(* 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/. *) let rec injection_tac ~term ~status:((proof, goal) as status) = 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,_ = List.find (function (m,_,_) -> m=goal) metasenv in let termty = (CicTypeChecker.type_of_aux' metasenv context term) in (match termty with (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]) when (U.eq equri (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind")) or (U.eq equri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) -> ( match tty with (C.MutInd (turi,typeno,exp_named_subst)) | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) -> ( 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) -> (* raise (ProofEngineTypes.Fail "Injection: nothing to do") ; *) T.id_tac | ((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 [],[] -> T.id_tac | hd1::tl1,hd2::tl2 -> T.then_ ~start:(injection1_tac ~i ~term) ~continuation:(traverse_list (i+1) tl1 tl2) | _ -> raise (ProofEngineTypes.Fail "Discriminate: i 2 termini hanno in testa lo stesso costruttore, ma applicato a un numero diverso di termini. possibile???") ; T.id_tac in traverse_list 1 applist1 applist2 | ((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 "Injection: not a projectable equality but a discriminable one") ; *) T.id_tac | _ -> (* raise (ProofEngineTypes.Fail "Injection: not a projectable equality") ; *) T.id_tac ) | _ -> raise (ProofEngineTypes.Fail "Injection: not a projectable equality") ) | _ -> raise (ProofEngineTypes.Fail "Injection: not an equation") ) ~status and injection1_tac ~term ~i ~status:((proof, goal) as status) = (* 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 _,metasenv,_,_ = proof in let _,context,_ = List.find (function (m,_,_) -> m=goal) metasenv in let termty = (CicTypeChecker.type_of_aux' metasenv context term) in match termty with (* an equality *) (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]) when (U.eq equri (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind")) or (U.eq equri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) -> ( match tty with (* some inductive type *) (C.MutInd (turi,typeno,exp_named_subst)) | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) -> prerr_endline ("XXXX term " ^ CicPp.ppterm term) ; prerr_endline ("XXXX termty " ^ CicPp.ppterm termty) ; prerr_endline ("XXXX t1 " ^ CicPp.ppterm t1) ; prerr_endline ("XXXX t2 " ^ CicPp.ppterm t2) ; prerr_endline ("XXXX tty " ^ CicPp.ppterm tty) ; 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 | _ -> raise (ProofEngineTypes.Fail "Injection: qui non dovrei capitarci mai") in let tty' = (CicTypeChecker.type_of_aux' metasenv context t1') in prerr_endline ("XXXX tty' " ^ CicPp.ppterm tty') ; prerr_endline ("XXXX t1' " ^ CicPp.ppterm t1') ; prerr_endline ("XXXX t2' " ^ CicPp.ppterm t2') ; prerr_endline ("XXXX consno " ^ string_of_int consno) ; let pattern = match (CicEnvironment.get_obj turi) with C.InductiveDefinition (ind_type_list,_,nr_ind_params_dx) -> let _,_,_,constructor_list = (List.nth ind_type_list typeno) in let i_constr_id,_ = List.nth constructor_list (consno - 1) in 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 <= nr_ind_params_dx) -> aux target (k+1) | C.Prod (binder,source,target) when (k > nr_ind_params_dx) -> let binder' = match binder with C.Name b -> C.Name b | C.Anonymous -> C.Name "y" in C.Lambda (binder',source,(aux target (k+1))) | _ -> let nr_param_constr = k - 1 - nr_ind_params_dx in if (id = i_constr_id) then C.Rel (nr_param_constr - i + 1) else S.lift (nr_param_constr + 1) t1' (* + 1 per liftare anche il lambda agguinto esternamente al case *) in aux reduced_cty 1 ) constructor_list | _ -> raise (ProofEngineTypes.Fail "Discriminate: object is not an Inductive Definition: it's imposible") in prerr_endline ("XXXX cominciamo!") ; T.thens ~start:(P.cut_tac (C.Appl [(C.MutInd (equri,0,[])) ; tty' ; t1' ; t2'])) ~continuations:[ T.then_ ~start:(injection_tac ~term:(C.Rel 1)) ~continuation:T.id_tac (* !!! qui devo anche fare clear di term tranne al primo passaggio *) ; T.then_ ~start: (fun ~status:((proof,goal) as status) -> let _,metasenv,_,_ = proof in let _,context,gty = List.find (function (m,_,_) -> m=goal) metasenv in prerr_endline ("XXXX goal " ^ string_of_int goal) ; prerr_endline ("XXXX gty " ^ CicPp.ppterm gty) ; prerr_endline ("XXXX old t1' " ^ CicPp.ppterm t1') ; prerr_endline ("XXXX change " ^ CicPp.ppterm (C.Appl [ C.Lambda (C.Name "x", tty, C.MutCase (turi, typeno, (C.Lambda ((C.Name "x"),(S.lift 1 tty),(S.lift 2 tty'))), (C.Rel 1), pattern)); t1])) ; let new_t1' = match gty with (C.Appl (C.MutInd (_,_,_)::arglist)) -> List.nth arglist 1 | _ -> raise (ProofEngineTypes.Fail "Injection: goal after cut is not correct") in prerr_endline ("XXXX new t1' " ^ CicPp.ppterm new_t1') ; P.change_tac ~what:new_t1' ~with_what: (C.Appl [ C.Lambda ( C.Name "x", tty, C.MutCase ( turi, typeno, (C.Lambda ( (C.Name "x"), (S.lift 1 tty), (S.lift 2 tty'))), (C.Rel 1), pattern ) ); t1] ) ~status ) ~continuation: (T.then_ ~start:(EqualityTactics.rewrite_simpl_tac ~term) ~continuation:EqualityTactics.reflexivity_tac ) ] ~status | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality") ) | _ -> raise (ProofEngineTypes.Fail "Discriminate: not an equality") ;; exception TwoDifferentSubtermsFound of int (* term ha tipo t1=t2; funziona solo se t1 e t2 hanno in testa costruttori diversi *) let discriminate'_tac ~term ~status:((proof, goal) as status) = 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,_ = List.find (function (m,_,_) -> m=goal) metasenv in let termty = (CicTypeChecker.type_of_aux' metasenv context term) in match termty with (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]) when (U.eq equri (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind")) or (U.eq equri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) -> ( match tty with (C.MutInd (turi,typeno,exp_named_subst)) | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) -> let consno2 = (* bruuutto: uso un eccezione per terminare con successo! buuu!! :-/ *) try let rec traverse t1 t2 = prerr_endline ("XXXX t1 " ^ CicPp.ppterm t1) ; prerr_endline ("XXXX t2 " ^ CicPp.ppterm t2) ; 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) -> 0 | ((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 l1 l2 = match l1,l2 with [],[] -> 0 | hd1::tl1,hd2::tl2 -> traverse hd1 hd2; traverse_list tl1 tl2 | _ -> raise (ProofEngineTypes.Fail "Discriminate: i 2 termini hanno in testa lo stesso costruttore, ma applicato a un numero diverso di termini. possibile???") in traverse_list applist1 applist2 | ((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 (TwoDifferentSubtermsFound consno2) | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality") in traverse t1 t2 with (TwoDifferentSubtermsFound consno2) -> consno2 in prerr_endline ("XXXX consno2 " ^ (string_of_int consno2)) ; if consno2 = 0 then raise (ProofEngineTypes.Fail "Discriminate: Discriminating terms are structurally equal") else let pattern = (* a list of "True" except for the element in position consno2 which is "False" *) match (CicEnvironment.get_obj turi) with C.InductiveDefinition (ind_type_list,_,nr_ind_params) -> prerr_endline ("XXXX nth " ^ (string_of_int (List.length ind_type_list)) ^ " " ^ (string_of_int typeno)) ; let _,_,_,constructor_list = (List.nth ind_type_list typeno) in prerr_endline ("XXXX nth " ^ (string_of_int (List.length constructor_list)) ^ " " ^ (string_of_int consno2)) ; let false_constr_id,_ = List.nth constructor_list (consno2 - 1) in prerr_endline ("XXXX nth funzionano ") ; List.map (function (id,cty) -> let red_ty = CicReduction.whd context cty in (* dubbio: e' corretto ridurre in questo context ??? *) let rec aux t k = match t with C.Prod (_,_,target) when (k <= nr_ind_params) -> aux target (k+1) | C.Prod (binder,source,target) when (k > nr_ind_params) -> C.Lambda (binder,source,(aux target (k+1))) | _ -> if (id = false_constr_id) then (C.MutInd (U.uri_of_string "cic:/Coq/Init/Logic/False.ind") 0 []) else (C.MutInd (U.uri_of_string "cic:/Coq/Init/Logic/True.ind") 0 []) in aux red_ty 1 ) constructor_list | _ -> raise (ProofEngineTypes.Fail "Discriminate: object is not an Inductive Definition: it's imposible") in let (proof',goals') = EliminationTactics.elim_type_tac ~term:(C.MutInd (U.uri_of_string "cic:/Coq/Init/Logic/False.ind") 0 [] ) ~status in (match goals' with [goal'] -> let _,metasenv',_,_ = proof' in let _,context',gty' = List.find (function (m,_,_) -> m=goal') metasenv' in prerr_endline ("XXXX gty " ^ CicPp.ppterm gty') ; prerr_endline ("XXXX tty " ^ CicPp.ppterm tty) ; prerr_endline ("XXXX t1 " ^ CicPp.ppterm t1) ; prerr_endline ("XXXX t2 " ^ CicPp.ppterm t2) ; ignore (List.map (fun t -> prerr_endline ("XXXX t " ^ CicPp.ppterm t)) pattern) ; prerr_endline ("XXXX case " ^ CicPp.ppterm (C.Appl [ C.Lambda ( C.Name "x", tty, C.MutCase ( turi, typeno, (C.Lambda ((C.Name "x"),tty,(C.Sort C.Prop))), (C.Rel 1), pattern ) ); t2])) ; T.then_ ~start: (P.change_tac ~what:gty' ~with_what: (C.Appl [ C.Lambda ( C.Name "x", tty, C.MutCase ( turi, typeno, (C.Lambda ((C.Name "x"),tty,(C.Sort C.Prop))), (C.Rel 1), pattern ) ); t2] ) ) ~continuation: ( prerr_endline ("XXXX rewrite<-: " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' (C.Appl [(C.MutInd (equri,0,[])) ; tty ; t1 ; t2]))); prerr_endline ("XXXX rewrite<-: " ^ CicPp.ppterm (C.Appl [(C.MutInd (equri,0,[])) ; tty ; t1 ; t2])) ; prerr_endline ("XXXX equri: " ^ U.string_of_uri equri) ; prerr_endline ("XXXX tty : " ^ CicPp.ppterm tty) ; prerr_endline ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1)) ; prerr_endline ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2)) ; if (CicTypeChecker.type_of_aux' metasenv' context' t1) <> tty then prerr_endline ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1)) ; if (CicTypeChecker.type_of_aux' metasenv' context' t2) <> tty then prerr_endline ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2)) ; if (CicTypeChecker.type_of_aux' metasenv' context' t1) <> (CicTypeChecker.type_of_aux' metasenv' context' t2) then prerr_endline ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1)) ; prerr_endline ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2)) ; prerr_endline ("XXXX rewrite<- " ^ CicPp.ppterm term ^ " : " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' term)); T.then_ ~start:(EqualityTactics.rewrite_back_simpl_tac ~term) ~continuation:(IntroductionTactics.constructor_tac ~n:1) ) ~status:(proof',goal') | _ -> raise (ProofEngineTypes.Fail "Discriminate: ElimType False left more (or less) than one goal") ) | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality") ) | _ -> raise (ProofEngineTypes.Fail "Discriminate: not an equality") ;; let discriminate_tac ~term ~status = 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 ;; let decide_equality_tac = (* il goal e' un termine della forma t1=t2\/~t1=t2; la tattica decide se l'uguaglianza e' vera o no e lo risolve *) Tacticals.id_tac ;; let compare_tac ~term ~status:((proof, goal) as status) = Tacticals.id_tac ~status (* (* term is in the form t1=t2; the tactic leaves two goals: in the first you have to *) (* demonstrate the goal with the additional hyp that t1=t2, in the second the hyp is ~t1=t2 *) 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,gty = List.find (function (m,_,_) -> m=goal) metasenv in let termty = (CicTypeChecker.type_of_aux' metasenv context term) in match termty with (C.Appl [(C.MutInd (uri, 0, [])); _; t1; t2]) when (uri = (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind")) -> let term' = (* (t1=t2)\/~(t1=t2) *) C.Appl [ (C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic/or.ind"), 0, [])) ; term ; C.Appl [ (C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic/eq.ind"), 1, [])) ; t1 ; C.Appl [C.Const ((U.uri_of_string "cic:/Coq/Init/Logic/not.con"), []) ; t2] ] ] in T.thens ~start:(P.cut_tac ~term:term') ~continuations:[ T.then_ ~start:(P.intros_tac) ~continuation:(P.elim_intros_simpl_tac ~term:(C.Rel 1)) ; decide_equality_tac] ~status | (C.Appl [(C.MutInd (uri, 0, [])); _; t1; t2]) when (uri = (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) -> let term' = (* (t1=t2) \/ ~(t1=t2) *) C.Appl [ (C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic/or.ind"), 0, [])) ; term ; C.Appl [ (C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind"), 1, [])) ; t1 ; C.Appl [C.Const ((U.uri_of_string "cic:/Coq/Init/Logic/not.con"), []) ; t2] ] ] in T.thens ~start:(P.cut_tac ~term:term') ~continuations:[ T.then_ ~start:(P.intros_tac) ~continuation:(P.elim_intros_simpl_tac ~term:(C.Rel 1)) ; decide_equality_tac] ~status | _ -> raise (ProofEngineTypes.Fail "Compare: Not an equality") *) ;; (* DISCRIMINTATE SENZA INJECTION exception TwoDifferentSubtermsFound of (Cic.term * Cic.term * int) let discriminate_tac ~term ~status:((proof, goal) as status) = 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,_ = List.find (function (m,_,_) -> m=goal) metasenv in let termty = (CicTypeChecker.type_of_aux' metasenv context term) in match termty with (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]) when (U.eq equri (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind")) or (U.eq equri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) -> ( match tty with (C.MutInd (turi,typeno,exp_named_subst)) | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) -> let (t1',t2',consno2') = (* bruuutto: uso un eccezione per terminare con successo! buuu!! :-/ *) try let rec traverse t1 t2 = prerr_endline ("XXXX t1 " ^ CicPp.ppterm t1) ; prerr_endline ("XXXX t2 " ^ CicPp.ppterm t2) ; 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) -> t1,t2,0 | ((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 l1 l2 = match l1,l2 with [],[] -> t1,t2,0 | hd1::tl1,hd2::tl2 -> traverse hd1 hd2; traverse_list tl1 tl2 | _ -> raise (ProofEngineTypes.Fail "Discriminate: i 2 termini hanno in testa lo stesso costruttore, ma applicato a un numero diverso di termini. possibile???") in traverse_list applist1 applist2 | ((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 (TwoDifferentSubtermsFound (t1,t2,consno2)) | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality") in traverse t1 t2 with (TwoDifferentSubtermsFound (t1,t2,consno2)) -> (t1,t2,consno2) in prerr_endline ("XXXX consno2' " ^ (string_of_int consno2')) ; if consno2' = 0 then raise (ProofEngineTypes.Fail "Discriminate: Discriminating terms are structurally equal") else let pattern = (* a list of "True" except for the element in position consno2' which is "False" *) match (CicEnvironment.get_obj turi) with C.InductiveDefinition (ind_type_list,_,nr_ind_params) -> prerr_endline ("XXXX nth " ^ (string_of_int (List.length ind_type_list)) ^ " " ^ (string_of_int