1		% (c) 2009-2026 Lehrstuhl fuer Softwaretechnik und Programmiersprachen,
2		% Heinrich Heine Universitaet Duesseldorf
3		% This software is licenced under EPL 1.0 (http://www.eclipse.org/org/documents/epl-v10.html)
4
5		:- module(closures,[construct_closure/4, is_closure/4, %is_closure_x/5,
6		construct_closure_if_necessary/4,
7		get_domain_range_for_closure_types/3,
8		construct_member_closure/5,
9		%construct_not_member_closure/4,
10		construct_complement_closure/3,
11		is_member_closure/5, is_member_closure_with_info/6,
12		is_not_member_closure/5,
13		is_not_member_value_closure/3,
14		is_not_member_value_closure_or_integerset/3,
15		construct_less_equal_closure/2, construct_greater_equal_closure/2,
16		is_lambda_value_domain_closure/5, % checks for special memoization closure
17		is_lambda_value_domain_normal_closure/5, % performs no check for memoization closures
18		is_lambda_closure/7,
19		is_lambda_comprehension_set/4,
20		select_equality/6,
21		is_special_infinite_closure/3,
22		is_id_closure_over/5,
23		is_full_id_closure/3,
24		is_closure_or_integer_set/4,
25		is_infinite_non_injective_closure/1,
26		is_symbolic_closure/1, is_symbolic_closure/3,
27		is_recursive_closure/1, is_recursive_closure/3,
28		get_recursive_identifier_of_closure/2, get_recursive_identifier_of_closure_body/2,
29		mark_closure_as_symbolic/2, mark_closure_as_recursive/2,
30		mark_closure_as_force/2, mark_closure/3
31		]).
32
33		:- use_module(module_information,[module_info/2]).
34		:- module_info(group,kernel).
35		:- module_info(description,'This module provides various utility functions to analyse ProB closures.').
36
37		construct_closure(Parameters, ParameterTypes, Body, Res) :-
38		Res = closure(Parameters, ParameterTypes, Body).
39		% Res = closure_x(Parameters, ParameterTypes, Body,_). %% STILL HAS PROBLEMS with delay, e.g. inside b_test_exists !!
40
41
42		% an optimized version of construct_closure, which will try to produce explicit values if possible
43		construct_closure_if_necessary(_,_,b(falsity,pred,_),Res) :- !, Res=[].
44		construct_closure_if_necessary([ID], [T1], b(Pred,pred,_), Res) :-
45		construct_unary_closure(Pred,ID,T1,SET),!,
46		Res = SET.
47		construct_closure_if_necessary(Parameters, ParameterTypes, Body, Res) :-
48		Res = closure(Parameters, ParameterTypes, Body).
49
50		:- use_module(b_global_sets,[try_b_type2global_set/2]).
51		:- use_module(custom_explicit_sets,[try_expand_and_convert_to_avl/2]).
52		construct_unary_closure(member(b(identifier(ID),T1,_),b(value(SET),set(T1),_)),ID,T1,Res) :- Res=SET.
53		construct_unary_closure(truth,_,T1,Res) :- try_b_type2global_set(T1,Res).
54		construct_unary_closure(equal(b(identifier(ID),T1,_),b(value(SET),T1,_)),ID,T1,Res) :-
55		try_expand_and_convert_to_avl([SET],Res).
56
57
58		:- use_module(self_check).
59		:- assert_must_succeed( closures:is_closure(closure([x],[integer],body),[x],[integer],body)).
60		%is_closure(closure_x(Parameters, ParameterTypes, Body, _Exp), Parameters, ParameterTypes, Body).
61		is_closure(closure(Parameters, ParameterTypes, Body), Parameters, ParameterTypes, Body).
62
63
64		:- use_module(btypechecker,[couplise_list/2]).
65		get_domain_range_for_closure_types(Types,Domain,Range) :-
66		couplise_list(Types,couple(Domain,Range)).
67
68
69		:- use_module(bsyntaxtree,[create_texpr/4, safe_create_texpr/4, extract_pos_infos/2]).
70		% following not useful: construct_member_closure currently always called where the construction is needed
71		%construct_member_closure(ID,_Type,ClosureSetExpression,Result) :-
72		% nonvar(ClosureSetExpression),ClosureSetExpression = value(S),!,
73		% print(construct_member_closure_value(ID,S)),nl, %%
74		% Result=S.
75		construct_member_closure(ID,Type,Info,ClosureSetExpression,Result) :-
76		check_result_instantiation(Result,construct_member_closure(ID)),
77		create_texpr(identifier(ID),Type,[],TIdentifier), % used to be [generated]
78		extract_pos_infos(Info,PosInfo), % Note: safe_create_texpr will copy WD info
79		safe_create_texpr(ClosureSetExpression,set(Type),PosInfo,TClosureSet), % TODO: we could store whether sub_expression_contains_wd_condition for next call
80		safe_create_texpr(member(TIdentifier,TClosureSet),pred,PosInfo,TPred),
81		construct_closure([ID],[Type],TPred,Result).
