr1),
65 clean_up_aux(Expr1,NonGroundExceptions,CExpr,[]).
66 clean_up_aux(Expr1,NonGroundExceptions,CExpr,Path) :- % performs no init
67 (preferences:get_preference(normalize_ast,true)
68 -> cleanups(normalize,Expr1,[],Expr2,Path)
69 ; Expr2=Expr1),
70 cleanups(pre,Expr2,[],TPExpr,Path),
71 remove_bt(TPExpr,PExpr,LExpr,TLExpr),
72 syntaxtransformation(PExpr,Subs,_,NewSubs,LExpr),
73 functor(PExpr,F,N),
74 % recursively clean up sub-expressions
75 clean_up_l(Subs,NonGroundExceptions,NewSubs,F/N,1,Path),
76 cleanups(post,TLExpr,[],CExpr,Path).
77 %, tools_printing:print_term_summary(cleaned_up(CExpr)),nl.
78
79 % just run post-phase
80 %cleanups_post(Expr,CleanedupExpr) :- cleanups(post,Expr,[],CleanedupExpr,[]).
81
82 clean_up_init(NonGroundExceptions,Expr,Expr2) :-
83 % ensure that WD info is available also for pre phase
84 % also pre-transform large set_extensions; they are only later transformed using eval_set_extension
85 (transform_bexpr_td_with_scoping(b_ast_cleanup:try_evaluate_set_extension,Expr,Expr1),
86 transform_bexpr(b_ast_cleanup:compute_wd_info_and_norm_record_types(NonGroundExceptions),Expr1,Expr2) -> true
87 ; add_internal_error('Call failed:',clean_up_init(NonGroundExceptions,Expr,_)), Expr2=Expr).
88
89
90 :- use_module(kernel_records,[normalise_record_types/4]).
91 :- use_module(bsyntaxtree,[transform_bexpr/3]).
92 compute_wd_info_and_norm_record_types(NonGroundExceptions,b(E,Type0,I),b(E,Type2,NInfo)) :-
93 ? (member(contains_wd_condition,I) -> NInfo=I
94 ? ; is_possibly_undefined(E)
95 -> NInfo = [contains_wd_condition|I]
96 ; NInfo = I
97 ),
98 (NonGroundExceptions = do_not_ground_types -> Type2=Type0
99 ; ground_type_to_any(Type0,NonGroundExceptions),
100 normalise_record_types(Type0,NonGroundExceptions,Type1,HasRecords),
101 % difference between Type1/0 in test 1906
102 (HasRecords == true,Type1 \= Type0 -> Type2=Type1 ; Type2=Type0)
103 ).
104
105 try_evaluate_set_extension(set_extension(List),Res,LocalIds) :-
106 (extension_should_be_evaluated(List),
107 evaluate_set_extension(List,EvaluatedList,LocalIds),
108 convert_to_avl(EvaluatedList,AVL)
109 % evaluate simple explicit set extensions: avoid storing & traversing position info & AST
110 -> (debug_mode(on) -> format('EVAL SET EXTENSION: ',[]), translate:print_bvalue(AVL),nl ; true),
111 Res=value(AVL)
112 ;
113 Res=set_extension(List) % avoid traversing inside set_extension, can be very large
114 ).
115 try_evaluate_set_extension(set_extension(List),Res,LocalIds) :-
116 (extension_should_be_evaluated(List),
117 evaluate_seq_extension_to_avl(List,AVL,LocalIds)
118 -> (debug_mode(on) -> format('EVAL SEQUENCE EXTENSION: ',[]), translate:print_bvalue(AVL),nl ; true),
119 Res=value(AVL)
120 ; Res=sequence_extension(List) % avoid traversing inside set_extension, can be very large
121 ).
122
123
124 :- use_module(library(ordsets),[ord_nonmember/2, ord_add_element/3]).
125 % apply the clean-up rules to an expression until all
126 % applicable rules are processed
127 % cleanups(Phase,Expr,AppliedRules,Result,Path):
128 % Phase: pre or post or normalize
129 % Expr: the expression to clean up
130 % AppliedRules: a sorted list of clean up rules that have been already applied
131 % and must only be apply once ("single" mode)
132 % Result: the cleaned-up expression
133 % Path: list of outer functors leading to this expression; can be used to decide about applicability of rules
134 cleanups(Phase,Expr,AppliedRules,Result,Path) :-
135 %% print(cleanups(Phase,Expr,AppliedRules,Result,Path)),nl,
136 % set up co-routines that ensure that "Rule" is not applied if
137 % is in the list AppliedRules
138 start_profile_rule(RuleInfos),
139 assure_single_rules(AppliedRules,Mode,Rule),
140 ? ( cleanup_phase(Phase,Expr,NExpr,Mode/Rule,Path) -> % try to apply a rule (matching the current phase)
141 ( Mode==single -> ord_add_element(AppliedRules,Rule,AppRules) % if the rule is marked as "single", we add to the list of already applied rules
142 ; Mode==multi -> AppRules = AppliedRules % if "multi", we do not add it to the list, the rule might be applied more than once
143 ; add_error_fail(b_ast_cleanup,'Unexpected rule mode ',Mode)
144 ),
145 stop_profile_rule(Rule,Mode,Phase,Expr,RuleInfos),
146 %(NExpr=b(_,_,I),bsyntaxtree:check_infos(I,Rule) -> true ; true),
147 cleanups(Phase,NExpr,AppRules,Result,Path) % continue recursively with the new expression
148 ; % if no rule matches anymore,
149 Result = Expr, % we leave the expression unmodified
150 Mode=multi, Rule=none). % and unblock the co-routine (see assure_single_rules/3)
151
152
153 :- if(environ(prob_safe_mode,true)).
154 start_profile_rule([R1,W1]) :- statistics(runtime,[R1,_]),statistics(walltime,[W1,_]).
155 stop_profile_rule(Rule,Mode,Phase,Expr,[R1,W1]) :-
156 statistics(runtime,[R2,_]),statistics(walltime,[W2,_]), DeltaW is W2-W1, DeltaR is R2-R1,
157 (DeltaW < 20 -> true ; format('Firing AST cleanup rule ~w (mode:~w) in phase ~w took ~w ms (~w ms walltime)~n',[Rule,Mode,Phase,DeltaR,DeltaW]), translate:print_span(Expr),nl),
158 runtime_profiler:register_profiler_runtime(Rule,ast_cleanup,unknown,DeltaR,DeltaW).
159 %%% print(fired_rule(Rule,Mode,Phase)),nl, translate:print_bexpr_or_subst(Expr), print(' ===> '),nl, translate:print_bexpr_or_subst(NExpr),nl, print_ast(NExpr),nl, %% COMMENT IN TO SEE applied RULES <---------------
160 %(map_over_typed_bexpr(b_ast_cleanup:check_valid_result,NExpr) -> true ; true), % comment in to check output after every firing of a rule
161 :- else.
162 start_profile_rule(_).
163 stop_profile_rule(_,_,_,_,_).
164 :- endif.
165
166 %check_valid_result(b(xexists([b(identifier(msgXX),integer,_)|_],_),pred,Infos)) :- nonmember(allow_to_lift_exists,Infos),print(missing_info),nl,trace,fail.
167
168 assure_single_rules([],_Mode,_Rule) :- !.
169 assure_single_rules(AppliedRules,Mode,Rule) :-
170 assure_single_rules2(AppliedRules,Mode,Rule).
171 :- block assure_single_rules2(?,-,?),assure_single_rules2(?,?,-).
172 assure_single_rules2(_AppliedRules,_,none) :- !.
173 assure_single_rules2(_AppliedRules,multi,_) :- !.
174 assure_single_rules2(AppliedRules,_,Rule) :-
175 % typically AppliedRules not very long; would also do: \+ member(Rule, AppliedRules).
176 ord_nonmember(Rule,AppliedRules).
177
178 cleanup_phase(Phase,OTExpr,NTExpr,Mode/Rule,Path) :-
179 create_texpr(OExpr,OType,OInfo,OTExpr),
180 check_generated_info(OInfo,entry,Path),
181 create_texpr(NExpr,NType,NInfo,NTExpr),
182 ? cleanup_phase2(Phase,OExpr,OType,OInfo,NExpr,NType,NInfo,Mode/Rule,Path),
183 check_generated_info(NInfo,Rule,Path).
184 cleanup_phase2(normalize,OExpr,OType,OInfo,NExpr,NType,NInfo,Mode/Rule,_Path) :-
185 decompose_rule(Mode_Rule,Mode,Rule),
186 cleanup_normalize(OExpr,OType,OInfo,NExpr,NType,NInfo,Mode_Rule),
187 (debug_mode(off) -> true
188 ; print('Rewritten: '), print_bexpr(b(OExpr,OType,OInfo)),nl,
189 print(' Into: '), print_bexpr(b(NExpr,NType,NInfo)),nl
190 ).
191 cleanup_phase2(pre,OExpr,OType,OInfo,NExpr,NType,NInfo,Mode/Rule,Path) :-
192 decompose_rule(Mode_Rule,Mode,Rule),
193 ? cleanup_pre_with_path(OExpr,OType,OInfo,NExpr,NType,NInfo,Mode_Rule,Path).
194 cleanup_phase2(post,OExpr,OType,OInfo,NExpr,NType,NInfo,Mode/Rule,Path) :-
195 decompose_rule(Mode_Rule,Mode,Rule),
196 ? cleanup_post_with_path(OExpr,OType,OInfo,NExpr,NType,NInfo,Mode_Rule,Path).
197 % check_ast(b(NExpr,NType,NInfo)),nl.
198
199 :- block decompose_rule(-,?,?).
200 decompose_rule(Mode_Rule,Mode,Rule) :-
201 (functor(Mode_Rule,'/',2)
202 -> Mode_Rule = Mode/Rule
203 ; add_internal_error('Illegal cleanup rule, missing mode: ',Mode_Rule),fail).
204
205 check_generated_info(Info,Rule,Path) :-
206 get_preference(prob_safe_mode,true),
207 (select(used_ids(_),Info,I1) -> member(used_ids(_),I1)),!,
208 format('Illegal used ids generated by ~w within ~w~n Infos=~w~n',[Rule,Path,Info]),
209 add_internal_error('Illegal Info generated by rule: ',Rule),
210 fail.
211 check_generated_info(_,_,_).
212
213 clean_up_l_wo_optimizations(Rest,NonGroundExceptions,CRest,SectionName) :-
214 maplist(clean_up_init(NonGroundExceptions),Rest,Rest1),
215 clean_up_l(Rest1,NonGroundExceptions,CRest,top_level(SectionName),1,[]).
216 clean_up_l([],_,[],_Functor,_Nr,_Path).
217 clean_up_l([Expr|Rest],NonGroundExceptions,[CExpr|CRest],Functor,ArgNr,Path) :-
218 clean_up_aux(Expr,NonGroundExceptions,CExpr,[path_arg(Functor,ArgNr)|Path]),
219 A1 is ArgNr+1,
220 clean_up_l(Rest,NonGroundExceptions,CRest,Functor,A1,Path).
221
222
223 % MAIN ENTRY POINT for b_machine_construction, bmachine_eventb, proz
224 % same as clean_up_l but also applies predicate_level_optimizations
225 % Context is just the name of the section/context in which the optimizations are run
226 clean_up_l_with_optimizations(Rest,NonGroundExceptions,CRest,Context) :-
227 %clean_up_l(Rest,NonGroundExceptions,CRest,top_level,1,[]).
228 (clean_up_l_with_opt(Rest,NonGroundExceptions,CleanedUpRest,top_level(Context),1,[]) -> CRest=CleanedUpRest
229 ; add_internal_error('Call failed:',clean_up_l_with_optimizations(Rest,NonGroundExceptions,CRest,Context)),
230 CRest=Rest
231 ).
232 clean_up_l_with_opt([],_,[],_Functor,_Nr,_Path).
233 clean_up_l_with_opt([Expr|Rest],NonGroundExceptions,[CExpr|CRest],Functor,ArgNr,Path) :-
234 %print('Cleaning up: '),translate:print_bexpr_or_subst(Expr),nl,
235 clean_up_init(NonGroundExceptions,Expr,Expr1),
236 clean_up_pred_or_expr_with_path(NonGroundExceptions,Expr1,CExpr,[path_arg(Functor,ArgNr)|Path]),
237 A1 is ArgNr+1,
238 clean_up_l_with_opt(Rest,NonGroundExceptions,CRest,Functor,A1,Path).
239
240 :- use_module(specfile,[animation_mode/1, animation_minor_mode/1]).
241 % cleanup_pre(OldExpr,OldType,OldInfo,NewExpr,NewType,NewInfo,Mode/Rule)
242
243 % optional normalization rules
244 % These rules are now generated using the prob_rule_compiler
245 %cleanup_normalize(empty_sequence,Type,Info,empty_set,Type,Info, multi/apply_normalization_rule(empty_sequence)). % rule probably not useful as empty_sequence converted to value([])?
246 cleanup_normalize(Expr,Type,Info,NewExpr,NewType,NewInfo, multi/apply_normalization_rule(Rule)) :-
247 b_ast_cleanup_rewrite_rules:normalization_rule_with_rename(Expr,Type,Info,NewExpr,NewType,NewInfo,Rule),
248 (debug_mode(off) -> true
249 ; format('Use rewrite_rule_normalize ~w~n',[Rule]),
250 print_bexpr(b(NewExpr,NewType,NewInfo)),nl
251 ),
252 (ground(NewExpr) -> true
253 ; print(not_ground_rewrite(Rule,Type,Info)),nl,
254 write(Expr),nl, write(' --> '),nl, write(NewExpr),nl,
255 fail).
256
257 never_transform_or_optimise(boolean_false).
258 never_transform_or_optimise(boolean_true).
259 %never_transform_or_optimise(bool_set).
260 never_transform_or_optimise(empty_set).
261 never_transform_or_optimise(empty_sequence). % except for normalization (cf above)
262 never_transform_or_optimise(falsity).
263 %never_transform_or_optimise(max_int).
264 %never_transform_or_optimise(min_int).
265 never_transform_or_optimise(truth).
266 never_transform_or_optimise(identifier(_)).
267 never_transform_or_optimise(integer(_)).
268 never_transform_or_optimise(real(_)).
269 never_transform_or_optimise(string(_)).
270 never_transform_or_optimise(value(_)) :- preferences:preference(normalize_ast, false).
271
272
273 % first check for a few expressions that never need to be optimised, rewritten:
274 cleanup_pre_with_path(E,_,_,_,_,_,_,_) :- never_transform_or_optimise(E),!,fail.
275 % TO DO: think about enabling the following clause
276 cleanup_pre_with_path(exists(AllIds,P),pred,I,exists(AllIds,P),pred,NewI,single/annotate_toplevel_exists,Path) :-
277 % mark the exists inside {paras| #(AllIds).(P)} as allowed to be lifted; relevant for test 1945 (although delayed semi_lifting in b_test_exists_wo_expansion also solves performance issue)
278 Path = [H|_], % TODO: also deal with lambda and other quantifications
279 H=path_arg(comprehension_set/2,1),
280 % % TO DO: add some conditions under which we allow to lift
281 get_preference(data_validation_mode,true), % TODO: check if we cannot enable this more generally
282 (debug_mode(off) -> true ; add_message(b_ast_cleanup,'Marking exists for lifting: ',AllIds,I)),
283 add_info_if_new(I,allow_to_lift_exists,NewI).
284 % mark existential quantifier as outermost: no need to delay it in b_interpreter:b_test_exists_wo_expansion
285 cleanup_pre_with_path(OExpr,OType,OInfo,NExpr,NType,NInfo,Mode_Rule,_) :-
286 ? cleanup_pre(OExpr,OType,OInfo,NExpr,NType,NInfo,Mode_Rule).
287
288 % Now cleanup_pre rules that do not require path:
289
290 cleanup_pre(block(TS),subst,_,Subst,subst,Info,multi/remove_block) :-
291 !,get_texpr_expr(TS,Subst),get_texpr_info(TS,Info).
292 % replace finite by truth
293 cleanup_pre(finite(S),pred,I,truth,pred,[was(finite(S))|I],multi/remove_finite) :-
294 % preferences:get_preference(disprover_mode,false), % keep finite in disprover goals
295 get_texpr_type(S,Type),
296 (typing_tools:is_provably_finite_type(Type) -> true
297 % ; is_infinite_ground_type(Type) -> fail
298 % ; print(no_longer_assuming_finite(Type)),nl,b_global_sets:portray_global_sets,nl,fail
299 ),!. % add_message(ast,'Removed : ',b(finite(S),pred,I),I).
300 /*
301 cleanup_pre(domain(SETC),Type,I,
302 comprehension_set(DomainIds,NewPred),Type,I,multi/dom_let_pred) :-
303 get_texpr_expr(SETC,comprehension_set(CompIds,CompPred)),
304 get_domain_range_ids(CompIds,DomainIds,[RangeId]),
305 get_texpr_ids(CompIds,UnsortedIds), sort(UnsortedIds,Blacklist),
306 conjunction_to_list(CompPred,Preds),
307 select_equality(TId,Preds,Blacklist,Expr,Rest,_UsedIds,check_well_definedness),
308 same_id(TId,RangeId,_),
309 !,
310 LetIds = [RangeId], Exprs = [Expr],
311 conjunct_predicates(Rest,RestPred),
312 NewPred = b(let_predicate(LetIds,Exprs,RestPred),pred,[generated(domain)]),
313 print('Translated dom({...,x|x=E&...}) into: '),
314 print_bexpr(b(comprehension_set(DomainIds,NewPred),Type,[])),nl.
315 */
316 /* strangely enough: this does not seem to buy anything:
317 cleanup_pre(domain(SETC),Type,I,
318 let_expression(LetIds,Exprs,NewExpr),Type,[generated(domain)|I],multi/dom_let_expr) :-
319 get_texpr_expr(SETC,comprehension_set(CompIds,CompPred)),
320 get_domain_range_ids(CompIds,DomainIds,[RangeId]),
321 get_texpr_ids(CompIds,UnsortedIds), sort(UnsortedIds,Blacklist),
322 conjunction_to_list(CompPred,Preds),
323 select_equality(TId,Preds,Blacklist,Expr,Rest,_UsedIds,check_well_definedness),
324 same_id(TId,RangeId,_),
325 !,
326 LetIds = [RangeId], Exprs = [Expr],
327 conjunct_predicates(Rest,RestPred),
328 get_texpr_info(SETC,CInfo),
329 NewExpr = b(comprehension_set(DomainIds,RestPred),Type,CInfo),
330 print('Translated dom({...,x|x=E&...}) into: '), print_bexpr(b(let_expression(LetIds,Exprs,NewExpr),Type,[])),nl.
331 */
332 % exchange quantified union by generalized union
333 cleanup_pre(QUANT,Type,I,
334 let_expression(LetIds,Exprs,NewExpr),Type,[generated(QuantOP)|I],multi/quant_union_inter_let) :-
335 get_preference(optimize_ast,true),
336 quantified_set_operator(QUANT,QuantOP,AllIds,Pred,Expr),
337 conjunction_to_nontyping_list(Pred,Preds),
338 % The ids are needed to build a "black list"
339 get_sorted_ids(AllIds,Ids),
340 find_one_point_rules(AllIds,Preds,Ids,LetIds,Exprs,RestIds,NewPreds),
341 % only succeed if we found at least one id which can be rewritten as let
342 LetIds = [_ID1|_],
343 !,
344 (RestIds=[],NewPreds=[] -> NewExpr=Expr
345 % UNION(x).(x=E|Expr) --> LET x BE x=E in Expr END
346 ; RestIds = [] -> conjunct_predicates_with_pos_info(NewPreds,NewPred),
347 % UNION(x).(x=E & NewPred|Expr) --> LET x BE x=E in IF NewPRED THEN Expr ELSE {} END END
348 NewExpr = b(if_then_else(NewPred,Expr,b(empty_set,Type,[])),Type,I)
349 ; conjunct_predicates_with_pos_info(NewPreds,NewPred),
350 quantified_set_operator(NewQUANT,QuantOP,RestIds,NewPred,Expr),
351 NewExpr = b(NewQUANT,Type,I)
352 ),
353 (debug_mode(off) -> true
354 ; print('Translated UNION/INTER into: '), print_bexpr(b(let_expression(LetIds,Exprs,NewExpr),Type,[])),nl).
355 cleanup_pre(quantified_union(Ids,Pred,Expr),Type,I,DomCOMPSET,Type,I,multi/quant_union_into_comprehension) :-
356 singleton_set_extension(Expr,CoupleExpr),
357 nested_couple_to_list(CoupleExpr,List), % we have UNION(..).(...| { A |-> B }) --> List = [A,B]
358 match_ids(List,Ids,AllIds,RestIds),
359 (RestIds = []
360 -> true % UNION(x,y).(x:INTEGER & y=x+1|{x|->y}) --> {x,y| x:INTEGER & y=x+1} = %x.(...).
361 ; % UNION(y,x,z).(x:INTEGER & y=x+1|{x|->y}) --> dom({x,y,z| x:INTEGER & y=x+1})
362 % used to fail test 1101; check on List relevant for test 2359
363 List = [_,_|_] % at least two ids, otherwise use quant_union translation below: ran( %(Ids).(Pred|One) )
364 ),
365 COMPSET = comprehension_set(AllIds,Pred),
366 generate_dom_for_ids(RestIds,COMPSET,Type,I,TDomCOMPSET), % add one dom(.) construct per ID that is projected away
367 (debug_mode(off) -> true
368 ; print('Translated UNION over identifier couples into: '), print_bexpr(TDomCOMPSET),nl),
369 % check_ast(TDomCOMPSET), will complain about redundant typing as we are still in pre phase
370 TDomCOMPSET = b(DomCOMPSET,Type,_).
371 cleanup_pre(quantified_union(Ids,Pred,Expr),Type,I,Res,Type,[was(quantified_union)|I],multi/quant_union_symbolic) :-
372 memberchk(prob_annotation('SYMBOLIC'),I),
373 % UNION(Ids).(Pred|Expr) --> {u| #Ids.(Pred & u:Expr)}
374 get_texpr_set_type(Expr,IdType),
375 !,
376 get_unique_id_inside('__UNION__',Pred,Expr,FRESHID),
377 NewTID = b(identifier(FRESHID),IdType,[]),
378 safe_create_texpr(member(NewTID,Expr),pred,Member),
379 create_exists_opt(Ids,[Pred,Member],Exists),
380 Res = comprehension_set([NewTID],Exists),
381 (debug_mode(off) -> true ; print('UNION @symbolic: '), print_bexpr(b(Res,Type,I)),nl).
382 % exchange quantified union by generalized union
383 cleanup_pre(quantified_union(Ids,Pred,Expr),Type,I,Res,Type,I,multi/quant_union) :-
384 !,
385 ((get_preference(convert_comprehension_sets_into_closures,false), % for test 1101: UNION is a form of let and forces computation at the moment; translating it into a construct without union means that it may be kept symbolic
386 singleton_set_extension(Expr,One) %, debug:bisect(Expr,[1,1,1,1,1,1,1])) % [1,1,1,1,1,1,1] slow; 1,1,0 1,1,1,0 fast
387 )
388 % UNION(Ids).(Pred|{One}) --> ran( %(Ids).(Pred|One) )
389 -> quantified_set_op(Ids,Pred,One,quantified_union,I,TRes),
390 get_texpr_expr(TRes,Res),
391 (debug_mode(off) -> true ; print('UNION - SINGLETON: '), print_bexpr(TRes),nl)
392 ;
393 % UNION(Ids).(Pred|Expr) --> union( ran( %(Ids).(Pred|Expr) ) )
394 quantified_set_op(Ids,Pred,Expr,quantified_union,I,Set),
395 Res = general_union(Set)
396 ).
397 %alternate encoding:
398 %cleanup_pre(quantified_union(Ids,Pred,Expr),Type,I,Set,Type,I,multi/quant_union) :-
399 %poses problem to test 614, 1101
400 % !,quantified_union_op(Ids,Pred,Expr,Type,Set).
401 % exchange quantified intersection by generalized intersection
402 cleanup_pre(quantified_intersection(Ids,Pred,Expr),Type,I,general_intersection(Set),Type,I,multi/quant_inter) :-
403 !,quantified_set_op(Ids,Pred,Expr,quantified_intersection,I,Set).
404 cleanup_pre(function(FUN,Argument),Type,I,Result,Type,I2,RULE) :-
405 cleanup_pre_function(FUN,Argument,Type,I,Result,I2,RULE).
406 cleanup_pre(first_projection(A,B),Type,I,Set,Type,[was(prj1),prob_annotation('SYMBOLIC')|I],multi/first_projection) :-
407 !,create_projection_set(A,B,first,Set).
408 cleanup_pre(second_projection(A,B),Type,I,Set,Type,[was(prj2),prob_annotation('SYMBOLIC')|I],multi/second_projection) :-
409 !,create_projection_set(A,B,second,Set).
410 cleanup_pre(event_b_first_projection(Rel),Type,I,Set,Type,[prob_annotation('SYMBOLIC')|I],multi/ev_first_projection) :-
411 !,create_event_b_projection_set(Rel,first,Set).
412 cleanup_pre(event_b_second_projection(Rel),Type,I,Set,Type,[prob_annotation('SYMBOLIC')|I],multi/ev_second_projection) :-
413 !,create_event_b_projection_set(Rel,second,Set).
414 cleanup_pre(event_b_first_projection_v2,Type,I,Set,Type,[prob_annotation('SYMBOLIC')|I],multi/ev2_first_projection) :-
415 !,create_event_b_projection_set_v2(Type,first,Set).
416 cleanup_pre(event_b_second_projection_v2,Type,I,Set,Type,[prob_annotation('SYMBOLIC')|I],multi/ev2_second_projection) :-
417 !,create_event_b_projection_set_v2(Type,second,Set).
418 cleanup_pre(image(Fun,SONE),T,I,Res,T,I,multi/succ_pred_image_optimisation) :-
419 singleton_set_extension(SONE,One), % succ[{h}] --> {h+1} and pred[{h}] --> {h-1} ; useful for alloy2b
420 precompute_pred_succ_function_call(Fun,One,FunOneRes),
421 !,
422 Res = set_extension([b(FunOneRes,integer,I)]).
423 cleanup_pre(union(Lambda1,Lambda2),T,I,lambda(TIDs1,TPred,TVal),T,I,multi/combine_lambdas_if_then_else) :-
424 Lambda1 = b(lambda(TIDs1,TPred1,TValue1),_,_), get_texpr_ids(TIDs1,Ids),
425 Lambda2 = b(lambda(TIDs2,TPred2,TValue2),_,_), get_texpr_ids(TIDs2,Ids),
426 % %x.(P & Cond1 | Val1) \/ %x.(P & not(Cond1) | Val2) ==> %x.(P| IF Cond1 THEN Val1 ELSE Val2 END)
427 conjunction_to_list(TPred1,L1),
428 conjunction_to_list(TPred2,L2),
429 append(Front1,[Last1],L1),
430 append(Front2,[Last2],L2),
431 maplist(same_texpr,Front1,Front2),
432 is_negation_of(Last1,Last2),
433 conjunct_predicates_with_pos_info(Front1,TPred),
434 get_texpr_type(TValue1,TV),
435 safe_create_texpr(if_then_else(Last1,TValue1,TValue2),TV,[],TVal),
436 (debug_mode(off) -> true
437 ; format('Union of lambdas converted to if-then-else: ',[]),
438 translate:print_bexpr(b(lambda(TIDs1,TPred,TVal),T,I)),nl
439 ).
440 cleanup_pre(event_b_comprehension_set(Ids,Expr,Pred),T,I,NewExpression,T,
441 [was(event_b_comprehension_set)|I],multi/ev_compset) :-
442 rewrite_event_b_comprehension_set(Ids,Expr,Pred, T, NewExpression).
443 cleanup_pre(domain_restriction(A,B),T,I,identity(A),T,I,multi/event_b_to_normal_identity1) :-
444 /* translate S <| id into id(S) */
445 is_event_b_identity(B).
446 cleanup_pre(range_restriction(B,A),T,I,identity(A),T,I,multi/event_b_to_normal_identity2) :-
447 /* translate id |> S into id(S) */
448 is_event_b_identity(B).
449 % what about translating id(TOTAL TYPE) into event_b_identity ??
450 cleanup_pre(ring(A,B),T,I,composition(B,A),T,I,multi/ring_composition). % replace backward composition by forward compositoin
451 cleanup_pre(less_equal(A,B),pred,I,less_equal_real(A,B),pred,I,multi/remove_ambiguous_leq_real) :-
452 get_texpr_type(A,real).
453 cleanup_pre(greater_equal(A,B),pred,I,less_equal_real(B,A),pred,I,multi/remove_ambiguous_geq_real) :-
454 get_texpr_type(A,real).
455 cleanup_pre(less(A,B),pred,I,less_real(A,B),pred,I,multi/remove_ambiguous_lt_real) :-
456 get_texpr_type(A,real).
457 cleanup_pre(greater(A,B),pred,I,less_real(B,A),pred,I,multi/remove_ambiguous_gt_real) :-
458 get_texpr_type(A,real).
459 cleanup_pre(unary_minus(A),real,I,unary_minus_real(A),real,I,multi/remove_ambiguous_unary_minus_real).
460 cleanup_pre(power_of(A,B),real,I,power_of_real(A,TB),real,I,multi/remove_ambiguous_unary_minus_real) :-
461 get_texpr_type(A,real),
462 safe_create_texpr(convert_real(B),real,[],TB). % TO DO: add pos
463 cleanup_pre(max(A),real,I,max_real(A),real,I,multi/remove_ambiguous_unary_max_real).
464 cleanup_pre(min(A),real,I,min_real(A),real,I,multi/remove_ambiguous_unary_min_real).
465 cleanup_pre(add(A,B),real,I,add_real(A,B),real,I,multi/remove_ambiguous_add_real).
466 cleanup_pre(div(A,B),real,I,div_real(A,B),real,I,multi/remove_ambiguous_div_real).
467
468 cleanup_pre(minus_or_set_subtract(A,B),integer,I,minus(A,B),integer,I,multi/remove_ambiguous_minus_int).
469 cleanup_pre(minus_or_set_subtract(A,B),real,I,minus_real(A,B),real,I,multi/remove_ambiguous_minus_real).
470 cleanup_pre(minus_or_set_subtract(A,B),Type,I,set_subtraction(A,B),Type,I,multi/remove_abiguous_minus_set) :-
471 is_set_type(Type,_).
472 cleanup_pre(mult_or_cart(A,B),integer,I,multiplication(A,B),integer,I,multi/remove_ambiguous_times_int).
473 cleanup_pre(mult_or_cart(A,B),real,I,multiplication_real(A,B),real,I,multi/remove_ambiguous_times_real).
474 cleanup_pre(mult_or_cart(A,B),Type,I,cartesian_product(A,B),Type,I,multi/remove_ambiguous_times_set) :-
475 is_set_type(Type,_).
476 cleanup_pre(E,T,Iin,E,T,Iout,multi/remove_rodinpos) :- % we use multi but can per construction only be applied once
477 selectchk(nodeid(rodinpos(_,[],_)),Iin,Iout). % remove rodinpos information with Name=[]
478 cleanup_pre(partition(X,[Set]),pred,I,equal(X,Set),pred,I,multi/remove_partition_one_element) :-
479 !,
480 % partition(X,Set) <=> X=Set
481 (debug_mode(off) -> true ;
482 print('Introducing equality for partition: '),
483 print_bexpr(X), print(' = '), print_bexpr(Set),nl).
484 cleanup_pre(case(Expression,CASES,Else),subst,I,NewSubst,subst,I,single/rewrite_case_to_if_then_else) :-
485 % translate CASE E OF EITHER e1 THEN ... ---> LET case_expr BE case_expr=E IN IF case_expr=e1 THEN ...
486 get_texpr_type(Expression,EType), get_texpr_info(Expression,EInfo),
487 ExprID = b(identifier(EID),EType,EInfo),
488 (get_texpr_id(Expression,EID)
489 -> NewSubst = if(IFLISTE) % no LET necessary
490 ; NewSubst = let([ExprID],Equal,b(if(IFLISTE),subst,I)),
491 get_unique_id_inside('case_expr',b(case(Expression,CASES,Else),subst,I),EID),
492 safe_create_texpr(equal(ExprID,Expression),pred,Equal)
493 ),
494 (maplist(gen_if_elsif(ExprID),CASES,IFLIST)
495 -> (get_texpr_expr(Else,skip) -> IFLISTE = IFLIST
496 ; TRUTH = b(truth,pred,[]), get_texpr_info(Else,EI),
497 append(IFLIST,[b(if_elsif(TRUTH,Else),subst,EI)],IFLISTE)
498 ),
499 (debug_mode(off) -> true
500 ; print('Translating CASE to IF-THEN-ELSE: '), print_bexpr(Expression),nl
501 %,translate:print_subst(b(NewSubst,subst,[])),nl
502 )
503 ; add_internal_error('Translation of CASE to IF-THEN-ELSE failed: ',CASES),fail
504 ).
505 cleanup_pre(exists(AllIds,Body),pred,I0,NewP1,pred,NewI,single/components_partition_exists) :-
506 get_preference(optimize_ast,true),
507 nonmember(partitioned_exists,I0), % avoid re-computing components on something that is already partitioned
508 Simplify=no_cleanup_and_simplify, % avoid loops
509 % Warning: the next call may make use of existing used_ids infos; if they are wrong we may have a problem!
510 b_interpreter_components:construct_optimized_exists(AllIds,Body,NewPred,Simplify,NrC),
511 (NrC = 1 % just one component; perform no change to avoid re-ordering ids, ... ; see test 510
512 -> NewP1=exists(AllIds,Body), NewI=I0
513 ; get_texpr_ids(AllIds,Ids), sort(Ids,SortedIds),
514 add_important_infos_to_exists_conjuncts(NewPred,I0,SortedIds, b(NewP1,pred,NewI)),
515 % important e.g. for test 1945; in particular allow_to_lift_exists
516 % Note: construct_optimized_exists can lift unrelated inner exists out (/ClearSy/2023/perf_0704/rule_genz.mch)
517 (debug_mode(on), NewP1 \= exists(_,_)
518 -> format('PARTITIONED EXISTS:~n ',[]), translate:nested_print_bexpr(b(NewP1,pred,NewI)),nl ; true)
519 ).
520 cleanup_pre(exists(AllIds,P),pred,I,NewP1,pred,I,single/factor_out) :- % REDUNDANT with rule above ??
521 conjunction_to_nontyping_list(P,Preds),
522 % move things which do not depend on AllIds outside
523 % transform, e.g., #(x).(y>2 & x=y) --> y>2 & #(x).(x=y)
524 get_preference(optimize_ast,true),
525 create_exists_opt(AllIds,Preds,b(NewP1,pred,_I),Modified),
526 %(Modified = true -> print(exists(AllIds)),nl,print_bexpr(b(NewP1,pred,_I)),nl),
527 % the rule will fire again on the newly generated sub predicate ! -> fix ?
528 Modified=true.% check if anything modified; otherwise don't fire rule
529
530 cleanup_pre(exists(AllIds,P),pred,Info0,NewP,pred,INew,multi/remove_single_use_equality) :-
531 % remove existentially quantified variables which are defined by an equation and are used only once
532 % e.g., Z1...Z4 in not(#(X,Y,Z,Z1,Z2,Z3,Z4).(X:INTEGER & X*Y=Z1 & Z1*Z = Z2 & Z*X = Z3 & Z3*Y = Z4 & Z2 /= Z4))
533 get_preference(optimize_ast,true),
534 (length_less(AllIds,100) -> true % otherwise the code becomes quite inefficient at the moment
535 ; perfmessage('Large existential quantifier, performing limited optimizations',Info0),
536 fail),
537 conjunction_to_list(P,Preds),
538 CheckWellDef=no_check,
539 ? select_equality(TId,Preds,[],_,IDEXPR,RestPreds,_,CheckWellDef),
540 get_texpr_id(TId,ID),
541 ? select(TIdE,AllIds,RestIds), get_texpr_id(TIdE,ID),
542 can_be_optimized_away(TIdE),
543 \+ occurs_in_expr(ID,IDEXPR), % we cannot inline #x.(x=y+x & ...)
544 always_defined_full_check_or_disprover_mode(IDEXPR), % otherwise we may remove WD issue by removing ID if Count=0 or move earlier/later if count=1
545 single_usage_identifier(ID,RestPreds,Count), % we could also remove if Expr is simple
546 (Count=0 -> debug_println(19,unused_equality_id(ID)),
547 PL=RestPreds
548 ; % Count should be 1
549 conjunct_predicates_with_pos_info(RestPreds,RestPred),
550 replace_id_by_expr(RestPred,ID,IDEXPR,E2),
551 conjunction_to_list(E2,PL)
552 ),
553 create_exists_opt(RestIds,PL,TNewP), % no need to computed used ids yet; we could do this:
554 %conjunct_predicates_with_pos_info(PL,PP), safe_create_texpr(exists(RestIds,PP),pred,TNewP),
555 (debug_mode(off) -> true
556 ; format('Remove existentially quantified identifier with single usage: ~w (count: ~w)~n',[ID,Count]), print_bexpr(IDEXPR),nl),
557 TNewP = b(NewP,pred,INew),!.
558 cleanup_pre(exists(AllIds,P),pred,I,let_predicate(LetIds,Exprs,NewP),pred,INew,multi/exists_to_let) :-
559 % rewrite predicates of the form #x.(x=E & P(x)) into (LET x==E IN P(x))
560 % side condition for #(ids).(id=E & P(ids)): no identifiers of ids occur in E
561 get_preference(optimize_ast,true),
562 conjunction_to_nontyping_list(P,Preds), % TO DO: avoid recomputing again (see line in clause above)
563 % The ids are needed to build a "black list"
564 get_sorted_ids(AllIds,Ids),
565 find_one_point_rules(AllIds,Preds,Ids,LetIds,Exprs,RestIds,NewPreds),
566 % no_check is not ok in the context of existential quantification and reification:
567 % #x.(1:dom(f) & x=f(1) & P) --> LET x=f(1) IN 1:dom(f) & P END
568 % it is not ok if the whole predicate gets reified in b_intepreter_check !! Hence we use always_defined_full_check_or_disprover_mode; see Well_def_1.9.0_b5 in private_examples
569 % only succeed if we found at least one id which can be rewritten as let
570 LetIds = [ID1|_],
571 !,
572 (atomic(ID1) -> add_internal_error(cleanup_pre,unwrapped_let_identifier(ID1)), INew=I
573 ; get_texpr_ids(LetIds,AtomicIDs),
574 remove_used_ids_from_info(AtomicIDs,I,INew)
575 ), % probably not necessary ?!
576 % see also the annotate_toplevel_exists rule above which adds allow_to_lift_exists; relevant, e.g., for test 1945
577 (member(allow_to_lift_exists,I) -> AddInfos=[allow_to_lift_exists] ; AddInfos=[]),
578 create_exists_opt(RestIds,NewPreds,AddInfos,NewP,_Modified),
579 (debug_mode(off) -> true
580 ; format('Extracted LET over ~w from exists (rest: ~w):~n ',[AtomicIDs,RestIds]),
581 translate:print_bexpr(b(let_predicate(LetIds,Exprs,NewP),pred,I)),nl
582 ).
583 % now the same LET extraction but for universal quantification:
584 cleanup_pre(forall(AllIds,P,Rhs),pred,I,let_predicate(LetIds,Exprs,NewP),pred,I,multi/forall_to_let) :-
585 get_preference(optimize_ast,true),
586 conjunction_to_nontyping_list(P,Preds),
587 % The ids are needed to build a "black list"
588 get_sorted_ids(AllIds,Ids),
589 check_forall_lhs_rhs(P,Rhs,I,Ids),
590 find_one_point_rules(AllIds,Preds,Ids,LetIds,Exprs,RestIds,NewPreds),
591 % only succeed if we found at least one id which can be rewritten as let
592 LetIds = [ID1|_],!,
593 (atomic(ID1) -> add_internal_error(cleanup_pre,unwrapped_let_identifier(ID1)) ; true),
594 conjunct_predicates_with_pos_info(NewPreds,NewLhs),
595 create_implication(NewLhs,Rhs,NewForallBody),
596 create_forall(RestIds,NewForallBody,NewP),
597 (debug_mode(on) -> print('Introduced let in forall: '), print(LetIds),nl ; true).
