X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=components%2Ftactics%2FdestructTactic.ml;fp=components%2Ftactics%2FdestructTactic.ml;h=a8bfc007d42ac395c2c5995686bc6cbc181daf33;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/components/tactics/destructTactic.ml b/components/tactics/destructTactic.ml new file mode 100644 index 000000000..a8bfc007d --- /dev/null +++ b/components/tactics/destructTactic.ml @@ -0,0 +1,592 @@ +(* Copyright (C) 2002, HELM Team. + * + * This file is part of HELM, an Hypertextual, Electronic + * Library of Mathematics, developed at the Computer Science + * Department, University of Bologna, Italy. + * + * HELM is free software; you can redistribute it and/or + * modify it under the terms of the GNU General Public License + * as published by the Free Software Foundation; either version 2 + * of the License, or (at your option) any later version. + * + * HELM is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with HELM; if not, write to the Free Software + * Foundation, Inc., 59 Temple Place - Suite 330, Boston, + * MA 02111-1307, USA. + * + * For details, see the HELM World-Wide-Web page, + * http://cs.unibo.it/helm/. + *) + +(* $Id$ *) + +module C = Cic +module U = UriManager +module P = PrimitiveTactics +module T = Tacticals +module CR = CicReduction +module PST = ProofEngineStructuralRules +module PET = ProofEngineTypes +module CTC = CicTypeChecker +module CU = CicUniv +module S = CicSubstitution +module RT = ReductionTactics +module PEH = ProofEngineHelpers +module ET = EqualityTactics +module DTI = DoubleTypeInference + +let debug = false +let debug_print = + if debug then (fun x -> prerr_endline (Lazy.force x)) else (fun _ -> ()) + +(* term ha tipo t1=t2; funziona solo se t1 e t2 hanno in testa costruttori +diversi *) + +let discriminate_tac ~term = + let true_URI = + match LibraryObjects.true_URI () with + Some uri -> uri + | None -> raise (PET.Fail (lazy "You need to register the default \"true\" definition first. Please use the \"default\" command")) in + let false_URI = + match LibraryObjects.false_URI () with + Some uri -> uri + | None -> raise (PET.Fail (lazy "You need to register the default \"false\" definition first. Please use the \"default\" command")) in + let fail msg = raise (PET.Fail (lazy ("Discriminate: " ^ msg))) in + let find_discriminating_consno t1 t2 = + let rec aux t1 t2 = + match t1, t2 with + | C.MutConstruct _, C.MutConstruct _ when t1 = t2 -> None + | C.Appl ((C.MutConstruct _ as constr1) :: args1), + C.Appl ((C.MutConstruct _ as constr2) :: args2) + when constr1 = constr2 -> + let rec aux_list l1 l2 = + match l1, l2 with + | [], [] -> None + | hd1 :: tl1, hd2 :: tl2 -> + (match aux hd1 hd2 with + | None -> aux_list tl1 tl2 + | Some _ as res -> res) + | _ -> (* same constructor applied to a different number of args *) + assert false + in + aux_list args1 args2 + | ((C.MutConstruct (_,_,consno1,subst1)), + (C.MutConstruct (_,_,consno2,subst2))) + | ((C.MutConstruct (_,_,consno1,subst1)), + (C.Appl ((C.MutConstruct (_,_,consno2,subst2)) :: _))) + | ((C.Appl ((C.MutConstruct (_,_,consno1,subst1)) :: _)), + (C.MutConstruct (_,_,consno2,subst2))) + | ((C.Appl ((C.MutConstruct (_,_,consno1,subst1)) :: _)), + (C.Appl ((C.MutConstruct (_,_,consno2,subst2)) :: _))) + when (consno1 <> consno2) || (subst1 <> subst2) -> + Some consno2 + | _ -> fail "not a discriminable equality" + in + aux t1 t2 + in + let mk_branches_and_outtype turi typeno consno context args = + (* a list of "True" except for the element in position consno which + * is "False" *) + match fst (CicEnvironment.get_obj CU.empty_ugraph turi) with + | C.InductiveDefinition (ind_type_list,_,paramsno,_) -> + let _,_,rty,constructor_list = List.nth ind_type_list typeno in + let false_constr_id,_ = List.nth constructor_list (consno - 1) in + let branches = + List.map + (fun (id,cty) -> + (* dubbio: e' corretto ridurre in questo context ??? *) + let red_ty = CR.whd context cty in + let rec aux t k = + match t with + | C.Prod (_,_,target) when (k <= paramsno) -> + S.subst (List.nth args (k-1)) + (aux target (k+1)) + | C.Prod (binder,source,target) when (k > paramsno) -> + C.Lambda (binder, source, (aux target (k+1))) + | _ -> + if (id = false_constr_id) + then (C.MutInd(false_URI,0,[])) + else (C.MutInd(true_URI,0,[])) + in + (S.lift 1 (aux red_ty 1))) + constructor_list in + let outtype = + let seed = ref 0 in + let rec mk_lambdas rev_left_args = + function + 0, args, C.Prod (_,so,ta) -> + C.Lambda + (C.Name (incr seed; "x" ^ string_of_int !seed), + so, + mk_lambdas rev_left_args (0,args,ta)) + | 0, args, C.Sort _ -> + let rec mk_rels = + function + 0 -> [] + | n -> C.Rel n :: mk_rels (n - 1) in + let argsno = List.length args in + C.Lambda + (C.Name "x", + (if argsno + List.length rev_left_args > 0 then + C.Appl + (C.MutInd (turi, typeno, []) :: + (List.map + (S.lift (argsno + 1)) + (List.rev rev_left_args)) @ + mk_rels argsno) + else + C.MutInd (turi,typeno,[])), + C.Sort C.Prop) + | 0, _, _ -> assert false (* seriously screwed up *) + | n, he::tl, C.Prod (_,_,ta) -> + mk_lambdas (he::rev_left_args)(n-1,tl,S.subst he ta) + | n,_,_ -> + assert false (* we should probably reduce in some context *) + in + mk_lambdas [] (paramsno, args, rty) + in + branches, outtype + | _ -> assert false + in + let discriminate'_tac ~term status = + let (proof, goal) = status in + let _,metasenv,_subst,_,_, _ = proof in + let _,context,_ = CicUtil.lookup_meta goal metasenv in + let termty,_ = + CTC.type_of_aux' metasenv context term CU.empty_ugraph + in + match termty with + | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2] + when LibraryObjects.is_eq_URI equri -> + let turi,typeno,exp_named_subst,args = + match tty with + | (C.MutInd (turi,typeno,exp_named_subst)) -> + turi,typeno,exp_named_subst,[] + | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::args)) -> + turi,typeno,exp_named_subst,args + | _ -> fail "not a discriminable equality" + in + let consno = + match find_discriminating_consno t1 t2 with + | Some consno -> consno + | None -> fail "discriminating terms are structurally equal" + in + let branches,outtype = + mk_branches_and_outtype turi typeno consno context args + in + PET.apply_tactic + (T.then_ + ~start:(EliminationTactics.elim_type_tac (C.MutInd (false_URI, 0, []))) + ~continuation: + (T.then_ + ~start: + (RT.change_tac + ~pattern:(PET.conclusion_pattern None) + (fun _ m u -> + C.Appl [ + C.Lambda ( C.Name "x", tty, + C.MutCase (turi, typeno, outtype, (C.Rel 1), branches)); + t2 ], + m, u)) + ~continuation: + (T.then_ + ~start: + (ET.rewrite_simpl_tac + ~direction:`RightToLeft + ~pattern:(PET.conclusion_pattern None) + term []) + ~continuation: + (IntroductionTactics.constructor_tac ~n:1)))) status + | _ -> fail "not an equality" + in + PET.mk_tactic (discriminate'_tac ~term) + +let