82
83		construct_not_member_closure(ID,Type,Info,ClosureSetExpression,Result) :-
84		check_result_instantiation(Result,construct_not_member_closure(ID)),
85		Type==integer,
86		interval_up_to_inf(ClosureSetExpression,Limit),
87		!,
88		construct_less_equal_closure(ID,Limit,Info,Result). % construct an interval closure; better support in kernel for it
89		construct_not_member_closure(ID,Type,Info,ClosureSetExpression,Result) :-
90		create_texpr(identifier(ID),Type,[],TIdentifier), % used to be [generated]
91		safe_create_texpr(ClosureSetExpression,set(Type),Info,TClosureSet),
92		safe_create_texpr(not_member(TIdentifier,TClosureSet),pred,Info,TPred),
93		construct_closure([ID],[Type],TPred,Result).
94
95		interval_up_to_inf(global_set('NATURAL'),-1).
96		interval_up_to_inf(global_set('NATURAL1'),0).
97		interval_up_to_inf(value(global_set('NATURAL')),-1).
98		interval_up_to_inf(value(global_set('NATURAL1')),0).
99
100
101		construct_less_equal_closure(X,Res) :-
102		construct_less_equal_closure('_zzzz_unary',X,[],Res).
103		construct_less_equal_closure(ID,X,Info,Res) :-
104		construct_closure([ID],[integer],
105		b(less_equal(b(identifier(ID),integer,[]),
106		b(value(int(X)),integer,[])), pred,Info),Res).
107
108		construct_greater_equal_closure(X,Res) :-
109		construct_closure(['_zzzz_unary'],[integer],
110		b(greater_equal(b(identifier('_zzzz_unary'),integer,[]),
111		b(value(int(X)),integer,[])), pred,[]),Res).
112
113		:- use_module(error_manager,[add_internal_error/2]).
114		% check that we do not instantiate result too early (rather than using equal_object)
115		check_result_instantiation(X,_) :- var(X),!.
116		check_result_instantiation(closure(_,_,_),_PP) :- !.
117		check_result_instantiation(X,PP) :-
118		add_internal_error('Result already instantiated in incompatible way: ',check_result_instantiation(X,PP)).
119
120		is_member_closure_with_info([ID],[TYPE],b(PRED,_Pred,Info), TYPE,Info,SET) :-
121		is_member_closure_aux(PRED, ID,TYPE,SET).
122		is_member_closure([ID],[TYPE],b(PRED,_Pred,_), TYPE,SET) :-
123		is_member_closure_aux(PRED, ID,TYPE,SET).
124
125		:- use_module(bsyntaxtree,[is_set_type/2]).
126		is_member_closure_aux(member(TID,TSET), ID,TYPE,SET) :-
127		TID = b(identifier(ID),IDTYPE,Info),
128		check_types_unify(IDTYPE,TYPE,Info), % see test 1948
129		TSET = b(SET,_SETTYPE,_).
130		is_member_closure_aux(subset(TID,BSET), ID,TYPE,SET) :-
131		TID = b(identifier(ID),IDTYPE,Info),
132		check_types_unify(IDTYPE,TYPE,Info),
133		SET = pow_subset(BSET).
134		% can we also detect pow1_subset ? {x| x/= {} & x<: BSET}
135
136
137		% detect not_member closures + integerset as special not_member_closures
138		is_not_member_value_closure_or_integerset(global_set(X),TYPE,SET) :- !,
139		is_not_member_global_set(X,TYPE,SET).
140		is_not_member_value_closure_or_integerset(C,TYPE,SET) :- is_not_member_value_closure(C,TYPE,SET).
141
142		is_not_member_global_set('INTEGER',integer,[]).
143		is_not_member_global_set('NATURAL',integer,X) :-
144		construct_less_equal_closure(-1,X). % {x|x<0}.
145		is_not_member_global_set('NATURAL1',integer,X) :-
146		construct_less_equal_closure(0,X). %X = {x|x<1}.
147
148		is_not_member_value_closure(closure(Par,T,B),TYPE,SET) :-
149		is_not_member_closure(Par,T,B,TYPE,value(SET)).
150		is_not_member_closure([ID],[TYPE],b(PRED,_Pred,_),TYPE,SET) :-
151		is_not_member_closure_aux(PRED,ID,TYPE,SET).
152
153		:- use_module(kernel_tools,[ground_value/1]).
154		is_not_member_closure_aux(not_member(b(identifier(ID),IDType,Info),b(SET,SType,_)),ID,TYPE,SET)
155		:-
156		check_types_unify(IDType,TYPE,Info),
157		is_set_type(SType,IDType).
