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(************************************************************************)
(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2019       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)

open Equality
open Names
open Pp
open Constr
open Termops
open CErrors
open Util
open Mod_subst
open Locus

(* Rewriting rules *)
type rew_rule = { rew_lemma: constr;
                  rew_type: types;
                  rew_pat: constr;
                  rew_ctx: Univ.ContextSet.t;
                  rew_l2r: bool;
                  rew_tac: Genarg.glob_generic_argument option }

let subst_hint subst hint =
  let cst' = subst_mps subst hint.rew_lemma in
  let typ' = subst_mps subst hint.rew_type in
  let pat' = subst_mps subst hint.rew_pat in
  let t' = Option.Smart.map (Genintern.generic_substitute subst) hint.rew_tac in
    if hint.rew_lemma == cst' && hint.rew_type == typ' && hint.rew_tac == t' then hint else
      { hint with
        rew_lemma = cst'; rew_type = typ';
        rew_pat = pat';        rew_tac = t' }

module HintIdent =
struct
  type t = int * rew_rule

  let compare (i, t) (j, t') = i - j

  let subst s (i,t) = (i,subst_hint s t)

  let constr_of (i,t) = t.rew_pat
end

module HintOpt =
struct
  let reduce c = c
  let direction = true
end

module HintDN = Term_dnet.Make(HintIdent)(HintOpt)

(* Summary and Object declaration *)
let rewtab =
  Summary.ref (String.Map.empty : HintDN.t String.Map.t) ~name:"autorewrite"

let raw_find_base bas = String.Map.find bas !rewtab

let find_base bas =
  try raw_find_base bas
  with Not_found ->
    user_err ~hdr:"AutoRewrite"
      (str "Rewriting base " ++ str bas ++ str " does not exist.")

let find_rewrites bas =
  List.rev_map snd (HintDN.find_all (find_base bas))

let find_matches bas pat =
  let base = find_base bas in
  let res = HintDN.search_pattern base pat in
  List.map snd res

let print_rewrite_hintdb bas =
  let env = Global.env () in
  let sigma = Evd.from_env env in
  (str "Database " ++ str bas ++ fnl () ++
           prlist_with_sep fnl
           (fun h ->
             str (if h.rew_l2r then "rewrite -> " else "rewrite <- ") ++
               Printer.pr_lconstr_env env sigma h.rew_lemma ++ str " of type " ++ Printer.pr_lconstr_env env sigma h.rew_type ++
               Option.cata (fun tac -> str " then use tactic " ++
               Pputils.pr_glb_generic env sigma tac) (mt ()) h.rew_tac)
           (find_rewrites bas))

type raw_rew_rule = (constr Univ.in_universe_context_set * bool * Genarg.raw_generic_argument option) CAst.t

(* Applies all the rules of one base *)
let one_base general_rewrite_maybe_in tac_main bas =
  let lrul = find_rewrites bas in
  let try_rewrite dir ctx c tc =
  Proofview.Goal.enter begin fun gl ->
    let sigma = Proofview.Goal.sigma gl in
    let subst, ctx' = UnivGen.fresh_universe_context_set_instance ctx in
    let c' = Vars.subst_univs_level_constr subst c in
    let sigma = Evd.merge_context_set Evd.univ_flexible sigma ctx' in
    Proofview.tclTHEN (Proofview.Unsafe.tclEVARS sigma)
    (general_rewrite_maybe_in dir c' tc)
  end in
  let open Proofview.Notations in
  Proofview.tclProofInfo [@ocaml.warning "-3"] >>= fun (_name, poly) ->
  let lrul = List.map (fun h ->
  let tac = match h.rew_tac with
  | None -> Proofview.tclUNIT ()
  | Some (Genarg.GenArg (Genarg.Glbwit wit, tac)) ->
    let ist = { Geninterp.lfun = Id.Map.empty
              ; poly
              ; extra = Geninterp.TacStore.empty } in
    Ftactic.run (Geninterp.interp wit ist tac) (fun _ -> Proofview.tclUNIT ())
  in
    (h.rew_ctx,h.rew_lemma,h.rew_l2r,tac)) lrul in
    Tacticals.New.tclREPEAT_MAIN (Proofview.tclPROGRESS (List.fold_left (fun tac (ctx,csr,dir,tc) ->
      Tacticals.New.tclTHEN tac
        (Tacticals.New.tclREPEAT_MAIN
            (Tacticals.New.tclTHENFIRST (try_rewrite dir ctx csr tc) tac_main)))
      (Proofview.tclUNIT()) lrul))