typeno)) ; let _,_,_,constructor_list = (List.nth ind_type_list typeno) in prerr_endline ("XXXX nth " ^ (string_of_int (List.length constructor_list)) ^ " " ^ (string_of_int consno2')) ; let false_constr_id,_ = List.nth constructor_list (consno2' - 1) in prerr_endline ("XXXX nth funzionano ") ; List.map (function (id,cty) -> let red_ty = CicReduction.whd context cty in (* dubbio: e' corretto ridurre in questo context ??? *) let rec aux t k = match t with C.Prod (_,_,target) when (k <= nr_ind_params) -> aux target (k+1) | C.Prod (binder,source,target) when (k > nr_ind_params) -> C.Lambda (binder,source,(aux target (k+1))) | _ -> if (id = false_constr_id) then (C.MutInd (U.uri_of_string "cic:/Coq/Init/Logic/False.ind") 0 []) else (C.MutInd (U.uri_of_string "cic:/Coq/Init/Logic/True.ind") 0 []) in aux red_ty 1 ) constructor_list | _ -> raise (ProofEngineTypes.Fail "Discriminate: object is not an Inductive Definition: it's imposible") in let (proof',goals') = EliminationTactics.elim_type_tac ~term:(C.MutInd (U.uri_of_string "cic:/Coq/Init/Logic/False.ind") 0 [] ) ~status in (match goals' with [goal'] -> let _,metasenv',_,_ = proof' in let _,context',gty' = List.find (function (m,_,_) -> m=goal') metasenv' in prerr_endline ("XXXX gty " ^ CicPp.ppterm gty') ; prerr_endline ("XXXX tty " ^ CicPp.ppterm tty) ; prerr_endline ("XXXX t1' " ^ CicPp.ppterm t1') ; prerr_endline ("XXXX t2' " ^ CicPp.ppterm t2') ; ignore (List.map (fun t -> prerr_endline ("XXXX t " ^ CicPp.ppterm t)) pattern) ; prerr_endline ("XXXX case " ^ CicPp.ppterm (C.Appl [ C.Lambda ( C.Name "x", tty, C.MutCase ( turi, typeno, (C.Lambda ((C.Name "x"),tty,(C.Sort C.Prop))), (C.Rel 1), pattern ) ); t2'])) ; T.then_ ~start: (P.change_tac ~what:gty' ~with_what: (C.Appl [ C.Lambda ( C.Name "x", tty, C.MutCase ( turi, typeno, (C.Lambda ((C.Name "x"),tty,(C.Sort C.Prop))), (C.Rel 1), pattern ) ); t2'] ) ) ~continuation: ( prerr_endline ("XXXX rewrite<-: " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' (C.Appl [(C.MutInd (equri,0,[])) ; tty ; t1' ; t2']))); prerr_endline ("XXXX rewrite<-: " ^ CicPp.ppterm (C.Appl [(C.MutInd (equri,0,[])) ; tty ; t1' ; t2'])) ; prerr_endline ("XXXX equri: " ^ U.string_of_uri equri) ; prerr_endline ("XXXX tty : " ^ CicPp.ppterm tty) ; prerr_endline ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1')) ; prerr_endline ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2')) ; if (CicTypeChecker.type_of_aux' metasenv' context' t1') <> tty then prerr_endline ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1')) ; if (CicTypeChecker.type_of_aux' metasenv' context' t2') <> tty then prerr_endline ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2')) ; if (CicTypeChecker.type_of_aux' metasenv' context' t1') <> (CicTypeChecker.type_of_aux' metasenv' context' t2') then prerr_endline ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1')) ; prerr_endline ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2')) ; let termty' = ProofEngineReduction.replace_lifting ~equality:(==) ~what:t1 ~with_what:t1' ~where:termty in let termty'' = ProofEngineReduction.replace_lifting ~equality:(==) ~what:t2 ~with_what:t2' ~where:termty' in prerr_endline ("XXXX rewrite<- " ^ CicPp.ppterm term ^ " : " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' term)); T.then_ ~start:(EqualityTactics.rewrite_back_simpl_tac ~term:term) ~continuation:(IntroductionTactics.constructor_tac ~n:1) ) ~status:(proof',goal') | _ -> raise (ProofEngineTypes.Fail "Discriminate: ElimType False left more (or less) than one goal") ) | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality") ) | _ -> raise (ProofEngineTypes.Fail "Discriminate: not an equality") ;; *)