598 % warning: used_identifier information not yet computed; translate may generate warnings
599 cleanup_pre(exists(AllIds,P),pred,I0,NewPE,pred,NewI,multi/exists_remove_typing) :-
600 (is_a_conjunct(P,Typing,Q) ; is_an_implication(P,Typing,Q)),
601 % TRUE & Q == TRUE => Q == Q
602 is_typing_predicate(Typing),
603 % remove typing so that other exists rules can fire
604 % we run as cleanup_pre: the other simplifications which remove typing have not run yet
605 % such typing conjuncts typicially come from Rodin translations
606 create_exists_opt(AllIds,[Q],b(NewPE,_,I1)),
607 add_important_info_from_super_expression(I0,I1,I2), % we could also copy node_id(_) from I0 ?
608 add_removed_typing_info(I2,NewI).
609 cleanup_pre(exists(AllIds,P),pred,I,disjunct(NewP1,NewP2),pred,I,single/partition_exists_implication) :-
610 is_a_disjunct_or_implication(P,_Type,Q,R),
611 /* note that even if R is only well-defined in case Q is false; it is ok to seperate this out
612 into two existential quantifiers: #x.(x=0 or 1/x=10) is ok to transform into #x.(x=0) or #x.(1/x=10) */
613 % this slows down test 1452, Cylinders, 'inv3/WD'; TO DO:investigate
614 create_exists_opt(AllIds,[Q],NewP1), % print('Q: '),print_bexpr(NewP1),nl,
615 create_exists_opt(AllIds,[R],NewP2). %, print('R: '),print_bexpr(NewP2),nl.
616 cleanup_pre(exists([B],P),pred,I,truth,pred,I,single/tautology_exists_min_max) :-
617 % ∃b·∀x0·(x0 ∈ FINITE ⇒ b ≤ x0) == TRUE : WD condition from Rodin for max; similar for min (TODO: check min)
618 B = b(identifier(ID1),integer,_),
619 get_texpr_expr(P,forall([X0],Left,Right)),
620 X0 = b(identifier(ID2),integer,_),
621 get_texpr_expr(Left,member(X1,FiniteSet)),
622 get_texpr_id(X1,ID2),
623 Right = b(COMP,pred,_),
624 (COMP = less_equal(B2,X2) ; COMP = greater_equal(B2,X2)),
625 get_texpr_id(B2,ID1), get_texpr_id(X2,ID2),
626 definitely_finite(FiniteSet),
627 (debug_mode(off) -> true ; format('Removing WD condition for min/max exists over ~w :',[ID1]), translate:print_bexpr(P),nl).
628 cleanup_pre(forall(AllIds,P,Rhs),pred,I,NewPred,pred,I,multi/forall_to_post_let) :-
629 % translate something like !(x,y).(y:1..100 & x=y*y => x<=y) into !(y).(y : 1 .. 100 => (#(x).( (x)=(y * y) & x <= y)))
630 post_let_forall(AllIds,P,Rhs,NewPred,modification),
631 !,
632 (debug_mode(on) -> print('POST LET INTRODUCTION: '), print_bexpr(b(NewPred,pred,[])),nl ; true).
633 cleanup_pre(set_extension(List),Type,I, set_extension(NList),Type,I, single/remove_pos) :-
634 remove_position_info_from_list(List,I,NList),!.
635 cleanup_pre(sequence_extension(List),Type,I, sequence_extension(NList),Type,I, single/remove_pos) :-
636 remove_position_info_from_list(List,I,NList),!.
637 cleanup_pre(if(List),Type,I, if(NList),Type,I, single/remove_if_elsif_pos) :-
638 % the pos info is not used for individual if_elsif entries; some models contain very large if-then-else constructs
639 maplist(remove_top_levelposition_info,List,NList),!.
640 %cleanup_pre(concat(A,B),string,I,Res,string,I,multi/concat_assoc_reorder) :-
641 % A = b(concat(A1,A2),string,I1),
642 % !, % reorder STRING concats for better efficiency, can only occur when allow_sequence_operators_on_strings is true
643 % % TO DO: extract information I2B from A2 and B
644 % Res = concat(A1,b(concat(A2,B),string,I2B)).
645 cleanup_pre(typeset,SType,I,Expr,SType,I,multi/remove_typeset) :- !,
646 % used, e.g., in test 1205 for recursive Event-B operator definition
647 ( ground(SType) ->
648 (is_set_type(SType,Type),
649 create_maximal_type_set(Type,b(MaxExpr,_,_)) -> Expr=MaxExpr
650 ; is_set_type(SType,Type) ->
651 add_error_and_fail(b_ast_cleanup,'Creating type expression for typeset failed: ',Type)
652 ;
653 add_error_and_fail(b_ast_cleanup,'Creating type expression for typeset failed, type is not a set: ',SType)
654 )
655 ; add_error_and_fail(b_ast_cleanup,'Non-ground type for typeset expression: ',SType)).
656 cleanup_pre(integer_set(S),Type,I,Expr,Type,[was(integer_set(S))|I],multi/remove_integer_set) :- !,
657 translate_integer_set(S,I,Expr),
658 (debug_mode(off) -> true
659 ; format('Rewrite ~w to: ',[S]),
660 print_bexpr(b(Expr,integer,I)),nl).
661 % should we move the rewrite_rules to normalize ??
662 cleanup_pre(Expr,Type,Info,NewExpr,NewType,NewInfo, multi/apply_rewrite_rule(Rule)) :-
663 rewrite_rule_with_rename(Expr,Type,Info,NewExpr,NewType,NewInfo,Rule), % from b_ast_cleanup_rewrite_rules
664 (debug_mode(off) -> true
665 ; format('Use rewrite_rule ~w~n',[Rule]),
666 print_bexpr(b(NewExpr,NewType,NewInfo)),nl),
667 (ground(NewExpr) -> true ; print(not_ground_rewrite(NewExpr)),nl,fail).
668 % 'x > y' to 'y < x'
669 cleanup_pre(greater(Lhs,Rhs), pred, I, less(Rhs,Lhs), pred, [was(greater(Lhs,Rhs))|I], single/normalize_greater) :-
670 preferences:get_preference(normalize_ast, true).
671 % 'x >= y' to 'y <= x'
672 cleanup_pre(greater_equal(Lhs,Rhs), pred, I, less_equal(Rhs,Lhs), pred, [was(greater_equal(Lhs,Rhs))|I], single/normalize_greater_equal) :-
673 preferences:get_preference(normalize_ast, true).
674 % 'x - y' to 'x + -y'
675 cleanup_pre(minus(Lhs,Rhs), integer, I, add(Lhs,b(unary_minus(Rhs),integer,[])), integer, [was(minus(Lhs,Rhs))|I], single/normalize_minus) :-
676 preferences:get_preference(normalize_ast, true).
677 cleanup_pre(value(CLOSURE), Type, I, comprehension_set(TIDs,B), Type, I, single/normalize_value_closure) :-
678 nonvar(CLOSURE), CLOSURE=closure(P,T,B),
679 preferences:get_preference(normalize_ast, true),
680 create_typed_ids(P,T,TIDs).
681 cleanup_pre(comprehension_set(TIDs,Body), Type, I, union(Set1,Set2), Type,I, single/extract_union) :-
682 preferences:get_preference(normalize_ast, true),
683 is_a_disjunct(Body,B1,B2), % should we also detect set difference, should we detect common prefix typing
684 % {x| P or Q} ==> {x|P} \/ {x|Q}
685 % such closure values are created by symbolic union, relevant for JSON trace replay for test 281
686 safe_create_texpr(comprehension_set(TIDs,B1),Type,I,Set1),
687 safe_create_texpr(comprehension_set(TIDs,B2),Type,I,Set2).
688 cleanup_pre(external_function_call('ASSERT_EXPR',[BOOL,MSG,EXPR]), Type, I,
689 assertion_expression(Pred,MsgStr,EXPR), Type,I, single/detect_assertion_expression) :-
690 % translate ASSERT_EXPR back to assertion_expression; dual to way it is printed in pretty printer
691 get_pred_from_bool(BOOL,Pred),
692 get_string(MSG,MsgStr).
693 cleanup_pre(external_pred_call(PRED,ARGS), pred, I,
694 EQ, pred,I, single/rewrite_external_pred_to_bool_function) :-
695 preferences:get_preference(normalize_ast,true),
696 synonym_for_external_predicate(PRED,FUNC),
697 % replace PRED(ARGS) by bool(FUNC(ARGS)=TRUE) as external functions can always be used wo DEFINITIONS
698 safe_create_texpr(external_function_call(FUNC,ARGS),boolean,[],FUNCALL),
699 EQ = equal(FUNCALL,b(boolean_true,boolean,[])),
700 (debug_mode(off) -> true ; print('REWRITTEN external predicate call to '), print_bexpr(FUNCALL),nl).
701
702
703 % Cleanup PRE for function calls:
704 % In reply to PROB-240: Check if arguments of Prj1/2 are types only using is_just_type:
705 cleanup_pre_function(TProjection,Argument,_Type,I,Result,I,multi/projection_call) :-
706 get_texpr_expr(TProjection,Projection),
707 cleanup_function_projection(Projection,Argument,I,Result),
708 !.
709 cleanup_pre_function(Lambda,Argument,Type,I,NewContextExpr,I,multi/lambda_guard1) :-
710 get_preference(optimize_ast,true),
711 get_texpr_expr(Lambda,LambdaExpr),
712 is_lambda_in_context(LambdaExpr,Type,TIds,TPre,TVal,NewContextExpr,NewExpr,LocalIds),
713 (is_just_typing_pred(TPre)
714 -> TPre1 = b(truth,pred,[]), % relevant for replace count below
715 get_texpr_expr(TVal,AssertionExpr)
716 ; TPre1=TPre,
717 AssertionExpr = assertion_expression(TPre1,ErrMsg,TVal)
718 ),
719 get_texpr_ids(TIds,Ids),
720 nested_couple_to_list(Argument,ArgList),
721 % translate %x.(TPre|TVal)(arg) -> LET x BE x=arg IN ASSERT_EXPR(TPre,Msg,TVal) END
722 same_length(ArgList,TIds),
723 \+ some_id_occurs_in_expr(LocalIds,Argument), % would trigger here LET x BE x=1+1 IN %y.(y:0..x|y+x+x) END (x) = res & x=0
724 ( same_ids_and_types(ArgList,TIds)
725 -> % lambda argument names and provided arguments are identical
726 NewExpr = AssertionExpr % no LET has to be introduced; relevant e.g. for rule_sgc335.mch
727 ; \+ ( sort(Ids,SIds),
728 some_id_occurs_in_expr(SIds,Argument)
729 %,format('Not inlining lambda, parameter id ~w occurs in : ',[Id]), print_bexpr(Argument),nl
730 %, add_message(ast_cleanup,'Not inlining parameter: ',Id,I)
731 ), % otherwise name clash and we would need a LET that can treat LET x BE x=x+1
732 TAssertionExpr = b(AssertionExpr,Type,I),
733 NewExpr = let_expression(TIds,ArgList,TAssertionExpr)
734 ; Ids = [Id1], ArgList = [Arg1] ->
735 %TODO: safely treat multiple args and things like (%(x,v).(x:INTEGER|x*v)(v|->v))=100
736 % In this case we need to substitute all args in one go
737 replace_id_by_expr_with_count(TPre1,Id1,Arg1,TPre2,Count1),
738 replace_id_by_expr_with_count(TVal,Id1,Arg1,TVal2,Count2),
739 Count is Count1+Count2,
740 is_replace_id_by_expr_ok(Arg1,Id1,Count,lambda_guard1),
741 NewExpr = assertion_expression(TPre2,ErrMsg,TVal2)
742 ),
743 % simplify_let will remove simple let expressions and vars used only once
744 % we used to call replace_ids_by_args in all cases, but this can duplicate arguments
745 % not replacing did lead to test 1284 taking very long, 191 seconds instead of 0.3 for 192 states
746 !,
747 ajoin_with_sep(Ids,',',IdsAtom),
748 get_texpr_info(Lambda,LambdaInfo), translate_span(LambdaInfo,LSpan),
749 (get_definition_context_from_span(LambdaInfo,LSpan2)
750 -> ajoin(['lambda function %(',IdsAtom,') ',LSpan,' (', LSpan2,
751 ') called outside of domain, condition false: '],ErrMsg)
752 ; ajoin(['lambda function %(',IdsAtom,') ',LSpan,
753 ' called outside of domain, condition false: '],ErrMsg)),
754 (debug_mode(off) -> true
755 ; add_message(ast_cleanup,'INLINED function application for: ',Ids,I),
756 translate:nested_print_bexpr(b(NewExpr,Type,I)),nl
757 ).
758 cleanup_pre_function(Fun,Arg,integer,I,ArithOp,I,multi/succ_pred_optimisation) :-
759 precompute_pred_succ_function_call(Fun,Arg,ArithOp).
760 /* cleanup_pre(event_b_comprehension_set([ID],ID,Pred),T,I,comprehension_set([Result],NewPred),T,
761 [was(event_b_comprehension_set)|I],multi/ev_compset_single_id) :-
762 % Event_B_Comprehension with a single ID which is also the expression
763 % TO DO: expand for multiple IDs
764 !,
765 Result = ID, NewPred=Pred. */
766 % Detect if_then_else; also done in cleanup_post (in pre we may be able to detect IF-THEN-ELSE before CSE has inserted lazy_lets
767 cleanup_pre_function(IFT,DUMMYARG,_Type,Info,if_then_else(IFPRED,THEN,ELSE),Info,multi/function_if_then_else) :-
768 is_if_then_else(IFT,pre,DUMMYARG,IFPRED,THEN,ELSE),
769 (debug_mode(off) -> true
770 ; print('% Recognised if-then-else expression (pre): IF '), print_bexpr(IFPRED),
771 print(' THEN '),print_bexpr(THEN), print(' ELSE '), print_bexpr(ELSE),nl
772 ).
773
774 % check if we detect a lambda or a lambda wrapped inside let_expressions
775 % e.g., LET one BE one=1 IN LET two BE two=2 IN %(x).(x:INTEGER|x+one+one+two+two)END END(y) = 7
776 % NewType: by moving the function application into the LETs the type of the LETs need to be adapted
777 is_lambda_in_context(let_expression(LetIds,Exprs,b(Lambda,_OldType,Info)),NewType,TIds,TPred,TValue,
778 let_expression(LetIds,Exprs,b(InnerCtxt,NewType,Info)),Hole,NewLocalIds) :- !,
779 is_lambda_in_context(Lambda,NewType,TIds,TPred,TValue,InnerCtxt,Hole,LocalIds),
780 get_texpr_ids(LetIds,Ids),
781 sort(Ids,SIds),
782 ord_union(SIds,LocalIds,NewLocalIds).
783 is_lambda_in_context(Lambda,_NewType,TIds,TPred,TValue,Context,ReplacementHole,[]) :-
784 Context=ReplacementHole,
785 is_lambda(Lambda, TIds, TPred,TValue).
786
787 :- use_module(closures,[is_lambda_closure/7, is_lambda_comprehension_set/4]).
788 is_lambda(lambda(TIds,TPred,TValue), TIds, TPred,TValue) :- !.
789 is_lambda(event_b_comprehension_set([TId],Expr,TPred), [TId], TPred, TValue) :- !,
790 % rewrite_event_b_comprehension_set does not seem to get called before the function/lambda rule is applied
791 % {ID.ID|->Val | PRed}
792 Expr = b(couple(LHS,RHS),_,_),
793 same_texpr(LHS,TId),
794 TValue=RHS.
795 is_lambda(value(Closure),[TId],TPred,TValue) :- !, nonvar(Closure), Closure = closure(Args,Types,Body),
796 is_lambda_closure(Args,Types,Body, [OtherID], [OtherType], TPred, TValue),
797 create_typed_id(OtherID,OtherType,TId). % TODO: accept lambdas with more than one argument TId
798 is_lambda(CompSet,TIds,Pred,Val) :- CompSet=comprehension_set(_,_),
799 is_lambda_comprehension_set(b(CompSet,any,[]),TIds,Pred,Val).
800 is_just_typing_pred(b(member(_,B),pred,_)) :- is_just_type(B). % would be removed by remove_type_member rule
801
802
803 :- use_module(external_function_declarations,[synonym_for_external_predicate/2]).
804
805 get_string(b(string(S),_,_),S).
806 get_string(b(value(V),_,_),S) :- nonvar(V), V=string(Str), atom(Str), S=Str.
807 % translate a boolean value into a predicate:
808 get_pred_from_bool(b(convert_bool(P),_,_),Pred) :- !, Pred=P.
809 get_pred_from_bool(BOOL,b(equal(BOOL,BTRUE),pred,[])) :- BTRUE = b(boolean_true,boolean,[]).
810
811 translate_integer_set('NAT',I,interval(b(integer(0),integer,I),b(max_int,integer,I))).
812 translate_integer_set('NAT1',I,interval(b(integer(1),integer,I),b(max_int,integer,I))).
813 translate_integer_set('INT',I,interval(b(min_int,integer,I),b(max_int,integer,I))).
814 %translate_integer_set('INTEGER',I,comprehension_set([b(identifier('_zzzz_unary'),integer,I)],
815 % b(truth,pred,[prob_annotation('SYMBOLIC')|I]))).
816 %translate_integer_set('NATURAL',I,comprehension_set([b(identifier('_zzzz_unary'),integer,I)],
817 % b(greater_equal(b(identifier('_zzzz_unary'),integer,I),
818 % b(integer(0),integer,I)),pred,[prob_annotation('SYMBOLIC')|I]))).
819 %translate_integer_set('NATURAL1',I,comprehension_set([b(identifier('_zzzz_unary'),integer,I)],
820 % b(greater_equal(b(identifier('_zzzz_unary'),integer,I),
821 % b(integer(1),integer,I)),pred,[prob_annotation('SYMBOLIC')|I]))).
822
823 % detect if an expression is equivalent to an integer set, does not check for interval yet
824 is_integer_set(integer_set(S),S).
825 is_integer_set(comprehension_set([b(identifier(ID),integer,_)],b(B,_,_)),S) :-
826 is_integer_set_constraint_pred(B,ID,S).
827 is_integer_set_constraint_pred(truth,_,'INTEGER').
828 is_integer_set_constraint_pred(Expr,ID,Set) :-
829 is_greater_equal(Expr,b(identifier(ID),integer,_),TNr),
830 get_integer(TNr,Nr),
831 (Nr=0 -> Set='NATURAL' ; Nr=1 -> Set='NATURAL1').
832 is_integer_set_constraint_pred(Expr,ID,Set) :-
833 is_greater(Expr,b(identifier(ID),integer,_),TNr),
834 get_integer(TNr,Nr),
835 (Nr = -1 -> Set='NATURAL' ; Nr=0 -> Set='NATURAL1').
836
837 is_greater_equal(greater_equal(A,B),A,B).
838 is_greater_equal(less_equal(B,A),A,B).
839 is_greater(greater(A,B),A,B).
840 is_greater(less(B,A),A,B).
841
842 is_inf_integer_set_with_lower_bound(b(X,_,_),Bound) :- is_integer_set(X,N),
843 (N='NATURAL' -> Bound=0 ; N='NATURAL1' -> Bound=1).
844
845
846
847 is_subset(subset(A,B),A,B).
848 is_subset(member(A,b(pow_subset(B),_,_)),A,B). % x : POW(T) <=> x <: T
849
850 % tool to translate CASE values to Test predicates for IF-THEN-ELSE
851 gen_if_elsif(CaseID,b(case_or(ListOfValues, Body),_,I),
852 b(if_elsif(Test,Body),subst,I)) :-
853 get_texpr_type(CaseID,T),
854 SEXT = b(set_extension(ListOfValues),set(T),I),
855 Test = b(member(CaseID,SEXT),pred,I).
856
857 % the case below happens frequently in data validation:
858 remove_position_info_from_list(List,I,NList) :-
859 member(nodeid(pos(C,FilePos,Line,From,Line,To)),I),
860 To-From > 1000, % the entire set/sequence extension is on one large line
861 length(List,Len), Len>100, % it has many elements
862 % we replace all position infos by the same top-level position info (enabling sharing)
863 maplist(remove_position_info(nodeid(pos(C,FilePos,Line,From,Line,To))),List,NList),
864 (debug_mode(off) -> true
865 ; format('SIMPLIFY POSITION INFO IN SET/SEQUENCE EXTENSION: line # ~w, length ~w~n',[Line,Len])).
866 remove_position_info(NI,b(Expr,Type,Infos),b(NExpr,Type,NewInfos)) :-
867 syntaxtransformation(Expr,Subs,_Names,NSubs,NExpr),
868 (select(nodeid(pos(_,_FilePos,_,_,_,_)),Infos,NT) -> NewInfos=[NI|NT] ; NewInfos=Infos),
869 maplist(remove_position_info(NI),Subs,NSubs).
870
871 :- use_module(bsyntaxtree,[delete_pos_info/2]).
872 % just remove position infos from top-lefel
873 remove_top_levelposition_info(b(Expr,Type,Infos),b(Expr,Type,NewInfos)) :-
874 delete_pos_info(Infos,NewInfos). % TODO: maybe remove other useless infos
875
876 % rules for function application of various projection functions
877 cleanup_function_projection(first_projection(A,B),Argument,I,Result) :-
878 gen_assertion_expression(A,B,Argument,first_of_pair(Argument),first,I,Result).
879 cleanup_function_projection(second_projection(A,B),Argument,I,Result) :-
880 gen_assertion_expression(A,B,Argument,second_of_pair(Argument),second,I,Result).
881 cleanup_function_projection(event_b_second_projection(A),Argument,_I,Result) :- % old style Rodin projection
882 check_is_just_type(A),Result = first_of_pair(Argument).
883 cleanup_function_projection(event_b_second_projection(A),Argument,_I,Result) :- % old style Rodin projection
884 check_is_just_type(A),Result = second_of_pair(Argument).
885 cleanup_function_projection(event_b_first_projection_v2,Argument,_I,Result) :- Result = first_of_pair(Argument).
886 cleanup_function_projection(event_b_second_projection_v2,Argument,_I,Result) :- Result = second_of_pair(Argument).
887
888 check_is_just_type(_A) :- preferences:get_preference(ignore_prj_types,true),!.
889 check_is_just_type(A) :- (is_just_type(A) -> true ; debug_println(9,not_type_for_prj(A)),fail).
890
891 :- use_module(bsyntaxtree,[get_texpr_set_type/2]).
892 gen_assertion_expression(A,B,_Argument,ProjExpr,_ProjType,_I,Result) :-
893 check_is_just_type(A),check_is_just_type(B),
894 !,
895 Result = ProjExpr.
896 % TO DO: add simplification rule for couple(x,y) : A*B with A or B being just types
897 gen_assertion_expression(A,B,Argument,ProjExpr,ProjType,Info,Result) :-
898 create_cartesian_product(A,B,CartAB),
899 safe_create_texpr(member(Argument,CartAB),pred,MemCheck),
900 ErrMsg = 'projection function called outside of domain: ', % TO DO: provide better user message with Argument result
901 (ProjType == first -> get_texpr_set_type(A,TT) ; get_texpr_set_type(B,TT)), %%
902 %get_texpr_pos_infos(Argument,Info), % add position infos
903 extract_pos_infos(Info,PosInfo),
904 safe_create_texpr(ProjExpr,TT,PosInfo,TProjExpr),
905 Result = assertion_expression(MemCheck,ErrMsg,TProjExpr).
906 :- use_module(bsyntaxtree,[is_set_type/2]).
907 create_cartesian_product(A,B,CartAB) :-
908 get_texpr_types([A,B],[STA,STB]),
909 is_set_type(STA,TypeA), is_set_type(STB,TypeB),
910 safe_create_texpr(cartesian_product(A,B),set(couple(TypeA,TypeB)),CartAB).
911
912
913 % rewriting Event-B comprehension sets into classical B style ones
914 rewrite_event_b_comprehension_set(IDs,CoupleExpr,Pred, _T, NewExpression) :-
915 % detect lambda expressions in classical B style
916 nested_couple_to_list(CoupleExpr,List),
917 check_ids(IDs,List,Expr),!,
918 NewExpression = lambda(IDs,Pred,Expr).
919 rewrite_event_b_comprehension_set(IDList,CoupleExpr,Pred, _T, NewExpression) :-
920 % Event_B_Comprehension with a several IDs which are also used as the couple expression
921 nested_couple_to_list(CoupleExpr,List),
922 List = IDList,
923 !,
924 NewExpression = comprehension_set(IDList,Pred).
925 rewrite_event_b_comprehension_set(Ids,Expr,Pred, T, NewExpression) :-
926 NewExpression = comprehension_set([Result],NewPred),
927 unify_types_strict(T,set(Type)),
928 % print(event_b_comprehension_set(Ids,Expr,Pred)),nl,
929 (select(Expr,Ids,RestIds)
930 -> % the Expr is an identifier which is part of Ids: we can avoid complicated translation below
931 % example {f,n•n:INT & f:1..n-->Digit|f} --translated-> {f|#(n).(n:INT & f:1..n-->Digit)}
932 % print(remove(Expr,RestIds)),nl,
933 ExPred=Pred, Result=Expr
934 ; get_unique_id_inside('__comp_result__',Pred,Expr,ResultId),
935 create_texpr(identifier(ResultId),Type,[],Result),
936 safe_create_texpr(equal(Result,Expr),pred,Equal),
937 conjunct_predicates_with_pos_info(Pred,Equal,ExPred), % put Equal after Pred for WD; used to be other order!
938 RestIds=Ids
939 ),
940 create_exists(RestIds,ExPred,NewPred). %, print(done_rewrite_event_b_comprehension_set),nl, print_bexpr(NewPred),nl.
941
942 check_ids([],[CoupleExpr],CoupleExpr). % we terminate with a single expression
943 check_ids([ID|T],[CoupleExprID|CT],Rest) :-
944 same_id(ID,CoupleExprID,_),
945 check_ids(T,CT,Rest).
946
947
948 evaluate_seq_extension_to_avl(List,AVL,LocalIds) :-
949 evaluate_set_extension(List,EvaluatedList,LocalIds),
950 convert_set_to_seq(EvaluatedList,1,ESeq),
951 convert_to_avl(ESeq,AVL).
952
953 evaluate_set_extension([],[],_).
954 evaluate_set_extension([H|List],[EH|EvaluatedList],LocalIds) :-
955 eval_set_extension_element(H,EH,LocalIds),
956 evaluate_set_extension(List,EvaluatedList,LocalIds).
957
958 extension_should_be_evaluated(List) :-
959 %preferences:has_default_value(use_solver_on_load), % Kodkod could not translate booleans back; now it can; check if we still need this
960 preferences:get_preference(optimize_ast,true),
961 List \= [],
962 List = [_|ListT], ListT \= []. % do not do this for singleton sets so as not to prevent triggering of other rules
963
964 :- use_module(kernel_reals,[construct_real/2, construct_negative_real/2]).
965 % construct a value term for a simple AST element:
966 eval_set_extension_element(b(E,T,_I),EE,LocalIds) :-
967 (eval_set_extension_aux(E,EE,LocalIds) -> true
968 ; eval_set_extension_typed_aux(E,T,EE,LocalIds)
969 % ; print('eval_set_extension failed: '),tools_printing:print_term_summary(E),nl,translate:print_span(_I),nl,fail
970 ).
971 eval_set_extension_aux(boolean_false,pred_false,_).
972 eval_set_extension_aux(boolean_true,pred_true,_).
973 eval_set_extension_aux(couple(A,B),(EA,EB),LocalIds) :-
974 eval_set_extension_element(A,EA,LocalIds), eval_set_extension_element(B,EB,LocalIds).
975 eval_set_extension_aux(integer(I),int(I),_).
976 eval_set_extension_aux(real(Atom),Real,_) :- construct_real(Atom,Real).
977 eval_set_extension_aux(unary_minus(b(Val,_,_)),Res,_) :- eval_set_ext_minus(Val,Res).
978 eval_set_extension_aux(string(S),string(S),_).
979 eval_set_extension_aux(empty_set,[],_).
980 eval_set_extension_aux(empty_sequence,[],_).
981 eval_set_extension_aux(value(V),V,_).
982 eval_set_extension_aux(rec(Fields),rec(EF),LocalIds) :- eval_set_extension_fields(Fields,EF,LocalIds).
983 %eval_set_extension_aux(interval(A,B),...) :- ...
984 eval_set_extension_aux(set_extension(List),AVL,LocalIds) :-
985 evaluate_set_extension(List,EvaluatedList,LocalIds),
986 convert_to_avl(EvaluatedList,AVL).
987 eval_set_extension_aux(sequence_extension(List),AVL,LocalIds) :-
988 evaluate_seq_extension_to_avl(List,AVL,LocalIds).
989
990
991 :- use_module(probsrc(kernel_freetypes),[registered_freetype_case_value/3, freetype_case_db/3]).
992 eval_set_extension_typed_aux(identifier(ID),TYPE,FDVal,LocalIds) :- LocalIds \= not_available,
993 (TYPE = global(GType)
994 -> b_global_sets:lookup_global_constant(ID,FDVal),
995 ord_nonmember(ID,LocalIds),
996 % we could check if enumerated_set_element entry in infos, cf is_just_type3 with given_set info
997 % may not yet be fully precompiled, hence we rely on pre_register_enumerated_set_with_elems
998 FDVal = fd(_,GType) % just check that the type matches, in case ID is a local name with different type
999 ; TYPE = freetype(FType)
1000 -> % see b_global_set_or_free_type; we could also accept global sets and freetype sets
1001 registered_freetype_case_value(ID,TYPE,FDVal),
1002 ord_nonmember(ID,LocalIds),
1003 FDVal = freeval(FType,_,_) % check type matches
1004 ).
1005 eval_set_extension_typed_aux(function(TID,Args),freetype(FreetypeId),V,LocalIds) :- LocalIds \= not_available,
1006 ground(FreetypeId),
1007 get_texpr_id(TID,CaseId),
1008 freetype_case_db(CaseId,FreetypeId,_CaseType),
1009 ord_nonmember(CaseId,LocalIds),
1010 %write(case(CaseId,FreetypeId,CaseType)),nl,
1011 eval_set_extension_element(Args,EArgs,LocalIds),
1012 V = freeval(FreetypeId,CaseId,EArgs).
1013 %eval_set_extension_typed_aux(E,T,_,_) :- print(uncov(E,T)),nl,nl,fail.
1014
1015
1016 eval_set_ext_minus(integer(I),int(R)) :- R is -I.
1017 eval_set_ext_minus(real(Atom),Real) :- construct_negative_real(Atom,Real).
1018
1019 eval_set_extension_fields([],[],_LocalIds).
1020 eval_set_extension_fields([field(Name,V)|T],[field(Name,EV)|ET],LocalIds) :- eval_set_extension_element(V,EV,LocalIds),
1021 eval_set_extension_fields(T,ET,LocalIds).
1022
1023 convert_set_to_seq([],_,[]).
1024 convert_set_to_seq([H|T],N,[(int(N),H)|CT]) :- N1 is N+1, convert_set_to_seq(T,N1,CT).
1025
1026
1027 post_let_forall(AllIds,P,Rhs,NewPred,modification) :-
1028 conjunction_to_list(P,Preds), reverse(Preds,RPreds),
1029 select_equality(TId,RPreds,[],_,Expr,RRest,UsedIds,no_check),
1030 select(TId,AllIds,RestIds),
1031 get_texpr_id(TId,Id),
1032 \+ member(Id,UsedIds), % not a recursive equality
1033 reverse(RRest,Rest),
1034 conjunct_predicates_with_pos_info(Rest,RestPred),
1035 \+ occurs_in_expr(Id,RestPred),
1036 !,
1037 NewRhs = b(let_predicate([TId],[Expr],Rhs),pred,[]),
1038 post_let_forall(RestIds,RestPred,NewRhs,NewPred,_).
1039 post_let_forall(AllIds,P,Rhs,NewPred, no_modification) :-
1040 create_implication(P,Rhs,NewForallBody),
1041 create_forall(AllIds,NewForallBody,NewP),
1042 get_texpr_expr(NewP,NewPred).
1043
1044
1045 is_interval(b(interval(A,B),_,_),A,B).
1046 is_interval(b(value(V),set(_),_),A,B) :- nonvar(V), V=closure(P,T,B),
1047 custom_explicit_sets:is_interval_closure(P,T,B,LOW,UP), integer(LOW),integer(UP),
1048 A=b(integer(LOW),integer,[]),
1049 B=b(integer(UP),integer,[]).
1050
1051 % a more flexible version, also detecting singleton set extension
1052 is_interval_or_singleton(I,A,B) :- is_interval(I,A,B),!.
1053 is_interval_or_singleton(b(set_extension([A]),set(integer),_),A,A).
1054
1055
1056
1057 % create a lambda expression for a projection
1058 create_projection_set(A,B,_Switch,Res) :-
1059 (definitely_empty_set(A) ; definitely_empty_set(B)),!,
1060 Res = empty_set.
1061 create_projection_set(A,B,Switch,lambda(Ids,SPred,Expr)) :- % generate lambda to be able to use function(lambda) rule
1062 Ids = [TArg1,TArg2],
1063 ( Switch==first -> Expr = TArg1
1064 ; Switch==second -> Expr = TArg2),
1065 get_texpr_type(A,TA1), unify_types_strict(TA1,set(Type1)),
1066 get_texpr_type(B,TB2), unify_types_strict(TB2,set(Type2)),
1067 (contains_no_ids(A,B) -> Arg1 = '_zzzz_unary', Arg2 = '_zzzz_binary' % avoid generating fresh ids; relevant for test 1313 and ticket PROB-346
1068 % TO DO: check whether _zzzz_unary/binary are actually used; we should avoid generating fresh ids whenever possible (otherwise syntactically identical formulas become different)
1069 ; get_unique_id_inside('_prj_arg1__',A,B,Arg1),
1070 get_unique_id_inside('_prj_arg2__',A,B,Arg2)),
1071 create_texpr(identifier(Arg1),Type1,[generated(Switch)],TArg1),
1072 create_texpr(identifier(Arg2),Type2,[generated(Switch)],TArg2),
1073 safe_create_texpr(member(TArg1,A),pred,MembA),
1074 safe_create_texpr(member(TArg2,B),pred,MembB),
1075 conjunct_predicates([MembA,MembB],Pred), SPred=Pred.
1076 % bsyntaxtree:mark_bexpr_as_symbolic(Pred,SPred). % TO DO: put mark code into another module; maybe only mark as symbolic if types large enough ??
1077
1078 contains_no_ids(A,B) :- contains_no_ids(A), contains_no_ids(B).
1079 contains_no_ids(b(E,_,_)) :- contains_no_ids_aux(E).
1080 contains_no_ids_aux(bool_set).
1081 contains_no_ids_aux(X) :- is_integer_set(X,_). % comprehension set may contain ids, but not visible to outside
1082 contains_no_ids_aux(mult_or_cart(A,B)) :- contains_no_ids(A),contains_no_ids(B).
1083 contains_no_ids_aux(relations(A,B)) :- contains_no_ids(A),contains_no_ids(B).
1084 contains_no_ids_aux(pow_subset(A)) :- contains_no_ids(A).
1085 contains_no_ids_aux(pow1_subset(A)) :- contains_no_ids(A).
1086 contains_no_ids_aux(real_set).
1087 contains_no_ids_aux(string_set).
1088 contains_no_ids_aux(interval(A,B)) :- contains_no_ids(A),contains_no_ids(B).
1089 % TO DO: add more
1090
1091 create_event_b_projection_set(Rel,Switch,lambda(Ids,SPred,Expr)) :-
1092 Ids = [TArg1,TArg2],
1093 ( Switch==first -> Expr = TArg1
1094 ; Switch==second -> Expr = TArg2),
1095 get_texpr_type(Rel,RT),unify_types_strict(RT,set(couple(Type1,Type2))),
1096 get_unique_id_inside('_prj_arg1__',Rel,Arg1),
1097 get_unique_id_inside('_prj_arg2__',Rel,Arg2),
1098 create_texpr(identifier(Arg1),Type1,[generated(Switch)],TArg1),
1099 create_texpr(identifier(Arg2),Type2,[generated(Switch)],TArg2),
1100 create_texpr(couple(TArg1,TArg2),couple(Type1,Type2),[],Couple),
1101 safe_create_texpr(member(Couple,Rel),pred,Member),
1102 SPred=Member.
1103 %bsyntaxtree:mark_bexpr_as_symbolic(Pred,SPred).
1104
1105 create_event_b_projection_set_v2(RelType,Switch,comprehension_set(Ids,SPred)) :-
1106 % we are generating {p1,p2,lambda | lambda=p1/p2}
1107 Ids = [TArg1,TArg2,TArg3],
1108 ( Switch==first -> ResultExpr = TArg1, Type1 = Type3
1109 ; Switch==second -> ResultExpr = TArg2, Type2 = Type3),
1110 unify_types_strict(RelType,set(couple(couple(Type1,Type2),T3))),
1111 (T3==Type3 -> true ; add_error(create_event_b_projection_set,'Unexpected return type: ',T3)),
1112 Arg1 = '_zzzz_unary',
1113 Arg2 = '_zzzz_binary',
1114 Arg3 = '_lambda_result_', % the comprehension set contains no other expressions: no clash possible
1115 create_texpr(identifier(Arg1),Type1,[generated(Switch)],TArg1),
1116 create_texpr(identifier(Arg2),Type2,[generated(Switch)],TArg2),
1117 create_texpr(identifier(Arg3),Type3,[lambda_result(Arg3),generated(Switch)],TArg3),
1118 safe_create_texpr(equal(TArg3,ResultExpr),pred,[prob_annotation('LAMBDA-EQUALITY')],Equal),
1119 SPred=Equal.
1120 % bsyntaxtree:mark_bexpr_as_symbolic(Pred,SPred).
1121 %,print(Pred),nl.
1122
1123 :- use_module(btypechecker,[couplise_list/2,prime_identifiers/2,prime_identifiers0/2, prime_atom0/2]).
1124 % create a comprehension set for quantified union or intersection UNION(x).(P|E) = ran(%x.(P|E))
1125 % TO DO: translate UNION into UNION(x).(P|E) = dom({r,x|P & r:E}) = ran({x,r|P & r:E}) which is considerably faster
1126 % also works for e.g., UNION(x).(x:1..2|{x+y}) = 12..13
1127 %quantified_union_op(Ids,Pred,Expr,SetType,Res) :- is_set_type(SetType,Type),
1128 % !,
1129 % Info = [generated(quantified_union)],
1130 % get_unique_id_inside('_zzzz_unary',Pred,Expr,FRESHID), % also include Expr !
1131 % NewID = b(identifier(FRESHID),Type,[]), %fresh
1132 % append(Ids,[NewID],NewIds),
1133 % safe_create_texpr(member(NewID,Expr),pred,[],Member),
1134 % conjunct_predicates([Pred,Member],Body),
1135 % get_texpr_types(NewIds,Types),couplise_list(Types,TupleType),
1136 % safe_create_texpr(comprehension_set(NewIds,Body),set(TupleType),Info,ComprSet),
1137 % Res = range(ComprSet).
1138 % %safe_create_texpr(range(ComprSet),set(set(Type)),Info,Set), print_bexpr(Set),nl.
1139 %quantified_union_op(Ids,Pred,Expr,SetType,Set) :-
1140 % add_internal_error('Could not translate quantified UNION operator: ',quantified_union_op(Ids,Pred,Expr,SetType,Set)),
1141 % fail.
1142
1143 % create a comprehension set for quantified union or intersection INTER(x).(P|E) = inter(ran(%x.(P|E)))
1144 % UNION could be treated by quantified_union_op above
1145 quantified_set_op(Ids,Pred,Expr,Loc,OuterInfos,Set) :-
1146 create_range_lambda(Ids,Pred,Expr,Loc,OuterInfos,Set),
1147 !. % , print(quantified),nl,print_bexpr(Set),nl.
1148 quantified_set_op(Ids,Pred,Expr,Loc,OuterInfos,Set) :-
1149 add_internal_error('Could not translate quantified set operator: ',
1150 quantified_set_op(Ids,Pred,Expr,Loc,OuterInfos,Set)),
1151 fail.