158		is_not_member_closure_aux(not_equal(b(identifier(ID),IDType,Info),ONE),ID,TYPE,SET) :-
159		(ONE = b(value(Val),_,_),
160		ground_value(Val)
161		-> custom_explicit_sets:construct_one_element_custom_set(Val,SetVal), SET = value(SetVal)
162		; SET = set_extension([ONE])),
163		check_types_unify(IDType,TYPE,Info).
164		%is_not_member_closure_aux(PRED,ID,TYPE,SET) :- print(check_not_mem(PRED,ID,TYPE,SET)),nl,fail.
165
166		:- use_module(btypechecker, [unify_types_strict/2]).
167		check_types_unify(IDType,TYPE,_) :- unify_types_strict(IDType,TYPE),!.
168		check_types_unify(IDType,TYPE,Info) :- add_error(closures,'Types do not match:',IDType-TYPE,Info),fail.
169
170
171		construct_complement_closure(Delta,Type,Closure) :-
172		% print(generating_complement_closure(GlobalSet,Delta,Type)),nl,
173		construct_not_member_closure('_zzzz_unary',Type,[],value(Delta),Closure).
174
175
176
177		/* lambda abstractions */
178		:- assert_must_succeed((closures:is_lambda_closure([x,y],[integer,integer],b(conjunct(b(member(b(identifier(x),integer,[nodeid(pos(0,0,0,0,0,0))]),b(value(global_set('NATURAL')),set(integer),[])),pred,[]),b(equal(b(identifier(y),integer,[]),b(multiplication(b(identifier(x),integer,[]),b(identifier(x),integer,[])),integer,[])),pred,[])),pred,[]),OtherIDs,OtherTypes,_DOMAINPRED,_Res), OtherIDs=[x], OtherTypes=[integer])).
179		:- assert_must_fail((closures:is_lambda_closure([x,y],[integer,integer],b(conjunct(b(conjunct(b(member(b(identifier(x),integer,[]),b(value(global_set('NATURAL')),set(integer),[])),pred,[]),b(equal(b(identifier(y),integer,[]),b(multiplication(b(identifier(x),integer,[]),b(identifier(x),integer,[])),integer,[])),pred,[])),pred,[]),b(less(b(identifier(y),integer,[]),b(value(int(10)),integer,[])),pred,[])),pred,[]),_,_,_D,_Res)
180		)).
181
182		:- use_module(bsyntaxtree,[conjunction_to_list/2,conjunct_predicates/2]).
183		is_lambda_closure(Args,Types,ClosurePred, OtherIDs, OtherTypes, DOMAINPRED,Res) :-
184		% TO DO: do this more efficiently: if LambdaID occurs in any non-equal predicate : stop searching
185		% TO DO: check if is_infinite_equality_closure is not a special case of lambda closure ?
186		append(OtherTypes,[LambdaType],Types), OtherTypes \= [],
187		append(OtherIDs,[LambdaID],Args),
188		Res=b(EXPR,LambdaType,EXPRINFO),
189		%used to call: b_interpreter:member_conjunct(EQ,ClosurePred,DOMAINPRED), ; but inlined below for efficiency
190		select_equality(ClosurePred,LambdaID,EXPR,LambdaType,EXPRINFO,DOMAINPRED),
191		!. % avoid backtracking member_conjunct
192		% tools:print_bt_message(is_lambda_closure(LambdaID)).
193		% Note: LAMBDA is usually '_lambda_result_'
194
195		identifier_equality(b(equal(b(LHS,Type,LHSInfo),b(RHS,_TypeRHS,RHSInfo)),pred,_),ID,Type,EXPR,EXPRINFO) :-
196		% no need to unify with TypeRHS; actually Prolog unification could fail due to seq types ?
197		identifier_equality_aux(LHS,LHSInfo,RHS,RHSInfo,ID,EXPR,EXPRINFO).
198		identifier_equality_aux(identifier(ID),_,EXPR,EXPRINFO,ID,EXPR,EXPRINFO) :- !.
199		identifier_equality_aux(EXPR,EXPRINFO,identifier(ID),_,ID,EXPR,EXPRINFO).
200
201		% find an equality ID = RHSExpr so that ID does not occur in RHSExpr nor in RestPred
202		% the identifier should be provided as input (for the cut below)
203		select_equality(ClosurePred,ID,RHSExpr,Type,Info,RestPred) :-
204		conjunction_to_list(ClosurePred,List),
205	?	select(EQ,List,RestList),
206		identifier_equality(EQ,ID,Type,RHSExpr,Info),
207		!, % once we find a first equality : no need to look for a second one as then does_not_occur in RestPred will always fail !
