src/Pure/Isar/locale.ML

Locales: new element constrains, parameter renaming with syntax,
experimental command instantiate withdrawn.

(*  Title:      Pure/Isar/locale.ML
    ID:         $Id$
    Author:     Clemens Ballarin, TU Muenchen; Markus Wenzel, LMU/TU Muenchen

Locales -- Isar proof contexts as meta-level predicates, with local
syntax and implicit structures.

Draws some basic ideas from Florian Kammueller's original version of
locales, but uses the richer infrastructure of Isar instead of the raw
meta-logic.  Furthermore, we provide structured import of contexts
(with merge and rename operations), as well as type-inference of the
signature parts, and predicate definitions of the specification text.

See also:

[1] Clemens Ballarin. Locales and Locale Expressions in Isabelle/Isar.
    In Stefano Berardi et al., Types for Proofs and Programs: International
    Workshop, TYPES 2003, Torino, Italy, LNCS 3085, pages 34-50, 2004.
*)

(* TODO:
- beta-eta normalisation of interpretation parameters
- no beta reduction of interpretation witnesses
- mix of locales with and without open in activate_elems
- dangling type frees in locales
*)

signature LOCALE =
sig
  type context
  datatype ('typ, 'term, 'fact) elem =
    Fixes of (string * 'typ option * mixfix option) list |
    Constrains of (string * 'typ) list |
    Assumes of ((string * Attrib.src list) * ('term * ('term list * 'term list)) list) list |
    Defines of ((string * Attrib.src list) * ('term * 'term list)) list |
    Notes of ((string * Attrib.src list) * ('fact * Attrib.src list) list) list
  datatype expr =
    Locale of string |
    Rename of expr * (string * mixfix option) option list |
    Merge of expr list
  val empty: expr
  datatype 'a elem_expr = Elem of 'a | Expr of expr

  (* Abstract interface to locales *)
  type element
  type element_i
  type locale
  val intern: Sign.sg -> xstring -> string
  val extern: Sign.sg -> string -> xstring
  val the_locale: theory -> string -> locale
  val intern_attrib_elem: theory ->
    ('typ, 'term, 'fact) elem -> ('typ, 'term, 'fact) elem
  val intern_attrib_elem_expr: theory ->
    ('typ, 'term, 'fact) elem elem_expr -> ('typ, 'term, 'fact) elem elem_expr

  (* Processing of locale statements *)
  val read_context_statement: xstring option -> element elem_expr list ->
    (string * (string list * string list)) list list -> context ->
    string option * (cterm list * cterm list) * context * context * 
      (term * (term list * term list)) list list
  val cert_context_statement: string option -> element_i elem_expr list ->
    (term * (term list * term list)) list list -> context ->
    string option * (cterm list * cterm list) * context * context *
      (term * (term list * term list)) list list

  (* Diagnostic functions *)
  val print_locales: theory -> unit
  val print_locale: theory -> expr -> element list -> unit
  val print_global_registrations: string -> theory -> unit
  val print_local_registrations': string -> context -> unit
  val print_local_registrations: string -> context -> unit

  (* Storing results *)
  val add_locale: bool -> bstring -> expr -> element list -> theory -> theory
  val add_locale_i: bool -> bstring -> expr -> element_i list -> theory -> theory
  val smart_note_thmss: string -> string option ->
    ((bstring * theory attribute list) * (thm list * theory attribute list) list) list ->
    theory -> theory * (bstring * thm list) list
  val note_thmss: string -> xstring ->
    ((bstring * Attrib.src list) * (thmref * Attrib.src list) list) list ->
    theory -> theory * (bstring * thm list) list
  val note_thmss_i: string -> string ->
    ((bstring * Attrib.src list) * (thm list * Attrib.src list) list) list ->
    theory -> theory * (bstring * thm list) list
  val add_thmss: string -> string -> ((string * thm list) * Attrib.src list) list ->
    theory * context -> (theory * context) * (string * thm list) list

  (* Locale interpretation *)
  val prep_global_registration:
    string * Attrib.src list -> expr -> string option list -> theory ->
    theory * ((string * term list) * term list) list * (theory -> theory)
  val prep_local_registration:
    string * Attrib.src list -> expr -> string option list -> context ->
    context * ((string * term list) * term list) list * (context -> context)
  val add_global_witness:
    string * term list -> thm -> theory -> theory
  val add_local_witness:
    string * term list -> thm -> context -> context
end;

structure Locale: LOCALE =
struct

(** locale elements and expressions **)

type context = ProofContext.context;

datatype ('typ, 'term, 'fact) elem =
  Fixes of (string * 'typ option * mixfix option) list |
  Constrains of (string * 'typ) list |
  Assumes of ((string * Attrib.src list) * ('term * ('term list * 'term list)) list) list |
  Defines of ((string * Attrib.src list) * ('term * 'term list)) list |
  Notes of ((string * Attrib.src list) * ('fact * Attrib.src list) list) list;

datatype expr =
  Locale of string |
  Rename of expr * (string * mixfix option) option list |
  Merge of expr list;

val empty = Merge [];

datatype 'a elem_expr =
  Elem of 'a | Expr of expr;

type element = (string, string, thmref) elem;
type element_i = (typ, term, thm list) elem;

type locale =
 {predicate: cterm list * thm list,
    (* CB: For old-style locales with "(open)" this entry is ([], []).
       For new-style locales, which declare predicates, if the locale declares
       no predicates, this is also ([], []).
       If the locale declares predicates, the record field is
       ([statement], axioms), where statement is the locale predicate applied
       to the (assumed) locale parameters.  Axioms contains the projections
       from the locale predicate to the normalised assumptions of the locale
       (cf. [1], normalisation of locale expressions.)
    *)
  import: expr,                                       (*dynamic import*)
  elems: (element_i * stamp) list,                    (*static content*)
  params: ((string * typ option) * mixfix option) list * string list}
                                                      (*all/local params*)


