src/Pure/Syntax/syntax_phases.ML

clarified term positions and markup: syntax = true means this is via concrete syntax;
clarified text color rendering;

(*  Title:      Pure/Syntax/syntax_phases.ML
    Author:     Makarius

Main phases of inner syntax processing, with standard implementations
of parse/unparse operations.
*)

signature SYNTAX_PHASES =
sig
  val markup_free: Proof.context -> string -> Markup.T list
  val reports_of_scope: Position.T list -> Position.report list
  val decode_sort: term -> sort
  val decode_typ: term -> typ
  val decode_term: Proof.context ->
    Position.report_text list * term Exn.result -> Position.report_text list * term Exn.result
  val parse_ast_pattern: Proof.context -> string * string -> Ast.ast
  val term_of_typ: Proof.context -> typ -> term
  val print_checks: Proof.context -> unit
  val typ_check: int -> string -> (Proof.context -> typ list -> typ list) ->
    Context.generic -> Context.generic
  val term_check: int -> string -> (Proof.context -> term list -> term list) ->
    Context.generic -> Context.generic
  val typ_uncheck: int -> string -> (Proof.context -> typ list -> typ list) ->
    Context.generic -> Context.generic
  val term_uncheck: int -> string -> (Proof.context -> term list -> term list) ->
    Context.generic -> Context.generic
  val typ_check': int -> string ->
    (typ list -> Proof.context -> (typ list * Proof.context) option) ->
    Context.generic -> Context.generic
  val term_check': int -> string ->
    (term list -> Proof.context -> (term list * Proof.context) option) ->
    Context.generic -> Context.generic
  val typ_uncheck': int -> string ->
    (typ list -> Proof.context -> (typ list * Proof.context) option) ->
    Context.generic -> Context.generic
  val term_uncheck': int -> string ->
    (term list -> Proof.context -> (term list * Proof.context) option) ->
    Context.generic -> Context.generic
end

structure Syntax_Phases: SYNTAX_PHASES =
struct

(** markup logical entities **)

fun markup_class ctxt c =
  [Name_Space.markup (Type.class_space (Proof_Context.tsig_of ctxt)) c];

fun markup_type ctxt c =
  [Name_Space.markup (Type.type_space (Proof_Context.tsig_of ctxt)) c];

fun markup_const ctxt c =
  [Name_Space.markup (Consts.space_of (Proof_Context.consts_of ctxt)) c];

fun markup_free ctxt x =
  let
    val strict = Variable.is_body ctxt andalso not (Syntax.is_pretty_global ctxt);
    val m1 = if Variable.is_fixed ctxt x orelse strict then [Variable.markup_fixed ctxt x] else [];
    val m2 = Variable.markup ctxt x;
  in m1 @ [m2] end;

fun markup_var xi = [Markup.name (Term.string_of_vname xi) Markup.var];

fun markup_bound def (ps: Term_Position.T list) (name, id) =
  Markup.bound ::
    map (fn {pos, ...} => Position.make_entity_markup def id Markup.boundN (name, pos)) ps;

fun markup_entity ctxt c =
  Syntax.get_consts (Proof_Context.syntax_of ctxt) c
  |> maps (Lexicon.unmark
     {case_class = markup_class ctxt,
      case_type = markup_type ctxt,
      case_const = markup_const ctxt,
      case_fixed = markup_free ctxt,
      case_default = K []});



(** reports of implicit variable scope **)

fun reports_of_scope [] = []
  | reports_of_scope (def_pos :: ps) =
      let
        val id = serial ();
        fun entity def = Position.make_entity_markup def id "" ("", def_pos);
      in
        map (rpair Markup.bound) (def_pos :: ps) @
        ((def_pos, entity {def = true}) :: map (rpair (entity {def = false})) ps)
      end;



(** decode parse trees **)

(* decode_sort *)

fun decode_sort tm =
  let
    fun err () = raise TERM ("decode_sort: bad encoding of classes", [tm]);

    fun class s = Lexicon.unmark_class s handle Fail _ => err ();

    fun classes (Const (s, _)) = [class s]
      | classes (Const ("_classes", _) $ Const (s, _) $ cs) = class s :: classes cs
      | classes _ = err ();

    fun sort (Const ("_dummy_sort", _)) = dummyS
      | sort (Const ("_topsort", _)) = []
      | sort (Const ("_sort", _) $ cs) = classes cs
      | sort (Const (s, _)) = [class s]
      | sort _ = err ();
  in sort tm end;


(* decode_typ *)

fun decode_pos (Free (x, _)) = if Term_Position.detect x then SOME x else NONE
  | decode_pos _ = NONE;

fun decode_typ tm =
  let
    fun err () = raise TERM ("decode_typ: bad encoding of type", [tm]);

    fun typ ps sort tm =
      (case tm of
        Const ("_tfree", _) $ t => typ ps sort t
      | Const ("_tvar", _) $ t => typ ps sort t
      | Const ("_ofsort", _) $ t $ s =>
          (case decode_pos s of
            SOME p => typ (p :: ps) sort t
          | NONE =>
              if is_none sort then typ ps (SOME (decode_sort s)) t
              else err ())
      | Const ("_dummy_ofsort", _) $ s => TFree ("'_dummy_", decode_sort s)
      | Free (x, _) => TFree (x, ps @ the_default dummyS sort)
      | Var (xi, _) => TVar (xi, ps @ the_default dummyS sort)
      | _ =>
          if null ps andalso is_none sort then
            let
              val (head, args) = Term.strip_comb tm;
              val a =
                (case head of
                  Const (c, _) => (Lexicon.unmark_type c handle Fail _ => err ())
                | _ => err ());
            in Type (a, map (typ [] NONE) args) end
          else err ());
  in typ [] NONE tm end;