208		(ID='_lambda_result_',EQ=b(_,_,I),
209		member(prob_annotation('LAMBDA-EQUALITY'),I)
210		-> true % no need to perform occurs check in RHS, but in RestPred, cf test 1874
211		; %format('Check occurs ~w : ',[ID]), translate:print_bexpr(b(RHSExpr,Type,Info)),nl,
212		does_not_occur_in(ID,b(RHSExpr,Type,Info))
213		),
214		conjunct_predicates(RestList,RestPred),
215		does_not_occur_in(ID,RestPred).
216
217
218		:- use_module(memoization,[is_lambda_value_domain_memoization_closure/5]).
219
220		% check whether we have a lambda closure and whether we can compute its domain
221		is_lambda_value_domain_closure(P,T,Pred, DomainValue,Expr) :-
222		is_lambda_value_domain_memoization_closure(P,T,Pred, DV,E),!,
223		DV \= fail, E\= fail,
224		DomainValue=DV, Expr=E.
225		is_lambda_value_domain_closure(Args,Types,B, DomainValue, EXPR) :-
226		is_lambda_value_domain_normal_closure(Args,Types,B, DomainValue, EXPR).
227
228		is_lambda_value_domain_normal_closure(Args,Types,B, DomainValue, EXPR) :-
229		% tools_printing:print_term_summary(try_is_lambda_domain(Args,Types,B)), %
230		is_lambda_closure(Args,Types,B, OtherIDs,OtherTypes, DomainPred, EXPR),!,
231		%print(lambda_closure(OtherIDs)), translate:print_bexpr(EXPR),nl,
232		construct_closure_if_necessary(OtherIDs,OtherTypes,DomainPred,DomClosure),
233		(is_symbolic_closure(Args,Types,B)
234		-> mark_closure_as_symbolic(DomClosure,DomainValue)
235		; DomainValue = DomClosure).
236		%print(lambda_domain(Args)),nl, (IDs=[_,_|_] -> trace ; true),
237		%translate:print_bvalue(DomainValue),nl.
238
239		% LAMBDARES is usually _lambda_result_, LAMBDARES cannot occur in DOMAIN (is value)
240
241		:- use_module(library(lists),[maplist/4]).
242		is_lambda_comprehension_set(b(comprehension_set(Parameters,Body),_,_),LambdaParas,DomainPred,EXPR) :-
243		maplist(get_names_and_types,Parameters,Args,Types),
244		is_lambda_closure(Args,Types,Body, OtherIDs,OtherTypes, DomainPred, EXPR),
245		maplist(combine_names_and_types,OtherIDs,OtherTypes,LambdaParas).
246
247		get_names_and_types(b(identifier(ID),Type,_),ID,Type).
248		combine_names_and_types(ID,Type,b(identifier(ID),Type,[])).
249
250		:- assert_must_succeed(closures:is_special_infinite_closure([x],[integer],b(truth,pred,[]))).
251		:- assert_must_succeed((X=b(identifier(x),integer,[]),N=b(integer(3),integer,[]),
252		closures:is_special_infinite_closure([x],[integer],b(greater(X,N),pred,[])))).
253		:- assert_must_succeed((X=b(identifier(x),integer,[]),N=b(integer(3),integer,[]),
254		closures:is_special_infinite_closure([x],[integer],b(greater(X,N),pred,[])))).
255		:- assert_must_succeed((X=b(identifier(x),integer,[]),N=b(integer(3),integer,[]),
256		closures:is_special_infinite_closure([x],[integer],b(less(X,N),pred,[])))).
257		:- assert_must_succeed((X=b(identifier(x),integer,[]),N=b(integer(3),integer,[]),
258		closures:is_special_infinite_closure([x],[integer],b(not_equal(X,N),pred,[])))).
259		:- assert_must_fail((X=b(identifier(x),integer,[]),N=b(integer(3),integer,[]),
260		closures:is_special_infinite_closure([x],[integer],b(equal(X,N),pred,[])))).
261		:- assert_must_succeed((X=b(identifier(x),integer,[]),N=b(integer(3),integer,[]),
262		closures:is_special_infinite_closure([x,y],[integer,integer],b(equal(X,N),pred,[])))).
263		:- assert_must_succeed((Y=b(identifier(y),integer,[]),N=b(integer(3),integer,[]),
264		closures:is_special_infinite_closure([x,y],[integer,integer],b(equal(Y,N),pred,[])))).
265
266		:- use_module(typing_tools,[is_infinite_type/1]).
267		/* checking for infinite closures */
268		%is_special_infinite_closure(_Par,T,b(truth,_Pred,_)) :- !, % now dealt with below
269		% member(Type,T), is_infinite_type(Type),!.
270		is_special_infinite_closure(Par,T,Body) :-
271	?	is_infinite_equality_closure(Par,T,Body),!.
272		%is_special_infinite_closure(Par,T,Body) :- is_full_id_closure(Par,T,Body,TYPE), is_infinite_type(TYPE).