(* CB: an internal (Int) locale element was either imported or included,
   an external (Ext) element appears directly in the locale text. *)

datatype ('a, 'b) int_ext = Int of 'a | Ext of 'b;



(** term and type instantiation, using symbol tables **)

(* instantiate TFrees *)

fun tinst_tab_type tinst T = if Symtab.is_empty tinst
      then T
      else Term.map_type_tfree
        (fn (v as (x, _)) => getOpt (Symtab.lookup (tinst, x), (TFree v))) T;

fun tinst_tab_term tinst t = if Symtab.is_empty tinst
      then t
      else Term.map_term_types (tinst_tab_type tinst) t;

fun tinst_tab_thm sg tinst thm = if Symtab.is_empty tinst
      then thm
      else let
          val cert = Thm.cterm_of sg;
          val certT = Thm.ctyp_of sg;
          val {hyps, prop, ...} = Thm.rep_thm thm;
          val tfrees = foldr Term.add_term_tfree_names [] (prop :: hyps);
          val tinst' = Symtab.dest tinst |>
                List.filter (fn (a, _) => a mem_string tfrees);
        in
          if null tinst' then thm
          else thm |> Drule.implies_intr_list (map cert hyps)
            |> Drule.tvars_intr_list (map #1 tinst')
            |> (fn (th, al) => th |> Thm.instantiate
                ((map (fn (a, T) => (certT (TVar (valOf (assoc (al, a)))), certT T)) tinst'),
                  []))
            |> (fn th => Drule.implies_elim_list th
                 (map (Thm.assume o cert o tinst_tab_term tinst) hyps))
        end;


(* instantiate TFrees and Frees *)

fun inst_tab_term (inst, tinst) = if Symtab.is_empty inst
      then tinst_tab_term tinst
      else (* instantiate terms and types simultaneously *)
        let
          fun instf (Const (x, T)) = Const (x, tinst_tab_type tinst T)
            | instf (Free (x, T)) = (case Symtab.lookup (inst, x) of
                 NONE => Free (x, tinst_tab_type tinst T)
               | SOME t => t)
            | instf (Var (xi, T)) = Var (xi, tinst_tab_type tinst T)
            | instf (b as Bound _) = b
            | instf (Abs (x, T, t)) = Abs (x, tinst_tab_type tinst T, instf t)
            | instf (s $ t) = instf s $ instf t
        in instf end;

fun inst_tab_thm sg (inst, tinst) thm = if Symtab.is_empty inst
      then tinst_tab_thm sg tinst thm
      else let
          val cert = Thm.cterm_of sg;
          val certT = Thm.ctyp_of sg;
          val {hyps, prop, ...} = Thm.rep_thm thm;
          (* type instantiations *)
          val tfrees = foldr Term.add_term_tfree_names [] (prop :: hyps);
          val tinst' = Symtab.dest tinst |>
                List.filter (fn (a, _) => a mem_string tfrees);
          (* term instantiations;
             note: lhss are type instantiated, because
                   type insts will be done first*)
          val frees = foldr Term.add_term_frees [] (prop :: hyps);
          val inst' = Symtab.dest inst |>
                List.mapPartial (fn (a, t) =>
                  get_first (fn (Free (x, T)) => 
                    if a = x then SOME (Free (x, tinst_tab_type tinst T), t)
                    else NONE) frees);
        in
          if null tinst' andalso null inst' then tinst_tab_thm sg tinst thm
          else thm |> Drule.implies_intr_list (map cert hyps)
            |> Drule.tvars_intr_list (map #1 tinst')
            |> (fn (th, al) => th |> Thm.instantiate
                ((map (fn (a, T) => (certT (TVar (valOf (assoc (al, a)))), certT T)) tinst'),
                  []))
            |> Drule.forall_intr_list (map (cert o #1) inst')
            |> Drule.forall_elim_list (map (cert o #2) inst') 
            |> (fn th => Drule.implies_elim_list th
                 (map (Thm.assume o cert o inst_tab_term (inst, tinst)) hyps))
        end;


(** registration management **)

structure Registrations :
  sig
    type T
    val empty: T
    val join: T * T -> T
    val dest: T -> (term list * ((string * Attrib.src list) * thm list)) list
    val lookup: Sign.sg -> T * term list ->
      ((string * Attrib.src list) * thm list) option
    val insert: Sign.sg -> term list * (string * Attrib.src list) -> T ->
      T * (term list * ((string * Attrib.src list) * thm list)) list
    val add_witness: term list -> thm -> T -> T
  end =
struct
  (* a registration consists of theorems instantiating locale assumptions
     and prefix and attributes, indexed by parameter instantiation *)
  type T = ((string * Attrib.src list) * thm list) Termtab.table;

  val empty = Termtab.empty;

  (* term list represented as single term, for simultaneous matching *)
  fun termify ts =
    Library.foldl (op $) (Const ("", map fastype_of ts ---> propT), ts);
  fun untermify t =
    let fun ut (Const _) ts = ts
          | ut (s $ t) ts = ut s (t::ts)
    in ut t [] end;

  (* joining of registrations: prefix and attributs of left theory,
     thms are equal, no attempt to subsumption testing *)
  fun join (r1, r2) = Termtab.join (fn (reg, _) => SOME reg) (r1, r2);

  fun dest regs = map (apfst untermify) (Termtab.dest regs);

  (* registrations that subsume t *)
  fun subsumers tsig t regs =
    List.filter (fn (t', _) => Pattern.matches tsig (t', t)) (Termtab.dest regs);