(* The AutoRewrite tactic *)
let autorewrite ?(conds=Naive) tac_main lbas =
  Tacticals.New.tclREPEAT_MAIN (Proofview.tclPROGRESS
    (List.fold_left (fun tac bas ->
       Tacticals.New.tclTHEN tac
        (one_base (fun dir c tac ->
          let tac = (tac, conds) in
            general_rewrite dir AllOccurrences true false ~tac (EConstr.of_constr c))
          tac_main bas))
      (Proofview.tclUNIT()) lbas))

let autorewrite_multi_in ?(conds=Naive) idl tac_main lbas =
  Proofview.Goal.enter begin fun gl ->
 (* let's check at once if id exists (to raise the appropriate error) *)
  let _ = List.map (fun id -> Tacmach.New.pf_get_hyp id gl) idl in
  let general_rewrite_in id dir cstr tac =
    let cstr = EConstr.of_constr cstr in
    general_rewrite_in dir AllOccurrences true ~tac:(tac, conds) false id cstr false
  in
 Tacticals.New.tclMAP (fun id ->
  Tacticals.New.tclREPEAT_MAIN (Proofview.tclPROGRESS
    (List.fold_left (fun tac bas ->
       Tacticals.New.tclTHEN tac (one_base (general_rewrite_in id) tac_main bas)) (Proofview.tclUNIT()) lbas)))
   idl
 end

let autorewrite_in ?(conds=Naive) id = autorewrite_multi_in ~conds [id]

let gen_auto_multi_rewrite conds tac_main lbas cl =
  let try_do_hyps treat_id l =
    autorewrite_multi_in ~conds (List.map treat_id l) tac_main lbas
  in
  if not (Locusops.is_all_occurrences cl.concl_occs) &&
     cl.concl_occs != NoOccurrences
  then
    Tacticals.New.tclZEROMSG (str"The \"at\" syntax isn't available yet for the autorewrite tactic.")
  else
    let compose_tac t1 t2 =
      match cl.onhyps with
        | Some [] -> t1
        | _ ->      Tacticals.New.tclTHENFIRST t1 t2
    in
    compose_tac
        (if cl.concl_occs != NoOccurrences then autorewrite ~conds tac_main lbas else Proofview.tclUNIT ())
        (match cl.onhyps with
           | Some l -> try_do_hyps (fun ((_,id),_) -> id) l
           | None ->
                 (* try to rewrite in all hypothesis
                    (except maybe the rewritten one) *)
               Proofview.Goal.enter begin fun gl ->
                 let ids = Tacmach.New.pf_ids_of_hyps gl in
                 try_do_hyps (fun id -> id)  ids
               end)

let auto_multi_rewrite ?(conds=Naive) lems cl =
  Proofview.V82.wrap_exceptions (fun () -> gen_auto_multi_rewrite conds (Proofview.tclUNIT()) lems cl)

let auto_multi_rewrite_with ?(conds=Naive) tac_main lbas cl =
  let onconcl = match cl.Locus.concl_occs with NoOccurrences -> false | _ -> true in
  match onconcl,cl.Locus.onhyps with
    | false,Some [_] | true,Some [] | false,Some [] ->
        (* autorewrite with .... in clause using tac n'est sur que
           si clause represente soit le but soit UNE hypothese
        *)
        Proofview.V82.wrap_exceptions (fun () -> gen_auto_multi_rewrite conds tac_main lbas cl)
    | _ ->
        Tacticals.New.tclZEROMSG (strbrk "autorewrite .. in .. using can only be used either with a unique hypothesis or on the conclusion.")

