X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=components%2Ftactics%2FdiscriminationTactics.ml;h=f12e4b3f5d2c8da1da429ba14bba162914e52f70;hb=6e01bb1ae52fe45ce77a7f950efb5feb295e82b1;hp=42da52bd60101f2c996fbc1eaed08cd0973006bf;hpb=ab16e7b1f7976674e6a4cb1043cd05f2c7f5ad20;p=helm.git diff --git a/components/tactics/discriminationTactics.ml b/components/tactics/discriminationTactics.ml index 42da52bd6..f12e4b3f5 100644 --- a/components/tactics/discriminationTactics.ml +++ b/components/tactics/discriminationTactics.ml @@ -25,275 +25,81 @@ (* $Id$ *) -let debug_print = fun _ -> () +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 -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 liftno l1 l2 = - match l1,l2 with - [],[] -> T.id_tac - | hd1::tl1,hd2::tl2 -> - if - fst - (CicReduction.are_convertible ~metasenv - context hd1 hd2 CicUniv.empty_ugraph) - then - traverse_list (i+1) liftno tl1 tl2 - else - T.then_ - ~start: - (injection1_tac ~i ~liftno - ~term:(CicSubstitution.lift liftno term)) - ~continuation: - (traverse_list (i+1) (liftno+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 0 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 (lazy "Injection: not a projectable equality but a discriminable one")) - | _ -> raise (ProofEngineTypes.Fail (lazy "Injection: not a projectable equality")) - ) - | _ -> 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 ~liftno = - 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 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))) - | _ -> -if id = i_constr_id then ( -prerr_endline ("k= " ^ string_of_int k); -prerr_endline ("paramsno= " ^ string_of_int paramsno); -prerr_endline ("nr_param_constr " ^ string_of_int (k - 1 - paramsno)); -prerr_endline ("rel= " ^ string_of_int (k - i)); -); - 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:[ - T.then_ - ~start:T.id_tac (*(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 -let aaa = - ProofEngineTypes.apply_tactic - (ReductionTactics.change_tac - ~pattern:(ProofEngineTypes.conclusion_pattern - (Some new_t1')) - (fun _ m u -> -let xxx = - C.Appl [ - C.Lambda - (C.Name "x", - tty, - C.MutCase - (turi,typeno,outtype,C.Rel 1,patterns)) ; - t1] -in -prerr_endline ("i=" ^ string_of_int i ^ "; liftno=" ^ string_of_int liftno); -prerr_endline ("XXX: " ^ CicPp.ppterm xxx); -prerr_endline ("WITH: " ^ CicPp.ppterm new_t1'); -xxx, - m, u)) - status -in -prerr_endline "OK"; -aaa - )) - ~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 debug = false +let debug_print = + if debug then (fun x -> prerr_endline (Lazy.force x)) else (fun _ -> ()) ;; -exception TwoDifferentSubtermsFound of int +(* funzione generale di rilocazione dei riferimenti locali *) + +let relocate_term map t = + let rec map_xnss k xnss = + let imap (uri, t) = uri, map_term k t in + List.map imap xnss + and map_mss k mss = + let imap = function + | None -> None + | Some t -> Some (map_term k t) + in + List.map imap mss + and map_fs len k fs = + let imap (name, i, ty, bo) = name, i, map_term k ty, map_term (k + len) bo in + List.map imap fs + and map_cfs len k cfs = + let imap (name, ty, bo) = name, map_term k ty, map_term (k + len) bo in + List.map imap cfs + and map_term k = function + | C.Rel m -> if m < k then C.Rel m else C.Rel (map (m - k)) + | C.Sort _ as t -> t + | C.Implicit _ as t -> t + | C.Var (uri, xnss) -> C.Var (uri, map_xnss k xnss) + | C.Const (uri, xnss) -> C.Const (uri, map_xnss k xnss) + | C.MutInd (uri, tyno, xnss) -> C.MutInd (uri, tyno, map_xnss k xnss) + | C.MutConstruct (uri, tyno, consno, xnss) -> + C.MutConstruct (uri, tyno, consno, map_xnss k xnss) + | C.Meta (i, mss) -> C.Meta(i, map_mss k mss) + | C.Cast (te, ty) -> C.Cast (map_term k te, map_term k ty) + | C.Appl ts -> C.Appl (List.map (map_term k) ts) + | C.MutCase (sp, i, outty, t, pl) -> + C.MutCase (sp, i, map_term k outty, map_term k t, List.map (map_term k) pl) + | C.Prod (n, s, t) -> C.Prod (n, map_term k s, map_term (succ k) t) + | C.Lambda (n, s, t) -> C.Lambda (n, map_term k s, map_term (succ k) t) + | C.LetIn (n, s, t) -> C.LetIn (n, map_term k s, map_term (succ k) t) + | C.Fix (i, fs) -> C.Fix (i, map_fs (List.length fs) k fs) + | C.CoFix (i, cfs) -> C.CoFix (i, map_cfs (List.length cfs) k cfs) + in + map_term 1 t + +let id n = n + +let comp f g n = f (g n) (* 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 discriminate_tac ~term = 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 + | 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 (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 + | 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 @@ -326,50 +132,86 @@ 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(false_URI,0,[])) - else (C.MutInd(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 = 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,_,_ = proof in + let _,metasenv,_subst,_,_, _ = proof in let _,context,_ = CicUtil.lookup_meta goal metasenv in let termty,_ = - CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph + CTC.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 = @@ -377,205 +219,319 @@ 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 (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") + 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: + (EqualityTactics.rewrite_simpl_tac + ~direction:`RightToLeft + ~pattern:(PET.conclusion_pattern None) + term []) + ~continuation: + (IntroductionTactics.constructor_tac ~n:1)))) status | _ -> fail "not an equality" in - ProofEngineTypes.mk_tactic (discriminate'_tac ~term) + PET.