273		%is_special_infinite_closure(Par,T,Body) :- is_prj1_closure(Par,T,Body,T1,_T2), is_infinite_type(T1).
274		%is_special_infinite_closure(Par,T,Body) :- is_prj2_closure(Par,T,Body,_T1,T2), is_infinite_type(T2).
275		is_special_infinite_closure(Par,T,Body) :-
276		is_not_member_closure(Par,T,Body,Type,value(_)), is_infinite_type(Type).
277
278		:- use_module(library(lists)).
279
280		greater_typing(greater(b(identifier(ID),integer,_),b(VUP,integer,_)),ID,UP) :- is_integer_val(VUP,UP).
281		greater_typing(greater_equal(b(identifier(ID),integer,_),b(VUP,integer,_)),ID,UP) :- is_integer_val(VUP,UP).
282		greater_typing(less(b(VUP,integer,_),b(identifier(ID),integer,_)),ID,UP) :- is_integer_val(VUP,UP).
283		greater_typing(less_equal(b(VUP,integer,_),b(identifier(ID),integer,_)),ID,UP) :- is_integer_val(VUP,UP).
284
285		less_typing(less(b(identifier(ID),integer,_),b(VUP,integer,_)),ID,UP) :- is_integer_val(VUP,UP).
286		less_typing(less_equal(b(identifier(ID),integer,_),b(VUP,integer,_)),ID,UP) :- is_integer_val(VUP,UP).
287		less_typing(greater(b(VUP,integer,_),b(identifier(ID),integer,_)),ID,UP) :- is_integer_val(VUP,UP).
288		less_typing(greater_equal(b(VUP,integer,_),b(identifier(ID),integer,_)),ID,UP) :- is_integer_val(VUP,UP).
289
290		is_integer_val(integer(UP),UP).
291		is_integer_val(value(V),UP) :- nonvar(V),V=int(UP).
292
293		is_static_expr_of_infinite_type(b(E,Type,_)) :- is_static_expr_of_infinite_type2(E,Type).
294		is_static_expr_of_infinite_type2(integer(_),_).
295		is_static_expr_of_infinite_type2(string(_),_).
296		is_static_expr_of_infinite_type2(real(_),_).
297		is_static_expr_of_infinite_type2(value(V),Type) :- is_val_of_infinite_type(V,Type).
298		is_static_expr_of_infinite_type2(empty_set,Type) :- is_infinite_type(Type).
299		is_static_expr_of_infinite_type2(empty_sequence,Type) :- is_infinite_type(Type).
300		% TODO: more typical expressions, set/sequence extension pairs
301
302		is_val_of_infinite_type(V,_) :- var(V),!,fail.
303		is_val_of_infinite_type(int(_),_).
304		is_val_of_infinite_type(string(_),_).
305		is_val_of_infinite_type(term(floating(_)),_).
306		is_val_of_infinite_type((A,B),couple(TA,TB)) :- (is_val_of_infinite_type(A,TA) -> true ; is_val_of_infinite_type(B,TB)).
307		is_val_of_infinite_type([],Type) :- is_infinite_type(Type).
308		is_val_of_infinite_type(avl_set(_),Type) :- is_infinite_type(Type).
309
310
311
312
313		% the following also translates global_set(NATURAL(1)) into closures
314		% TO DO: probably better to remove global_set(INTSET) all together and rewrite in ast_cleanup to closure
315		is_closure_or_integer_set(closure(P,T,B),P,T,B).
316		is_closure_or_integer_set(global_set(INTSET),
317		['_zzzz_unary'],[integer],
318		b(greater_equal(
319		b(identifier('_zzzz_unary'),integer,[]),
320		b(integer(BOUND),integer,[])
321		),
322		pred,
323		[prob_annotation('SYMBOLIC')])
324		) :-
325		get_bound(INTSET,BOUND).
326		get_bound('NATURAL',0).
327		get_bound('NATURAL1',1).
328		% TO DO: allow INTEGER / maximal sets ? -> truth; could get rid of complement sets?
329
330		% to do: extend; could be value(infinite_closure)...
331
332
333
334		/* Equality closures {x1,x2,...|id=E2}, where id does not occur in E2 and id =xi */
335		% should cover id, prj1, prj2
336		% {x,y|y:BOOL & x=f(y) } or %x.(x:NATURAL|Expr(x))
337		% would not be infinite {x,y|x:BOOL & x=f(g(x)*y)} , g={FALSE|->0, TRUE|->1}, f = ...
