(* 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/. *) (* $Id$ *) let debug_print = fun _ -> () let rec injection_tac ~first_time ~term ~liftno ~continuation = let injection_tac ~term status = let (proof, goal) = status in let module C = Cic in let module U = UriManager in let module P = PrimitiveTactics in let module T = Tacticals in let _,metasenv,_,_ = proof in let _,context,_ = CicUtil.lookup_meta goal metasenv in let term = CicSubstitution.lift liftno term in let termty,_ = (* TASSI: FIXME *) CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in ProofEngineTypes.apply_tactic (match termty with (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]) when LibraryObjects.is_eq_URI equri -> begin match tty with (C.MutInd (turi,typeno,exp_named_subst)) | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) -> begin match t1,t2 with ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)), (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))) when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) -> if first_time then raise (ProofEngineTypes.Fail (lazy "Injection: nothing to do")) else continuation ~liftno | C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::applist1), C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::applist2) when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) -> let rec traverse_list i l1 l2 = match l1,l2 with [],[] -> if first_time then continuation else (match term with C.Rel n -> (match List.nth context (n-1) with Some (C.Name id,_) -> fun ~liftno -> T.then_ ~start: (ProofEngineStructuralRules.clear ~hyps:[id]) ~continuation:(continuation ~liftno) | _ -> assert false) | _ -> assert false) | hd1::tl1,hd2::tl2 -> if fst (CicReduction.are_convertible ~metasenv context hd1 hd2 CicUniv.empty_ugraph) then traverse_list (i+1) tl1 tl2 else injection1_tac ~i ~term ~continuation:(traverse_list (i+1) tl1 tl2) | _ -> raise (ProofEngineTypes.Fail (lazy "Discriminate: i 2 termini hanno in testa lo stesso costruttore, ma applicato a un numero diverso di termini. possibile???")) in traverse_list 1 applist1 applist2 ~liftno | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)), (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))) | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)), (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_))) | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)), (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))) | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)), (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_))) when (consno1 <> consno2) || (exp_named_subst1 <> exp_named_subst2) -> raise (ProofEngineTypes.Fail (lazy "Injection: not a projectable equality but a discriminable one")) | _ -> if first_time then raise (ProofEngineTypes.Fail (lazy "Injection: not a projectable equality")) else continuation ~liftno end | _ -> if first_time then raise (ProofEngineTypes.Fail (lazy "Injection: not a projectable equality")) else continuation ~liftno end | _ -> raise (ProofEngineTypes.Fail (lazy "Injection: not an equation")) ) status in ProofEngineTypes.mk_tactic (injection_tac ~term) and injection1_tac ~term ~i ~liftno ~continuation = let injection1_tac ~term ~i 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 module C = Cic in let module S = CicSubstitution in let module U = UriManager in let module P = PrimitiveTactics in let module T = Tacticals in let term = CicSubstitution.lift liftno term in let _,metasenv,_,_ = proof in let _,context,_ = CicUtil.lookup_meta goal metasenv in let termty,_ = (* TASSI: FIXME *) CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in match termty with (* an equality *) (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]) when LibraryObjects.is_eq_URI equri -> ( match tty with (* some inductive type *) (C.MutInd (turi,typeno,exp_named_subst)) | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) -> let t1',t2',consno = (* sono i due sottotermini che differiscono *) match t1,t2 with ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::applist1)), (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::applist2))) when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) -> (* controllo ridondante *) (List.nth applist1 (i-1)),(List.nth applist2 (i-1)),consno2 | _ -> assert false in let tty',_ = CicTypeChecker.type_of_aux' metasenv context t1' CicUniv.empty_ugraph in let patterns,outtype = match fst (CicEnvironment.get_obj CicUniv.empty_ugraph turi) with C.InductiveDefinition (ind_type_list,_,paramsno,_)-> let _,_,_,constructor_list = List.nth ind_type_list typeno in let i_constr_id,_ = List.nth constructor_list (consno - 1) in let seed = ref 0 in let patterns = List.map (function (id,cty) -> let reduced_cty = CicReduction.whd context cty in let rec aux t k = match t with C.Prod (_,_,target) when k <= paramsno -> aux target (k+1) | C.Prod (binder,source,target) when k > paramsno -> let binder' = match binder with C.Name _ -> binder | C.Anonymous -> C.Name (incr seed; "y" ^ string_of_int !seed) in C.Lambda (binder',source,(aux target (k+1))) | _ -> let nr_param_constr = k - 1 - paramsno in if id = i_constr_id then C.Rel (k - i) else S.lift (nr_param_constr + 1) t1' (* + 1 per liftare anche il lambda aggiunto esternamente al case *) in aux reduced_cty 1 ) constructor_list in let outtype = let seed = ref 0 in let rec to_lambdas te head = match CicReduction.whd context te with | C.Prod (binder,so,ta) -> let binder' = match binder with C.Name _ -> binder | C.Anonymous -> C.Name (incr seed; "d" ^ string_of_int !seed) in C.Lambda (binder',so,to_lambdas ta head) | _ -> head in let rec skip_prods n te = match n, CicReduction.whd context te with 0, _ -> te | n, C.Prod (_,_,ta) -> skip_prods (n - 1) ta | _, _ -> assert false in let abstracted_tty = match CicSubstitution.lift (paramsno + 1) tty with C.MutInd _ as tty' -> tty' | C.Appl l -> let keep,abstract = HExtlib.split_nth (paramsno +1) l in let rec mk_rels = function 0 -> [] | n -> C.Rel n :: (mk_rels (n - 1)) in C.Appl (keep@mk_rels (List.length abstract)) | _ -> assert false in match ind_type_list with [] -> assert false | (_,_,ty,_)::_ -> to_lambdas (skip_prods paramsno ty) (C.Lambda (C.Name "x", abstracted_tty, S.lift (2+paramsno) tty')) in patterns,outtype | _ -> raise (ProofEngineTypes.Fail (lazy "Discriminate: object is not an Inductive Definition: it's imposible")) in ProofEngineTypes.apply_tactic (T.thens ~start: (P.cut_tac (C.Appl [C.MutInd (equri,0,[]) ; tty' ; t1' ; t2'])) ~continuations: [ injection_tac ~first_time:false ~liftno:0 ~term:(C.Rel 1) (* here I need to lift all the continuations by 1; since I am setting back liftno to 0, I actually need to lift all the continuations by liftno + 1 *) ~continuation: (fun ~liftno:x -> continuation ~liftno:(liftno + 1 + x)) ; T.then_ ~start:(ProofEngineTypes.mk_tactic (fun status -> let (proof, goal) = status in let _,metasenv,_,_ = proof in let _,context,gty = CicUtil.lookup_meta goal metasenv in let new_t1' = match gty with (C.Appl (C.MutInd (_,_,_)::arglist)) -> List.nth arglist 1 | _ -> raise (ProofEngineTypes.Fail (lazy "Injection: goal after cut is not correct")) in ProofEngineTypes.apply_tactic (ReductionTactics.change_tac ~pattern:(ProofEngineTypes.conclusion_pattern (Some new_t1')) (fun _ m u -> C.Appl [ C.Lambda (C.Name "x", tty, C.MutCase (turi,typeno,outtype,C.Rel 1,patterns)) ; t1], m, u)) status )) ~continuation: (T.then_ ~start: (EqualityTactics.rewrite_simpl_tac ~direction:`LeftToRight ~pattern:(ProofEngineTypes.conclusion_pattern None) term) ~continuation:EqualityTactics.reflexivity_tac) ]) status | _ -> raise (ProofEngineTypes.Fail (lazy "Injection: not an equality over elements of an inductive type")) ) | _ -> raise (ProofEngineTypes.Fail (lazy "Injection: not an equality")) in ProofEngineTypes.mk_tactic (injection1_tac ~term ~i) ;; let injection_tac = injection_tac ~first_time:true ~liftno:0 ~continuation:(fun ~liftno -> Tacticals.id_tac) ;; (* term ha tipo t1=t2; funziona solo se t1 e t2 hanno in testa costruttori diversi *) let discriminate'_tac ~term = let module C = Cic in let module U = UriManager in let module P = PrimitiveTactics in let module T = Tacticals in let true_URI = match LibraryObjects.true_URI () with Some uri -> uri | None -> raise (ProofEngineTypes.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 (ProofEngineTypes.Fail (lazy "You need to register the default \"false\" definition first. Please use the \"default\" command")) in let fail msg = raise (ProofEngineTypes.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 CicUniv.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 = CicReduction.whd context cty in let rec aux t k = match t with | C.Prod (_,_,target) when (k <= paramsno) -> CicSubstitution.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 (CicSubstitution.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 (CicSubstitution.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,CicSubstitution.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,_,_ = proof in let _,context,_ = CicUtil.lookup_meta goal metasenv in let termty,_ = CicTypeChecker.type_of_aux' metasenv context term CicUniv.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 ProofEngineTypes.apply_tactic (T.then_ ~start:(EliminationTactics.elim_type_tac (C.MutInd (false_URI, 0, []))) ~continuation: (T.then_ ~start: (ReductionTactics.change_tac ~pattern:(ProofEngineTypes.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: (EqualityTactics.rewrite_simpl_tac ~direction:`RightToLeft ~pattern:(ProofEngineTypes.conclusion_pattern None) term) ~continuation: (IntroductionTactics.constructor_tac ~n:1)))) status | _ -> fail "not an equality" in ProofEngineTypes.mk_tactic (discriminate'_tac ~term) let discriminate_tac ~term = let discriminate_tac ~term status = ProofEngineTypes.apply_tactic (Tacticals.then_ ~start:(* (injection_tac ~term) *) Tacticals.id_tac ~continuation:(discriminate'_tac ~term)) (* NOOO!!! non term ma una (qualunque) delle nuove hyp introdotte da inject *) status in ProofEngineTypes.mk_tactic (discriminate_tac ~term)