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(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_symbolic_closure/1, is_symbolic_closure/3,
26		is_recursive_closure/1, is_recursive_closure/3,
27		get_recursive_identifier_of_closure/2, get_recursive_identifier_of_closure_body/2,
28		mark_closure_as_symbolic/2, mark_closure_as_recursive/2, mark_closure/3
29		]).
30
31		:- use_module(module_information,[module_info/2]).
32		:- module_info(group,kernel).
33		:- module_info(description,'This module provides various utility functions to analyse ProB closures.').
34
35		construct_closure(Parameters, ParameterTypes, Body, Res) :-
36		Res = closure(Parameters, ParameterTypes, Body).
37		% Res = closure_x(Parameters, ParameterTypes, Body,_). %% STILL HAS PROBLEMS with delay, e.g. inside b_test_exists !!
38
39
40		% an optimized version of construct_closure, which will try to produce explicit values if possible
41		construct_closure_if_necessary(_,_,b(falsity,pred,_),Res) :- !, Res=[].
42		construct_closure_if_necessary([ID], [T1], b(Pred,pred,_), Res) :-
43		construct_unary_closure(Pred,ID,T1,SET),!,
44		Res = SET.
45		construct_closure_if_necessary(Parameters, ParameterTypes, Body, Res) :-
46		Res = closure(Parameters, ParameterTypes, Body).
47
48		:- use_module(b_global_sets,[try_b_type2global_set/2]).
49		:- use_module(custom_explicit_sets,[try_expand_and_convert_to_avl/2]).
50		construct_unary_closure(member(b(identifier(ID),T1,_),b(value(SET),set(T1),_)),ID,T1,Res) :- Res=SET.
51		construct_unary_closure(truth,_,T1,Res) :- try_b_type2global_set(T1,Res).
52		construct_unary_closure(equal(b(identifier(ID),T1,_),b(value(SET),T1,_)),ID,T1,Res) :-
53		try_expand_and_convert_to_avl([SET],Res).
54
55
56		:- use_module(self_check).
57		:- assert_must_succeed( closures:is_closure(closure([x],[integer],body),[x],[integer],body)).
58		%is_closure(closure_x(Parameters, ParameterTypes, Body, _Exp), Parameters, ParameterTypes, Body).
59		is_closure(closure(Parameters, ParameterTypes, Body), Parameters, ParameterTypes, Body).
60
61
62		:- use_module(btypechecker,[couplise_list/2]).
63		get_domain_range_for_closure_types(Types,Domain,Range) :-
64		couplise_list(Types,couple(Domain,Range)).
65
66
67		:- use_module(bsyntaxtree,[create_texpr/4, safe_create_texpr/4, extract_pos_infos/2]).
68		% following not useful: construct_member_closure currently always called where the construction is needed
69		%construct_member_closure(ID,_Type,ClosureSetExpression,Result) :-
70		% nonvar(ClosureSetExpression),ClosureSetExpression = value(S),!,
71		% print(construct_member_closure_value(ID,S)),nl, %%
72		% Result=S.
73		construct_member_closure(ID,Type,Info,ClosureSetExpression,Result) :-
74		check_result_instantiation(Result,construct_member_closure(ID)),
75		create_texpr(identifier(ID),Type,[],TIdentifier), % used to be [generated]
76		extract_pos_infos(Info,PosInfo), % Note: safe_create_texpr will copy WD info
77		safe_create_texpr(ClosureSetExpression,set(Type),PosInfo,TClosureSet), % TODO: we could store whether sub_expression_contains_wd_condition for next call
78		safe_create_texpr(member(TIdentifier,TClosureSet),pred,PosInfo,TPred),
79		construct_closure([ID],[Type],TPred,Result).
80
81		construct_not_member_closure(ID,Type,Info,ClosureSetExpression,Result) :-
82		check_result_instantiation(Result,construct_not_member_closure(ID)),
83		Type==integer,
84		interval_up_to_inf(ClosureSetExpression,Limit),
85		!,
86		construct_less_equal_closure(ID,Limit,Info,Result). % construct an interval closure; better support in kernel for it
87		construct_not_member_closure(ID,Type,Info,ClosureSetExpression,Result) :-
88		create_texpr(identifier(ID),Type,[],TIdentifier), % used to be [generated]
89		safe_create_texpr(ClosureSetExpression,set(Type),Info,TClosureSet),
90		safe_create_texpr(not_member(TIdentifier,TClosureSet),pred,Info,TPred),
91		construct_closure([ID],[Type],TPred,Result).
