(*  Title:      Pure/sign.ML

    ID:         $Id$

    Author:     Lawrence C Paulson and Markus Wenzel

The abstract type "sg" of signatures.

*)

(*base names*)

type bstring = string;

type bclass = class;

(*external forms -- partially qualified names*)

type xstring = string;

type xclass = class;

type xsort = sort;

type xtyp = typ;

type xterm = term;

signature SIGN =

sig

  type sg

  type sg_ref

  type data

  val rep_sg: sg ->

   {self: sg_ref,

    tsig: Type.type_sig,

    const_tab: typ Symtab.table,

    syn: Syntax.syntax,

    path: string list,

    spaces: (string * NameSpace.T) list,

    data: data}

  val name_of: sg -> string

  val stamp_names_of: sg -> string list

  val tsig_of: sg -> Type.type_sig

  val deref: sg_ref -> sg

  val self_ref: sg -> sg_ref

  val subsig: sg * sg -> bool

  val eq_sg: sg * sg -> bool

  val same_sg: sg * sg -> bool

  val is_draft: sg -> bool

  val is_stale: sg -> bool

  val const_type: sg -> string -> typ option

  val classes: sg -> class list

  val defaultS: sg -> sort

  val subsort: sg -> sort * sort -> bool

  val nodup_Vars: term -> unit

  val norm_sort: sg -> sort -> sort

  val nonempty_sort: sg -> sort list -> sort -> bool

  val of_sort: sg -> typ * sort -> bool

  val long_names: bool ref

  val classK: string

  val typeK: string

  val constK: string

  val full_name: sg -> bstring -> string

  val full_name_path: sg -> string -> bstring -> string

  val base_name: string -> bstring

  val intern: sg -> string -> xstring -> string

  val extern: sg -> string -> string -> xstring

  val cond_extern: sg -> string -> string -> xstring

  val intern_class: sg -> xclass -> class

  val intern_tycon: sg -> xstring -> string

  val intern_const: sg -> xstring -> string

  val intern_sort: sg -> xsort -> sort

  val intern_typ: sg -> xtyp -> typ

  val intern_term: sg -> xterm -> term

  val intern_tycons: sg -> xtyp -> typ

  val pretty_sg: sg -> Pretty.T

  val str_of_sg: sg -> string

  val pprint_sg: sg -> pprint_args -> unit

  val pretty_term: sg -> term -> Pretty.T

  val pretty_typ: sg -> typ -> Pretty.T

  val pretty_sort: sg -> sort -> Pretty.T

  val pretty_classrel: sg -> class * class -> Pretty.T

  val pretty_arity: sg -> string * sort list * sort -> Pretty.T

  val string_of_term: sg -> term -> string

  val string_of_typ: sg -> typ -> string

  val string_of_sort: sg -> sort -> string

  val str_of_sort: sg -> sort -> string

  val str_of_classrel: sg -> class * class -> string

  val str_of_arity: sg -> string * sort list * sort -> string

  val pprint_term: sg -> term -> pprint_args -> unit

  val pprint_typ: sg -> typ -> pprint_args -> unit

  val certify_typ: sg -> typ -> typ

  val certify_term: sg -> term -> term * typ * int

  val read_raw_typ: sg * (indexname -> sort option) -> string -> typ

  val read_typ: sg * (indexname -> sort option) -> string -> typ

  val infer_types: sg -> (indexname -> typ option) ->

    (indexname -> sort option) -> string list -> bool

    -> xterm list * typ -> term * (indexname * typ) list

  val infer_types_simult: sg -> (indexname -> typ option) ->

    (indexname -> sort option) -> string list -> bool

    -> (xterm list * typ) list -> term list * (indexname * typ) list

  val add_classes: (bclass * xclass list) list -> sg -> sg

  val add_classes_i: (bclass * class list) list -> sg -> sg

  val add_classrel: (xclass * xclass) list -> sg -> sg

  val add_classrel_i: (class * class) list -> sg -> sg

  val add_defsort: xsort -> sg -> sg

  val add_defsort_i: sort -> sg -> sg

  val add_types: (bstring * int * mixfix) list -> sg -> sg

  val add_nonterminals: bstring list -> sg -> sg

  val add_tyabbrs: (bstring * string list * string * mixfix) list -> sg -> sg

  val add_tyabbrs_i: (bstring * string list * typ * mixfix) list -> sg -> sg

  val add_arities: (xstring * xsort list * xsort) list -> sg -> sg

  val add_arities_i: (string * sort list * sort) list -> sg -> sg

  val add_consts: (bstring * string * mixfix) list -> sg -> sg

  val add_consts_i: (bstring * typ * mixfix) list -> sg -> sg

  val add_syntax: (bstring * string * mixfix) list -> sg -> sg

  val add_syntax_i: (bstring * typ * mixfix) list -> sg -> sg

  val add_modesyntax: (string * bool) * (bstring * string * mixfix) list -> sg -> sg

  val add_modesyntax_i: (string * bool) * (bstring * typ * mixfix) list -> sg -> sg

  val add_trfuns:

