open Names
open Pp
open Constr
open Libnames
open Globnames
open Refiner

let mk_prefix pre id = Id.of_string (pre^(Id.to_string id))
let mk_rel_id = mk_prefix "R_"
let mk_correct_id id = Nameops.add_suffix (mk_rel_id id) "_correct"
let mk_complete_id id = Nameops.add_suffix (mk_rel_id id) "_complete"
let mk_equation_id id = Nameops.add_suffix id "_equation"

let msgnl m =
  ()

let fresh_id avoid s = Namegen.next_ident_away_in_goal (Id.of_string s) (Id.Set.of_list avoid)

let fresh_name avoid s = Name (fresh_id avoid s)

let get_name avoid ?(default="H") = function
  | Anonymous -> fresh_name avoid default
  | Name n -> Name n

let array_get_start a =
  Array.init
    (Array.length a - 1)
    (fun i -> a.(i))

let id_of_name = function
    Name id -> id
  | _ -> raise Not_found

let locate  ref =
    let {CAst.v=qid} = qualid_of_reference ref in
    Nametab.locate qid

let locate_ind ref =
  match locate ref with
    | IndRef x -> x
    | _ -> raise Not_found

let locate_constant ref =
  match locate ref with
    | ConstRef x -> x
    | _ -> raise Not_found


let locate_with_msg msg f x =
  try f x
  with Not_found -> raise (CErrors.UserError(None, msg))


let filter_map filter f =
  let rec it = function
    | [] -> []
    | e::l ->
	if filter e
	then
	  (f e) :: it l
	else it l
  in
  it


let chop_rlambda_n  =
  let rec chop_lambda_n acc n rt =
      if n == 0
      then List.rev acc,rt
      else
	match DAst.get rt with
	  | Glob_term.GLambda(name,k,t,b) -> chop_lambda_n ((name,t,None)::acc) (n-1) b
	  | Glob_term.GLetIn(name,v,t,b) -> chop_lambda_n ((name,v,t)::acc) (n-1) b
	  | _ ->
	      raise (CErrors.UserError(Some "chop_rlambda_n",
				    str "chop_rlambda_n: Not enough Lambdas"))
  in
  chop_lambda_n []

let chop_rprod_n  =
  let rec chop_prod_n acc n rt =
      if n == 0
      then List.rev acc,rt
      else
	match DAst.get rt with
	  | Glob_term.GProd(name,k,t,b) -> chop_prod_n ((name,t)::acc) (n-1) b
	  | _ -> raise (CErrors.UserError(Some "chop_rprod_n",str "chop_rprod_n: Not enough products"))
  in
  chop_prod_n []



let list_union_eq eq_fun l1 l2 =
  let rec urec = function
    | [] -> l2
    | a::l -> if List.exists (eq_fun a) l2 then urec l else a::urec l
  in
  urec l1

let list_add_set_eq eq_fun x l =
  if List.exists (eq_fun x) l then l else x::l

let const_of_id id =
  let princ_ref = qualid_of_ident id in
  try Constrintern.locate_reference princ_ref
  with Not_found ->
    CErrors.user_err ~hdr:"IndFun.const_of_id"
      (str "cannot find " ++ Id.print id)

let def_of_const t =
   match Constr.kind t with
    Const sp ->
      (try (match Environ.constant_opt_value_in (Global.env()) sp with
             | Some c -> c
	     | _ -> assert false)
       with Not_found -> assert false)
    |_ -> assert false

let coq_constant s =
  UnivGen.constr_of_global @@
  Coqlib.gen_reference_in_modules "RecursiveDefinition"
    Coqlib.init_modules s;;

let find_reference sl s =
  let dp = Names.DirPath.make (List.rev_map Id.of_string sl) in
  Nametab.locate (make_qualid dp (Id.of_string s))

let eq = lazy(EConstr.of_constr (coq_constant "eq"))
let refl_equal = lazy(EConstr.of_constr (coq_constant "eq_refl"))

