1 % (c) 2020-2025 Lehrstuhl fuer Softwaretechnik und Programmiersprachen,
2 % Heinrich Heine Universitaet Duesseldorf
3 % This software is licenced under EPL 1.0 (http://www.eclipse.org/org/documents/epl-v10.html
4
5 :- module(well_def_hyps, [empty_hyps/1,
6 portray_hyps/1,
7 get_hyp_vars/2,
8 get_hyp_var_type/3,
9 push_hyp/4, push_hyps/4,
10 push_hyps_wo_renaming/4,
11 %push_normalized_hyp/3,
12 add_new_hyp_variables/3,
13 add_new_hyp_any_vars/3,
14 copy_hyp_variables/3,
15 is_hyp_var/2,
16 get_clash_renaming_subst/2,
17 get_renamed_expression/3,
18 get_normalized_and_renamed_predicate/4,
19 translate_norm_expr_with_limit/3,
20 negate_hyp/2,
21 negate_op/2,
22 is_finite_type_for_wd/2
23 ]).
24
25 :- use_module(probsrc(module_information),[module_info/2]).
26 :- module_info(group,well_def_prover).
27 :- module_info(description,'This module provides hypotheses stack management.').
28
29
30
31 :- use_module(wdsrc(well_def_tools), [not_occurs/2]).
32 :- use_module(probsrc(error_manager)).
33 :- use_module(probsrc(debug)).
34 :- use_module(library(avl)).
35 :- use_module(library(ordsets)).
36 :- use_module(probsrc(avl_tools),[avl_fetch_bin/4]).
37
38 % ------------------------------
39
40 % Hypotheses stack management:
41
42
43 % create an empty hyp stack
44 empty_hyps(hyp_rec(E,HI2)) :- empty_avl(E),
45 avl_store(hyp_typed_vars,E,[],HI1), % typed variables of the hypotheses (implicitly universally quantified)
46 avl_store(hyp_clash_vars,HI1,clash_rec(0,E),HI2). % variables which are currently in clash
47
48 :- use_module(probsrc(bsyntaxtree), [conjunct_predicates/2]).
49 % display the hypotheses stack:
50 portray_hyps(hyp_rec(AVL,HInfos)) :- fetch_hyp_vars(HInfos,Vars),
51 get_clashed_vars(HInfos,CVars),
52 (debug_mode(on) -> portray_hyp_vars(hyp_rec(AVL,HInfos)),nl ; true),
53 %b_global_sets:portray_global_sets,
54 !,
55 format('Hypotheses over ~w (clashes: ~w):~n',[Vars,CVars]),
56 %avl_domain(AVL,D), lists:maplist(well_def_hyps:println_nhyp,D),
57 avl_range(AVL,Hyp),
58 conjunct_predicates(Hyp,HypC),
59 translate:nested_print_bexpr(HypC),nl,nl.
60 portray_hyps(H) :- !, format('** ILLEGAL Hypotheses: ~w~n',[H]).
61
62 print_tvar(b(identifier(ID),Type,_)) :- format(' ~w : ~w~n',[ID,Type]).
63 :- use_module(library(lists),[maplist/2]).
64 portray_hyp_vars(hyp_rec(_,HInfos)) :- fetch_hyp_typed_vars(HInfos,TVars),!,
65 length(TVars,Len),
66 format('Typed vars in hyps (~w):~n',[Len]),
67 maplist(print_tvar,TVars).
68 portray_hyp_vars(H) :- !, format('** ILLEGAL Hypotheses: ~w~n',[H]).
69
70
71 %println_nhyp(NH) :- format(' --> ~w~n',[NH]).
72
73
74 % ---------------------
75
76 % for debugging:
77 :- public hyp_portray_hook/1.
78 hyp_portray_hook(X) :- nonvar(X), X= hyp_rec(AVL,HInfos),
79 avl_size(AVL,Size),
80 avl_size(HInfos,ISize),
81 format('hyp_rec(#~w,#~w)',[Size,ISize]).
82
83 :- public install_hyp_portray_hook/0.
84 install_hyp_portray_hook :- % mainly for the Prolog debugger
85 assertz(( user:portray(X) :- well_def_hyps:hyp_portray_hook(X) )).
86
87 %:- install_hyp_portray_hook.
88
89
90 % ------------------------
91
92 % get the variable ids currently in scope
93 get_hyp_vars(hyp_rec(_,HInfos),Res) :- get_hyp_vars(HInfos,Vars),!,Res=Vars.
94 get_hyp_vars(H,R) :- add_internal_error('Illegal hyps: ',get_hyp_vars(H,R)), R=[].
95
96 :- use_module(probsrc(bsyntaxtree), [def_get_texpr_ids/2]).
97 fetch_hyp_vars(HInfos,Vars) :- avl_fetch(hyp_typed_vars,HInfos,TVars),
98 def_get_texpr_ids(TVars,Vars).
99 fetch_hyp_typed_vars(HInfos,Vars) :-
100 avl_fetch(hyp_typed_vars,HInfos,Vars).
101 get_clashed_vars(HInfos,Vars) :- avl_fetch(hyp_clash_vars,HInfos,clash_rec(_,AVL)),
102 avl_domain(AVL,Vars).
103 get_clash_renaming(HInfos,Renamings) :- avl_fetch(hyp_clash_vars,HInfos,clash_rec(_,AVL)),
104 findall(rename(ID,FreshID), avl_member(ID,AVL,FreshID), Renamings).
105
106 % check if a variable id is currently in the scope of the hypotheses
107 % if not, it is a global identifier (e.g., enumerated or deferred set)
108 is_hyp_var(Var,hyp_rec(_,HInfos)) :- atomic(Var), nonvar(HInfos),!,
109 fetch_hyp_vars(HInfos,Vars),
110 ord_member(Var,Vars).
111 is_hyp_var(V,H) :- add_internal_error('Illegal call: ',is_hyp_var(V,H)),fail.
112
113 :- use_module(probsrc(tools_lists),[ord_member_nonvar_chk/2]).
114 get_hyp_var_type(Var,hyp_rec(_,HInfos),Type) :- atomic(Var),!,
115 fetch_hyp_typed_vars(HInfos,TVars),
116 TVar = b(identifier(Var),Type,_),
117 ord_member_nonvar_chk(TVar,TVars).