    (string * (ast list -> ast)) list *

    (string * (term list -> term)) list *

    (string * (term list -> term)) list *

    (string * (ast list -> ast)) list -> sg -> sg

  val add_trfunsT:

    (string * (bool -> typ -> term list -> term)) list -> sg -> sg

  val add_tokentrfuns:

    (string * string * (string -> string * int)) list -> sg -> sg

  val add_trrules: (xstring * string) Syntax.trrule list -> sg -> sg

  val add_trrules_i: ast Syntax.trrule list -> sg -> sg

  val add_path: string -> sg -> sg

  val add_space: string * string list -> sg -> sg

  val add_name: string -> sg -> sg

  val data_kinds: data -> string list

  val init_data: Object.kind * (Object.T * (Object.T -> Object.T) *

    (Object.T * Object.T -> Object.T) * (sg -> Object.T -> unit)) -> sg -> sg

  val get_data: Object.kind -> (Object.T -> 'a) -> sg -> 'a

  val put_data: Object.kind -> ('a -> Object.T) -> 'a -> sg -> sg

  val print_data: Object.kind -> sg -> unit

  val merge_refs: sg_ref * sg_ref -> sg_ref

  val merge: sg * sg -> sg

  val prep_ext: sg -> sg

  val nontriv_merge: sg * sg -> sg

  val pre_pure: sg

  val const_of_class: class -> string

  val class_of_const: string -> class

end;

structure Sign: SIGN =

struct

(** datatype sg **)

(* types sg, data, sg_ref *)

datatype sg =

  Sg of

   {id: string ref,                             (*id*)

    stamps: string ref list} *                  (*unique theory indentifier*)

   {self: sg_ref,                               (*mutable self reference*)

    tsig: Type.type_sig,                        (*order-sorted signature of types*)

    const_tab: typ Symtab.table,                (*type schemes of constants*)

    syn: Syntax.syntax,                         (*syntax for parsing and printing*)

    path: string list,                          (*current name space entry prefix*)

    spaces: (string * NameSpace.T) list,        (*name spaces for consts, types etc.*)

    data: data}                                 (*anytype data*)

and data =

  Data of

    (Object.kind *				(*kind (for authorization)*)

      (Object.T *				(*value*)

        ((Object.T -> Object.T) *               (*prepare extend method*)

          (Object.T * Object.T -> Object.T) *   (*merge and prepare extend method*)

          (sg -> Object.T -> unit))))           (*print method*)

    Symtab.table

and sg_ref =

  SgRef of sg ref option;

(*make signature*)

fun make_sign (id, self, tsig, const_tab, syn, path, spaces, data, stamps) =

  Sg ({id = id, stamps = stamps}, {self = self, tsig = tsig, const_tab = const_tab,

    syn = syn, path = path, spaces = spaces, data = data});

(* basic operations *)

fun rep_sg (Sg (_, args)) = args;

(*show stamps*)

fun stamp_names_of (Sg ({stamps, ...}, _)) = rev (map ! stamps);

fun pretty_sg sg = Pretty.str_list "{" "}" (stamp_names_of sg);

val str_of_sg = Pretty.str_of o pretty_sg;

val pprint_sg = Pretty.pprint o pretty_sg;

val tsig_of = #tsig o rep_sg;

fun const_type (Sg (_, {const_tab, ...})) c = Symtab.lookup (const_tab, c);

(* id and self *)

fun check_stale (sg as Sg ({id, ...},

        {self = SgRef (Some (ref (Sg ({id = id', ...}, _)))), ...})) =

      if id = id' then sg

      else raise TERM ("Stale signature: " ^ str_of_sg sg, [])

  | check_stale _ = sys_error "Sign.check_stale";

fun is_stale sg = (check_stale sg; false) handle TERM _ => true;

fun self_ref (sg as Sg (_, {self, ...})) = (check_stale sg; self);

fun deref (SgRef (Some (ref sg))) = sg

  | deref (SgRef None) = sys_error "Sign.deref";

fun name_of (sg as Sg ({id = ref name, ...}, _)) =

  if name = "" orelse ord name = ord "#" then

    raise TERM ("Nameless signature " ^ str_of_sg sg, [])

  else name;

(* inclusion and equality *)

local

  (*avoiding polymorphic equality: factor 10 speedup*)

  fun mem_stamp (_:string ref, []) = false

    | mem_stamp (x, y :: ys) = x = y orelse mem_stamp (x, ys);

  fun subset_stamp ([], ys) = true

    | subset_stamp (x :: xs, ys) =

        mem_stamp (x, ys) andalso subset_stamp (xs, ys);

