1 (* Copyright (C) 2019, HELM Team.
3 * This file is part of HELM, an Hypertextual, Electronic
4 * Library of Mathematics, developed at the Computer Science
5 * Department, University of Bologna, Italy.
7 * HELM is free software; you can redistribute it and/or
8 * modify it under the terms of the GNU General Public License
9 * as published by the Free Software Foundation; either version 2
10 * of the License, or (at your option) any later version.
12 * HELM is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 * GNU General Public License for more details.
17 * You should have received a copy of the GNU General Public License
18 * along with HELM; if not, write to the Free Software
19 * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
22 * For details, see the HELM World-Wide-Web page,
23 * http://cs.unibo.it/helm/.
26 open Continuationals.Stack
27 module Ast = NotationPt
31 type just = [ `Term of NTacStatus.tactic_term | `Auto of NnAuto.auto_params ]
33 let mk_just status goal =
35 `Auto (l,params) -> NnAuto.auto_lowtac ~params:(l,params) status goal
36 | `Term t -> apply_tac t
39 exception FirstTypeWrong
40 exception NotEquivalentTypes
42 let extract_first_goal_from_status status =
43 let s = status#stack in
45 | [] -> fail (lazy "There's nothing to prove")
46 | (g1, _, k, tag1, _) :: tl ->
47 let goals = filter_open g1 in
49 [] -> fail (lazy "No goals under focus")
51 let goal = goal_of_loc (loc) in
54 let extract_conclusion_type status goal =
55 let gty = get_goalty status goal in
56 let ctx = ctx_of gty in
57 let status,gty = term_of_cic_term status gty ctx in
61 let alpha_eq_tacterm_kerterm ty t status goal =
62 let gty = get_goalty status goal in
63 let ctx = ctx_of gty in
64 let status,cicterm = disambiguate status ctx ty `XTNone (*(`XTSome (mk_cic_term ctx t))*) in
65 let (_,_,metasenv,subst,_) = status#obj in
66 let status,ty = term_of_cic_term status cicterm ctx in
67 if NCicReduction.alpha_eq status metasenv subst ctx t ty then
73 let are_convertible ty1 ty2 status goal =
74 let gty = get_goalty status goal in
75 let ctx = ctx_of gty in
76 let status,cicterm1 = disambiguate status ctx ty1 `XTNone in
77 let status,cicterm2 = disambiguate status ctx ty2 `XTNone in
78 NTacStatus.are_convertible status ctx cicterm1 cicterm2
80 let clear_volatile_params_tac status =
81 match status#stack with
82 [] -> fail (lazy "Empty stack")
83 | (g,t,k,tag,p)::tl ->
84 let rec remove_volatile = function
86 | (k,v as hd')::tl' ->
87 let re = Str.regexp "volatile_.*" in
88 if Str.string_match re k 0 then
91 hd'::(remove_volatile tl')
93 let newp = remove_volatile p in
94 status#set_stack ((g,t,k,tag,newp)::tl)
97 let add_parameter_tac key value status =
98 match status#stack with
100 | (g,t,k,tag,p) :: tl -> status#set_stack ((g,t,k,tag,(key,value)::p)::tl)
104 (* LCF-like tactic that checks whether the conclusion of the sequent of the given goal is a product, checks that
105 the type of the conclusion's bound variable is the same as t1 and then uses an exact_tac with
106 \lambda id: t1. ?. If a t2 is given it checks that t1 ~_{\beta} t2 and uses and exact_tac with \lambda id: t2. ?