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) +let exn_nonproj = + PET.Fail (lazy "Injection: not a projectable equality") +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") -(* DISCRIMINTATE SENZA INJECTION +let pp ctx t = + let names = List.map (function Some (n,_) -> Some n | None -> None) ctx in + CicPp.pp t names -exception TwoDifferentSubtermsFound of (Cic.term * Cic.term * int) +let clear_term first_time context term = + let g () = if first_time then raise exn_nothingtodo else T.id_tac in + match term with + | C.Rel n -> + begin match List.nth context (pred n) with + | Some (C.Name id, _) -> PST.clear ~hyps:[id] + | _ -> assert false + end + | _ -> g () -let discriminate_tac ~term status = - 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")) -> ( - match tty with - (C.MutInd (turi,typeno,exp_named_subst)) - | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) -> +let simpl_in_term context = function + | Cic.Rel i -> + let name = match List.nth context (pred i) with + | Some (Cic.Name s, Cic.Def _) -> s + | Some (Cic.Name s, Cic.Decl _) -> s + | _ -> assert false + in + RT.simpl_tac ~pattern:(None,[name,Cic.Implicit (Some `Hole)],None) + | _ -> raise exn_nonproj - 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 +(* ~term vive nel contesto della tattica + * ~continuation riceve la mappa relativa + *) +let rec injection_tac ~term ~i ~continuation = + 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 termty,_ = + CTC.type_of_aux' metasenv context term CicUniv.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 (i-1),List.nth applist2 (i-1),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 CicUniv.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 + CicUniv.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 + PET.apply_tactic T.id_tac status (* FG: ??????? *) + else + let tac term = + let tac 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); + EqualityTactics.rewrite_simpl_tac + ~direction:`LeftToRight + ~pattern:(PET.conclusion_pattern None) + term []; + EqualityTactics.reflexivity_tac + ] in + PET.apply_tactic tac status + in + PET.mk_tactic tac + in + debug_print (lazy ("CUT: " ^ pp context cutted)); + let continuation ~map = continuation ~map:(comp succ map) in + PET.apply_tactic + (T.thens ~start: (P.cut_tac cutted) + ~continuations:[ + (qnify_tac ~first_time:false ~term:(C.Rel 1) ~map:id + ~continuation); + tac term] + ) status + | _ -> raise exn_noneq + in + PET.mk_tactic injection_tac - | ((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) +(* ~term vive nel contesto della tattica una volta ~mappato + * ~continuation riceve la mappa relativa + *) +and qnify_tac ~first_time ~map ~term ~continuation = + let are_convertible hd1 hd2 metasenv context = + fst (CR.are_convertible ~metasenv context hd1 hd2 CicUniv.empty_ugraph) + in + let qnify_tac status = + let (proof, goal) = status in + let _,metasenv,_subst, _,_, _ = proof in + let _,context,_ = CicUtil.lookup_meta goal metasenv in + let term = relocate_term map term in + let termty,_ = + CTC.type_of_aux' metasenv context term CicUniv.empty_ugraph + in + debug_print (lazy ("\nqnify su: " ^ pp context termty)); + let tac = match termty with + | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2] + when LibraryObjects.is_eq_URI equri -> begin + match (CR.whd ~delta:true context tty) with + | C.MutInd _ + | C.Appl (C.MutInd _ :: _) -> + begin match t1,t2 with + | C.MutConstruct _, + C.MutConstruct _ + when t1 = t2 -> + T.then_ ~start:(clear_term first_time context term) + ~continuation:(continuation ~map:id) + | C.Appl (C.MutConstruct _ as mc1 :: applist1), + C.Appl (C.MutConstruct _ as mc2 :: applist2) + when mc1 = mc2 -> + let rec traverse_list i l1 l2 = match l1, l2 with + | [], [] -> + T.then_ ~start:(clear_term first_time context term) + ~continuation:(continuation ~map:id) + | hd1 :: tl1, hd2 :: tl2 -> + if are_convertible hd1 hd2 metasenv context then + traverse_list (succ i) tl1 tl2 + else + injection_tac ~i ~term ~continuation: + (qnify_tac ~first_time:false ~term ~continuation) + | _ -> assert false + (* i 2 termini hanno in testa lo stesso costruttore, + * ma applicato a un numero diverso di termini *) 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' - 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") - ) - | _ -> raise (ProofEngineTypes.Fail "Discriminate: not an equality") -;; - -*) - - + traverse_list 1 applist1 applist2 + | 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 + | _ when not first_time -> continuation ~map:id + | _ (* when first_time *) -> + T.then_ ~start:(simpl_in_term context term) + ~continuation:(qnify_tac ~first_time:false ~term ~map:id ~continuation) + end + | _ when not first_time -> continuation ~map:id + | _ (* when first_time *) -> raise exn_nonproj + end + | _ -> raise exn_nonproj + in + PET.apply_tactic tac status + in + PET.mk_tactic qnify_tac +(* destruct performs either injection or discriminate *) +(* equivalent to Coq's "analyze equality" *) +let destruct_tac = + qnify_tac + ~first_time:true ~map:id ~continuation:(fun ~map -> T.id_tac)