  (*fast partial test*)

  fun fast_sub ([]: string ref list, _) = true

    | fast_sub (_, []) = false

    | fast_sub (x :: xs, y :: ys) =

        if x = y then fast_sub (xs, ys)

        else fast_sub (x :: xs, ys);

in

  fun eq_sg (sg1 as Sg ({id = id1, ...}, _), sg2 as Sg ({id = id2, ...}, _)) =

    (check_stale sg1; check_stale sg2; id1 = id2);

  fun subsig (sg1 as Sg ({stamps = s1, ...}, _), sg2 as Sg ({stamps = s2, ...}, _)) =

    eq_sg (sg1, sg2) orelse subset_stamp (s1, s2);

  fun fast_subsig (sg1 as Sg ({stamps = s1, ...}, _), sg2 as Sg ({stamps = s2, ...}, _)) =

    eq_sg (sg1, sg2) orelse fast_sub (s1, s2);

end;

(*test if same theory names are contained in signatures' stamps,

  i.e. if signatures belong to same theory but not necessarily to the

  same version of it*)

fun same_sg (sg1 as Sg ({stamps = s1, ...}, _), sg2 as Sg ({stamps = s2, ...}, _)) =

  eq_sg (sg1, sg2) orelse eq_set_string (pairself (map (op !)) (s1, s2));

(*test for drafts*)

fun is_draft (Sg ({stamps = ref name :: _, ...}, _)) = name = "" orelse ord name = ord "#";

(* classes and sorts *)

val classes = #classes o Type.rep_tsig o tsig_of;

val defaultS = Type.defaultS o tsig_of;

val subsort = Type.subsort o tsig_of;

val norm_sort = Type.norm_sort o tsig_of;

val nonempty_sort = Type.nonempty_sort o tsig_of;

fun of_sort (Sg (_, {tsig, ...})) =

  Sorts.of_sort (#classrel (Type.rep_tsig tsig)) (#arities (Type.rep_tsig tsig));

(** signature data **)

(* errors *)

fun of_theory sg = "\nof theory " ^ str_of_sg sg;

fun err_inconsistent kinds =

  error ("Attempt to merge different versions of " ^ commas_quote kinds ^ " data");

fun err_method name kind =

  error ("Error while invoking " ^ quote kind ^ " " ^ name ^ " method");

fun err_dup_init sg kind =

  error ("Duplicate initialization of " ^ quote kind ^ " data" ^ of_theory sg);

fun err_uninit sg kind =

  error ("Tried to access uninitialized " ^ quote kind ^ " data" ^ of_theory sg);

fun err_access sg kind =

  error ("Unauthorized access to " ^ quote kind ^ " data" ^ of_theory sg);

(* prepare data *)

val empty_data = Data Symtab.empty;

fun merge_data (Data tab1, Data tab2) =

  let

    val data1 = map snd (Symtab.dest tab1);

    val data2 = map snd (Symtab.dest tab2);

    val all_data = data1 @ data2;

    val kinds = gen_distinct Object.eq_kind (map fst all_data);

   fun entry data kind =

     (case gen_assoc Object.eq_kind (data, kind) of

       None => []

     | Some x => [(kind, x)]);

    fun merge_entries [(kind, (e, mths as (ext, _, _)))] =

          (kind, (ext e handle _ => err_method "prep_ext" (Object.name_of_kind kind), mths))

      | merge_entries [(kind, (e1, mths as (_, mrg, _))), (_, (e2, _))] =

          (kind, (mrg (e1, e2) handle _ => err_method "merge" (Object.name_of_kind kind), mths))

      | merge_entries _ = sys_error "merge_entries";

    val data = map (fn k => merge_entries (entry data1 k @ entry data2 k)) kinds;

    val data_idx = map (fn (k, x) => (Object.name_of_kind k, (k, x))) data;

  in

    Data (Symtab.make data_idx)

      handle Symtab.DUPS dups => err_inconsistent dups

  end;

fun prep_ext_data data = merge_data (data, empty_data);

fun init_data_sg sg (Data tab) kind e ext mrg prt =

  let val name = Object.name_of_kind kind in

    Data (Symtab.update_new ((name, (kind, (e, (ext, mrg, prt)))), tab))

      handle Symtab.DUP _ => err_dup_init sg name

  end;

(* access data *)

fun data_kinds (Data tab) = map fst (Symtab.dest tab);

fun lookup_data sg tab kind =

  let val name = Object.name_of_kind kind in

    (case Symtab.lookup (tab, name) of

      Some (k, x) =>

        if Object.eq_kind (kind, k) then x

        else err_access sg name

    | None => err_uninit sg name)

  end;

fun get_data kind f (sg as Sg (_, {data = Data tab, ...})) =

  let val x = fst (lookup_data sg tab kind)

  in f x handle Match => Object.kind_error kind end;

fun print_data kind (sg as Sg (_, {data = Data tab, ...})) =

  let val (e, (_, _, prt)) = lookup_data sg tab kind

  in prt sg e handle _ => err_method ("print" ^ of_theory sg) (Object.name_of_kind kind) end;

fun put_data_sg sg (Data tab) kind f x =

  Data (Symtab.update ((Object.name_of_kind kind,

    (kind, (f x, snd (lookup_data sg tab kind)))), tab));