92
93		interval_up_to_inf(global_set('NATURAL'),-1).
94		interval_up_to_inf(global_set('NATURAL1'),0).
95		interval_up_to_inf(value(global_set('NATURAL')),-1).
96		interval_up_to_inf(value(global_set('NATURAL1')),0).
97
98
99		construct_less_equal_closure(X,Res) :-
100		construct_less_equal_closure('_zzzz_unary',X,[],Res).
101		construct_less_equal_closure(ID,X,Info,Res) :-
102		construct_closure([ID],[integer],
103		b(less_equal(b(identifier(ID),integer,[]),
104		b(value(int(X)),integer,[])), pred,Info),Res).
105
106		construct_greater_equal_closure(X,Res) :-
107		construct_closure(['_zzzz_unary'],[integer],
108		b(greater_equal(b(identifier('_zzzz_unary'),integer,[]),
109		b(value(int(X)),integer,[])), pred,[]),Res).
110
111		:- use_module(error_manager,[add_internal_error/2]).
112		% check that we do not instantiate result too early (rather than using equal_object)
113		check_result_instantiation(X,_) :- var(X),!.
114		check_result_instantiation(closure(_,_,_),_PP) :- !.
115		check_result_instantiation(X,PP) :-
116		add_internal_error('Result already instantiated in incompatible way: ',check_result_instantiation(X,PP)).
117
118		is_member_closure_with_info([ID],[TYPE],b(PRED,_Pred,Info), TYPE,Info,SET) :-
119		is_member_closure_aux(PRED, ID,TYPE,SET).
120		is_member_closure([ID],[TYPE],b(PRED,_Pred,_), TYPE,SET) :-
121		is_member_closure_aux(PRED, ID,TYPE,SET).
122
123		:- use_module(bsyntaxtree,[is_set_type/2]).
124		is_member_closure_aux(member(TID,TSET), ID,TYPE,SET) :-
125		TID = b(identifier(ID),TYPE,_),
126		TSET = b(SET,SETTYPE,_),
127		is_set_type(SETTYPE,TYPE).
128		is_member_closure_aux(subset(TID,BSET), ID,TYPE,SET) :-
129		TID = b(identifier(ID),TYPE,_),
130		SET = pow_subset(BSET).
131		% can we also detect pow1_subset ? {x| x/= {} & x<: BSET}
132
133
134		% detect not_member closures + integerset as special not_member_closures
135		is_not_member_value_closure_or_integerset(global_set(X),TYPE,SET) :- !,
136		is_not_member_global_set(X,TYPE,SET).
137		is_not_member_value_closure_or_integerset(C,TYPE,SET) :- is_not_member_value_closure(C,TYPE,SET).
138
139		is_not_member_global_set('INTEGER',integer,[]).
140		is_not_member_global_set('NATURAL',integer,X) :-
141		construct_less_equal_closure(-1,X). % {x|x<0}.
142		is_not_member_global_set('NATURAL1',integer,X) :-
143		construct_less_equal_closure(0,X). %X = {x|x<1}.
144
145		is_not_member_value_closure(closure(Par,T,B),TYPE,SET) :-
146		is_not_member_closure(Par,T,B,TYPE,value(SET)).
147		is_not_member_closure([ID],[TYPE],b(PRED,_Pred,_),TYPE,SET) :-
148		is_not_member_closure_aux(PRED,ID,TYPE,SET).
149
150		:- use_module(kernel_tools,[ground_value/1]).
151		is_not_member_closure_aux(not_member(b(identifier(ID),TYPE,_),b(SET,set(TYPE),_)),ID,TYPE,SET).
152		is_not_member_closure_aux(not_equal(b(identifier(ID),TYPE,_),ONE),ID,TYPE,SET) :-
153		(ONE = b(value(Val),_,_),
154		ground_value(Val)
155		-> custom_explicit_sets:construct_one_element_custom_set(Val,SetVal), SET = value(SetVal)
156		; SET = set_extension([ONE])).
157		%is_not_member_closure_aux(PRED,ID,TYPE,SET) :- print(check_not_mem(PRED,ID,TYPE,SET)),nl,fail.