338		% we assume Well-Definedness
339		% we also accept closures without equality now
340
341		is_infinite_equality_closure(IDs, TYPES, Body) :-
342		%IDs = [_,_|_], % we used to require at least at least two variables
343		\+ Body = b(member(_,_),_,_), % simple member closure; we deal with it separately (and avoid blow-up of checks, cf test 2283)
344	?	check_inf_cl_body(Body,[],OutConstrained),
345		% if we arrive here, we know that the body constraint is satisfiable
346		(member(_ID/infinite,OutConstrained) -> true
347		; contains_infinite_type(IDs,TYPES,OutConstrained)).
348
349		contains_infinite_type([ID|IT],[H|T],OutConstrained) :-
350		(is_infinite_type(H),
351	?	\+ member(ID/_,OutConstrained)
352		-> true ; contains_infinite_type(IT,T,OutConstrained)).
353
354		:- use_module(library(ordsets),[ord_member/2]).
355		is_quantified(SIds,ID/_) :- ord_member(ID,SIds).
356		is_lambda_equality(b(equal(_,_),_,Infos)) :- member(prob_annotation('LAMBDA-EQUALITY'),Infos).
357
358		:- use_module(b_ast_cleanup,[definitely_not_empty_and_finite/1, definitely_infinite/1]).
359		:- use_module(external_functions,[external_pred_always_true/1]).
360		:- use_module(bsyntaxtree, [get_texpr_id/2, get_texpr_type/2, definitely_not_empty_set/1]).
361		check_inf_cl_body(b(B,pred,_),InConstrained,OutConstrained) :-
362	?	check_bdy_aux(B,InConstrained,OutConstrained).
363
364		l_check_inf_cl_body([]) --> [].
365		l_check_inf_cl_body([H|T]) --> check_inf_cl_body(H), l_check_inf_cl_body(T).
366
367		:- use_module(probsrc(tools),[split_list/4]).
368
369		check_bdy_aux(conjunct(A,B),InConstrained,OutConstrained) :- !,
370		conjunction_to_list(b(conjunct(A,B),pred,[]),List),
371		split_list(is_lambda_equality,List,LambdaEq,Rest),
372		l_check_inf_cl_body(LambdaEq,InConstrained,OutConstrained1), % treat lambda equalities first
373		% reason: avoid failing due to rhs_safe checks; ideally we should do topological sorting
374		% or keep track of really used ids in each equality
375		l_check_inf_cl_body(Rest,OutConstrained1,OutConstrained).
376		check_bdy_aux(disjunct(A,B),InConstrained,OutConstrained) :- !,
377		(check_inf_cl_body(A,InConstrained,OutConstrained) -> true
378		; check_inf_cl_body(B,InConstrained,OutConstrained)).
379		check_bdy_aux(exists(TIds,ExistsBody), Constrained, OutConstrained) :- !,
380		bsyntaxtree:get_texpr_ids(TIds,Ids), sort(Ids,SIds),
381		% happens in Event-B style compr. sets, cf test 2514
382		% Example: bap={i,x,y• i:INTEGER & x=y & x:INTEGER|i|->(x|->y)} & bap[{100}][1..2]=res
383		exclude(is_quantified(SIds),Constrained,C1), % remove any var that is clashing with exists ids
384		check_inf_cl_body(ExistsBody,C1,C2),
385		exclude(is_quantified(SIds),C2,OutConstrained).
386		% remove quantified ids; should not count towards outer infinity, unless linked via equal to an outer id
387		% example, UNION(x,y,z).(x:INTEGER & y=x*x & z=x+x|{x|->(y|->z)}) = s & not(s:FIN(s))
388
389		check_bdy_aux(equal(LHS,RHS), Constrained, OutConstrained) :- !,
390		(check_bdy_equal(LHS,RHS,Constrained,OutConstrained) -> true
391		; check_bdy_equal(RHS,LHS,Constrained,OutConstrained)),!.
392		check_bdy_aux(member(b(identifier(ID),TYPE,_),SET),Constrained,[ID/INFINITE|Constrained]) :- !,
393		\+ member(ID/_,Constrained),
394		rhs_safe(Constrained,SET), % avoid ID : {ID+1, ID+2}
395		(is_infinite_type(TYPE)
396		-> %check that SET is infinite; otherwise remove from IDs
397		(definitely_infinite(SET) -> INFINITE=infinite;
398		definitely_not_empty_and_finite(SET) -> INFINITE = finite
399		)
400		; definitely_not_empty_and_finite(SET), % otherwise we may have no solution and the entire closure is empty
401		INFINITE = finite
402		).
403		check_bdy_aux(member(LHS,RHS),Constrained,[ID/infinite|Constrained]) :- !, % ID'Field : SET
404		record_field_access_with_infinite_rest_type(LHS,RHS,Constrained,ID), % should we also cater for finite rest?
405		definitely_not_empty_set(RHS).
