X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=components%2Ftactics%2FdiscriminationTactics.ml;h=ebf7728449dad2d03de6b08744529171c667ae34;hb=3f586b01da59fe16b3d7f37da28bdd71f2225131;hp=0ffa2c52b4ceb70d0bff28a98a7182e4611c8b60;hpb=9a17bf0f4213f5f130326d658ce7ee4b41f6d6f2;p=helm.git diff --git a/components/tactics/discriminationTactics.ml b/components/tactics/discriminationTactics.ml index 0ffa2c52b..ebf772844 100644 --- a/components/tactics/discriminationTactics.ml +++ b/components/tactics/discriminationTactics.ml @@ -27,185 +27,22 @@ let debug_print = fun _ -> () -let rec injection_tac ~term = - 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 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 -> ( - 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 (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 - | ((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 (lazy "Injection: not a projectable equality")) - ) - | _ -> raise (ProofEngineTypes.Fail (lazy "Injection: not an equation")) - ) status - in - ProofEngineTypes.mk_tactic (injection_tac ~term) - -and injection1_tac ~term ~i = - 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 _,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 pattern = - match fst(CicEnvironment.get_obj - CicUniv.empty_ugraph 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 (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:[ - 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:(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, - (C.Lambda ((C.Name "x"), - (S.lift 1 tty), - (S.lift 2 tty'))), - (C.Rel 1), pattern - ) - ); - 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 "Discriminate: not a discriminable equality")) - ) - | _ -> raise (ProofEngineTypes.Fail (lazy "Discriminate: not an equality")) - in - ProofEngineTypes.mk_tactic (injection1_tac ~term ~i) -;; - -exception TwoDifferentSubtermsFound of int - (* term ha tipo t1=t2; funziona solo se t1 e t2 hanno in testa costruttori diversi *) -let discriminate'_tac ~term = +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 = @@ -239,33 +76,69 @@ let discriminate'_tac ~term = in aux t1 t2 in - let mk_pattern turi typeno consno context left_args = + 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,_,nr_ind_params,_) -> - let _,_,_,constructor_list = List.nth ind_type_list typeno in + | 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 - 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 <= nr_ind_params) -> - CicSubstitution.subst (List.nth left_args (k-1)) - (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(LibraryObjects.false_URI (),0,[])) - else (C.MutInd(LibraryObjects.true_URI (),0,[])) - in - (CicSubstitution.lift 1 (aux red_ty 1))) - constructor_list - | _ -> (* object is not an inductive definition *) - assert false + 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 @@ -275,14 +148,14 @@ let discriminate'_tac ~term = 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,left_args = + | 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)::left_args)) -> - turi,typeno,exp_named_subst,left_args + | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::args)) -> + turi,typeno,exp_named_subst,args | _ -> fail "not a discriminable equality" in let consno = @@ -290,205 +163,316 @@ let discriminate'_tac ~term = | Some consno -> consno | None -> fail "discriminating terms are structurally equal" in - let pattern = mk_pattern turi typeno consno context left_args in - let (proof',goals') = - ProofEngineTypes.apply_tactic - (EliminationTactics.elim_type_tac - (C.MutInd (LibraryObjects.false_URI (), 0, []))) - status + let branches,outtype = + mk_branches_and_outtype turi typeno consno context args in - (match goals' with - | [goal'] -> - let _,metasenv',_,_ = proof' in - let _,context',gty' = CicUtil.lookup_meta goal' metasenv' in - ProofEngineTypes.apply_tactic - (T.then_ - ~start: - (ReductionTactics.change_tac - ~pattern:(ProofEngineTypes.conclusion_pattern (Some gty')) - (fun _ m u -> - C.Appl [ - C.Lambda ( C.Name "x", tty, - C.MutCase (turi, typeno, - (C.Lambda ((C.Name "x"), - (CicSubstitution.lift 1 tty), - (C.Sort C.Prop))), - (C.Rel 1), pattern)); - 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))) - (proof',goal') - | [] -> fail "ElimType False left no goals" - | _ -> fail "ElimType False left more than one goal") + 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) - -(* DISCRIMINTATE SENZA INJECTION - -exception TwoDifferentSubtermsFound of (Cic.term * Cic.term * int) - -let discriminate_tac ~term status = +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 (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) 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")) -> ( + 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) + | _ -> assert false (* i 2 termini hanno in testa lo stesso costruttore, ma applicato a un numero diverso di termini *) + 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) -> + discriminate_tac ~term + (*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) - let (t1',t2',consno2') = (* bruuutto: uso un eccezione per terminare con successo! buuu!! :-/ *) - try - let rec traverse t1 t2 = -debug_print (lazy ("XXXX t1 " ^ CicPp.ppterm t1)) ; -debug_print (lazy ("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 -debug_print (lazy ("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 fst(CicEnvironment.get_obj turi - CicUniv.empty_ugraph) with - C.InductiveDefinition (ind_type_list,_,nr_ind_params) -> -debug_print (lazy ("XXXX nth " ^ (string_of_int (List.length ind_type_list)) ^ " " ^ (string_of_int typeno))) ; - let _,_,_,constructor_list = (List.nth ind_type_list typeno) in -debug_print (lazy ("XXXX nth " ^ (string_of_int (List.length constructor_list)) ^ " " ^ (string_of_int consno2'))) ; - let false_constr_id,_ = List.nth constructor_list (consno2' - 1) in -debug_print (lazy "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' = - CicUtil.lookup_meta goal' metasenv' +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 - 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: - ( -debug_print (lazy ("XXXX rewrite<-: " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' (C.Appl [(C.MutInd (equri,0,[])) ; tty ; t1' ; t2'])))); -debug_print (lazy ("XXXX rewrite<-: " ^ CicPp.ppterm (C.Appl [(C.MutInd (equri,0,[])) ; tty ; t1' ; t2']))) ; -debug_print (lazy ("XXXX equri: " ^ U.string_of_uri equri)) ; -debug_print (lazy ("XXXX tty : " ^ CicPp.ppterm tty)) ; -debug_print (lazy ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1'))) ; -debug_print (lazy ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2'))) ; -if (CicTypeChecker.type_of_aux' metasenv' context' t1') <> tty then debug_print (lazy ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1'))) ; -if (CicTypeChecker.type_of_aux' metasenv' context' t2') <> tty then debug_print (lazy ("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 debug_print (lazy ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' - metasenv' context' t1'))) ; debug_print (lazy ("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 - -debug_print (lazy ("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) - ) - (proof',goal') - | _ -> raise (ProofEngineTypes.Fail "Discriminate: ElimType False left more (or less) than one goal") - ) - | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality") + 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 "Discriminate: not an equality") + | _ -> raise (ProofEngineTypes.Fail (lazy "Injection: not an equality")) + in + ProofEngineTypes.mk_tactic (injection1_tac ~term ~i) ;; -*) - - - +(* destruct performs either injection or discriminate *) +(* equivalent to Coq's "analyze equality" *) +let destruct_tac = + injection_tac + ~first_time:true ~liftno:0 ~continuation:(fun ~liftno -> Tacticals.id_tac) +;;