  (* look up registration, pick one that subsumes the query *)
  fun lookup sign (regs, ts) =
    let
      val tsig = Sign.tsig_of sign;
      val t = termify ts;
      val subs = subsumers tsig t regs;
    in (case subs of
        [] => NONE
      | ((t', (attn, thms)) :: _) => let
            val (tinst, inst) = Pattern.match tsig (t', t);
            (* thms contain Frees, not Vars *)
            val tinst' = tinst |> Vartab.dest
                 |> map (fn ((x, 0), (_, T)) => (x, Type.unvarifyT T))
                 |> Symtab.make;
            val inst' = inst |> Vartab.dest
                 |> map (fn ((x, 0), (_, t)) => (x, Logic.unvarify t))
                 |> Symtab.make;
          in
            SOME (attn, map (inst_tab_thm sign (inst', tinst')) thms)
          end)
    end;

  (* add registration if not subsumed by ones already present,
     additionally returns registrations that are strictly subsumed *)
  fun insert sign (ts, attn) regs =
    let
      val tsig = Sign.tsig_of sign;
      val t = termify ts;
      val subs = subsumers tsig t regs ;
    in (case subs of
        [] => let
                val sups =
                  List.filter (fn (t', _) => Pattern.matches tsig (t, t')) (Termtab.dest regs);
                val sups' = map (apfst untermify) sups
              in (Termtab.update ((t, (attn, [])), regs), sups') end
      | _ => (regs, []))
    end;

  (* add witness theorem to registration,
     only if instantiation is exact, otherwise exception Option raised *)
  fun add_witness ts thm regs =
    let
      val t = termify ts;
      val (x, thms) = valOf (Termtab.lookup (regs, t));
    in
      Termtab.update ((t, (x, thm::thms)), regs)
    end;
end;

(** theory data **)

structure GlobalLocalesArgs =
struct
  val name = "Isar/locales";
  type T = NameSpace.T * locale Symtab.table * Registrations.T Symtab.table;
    (* 1st entry: locale namespace,
       2nd entry: locales of the theory,
       3rd entry: registrations, indexed by locale name *)

  val empty = (NameSpace.empty, Symtab.empty, Symtab.empty);
  val copy = I;
  val prep_ext = I;

  fun join_locs ({predicate, import, elems, params}: locale,
      {elems = elems', ...}: locale) =
    SOME {predicate = predicate, import = import,
      elems = gen_merge_lists eq_snd elems elems',
      params = params};
  fun merge ((space1, locs1, regs1), (space2, locs2, regs2)) =
    (NameSpace.merge (space1, space2), Symtab.join join_locs (locs1, locs2),
     Symtab.join (SOME o Registrations.join) (regs1, regs2));

  fun print _ (space, locs, _) =
    Pretty.strs ("locales:" :: map (NameSpace.extern space o #1) (Symtab.dest locs))
    |> Pretty.writeln;
end;

structure GlobalLocalesData = TheoryDataFun(GlobalLocalesArgs);
val _ = Context.add_setup [GlobalLocalesData.init];



(** context data **)

structure LocalLocalesArgs =
struct
  val name = "Isar/locales";
  type T = Registrations.T Symtab.table;
    (* registrations, indexed by locale name *)
  fun init _ = Symtab.empty;
  fun print _ _ = ();
end;

structure LocalLocalesData = ProofDataFun(LocalLocalesArgs);
val _ = Context.add_setup [LocalLocalesData.init];


(* access locales *)

val print_locales = GlobalLocalesData.print;

val intern = NameSpace.intern o #1 o GlobalLocalesData.get_sg;
val extern = NameSpace.extern o #1 o GlobalLocalesData.get_sg;

fun declare_locale name thy =
  thy |> GlobalLocalesData.map (fn (space, locs, regs) =>
    (Sign.declare_name (Theory.sign_of thy) name space, locs, regs));

fun put_locale name loc =
  GlobalLocalesData.map (fn (space, locs, regs) =>
    (space, Symtab.update ((name, loc), locs), regs));

fun get_locale thy name = Symtab.lookup (#2 (GlobalLocalesData.get thy), name);

fun the_locale thy name =
  (case get_locale thy name of
    SOME loc => loc
  | NONE => error ("Unknown locale " ^ quote name));


(* access registrations *)

(* Ids of global registrations are varified,
   Ids of local registrations are not.
   Thms of registrations are never varified. *)

(* retrieve registration from theory or context *)

fun gen_get_registrations get thy_ctxt name =
  case Symtab.lookup (get thy_ctxt, name) of
      NONE => []
    | SOME reg => Registrations.dest reg;

val get_global_registrations =
     gen_get_registrations (#3 o GlobalLocalesData.get);
val get_local_registrations =
     gen_get_registrations LocalLocalesData.get;

fun gen_get_registration get get_sg thy_ctxt (name, ps) =
  case Symtab.lookup (get thy_ctxt, name) of
      NONE => NONE
    | SOME reg => Registrations.lookup (get_sg thy_ctxt) (reg, ps);

val get_global_registration =
     gen_get_registration (#3 o GlobalLocalesData.get) Theory.sign_of;
val get_local_registration =
     gen_get_registration LocalLocalesData.get ProofContext.sign_of;

val test_global_registration = isSome oo get_global_registration;
val test_local_registration = isSome oo get_local_registration;
fun smart_test_registration ctxt id =
  let
    val thy = ProofContext.theory_of ctxt;
  in
    test_global_registration thy id orelse test_local_registration ctxt id
  end;