406		check_bdy_aux(not_equal(A,B),Constrained,[ID/infinite|TC]) :- !,
407		(get_texpr_id(A,ID)
408		-> is_static_expr_of_infinite_type(B) % we have to be careful that B does not directly or indirectly reference A
409		; get_texpr_id(B,ID),
410		is_static_expr_of_infinite_type(A)
411		),
412		(select(ID/Kind,Constrained,TC)
413		-> Kind=infinite % if it was infinite it will remain infinite, we only discard a single static value
414		; TC=Constrained).
415		check_bdy_aux(truth,Constrained,OutConstrained) :- !, OutConstrained=Constrained.
416		check_bdy_aux(external_pred_call(FunName,_Args),Constrained,Constrained) :- !,
417		external_pred_always_true(FunName).
418		check_bdy_aux(EXPR,Constrained,[ID/infinite|Constrained]) :-
419		%% TO DO: store bounds in ID/... list to check if the domain remains infinite!
420		greater_typing(EXPR,ID,_UP),
421		\+ member(ID/_,Constrained).
422		check_bdy_aux(EXPR,Constrained,[ID/infinite|Constrained]) :-
423		less_typing(EXPR,ID,_UP),
424		\+ member(ID/_,Constrained).
425
426
427		check_bdy_equal(LHS,RHS, Constrained, [ID/equal|Constrained]) :-
428		get_texpr_id(LHS,ID),
429		\+ member(ID/_,Constrained), % no constraints on ID so far
430		does_not_occur_in(ID,RHS), % we have no direct equation like ID=ID+1
431		rhs_safe(Constrained,RHS),
432		!. % the equation must have a solution; assuming well-definedness
433		check_bdy_equal(LHS,RHS, Constrained, [ID/infinite|Constrained]) :- % ID'FieldName = RHS
434		% detect closures like {x|x:struct(a:INTEGER,b:BOOL) & x'b=FALSE}, see test 2483
435		record_field_access_with_infinite_rest_type(LHS,RHS,Constrained,ID),!.
436
437		% check if the RHS is sufficiently unconstrained so that equality with a new variable will succeed
438		% see test 2483, card({x,y,v|x:INTEGER & y:{v+1,v+2} & v=y}) = 0
439		% TODO: maybe faster to find_identifier_uses once rather than calling does_not_occur_in repeatedly
440		% TODO: detect if an identifier is used only once, then we do not need to check RHS (LAMBDA-EQUALITY)
441		rhs_safe([],_).
442		rhs_safe([HID/Kind|TConstrained],RHS) :-
443		(Kind=infinite -> true % CHECK! happens for HID=b in 2283
444		; %HID could be bound to new ID, e.g., via HID=NewID+1 and equation NewID=HID would have no solution
445		does_not_occur_in(HID,RHS)
446		),
447		rhs_safe(TConstrained,RHS).
448
449		% see if we have LHS = ID'FieldName and ID does not occur in RHS and other fields are still infinite
450		record_field_access_with_infinite_rest_type(LHS,RHS,Constrained,ID) :-
451		LHS = b(record_field(TID,FieldName),_,_),
452		get_texpr_id(TID,ID),
453		\+ member(ID/_,Constrained), % no constraints on ID so far
454		get_texpr_type(TID,record(FieldTypes)),
455		select(field(FieldName,_),FieldTypes,RestTypes),
456		% we now have only a single value for field FieldName
457		is_infinite_type(record(RestTypes)), % there are still infinitely many values left given the other fields
458		does_not_occur_in(ID,RHS),
459		rhs_safe(Constrained,RHS),!.
460
461
462		:- use_module(bsyntaxtree,[occurs_in_expr/2]).
463		does_not_occur_in(ID,EXPR) :- \+ occurs_in_expr(ID,EXPR).
464
465
466
467		% check if we have a closure of type id(SetValue)
468
469		is_id_closure_over([ID1,ID2], [TYPE,TYPE],Body, ID_Domain, Full) :- nonvar(Body),
470		Body=b(equal(b(identifier(ID1),TYPE,_),b(identifier(ID2),TYPE,_)),pred,_),
471		!,
472		convert_type_to_value(TYPE,ID_Domain), Full=true.
473		is_id_closure_over(Par,Types,Body,ID_Domain,Full) :- nonvar(Par),nonvar(Body),
474		is_member_closure(Par,Types,Body,_,Set), % print(member_closure(Set)),nl,
475		nonvar(Set),
476		Set = identity(b(VAL,SType,_)),
477		is_set_type(SType,_),
478		nonvar(VAL), VAL=value(ID_Domain),
479		(custom_explicit_sets:is_definitely_maximal_set(ID_Domain) -> Full=true ; Full=false).
480
481		%:- use_module(kernel_objects,[all_strings_wf/2]).
482		convert_type_to_value(integer,global_set('INTEGER')).
483		convert_type_to_value(global(G),global_set(G)).
484		convert_type_to_value(boolean,BS) :- BS=[pred_true /* bool_true */,pred_false /* bool_false */]. % TO DO: generate AVL ?