(** build signatures **)

fun ext_stamps stamps (id as ref name) =

  let val stmps = (case stamps of ref "#" :: ss => ss | ss => ss) in

    if exists (equal name o !) stmps then

      error ("Theory already contains a " ^ quote name ^ " component")

    else id :: stmps

  end;

fun create_sign self stamps name (syn, tsig, ctab, (path, spaces), data) =

  let

    val id = ref name;

    val sign =

      make_sign (id, self, tsig, ctab, syn, path, spaces, data, ext_stamps stamps id);

  in

    (case self of

      SgRef (Some r) => r := sign

    | _ => sys_error "Sign.create_sign");

    sign

  end;

fun extend_sign keep extfun name decls

    (sg as Sg ({id = _, stamps}, {self, tsig, const_tab, syn, path, spaces, data})) =

  let

    val _ = check_stale sg;

    val (self', data') =

      if is_draft sg andalso keep then (self, data)

      else (SgRef (Some (ref sg)), prep_ext_data data);

  in

    create_sign self' stamps name

      (extfun (syn, tsig, const_tab, (path, spaces), data') decls)

  end;

(** name spaces **)

(*prune names on output by default*)

val long_names = ref false;

(* kinds *)

val classK = "class";

val typeK = "type";

val constK = "const";

(* add and retrieve names *)

fun space_of spaces kind =

  if_none (assoc (spaces, kind)) NameSpace.empty;

(*input and output of qualified names*)

fun intrn spaces kind = NameSpace.intern (space_of spaces kind);

fun extrn spaces kind = NameSpace.extern (space_of spaces kind);

(*add names*)

fun add_names spaces kind names =

  let val space' = NameSpace.extend (space_of spaces kind, names) in

    overwrite (spaces, (kind, space'))

  end;

(*make full names*)

fun full path name =

  if name = "" then error "Attempt to declare empty name \"\""

  else if NameSpace.qualified name then

    error ("Attempt to declare qualified name " ^ quote name)

  else NameSpace.pack (path @ [name]);

(*base name*)

val base_name = NameSpace.base;

(* intern / extern names *)

local

  (*prepare mapping of names*)

  fun mapping f add_xs t =

    let

      fun f' x = let val y = f x in if x = y then None else Some (x, y) end;

      val table = mapfilter f' (add_xs (t, []));

      fun lookup x = if_none (assoc (table, x)) x;

    in lookup end;

  (*intern / extern typ*)

  fun trn_typ trn T =

    T |> map_typ

      (mapping (trn classK) add_typ_classes T)

      (mapping (trn typeK) add_typ_tycons T);

  (*intern / extern term*)

  fun trn_term trn t =

    t |> map_term

      (mapping (trn classK) add_term_classes t)

      (mapping (trn typeK) add_term_tycons t)

      (mapping (trn constK) add_term_consts t);

  val spaces_of = #spaces o rep_sg;

in

  fun intrn_class spaces = intrn spaces classK;

  fun extrn_class spaces = extrn spaces classK;

  val intrn_sort = map o intrn_class;

  val intrn_typ = trn_typ o intrn;

  val intrn_term = trn_term o intrn;

  val extrn_sort = map o extrn_class;

  val extrn_typ = trn_typ o extrn;

  val extrn_term = trn_term o extrn;

  fun intrn_tycons spaces T =

    map_typ I (mapping (intrn spaces typeK) add_typ_tycons T) T;

  val intern = intrn o spaces_of;

  val extern = extrn o spaces_of;

  fun cond_extern sg kind = if ! long_names then I else extern sg kind;

  val intern_class = intrn_class o spaces_of;

  val intern_sort = intrn_sort o spaces_of;

  val intern_typ = intrn_typ o spaces_of;

  val intern_term = intrn_term o spaces_of;

  fun intern_tycon sg = intrn (spaces_of sg) typeK;

  fun intern_const sg = intrn (spaces_of sg) constK;

  val intern_tycons = intrn_tycons o spaces_of;

  val full_name = full o #path o rep_sg;

  fun full_name_path sg elems name =

    full (#path (rep_sg sg) @ NameSpace.unpack elems) name;

end;

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

fun pretty_term (sg as Sg ({stamps, ...}, {syn, spaces, ...})) t =

  Syntax.pretty_term syn

    (exists (equal "CPure" o !) stamps)