108 let lambda_abstract_tac id t1 status goal =
109 match extract_conclusion_type status goal with
110 | NCic.Prod (_,t,_) ->
111 if alpha_eq_tacterm_kerterm t1 t status goal then
113 block_tac [exact_tac ("",0,(Ast.Binder (`Lambda,(Ast.Ident (id,None),Some t1),Ast.Implicit
114 `JustOne))); clear_volatile_params_tac;
115 add_parameter_tac "volatile_newhypo" id] status
118 | _ -> raise NotAProduct
120 let assume name ty status =
121 let goal = extract_first_goal_from_status status in
122 try lambda_abstract_tac name ty status goal
124 | NotAProduct -> fail (lazy "You can't assume without an universal quantification")
125 | FirstTypeWrong -> fail (lazy "The assumed type is wrong")
126 | NotEquivalentTypes -> fail (lazy "The two given types are not equivalent")
129 let suppose t1 id status =
130 let goal = extract_first_goal_from_status status in
131 try lambda_abstract_tac id t1 status goal
133 | NotAProduct -> fail (lazy "You can't suppose without a logical implication")
134 | FirstTypeWrong -> fail (lazy "The supposed proposition is different from the premise")
135 | NotEquivalentTypes -> fail (lazy "The two given propositions are not equivalent")
138 let assert_tac t1 t2 status goal continuation =
139 let t = extract_conclusion_type status goal in
140 if alpha_eq_tacterm_kerterm t1 t status goal then
142 | None -> continuation
144 let status,res = are_convertible t1 t2 status goal in
145 if res then continuation
147 raise NotEquivalentTypes
151 let branch_dot_tac status =
152 match status#stack with
153 ([],t,k,tag,p) :: tl ->
154 if List.length t > 0 then
155 status#set_stack (([List.hd t],List.tl t,k,tag,p)::tl)
161 let status_parameter key status =
162 match status#stack with
164 | (g,t,k,tag,p)::_ -> try List.assoc key p with _ -> ""
167 let beta_rewriting_step t status =
168 let ctx = status_parameter "volatile_context" status in
169 if ctx <> "beta_rewrite" then
171 let newhypo = status_parameter "volatile_newhypo" status in
173 fail (lazy "Invalid use of 'or equivalently'")
175 change_tac ~where:("",0,(None,[newhypo,Ast.UserInput],None)) ~with_what:t status
178 change_tac ~where:("",0,(None,[],Some
179 Ast.UserInput)) ~with_what:t status
182 let done_continuation status =
183 let rec continuation l =
186 | (_,t,_,tag,p)::tl ->
187 if tag = `BranchTag then
188 if List.length t > 0 then
191 try List.assoc "context" p
194 ctx <> "induction" && ctx <> "cases"
196 if continue then [clear_volatile_params_tac;branch_dot_tac] else
197 [clear_volatile_params_tac]
199 [merge_tac] @ (continuation tl)
203 continuation status#stack
206 let bydone just status =
207 let goal = extract_first_goal_from_status status in
208 let continuation = done_continuation status in
209 let l = [mk_just status goal just] @ continuation in
213 let push_goals_tac status =
214 match status#stack with
215 [] -> fail (lazy "Error pushing goals")
216 | (g1,t1,k1,tag1,p1) :: (g2,t2,k2,tag2,p2) :: tl ->
217 if List.length g2 > 0 then
218 status#set_stack ((g1,t1 @+ g2,k1,tag1,p1) :: ([],t2,k2,tag2,p2) :: tl)
219 else status (* Nothing to push *)
222 let we_need_to_prove t id status =
223 let goal = extract_first_goal_from_status status in
227 try assert_tac t None status goal (add_parameter_tac "volatile_context" "beta_rewrite" status)
229 | FirstTypeWrong -> fail (lazy "The given proposition is not the same as the conclusion")
233 block_tac [clear_volatile_params_tac; cut_tac t; branch_tac; shift_tac; intro_tac id; merge_tac; branch_tac;
234 push_goals_tac; add_parameter_tac "volatile_context" "beta_rewrite"
239 let by_just_we_proved just ty id status =
240 let goal = extract_first_goal_from_status status in
241 let wrappedjust = just in