(* add registration to theory or context, ignored if subsumed *)

fun gen_put_registration map_data get_sg (name, ps) attn thy_ctxt =
  map_data (fn regs =>
    let
      val sg = get_sg thy_ctxt;
      val reg = getOpt (Symtab.lookup (regs, name), Registrations.empty);
      val (reg', sups) = Registrations.insert sg (ps, attn) reg;
      val _ = if not (null sups) then warning
                ("Subsumed interpretation(s) of locale " ^
                 quote (extern sg name) ^
                 "\nby interpretation(s) with the following prefix(es):\n" ^
                  commas_quote (map (fn (_, ((s, _), _)) => s) sups))
              else ();
    in Symtab.update ((name, reg'), regs) end) thy_ctxt;

val put_global_registration =
     gen_put_registration (fn f =>
       GlobalLocalesData.map (fn (space, locs, regs) =>
         (space, locs, f regs))) Theory.sign_of;
val put_local_registration =
     gen_put_registration LocalLocalesData.map ProofContext.sign_of;

(* TODO: needed? *)
(*
fun smart_put_registration id attn ctxt =
  (* ignore registration if already present in theory *)
     let
       val thy = ProofContext.theory_of ctxt;
     in case get_global_registration thy id of
          NONE => put_local_registration id attn ctxt
        | SOME _ => ctxt
     end;
*)

(* add witness theorem to registration in theory or context,
   ignored if registration not present *)

fun gen_add_witness map (name, ps) thm =
  map (fn regs =>
      let
        val reg = valOf (Symtab.lookup (regs, name));
      in
        Symtab.update ((name, Registrations.add_witness ps thm reg), regs)
      end handle Option => regs);

val add_global_witness =
     gen_add_witness (fn f =>
       GlobalLocalesData.map (fn (space, locs, regs) =>
         (space, locs, f regs)));
val add_local_witness = gen_add_witness LocalLocalesData.map;


(* import hierarchy
   implementation could be more efficient, eg. by maintaining a database
   of dependencies *)

fun imports thy (upper, lower) =
  let
    val sign = sign_of thy;
    fun imps (Locale name) low = (name = low) orelse
      (case get_locale thy name of
           NONE => false
         | SOME {import, ...} => imps import low)
      | imps (Rename (expr, _)) low = imps expr low
      | imps (Merge es) low = exists (fn e => imps e low) es;
  in
    imps (Locale (intern sign upper)) (intern sign lower)
  end;


(* printing of registrations *)

fun gen_print_registrations get_regs mk_ctxt msg loc thy_ctxt =
  let
    val ctxt = mk_ctxt thy_ctxt;
    val thy = ProofContext.theory_of ctxt;
    val sg = Theory.sign_of thy;

    val prt_term = Pretty.quote o ProofContext.pretty_term ctxt;
    val prt_atts = Args.pretty_attribs ctxt;
    fun prt_inst (ts, (("", []), thms)) =
          Pretty.enclose "(" ")" (Pretty.breaks (map prt_term ts))
      | prt_inst (ts, ((prfx, atts), thms)) =
          Pretty.block (
            (Pretty.breaks (Pretty.str prfx :: prt_atts atts) @
              [Pretty.str ":", Pretty.brk 1,
                Pretty.enclose "(" ")" (Pretty.breaks (map prt_term ts))]));

    val loc_int = intern sg loc;
    val regs = get_regs thy_ctxt;
    val loc_regs = Symtab.lookup (regs, loc_int);
  in
    (case loc_regs of
        NONE => Pretty.str ("No interpretations in " ^ msg ^ ".")
      | SOME r => let
            val r' = Registrations.dest r;
            val r'' = Library.sort_wrt (fn (_, ((prfx, _), _)) => prfx) r';
          in Pretty.big_list ("Interpretations in " ^ msg ^ ":")
            (map prt_inst r'')
          end)
    |> Pretty.writeln
  end;

val print_global_registrations =
     gen_print_registrations (#3 o GlobalLocalesData.get)
       ProofContext.init "theory";
val print_local_registrations' =
     gen_print_registrations LocalLocalesData.get
       I "context";
fun print_local_registrations loc ctxt =
  (print_global_registrations loc (ProofContext.theory_of ctxt);
   print_local_registrations' loc ctxt);


(* diagnostics *)

fun err_in_locale ctxt msg ids =
  let
    val sign = ProofContext.sign_of ctxt;
    fun prt_id (name, parms) =
      [Pretty.block (Pretty.breaks (map Pretty.str (extern sign name :: parms)))];
    val prt_ids = List.concat (separate [Pretty.str " +", Pretty.brk 1] (map prt_id ids));
    val err_msg =
      if forall (equal "" o #1) ids then msg
      else msg ^ "\n" ^ Pretty.string_of (Pretty.block
        (Pretty.str "The error(s) above occurred in locale:" :: Pretty.brk 1 :: prt_ids));
  in raise ProofContext.CONTEXT (err_msg, ctxt) end;

(* Version for identifiers with axioms *)

fun err_in_locale' ctxt msg ids' = err_in_locale ctxt msg (map fst ids');


(** primitives **)

(* map elements *)

fun map_elem {name, var, typ, term, fact, attrib} =
  fn Fixes fixes => Fixes (fixes |> map (fn (x, T, mx) =>
       let val (x', mx') = var (x, mx) in (x', Option.map typ T, mx') end))
   | Constrains csts => Constrains (csts |> map (fn (x, T) =>
       let val (x', _) = var (x, SOME Syntax.NoSyn) in (x', typ T) end))
   | Assumes asms => Assumes (asms |> map (fn ((a, atts), propps) =>
      ((name a, map attrib atts), propps |> map (fn (t, (ps, qs)) =>
        (term t, (map term ps, map term qs))))))
   | Defines defs => Defines (defs |> map (fn ((a, atts), (t, ps)) =>
      ((name a, map attrib atts), (term t, map term ps))))
   | Notes facts => Notes (facts |> map (fn ((a, atts), bs) =>
      ((name a, map attrib atts), bs |> map (fn (ths, btts) => (fact ths, map attrib btts)))));

fun map_values typ term thm = map_elem
  {name = I, var = I, typ = typ, term = term, fact = map thm,
    attrib = Args.map_values I typ term thm};