158
159		construct_complement_closure(Delta,Type,Closure) :-
160		% print(generating_complement_closure(GlobalSet,Delta,Type)),nl,
161		construct_not_member_closure('_zzzz_unary',Type,[],value(Delta),Closure).
162
163
164
165		/* lambda abstractions */
166		:- 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])).
167		:- 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)
168		)).
169
170		:- use_module(bsyntaxtree,[conjunction_to_list/2,conjunct_predicates/2]).
171		is_lambda_closure(Args,Types,ClosurePred, OtherIDs, OtherTypes, DOMAINPRED,Res) :-
172		% TO DO: do this more efficiently: if LambdaID occurs in any non-equal predicate : stop searching
173		% TO DO: check if is_infinite_equality_closure is not a special case of lambda closure ?
174		append(OtherTypes,[LambdaType],Types), OtherTypes \= [],
175		append(OtherIDs,[LambdaID],Args),
176		Res=b(EXPR,LambdaType,EXPRINFO),
177		%used to call: b_interpreter:member_conjunct(EQ,ClosurePred,DOMAINPRED), ; but inlined below for efficiency
178		select_equality(ClosurePred,LambdaID,EXPR,LambdaType,EXPRINFO,DOMAINPRED),
179		!. % avoid backtracking member_conjunct
180		% tools:print_bt_message(is_lambda_closure(LambdaID)).
181		% Note: LAMBDA is usually '_lambda_result_'
182
183		identifier_equality(b(equal(b(LHS,Type,LHSInfo),b(RHS,_TypeRHS,RHSInfo)),pred,_),ID,Type,EXPR,EXPRINFO) :-
184		% no need to unify with TypeRHS; actually Prolog unification could fail due to seq types ?
185		identifier_equality_aux(LHS,LHSInfo,RHS,RHSInfo,ID,EXPR,EXPRINFO).
186		identifier_equality_aux(identifier(ID),_,EXPR,EXPRINFO,ID,EXPR,EXPRINFO) :- !.
187		identifier_equality_aux(EXPR,EXPRINFO,identifier(ID),_,ID,EXPR,EXPRINFO).
188
189		% find an equality ID = RHSExpr so that ID does not occur in RHSExpr nor in RestPred
190		% the identifier should be provided as input (for the cut below)
191		select_equality(ClosurePred,ID,RHSExpr,Type,Info,RestPred) :-
192		conjunction_to_list(ClosurePred,List),
193	?	select(EQ,List,RestList),
194		identifier_equality(EQ,ID,Type,RHSExpr,Info),
195		!, % once we find a first equality : no need to look for a second one as then does_not_occur in RestPred will always fail !
196		(ID='_lambda_result_',EQ=b(_,_,I),
197	?	member(prob_annotation('LAMBDA-EQUALITY'),I)
198		-> true % no need to perform occurs check in RHS, but in RestPred, cf test 1874
199		; %format('Check occurs ~w : ',[ID]), translate:print_bexpr(b(RHSExpr,Type,Info)),nl,
200		does_not_occur_in(ID,b(RHSExpr,Type,Info))
201		),
202		conjunct_predicates(RestList,RestPred),
203		does_not_occur_in(ID,RestPred).
204
205
206		:- use_module(memoization,[is_lambda_value_domain_memoization_closure/5]).
207
208		% check whether we have a lambda closure and whether we can compute its domain
209		is_lambda_value_domain_closure(P,T,Pred, DomainValue,Expr) :-
210	?	is_lambda_value_domain_memoization_closure(P,T,Pred, DV,E),!,
211		DV \= fail, E\= fail,
212		DomainValue=DV, Expr=E.
213		is_lambda_value_domain_closure(Args,Types,B, DomainValue, EXPR) :-
214		is_lambda_value_domain_normal_closure(Args,Types,B, DomainValue, EXPR).
215
216		is_lambda_value_domain_normal_closure(Args,Types,B, DomainValue, EXPR) :-
217		% tools_printing:print_term_summary(try_is_lambda_domain(Args,Types,B)), %
218		is_lambda_closure(Args,Types,B, OtherIDs,OtherTypes, DomainPred, EXPR),!,
219		%print(lambda_closure(OtherIDs)), translate:print_bexpr(EXPR),nl,
220		construct_closure_if_necessary(OtherIDs,OtherTypes,DomainPred,DomClosure),
221	?	(is_symbolic_closure(Args,Types,B)
222		-> mark_closure_as_symbolic(DomClosure,DomainValue)
223		; DomainValue = DomClosure).