242 let just = mk_just status goal just in
245 assert_tac ty None status goal (block_tac [clear_volatile_params_tac; add_parameter_tac
246 "volatile_context" "beta_rewrite"] status)
249 block_tac [cut_tac ty; branch_tac; just; shift_tac; intro_tac id; merge_tac;
250 clear_volatile_params_tac; add_parameter_tac "volatile_newhypo" id] status
254 let existselim just id1 t1 t2 id2 status =
255 let goal = extract_first_goal_from_status status in
258 let just = mk_just status goal just in
260 cut_tac ("",0,(Ast.Appl [Ast.Ident ("ex",None); t1; Ast.Binder (`Lambda,(Ast.Ident
261 (id1,None), Some t1),t2)]));
262 branch_tac ~force:false;
266 intros_tac ~names_ref:(ref []) [id1;id2];
268 clear_volatile_params_tac
272 let andelim just t1 id1 t2 id2 status =
273 let goal = extract_first_goal_from_status status in
276 let just = mk_just status goal just in
278 cut_tac ("",0,(Ast.Appl [Ast.Ident ("And",None); t1 ; t2]));
279 branch_tac ~force:false;
283 intros_tac ~names_ref:(ref []) [id1;id2];
285 clear_volatile_params_tac
289 let type_of_tactic_term status ctx t =
290 let status,cicterm = disambiguate status ctx t `XTNone in
291 let (_,cicty) = typeof status ctx cicterm in
294 let swap_first_two_goals_tac status =
296 match status#stack with
298 | (g,t,k,tag,p) :: s ->
300 | (loc1) :: (loc2) :: tl ->
301 ([loc2;loc1] @+ tl,t,k,tag,p) :: s
304 status#set_stack gstatus
306 let thesisbecomes t1 = we_need_to_prove t1 None
309 let obtain id t1 status =
310 let goal = extract_first_goal_from_status status in
311 let cicgty = get_goalty status goal in
312 let ctx = ctx_of cicgty in
313 let cicty = type_of_tactic_term status ctx t1 in
314 let _,ty = term_of_cic_term status cicty ctx in
316 block_tac [ cut_tac ("",0,(Ast.Appl [Ast.Ident ("eq",None); Ast.NCic ty; t1; Ast.Implicit
318 swap_first_two_goals_tac;
319 branch_tac; shift_tac; shift_tac; intro_tac id; merge_tac; branch_tac; push_goals_tac;
320 add_parameter_tac "volatile_context" "rewrite"
325 let conclude t1 status =
326 let goal = extract_first_goal_from_status status in
327 let cicgty = get_goalty status goal in
328 let ctx = ctx_of cicgty in
329 let _,gty = term_of_cic_term status cicgty ctx in
331 (* The first term of this Appl should probably be "eq" *)
332 NCic.Appl [_;_;plhs;_] ->
333 if alpha_eq_tacterm_kerterm t1 plhs status goal then
334 add_parameter_tac "volatile_context" "rewrite" status
336 fail (lazy "The given conclusion is different from the left-hand side of the current conclusion")
337 | _ -> fail (lazy "Your conclusion needs to be an equality")
340 let rewritingstep rhs just last_step status =
341 let ctx = status_parameter "volatile_context" status in
342 if ctx = "rewrite" then
344 let goal = extract_first_goal_from_status status in
345 let cicgty = get_goalty status goal in
346 let ctx = ctx_of cicgty in
347 let _,gty = term_of_cic_term status cicgty ctx in
348 let cicty = type_of_tactic_term status ctx rhs in
349 let _,ty = term_of_cic_term status cicty ctx in
350 let just' = (* Extraction of the ""justification"" from the ad hoc justification *)
352 `Auto (univ, params) ->
354 if not (List.mem_assoc "timeout" params) then
355 ("timeout","3")::params
359 if not (List.mem_assoc "paramodulation" params) then
360 ("paramodulation","1")::params
363 if params = params' then NnAuto.auto_lowtac ~params:(univ, params) status goal
365 first_tac [NnAuto.auto_lowtac ~params:(univ, params) status goal; NnAuto.auto_lowtac
366 ~params:(univ, params') status goal]
367 | `Term just -> apply_tac just
368 | `SolveWith term -> NnAuto.demod_tac ~params:(Some [term], ["all","1";"steps","1"; "use_ctx","false"])
371 let plhs,prhs,prepare =
372 match gty with (* Extracting the lhs and rhs of the previous equality *)