(* Functions necessary to the library object declaration *)
let cache_hintrewrite (_,(rbase,lrl)) =
  let base = try raw_find_base rbase with Not_found -> HintDN.empty in
  let max = try fst (Util.List.last (HintDN.find_all base)) with Failure _ -> 0
  in
  let lrl = HintDN.refresh_metas lrl in
  let lrl = HintDN.map (fun (i,h) -> (i + max, h)) lrl in
    rewtab:=String.Map.add rbase (HintDN.union lrl base) !rewtab


let subst_hintrewrite (subst,(rbase,list as node)) =
  let list' = HintDN.subst subst list in
    if list' == list then node else
      (rbase,list')

(* Declaration of the Hint Rewrite library object *)
let inHintRewrite : string * HintDN.t -> Libobject.obj =
  let open Libobject in
  declare_object @@ superglobal_object_nodischarge "HINT_REWRITE"
    ~cache:cache_hintrewrite
    ~subst:(Some subst_hintrewrite)

open Clenv

type hypinfo = {
  hyp_cl : clausenv;
  hyp_prf : constr;
  hyp_ty : types;
  hyp_car : constr;
  hyp_rel : constr;
  hyp_l2r : bool;
  hyp_left : constr;
  hyp_right : constr;
}

let decompose_applied_relation metas env sigma c ctype left2right =
  let find_rel ty =
    let eqclause = Clenv.mk_clenv_from_env env sigma None (EConstr.of_constr c,ty) in
    let eqclause =
      if metas then eqclause
      else fst (clenv_pose_metas_as_evars eqclause (Evd.undefined_metas eqclause.evd))
    in
    let (equiv, args) = EConstr.decompose_app sigma (Clenv.clenv_type eqclause) in
    let rec split_last_two = function
      | [c1;c2] -> [],(c1, c2)
      | x::y::z ->
          let l,res = split_last_two (y::z) in x::l, res
      | _ -> raise Not_found
    in
      try
        let others,(c1,c2) = split_last_two args in
        let ty1, ty2 = Typing.unsafe_type_of env eqclause.evd c1, Typing.unsafe_type_of env eqclause.evd c2 in
        (* XXX: It looks like mk_clenv_from_env should be fixed instead? *)
        let open EConstr in
        let hyp_ty = Unsafe.to_constr ty in
        let hyp_car = Unsafe.to_constr ty1 in
        let hyp_prf = Unsafe.to_constr @@ Clenv.clenv_value eqclause in
        let hyp_rel = Unsafe.to_constr @@ mkApp (equiv, Array.of_list others) in
        let hyp_left = Unsafe.to_constr @@ c1 in
        let hyp_right = Unsafe.to_constr @@ c2 in
(*           if not (evd_convertible env eqclause.evd ty1 ty2) then None *)
(*           else *)
        Some { hyp_cl=eqclause; hyp_prf; hyp_ty; hyp_car; hyp_rel; hyp_l2r=left2right; hyp_left; hyp_right; }
      with Not_found -> None
  in
    match find_rel ctype with
    | Some c -> Some c
    | None ->
        let ctx,t' = Reductionops.splay_prod_assum env sigma ctype in (* Search for underlying eq *)
        match find_rel (it_mkProd_or_LetIn t' ctx) with
        | Some c -> Some c
        | None -> None

let find_applied_relation ?loc metas env sigma c left2right =
  let ctype = Typing.unsafe_type_of env sigma (EConstr.of_constr c) in
    match decompose_applied_relation metas env sigma c ctype left2right with
    | Some c -> c
    | None ->
        user_err ?loc ~hdr:"decompose_applied_relation"
                    (str"The type" ++ spc () ++ Printer.pr_econstr_env env sigma ctype ++
                       spc () ++ str"of this term does not end with an applied relation.")

(* To add rewriting rules to a base *)
let add_rew_rules base lrul =
  let counter = ref 0 in
  let env = Global.env () in
  let sigma = Evd.from_env env in
  let ist = Genintern.empty_glob_sign (Global.env ()) in
  let intern tac = snd (Genintern.generic_intern ist tac) in
  let lrul =
    List.fold_left
      (fun dn {CAst.loc;v=((c,ctx),b,t)} ->
        let sigma = Evd.merge_context_set Evd.univ_rigid sigma ctx in
        let info = find_applied_relation ?loc false env sigma c b in
        let pat = if b then info.hyp_left else info.hyp_right in
        let rul = { rew_lemma = c; rew_type = info.hyp_ty;
                    rew_pat = pat; rew_ctx = ctx; rew_l2r = b;
                    rew_tac = Option.map intern t}
        in incr counter;
          HintDN.add pat (!counter, rul) dn) HintDN.empty lrul
  in Lib.add_anonymous_leaf (inHintRewrite (base,lrul))
tactics/autorewrite.ml

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