224		%print(lambda_domain(Args)),nl, (IDs=[_,_|_] -> trace ; true),
225		%translate:print_bvalue(DomainValue),nl.
226
227		% LAMBDARES is usually _lambda_result_, LAMBDARES cannot occur in DOMAIN (is value)
228
229		:- use_module(library(lists),[maplist/4]).
230		is_lambda_comprehension_set(b(comprehension_set(Parameters,Body),_,_),LambdaParas,DomainPred,EXPR) :-
231		maplist(get_names_and_types,Parameters,Args,Types),
232		is_lambda_closure(Args,Types,Body, OtherIDs,OtherTypes, DomainPred, EXPR),
233		maplist(combine_names_and_types,OtherIDs,OtherTypes,LambdaParas).
234
235		get_names_and_types(b(identifier(ID),Type,_),ID,Type).
236		combine_names_and_types(ID,Type,b(identifier(ID),Type,[])).
237
238		:- assert_must_succeed(closures:is_special_infinite_closure([x],[integer],b(truth,pred,[]))).
239		:- assert_must_succeed((X=b(identifier(x),integer,[]),N=b(integer(3),integer,[]),
240		closures:is_special_infinite_closure([x],[integer],b(greater(X,N),pred,[])))).
241		:- assert_must_succeed((X=b(identifier(x),integer,[]),N=b(integer(3),integer,[]),
242		closures:is_special_infinite_closure([x],[integer],b(greater(X,N),pred,[])))).
243		:- assert_must_succeed((X=b(identifier(x),integer,[]),N=b(integer(3),integer,[]),
244		closures:is_special_infinite_closure([x],[integer],b(less(X,N),pred,[])))).
245		:- assert_must_succeed((X=b(identifier(x),integer,[]),N=b(integer(3),integer,[]),
246		closures:is_special_infinite_closure([x],[integer],b(not_equal(X,N),pred,[])))).
247		:- assert_must_fail((X=b(identifier(x),integer,[]),N=b(integer(3),integer,[]),
248		closures:is_special_infinite_closure([x],[integer],b(equal(X,N),pred,[])))).
249		:- assert_must_succeed((X=b(identifier(x),integer,[]),N=b(integer(3),integer,[]),
250		closures:is_special_infinite_closure([x,y],[integer,integer],b(equal(X,N),pred,[])))).
251		:- assert_must_succeed((Y=b(identifier(y),integer,[]),N=b(integer(3),integer,[]),
252		closures:is_special_infinite_closure([x,y],[integer,integer],b(equal(Y,N),pred,[])))).
253
254		:- use_module(typing_tools,[is_infinite_type/1]).
255		/* checking for infinite closures */
256		%is_special_infinite_closure(_Par,T,b(truth,_Pred,_)) :- !, % now dealt with below
257		% member(Type,T), is_infinite_type(Type),!.
258		is_special_infinite_closure(Par,T,Body) :-
259	?	is_infinite_equality_closure(Par,T,Body),!.
260		%is_special_infinite_closure(Par,T,Body) :- is_full_id_closure(Par,T,Body,TYPE), is_infinite_type(TYPE).
261		%is_special_infinite_closure(Par,T,Body) :- is_prj1_closure(Par,T,Body,T1,_T2), is_infinite_type(T1).
262		%is_special_infinite_closure(Par,T,Body) :- is_prj2_closure(Par,T,Body,_T1,T2), is_infinite_type(T2).
263		is_special_infinite_closure(Par,T,Body) :-
264		is_not_member_closure(Par,T,Body,Type,value(_)), is_infinite_type(Type).
265
266		:- use_module(library(lists)).
267
268		greater_typing(greater(b(identifier(ID),integer,_),b(VUP,integer,_)),ID,UP) :- is_integer_val(VUP,UP).
269		greater_typing(greater_equal(b(identifier(ID),integer,_),b(VUP,integer,_)),ID,UP) :- is_integer_val(VUP,UP).