118 get_hyp_var_type(V,H,T) :- add_internal_error('Illegal call: ',is_hyp_var_type(V,H,T)),fail.
119
120 :- use_module(probsrc(bsyntaxtree), [conjunction_to_list/2]).
121 % push a new Hypothesis H on the hyp stack
122 push_hyp(Hyps,H,Options,NewHyps) :-
123 check_valid_hyp_rec(Hyps,push_hyp),
124 conjunction_to_list(H,Hs),
125 push_hyps(Hyps,Hs,Options,NewHyps).
126
127 check_valid_hyp_rec(Hyps,PP) :- var(Hyps),!,
128 add_internal_error('Illegal variable hyp_rec: ',check_hyp_rec(Hyps,PP)),fail.
129 check_valid_hyp_rec(Hyps,PP) :- Hyps \= hyp_rec(_,_),!,
130 add_internal_error('Illegal hyp_rec: ',check_valid_hyp_rec(Hyps,PP)),fail.
131 check_valid_hyp_rec(_,_).
132
133 % push a list of hypotheses
134 push_hyps(hyp_rec(NHyps,HInfos),Hs,Options,hyp_rec(NewNHyps,HInfos)) :- !,
135 get_clash_renaming(HInfos,ClashRenaming),
136 push_hyp_aux(Hs,ClashRenaming,Options,NHyps,NewNHyps).
137 push_hyps(A,B,C,D) :- add_internal_error('Illegal call: ', push_hyps(A,B,C,D)),fail.
138
139 % useful if renaming done outside, e.g., for treating x:=x-1 in WD analyser
140 push_hyps_wo_renaming(hyp_rec(NHyps,HInfos),Hs,Options,hyp_rec(NewNHyps,HInfos)) :- !, ClashRenaming=[],
141 push_hyp_aux(Hs,ClashRenaming,Options,NHyps,NewNHyps).
142 push_hyps_wo_renaming(A,B,C,D) :- add_internal_error('Illegal call: ', push_hyps(A,B,C,D)),fail.
143
144 push_hyp_aux(Hyps,_,_,_,_) :- var(Hyps),!, add_internal_error('Unbound hyps: ',push_hyps(Hyps)),fail.
145 push_hyp_aux([],_,_,NH,NH).
146 push_hyp_aux([H|T],ClashRenaming,Options,NHyps,NewNHyps) :-
147 ((var(NHyps) ; NHyps=hyp_rec(_,_)) -> add_internal_error('Illegal AVL: ',NHyps),fail ; true),
148 push_individual_hyp(H,ClashRenaming,Options,NHyps,NHyps3),
149 push_hyp_aux(T,ClashRenaming,Options,NHyps3,NewNHyps).
150
151 % sometimes we still have conjuncts in the list of hypotheses (e.g., coming from Rodin)
152 push_individual_hyp(b(conjunct(H1,H2),_,_),ClashRenaming,Options,NHyps,NHyps3) :- !,
153 push_individual_hyp(H1,ClashRenaming,Options,NHyps,NHyps2),
154 push_individual_hyp(H2,ClashRenaming,Options,NHyps2,NHyps3).
155 push_individual_hyp(H,ClashRenaming,Options,NHyps,NHyps3) :-
156 normalize_and_rename_predicate(ClashRenaming,H,RenH,NH),
157 % print('PUSH: '),nl, debug:print_quoted_with_max_depth(NH,6), print(' '), error_manager:print_message_span(H),nl,
158 push_normalized_hyp_aux(NH,RenH,Options,NHyps,NHyps3).
159
160 % utility: used to push already normalized and renamed hyp from within prover for normalized sub-goals
161 %push_normalized_hyp(NH,hyp_rec(NHyps,I),hyp_rec(NHyps3,I)) :- norm_aux(NH,NormPred),
162 % push_normalized_hyp_aux(NormPred,unknown,[],NHyps,NHyps3).
163
164 push_normalized_hyp_aux(NH0,RenH,Options,NHyps,NHyps2) :-
165 simplify_hyp(NH0,NHyps,NH),
166 ((useful_hyp(NH) ; safe_ord_member(create_full_po,Options)
167 ; potentially_useful_for_hyp_rule(NH), safe_ord_member(push_more_hyps,Options)
168 ; useful_implication(NH,Options),
169 true %safe_ord_member(push_more_hyps,Options) % seems useful for Event-B benchmark models, enable by default?
170 )
171 -> avl_store_with_commutes_if_new(NH,NHyps,RenH,NHyps2,Options)
172 ; push_commutative_hyps(NH,RenH,Options,NHyps,NHyps2)
173 % hypothesis not directly used by prover, but there could be alternatives e.g., for disjunct
174 %,functor(NH,FF,NN), print(not_pushing(FF,NN)),nl
175 ).
176
177
178
179 % push equivalent or implied hypotheses on the stack:
180 push_commutative_hyps(NH,RenH,Options,NHyps1,NHyps2) :-
181 ? commute_bin_op(NH,_,Options), % somehow faster than using findall directly
182 !,
183 findall(NH3,commute_bin_op(NH,NH3,Options),NH3s),
184 l_avl_store_nhyps(NH3s,NHyps1,RenH,NHyps2,Options).
185 push_commutative_hyps(_,_,_,NHyps,NHyps).
186
187 safe_ord_member(El,List) :- var(List),!, add_internal_error('Illegal call: ',safe_ord_member(El,List)),fail.
188 safe_ord_member(El,List) :- ord_member(El,List).
189
190 l_avl_store_nhyps([],NHyps,_,NHyps,_Options).
191 l_avl_store_nhyps([NH1|TNH],NHyps1,RenH,NHyps3,Options) :-
192 simplify_hyp(NH1,NHyps1,NH1s),
193 avl_store_if_new(NH1s,NHyps1,RenH,NHyps2,Options),
194 l_avl_store_nhyps(TNH,NHyps2,RenH,NHyps3,Options).
195
196 % store a hypothesis if new (without storing commutative versions of it)
197 avl_store_if_new(NH,H,_,H2,_) :- avl_fetch(NH,H),!, H2=H.
198 avl_store_if_new(NH,H1,RH,H3,Options) :- %write(prop_new(NH)),nl, avl_domain(H1,H1D), write(H1D),nl,nl,
199 propagate_resolution_with_hyp(NH,H1,H2,Options),
200 avl_store(NH,H2,RH,H3).