(*****************************************************************)
(* Copy of the standart save mechanism but without the much too  *)
(* slow reduction function                                       *)
(*****************************************************************)
open Entries
open Decl_kinds
open Declare

let definition_message = Declare.definition_message

let get_locality = function
| Discharge -> true
| Local -> true
| Global -> false

let save with_clean id const (locality,_,kind) hook =
  let fix_exn = Future.fix_exn_of const.const_entry_body in
  let l,r = match locality with
    | Discharge when Lib.sections_are_opened () ->
        let k = Kindops.logical_kind_of_goal_kind kind in
	let c = SectionLocalDef const in
	let _ = declare_variable id (Lib.cwd(), c, k) in
	(Local, VarRef id)
    | Discharge | Local | Global ->
        let local = get_locality locality in
        let k = Kindops.logical_kind_of_goal_kind kind in
        let kn = declare_constant id ~local (DefinitionEntry const, k) in
	(locality, ConstRef kn)
  in
  if with_clean then Proof_global.discard_current ();
  CEphemeron.iter_opt hook (fun f -> Lemmas.call_hook fix_exn f l r);
  definition_message id



let cook_proof _ =
  let (id,(entry,_,strength)) = Pfedit.cook_proof () in
  (id,(entry,strength))

let get_proof_clean do_reduce =
  let result = cook_proof do_reduce in
  Proof_global.discard_current ();
  result

let with_full_print f a =
  let old_implicit_args = Impargs.is_implicit_args ()
  and old_strict_implicit_args =  Impargs.is_strict_implicit_args ()
  and old_contextual_implicit_args = Impargs.is_contextual_implicit_args () in
  let old_rawprint = !Flags.raw_print in
  let old_printuniverses = !Constrextern.print_universes in
  let old_printallowmatchdefaultclause = !Detyping.print_allow_match_default_clause in
  Constrextern.print_universes := true;
  Detyping.print_allow_match_default_clause := false;
  Flags.raw_print := true;
  Impargs.make_implicit_args false;
  Impargs.make_strict_implicit_args false;
  Impargs.make_contextual_implicit_args false;
  Dumpglob.pause ();
  try
    let res = f a in
    Impargs.make_implicit_args old_implicit_args;
    Impargs.make_strict_implicit_args old_strict_implicit_args;
    Impargs.make_contextual_implicit_args old_contextual_implicit_args;
    Flags.raw_print := old_rawprint;
    Constrextern.print_universes := old_printuniverses;
    Detyping.print_allow_match_default_clause := old_printallowmatchdefaultclause;
    Dumpglob.continue ();
    res
  with
    | reraise ->
	Impargs.make_implicit_args old_implicit_args;
	Impargs.make_strict_implicit_args old_strict_implicit_args;
	Impargs.make_contextual_implicit_args old_contextual_implicit_args;
	Flags.raw_print := old_rawprint;
	Constrextern.print_universes := old_printuniverses;
        Detyping.print_allow_match_default_clause := old_printallowmatchdefaultclause;
	Dumpglob.continue ();
	raise reraise






(**********************)

type function_info =
    {
      function_constant : Constant.t;
      graph_ind : inductive;
      equation_lemma : Constant.t option;
      correctness_lemma : Constant.t option;
      completeness_lemma : Constant.t option;
      rect_lemma : Constant.t option;
      rec_lemma : Constant.t option;
      prop_lemma : Constant.t option;
      is_general : bool; (* Has this function been defined using general recursive definition *)
    }


(* type function_db  = function_info list *)

(* let function_table = ref ([] : function_db) *)


let from_function = Summary.ref Cmap_env.empty ~name:"functions_db_fn"
let from_graph = Summary.ref Indmap.empty ~name:"functions_db_gr"

(*
let rec do_cache_info finfo = function
  | [] -> raise Not_found
  | (finfo'::finfos as l) ->
      if finfo' == finfo then l
      else if finfo'.function_constant = finfo.function_constant
      then finfo::finfos
      else
	let res = do_cache_info finfo finfos in
	if res == finfos then l else  finfo'::l


let cache_Function (_,(finfos)) =
  let new_tbl =
    try do_cache_info finfos !function_table
    with Not_found -> finfos::!function_table
  in
  if new_tbl != !function_table
  then function_table := new_tbl
*)

let cache_Function (_,finfos) =
  from_function := Cmap_env.add finfos.function_constant finfos !from_function;
  from_graph := Indmap.add finfos.graph_ind finfos !from_graph