270		greater_typing(less(b(VUP,integer,_),b(identifier(ID),integer,_)),ID,UP) :- is_integer_val(VUP,UP).
271		greater_typing(less_equal(b(VUP,integer,_),b(identifier(ID),integer,_)),ID,UP) :- is_integer_val(VUP,UP).
272
273		less_typing(less(b(identifier(ID),integer,_),b(VUP,integer,_)),ID,UP) :- is_integer_val(VUP,UP).
274		less_typing(less_equal(b(identifier(ID),integer,_),b(VUP,integer,_)),ID,UP) :- is_integer_val(VUP,UP).
275		less_typing(greater(b(VUP,integer,_),b(identifier(ID),integer,_)),ID,UP) :- is_integer_val(VUP,UP).
276		less_typing(greater_equal(b(VUP,integer,_),b(identifier(ID),integer,_)),ID,UP) :- is_integer_val(VUP,UP).
277
278		is_integer_val(integer(UP),UP).
279		is_integer_val(value(V),UP) :- nonvar(V),V=int(UP).
280
281		is_static_expr_of_infinite_type(b(E,Type,_)) :- is_static_expr_of_infinite_type2(E,Type).
282		is_static_expr_of_infinite_type2(integer(_),_).
283		is_static_expr_of_infinite_type2(string(_),_).
284		is_static_expr_of_infinite_type2(real(_),_).
285		is_static_expr_of_infinite_type2(value(V),Type) :- is_val_of_infinite_type(V,Type).
286		is_static_expr_of_infinite_type2(empty_set,Type) :- is_infinite_type(Type).
287		is_static_expr_of_infinite_type2(empty_sequence,Type) :- is_infinite_type(Type).
288		% TODO: more typical expressions, set/sequence extension pairs
289
290		is_val_of_infinite_type(V,_) :- var(V),!,fail.
291		is_val_of_infinite_type(int(_),_).
292		is_val_of_infinite_type(string(_),_).
293		is_val_of_infinite_type(term(floating(_)),_).
294		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)).
295		is_val_of_infinite_type([],Type) :- is_infinite_type(Type).
296		is_val_of_infinite_type(avl_set(_),Type) :- is_infinite_type(Type).
297
298
299
300
301		% the following also translates global_set(NATURAL(1)) into closures
302		% TO DO: probably better to remove global_set(INTSET) all together and rewrite in ast_cleanup to closure
303		is_closure_or_integer_set(closure(P,T,B),P,T,B).
304		is_closure_or_integer_set(global_set(INTSET),
305		['_zzzz_unary'],[integer],
306		b(greater_equal(
307		b(identifier('_zzzz_unary'),integer,[]),
308		b(integer(BOUND),integer,[])
309		),
310		pred,
311		[prob_annotation('SYMBOLIC')])
312		) :-
313		get_bound(INTSET,BOUND).
314		get_bound('NATURAL',0).
315		get_bound('NATURAL1',1).
316		% TO DO: allow INTEGER / maximal sets ? -> truth; could get rid of complement sets?
317
318		% to do: extend; could be value(infinite_closure)...
319
320
321
322		/* Equality closures {x1,x2,...|id=E2}, where id does not occur in E2 and id =xi */
323		% should cover id, prj1, prj2
324		% {x,y|y:BOOL & x=f(y) } or %x.(x:NATURAL|Expr(x))
325		% would not be infinite {x,y|x:BOOL & x=f(g(x)*y)} , g={FALSE|->0, TRUE|->1}, f = ...
326		% we assume Well-Definedness
327		% we also accept closures without equality now
328
329		is_infinite_equality_closure(IDs, TYPES, Body) :-
330		%IDs = [_,_|_], % we used to require at least at least two variables
331	?	check_inf_cl_body(Body,[],OutConstrained),
332	?	(member(_ID/infinite,OutConstrained) -> true
333		; contains_infinite_type(IDs,TYPES,OutConstrained)). % , print(infinite(IDs)),nl.
334
335		contains_infinite_type([ID|IT],[H|T],OutConstrained) :-
336		(is_infinite_type(H),
337	?	\+ member(ID/_,OutConstrained)
338		-> true ; contains_infinite_type(IT,T,OutConstrained)).
339
340		:- use_module(b_ast_cleanup,[definitely_not_empty_and_finite/1, definitely_infinite/1]).