201
202 % propagate new hyp by applying (simple) resolution: Hyp & not(Hyp) -> add false as hypothesis
203 % also propagates implications Hyp => Q -> add Q as hypothesis
204 propagate_resolution_with_hyp(NormHyp,Hyps,H2,_) :- negate_norm_op(NormHyp,NegNormHyp),
205 avl_fetch(NegNormHyp,Hyps),!,
206 debug_println(9,contradiction_found_in_hypotheses(NormHyp)),
207 avl_store(falsity,Hyps,b(falsity,pred,[neg_hyp]),H2). % false_hyp rule can later trigger
208 propagate_resolution_with_hyp(NH,Hyps,H2,Options) :-
209 %write(fetch_impl),nl, avl_domain(Hyps,D), write(hyps(D)),nl,
210 findall(NRHS,avl_fetch_bin(NH,implication,Hyps,NRHS),TriggeredImplications),
211 propagate_implications(TriggeredImplications,NH,Hyps,H2,Options).
212
213 negate_norm_op(NormHyp,NegNormHyp) :- negate_op(NormHyp,NegNH),
214 norm_aux(NegNH,NegNormHyp).
215
216 propagate_implications([],_,Hyps,Hyps,_).
217 propagate_implications([NRHS|TR],NLHS,NHyps1,NHyps4,Options) :-
218 (avl_delete(implication(NLHS,NRHS),NHyps1,TE,NHyps2)
219 -> % write('propagate : '),translate:print_bexpr(TE),nl,
220 (TE=b(implication(_,RHS),_,_) -> true
221 ; TE=b(disjunct(_,RHS),_,_) -> true
222 ; unknown_source_term(RHS),
223 true %add_warning(wd_prover,'Unexpected un-normalised hyp: ',TE)
224 ),
225 simplify_hyp(NRHS,NHyps2,NRHS2),
226 avl_store_with_commutes_if_new(NRHS2,NHyps2,RHS,NHyps3,Options)
227 ; % implication has already been triggered by processing a previous NRHS in the list
228 NHyps3=NHyps1
229 ),
230 propagate_implications(TR,NLHS,NHyps3,NHyps4,Options).
231
232 unknown_source_term(b(unknown,pred,[trigger_implication])).
233
234 avl_store_with_commutes_if_new(NH,H,_,H2,_) :- avl_fetch(NH,H),!, H2=H.
235 avl_store_with_commutes_if_new(conjunct(NH1,NH2),H0,TE,H2,Options) :- !,
236 (TE=b(conjunct(TE1,TE2),_,_) -> true ; unknown_source_term(TE1), unknown_source_term(TE2)),
237 simplify_hyp(NH1,H0,SNH1),
238 avl_store_with_commutes_if_new(SNH1,H0,TE1,H1,Options),
239 simplify_hyp(NH2,H1,SNH2),
240 avl_store_with_commutes_if_new(SNH2,H1,TE2,H2,Options).
241 avl_store_with_commutes_if_new(NH,H0,RH,H3,Options) :- %write(prop_new(NH)),nl, avl_domain(H,H1D), write(H1D),nl,nl,
242 avl_store(NH,H0,RH,H1),
243 propagate_resolution_with_hyp(NH,H1,H2,Options),
244 push_commutative_hyps(NH,RH,Options,H2,H3).
245
246 :- use_module(probsrc(bsyntaxtree), [rename_bt/3]).
247 normalize_and_rename_predicate(_,H,_,_) :- var(H),!,
248 add_internal_error('Unbound predicate: ',normalize_and_rename_predicate(H)),fail.
249 normalize_and_rename_predicate([],H,RenH,NH) :- !, RenH=H,
250 normalize_predicate(H,NH).
251 normalize_and_rename_predicate(ClashRenaming,H,RenH,NH) :- !,
252 %format('Rename Hyp: ~w ',[ClashRenaming]),translate:print_bexpr(H),nl,
253 rename_bt(H,ClashRenaming,RenH),
254 %print(' > renamed Hyp: '),translate:print_bexpr(RenH),nl,
255 normalize_predicate(RenH,NH).
256
257 % :- use_module(probsrc(bsyntaxtree),[expand_all_lets/2]).
258 % TO DO: expand lets; but can be very expensive; e.g., B/Tickets/Schneider3_Trees/NewSolver_v2.mch -wd-check
259 normalize_predicate(Pred,NormPred) :-
260 b_interpreter_check:norm_pred_check(Pred,NP),
261 norm_aux(NP,NormPred).
262
263
264 % put identifiers first, so that we can more efficiently do lookups;
265 % hence we try and replace less/greater by less_equal/greater_equal when possible
266 norm_aux(equal(A,B),equal(NA,NB)) :- !, norm_equal(A,B,NA,NB).
267 norm_aux(greater(Val,Nr),greater_equal(Val,N1)) :- integer(Nr),!, N1 is Nr+1.
268 norm_aux(greater(Nr,Val),greater_equal(N1,Val)) :- integer(Nr),!, N1 is Nr-1.
269 norm_aux(greater(A,B),less(B,A)) :- !. % we only look up less (when both args are known)
270 norm_aux(less(Val,Nr),less_equal(Val,N1)) :- integer(Nr),!, N1 is Nr-1.
271 norm_aux(less(Nr,Val),less_equal(N1,Val)) :- integer(Nr),!, N1 is Nr+1.
272 norm_aux(not_equal(Val,EMPTY),not_equal(Val,empty_set)) :- is_empty_set_alternative(EMPTY),!.
273 norm_aux(not_equal(EMPTY,Val),not_equal(Val,empty_set)) :- is_empty_set_alternative(EMPTY),!.
274 norm_aux(negation(Pred),NormPred) :- negate_op(Pred,NP),!, norm_aux(NP,NormPred).
275 norm_aux(implication(Pred1,Pred2),NormPred) :- !,
276 norm_implication(Pred1,Pred2,NormPred).
277 norm_aux(disjunct(Pred1,Pred2),disjunct(NormPred1,NormPred2)) :- !,
278 norm_aux(Pred1,NormPred1),norm_aux(Pred2,NormPred2).