(* map attributes *)

fun map_attrib_specs f = map (apfst (apsnd (map f)));
fun map_attrib_facts f = map (apfst (apsnd (map f)) o apsnd (map (apsnd (map f))));

fun map_attrib_elem f = map_elem {name = I, var = I, typ = I, term = I, fact = I, attrib = f};

fun intern_attrib_elem thy = map_attrib_elem (Attrib.intern_src (Theory.sign_of thy));

fun intern_attrib_elem_expr thy (Elem elem) = Elem (intern_attrib_elem thy elem)
  | intern_attrib_elem_expr _ (Expr expr) = Expr expr;


(* renaming *)

(* ren maps names to (new) names and syntax; represented as association list *)

fun rename_var ren (x, mx) =
  case assoc_string (ren, x) of
      NONE => (x, mx)
    | SOME (x', NONE) =>
        (x', if mx = NONE then mx else SOME Syntax.NoSyn)     (*drop syntax*)
    | SOME (x', SOME mx') =>
        if mx = NONE then raise ERROR_MESSAGE
          ("Attempt to change syntax of structure parameter " ^ quote x)
        else (x', SOME mx');                                (*change syntax*)

fun rename ren x =
  case assoc_string (ren, x) of
      NONE => x
    | SOME (x', _) => x';                                   (*ignore syntax*)

fun rename_term ren (Free (x, T)) = Free (rename ren x, T)
  | rename_term ren (t $ u) = rename_term ren t $ rename_term ren u
  | rename_term ren (Abs (x, T, t)) = Abs (x, T, rename_term ren t)
  | rename_term _ a = a;

fun rename_thm ren th =
  let
    val {sign, hyps, prop, maxidx, ...} = Thm.rep_thm th;
    val cert = Thm.cterm_of sign;
    val (xs, Ts) = Library.split_list (Library.foldl Term.add_frees ([], prop :: hyps));
    val xs' = map (rename ren) xs;
    fun cert_frees names = map (cert o Free) (names ~~ Ts);
    fun cert_vars names = map (cert o Var o apfst (rpair (maxidx + 1))) (names ~~ Ts);
  in
    if xs = xs' then th
    else
      th
      |> Drule.implies_intr_list (map cert hyps)
      |> Drule.forall_intr_list (cert_frees xs)
      |> Drule.forall_elim_list (cert_vars xs)
      |> Thm.instantiate ([], cert_vars xs ~~ cert_frees xs')
      |> (fn th' => Drule.implies_elim_list th' (map (Thm.assume o cert o rename_term ren) hyps))
  end;

fun rename_elem ren =
  map_values I (rename_term ren) (rename_thm ren) o
  map_elem {name = I, typ = I, term = I, fact = I, attrib = I, var = rename_var ren};

fun rename_facts prfx =
  map_elem {var = I, typ = I, term = I, fact = I, attrib = I, name = NameSpace.qualified prfx};


(* type instantiation *)

fun inst_type [] T = T
  | inst_type env T = Term.map_type_tfree (fn v => getOpt (assoc (env, v), TFree v)) T;

fun inst_term [] t = t
  | inst_term env t = Term.map_term_types (inst_type env) t;

fun inst_thm _ [] th = th
  | inst_thm ctxt env th =
      let
        val sign = ProofContext.sign_of ctxt;
        val cert = Thm.cterm_of sign;
        val certT = Thm.ctyp_of sign;
        val {hyps, prop, maxidx, ...} = Thm.rep_thm th;
        val tfrees = foldr Term.add_term_tfree_names [] (prop :: hyps);
        val env' = List.filter (fn ((a, _), _) => a mem_string tfrees) env;
      in
        if null env' then th
        else
          th
          |> Drule.implies_intr_list (map cert hyps)
          |> Drule.tvars_intr_list (map (#1 o #1) env')
          |> (fn (th', al) => th' |>
            Thm.instantiate ((map (fn ((a, _), T) =>
              (certT (TVar (valOf (assoc (al, a)))), certT T)) env'), []))
          |> (fn th'' => Drule.implies_elim_list th''
              (map (Thm.assume o cert o inst_term env') hyps))
      end;

fun inst_elem ctxt env =
  map_values (inst_type env) (inst_term env) (inst_thm ctxt env);


(* term and type instantiation, variant using symbol tables *)

(* instantiate TFrees *)

fun tinst_tab_elem sg tinst =
  map_values (tinst_tab_type tinst) (tinst_tab_term tinst) (tinst_tab_thm sg tinst);

(* instantiate TFrees and Frees *)

fun inst_tab_elem sg (inst as (_, tinst)) =
  map_values (tinst_tab_type tinst) (inst_tab_term inst) (inst_tab_thm sg inst);

fun inst_tab_elems sign inst ((n, ps), elems) =
      ((n, map (inst_tab_term inst) ps), map (inst_tab_elem sign inst) elems);


(** structured contexts: rename + merge + implicit type instantiation **)

(* parameter types *)