(* parsetree_to_ast *)

fun parsetree_literals (Parser.Markup (_, ts)) = maps parsetree_literals ts
  | parsetree_literals (Parser.Node _) = []
  | parsetree_literals (Parser.Tip tok) =
      if Lexicon.is_literal tok andalso
        not (null (Lexicon.literal_markup (Lexicon.str_of_token tok)))
      then filter Position.is_reported [Lexicon.pos_of_token tok] else [];

fun parsetree_to_ast ctxt trf parsetree =
  let
    val reports = Unsynchronized.ref ([]: Position.report_text list);
    fun report pos = Term_Position.store_reports reports [pos];
    val append_reports = Position.append_reports reports;

    fun report_pos tok =
      if Lexicon.is_literal tok andalso null (Lexicon.literal_markup (Lexicon.str_of_token tok))
      then Position.none else Lexicon.pos_of_token tok;

    val markup_cache = Symtab.apply_unsynchronized_cache (markup_entity ctxt);

    val ast_of_pos = Ast.Variable o Term_Position.encode;
    val ast_of_position = Ast.Variable o Term_Position.encode_no_syntax o single o report_pos;

    val syntax_ast_of_pos = Ast.Variable o Term_Position.encode_syntax;
    val syntax_ast_of_position = syntax_ast_of_pos o single o report_pos;
    fun syntax_ast_of_position' a = Ast.constrain (Ast.Constant a) o syntax_ast_of_position;

    fun asts_of_token tok =
      if Lexicon.valued_token tok
      then [Ast.Variable (Lexicon.str_of_token tok)]
      else [];

    fun asts_of_position c tok =
      [Ast.Appl [Ast.Constant c, ast_of (Parser.Tip tok), ast_of_position tok]]

    and asts_of (Parser.Markup ({markup, range = (pos, _), ...}, pts)) =
          let
            val asts = maps asts_of pts;
            val _ = append_reports (map (pair pos) markup);
          in asts end
      | asts_of (Parser.Node ({const = "", ...}, pts)) = maps asts_of pts
      | asts_of (Parser.Node ({const = "_class_name", ...}, [Parser.Tip tok])) =
          let
            val pos = report_pos tok;
            val (c, rs) = Proof_Context.check_class ctxt (Lexicon.str_of_token tok, pos);
            val _ = append_reports rs;
          in [Ast.Constant (Lexicon.mark_class c)] end
      | asts_of (Parser.Node ({const = "_type_name", ...}, [Parser.Tip tok])) =
          let
            val pos = report_pos tok;
            val (c, rs) =
              Proof_Context.check_type_name {proper = true, strict = false} ctxt
                (Lexicon.str_of_token tok, pos)
              |>> dest_Type_name;
            val _ = append_reports rs;
          in [Ast.Constant (Lexicon.mark_type c)] end
      | asts_of (Parser.Node ({const = "_DDDOT", ...}, [Parser.Tip tok])) =
          [Ast.constrain (Ast.Variable Auto_Bind.dddot_vname) (syntax_ast_of_position tok)]
      | asts_of (Parser.Node ({const = "_position", ...}, [Parser.Tip tok])) =
          asts_of_position "_constrain" tok
      | asts_of (Parser.Node ({const = "_position_sort", ...}, [Parser.Tip tok])) =
          asts_of_position "_ofsort" tok
      | asts_of (Parser.Node ({const = a as "\<^const>Pure.dummy_pattern", ...}, [Parser.Tip tok])) =
          [syntax_ast_of_position' a tok]
      | asts_of (Parser.Node ({const = a as "_idtdummy", ...}, [Parser.Tip tok])) =
          [syntax_ast_of_position' a tok]
      | asts_of (Parser.Node ({const = "_idtypdummy", ...}, pts as [Parser.Tip tok, _, _])) =
          let val args = maps asts_of pts
          in [Ast.Appl (Ast.Constant "_constrain" :: syntax_ast_of_position' "_idtdummy" tok :: args)] end
      | asts_of (Parser.Node ({const = a, ...}, pts)) =
          let
            val ps = map Term_Position.syntax (maps parsetree_literals pts);
            val args = maps asts_of pts;
            fun head () =
              if not (null ps) andalso (Lexicon.is_fixed a orelse Lexicon.is_const a)
              then Ast.constrain (Ast.Constant a) (ast_of_pos ps)
              else Ast.Constant a;
            val _ = List.app (fn pos => report pos markup_cache a) ps;
          in
            [case trf a of
              SOME f => f ctxt args
            | NONE => Ast.mk_appl (head ()) args]
          end
      | asts_of (Parser.Tip tok) = asts_of_token tok

    and ast_of pt =
      (case asts_of pt of
        [ast] => ast
      | asts => raise Ast.AST ("parsetree_to_ast: malformed parsetree", asts));

    val ast = Exn.result ast_of parsetree;
  in (! reports, ast) end;


(* ast_to_term *)

fun ast_to_term ctxt trf =
  let
    fun trans a args =
      (case trf a of
        NONE => Term.list_comb (Syntax.const a, args)
      | SOME f => f ctxt args);

    fun term_of (Ast.Constant a) = trans a []
      | term_of (Ast.Variable x) = Lexicon.read_var x
      | term_of (Ast.Appl (Ast.Constant a :: (asts as _ :: _))) =
          trans a (map term_of asts)
      | term_of (Ast.Appl (ast :: (asts as _ :: _))) =
          Term.list_comb (term_of ast, map term_of asts)
      | term_of (ast as Ast.Appl _) = raise Ast.AST ("ast_to_term: malformed ast", [ast]);
  in term_of end;


(* decode_term -- transform parse tree into raw term *)

fun decode_const ctxt (c, ps) =
  Proof_Context.check_const {proper = true, strict = false} ctxt (c, ps)
  |>> dest_Const_name;

fun decode_term ctxt =
  let
    val markup_free_cache = Symtab.apply_unsynchronized_cache (markup_free ctxt);
    val markup_const_cache = Symtab.apply_unsynchronized_cache (markup_const ctxt);

    fun decode (result as (_: Position.report_text list, Exn.Exn _)) = result
      | decode (reports0, Exn.Res tm) =
          let
            val reports = Unsynchronized.ref reports0;
            fun report ps = Term_Position.store_reports reports ps;
            val append_reports = Position.append_reports reports;

            fun decode ps qs bs (Const ("_constrain", _) $ t $ typ) =
                  (case Term_Position.decode_position typ of
                    SOME (ps', T) => Type.constraint T (decode (ps' @ ps) qs bs t)
                  | NONE => Type.constraint (decode_typ typ) (decode ps qs bs t))
              | decode ps qs bs (Const ("_constrainAbs", _) $ t $ typ) =
                  (case Term_Position.decode_position typ of
                    SOME (qs', T) => Type.constraint (T --> dummyT) (decode ps (qs' @ qs) bs t)
                  | NONE => Type.constraint (decode_typ typ --> dummyT) (decode ps qs bs t))
              | decode _ qs bs (Abs (x, T, t)) =
                  let
                    val id = serial ();
                    val _ = report qs (markup_bound {def = true} qs) (x, id);
                  in Abs (x, T, decode [] [] ((qs, (x, id)) :: bs) t) end
              | decode _ _ bs (t $ u) = decode [] [] bs t $ decode [] [] bs u
              | decode ps _ _ (Const (a, T)) =
                  (case try Lexicon.unmark_fixed a of
                    SOME x => Free (x, T)
                  | NONE =>
                      (case try Lexicon.unmark_const a of
                        SOME c => Const (c, T)
                      | NONE =>
                          let val c = #1 (decode_const ctxt (a, []))
                          in report ps markup_const_cache c; Const (c, T) end))
              | decode ps _ _ (Free (a, T)) =
                  ((Name.reject_internal (a, map #pos ps) handle ERROR msg =>
                      error (msg ^ Proof_Context.consts_completion_message ctxt (a, map #pos ps)));
                    (case Proof_Context.lookup_free ctxt a of
                      SOME x => (report ps markup_free_cache x; Free (x, T))
                    | NONE =>
                        let
                          val (c, rs) = decode_const ctxt (a, map #pos ps);
                          val _ = append_reports rs;
                        in Const (c, T) end))
              | decode ps _ _ (Var (xi, T)) = (report ps markup_var xi; Var (xi, T))
              | decode ps _ bs (t as Bound i) =
                  (case try (nth bs) i of
                    SOME (qs, (x, id)) => (report ps (markup_bound {def = false} qs) (x, id); t)
                  | NONE => t);

            val tm' = Exn.result (fn () => decode [] [] [] tm) ();
          in (! reports, tm') end;

  in decode end;



(** parse **)

(* results *)

fun proper_results results = map_filter (fn (y, Exn.Res x) => SOME (y, x) | _ => NONE) results;
fun failed_results results = map_filter (fn (y, Exn.Exn e) => SOME (y, e) | _ => NONE) results;

fun report_result ctxt pos ambig_msgs results =
  (case (proper_results results, failed_results results) of
    ([], (reports, exn) :: _) => (Context_Position.reports_text ctxt reports; Exn.reraise exn)
  | ([(reports, x)], _) => (Context_Position.reports_text ctxt reports; x)
  | _ =>
      if null ambig_msgs then
        error ("Parse error: ambiguous syntax" ^ Position.here pos)
      else error (cat_lines ambig_msgs));


(* parse raw asts *)

fun parse_asts ctxt raw root (syms, pos) =
  let
    val syn = Proof_Context.syntax_of ctxt;
    val ast_tr = Syntax.parse_ast_translation syn;

    val toks = Syntax.tokenize syn raw syms;
    val _ = Context_Position.reports ctxt (maps Lexicon.reports_of_token toks);

    val pts = Syntax.parse syn root (filter Lexicon.is_proper toks)
      handle ERROR msg =>
        error (msg ^ Markup.markup_report (implode (map (Lexicon.reported_token_range ctxt) toks)));
    val len = length pts;

    val limit = Config.get ctxt Syntax.ambiguity_limit;
    val ambig_msgs =
      if len <= 1 then []
      else
        [cat_lines
          (("Ambiguous input" ^ Position.here (Position.no_range_position pos) ^
            " produces " ^ string_of_int len ^ " parse trees" ^
            (if len <= limit then "" else " (" ^ string_of_int limit ^ " displayed)") ^ ":") ::
            map (Pretty.string_of o Pretty.item o Parser.pretty_tree) (take limit pts))];

  in (ambig_msgs, map (parsetree_to_ast ctxt ast_tr) pts) end;

fun parse_tree ctxt root input =
  let
    val syn = Proof_Context.syntax_of ctxt;
    val tr = Syntax.parse_translation syn;
    val normalize = Ast.normalize ctxt {permissive_constraints = false} (Syntax.parse_rules syn);
    val (ambig_msgs, asts) = parse_asts ctxt false root input;
    val results = (map o apsnd o Exn.maps_res) (normalize #> Exn.result (ast_to_term ctxt tr)) asts;
  in (ambig_msgs, results) end;


(* parse logical entities *)

fun parse_failed ctxt pos msg kind =
  cat_error msg ("Failed to parse " ^ kind ^
    Markup.markup_report (Context_Position.reported_text ctxt pos (Markup.bad ()) ""));

fun parse_sort ctxt =
  Syntax.parse_input ctxt Term_XML.Decode.sort Markup.language_sort
    (fn (syms, pos) =>
      parse_tree ctxt "sort" (syms, pos)
      |> uncurry (report_result ctxt pos)
      |> decode_sort
      |> Type.minimize_sort (Proof_Context.tsig_of ctxt)
      handle ERROR msg => parse_failed ctxt pos msg "sort");

fun parse_typ ctxt =
  Syntax.parse_input ctxt Term_XML.Decode.typ Markup.language_type
    (fn (syms, pos) =>
      parse_tree ctxt "type" (syms, pos)
      |> uncurry (report_result ctxt pos)
      |> decode_typ
      handle ERROR msg => parse_failed ctxt pos msg "type");

fun parse_term is_prop ctxt =
  let
    val (markup, kind, root, constrain) =
      if is_prop
      then (Markup.language_prop, "prop", "prop", Type.constraint propT)
      else (Markup.language_term, "term", Config.get ctxt Syntax.root, I);
    val decode = constrain o Term_XML.Decode.term (Proof_Context.consts_of ctxt);
  in
    Syntax.parse_input ctxt decode markup
      (fn (syms, pos) =>
        let
          val (ambig_msgs, results) = parse_tree ctxt root (syms, pos) ||> map (decode_term ctxt);
          val parsed_len = length (proper_results results);

          val ambiguity_warning = Config.get ctxt Syntax.ambiguity_warning;
          val limit = Config.get ctxt Syntax.ambiguity_limit;

          (*brute-force disambiguation via type-inference*)
          fun check t =
            (Syntax.check_term (Proof_Context.allow_dummies ctxt) (constrain t); Exn.Res t)
              handle exn as ERROR _ => Exn.Exn exn;

          fun par_map xs = Par_List.map' {name = "Syntax_Phases.parse_term", sequential = false} xs;
          val results' =
            if parsed_len > 1 then (grouped 10 par_map o apsnd o Exn.maps_res) check results
            else results;
          val reports' = fst (hd results');

          val errs = map snd (failed_results results');
          val checked = map snd (proper_results results');
          val checked_len = length checked;

          val pretty_term = Syntax.pretty_term (Config.put Printer.show_brackets true ctxt);
        in
          if checked_len = 0 then
            report_result ctxt pos []
              [(reports', Exn.Exn (Exn.EXCEPTIONS (map ERROR ambig_msgs @ errs)))]
          else if checked_len = 1 then
            (if not (null ambig_msgs) andalso ambiguity_warning andalso
                Context_Position.is_visible ctxt then
              warning
                (cat_lines (ambig_msgs @
                  ["Fortunately, only one parse tree is well-formed and type-correct,\n\
                   \but you may still want to disambiguate your grammar or your input."]))
             else (); report_result ctxt pos [] results')
          else
            report_result ctxt pos []
              [(reports', Exn.Exn (ERROR (cat_lines (ambig_msgs @
                (("Ambiguous input\n" ^ string_of_int checked_len ^ " terms are type correct" ^
                  (if checked_len <= limit then ""
                   else " (" ^ string_of_int limit ^ " displayed)") ^ ":") ::
                  map (Pretty.string_of o Pretty.item o single o pretty_term)
                    (take limit checked))))))]
        end handle ERROR msg => parse_failed ctxt pos msg kind)
  end;


(* parse_ast_pattern *)

fun parse_ast_pattern ctxt (root, str) =
  let
    val syn = Proof_Context.syntax_of ctxt;

    val reports = Unsynchronized.ref ([]: Position.report_text list);
    fun report ps = Term_Position.store_reports reports ps;

    val markup_cache = Symtab.apply_unsynchronized_cache (markup_entity ctxt);

    fun decode_const ps c = (report ps markup_cache c; Ast.Constant c);
    fun decode_var ps x = (report ps (fn () => [Markup.name x Markup.free]) (); Ast.Variable x);
    fun decode_appl ps asts = Ast.Appl (map (decode ps) asts)
    and decode ps (Ast.Constant c) = decode_const ps c
      | decode ps (Ast.Variable x) =
          if Syntax.is_const syn x orelse Long_Name.is_qualified x
          then decode_const ps x
          else decode_var ps x
      | decode ps (Ast.Appl (asts as (Ast.Constant c :: ast :: Ast.Variable x :: args))) =
          if member (op =) Term_Position.markers c then
            (case Term_Position.decode x of
              [] => decode_appl ps asts
            | ps' => Ast.mk_appl (decode (ps' @ ps) ast) (map (decode ps) args))
          else decode_appl ps asts
      | decode ps (Ast.Appl asts) = decode_appl ps asts;

    val source = Syntax.read_input str;
    val pos = Input.pos_of source;
    val syms = Input.source_explode source;
    val ast =
      parse_asts ctxt true root (syms, pos)
      |> uncurry (report_result ctxt pos)
      |> decode [];
    val _ = Context_Position.reports_text ctxt (! reports);
  in ast end;



(** encode parse trees **)

(* term_of_sort *)

fun term_of_sort S =
  let
    val class = Syntax.const o Lexicon.mark_class;

    fun classes [c] = class c
      | classes (c :: cs) = Syntax.const "_classes" $ class c $ classes cs;
  in
    if S = dummyS then Syntax.const "_dummy_sort"
    else
      (case S of
        [] => Syntax.const "_topsort"
      | [c] => class c
      | cs => Syntax.const "_sort" $ classes cs)
  end;


(* term_of_typ *)

fun term_of_typ ctxt ty =
  let
    val show_sorts = Config.get ctxt show_sorts orelse Config.get ctxt show_markup;

    fun ofsort t raw_S =
      if show_sorts then
        let val S = #2 (Term_Position.decode_positionS raw_S)
        in if S = dummyS then t else Syntax.const "_ofsort" $ t $ term_of_sort S end
      else t;

    fun term_of (Type (a, Ts)) =
          Term.list_comb (Syntax.const (Lexicon.mark_type a), map term_of Ts)
      | term_of (TFree (x, S)) =
          if Term_Position.detect x then Syntax.free x
          else ofsort (Syntax.const "_tfree" $ Syntax.free x) S
      | term_of (TVar (xi, S)) = ofsort (Syntax.const "_tvar" $ Syntax.var xi) S;
  in term_of ty end;


(* simple_ast_of *)

fun simple_ast_of ctxt =
  let
    val tune_var = if Config.get ctxt show_question_marks then I else unprefix "?";
    fun ast_of (Const (c, _)) = Ast.Constant c
      | ast_of (Free (x, _)) = Ast.Variable x
      | ast_of (Var (xi, _)) = Ast.Variable (tune_var (Term.string_of_vname xi))
      | ast_of (t as _ $ _) =
          let val (f, args) = strip_comb t
          in Ast.mk_appl (ast_of f) (map ast_of args) end
      | ast_of (Bound i) = Ast.Appl [Ast.Constant "_loose", Ast.Variable ("B." ^ string_of_int i)]
      | ast_of (Abs _) = raise Fail "simple_ast_of: Abs";
  in ast_of end;


(* sort_to_ast and typ_to_ast *)

fun ast_of_termT ctxt trf tm =
  let
    val ctxt' = Config.put show_sorts false ctxt;
    fun ast_of (t as Const ("_tfree", _) $ Free _) = simple_ast_of ctxt t
      | ast_of (t as Const ("_tvar", _) $ Var _) = simple_ast_of ctxt t
      | ast_of (Const (a, _)) = trans a []
      | ast_of (t as _ $ _) =
          (case strip_comb t of
            (Const (a, _), args) => trans a args
          | (f, args) => Ast.Appl (map ast_of (f :: args)))
      | ast_of t = simple_ast_of ctxt t
    and trans a args = ast_of (trf a ctxt' dummyT args)
      handle Match => Ast.mk_appl (Ast.Constant a) (map ast_of args);
  in ast_of tm end;

fun sort_to_ast ctxt trf S = ast_of_termT ctxt trf (term_of_sort S);
fun typ_to_ast ctxt trf T = ast_of_termT ctxt trf (term_of_typ ctxt T);


(* term_to_ast *)

local

fun mark_aprop tm =
  let
    fun aprop t = Syntax.const "_aprop" $ t;

    fun is_prop Ts t =
      Type_Annotation.clean (Type_Annotation.fastype_of Ts t) = propT
        handle TERM _ => false;

    fun is_term (Const ("Pure.term", _) $ _) = true
      | is_term _ = false;

    fun mark _ (t as Const _) = t
      | mark Ts (t as Const ("_bound", _) $ u) = if is_prop Ts u then aprop t else t
      | mark Ts (t as Free _) = if is_prop Ts t then aprop t else t
      | mark Ts (t as Var _) = if is_prop Ts t then aprop t else t
      | mark Ts (t as Bound _) = if is_prop Ts t then aprop t else t
      | mark Ts (Abs (x, T, t)) = Abs (x, T, mark (T :: Ts) t)
      | mark Ts (t as t1 $ (t2 as Const ("Pure.type", Type ("itself", [T])))) =
          if is_prop Ts t andalso not (is_term t) then Const ("_type_prop", T) $ mark Ts t1
          else mark Ts t1 $ mark Ts t2
      | mark Ts (t as t1 $ t2) =
          (if is_Const (Term.head_of t) orelse not (is_prop Ts t) then I else aprop)
            (mark Ts t1 $ mark Ts t2);
  in mark [] tm end;

fun prune_types tm =
  let
    fun regard t t' seen =
      if Type_Annotation.is_omitted (Type_Annotation.fastype_of [] t) then (t, seen)
      else if member (op aconv) seen t then (t', seen)
      else (t, t :: seen);

    fun prune (t as Const _, seen) = (t, seen)
      | prune (t as Free (x, T), seen) = regard t (Free (x, Type_Annotation.ignore_type T)) seen
      | prune (t as Var (xi, T), seen) = regard t (Var (xi, Type_Annotation.ignore_type T)) seen
      | prune (t as Bound _, seen) = (t, seen)
      | prune (Abs (x, T, t), seen) =
          let val (t', seen') = prune (t, seen);
          in (Abs (x, T, t'), seen') end
      | prune (t1 $ t2, seen) =
          let
            val (t1', seen') = prune (t1, seen);
            val (t2', seen'') = prune (t2, seen');
          in (t1' $ t2', seen'') end;
  in #1 (prune (tm, [])) end;

fun mark_atoms ctxt tm =
  let
    val {structs, fixes} = Syntax_Trans.get_idents ctxt;
    val show_structs = Config.get ctxt show_structs;

    fun mark ((t as Const (c, _)) $ u) =
          if member (op =) Pure_Thy.token_markers c
          then t $ u else mark t $ mark u
      | mark (t $ u) = mark t $ mark u
      | mark (Abs (x, T, t)) = Abs (x, T, mark t)
      | mark (t as Const (c, T)) =
          if Proof_Context.is_syntax_const ctxt c then t
          else Const (Lexicon.mark_const c, T)
      | mark (t as Free (x, T)) =
          let val i = find_index (fn s => s = x) structs + 1 in
            if i = 0 andalso member (op =) fixes x then
              Const (Lexicon.mark_fixed x, T)
            else if i = 1 andalso not show_structs then
              Syntax.const "_struct" $ Syntax.const "_indexdefault"
            else Syntax.const "_free" $ t
          end
      | mark (t as Var (xi, T)) =
          if xi = Auto_Bind.dddot_indexname then Const ("_DDDOT", T)
          else Syntax.const "_var" $ t
      | mark a = a;
  in mark tm end;

in

fun term_to_ast ctxt trf =
  let
    val show_types = Config.get ctxt show_types orelse Config.get ctxt show_sorts;
    val show_markup = Config.get ctxt show_markup;
    val show_consts_markup = Config.get ctxt show_consts_markup;

    val show_const_types = show_markup andalso show_consts_markup;
    val show_var_types = show_types orelse show_markup;
    val clean_var_types = show_markup andalso not show_types;

    fun constrain clean T ast =
      let val U = Type_Annotation.print clean T in
        if U = dummyT then ast
        else Ast.constrain ast (ast_of_termT ctxt trf (term_of_typ ctxt U))
      end;

    fun main tm =
      (case strip_comb tm of
        (t as Abs _, ts) => Ast.mk_appl (main (Syntax_Trans.abs_tr' ctxt t)) (map main ts)
      | ((c as Const ("_free", _)), Free (x, T) :: ts) =>
          Ast.mk_appl (variable (c $ Syntax.free x) T) (map main ts)
      | ((c as Const ("_var", _)), Var (xi, T) :: ts) =>
          Ast.mk_appl (variable (c $ Syntax.var xi) T) (map main ts)
      | ((c as Const ("_bound", B)), Free (x, T) :: ts) =>
          let
            val X =
              if show_markup andalso not show_types orelse B <> dummyT then T
              else dummyT;
          in Ast.mk_appl (variable (c $ Syntax.free x) X) (map main ts) end
      | (Const ("_idtdummy", T), ts) =>
          Ast.mk_appl (variable (Syntax.const "_idtdummy") T) (map main ts)
      | (Const (c, T), ts) => constant c T ts
      | (t, ts) => Ast.mk_appl (simple_ast_of ctxt t) (map main ts))

    and constant a T args =
      (case SOME (trf a ctxt (Type_Annotation.smash T) args) handle Match => NONE of
        SOME t => main t
      | NONE =>
          let val c = Ast.Constant a |> show_const_types ? constrain {clean = true} T
          in Ast.mk_appl c (map main args) end)

    and variable v T =
      simple_ast_of ctxt v
      |> show_var_types ? constrain {clean = clean_var_types} T;
  in
    mark_aprop
    #> show_types ? prune_types
    #> Variable.revert_bounds ctxt
    #> mark_atoms ctxt
    #> main
  end;

end;



(** unparse **)

local

fun extern ctxt c =
  (case Syntax.get_consts (Proof_Context.syntax_of ctxt) c of
    [b] => b
  | bs =>
      (case filter Lexicon.is_marked bs of
        [] => c
      | [b] => b
      | _ => error ("Multiple logical entities for " ^ quote c ^ ": " ^ commas_quote bs)))
  |> Proof_Context.extern_entity ctxt;

fun pretty_free ctxt x =
  Pretty.marks_str (markup_free ctxt x, Proof_Context.extern_fixed ctxt x);

fun pretty_var s =
  (case Lexicon.read_variable s of
    SOME (x, i) =>
      (case try Name.dest_skolem x of
        SOME x' => (Markup.skolem, Term.string_of_vname (x', i))
      | NONE => (Markup.var, s))
  | NONE => (Markup.var, s))
  |> Pretty.mark_str;

val typing_elem = YXML.output_markup_elem Markup.typing;
val sorting_elem = YXML.output_markup_elem Markup.sorting;

fun exclude_consts ast ctxt =
  let
    val s = the_default "" (Syntax_Trans.default_struct ctxt);

    fun exclude (Ast.Appl [Ast.Constant "_struct", Ast.Constant "_indexdefault"]) = Symset.insert s
      | exclude (Ast.Constant c) =
          if Lexicon.is_fixed c then Symset.insert (Lexicon.unmark_fixed c) else I
      | exclude (Ast.Appl [Ast.Constant "_bound", Ast.Variable x]) = Symset.insert x
      | exclude (Ast.Appl [Ast.Constant "_free", Ast.Variable x]) = Symset.insert x
      | exclude (Ast.Appl asts) = fold exclude asts
      | exclude _ = I;
  in Proof_Context.exclude_consts (Symset.build (exclude ast)) ctxt end;

fun unparse_t t_to_ast pretty_flags language_markup ctxt0 t =
  let
    val syn = Proof_Context.syntax_of ctxt0;
    val prtabs = Syntax.print_mode_tabs syn;
    val trf = Syntax.print_ast_translation syn;

    val ast = t_to_ast ctxt0 (Syntax.print_translation syn) t;
    val ctxt = exclude_consts ast ctxt0;

    val show_markup = Config.get ctxt show_markup;
    val show_sorts = Config.get ctxt show_sorts;
    val show_types = Config.get ctxt show_types orelse show_sorts;

    val pretty_free_cache = Symtab.apply_unsynchronized_cache (pretty_free ctxt);
    val pretty_var_cache = Symtab.apply_unsynchronized_cache pretty_var;

    val markup_syntax_cache =
      Symtab.apply_unsynchronized_cache (markup_entity ctxt #> map (Markup.syntax_properties true));

    val pretty_entity_cache =
      Symtab.apply_unsynchronized_cache (fn a =>
        Pretty.marks_str (markup_entity ctxt a, extern ctxt a));

    val cache1 = Unsynchronized.ref (Ast.Table.empty: Markup.output Pretty.block Ast.Table.table);
    val cache2 = Unsynchronized.ref (Ast.Table.empty: Markup.output Pretty.block Ast.Table.table);

    fun token_trans "_tfree" x = SOME (Pretty.mark_str (Markup.tfree, x))
      | token_trans "_tvar" x = SOME (Pretty.mark_str (Markup.tvar, x))
      | token_trans "_free" x = SOME (pretty_free_cache x)
      | token_trans "_bound" x = SOME (Pretty.mark_str (Markup.bound, x))
      | token_trans "_loose" x = SOME (Pretty.mark_str (Markup.bad (), x))
      | token_trans "_var" x = SOME (pretty_var_cache x)
      | token_trans "_numeral" x = SOME (Pretty.mark_str (Markup.numeral, x))
      | token_trans "_inner_string" x = SOME (Pretty.mark_str (Markup.inner_string, x))
      | token_trans _ _ = NONE;

    fun markup_trans a [Ast.Variable x] = token_trans a x
      | markup_trans "_constrain" [t, ty] = constrain_trans t ty
      | markup_trans "_idtyp" [t, ty] = constrain_trans t ty
      | markup_trans "_ofsort" [ty, s] = ofsort_trans ty s
      | markup_trans _ _ = NONE

    and constrain_trans t ty =
      if show_markup andalso not show_types
      then SOME (markup_ast true t ty) else NONE

    and ofsort_trans ty s =
      if show_markup andalso not show_sorts
      then SOME (markup_ast false ty s) else NONE

    and pretty_ast flags m =
      Printer.pretty flags ctxt prtabs
        {trf = trf, constrain_block = constrain_block true, constrain_trans = constrain_trans,
          markup_trans = markup_trans, markup_syntax = markup_syntax_cache,
          pretty_entity = pretty_entity_cache}
      #> Pretty.markup m

    and markup_ast is_typing a A =
      Pretty.make_block (constrain_block is_typing A)
        [pretty_ast (if is_typing then pretty_flags else Printer.type_mode_flags) Markup.empty a]

    and constrain_block is_typing A =
      let val cache = if is_typing then cache1 else cache2 in
        (case Ast.Table.lookup (! cache) A of
          SOME block => block
        | NONE =>
            let
              val ((bg1, bg2), en) = if is_typing then typing_elem else sorting_elem;
              val B = Pretty.symbolic_output (pretty_ast Printer.type_mode_flags Markup.empty A);
              val bg = implode (bg1 :: Bytes.contents B @ [bg2]);
              val block = {markup = (bg, en), open_block = false, consistent = false, indent = 0};
            in Unsynchronized.change cache (Ast.Table.update (A, block)); block end)
      end;
  in
    Ast.normalize ctxt {permissive_constraints = true} (Syntax.print_rules syn) ast
    |> pretty_ast pretty_flags language_markup
  end;

in

val unparse_sort = unparse_t sort_to_ast Printer.type_mode_flags (Markup.language_sort false);
val unparse_typ = unparse_t typ_to_ast Printer.type_mode_flags (Markup.language_type false);

fun unparse_term ctxt =
  let
    val thy = Proof_Context.theory_of ctxt;
    val pretty_flags = {type_mode = false, curried = not (Pure_Thy.old_appl_syntax thy)};
  in unparse_t term_to_ast pretty_flags (Markup.language_term false) ctxt end;

end;



(** translations **)

(* type propositions *)

fun type_prop_tr' ctxt T [Const ("\<^const>Pure.sort_constraint", _)] =
      Syntax.const "_sort_constraint" $ term_of_typ (Config.put show_sorts true ctxt) T
  | type_prop_tr' ctxt T [t] =
      Syntax.const "_ofclass" $ term_of_typ ctxt T $ t
  | type_prop_tr' _ T ts = raise TYPE ("type_prop_tr'", [T], ts);


(* type reflection *)

fun type_tr' ctxt (ty as Type ("itself", [T])) ts =
      Term.list_comb (Const ("_TYPE", ty) $ term_of_typ ctxt T, ts)
  | type_tr' _ _ _ = raise Match;


(* type constraints *)

fun type_constraint_tr' ctxt (Type ("fun", [T, _])) (t :: ts) =
      Term.list_comb (Syntax.const "_constrain" $ t $ term_of_typ ctxt T, ts)
  | type_constraint_tr' _ _ _ = raise Match;


(* authentic syntax *)

fun const_ast_tr intern ctxt asts =
  (case asts of
    [Ast.Appl [Ast.Constant "_constrain", Ast.Variable c, T as Ast.Variable p]] =>
      let
        val (c', _) = decode_const ctxt (c, map #pos (Term_Position.decode p));
        val d = if intern then Lexicon.mark_const c' else c;
      in Ast.constrain (Ast.Constant d) T end
  | _ => raise Ast.AST ("const_ast_tr", asts));


(* setup translations *)

val _ = Theory.setup
 (Sign.parse_ast_translation
   [("_context_const", const_ast_tr true),
    ("_context_xconst", const_ast_tr false)] #>
  Sign.typed_print_translation
   [("_type_prop", type_prop_tr'),
    ("\<^const>Pure.type", type_tr'),
    ("_type_constraint_", type_constraint_tr')]);



(** check/uncheck **)

(* context-sensitive (un)checking *)

type key = int * bool;

structure Checks = Generic_Data
(
  type 'a check = 'a list -> Proof.context -> ('a list * Proof.context) option;
  type T =
    ((key * ((string * typ check) * stamp) list) list *
     (key * ((string * term check) * stamp) list) list);
  val empty = ([], []);
  fun merge ((typ_checks1, term_checks1), (typ_checks2, term_checks2)) : T =
    (AList.join (op =) (K (Library.merge (eq_snd (op =)))) (typ_checks1, typ_checks2),
     AList.join (op =) (K (Library.merge (eq_snd (op =)))) (term_checks1, term_checks2));
);

fun print_checks ctxt =
  let
    fun split_checks checks =
      List.partition (fn ((_, un), _) => not un) checks
      |> apply2 (map (fn ((i, _), fs) => (i, map (fst o fst) fs))
          #> sort (int_ord o apply2 fst));
    fun pretty_checks kind checks =
      checks |> map (fn (i, names) => Pretty.block
        [Pretty.str (kind ^ " (stage " ^ signed_string_of_int i ^ "):"),
          Pretty.brk 1, Pretty.strs names]);

    val (typs, terms) = Checks.get (Context.Proof ctxt);
    val (typ_checks, typ_unchecks) = split_checks typs;
    val (term_checks, term_unchecks) = split_checks terms;
  in
    pretty_checks "typ_checks" typ_checks @
    pretty_checks "term_checks" term_checks @
    pretty_checks "typ_unchecks" typ_unchecks @
    pretty_checks "term_unchecks" term_unchecks
  end |> Pretty.writeln_chunks;


local

fun context_check which (key: key) name f =
  Checks.map (which (AList.map_default op = (key, []) (cons ((name, f), stamp ()))));

fun simple_check eq f xs ctxt =
  let val xs' = f ctxt xs
  in if eq_list eq (xs, xs') then NONE else SOME (xs', ctxt) end;

in

fun typ_check' stage = context_check apfst (stage, false);
fun term_check' stage = context_check apsnd (stage, false);
fun typ_uncheck' stage = context_check apfst (stage, true);
fun term_uncheck' stage = context_check apsnd (stage, true);

fun typ_check key name f = typ_check' key name (simple_check (op =) f);
fun term_check key name f = term_check' key name (simple_check (op aconv) f);
fun typ_uncheck key name f = typ_uncheck' key name (simple_check (op =) f);
fun term_uncheck key name f = term_uncheck' key name (simple_check (op aconv) f);

end;


local

fun check_stage fs = perhaps_loop (perhaps_apply (map uncurry fs));
fun check_all fs = perhaps_apply (map check_stage fs);

fun check which uncheck ctxt0 xs0 =
  let
    val funs = which (Checks.get (Context.Proof ctxt0))
      |> map_filter (fn ((i, u), fs) => if uncheck = u then SOME (i, map (snd o fst) fs) else NONE)
      |> Library.sort (int_ord o apply2 fst) |> map snd
      |> not uncheck ? map rev;
  in #1 (perhaps (check_all funs) (xs0, ctxt0)) end;

val apply_typ_check = check fst false;
val apply_term_check = check snd false;
val apply_typ_uncheck = check fst true;
val apply_term_uncheck = check snd true;

in

fun check_typs ctxt raw_tys =
  let
    val (sorting_report, tys) = Proof_Context.prepare_sortsT ctxt raw_tys;
    val _ = if Context_Position.reports_enabled ctxt then Output.report sorting_report else ();
  in
    tys
    |> apply_typ_check ctxt
    |> Term_Sharing.typs (Proof_Context.theory_of ctxt)
  end;

fun check_terms ctxt raw_ts =
  let
    val (sorting_report, raw_ts') = Proof_Context.prepare_sorts ctxt raw_ts;
    val (ts, ps) = Type_Infer_Context.prepare_positions ctxt raw_ts';

    val tys = map (Logic.mk_type o snd) ps;
    val (ts', tys') = ts @ tys
      |> apply_term_check ctxt
      |> chop (length ts);
    val typing_report =
      fold2 (fn ({pos, ...}, _) => fn ty =>
        if Position.is_reported pos then
          cons (Position.reported_text pos Markup.typing
            (Syntax.string_of_typ ctxt (Logic.dest_type ty)))
        else I) ps tys' [];

    val _ =
      if Context_Position.reports_enabled ctxt
      then Output.report (sorting_report @ typing_report) else ();
  in Term_Sharing.terms (Proof_Context.theory_of ctxt) ts' end;

fun check_props ctxt = map (Type.constraint propT) #> check_terms ctxt;

val uncheck_typs = apply_typ_uncheck;
val uncheck_terms = apply_term_uncheck;

end;


(* install operations *)

val _ =
  Theory.setup
   (Syntax.install_operations
     {parse_sort = parse_sort,
      parse_typ = parse_typ,
      parse_term = parse_term false,
      parse_prop = parse_term true,
      unparse_sort = unparse_sort,
      unparse_typ = unparse_typ,
      unparse_term = unparse_term,
      check_typs = check_typs,
      check_terms = check_terms,
      check_props = check_props,
      uncheck_typs = uncheck_typs,
      uncheck_terms = uncheck_terms});

end;


(* standard phases *)

val _ = Context.>>
 (Syntax_Phases.typ_check 0 "standard" Proof_Context.standard_typ_check #>
  Syntax_Phases.term_check 0 "standard"
    (fn ctxt => Type_Infer_Context.infer_types ctxt #> map (Proof_Context.expand_abbrevs ctxt)) #>
  Syntax_Phases.term_check 100 "standard_finish" Proof_Context.standard_term_check_finish #>
  Syntax_Phases.term_uncheck 0 "standard" Proof_Context.standard_term_uncheck);