(************************************************************************)
(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \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)         *)
(************************************************************************)

(* Created by Hugo Herbelin from contents related to inductive schemes
   initially developed by Christine Paulin (induction schemes), Vincent
   Siles (decidable equality and boolean equality) and Matthieu Sozeau
   (combined scheme) in file command.ml, Sep 2009 *)

(* This file provides entry points for manually or automatically
   declaring new schemes *)

open Pp
open Util
open Declarations
open Term
open Goptions
open Vernacexpr
open Ind_tables
open Auto_ind_decl
open Eqschemes
open Elimschemes
open Sorts

(** Data of an inductive scheme with name resolved *)
type resolved_scheme = Names.Id.t CAst.t * Indrec.dep_flag * Names.inductive * UnivGen.QualityOrSet.t

(** flag for internal message display *)
type internal_flag =
  | UserAutomaticRequest (* kernel action, a message is displayed *)
  | UserIndividualRequest   (* user action, a message is displayed *)

(* Flags governing automatic synthesis of schemes *)

let elim_flag = ref true
let () =
  declare_bool_option
    { optstage = Summary.Stage.Interp;
      optdepr  = None;
      optkey   = ["Elimination";"Schemes"];
      optread  = (fun () -> !elim_flag) ;
      optwrite = (fun b -> elim_flag := b) }

let bifinite_elim_flag = ref false
let () =
  declare_bool_option
    { optstage = Summary.Stage.Interp;
      optdepr  = None;
      optkey   = ["Nonrecursive";"Elimination";"Schemes"];
      optread  = (fun () -> !bifinite_elim_flag) ;
      optwrite = (fun b -> bifinite_elim_flag := b) }

let case_flag = ref false
let () =
  declare_bool_option
    { optstage = Summary.Stage.Interp;
      optdepr  = None;
      optkey   = ["Case";"Analysis";"Schemes"];
      optread  = (fun () -> !case_flag) ;
      optwrite = (fun b -> case_flag := b) }

let eq_flag = ref false
let () =
  declare_bool_option
    { optstage = Summary.Stage.Interp;
      optdepr  = None;
      optkey   = ["Boolean";"Equality";"Schemes"];
      optread  = (fun () -> !eq_flag) ;
      optwrite = (fun b -> eq_flag := b) }

let is_eq_flag () = !eq_flag

let eq_dec_flag = ref false
let () =
  declare_bool_option
    { optstage = Summary.Stage.Interp;
      optdepr  = None;
      optkey   = ["Decidable";"Equality";"Schemes"];
      optread  = (fun () -> !eq_dec_flag) ;
      optwrite = (fun b -> eq_dec_flag := b) }

let rewriting_flag = ref false
let () =
  declare_bool_option
    { optstage = Summary.Stage.Interp;
      optdepr  = None;
      optkey   = ["Rewriting";"Schemes"];
      optread  = (fun () -> !rewriting_flag) ;
      optwrite = (fun b -> rewriting_flag := b) }

(* Util *)
let define ~poly ?loc name sigma c types =
  let univs = Evd.univ_entry ~poly sigma in
  let entry = Declare.definition_entry ~univs ?types c in
  let kind = Decls.(IsDefinition Scheme) in
  let kn = Declare.declare_constant ?loc ~kind ~name (Declare.DefinitionEntry entry) in
  Declare.definition_message name;
  kn

(* Boolean equality *)

let declare_beq_scheme_gen ?locmap names kn =
  ignore (define_mutual_scheme ?locmap beq_scheme_kind names kn)

let debug = CDebug.create ~name:"indschemes" ()

let alarm what internal msg =
  match internal with
  | UserAutomaticRequest ->
    debug Pp.(fun () ->
        hov 0 msg ++ fnl () ++ what ++ str " not defined.");
    None
  | UserIndividualRequest -> Some msg