279 norm_aux(equivalence(Pred1,Pred2),equivalence(NormPred1,NormPred2)) :- !,
280 norm_aux(Pred1,NormPred1),norm_aux(Pred2,NormPred2).
281 %norm_aux(Term,NormPred) :- print(Term),nl,functor(Term,union,2),flatten(Term,union,List,[]), print(union(List)),nl,
282 % sort(List,SL),print(sorted(SL)),nl,fail.
283 norm_aux(V,V).
284 % TO DO: subset_strict -> subset and not_equal
285 % TO DO: normalize value(X) terms -> value(int(Nr)) -> Nr, ...
286 % TO DO: maybe process a few rules here x<: dom(f) or x = dom(f) - other
287
288 norm_equal(A,B,RA,RB) :- peel_eq(A,B,SA,SB),
289 (SB='$'(_), SA \= '$'(_) -> RA=SB,RB=SA ; RA=SA, RB=SB).
290
291 peel_eq(reverse(A),reverse(B),SA,SB) :- !, peel_eq(A,B,SA,SB).
292 % TODO: add other injective/reversible operators; also cf. simplify_hyp
293 peel_eq(A,B,A,B).
294
295 norm_implication(conjunct(A,B),Pred2,Implication) :- !,
296 % A & B => C ---> A => (B => C) (so that we can use avl_fetch on LHS of implication)
297 norm_implication(B,Pred2,Implication2),
298 norm_implication(A,Implication2,Implication).
299 norm_implication(Pred1,Pred2,implication(NormPred1,NormPred2)) :-
300 norm_aux(Pred1,NormPred1),norm_aux(Pred2,NormPred2).
301
302
303 % TO DO: flatten and sort union and possibly other operators:
304 %flatten(Term,BOP) --> {functor(Term,BOP,2), arg(1,Term,B1), arg(2,Term,B2)},!,
305 % flatten(B1,BOP), flatten(B2,BOP).
306 %flatten(Term,_) --> [Term].
307
308 is_empty_set_alternative(empty_sequence).
309 is_empty_set_alternative(value(V)) :- V==[]. % should now be handled in norm_expr / norm_value
310
311 negate_op(truth,falsity).
312 negate_op(falsity,truth).
313 negate_op(equal(A,B),not_equal(A,B)).
314 negate_op(not_equal(A,B),equal(A,B)).
315 negate_op(less(A,B),less_equal(B,A)).
316 negate_op(greater(A,B),less_equal(A,B)).
317 negate_op(less_equal(A,B),less(B,A)).
318 negate_op(greater_equal(A,B),less(A,B)).
319 negate_op(less_real(A,B),less_equal_real(B,A)).
320 negate_op(less_equal_real(A,B),less_real(B,A)).
321 negate_op(negation(P),P).
322 negate_op(not_member(A,B),member(A,B)).
323 negate_op(member(A,B),not_member(A,B)). % should we do this?
324 negate_op(not_subset(A,B),subset(A,B)).
325 negate_op(subset(A,B),not_subset(A,B)).
326 negate_op(not_subset_strict(A,B),subset_strict(A,B)).
327 negate_op(subset_strict(A,B),not_subset_strict(A,B)).
328 % should we negate_op(conjunct ...), we also treat negation in prove_po/prove_negated_po
329
330 % for commutative binary operators: also store commutative version to enable lookup on either argument
331 commute_bin_op(OpTerm,CommutativeOrDerivedVersion,_Options) :-
332 ? commute_bin_op(OpTerm,CommutativeOrDerivedVersion).
333 commute_bin_op(OpTerm,CommutativeOrDerivedVersion,Options) :-
334 safe_ord_member(push_more_hyps,Options),
335 ? commute_bin_op_aggressive(OpTerm,CommutativeOrDerivedVersion,Options).
336
337 ?commute_bin_op(equal(A,B),Pred) :- compute_bin_op_equal(A,B,Pred).
338 % not_equal: no need to reverse: we always know both values when doing a lookup
339 commute_bin_op(greater_equal(A,B),less_equal(B,A)) :- can_be_used_for_lookups(B).
340 commute_bin_op(greater(A,B),Pred) :- compute_bin_op_less(B,A,Pred).
341 ?commute_bin_op(less_equal(A,B),Pred) :- compute_bin_op_less_equal(A,B,Pred).
342 ?commute_bin_op(less(A,B),Pred) :- compute_bin_op_less(A,B,Pred).
343 commute_bin_op(less_real(A,B),not_equal(A,B)). % TO DO: extend
344 ?commute_bin_op(subset_strict(A,B),Pred) :- gen_subset(A,B,Pred).
345 commute_bin_op(subset_strict(A,B),not_equal(A,B)).
346 commute_bin_op(subset(A,B),superset(B,A)) :- % new operator, for efficient lookups !
347 can_be_used_for_lookups(B).
348 commute_bin_op(subset(A,cartesian_product(Dom,Ran)),member(A,relations(Dom,Ran))) :-
349 can_be_used_for_lookups(A).
350 commute_bin_op(subset_strict(A,cartesian_product(Dom,Ran)),member(A,relations(Dom,Ran))) :-
351 can_be_used_for_lookups(A).
352 commute_bin_op(not_subset(A,B),not_equal(A,B)). % also implies not_subset_strict
353 commute_bin_op(member(_,Set),not_equal(Set,empty_set)).
354 commute_bin_op(member(couple(A,B),C),NewHyp) :-
355 ( NewHyp = member(A,domain(C)) % A|->B : C ==> A : dom(C)
356 ; NewHyp = member(B,range(C)) ). % A|->B : C ==> B : ran(C)
357 commute_bin_op(member(X,interval(Low,Up)),NewHyp) :-
358 (NewHyp = less_equal(Low,Up) % x : Low..Up => Low <= Up
359 ; NewHyp = less_equal(Low,X) % Low <= X if X: Low..UP
360 ; can_be_used_for_lookups(X), NewHyp = greater_equal(X,Low)
361 ; NewHyp = less_equal(X,Up) % X <= UP if X: Low..UP
362 ; can_be_used_for_lookups(Up), NewHyp = greater_equal(Up,X)
363 ).