1152
1153 create_range_lambda(Ids,Pred,Expr,Loc,OuterInfos,Set) :-
1154 Info = [generated(Loc)|OuterInfos],
1155 get_texpr_types(Ids,Types),couplise_list(Types,ArgType),
1156 get_texpr_type(Expr,ExprType),
1157 safe_create_texpr(lambda(Ids,Pred,Expr),set(couple(ArgType,ExprType)),Info,Lambda),
1158 safe_create_texpr(range(Lambda),set(ExprType),Info,Set).
1159
1160
1161 quantified_set_operator(quantified_union(AllIds,Pred,Expr),quantified_union,AllIds,Pred,Expr).
1162 quantified_set_operator(quantified_intersection(AllIds,Pred,Expr),quantified_intersection,AllIds,Pred,Expr).
1163
1164 % match_ids(List1,List2, AllIds,Rest) find all ids in List1 in List2; ids in List2 not in List1 are put in Rest
1165 match_ids([],List,List,List).
1166 match_ids([TID|T],List,[TID2|T2],Rest) :- select(TID2,List,L2),
1167 same_id(TID,TID2,_),!,
1168 match_ids(T,L2,T2,Rest).
1169
1170 % generate dom(.) operators for TypedIds which have to be projected away
1171 generate_dom_for_ids([],E,T,I,b(E,T,I)).
1172 generate_dom_for_ids([TID|Ts],E,T,I,Res) :- T = set(T1),
1173 get_texpr_type(TID,TIDType),
1174 generate_dom_for_ids(Ts,E,set(couple(T1,TIDType)),I,DE),
1175 safe_create_texpr(domain(DE),T,Res).
1176
1177 :- use_module(tools_strings,[ajoin/2,ajoin_with_sep/3]).
1178 % we ensure that this check is only done once, for user machines,... not for generated formulas
1179 check_forall_lhs_rhs(_,_,_,_) :- preferences:get_preference(perform_stricter_static_checks,false),!.
1180 check_forall_lhs_rhs(_,_,_,_) :- preferences:get_preference(disprover_mode,true),!.
1181 check_forall_lhs_rhs(_,_,_,_) :- animation_minor_mode(eventb),!. % typing predicates get removed it seems
1182 check_forall_lhs_rhs(_,_,I,_) :- member(removed_typing,I),!. % means that typing was possibly removed
1183 check_forall_lhs_rhs(Lhs,_,_,_) :- member_in_conjunction(PC,Lhs),
1184 get_texpr_info(PC,PI),member(II,PI),
1185 removed_typing(II),!. % it was something else; does not seem to detect all removed conjunctions, hence we also check I above
1186 check_forall_lhs_rhs(P,_,I,Ids) :- find_identifier_uses_if_necessary(P,[],LhsUsed),
1187 ord_subtract(Ids,LhsUsed,NotDefined),
1188 NotDefined=[_|_],
1189 ajoin_with_sep(NotDefined,',',S),
1190 translate:translate_bexpression(P,PS),
1191 ajoin(['Left-hand side "', PS, '" of forall does not define identifier(s): '],Msg),
1192 add_warning(bmachine_static_checks,Msg,S,I),
1193 fail.
1194 check_forall_lhs_rhs(_,Rhs,I,Ids) :-
1195 find_identifier_uses_if_necessary(Rhs,[],RhsUsed),
1196 (ord_intersect(Ids,RhsUsed) -> true
1197 ; ajoin_with_sep(Ids,',',S),
1198 add_warning(bmachine_static_checks,'Right-hand side of forall does not use identifiers: ',S,I)
1199 ).
1200 removed_typing(removed_typing). removed_typing(was(_)).
1201
1202 :- use_module(kernel_records,[normalise_record_type/2]).
1203 :- use_module(library(lists),[last/2]).
1204
1205 % first the rules that require the path:
1206 cleanup_post_with_path(assign([b(identifier(ID),TYPE,INFO)],[EXPR]),subst,I,
1207 assign_single_id(b(identifier(ID),TYPE,INFO),EXPR),subst,I,single/assign_single_id,Path) :-
1208 \+ animation_minor_mode(eventb), % there is no support in the Event-B interpreter for assign_single_id yet
1209 ? (simple_expression(EXPR) % the assign_single_id is not guarded by a waitflag; EXPR should not be too expensive too calculate
1210 -> true
1211 ; % if we are in an unguarded context; then we do not need to guard EXPR by waitflag anyway
1212 ? maplist(unguarded,Path)
1213 ),
1214 !,
1215 (debug_level_active_for(4) -> format('Single Assignment to ~w~n',[ID])
1216 %translate:print_subst(b(assign([b(identifier(ID),TYPE,INFO)],[EXPR]),subst,I)),nl
1217 ; true).
1218 cleanup_post_with_path(any(Ids,Pred,Subst),subst,Info,any(Ids,Pred,NewSubst),subst,NewInfo,multi/remove_useless_assign,_Path) :-
1219 get_preference(optimize_ast,true),
1220 member_in_conjunction(b(equal(TID1,TID2),pred,_),Pred),
1221 get_texpr_id(TID1,ID1),
1222 get_texpr_id(TID2,ID2), % we have an equality of the form x=x' (as generated by TLA2B)
1223 delete_assignment(Subst,TID3,TID4,NewSubst),
1224 get_texpr_id(TID4,ID4), get_texpr_id(TID3,ID3),
1225 ( c(ID1,ID2) = c(ID3,ID4) ; c(ID1,ID2) = c(ID4,ID3)), % we have an assignment x:=x' or x':=x
1226 % the cleanup rule recompute_accessed_vars below recomputes the info fields for enclosing operations! get_accessed_vars is currently called before ast_cleanup
1227 ajoin([ID3,' := ',ID4],Assign),
1228 add_hint_message(remove_useless_assign,'Removing useless assignment: ',Assign,Info),
1229 (member(removed_useless_assign,Info) -> NewInfo=Info ; NewInfo=[removed_useless_assign|Info]).
1230 cleanup_post_with_path(operation(TName,Res,Params,TBody),Type,Info,
1231 operation(TName,Res,Params,NewTBody),Type,NewInfos,single/recompute_accessed_vars,_Path) :-
1232 TBody=b(Body,subst,BInfos),
1233 select(removed_useless_assign,BInfos,NewBInfos),
1234 btypechecker:compute_accessed_vars_infos_for_operation(TName,Res,Params,TBody,Modifies,_,_,NewRWInfos),
1235 debug_format(19,'Recomputing read/write infos for ~w (~w)~n',[TName,Modifies]),
1236 update_infos(NewRWInfos,Info,NewInfos),
1237 NewTBody=b(Body,subst,NewBInfos).
1238 cleanup_post_with_path(any(Ids,Pred,Subst),subst,I,Result,subst,[generated|I],single/transform_any_into_let,Path) :-
1239 (last(Path,path_arg(top_level(_),_))
1240 /* do not remove top-level ANY if show_eventb_any_arguments is true; see, e.g., test 1271 */
1241 -> preferences:preference(show_eventb_any_arguments,false) ; true),
1242 conjunction_to_list(Pred,Preds),
1243 get_sorted_ids(Ids,BlacklistIds),
1244 find_one_point_rules(Ids,Preds,BlacklistIds,LetIDs,Exprs,RestIds,RestPreds),
1245 LetIDs \= [],
1246 maplist(create_equality,LetIDs,Exprs,LetDefs),
1247 % print(found_lets(LetIDs,RestIds,RestPred)),nl,print(Path),nl,
1248 conjunct_predicates_with_pos_info(LetDefs,LetDefPred),
1249 (RestIds = [], RestPreds=[] % complete ANY can be translated to LET
1250 -> Result = let(LetIDs,LetDefPred,Body), Body = Subst
1251 ; split_predicates(RestPreds,Ids,RestUsingIds,RestNotUsingIds),
1252 conjunct_predicates_with_pos_info(RestPreds,RestPred),
1253 % print('USING: '), print_bexpr(RestUsingIds),nl, print('NOT USING: '), print_bexpr(RestNotUsingIds),nl,
1254 (RestIds = []
1255 -> (is_truth(RestUsingIds)
1256 % RestPred does not use the LET identifiers; move outside of the LET !
1257 -> Result = select([b(select_when(RestPred,SelectBody),subst,[generated|I])]),
1258 SelectBody = b(let(LetIDs,LetDefPred,Subst),subst,[generated|I])
1259 ; is_truth(RestNotUsingIds)
1260 % RestPred uses LET identifiers in all conjuncts; move inside LET
1261 -> Result = let(LetIDs,LetDefPred,LetBody),
1262 LetBody = b(select([b(select_when(RestPred,Subst),subst,[])]),subst,[generated|I])
1263 ;
1264 % we would need to generate an outer and inner select; transformation probably not worth it
1265 fail
1266 )
1267 ; is_truth(RestUsingIds)
1268 % RestPred does not use LET identifiers move outside of LET
1269 -> Result = any(RestIds,RestPred,SelectBody),
1270 SelectBody = b(let(LetIDs,LetDefPred,Subst),subst,[generated|I])
1271 ; is_truth(RestNotUsingIds)
1272 % RestPred uses LET identifiers in all conjuncts; move inside LET
1273 -> Result = let(LetIDs,LetDefPred,LetBody),
1274 LetBody = b(any(RestIds,RestPred,Subst),subst,I)
1275 ;
1276 % we would need to generate an outer and inner any; transformation probably not worth it
1277 fail
1278 )
1279 ),
1280 !. %,translate:print_subst(b(Result,subst,[])),nl.
1281 cleanup_post_with_path(operation(TName,Res,Params,Body),Type,Info,
1282 operation(TName,Res,Params,NewBody),Type,Info,single/lts_min_guard_splitting,Path) :-
1283 (get_preference(ltsmin_guard_splitting,true) ; \+ get_preference(pge,off)), % equivalent to pge_algo:is_pge_opt_on),
1284 Path = [path_arg(top_level(operation_bodies),_)], % only apply at top-level and TO DO: only for top-most machine !!
1285 % TO DO: also apply for Event-B models
1286 get_texpr_id(TName,Name),
1287 (get_operation_propositional_guards(Name,Res,Params,Body,Guards,RestBody)
1288 -> true
1289 ; add_warning(ltsmin_guard_splitting,'Cannot extract guard for:',Name),fail),
1290 Guards \= [],
1291 conjunct_predicates_with_pos_info(Guards,G),
1292 get_texpr_info(Body,BInfo),
1293 NewBody = b(precondition(G,RestBody),subst,[prob_annotation('LTSMIN-GUARD')|BInfo]), % a SELECT would be more appropriate
1294 (debug_mode(off) -> true
1295 ; format('Extracting LTS Min guard for ~w~n',[Name]),translate:print_subst(NewBody),nl).
1296 cleanup_post_with_path(exists(Ids,B),Type,OInfo,exists(Ids,B),Type,NInfo,single/invalidate_used_ids,_Path) :-
1297 delete(OInfo,used_ids(_),NInfo). % the changes done by cleanups, e.g, removing unused predicates can affect used_ids
1298 cleanup_post_with_path(forall(Ids,LHS,RHS),Type,OInfo,forall(Ids,LHS,RHS),Type,NInfo,single/invalidate_used_ids,_Path) :-
1299 delete(OInfo,used_ids(_),NInfo). % ditto
1300 cleanup_post_with_path(OExpr,OType,OInfo,NExpr,NType,NInfo,Mode/Rule,Path) :-
1301 get_preference(optimize_ast,true),
1302 cleanup_post_ne_with_path(OExpr,OType,OInfo,NExpr,NType,NInfo,Mode/Rule,Path).
1303 cleanup_post_with_path(OExpr,OType,OInfo,NExpr,NType,NInfo,Mode/Rule,_Path) :-
1304 ? cleanup_post_essential(OExpr,OType,OInfo,NExpr,NType,NInfo,Mode/Rule).
1305
1306 % delete an assignment from a substitution
1307 delete_assignment(b(assign(LHS,RHS),subst,Info),ID,IDRHS,b(RES,subst,Info)) :-
1308 nth1(Pos,LHS,ID,RestLHS),
1309 nth1(Pos,RHS,IDRHS,RestRHS),
1310 (RestLHS = [] -> RES = skip ; RES = assign(RestLHS,RestRHS)).
1311 % TO DO: also deal with parallel and possibly other constructs assign_single_id,...
1312
1313 %unguarded(path_arg(sequence/1,1)). % first argument of sequence is not guarded
1314 ?unguarded(path_arg(X,_)) :- unguarded_aux(X).
1315 unguarded_aux(top_level(_)).
1316 unguarded_aux(operation/4).
1317 unguarded_aux(parallel/1).
1318 unguarded_aux(var/2).
1319 unguarded_aux(let/3).
1320 % what about choice/2 ??
1321
1322 :- load_files(library(system), [when(compile_time), imports([environ/2])]).
1323
1324
1325 % ---------------------
1326
1327 % now the rules which do not need the Path
1328
1329 % first check for a few expressions that never need to be optimised, rewritten:
1330 cleanup_post_essential(E,_,_,_,_,_,_) :- never_transform_or_optimise(E),!,fail.
1331
1332 cleanup_post_essential(Expr,Type,I,Expr,Type,I2,single/remove_erroneous_info_field) :-
1333 \+ ground(I),!,
1334 functor(Expr,F,_N),
1335 add_internal_error('Information field not ground: ',I:F),
1336 I2=[].
1337 cleanup_post_essential(comprehension_set(Ids,E),Type,I,comprehension_set(Ids,E),Type,I,single/sanity_check) :-
1338 get_preference(prob_safe_mode,true),
1339 get_texpr_ids(Ids,UnsortedIds),sort(UnsortedIds,SIds),
1340 \+ same_length(UnsortedIds,SIds),
1341 add_error(cleanup_post,'Identifier clash in comprehension set: ',UnsortedIds),
1342 print(E),nl,
1343 fail.
1344
1345
1346 cleanup_post_essential(lambda(Ids,Pred,Expr),Type,I,
1347 comprehension_set(CompIds,CompPred),Type,NewInfo,multi/remove_lambda) :- !,
1348 unify_types_strict(Type,set(couple(_ArgType,ResType))),
1349 get_unique_id_inside('_lambda_result_',Pred,Expr,ResultId),
1350 def_get_texpr_id(Result,ResultId),
1351 get_texpr_type(Result,ResType),
1352 get_texpr_info(Result,[lambda_result(ResultId)]),
1353 append(Ids,[Result],CompIds),
1354 get_texpr_expr(Equal,equal(Result,Expr)),
1355 get_texpr_type(Equal,pred),
1356 extract_important_info_from_subexpression(Expr,EqInfo), % mark equality with wd condition if Expr has wd condition
1357 (member(prob_annotation('SYMBOLIC'),EqInfo)
1358 -> % something like %p.(p : BOOL|%t.(t : NATURAL|t .. t + 7))
1359 (debug_mode(off) -> true
1360 ; write('Marking lambda as symbolic because result is symbolic: '),print_bexpr(Expr),nl),
1361 add_info_if_new(I,prob_annotation('SYMBOLIC'),NewInfo)
1362 ; infinite_or_symbolic_domain_for_lambda(Ids,Pred,Kind)
1363 -> % something like %t.(t : NATURAL|t .. t + 7)
1364 (debug_mode(off) -> true
1365 ; get_texpr_ids(Ids,AIds),
1366 format('Marking lambda over ~w as symbolic because the domain is ~w: ',[AIds,Kind]),
1367 print_bexpr(Pred),nl),
1368 add_info_if_new(I,prob_annotation('SYMBOLIC'),NewInfo)
1369 ; NewInfo = I),
1370 get_texpr_info(Equal,[prob_annotation('LAMBDA-EQUALITY')|EqInfo]),
1371 conjunct_predicates_with_pos_info(Pred,Equal,CompPred0),
1372 add_texpr_infos(CompPred0,[prob_annotation('LAMBDA')],CompPred). % checked e.g. in is_converted_lambda_closure
1373 %print_bexpr(b(comprehension_set(CompIds,CompPred),Type,NewInfo)),nl.
1374
1375 cleanup_post_essential(reflexive_closure(Rel),Type,I, UNION,Type,NewInfo,multi/remove_reflexive_closure) :- !,
1376 NewInfo = [was(reflexive_closure)|I],
1377 safe_create_texpr(closure(Rel),Type,I,CL),
1378 UNION = union(b(event_b_identity,Type,IdInfo), CL), % closure(R) = id \/ closure1(R)
1379 (is_infinite_ground_type(Type) -> IdInfo = [prob_annotation('SYMBOLIC')|I] ; IdInfo =I),
1380 (debug_mode(on) -> print('Rewriting closure to: '), print_bexpr(b(UNION,Type,[])),nl ; true).
1381 cleanup_post_essential(evb2_becomes_such(Ids,Pred),subst,I,becomes_such(Ids,Pred2),subst,I,multi/ev2_becomes_such) :-
1382 % we translate a Classical-B becomes_such with id -> id$0, id' -> id
1383 % classical B: Dec = BEGIN level : (level>=0 & level> level$0-5 & level < level$0) END
1384 % Event-B: level'>= 0, level' > level-5 ...
1385 !,
1386 prime_identifiers(Ids,PIds),
1387 maplist(gen_rename,PIds,Ids,RenameList1), % id' -> id
1388 prime_identifiers0(Ids,PIds0),
1389 maplist(gen_rename,Ids,PIds0,RenameList2), % id -> id$0
1390 append(RenameList1,RenameList2,RenameList),
1391 rename_bt(Pred,RenameList,Pred2),
1392 (debug_mode(off) -> true
1393 ; format('Converting Event-B becomes_such: ',[]), print_bexpr(Pred2),nl).
1394 cleanup_post_essential(successor,Type,I,Compset,Type,[was(successor)|I],multi/successor) :- !,
1395 % translation of succ
1396 pred_succ_compset(add,Compset).
1397 cleanup_post_essential(rev(A),string,I,ExtFunCall,string,[was(rev)|I],multi/rev_for_string) :- !,
1398 % translation of rev for STRINGs, this can only occur when allow_sequence_operators_on_strings is true
1399 ExtFunCall = external_function_call('STRING_REV',[A]).
1400 cleanup_post_essential(concat(A,B),string,I,ExtFunCall,string,[was(concat)|I],multi/concat_for_string) :- !,
1401 % translation of concat (^) for STRINGs, can only occur when allow_sequence_operators_on_strings is true
1402 construct_string_append(A,B,ExtFunCall).
1403 cleanup_post_essential(general_concat(A),string,I,ExtFunCall,string,[was(general_concat)|I],multi/concat_for_string) :-
1404 !, % translation of conc for seq(STRING) --> STRING, can only occur when allow_sequence_operators_on_strings is true
1405 ExtFunCall = external_function_call('STRING_CONC',[A]).
1406 cleanup_post_essential(size(A),integer,I,ExtFunCall,integer,[was(A)|I],multi/concat_for_string) :-
1407 get_texpr_type(A,string),!,
1408 % translation of size for STRING, this can only occur when allow_sequence_operators_on_strings is true
1409 ExtFunCall = external_function_call('STRING_LENGTH',[A]).
1410 cleanup_post_essential(predecessor,Type,I,Compset,Type,[was(predecessor)|I],multi/predecessor) :- !,
1411 % translation of pred
1412 pred_succ_compset(minus,Compset).
1413 cleanup_post_essential(becomes_such(Ids1,Pred),subst,I,becomes_such(Ids2,Pred),subst,I,single/becomes_such) :- !,
1414 annotate_becomes_such_vars(Ids1,Pred,Ids2).
1415 cleanup_post_essential(Expr,Type,I,Expr,Type,[contains_wd_condition|I],multi/possibly_undefined) :-
1416 % multi: rule can only be applied once anyway, no need to check
1417 nonmember(contains_wd_condition,I),
1418 % print(' - CHECK WD: '), print_bexpr(Expr),nl, %%
1419 is_possibly_undefined(Expr),!,
1420 %% print('CONTAINS WD: '), print_bexpr(Expr),nl, %%
1421 %(translate:translate_bexpression(Expr,'{min(xunits)}') -> trace ; true),
1422 true.
1423 % if a substitution has a sub-expression that is a substitution with that refers to the original
1424 % value of a variable, we mark this substitution, too.
1425
1426 % If the substitution of an operation contains a while whose invariant contains references x$0
1427 % to the original value of a variable x, we must insert a LET substitution to preserve the original value.
1428 cleanup_post_essential(operation(Id,Results,Args,Body),Type,I,operation(Id,Results,Args,NewBody),Type,I,single/refers_to_old_state_let) :-
1429 get_texpr_info(Body,BodyInfo),
1430 memberchk(refers_to_old_state(References),BodyInfo),!,
1431 create_equalities_for_let(References,Ids,Equalities),
1432 conjunct_predicates_with_pos_info(Equalities,P),
1433 insert_let(Body,Ids,P,NewBody).
1434 cleanup_post_essential(Subst,subst,I,Subst,subst,NI,single/refers_to_old_state) :-
1435 safe_syntaxelement_det(Subst,Subs,_,_,_),
1436 % check if a child contains the refers_to_old_state flag
1437 findall(Reference, (member(Sub,Subs),
1438 get_texpr_info(Sub,SubInfo),
1439 memberchk(refers_to_old_state(References),SubInfo),
1440 member(Reference,References)), ReferedIds),
1441 ReferedIds \= [],
1442 !,
1443 sort(ReferedIds,SortedIds),
1444 NI = [refers_to_old_state(SortedIds)|I].
1445
1446 cleanup_post_essential(let_predicate([],[],TExpr),Type,Iin,Expr,Type,Iout,multi/remove_let_predicate) :- !,
1447 % same as above, just for predicates
1448 get_texpr_expr(TExpr,Expr),
1449 get_texpr_info(TExpr,I),
1450 % The next is done to prevent removing position information (in case of Event-B invariants, theorems,...)
1451 propagate_pos_info_if_useful(I,Iin,Iout).
1452
1453 cleanup_post_essential(OExpr,OType,OInfo,NExpr,NType,NInfo,Mode/Rule) :-
1454 get_preference(optimize_ast,true),
1455 ? cleanup_post(OExpr,OType,OInfo,NExpr,NType,NInfo,Mode/Rule).
1456
1457 % moved these rule below the simplifciation rules above to avoid re-computing used_id infos
1458 cleanup_post_essential(forall(Ids,Lhs,Rhs),pred,IOld,Res,pred,INew,single/forall_used_identifier) :-
1459 reconstruct_forall(Ids,Lhs,Rhs,IOld, b(Res,pred,INew)).
1460 cleanup_post_essential(exists(Ids,P),pred,IOld,exists(Ids,NP),pred,ResInfo,single/exists_used_identifier) :-
1461 inner_predicate_level_optimizations(P,NP),
1462 add_used_identifier_info(Ids,NP,IOld,INew0),
1463 add_used_ids_defined_by_equality(Ids,NP,INew0,INew),
1464 %print('* POST => '),print_bexpr(b(exists(Ids,NP),pred,INew)),nl,
1465 %print(' INFO=> '),print(INew),nl,
1466 % TO DO: also compute which identifiers are worth waiting for; do not wait for res in #x.(x:E & ... & res=min(f(x)))
1467 add_removed_typing_info(INew,ResInfo).
1468 cleanup_post_essential(Construct,Type,I,NewConstruct,Type,I,single/detect_partitions) :-
1469 contains_predicate(Construct,Type,Pred,NewConstruct,NewPred),!, % something like a select or other substitution
1470 predicate_level_optimizations(Pred,NewPred).
1471 cleanup_post_essential(Construct,Type,I,NewConstruct,Type,I,single/detect_partitions2) :-
1472 contains_predicates(Construct,Type,Preds,NewConstruct,NewPreds),!,
1473 maplist(predicate_level_optimizations,Preds,NewPreds) % TO DO: do CSE together (in some cases) !
1474 . %, (Preds=NewPreds -> true ; print('Found partitions: '), translate:print_subst(b(NewConstruct,Type,I)),nl).
1475
1476 construct_inner_forall(Ids,LHS,RHS,OldInfo,Res) :-
1477 delete(OldInfo,used_ids(_),I1), % we construct a changed forall construct; old used_ids info possibly incorrect
1478 reconstruct_forall(Ids,LHS,RHS,I1,Res).
1479 % use when in cleanup_post you construct a forall which will not be at the top-level
1480 % (meaning that the above essential rules will not run)
1481 reconstruct_forall(Ids,LHS,RHS,OldInfo, b(Res,pred,NewInfo)) :-
1482 inner_predicate_level_optimizations(LHS,NLhs),
1483 inner_predicate_level_optimizations(RHS,NRhs),
1484 construct_forall_opt(Ids,NLhs,NRhs,OldInfo, Res,NewInfo).
1485
1486 construct_forall_opt(IDs,NLhs,NRhs,Info, Res,NewInfo) :-
1487 (is_truth(NRhs) ; is_falsity(NLhs)),!,
1488 add_hint_message(remove_useless_assign,'Removing useless universal quantification','',Info),
1489 Res= truth, NewInfo = [was(forall(IDs,NLhs,NRhs))|Info].
1490 % TO DO: is the following rule useful ?: will require adapting test 510 output file
1491 % triggers e.g. for test 1447
1492 %construct_forall_opt([TID],LHS,RHS,Info, Res,NewInfo) :- % !x. (x:SetA => x:SetB) ---> SetA <: SetB
1493 % is_valid_id_member_check(LHS,TID,SetA), is_valid_id_member_check(RHS,TID,SetB),
1494 % !,
1495 % (debug_mode(off) -> true
1496 % ; format('Replacing forall ~w by subset: ',[TID]), print_bexpr(b(subset(SetA,SetB),pred,Info)),nl
1497 % ),
1498 % Res = subset(SetA,SetB), NewInfo = [was(forall)|Info].
1499 construct_forall_opt(Ids,NLhs,NRhs,OldInfo, forall(Ids,NLhs,NRhs),ResInfo) :-
1500 conjunct_predicates([NLhs,NRhs],P),
1501 add_used_identifier_info(Ids,P,OldInfo,Info),
1502 add_removed_typing_info(Info,ResInfo).
1503
1504 add_removed_typing_info(Info,ResInfo) :-
1505 (memberchk(removed_typing,Info) -> ResInfo = Info ; ResInfo = [removed_typing|Info]).
1506
1507 disjoint_ids(Ids1,Ids2) :-
1508 get_texpr_ids(Ids1,I1), sort(I1,SI1),
1509 get_texpr_ids(Ids2,I2), sort(I2,SI2),
1510 ord_disjoint(SI1,SI2).
1511
1512
1513 % translate concat(^) of strings:
1514 construct_string_append(A,B,ExtCall) :-
1515 is_string_conc_or_append(A,List,InfoA), !, % nested concat -> translate to STRING_CONC to enable optimisations
1516 append(List,[B],NewList),
1517 ExtCall = external_function_call('STRING_CONC',[S]),
1518 get_texpr_info(B,IB),merge_info(InfoA,IB,Info),
1519 S = b(sequence_extension(NewList),seq(string),Info).
1520 construct_string_append(A,B,external_function_call('STRING_APPEND',[A,B])).
1521
1522 is_string_conc_or_append(b(external_function_call(F,FArgs),_,Info),Args,Info) :-
1523 (F='STRING_APPEND' -> Args = FArgs
1524 ; F='STRING_CONC',
1525 FArgs = b(sequence_extension(SArgs),_,_)
1526 -> Args = SArgs).
1527
1528 % ---------------------
1529
1530 % non-essential post cleanup rules; only applied when optimize_ast is TRUE
1531
1532 % WITH PATH:
1533
1534 cleanup_post_ne_with_path(member(E,b(image(Rel,SONE),TypeImg,InfoImg)),pred,I,member(Couple,Rel),pred,I,multi/replace_image_by_member,Path) :-
1535 % x : Rel[{One}] => One|->x : Rel
1536 Path \= [path_arg(forall/3,1)|_], % not LHS of a forall
1537 %% do not do this if it is the LHS of a forall: !(aus2).( aus2 : helper[{mm}] => RHS) (as we no longer can apply the optimized set treatment for forall
1538 singleton_set_extension(SONE,One),
1539 %% Rel \= b(inverse(_),_,_), %% TO DO: maybe exclude this; here user maybe wants to explicitly compute image ?
1540 !,
1541 create_couple(One,E,Couple),
1542 (debug_mode(off) -> true
1543 ; print('Member of Image: '),print_bexpr(b(member(E,b(image(Rel,SONE),TypeImg,InfoImg)),pred,I)),nl,
1544 print(' replaced by: '),print_bexpr(b(member(Couple,Rel),pred,I)),nl
1545 ).
1546
1547
1548 % WITHOUT PATH:
1549
1550 cleanup_post(conjunct(b(truth,pred,I1),b(B,pred,I2)),pred,I0,B,pred,NewI,multi/remove_truth_conj1) :- !,
1551 include_important_info_from_removed_pred(I1,I2,I3), % ensure was,... information propagated
1552 add_important_info_from_super_expression(I0,I3,NewI).
1553 cleanup_post(conjunct(b(A,pred,I2),b(truth,pred,I1)),pred,I0,A,pred,NewI,multi/remove_truth_conj2) :- !,
1554 include_important_info_from_removed_pred(I1,I2,I3),
1555 add_important_info_from_super_expression(I0,I3,NewI).
1556 cleanup_post(conjunct(b(falsity,pred,I1),b(_,_,I2)),pred,I0,falsity,pred,NewI,multi/simplify_falsity_conj1) :- !,
1557 include_important_info_from_removed_pred(I2,I1,I3),
1558 add_important_info_from_super_expression(I0,I3,NewI).
1559 cleanup_post(conjunct(LHS,b(falsity,pred,I2)),pred,I0,falsity,pred,NewI,multi/simplify_falsity_conj2) :-
1560 always_well_defined_or_wd_reorderings_allowed(LHS), % we can only improve WD here,
1561 % also checks allow_improving_wd_mode preference
1562 !, % Note: ProB would treat falsity first anyway; so in principle this could be done always for solving
1563 get_texpr_info(LHS,I1),
1564 include_important_info_from_removed_pred(I1,I2,I3),
1565 add_important_info_from_super_expression(I0,I3,NewI).
1566 % we use FInfo: in case it has a was(.) field, e.g., for pretty printing and unsat core generation and unsatCore.groovy test
1567 cleanup_post(conjunct(AA,BB),pred,I,Res,pred,I,multi/modus_ponens) :-
1568 Impl = b(implication(A,B),pred,_),
1569 ((AA,BB) = (Impl,A2) ; (BB,AA) = (Impl,A2)),
1570 same_texpr(A,A2),
1571 % arises e.g., for predicates such as IF x:0..3 THEN y=2 ELSE 1=0 END ; works with simplify_falsity_impl3 rule
1572 % rewrite (A=>B) & A into (A&B)
1573 !,
1574 (debug_mode(off) -> true ; print('Modus Ponens: '),print_bexpr(A), print(' => '), print_bexpr(B),nl),
1575 Res = conjunct(A,B).
1576 %cleanup_post(conjunct(TLHS,P1),pred,_,LHS,pred,Info,multi/duplicate_pred) :-
1577 % % TO DO: implement an efficient version of this; currently very slow e.g. for test 293
1578 % b_interpreter:member_conjunct(P2,TLHS,_),
1579 % same_texpr(P1,P2),
1580 % TLHS = b(LHS,pred,Info),
1581 % print('remove_duplicate: '), print_bexpr(P1),nl.
1582 cleanup_post(conjunct(LHS,b(Comparison1,pred,_)),pred,I0,Result,pred,RInfo,multi/detect_interval1) :-
1583 % X <= UpBound & X >= LowBound <=> X : UpBound .. LowBound (particularly useful when CLPFD FALSE, causes problem with test 1771)
1584 % Note: x>18 & y<1024 & x<20 & y>1020 now works, it is bracketed ((()) & y>1020)
1585 get_preference(use_clpfd_solver,false),
1586 \+ data_validation_mode, % this rule may lead to additional enumerations
1587 get_leq_comparison(Comparison1,X,UpBound),
1588 ? select_conjunct(b(Comparison2,_,_),LHS,Prefix,Suffix),
1589 get_geq_comparison(Comparison2,X2,LowBound),
1590 same_texpr(X,X2),
1591 (always_well_defined_or_disprover_mode(UpBound)
1592 -> true
1593 ; % as we may move valuation earlier, we have to be careful
1594 % we check if Comparison2 is last conjunct; x=7 & x:8..(1/0) raises no WD error in ProB
1595 Suffix=[]
1596 ),
1597 !,
1598 create_interval_member(X,LowBound,UpBound,Member),
1599 append(Prefix,[Member|Suffix],ResultList),
1600 conjunct_predicates(ResultList,TResult),
1601 TResult = b(Result,pred,I1),
1602 add_important_info_from_super_expression(I0,I1,RInfo),
1603 (debug_mode(off) -> true ; print(' Detected interval membership (1): '),print_bexpr(b(Result,pred,RInfo)),nl).
1604 cleanup_post(conjunct(LHS,b(Comparison1,pred,_)),pred,I0,Result,pred,RInfo,multi/detect_interval2) :-
1605 % X >= LowBound & X <= UpBound <=> X : UpBound .. LowBound
1606 get_preference(use_clpfd_solver,false),
1607 \+ data_validation_mode, % this rule may lead to additional enumerations
1608 get_geq_comparison(Comparison1,X,LowBound),
1609 ? select_conjunct(b(Comparison2,_,_),LHS,Prefix,Suffix),
1610 get_leq_comparison(Comparison2,X2,UpBound),
1611 same_texpr(X,X2),
1612 (always_well_defined_or_disprover_mode(LowBound)
1613 -> true
1614 ; % as we may move valuation earlier, we have to be careful
1615 % we check if Comparison2 is last conjunct; x=7 & x:8..(1/0) raises no WD error in ProB
1616 Suffix=[]
1617 ),
1618 !,
1619 create_interval_member(X,LowBound,UpBound,Member),
1620 append(Prefix,[Member|Suffix],ResultList),
1621 conjunct_predicates(ResultList,TResult),
1622 TResult = b(Result,pred,I1),
1623 add_important_info_from_super_expression(I0,I1,RInfo),
1624 (debug_mode(off) -> true ; print(' Detected interval membership (2): '),print_bexpr(b(Result,pred,RInfo)),nl).
1625
1626 cleanup_post(disjunct(b(truth,pred,I1),_),pred,I0,truth,pred,I,multi/simplify_truth_disj1) :- !,
1627 add_important_info_from_super_expression(I0,I1,I).
1628 cleanup_post(disjunct(b(A,pred,I1),b(falsity,pred,_)),pred,I0,A,pred,I,multi/remove_falsity_disj1) :- !,
1629 add_important_info_from_super_expression(I0,I1,I).
1630 cleanup_post(disjunct(b(falsity,pred,_),b(B,pred,I1)),pred,I0,B,pred,I,multi/remove_falsity_disj2) :- !,
1631 add_important_info_from_super_expression(I0,I1,I).
1632 cleanup_post(disjunct(Expr1,b(truth,pred,I1)),pred,I0,truth,pred,I,multi/simplify_truth_disj2) :-
1633 always_well_defined_or_wd_reorderings_allowed(Expr1), !, % we can only improve WD here
1634 add_important_info_from_super_expression(I0,I1,I).
1635 cleanup_post(disjunct(Equality1,Equality2),pred,I,New,pred,I,multi/rewrite_disjunct_to_member1) :-
1636 identifier_equality(Equality2,ID,_,Expr2),
1637 always_well_defined_or_disprover_mode(Expr2),
1638 get_texpr_type(Expr2,Type2),
1639 type_contains_no_sets(Type2), % we do not want to generate sets of sets, or worse sets with infinite sets (x=NATURAL1 or ...) which cannot be converted to AVL
1640 identifier_equality(Equality1,ID,TID,Expr1),
1641 % Rewrite (ID = Expr1 or ID = Expr2) into ID: {Expr1,Expr2} ; good if FD information can be extracted for ID
1642 % But: can be bad for reification, in particular when set extension cannot be computed fully
1643 % TO DO: also deal with ID : {Values} and more general extraction of more complicated disjuncts
1644 % TO DO: also apply for implication (e.g., ID /= E1 => ID=E2)
1645 !,
1646 construct_set_extension(Expr1,Expr2,SetX),
1647 New=member(TID,SetX),
1648 (debug_mode(off) -> true
1649 ; format('Rewrite disjunct (1) ~w: ',[ID]),print_bexpr(SetX),nl).
1650 cleanup_post(disjunct(LHS1,LHS2),pred,I,New,pred,I,multi/rewrite_disjunct_to_member2) :-
1651 id_member_of_set_extension(LHS2,ID,TID1,LExpr2), % also detects equalities
1652 get_texpr_type(TID1,Type),
1653 get_preference(use_clpfd_solver,true),type_contains_fd_index(Type), % merging is potentially useful
1654 maplist(always_well_defined_or_disprover_mode,LExpr2), % TODO: check that merging makes sense, e.g., definite FD values or simple identfiiers
1655 id_member_of_set_extension(LHS1,ID,TID,LExpr1),
1656 % Rewrite (ID : {Expr1,...} or ID : {Expr2,...} into ID: {Expr1,Expr2}
1657 l_construct_set_extension(LExpr1,LExpr2,SetX),
1658 New=member(TID,SetX),
1659 (debug_mode(off) -> true
1660 ; format('Rewrite disjunct (2) ~w: ',[ID]),print_bexpr(SetX),nl).
1661 cleanup_post(disjunct(P1,NegP1),pred,Info,truth,pred,Info,multi/tautology_disjunction) :-
1662 % P1 or not(P1) == truth (was created by Rodin for WD)
1663 (get_texpr_expr(NegP1,negation(P1bis)) -> same_texpr(P1,P1bis)
1664 ; get_texpr_expr(P1,negation(NP1)) -> same_texpr(NP1,NegP1)),
1665 (debug_mode(off) -> true
1666 ; format('Detected useless disjunction (tautology): ',[]),print_bexpr(b(disjunct(P1,NegP1),pred,Info)),nl).
1667 cleanup_post(disjunct(CEquality1,CEquality2),pred,IOld,New,pred,INew,multi/factor_common_pred_in_disjunction) :-
1668 % (x=2 & y=3) or (x=2 & y=4) -> x=2 & (y=3 or y=4) to improve constraint propagation
1669 factor_disjunct(CEquality1,CEquality2,IOld,New,INew),
1670 (debug_mode(off) -> true
1671 ; format('Factor disjunct: ',[]),print_bexpr(b(New,pred,INew)),nl).
1672 cleanup_post(implication(b(truth,pred,_),b(B,pred,I1)),pred,I0,B,pred,I,multi/remove_truth_impl1) :- !,
1673 add_important_info_from_super_expression(I0,I1,I).
1674 cleanup_post(implication(b(falsity,pred,I1),_),pred,I0,truth,pred,I,multi/simplify_falsity_impl1) :- !,
1675 add_important_info_from_super_expression(I0,I1,I).
1676 cleanup_post(implication(_,b(truth,pred,I1)),pred,I0,truth,pred,I,multi/simplify_truth_impl2) :- !,
1677 add_important_info_from_super_expression(I0,I1,I).
1678 cleanup_post(implication(P,b(falsity,pred,_)),pred,I,NotP,pred,[was(implication)|I],multi/simplify_falsity_impl3) :- !,
1679 create_negation(P,TNotP),
1680 (debug_mode(off) -> true ; print_bexpr(P), print(' => FALSE simplified'),nl),
1681 get_texpr_expr(TNotP,NotP).
1682 % TO DO: is the following rule useful ?:
1683 %cleanup_post(implication(A,b(implication(B,C),pred,_)),pred,IOld,
1684 % implication(AB,C),pred,IOld,single/replace_implication_by_and) :-
1685 % % (A => B => C <==> (A & B) => C
1686 % conjunct_predicates([A,B],AB),
1687 % (debug_mode(off) -> true ; print('Simplifying double implication: '), print_bexpr(b(implication(AB,C),pred,IOld)),nl).