let try_declare_scheme ?locmap what f internal names kn =
  try f ?locmap names kn
  with e when CErrors.noncritical e ->
  let e = Exninfo.capture e in
  let rec extract_exn = function Logic_monad.TacticFailure e -> extract_exn e | e -> e in
  let msg = match extract_exn (fst e) with
    | ParameterWithoutEquality cst ->
        alarm what internal
          (str "Boolean equality not found for parameter " ++ Printer.pr_global cst ++
           str".")
    | InductiveWithProduct ->
        alarm what internal
          (str "Unable to decide equality of functional arguments.")
    | InductiveWithSort ->
        alarm what internal
          (str "Unable to decide equality of type arguments.")
    | NonSingletonProp ind ->
        alarm what internal
          (str "Cannot extract computational content from proposition " ++
           quote (Printer.pr_inductive (Global.env()) ind) ++ str ".")
    | EqNotFound ind' ->
        alarm what internal
          (str "Boolean equality on " ++
           quote (Printer.pr_inductive (Global.env()) ind') ++
           strbrk " is missing.")
    | UndefinedCst s ->
        alarm what internal
          (strbrk "Required constant " ++ str s ++ str " undefined.")
    | DeclareUniv.AlreadyDeclared (kind, id) as exn ->
      let msg = CErrors.print exn in
      alarm what internal msg
    | DecidabilityMutualNotSupported ->
        alarm what internal
          (str "Decidability lemma for mutual inductive types not supported.")
    | EqUnknown s ->
         alarm what internal
           (str "Found unsupported " ++ str s ++ str " while building Boolean equality.")
    | NoDecidabilityCoInductive ->
         alarm what internal
           (str "Scheme Equality is only for inductive types.")
    | DecidabilityIndicesNotSupported ->
         alarm what internal
           (str "Inductive types with indices not supported.")
    | ConstructorWithNonParametricInductiveType ind ->
         alarm what internal
           (strbrk "Unsupported constructor with an argument whose type is a non-parametric inductive type." ++
            strbrk " Type " ++ quote (Printer.pr_inductive (Global.env()) ind) ++
            str " is applied to an argument which is not a variable.")
    | InternalDependencies ->
         alarm what internal
           (strbrk "Inductive types with internal dependencies in constructors not supported.")
    | e ->
        alarm what internal
          (str "Unexpected error during scheme creation: " ++ CErrors.print e)
  in
  match msg with
  | None -> ()
  | Some msg -> Exninfo.iraise (CErrors.UserError msg, snd e)

let beq_scheme_msg mind =
  let mib = Global.lookup_mind mind in
  (* TODO: mutual inductive case *)
  str "Boolean equality on " ++
    pr_enum (fun ind -> quote (Printer.pr_inductive (Global.env()) ind))
    (List.init (Array.length mib.mind_packets) (fun i -> (mind,i)))

let declare_beq_scheme_with ?locmap l kn =
  try_declare_scheme (beq_scheme_msg kn) declare_beq_scheme_gen UserIndividualRequest l kn

let try_declare_beq_scheme ?locmap kn =
  (* TODO: handle Fix, eventually handle
      proof-irrelevance; improve decidability by depending on decidability
      for the parameters rather than on the bl and lb properties *)
  try_declare_scheme (beq_scheme_msg kn) declare_beq_scheme_gen UserAutomaticRequest [] kn

let declare_beq_scheme ?locmap mi = declare_beq_scheme_with ?locmap [] mi

(* Case analysis schemes *)
let declare_one_case_analysis_scheme ?loc ind =
  let (mib, mip) as specif = Global.lookup_inductive ind in
  let kind = Indrec.pseudo_sort_quality_for_elim ind mip in
  let dep, suff =
    if Sorts.Quality.is_qprop kind then case_nodep, Some "case"
    else if not (Inductiveops.has_dependent_elim specif) then
      case_nodep, None
    else case_dep, Some "case" in
  let id = match suff with
    | None -> None
    | Some suff ->
      (* the auto generated eliminator may be called "case" instead of eg "case_nodep" *)
      Some Names.(Id.of_string (Id.to_string mip.mind_typename ^ "_" ^ suff))
  in
  let kelim = Inductiveops.elim_sort (mib,mip) in
  if Sorts.Quality.eliminates_to kelim Sorts.Quality.qtype then
    define_individual_scheme ?loc dep id ind

