(* ||M|| This file is part of HELM, an Hypertextual, Electronic ||A|| Library of Mathematics, developed at the Computer Science ||T|| Department, University of Bologna, Italy. ||I|| ||T|| HELM is free software; you can redistribute it and/or ||A|| modify it under the terms of the GNU General Public License \ / version 2 or (at your option) any later version. \ / This software is distributed as is, NO WARRANTY. V_______________________________________________________________ *) (* $Id: nCic.ml 9058 2008-10-13 17:42:30Z tassi $ *) (*let pp m = prerr_endline (Lazy.force m);;*) let pp _ = ();; let fresh_name = let i = ref 0 in function () -> incr i; "z" ^ string_of_int !i ;; let mk_id id = let id = if id = "_" then fresh_name () else id in NotationPt.Ident (id,None) ;; let rec split_arity status ~subst context te = match NCicReduction.whd status ~subst context te with | NCic.Prod (name,so,ta) -> split_arity status ~subst ((name, (NCic.Decl so))::context) ta | t -> context, t ;; let mk_appl = function [] -> assert false | [x] -> x | l -> NotationPt.Appl l ;; let rec mk_prods l t = match l with [] -> t | hd::tl -> NotationPt.Binder (`Forall, (mk_id hd, None), mk_prods tl t) ;; let rec mk_arrows ?(pattern=false) xs ys selection target = match selection,xs,ys with [],[],[] -> target | false :: l,x::xs,y::ys -> mk_arrows ~pattern xs ys l target | true :: l,x::xs,y::ys -> NotationPt.Binder (`Forall, (mk_id "_", Some (mk_appl [if pattern then NotationPt.Implicit `JustOne else mk_id "eq" ; NotationPt.Implicit `JustOne;x;y])), mk_arrows ~pattern xs ys l target) | _ -> raise (Invalid_argument "ninverter: the selection doesn't match the arity of the specified inductive type") ;; let subst_metasenv_and_fix_names status = let u,h,metasenv, subst,o = status#obj in let o = NCicUntrusted.map_obj_kind ~skip_body:true (NCicUntrusted.apply_subst status subst []) o in status#set_obj(u,h,NCicUntrusted.apply_subst_metasenv status subst metasenv,subst,o) ;; let mk_inverter name is_ind it leftno ?selection outsort (status: #NCic.status) baseuri = pp (lazy ("leftno = " ^ string_of_int leftno)); let _,ind_name,ty,cl = it in pp (lazy ("arity: " ^ status#ppterm ~metasenv:[] ~subst:[] ~context:[] ty)); let ncons = List.length cl in (**)let params,ty = NCicReduction.split_prods status ~subst:[] [] leftno ty in let params = List.rev_map (function name,_ -> mk_id name) params in pp (lazy ("lunghezza params = " ^ string_of_int (List.length params)));(**) let args,sort= split_arity status ~subst:[] [] ty in pp (lazy ("arity sort: " ^ status#ppterm ~metasenv:[] ~subst:[] ~context:args sort)); (**)let args = List.rev_map (function name,_ -> mk_id name) args in pp (lazy ("lunghezza args = " ^ string_of_int (List.length args)));(**) let nparams = List.length args in pp (lazy ("nparams = " ^ string_of_int nparams)); if nparams = 0 then raise (Failure "inverter: the type must have at least one right parameter") else let xs = List.map (fun n -> "x" ^ (string_of_int n)) (HExtlib.list_seq 1 (leftno+nparams+1)) in pp (lazy ("lunghezza xs = " ^ string_of_int (List.length xs))); let ls, rs = HExtlib.split_nth leftno xs in pp (lazy ("lunghezza ls = " ^ string_of_int (List.length ls))); pp (lazy ("lunghezza rs = " ^ string_of_int (List.length rs))); let ys = List.map (fun n -> "y" ^ (string_of_int n)) (HExtlib.list_seq (leftno+1) (leftno+nparams+1)) in let _id_xs = List.map mk_id xs in let id_ls = List.map mk_id ls in let id_rs = List.map mk_id rs in let id_ys = List.map mk_id ys in (* pseudocode let t = Lambda y1 ... yr. xs_ = ys_ -> pred *) (* check: assuming we have more than one right parameter *) (* pred := P yr- *) let pred = mk_appl ((mk_id "P")::id_ys) in let selection = match selection with None -> HExtlib.mk_list true (List.length ys) | Some s -> s in let prods = mk_arrows id_rs id_ys selection pred in let hyplist = let rec hypaux k = function 0 -> [] | n -> ("H" ^ string_of_int k) :: hypaux (k+1) (n-1) in (hypaux 1 ncons) in pp (lazy ("lunghezza ys = " ^ string_of_int (List.length ys))); let outsort, suffix = NCicElim.ast_of_sort outsort in let theorem = mk_prods xs (NotationPt.Binder (`Forall, (mk_id "P", Some (mk_prods (HExtlib.mk_list "_" (List.length ys)) (NotationPt.Sort outsort))), mk_prods hyplist (NotationPt.Binder (`Forall, (mk_id "Hterm", Some (mk_appl (List.map mk_id (ind_name::xs)))), mk_appl (mk_id "P"::id_rs))))) in let status, theorem = GrafiteDisambiguate.disambiguate_nobj status ~baseuri (baseuri ^ name ^ ".def",0, NotationPt.Theorem (`Theorem,name,theorem, Some (NotationPt.Implicit (`Tagged "inv")),`InversionPrinciple)) in let uri,height,nmenv,nsubst,nobj = theorem in let ninitial_stack = Continuationals.Stack.of_nmetasenv nmenv in let status = status#set_obj theorem in let status = status#set_stack ninitial_stack in let status = subst_metasenv_and_fix_names status in let cut_theorem = let rs = List.map (fun x -> mk_id x) rs in mk_arrows rs rs selection (mk_appl (mk_id "P"::rs)) in let cut = mk_appl [NotationPt.Binder (`Lambda, (mk_id "Hcut", Some cut_theorem), NotationPt.Implicit (`Tagged "end")); NotationPt.Implicit (`Tagged "cut")] in let intros = List.map (fun x -> pp (lazy x); NTactics.intro_tac x) (xs@["P"]@hyplist@["Hterm"]) in let where = "",0,(None,[], Some ( mk_arrows ~pattern:true (HExtlib.mk_list (NotationPt.Implicit `JustOne) (List.length ys)) (HExtlib.mk_list NotationPt.UserInput (List.length ys)) selection NotationPt.UserInput)) in let elim_tac = if is_ind then NTactics.elim_tac else NTactics.cases_tac in let status = NTactics.block_tac (NTactics.branch_tac :: NTactics.case_tac "inv" :: (intros @ [NTactics.apply_tac ("",0,cut); NTactics.branch_tac; NTactics.case_tac "end"; NTactics.apply_tac ("",0,mk_id "Hcut"); NTactics.apply_tac ("",0,mk_id "refl"); NTactics.shift_tac; elim_tac ~what:("",0,mk_id "Hterm") ~where; NTactics.branch_tac ~force:true] @ HExtlib.list_concat ~sep:[NTactics.shift_tac] (List.map (fun id-> [NTactics.apply_tac ("",0,mk_id id)]) hyplist) @ [NTactics.merge_tac; NTactics.merge_tac; NTactics.merge_tac; NTactics.skip_tac])) status in pp (lazy "inv 3"); status,status#obj ;;