1688 cleanup_post(equivalence(b(truth,pred,_),b(B,pred,I1)),pred,I0,B,pred,I,multi/remove_truth_equiv1) :- !,
1689 add_important_info_from_super_expression(I0,I1,I).
1690 cleanup_post(equivalence(b(A,pred,I),b(truth,pred,I1)),pred,I0,A,pred,I,multi/remove_truth_equiv2) :- !,
1691 add_important_info_from_super_expression(I0,I1,I).
1692 % TO DO: more rules for implication/equivalence to introduce negations (A <=> FALSITY ---> not(A)) ?
1693 % detect certain tautologies/inconsistencies
1694 cleanup_post(lazy_let_pred(_ID,_,b(Sub,pred,I1)),pred,I0,Sub,pred,I,multi/remove_lazy_let_pred) :-
1695 (Sub=truth ; Sub=falsity), !,
1696 add_important_info_from_super_expression(I0,I1,I).
1697 cleanup_post(IFTHENELSE,T,_,Res,T,[was(ifthenelse)|NI],single/remove_if_then_else) :-
1698 explicit_if_then_else(IFTHENELSE,IF,THEN,ELSE),
1699 (is_falsity(IF) -> b(Res,_,NI)=ELSE
1700 ; is_truth(IF) -> b(Res,_,NI)=THEN
1701 ),
1702 (debug_mode(off) -> true
1703 ; print('Simplified IF-THEN-ELSE: '), print_bexpr(IF),nl).
1704 cleanup_post(member(X,B),pred,I,truth,pred,[was(member(X,B))|I],multi/remove_type_member) :-
1705 is_just_type(B),
1706 nonmember(label(_),I), % the user has explicitly labeled this conjunct
1707 !. % print('REMOVE: '),print_bexpr(b(member(X,B),pred,[])),nl, print(I),nl.
1708 %cleanup_post(member(X,SET),pred,I,greater_equal(X,TBound),pred,[was(member(X,SET))|I],multi/remove_type_member) :-
1709 % disabled at the moment: we need to adapt test 1383, 767, 1703, 1003
1710 % is_inf_integer_set_with_lower_bound(SET,Bound),
1711 % Replace x:NATURAL by x>=0 and x:NATURAL1 by x>=1 ; is usually much more efficient
1712 % note : removes virtual timeout in test 290
1713 % !,
1714 % TBound = b(integer(Bound),integer,[]), print('REPLACE: '),print_bexpr(b(member(X,SET),pred,I)),nl, print_bexpr(b(greater_equal(X,TBound),pred,I)),nl.
1715 cleanup_post(not_member(X,B),pred,I,falsity,pred,[was(not_member(X,B))|I],multi/remove_type_not_member) :-
1716 is_just_type(B),
1717 nonmember(label(_),I), % the user has explicitly labeled this conjunct
1718 !.
1719 cleanup_post(member(X,TSet),pred,I,equal(X,One),pred,I,multi/remove_member_one_element_set) :-
1720 singleton_set_extension(TSet,One),
1721 !,
1722 % X:{One} <=> X=One
1723 true. %,print('Introducing equality: '),print_bexpr(X), print(' = '), print_bexpr(One),nl.
1724 cleanup_post(member(X,b(Set,_,_)),pred,I,not_equal(X,One),pred,I,multi/remove_member_setdiff) :-
1725 Set = set_subtraction(MaximalSet,SONE),
1726 singleton_set_extension(SONE,One),
1727 definitely_maximal_set(MaximalSet),
1728 !, % x : INTEGER-{One} <=> x/=One
1729 (debug_mode(off) -> true
1730 ; print('Replacing member of set_subtraction: '), print_bexpr(MaximalSet), print(' - '), print_bexpr(SONE),nl).
1731 cleanup_post(not_member(X,TSet),pred,I,not_equal(X,One),pred,I,multi/remove_member_one_element_set) :-
1732 singleton_set_extension(TSet,One),
1733 !,
1734 % X/:{One} <=> X/=One
1735 true.
1736 cleanup_post(member(E,b(fin_subset(E2),_,_)),pred,I,finite(E),pred,I,multi/introduce_finite) :-
1737 (same_texpr(E,E2); is_just_type(E2)),!. % print(introduce(finite(E))),nl.
1738 cleanup_post(not_member(E,b(fin_subset(E2),_,_)),pred,I,NotFinite,pred,I,multi/introduce_not_finite) :-
1739 (same_texpr(E,E2); is_just_type(E2)),!,
1740 create_negation(b(finite(E),pred,I),TNotP), get_texpr_expr(TNotP,NotFinite).
1741 /* do we want need this rule ?:
1742 clenaup_post(member(b(couple(A,B),couple(TA,TB),IC),ID),pred,I,equal(A,B),pred,I,multi/replace_member_id) :-
1743 is_is_event_b_identity(ID), !.
1744 */
1745 cleanup_post(member(b(couple(A,B),couple(TA,TB),IC),b(reverse(Rel),_,_)),pred,I,member(ICouple,Rel),pred,I,multi/remove_reverse) :- !,
1746 % (A,B) : Rel~ ===> (B,A) : Rel
1747 % can be detrimental for performance when A is known and B is not and Rel is large
1748 \+ data_validation_mode,
1749 (debug_mode(off) -> true ; print('Removed inverse (~): '),print_bexpr(Rel),nl),
1750 ICouple = b(couple(B,A),couple(TB,TA),IC).
1751 cleanup_post(member(LHS,ITE),pred,I,Result,pred,I,multi/member_if_then_else) :-
1752 get_texpr_expr(ITE,if_then_else(IFPRED,THEN,ELSE)),
1753 (definitely_empty_set(ELSE)
1754 -> A=THEN, P = IFPRED
1755 ; definitely_empty_set(THEN)
1756 -> A=ELSE, create_negation(IFPRED,P)
1757 ),
1758 % x: IF P THEN A ELSE {} END --> P & x:A
1759 % x: IF P THEN {} ELSE A END --> not(P) & x:A
1760 % appears in some generated Caval machines
1761 % x: IF a=TRUE THEN {11} ELSE {} END & x>11 can now be solved deterministically
1762 MEM = b(member(LHS,A),pred,I),
1763 conjunct_predicates([P,MEM],TR),
1764 (debug_mode(off) -> true ; print('Replace member of if-then-else by: '),print_bexpr(TR),nl),
1765 get_texpr_expr(TR,Result).
1766 cleanup_post(member(LHS,Comprehension),pred,I,Result,pred,NewInfo,multi/remove_member_comprehension) :-
1767 Comprehension = b(ComprSet,_,_),
1768 is_comprehension_set(ComprSet,[TID],Body),
1769 get_texpr_id(TID,ID),
1770 % LHS:{x|P(x)} ==> P(LHS)
1771 replace_id_by_expr_with_count(Body,ID,LHS,TResult,Count),
1772 % rewrite could duplicate LHS: not an issue in CSE mode; optimization relevant in normalize_ast mode
1773 is_replace_id_by_expr_ok(LHS,ID,Count,remove_member_comprehension),
1774 !,
1775 % could introduce LET if necessary because ID occurs multiple times (Count>1)
1776 get_texpr_expr(TResult,Result),
1777 get_texpr_info(TResult,I1),
1778 add_important_info_from_super_expression(I,I1,NewInfo),
1779 (debug_mode(off) -> true ; print('Remove element of comprehension_set: '),print_bexpr(Comprehension),nl,
1780 format(' rewriting to (~w): ',[Count]),print_bexpr(TResult),nl).
1781 cleanup_post(not_member(LHS,Comprehension),pred,I,Result,pred,I,multi/remove_not_member_comprehension) :-
1782 Comprehension = b(ComprSet,_,_),
1783 is_comprehension_set(ComprSet,[TID],Body),
1784 get_texpr_id(TID,ID),
1785 % LHS/:{x|P(x)} ==> not(P(LHS))
1786 replace_id_by_expr_with_count(Body,ID,LHS,TResult,Count),
1787 % rewrite could duplicate LHS: not an issue in CSE mode; optimization relevant in normalize_ast mode
1788 is_replace_id_by_expr_ok(LHS,ID,Count,remove_not_member_comprehension),
1789 !,
1790 Result = negation(TResult),
1791 (debug_mode(off) -> true ; print('Remove not element of comprehension_set: '),print_bexpr(Comprehension),nl,
1792 format(' rewriting to (~w): not(',[Count]),print_bexpr(TResult),print(')'),nl).
1793 cleanup_post(comprehension_set(Ids,Body),Type,I,NewExpr,Type,I2,Rule) :-
1794 ? cleanup_comprehension_set(Ids,Body,Type,I,NewExpr,I2,Rule),
1795 !.
1796 cleanup_post(subset(A,B),pred,I,truth,pred,[was(subset(A,B))|I],multi/remove_type_subset) :-
1797 is_just_type(B),
1798 nonmember(label(_),I), % the user has explicitly labeled this conjunct
1799 !.
1800 cleanup_post(not_subset(A,B),pred,I,falsity,pred,[was(not_subset(A,B))|I],multi/remove_type_not_subset) :-
1801 is_just_type(B),
1802 nonmember(label(_),I), % the user has explicitly labeled this conjunct
1803 !.
1804 cleanup_post(SUB,pred,I,NewPred,pred,[generated_conjunct|I],multi/replace_subset_by_element) :-
1805 is_subset(SUB,A,B),
1806 is_set_extension(A,List),
1807 !, % for sequence extension we don't need this as the interpreter knows exactly the cardinality of a sequence_extension ?
1808 % applying rule {x1,x2,...} <: B <=> x1:B & x2:B & ...
1809 maplist(gen_member_predicates(B),List,Conjuncts),
1810 conjunct_predicates(Conjuncts,TNewPred),
1811 % print('detected subset-member rule: '),print_bexpr(TNewPred),nl,
1812 get_texpr_expr(TNewPred,NewPred).
1813 cleanup_post(SUB,pred,I,NewPred,pred,[generated_conjunct|I],multi/replace_union_subset) :-
1814 is_subset(SUB,A,B),
1815 % mark conjunct as generated: used e.g. by flatten_conjunct in predicate_evaluator
1816 get_texpr_expr(A,union(_,_)),!,
1817 % applying rule A1 \/ A2 <: B <=> A1 <: B & A2 <: B
1818 % could be detrimental if checking that something is an element of B is expensive
1819 extract_unions(A,As),
1820 findall(Subi,(member(Ai,As),safe_create_texpr(subset(Ai,B),pred,I,Subi)),Conj), % we could try and re-run clean-up ? safe_create_texpr will ensure WD info set
1821 conjunct_predicates(Conj,TNewPred),
1822 get_texpr_expr(TNewPred,NewPred).
1823 cleanup_post(Comp,pred,I,SComp,pred,I,multi/simplify_cse_comparison) :-
1824 % simplify comparison operations; can result in improved constraint propagation
1825 % e.g., ia + CSE1 * 2 > ia + fa <=> CSE1 * 2 > fa for Setlog/prob-ttf/qsee-TransmitMemoryDumpOk21_SP_3.prob
1826 comparison(Comp,A,B,SComp,SA,SB),
1827 simplify_comparison_terms(A,B,SA,SB),!,
1828 (debug_mode(off) -> true
1829 ; print('Simplified: '),print_bexpr(b(Comp,pred,I)),
1830 print(' <=> '),print_bexpr(b(SComp,pred,I)),nl).
1831 cleanup_post(EMPTYSET,T,I,empty_set,T,[was(EMPTYSET)|I],multi/detect_emptyset) :- EMPTYSET \= empty_set,
1832 definitely_empty_set(b(EMPTYSET,T,I)),
1833 (debug_mode(off) -> true
1834 ; print('Detected empty set: '), print_bexpr(b(EMPTYSET,T,I)),nl).
1835 cleanup_post(equal(A,B),pred,I,truth,pred,[was(equal(A,B))|I],multi/remove_equality) :-
1836 same_texpr(A,B),always_well_defined_or_disprover_mode(A),!. % ,print(removed_equal(A,B)),nl.
1837 cleanup_post(equal(A,B),pred,I,equal(A2,B2),pred,I,multi/simplify_equality) :-
1838 simplify_equality(A,B,A2,B2).
1839 cleanup_post(not_equal(A,B),pred,I,not_equal(A2,B2),pred,I,multi/simplify_inequality) :-
1840 simplify_equality(A,B,A2,B2).
1841 cleanup_post(equal(A,B),pred,I,falsity,pred,[was(equal(A,B))|I],multi/remove_equality_false) :-
1842 different_texpr_values(A,B),!. %,print(removed_equal_false(A,B)),nl.
1843 cleanup_post(equal(A,B),pred,I,greater(Low,Up),pred,I,multi/remove_equality) :-
1844 % Low..Up = {} <=> Low>Up % is also handled by constraint solver; but other simplifications can apply here
1845 (definitely_empty_set(B), is_interval(A,Low,Up) ;
1846 definitely_empty_set(A), is_interval(B,Low,Up)),!,
1847 (debug_mode(off) -> true
1848 ; print('Simplified: '), print_bexpr(b(equal(A,B),pred,I)), print(' <=> '),
1849 print_bexpr(b(greater(Low,Up),pred,I)),nl).
1850 cleanup_post(CardGt0Expr,pred,I,not_equal(X,EmptySet),pred,I,multi/remove_cardgt0) :-
1851 get_geq_comparison(CardGt0Expr,Card,One),
1852 % card(P) > 0 -> P\={} if wd guaranteed; also rewrites card(P) >= 1
1853 Card = b(card(X),integer,_), get_integer(One,1),
1854 finite_set_or_disprover_mode(X), % as we keep X, it is sufficient for X to be finite for the rule to be ok
1855 get_texpr_type(X,TX), get_texpr_info(One,I0),
1856 EmptySet = b(empty_set,TX,I0),!,
1857 (debug_mode(off) -> true ; print('Removed card(.) > 0 for set: '), print_bexpr(X), nl).
1858 cleanup_post(CardEq0Expr,pred,I,equal(X,EmptySet),pred,I,multi/remove_cardeq0) :-
1859 is_equality(b(CardEq0Expr,pred,I),Card,Zero),
1860 % card(P) = 0 -> P={} if wd guaranteed
1861 Card = b(card(X),integer,_), get_integer(Zero,0),
1862 finite_set_or_disprover_mode(X),
1863 get_texpr_type(X,TX), get_texpr_info(Zero,I0),
1864 EmptySet = b(empty_set,TX,I0),!,
1865 (debug_mode(off) -> true ; print('Removed card(.) = 0 for set: '), print_bexpr(X), nl).
1866 cleanup_post(CardLt1Expr,pred,I,equal(X,EmptySet),pred,I,multi/remove_cardlt1) :-
1867 get_leq_comparison(CardLt1Expr,Card,Zero),
1868 % card(P) <= 0 -> P={} if wd guaranteed; TODO: also detect card(P) < 1
1869 Card = b(card(X),integer,_), get_integer(Zero,0),
1870 finite_set_or_disprover_mode(X),
1871 get_texpr_type(X,TX), get_texpr_info(Zero,I0),
1872 EmptySet = b(empty_set,TX,I0),!,
1873 (debug_mode(off) -> true ; print('Removed card(.) <= 0 for set: '), print_bexpr(X), nl).
1874 cleanup_post(member(Card,Natural),pred,I,truth,pred,I,multi/remove_card_natural) :-
1875 % card(P) : NATURAL -> truth if wd guaranteed
1876 Card = b(card(X),integer,_),
1877 is_integer_set(Natural,'NATURAL'),
1878 always_well_defined_or_disprover_mode(Card),
1879 !,
1880 (debug_mode(off) -> true ; print('Removed card(.):NATURAL for set: '), print_bexpr(X), nl).
1881 cleanup_post(not_equal(A,B),pred,I,less_equal(Low,Up),pred,I,multi/remove_equality) :-
1882 % Low..Up \= {} <=> Low<=Up % is also handled by constraint solver; but other simplifications can apply here
1883 (definitely_empty_set(B), is_interval(A,Low,Up) ;
1884 definitely_empty_set(A), is_interval(B,Low,Up)),!,
1885 (debug_mode(off) -> true
1886 ; print('Simplified: '), print_bexpr(b(equal(A,B),pred,I)), print(' <=> '),
1887 print_bexpr(b(less_equal(Low,Up),pred,I)),nl).
1888 cleanup_post(equal(A,B),pred,I,equal(A,RLet),pred,I,single/detect_recursion) :-
1889 % "A" should be an identifier
1890 get_texpr_id(A,ID),
1891 % check if some side conditions are fulfilled where the recursion detection can be enabled
1892 recursion_detection_enabled(A,B,I),
1893 % A must be recursively used in B:
1894 find_recursive_usage(B,ID),
1895 % TO DO: also find mutual recursion !
1896 debug_println(9,recursion_detected(ID)),
1897 !, % create an recursive_let where the body is annotated to be symbolic
1898 get_texpr_type(B,Type), add_texpr_infos(B,[prob_annotation('SYMBOLIC')],B2),
1899 mark_recursion(B2,ID,B3),
1900 %print(marked_recursion(ID)),nl,
1901 safe_create_texpr(recursive_let(A,B3),Type,RLet).
1902 cleanup_post(recursive_let(TID,TBody),T,_,Body,T,I2,single/remove_recursive_let) :- get_texpr_id(TID,ID),
1903 \+ occurs_in_expr(ID,TBody),
1904 debug_println(19,removing_recursive_let(ID)), % required for test 1225
1905 TBody = b(Body,_,I2).
1906 cleanup_post(equal(A,B),pred,Info1,ResultExpr,pred,Info3,multi/simplify_bool_true_false) :-
1907 % simplify bool(X)=TRUE -> X and bool(X)=FALSE -> not(X)
1908 ( get_texpr_expr(A,convert_bool(X)), get_texpr_boolean(B,BOOLVAL)
1909 ;
1910 get_texpr_boolean(A,BOOLVAL),get_texpr_expr(B,convert_bool(X))
1911 ),
1912 get_texpr_info(X,Info2),
1913 add_important_info_from_super_expression(Info1,Info2,Info3),
1914 (BOOLVAL = boolean_true -> get_texpr_expr(X,ResultExpr) ;
1915 BOOLVAL = boolean_false -> create_negation(X,TNX), get_texpr_expr(TNX,ResultExpr)),
1916 !,
1917 (debug_mode(off) -> true
1918 ; format('Simplifying bool(.)=~w to ',[BOOLVAL]),translate:print_bexpr(b(ResultExpr,pred,Info3)),nl).
1919 %cleanup_post(equal(A,B),pred,Info1,equal(REL,CartProd),pred,Info1,multi/simplify_image) :-
1920 % cannot be applied yet; SETS not precompiled yet !
1921 % A = b(image(REL,SetExt),_,_),
1922 % % REL[{OneEl}] = B ----> REL = {OneEl}*B if OneEl is the only possible value
1923 % % such signature appear in Alloy generated code
1924 % SetExt = b(set_extension([_]),set(global(GlobalSetName)),_),
1925 % %bmachine:b_get_named_machine_set_calc(GlobalSetName,_,[_]),
1926 % b_global_set_cardinality(Type,1), % cannot be called yet; global sets not precompiled
1927 % !,
1928 % get_texpr_type(REL,RelType),
1929 % safe_create_texpr(cartesian_product(SetExt,B),RelType,CartProd),
1930 % format('Translating image for singleton set'), print_bexpr(b(equal(REL,CartProd),pred,[])),nl.
1931 cleanup_post(not_equal(A,B),pred,I,falsity,pred,[was(not_equal(A,B))|I],multi/remove_disequality) :-
1932 same_texpr(A,B),always_well_defined_or_disprover_mode(A),!. % ,print(removed_not_equal(A,B)),nl.
1933 % sometimes one uses & TRUE=TRUE to finish off guards, invariants, ...
1934 % exchange lambda expressions by a comprehension set
1935 % TO DO: also add rule for bool(X)=FALSE -> not(X)
1936 cleanup_post(not_equal(A,B),pred,I,truth,pred,[was(not_equal(A,B))|I],multi/remove_disequality_false) :-
1937 different_texpr_values(A,B),!. % ,print(removed_not_equal_false(A,B)),nl.
1938 cleanup_post(not_equal(A,B),pred,I,NewP,pred,[was(not_equal(A,B))|I],multi/not_disjoint_disequality) :-
1939 /* Set1 /\ Set2 /= {} <===> #(zz).(zz:Set1 & zz:Set2) */
1940 preferences:preference(use_smt_mode,true), /* currently this rewriting makes test 1112 fail; TO DO: investigate */
1941 definitely_empty_set(B),
1942 get_texpr_expr(A,intersection(Set1,Set2)),!,
1943 get_texpr_type(Set1,Set1Type), unify_types_strict(Set1Type,set(T)),
1944 ID = b(identifier('_zzzz_unary'),T,[generated]),
1945 ESet1 = b(member(ID,Set1),pred,[]),
1946 ESet2 = b(member(ID,Set2),pred,[]),
1947 create_exists_opt([ID],[ESet1,ESet2],NewPredicate),
1948 (debug_mode(off) -> true
1949 ; print('Transformed not disjoint disequality: '),print_bexpr(NewPredicate),nl),
1950 get_texpr_expr(NewPredicate,NewP).
1951 cleanup_post(equal(b(intersection(A,B),_,_),Empty),pred,I,not_equal(El1,El2),pred,[was(intersection)|I],multi/detect_not_equal) :-
1952 % {El1} /\ {El2} = {} --> El1 \= El2 (disjoint sets)
1953 singleton_set_extension(A,El1),
1954 singleton_set_extension(B,El2),
1955 definitely_empty_set(Empty).
1956 cleanup_post(equal(b(intersection(A,B),_,_),Empty),pred,I,NewDisequality,pred,[was(intersection)|I],multi/detect_disjoint_set_extensions) :-
1957 % {El1,...} /\ {El2,...} = {} --> El1 \= El2 & .... (disjoint sets)
1958 get_texpr_expr(A,set_extension(Els1)), length(Els1,Len1), Len1 < 20,
1959 get_texpr_expr(B,set_extension(Els2)), length(Els2,Len2), Len2 < 20,
1960 Len1 * Len2 < 100,
1961 definitely_empty_set(Empty),
1962 maplist(simple_expression,Els1), % avoid duplication of computation
1963 maplist(simple_expression,Els2), % ditto
1964 findall(NotEqual, (member(A1,Els1),member(B1,Els2),safe_create_texpr(not_equal(A1,B1),pred,NotEqual)),
1965 NotEquals),
1966 conjunct_predicates(NotEquals,TRes),
1967 (debug_mode(off) -> true
1968 ; write('Expanding disjoint set constraint: '),translate:print_bexpr(TRes),nl
1969 ),
1970 get_texpr_expr(TRes,NewDisequality).
1971 cleanup_post(greater(A,B),pred,I,Res,pred,[was(greater(A,B))|I],multi/eval_greater) :-
1972 get_integer(A,IA), get_integer(B,IB),
1973 (IA>IB -> Res = truth ; Res=falsity).
1974 cleanup_post(less(A,B),pred,I,Res,pred,[was(less(A,B))|I],multi/eval_less) :-
1975 get_integer(A,IA), get_integer(B,IB),
1976 (IA<IB -> Res = truth ; Res=falsity).
1977 cleanup_post(greater_equal(A,B),pred,I,Res,pred,[was(greater_equal(A,B))|I],multi/eval_greater_equal) :-
1978 get_integer(A,IA), get_integer(B,IB),
1979 (IA >= IB -> Res = truth ; Res=falsity).
1980 cleanup_post(less_equal(A,B),pred,I,Res,pred,[was(less_equal(A,B))|I],multi/eval_less_equal) :-
1981 get_integer(A,IA), get_integer(B,IB),
1982 (IA =< IB -> Res = truth ; Res=falsity).
1983 % TODO: similar things for less_real ?
1984 cleanup_post(CHOOSE,real,I,div_real(A,B),real,I,multi/replace_tla_real_division) :-
1985 is_tla_real_division(CHOOSE,A,B),
1986 % Detect TLA real division defined by Div_1(a, b) == CHOOSE({m|m:REAL & m*b=a})
1987 add_debug_message(ast_cleanup,'Translated TLA+ division to real division: ',b(div_real(A,B),real,I),I).
1988 cleanup_post(negation(A),pred,I,falsity,pred,[was(negation(A))|I],multi/remove_negation_truth) :-
1989 is_truth(A),!. % ,print(negation(A)),nl.
1990 cleanup_post(negation(A),pred,I,truth,pred,[was(negation(A))|I],multi/remove_negation_falsity) :-
1991 is_falsity(A),!. % ,print(negation(A)),nl.
1992 cleanup_post(convert_bool(A),boolean,I,Res,boolean,I,multi/remove_convert_bool) :-
1993 (is_truth(A) -> Res = boolean_true
1994 ; is_falsity(A) -> Res = boolean_false
1995 ; is_equality(A,LHS,BoolTRUE), get_texpr_boolean(BoolTRUE,boolean_true) % bool(LHS=TRUE) --> LHS
1996 -> get_texpr_expr(LHS,Res)
1997 ; A=not_equal(LHS,BoolFALSE), get_texpr_boolean(BoolFALSE,boolean_false) % bool(LHS/=FALSE) --> LHS
1998 -> get_texpr_expr(LHS,Res)
1999 ),!.
2000 cleanup_post(assertion_expression(Cond,_ErrMsg,Expr),_T,I0,BE,TE,IE,multi/remove_assertion_expression) :-
2001 is_truth(Cond),!,
2002 Expr = b(BE,TE,I1),
2003 add_important_info_from_super_expression(I0,I1,IE).
2004 cleanup_post(card(INTERVAL), T, I, Res, T, I, single/card_of_interval) :-
2005 % e.g., card(1..4) -> 4
2006 is_interval(INTERVAL, LowerBound, UpperBound),
2007 get_integer(LowerBound, L),
2008 number(L),
2009 get_integer(UpperBound, U),
2010 number(U),
2011 (L > U -> Card = 0 ; Card is 1+(U - L)),
2012 !,
2013 Res = integer(Card).
2014 cleanup_post(member(Empty,TPow),T,I,Res,T,I,single/empty_set_in_pow_subset) :-
2015 definitely_empty_set(Empty), % useful for z3 integration to prevent powerset constraint
2016 TPow = b(POW,_,_),
2017 (POW=pow_subset(_) -> RT=truth
2018 ; POW=fin_subset(_) -> RT=truth
2019 ; POW=pow1_subset(_) -> RT=falsity
2020 ; POW=fin1_subset(_) -> RT=falsity),
2021 always_well_defined_or_disprover_mode(TPow),
2022 !,
2023 Res = RT.
2024 cleanup_post(card(Empty),T,I,Res,T,I,single/card_singleton_set) :-
2025 Empty = b(empty_set,_,_), % useful for z3 integration to prevent cardinality constraint
2026 !,
2027 Res = integer(0).
2028 cleanup_post(card(SONE),T,I,Res,T,I,single/card_singleton_set) :-
2029 singleton_set_extension(SONE,One), % card({One}) = 1 ; useful for alloy2b
2030 always_well_defined_or_disprover_mode(One),
2031 !,
2032 Res = integer(1).
2033 cleanup_post(cartesian_product(A,B),T,I,Res,T,I,single/cartesian_product_to_pair) :-
2034 singleton_set_extension(A,El1),
2035 singleton_set_extension(B,El2), % {A}*{B} -> {A|->B} ; happens in Alloy translations a lot
2036 !,
2037 get_texpr_type(El1,T1), get_texpr_type(El2,T2),
2038 safe_create_texpr(couple(El1,El2),couple(T1,T2),Pair),
2039 Res = set_extension([Pair]).
2040 cleanup_post(image(Fun,Empty),T,I,empty_set,T,I,multi/image_empty_optimisation) :-
2041 definitely_empty_set(Empty),
2042 always_well_defined_or_wd_improvements_allowed(Fun),
2043 !,
2044 (debug_mode(off) -> true
2045 ; add_message(ast_cleanup,'Removing unnecessary image of empty set: ',Fun,I)).
2046 cleanup_post(union(A,B),T,I,Res,T,[add_element_to_set|I],multi/add_element_to_set) :- % multi: cycle check done in info field
2047 ? \+ member(add_element_to_set,I),
2048 ( singleton_set_extension(B,_El) -> Res = union(A,B)
2049 ; singleton_set_extension(A,_El) -> Res = union(B,A)),
2050 !. %,print(detected_add_singleton_element(_El)),nl.
2051 cleanup_post(union(A,B),T,I,Res,T,I,multi/union_empty_set) :-
2052 ( definitely_empty_set(A) -> get_texpr_expr(B,Res) % {} \/ B = B
2053 ; definitely_empty_set(B) -> get_texpr_expr(A,Res) % A \/ {} = A
2054 ),
2055 !.
2056 cleanup_post(intersection(A,B),T,I,empty_set,T,I,multi/intersection_empty_set) :-
2057 ( definitely_empty_set(A) -> true % A /\ {} = {}
2058 ; definitely_empty_set(B) -> true % {} /\ B = {}
2059 ),
2060 !.
2061 cleanup_post(set_subtraction(A,B),T,I,Res,T,I,multi/intersection_empty_set) :-
2062 ( definitely_empty_set(A) -> Res=empty_set % {} - B = {}
2063 ; definitely_empty_set(B) -> get_texpr_expr(A,Res) % A - {} = A
2064 ),
2065 !.
2066 cleanup_post(general_union(SetExt),Type,I0,Res,Type,Info,multi/general_union_set_extension) :- % union_generalized
2067 % union({a,b,c,...}) = a \/ b \/ c ...
2068 SetExt = b(set_extension(LIST),_,I1),
2069 add_important_info_from_super_expression(I0,I1,Info),
2070 % no need to apply rule if already transformed into avl in cleanup_pre, hence we do not call is_set_extension
2071 construct_union_from_list(LIST,Type,Info,TRes),
2072 !,
2073 (debug_mode(on) -> print('translated_general_union: '), print_bexpr(TRes),nl ; true),
2074 get_texpr_expr(TRes,Res).
2075 cleanup_post(general_intersection(SetExt),Type,I0,Res,Type,Info,multi/general_inter_set_extension) :- % inter_generalized
2076 % inter({a,b,c,...}) = a /\ b /\ c ...
2077 SetExt = b(set_extension(LIST),_,I1),
2078 add_important_info_from_super_expression(I0,I1,Info),
2079 % no need to apply rule if already transformed into avl in cleanup_pre, hence we do not call is_set_extension
2080 construct_inter_from_list(LIST,Type,Info,TRes),
2081 !,
2082 (debug_mode(on) -> print('translated_general_intersection: '), print_bexpr(TRes),nl ; true),
2083 get_texpr_expr(TRes,Res).
2084 cleanup_post(SUB,pred,I0,FORALL,pred,FInfo,multi/general_union_subset) :-
2085 is_subset(SUB,UNION,T),
2086 % union(S) <: T ===> !x.(x:S => x <: T)
2087 % currently: subsets of T may be generated, but it does not propagate well to S
2088 UNION = b(general_union(S),_,_),
2089 !,
2090 get_unique_id_inside('_zzzz_unary',S,T,ID),
2091 get_texpr_type(S,SType), is_set_type(SType,IDType),
2092 TID = b(identifier(ID),IDType,[generated]),
2093 safe_create_texpr(member(TID,S),pred,LHS),
2094 safe_create_texpr(subset(TID,T),pred,RHS),
2095 create_implication(LHS,RHS,NewForallBody),
2096 create_forall([TID],NewForallBody,TFORALL),
2097 TFORALL = b(FORALL,pred,I1),
2098 add_important_info_from_super_expression(I0,I1,FInfo),
2099 % see test 1854, and ProZ ROZ/model.tex
2100 (debug_mode(on) -> print('translated_general_union subset: '), print_bexpr(TFORALL),nl ; true).
2101 cleanup_post(size(Seq),integer,Info,Res,integer,Info,multi/size_append) :-
2102 get_texpr_expr(Seq,concat(A,B)),
2103 % size(A^B) = size(A)+size(B) useful e.g. for test 1306
2104 !,
2105 Res = add(b(size(A),integer,Info),b(size(B),integer,Info)).
2106 cleanup_post(concat(A,B),Type,I0,Seq,Type,[was(concat)|NewInfo],multi/concat_empty) :-
2107 ( definitely_empty_set(A) -> b(Seq,_,I1)=B
2108 ; definitely_empty_set(B) -> b(Seq,_,I1)=A
2109 ),!,
2110 add_important_info_from_super_expression(I0,I1,NewInfo).
2111 cleanup_post(concat(A,B),Type,I0,Seq,Type,[was(concat)|I0],multi/concat_singleton_seq) :-
2112 ( is_singleton_sequence(B,Element) -> Seq = insert_tail(A,Element)
2113 ; is_singleton_sequence(A,Element) -> Seq = insert_front(Element,B)
2114 ),!,
2115 debug_format(19,'Concat with singleton sequence detected~n',[]).
2116 cleanup_post(E,integer,I,Res,integer,[was(Operator)|I],multi/constant_expression) :-
2117 pre_compute_static_int_expression(E,Result),!,
2118 functor(E,Operator,_),
2119 % format('Precomputed: ~w for ',[Result]), translate:print_bexpr(b(E,integer,[])),nl,
2120 Res = integer(Result).
2121 cleanup_post(min(Interval),integer,I0,Res,integer,Info,multi/eval_min_interval) :-
2122 is_interval_or_singleton(Interval,Low,Up),
2123 get_integer(Low,L), number(L),
2124 get_integer(Up,U), number(U), L =< U, % non-empty interval
2125 debug_println(5,simplified_min_interval(L,U,L)),
2126 Res = integer(L), get_texpr_info(Low,I1),
2127 add_important_info_from_super_expression(I0,I1,Info).
2128 cleanup_post(max(Interval),integer,I0,Res,integer,Info,multi/eval_max_interval) :-
2129 is_interval_or_singleton(Interval,Low,Up),
2130 get_integer(Low,L), number(L),
2131 get_integer(Up,U), number(U), L =< U, % non-empty interval
2132 debug_println(5,simplified_max_interval(L,U,U)),
2133 Res = integer(U), get_texpr_info(Low,I1),
2134 add_important_info_from_super_expression(I0,I1,Info).
2135 cleanup_post(first(Seq),Type,I0,Res,Type,Info,multi/first_seq_extension) :-
2136 is_sequence_extension(Seq,List), List = [First|Rest],
2137 (Rest == [] -> true ; preferences:get_preference(disprover_mode,true)), % we may remove WD issue otherwise (TO DO: check if Rest contains any problematic elements)
2138 !,
2139 First = b(Res,Type,I1),
2140 add_important_info_from_super_expression(I0,I1,Info).
2141 cleanup_post(last(Seq),Type,I0,Res,Type,Info,multi/first_seq_extension) :-
2142 is_sequence_extension(Seq,List), List = [First|Rest],
2143 (Rest == [] -> true ; preferences:get_preference(disprover_mode,true)), % we may remove WD issue otherwise (TO DO: check if list contains any problematic elements)
2144 !,
2145 last([First|Rest],b(Res,Type,I1)),
2146 add_important_info_from_super_expression(I0,I1,Info).
2147 cleanup_post(function(Fun,Arg),Type,Info,New,Type,NewInfo,Rule) :-
2148 cleanup_post_function(Fun,Arg,Type,Info,New,NewInfo,Rule).
2149 cleanup_post(range(SETC),Type,I, comprehension_set(RangeIds2,NewCompPred),Type,I,single/range_setcompr) :-
2150 % translate ran({x1,...xn|P}) into {xn| #(x1,...).(P)} ; particularly interesting if x1... contains large datavalues (e.g., C_02_001.mch from test 1131)
2151 get_texpr_expr(SETC,comprehension_set(CompIds,CompPred)),
2152 get_domain_range_ids(CompIds,DomainIds,RangeIds), % print(range(CompIds,DomainIds,RangeIds)),nl,
2153 %\+((member(ID,RangeIds),get_texpr_id(ID,'_lambda_result_'))), % for test 612; maybe disable optimisation if memory consumption of variables small
2154 !, % TO DO: also detect patterns such as dom(dom( or ran(ran( ... [Done ??]
2155 rename_lambda_result_id(RangeIds,CompPred,RangeIds2,CompPred1),
2156 rename_lambda_result_id(DomainIds,CompPred1,DomainIds2,CompPred2),
2157 create_outer_exists_for_dom_range(DomainIds2,CompPred2,NewCompPred), % will mark the exists; so that during expansion we will treat it differently for enumeration
2158 (debug_mode(off) -> true
2159 ; print('Encode range as existential quantification: '), print_bexpr(NewCompPred),nl).
2160 cleanup_post(domain(SETC),Type,I, comprehension_set(DomainIds2,NewCompPred),Type,I,single/domain_setcompr) :-
2161 % translate dom({x1,...xn|P}) into {x1,..| #(xn).(P)} ; particularly interesting if xn contains large datavalues
2162 % used to fail test 306 ; fixed by allow_to_lift_exists annotation
2163 \+ data_validation_mode, % sometimes this optimisation is counter-productive for data_validation, problem: test 1945
2164 get_texpr_expr(SETC,comprehension_set(CompIds,CompPred)),
2165 get_domain_range_ids(CompIds,DomainIds,RangeIds), % print(domain(CompIds,DomainIds,RangeIds)),nl,
2166 % \+ (member(ID,CompIds),get_texpr_id(ID,'_lambda_result_')),
2167 % WE HAVE TO BE CAREFUL if xn = LAMBDA_RESULT ; TO DO rename like above for range
2168 % example from test 292: rel(fnc({x,y|x:1..10 & y:1..x})) = {x,y|x:1..10 & y:1..x}
2169 %\+ data_validation_mode, % test 1945 fails with WD errors if we disable this rule
2170 !,
2171 % TO DO: detect when closure is lambda; e.g., for e.g. dom(pred) = INTEGER in test 292 : split(CompIds,Args,Types), closures:is_lambda_value_domain_closure(Args,Types,B, DomainValue, _),; currently create_exists_opt deals with most of this
2172 rename_lambda_result_id(DomainIds,CompPred,DomainIds2,CompPred1),
2173 rename_lambda_result_id(RangeIds,CompPred1,RangeIds2,CompPred2),
2174 create_outer_exists_for_dom_range(RangeIds2,CompPred2,NewCompPred),
2175 (debug_mode(off) -> true
2176 ; get_texpr_ids(DomainIds,DIS), get_texpr_ids(RangeIds,RIS),
2177 ajoin(['Encode domain over ',DIS,' as existential quantification over ',RIS,' : '],Msg),
2178 add_message(ast_cleanup,Msg,NewCompPred,I)).
2179 cleanup_post(domain(SETC),Type,I, comprehension_set(DomainIds,RestPred),Type,I,single/domain_setcompr) :-
2180 % translate dom({x1,...xn|P & xn=E}) into {x1,..| P} ; particularly interesting if xn contains large datavalues
2181 get_texpr_expr(SETC,comprehension_set(CompIds,CompPred)),
2182 get_domain_range_ids(CompIds,DomainIds,RangeIds), % print(domain(CompIds,DomainIds,RangeIds)),nl,
2183 \+ (member(ID,CompIds),get_texpr_id(ID,'_lambda_result_')),
2184 conjunction_to_list(CompPred,Preds),
2185 RangeIds = [TId],
2186 get_sorted_ids(RangeIds,Blacklist),
2187 select_equality(TId,Preds,Blacklist,_Eq,_Expr,RestPreds,_,check_well_definedness), % We could do check_well_definedness only if preference set
2188 conjunct_predicates_with_pos_info(RestPreds,RestPred),
2189 not_occurs_in_predicate(Blacklist,RestPred),
2190 !,
2191 % TO DO: use create_optimized exists; also treat inner existential quantification and merge
2192 (debug_mode(off) -> true
2193 ; write('Encode domain of lambda abstraction: '),print_bexpr(RestPred),nl).
2194 cleanup_post(precondition(TP,TS),subst,I0,S,subst,Info,multi/remove_triv_precondition) :-
2195 % remove trivial preconditions
2196 get_texpr_expr(TP,truth),!,
2197 get_texpr_expr(TS,S),get_texpr_info(TS,I1),
2198 add_important_info_from_super_expression(I0,I1,Info).