(* CB: frozen_tvars has the following type:
  ProofContext.context -> Term.typ list -> (Term.indexname * (sort * Term.typ)) list *)

fun frozen_tvars ctxt Ts =
  let
    val tvars = rev (Library.foldl Term.add_tvarsT ([], Ts));
    val tfrees = map TFree
      (Term.invent_names (ProofContext.used_types ctxt) "'a" (length tvars) ~~ map #2 tvars);
  in map (fn ((x, S), y) => (x, (S, y))) (tvars ~~ tfrees) end;

fun unify_frozen ctxt maxidx Ts Us =
  let
    fun paramify (i, NONE) = (i, NONE)
      | paramify (i, SOME T) = apsnd SOME (TypeInfer.paramify_dummies (i, T));

    val (maxidx', Ts') = foldl_map paramify (maxidx, Ts);
    val (maxidx'', Us') = foldl_map paramify (maxidx', Us);
    val tsig = Sign.tsig_of (ProofContext.sign_of ctxt);

    fun unify (env, (SOME T, SOME U)) = (Type.unify tsig env (U, T)
          handle Type.TUNIFY =>
            raise TYPE ("unify_frozen: failed to unify types", [U, T], []))
      | unify (env, _) = env;
    val (unifier, _) = Library.foldl unify ((Vartab.empty, maxidx''), Ts' ~~ Us');
    val Vs = map (Option.map (Envir.norm_type unifier)) Us';
    val unifier' = Vartab.extend (unifier, frozen_tvars ctxt (List.mapPartial I Vs));
  in map (Option.map (Envir.norm_type unifier')) Vs end;

fun params_of elemss = gen_distinct eq_fst (List.concat (map (snd o fst) elemss));
fun params_of' elemss = gen_distinct eq_fst (List.concat (map (snd o fst o fst) elemss));
fun params_syn_of syn elemss =
  gen_distinct eq_fst (List.concat (map (snd o fst) elemss)) |>
    map (apfst (fn x => (x, valOf (Symtab.lookup (syn, x)))));


(* CB: param_types has the following type:
  ('a * 'b option) list -> ('a * 'b) list *)
fun param_types ps = List.mapPartial (fn (_, NONE) => NONE | (x, SOME T) => SOME (x, T)) ps;


fun merge_syntax ctxt ids ss = Symtab.merge (op =) ss
  handle Symtab.DUPS xs => err_in_locale ctxt
    ("Conflicting syntax for parameter(s): " ^ commas_quote xs) (map fst ids);


(* flatten expressions *)

local

(* CB: OUTDATED unique_parms has the following type:
     'a ->
     (('b * (('c * 'd) list * Symtab.key list)) * 'e) list ->
     (('b * ('c * 'd) list) * 'e) list  *)

fun unique_parms ctxt elemss =
  let
    val param_decls =
      List.concat (map (fn (((name, (ps, qs)), _), _) => map (rpair (name, ps)) qs) elemss)
      |> Symtab.make_multi |> Symtab.dest;
  in
    (case find_first (fn (_, ids) => length ids > 1) param_decls of
      SOME (q, ids) => err_in_locale ctxt ("Multiple declaration of parameter " ^ quote q)
          (map (apsnd (map fst)) ids)
    | NONE => map (apfst (apfst (apsnd #1))) elemss)
  end;

fun unify_parms ctxt (fixed_parms : (string * typ) list)
  (raw_parmss : (string * typ option) list list) =
  let
    val sign = ProofContext.sign_of ctxt;
    val tsig = Sign.tsig_of sign;
    val maxidx = length raw_parmss;
    val idx_parmss = (0 upto maxidx - 1) ~~ raw_parmss;

    fun varify i = Term.map_type_tfree (fn (a, S) => TVar ((a, i), S));
    fun varify_parms (i, ps) = map (apsnd (varify i)) (param_types ps);
    val parms = fixed_parms @ List.concat (map varify_parms idx_parmss);

    fun unify T ((env, maxidx), U) =
      Type.unify tsig (env, maxidx) (U, T)
      handle Type.TUNIFY =>
        let val prt = Sign.string_of_typ sign
        in raise TYPE ("unify_parms: failed to unify types " ^
          prt U ^ " and " ^ prt T, [U, T], [])
        end
    fun unify_list (envir, T :: Us) = Library.foldl (unify T) (envir, Us)
      | unify_list (envir, []) = envir;
    val (unifier, _) = Library.foldl unify_list
      ((Vartab.empty, maxidx), map #2 (Symtab.dest (Symtab.make_multi parms)));

    val parms' = map (apsnd (Envir.norm_type unifier)) (gen_distinct eq_fst parms);
    val unifier' = Vartab.extend (unifier, frozen_tvars ctxt (map #2 parms'));

    fun inst_parms (i, ps) =
      foldr Term.add_typ_tfrees [] (List.mapPartial snd ps)
      |> List.mapPartial (fn (a, S) =>
          let val T = Envir.norm_type unifier' (TVar ((a, i), S))
          in if T = TFree (a, S) then NONE else SOME ((a, S), T) end)
  in map inst_parms idx_parmss end : ((string * Term.sort) * Term.typ) list list;

in

fun unify_elemss _ _ [] = []
  | unify_elemss _ [] [elems] = [elems]
  | unify_elemss ctxt fixed_parms elemss =
      let
        val envs = unify_parms ctxt fixed_parms (map (#2 o #1 o #1) elemss);
        fun inst ((((name, ps), axs), elems), env) =
          (((name, map (apsnd (Option.map (inst_type env))) ps), 
            map (inst_thm ctxt env) axs), map (inst_elem ctxt env) elems);
      in map inst (elemss ~~ envs) end;

(* like unify_elemss, but does not touch axioms,
   additional parameter for enforcing further constraints (eg. syntax) *)

fun unify_elemss' _ _ [] [] = []
  | unify_elemss' _ [] [elems] [] = [elems]
  | unify_elemss' ctxt fixed_parms elemss c_parms =
      let
        val envs = unify_parms ctxt fixed_parms (map (#2 o #1 o #1) elemss @ map single c_parms);
        fun inst ((((name, ps), axs), elems), env) =
          (((name, map (apsnd (Option.map (inst_type env))) ps),  axs),
           map (inst_elem ctxt env) elems);
      in map inst (elemss ~~ (Library.take (length elemss, envs))) end;

(* flatten_expr:
   Extend list of identifiers by those new in locale expression expr.
   Compute corresponding list of lists of locale elements (one entry per
   identifier).