373 NCic.Appl [_;_;plhs;prhs] -> plhs,prhs,(fun continuation -> continuation status)
374 | _ -> fail (lazy "You are not building an equaility chain")
378 let todo = [just'] @ (done_continuation status) in
381 let (_,_,rhs) = rhs in
382 block_tac [apply_tac ("",0,Ast.Appl [Ast.Ident ("trans_eq",None); Ast.NCic ty; Ast.NCic plhs;
383 rhs; Ast.NCic prhs]); branch_tac; just'; merge_tac]
388 fail (lazy "You are not building an equality chain")
391 let rec pp_metasenv_names (metasenv:NCic.metasenv) =
396 let meta_attrs,_,_ = conj in
397 let rec find_name_aux meta_attrs = match meta_attrs with
399 | hd :: tl -> match hd with
401 | _ -> find_name_aux tl
403 let name = find_name_aux meta_attrs
405 "[Goal: " ^ (string_of_int n) ^ ", Name: " ^ name ^ "]; " ^ (pp_metasenv_names tl)
408 let print_goals_names_tac s (status:#NTacStatus.tac_status) =
409 let (_,_,metasenv,_,_) = status#obj in
410 prerr_endline (s ^" -> Metasenv: " ^ (pp_metasenv_names metasenv)); status
412 (* Useful as it does not change the order in the list *)
413 let rec list_change_assoc k v = function
415 | (k',v' as hd) :: tl -> if k' = k then (k',v) :: tl else hd :: (list_change_assoc k v tl)
418 let add_names_to_goals_tac (cl:NCic.constructor list ref) (status:#NTacStatus.tac_status) =
419 let add_name_to_goal name goal metasenv =
420 let (mattrs,ctx,t as conj) = try List.assoc goal metasenv with _ -> assert false in
421 let mattrs = (`Name name) :: (List.filter (function `Name _ -> false | _ -> true) mattrs) in
422 let newconj = (mattrs,ctx,t) in
423 list_change_assoc goal newconj metasenv
426 (* It's important that this tactic is called before branching and right after the creation of
427 * the new goals, when they are still under focus *)
428 match status#stack with
429 [] -> fail (lazy "Can not add names to an empty stack")
430 | (g,_,_,_,_) :: tl ->
431 let rec sublist n = function
433 | hd :: tl -> if n = 0 then [] else hd :: (sublist (n-1) tl)
435 List.map (fun _,sw -> goal_of_switch sw) (sublist (List.length !cl) g)
437 let rec add_names_to_goals g cl metasenv =
440 | hd::tl, (_,consname,_)::tl' ->
441 add_names_to_goals tl tl' (add_name_to_goal consname hd metasenv)
442 | _,_ -> fail (lazy "There are less goals than constructors")
444 let (olduri,oldint,metasenv,oldsubst,oldkind) = status#obj in
445 let newmetasenv = add_names_to_goals new_goals !cl metasenv
446 in status#set_obj(olduri,oldint,newmetasenv,oldsubst,oldkind)
449 let (olduri,oldint,metasenv,oldsubst,oldkind) = status#obj in
450 let remove_name_from_metaattrs =
451 List.filter (function `Name _ -> false | _ -> true) in
452 let rec add_names_to_metasenv cl metasenv =
453 match cl,metasenv with
455 | hd :: tl, mhd :: mtl ->
456 let _,consname,_ = hd in
457 let gnum,conj = mhd in
458 let mattrs,ctx,t = conj in
459 let mattrs = [`Name consname] @ (remove_name_from_metaattrs mattrs)
461 let newconj = mattrs,ctx,t in
462 let newmeta = gnum,newconj in
463 newmeta :: (add_names_to_metasenv tl mtl)
464 | _,[] -> assert false
466 let newmetasenv = add_names_to_metasenv !cl metasenv in
467 status#set_obj (olduri,oldint,newmetasenv,oldsubst,oldkind)
470 let unfocus_branch_tac status =
471 match status#stack with
473 | (g,t,k,tag,p) :: tl -> status#set_stack (([],g @+ t,k,tag,p)::tl)
476 let we_proceed_by_induction_on t1 t2 status =
477 let goal = extract_first_goal_from_status status in
478 let txt,len,t1 = t1 in
479 let t1 = txt, len, Ast.Appl [t1; Ast.Implicit `Vector] in
480 let indtyinfo = ref None in
481 let sort = ref (NCic.Rel 1) in
482 let cl = ref [] in (* this is a ref on purpose, as the block of code after sort_of_goal_tac in
483 block_tac acts as a block of asynchronous code, in which cl gets modified with the info retrieved