2199 cleanup_post(external_function_call('ENUM',[TA]),T,I,A,T,[prob_annotation('ENUM')|I],single/process_ENUM) :-
2200 (debug_mode(on) -> format(' Processing ENUM (~w): ',[T]),translate:print_bexpr(TA),nl ; true),
2201 % TO DO: do not process in DEFINITION of ENUM in LibraryProB.def
2202 get_texpr_expr(TA,A).
2203 cleanup_post(comprehension_set(TIds,Body),T,I1,comprehension_set(TIds,Body2),T,I1,single/detect_lambda_result_auto) :-
2204 get_texpr_info(Body,BI),
2205 (TIds=[_,_,_|_] % check if at least three ids
2206 -> true % for example useful here: {x,y,v| x:INTEGER & y:INTEGER & #z.(z=x+1 & x = y*y & v=z*z & y:1..10)} it could be useful to detect x as DO_NOT_ENUMERATE; currently we only enable this analysis for four ids at least
2207 ; nonmember(prob_annotation('LAMBDA'),BI) % it is a lambda with one argument, no use to do analysis
2208 ),
2209 perform_do_not_enumerate_analysis(TIds,Body,'SET COMPREHENSION',I1,Body2).
2210 cleanup_post(comprehension_set(Ids1,E1),T,I,comprehension_set(Ids2,E2),T,I,multi/detect_lambda_result_user_ann) :-
2211 get_texpr_expr(DNE,external_pred_call('DO_NOT_ENUMERATE',[TID])),
2212 get_texpr_id(TID,ID),
2213 member_in_conjunction(DNE,E1),
2214 NewInfo = prob_annotation('DO_NOT_ENUMERATE'(ID)), % similar to lambda_result
2215 E1 = b(PRED,pred,I1),
2216 nonmember(NewInfo,I1),
2217 get_texpr_id(TID,ID),
2218 nth1(Pos,Ids1,TID1,Rest),
2219 add_texpr_infos(TID1,[NewInfo],TID2),
2220 nth1(Pos,Ids2,TID2,Rest),
2221 add_message(detect_lambda_result,'Annotating comprehension set identifier with DO_NOT_ENUMERATE: ',ID,I1),
2222 E2 = b(PRED,pred,[NewInfo|I1]).
2223 cleanup_post(record_field(b(rec(Fields),TR,IR),Field),T,I,FieldVal,T,I, single/remove_field_access) :-
2224 always_well_defined_or_disprover_mode(b(rec(Fields),TR,IR)),
2225 member(field(Field,TFieldVal),Fields),!,
2226 (debug_mode(off) -> true ; add_message(remove_field_access,'Remove static field access: ',Field,I)), % cf test 1294
2227 get_texpr_expr(TFieldVal,FieldVal).
2228 cleanup_post(sequence([S1,b(sequence(S2),subst,_)]),subst,I,sequence([S1|S2]),subst,I, single/flatten_sequence2) :-
2229 debug_println(9,flatten_sequence2). % do we need something for longer sequences?
2230 cleanup_post(sequence([b(sequence(S1),subst,_)|S2]),subst,I,sequence(NewSeq),subst,I, single/flatten_sequence1) :-
2231 append(S1,S2,NewSeq),
2232 % avoid maybe calling filter_useless_subst_in_sequence again
2233 debug_println(9,flatten_sequence1).
2234 cleanup_post(sequence(S1),subst,I,sequence(S2),subst,I, single/remove_useless_subst_in_seuence) :-
2235 get_preference(useless_code_elimination,true),
2236 filter_useless_subst_in_sequence(S1,Change,S2), debug_println(filter_sequence(9,Change)).
2237 cleanup_post(sequence(Statements),subst,I,Result,subst,I, single/sequence_to_multi_assign) :-
2238 % merge sequence of assignments if possible
2239 merge_assignments(Statements,Merge,New), Merge==merged,
2240 construct_sequence(New,Result).
2241 % nl,print('Merged: '),translate:print_subst(b(Result,subst,I)),nl,nl.
2242 cleanup_post(parallel(Statements),subst,I,Result,subst,I, single/parallel_to_multi_assign) :-
2243 % this merges multiple assignments into a single one: advantage: only one waitflag set up
2244 % should probably not be done in INITIALISATION
2245 % print(parallel(Statements)),nl,trace,
2246 extract_assignments(Statements,LHS,RHS,Rest,Nr), % print(extracted(Nr,LHS)),nl,
2247 Nr>1,!,
2248 (debug_mode(on) ->
2249 print('Parallel to Assignment: '), translate:print_subst(b(parallel(Statements),subst,I)),nl
2250 ; true),
2251 (Rest == [] -> Result = assign(LHS,RHS)
2252 ; Result = parallel([b(assign(LHS,RHS),subst,[])|Rest])).
2253 %translate:print_subst(b(Result,subst,I)),nl.
2254 cleanup_post(select([CHOICE|Rest]),subst,I0,S,subst,Info,single/remove_select) :-
2255 Rest = [], % SELECT can have multiple true branches
2256 CHOICE=b(select_when(TRUTH,Subst),subst,_),
2257 is_truth(TRUTH),!,
2258 debug_println(19,'Removing useless SELECT'),
2259 get_texpr_expr(Subst,S),get_texpr_info(Subst,I1),
2260 add_hint_message(remove_select,'Removing useless SELECT','',I1),
2261 add_important_info_from_super_expression(I0,I1,Info).
2262 cleanup_post(select([CHOICE|Rest],_ELSE),subst,OldInfo,Res,subst,I,single/remove_select_else) :-
2263 CHOICE=b(select_when(TRUTH,Subst),subst,_),
2264 is_truth(TRUTH),!,
2265 (Rest = [] % completely useless SELECT
2266 -> add_hint_message(remove_select_else,'Removing useless SELECT','',OldInfo),
2267 get_texpr_expr(Subst,Res),get_texpr_info(Subst,I1),
2268 add_important_info_from_super_expression(OldInfo,I1,I)
2269 ; add_hint_message(remove_select_else,'Removing useless SELECT ELSE branch','',OldInfo),
2270 Res = select([CHOICE|Rest]), I=OldInfo).
2271 cleanup_post(let_expression([],[],TExpr),Type,I0,Expr,Type,I,multi/remove_let_expression) :- !,
2272 % remove trivial let expressions without any introduced identifiers
2273 % this rule makes only sense in combination with the next rule which removes
2274 % simple let identifiers
2275 get_texpr_expr(TExpr,Expr),
2276 get_texpr_info(TExpr,I1),
2277 add_important_info_from_super_expression(I0,I1,I).
2278 cleanup_post(let([],Pred,TExpr),Type,I0,Expr,Type,I,multi/remove_let) :- is_truth(Pred),!,
2279 % remove trivial let expressions without any introduced identifiers
2280 % this rule makes only sense in combination with the next rule which removes
2281 % simple let identifiers
2282 get_texpr_expr(TExpr,Expr),
2283 get_texpr_info(TExpr,I1),
2284 add_important_info_from_super_expression(I0,I1,I).
2285 cleanup_post(let_expression(TIds,Exprs,Expr),Type,I,
2286 let_expression(NIds,NExprs,NExpr),Type,I,multi/remove_let_expression2) :-
2287 simplify_let(TIds,Exprs,Expr,NIds,NExprs,NExpr),!,
2288 %format('~n Simplified Let ~w --> ~w~n',[TIds,NIds]),
2289 true.
2290 cleanup_post(let_predicate(TIds,Exprs,Body),Type,I,
2291 let_predicate(NIds,NExprs,NBody),Type,I,multi/remove_let_predicate2) :-
2292 simplify_let(TIds,Exprs,Body,NIds,NExprs,NBody),!,
2293 %format('~n Simplified Let ~w --> ~w~n',[TIds,NIds]),
2294 (is_truth(NBody) -> print(useless_let),nl,nl ; true).
2295 cleanup_post(let_predicate(TIds,Exprs,Body),Type,I,
2296 NewExpr,Type,NewI,single/useless_let_message_or_removal) :-
2297 is_truth(Body),
2298 nonmember(useless_let,I),
2299 get_texpr_ids(TIds,Ids),
2300 TE=b(let_predicate(TIds,Exprs,Body),Type,I),
2301 (always_well_defined_or_wd_improvements_allowed(TE)
2302 -> NewExpr = truth, delete(I,contains_wd_condition,NewI),
2303 (always_well_defined_or_disprover_mode(TE)
2304 -> true
2305 ; TIds=[TID1|_],
2306 add_message(b_ast_cleanup,'Removing useless existentially quantified variables: ',Ids,TID1)
2307 )
2308 ; NewExpr = let_predicate(TIds,Exprs,Body), NewI=[useless_let|I],
2309 TIds= [TID1|_], get_texpr_info(TID1,BInfo),
2310 nonmember(generated_exists_parameter,BInfo),
2311 % otherwise this was generated programmatically, e.g., in get_operation_enabling_condition, see test 625
2312 (nonmember(allow_to_lift_exists,I) -> true % ditto, e.g., by create_outer_exists_for_dom_range, see test 1945
2313 ; get_preference(data_validation_mode,true)),
2314 add_message(b_ast_cleanup,'Useless existentially quantified variables: ',Ids,TIds)
2315 ).
2316 % was disabled because simplify_let_subst also replaced in RHS of assignments
2317 % but now we check that a LET/ANY variable cannot be assigned to statically
2318 % so it should be safe now to replace simple equalities:
2319 cleanup_post(let(Ids,Pred,Subst),Type,I,
2320 let(NIds,NPred,NSubst),Type,I,multi/remove_let_subst2) :-
2321 simplify_let_subst(Ids,Pred,Subst,NIds,NPred,NSubst),! ,
2322 true. % translate:print_subst(b(let(NIds,NPred,NSubst),subst,[])),nl.
2323 /* this is not used currently; as the generic code's performance has been improved
2324 and better propagation is ensured by b_compute_arith_expression which (partially) instantiates its argument (known to be an integer)
2325 cleanup_post(ArithPredicate,pred,Info,ArithPredicate,pred,NewInfo,single/add_arith_pred_info) :-
2326 comparison(ArithPredicate,LHS,RHS,_,_,_),
2327 \+ clpfd_arith_integer_expression(LHS),
2328 \+ clpfd_arith_integer_expression(RHS),
2329 !,
2330 % store the information that there is no use in doing b_compute_arith_expression special treatment
2331 NewInfo = [no_clpfd_arith_integer_expression|Info].
2332 */
2333
2334 cleanup_post(forall([ID],LHS,RHS),pred,IOld,Res,pred,IOld,single/expand_forall_set_extension) :-
2335 % expand !x.(x:{a,b,...} => RHS) into conjunction
2336 % can be useful e.g. for KODKOD when we pick an element from a set of sets
2337 \+ preferences:has_default_value(use_solver_on_load), % prob, used to be only enabled in Kodkod mode
2338 % TO DO: enable always; but maybe check that set_extension can be computed (which eval_set_extension will do) to avoid duplicating checks (!y.(y:{v,w} => expensive_pred) + what if v=w
2339 nonmember(do_not_optimize_away,IOld),
2340 get_texpr_expr(LHS,member(ID2,Set)),
2341 same_texpr(ID,ID2),
2342 is_set_extension(Set,SList),
2343 get_texpr_id(ID,AID),
2344 debug_format(19,'Expanding forall ~w ',[AID]),
2345 findall(C, (member(SEL,SList),replace_id_by_expr(RHS,AID,SEL,C)),Conjuncts),
2346 conjunct_predicates_with_pos_info(Conjuncts,ExpandedForAll),
2347 (silent_mode(on) -> true ; print_bexpr(ExpandedForAll),nl),
2348 get_texpr_expr(ExpandedForAll,Res).
2349 cleanup_post(forall(Ids1,LHS,RHS),pred,IOld,
2350 forall(Ids,NewLHS,NewRHS),pred,INew,multi/merge_forall) :-
2351 is_truth(LHS),
2352 RHS = b(forall(Ids2,NewLHS,NewRHS),pred,_),
2353 %((member(b(identifier(_),Type,_),Ids1), is_infinite_ground_type(Type)) -> true), % could be useful for tests 1441, 1447 ??
2354 (disjoint_ids(Ids1,Ids2)
2355 -> append(Ids1,Ids2,Ids),
2356 % !x.(truth => !y.(P=>Q) <==> !(x,y).(P=>Q)
2357 (debug_mode(off) -> true ; format('Merging forall ~w: ',[Ids]), print_bexpr(NewLHS),nl),
2358 add_removed_typing_info(IOld,INew)
2359 ; \+ preferences:get_preference(disprover_mode,true),
2360 translate:translate_bexpression(b(forall(Ids1,LHS,RHS),pred,IOld),PS),
2361 add_warning(b_ast_cleanup,'Variable clash in nested universal quantification: ',PS,IOld),
2362 fail
2363 ).
2364 cleanup_post(forall(Ids,LHS,RHS),pred,IOld,
2365 implication(Outer,FORALL),pred,IOld,single/detect_global_preds_forall1) :-
2366 % !x.(P(x) & Q => R(x) <==> Q => !x.(P(x) => R(x))
2367 % TO DO: maybe we should not lift things like printf, ... ?
2368 bsyntaxtree:detect_global_predicates(Ids,LHS,Outer,Inner),
2369 (debug_mode(off) -> true ; format('Lifting predicate (lhs) of forall ~w: ',[Ids]), print_bexpr(Outer),nl),
2370 construct_inner_forall(Ids,Inner,RHS,IOld,FORALL).
2371 % TO DO: implement similar lifting rules for exists(Ids,P)
2372 cleanup_post(forall(Ids,LHS,RHS),pred,IOld,
2373 conjunct(Outer,FORALL),pred,IOld,single/detect_global_preds_forall2) :-
2374 is_truth(LHS),
2375 % !x.(truth => Q & R(x) <==> Q & !x.(truth => R(x))
2376 bsyntaxtree:detect_global_predicates(Ids,RHS,Outer,Inner),
2377 (debug_mode(off) -> true ; format('Lifting predicate (rhs &) of forall ~w: ',[Ids]), print_bexpr(Outer),nl),
2378 construct_inner_forall(Ids,LHS,Inner,IOld, FORALL). % print_bexpr(FORALL),nl,nl.
2379 cleanup_post(forall(Ids,LHS,RHS),pred,IOld,
2380 implication(Outer,FORALL),pred,IOld,single/detect_global_preds_forall3) :-
2381 is_truth(LHS),
2382 RHS = b(implication(RHS1,RHS2),pred,_),
2383 % !x.(truth => (Q & R(x) => S(x)) <==> Q => !x.(truth => R(x) => S(x))
2384 bsyntaxtree:detect_global_predicates(Ids,RHS1,Outer,Inner),
2385 create_implication(Inner,RHS2,NewRHS),
2386 (debug_mode(off) -> true ; format('Lifting predicate (rhs =>) of forall ~w: ',[Ids]), print_bexpr(Outer),nl),
2387 construct_inner_forall(Ids,LHS,NewRHS,IOld, FORALL).
2388 cleanup_post(forall([TID1,TID2|OTHER],LHS,RHS),pred,IOld,
2389 forall([TID1,TID2|OTHER],NewLHS,RHS),pred,[prob_symmetry(ID1,ID2)|IOld],single/symmetry_detection) :-
2390 % DETECT Symmetries such as !(x,y).(x /= y => x=TRUE or y=TRUE)
2391 % !(x2,y).(x2 /= y & x2:s & y:s => x2=aa or y=aa)
2392 % f:1..n --> 1..(n-1) & !(x,y).(x/=y &x:dom(f) & y:1..n => f(x) /= f(y)) & n=9 (runtime 1 sec -> 0.78 sec)
2393 get_texpr_type(TID1,T), get_texpr_type(TID2,T),
2394 \+ preferences:get_preference(use_solver_on_load,kodkod), % e.g., Kodkod cannot properly deal with LEQ_SYM_BREAK, treats it like truth
2395 preferences:get_preference(use_static_symmetry_detection,true),
2396 sym_break_supported_type(T), % LEQ_SYM_BREAK not yet fully functional with SET types; TO DO: fix
2397 get_texpr_id(TID1,ID1), get_texpr_id(TID2,ID2),
2398 nonmember(prob_symmetry(ID1,ID2),IOld),
2399 rename_bt(LHS,[rename(ID1,ID2),rename(ID2,ID1)],LHS2),
2400 same_norm_texpr(LHS,LHS2),
2401 rename_bt(RHS,[rename(ID1,ID2),rename(ID2,ID1)],RHS2),
2402 same_norm_texpr(RHS,RHS2),
2403 construct_sym_break(T,TID1,TID2,LHS,SYMBREAK),
2404 conjunct_predicates_with_pos_info(LHS,SYMBREAK,NewLHS),
2405 (debug_mode(off) -> true
2406 ; format('SYMMETRY BREAKING FORALL: !(~w,~w).(',[ID1,ID2]),print_bexpr(NewLHS),
2407 print(' => '), print_bexpr(RHS),print(')'),nl).
2408 cleanup_post(forall(AllIds,P,Rhs),pred,I,NewPred,pred,INew,multi/forall_splitting) :-
2409 AllIds = [TID1|TRestIDs], TRestIDs = [_|_], % TO DO: maybe not require that TID1 is the first id
2410 get_preference(use_clpfd_solver,true), % with CLPFD false: maybe more likely to reduce performance
2411 % NOTE: we could destroy symmetry reduction detection if TRestIDs = [TID2], but we run after symmetry detection
2412 % !(x,y,...).(x:SET & RestPred => Rhs) == !x.(x:SET => !(y,..).(RestPred => Rhs))
2413 conjunction_to_list(P,[MEM|RestPreds]),
2414 is_membership(MEM,TID,Set),
2415 same_id(TID1,TID,ID),
2416 \+ definitely_infinite(Set), % prevent !(x,y).(x:NATURAL & x<10 & y :1..x => x+y<20)
2417 %\+ known_set(Set), % rewriting makes sense if Set is not fully known and will be instantiated during solving
2418 % used to prevent known sets, but rewriting also useful for known sets (QueensWithEvents_ForallTest2b)
2419 get_sorted_ids(TRestIDs,RestIDs),
2420 not_occurs_in_predicate(RestIDs,Set),
2421 NewPred = forall([TID1],MEM,InnerForall),
2422 conjunct_predicates_with_pos_info(RestPreds,InnerForallLhs),
2423 construct_inner_forall(TRestIDs,InnerForallLhs,Rhs,I,InnerForall),
2424 !,
2425 delete(I,used_ids(_),I1), % should in principle still be ok at outer level; but just be sure
2426 add_removed_typing_info(I1,INew),
2427 (debug_mode(on) -> format('FORALL SPLITTING ~w (from ~w) for better propagation: ',[ID,RestIDs]),
2428 print_bexpr(b(NewPred,pred,INew)),nl
2429 ; true).
2430 cleanup_post(exists([TID],MemPred),pred,IOld,
2431 Res,pred,IOld, single/replace_exists_by_not_empty) :-
2432 % simplify #ID.(ID:E) <=> E /= {}
2433 % simplify #ID.(ID:E1 & ID:E2) <=> E1 /\ E2 /= {} , etc...
2434 % important e.g. for y:20..30000000000 & not(#x.(x:1..10 & x:8..y))
2435 is_valid_id_member_check(MemPred,TID,E),
2436 !,
2437 (definitely_not_empty_set(E) -> Res= truth
2438 ; get_texpr_type(E,Type), EmptySet=b(empty_set,Type,[]),
2439 Res = not_equal(E,EmptySet)),
2440 (debug_mode(off) -> true
2441 ; get_texpr_id(TID,ID),
2442 format('Removing existential quantifier: ~w~n',[ID]),
2443 print_bexpr(b(Res,pred,IOld)),nl).
2444 cleanup_post(exists([TID],b(NotMemPred,_,_)),pred,IOld,
2445 not_equal(E,TypeExpr),pred,IOld, single/replace_exists_by_not_full) :-
2446 % simplify #ID.(ID/:E) <=> E /= FullType
2447 % important e.g. for y:7..30000000000 & not(#x.(x /: 1..y))
2448 is_not_member(NotMemPred,MID,E),
2449 same_id(TID,MID,SID),
2450 % + check that MID does not occur in E
2451 \+ occurs_in_expr(SID,E),
2452 get_texpr_type(E,SType),
2453 is_set_type(SType,Type),
2454 create_maximal_type_set(Type,TypeExpr), % Note: no longer introduces identifiers but value(.) results
2455 !,
2456 (debug_mode(off) -> true
2457 ; format('Removing existential quantifier: ~w~n',[SID]),
2458 print_bexpr(b(not_equal(E,TypeExpr),pred,IOld)),nl).
2459 cleanup_post(exists([TID],b(Pred,_,_)),pred,IOld,
2460 truth,pred,IOld, single/replace_exists_by_truth) :-
2461 b_interpreter_check:arithmetic_op(Pred,_Op,X,Y),
2462 ( (same_id(TID,X,SID), \+ occurs_in_expr(SID,Y), always_well_defined_or_disprover_mode(Y)) ;
2463 (same_id(TID,Y,SID), \+ occurs_in_expr(SID,X), always_well_defined_or_disprover_mode(X))
2464 ),
2465 !, % we have a formula of the form #SID.(SID > Expr); provided Expr is well-defined, this is always true
2466 (debug_mode(off) -> true
2467 ; format('Removing existential quantifier: ~w~n',[SID]),
2468 print_bexpr(b(Pred,pred,[])),nl).
2469 cleanup_post(exists([TID1,TID2|OTHER],RHS),pred,IOld,
2470 exists([TID1,TID2|OTHER],NewRHS),pred,[prob_symmetry(ID1,ID2)|IOld],single/symmetry_detection) :-
2471 % DETECT Symmetries such as #(x,y).(x /= y & (x=TRUE or y=TRUE))
2472 % #(x2,y).(x2 /= y & x2:s & y:s & x2=aa or y=aa)
2473 get_texpr_type(TID1,T), get_texpr_type(TID2,T),
2474 \+ preferences:get_preference(use_solver_on_load,kodkod),
2475 preferences:get_preference(use_static_symmetry_detection,true),
2476 sym_break_supported_type(T), % LESS not yet fully functional with SET types; TO DO: fix
2477 get_texpr_id(TID1,ID1), get_texpr_id(TID2,ID2),
2478 nonmember(prob_symmetry(ID1,ID2),IOld),
2479 ? \+(contains_equality(TID1,TID2,RHS)), % IDs are already equal; no use in sym breaking
2480 rename_bt(RHS,[rename(ID1,ID2),rename(ID2,ID1)],RHS2),
2481 same_norm_texpr(RHS,RHS2),
2482 construct_sym_break(T,TID1,TID2,RHS,SYMBREAK),
2483 conjunct_predicates_with_pos_info(RHS,SYMBREAK,NewRHS),
2484 (debug_mode(off) -> true
2485 ; format('SYMMETRY BREAKING EXISTS: #(~w,~w).(',[ID1,ID2]),print_bexpr(NewRHS),print(')'),nl).
2486 cleanup_post(Expr,T,I1,NewExpr,T,I1,single/detect_lambda_result_quant_auto) :-
2487 construct_for_find_do_not_enumerate(Expr,KIND,TIds,Body,NewExpr,NewBody),
2488 perform_do_not_enumerate_analysis(TIds,Body,KIND,I1,NewBody).
2489 % sort args of commutative operators by term size
2490 cleanup_post(Expr, Type, I, NExpr, Type, NI, single/normalize_commutative_args) :-
2491 preferences:get_preference(normalize_ast_sort_commutative, true),
2492 sort_commutative_args(Expr, I, NExpr, NI).
2493 %,(NExpr=Expr -> true ; print('COMMUTE: '), translate:print_bexpr(b(Expr,Type,I)),nl, print(' TO: '), translate:print_bexpr(b(NExpr,Type,NI)),nl).
2494 %% COMMENT IN NEXT LINE TO CHECK validity of AST per NODE (helps find bugs)
2495 %%cleanup_post(Expr,pred,I,Expr,pred,I,single/checked) :- check_ast(true,b(Expr,pred,I)),fail.
2496 %%
2497 cleanup_post(Expr, pred, I, Expr, pred, [DI|I], single/detect_prob_ignore) :-
2498 get_info_labels(I,Labels), member(Label,Labels),
2499 is_prob_ignore_label(Label),
2500 !,
2501 DI=description('prob-ignore'), % detected by info_has_ignore_pragma/1
2502 nonmember(DI,I),
2503 add_message(detect_prob_ignore,'Detected prob-ignore label: ',Label,I).
2504
2505 is_prob_ignore_label(Label) :-
2506 atom_codes(Label,Cs),
2507 IGNORE = [112,114,111,98,DASH,105,103,110,111,114,101|_],
2508 % used to be: append("prob-ignore",_,IGNORE), but Rodin editor sometimes puts Dash 8722 rather than 45 in label
2509 suffix(Cs,IGNORE), % accept prob-ignore somewhere in the label
2510 member(DASH,[45, 8722, 95, 46, 32, 126, 61, 43, 35]). % "--_. ~=+#"
2511 % used to call reverse and match "erongi-borp"
2512
2513 cleanup_post_function(Override,X,_Type,I0,Res,Info,multi/function_override) :-
2514 preferences:get_preference(disprover_mode,true), % only applied in Disprover mode as it can remove WD problem; TO DO make it also applicable in normal mode
2515 get_texpr_expr(Override,overwrite(_F,SEXt)),
2516 SEXt = b(set_extension(LIST),_,_),
2517 member(b(couple(From,To),_,_),LIST),
2518 same_texpr(From,X),
2519 % ( F <+ { ... X|->To ...}) (X) ==> To
2520 %print_bexpr(b(function(Override,X),Type,_I)), print(' ==> '), print_bexpr(To),nl,
2521 !,
2522 get_texpr_expr(To,Res),
2523 get_texpr_info(To,I1),
2524 add_important_info_from_super_expression(I0,I1,Info).
2525 cleanup_post_function(Override,X,Type,Info,Res,Info,multi/function_override_ifte) :-
2526 preferences:get_preference(disprover_mode,true), % only applied in Disprover mode as it can remove WD
2527 % TO DO: should we do this generally? or simply deal with overwrite symbolically always?
2528 get_texpr_expr(Override,overwrite(F,SEXt)),
2529 SEXt = b(set_extension([Couple]),_,_),
2530 Couple = b(couple(From,To),_,_),
2531 % (f <+ {A|->B}) (x) -> if_then_else(x=A,B,f(x)) ; avoids having to explicitly compute f<+{A|->B}
2532 Res = if_then_else(EqXFrom,To,FX),
2533 safe_create_texpr(equal(X,From),pred,EqXFrom),
2534 safe_create_function_call(F,X,Type,Info,FX).
2535 cleanup_post_function(SEXt,ARG,_Type,I0,Res,Info,multi/function_set_extension) :-
2536 SEXt = b(set_extension(LIST),_,ListInfos), % TO DO: also support b(value(avl_set(A)),_,_)
2537 eval_set_extension_element(ARG,Value,not_available),
2538 select(b(couple(LHS,RHS),_,_),LIST,REST),
2539 (member(contains_wd_condition,ListInfos) % then we could remove WD problem, e.g., r = {1|->2, 2|-> 1/0}(1)
2540 -> (preferences:preference(find_abort_values,false) ;
2541 preferences:get_preference(disprover_mode,true))
2542 ; true),
2543 eval_set_extension_element(LHS,Value,not_available), %nl,print(found(RHS)),nl,
2544 % WE NEED TO Check that all LHS can be compared against ARG
2545 \+ member((b(couple(LHS2,_),_,_),REST),eval_set_extension_element(LHS2,Value,not_available)), % no other potential match
2546 \+ member((b(couple(LHS3,_),_,_),LIST), \+ eval_set_extension_element(LHS3,_,not_available)), % all left-hand-sides can be evaluated
2547 !, get_texpr_expr(RHS,Res), get_texpr_info(RHS,I1),
2548 add_important_info_from_super_expression(I0,I1,Info).
2549 % Detect if_then_else in format as printed by pp_expr2(if_then_else( ....)...) or as generated by B2TLA:
2550 cleanup_post_function(IFT,DUMMYARG,_Type,Info,if_then_else(IFPRED,THEN,ELSE),Info,multi/function_if_then_else) :-
2551 is_if_then_else(IFT,post,DUMMYARG,IFPRED,THEN,ELSE),
2552 (debug_mode(off) -> true
2553 ; print('% Recognised if-then-else expression: IF '), print_bexpr(IFPRED),
2554 print(' THEN '),print_bexpr(THEN), print(' ELSE '),print_bexpr(ELSE),nl
2555 ).
2556 cleanup_post_function(Composition,X,Type,Info,NewExpr,Info,multi/function_composition) :-
2557 (data_validation_mode ;
2558 get_preference(convert_comprehension_sets_into_closures,true)
2559 % there it can make a big difference in particular since relational composition (rel_composition_wf -> rel_compose_with_inf_fun case) was not fully symbolic; see Systerel data validation examples
2560 ),
2561 % (F;G)(X) --> G(F(X)) (F;G;H)(X) --> H(G(F(X))) ...
2562 peel_rel_composition(Composition,Type,Info,X,Result,Level),
2563 Level>0,
2564 Result = b(NewExpr,_,_),
2565 %check_ast(Result), % <---
2566 (debug_mode(off) -> true
2567 ; format('Function application of COMPOSITION (Nesting: ~w) translated to: ',[Level]),print_bexpr(Result),nl).
2568 cleanup_post_function(Fun,Arg,_Type,Info,function(Fun,Arg),NewInfo,single/function_inversion_annotation) :-
2569 data_validation_mode, % TODO: activate in general
2570 limited_propagation(Arg),
2571 NewInfo = [prob_annotation('INVERSION_PENALTY')|Info],
2572 (debug_mode(off) -> true
2573 ; add_message(ast_cleanup,'Function application not suited for propagation from result to argument: ',Arg,Info)).
2574
2575 % statically detect whether there is potential for propagating result values onto these expressions
2576 limited_propagation(b(Expr,_,_)) :- limited_prop_aux(Expr).
2577 limited_prop_aux(function(_,_)). % we need to propagate through at least one more function call
2578 limited_prop_aux(composition(_,_)). % argument is a function, composed of two other functions
2579 limited_prop_aux(iteration(_,_)).
2580 limited_prop_aux(record_field(Rec,_)) :- limited_propagation(Rec). % we only know part of the record; TODO: add a penalty even if Rec allows propagation
2581 %limited_prop_aux(external_function_call(_,_)). % MU probably ok, for other funs it depends
2582 limited_prop_aux(couple(A,B)) :-
2583 (limited_propagation(A)
2584 -> % back propagation on A not useful,
2585 (limited_propagation(B) -> true % back propagation on both arguments is not useful
2586 ; is_constant(B) % B is a constant and could only filter (if TRY_FIND_ABORT / find_abort_values false)
2587 )
2588 ; is_constant(A), limited_propagation(B) % what if both are a constant ?
2589 ).
2590 limited_prop_aux(minus(A,B)) :- (limited_propagation(A) -> true ; limited_propagation(B)).
2591 limited_prop_aux(add(A,B)) :- (limited_propagation(A) -> true ; limited_propagation(B)).
2592 limited_prop_aux(div(A,B)) :- (limited_propagation(A) -> true ; limited_propagation(B)).
2593 limited_prop_aux(multiplication(A,B)) :- (limited_propagation(A) -> true ; limited_propagation(B)).
2594 limited_prop_aux(let_expression(_,_,C)) :- limited_propagation(C).
2595 % TODO: detect more cases where propagating from result of function application to argument is of limited value
2596 % sequence operators: insert_tail, first, last, ..., sequence_extension (cf test 2387)
2597
2598 is_constant(b(C,_,_)) :- is_const_aux(C).
2599 is_const_aux(boolean_false).
2600 is_const_aux(boolean_true).
2601 is_const_aux(couple(A,B)) :- is_constant(A),is_constant(B).
2602 is_const_aux(empty_set).
2603 is_const_aux(empty_sequence).
2604 is_const_aux(integer(_)).
2605 is_const_aux(real(_)).
2606 is_const_aux(string(_)).
2607 % not covered yet: value(_) and record(_)
2608
2609
2610 % detect comprehension set or closure values
2611 is_comprehension_set(comprehension_set(TypedIds,Body),TypedIds,Body).
2612 is_comprehension_set(value(Closure),TypedIds,Body) :- nonvar(Closure),
2613 Closure = closure(P,T,Body),
2614 \+ custom_explicit_sets:is_interval_closure_or_integerset(Closure,_,_), % this is already a value
2615 % TO DO: also detect simple member closures like seq(0..1)
2616 create_typed_ids(P,T,TypedIds).
2617
2618 cleanup_comprehension_set([TID],b(member(LHS,TSet),pred,_),Type,I,Set,I2,multi/remove_useless_comprehension_set) :-
2619 get_texpr_id(TID,ID),
2620 get_texpr_id(LHS,ID),
2621 % {ID|ID:Set} ==> Set
2622 not_occurs_in_expr(ID,TSet),
2623 TSet=b(Set,Type,I2),
2624 !,
2625 add_hint_message(remove_useless_comprehension_set,'Removing useless comprehension set over: ',ID,I).
2626 cleanup_comprehension_set([TID],Body,_Type,I,NewExpr,NewInfo,single/detect_seq_comprehension_set) :-
2627 get_texpr_id(TID,ID),
2628 % {ID | #LenID. (ID : 1..LenID --> Set)} ==> seq(Set)
2629 % {ID | #LenID. (ID : 1..LenID >-> Set)} ==> iseq(Set)
2630 get_texpr_expr(Body,exists([TLen],TIBody)),
2631 get_texpr_id(TLen,LenID), LenID \= ID,
2632 get_texpr_expr(TIBody,IBody),
2633 get_member(IBody,LenID,ISet,TID2,FUNCTION),
2634 get_texpr_id(TID2,ID),
2635 get_seq_fun_aux(FUNCTION,ISet,Interval,SeqTypeSet),
2636 get_texpr_expr(Interval,interval(ONE,TLen2)),
2637 get_texpr_id_with_offset(TLen2,LenID,Offset), % LenID or something like LenID-1
2638 get_integer(ONE,StartingIndex),!,
2639 (StartingIndex = 1, Offset=0 % TODO: check if a negative offset is always ok for all Seq Types
2640 -> add_hint_message(detect_seq_comprehension_set,'Detecting sequence operator: ',ID,I),
2641 NewExpr = SeqTypeSet, NewInfo=I
2642 ; % we have something sequence like but with indexes not starting at 1, maybe at 0
2643 % e.g. {ID | #LenID. (ID : 0..LenID-1 --> Set)}; happens in Soton/UML-B drone model
2644 add_hint_message(detect_seq_comprehension_set,'Marking sequence like operator as symbolic, indexes are not starting at 1: ',ID,I),
2645 NewExpr = comprehension_set([TID],Body),
2646 %add_texpr_infos(Body,[prob_annotation('SYMBOLIC')],Body2),
2647 add_info_if_new(I,prob_annotation('SYMBOLIC'),NewInfo)
2648 ).
2649 % {RANGE_LAMBDA__|#x.(x : dom(F) & RANGE_LAMBDA__ = F(x))} --> ran(F) // generated by TLC4B -> TLA2B
2650 % TO DO: detect {R|R:INTEGER & #D.(D|->R:F)} as ran(F)
2651 cleanup_comprehension_set([TID],Body, _Type, I, range(Func), I, multi/detect_tla_range_comprehension_set) :-
2652 Body = b(exists([DomTID],EBody),pred,_),
2653 EBody = b(conjunct(LHS,RHS),pred,_),
2654 is_membership(LHS,DomTID1,b(domain(Func),_,_)),
2655 same_id(DomTID,DomTID1,_),
2656 is_equality(RHS,TID1,FunCall),
2657 FunCall = b(function(Func1,DomTID2),_,_),
2658 same_id(TID,TID1,_),
2659 same_id(DomTID,DomTID2,_),
2660 same_texpr(Func,Func1),
2661 always_well_defined_or_disprover_mode(FunCall), % we could also allow TLA minor mode
2662 add_hint_message(detect_tla_range_comprehension_set,'Detected range set-comprehension: ',Func,I).
2663 cleanup_comprehension_set([TID],Pred,Type,I,
2664 struct(b(rec(NewFieldSets),record(FieldTypes),I)),
2665 I,single/simplify_record) :-
2666 % {r|r'a : 1..1000 & r'b : 1..100 & r:struct(a:INTEGER,b:NAT,c:BOOL)} --> struct(a:1..1000,b:1..100,c:BOOL)
2667 % these kind of set comprehensions are generated by ProZ, see ROZ example model.tex test 1858
2668 % TO DO: maybe generalise this optimisation: currently it only works if all predicates can be assimilated into struct expression
2669 TID = b(identifier(ID),record(FieldTypes),_),
2670 conjunction_to_list(Pred,PL),
2671 l_update_record_field_membership(PL,ID,[],FieldSetsOut),
2672 maplist(construct_field_sets(FieldSetsOut),FieldTypes,NewFieldSets),
2673 (debug_mode(off) -> true
2674 ; print('Detected Record set comprehension: '),
2675 print_bexpr(b(struct(b(rec(NewFieldSets),record(FieldTypes),I)),Type,I)),nl).
2676 cleanup_comprehension_set(Ids1,E,_Type,I,comprehension_set(Ids2,E2),I,single/detect_lambda) :-
2677 preferences:get_preference(detect_lambdas,true),
2678 % used to lead to *** Enumerating lambda result warnings for test 1162, not anymore
2679 % does not yet detect: f = {x,y|x:NATURAL & (x> 1 &y=x+2)} & res = f[3..4]
2680 E = b(conjunct(LHS,Equality),pred,Info),
2681 nonmember(prob_annotation('LAMBDA'),Info), % not already processed
2682 ? identifier_equality(Equality,ID,TID1,Expr1),
2683 last(Ids1,TID), get_texpr_id(TID,ID),
2684 not_occurs_in_expr(ID,Expr1),
2685 not_occurs_in_predicate([ID],LHS),
2686 !,
2687 get_texpr_info(Equality,EqInfo),
2688 get_unique_id_inside('_lambda_result_',LHS,Expr1,ResultId), % currently the info field lambda_result is not enough: several parts of the ProB kernel match on the identifier name '_lambda_result_'
2689 TID1 = b(identifier(_),Type1,Info1),
2690 add_texpr_infos(b(identifier(ResultId),Type1,Info1),[lambda_result(ResultId),lambda_result_id_was(ID)],TID2),
2691 Equality2 = b(equal(TID2,Expr1),pred,[prob_annotation('LAMBDA-EQUALITY')|EqInfo]),
2692 E2 = b(conjunct(LHS,Equality2),pred,[prob_annotation('LAMBDA')|Info]),
2693 append(Ids0,[_],Ids1),
2694 append(Ids0,[TID2],Ids2),
2695 % code exists which is simpler, but has disadvantage of losing position info for equality
2696 (debug_mode(off) -> true ; format('Lambda using ~w detected: ',[ID]),print_bexpr(E2),nl).
2697
2698
2699 % extract membership for ID and detect optional restrictions for Length identfier LenID
2700 get_member(conjunct(TA,TB),LenID,ISet,TID2,FUNCTION) :-
2701 get_texpr_expr(TA,A), % detect LenId : NATURAL(1)
2702 get_mem_of_integerset(A,LenID,ISet), % TO DO: detect LenID>0, or LenID /=0
2703 get_texpr_expr(TB,B),
2704 get_member1(B,TID2,FUNCTION).
2705 get_member(IBody,_,'NATURAL',TID2,F) :- get_member1(IBody,TID2,F).
2706 get_member1(member(TID2,b(FUNCTION,_,_)),TID2,FUNCTION).
2707
2708 get_mem_of_integerset(member(TID2,b(SET,_,_)),LenID,ISet) :- !,
2709 get_texpr_id(TID2,LenID),
2710 is_integer_set(SET,ISet).
2711 get_mem_of_integerset(Pred,LenID,ISet) :-
2712 is_integer_set_constraint_pred(Pred,LenID,ISet).
2713
2714
2715 get_texpr_id_with_offset(Expr,ID,0) :- get_texpr_id(Expr,ID).
2716 get_texpr_id_with_offset(b(add(TID,Expr),integer,_),ID,Offset) :-
2717 get_texpr_id(TID,ID), get_integer(Expr,Offset).