341		:- use_module(external_functions,[external_pred_always_true/1]).
342		:- use_module(bsyntaxtree, [get_texpr_id/2, get_texpr_type/2]).
343		check_inf_cl_body(b(B,pred,_),InConstrained,OutConstrained) :-
344	?	check_bdy_aux(B,InConstrained,OutConstrained).
345		check_bdy_aux(conjunct(A,B),InConstrained,OutConstrained) :- !,
346	?	check_inf_cl_body(A,InConstrained,OutConstrained1),
347	?	check_inf_cl_body(B,OutConstrained1,OutConstrained).
348		check_bdy_aux(disjunct(A,B),InConstrained,OutConstrained) :- !,
349	?	(check_inf_cl_body(A,InConstrained,OutConstrained) -> true
350	?	; check_inf_cl_body(B,InConstrained,OutConstrained)).
351		check_bdy_aux(equal(LHS,RHS), Constrained, [ID/equal|Constrained]) :-
352		get_texpr_id(LHS,ID),
353	?	\+ member(ID/_,Constrained), % no constraints on ID so far
354		does_not_occur_in(ID,RHS),!. % the equation must have a solution; assuming well-definedness
355		check_bdy_aux(equal(LHS,RHS), Constrained, [ID/equal|Constrained]) :- % symmetric to case above
356		get_texpr_id(RHS,ID),
357	?	\+ member(ID/_,Constrained),
358		does_not_occur_in(ID,LHS),!.
359		check_bdy_aux(member(b(identifier(ID),TYPE,_),SET),Constrained,[ID/INFINITE|Constrained]) :-
360		\+ member(ID/_,Constrained),
361		(is_infinite_type(TYPE)
362		-> %check that SET is infinite; otherwise remove from IDs
363	?	(definitely_infinite(SET) -> INFINITE=infinite;
364		definitely_not_empty_and_finite(SET) -> INFINITE = finite
365		)
366		; definitely_not_empty_and_finite(SET), % otherwise we may have no solution and the entire closure is empty
367		INFINITE = finite
368		).
369		check_bdy_aux(EXPR,Constrained,[ID/infinite|Constrained]) :-
370		%% TO DO: store bounds in ID/... list to check if the domain remains infinite!
371		greater_typing(EXPR,ID,_UP),
372	?	\+ member(ID/_,Constrained).
373		check_bdy_aux(EXPR,Constrained,[ID/infinite|Constrained]) :-
374		less_typing(EXPR,ID,_UP),
375		\+ member(ID/_,Constrained).
376		check_bdy_aux(not_equal(A,B),Constrained,[ID/infinite|TC]) :-
377		(get_texpr_id(A,ID)
378		-> is_static_expr_of_infinite_type(B) % we have to be careful that B does not directly or indirectly reference A
379		; get_texpr_id(B,ID),
380		is_static_expr_of_infinite_type(A)
381		),
382	?	(select(ID/Kind,Constrained,TC)
383		-> Kind=infinite % if it was infinite it will remain infinite, we only discard a single static value
384		; TC=Constrained).
385		check_bdy_aux(truth,Constrained,Constrained).
386		check_bdy_aux(external_pred_call(FunName,_Args),Constrained,Constrained) :-
387		external_pred_always_true(FunName).
388
389
390		:- use_module(bsyntaxtree,[occurs_in_expr/2]).
391		does_not_occur_in(ID,EXPR) :- \+ occurs_in_expr(ID,EXPR).
392
393
394
395		% check if we have a closure of type id(SetValue)
396
397		is_id_closure_over([ID1,ID2], [TYPE,TYPE],Body, ID_Domain, Full) :- nonvar(Body),
398		Body=b(equal(b(identifier(ID1),TYPE,_),b(identifier(ID2),TYPE,_)),pred,_),
399		!,
400		convert_type_to_value(TYPE,ID_Domain), Full=true.
401		is_id_closure_over(Par,Types,Body,ID_Domain,Full) :- nonvar(Par),nonvar(Body),
402		is_member_closure(Par,Types,Body,_,Set), % print(member_closure(Set)),nl,
403		nonvar(Set),
404		Set = identity(b(VAL,set(_TYPE),_)),
405		nonvar(VAL), VAL=value(ID_Domain),
406		(custom_explicit_sets:is_definitely_maximal_set(ID_Domain) -> Full=true ; Full=false).
407
408		%:- use_module(kernel_objects,[all_strings_wf/2]).
409		convert_type_to_value(integer,global_set('INTEGER')).
410		convert_type_to_value(global(G),global_set(G)).
411		convert_type_to_value(boolean,BS) :- BS=[pred_true /* bool_true */,pred_false /* bool_false */]. % TO DO: generate AVL ?
412		convert_type_to_value(string,global_set('STRING')). % :- all_strings_wf(S,WF).
413		%convert_type_to_value(Type,closure([x],[Type],TRUTH)) :- ... TO DO
414
415
416
417		/* Event-B id closure over full Type */
418
419		is_full_id_closure(P,T,B) :- is_id_closure_over(P,T,B,_,true).
420
421
422		% currently commented out in is_special_infinite_closure
423		%is_prj1_closure([ID1,_ID2,RESID],[Type1,Type2,Type1],
424		% b(equal(b(identifier(RESID),Type1,_),b(identifier(ID1),Type1,_)),pred,_),Type1,Type2).
425		%is_prj2_closure([_ID1,ID2,RESID],[Type1,Type2,Type2],
426		% b(equal(b(identifier(RESID),Type2,_),b(identifier(ID2),Type2,_)),pred,_),Type1,Type2).
427
428
429		% ---- SYMBOLIC and RECURSIVE annotations
430
431		get_recursive_identifier_of_closure(V,RID) :- nonvar(V), V=closure(_P,_T,B),
432		get_recursive_identifier_of_closure_body(B,RID).
433	?	get_recursive_identifier_of_closure_body(b(_,_,BodyInfo),RID) :- member(prob_annotation(recursive(RID)),BodyInfo).
434
435		is_recursive_closure(V) :- nonvar(V), V=closure(P,T,B),
436		is_recursive_closure(P,T,B).
437
438		is_recursive_closure(_P,_T,b(_,_,INFO)) :-
439		member(prob_annotation('RECURSIVE'),INFO).
440		% we also have prob_annotation(recursive(TID)) annotation
441
442		is_symbolic_closure(V) :- nonvar(V), V=closure(P,T,B),
443	?	is_symbolic_closure(P,T,B).
444
445		is_symbolic_closure(_P,_T,b(_,_,INFO)) :-
446	?	member(prob_annotation('SYMBOLIC'),INFO).
447
448		% see also is_converted_lambda_closure
449
450
451		:- use_module(error_manager,[add_internal_error/2, add_error/3]).
452		:- use_module(debug,[debug_println/2]).
453
454		% mark a closure as symbolic by marking the info field of the body predicate
455		mark_closure_as_symbolic(C,R) :-
456		mark_closure3(C,['SYMBOLIC'],R).
457		mark_closure_as_recursive(C,R) :-
458		mark_closure3(C,['SYMBOLIC','RECURSIVE'],R).
459		mark_closure3(_,ANN,R) :- nonvar(R), % we could use equal_object
460		add_internal_error('Result already instantiated: ',mark_closure3(_,ANN,R)),fail.
461		mark_closure3(C,ANN,R) :- var(C), % we could use equal_object
462		!,
463		debug_println(19,not_marking_var_closure(C,ANN)),
464		R=C.
465		mark_closure3(C,ANN,R) :- mark_closure(C,ANN,R).
466		%:- block mark_closure(-,?,?).
467		mark_closure(closure(P,T,B),ANN,R) :- !, mark_aux(P,T,B,ANN,R).
468		mark_closure(A,_,Res) :- A=Res. % not a closure
469		%:- block mark_aux(?,?,-,?,?).
470		mark_aux(P,T,b(Pred,pred,INFO),ANN,Res) :-
471		(ground(INFO)
472		-> mark_info(ANN,INFO,RINFO)
473		; add_error(mark_aux,'Info field not set: ',closure(P,T,b(Pred,pred,INFO))),
474		RINFO=INFO),
475		Res = closure(P,T,b(Pred,pred,RINFO)).
476
477		mark_info([],INFO,INFO).
478		mark_info([ANN|T],INFO,Res) :-
479	?	(member(prob_annotation(ANN),INFO) -> Res=TRes ; Res = [prob_annotation(ANN)|TRes]),
480		mark_info(T,INFO,TRes).
481