364 commute_bin_op(member(X,Rel),NewHyp) :- is_total_relation(Rel,Domain),
365 % we cannot efficiently lookup this info from Domain
366 can_be_used_for_lookups(Domain),
367 NewHyp = equal(Domain,domain(X)).
368 commute_bin_op(member(X,Rel),NewHyp) :- is_surjective_relation(Rel,Range),
369 % we cannot efficiently lookup this info from Range
370 can_be_used_for_lookups(Range),
371 NewHyp = equal(Range,range(X)).
372 commute_bin_op(member(card(X),_),NewHyp) :- can_be_used_for_lookups(X),
373 NewHyp=finite(X).
374 ?commute_bin_op(disjunct(LHS,RHS),NewHyp) :- get_member_pred(LHS,X,A), get_member_pred(RHS,X,B),
375 NewHyp = member(X,union(A,B)).
376 commute_bin_op(disjunct(LHS,RHS),NewHyp) :- get_subset_pred(LHS,X,A), get_subset_pred(RHS,X,B),
377 NewHyp = subset(X,union(A,B)).
378 commute_bin_op(partition(A,List),equal(A,UNION)) :- gen_union(List,UNION).
379 % TO DO: is there a use in the all_disjoint feature?
380 commute_bin_op(forall(['$'(X)],LHSPred,RHSPred), Pred) :-
381 get_member_lhs(LHSPred,'$'(X),Set),
382 ? get_member_rhs(RHSPred,'$'(X),SET2),
383 useful_forall_superset(SET2),
384 % !x.(x:SET => x:dom(F)) => SET <: dom(F)
385 % !x.(x:SET => x:SET2) => SET <: SET2
386 not_occurs(Set,X),
387 not_occurs(SET2,X), %print(subset1(Set,SET2)),nl,
388 ? gen_subset(Set,SET2,Pred).
389 commute_bin_op(forall(['$'(X),'$'(Y)],LHSPred,RHSPred), Pred) :- % TO DO: generalise
390 get_member_lhs(LHSPred,couple('$'(X),'$'(Y)),Set), %TO DO: generalise -> domain/range
391 get_member_rhs(RHSPred,'$'(X),SET2),
392 useful_forall_superset(SET2),
393 % !x,y.(x|->y:SET => x:dom(F)) => dom(SET) <: dom(F)
394 % !x,y.(x|->y:SET => x:SET2) => dom(SET) <: SET2
395 not_occurs(Set,X),
396 not_occurs(Set,Y),
397 not_occurs(SET2,X), %print(subset2(Set,SET2)),nl,
398 ? gen_subset(domain(Set),SET2,Pred).
399 commute_bin_op(equal(A,reverse(B)),equal(B,reverse(A))).
400 commute_bin_op(not_equal(A,B),equal(A,NB)) :- negate_boolean_like_value(B,NB).
401 commute_bin_op(not_equal(intersection(Set1,Set2),empty_set), Pred) :-
402 % Set /\ {a} /= {} => a : Set
403 (Set1=set_extension([A]),B=Set2 -> true ; Set2=set_extension([A]),B=Set1),
404 Pred = member(A,B).
405 %commute_bin_op(X,_) :- print(binop(X)),nl,fail.
406
407 % transform disjuncts/equivalences/... into implications that we propagate:
408 commute_bin_op_aggressive(disjunct(LHS,RHS),implication(NegLHS,RHS),Options) :-
409 negate_norm_op(LHS,NegLHS), useful_hyp_or_imp(RHS,Options).
410 commute_bin_op_aggressive(disjunct(RHS,LHS),implication(NegLHS,RHS),Options) :-
411 negate_norm_op(LHS,NegLHS), useful_hyp_or_imp(RHS,Options).
412 commute_bin_op_aggressive(implication(LHS,RHS),implication(NegRHS,NegLHS),_) :- % contra-positive implication
413 negate_norm_op(LHS,NegLHS),
414 negate_norm_op(RHS,NegRHS).
415 commute_bin_op_aggressive(equivalence(LHS,RHS),implication(LHS,RHS),Options) :-
416 useful_hyp_or_imp(RHS,Options).
417 commute_bin_op_aggressive(equivalence(RHS,LHS),implication(LHS,RHS),Options) :-
418 useful_hyp_or_imp(RHS,Options).
419
420 % extract a membership predicate
421 get_member_pred(member(X,A),X,A).
422 get_member_pred(equal(X,A),X,set_extension([A])).
423 get_member_pred(equal(A,X),X,set_extension([A])).
424 ?get_member_pred(disjunct(LHS,RHS),X,union(A,B)) :- get_member_pred(LHS,X,A), get_member_pred(RHS,X,B).
425 % TO DO: same for subset?
426 get_subset_pred(subset(X,A),X,A).
427 get_subset_pred(subset_strict(X,A),X,A).
428 %get_subset_pred(member(X,power_set(A)),X,A).
429 get_subset_pred(disjunct(LHS,RHS),X,union(A,B)) :- get_subset_pred(LHS,X,A), get_subset_pred(RHS,X,B).
430
431 % for which supersets is it useful to derive informations from forall quantifier:
432 useful_forall_superset(domain(_)).
433 useful_forall_superset(range(_)).
434 useful_forall_superset(finite(_)).
435 useful_forall_superset(seq(_)).
436 useful_forall_superset(seq1(_)).
437 useful_forall_superset(iseq(_)).
438 useful_forall_superset(iseq1(_)).
439 useful_forall_superset(perm(_)).
440 useful_forall_superset(partial_function(_,_)).
441 useful_forall_superset(total_function(_,_)).
442 useful_forall_superset(total_injection(_,_)).
443 useful_forall_superset(total_surjection(_,_)).
444 useful_forall_superset('$'(_)).
445 useful_forall_superset(pow1_subset(_)). % not empty
446 useful_forall_superset(fin1_subset(_)). % not empty and finite
447 useful_forall_superset(fin_subset(_)). % finite info
448 % TO DO: more
449
450 is_total_relation(total_function(A,_),A).
451 is_total_relation(total_injection(A,_),A).
452 is_total_relation(total_surjection(A,_),A).
453 is_total_relation(total_bijection(A,_),A).
454 is_total_relation(total_surjection_relation(A,_),A).
455
456
457 is_surjective_relation(partial_surjection(_,B),B).
458 is_surjective_relation(surjection_relation(_,B),B).
459 is_surjective_relation(total_surjection(_,B),B).
460 is_surjective_relation(total_bijection(_,B),B).