2718 get_texpr_id_with_offset(b(minus(TID,Expr),integer,_),ID,NegOffset) :-
2719 get_texpr_id(TID,ID), get_integer(Expr,Offset), NegOffset is -Offset.
2720
2721 get_seq_fun_aux(total_function(Interval,TargetSet),'NATURAL',Interval,seq(TargetSet)).
2722 get_seq_fun_aux(total_function(Interval,TargetSet),'NATURAL1',Interval,seq1(TargetSet)).
2723 get_seq_fun_aux(total_injection(Interval,TargetSet),'NATURAL',Interval,iseq(TargetSet)).
2724 get_seq_fun_aux(total_injection(Interval,TargetSet),'NATURAL1',Interval,iseq1(TargetSet)).
2725 get_seq_fun_aux(total_bijection(Interval,TargetSet),'NATURAL',Interval,perm(TargetSet)).
2726 get_seq_fun_aux(total_bijection(Interval,TargetSet),'NATURAL1',Interval,perm(TargetSet)) :-
2727 definitely_not_empty_set(TargetSet).
2728
2729 % Detect TLA real division defined by Div_1(a, b) == CHOOSE({m|m:REAL & m*b=a})
2730 is_tla_real_division(external_function_call('CHOOSE',[SETCOMPR]),TA,TB) :-
2731 get_texpr_expr(SETCOMPR,comprehension_set([TID1],BODY)),
2732 get_texpr_id(TID1,ID),
2733 is_equality( BODY, MUL, TA),
2734 get_texpr_expr(MUL,multiplication_real(TID2,TB)),
2735 get_texpr_id(TID2,ID).
2736
2737
2738 % --------------------------------
2739
2740 construct_for_find_do_not_enumerate(exists(TIds,Pred),'EXISTS',TIds,Pred,exists(TIds,Pred2),Pred2).
2741 construct_for_find_do_not_enumerate(any(TIds,Pred,Body),'ANY',TIds,Pred,any(TIds,Pred2,Body),Pred2) :-
2742 data_validation_mode. % as we do not examine Body of the Any, we do not know if there are additional constraints on TIds in the body
2743 % tests where ANYs would be annotated 471, 565, 808, 1196, 1489, 1850
2744
2745 % try and perform analysis for a body of either exists, any or set_comprehension
2746 perform_do_not_enumerate_analysis(TIds,Body,KIND,Span,NewBody) :-
2747 get_preference(perform_enumeration_order_analysis,true),
2748 get_texpr_info(Body,BI),
2749 nonmember(prob_annotation('DO_NOT_ENUMERATE'(_)),BI), % analysis was already performed or manually annotated
2750 find_do_not_enumerate_variables(TIds,Body,SortedVs,DelayVsInOrder),
2751 !,
2752 findall(prob_annotation('DELAY_ENUMERATION'(PosNr,DNID)),nth1(PosNr,DelayVsInOrder,DNID),I1),
2753 (SortedVs = []
2754 -> NewInfos = [prob_annotation('DO_NOT_ENUMERATE'('$$NONE$$'))|I1] % dummy marking to avoid running analysis again
2755 ; findall(prob_annotation('DO_NOT_ENUMERATE'(DNID)),member(DNID,SortedVs),NewInfos,I1)
2756 ),
2757 (debug_mode(off) -> true
2758 ; I1=[], SortedVs=[] -> true
2759 ; ajoin(['Annotating ',KIND,' identifiers with DO_NOT_ENUMERATE: '],Msg),
2760 %write(SortedVs),nl,
2761 add_message(detect_lambda_result_auto,Msg,SortedVs:DelayVsInOrder,Span)
2762 ),
2763 add_texpr_infos(Body,NewInfos,NewBody).
2764 perform_do_not_enumerate_analysis(_,Body,_,_,Body).
2765
2766 :- public check_do_not_enum_result/2.
2767 % check if there is a difference with stored result in info field if it exists
2768 check_do_not_enum_result(NewInfos,BInfo) :- member(prob_annotation('DO_NOT_ENUMERATE'(_)),BInfo),!,
2769 findall(DNID,
2770 (member(prob_annotation('DO_NOT_ENUMERATE'(DNID)),BInfo), DNID \= '$$NONE$$'), OldIds),
2771 findall(DNID,
2772 (member(prob_annotation('DO_NOT_ENUMERATE'(DNID)),NewInfos), DNID \= '$$NONE$$'), NewIds),
2773 (OldIds = NewIds
2774 -> format('Same DO_NOT_ENUMERATE result: ~w~n',[OldIds])
2775 ; format('Difference in DO_NOT_ENUMERATE result:~nOLD: ~w~nNEW: ~w~n',[OldIds,NewIds])
2776 ).
2777 check_do_not_enum_result(_,_).
2778
2779 % --------------------
2780
2781 % we only sort at the top-level, as cleanup_post will work its way bottom-up:
2782 sort_commutative_args(Expr, I, Sorted, NI) :- nonvar(Expr),
2783 functor(Expr, Functor, 2),
2784 is_commutative(Functor),
2785 !,
2786 arg(1, Expr, Lhs),
2787 arg(2, Expr, Rhs),
2788 remove_all_infos_and_ground(Lhs,CNLhs), % remove infos for comparison
2789 remove_all_infos_and_ground(Rhs,CNRhs),
2790 get_texpr_expr(CNLhs,N1),
2791 get_texpr_expr(CNRhs,N2),
2792 ( N1 @> N2
2793 -> Sorted =.. [Functor,Rhs,Lhs],
2794 NI = [was(Expr)|I]
2795 ; Sorted =.. [Functor,Lhs,Rhs],
2796 NI = I
2797 ).
2798
2799
2800 is_commutative(conjunct).
2801 is_commutative(disjunct).
2802 is_commutative(equivalence).
2803 is_commutative(equal).
2804 is_commutative(not_equal).
2805 is_commutative(add).
2806 is_commutative(multiplication).
2807 is_commutative(union).
2808 is_commutative(intersection).
2809
2810 % --------------------
2811
2812 factor_disjunct(CEquality1,CEquality2,IOld,New,INew) :-
2813 % (x=2 & y=3) or (x=2 & y=4) -> x=2 & (y=3 or y=4) to improve constraint propagation
2814 Blacklist=[],
2815 conjunction_to_list(CEquality1,Preds1),
2816 conjunction_to_list(CEquality2,Preds2),
2817 select_equality(TId1,Preds1,Blacklist,TEqual,Expr1,RestPreds1,_,check_well_definedness), % also allow other preds, use safe_select(check_well_definedness,TEqual,Preds,Rest),
2818 get_texpr_id(TId1,Id),
2819 get_texpr_id(TId2,Id),
2820 select_equality(TId2,Preds2,Blacklist,_,Expr2,RestPreds2,_,check_well_definedness),
2821 same_texpr(Expr1,Expr2),
2822 conjunct_predicates_with_pos_info(RestPreds1,P1),
2823 conjunct_predicates_with_pos_info(RestPreds2,P2),
2824 % TO DO: do not recursively start from scratch in P1, one should start from the right of CEquality1:
2825 (fail, % disable recursive looking
2826 factor_disjunct(P1,P2,IOld,P12,INew) -> NewDisj = b(P12,pred,INew)
2827 ; disjunct_predicates_with_pos_info(P1,P2,NewDisj)),
2828 conjunct_predicates_with_pos_info(TEqual,NewDisj,NewPred),
2829 NewPred=b(New,pred,I2),
2830 include_important_info_from_removed_pred(IOld,I2,INew).
2831
2832 % ------------------------------------------
2833
2834 gen_rename(TID1,TID2,rename(ID1,ID2)) :- def_get_texpr_id(TID1,ID1), def_get_texpr_id(TID2,ID2).
2835
2836 is_not_member(not_member(LHS,RHS),LHS,RHS).
2837 is_not_member(negation(b(member(LHS,RHS),pred,_)),LHS,RHS).
2838
2839
2840 :- use_module(typing_tools,[create_maximal_type_set/2]).
2841 is_valid_id_member_check(b(member(MID,E),_,_),ID,E) :- same_id(ID,MID,SID),
2842 % + check that MID does not occur in E
2843 \+ occurs_in_expr(SID,E).
2844 is_valid_id_member_check(b(truth,_,_),ID,TypeExpr) :-
2845 get_texpr_type(ID,SType),
2846 create_maximal_type_set(SType,TypeExpr). % Note: this no longer introduces identifiers, which could clash
2847 is_valid_id_member_check(b(conjunct(A,B),_,_),ID,Res) :-
2848 ? is_valid_id_member_check(A,ID,EA),
2849 is_valid_id_member_check(B,ID,EB),
2850 get_texpr_type(EA,Type),
2851 safe_create_texpr(intersection(EA,EB),Type,Res).
2852
2853 contains_equality(TID1,TID2,RHS) :-
2854 ? b_interpreter:member_conjunct(b(equal(A,B),pred,_),RHS,_),
2855 (same_id(A,TID1,_),same_id(B,TID2,_) ; same_id(A,TID2,_),same_id(B,TID1,_)).
2856
2857 simplify_let_subst(Ids,Pred,Subst,NIds,RestPred,NewSubst) :-
2858 % remove let identifiers whose definitions are very simple, i.e. identifiers
2859 Eq = b(equal(TypID,TExpr),pred,_),
2860 can_be_optimized_away(TypID),
2861 get_texpr_id(TypID,ToReplace),
2862 b_interpreter:member_conjunct(Eq,Pred,RestPred),
2863 is_simple_expression(TExpr),
2864 nth0(_N,Ids,TI,NIds),get_texpr_id(TI,ToReplace),
2865 !,
2866 % Intitially there was an issue as we may also replace in the LHS of assignments
2867 % see e.g. TestLet = LET cnt BE cnt=1 IN IF cnt=0 THEN ABORT ELSE cnt :: {0,1} END END; in SubstitutionLaws
2868 % However, now the static type checker rejects those assignments
2869 replace_id_by_expr(Subst,ToReplace,TExpr,NSubst),
2870 % TO DO: it seems like cleanup rules are not applied on NSubst, e.g., function for set_extension rules
2871 debug_println(9,replaced_let_subst_id(ToReplace)),
2872 (Subst==NSubst -> NewSubst=NSubst ; clean_up(NSubst,[],NewSubst)).
2873
2874 can_be_optimized_away(b(_,_,I)) :- nonmember(do_not_optimize_away,I).
2875
2876 %replace_in_rhs(ID,E,RHS,CleanNewRHS) :- replace_id_by_expr(RHS,ID,E,NewRHS), clean_up(NewRHS,[],CleanNewRHS).
2877
2878 can_be_replaced(RHS,_,Ids) :- get_texpr_id(RHS,RHSID),!,
2879 \+ (member(TID2,Ids), get_texpr_id(TID2,RHSID)). % ID occurs in Ids, replacing it in Expr will move the scope
2880 % example: Z Test (\LET x==1 @ (\LET x==x+1; y==x @ 7*x+y)) = 15
2881 can_be_replaced(_RHS,UsedIds,Ids) :- % TO DO: compute used ids
2882 %find_identifier_uses(RHS,[],UsedIds),
2883 get_texpr_ids(Ids,AtomicIds), sort(AtomicIds,SortedIds),
2884 \+ ord_intersect(UsedIds,SortedIds).
2885
2886 % simplify LET Ids BE Ids=Exprs IN Expr END by moving one identifier Id inside
2887 simplify_let(Ids,Exprs,Expr,NIds,NExprs,CleanNewExpr) :-
2888 nth0(N,Ids,TId,NIds),
2889 get_texpr_id(TId,Id),
2890 can_be_optimized_away(TId),
2891 nth0(N,Exprs,LetExpr,NExprs),
2892 find_identifier_uses_if_necessary(LetExpr,[],LetExprIds),
2893 \+ ord_member(Id,LetExprIds), %\+ occurs_in_expr(Id,LetExpr), % illegal let, e.g., i = i+1;
2894 can_be_replaced(LetExpr,LetExprIds,Ids), % moving LetExpr will not produce scoping issues
2895 maplist(not_occurs_in_expr(Id),NExprs), % The ID is not used for defining other RHS in the same let
2896 simplify_let_aux(TId,Id,LetExpr,Expr,CleanNewExpr).
2897
2898 simplify_let_aux(_TId,Id,LetExpr,Expr,CleanNewExpr) :-
2899 % remove let identifiers whose definitions are very simple, i.e. identifiers
2900 is_simple_expression(LetExpr),
2901 % TId = LetExpr
2902 % TO DO: do not do this to outer variables which the user cares about !!
2903 !,
2904 %maplist(replace_in_rhs(Id,LetExpr),NExprs,NewExprs),
2905 replace_id_by_expr(Expr,Id,LetExpr,NExpr),
2906 clean_up(NExpr,[],CleanNewExpr). % clean up adjust eg used_ids info; necessary for test 568 in prob_safe_mode
2907 simplify_let_aux(TId,Id,LetExpr,Expr,CleanNewExpr) :-
2908 % push the let expression down the AST. E.g. "LET a=E IN (4*(a+z*a) + z)" would
2909 % be transformed to "4*(LET a=E IN (a+z*a)) + z"
2910 % If the final form is like "LET a=E IN a" it will be simplified to E.
2911 \+ do_not_to_move_let_inside(Expr),
2912 !,
2913 ( identifier_sub_ast(Expr,Id,SubPosition) ->
2914 prune_sub_ast_pos_list(SubPosition,Id,LetExpr,Expr,SafeSubPosition),
2915 SafeSubPosition = [_|_], % The LET can actually be moved down
2916 % SubPosition points to the highest point in the AST coveringa all occurences
2917 exchange_ast_position(SafeSubPosition,Expr,OldInner,NewInner,NExpr),
2918 get_texpr_type(OldInner,Type),
2919 ( get_texpr_id(OldInner,Id) -> % There is only one reference to Id,
2920 debug_format(19,'Simplified LET for ~w away, single usage~n',[Id]),
2921 NewInner = LetExpr % replace it with the expression
2922 % We need to check that we are not simply just exchanging lets with each other
2923 ; cycle_detection(Id,SafeSubPosition,Expr) -> debug_println(9,cycle(Id)),fail
2924 ; Type=pred -> % print(created_let_predicate(N,Id,SafeSubPosition,NIds)),nl,
2925 extract_important_info_from_subexpressions(LetExpr,OldInner,NewLetInfo), % maybe no longer necessary because of cleanups call below
2926 create_texpr(let_predicate([TId],[LetExpr],OldInner),pred,NewLetInfo,NewInner)
2927 ; % print(create_let_expression(TId)),nl,
2928 extract_important_info_from_subexpressions(LetExpr,OldInner,NewLetInfo), % maybe no longer necessary because of cleanups call below
2929 create_texpr(let_expression([TId],[LetExpr],OldInner),Type,NewLetInfo,NewInner)),
2930 clean_up(NExpr,[],CleanNewExpr) % maybe we only need WD post rules ?
2931 ; always_well_defined_or_wd_improvements_allowed(LetExpr) ->
2932 % Id does not occur in the expression -> just remove the LET
2933 add_debug_message(b_ast_cleanup,'Identifier of LET not used: ',Id,Expr),
2934 CleanNewExpr = Expr
2935 ; gen_unused_let_id_msg(TId,Id,LetExpr),fail
2936 ),!.
2937 simplify_let_aux(TId,Id,LetExpr,Expr,CleanNewExpr) :- % do_not_to_move_let_inside has succeeded
2938 not_occurs_in_expr(Id,Expr),
2939 (always_well_defined_or_wd_improvements_allowed(LetExpr)
2940 -> add_debug_message(b_ast_cleanup,'Identifier of LET not used: ',Id,Expr)
2941 ; gen_unused_let_id_msg(TId,Id,LetExpr), fail
2942 ),
2943 CleanNewExpr=Expr.
2944
2945 gen_unused_let_id_msg(TID,Id,LetExpr) :- get_texpr_info(TID,Infos), member(generated_exists_parameter,Infos),!,
2946 add_debug_message(b_ast_cleanup,'Cannot remove unused identifier in (auto-generated) LET due to WD condition: ',Id,LetExpr).
2947 gen_unused_let_id_msg(_TID,Id,LetExpr) :-
2948 add_message(b_ast_cleanup,'Cannot remove unused identifier in LET due to WD condition: ',Id,LetExpr).
2949
2950
2951 % this has to be checked not just at the top-level but along the SubPosition path
2952 do_not_to_move_let_inside(b(E,_T,Infos)) :-
2953 (do_not_to_move_let_inside_aux(E) -> true
2954 ; E=exists(_,_), (get_preference(lift_existential_quantifiers,true) ; member(allow_to_lift_exists,Infos))
2955 ).
2956 %add_message(simplify_let,'Not moving LET inside: ',b(E,_T,Infos),Infos).
2957 % exists can be lifted which can also lead to duplication allow_to_lift_exists
2958 % for those quantifiers we may duplicate the computation of a let by moving it inside:
2959 do_not_to_move_let_inside_aux(forall(_,_,_)). % otherwise we may compute the let multiple times
2960 do_not_to_move_let_inside_aux(comprehension_set(_,_)). % ditto
2961 do_not_to_move_let_inside_aux(general_product(_,_,_)). % ditto (PI)
2962 do_not_to_move_let_inside_aux(general_sum(_,_,_)). % ditto (SIGMA)
2963 do_not_to_move_let_inside_aux(lambda(_,_,_)). % ditto
2964 do_not_to_move_let_inside_aux(quantified_intersection(_,_,_)). % ditto
2965 do_not_to_move_let_inside_aux(quantified_union(_,_,_)). % ditto
2966 %do_not_to_move_let_inside_aux(exists(_,_)). % can lead to duplication upon lifting or semi-lifting, e.g., if two exists are nested?
2967 % TODO: investigate if we should disable moving LET into exists in general
2968 do_not_to_move_let_inside_aux(convert_bool(_)). % can lead to duplication if reification fails
2969
2970
2971 not_occurs_in_expr(Id,Expr) :- \+ occurs_in_expr(Id,Expr).
2972
2973 cycle_detection(Id,SubPosition,Expr) :-
2974 (get_constructor(SubPosition,Expr,CC),
2975 \+ let_constructor(CC) -> fail % at least one other constructor found
2976 ; debug_println(9,cycle_let_detection(Id))
2977 ).
2978 % we have a let constructor which can be modified by simplify_let:
2979 let_constructor(let_expression).
2980 let_constructor(let_predicate).
2981 let_constructor(let_substitution).
2982
2983 % traverse a SubPositions List from identifier_sub_ast and check for potential duplication
2984 % by quantifiers, if found: prune list at that point
2985 prune_sub_ast_pos_list([],_,_,_,[]).
2986 prune_sub_ast_pos_list([Pos|T],Id,LetExpr,OldTExpr,Res) :-
2987 remove_bt(OldTExpr,OldExpr,NewExpr,_NewTExpr),
2988 (do_not_to_move_let_inside(OldTExpr)
2989 -> Res=[],
2990 (debug_mode(off) -> true ; add_message(simplify_let,'Not moving LET inside quantifier/bool: ',Id,OldTExpr))
2991 ; Res = [Pos|TR],
2992 syntaxtransformation(OldExpr,Subs,_Names,_NSubs,NewExpr),
2993 nth0(Pos,Subs, OldSelected,_Rest),
2994 prune_sub_ast_pos_list(T,Id,LetExpr,OldSelected,TR),
2995 (TR=[], avoid_top_level_let_within(OldExpr)
2996 -> Res=[] % we would create a let at the top-level of this
2997 ; Res = [Pos|TR]
2998 )
2999 ).
3000
3001 avoid_top_level_let_within(card(_)). % reification of card does not work yet with top-level let_predicate, for test 1562
3002 % Note: maybe it is best to avoid pushing into card completely, as even at the next
3003 % level the let could disturb the reification small set detection?
3004
3005 % get a SubPosition path (as produced by identifier_sub_ast) and
3006 % generate upon backtracking all constructors that are used along the Path
3007 get_constructor([Pos|T],OldTExpr,ConstructorForPos) :-
3008 remove_bt(OldTExpr,OldExpr,NewExpr,_NewTExpr),
3009 (functor(OldExpr,ConstructorForPos,_)
3010 ; syntaxtransformation(OldExpr,Subs,_Names,_NSubs,NewExpr),
3011 nth0(Pos,Subs, OldSelected,_Rest),
3012 get_constructor(T,OldSelected,ConstructorForPos)
3013 ).
3014
3015 is_simple_expression(TExpr) :-
3016 get_texpr_expr(TExpr,Expr),
3017 is_simple_expression2(Expr),!.
3018 is_simple_expression(TExpr) :-
3019 is_just_type(TExpr).
3020 is_simple_expression2(identifier(_)).
3021 is_simple_expression2(integer(_)).
3022 is_simple_expression2(real(_)).
3023 is_simple_expression2(string(_)).
3024 is_simple_expression2(boolean_true).
3025 is_simple_expression2(boolean_false).
3026 is_simple_expression2(empty_set).
3027 is_simple_expression2(empty_sequence).
3028 %is_simple_expression2(interval(Low,Up)) :- is_simple_expression(Low), is_simple_expression(Up).
3029 % TODO: simple couples? simple records?
3030
3031 % a variation of is_simple_expression, allowing some simple constructs
3032 is_simple_expression_lvl(TExpr,Lvl) :-
3033 get_texpr_expr(TExpr,Expr),
3034 is_simple_expression2_lvl(Expr,Lvl),!.
3035 is_simple_expression2_lvl(Cons,Lvl) :- simple_binary_constructor(Cons,A,B), !,
3036 Lvl>0, L1 is Lvl-1,
3037 is_simple_expression_lvl(A,L1),is_simple_expression_lvl(B,L1).
3038 is_simple_expression2_lvl(Cons,Lvl) :- simple_unary_constructor(Cons,A),!,
3039 Lvl>0, L1 is Lvl-1,
3040 is_simple_expression_lvl(A,L1).
3041 is_simple_expression2_lvl(E,_) :- is_simple_expression2(E).
3042
3043 simple_binary_constructor(function(A,B),A,B).
3044 simple_binary_constructor(couple(A,B),A,B).
3045 % TODO: simple records?
3046 simple_unary_constructor(reverse(A),A).
3047 simple_unary_constructor(set_extension([A]),A).
3048 simple_unary_constructor(sequence_extension([A]),A).
3049
3050 % check for duplication of complex LHS expressions by replacing ID with LHS NrOccurences of times for Rule
3051 is_replace_id_by_expr_ok(_LHS,_ID,NrOccurences,_Rule) :- NrOccurences < 2.
3052 is_replace_id_by_expr_ok(_LHS,_ID,_,_Rule) :-
3053 get_preference(normalize_ast,true),!. % is necessary at least for remove_member_comprehension, remove_not_member_comprehension
3054 is_replace_id_by_expr_ok(_LHS,_ID,_,_Rule) :-
3055 get_preference(use_common_subexpression_elimination,true),!.
3056 is_replace_id_by_expr_ok(LHS,_ID,NrOccurences,_Rule) :-
3057 (NrOccurences<3 -> Lvl=2 ; NrOccurences<6 -> Lvl=1 ; Lvl=0), % what heuristic should we use here; test 1750 seems to indicate that Lvl=4 would still be beneficial for NrOccurences=2 and lambda_guard1 rule
3058 is_simple_expression_lvl(LHS,Lvl).
3059 is_replace_id_by_expr_ok(LHS,ID,Count,Rule) :-
3060 debug_mode(on),
3061 format('replace ~w (~w times) not ok for ~w using: ',[ID,Count,Rule]), translate:print_bexpr(LHS),nl,fail.
3062
3063
3064 % detect either Event-B identity or id over full type
3065 is_event_b_identity(b(X,_,_)) :- is_event_b_identity_aux(X).
3066 is_event_b_identity_aux(event_b_identity).
3067 is_event_b_identity_aux(identity(T)) :- is_just_type(T).
3068
3069 :- use_module(library(avl),[avl_member/2]).
3070 % check if we have a set extension and return list of terms
3071 is_set_extension(b(S,T,I),L) :- is_set_extension_aux(S,T,I,L).
3072 is_set_extension_aux(set_extension(L),_,_,L).
3073 % TO DO: detect sequence_extension
3074 is_set_extension_aux(value(avl_set(A)),SetType,I,L) :- % computed by eval_set_extension
3075 is_set_type(SetType,Type),
3076 findall(b(value(M),Type,I),avl_member(M,A),L).
3077
3078 is_sequence_extension(b(S,T,I),L) :- is_sequence_extension_aux(S,T,I,L).
3079 is_sequence_extension_aux(sequence_extension(L),_,_,L).
3080 % TO DO: detect value/set_extensions
3081
3082 recursion_detection_enabled(A,B,I) :-
3083 (recursion_detection_enabled_aux(A,B,I) -> true).
3084 recursion_detection_enabled_aux(A,_B,I) :-
3085 animation_mode(b), % in B mode,
3086 memberchk(section(properties),I), % the rule should be only applied to properties
3087 % and where A is an abstract constant.
3088 get_texpr_info(A,AInfo),memberchk(loc(_,_,abstract_constants),AInfo).
3089 recursion_detection_enabled_aux(A,_B,_I) :-
3090 animation_minor_mode(eventb), % in Event-B,
3091 %TODO: Limit application to axioms
3092 get_texpr_info(A,AInfo), % A must be a constant
3093 memberchk(loc(_,constants),AInfo).
3094 recursion_detection_enabled_aux(_A,_B,_I) :-
3095 animation_minor_mode(z). % use always in Z
3096 recursion_detection_enabled_aux(_A,_B,Infos) :- % check for @desc recursive_let pragma
3097 member(description(D),Infos), rec_let_pragma(D).
3098
3099 rec_let_pragma(recursive_let).
3100 rec_let_pragma(letrec). % more compact exists in other languages
3101 rec_let_pragma(reclet). % Z syntax
3102
3103 % peel of relational compositions and replace with function application
3104 % used to translate (F;G)(X) --> G(F(X)) or (F;G;H)(X) --> H(G(F(X))) ...
3105 peel_rel_composition(b(composition(F,G),_,_),TypeGArg,Info,Arg,GFres,L1) :-
3106 get_texpr_type(G,SType),
3107 bsyntaxtree:is_set_type(SType,couple(TypeFArg,_)),
3108 !,
3109 %Note: rule is multi: we will detect compositions inside G at next iteration
3110 peel_rel_composition(F,TypeFArg,Info,Arg,FRes,Level), L1 is Level+1,
3111 safe_create_function_call(G,FRes,TypeGArg,Info,GFres).
3112 peel_rel_composition(Fun,TypeFArg,Info,Arg,FArg,0) :-
3113 safe_create_function_call(Fun,Arg,TypeFArg,Info,FArg). % TODO: apply function_call_opt
3114
3115 % create a function call and detect certain optimisations like lambda inlining
3116 safe_create_function_call(Fun,Arg,TypeFArg,Info,Res) :-
3117 safe_create_texpr(function(Fun,Arg),TypeFArg,Info,FArg),
3118 (cleanup_pre_function(Fun,Arg,TypeFArg,Info,CleanupRes,Info2,_)
3119 -> Res = b(CleanupRes,TypeFArg,Info2)
3120 ; Res=FArg
3121 ).
3122
3123
3124 construct_union_from_list([X],_,_,Res) :- !, Res=X.
3125 construct_union_from_list([X,Y|T],Type,Info,Res) :-
3126 construct_union_from_list([Y|T],Type,Info,RHS),
3127 Res = b(union(X,RHS),Type,Info).
3128 construct_inter_from_list([X],_,_,Res) :- !, Res=X.
3129 construct_inter_from_list([X,Y|T],Type,Info,Res) :-
3130 construct_inter_from_list([Y|T],Type,Info,RHS),
3131 Res = b(intersection(X,RHS),Type,Info).
3132
3133 % LEQ_SYM_BREAK / LEQ_SYM does not support all types yet:
3134 sym_break_supported_type(Var) :- var(Var),!,fail.
3135 sym_break_supported_type(integer).
3136 sym_break_supported_type(boolean).
3137 sym_break_supported_type(real).
3138 sym_break_supported_type(string).
3139 sym_break_supported_type(global(_)).
3140 sym_break_supported_type(couple(A,B)) :- sym_break_supported_type(A), sym_break_supported_type(B).
3141 sym_break_supported_type(record(F)) :- maplist(sym_break_supported_field,F).
3142 sym_break_supported_field(field(_,T)) :- sym_break_supported_type(T).
3143 % example with pairs: !(x,y).(x:s2 & y:s2 & x/=y => prj1(INTEGER,INTEGER)(x)/=prj1(INTEGER,INTEGER)(y)) (with let s2 = {x,y|x:1..10000 & y:{x+1}}); here we get a slow-down; maybe we should check if RHS complicated enough
3144 % here it is beneficial: !(x,y).(x:dom(s)&y:dom(s)&x/=y => s(x)+s(y)>0) with let s={x,y,v|x:1..10&y:1..50&v=x+y}; runtime goes down from 9.7 to 6.1 seconds
3145
3146 construct_sym_break(integer,TID1,TID2,Pred,Res) :- member_in_conjunction(Neq,Pred), is_id_inequality(Neq,TID1,TID2),
3147 !, get_texpr_info(TID1,Info1),
3148 Res = b(less(TID1,TID2),pred,Info1). % we don't need the external function; we can used <
3149 construct_sym_break(integer,TID1,TID2,_Pred,Res) :- !, get_texpr_info(TID1,Info1),
3150 Res = b(less_equal(TID1,TID2),pred,Info1). % we don't need the external function; we can used <= ; we could check whether < or <= already in Pred ? occurs in test 1360: #(vv,ww).(vv < ww & ww < vv)
3151 construct_sym_break(_,TID1,TID2,_,Res) :- get_texpr_info(TID1,Info1),
3152 Res = b(external_pred_call('LEQ_SYM',[TID1,TID2]),pred,Info1).
3153
3154 % construct {Expr1,Expr2}
3155 construct_set_extension(Expr1,Expr2,Res) :- same_texpr(Expr1,Expr2),!,
3156 get_texpr_type(Expr1,Type),
3157 extract_info(Expr1,Infos), % will also copy used_ids; ok as this does not change by adding set_extension
3158 Res = b(set_extension([Expr1]),set(Type),Infos).
3159 construct_set_extension(Expr1,Expr2,Res) :-
3160 get_texpr_type(Expr1,Type),
3161 extract_info(Expr1,Expr2,Infos),
3162 (Expr1 @=< Expr2 -> Lst=[Expr1,Expr2] ; Lst=[Expr2,Expr1]), % solves issue with ParserTests; {FALSE,TRUE}
3163 Res = b(set_extension(Lst),set(Type),Infos).
3164
3165 l_construct_set_extension([E1],[E2],Res) :- !, construct_set_extension(E1,E2,Res).
3166 l_construct_set_extension(L1,L2,Res) :- append(L1,L2,L12),
3167 L12=[Expr1|T],!,
3168 get_texpr_type(Expr1,Type),
3169 last(T,Expr2),
3170 extract_info(Expr1,Expr2,Infos), % TODO: improve info extraction; sort L12 values?
3171 Res = b(set_extension(L12),set(Type),Infos).
3172 l_construct_set_extension(A,B,Res) :-
3173 add_internal_error('Requires at least two els:',l_construct_set_extension(A,B,Res)),fail.
3174
3175 is_id_inequality(b(not_equal(A,B),pred,_),X,Y) :-
3176 (same_texpr(A,X) -> same_texpr(B,Y) ; same_texpr(A,Y), same_texpr(B,X)).
3177
3178
3179 %known_set(b(integer_set(_),set(integer),_)). % used for forall splitting; TODO: use is_integer_set ??
3180 %known_set(b(interval(_,_),set(integer),_)).
3181
3182 % detect if we have an if-then-else function (which is then applied to a dummy argument)
3183 is_if_then_else(b(comprehension_set([TDummyID1,ID2],CONJ),_Type,_),_,_DUMMYARG,IFPRED,THEN,ELSE) :-
3184 % we ignore the _DUMMYARG as here we do not check the value of DUMMYARG in the body
3185 % TO DO: also allow removal of equalities as in TLA case below
3186 % DETECT {Dummy,Res| Test => Res=THEN & not(Test) => Res=ELSE}
3187 get_texpr_id(ID2,LambdaID), get_texpr_id(TDummyID1,DummyID),
3188 is_ifte_case_conjunct(CONJ,IFPRED,EQ1,EQ2),
3189 is_equality_conj(EQ1,II1,THEN), get_texpr_id(II1,LambdaID),
3190 is_equality_conj(EQ2,II2,ELSE), get_texpr_id(II2,LambdaID),
3191 \+ occurs_in_expr(DummyID,IFPRED),\+ occurs_in_expr(LambdaID,IFPRED),
3192 \+ occurs_in_expr(DummyID,THEN), \+ occurs_in_expr(LambdaID,THEN),
3193 \+ occurs_in_expr(DummyID,ELSE), \+ occurs_in_expr(LambdaID,ELSE).
3194
3195 % Recognize B2TLA encodings as well: %((x).(x=0 & PRED|C1)\/%(x).(x=0 & not(PRED)|C2)) (0)
3196 %is_if_then_else(IF,_,_,_,_) :- nl,print(IF),nl,nl,fail.
3197 is_if_then_else(b(union(COMP1,COMP2),_Type,_),_,DUMMYARG,IFPRED,THEN,ELSE) :-
3198 if_then_else_lambda(COMP1,DUMMYARG,IFPRED,THEN),
3199 if_then_else_lambda(COMP2,DUMMYARG,NOT_IFPRED,ELSE),
3200 is_negation_of(IFPRED,NOT_IFPRED).
3201
3202 is_if_then_else(b(set_extension([CASE1,CASE2]),_,Info),POST,Arg,IFPRED,THEN,ELSE) :-
3203 (POST=post -> true ; data_validation_mode), % in cleanup_pre the wd info is not yet computed
3204 Arg = b(convert_bool(IFPRED),boolean,_),
3205 % {TRUE|->v1,FALSE|->v2}(bool(TEST)) --> IF TEST THEN v1 ELSE v2 END
3206 % example: {TRUE|->1,FALSE|->2}(bool(2>3)) --> IF 2>3 THEN 1 ELSE 2 END
3207 CASE1 = b(couple(b(B1,boolean,_),Val1),_,_),
3208 CASE2 = b(couple(b(B2,boolean,_),Val2),_,_),
3209 ( B1=boolean_true,B2=boolean_false -> THEN=Val1,ELSE=Val2
3210 ; B2=boolean_true,B1=boolean_false -> THEN=Val2,ELSE=Val1),
3211 (always_well_defined_or_disprover_mode(THEN),
3212 always_well_defined_or_disprover_mode(ELSE) -> true
3213 %,add_message(function_if_then_else,'Detected {TRUE|->v1,FALSE|->v2}(bool(TEST)) construct without WD condition, rewriting it to IF TEST THEN v1 ELSE v2 END','',Info)
3214 % otherwise: the transformation to IF-THEN-ELSE may remove WD problem
3215 ; silent_mode(on) -> true
3216 ; %data_validation_mode,
3217 add_message(function_if_then_else,'Detected {TRUE|->v1,FALSE|->v2}(bool(TEST)) construct with WD condition, you should probably rewrite it to IF TEST THEN v1 ELSE v2 END','',Info),
3218 true % fail
3219 ).
3220
3221 if_then_else_lambda(b(comprehension_set([TDummyID,TLAMBDAID],CONJ),_,_),DUMMYARG,IFPRED,RESULT) :-
3222 conjunction_to_nontyping_list(CONJ,CL),
3223 get_texpr_id(TDummyID,DummyID),
3224 get_texpr_id(TLAMBDAID,LambdaID),
3225 (remove_equality(DummyID,DUMMYVAL,CL,ConjList) % look if there is an equality for the DummyID
3226 -> same_texpr(DUMMYVAL,DUMMYARG), % TO DO: check that we apply the function with this value
3227 \+ occurs_in_expr(LambdaID,DUMMYVAL), % ensure this is really the same value
3228 \+ occurs_in_expr(DummyID,DUMMYVAL)
3229 ; ConjList=CL),
3230 remove_equality(LambdaID,RESULT,ConjList,RestList),
3231 \+ occurs_in_expr(LambdaID,RESULT),
3232 \+ occurs_in_expr(DummyID,RESULT), % otherwise this is not really a dummy identifier
3233 conjunct_predicates_with_pos_info(RestList,IFPRED),
3234 \+ occurs_in_expr(DummyID,IFPRED).
3235
3236 % DETECT (IFPRED => EQ1) & (not(IFPRED) => EQ2)
3237 is_ifte_case_conjunct(CONJ,IFPRED,EQ1,EQ2) :-
3238 is_a_conjunct(CONJ,IMP1,IMP2),
3239 is_an_implication_conj(IMP1,IFPRED,EQ1),
3240 is_an_implication_conj(IMP2,NOT_IFPRED,EQ2),
3241 is_negation_of(IFPRED,NOT_IFPRED).
3242 % TO DO: also deal with lazy_lets wrapped around
3243 %is_ifte_case_conjunct(lazy_let_pred(ID,IFPRED,CONJ),IFPRED,EQ1,EQ2) :-
3244 % is_a_conjunct(CONJ,IMP1,IMP2),
3245 % is_an_implication(IMP1,IFPRED,EQ1),
3246 % is_an_implication(IMP2,NOT_IFPRED,EQ2),
3247 % is_negation_of(IFPRED,NOT_IFPRED).
3248
3249 % detect explicit if-then-else for cleanup_post:
3250 explicit_if_then_else(if_then_else(IF,THEN,ELSE),IF,THEN,ELSE).
3251 explicit_if_then_else(if([b(if_elsif(IF,THEN),subst,_)|TAIL]),IF,THEN,ELSE) :-
3252 (TAIL = [b(if_elsif(b(truth,pred,_),EE),subst,_)|_] -> ELSE = EE
3253 ; TAIL = [] -> ELSE = b(skip,subst,[generated])
3254 ).
3255
3256 % just like is_an_implication but allow typing conjuncts (not yet removed in pre-phase)
3257 is_an_implication_conj(Pred,LHS,RHS) :- is_an_implication(Pred,LHS,RHS),!.
3258 is_an_implication_conj(b(conjunct(A,B),pred,_),LHS,RHS) :-
3259 (is_typing_predicate(A) -> is_an_implication_conj(B,LHS,RHS)
3260 ; is_typing_predicate(B) -> is_an_implication_conj(A,LHS,RHS)).
3261
3262 % just like is_equality but allow typing conjuncts (not yet removed in pre-phase)
3263 is_equality_conj(EQ,LHS,RHS) :- is_equality(EQ,LHS,RHS).
3264 is_equality_conj(b(conjunct(A,B),pred,_),LHS,RHS) :-
3265 (is_typing_predicate(A) -> is_equality_conj(B,LHS,RHS)
3266 ; is_typing_predicate(B) -> is_equality_conj(A,LHS,RHS)).
3267
3268 % remove a dummy equality from list
3269 remove_equality(ID,RHS,ConjList,Rest) :-
3270 DummyEQ = b(equal(DID,RHS),pred,_), % TO DO: also accept simple typing memberships ?
3271 get_texpr_id(DID,ID),
3272 select(DummyEQ,ConjList,Rest). %, print(eq(DID,RHS)),nl.
3273
3274 get_texpr_boolean(b(X,_,_),Res) :- is_boolan_expr(X,Res).
3275 is_boolan_expr(boolean_true,boolean_true).
3276 is_boolan_expr(boolean_false,boolean_false).
3277 is_boolan_expr(value(X),Res) :- nonvar(X), conv_bool_val(X,Res).
3278 conv_bool_val(pred_true,boolean_true).
3279 conv_bool_val(pred_false,boolean_false).
3280
3281 is_typing_conjunct(b(member(_,B),_,_)) :- is_just_type(B).
3282 is_typing_predicate(Typing) :- conjunction_to_list(Typing,LT), maplist(is_typing_conjunct,LT).
3283 conjunction_to_nontyping_list(Pred,List) :- conjunction_to_list(Pred,TList), exclude(is_typing_conjunct,TList,List).