(* Induction/recursion schemes *)

let declare_one_induction_scheme ?loc ind =
  let (mib,mip) as specif = Global.lookup_inductive ind in
  let kind = Indrec.pseudo_sort_quality_for_elim ind mip in
  let from_prop = Sorts.Quality.is_qprop kind in
  let depelim = Inductiveops.has_dependent_elim specif in
  let kelim = Inductiveops.constant_sorts_below
              @@ Inductiveops.elim_sort (mib,mip) in
  let kelim =
    if Global.sprop_allowed ()
    then kelim
    else List.filter (fun s -> not (UnivGen.QualityOrSet.is_sprop s)) kelim
  in
  let elims =
    List.filter (fun (sort,_) -> List.mem_f UnivGen.QualityOrSet.equal sort kelim)
      (* NB: the order is important, it makes it so that _rec is
         defined using _rect but _ind is not. *)
      [(UnivGen.QualityOrSet.qtype, "rect");
       (UnivGen.QualityOrSet.prop, "ind");
       (UnivGen.QualityOrSet.set, "rec");
       (UnivGen.QualityOrSet.sprop, "sind")]
  in
  let elims = List.map (fun (to_kind,dflt_suff) ->
      if from_prop then elim_scheme ~dep:false ~to_kind, Some dflt_suff
      else if depelim then elim_scheme ~dep:true ~to_kind, Some dflt_suff
      else elim_scheme ~dep:false ~to_kind, None)
      elims
  in
  List.iter (fun (kind, suff) ->
      let id = match suff with
        | None -> None
        | Some suff ->
          (* the auto generated eliminator may be called "rect" instead of eg "rect_dep" *)
          Some Names.(Id.of_string (Id.to_string mip.mind_typename ^ "_" ^ suff))
      in
      define_individual_scheme ?loc kind id ind)
         elims

let declare_induction_schemes ?(locmap=Locmap.default None) kn =
  let mib = Global.lookup_mind kn in
  if mib.mind_finite <> Declarations.CoFinite then begin
    for i = 0 to Array.length mib.mind_packets - 1 do
      let loc = Ind_tables.Locmap.lookup ~locmap (kn,i) in
      declare_one_induction_scheme (kn,i) ?loc;
    done;
  end

(* Decidable equality *)

let declare_eq_decidability_gen ?locmap names kn =
  let mib = Global.lookup_mind kn in
  if mib.mind_finite <> Declarations.CoFinite then
    define_mutual_scheme ?locmap eq_dec_scheme_kind names kn

let eq_dec_scheme_msg ind = (* TODO: mutual inductive case *)
  str "Decidable equality on " ++ quote (Printer.pr_inductive (Global.env()) ind)

let declare_eq_decidability_scheme_with ?locmap l kn =
  try_declare_scheme ?locmap (eq_dec_scheme_msg (kn,0))
    declare_eq_decidability_gen UserIndividualRequest l kn

let try_declare_eq_decidability ?locmap kn =
  try_declare_scheme ?locmap (eq_dec_scheme_msg (kn,0))
    declare_eq_decidability_gen UserAutomaticRequest [] kn

let declare_eq_decidability ?locmap mi = declare_eq_decidability_scheme_with ?locmap [] mi

let ignore_error f x =
  try f x with e when CErrors.noncritical e -> ()

let declare_rewriting_schemes ?loc ind =
  if Hipattern.is_inductive_equality (Global.env ()) ind then begin
    define_individual_scheme ?loc rew_r2l_scheme_kind None ind;
    define_individual_scheme ?loc rew_r2l_dep_scheme_kind None ind;
    define_individual_scheme ?loc rew_r2l_forward_dep_scheme_kind None ind;
    (* These ones expect the equality to be symmetric; the first one also *)
    (* needs eq *)
    ignore_error (define_individual_scheme rew_l2r_scheme_kind None) ind;
    ignore_error
      (define_individual_scheme ?loc sym_involutive_scheme_kind None) ind;
    ignore_error
      (define_individual_scheme ?loc rew_l2r_dep_scheme_kind None) ind;
    ignore_error
      (define_individual_scheme ?loc rew_l2r_forward_dep_scheme_kind None) ind
  end