let load_Function _  = cache_Function
let subst_Function (subst,finfos) =
  let do_subst_con c = Mod_subst.subst_constant subst c
  and do_subst_ind i = Mod_subst.subst_ind subst i
  in
  let function_constant' = do_subst_con finfos.function_constant in
  let graph_ind' = do_subst_ind finfos.graph_ind in
  let equation_lemma' = Option.Smart.map do_subst_con finfos.equation_lemma in
  let correctness_lemma' = Option.Smart.map do_subst_con finfos.correctness_lemma in
  let completeness_lemma' = Option.Smart.map do_subst_con finfos.completeness_lemma in
  let rect_lemma' = Option.Smart.map do_subst_con finfos.rect_lemma in
  let rec_lemma' = Option.Smart.map do_subst_con finfos.rec_lemma in
  let prop_lemma' =  Option.Smart.map do_subst_con finfos.prop_lemma in
  if function_constant' == finfos.function_constant &&
    graph_ind' == finfos.graph_ind &&
    equation_lemma' == finfos.equation_lemma &&
    correctness_lemma' == finfos.correctness_lemma &&
    completeness_lemma' == finfos.completeness_lemma &&
    rect_lemma' == finfos.rect_lemma &&
    rec_lemma' == finfos.rec_lemma &&
    prop_lemma' == finfos.prop_lemma
  then finfos
  else
    { function_constant = function_constant';
      graph_ind = graph_ind';
      equation_lemma = equation_lemma' ;
      correctness_lemma = correctness_lemma' ;
      completeness_lemma = completeness_lemma' ;
      rect_lemma = rect_lemma' ;
      rec_lemma = rec_lemma';
      prop_lemma = prop_lemma';
      is_general = finfos.is_general
    }

let classify_Function infos = Libobject.Substitute infos


let discharge_Function (_,finfos) =
  let function_constant' = Lib.discharge_con finfos.function_constant
  and graph_ind' = Lib.discharge_inductive finfos.graph_ind
  and equation_lemma' = Option.Smart.map Lib.discharge_con finfos.equation_lemma
  and correctness_lemma' = Option.Smart.map Lib.discharge_con finfos.correctness_lemma
  and completeness_lemma' = Option.Smart.map Lib.discharge_con finfos.completeness_lemma
  and rect_lemma' = Option.Smart.map Lib.discharge_con finfos.rect_lemma
  and rec_lemma' = Option.Smart.map Lib.discharge_con finfos.rec_lemma
  and prop_lemma' = Option.Smart.map Lib.discharge_con finfos.prop_lemma
  in
  if function_constant' == finfos.function_constant &&
    graph_ind' == finfos.graph_ind &&
    equation_lemma' == finfos.equation_lemma &&
    correctness_lemma' == finfos.correctness_lemma &&
    completeness_lemma' == finfos.completeness_lemma &&
    rect_lemma' == finfos.rect_lemma &&
    rec_lemma' == finfos.rec_lemma &&
    prop_lemma' == finfos.prop_lemma
  then Some finfos
  else
    Some { function_constant = function_constant' ;
	   graph_ind = graph_ind' ;
	   equation_lemma = equation_lemma' ;
	   correctness_lemma = correctness_lemma' ;
	   completeness_lemma = completeness_lemma';
	   rect_lemma = rect_lemma';
	   rec_lemma = rec_lemma';
	   prop_lemma = prop_lemma' ;
	   is_general = finfos.is_general
	 }

let pr_ocst c =
  let sigma, env = Pfedit.get_current_context () in
  Option.fold_right (fun v acc -> Printer.pr_lconstr_env env sigma (mkConst v)) c (mt ())

let pr_info f_info =
  let sigma, env = Pfedit.get_current_context () in
  str "function_constant := " ++
  Printer.pr_lconstr_env env sigma (mkConst f_info.function_constant)++ fnl () ++
  str "function_constant_type := " ++
  (try
     Printer.pr_lconstr_env env sigma
       (fst (Global.type_of_global_in_context env (ConstRef f_info.function_constant)))
   with e when CErrors.noncritical e -> mt ()) ++ fnl () ++
  str "equation_lemma := " ++ pr_ocst f_info.equation_lemma ++ fnl () ++
  str "completeness_lemma :=" ++ pr_ocst f_info.completeness_lemma ++ fnl () ++
  str "correctness_lemma := " ++ pr_ocst f_info.correctness_lemma ++ fnl () ++
  str "rect_lemma := " ++ pr_ocst f_info.rect_lemma ++ fnl () ++
  str "rec_lemma := " ++ pr_ocst f_info.rec_lemma ++ fnl () ++
  str "prop_lemma := " ++ pr_ocst f_info.prop_lemma ++ fnl () ++
  str "graph_ind := " ++ Printer.pr_lconstr_env env sigma (mkInd f_info.graph_ind) ++ fnl ()