   Identifiers represent locale fragments and are in an extended form:
     ((name, ps), (ax_ps, axs))
   (name, ps) is the locale name with all its parameters.
   (ax_ps, axs) is the locale axioms with its parameters;
     axs are always taken from the top level of the locale hierarchy,
     hence axioms may contain additional parameters from later fragments:
     ps subset of ax_ps.  axs is either singleton or empty.

   Elements are enriched by identifier-like information:
     (((name, ax_ps), axs), elems)
   The parameters in ax_ps are the axiom parameters, but enriched by type
   info: now each entry is a pair of string and typ option.  Axioms are
   type-instantiated.

*)

fun flatten_expr ctxt ((prev_idents, prev_syntax), expr) =
  let
    val thy = ProofContext.theory_of ctxt;
    (* thy used for retrieval of locale info,
       ctxt for error messages, parameter unification and instantiation
       of axioms *)
    (* TODO: consider err_in_locale with thy argument *)

    fun renaming (SOME x :: xs) (y :: ys) = (y, x) :: renaming xs ys
      | renaming (NONE :: xs) (y :: ys) = renaming xs ys
      | renaming [] _ = []
      | renaming xs [] = raise ERROR_MESSAGE ("Too many arguments in renaming: " ^
          commas (map (fn NONE => "_" | SOME x => quote (fst x)) xs));

    fun rename_parms top ren ((name, ps), (parms, axs)) =
      let val ps' = map (rename ren) ps in
        (case duplicates ps' of [] => ((name, ps'),
          if top then (map (rename ren) parms, map (rename_thm ren) axs)
          else (parms, axs))
        | dups => err_in_locale ctxt ("Duplicate parameters: " ^ commas_quote dups) [(name, ps')])
      end;

    fun identify top (Locale name) =
    (* CB: ids_ax is a list of tuples of the form ((name, ps), axs),
       where name is a locale name, ps a list of parameter names and axs
       a list of axioms relating to the identifier, axs is empty unless
       identify at top level (top = true);
       parms is accumulated list of parameters *)
          let
            val {predicate = (_, axioms), import, params, ...} =
              the_locale thy name;
            val ps = map (#1 o #1) (#1 params);
            val (ids', parms', _) = identify false import;
                (* acyclic import dependencies *)
            val ids'' = ids' @ [((name, ps), ([], []))];
            val ids_ax = if top then snd
                 (* get the right axioms, only if at top level *)
                 (foldl_map (fn (axs, ((name, parms), _)) => let
                   val {elems, ...} = the_locale thy name;
                   val ts = List.concat (List.mapPartial (fn (Assumes asms, _) =>
                     SOME (List.concat (map (map #1 o #2) asms)) | _ => NONE) elems);
                   val (axs1, axs2) = splitAt (length ts, axs);
                 in (axs2, ((name, parms), (ps, axs1))) end) (axioms, ids''))
               else ids'';
            val syn = Symtab.make (map (apfst fst) (#1 params));
          in (ids_ax, merge_lists parms' ps, syn) end
      | identify top (Rename (e, xs)) =
          let
            val (ids', parms', syn') = identify top e;
            val ren = renaming xs parms'
              handle ERROR_MESSAGE msg => err_in_locale' ctxt msg ids';
            val ids'' = gen_distinct eq_fst (map (rename_parms top ren) ids');
            val parms'' = distinct (List.concat (map (#2 o #1) ids''));
            val syn'' = syn' |> Symtab.dest |> map (rename_var ren) |>
                  Symtab.make;
            (* check for conflicting syntax? *)
          in (ids'', parms'', syn'') end
      | identify top (Merge es) =
          Library.foldl (fn ((ids, parms, syn), e) => let
                     val (ids', parms', syn') = identify top e
                   in (gen_merge_lists eq_fst ids ids',
                       merge_lists parms parms',
                       merge_syntax ctxt ids' (syn, syn')) end)
            (([], [], Symtab.empty), es);

    (* CB: enrich identifiers by parameter types and 
       the corresponding elements (with renamed parameters),
       also takes care of parameter syntax *)

    fun eval syn ((name, xs), axs) =
      let
        val {params = (ps, qs), elems, ...} = the_locale thy name;
        val ps' = map #1 ps;
        val ren = map #1 ps' ~~
              map (fn x => (x, valOf (Symtab.lookup (syn, x)))) xs;
        val (params', elems') =
          if null ren then ((ps', qs), map #1 elems)
          else ((map (apfst (rename ren)) ps', map (rename ren) qs),
            map (rename_elem ren o #1) elems);
        val elems'' = map (rename_facts (space_implode "_" xs)) elems';
      in (((name, params'), axs), elems'') end;

    (* type constraint for renamed parameter with syntax *)
    fun type_syntax NONE = NONE
      | type_syntax (SOME mx) = let
            val Ts = map (fn x => TFree (x, [])) (Term.invent_names [] "'mxa"
              (Syntax.mixfix_args mx + 1))
          in Ts |> Library.split_last |> op ---> |> SOME end;