    (if ! long_names then t else extrn_term spaces t);

fun pretty_typ (Sg (_, {syn, spaces, ...})) T =

  Syntax.pretty_typ syn

    (if ! long_names then T else extrn_typ spaces T);

fun pretty_sort (Sg (_, {syn, spaces, ...})) S =

  Syntax.pretty_sort syn

    (if ! long_names then S else extrn_sort spaces S);

fun pretty_classrel sg (c1, c2) = Pretty.block

  [pretty_sort sg [c1], Pretty.str " <", Pretty.brk 1, pretty_sort sg [c2]];

fun pretty_arity sg (t, Ss, S) =

  let

    val t' = cond_extern sg typeK t;

    val dom =

      if null Ss then []

      else [Pretty.list "(" ")" (map (pretty_sort sg) Ss), Pretty.brk 1];

  in

    Pretty.block

      ([Pretty.str (t' ^ " ::"), Pretty.brk 1] @ dom @ [pretty_sort sg S])

  end;

fun string_of_term sg t = Pretty.string_of (pretty_term sg t);

fun string_of_typ sg T = Pretty.string_of (pretty_typ sg T);

fun string_of_sort sg S = Pretty.string_of (pretty_sort sg S);

fun str_of_sort sg S = Pretty.str_of (pretty_sort sg S);

fun str_of_classrel sg c1_c2 = Pretty.str_of (pretty_classrel sg c1_c2);

fun str_of_arity sg ar = Pretty.str_of (pretty_arity sg ar);

fun pprint_term sg = Pretty.pprint o Pretty.quote o (pretty_term sg);

fun pprint_typ sg = Pretty.pprint o Pretty.quote o (pretty_typ sg);

(** read types **)  (*exception ERROR*)

fun err_in_type s =

  error ("The error(s) above occurred in type " ^ quote s);

fun rd_raw_typ syn tsig spaces def_sort str =

  intrn_tycons spaces

    (Syntax.read_typ syn (Type.get_sort tsig def_sort (intrn_sort spaces)) str

      handle ERROR => err_in_type str);

fun read_raw_typ (sg as Sg (_, {tsig, syn, spaces, ...}), def_sort) str =

  (check_stale sg; rd_raw_typ syn tsig spaces def_sort str);

(*read and certify typ wrt a signature*)

fun read_typ (sg, def_sort) str =

  (Type.cert_typ (tsig_of sg) (read_raw_typ (sg, def_sort) str)

      handle TYPE (msg, _, _) => (error_msg msg; err_in_type str));

(** certify types and terms **)   (*exception TYPE*)

(* certify_typ *)

val certify_typ = Type.cert_typ o tsig_of;

(* certify_term *)

(*check for duplicate TVars with distinct sorts*)

fun nodup_TVars (tvars, T) =

  (case T of

    Type (_, Ts) => nodup_TVars_list (tvars, Ts)

  | TFree _ => tvars

  | TVar (v as (a, S)) =>

      (case assoc_string_int (tvars, a) of

        Some S' =>

          if S = S' then tvars

          else raise TYPE ("Type variable " ^ Syntax.string_of_vname a ^

            " has two distinct sorts", [TVar (a, S'), T], [])

      | None => v :: tvars))

(*equivalent to foldl nodup_TVars_list, but 3X faster under Poly/ML*)

and nodup_TVars_list (tvars, []) = tvars

  | nodup_TVars_list (tvars, T :: Ts) =

      nodup_TVars_list (nodup_TVars (tvars, T), Ts);

(*check for duplicate Vars with distinct types*)

fun nodup_Vars tm =

  let

    fun nodups vars tvars tm =

      (case tm of

        Const (c, T) => (vars, nodup_TVars (tvars, T))

      | Free (a, T) => (vars, nodup_TVars (tvars, T))

      | Var (v as (ixn, T)) =>

          (case assoc_string_int (vars, ixn) of

            Some T' =>

              if T = T' then (vars, nodup_TVars (tvars, T))

              else raise TYPE ("Variable " ^ Syntax.string_of_vname ixn ^

                " has two distinct types", [T', T], [])

          | None => (v :: vars, tvars))

      | Bound _ => (vars, tvars)

      | Abs (_, T, t) => nodups vars (nodup_TVars (tvars, T)) t

      | s $ t =>

          let val (vars',tvars') = nodups vars tvars s in

            nodups vars' tvars' t

          end);

  in nodups [] [] tm; () end;

(*compute and check type of the term*)

fun type_check sg tm =

  let

    val prt =

      setmp Syntax.show_brackets true

        (setmp long_names true (pretty_term sg));

    val prT = setmp long_names true (pretty_typ sg);