485		convert_type_to_value(string,global_set('STRING')). % :- all_strings_wf(S,WF).
486		%convert_type_to_value(Type,closure([x],[Type],TRUTH)) :- ... TO DO
487
488
489
490		/* Event-B id closure over full Type */
491
492		is_full_id_closure(P,T,B) :- is_id_closure_over(P,T,B,_,true).
493
494
495		% currently commented out in is_special_infinite_closure
496		%is_prj1_closure([ID1,_ID2,RESID],[Type1,Type2,Type1],
497		% b(equal(b(identifier(RESID),Type1,_),b(identifier(ID1),Type1,_)),pred,_),Type1,Type2).
498		%is_prj2_closure([_ID1,ID2,RESID],[Type1,Type2,Type2],
499		% b(equal(b(identifier(RESID),Type2,_),b(identifier(ID2),Type2,_)),pred,_),Type1,Type2).
500
501
502		% ---- SYMBOLIC and RECURSIVE annotations
503
504		get_recursive_identifier_of_closure(V,RID) :- nonvar(V), V=closure(_P,_T,B),
505		get_recursive_identifier_of_closure_body(B,RID).
506		get_recursive_identifier_of_closure_body(b(_,_,BodyInfo),RID) :- member(prob_annotation(recursive(RID)),BodyInfo).
507
508		is_recursive_closure(V) :- nonvar(V), V=closure(P,T,B),
509		is_recursive_closure(P,T,B).
510
511		is_recursive_closure(_P,_T,b(_,_,INFO)) :-
512		member(prob_annotation('RECURSIVE'),INFO).
513		% we also have prob_annotation(recursive(TID)) annotation
514
515		is_symbolic_closure(V) :- nonvar(V), V=closure(P,T,B),
516	?	is_symbolic_closure(P,T,B).
517
518		is_symbolic_closure(_P,_T,b(_,_,INFO)) :-
519	?	member(prob_annotation('SYMBOLIC'),INFO).
520
521		% see also is_converted_lambda_closure
522
523
524		:- use_module(error_manager,[add_internal_error/2, add_error/3]).
525		:- use_module(debug,[debug_println/2]).
526
527		% mark a closure as symbolic by marking the info field of the body predicate
528		mark_closure_as_symbolic(C,R) :-
529		mark_closure3(C,['SYMBOLIC'],R).
530		mark_closure_as_recursive(C,R) :-
531		mark_closure3(C,['SYMBOLIC','RECURSIVE'],R).
532		mark_closure_as_force(C,R) :-
533		mark_closure3(C,['FORCE'],R).
534		mark_closure3(_,ANN,R) :- nonvar(R), % we could use equal_object
535		add_internal_error('Result already instantiated: ',mark_closure3(_,ANN,R)),fail.
536		mark_closure3(C,ANN,R) :- var(C), % we could use equal_object
537		!,
538		debug_println(19,not_marking_var_closure(C,ANN)),
539		R=C.
540		mark_closure3(C,ANN,R) :- mark_closure(C,ANN,R).
541		%:- block mark_closure(-,?,?).
542		mark_closure(closure(P,T,B),ANN,R) :- !, mark_aux(P,T,B,ANN,R).
543		mark_closure(A,_,Res) :- A=Res. % not a closure
544		%:- block mark_aux(?,?,-,?,?).
545		mark_aux(P,T,b(Pred,pred,INFO),ANN,Res) :-
546		(ground(INFO)
547		-> mark_info(ANN,INFO,RINFO)
548		; add_error(mark_aux,'Info field not set: ',closure(P,T,b(Pred,pred,INFO))),
549		RINFO=INFO),
550		Res = closure(P,T,b(Pred,pred,RINFO)).
551
552		mark_info([],INFO,INFO).
553		mark_info([ANN|T],INFO,Res) :-
554		(member(prob_annotation(ANN),INFO) -> Res=TRes ; Res = [prob_annotation(ANN)|TRes]),
555		mark_info(T,INFO,TRes).
556
557
558
559		% this will detect prj1/prj2 style functions which project away an infinite number of args
560		% such non-injective functions/relations remain infinite when composed with a finite set
561		is_infinite_non_injective_closure(closure(P,T,Body)) :-
562		%see also bsyntaxtree:get_lambda_equality(Body,LambdaID,RestBody,ResultExpr),
563		Body = b(equal(LHS,RHS),pred,_),
564		get_texpr_id(LHS,LambdaID),
565		get_texpr_id(RHS,ProjID), % TODO: get used ids and see if the rest is infinite
566		append(Args,[LambdaID],P), Args = [_,_|_],
567		nth1(Nr,Args,ProjID),
568		nth1(Nr2,T,NonProjectedType),
569		Nr2 \= Nr,
570		is_infinite_type(NonProjectedType).