3284
3285 % used e.g. for translating : ran({x1,...xn|P}) --> {xn| #(x1,...).(P)}
3286 % we annotate this exists as allow_to_lift; as the origin is a set comprehension which originally had all variables at the top-level (including the existentially quantified ones)
3287 create_outer_exists_for_dom_range(Ids,CompPred,NewCompPred) :-
3288 create_outer_exists_for_dom_range2(Ids,CompPred,NewCompPred1),
3289 compute_used_ids_info_if_necessary(NewCompPred1,NewCompPred).
3290 create_outer_exists_for_dom_range2(Ids,b(exists(InnerIds,P),pred,Infos),New) :-
3291 member(allow_to_lift_exists,Infos),
3292 append(Ids,InnerIds,NewIds),!, % simply add Ids to existing existential quantifier
3293 New = b(exists(NewIds,P),pred,NewInfos),
3294 remove_from_used_ids(Infos,Ids,NewInfos).
3295 create_outer_exists_for_dom_range2(Ids,P,New) :-
3296 % we could also use construct_optimized_exists/3 it does a full partitioning of P; see also components_partition_exists rule above
3297 create_exists_opt_liftable(Ids,P,New). % marked as liftable as origin is a set comprehension with all ids
3298 % calls create_exists_opt: detects also simple tautologies like #x.(x=E)
3299 % + predicates that do not use one of the quantified identifiers are moved outside
3300 %N=b(P2,T2,[allow_to_lift_exists|I2]). %, check_ast(N).
3301
3302 % remove newly quantified Typed IDs from used_ids info; if the info exists
3303 remove_from_used_ids(OldInfo,NewQuantifiedTIds,NewInfo) :-
3304 select(used_ids(OldUsed),OldInfo,I1),!,
3305 get_texpr_ids(NewQuantifiedTIds,NewQ),
3306 NewInfo = [used_ids(NewUsed)|I1],
3307 ord_subtract(OldUsed,NewQ,NewUsed).
3308 remove_from_used_ids(I,_,I).
3309
3310 % if _lambda_result_ occurs in list; rename it so that we do not get issues with enumeration
3311 rename_lambda_result_id(Ids,CompPred,NewIds,NewCompPred) :-
3312 select(ID,Ids,Rest),
3313 get_texpr_id(ID,'_lambda_result_'),
3314 !,
3315 get_unique_id_inside('__RANGE_LAMBDA__',CompPred,FRESHID), % if we don't rename then _lambda_result_ will not be enumerated ! TO DO: also check different from Ids if we want to remove __ prefix
3316 % TO DO: remove lambda_result(Info)
3317 rename_bt(CompPred,[rename('_lambda_result_',FRESHID)],NewCompPred),
3318 get_texpr_type(ID,IDType), get_texpr_info(ID,IDInfo),
3319 NewIds = [b(identifier(FRESHID),IDType,IDInfo)|Rest].
3320 rename_lambda_result_id(Ids,CompPred,Ids,CompPred).
3321
3322 contains_predicate(convert_bool(Pred),boolean,Pred,
3323 convert_bool(NewP),NewP).
3324 contains_predicate(comprehension_set(CompIds,Pred),_,Pred,
3325 comprehension_set(CompIds,NewP),NewP).
3326 contains_predicate(general_sum(Ids,Pred,Expression),integer,Pred,
3327 general_sum(Ids,NewP,Expression),NewP).
3328 contains_predicate(general_product(Ids,Pred,Expression),integer,Pred,
3329 general_product(Ids,NewP,Expression),NewP).
3330 contains_predicate(if_then_else(Pred,Then,Else),_,Pred,
3331 if_then_else(NewP,Then,Else),NewP).
3332 contains_predicate(assertion_expression(Pred,ErrMsg,Expr),_,Pred,
3333 assertion_expression(NewP,ErrMsg,Expr),NewP).
3334 contains_predicate(precondition(Pred,Body),subst,Pred,
3335 precondition(NewP,Body),NewP).
3336 contains_predicate(assertion(Pred,Body),subst,Pred,
3337 assertion(NewP,Body),NewP).
3338 contains_predicate(witness_then(Pred,Body),subst,Pred,
3339 witness_then(NewP,Body),NewP).
3340 contains_predicate(becomes_such(Vars,Pred),subst,Pred,
3341 becomes_such(Vars,NewP),NewP).
3342 contains_predicate(any(Parameters,Pred,Body),subst,Pred,
3343 any(Parameters,NewP,Body),NewP).
3344 contains_predicate(lazy_let_expr(ID,SharedExpr,MainExpr),pred, SharedExpr,
3345 lazy_let_expr(ID,NewSharedExpr,MainExpr), NewSharedExpr) :-
3346 get_texpr_type(SharedExpr,pred).
3347 contains_predicate(lazy_let_subst(ID,SharedExpr,MainExpr),pred, SharedExpr,
3348 lazy_let_subst(ID,NewSharedExpr,MainExpr), NewSharedExpr) :-
3349 get_texpr_type(SharedExpr,pred).
3350 contains_predicate(lazy_let_pred(ID,SharedExpr,MainExpr),pred, MainExpr,
3351 lazy_let_pred(ID,SharedExpr,NewMainExpr), NewMainExpr) :-
3352 \+ get_texpr_type(SharedExpr,pred).
3353 % while(COND,STMT,INV,VARIANT), select, if --> can have multiple predicates !!
3354 contains_predicates(while(Cond, Stmt,Invariant,Variant),subst, [Cond,Invariant],
3355 while(NewCond,Stmt,NewInv, Variant), [NewCond,NewInv]).
3356 contains_predicates(if(Whens),subst,Preds,
3357 if(NewWhens),NewPreds) :-
3358 get_predicates_from_list_of_cases(Whens,Preds,NewWhens,NewPreds).
3359 contains_predicates(select(Whens),subst,Preds,
3360 select(NewWhens),NewPreds) :-
3361 get_predicates_from_list_of_cases(Whens,Preds,NewWhens,NewPreds).
3362 contains_predicates(select(Whens,Else),subst,Preds,
3363 select(NewWhens,Else),NewPreds) :-
3364 get_predicates_from_list_of_cases(Whens,Preds,NewWhens,NewPreds).
3365 contains_predicates(lazy_let_pred(ID,SharedExpr,MainExpr),pred, [SharedExpr,MainExpr],
3366 lazy_let_pred(ID,NSharedExpr,NMainExpr), [NSharedExpr,NMainExpr]) :-
3367 get_texpr_type(SharedExpr,pred).
3368
3369 get_predicates_from_list_of_cases([],[],[],[]).
3370 get_predicates_from_list_of_cases([H|T],Preds,[NewH|NewT],NewPreds) :-
3371 (get_single_predicate(H,Pred,NH,NewPred)
3372 -> NewH=NH, Preds=[Pred|TP], NewPreds = [NewPred|NTP]
3373 ; NewH=H, Preds=TP, NewPreds = NTP
3374 ),
3375 get_predicates_from_list_of_cases(T,TP,NewT,NTP).
3376
3377 get_single_predicate(b(E,T,I),Preds,b(NewE,T,I),NewPreds) :-
3378 get_single_predicate_aux(E,Preds,NewE,NewPreds).
3379 get_single_predicate_aux(select_when(Pred,Body),Pred,select_when(NewPred,Body),NewPred).
3380 get_single_predicate_aux(if_elsif(Pred,Body),Pred,if_elsif(NewPred,Body),NewPred).
3381
3382
3383 % Detect useless statements in sequential compositions:
3384 % useful for LCHIP code, e.g., where dummy code is added for the code generator: i9 : (i9 : BOOL); i9 := TRUE
3385 % in test 1660 we remove an assignment that reads an unitialised variable
3386 filter_useless_subst_in_sequence([],_,R) :- !, R=[].
3387 filter_useless_subst_in_sequence([S1],_,R) :- !, R=[S1].
3388 filter_useless_subst_in_sequence([S1|S2],change,R) :- useless_subst_in_sequence(S1,S2),!,
3389 add_hint_message(filter_useless_subst_in_sequence,'Removing useless substitution in sequence','',S1),
3390 filter_useless_subst_in_sequence(S2,_,R).
3391 filter_useless_subst_in_sequence([S1|S2],Change,[S1|RS]) :- filter_useless_subst_in_sequence(S2,Change,RS).
3392
3393 useless_subst_in_sequence(b(Subst,subst,Info),Sequence2) :- % print(check(Subst,Sequence2)),nl,
3394 useless_code_before_sequence(Subst,Info,Sequence2).
3395
3396 useless_code_before_sequence(skip,_,_) :- !.
3397 useless_code_before_sequence(Subst,_,SubstList) :- is_non_failing_assignment(Subst,TID), def_get_texpr_id(TID,ID),
3398 is_dead(ID,SubstList).
3399
3400 % first naive version to compute if the variable ID is dead when followed by a list of substitutions
3401 is_dead(ID,[b(Subst,subst,Info)|_]) :- % we currently only look at first statement; TO DO: improve
3402 is_dead_aux(Subst,Info,ID).
3403 is_dead_aux(assign_single_id(TID,RHS),_Info,ID) :-
3404 get_texpr_id(TID,ID), % we assign to ID; TO DO: deal with other assignments and assignments to functions f(i) := ...
3405 find_identifier_uses_if_necessary(RHS,[],UsedIds),
3406 \+ ord_member(ID,UsedIds).
3407
3408 % non failing assignment without WD condition, note that we may still try and read identifiers that have not been initialised (having term(undefined) as value), see test 1660
3409 is_non_failing_assignment(becomes_such([TID],Pred),TID) :- is_truth(Pred).
3410 is_non_failing_assignment(becomes_element_of([TID],Set),TID) :- definitely_not_empty_set(Set).
3411 is_non_failing_assignment(assign_single_id(TID,RHS),TID) :- always_well_defined_or_disprover_mode(RHS).
3412 is_non_failing_assignment(assign([LHS],[RHS]),TID) :- always_well_defined_or_disprover_mode(RHS),
3413 get_lhs_assigned_identifier(LHS,TID).
3414
3415
3416 % ---------------------------------------------
3417
3418 :- use_module(extrasrc(b_expression_sharing),[cse_optimize_predicate/2]).
3419 % these are "global" optimizations at the predicate level
3420 % they are only called once a predicate has been completely constructed
3421 predicate_level_optimizations(Pred,NewPred) :-
3422 predicate_level_optimizations(Pred,NewPred,[]).
3423 predicate_level_optimizations(Pred,NewPred,Path) :-
3424 inner_predicate_level_optimizations(Pred,Pred1),
3425 (get_preference(use_common_subexpression_elimination,true),
3426 \+ do_not_optimise_in_context(Path)
3427 -> cse_optimize_predicate(Pred1,NewPred)
3428 ; NewPred=Pred1
3429 ). %,print_opt_debug_info(Pred,NewPred,Path).
3430 /*
3431 print_opt_debug_info(Pred,NewPred,Path) :-
3432 (Pred==NewPred -> true
3433 ; same_texpr(Pred,NewPred) -> true
3434 ; format('Optimized pred ~w: ',[Path]), print_bexpr(NewPred),nl
3435 % , (Path=[] -> trace ; true)
3436 ).
3437 */
3438
3439 do_not_optimise_in_context([path_arg(top_level(invariant),Nr)]) :-
3440 get_preference(use_po,true),
3441 debug_format(19,'% NOT applying CSE to Invariant Nr ~w (PROOF_INFO = TRUE)~n',[Nr]).
3442
3443 :- use_module(partition_detection,[detect_all_partitions_in_predicate/2]).
3444 % this predicate is also called for exists, forall, ...:
3445 inner_predicate_level_optimizations(Pred,NewPred) :-
3446 detect_all_partitions_in_predicate(Pred,NewPred1),
3447 (get_preference(remove_implied_constraints,true)
3448 -> remove_implied_constraints(NewPred1,NewPred)
3449 ; NewPred=NewPred1)
3450 . %,(Pred==NewPred -> true ; print('Optimized pred: '), print_bexpr(NewPred),nl).
3451
3452
3453
3454 % ----------------------------------
3455
3456 remove_implied_constraints(Predicate,NewPredicate) :-
3457 conjunction_to_list(Predicate,PList),
3458 remove_implied_constraints(PList,[],PNew),
3459 conjunct_predicates_with_pos_info(PNew,NewPredicate).
3460
3461 % remove constraints which are redundant for ProB
3462 % example:
3463 % n=1000 & f:1..n --> BOOL & f:1..n +-> BOOL & !x.(x:dom(f) => f(x) = bool(x>50)) & f: 1..n <-> BOOL & dom(f)=1..n
3464 % runtime goes from 500 ms down to 300 ms by remove +->, <-> and dom(f) checks
3465 % but test 1442 has issue: still unclear how useful this static detection is
3466 % it is probably most useful for proving/disproving where we have lots of redundant/derived hypotheses
3467
3468 remove_implied_constraints([],_,[]).
3469 remove_implied_constraints([Constraint|T],SoFar,Result) :-
3470 % print('Checking: '), print_bexpr(Constraint),nl,
3471 possible_implied_constraint(Constraint,C1),
3472 % print('Checking if implied constraint: '), print_bexpr(Constraint),nl,
3473 (member(TC2,T) ; member(TC2,SoFar)),
3474 get_texpr_expr(TC2,C2),
3475 implied_constraint2(C2,C1),
3476 (debug_mode(off) -> true
3477 ; print('Removing implied constraint: '), print_bexpr(Constraint),
3478 print(' <=== '), print_bexpr(TC2),nl),
3479 !,
3480 remove_implied_constraints(T,SoFar,Result).
3481 remove_implied_constraints([H|T],SoFar,[H|RT]) :- remove_implied_constraints(T,[H|SoFar],RT).
3482
3483 possible_implied_constraint(b(E,T,I),E) :-
3484 (possible_implied_constraint2(E,T,I) -> true).
3485 possible_implied_constraint2(member(_,b(FUNCTION,_,_)),_,_) :- functor(FUNCTION,F,2),
3486 (function_implication2(F,_) -> true ; F = relations).
3487 possible_implied_constraint2(equal(b(domain(_),_,_),_),_,_). % TO DO: other way around
3488
3489 % f: A --> B ==> f: A +-> B, f: A<->B, dom(f) = A
3490 % test 1442: issue with surjection
3491 implied_constraint2(member(Fun1,b(FUNCTION1,T,_)), member(Fun2,b(FUNCTION2,T,_))) :-
3492 functor(FUNCTION1,F1,2), arg(1,FUNCTION1,X1), arg(2,FUNCTION1,Y1),
3493 functor(FUNCTION2,F2,2), arg(1,FUNCTION2,X2), arg(2,FUNCTION2,Y2),
3494 function_implication(F1,F2),
3495 same_texpr(Fun1,Fun2),
3496 same_texpr(X1,X2),
3497 same_texpr(Y1,Y2).
3498 % f: A --> B ==> dom(f) = A
3499 implied_constraint2(member(Fun2,b(FUNCTION2,_,_)), equal(b(domain(Fun1),_,_),Domain)) :-
3500 functor(FUNCTION2,F2,2), arg(1,FUNCTION2,Domain2),
3501 total_function(F2),
3502 same_texpr(Fun1,Fun2),
3503 same_texpr(Domain,Domain2).
3504 % TODO: f: A -->> B ==> ran(f) = B ?
3505
3506
3507 total_function(total_bijection).
3508 total_function(total_injection).
3509 total_function(total_surjection).
3510 total_function(total_function).
3511 %total_relation(total_surjection_relation). % not sure if in this case the constraint is maybe not useful after all?
3512 %total_relation(total_relation).
3513
3514 function_implication(F1,F2) :- function_implication2(F1,F2).
3515 function_implication(F1,F2) :- function_implication2(F1,Z), function_implication(Z,F2).
3516
3517 function_implication2(total_bijection,total_injection).
3518 function_implication2(total_bijection,total_surjection).
3519 function_implication2(total_injection,total_function).
3520 function_implication2(total_surjection,total_function).
3521 function_implication2(total_function,partial_function).
3522 function_implication2(partial_function,relations).
3523 function_implication2(partial_injection,partial_function). % >+>
3524 function_implication2(partial_surjection,partial_function).
3525 %function_implication2(partial_bijection,partial_injection).
3526 %function_implication2(partial_bijection,partial_surjection).
3527 function_implication2(total_relation,relations).
3528 function_implication2(surjection_relation,relations).
3529 function_implication2(total_surjection_relation,total_relation).
3530 function_implication2(total_surjection_relation,surjection_relation).
3531
3532 % ------------------
3533
3534
3535 % divide a list of identifiers into domain and range identifiers
3536 get_domain_range_ids([D,R],[D],[R]) :- !.
3537 get_domain_range_ids([D1,D2|T],[D1|DT],R) :- get_domain_range_ids([D2|T],DT,R).
3538
3539
3540 % detect whether there is a pattern of a recursive usage of the identifier: ID(x) or ID[x] or x:ID
3541 find_recursive_usage(TExpr,ID) :-
3542 syntaxtraversion(TExpr,Expr,_,_,Subs,TNames), % print(try_id(ID,Expr,Subs,TNames)),nl,
3543 ( Expr = function(Fun,_), get_texpr_id(Fun,ID) -> true
3544 ; Expr = image(Rel,_), get_texpr_id(Rel,ID) -> true
3545 ; Expr = member(_,Set), get_texpr_id(Set,ID) -> true
3546 ; \+ (member(ID1,TNames),get_texpr_id(ID1,ID)), % new local variable with same name
3547 member(Sub,Subs), find_recursive_usage(Sub,ID)
3548 ).
3549
3550 :- use_module(bsyntaxtree,[transform_bexpr/3]).
3551 % find comprehension sets and mark them as recursive if they use the recursive ID
3552 mark_recursion(TExpr,RecID,NewTExpr) :-
3553 (transform_bexpr(b_ast_cleanup:mark_comprehension_set(RecID),TExpr,NewTExpr)
3554 -> true
3555 ; add_internal_error('Call failed: ',transform_bexpr(b_ast_cleanup:mark_comprehension_set(RecID),TExpr,NewTExpr)),
3556 NewTExpr=TExpr).
3557
3558 :- public mark_comprehension_set/3.
3559 mark_comprehension_set(RecID,b(lambda(Ids,P,Expr),Type,Info),
3560 b(lambda(Ids,P,Expr),Type,NInfo)) :-
3561 (find_recursive_usage(P,RecID) -> true ; find_recursive_usage(Expr,RecID)),
3562 get_texpr_ids(Ids,AtomicIds),
3563 (silent_mode(on) -> true
3564 ; format('Recursive lambda using ~w detected (name: ~w)~n',[AtomicIds,RecID]),
3565 error_manager:print_message_span(Info),nl
3566 ),
3567 add_texpr_infos(Info,[prob_annotation('SYMBOLIC'),prob_annotation('RECURSIVE')],NInfo).
3568 mark_comprehension_set(RecID,b(comprehension_set(Ids,P),Type,Info),
3569 b(comprehension_set(Ids,P),Type,NInfo)) :-
3570 % DO NOT MARK IT IF IT IS IN RESULT POSITION of recursive function ?
3571 find_recursive_usage(P,RecID),
3572 get_texpr_ids(Ids,AtomicIds),
3573 (silent_mode(on) -> true
3574 ; format('Recursive comprehension set using ~w detected (name: ~w)~n',[AtomicIds,RecID]),
3575 error_manager:print_message_span(Info),nl
3576 ),
3577 NInfo = [prob_annotation('SYMBOLIC'),prob_annotation('RECURSIVE')|Info]. % TO DO: only add if not already there
3578
3579
3580 % pred(h) --> h-1, succ(h) --> h+1
3581 precompute_pred_succ_function_call(Fun,Arg,ArithOp) :-
3582 get_texpr_expr(Fun,PS),
3583 ( PS=predecessor -> Op=minus
3584 ; PS=successor -> Op=add), % we could use add_one predicate
3585 ArithOp =.. [Op,Arg,Integer],
3586 create_texpr(integer(1),integer,[],Integer).
3587
3588 %
3589 one(b(integer(1),integer,[])).
3590 create_interval_member(X,LowBound,UpBound,Member) :-
3591 safe_create_texpr(interval(LowBound,UpBound),set(integer),Interval),
3592 safe_create_texpr(member(X,Interval),pred,Member).
3593
3594 get_leq_comparison(less(A,B),A,B1) :- minus_one(B,BM1),
3595 safe_create_texpr(BM1,integer,B1).
3596 get_leq_comparison(greater(B,A),A,B1) :- get_leq_comparison(less(A,B),A,B1).
3597 get_leq_comparison(less_equal(A,B),A,B).
3598 get_leq_comparison(greater_equal(B,A),A,B).
3599
3600 minus_one(b(integer(I),integer,_),Res) :- !, I1 is I-1, Res=integer(I1).
3601 minus_one(B,minus(B,One)) :- one(One).
3602 add_one(b(integer(I),integer,_),Res) :- !, I1 is I+1, Res=integer(I1).
3603 add_one(B,add(B,One)) :- one(One).
3604
3605 % get_geq_comparison(Expr,LHS,RHS) ; RHS can be shifted by 1
3606 get_geq_comparison(less(B,A),A,B1) :- get_geq_comparison(greater(A,B),A,B1).
3607 get_geq_comparison(greater(A,B),A,B1) :- add_one(B,BP1),
3608 safe_create_texpr(BP1,integer,B1).
3609 get_geq_comparison(less_equal(B,A),A,B).
3610 get_geq_comparison(greater_equal(A,B),A,B).
3611 get_geq_comparison(member(A,SET),A,b(integer(Bound),integer,[])) :-
3612 is_inf_integer_set_with_lower_bound(SET,Bound).
3613 % comparison operators:
3614 comparison(equal(A,B),A,B,equal(SA,SB),SA,SB).
3615 comparison(not_equal(A,B),A,B,not_equal(SA,SB),SA,SB).
3616 comparison(greater(A,B),A,B,greater(SA,SB),SA,SB).
3617 comparison(less(A,B),A,B,less(SA,SB),SA,SB).
3618 comparison(greater_equal(A,B),A,B,greater_equal(SA,SB),SA,SB).
3619 comparison(less_equal(A,B),A,B,less_equal(SA,SB),SA,SB).
3620 % rules to simplify binary comparison arguments
3621 simplify_comparison_terms(b(A,T,_IA),b(B,T,_IB),RA,RB) :-
3622 simplify_comparison_terms2(A,B,RA,RB).
3623 % TO DO: expand into much better simplifier !
3624 simplify_comparison_terms2(minus(A1,A2),minus(B1,B2),ResA,ResB) :-
3625 ( same_texpr(A1,B1) -> ResA=B2, ResB=A2 % X-A2 < X-B2 <=> B2 < A2
3626 ; same_texpr(A2,B2) -> ResA=A1, ResB=B1). % A1-X < B1-X <=> A1 < B1
3627 simplify_comparison_terms2(add(A1,A2),add(B1,B2),ResA,ResB) :-
3628 ( same_texpr(A1,B1) -> ResA=A2, ResB=B2 % X+A2 < X+B2 <=> A2 < B2
3629 ; same_texpr(A2,B2) -> ResA=A1, ResB=B1 % A1+X < B1+X <=> A1 < B1
3630 ; same_texpr(A1,B2) -> ResA=A2, ResB=B1 % X+A2 < B1+X <=> A2 < B1
3631 ; same_texpr(A2,B1) -> ResA=A1, ResB=B2). % A1+X < X+B2 <=> A1 < B2
3632 % multiplication: beware of sign, same with division
3633
3634 /* not used at the moment:
3635 clpfd_arith_integer_expression(b(E,integer,_)) :- clpfd_arith_integer_expression_aux(E).
3636 % check if we have an expression that can be dealt with by b_compute_arith_expression
3637 clpfd_arith_integer_expression_aux(unary_minus(X)) :-
3638 X \= b(integer(_),integer,_). % if it is an explicit integer we can compute it normally
3639 clpfd_arith_integer_expression_aux(add(_,_)).
3640 clpfd_arith_integer_expression_aux(minus(_,_)).
3641 clpfd_arith_integer_expression_aux(multiplication(_,_)).
3642 */
3643
3644 % simplify equality/inequality Unifications:
3645 simplify_equality(b(A,T,_),b(B,T,_),A2,B2) :-
3646 simplify_equality_aux(A,B,T,A2,B2).
3647 simplify_equality_aux(set_extension([A1]),set_extension([B1]),_,A2,B2) :- !,
3648 opt_simplify_equality(A1,B1,A2,B2).
3649 simplify_equality_aux(CoupleA,Type,CoupleB,A3,B3) :-
3650 get_couple(CoupleA,Type,A1,A2),
3651 get_couple(CoupleB,Type,B1,B2),
3652 (same_texpr(A1,B1), % (1,x)=(1,3) -> x=3
3653 always_well_defined_or_disprover_mode(A1)
3654 -> opt_simplify_equality(A2,B2,A3,B3)
3655 ; same_texpr(A2,B2),always_well_defined_or_disprover_mode(A2)
3656 -> opt_simplify_equality(A1,B1,A3,B3)
3657 ; different_texpr_values(A1,B1), % (1,x)=(2,3) -> 1=2
3658 always_well_defined_or_wd_improvements_allowed(A2),
3659 always_well_defined_or_wd_improvements_allowed(B2)
3660 -> (A3,B3) = (A1,B1) % no need to compare A2,B2
3661 ; different_texpr_values(A2,B2), always_well_defined_or_wd_improvements_allowed(A1),
3662 always_well_defined_or_wd_improvements_allowed(B1)
3663 -> (A3,B3) = (A2,B2) % no need to compare A1,B1
3664 ).
3665
3666 % flexibly get a couple from either AST or value:
3667 get_couple(couple(A1,A2),_,A1,A2).
3668 get_couple(value(CVal),couple(T1,T2),A1,A2) :- nonvar(CVal), CVal=(V1,V2),
3669 A1=b(value(V1),T1,[]), A2=b(value(V2),T2,[]).
3670
3671 opt_simplify_equality(A1,B1,A2,B2) :-
3672 (simplify_equality(A1,B1,A2,B2) -> true ; A2=A1, B2=B1).
3673
3674 % record field set extraction:
3675 construct_field_sets(FieldsSetsOut, field(Name,Type), field(Name,NewSet)) :-
3676 (member(field_set(Name,NewSet),FieldsSetsOut)
3677 -> true
3678 ; create_maximal_type_set(Type,NewSet)
3679 ).
3680
3681 % traverse a list of conjuncts and check that they all restrict fields of a record ID
3682 % all sets are combined via intersection
3683 l_update_record_field_membership([],_) --> [].
3684 l_update_record_field_membership([H|T],ID) -->
3685 update_record_field_membership(H,ID), l_update_record_field_membership(T,ID).
3686 update_record_field_membership(b(member(b(LHS,_,_),TRHS),pred,_),ID) --> update2(LHS,TRHS,ID).
3687 update2(record_field(RECID,FieldName),TRHS,ID) --> {get_texpr_id(RECID,ID)},add_field_restriction(FieldName,TRHS).
3688 update2(identifier(ID),b(struct(b(rec(FieldSets),_,_)),_,_),ID) -->
3689 l_add_field_restriction(FieldSets).
3690
3691 l_add_field_restriction([]) --> [].
3692 l_add_field_restriction([field(FieldName,TRHS)|T]) -->
3693 add_field_restriction(FieldName,TRHS), l_add_field_restriction(T).
3694 add_field_restriction(FieldName,TRHS,FieldsIn,FieldsOut) :-
3695 (select(field_set(FieldName,OldSet),FieldsIn,F2)
3696 -> OldSet = b(_,Type,_),
3697 safe_create_texpr(intersection(OldSet,TRHS),Type,NewSet),
3698 FieldsOut = [field_set(FieldName,NewSet)|F2]
3699 ; FieldsOut = [field_set(FieldName,TRHS)|FieldsIn]).
3700 % end record field extraction
3701
3702
3703 extract_unions(A,R) :- get_texpr_expr(A,union(A1,A2)),!,
3704 extract_unions(A1,R1), extract_unions(A2,R2),
3705 append(R1,R2,R).
3706 extract_unions(A,[A]).
3707
3708 gen_member_predicates(B,SEl,TExpr) :- safe_create_texpr(member(SEl,B),pred,TExpr).
3709
3710 % when constructing an expression/predicate: important to ripple wd information up
3711 extract_important_info_from_subexpression(b(_,_,Info),NewInfo) :-
3712 include(important_info_from_sub_expr,Info,NewInfo).
3713
3714 extract_important_info_from_subexpressions(b(_,_,Info1),b(_,_,Info2),NewInfo) :-
3715 include(important_info_from_sub_expr,Info1,II1),
3716 (memberchk(contains_wd_condition,Info2), nonmember(contains_wd_condition,II1)
3717 -> NewInfo = [contains_wd_condition|II1]
3718 ; NewInfo=II1). % TO DO: maybe also import other Infos? merge position info (nodeid(_))?
3719 % other important ones: removed_typing ??
3720
3721 % include important info from removed conjunct (note: see also extract_info in bsyntaxtree)
3722 % include_important_info(RemovedPredInfo,RemainingPredInfo,NewInfo)
3723 include_important_info_from_removed_pred([],Info2,Info2).
3724 include_important_info_from_removed_pred([H1|Info1],Info2,NewInfo2) :-
3725 (is_removed_typing_info(H1), nonmember(removed_typing,Info2)
3726 -> NewInfo2 = [removed_typing|Info2]
3727 ; include_important_info_from_removed_pred(Info1,Info2,NewInfo2)).
3728
3729 is_removed_typing_info(was(_)).
3730 is_removed_typing_info(removed_typing).
3731
3732 important_info_from_sub_expr(removed_typing).
3733 important_info_from_sub_expr(contains_wd_condition).
3734 important_info_from_sub_expr(prob_annotation(_)).
3735 important_info_from_sub_expr(nodeid(_)).
3736 important_info_from_sub_expr(was(_)).
3737 %important_info(allow_to_lift_exists). % important but only for exists; should not be copied to outer predicates
3738
3739 % add important infos in case an expression gets simplified into a sub-expression, e.g., bool(X)=TRUE -> X
3740 add_important_info_from_super_expression(Infos,SubInfos,NewSubInfos) :-
3741 include(important_info_from_super_expression,Infos,Important), % print(add_important(Important)),nl,
3742 add_infos_if_new(Important,SubInfos,NewSubInfos).
3743
3744
3745 important_info_from_super_expression(label(_)).
3746 important_info_from_super_expression(P) :- is_rodin_label_info(P). % important for Rodin proof info; if an invariant is partioned
3747 %add_important_info_to_texpr_from_super(Infos,b(Sub,T,SubInfos),b(Sub,T,NewSubInfos)) :- !,
3748 % add_important_info_from_super_expression(Infos,SubInfos,NewSubInfos).
3749
3750 important_info_for_exists(allow_to_lift_exists).
3751 important_info_for_exists(Label) :- important_info_from_super_expression(Label).
3752 % add important infos to individual conjuncts which are exists constructs; used when partitioning of exists:
3753 add_important_infos_to_exists_conjuncts(TPred,SuperInfos,SuperIds,NewTPred) :-
3754 include(important_info_for_exists,SuperInfos,Important),
3755 (Important=[]
3756 -> NewTPred=TPred
3757 ; add_to_conjuncts_aux(TPred,Important,SuperIds,NewTPred)
3758 ).
3759 add_to_conjuncts_aux(b(Pred,Type,Infos),Important,SuperIds,b(NP,Type,NewSubInfos)) :-
3760 (Pred=conjunct(A,B)
3761 -> NP=conjunct(NA,NB), NewSubInfos=Infos,
3762 add_to_conjuncts_aux(A,Important,SuperIds,NA),
3763 add_to_conjuncts_aux(B,Important,SuperIds,NB)
3764 ; Pred=exists(InnerIds,_), member(TID,InnerIds),
3765 def_get_texpr_id(TID,ID),
3766 ord_member(ID,SuperIds) % the exists is probably related to the outer exists
3767 % (TODO: it could be a lifted clashing one: perform this annotation directly in construct_optimized_exists !!)
3768 -> append(Important,Infos,NewSubInfos), % copy infos from original exists
3769 NP=Pred
3770 ; NP=Pred, NewSubInfos=Infos).
3771
3772 % extract all assignments from a list of statements; last arg is the number of assignments extracted
3773 extract_assignments([],[],[],[],0).
3774 extract_assignments([H|T],ResLHS,ResRHS,Rest,Nr) :-
3775 is_ordinary_assignment(H,LHS,RHS,Cnt),!,
3776 extract_assignments(T,LT,RT,Rest,N),
3777 append(LHS,LT,ResLHS), append(RHS,RT,ResRHS), Nr is N+Cnt.
3778 extract_assignments([H|T],LT,RT,[H|Rest],Nr) :-
3779 extract_assignments(T,LT,RT,Rest,Nr).
3780 % assigned_after(Primed),modifies(Var)
3781
3782 % check if we have an ordinary assignment that can be merged, optimised:
3783 is_ordinary_assignment(b(S,_,Info),LHS,RHS,Cnt) :- is_ordinary_assignment_aux(S,Info,LHS,RHS,Cnt).
3784 is_ordinary_assignment_aux(skip,_Info,[],[],0).
3785 is_ordinary_assignment_aux(assign_single_id(LHS,RHS),_Info,[LHS],[RHS],0). % count=0: used for parallel merge: assign_single_id less useful to merge with
3786 is_ordinary_assignment_aux(assign(LHS,RHS),Info,LHS,RHS,1) :-
3787 \+ member(assigned_after(_),Info), % these assignments are treated in a special way
3788 \+ member(modifies(_),Info).
3789
3790 % merge assignments in a list of statements to be executed by sequential composition:
3791 merge_assignments([S1,S2|T],merged,Res) :- merge_two_assignments(S1,S2,New),!,
3792 merge_assignments([New|T],_,Res).
3793 merge_assignments([],no_merge,[]).
3794 merge_assignments([H|T],Merge,[H|TR]) :- merge_assignments(T,Merge,TR).
3795
3796 :- use_module(b_read_write_info,[get_lhs_assigned_identifier/2]).
3797 get_lhs_assigned_ids(LHS,SortedIds) :-
3798 maplist(get_lhs_assigned_identifier,LHS,TLHSAssign),
3799 get_sorted_ids(TLHSAssign,SortedIds).
3800 merge_two_assignments(S1,S2,NewAssignment) :-
3801 is_ordinary_assignment(S1,LHS1,RHS1,_),
3802 is_ordinary_assignment(S2,LHS2,RHS2,_),
3803 get_lhs_assigned_ids(LHS1,SortedIDs1),
3804 get_lhs_assigned_ids(LHS2,SortedIDs2),
3805 ord_disjoint(SortedIDs1,SortedIDs2), % no race condition
3806 maplist(not_occurs_in_predicate(SortedIDs1),RHS2),
3807 maplist(not_occurs_in_predicate(SortedIDs1),LHS2), % not used in left-hand side, e.g., f(x+y) := RHS
3808 get_texpr_info(S1,I1), get_texpr_info(S2,I2),
3809 merge_info(I1,I2,Infos),
3810 append(LHS1,LHS2,NewLHS),
3811 append(RHS1,RHS2,NewRHS),
3812 NewAssignment = b(assign(NewLHS,NewRHS),subst,Infos),
3813 (debug_mode(off) -> true ; print('Merged assignments: '),translate:print_subst(NewAssignment),nl).
3814 construct_sequence([],skip).
3815 construct_sequence([TH],H) :- !, TH=b(H,_,_).
3816 construct_sequence(List,sequence(List)).
3817
3818 % check if we have a simple expression which will not be complicated to calculate
3819 ?simple_expression(b(E,_,_)) :- simple2(E).
3820 % (simple2(E) -> true ; print(not_simple(E)),nl).
3821 simple2(bool_set).
3822 simple2(boolean_false).
3823 simple2(boolean_true).
3824 simple2(empty_sequence).
3825 simple2(empty_set).
3826 simple2(identifier(_)).
3827 %simple2(integer_set(_)).
3828 simple2(integer(_)).
3829 simple2(lazy_lookup_expr(_)).
3830 simple2(lazy_let_expr(_,A,B)) :- simple2(B), simple_expr_or_pred(A).
3831 simple2(max_int).
3832 simple2(min_int).
3833 simple2(real_set).
3834 simple2(real(_)).
3835 simple2(string_set).
3836 simple2(string(_)).
3837 simple2(value(_)).
3838 simple2(first_of_pair(_)). simple2(second_of_pair(_)).
3839 simple2(couple(A,B)) :- simple_expression(A), simple_expression(B).
3840 simple2(interval(A,B)) :- simple_expression(A), simple_expression(B).
3841 ?simple2(add(A,B)) :- simple_expression(A), simple_expression(B).
3842 simple2(minus(A,B)) :- simple_expression(A), simple_expression(B).
3843 simple2(multiplication(A,B)) :- simple_expression(A), simple_expression(B).
3844 simple2(unary_minus(A)) :- simple_expression(A).
3845 simple2(convert_bool(A)) :- simple_predicate(A).
3846 simple2(sequence_extension(A)) :- maplist(simple_expression,A).
3847 simple2(set_extension(A)) :- maplist(simple_expression,A). % a bit more expensive than sequence_extension: elements need to be compared
3848 simple2(X) :- is_integer_set(X,_).
3849
3850 simple_expr_or_pred(b(E,T,_)) :- (T=pred -> simplep2(E) ; simple2(E)).
3851
3852 simple_predicate(b(E,_,_)) :- simplep2(E).
3853 simplep2(equal(A,B)) :- simple_expression(A), simple_expression(B). % could be slightly more expensive if set type
3854 simplep2(not_equal(A,B)) :- simple_expression(A), simple_expression(B). % ditto
3855 simplep2(lazy_let_pred(_,A,B)) :- simple_predicate(B), simple_expr_or_pred(A).
3856 simplep2(less(A,B)) :- simple_expression(A), simple_expression(B).
3857 simplep2(less_equal(A,B)) :- simple_expression(A), simple_expression(B).
3858 simplep2(greater(A,B)) :- simple_expression(A), simple_expression(B).
3859 simplep2(greater_equal(A,B)) :- simple_expression(A), simple_expression(B).
3860
3861 % detect ID = Expr or Expr = ID
3862 identifier_equality(TExpr,ID,TID,Expr) :- is_equality(TExpr,LHS,RHS),
3863 ( get_texpr_id(LHS,ID), TID=LHS, Expr = RHS
3864 ; get_texpr_id(RHS,ID), TID=RHS, Expr = LHS).
3865
3866
3867 id_member_of_set_extension(TExpr,ID,TID,[Expr]) :- identifier_equality(TExpr,ID,TID,Expr).
3868 id_member_of_set_extension(b(member(TID,SEXT),pred,_),ID,TID,SList) :- get_texpr_id(TID,ID),
3869 is_set_extension(SEXT,SList).
3870
3871 % check if merging disjunctions of set_extensionts of this type is useful in CLP(FD) mode
3872 % see get_fd_type in clpfd_tables, ...
3873 type_contains_fd_index(V) :- var(V),!,fail.
3874 type_contains_fd_index(couple(A,_)) :- type_contains_fd_index(A).
3875 type_contains_fd_index(record([field(_,T1)|_])) :- type_contains_fd_index(T1).
3876 type_contains_fd_index(global(_)).
3877 type_contains_fd_index(integer).
3878 type_contains_fd_index(boolean).
3879
3880
3881 create_equalities_for_let(ORefs,Primed,Equalities) :-
3882 maplist(create_equality_for_let,ORefs,Primed,Equalities).
3883 create_equality_for_let(oref(PrimedId,OrigId,Type),TPrimed,Equality) :-
3884 create_texpr(identifier(OrigId),Type,[],TOrig),
3885 create_texpr(identifier(PrimedId),Type,[],TPrimed),
3886 safe_create_texpr(equal(TPrimed,TOrig),pred,Equality).
3887
3888 % inserts a let statement. If the original statement is a precondition or any, the let is moved
3889 % inside the original statement to prevent strange side-effects. This can be used for other,
3890 % non-value changing substitutions as well.
3891 insert_let(TExpr,Ids,P,NTExpr) :-
3892 remove_bt(TExpr,Expr,NewExpr,NTExpr),
3893 move_let_inside(Expr,Old,New,NewExpr),!,
3894 insert_let(Old,Ids,P,New).