    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 text = cat_lines

         ["Type error in application: " ^ why,

          "",

          Pretty.string_of (Pretty.block [Pretty.str "Operator:", Pretty.brk 2, prt t',

            Pretty.str " :: ", prT T]),

          Pretty.string_of (Pretty.block [Pretty.str "Operand:", Pretty.brk 3, prt u',

            Pretty.str " :: ", prT U]), ""];

      in raise TYPE (text, [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 (nth_elem (i, bs) handle LIST _ =>

          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 certify_term sg tm =

  let

    val _ = check_stale sg;

    val tsig = tsig_of sg;

    fun show_const a T = quote a ^ " :: " ^ quote (string_of_typ sg T);

    fun atom_err (errs, Const (a, T)) =

        (case const_type sg a of

          None => ("Undeclared constant " ^ show_const a T) :: errs

        | Some U =>

            if Type.typ_instance (tsig, T, U) then errs

            else ("Illegal type for constant " ^ show_const a T) :: errs)

      | atom_err (errs, Var ((x, i), _)) =

          if i < 0 then ("Negative index for Var " ^ quote x) :: errs else errs

      | atom_err (errs, _) = errs;

    val norm_tm =

      (case it_term_types (Type.typ_errors tsig) (tm, []) of

        [] => map_term_types (Type.norm_typ tsig) tm

      | errs => raise TYPE (cat_lines errs, [], [tm]));

    val _ = nodup_Vars norm_tm;

  in

    (case foldl_aterms atom_err ([], norm_tm) of

      [] => (norm_tm, type_check sg norm_tm, maxidx_of_term norm_tm)

    | errs => raise TYPE (cat_lines errs, [], [norm_tm]))

  end;

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

(*

  def_type: partial map from indexnames to types (constrains Frees, Vars)

  def_sort: partial map from indexnames to sorts (constrains TFrees, TVars)

  used: list 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 sg def_type def_sort used freeze args =

  let

    val tsig = tsig_of sg;

    val prt =

      setmp Syntax.show_brackets true

        (setmp long_names true (pretty_term sg));

    val prT = setmp long_names true (pretty_typ sg);

    val termss = foldr multiply (map fst args, [[]]);

    val typs =

      map (fn (_, T) => certify_typ sg T handle TYPE (msg, _, _) => error msg) args;

    fun infer ts = OK

      (Type.infer_types prt prT tsig (const_type sg) def_type def_sort

        (intern_const sg) (intern_tycons sg) (intern_sort sg) used freeze typs ts)

      handle TYPE (msg, _, _) => Error msg;

    val err_results = map infer termss;

    val errs = mapfilter get_error err_results;

    val results = mapfilter get_ok err_results;

    val ambiguity = length termss;	(* FIXME !? *)

    (* FIXME to syntax.ML!? *)

    fun ambig_msg () =

      if ambiguity > 1 andalso ambiguity <= ! Syntax.ambiguity_level

      then

        error_msg "Got more than one parse tree.\n\

          \Retry with smaller Syntax.ambiguity_level for more information."

      else ();

  in

    if null results then (ambig_msg (); error (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 (ambig_msg (); error ("More than one term is type correct:\n" ^

      (cat_lines (map (Pretty.string_of o prt) (flat (map fst results))))))

  end;

fun infer_types sg def_type def_sort used freeze tsT =

  apfst hd (infer_types_simult sg def_type def_sort used freeze [tsT]);

(** extend signature **)    (*exception ERROR*)

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

fun decls_of path name_of mfixs =

  map (fn (x, y, mx) => (full path (name_of x mx), y)) mfixs;

fun no_read _ _ _ decl = decl;

(* add default sort *)

fun ext_defsort int (syn, tsig, ctab, (path, spaces), data) S =

  (syn, Type.ext_tsig_defsort tsig (if int then intrn_sort spaces S else S),

    ctab, (path, spaces), data);

(* add type constructors *)

fun ext_types (syn, tsig, ctab, (path, spaces), data) types =

  let val decls = decls_of path Syntax.type_name types in

    (Syntax.extend_type_gram syn types,

      Type.ext_tsig_types tsig decls, ctab,

      (path, add_names spaces typeK (map fst decls)), data)

  end;

fun ext_nonterminals sg nonterms =

  ext_types sg (map (fn n => (n, 0, Syntax.NoSyn)) nonterms);

(* add type abbreviations *)

fun read_abbr syn tsig spaces (t, vs, rhs_src) =

  (t, vs, rd_raw_typ syn tsig spaces (K None) rhs_src)

    handle ERROR => error ("in type abbreviation " ^ t);

fun ext_abbrs rd_abbr (syn, tsig, ctab, (path, spaces), data) abbrs =

  let

    fun mfix_of (t, vs, _, mx) = (t, length vs, mx);

    val syn' = Syntax.extend_type_gram syn (map mfix_of abbrs);

    val abbrs' =

      map (fn (t, vs, rhs, mx) =>

        (full path (Syntax.type_name t mx), vs, rhs)) abbrs;

    val spaces' = add_names spaces typeK (map #1 abbrs');

    val decls = map (rd_abbr syn' tsig spaces') abbrs';

  in

    (syn', Type.ext_tsig_abbrs tsig decls, ctab, (path, spaces'), data)

  end;

fun ext_tyabbrs abbrs = ext_abbrs read_abbr abbrs;

fun ext_tyabbrs_i abbrs = ext_abbrs no_read abbrs;