let warn_cannot_build_congruence =
  CWarnings.create ~name:"cannot-build-congruence" ~category:CWarnings.CoreCategories.automation
         (fun () ->
          strbrk "Cannot build congruence scheme because eq is not found")

let declare_congr_scheme ?loc ind =
  let env = Global.env () in
  if Hipattern.is_inductive_equality env ind then begin
    if
      try Rocqlib.check_required_library Rocqlib.logic_module_name; true
      with e when CErrors.noncritical e -> false
    then
      define_individual_scheme ?loc congr_scheme_kind None ind
    else
      warn_cannot_build_congruence ()
  end

let declare_sym_scheme ?loc ind =
  if Hipattern.is_inductive_equality (Global.env ()) ind then
    (* Expect the equality to be symmetric *)
    ignore_error (define_individual_scheme ?loc sym_scheme_kind None) ind

(* Scheme command *)

(* Boolean on scheme_type cheking if it considered dependent *)
let sch_isdep = function
| SchemeInduction  | SchemeElimination -> true
| SchemeMinimality | SchemeCase        -> false

let sch_isrec = function
| SchemeInduction | SchemeMinimality -> true
| SchemeElimination | SchemeCase -> false

(* Generate suffix for scheme given a target sort *)
let scheme_suffix_gen {sch_type; sch_sort} sort =
  let open Quality in
  (* The _ind/_rec_/case suffix *)
  let ind_suffix = match sch_isrec sch_type, sch_sort with
    | true  , Qual (QConstant QSProp | QConstant QProp) -> "_ind"
    | true  , _ -> "_rec"
    | false , _ -> "_case" in
  (* SProp and Type have an auxillary ending to the _ind suffix *)
  let aux_suffix = match sch_sort with
    | Qual (QConstant QSProp) -> "s"
    | Qual (QConstant QType) -> "t"
    | _ -> "" in
  (* Some schemes are deliminated with _dep or no_dep *)
  let dep_suffix = match sch_isdep sch_type , sort with
    | true  , QConstant QProp  -> "_dep"
    | false , QConstant QType
    | false , QConstant QSProp -> "_nodep"
    | _ , _                    -> "" in
  ind_suffix ^ aux_suffix ^ dep_suffix

let smart_ind qid =
  let ind = Smartlocate.smart_global_inductive qid in
  if Dumpglob.dump() then Dumpglob.add_glob ?loc:qid.loc (IndRef ind);
  ind

(* Resolve the name of a scheme using an environment and extract some
   important data such as the inductive type involved, whether it is a dependent
   eliminator and its sort. *)
let name_and_process_scheme env = function
  | (Some id, {sch_type; sch_qualid; sch_sort}) ->
    (id, sch_isdep sch_type, smart_ind sch_qualid, sch_sort)
  | (None, ({sch_type; sch_qualid; sch_sort} as sch)) ->
    (* If no name has been provided, we build one from the types of the ind requested *)
    let ind = smart_ind sch_qualid in
    let sort_of_ind =
      Indrec.pseudo_sort_quality_for_elim ind
        (snd (Inductive.lookup_mind_specif env ind))
    in
    let suffix = scheme_suffix_gen sch sort_of_ind in
    let newid = Nameops.add_suffix (Nametab.basename_of_global (Names.GlobRef.IndRef ind)) suffix in
    let newref = CAst.make newid in
    (newref, sch_isdep sch_type, ind, sch_sort)