let pr_table tb =
  let l = Cmap_env.fold (fun k v acc -> v::acc) tb [] in
  Pp.prlist_with_sep fnl pr_info l

let in_Function : function_info -> Libobject.obj =
  Libobject.declare_object
    {(Libobject.default_object "FUNCTIONS_DB") with
       Libobject.cache_function = cache_Function;
       Libobject.load_function  = load_Function;
       Libobject.classify_function  = classify_Function;
       Libobject.subst_function = subst_Function;
       Libobject.discharge_function = discharge_Function
(*        Libobject.open_function = open_Function; *)
    }


let find_or_none id =
  try Some
    (match Nametab.locate (qualid_of_ident id) with ConstRef c -> c | _ -> CErrors.anomaly (Pp.str "Not a constant.")
    )
  with Not_found -> None



let find_Function_infos f =
  Cmap_env.find f !from_function


let find_Function_of_graph ind =
  Indmap.find ind !from_graph

let update_Function finfo =
  (* Pp.msgnl (pr_info finfo); *)
  Lib.add_anonymous_leaf (in_Function finfo)
			 

let add_Function is_general f =
  let f_id = Label.to_id (Constant.label f) in
  let equation_lemma = find_or_none (mk_equation_id f_id)
  and correctness_lemma = find_or_none (mk_correct_id f_id)
  and completeness_lemma = find_or_none (mk_complete_id f_id)
  and rect_lemma = find_or_none (Nameops.add_suffix f_id "_rect")
  and rec_lemma = find_or_none (Nameops.add_suffix f_id "_rec")
  and prop_lemma = find_or_none (Nameops.add_suffix f_id "_ind")
  and graph_ind =
    match Nametab.locate (qualid_of_ident (mk_rel_id f_id))
    with | IndRef ind -> ind | _ -> CErrors.anomaly (Pp.str "Not an inductive.")
  in
  let finfos =
    { function_constant = f;
      equation_lemma = equation_lemma;
      completeness_lemma = completeness_lemma;
      correctness_lemma = correctness_lemma;
      rect_lemma = rect_lemma;
      rec_lemma = rec_lemma;
      prop_lemma = prop_lemma;
      graph_ind = graph_ind;
      is_general = is_general

    }
  in
  update_Function finfos

let pr_table () = pr_table !from_function
(*********************************)
(* Debuging *)
let functional_induction_rewrite_dependent_proofs = ref true
let function_debug = ref false
open Goptions

let functional_induction_rewrite_dependent_proofs_sig = 
  {
    optdepr = false;
    optname = "Functional Induction Rewrite Dependent";
    optkey =  ["Functional";"Induction";"Rewrite";"Dependent"];
    optread = (fun () -> !functional_induction_rewrite_dependent_proofs);
    optwrite = (fun b -> functional_induction_rewrite_dependent_proofs := b)
  }
let _ = declare_bool_option functional_induction_rewrite_dependent_proofs_sig

let do_rewrite_dependent () = !functional_induction_rewrite_dependent_proofs = true

let function_debug_sig =
  {
    optdepr = false;
    optname = "Function debug";
    optkey =  ["Function_debug"];
    optread = (fun () -> !function_debug);
    optwrite = (fun b -> function_debug := b)
  }

let _ = declare_bool_option function_debug_sig


let do_observe () = !function_debug 



let strict_tcc = ref false
let is_strict_tcc () = !strict_tcc
let strict_tcc_sig =
  {
    optdepr = false;
    optname = "Raw Function Tcc";
    optkey =  ["Function_raw_tcc"];
    optread = (fun () -> !strict_tcc);
    optwrite = (fun b -> strict_tcc := b)
  }