(* add type arities *)

fun ext_arities int (syn, tsig, ctab, (path, spaces), data) arities =

  let

    fun intrn_arity (c, Ss, S) =

      (intrn spaces typeK c, map (intrn_sort spaces) Ss, intrn_sort spaces S);

    val intrn = if int then map intrn_arity else I;

    val tsig' = Type.ext_tsig_arities tsig (intrn arities);

    val log_types = Type.logical_types tsig';

  in

    (Syntax.extend_log_types syn log_types, tsig', ctab, (path, spaces), data)

  end;

(* add term constants and syntax *)

fun const_name path c mx =

  full path (Syntax.const_name c mx);

fun err_in_const c =

  error ("in declaration of constant " ^ quote c);

fun err_dup_consts cs =

  error ("Duplicate declaration of constant(s) " ^ commas_quote cs);

fun read_const syn tsig (path, spaces) (c, ty_src, mx) =

  (c, rd_raw_typ syn tsig spaces (K None) ty_src, mx)

    handle ERROR => err_in_const (const_name path c mx);

fun ext_cnsts rd_const syn_only prmode (syn, tsig, ctab, (path, spaces), data) raw_consts =

  let

    fun prep_const (c, ty, mx) =

      (c, compress_type (Type.varifyT (Type.cert_typ tsig (Type.no_tvars ty))), mx)

        handle TYPE (msg, _, _) =>

          (error_msg msg; err_in_const (const_name path c mx));

    val consts = map (prep_const o rd_const syn tsig (path, spaces)) raw_consts;

    val decls =

      if syn_only then []

      else decls_of path Syntax.const_name consts;

  in

    (Syntax.extend_const_gram syn prmode consts, tsig,

      Symtab.extend (ctab, decls)

        handle Symtab.DUPS cs => err_dup_consts cs,

      (path, add_names spaces constK (map fst decls)), data)

  end;

fun ext_consts_i sg = ext_cnsts no_read false ("", true) sg;

fun ext_consts sg = ext_cnsts read_const false ("", true) sg;

fun ext_syntax_i sg = ext_cnsts no_read true ("", true) sg;

fun ext_syntax sg = ext_cnsts read_const true ("", true) sg;

fun ext_modesyntax_i sg (prmode, consts) = ext_cnsts no_read true prmode sg consts;

fun ext_modesyntax sg (prmode, consts) = ext_cnsts read_const true prmode sg consts;

(* add type classes *)

fun const_of_class c = c ^ "_class";

fun class_of_const c_class =

  let

    val c = implode (take (size c_class - size "_class", explode c_class));

  in

    if const_of_class c = c_class then c

    else raise TERM ("class_of_const: bad name " ^ quote c_class, [])

  end;

fun ext_classes int (syn, tsig, ctab, (path, spaces), data) classes =

  let

    val names = map fst classes;

    val consts =

      map (fn c => (const_of_class c, a_itselfT --> propT, NoSyn)) names;

    val full_names = map (full path) names;

    val spaces' = add_names spaces classK full_names;

    val intrn = if int then map (intrn_class spaces') else I;

    val classes' =

      ListPair.map (fn (c, (_, cs)) => (c, intrn cs)) (full_names, classes);

  in

    ext_consts_i

      (Syntax.extend_consts syn names,

        Type.ext_tsig_classes tsig classes', ctab, (path, spaces'), data)

    consts

  end;

(* add to classrel *)

fun ext_classrel int (syn, tsig, ctab, (path, spaces), data) pairs =

  let val intrn = if int then map (pairself (intrn_class spaces)) else I in

    (syn, Type.ext_tsig_classrel tsig (intrn pairs), ctab, (path, spaces), data)

  end;

(* add translation rules *)

fun ext_trrules (syn, tsig, ctab, (path, spaces), data) args =

  (Syntax.extend_trrules syn

    (map (Syntax.map_trrule (fn (root, str) => (intrn spaces typeK root, str))) args),

      tsig, ctab, (path, spaces), data);

(* add to syntax *)

fun ext_syn extfun (syn, tsig, ctab, names, data) args =

  (extfun syn args, tsig, ctab, names, data);

(* add to path *)

fun ext_path (syn, tsig, ctab, (path, spaces), data) elems =

  let

    val path' =

      if elems = ".." andalso not (null path) then fst (split_last path)

      else if elems = "/" then []

      else path @ NameSpace.unpack elems;

  in

    (syn, tsig, ctab, (path', spaces), data)

  end;      