461 is_surjective_relation(total_surjection_relation(_,B),B).
462 is_surjective_relation(perm(B),B).
463
464 negate_boolean_like_value(boolean_true,boolean_false).
465 negate_boolean_like_value(boolean_false,boolean_true).
466 % TO DO: also treat enumerated sets with exactly two values
467
468 % must match completely
469 get_member_lhs(member(X,Set),X,Set).
470 get_member_lhs(truth,_,typeset).
471
472 % must be an conjunct in rhs
473 get_member_rhs(member(X,Set),X,Set).
474 ?get_member_rhs(conjunct(A,B),X,Set) :- get_member_rhs(A,X,Set) ; get_member_rhs(B,X,Set).
475 get_member_rhs(not_equal(empty_set,X),X,pow1_subset(typeset)).
476 get_member_rhs(not_equal(X,empty_set),X,pow1_subset(typeset)).
477 get_member_rhs(finite(X),X,fin_subset(typeset)).
478
479
480 compute_bin_op_less_equal(A,B,greater_equal(B,A)) :- can_be_used_for_lookups(B).
481 compute_bin_op_less_equal(card(X),_,finite(X)) :- can_be_used_for_lookups(X).
482
483 compute_bin_op_less(A,B,less_equal(A,B)).
484 compute_bin_op_less(A,B,greater_equal(B,A)) :- can_be_used_for_lookups(B). % we do not lookup greater
485 compute_bin_op_less(A,B,not_equal(A,B)). % for not_equal we only need to store one direction
486 compute_bin_op_less(card(X),_,finite(X)) :- can_be_used_for_lookups(X). % actually card(X)>1 also implies finite(X)
487
488 compute_bin_op_equal(A,B,equal(B,A)) :-
489 can_be_used_for_lookups(B).
490 compute_bin_op_equal(A,B,falsity) :- % sometimes we have FALSE=TRUE as an alternative to falsity
491 is_explicit_value(A,VA),
492 is_explicit_value(B,VB),
493 VA \= VB.
494 compute_bin_op_equal(Set,A,Pred) :-
495 % e.g., A = B \ C => A <: B, useful for examples/B/Alstom/etcs/actions_scn_f6_372_bis.mch
496 ? derive_superset(Set,B), B \= A,
497 gen_superset(B,A,Pred). % only generate superset rule; for subset there are rules to treat set_subtraction
498 compute_bin_op_equal(A,Set,Pred) :- % interchange args
499 ? derive_superset(Set,B), B \= A,
500 gen_superset(B,A,Pred).
501 compute_bin_op_equal(A,Set,subset(B,A)) :- % A = B \/ C => B <: A ; useful to allow lookups of B
502 ? derive_subset(Set,B),
503 can_be_used_for_lookups(B), B \= A.
504 compute_bin_op_equal(A,Add,Res) :- is_add_with_nr(Add,B,Nr),
505 % A = B+Nr => B < A
506 ? (Nr>0 -> compute_bin_op_less(B,A,Res)
507 ? ; Nr<0 -> compute_bin_op_less(A,B,Res)
508 ; Res = equal(A,B)).
509 compute_bin_op_equal(A,B,finite(X)) :-
510 (A=card(X);B=card(X)), can_be_used_for_lookups(X). % actually: if any sub-expression uses card(.) we could add it?
511
512 % cf is_explicit_value/3 in well_def_prover
513 % explicit value that can be compared using Prolog unification:
514 is_explicit_value(boolean_true,pred_true).
515 is_explicit_value(boolean_false,pred_false).
516 is_explicit_value(string(A),A).
517 is_explicit_value(Nr,Nr) :- number(Nr).
518
519 is_add_with_nr(add(A,B),X,Nr) :- (number(B) -> (X,Nr)=(A,B) ; number(A) -> (X,Nr)=(B,A)).
520 is_add_with_nr(minus(A,B),A,Nr) :- number(B), Nr is -B.
521
522 derive_superset(set_subtraction(B,_),B). % B \ C <: B
523 derive_superset(intersection(B,_),B). % B /\ C <: B
524 derive_superset(intersection(_,C),C). % B /\ C <: C
525
526 derive_subset(union(B,_),B). % B <: B \/ C
527 derive_subset(union(_,C),C). % C <: B /\ C
528
529 gen_subset(A,B,subset(A,B)) :- can_be_used_for_lookups(A).
530 gen_subset(A,B,superset(B,A)) :- can_be_used_for_lookups(B).
531
532 gen_superset(A,B,superset(A,B)) :- can_be_used_for_lookups(A).
533
534 gen_union([],emptyset).
535 gen_union([X],R) :- !, R=X.
536 gen_union([X|T],union(X,UT)) :- gen_union(T,UT).
537
538 % true if we are likely to need looking up these kinds of terms
539 can_be_used_for_lookups('$'(_)).
540 %can_be_used_for_lookups(Nr) :- number(Nr).
541 can_be_used_for_lookups(domain(_)). % lookup domain of a function
542 can_be_used_for_lookups(range(_)).
543 can_be_used_for_lookups(card(_)).
544 can_be_used_for_lookups(size(_)). % TO DO: normalize size to card, we assume hyps are WD; so no difference
545 can_be_used_for_lookups(interval(_,_)).
546 % ADD: records,...
547
548 useful_hyp(finite(_)).
549 %useful_hyp(partition(_,_)). % now rewritten
550 useful_hyp(member(_,_)).
551 useful_hyp(subset(_,_)).
552 useful_hyp(equal(_,_)).
553 useful_hyp(greater_equal(_,_)).
554 useful_hyp(less_equal(_,_)).
555 useful_hyp(less_equal_real(_,_)).
556 %useful_hyp(less(_,_)). % less is now no longer looked up; we look up not_equal
557 useful_hyp(not_equal(_,_)).
558 useful_hyp(not_member(_,_)). % used in check_not_member_of_set
559 %useful_hyp(equal(A,B)) :- check if A is ID which occurs in B; e.g, x = x*1 not useful
560
561 useful_implication(implication(_,RHS),Options) :-
562 useful_hyp_or_imp(RHS,Options).