3895 insert_let(TExpr,Ids,P,NTExpr) :-
3896 create_texpr(let(Ids,P,TExpr),subst,[],NTExpr).
3897 move_let_inside(precondition(Cond,Old),Old,New,precondition(Cond,New)).
3898 move_let_inside(any(Any,Where,Old),Old,New,any(Any,Where,New)).
3899
3900 % find_one_point_rules(+TypedIds,+Blacklist,+Predicates,
3901 % -LetIds,-LetExprs,-RemainingIds,-RemainingPredicates)
3902 % TypedIds: The ids that are quantified in the exists clause
3903 % Blacklist: All ids that must not be used in the found expression
3904 % Predicates: The predicates of the exists (without already used id=E predicates)
3905 % LetIds: The ids that can be introduced as LET
3906 % LetExprs. For each id (in LetIds) the corresponding expression
3907 % RemainingIds: The ids that are not converted into LETs
3908 % RemainingPredicates: The predicates after removing the id=E predicates
3909 % (e.g., f = {1|->2} & !e.(2:dom(f) & e=f(2) => e>100) should not generate a WD-error)
3910 find_one_point_rules(TIds,Preds,Blacklist,LetIds,Exprs,RestIds,NewPreds) :-
3911 typed_ids_to_avl(TIds,AVL),
3912 find_one_point_equalities(Preds,is_leftmost,AVL,Blacklist,LetIds,Exprs,RestIds,NewPreds).
3913
3914 :- use_module(library(avl),[avl_range/2, avl_fetch/3, avl_delete/4, empty_avl/1]).
3915 :- use_module(bsyntaxtree,[is_equality/3]).
3916 find_one_point_equalities([],_,AVL,_,[],[],RestIds,[]) :-
3917 avl_range(AVL,RestIds).
3918 find_one_point_equalities([TEqual|TPreds],WDLEFT,AVL,Blacklist,LetIds,Exprs,RestIds,NewPreds) :-
3919 split_equality(TEqual,TEq1,TEq2),
3920 %print('Splitting equality: '), translate:print_bexpr(TEqual),nl,
3921 !,
3922 find_one_point_equalities([TEq1,TEq2|TPreds],WDLEFT,AVL,Blacklist,LetIds,Exprs,RestIds,NewPreds).
3923 find_one_point_equalities([TEqual|TPreds],WDLEFT,AVL,Blacklist,[LetID|LetIds],[Expr|Exprs],RestIds,NewPreds) :-
3924 is_equality(TEqual,TA,TB),
3925 ( get_texpr_id(TA,Id),TB=Expr ; get_texpr_id(TB,Id),TA=Expr ),
3926 avl_fetch(Id,AVL,LetID), % we have an equality involving a quantified identifier
3927 %print(wdleft(WDLEFT,Id)),nl, print_bexpr(Expr),nl,
3928 (WDLEFT=is_leftmost
3929 -> true % all the expressions to the left of the equality are well-defined
3930 ; always_defined_full_check_or_disprover_mode(Expr)), % we can lift Id=Expr to an outer LET
3931 % example: UNION(x).(1:dom(f) & x=f(1)|{x}) --> do not lift x=f(1) out if f(1) is not WD, see test 2195
3932 find_identifier_uses_if_necessary(Expr,[],UsedIds),
3933 ord_disjoint(Blacklist,UsedIds),
3934 % TODO: what if we have an equality between two quantified ids in the blacklist?
3935 !,
3936 avl_delete(Id,AVL,_,AVL2),
3937 (empty_avl(AVL2) % check if we have found equalities for all ids
3938 -> NewPreds=TPreds, LetIds=[],Exprs=[],RestIds=[]
3939 ; % should we add Id to Blacklist; usually all ids are already in the blacklist
3940 % WDLEFT remains unchanged
3941 update_wd_to_left(WDLEFT,Expr,NewWDLEFT),
3942 find_one_point_equalities(TPreds,NewWDLEFT,AVL2,Blacklist,LetIds,Exprs,RestIds,NewPreds)
3943 ).
3944 find_one_point_equalities([TEqual|TPreds],_WDLEFT,AVL,Blacklist,LetIds,Exprs,RestIds,[TEqual|NewPreds]) :-
3945 %update_wd_to_left(WDLEFT,Expr,NewWDLEFT),
3946 find_one_point_equalities(TPreds,not_leftmost,AVL,Blacklist,LetIds,Exprs,RestIds,NewPreds).
3947
3948 % update information about whether the next conjunct should still be considered as leftmost concerning WD
3949 update_wd_to_left(is_leftmost,Expr,NewWD) :- always_defined_full_check_or_disprover_mode(Expr),!,
3950 NewWD = is_leftmost.
3951 update_wd_to_left(_,_,not_leftmost).
3952
3953
3954 :- use_module(library(avl),[list_to_avl/2]).
3955 get_avl_aux(TID,Id-TID) :- get_texpr_id(TID,Id).
3956
3957 % convert an unsorted typed identifier list to an AVL tree
3958 typed_ids_to_avl(TIds,AVL) :-
3959 maplist(get_avl_aux,TIds,L),
3960 list_to_avl(L,AVL).
3961
3962
3963 % select a predicate from Preds of the form id=Expr (or Expr=id) where Expr does not contain
3964 % references to identifiers in Blacklist. Rest is Preds without id=Expr
3965 select_equality(TId,Preds,Blacklist,TEqual,Expr,Rest,UsedIds,CheckWellDef) :-
3966 get_texpr_id(TId,Id),
3967 ? safe_select(CheckWellDef,TEqual,Preds,Rest),
3968 is_equality(TEqual,TA,TB), % the ast_cleanup rules have not run yet on the sub-expressions of the exists: detect more equalities
3969 ( get_texpr_id(TA,Id),TB=Expr ; get_texpr_id(TB,Id),TA=Expr ),
3970 find_identifier_uses_if_necessary(Expr,[],UsedIds),
3971 ord_disjoint(Blacklist,UsedIds).
3972
3973
3974 % safely select a predicate from List, preserving WD (well-definedness)
3975 safe_select(check_well_definedness,Element,[H|T],Rest) :- !,
3976 (Element=H,Rest=T % either first element
3977 ; % or if later element; then it must be well-defined; otherwise H could fail
3978 select(Element,T,TRest), Rest=[H|TRest],
3979 always_defined_full_check_or_disprover_mode(Element) % we cannot use always_well_defined(Element) in cleanup_pre; it is only computed in cleanup_post at the moment; TO DO: we now do compute in pre phase
3980 %, print(always_wd(Element)),nl
3981 ).
3982 ?safe_select(_,Element,List,Rest) :- select(Element,List,Rest).
3983
3984 % split predicate list into conjuncts using a certain list of ids and those not
3985 split_predicates(LP,Ids,UsingIds,NotUsingIds) :-
3986 get_sorted_ids(Ids,SIds),
3987 filter(not_occurs_in_predicate(SIds),LP,NP,UP),
3988 conjunct_predicates_with_pos_info(NP,NotUsingIds),
3989 conjunct_predicates_with_pos_info(UP,UsingIds).
3990
3991 not_occurs_in_predicate([],_Pred) :- !.
3992 not_occurs_in_predicate(SortedIDs,Pred) :- SortedIDs = [ID1|_],
3993 (ID1 = b(_,_,_) -> add_internal_error('Wrapped identifiers: ',not_occurs_in_predicate(SortedIDs,Pred)) ; true),
3994 find_identifier_uses_if_necessary(Pred,[],UsedIds),
3995 ord_disjoint(SortedIDs,UsedIds).
3996 get_sorted_ids(Ids,SIds) :-
3997 get_texpr_ids(Ids,UnsortedIds),sort(UnsortedIds,SIds).
3998
3999 pred_succ_compset(Op,comprehension_set([A,B],Pred)) :-
4000 %get_unique_id('_a_',AId),get_unique_id('_b_',BId),
4001 BId = '_lambda_result_',
4002 (Op = add -> AId = '_succ_' ; AId='_pred_'),
4003 create_texpr(identifier(AId),integer,[],A),
4004 create_texpr(identifier(BId),integer,[lambda_result(BId)],B),
4005 create_texpr(integer(1),integer,[],Integer),
4006 create_texpr(ArithOp,integer,[],TArithOp),
4007 ArithOp =.. [Op,A,Integer],
4008 safe_create_texpr(equal(B,TArithOp),pred,[prob_annotation('LAMBDA-EQUALITY')],Pred).
4009
4010 add_used_identifier_info(_Ids,_P,IOld,INew) :-
4011 member(used_ids(_),IOld),!,INew=IOld.
4012 add_used_identifier_info(Ids,P,IOld,[used_ids(FoundIds)|IOld]) :-
4013 % add used identifiers to information
4014 get_sorted_ids(Ids,Ignore),
4015 find_identifier_uses(P,Ignore,FoundIds).
4016
4017 add_used_ids_defined_by_equality(_Ids,P,IOld,INew) :-
4018 ? member(used_ids(UsedIds),IOld),!,
4019 findall(ID, (member_in_conjunction(Equality,P),
4020 identifier_equality(Equality,ID,_TID,Expr),
4021 ord_member(ID,UsedIds),
4022 not_occurs_in_expr(ID,Expr)), % TO DO: we could check also other ids defined by equality already found
4023 IdsDefinedByEquality),
4024 (select(used_ids_defined_by_equality(_),IOld,I1) -> true ; I1=IOld),
4025 (IdsDefinedByEquality=[] -> INew=I1
4026 ; %debug_println(9,used_ids_defined_by_equality(IdsDefinedByEquality)),
4027 INew = [used_ids_defined_by_equality(IdsDefinedByEquality)|I1]
4028 ).
4029 add_used_ids_defined_by_equality(Ids,P,IOld,INew) :-
4030 add_internal_error('No used_ids info:',add_used_ids_defined_by_equality(Ids,P,IOld,INew)),
4031 INew=IOld.
4032
4033
4034 % can be used to check the validity of the used_ids field, e.g., for existential quantifier
4035 check_used_ids_info(Parameters,Predicate,StoredUsedIds,PP) :-
4036 % get_global_identifiers(Ignored), and add to Parameters ??
4037 (add_used_identifier_info(Parameters,Predicate,[],[used_ids(UsedIds)])
4038 -> (StoredUsedIds=UsedIds -> true
4039 ; ord_subset(UsedIds,StoredUsedIds)
4040 -> format('Suboptimal used_ids info: ~w (actual ~w) [origin ~w with ~w]~n',[StoredUsedIds,UsedIds,PP,Parameters])
4041 %, print_bexpr(Predicate),nl
4042 ; add_internal_error('Incorrect used_ids info: ', check_used_ids_info(Parameters,Predicate,UsedIds,PP)),
4043 print_bexpr(Predicate),nl,
4044 (extract_span_description(Predicate,PosMsg) -> format('Location: ~w~n',[PosMsg]) ; true),
4045 ord_subtract(UsedIds,StoredUsedIds,Delta),
4046 format('Incorrect used_ids info: ~w (actual ~w)~nNot included: ~w~n~n',[StoredUsedIds,UsedIds,Delta])
4047 %, print_bexpr(Predicate),nl
4048 )
4049 ; add_internal_error('Could not computed used ids:',
4050 add_used_identifier_info(Parameters,Predicate,[],[used_ids(_)]))
4051 ).
4052
4053 % update used_ids_info for existential and universal quantifier (at top-level only !)
4054 recompute_used_ids_info(b(E,pred,Info0),Res) :-
4055 delete(Info0,used_ids(_),Info1),
4056 recompute_used_ids_info_aux(E,Info1,Info2),!, Res= b(E,pred,Info2).
4057 recompute_used_ids_info(TE,TE).
4058
4059 compute_used_ids_info_if_necessary(b(E,pred,Info1),Res) :-
4060 recompute_used_ids_info_aux(E,Info1,Info2),!, Res= b(E,pred,Info2).
4061 compute_used_ids_info_if_necessary(TE,TE).
4062
4063 recompute_used_ids_info_aux(exists(Parameters,Predicate),Info1,Info2) :-
4064 add_used_identifier_info(Parameters,Predicate,Info1,Info2).
4065 recompute_used_ids_info_aux(forall(Parameters,Lhs,Rhs),Info1,Info2) :-
4066 conjunct_predicates([Lhs,Rhs],Predicate),
4067 add_used_identifier_info(Parameters,Predicate,Info1,Info2).
4068 % for while loop we could recompute modifies and reads info
4069
4070 % generation of unique identifiers
4071 :- dynamic unique_id_counter/1.
4072 unique_id_counter(1).
4073
4074 get_unique_id_inside(Prefix,Pred,ResultId) :-
4075 (\+ occurs_in_expr(Prefix,Pred) % first try and see whether we need to append a number
4076 -> ResultId = Prefix
4077 ; get_unique_id(Prefix,ResultId)
4078 ).
4079 get_unique_id_inside(Prefix,Pred,Expr,ResultId) :-
4080 ( \+ occurs_in_expr(Prefix,Pred),
4081 \+ occurs_in_expr(Prefix,Expr) % first try and see whether we need to append a number
4082 -> ResultId = Prefix
4083 ; get_unique_id(Prefix,ResultId)
4084 ).
4085
4086 get_unique_id(Prefix,Id) :-
4087 retract(unique_id_counter(Old)),
4088 New is Old + 1,
4089 assertz(unique_id_counter(New)),
4090 safe_atom_chars(Prefix,CPrefix,get_unique_id1),
4091 number_chars(Old,CNumber),
4092 append(CPrefix,CNumber,CId),
4093 safe_atom_chars(Id,CId,get_unique_id2).
4094
4095 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
4096 % replace all variables in types by "any"
4097
4098 ground_type_to_any(T,Exceptions) :- var(T),!,
4099 ( exact_member(T,Exceptions) -> ! % any variable exact member in list is not grounded
4100 ; T=any).
4101 ground_type_to_any(record(Fields),Exceptions) :- !,
4102 % treat records separately, we do not want the list of fields to be bound to any; see B/Tickets/RecordPartiallyTyped
4103 ground_field_types(Fields,Exceptions).
4104 ground_type_to_any(seq(T),Exceptions) :- !, ground_type_to_any(T,Exceptions).
4105 ground_type_to_any(set(T),Exceptions) :- !, ground_type_to_any(T,Exceptions).
4106 ground_type_to_any(couple(A,B),Exceptions) :- !, ground_type_to_any(A,Exceptions), ground_type_to_any(B,Exceptions).
4107 ground_type_to_any(global(_),_) :- !.
4108 ground_type_to_any(freetype(_),_) :- !.
4109 ground_type_to_any(T,_) :- ground(T),!.
4110 ground_type_to_any(T,Exceptions) :-
4111 functor(T,_,Arity),
4112 ground_type_args(Arity,T,Exceptions).
4113 ground_type_args(0,_T,_Exceptions) :- !.
4114 ground_type_args(N,T,Exceptions) :-
4115 arg(N,T,Arg),
4116 ground_type_to_any(Arg,Exceptions),
4117 N2 is N-1,
4118 ground_type_args(N2,T,Exceptions).
4119
4120 ground_field_types(T,Exceptions) :- var(T),!,
4121 ( exact_member(T,Exceptions) -> ! % any variable exact member in list is not grounded
4122 ; print(grounding_open_ended_record),nl, % should we generate a warning here ?
4123 T=[]
4124 ).
4125 ground_field_types([],_) :- !.
4126 ground_field_types([field(Name,Type)|T],Exceptions) :- !,
4127 (var(Name)
4128 -> add_internal_error('Unbound record field name: ',ground_field_types([field(Name,Type)|T],Exceptions))
4129 ; true),
4130 ground_type_to_any(Type,Exceptions),
4131 ground_field_types(T,Exceptions).
4132 ground_field_types(Other,Exceptions) :-
4133 add_internal_error('Illegal record field list: ',ground_field_types(Other,Exceptions)).
4134
4135 % annote variables of becomes_such with before_substitution infos
4136 annotate_becomes_such_vars(Ids1,Pred,Ids2) :-
4137 find_used_primed_ids(Pred,Ids1,BeforeAfter),
4138 maplist(add_before_after_info(BeforeAfter),Ids1,Ids2).
4139 % put optional before/after usage into the information of the identifiers
4140 % makes only sense in the context of becomes_such substitutions
4141 add_before_after_info(BeforeAfter,TId,TId2) :-
4142 def_get_texpr_id(TId,Id),
4143 ( member(ba(Id,BeforeId),BeforeAfter) ->
4144 get_texpr_type(TId,Type), get_texpr_info(TId,Info),
4145 create_texpr(identifier(Id),Type,[before_substitution(Id,BeforeId)|Info],TId2)
4146 ; TId = TId2 ).
4147
4148 % find all used pairs of before/after variables, e.g. ba(x,'x$0')
4149 % see becomes_such substitutions
4150 find_used_primed_ids(TExpr,PossibleIds,Uses) :-
4151 prime_identifiers0(PossibleIds,TP0),
4152 get_sorted_ids(TP0,SP0), % sorted list of primed ids
4153 find_used_primed_ids2(SP0,TExpr,[],Uses).
4154 find_used_primed_ids2(SP0,TExpr,In,Out) :-
4155 syntaxtraversion(TExpr,Expr,_,_Infos,Subs,_),
4156 ( (Expr = identifier(FullId),
4157 %member(before_substitution(Id,FullId),Infos) % this info is not available in Event-B mode
4158 ord_member(FullId,SP0),
4159 prime_atom0(Id,FullId))
4160 -> ord_add_element(In,ba(Id,FullId),Uses)
4161 ; In = Uses ),
4162 foldl(find_used_primed_ids2(SP0),Subs,Uses,Out).
4163
4164 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
4165 % find expressions which are possibly not well-defined
4166 is_possibly_undefined(Expr) :- always_wd(Expr),!,fail.
4167 is_possibly_undefined(Expr) :-
4168 safe_syntaxelement_det(Expr,Subs,_Names,_,_),
4169 % note: can be very long list Subs for set_extension
4170 ? member(Sub,Subs),
4171 get_texpr_info(Sub,Info),
4172 memberchk(contains_wd_condition,Info),!.
4173 is_possibly_undefined(Expr) :- % TODO: detect freetype constructors as not having a WD condition
4174 ? has_top_level_wd_condition(Expr). %%,print(wd(F,Expr)),nl.
4175
4176 has_top_level_wd_condition(Expr) :- functor(Expr,F,_),
4177 ? has_wd_condition(F,Expr).
4178
4179 % a few common cases which are always defined:
4180 always_wd(bool_set).
4181 always_wd(boolean_false).
4182 always_wd(boolean_true).
4183 always_wd(empty_set).
4184 always_wd(identifier(_)).
4185 always_wd(integer(_)).
4186 always_wd(integer_set(_)).
4187 always_wd(real_set).
4188 always_wd(real(_)).
4189 always_wd(string(_)).
4190 always_wd(string_set).
4191 %always_wd(value(_)). ?
4192 always_wd(truth).
4193
4194
4195 always_defined_full_check_or_disprover_mode(_) :- preferences:get_preference(disprover_mode,true),!.
4196 always_defined_full_check_or_disprover_mode(BExpr) :- \+ full_check_is_possibly_undefined(BExpr).
4197
4198 % a version which does the full traversal; can be used before contains_wd_condition has been computed
4199 full_check_is_possibly_undefined(BExpr) :- get_texpr_expr(BExpr,Expr),
4200 full_check_is_possibly_undefined_aux(Expr).
4201 full_check_is_possibly_undefined_aux(Expr) :-
4202 functor(Expr,F,_),has_wd_condition(F,Expr),!.
4203 full_check_is_possibly_undefined_aux(Expr) :-
4204 syntaxtraversion(_,Expr,_,_,Subs,_),
4205 member(Sub,Subs),
4206 full_check_is_possibly_undefined(Sub),!.
4207
4208 :- use_module(external_functions,[external_fun_has_wd_condition/1]).
4209 % determine if an operator has an attached WD condition (used to compute contains_wd_condition)
4210 % division and module must not divide by zero
4211 has_wd_condition(div,Expr) :- arg(2,Expr,DIV),
4212 ? \+ definitely_not_zero(DIV).
4213 has_wd_condition(floored_div,Expr) :- arg(2,Expr,DIV),
4214 \+ definitely_not_zero(DIV).
4215 has_wd_condition(div_real,Expr) :- arg(2,Expr,DIV),
4216 \+ definitely_not_zero(DIV).
4217 % functions must not be applied to values outside their domain
4218 has_wd_condition(function,_Expr). % if lambda over total domain we could remove wd_condition, but ast_cleanup rule then already replaces it with assertion_expression, which gets optimised away in this case
4219 has_wd_condition(assertion_expression,_). % gets translated from function application
4220 has_wd_condition(modulo,Expr) :- arg(2,Expr,DIV),
4221 ? (\+ definitely_not_zero(DIV) ;
4222 \+ definitely_not_negative(DIV) ;
4223 arg(1,Expr,A1), \+ definitely_not_negative(A1)).
4224 % power_of must have a non-negative exponent (?)
4225 has_wd_condition(power_of,Expr) :- arg(2,Expr,EXP),
4226 \+ definitely_not_negative(EXP).
4227 has_wd_condition(power_of_real,Expr) :- arg(1,Expr,Base), arg(2,Expr,EXP),
4228 (definitely_not_negative(Base)
4229 -> (definitely_not_zero(Base) -> fail % no WD if base > 0
4230 ; definitely_not_negative(EXP) -> fail % 0.0 ^ EXP is defined if EXP >=0
4231 ; true % 0.0 ^ -1.0 is a division by zero
4232 )
4233 ; true). % things like -1.0 ^ 0.5 is not a real number; we could check if EXP is guaranteed an integ
4234 % Note: REAL ** INTEGER has no WD condition, but power_of_real has a WD condition
4235 has_wd_condition(iteration,Expr) :- arg(2,Expr,Idx),
4236 \+ definitely_not_negative(Idx).
4237 % min and max need a non-empty set
4238 % also Atelier-B manual requires the set to have an upper limit
4239 has_wd_condition(max,Expr) :- arg(1,Expr,S), \+ definitely_not_empty_and_finite(S).
4240 has_wd_condition(min,Expr) :- arg(1,Expr,S), \+ definitely_not_empty_and_finite(S).
4241 has_wd_condition(max_real,Expr) :- arg(1,Expr,S), \+ definitely_not_empty_and_finite(S).
4242 has_wd_condition(min_real,Expr) :- arg(1,Expr,S), \+ definitely_not_empty_and_finite(S).
4243 % all the sequence operations must not be applied to non-sequence
4244 % relations and some must not be applied to empty-sequences
4245 has_wd_condition(size,E) :- arg(1,E,S), \+ definitely_sequence(S).
4246 has_wd_condition(first,E) :- arg(1,E,S), \+ definitely_not_empty_sequence(S).
4247 has_wd_condition(last,E) :- arg(1,E,S), \+ definitely_not_empty_sequence(S).
4248 has_wd_condition(front,E) :- arg(1,E,S), \+ definitely_not_empty_sequence(S).
4249 has_wd_condition(tail,E) :- arg(1,E,S), \+ definitely_not_empty_sequence(S).
4250 has_wd_condition(rev,E) :- arg(1,E,S), \+ definitely_sequence(S).
4251 has_wd_condition(concat,_).
4252 has_wd_condition(insert_front,_).
4253 has_wd_condition(insert_tail,_).
4254 has_wd_condition(restrict_front,_).
4255 has_wd_condition(restrict_tail,_).
4256 has_wd_condition(general_concat,_).
4257 % the general intersection must not be applied to an empty set of sets
4258 has_wd_condition(general_intersection,Expr) :- arg(1,Expr,S),
4259 \+ definitely_not_empty(S).
4260 has_wd_condition(quantified_intersection,_). % gets translated to general_intersection
4261 % card must not be applied to infinite sets:
4262 has_wd_condition(card,Expr) :- arg(1,Expr,S), \+ definitely_finite(S).
4263 has_wd_condition(general_sum,_). % TO DO: \+ definitely_finite2(comprehension_set(Ids,P))
4264 has_wd_condition(general_product,_). % ditto; note: sets which are summed/multiplied must be finite
4265 has_wd_condition(mu,_). % Z MU Operator
4266 has_wd_condition(freetype_destructor,_).
4267 has_wd_condition(external_function_call,Expr) :- arg(1,Expr,FunName),
4268 external_fun_has_wd_condition(FunName).
4269 has_wd_condition(external_pred_call,Expr) :- arg(1,Expr,FunName),
4270 external_fun_has_wd_condition(FunName).
4271 % external_subst_call?
4272 has_wd_condition(operation_call_in_expr,_). % we now assume all operation calls may have PRE-conditions
4273 % or involve recursion, and thus may loop; TO DO: compute this information per operation by a fixpoint algorithm
4274
4275 definitely_not_zero(b(integer(X),integer,_)) :- integer(X), X \= 0.
4276 definitely_not_zero(b(real(X),real,_)) :- atom(X), construct_real(X,R), R \= 0.0.
4277 definitely_not_negative(b(integer(X),integer,_)) :- number(X), X >= 0.
4278 % to do add more ?: card(_), ...
4279
4280 definitely_not_empty(b(S,_,_)) :- def_not_empty2(S).
4281 def_not_empty2(set_extension([_|_])).
4282 def_not_empty2(sequence_extension([_|_])).
4283 def_not_empty2(union(A,B)) :- (definitely_not_empty(A) -> true ; definitely_not_empty(B)).
4284 def_not_empty2(value(S)) :- % what about closures ?
4285 definitely_not_empty_finite_value(S).
4286 % TODO: add more cases; but currently only used for general_intersection
4287
4288 definitely_not_empty_and_finite(b(S,_,_)) :- def_not_empty_fin2(S).
4289 def_not_empty_fin2(bool_set).
4290 def_not_empty_fin2(set_extension([_|_])).
4291 def_not_empty_fin2(sequence_extension([_|_])).
4292 def_not_empty_fin2(cartesian_product(A,B)) :- definitely_not_empty_and_finite(A), definitely_not_empty_and_finite(B).
4293 def_not_empty_fin2(union(A,B)) :- definitely_not_empty_and_finite(A), definitely_not_empty_and_finite(B).
4294 def_not_empty_fin2(overwrite(A,B)) :- definitely_not_empty_and_finite(A),definitely_not_empty_and_finite(B).
4295 def_not_empty_fin2(interval(A,B)) :- definitely_not_empty_set(b(interval(A,B),set(integer),[])).
4296 def_not_empty_fin2(value(S)) :- % what about closures ?
4297 definitely_not_empty_finite_value(S). %kernel_objects:not_empty_set(S).
4298
4299
4300 definitely_not_empty_sequence(b(S,_,_)) :- definitely_not_empty_sequence2(S).
4301 definitely_not_empty_sequence2(sequence_extension(_)).
4302
4303 definitely_sequence(b(S,_,_)) :- definitely_sequence2(S).
4304 definitely_sequence2(empty_sequence).
4305 definitely_sequence2(sequence_extension(_)).
4306
4307 :- use_module(typing_tools,[is_provably_finite_type/1, is_infinite_type/1]).
4308 is_infinite_ground_type(Type) :-
4309 ground(Type), is_infinite_type(Type). % non-ground types happen e.g. in test 472
4310
4311 definitely_finite(b(S,Type,_)) :-
4312 (ground(Type)
4313 -> (is_provably_finite_type(Type)
4314 -> true
4315 ; definitely_finite2(S) -> true
4316 %; \+ is_infinite_type(Type) -> print(no_longer_assuming_finite(Type)),nl,nl,fail
4317 )
4318 ; definitely_finite2(S)).
4319 definitely_finite2(bool_set).
4320 definitely_finite2(empty_set).
4321 definitely_finite2(empty_sequence).
4322 definitely_finite2(set_extension(_)).
4323 definitely_finite2(sequence_extension(_)).
4324 definitely_finite2(cartesian_product(A,B)) :- definitely_finite(A), definitely_finite(B).
4325 definitely_finite2(overwrite(A,B)) :- definitely_finite(A), definitely_finite(B).
4326 definitely_finite2(union(A,B)) :- definitely_finite(A), definitely_finite(B).
4327 definitely_finite2(intersection(A,B)) :- (definitely_finite(A) -> true ; definitely_finite(B)).
4328 definitely_finite2(set_subtraction(A,_)) :- definitely_finite(A).
4329 definitely_finite2(domain_restriction(_,B)) :- definitely_finite(B). % A finite does not guarantee finite relation
4330 definitely_finite2(domain_subtraction(_,B)) :- definitely_finite(B).
4331 definitely_finite2(range_restriction(A,_)) :- definitely_finite(A). % B finite does not guarantee finite relation
4332 definitely_finite2(range_subtraction(A,_)) :- definitely_finite(A).
4333 definitely_finite2(interval(_,_)).
4334 definitely_finite2(value(S)) :- nonvar(S),(S=[] ; S=avl_set(_)).
4335 % TO DO: add other operators : comprehension_set(Ids,P)
4336
4337
4338 definitely_infinite(b(S,_,_)) :- !,definitely_infinite2(S).
4339 definitely_infinite(S) :- add_internal_error('AST not wrapped:',definitely_infinite(S)),fail.
4340 definitely_infinite2(string_set).
4341 definitely_infinite2(real_set).
4342 definitely_infinite2(integer_set(X)) :-
4343 X='NATURAL' ; X='NATURAL1' ; X='INTEGER'.
4344 definitely_infinite2(seq1(S)) :- definitely_not_empty_set(S).
4345 definitely_infinite2(seq(S)) :- definitely_not_empty_set(S).
4346 definitely_infinite2(cartesian_product(A,B)) :- is_infinite_cart_prod(A,B).
4347 definitely_infinite2(pow_subset(S)) :- definitely_infinite(S).
4348 definitely_infinite2(pow1_subset(S)) :- definitely_infinite(S).
4349 definitely_infinite2(fin_subset(S)) :- definitely_infinite(S). % the set of finite subsets is infinite
4350 definitely_infinite2(fin1_subset(S)) :- definitely_infinite(S).
4351 definitely_infinite2(iseq(S)) :- definitely_infinite(S).
4352 definitely_infinite2(iseq1(S)) :- definitely_infinite(S).
4353 definitely_infinite2(perm(S)) :- definitely_infinite(S).
4354 definitely_infinite2(value(V)) :- infinite_value_set(V).
4355 definitely_infinite2(relations(A,B)) :- is_infinite_cart_prod(A,B).
4356 definitely_infinite2(partial_function(A,B)) :- is_infinite_cart_prod(A,B).
4357 definitely_infinite2(total_function(A,B)) :-
4358 (definitely_infinite(A) -> definitely_not_empty_set_card_gt1(B) % INTEGER-->{1} is finite, INTEGER-->BOOL is inf.
4359 ; definitely_infinite(B) -> definitely_not_empty_set(A)). % {TRUE} --> INTEGER is infinite
4360 definitely_infinite2(total_relation(A,B)) :- definitely_infinite2(total_function(A,B)).
4361 % TODO: partial_injection, total_injection, partial_surjection, total_surjection, total_bijection, partial_bijection,
4362 % surjection_relation, total_surjection_relation
4363 % cf total_surjection_card
4364
4365 % non empty sets with at least two elements:
4366 definitely_not_empty_set_card_gt1(bool_set).
4367 definitely_not_empty_set_card_gt1(A) :- definitely_infinite(A).
4368
4369 is_infinite_cart_prod(A,B) :-
4370 (definitely_infinite(A) -> definitely_not_empty_set(B) % INTEGER*{} is finite
4371 ; definitely_infinite(B) -> definitely_not_empty_set(A)).
4372
4373 infinite_value_set(V) :- var(V),!,fail.
4374 infinite_value_set(global_set(X)) :-
4375 X='NATURAL' ; X='NATURAL1' ; X='INTEGER'.
4376 infinite_value_set(closure(P,T,B)) :-
4377 % T \= [integer], % otherwise we could intersect with NATURAL,... ????
4378 custom_explicit_sets:is_infinite_closure(P,T,B).
4379 infinite_value_set(freetype(ID)) :- kernel_freetypes:is_infinite_freetype(ID).
4380
4381
4382
4383
4384 % check if %(Ids).(Pred|_) is infinite
4385 infinite_or_symbolic_domain_for_lambda(Ids,b(Expr,pred,_),Kind) :-
4386 inf_dom_aux(Expr,Ids,Kind).
4387 inf_dom_aux(member(TID2,InfSet),[TID],infinite) :- same_id(TID,TID2,_),
4388 definitely_infinite(InfSet).
4389 inf_dom_aux(truth,Ids,infinite) :-
4390 member(TID,Ids), get_texpr_type(TID,Type),
4391 is_infinite_ground_type(Type).
4392 inf_dom_aux(COMP,[TID|_],infinite) :- % A \= "" or A \= 0 or A \= B+1 or A < B*B or ...
4393 binary_inf_comparison(COMP,A,B),
4394 get_texpr_type(TID,Type), is_infinite_ground_type(Type),
4395 same_id(A,TID,ID),
4396 not_occurs_in_expr(ID,B). % ensure B does not depend on A; e.g. we have %x.(x/=x | E) is empty
4397 inf_dom_aux(equal(EXTFUN,BOOL),Ids,symbolic) :-
4398 % something like f = %s.(s:STRING & REGEX_MATCH(s,"[a-z]+")=TRUE | s)
4399 get_texpr_expr(EXTFUN,external_function_call(FUN,Args)),
4400 get_texpr_boolean(BOOL,_),
4401 is_symbolic_ext_pred(FUN,Args,Ids).
4402 inf_dom_aux(external_pred_call(FUN,Args),Ids,symbolic) :-
4403 is_symbolic_ext_pred(FUN,Args,Ids).
4404
4405 % a comparator which allows infinitely many values for first argument with fixed second argument
4406 binary_inf_comparison(not_equal(A,B),AA,BB) :- sym_unify(A,B,AA,BB).
4407 binary_inf_comparison(less(A,B),AA,BB) :- sym_unify(A,B,AA,BB).
4408 binary_inf_comparison(less_equal(A,B),AA,BB) :- sym_unify(A,B,AA,BB).
4409 binary_inf_comparison(greater(A,B),AA,BB) :- sym_unify(A,B,AA,BB).
4410 binary_inf_comparison(greater_equal(A,B),AA,BB) :- sym_unify(A,B,AA,BB).
4411
4412 sym_unify(A,B,A,B).
4413 sym_unify(A,B,B,A).
4414
4415 % not guaranteed to be infinite, but makes sense to keep symbolic
4416 is_symbolic_ext_pred(FUN,Args,[TID|_]) :-
4417 symbolic_ext_pred(FUN),
4418 def_get_texpr_id(TID,ID),
4419 (member(A,Args), occurs_in_expr(ID,A) -> true). % ensure the condition is not static and depends on an argument
4420
4421 % external predicates which indicate that the corresponding function should be kept symbolic
4422 symbolic_ext_pred('IS_REGEX').
4423 symbolic_ext_pred('GET_IS_REGEX').
4424 symbolic_ext_pred('REGEX_MATCH').
4425 symbolic_ext_pred('REGEX_IMATCH').
4426 symbolic_ext_pred('GET_IS_REGEX_MATCH').
4427 symbolic_ext_pred('GET_IS_REGEX_IMATCH').
4428 symbolic_ext_pred('STRING_EQUAL_CASE_INSENSITIVE').
4429 symbolic_ext_pred('STRING_IS_ALPHANUMERIC').
4430 symbolic_ext_pred('STRING_IS_DECIMAL').
4431 symbolic_ext_pred('STRING_IS_NUMBER').
4432 symbolic_ext_pred('GET_STRING_EQUAL_CASE_INSENSITIVE').
4433 symbolic_ext_pred('GET_STRING_IS_ALPHANUMERIC').
4434 symbolic_ext_pred('GET_STRING_IS_DECIMAL').
4435 symbolic_ext_pred('GET_STRING_IS_NUMBER').
4436 symbolic_ext_pred('GET_STRING_IS_INT').
4437 symbolic_ext_pred('FILE_EXISTS').
4438 symbolic_ext_pred('GET_FILE_EXISTS').
4439 symbolic_ext_pred('DIRECTORY_EXISTS').
4440 symbolic_ext_pred('GET_DIRECTORY_EXISTS').
4441 % TODO: add more external predicates
4442 %symbolic_ext_pred(X) :- nl,print(not_symbolic(X)),nl,fail.
4443
4444
4445 :- use_module(custom_explicit_sets,[quick_is_definitely_maximal_set/1]).
4446 % should we use is_just_type/1 instead ?? TO DO: check
4447 definitely_maximal_set(b(S,_,_)) :- definitely_maximal2(S).
4448 definitely_maximal2(integer_set('INTEGER')).
4449 definitely_maximal2(bool_set).
4450 definitely_maximal2(string_set).
4451 definitely_maximal2(typeset).
4452 definitely_maximal2(comprehension_set(_,b(truth,_,_))). % also covers is_integer_set(X,'INTEGER')
4453 definitely_maximal2(value(S)) :- nonvar(S),quick_is_definitely_maximal_set(S).
4454 % TO DO: cartesian product, records, ... if useful
4455
4456
4457 % just a sequence consisting of a single element
4458 is_singleton_sequence(b(sequence_extension([ELEMENT]),_,_),ELEMENT).
4459
4460 % check if type does not contain sets
4461 type_contains_no_sets(X) :- var(X),!,fail. % in test 472 we have a variable type
4462 type_contains_no_sets(integer).
4463 type_contains_no_sets(boolean).
4464 type_contains_no_sets(string).
4465 type_contains_no_sets(global(_)).
4466 type_contains_no_sets(couple(A,B)) :- type_contains_no_sets(A), type_contains_no_sets(B).
4467 type_contains_no_sets(record(Fields)) :- field_types_ok(Fields).
4468 field_types_ok([]).
4469 field_types_ok([field(_,Type)|T]) :- type_contains_no_sets(Type), field_types_ok(T).
4470
4471 % ----------------------------------
4472
4473
4474 select_conjunct(Predicate,Conjunction,Prefix,Suffix) :-
4475 conjunction_to_list(Conjunction,List),
4476 append(Prefix,[Predicate|Suffix],List).
4477
4478
4479 data_validation_mode :-
4480 (get_preference(data_validation_mode,true) -> true
4481 ; environ(prob_data_validation_mode,true)).
4482
4483 % optionally provide hints about rewritings or potential improvements
4484 add_hint_message(_,_Msg,_Term,_Span) :- debug_mode(off),
4485 get_preference(performance_monitoring_on,false), % should we use another preference?
4486 !.
4487 add_hint_message(Src,Msg,Term,Span) :-
4488 add_message(Src,Msg,Term,Span).
4489
4490 % ------------------------
4491
4492 % mini partial evaluation / constant expression evaluation of B expressions
4493 % TO DO: unify with b_compile and b_expression_sharing !
4494 % But this one only pre-computes top-level operators; assumes bottom-up traversal
4495
4496 :- use_module(kernel_card_arithmetic,[safe_pown/3]).
4497 pre_compute_static_int_expression(add(A,B),Result) :- % plus
4498 get_integer(A,IA), get_integer(B,IB),
4499 Result is IA+IB.
4500 pre_compute_static_int_expression(minus(A,B),Result) :- % plus
4501 get_integer(A,IA), get_integer(B,IB),
4502 Result is IA-IB.
4503 pre_compute_static_int_expression(unary_minus(A),Result) :- % plus
4504 get_integer(A,IA),
4505 Result is -IA.
4506 pre_compute_static_int_expression(multiplication(A,B),Result) :-
4507 get_integer(A,IA), get_integer(B,IB),
4508 Result is IA*IB.
4509 pre_compute_static_int_expression(div(A,B),Result) :- % TO DO: also add floored_div
4510 get_integer(B,IB), IB \= 0,
4511 get_integer(A,IA),
4512 Result is IA//IB.
4513 pre_compute_static_int_expression(modulo(A,B),Result) :-
4514 get_integer(B,IB), IB > 0,
4515 get_integer(A,IA), IA >= 0,
4516 Result is IA mod IB.
4517 pre_compute_static_int_expression(power_of(A,B),Result) :-
4518 get_integer(A,IA), get_integer(B,IB), IB >= 0,
4519 safe_pown(IA,IB,Result), number(Result).
4520
4521 % ----------------------------------------
4522