let do_mutual_induction_scheme ?(force_mutual=false) env ?(isrec=true) l =
  let sigma, inst =
    let _,_,ind,_ = match l with | x::_ -> x | [] -> assert false in
    let _, ctx = Typeops.type_of_global_in_context env (Names.GlobRef.IndRef ind) in
    let u, ctx = UnivGen.fresh_instance_from ctx None in
    let u = EConstr.EInstance.make u in
    let sigma = Evd.from_ctx (UState.of_context_set ctx) in
    sigma, u
  in
  let sigma, lrecspec =
    List.fold_left_map (fun sigma (_,dep,ind,sort) ->
        let sigma, sort = Evd.fresh_sort_in_quality ~rigid:UnivRigid sigma sort in
        (sigma, ((ind,inst),dep,sort)))
      sigma
      l
  in
  let sigma, listdecl =
    if isrec then Indrec.build_mutual_induction_scheme env sigma ~force_mutual lrecspec
    else
      List.fold_left_map (fun sigma (ind,dep,sort) ->
          let sigma, c = Indrec.build_case_analysis_scheme env sigma ind dep sort in
          let c, _ = Indrec.eval_case_analysis c in
          sigma, c)
        sigma lrecspec
  in
  let poly =
    (* NB: build_mutual_induction_scheme forces nonempty list of mutual inductives
       (force_mutual is about the generated schemes) *)
    let _,_,ind,_ = List.hd l in
    Global.is_polymorphic (Names.GlobRef.IndRef ind)
  in
  let declare decl ({CAst.v=fi; loc},dep,ind, sort) =
    let decltype = Retyping.get_type_of env sigma decl in
    let decltype = EConstr.to_constr sigma decltype in
    let decl = EConstr.to_constr sigma decl in
    let cst = define ?loc ~poly fi sigma decl (Some decltype) in
    let kind =
      let open Elimschemes in
      let open UnivGen.QualityOrSet in
      if isrec then Some (elim_scheme ~dep ~to_kind:sort)
      else match sort with
        | Qual (QConstant QType) -> Some (if dep then case_dep else case_nodep)
        | Qual (QConstant QProp) -> Some (if dep then casep_dep else casep_nodep)
        | Set | Qual (QConstant QSProp | QVar _) ->
          (* currently we don't have standard scheme kinds for this *)
          None
    in
    match kind with
    | None -> ()
    | Some kind ->
      (* TODO locality *)
      DeclareScheme.declare_scheme SuperGlobal (Ind_tables.scheme_kind_name kind) (ind,cst)
  in
  let () = List.iter2 declare listdecl l in
  let lrecnames = List.map (fun ({CAst.v},_,_,_) -> v) l in
  Declare.fixpoint_message None lrecnames

let do_scheme env l =
  let isrec = match l with
    | [_, sch] -> sch_isrec sch.sch_type
    | _ ->
      if List.for_all (fun (_,sch) -> sch_isrec sch.sch_type) l
      then true
      else CErrors.user_err Pp.(str "Mutually defined schemes should be recursive.")
  in
  let lnamedepindsort = List.map (name_and_process_scheme env) l in
  do_mutual_induction_scheme env ~isrec lnamedepindsort

let do_scheme_equality ?locmap sch id =
  let mind,_ = smart_ind id in
  let dec = match sch with SchemeBooleanEquality -> false | SchemeEquality -> true in
  declare_beq_scheme ?locmap mind;
  if dec then declare_eq_decidability ?locmap mind

(**********************************************************************)
(* Combined scheme *)
(* Matthieu Sozeau, Dec 2006 *)

let list_split_rev_at index l =
  let rec aux i acc = function
      hd :: tl when Int.equal i index -> acc, tl
    | hd :: tl -> aux (succ i) (hd :: acc) tl
    | [] -> failwith "List.split_when: Invalid argument"
  in aux 0 [] l

let fold_left' f = function
    [] -> invalid_arg "fold_left'"
  | hd :: tl -> List.fold_left f hd tl

let mk_rocq_and sigma = Evd.fresh_global (Global.env ()) sigma (Rocqlib.lib_ref "core.and.type")
let mk_rocq_conj sigma = Evd.fresh_global (Global.env ()) sigma (Rocqlib.lib_ref "core.and.conj")

let mk_rocq_prod sigma = Evd.fresh_global (Global.env ()) sigma (Rocqlib.lib_ref "core.prod.type")
let mk_rocq_pair sigma = Evd.fresh_global (Global.env ()) sigma (Rocqlib.lib_ref "core.prod.intro")