563 useful_hyp_or_imp(RHS,Options) :-
564 (useful_hyp(RHS) -> true
565 ; useful_implication_body(RHS,Options)). % useful upon pushing hyps in propagate_resolution_with_hyp
566
567 % implication or similar which could be useful (i.e., triggered so that it produces a really useful hypothesis)
568 useful_implication_body(implication(_,RHS),Options) :-
569 useful_hyp_or_imp(RHS,Options).
570 useful_implication_body(equivalence(_,_),Options) :- safe_ord_member(push_more_hyps,Options).
571 useful_implication_body(disjunct(_,_),Options) :- safe_ord_member(push_more_hyps,Options).
572 useful_implication_body(conjunct(LHS,RHS),Options) :-
573 (useful_hyp_or_imp(LHS,Options) -> true ; useful_hyp_or_imp(RHS,Options)).
574
575 % check if we can simplify the hypothesis
576 simplify_hyp(implication(LHS,RHS),Hyps,Res) :- % true => RHS --> RHS
577 %write(check_imp_lhs_hyp(LHS)),nl, avl_domain(Hyps,D), write(dom(D)),nl,
578 avl_fetch(LHS,Hyps),!, % LHS is in the hyps
579 %write(simplify_imp(LHS,RHS)),nl,
580 simplify_hyp(RHS,Hyps,Res).
581 % TODO: disjunction, ...
582 simplify_hyp(Hyp,_,Hyp).
583
584
585 % a few more binary operations that are potentially useful for :prove, particularly if negation in goal
586 potentially_useful_for_hyp_rule(less(_,_)).
587 potentially_useful_for_hyp_rule(less_real(_,_)).
588 potentially_useful_for_hyp_rule(not_subset(_,_)).
589 potentially_useful_for_hyp_rule(not_subset_strict(_,_)).
590 potentially_useful_for_hyp_rule(subset_strict(_,_)).
591 potentially_useful_for_hyp_rule(partition(_,_)).
592
593 get_clash_renaming_subst(hyp_rec(_,HInfos),ClashRenaming) :- !,
594 get_clash_renaming(HInfos,ClashRenaming).
595 get_clash_renaming_subst(H,R) :- add_internal_error('Illegal hyps:',get_clash_renaming_subst(H,R)),fail.
596
597 % rename an expression or predicate given the current variable clashes
598 get_renamed_expression(Expr,Hyps,RenExpr) :-
599 get_clash_renaming_subst(Hyps,ClashRenaming),
600 rename_bt(Expr,ClashRenaming,RenExpr).
601
602 get_normalized_and_renamed_predicate(Pred,Hyps,RenPred,NormPred) :-
603 get_clash_renaming_subst(Hyps,ClashRenaming),
604 normalize_and_rename_predicate(ClashRenaming,Pred,RenPred,NormPred).
605
606 :- use_module(library(lists),[maplist/3]).
607 % add new quantified $ untyped variables to the hyp stack
608 create_any_type($(ID),b(identifier(ID),any,[])).
609 add_new_hyp_any_vars(H,DollarIDs,H2) :-
610 maplist(create_any_type,DollarIDs,TVars),!,
611 add_new_hyp_variables(H,TVars,H2).
612 add_new_hyp_any_vars(H,I,H2) :- add_internal_error('Illegal Ids:',add_new_hyp_any_vars(H,I,H)),
613 H2=H.
614
615 % add new quantified typed variables to the hyp stack
616 add_new_hyp_variables(H,[],R) :- !, R=H.
617 add_new_hyp_variables(hyp_rec(NH,HInfos1),NewAddedTVars,hyp_rec(NH,HInfos3)) :-
618 fetch_hyp_typed_vars(HInfos1,TVars),
619 list_to_ord_set(NewAddedTVars,SortedNewTVars),
620 add_new_hyp_vars(SortedNewTVars,TVars,NewTVars2,ClashTVars),
621 (ClashTVars=[] -> HInfos2=HInfos1, NewTVars3=NewTVars2
622 ; (debug_mode(off) -> true
623 ; add_message(well_def_analyser,'Variable clash, will rename future predicates: ', ClashTVars,ClashTVars)
624 ),
625 avl_fetch(hyp_clash_vars,HInfos1,clash_rec(GenSymCount,OldClashAVL)),
626 ren_clash_variables(ClashTVars,RenClashTVars,GenSymCount,NewGSC,OldClashAVL,NewClashAVL),
627 avl_store(hyp_clash_vars,HInfos1,clash_rec(NewGSC,NewClashAVL),HInfos2),
628 list_to_ord_set(RenClashTVars,SRenClashTVars),
629 ord_union(SRenClashTVars,NewTVars2,NewTVars3)
630 ),
631 avl_store(hyp_typed_vars,HInfos2,NewTVars3,HInfos3).
632
633 % add_new_typed_vars(AddedTVars,OldTVars,NewTVars,ClashVars)
634 add_new_hyp_vars([],TVars,NewTVars,[]) :- !, NewTVars=TVars.
635 add_new_hyp_vars(AddedTVars,[],NewTVars,[]) :- !,NewTVars=AddedTVars.
636 add_new_hyp_vars([b(identifier(ID1),Type1,I1)|T1],[b(identifier(ID2),Type2,I2)|T2],NewTVars,Clash) :- !,
637 (ID1 @> ID2
638 -> NewTVars = [b(identifier(ID2),Type2,I2)|NewT],
639 add_new_hyp_vars([b(identifier(ID1),Type1,I1)|T1],T2,NewT,Clash)
640 ; ID1 @< ID2
641 -> NewTVars = [b(identifier(ID1),Type1,I1)|NewT],
642 add_new_hyp_vars(T1,[b(identifier(ID2),Type2,I2)|T2],NewT,Clash)
643 ; NewTVars = [b(identifier(ID2),Type2,I2)|NewT],
644 Clash = [b(identifier(ID1),Type1,I1)|NewClash],
645 add_new_hyp_vars(T1,T2,NewT,NewClash)
646 ).
647 add_new_hyp_vars(T1,T2,_,_) :- add_internal_error('Illegal call: ',add_new_hyp_vars(T1,T2,_,_)),fail.
648
649 % add clash ids and their renaming to the clash AVL
650 ren_clash_variables([],[],C,C,Avl,Avl).