let _ = declare_bool_option strict_tcc_sig


exception Building_graph of exn
exception Defining_principle of exn
exception ToShow of exn

let jmeq () =
  try
    Coqlib.check_required_library Coqlib.jmeq_module_name;
    EConstr.of_constr @@
    UnivGen.constr_of_global @@
      Coqlib.coq_reference "Function" ["Logic";"JMeq"] "JMeq"
  with e when CErrors.noncritical e -> raise (ToShow e)

let jmeq_refl () =
  try
    Coqlib.check_required_library Coqlib.jmeq_module_name;
    EConstr.of_constr @@
    UnivGen.constr_of_global @@
      Coqlib.coq_reference "Function" ["Logic";"JMeq"] "JMeq_refl"
  with e when CErrors.noncritical e -> raise (ToShow e)

let h_intros l =
  tclMAP (fun x -> Proofview.V82.of_tactic (Tactics.Simple.intro x)) l

let h_id = Id.of_string "h"
let hrec_id = Id.of_string "hrec"
let well_founded = function () -> EConstr.of_constr (coq_constant "well_founded")
let acc_rel = function () -> EConstr.of_constr (coq_constant "Acc")
let acc_inv_id = function () -> EConstr.of_constr (coq_constant "Acc_inv")

let well_founded_ltof () = EConstr.of_constr @@ UnivGen.constr_of_global @@
    Coqlib.coq_reference "" ["Arith";"Wf_nat"] "well_founded_ltof"

let ltof_ref = function  () -> (find_reference ["Coq";"Arith";"Wf_nat"] "ltof")

let evaluable_of_global_reference r = (* Tacred.evaluable_of_global_reference (Global.env ()) *)
  match r with
      ConstRef sp -> EvalConstRef sp
    | VarRef id -> EvalVarRef id
    | _ -> assert false;;

let list_rewrite (rev:bool) (eqs: (EConstr.constr*bool) list) =
  tclREPEAT
    (List.fold_right
       (fun (eq,b) i -> tclORELSE (Proofview.V82.of_tactic ((if b then Equality.rewriteLR else Equality.rewriteRL) eq)) i)
       (if rev then (List.rev eqs) else eqs) (tclFAIL 0 (mt())));;

let decompose_lam_n sigma n =
  if n < 0 then CErrors.user_err Pp.(str "decompose_lam_n: integer parameter must be positive");
  let rec lamdec_rec l n c =
    if Int.equal n 0 then l,c
    else match EConstr.kind sigma c with
      | Lambda (x,t,c) -> lamdec_rec ((x,t)::l) (n-1) c
      | Cast (c,_,_)     -> lamdec_rec l n c
      | _ -> CErrors.user_err Pp.(str "decompose_lam_n: not enough abstractions")
  in
  lamdec_rec [] n

let lamn n env b =
  let open EConstr in
  let rec lamrec = function
    | (0, env, b)        -> b
    | (n, ((v,t)::l), b) -> lamrec (n-1,  l, mkLambda (v,t,b))
    | _ -> assert false
  in
  lamrec (n,env,b)

(* compose_lam [xn:Tn;..;x1:T1] b = [x1:T1]..[xn:Tn]b *)
let compose_lam l b = lamn (List.length l) l b

(* prodn n [xn:Tn;..;x1:T1;Gamma] b = (x1:T1)..(xn:Tn)b *)
let prodn n env b =
  let open EConstr in
  let rec prodrec = function
    | (0, env, b)        -> b
    | (n, ((v,t)::l), b) -> prodrec (n-1,  l, mkProd (v,t,b))
    | _ -> assert false
  in
  prodrec (n,env,b)

(* compose_prod [xn:Tn;..;x1:T1] b = (x1:T1)..(xn:Tn)b *)
let compose_prod l b = prodn (List.length l) l b

type tcc_lemma_value =
  | Undefined
  | Value of constr
  | Not_needed

(* We only "purify" on exceptions. XXX: What is this doing here? *)
let funind_purify f x =
  let st = Vernacstate.freeze_interp_state `No in
  try f x
  with e ->
    let e = CErrors.push e in
    Vernacstate.unfreeze_interp_state st;
    Exninfo.iraise e