484 with analize_indty_tac, and later used to label each new goal with a costructor name. Using a
485 plain list this doesn't seem to work, as add_names_to_goals_tac would immediately act on an empty
486 list, instead of acting on the list of constructors *)
488 assert_tac t2 None status goal (block_tac [
489 analyze_indty_tac ~what:t1 indtyinfo;
490 sort_of_goal_tac sort;
492 let ity = HExtlib.unopt !indtyinfo in
493 let NReference.Ref (uri, _) = ref_of_indtyinfo ity in
495 NUri.name_of_uri uri ^ "_" ^
496 snd (NCicElim.ast_of_sort
497 (match !sort with NCic.Sort x -> x | _ -> assert false))
500 let l = [Ast.Ident (name,None)] in
501 (* Generating an implicit for each argument of the inductive type, plus one the
502 * predicate, plus an implicit for each constructor of the inductive type *)
503 let l = l @ HExtlib.mk_list (Ast.Implicit `JustOne) (ity.leftno+1+ity.consno) in
509 exact_tac ("",0,eliminator) status);
510 add_names_to_goals_tac cl;
514 add_parameter_tac "context" "induction"
517 | FirstTypeWrong -> fail (lazy "What you want to prove is different from the conclusion")
520 let we_proceed_by_cases_on ((txt,len,ast1) as t1) t2 status =
521 let goal = extract_first_goal_from_status status in
522 let npt1 = txt, len, Ast.Appl [ast1; Ast.Implicit `Vector] in
523 let indtyinfo = ref None in
526 assert_tac t2 None status goal (block_tac [
527 analyze_indty_tac ~what:npt1 indtyinfo;
528 cases_tac ~what:t1 ~where:("",0,(None,[],Some
532 let ity = HExtlib.unopt !indtyinfo in
533 cl := ity.cl; add_names_to_goals_tac cl status
535 branch_tac; push_goals_tac;
537 add_parameter_tac "context" "cases"
540 | FirstTypeWrong -> fail (lazy "What you want to prove is different from the conclusion")
543 let byinduction t1 id = suppose t1 id ;;
545 let name_of_conj conj =
546 let mattrs,_,_ = conj in
547 let rec search_name mattrs =
553 | _ -> search_name tl
557 let rec loc_of_goal goal l =
559 [] -> fail (lazy "Reached the end")
562 let g = goal_of_switch sw in
564 else loc_of_goal goal tl
567 let has_focused_goal status =
568 match status#stack with
570 | ([],_,_,_,_) :: tl -> false
574 let focus_on_case_tac case status =
575 let (_,_,metasenv,_,_) = status#obj in
576 let rec goal_of_case case metasenv =
578 [] -> fail (lazy "The given case does not exist")
579 | (goal,conj) :: tl ->
580 if name_of_conj conj = case then goal
581 else goal_of_case case tl
583 let goal_to_focus = goal_of_case case metasenv in
585 match status#stack with
586 [] -> fail (lazy "There is nothing to prove")
587 | (g,t,k,tag,p) :: s ->
590 loc_of_goal goal_to_focus t
591 with _ -> fail (lazy "The given case is not part of the current induction/cases analysis
594 let curloc = if has_focused_goal status then
595 let goal = extract_first_goal_from_status status in
599 (((g @- curloc) @+ [loc]),(curloc @+ (t @- [loc])),k,tag,p) :: s
601 status#set_stack gstatus
604 let case id l status =
605 let ctx = status_parameter "context" status in
606 if ctx <> "induction" && ctx <> "cases" then fail (lazy "You can't use case outside of an
607 induction/cases analysis context")
610 if has_focused_goal status then fail (lazy "Finish the current case before switching")
614 let goal = extract_first_goal_from_status status in
615 let (_,_,metasenv,_,_) = status#obj in
616 let conj = NCicUtils.lookup_meta goal metasenv in
617 let name = name_of_conj conj in
624 (try_tac (assume id ("",0,ty))) :: (aux tl)
628 (* if name = id then block_tac continuation status *)
630 block_tac ([focus_on_case_tac id] @ continuation) status
635 let print_stack status = prerr_endline ("PRINT STACK: " ^ (pp status#stack)); id_tac status ;;
637 (* vim: ts=2: sw=0: et: