src/Pure/sign.ML

simplified add_abbrev -- single argument;

(*  Title:      Pure/sign.ML
    ID:         $Id$
    Author:     Lawrence C Paulson and Markus Wenzel

Logical signature content: naming conventions, concrete syntax, type
signature, polymorphic constants.
*)

signature SIGN_THEORY =
sig
  val add_defsort: string -> theory -> theory
  val add_defsort_i: sort -> theory -> theory
  val add_types: (bstring * int * mixfix) list -> theory -> theory
  val add_typedecls: (bstring * string list * mixfix) list -> theory -> theory
  val add_nonterminals: bstring list -> theory -> theory
  val add_tyabbrs: (bstring * string list * string * mixfix) list -> theory -> theory
  val add_tyabbrs_i: (bstring * string list * typ * mixfix) list -> theory -> theory
  val add_syntax: (bstring * string * mixfix) list -> theory -> theory
  val add_syntax_i: (bstring * typ * mixfix) list -> theory -> theory
  val add_modesyntax: Syntax.mode -> (bstring * string * mixfix) list -> theory -> theory
  val add_modesyntax_i: Syntax.mode -> (bstring * typ * mixfix) list -> theory -> theory
  val del_modesyntax: Syntax.mode -> (bstring * string * mixfix) list -> theory -> theory
  val del_modesyntax_i: Syntax.mode -> (bstring * typ * mixfix) list -> theory -> theory
  val add_consts: (bstring * string * mixfix) list -> theory -> theory
  val add_consts_i: (bstring * typ * mixfix) list -> theory -> theory
  val add_const_constraint: xstring * string option -> theory -> theory
  val add_const_constraint_i: string * typ option -> theory -> theory
  val primitive_class: string * class list -> theory -> theory
  val primitive_classrel: class * class -> theory -> theory
  val primitive_arity: arity -> theory -> theory
  val add_trfuns:
    (string * (ast list -> ast)) list *
    (string * (term list -> term)) list *
    (string * (term list -> term)) list *
    (string * (ast list -> ast)) list -> theory -> theory
  val add_trfunsT:
    (string * (bool -> typ -> term list -> term)) list -> theory -> theory
  val add_advanced_trfuns:
    (string * (Context.generic -> ast list -> ast)) list *
    (string * (Context.generic -> term list -> term)) list *
    (string * (Context.generic -> term list -> term)) list *
    (string * (Context.generic -> ast list -> ast)) list -> theory -> theory
  val add_advanced_trfunsT:
    (string * (Context.generic -> bool -> typ -> term list -> term)) list -> theory -> theory
  val add_tokentrfuns:
    (string * string * (string -> string * real)) list -> theory -> theory
  val add_mode_tokentrfuns: string -> (string * (string -> string * real)) list
    -> theory -> theory
  val parse_ast_translation: bool * string -> theory -> theory
  val parse_translation: bool * string -> theory -> theory
  val print_translation: bool * string -> theory -> theory
  val typed_print_translation: bool * string -> theory -> theory
  val print_ast_translation: bool * string -> theory -> theory
  val token_translation: string -> theory -> theory
  val add_trrules: (xstring * string) Syntax.trrule list -> theory -> theory
  val del_trrules: (xstring * string) Syntax.trrule list -> theory -> theory
  val add_trrules_i: ast Syntax.trrule list -> theory -> theory
  val del_trrules_i: ast Syntax.trrule list -> theory -> theory
  val add_path: string -> theory -> theory
  val parent_path: theory -> theory
  val root_path: theory -> theory
  val absolute_path: theory -> theory
  val local_path: theory -> theory
  val no_base_names: theory -> theory
  val qualified_names: theory -> theory
  val sticky_prefix: string -> theory -> theory
  val set_policy: (string -> bstring -> string) * (string list -> string list list) ->
    theory -> theory
  val restore_naming: theory -> theory -> theory
  val hide_classes: bool -> xstring list -> theory -> theory
  val hide_classes_i: bool -> string list -> theory -> theory
  val hide_types: bool -> xstring list -> theory -> theory
  val hide_types_i: bool -> string list -> theory -> theory
  val hide_consts: bool -> xstring list -> theory -> theory
  val hide_consts_i: bool -> string list -> theory -> theory
  val hide_names: bool -> string * xstring list -> theory -> theory
  val hide_names_i: bool -> string * string list -> theory -> theory
end

signature SIGN =
sig
  val init_data: theory -> theory
  val rep_sg: theory ->
   {naming: NameSpace.naming,
    syn: Syntax.syntax,
    tsig: Type.tsig,
    consts: Consts.T}
  val naming_of: theory -> NameSpace.naming
  val base_name: string -> bstring
  val full_name: theory -> bstring -> string
  val full_name_path: theory -> string -> bstring -> string
  val declare_name: theory -> string -> NameSpace.T -> NameSpace.T
  val syn_of: theory -> Syntax.syntax
  val tsig_of: theory -> Type.tsig
  val classes_of: theory -> Sorts.algebra
  val classes: theory -> class list
  val super_classes: theory -> class -> class list
  val defaultS: theory -> sort
  val subsort: theory -> sort * sort -> bool
  val of_sort: theory -> typ * sort -> bool
  val witness_sorts: theory -> sort list -> sort list -> (typ * sort) list
  val universal_witness: theory -> (typ * sort) option
  val all_sorts_nonempty: theory -> bool
  val typ_instance: theory -> typ * typ -> bool
  val typ_equiv: theory -> typ * typ -> bool
  val typ_match: theory -> typ * typ -> Type.tyenv -> Type.tyenv
  val typ_unify: theory -> typ * typ -> Type.tyenv * int -> Type.tyenv * int
  val is_logtype: theory -> string -> bool
  val consts_of: theory -> Consts.T
  val const_constraint: theory -> string -> typ option
  val the_const_constraint: theory -> string -> typ
  val const_type: theory -> string -> typ option
  val the_const_type: theory -> string -> typ
  val declared_tyname: theory -> string -> bool
  val declared_const: theory -> string -> bool
  val const_monomorphic: theory -> string -> bool
  val const_syntax_name: theory -> string -> string
  val const_typargs: theory -> string * typ -> typ list
  val const_instance: theory -> string * typ list -> typ
  val class_space: theory -> NameSpace.T
  val type_space: theory -> NameSpace.T
  val const_space: theory -> NameSpace.T
  val intern_class: theory -> xstring -> string
  val extern_class: theory -> string -> xstring
  val intern_type: theory -> xstring -> string
  val extern_type: theory -> string -> xstring
  val intern_const: theory -> xstring -> string
  val extern_const: theory -> string -> xstring
  val intern_sort: theory -> sort -> sort
  val extern_sort: theory -> sort -> sort
  val intern_typ: theory -> typ -> typ
  val extern_typ: theory -> typ -> typ
  val intern_term: theory -> term -> term
  val extern_term: (string -> xstring) -> theory -> term -> term
  val intern_tycons: theory -> typ -> typ
  val pretty_term': Context.generic -> Syntax.syntax -> (string -> xstring) -> term -> Pretty.T
  val pretty_term: theory -> term -> Pretty.T
  val pretty_typ: theory -> typ -> Pretty.T
  val pretty_sort: theory -> sort -> Pretty.T
  val pretty_classrel: theory -> class list -> Pretty.T
  val pretty_arity: theory -> arity -> Pretty.T
  val string_of_term: theory -> term -> string
  val string_of_typ: theory -> typ -> string
  val string_of_sort: theory -> sort -> string
  val string_of_classrel: theory -> class list -> string
  val string_of_arity: theory -> arity -> string
  val pp: theory -> Pretty.pp
  val arity_number: theory -> string -> int
  val arity_sorts: theory -> string -> sort -> sort list
  val certify_class: theory -> class -> class
  val certify_sort: theory -> sort -> sort
  val certify_typ: theory -> typ -> typ
  val certify_typ_syntax: theory -> typ -> typ
  val certify_typ_abbrev: theory -> typ -> typ
  val certify': bool -> bool -> Pretty.pp -> Consts.T -> theory -> term -> term * typ * int
  val certify_term: theory -> term -> term * typ * int
  val certify_prop: theory -> term -> term * typ * int
  val cert_term: theory -> term -> term
  val cert_prop: theory -> term -> term
  val no_vars: Pretty.pp -> term -> term
  val cert_def: Pretty.pp -> term -> (string * typ) * term
  val read_class: theory -> xstring -> class
  val read_sort': Syntax.syntax -> Context.generic -> string -> sort
  val read_sort: theory -> string -> sort
  val read_arity: theory -> xstring * string list * string -> arity
  val cert_arity: theory -> arity -> arity
  val read_typ': Syntax.syntax -> Context.generic ->
    (indexname -> sort option) -> string -> typ
  val read_typ_syntax': Syntax.syntax -> Context.generic ->
    (indexname -> sort option) -> string -> typ
  val read_typ_abbrev': Syntax.syntax -> Context.generic ->
    (indexname -> sort option) -> string -> typ
  val read_typ: theory * (indexname -> sort option) -> string -> typ
  val read_typ_syntax: theory * (indexname -> sort option) -> string -> typ
  val read_typ_abbrev: theory * (indexname -> sort option) -> string -> typ
  val read_tyname: theory -> string -> typ
  val read_const: theory -> string -> term
  val infer_types_simult: Pretty.pp -> theory -> Consts.T -> (indexname -> typ option) ->
    (indexname -> sort option) -> Name.context -> bool
    -> (term list * typ) list -> term list * (indexname * typ) list
  val infer_types: Pretty.pp -> theory -> Consts.T -> (indexname -> typ option) ->
    (indexname -> sort option) -> Name.context -> bool
    -> term list * typ -> term * (indexname * typ) list
  val read_def_terms': Pretty.pp -> (string -> bool) -> Syntax.syntax -> Consts.T ->
    Context.generic -> (indexname -> typ option) * (indexname -> sort option) ->
    Name.context -> bool -> (string * typ) list -> term list * (indexname * typ) list
  val read_def_terms:
    theory * (indexname -> typ option) * (indexname -> sort option) ->
    string list -> bool -> (string * typ) list -> term list * (indexname * typ) list
  val simple_read_term: theory -> typ -> string -> term
  val read_term: theory -> string -> term
  val read_prop: theory -> string -> term
  val add_consts_authentic: (bstring * typ * mixfix) list -> theory -> theory
  val add_notation: Syntax.mode -> (term * mixfix) list -> theory -> theory
  val add_abbrev: string -> bstring * term -> theory -> ((string * typ) * term) * theory
  include SIGN_THEORY
end

structure Sign: SIGN =
struct


(** datatype sign **)

datatype sign = Sign of
 {naming: NameSpace.naming,     (*common naming conventions*)
  syn: Syntax.syntax,           (*concrete syntax for terms, types, sorts*)
  tsig: Type.tsig,              (*order-sorted signature of types*)
  consts: Consts.T};            (*polymorphic constants*)

fun make_sign (naming, syn, tsig, consts) =
  Sign {naming = naming, syn = syn, tsig = tsig, consts = consts};

structure SignData = TheoryDataFun
(struct
  val name = "Pure/sign";
  type T = sign;
  val copy = I;
  fun extend (Sign {syn, tsig, consts, ...}) =
    make_sign (NameSpace.default_naming, syn, tsig, consts);

  val empty =
    make_sign (NameSpace.default_naming, Syntax.basic_syn, Type.empty_tsig, Consts.empty);

  fun merge pp (sign1, sign2) =
    let
      val Sign {naming = _, syn = syn1, tsig = tsig1, consts = consts1} = sign1;
      val Sign {naming = _, syn = syn2, tsig = tsig2, consts = consts2} = sign2;

      val naming = NameSpace.default_naming;
      val syn = Syntax.merge_syntaxes syn1 syn2;
      val tsig = Type.merge_tsigs pp (tsig1, tsig2);
      val consts = Consts.merge (consts1, consts2);
    in make_sign (naming, syn, tsig, consts) end;

  fun print _ _ = ();
end);

val init_data = SignData.init;

fun rep_sg thy = SignData.get thy |> (fn Sign args => args);

fun map_sign f = SignData.map (fn Sign {naming, syn, tsig, consts} =>
  make_sign (f (naming, syn, tsig, consts)));

fun map_naming f = map_sign (fn (naming, syn, tsig, consts) => (f naming, syn, tsig, consts));
fun map_syn f = map_sign (fn (naming, syn, tsig, consts) => (naming, f syn, tsig, consts));
fun map_tsig f = map_sign (fn (naming, syn, tsig, consts) => (naming, syn, f tsig, consts));
fun map_consts f = map_sign (fn (naming, syn, tsig, consts) => (naming, syn, tsig, f consts));


(* naming *)

val naming_of = #naming o rep_sg;
val base_name = NameSpace.base;
val full_name = NameSpace.full o naming_of;
fun full_name_path thy elems = NameSpace.full (NameSpace.add_path elems (naming_of thy));
val declare_name = NameSpace.declare o naming_of;


(* syntax *)

val syn_of = #syn o rep_sg;


(* type signature *)

val tsig_of = #tsig o rep_sg;
val classes_of = #2 o #classes o Type.rep_tsig o tsig_of;
val classes = Sorts.classes o classes_of;
val super_classes = Sorts.super_classes o classes_of;
val defaultS = Type.defaultS o tsig_of;
val subsort = Type.subsort o tsig_of;
val of_sort = Type.of_sort o tsig_of;
val witness_sorts = Type.witness_sorts o tsig_of;
val universal_witness = Type.universal_witness o tsig_of;
val all_sorts_nonempty = is_some o universal_witness;
val typ_instance = Type.typ_instance o tsig_of;
fun typ_equiv thy (T, U) = typ_instance thy (T, U) andalso typ_instance thy (U, T);
val typ_match = Type.typ_match o tsig_of;
val typ_unify = Type.unify o tsig_of;
val is_logtype = member (op =) o Type.logical_types o tsig_of;


(* polymorphic constants *)

val consts_of = #consts o rep_sg;
val the_const_constraint = Consts.constraint o consts_of;
val const_constraint = try o the_const_constraint;
val the_const_type = Consts.declaration o consts_of;
val const_type = try o the_const_type;
val const_monomorphic = Consts.monomorphic o consts_of;
val const_syntax_name = Consts.syntax_name o consts_of;
val const_typargs = Consts.typargs o consts_of;
val const_instance = Consts.instance o consts_of;

val declared_tyname = Symtab.defined o #2 o #types o Type.rep_tsig o tsig_of;
val declared_const = is_some oo const_constraint;



(** intern / extern names **)

val class_space = #1 o #classes o Type.rep_tsig o tsig_of;
val type_space = #1 o #types o Type.rep_tsig o tsig_of;
val const_space = Consts.space_of o consts_of;

val intern_class = NameSpace.intern o class_space;
val extern_class = NameSpace.extern o class_space;
val intern_type = NameSpace.intern o type_space;
val extern_type = NameSpace.extern o type_space;
val intern_const = NameSpace.intern o const_space;
val extern_const = NameSpace.extern o const_space;

val intern_sort = map o intern_class;
val extern_sort = map o extern_class;

local

fun map_typ f g (Type (c, Ts)) = Type (g c, map (map_typ f g) Ts)
  | map_typ f _ (TFree (x, S)) = TFree (x, map f S)
  | map_typ f _ (TVar (xi, S)) = TVar (xi, map f S);

fun map_term f g h (Const (c, T)) = Const (h c, map_typ f g T)
  | map_term f g _ (Free (x, T)) = Free (x, map_typ f g T)
  | map_term f g _ (Var (xi, T)) = Var (xi, map_typ f g T)
  | map_term _ _ _ (t as Bound _) = t
  | map_term f g h (Abs (x, T, t)) = Abs (x, map_typ f g T, map_term f g h t)
  | map_term f g h (t $ u) = map_term f g h t $ map_term f g h u;

val add_classesT = Term.fold_atyps
  (fn TFree (_, S) => fold (insert (op =)) S
    | TVar (_, S) => fold (insert (op =)) S
    | _ => I);

fun add_tyconsT (Type (c, Ts)) = insert (op =) c #> fold add_tyconsT Ts
  | add_tyconsT _ = I;

val add_consts = Term.fold_aterms (fn Const (c, _) => insert (op =) c | _ => I);

fun mapping add_names f t =
  let
    fun f' (x: string) = let val y = f x in if x = y then NONE else SOME (x, y) end;
    val tab = map_filter f' (add_names t []);
    fun get x = the_default x (AList.lookup (op =) tab x);
  in get end;

fun typ_mapping f g thy T =
  T |> map_typ
    (mapping add_classesT (f thy) T)
    (mapping add_tyconsT (g thy) T);

fun term_mapping f g h thy t =
  t |> map_term
    (mapping (Term.fold_types add_classesT) (f thy) t)
    (mapping (Term.fold_types add_tyconsT) (g thy) t)
    (mapping add_consts (h thy) t);

in

val intern_typ = typ_mapping intern_class intern_type;
val extern_typ = typ_mapping extern_class extern_type;
val intern_term = term_mapping intern_class intern_type intern_const;
fun extern_term h = term_mapping extern_class extern_type (K h);
val intern_tycons = typ_mapping (K I) intern_type;

end;



(** pretty printing of terms, types etc. **)

fun pretty_term' context syn ext t =
  let val curried = Context.exists_name Context.CPureN (Context.theory_of context)
  in Syntax.pretty_term ext context syn curried t end;

fun pretty_term thy t =
  pretty_term' (Context.Theory thy) (syn_of thy) (Consts.extern (consts_of thy))
    (extern_term (Consts.extern_early (consts_of thy)) thy t);

fun pretty_typ thy T = Syntax.pretty_typ (Context.Theory thy) (syn_of thy) (extern_typ thy T);
fun pretty_sort thy S = Syntax.pretty_sort (Context.Theory thy) (syn_of thy) (extern_sort thy S);

fun pretty_classrel thy cs = Pretty.block (flat
  (separate [Pretty.str " <", Pretty.brk 1] (map (single o pretty_sort thy o single) cs)));

fun pretty_arity thy (a, Ss, S) =
  let
    val a' = extern_type thy a;
    val dom =
      if null Ss then []
      else [Pretty.list "(" ")" (map (pretty_sort thy) Ss), Pretty.brk 1];
  in Pretty.block ([Pretty.str (a' ^ " ::"), Pretty.brk 1] @ dom @ [pretty_sort thy S]) end;

val string_of_term = Pretty.string_of oo pretty_term;
val string_of_typ = Pretty.string_of oo pretty_typ;
val string_of_sort = Pretty.string_of oo pretty_sort;
val string_of_classrel = Pretty.string_of oo pretty_classrel;
val string_of_arity = Pretty.string_of oo pretty_arity;

fun pp thy = Pretty.pp (pretty_term thy, pretty_typ thy, pretty_sort thy,
  pretty_classrel thy, pretty_arity thy);



(** certify entities **)    (*exception TYPE*)

(* certify wrt. type signature *)

val arity_number = Type.arity_number o tsig_of;
fun arity_sorts thy = Type.arity_sorts (pp thy) (tsig_of thy);

fun certify cert = cert o tsig_of o Context.check_thy;

val certify_class      = certify Type.cert_class;
val certify_sort       = certify Type.cert_sort;
val certify_typ        = certify Type.cert_typ;
val certify_typ_syntax = certify Type.cert_typ_syntax;
val certify_typ_abbrev = certify Type.cert_typ_abbrev;


(* certify term/prop *)

local

fun type_check pp tm =
  let
    fun err_appl why bs t T u U =
      let
        val xs = map Free bs;           (*we do not rename here*)
        val t' = subst_bounds (xs, t);
        val u' = subst_bounds (xs, u);
        val msg = cat_lines
          (TypeInfer.appl_error (Syntax.pp_show_brackets pp) why t' T u' U);
      in raise TYPE (msg, [T, U], [t', u']) end;

    fun typ_of (_, Const (_, T)) = T
      | typ_of (_, Free  (_, T)) = T
      | typ_of (_, Var (_, T)) = T
      | typ_of (bs, Bound i) = snd (List.nth (bs, i) handle Subscript =>
          raise TYPE ("Loose bound variable: B." ^ string_of_int i, [], [Bound i]))
      | typ_of (bs, Abs (x, T, body)) = T --> typ_of ((x, T) :: bs, body)
      | typ_of (bs, t $ u) =
          let val T = typ_of (bs, t) and U = typ_of (bs, u) in
            (case T of
              Type ("fun", [T1, T2]) =>
                if T1 = U then T2 else err_appl "Incompatible operand type" bs t T u U
            | _ => err_appl "Operator not of function type" bs t T u U)
          end;
  in typ_of ([], tm) end;

fun err msg = raise TYPE (msg, [], []);

fun check_vars (t $ u) = (check_vars t; check_vars u)
  | check_vars (Abs (_, _, t)) = check_vars t
  | check_vars (Var (xi as (_, i), _)) =
      if i < 0 then err ("Malformed variable: " ^ quote (Term.string_of_vname xi)) else ()
  | check_vars _ = ();

in

fun certify' normalize prop pp consts thy tm =
  let
    val _ = Context.check_thy thy;
    val _ = check_vars tm;
    val tm' = Term.map_types (certify_typ thy) tm;
    val T = type_check pp tm';
    val _ = if prop andalso T <> propT then err "Term not of type prop" else ();
    val tm'' = Consts.certify pp (tsig_of thy) consts tm';
    val tm'' = if normalize then tm'' else tm';
  in (if tm = tm'' then tm else tm'', T, Term.maxidx_of_term tm'') end;

fun certify_term thy = certify' true false (pp thy) (consts_of thy) thy;
fun certify_prop thy = certify' true true (pp thy) (consts_of thy) thy;

fun cert_term_abbrev thy = #1 o certify' false false (pp thy) (consts_of thy) thy;
val cert_term = #1 oo certify_term;
val cert_prop = #1 oo certify_prop;

end;


(* specifications *)

fun no_vars pp tm =
  (case (Term.add_vars tm [], Term.add_tvars tm []) of
    ([], []) => tm
  | (vars, tvars) => error (Pretty.string_of (Pretty.block (Pretty.breaks
      (Pretty.str "Illegal schematic variable(s) in term:" ::
       map (Pretty.term pp o Var) vars @ map (Pretty.typ pp o TVar) tvars)))));

fun cert_def pp tm =
  let val ((lhs, rhs), _) = tm
    |> no_vars pp
    |> Logic.strip_imp_concl
    |> Logic.dest_def pp Term.is_Const (K false) (K false)
  in (Term.dest_Const (Term.head_of lhs), rhs) end
  handle TERM (msg, _) => error msg;



(** read and certify entities **)    (*exception ERROR*)

(* classes and sorts *)

fun read_class thy c = certify_class thy (intern_class thy c)
  handle TYPE (msg, _, _) => error msg;

fun read_sort' syn context str =
  let
    val thy = Context.theory_of context;
    val _ = Context.check_thy thy;
    val S = intern_sort thy (Syntax.read_sort context syn str);
  in certify_sort thy S handle TYPE (msg, _, _) => error msg end;

fun read_sort thy str = read_sort' (syn_of thy) (Context.Theory thy) str;


(* type arities *)

fun prep_arity prep_tycon prep_sort thy (t, Ss, S) =
  let val arity = (prep_tycon thy t, map (prep_sort thy) Ss, prep_sort thy S)
  in Type.add_arity (pp thy) arity (tsig_of thy); arity end;

val read_arity = prep_arity intern_type read_sort;
val cert_arity = prep_arity (K I) certify_sort;


(* types *)

local

fun gen_read_typ' cert syn context def_sort str =
  let
    val thy = Context.theory_of context;
    val _ = Context.check_thy thy;
    val get_sort = TypeInfer.get_sort (tsig_of thy) def_sort (intern_sort thy);
    val T = intern_tycons thy (Syntax.read_typ context syn get_sort (intern_sort thy) str);
  in cert thy T handle TYPE (msg, _, _) => error msg end
  handle ERROR msg => cat_error msg ("The error(s) above occurred in type " ^ quote str);

fun gen_read_typ cert (thy, def_sort) str =
  gen_read_typ' cert (syn_of thy) (Context.Theory thy) def_sort str;

in

fun no_def_sort thy = (thy: theory, K NONE);

val read_typ'        = gen_read_typ' certify_typ;
val read_typ_syntax' = gen_read_typ' certify_typ_syntax;
val read_typ_abbrev' = gen_read_typ' certify_typ_abbrev;
val read_typ         = gen_read_typ certify_typ;
val read_typ_syntax  = gen_read_typ certify_typ_syntax;
val read_typ_abbrev  = gen_read_typ certify_typ_abbrev;

end;


(* type and constant names *)

fun read_tyname thy raw_c =
  let val c = intern_type thy raw_c
  in Type (c, replicate (arity_number thy c) dummyT) end;

val read_const = Consts.read_const o consts_of;



(** infer_types **)         (*exception ERROR*)

(*
  def_type: partial map from indexnames to types (constrains Frees and Vars)
  def_sort: partial map from indexnames to sorts (constrains TFrees and TVars)
  used: context of already used type variables
  freeze: if true then generated parameters are turned into TFrees, else TVars

  termss: lists of alternative parses (only one combination should be type-correct)
  typs: expected types
*)

fun infer_types_simult pp thy consts def_type def_sort used freeze args =
  let
    val termss = fold_rev (multiply o fst) args [[]];
    val typs =
      map (fn (_, T) => certify_typ thy T handle TYPE (msg, _, _) => error msg) args;

    fun infer ts = Result (TypeInfer.infer_types (Syntax.pp_show_brackets pp) (tsig_of thy)
        (try (Consts.constraint consts)) def_type def_sort (Consts.intern consts)
        (intern_tycons thy) (intern_sort thy) used freeze typs ts)
      handle TYPE (msg, _, _) => Exn (ERROR msg);

    val err_results = map infer termss;
    val errs = map_filter (fn Exn (ERROR msg) => SOME msg | _ => NONE) err_results;
    val results = map_filter get_result err_results;

    val ambiguity = length termss;
    fun ambig_msg () =
      if ambiguity > 1 andalso ambiguity <= ! Syntax.ambiguity_level then
        "Got more than one parse tree.\n\
        \Retry with smaller Syntax.ambiguity_level for more information."
      else "";
  in
    if null results then (cat_error (ambig_msg ()) (cat_lines errs))
    else if length results = 1 then
      (if ambiguity > ! Syntax.ambiguity_level then
        warning "Fortunately, only one parse tree is type correct.\n\
          \You may still want to disambiguate your grammar or your input."
      else (); hd results)
    else (cat_error (ambig_msg ()) ("More than one term is type correct:\n" ^
      cat_lines (map (Pretty.string_of_term pp) (maps fst results))))
  end;

fun infer_types pp thy consts def_type def_sort used freeze tsT =
  apfst hd (infer_types_simult pp thy consts def_type def_sort used freeze [tsT]);


(* read_def_terms -- read terms and infer types *)    (*exception ERROR*)

fun read_def_terms' pp is_logtype syn consts context (types, sorts) used freeze sTs =
  let
    val thy = Context.theory_of context;
    fun read (s, T) =
      let val T' = certify_typ thy T handle TYPE (msg, _, _) => error msg
      in (Syntax.read context is_logtype syn T' s, T') end;
  in infer_types_simult pp thy consts types sorts used freeze (map read sTs) end;

fun read_def_terms (thy, types, sorts) used freeze sTs =
  let
    val pp = pp thy;
    val consts = consts_of thy;
    val cert_consts = Consts.certify pp (tsig_of thy) consts;
    val (ts, inst) =
      read_def_terms' pp (is_logtype thy) (syn_of thy) consts
        (Context.Theory thy) (types, sorts) (Name.make_context used) freeze sTs;
  in (map cert_consts ts, inst) end;

fun simple_read_term thy T s =
  let val ([t], _) = read_def_terms (thy, K NONE, K NONE) [] true [(s, T)]
  in t end handle ERROR msg => cat_error msg ("The error(s) above occurred for term " ^ s);

fun read_term thy = simple_read_term thy TypeInfer.logicT;
fun read_prop thy = simple_read_term thy propT;



(** signature extension functions **)  (*exception ERROR/TYPE*)

(* add default sort *)

fun gen_add_defsort prep_sort s thy =
  thy |> map_tsig (Type.set_defsort (prep_sort thy s));

val add_defsort = gen_add_defsort read_sort;
val add_defsort_i = gen_add_defsort certify_sort;


(* add type constructors *)

fun add_types types thy = thy |> map_sign (fn (naming, syn, tsig, consts) =>
  let
    val syn' = Syntax.extend_type_gram types syn;
    val decls = map (fn (a, n, mx) => (Syntax.type_name a mx, n)) types;
    val tsig' = Type.add_types naming decls tsig;
  in (naming, syn', tsig', consts) end);

fun add_typedecls decls thy =
  let
    fun type_of (a, vs: string list, mx) =
      if not (has_duplicates (op =) vs) then (a, length vs, mx)
      else error ("Duplicate parameters in type declaration: " ^ quote a);
  in add_types (map type_of decls) thy end;


(* add nonterminals *)

fun add_nonterminals ns thy = thy |> map_sign (fn (naming, syn, tsig, consts) =>
  let
    val syn' = Syntax.extend_consts ns syn;
    val tsig' = Type.add_nonterminals naming ns tsig;
  in (naming, syn', tsig', consts) end);


(* add type abbreviations *)

fun gen_add_tyabbr prep_typ (a, vs, rhs, mx) thy =
  thy |> map_sign (fn (naming, syn, tsig, consts) =>
    let
      val syn' = Syntax.extend_type_gram [(a, length vs, mx)] syn;
      val a' = Syntax.type_name a mx;
      val abbr = (a', vs, prep_typ thy rhs)
        handle ERROR msg => cat_error msg ("in type abbreviation " ^ quote a');
      val tsig' = Type.add_abbrevs naming [abbr] tsig;
    in (naming, syn', tsig', consts) end);

val add_tyabbrs = fold (gen_add_tyabbr (read_typ_syntax o no_def_sort));
val add_tyabbrs_i = fold (gen_add_tyabbr certify_typ_syntax);


(* modify syntax *)

fun gen_syntax change_gram prep_typ mode args thy =
  let
    fun prep (c, T, mx) = (c, prep_typ thy T, mx) handle ERROR msg =>
      cat_error msg ("in syntax declaration " ^ quote (Syntax.const_name c mx));
  in thy |> map_syn (change_gram (is_logtype thy) mode (map prep args)) end;

fun gen_add_syntax x = gen_syntax Syntax.extend_const_gram x;

val add_modesyntax = gen_add_syntax (read_typ_syntax o no_def_sort);
val add_modesyntax_i = gen_add_syntax certify_typ_syntax;
val add_syntax = add_modesyntax Syntax.default_mode;
val add_syntax_i = add_modesyntax_i Syntax.default_mode;
val del_modesyntax = gen_syntax Syntax.remove_const_gram (read_typ_syntax o no_def_sort);
val del_modesyntax_i = gen_syntax Syntax.remove_const_gram certify_typ_syntax;

fun const_syntax thy (Const (c, _), mx) = try (Consts.syntax (consts_of thy)) (c, mx)
  | const_syntax _ _ = NONE;

fun add_notation mode args thy =
  thy |> add_modesyntax_i mode (map_filter (const_syntax thy) args);


(* add constants *)

local

fun gen_add_consts prep_typ authentic raw_args thy =
  let
    val prepT = Compress.typ thy o Logic.varifyT o Type.no_tvars o Term.no_dummyT o prep_typ thy;
    fun prep (raw_c, raw_T, raw_mx) =
      let
        val (c, mx) = Syntax.const_mixfix raw_c raw_mx;
        val c' = if authentic then Syntax.constN ^ full_name thy c else c;
        val T = (prepT raw_T handle TYPE (msg, _, _) => error msg) handle ERROR msg =>
          cat_error msg ("in declaration of constant " ^ quote c);
      in (((c, T), authentic), (c', T, mx)) end;
    val args = map prep raw_args;
  in
    thy
    |> map_consts (fold (Consts.declare (naming_of thy) o #1) args)
    |> add_syntax_i (map #2 args)
  end;

in

val add_consts = gen_add_consts (read_typ o no_def_sort) false;
val add_consts_i = gen_add_consts certify_typ false;
val add_consts_authentic = gen_add_consts certify_typ true;

end;


(* add abbreviations *)

fun add_abbrev mode (c, raw_t) thy =
  let
    val prep_tm = Compress.term thy o Term.no_dummy_patterns o cert_term_abbrev thy;
    val t = (prep_tm raw_t handle TYPE (msg, _, _) => error msg | TERM (msg, _) => error msg)
      handle ERROR msg => cat_error msg ("in constant abbreviation " ^ quote c);
    val (res, consts') = consts_of thy
      |> Consts.abbreviate (pp thy) (tsig_of thy) (naming_of thy) mode ((c, t), true);
  in (res, thy |> map_consts (K consts')) end;


(* add constraints *)

fun gen_add_constraint int_const prep_typ (raw_c, opt_T) thy =
  let
    val c = int_const thy raw_c;
    fun prepT raw_T =
      let val T = Logic.varifyT (Type.no_tvars (Term.no_dummyT (prep_typ thy raw_T)))
      in cert_term thy (Const (c, T)); T end
      handle TYPE (msg, _, _) => error msg;
  in thy |> map_consts (Consts.constrain (c, Option.map prepT opt_T)) end;

val add_const_constraint = gen_add_constraint intern_const (read_typ o no_def_sort);
val add_const_constraint_i = gen_add_constraint (K I) certify_typ;


(* primitive classes and arities *)

fun primitive_class (bclass, classes) thy =
  thy |> map_sign (fn (naming, syn, tsig, consts) =>
    let
      val syn' = Syntax.extend_consts [bclass] syn;
      val tsig' = Type.add_class (pp thy) naming (bclass, classes) tsig;
    in (naming, syn', tsig', consts) end)
  |> add_consts_i [(Logic.const_of_class bclass, Term.a_itselfT --> propT, NoSyn)];

fun primitive_classrel arg thy = thy |> map_tsig (Type.add_classrel (pp thy) arg);
fun primitive_arity arg thy = thy |> map_tsig (Type.add_arity (pp thy) arg);


(* add translation functions *)

local

fun mk trs = map Syntax.mk_trfun trs;

fun gen_add_trfuns ext non_typed (atrs, trs, tr's, atr's) =
  map_syn (ext (mk atrs, mk trs, mk (map (apsnd non_typed) tr's), mk atr's));

fun gen_add_trfunsT ext tr's = map_syn (ext ([], [], mk tr's, []));

in

val add_trfuns = gen_add_trfuns Syntax.extend_trfuns Syntax.non_typed_tr';
val add_trfunsT = gen_add_trfunsT Syntax.extend_trfuns;
val add_advanced_trfuns = gen_add_trfuns Syntax.extend_advanced_trfuns Syntax.non_typed_tr'';
val add_advanced_trfunsT = gen_add_trfunsT Syntax.extend_advanced_trfuns;

end;

val add_tokentrfuns = map_syn o Syntax.extend_tokentrfuns;
fun add_mode_tokentrfuns m = add_tokentrfuns o map (fn (s, f) => (m, s, f));


(* compile translation functions *)

local

fun advancedT false = ""
  | advancedT true = "Context.generic -> ";

fun advancedN false = ""
  | advancedN true = "advanced_";

in

fun parse_ast_translation (a, txt) =
  txt |> Context.use_let ("val parse_ast_translation: (string * (" ^ advancedT a ^
      "Syntax.ast list -> Syntax.ast)) list")
    ("Sign.add_" ^ advancedN a ^ "trfuns (parse_ast_translation, [], [], [])");

fun parse_translation (a, txt) =
  txt |> Context.use_let ("val parse_translation: (string * (" ^ advancedT a ^
      "term list -> term)) list")
    ("Sign.add_" ^ advancedN a ^ "trfuns ([], parse_translation, [], [])");

fun print_translation (a, txt) =
  txt |> Context.use_let ("val print_translation: (string * (" ^ advancedT a ^
      "term list -> term)) list")
    ("Sign.add_" ^ advancedN a ^ "trfuns ([], [], print_translation, [])");

fun print_ast_translation (a, txt) =
  txt |> Context.use_let ("val print_ast_translation: (string * (" ^ advancedT a ^
      "Syntax.ast list -> Syntax.ast)) list")
    ("Sign.add_" ^ advancedN a ^ "trfuns ([], [], [], print_ast_translation)");

fun typed_print_translation (a, txt) =
  txt |> Context.use_let ("val typed_print_translation: (string * (" ^ advancedT a ^
      "bool -> typ -> term list -> term)) list")
    ("Sign.add_" ^ advancedN a ^ "trfunsT typed_print_translation");

val token_translation =
  Context.use_let "val token_translation: (string * string * (string -> string * real)) list"
    "Sign.add_tokentrfuns token_translation";

end;


(* translation rules *)

fun gen_trrules f args thy = thy |> map_syn (fn syn =>
  let val rules = map (Syntax.map_trrule (apfst (intern_type thy))) args
  in f (Context.Theory thy) (is_logtype thy) syn rules syn end);

val add_trrules = gen_trrules Syntax.extend_trrules;
val del_trrules = gen_trrules Syntax.remove_trrules;
val add_trrules_i = map_syn o Syntax.extend_trrules_i;
val del_trrules_i = map_syn o Syntax.remove_trrules_i;


(* modify naming *)

val add_path        = map_naming o NameSpace.add_path;
val no_base_names   = map_naming NameSpace.no_base_names;
val qualified_names = map_naming NameSpace.qualified_names;
val sticky_prefix   = map_naming o NameSpace.sticky_prefix;
val set_policy      = map_naming o NameSpace.set_policy;
val restore_naming  = map_naming o K o naming_of;

val parent_path   = add_path "..";
val root_path     = add_path "/";
val absolute_path = add_path "//";

fun local_path thy = thy |> root_path |> add_path (Context.theory_name thy);


(* hide names *)

fun hide_classes b xs thy = thy |> map_tsig (Type.hide_classes b (map (intern_class thy) xs));
val hide_classes_i = map_tsig oo Type.hide_classes;
fun hide_types b xs thy = thy |> map_tsig (Type.hide_types b (map (intern_type thy) xs));
val hide_types_i = map_tsig oo Type.hide_types;
fun hide_consts b xs thy = thy |> map_consts (fold (Consts.hide b o intern_const thy) xs);
val hide_consts_i = map_consts oo (fold o Consts.hide);

local

val kinds =
 [("class", (intern_class, can o certify_class, hide_classes_i)),
  ("type", (intern_type, declared_tyname, hide_types_i)),
  ("const", (intern_const, declared_const, hide_consts_i))];

fun gen_hide int b (kind, xnames) thy =
  (case AList.lookup (op =) kinds kind of
    SOME (intern, check, hide) =>
      let
        val names = if int then map (intern thy) xnames else xnames;
        val bads = filter_out (check thy) names;
      in
        if null bads then hide b names thy
        else error ("Attempt to hide undeclared item(s): " ^ commas_quote bads)
      end
  | NONE => error ("Bad name space specification: " ^ quote kind));

in

val hide_names = gen_hide true;
val hide_names_i = gen_hide false;

end;

end;