let build_combined_scheme env schemes =
  let sigma = Evd.from_env env in
  let sigma, defs = List.fold_left_map (fun sigma cst ->
    let sigma, c = Evd.fresh_constant_instance env sigma cst in
    sigma, (c, Typeops.type_of_constant_in env c)) sigma schemes in
  let find_inductive ty =
    let (ctx, arity) = decompose_prod ty in
    let (_, last) = List.hd ctx in
      match Constr.kind last with
        | Constr.App (ind, args) ->
            let ind = Constr.destInd ind in
            let (_,spec) = Inductive.lookup_mind_specif env (fst ind) in
              ctx, ind, spec.mind_nrealargs
        | _ -> ctx, Constr.destInd last, 0
  in
  let (c, t) = List.hd defs in
  let ctx, ind, nargs = find_inductive t in
  (* We check if ALL the predicates are in Prop, if so we use propositional
     conjunction '/\', otherwise we use the simple product '*'.
  *)
  let inprop =
    let inprop (_,t) =
      UnivGen.QualityOrSet.is_prop
        (Retyping.get_sort_quality_of env sigma (EConstr.of_constr t))
    in
    List.for_all inprop defs
  in
  let mk_and, mk_conj =
    if inprop
    then (mk_rocq_and, mk_rocq_conj)
    else (mk_rocq_prod, mk_rocq_pair)
  in
  (* Number of clauses, including the predicates quantification *)
  let prods = Termops.nb_prod sigma (EConstr.of_constr t) - (nargs + 1) in
  let sigma, rocqand  = mk_and sigma in
  let sigma, rocqconj = mk_conj sigma in
  let relargs = Termops.rel_vect 0 prods in
  let concls = List.rev_map
    (fun (cst, t) ->
      Constr.mkApp(Constr.mkConstU cst, relargs),
      snd (decompose_prod_n prods t)) defs in
  let concl_bod, concl_typ =
    fold_left'
      (fun (accb, acct) (cst, x) ->
        Constr.mkApp (EConstr.to_constr sigma rocqconj, [| x; acct; cst; accb |]),
        Constr.mkApp (EConstr.to_constr sigma rocqand, [| x; acct |])) concls
  in
  let ctx, _ =
    list_split_rev_at prods
      (List.rev_map (fun (x, y) -> Context.Rel.Declaration.LocalAssum (x, y)) ctx) in
  let typ = List.fold_left (fun d c -> Term.mkProd_wo_LetIn c d) concl_typ ctx in
  let body = it_mkLambda_or_LetIn concl_bod ctx in
  let sigma = Typing.check env sigma (EConstr.of_constr body) (EConstr.of_constr typ) in
  (sigma, body, typ)

let do_combined_scheme name csts =
  let open CAst in
  let sigma,body,typ = build_combined_scheme (Global.env ()) csts in
  (* It is possible for the constants to have different universe
     polymorphism from each other, however that is only when the user
     manually defined at least one of them (as Scheme would pick the
     polymorphism of the inductive block). In that case if they want
     some other polymorphism they can also manually define the
     combined scheme. *)
  let poly = Global.is_polymorphic (Names.GlobRef.ConstRef (List.hd csts)) in
  ignore (define ~poly ?loc:name.loc name.v sigma body (Some typ));
  Declare.fixpoint_message None [name.v]

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

let map_inductive_block ?(locmap=Locmap.default None) f kn n =
  for i=0 to n-1 do
    let loc = Ind_tables.Locmap.lookup ~locmap (kn,i) in
    f ?loc (kn,i)
  done

let declare_default_schemes ?locmap kn =
  let mib = Global.lookup_mind kn in
  let n = Array.length mib.mind_packets in
  if !elim_flag && (mib.mind_finite <> Declarations.BiFinite || !bifinite_elim_flag)
     && mib.mind_typing_flags.check_positive then
    declare_induction_schemes kn ?locmap;
  if !case_flag then map_inductive_block ?locmap declare_one_case_analysis_scheme kn n;
  if is_eq_flag() then try_declare_beq_scheme kn ?locmap;
  if !eq_dec_flag then try_declare_eq_decidability kn ?locmap;
  if !rewriting_flag then map_inductive_block ?locmap declare_congr_scheme kn n;
  if !rewriting_flag then map_inductive_block ?locmap declare_sym_scheme kn n;
  if !rewriting_flag then map_inductive_block ?locmap declare_rewriting_schemes kn n