exn_noneq = + PET.Fail (lazy "Injection: not an equality") +let exn_nothingtodo = + PET.Fail (lazy "Nothing to do") +let exn_discrnonind = + PET.Fail (lazy "Discriminate: object is not an Inductive Definition: it's imposible") +let exn_injwronggoal = + PET.Fail (lazy "Injection: goal after cut is not correct") +let exn_noneqind = + PET.Fail (lazy "Injection: not an equality over elements of an inductive type") + +let pp ctx t = + let names = List.map (function Some (n,_) -> Some n | None -> None) ctx in + CicPp.pp t names + +let clear_term first_time lterm = + let clear_term status = + let (proof, goal) = status in + let _,metasenv,_subst,_,_, _ = proof in + let _,context,_ = CicUtil.lookup_meta goal metasenv in + let term, metasenv, _ugraph = lterm context metasenv CU.empty_ugraph in + debug_print (lazy ("\nclear di: " ^ pp context term)); + debug_print (lazy ("nel contesto:\n" ^ CicPp.ppcontext context)); + let g () = if first_time then raise exn_nothingtodo else T.id_tac in + let tactic = match term with + | C.Rel n -> + begin match List.nth context (pred n) with + | Some (C.Name id, _) -> + T.if_ ~fail:(g ()) ~start:(PST.clear ~hyps:[id]) ~continuation:T.id_tac + | _ -> assert false + end + | _ -> g () + in + PET.apply_tactic tactic status + in + PET.mk_tactic clear_term + +let exists context = function + | C.Rel i -> List.nth context (pred i) <> None + | _ -> true + +let recur_on_child_tac ~before ~after = + let recur_on_child status = + let (proof, goal) = status in + let _, metasenv, _subst, _, _, _ = proof in + let _, context, _ = CicUtil.lookup_meta goal metasenv in + debug_print (lazy ("\nrecur_on_child")); + debug_print (lazy ("nel contesto:\n" ^ CicPp.ppcontext context)); + let mk_lterm term c m ug = + let distance = List.length c - List.length context in + S.lift distance term, m, ug + in + let lterm = mk_lterm (Cic.Rel 1) in + let tactic = T.then_ ~start:before ~continuation:(after lterm) in + PET.apply_tactic tactic status + in + PET.mk_tactic recur_on_child + +let injection_tac ~lterm ~i ~continuation ~recur = + let give_name seed = function + | C.Name _ as name -> name + | C.Anonymous -> C.Name (incr seed; "y" ^ string_of_int !seed) + in + let rec mk_rels = function | 0 -> [] | n -> C.Rel n :: (mk_rels (n - 1)) in + let injection_tac status = + let (proof, goal) = status in + (* precondizione: t1 e t2 hanno in testa lo stesso costruttore ma + * differiscono (o potrebbero differire?) nell'i-esimo parametro + * del costruttore *) + let _,metasenv,_subst,_,_, _ = proof in + let _,context,_ = CicUtil.lookup_meta goal metasenv in + let term, metasenv, _ugraph = lterm context metasenv CU.empty_ugraph in + let termty,_ = + CTC.type_of_aux' metasenv context term CU.empty_ugraph + in + debug_print (lazy ("\ninjection su : " ^ pp context termty)); + match termty with (* an equality *) + | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2] + when LibraryObjects.is_eq_URI equri -> + let turi,typeno,ens,params = + match tty with (* some inductive type *) + | C.MutInd (turi,typeno,ens) -> turi,typeno,ens,[] + | C.Appl (C.MutInd (turi,typeno,ens)::params) -> turi,typeno,ens,params + | _ -> raise exn_noneqind + in + let t1',t2',consno = (* sono i due sottotermini che differiscono *) + match t1,t2 with + | C.Appl ((C.MutConstruct (uri1,typeno1,consno1,ens1))::applist1), + C.Appl ((C.MutConstruct (uri2,typeno2,consno2,ens2))::applist2) + when (uri1 = uri2) && (typeno1 = typeno2) && + (consno1 = consno2) && (ens1 = ens2) -> + (* controllo ridondante *) + List.nth applist1 (pred i),List.nth applist2 (pred i),consno2 + | _ -> assert false + in + let tty',_ = CTC.type_of_aux' metasenv context t1' CU.empty_ugraph in + let patterns,outtype = + match fst (CicEnvironment.get_obj CU.empty_ugraph turi) with + | C.InductiveDefinition (ind_type_list,_,paramsno,_)-> + let left_params, right_params = HExtlib.split_nth paramsno params in + let _,_,_,constructor_list = List.nth ind_type_list typeno in + let i_constr_id,_ = List.nth constructor_list (consno - 1) in + let patterns = + let seed = ref 0 in + List.map + (function (id,cty) -> + let reduced_cty = CR.whd context cty in + let rec aux k = function + | C.Prod (_,_,tgt) when k <= paramsno -> + let left = List.nth left_params (k-1) in + aux (k+1) (S.subst left tgt) + | C.Prod (binder,source,target) when k > paramsno -> + let binder' = give_name seed binder in + C.Lambda (binder',source,(aux (k+1) target)) + | _ -> + let nr_param_constr = k - paramsno - 1 in + if id = i_constr_id then C.Rel (k - i) + else S.lift nr_param_constr t1' + (* + 1 per liftare anche il lambda aggiunto + * esternamente al case *) + in S.lift 1 (aux 1 reduced_cty)) + constructor_list + in + (* this code should be taken from cases_tac *) + let outtype = + let seed = ref 0 in + let rec to_lambdas te head = + match CR.whd context te with + | C.Prod (binder,so,ta) -> + let binder' = give_name seed binder in + C.Lambda (binder',so,to_lambdas ta head) + | _ -> head + in + let rec skip_prods params te = + match params, CR.whd context te with + | [], _ -> te + | left::tl, C.Prod (_,_,ta) -> + skip_prods tl (S.subst left ta) + | _, _ -> assert false + in + let abstracted_tty = + let tty = + List.fold_left (fun x y -> S.subst y x) tty left_params + in + (* non lift, ma subst coi left! *) + match S.lift 1 tty with + | C.MutInd _ as tty' -> tty' + | C.Appl l -> + let keep,abstract = HExtlib.split_nth (paramsno +1) l in + let keep = List.map (S.lift paramsno) keep in + C.Appl (keep@mk_rels (List.length abstract)) + | _ -> assert false + in + match ind_type_list with + | [] -> assert false + | (_,_,ty,_)::_ -> + (* this is in general wrong, do as in cases_tac *) + to_lambdas (skip_prods left_params ty) + (C.Lambda + (C.Name "cased", abstracted_tty, + (* here we should capture right parameters *) + (* 1 for his Lambda, one for the Lambda outside the match + * and then one for each to_lambda *) + S.lift (2+List.length right_params) tty')) + in + patterns,outtype + | _ -> raise exn_discrnonind + in + let cutted = C.Appl [C.MutInd (equri,0,[]) ; tty' ; t1' ; t2'] in + let changed = + C.Appl [ C.Lambda (C.Name "x", tty, + C.MutCase (turi,typeno,outtype,C.Rel 1,patterns)) ; t1] + in + (* check if cutted and changed are well typed and if t1' ~ changed *) + let go_on = + try + let _,g = CTC.type_of_aux' metasenv context cutted + CU.empty_ugraph + in + let _,g = CTC.type_of_aux' metasenv context changed g in + fst (CR.are_convertible ~metasenv context t1' changed g) + with + | CTC.TypeCheckerFailure _ -> false + in + if not go_on then begin + HLog.warn "destruct: injection failed"; + PET.apply_tactic continuation status + end else + let fill_cut_tac term = + let fill_cut status = + debug_print (lazy "riempio il cut"); + let (proof, goal) = status in + let _,metasenv,_subst,_,_, _ = proof in + let _,context,gty = CicUtil.lookup_meta goal metasenv in + let gty = Unshare.unshare gty in + let new_t1' = match gty with + | (C.Appl (C.MutInd (_,_,_)::_::t::_)) -> t + | _ -> raise exn_injwronggoal + in + debug_print (lazy ("metto: " ^ pp context changed)); + debug_print (lazy ("al posto di: " ^ pp context new_t1')); + debug_print (lazy ("nel goal: " ^ pp context gty)); + debug_print (lazy ("nel contesto:\n" ^ CicPp.ppcontext context)); + debug_print (lazy ("e poi rewrite con: "^pp context term)); + let tac = T.seq ~tactics:[ + RT.change_tac + ~pattern:(None, [], Some (PEH.pattern_of ~term:gty [new_t1'])) + (fun _ m u -> changed,m,u); + ET.rewrite_simpl_tac + ~direction:`LeftToRight + ~pattern:(PET.conclusion_pattern None) + term []; + ET.reflexivity_tac + ] in + PET.apply_tactic tac status + in + PET.mk_tactic fill_cut + in + debug_print (lazy ("CUT: " ^ pp context cutted)); + let tactic = + T.thens ~start: (P.cut_tac cutted) + ~continuations:[ + recur_on_child_tac continuation recur; + fill_cut_tac term + ] + in + PET.apply_tactic tactic status + | _ -> raise exn_noneq + in + PET.mk_tactic injection_tac + +let subst_tac ~lterm ~direction ~where ~continuation ~recur = + let subst_tac status = + let (proof, goal) = status in + let _,metasenv,_subst,_,_, _ = proof in + let _,context,_ = CicUtil.lookup_meta goal metasenv in + let term, metasenv, _ugraph = lterm context metasenv CU.empty_ugraph in + debug_print (lazy ("\nsubst " ^ (match direction with `LeftToRight -> "->" | `RightToLeft -> "<-") ^ " di: " ^ pp context term)); + let tactic = match where with + | None -> + debug_print (lazy ("nella conclusione")); + let pattern = PET.conclusion_pattern None in + let tactic = ET.rewrite_tac ~direction ~pattern term [] in + T.then_ ~start:(T.try_tactic ~tactic) ~continuation + | Some name -> + debug_print (lazy ("nella premessa: " ^ name)); + let pattern = None, [name, PET.hole], None in + let start = ET.rewrite_tac ~direction ~pattern term [] in + let ok_tactic = recur_on_child_tac continuation recur in + T.if_ ~start ~continuation:ok_tactic ~fail:continuation + in + PET.apply_tactic tactic status + in + PET.mk_tactic subst_tac + +let rec destruct ~first_time lterm = + let are_convertible hd1 hd2 metasenv context = + fst (CR.are_convertible ~metasenv context hd1 hd2 CU.empty_ugraph) + in + let recur = destruct ~first_time:false in + let destruct status = + let (proof, goal) = status in + let _,metasenv,_subst, _,_, _ = proof in + let _,context,_ = CicUtil.lookup_meta goal metasenv in + let term, metasenv, _ugraph = lterm context metasenv CU.empty_ugraph in + let tactic = if not (first_time || exists context term) then T.id_tac else begin + debug_print (lazy ("\ndestruct di: " ^ pp context term)); + debug_print (lazy ("nel contesto:\n" ^ CicPp.ppcontext context)); + let termty,_ = CTC.type_of_aux' metasenv context term CU.empty_ugraph in + debug_print (lazy ("\ndestruct su: " ^ pp context termty)); + let mk_lterm term c m ug = + let distance = List.length c - List.length context in + S.lift distance term, m, ug + in + let lterm = mk_lterm term in + let mk_subst_chain direction index with_what what = + let k = match term with C.Rel i -> i | _ -> -1 in + let rec traverse_context first_time j = function + | [] -> + let continuation = + T.seq ~tactics:[ + clear_term first_time lterm; + clear_term false (mk_lterm what); + clear_term false (mk_lterm with_what) + ] + in + subst_tac ~direction ~lterm ~where:None ~continuation ~recur + | Some (C.Name name, _) :: tl when j < index && j <> k -> + debug_print (lazy ("\nsubst programmata: cosa: " ^ string_of_int index ^ ", dove: " ^ string_of_int j)); + subst_tac ~direction ~lterm ~where:(Some name) ~recur + ~continuation:(traverse_context false (succ j) tl) + | _ :: tl -> traverse_context first_time (succ j) tl + in + traverse_context first_time 1 context + in + match termty with + | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2] + when LibraryObjects.is_eq_URI equri -> + begin match t1,t2 with +(* injection part *) + | C.MutConstruct _, + C.MutConstruct _ + when t1 = t2 -> clear_term first_time lterm + | C.Appl (C.MutConstruct _ as mc1 :: applist1), + C.Appl (C.MutConstruct _ as mc2 :: applist2) + when mc1 = mc2 -> + let rec traverse_list first_time i l1 l2 = + match l1, l2 with + | [], [] -> clear_term first_time lterm + | hd1 :: tl1, hd2 :: tl2 -> + if are_convertible hd1 hd2 metasenv context then + traverse_list first_time (succ i) tl1 tl2 + else + injection_tac ~i ~lterm ~recur ~continuation: + (traverse_list false (succ i) tl1 tl2) + | _ -> assert false + (* i 2 termini hanno in testa lo stesso costruttore, + * ma applicato a un numero diverso di termini *) + in + traverse_list first_time 1 applist1 applist2 +(* discriminate part *) + | C.MutConstruct (_,_,consno1,ens1), + C.MutConstruct (_,_,consno2,ens2) + | C.MutConstruct (_,_,consno1,ens1), + C.Appl ((C.MutConstruct (_,_,consno2,ens2))::_) + | C.Appl ((C.MutConstruct (_,_,consno1,ens1))::_), + C.MutConstruct (_,_,consno2,ens2) + | C.Appl ((C.MutConstruct (_,_,consno1,ens1))::_), + C.Appl ((C.MutConstruct (_,_,consno2,ens2))::_) + when (consno1 <> consno2) || (ens1 <> ens2) -> + discriminate_tac ~term +(* subst part *) + | C.Rel _, C.Rel _ when t1 = t2 -> + T.seq ~tactics:[ + clear_term first_time lterm; + clear_term false (mk_lterm t1) + ] + | C.Rel i1, C.Rel i2 when i1 < i2 -> + mk_subst_chain `LeftToRight i1 t2 t1 + | C.Rel i1, C.Rel i2 when i1 > i2 -> + mk_subst_chain `RightToLeft i2 t1 t2 + | C.Rel i1, _ when DTI.does_not_occur i1 t2 -> + mk_subst_chain `LeftToRight i1 t2 t1 + | _, C.Rel i2 when DTI.does_not_occur i2 t1 -> + mk_subst_chain `RightToLeft i2 t1 t2 +(* else part *) + | _ when first_time -> raise exn_nothingtodo + | _ (* when not first time *) -> T.id_tac + end + | _ when first_time -> raise exn_nothingtodo + | _ (* when not first time *) -> T.id_tac + end in + PET.apply_tactic tactic status + in + PET.mk_tactic destruct + +(* destruct performs either injection or discriminate or subst *) +let destruct_tac xterms = + let destruct status = + let (proof, goal) = status in + let _,metasenv,_subst,_,_, _ = proof in + let _,context,_ = CicUtil.lookup_meta goal metasenv in + let mk_lterm term c m ug = + let distance = List.length c - List.length context in + S.lift distance term, m, ug + in + let tactics = match xterms with + | Some terms -> + let map term = destruct ~first_time:false (mk_lterm term) in + List.map map terms + | None -> + let rec mk_tactics first_time i tacs = function + | [] -> List.rev tacs + | Some _ :: tl -> + let lterm = mk_lterm (C.Rel i) in + let tacs = destruct ~first_time lterm :: tacs in + mk_tactics false (succ i) tacs tl + | _ :: tl -> mk_tactics first_time (succ i) tacs tl + in + mk_tactics false 1 [] context + in + PET.apply_tactic (T.seq ~tactics) status + in + PET.mk_tactic destruct