651 ren_clash_variables([b(identifier(ID1),Type1,I1)|T1],
652 [b(identifier(RenamedID),Type1,[was(ID1)|I1])|T2], Cin,Cout,AvlIn,AvlOut) :-
653 number_codes(Cin,NC), atom_codes(Ain,NC),
654 atom_concat('$wd_rename_',Ain,RenamedID), % print(rename(ID,RenamedID)),nl,
655 C1 is Cin+1,
656 avl_store(ID1,AvlIn,RenamedID,Avl2),
657 ren_clash_variables(T1,T2,C1,Cout,Avl2,AvlOut).
658
659 % make a fresh copy of existing variables (the variables are not typed but atomic ids)
660 copy_hyp_variables(hyp_rec(NH,HInfos1),ExistingVars,Hyp2) :-
661 fetch_hyp_typed_vars(HInfos1,TVars),
662 list_to_ord_set(ExistingVars,SortedIds),
663 get_existing_tids(SortedIds,TVars,ResTVars),
664 add_new_hyp_variables(hyp_rec(NH,HInfos1),ResTVars,Hyp2).
665
666 get_existing_tids([],_,[]).
667 get_existing_tids([ID|TI],TIDs,Res) :- get_aux(TIDs,ID,TI,Res).
668 :- use_module(probsrc(bsyntaxtree), [get_texpr_id/2]).
669 get_aux([],ID,_,Res) :- add_internal_error('Cannot find existing hyp variable:',ID), Res=[].
670 get_aux([TID|TT],ID,TI,Res) :-
671 (get_texpr_id(TID,ID) -> Res=[TID|ResT], get_existing_tids(TI,TT,ResT)
672 ; get_aux(TT,ID,TI,Res)
673 ).
674
675
676 % similar to create_negation in bsyntaxtree but more rules adapted for hypotheses and WD prover
677
678 :- use_module(probsrc(bsyntaxtree),[extract_info/2]).
679 negate_hyp(b(P,pred,I),Res) :- create_negation_aux(P,I,R),!,Res=R.
680 negate_hyp(Pred,b(negation(Pred),pred,Infos)) :-
681 extract_info(Pred,Infos).
682
683 create_negation_aux(truth,I,R) :- !, R=b(falsity,pred,I).
684 create_negation_aux(falsity,I,R) :- !, R=b(truth,pred,I).
685 create_negation_aux(disjunct(A,B),I,R) :- !,
686 negate_hyp(A,NA), negate_hyp(B,NB), R = b(conjunct(NA,NB),pred,I).
687 create_negation_aux(implication(A,B),I,R) :- !, % not(A=>B) <===> A & not(B)
688 negate_hyp(B,NB), R = b(conjunct(A,NB),pred,I).
689 create_negation_aux(negation(Pred),_,R) :- !, R=Pred.
690 create_negation_aux(BOP,I,R) :- negate_op_aux(BOP,NBOP), R=b(NBOP,pred,I).
691 % no rule for conjunct(A,B)
692
693 % TODO: should we use negate_op ??
694 negate_op_aux(equal(A,B),not_equal(A,B)).
695 negate_op_aux(not_equal(A,B),equal(A,B)).
696 negate_op_aux(less(A,B),greater_equal(A,B)).
697 negate_op_aux(less_equal(A,B),greater(A,B)).
698 negate_op_aux(greater(A,B),less_equal(A,B)).
699 negate_op_aux(greater_equal(A,B),less(A,B)).
700
701 % --------------------
702
703 :- use_module(probsrc(preferences), [get_preference/2]).
704 :- use_module(probsrc(typing_tools),[is_finite_type_in_context/2]).
705 is_finite_type_for_wd(Type,_) :-
706 get_preference(wd_analysis_for_animation,true),!,
707 is_finite_type_in_context(animation,Type).
708 is_finite_type_for_wd(Type,_Hyps) :-
709 is_finite_type_in_context(proving,Type).
710
711
712 % -------------------
713
714 % convert a normalized expression to a raw expression (e.g., for pretty printing translate:print_raw_bexpr
715 % or translate:transform_raw)
716
717 convert_norm_expr_to_raw('$'(ID),Res) :- !, Res=identifier(unknown,ID).
718 convert_norm_expr_to_raw(Int,Res) :- integer(Int),!,Res=integer(unknown,Int).
719 convert_norm_expr_to_raw(Nr,Res) :- float(Nr),!,Res=real(unknown,Nr).
720 convert_norm_expr_to_raw(set_extension(List),Res) :- !,
721 Res = set_extension(unknown,RList),
722 l_convert_norm(List,RList).
723 convert_norm_expr_to_raw(sequence_extension(List),Res) :- !,
724 Res = sequence_extension(unknown,RList),
725 l_convert_norm(List,RList).
726 convert_norm_expr_to_raw(forall(List,LHS,RHS),Res) :- !,
727 Res = forall(unknown,RList,RLHS,RRHS),
728 l_convert_norm(List,RList),
729 convert_norm_expr_to_raw(LHS,RLHS),
730 convert_norm_expr_to_raw(RHS,RRHS).
731 convert_norm_expr_to_raw(exists(List,Pred),Res) :- !,
732 Res = exists(unknown,RList,RPred),
733 l_convert_norm(List,RList),
734 convert_norm_expr_to_raw(Pred,RPred).
735 convert_norm_expr_to_raw(function(Functor,List),Res) :- !,
736 Res = function(unknown,RFunctor,RList),
737 l_convert_norm(List,RList),
738 convert_norm_expr_to_raw(Functor,RFunctor).
739 % TODO: more special cases where generic code below does not work:
740 convert_norm_expr_to_raw(Term,Res) :- Term =.. [Functor|Args],
741 l_convert_norm(Args,RawArgs),
742 Res =.. [Functor,unknown|RawArgs].
743
744 l_convert_norm([],[]).
745 l_convert_norm([H|T],[RH|RT]) :- convert_norm_expr_to_raw(H,RH), l_convert_norm(T,RT).
746
747 :- use_module(probsrc(translate),[translate_raw_bexpr_with_limit/3]).
748 translate_norm_expr_with_limit(NormExpr,Limit,Str) :-
749 (convert_norm_expr_to_raw(NormExpr,RawExpr)
750 -> translate_raw_bexpr_with_limit(RawExpr,Limit,Str)
751 ; add_error(translate_norm_expr,'Cannot translate norm expression:',NormExpr),
752 Str = '???'
753 ).