(* add to name space *)

fun ext_space (syn, tsig, ctab, (path, spaces), data) (kind, names) =

  (syn, tsig, ctab, (path, add_names spaces kind names), data);

(* signature data *)

fun ext_init_data sg (syn, tsig, ctab, names, data) (kind, (e, ext, mrg, prt)) =

  (syn, tsig, ctab, names, init_data_sg sg data kind e ext mrg prt);

fun ext_put_data sg (syn, tsig, ctab, names, data) (kind, f, x) =

  (syn, tsig, ctab, names, put_data_sg sg data kind f x);

(* the external interfaces *)

val add_classes       = extend_sign true (ext_classes true) "#";

val add_classes_i     = extend_sign true (ext_classes false) "#";

val add_classrel      = extend_sign true (ext_classrel true) "#";

val add_classrel_i    = extend_sign true (ext_classrel false) "#";

val add_defsort       = extend_sign true (ext_defsort true) "#";

val add_defsort_i     = extend_sign true (ext_defsort false) "#";

val add_types         = extend_sign true ext_types "#";

val add_nonterminals  = extend_sign true ext_nonterminals "#";

val add_tyabbrs       = extend_sign true ext_tyabbrs "#";

val add_tyabbrs_i     = extend_sign true ext_tyabbrs_i "#";

val add_arities       = extend_sign true (ext_arities true) "#";

val add_arities_i     = extend_sign true (ext_arities false) "#";

val add_consts        = extend_sign true ext_consts "#";

val add_consts_i      = extend_sign true ext_consts_i "#";

val add_syntax        = extend_sign true ext_syntax "#";

val add_syntax_i      = extend_sign true ext_syntax_i "#";

val add_modesyntax    = extend_sign true ext_modesyntax "#";

val add_modesyntax_i  = extend_sign true ext_modesyntax_i "#";

val add_trfuns        = extend_sign true (ext_syn Syntax.extend_trfuns) "#";

val add_trfunsT       = extend_sign true (ext_syn Syntax.extend_trfunsT) "#";

val add_tokentrfuns   = extend_sign true (ext_syn Syntax.extend_tokentrfuns) "#";

val add_trrules       = extend_sign true ext_trrules "#";

val add_trrules_i     = extend_sign true (ext_syn Syntax.extend_trrules_i) "#";

val add_path          = extend_sign true ext_path "#";

val add_space         = extend_sign true ext_space "#";

fun init_data arg sg  = extend_sign true (ext_init_data sg) "#" arg sg;

fun put_data k f x sg = extend_sign true (ext_put_data sg) "#" (k, f, x) sg;

fun add_name name sg  = extend_sign true K name () sg;

fun prep_ext sg       = extend_sign false K "#" () sg;

(** merge signatures **)    	(*exception TERM*)

(* merge_stamps *)

fun merge_stamps stamps1 stamps2 =

  let val stamps = merge_rev_lists stamps1 stamps2 in

    (case duplicates (map ! stamps) of

      [] => stamps

    | dups => raise TERM ("Attempt to merge different versions of theories "

        ^ commas_quote dups, []))

  end;

(* implicit merge -- trivial only *)

fun merge_refs (sgr1 as SgRef (Some (ref (sg1 as Sg ({stamps = s1, ...}, _)))),

        sgr2 as SgRef (Some (ref (sg2 as Sg ({stamps = s2, ...}, _))))) =

      if fast_subsig (sg2, sg1) then sgr1

      else if fast_subsig (sg1, sg2) then sgr2

      else if subsig (sg2, sg1) then sgr1

      else if subsig (sg1, sg2) then sgr2

      else (merge_stamps s1 s2; (*check for different versions*)

        raise TERM ("Attempt to do non-trivial merge of signatures", []))

  | merge_refs _ = sys_error "Sign.merge_refs";

val merge = deref o merge_refs o pairself self_ref;

(* proper merge *)

fun merge_aux (sg1, sg2) =

  if subsig (sg2, sg1) then sg1

  else if subsig (sg1, sg2) then sg2

  else if is_draft sg1 orelse is_draft sg2 then

    raise TERM ("Attempt to merge draft signatures", [])

  else

    (*neither is union already; must form union*)

    let

      val Sg ({id = _, stamps = stamps1}, {self = _, tsig = tsig1, const_tab = const_tab1,

        syn = syn1, path = _, spaces = spaces1, data = data1}) = sg1;

      val Sg ({id = _, stamps = stamps2}, {self = _, tsig = tsig2, const_tab = const_tab2,

        syn = syn2, path = _, spaces = spaces2, data = data2}) = sg2;

      val id = ref "";

      val self_ref = ref sg1;                   (*dummy value*)

      val self = SgRef (Some self_ref);