    (* compute identifiers and syntax, merge with previous ones *)
    val (ids, _, syn) = identify true expr;
    val idents = gen_rems eq_fst (ids, prev_idents);
    val syntax = merge_syntax ctxt ids (syn, prev_syntax);
    (* add types to params, check for unique params and unify them *)
    val raw_elemss = unique_parms ctxt (map (eval syntax) idents);
    val elemss = unify_elemss' ctxt [] raw_elemss
         (map (apsnd type_syntax) (Symtab.dest syntax));
    (* replace params in ids by params from axioms,
       adjust types in axioms *)
    val all_params' = params_of' elemss;
    val all_params = param_types all_params';
    val elemss' = map (fn (((name, _), (ps, axs)), elems) =>
         (((name, map (fn p => (p, assoc (all_params, p))) ps), axs), elems))
         elemss;
    fun inst_ax th = let
         val {hyps, prop, ...} = Thm.rep_thm th;
         val ps = map (apsnd SOME) (Library.foldl Term.add_frees ([], prop :: hyps));
         val [env] = unify_parms ctxt all_params [ps];
         val th' = inst_thm ctxt env th;
       in th' end;
    val final_elemss = map (fn ((id, axs), elems) =>
         ((id, map inst_ax axs), elems)) elemss';
  in ((prev_idents @ idents, syntax), final_elemss) end;

end;


(* activate elements *)

local

fun export_axioms axs _ hyps th =
  th |> Drule.satisfy_hyps axs
     (* CB: replace meta-hyps, using axs, by a single meta-hyp. *)
  |> Drule.implies_intr_list (Library.drop (length axs, hyps))
     (* CB: turn remaining hyps into assumptions. *)
  |> Seq.single

fun activate_elem _ ((ctxt, axs), Fixes fixes) =
      ((ctxt |> ProofContext.add_fixes fixes, axs), [])
  | activate_elem _ ((ctxt, axs), Constrains _) = ((ctxt, axs), [])
  | activate_elem _ ((ctxt, axs), Assumes asms) =
      let
        val asms' = map_attrib_specs (Attrib.context_attribute_i ctxt) asms;
        val ts = List.concat (map (map #1 o #2) asms');
        val (ps, qs) = splitAt (length ts, axs);
        val (ctxt', _) =
          ctxt |> ProofContext.fix_frees ts
          |> ProofContext.assume_i (export_axioms ps) asms';
      in ((ctxt', qs), []) end
  | activate_elem _ ((ctxt, axs), Defines defs) =
      let
        val defs' = map_attrib_specs (Attrib.context_attribute_i ctxt) defs;
        val (ctxt', _) =
        ctxt |> ProofContext.assume_i ProofContext.export_def
          (defs' |> map (fn ((name, atts), (t, ps)) =>
            let val (c, t') = ProofContext.cert_def ctxt t
            in ((if name = "" then Thm.def_name c else name, atts), [(t', (ps, []))]) end))
      in ((ctxt', axs), []) end
  | activate_elem is_ext ((ctxt, axs), Notes facts) =
      let
        val facts' = map_attrib_facts (Attrib.context_attribute_i ctxt) facts;
        val (ctxt', res) = ctxt |> ProofContext.note_thmss_i facts';
      in ((ctxt', axs), if is_ext then res else []) end;

fun activate_elems (((name, ps), axs), elems) ctxt =
  let val ((ctxt', _), res) =
    foldl_map (activate_elem (name = "")) ((ProofContext.qualified_names ctxt, axs), elems)
      handle ProofContext.CONTEXT (msg, ctxt) => err_in_locale ctxt msg [(name, map fst ps)]
    val ctxt'' = if name = "" then ctxt'
          else let
              val ps' = map (fn (n, SOME T) => Free (n, T)) ps;
              val ctxt'' = put_local_registration (name, ps') ("", []) ctxt'
            in foldl (fn (ax, ctxt) =>
              add_local_witness (name, ps') (Thm.assume (Thm.cprop_of ax)) ctxt) ctxt'' axs
            end
  in (ProofContext.restore_naming ctxt ctxt'', res) end;

fun activate_elemss prep_facts = foldl_map (fn (ctxt, (((name, ps), axs), raw_elems)) =>
  let
    val elems = map (prep_facts ctxt) raw_elems;
    val (ctxt', res) = apsnd List.concat (activate_elems (((name, ps), axs), elems) ctxt);
    val elems' = map (map_attrib_elem Args.closure) elems;
  in (ctxt', (((name, ps), elems'), res)) end);

in

(* CB: activate_facts prep_facts (ctxt, elemss),
   where elemss is a list of pairs consisting of identifiers and
   context elements, extends ctxt by the context elements yielding
   ctxt' and returns (ctxt', (elemss', facts)).
   Identifiers in the argument are of the form ((name, ps), axs) and
   assumptions use the axioms in the identifiers to set up exporters
   in ctxt'.  elemss' does not contain identifiers and is obtained
   from elemss and the intermediate context with prep_facts.
   If read_facts or cert_facts is used for prep_facts, these also remove
   the internal/external markers from elemss. *)

fun activate_facts prep_facts arg =
  apsnd (apsnd List.concat o Library.split_list) (activate_elemss prep_facts arg);

fun activate_note prep_facts (ctxt, args) =
  let
    val (ctxt', ([(_, [Notes args'])], facts)) =
      activate_facts prep_facts (ctxt, [((("", []), []), [Ext (Notes args)])]);
  in (ctxt', (args', facts)) end;

end;


(* register elements *)

fun register_elems (((_, ps), (((name, ax_ps), axs), _)), ctxt) =
  if name = "" then ctxt
      else let val ps' = map (fn (n, SOME T) => Free (n, T)) ax_ps
          val ctxt' = put_local_registration (name, ps') ("", []) ctxt
        in foldl (fn (ax, ctxt) =>
          add_local_witness (name, ps') ax ctxt) ctxt' axs
        end;

fun register_elemss id_elemss ctxt = 
  foldl register_elems ctxt id_elemss;


(** prepare context elements **)

(* expressions *)

fun intern_expr sg (Locale xname) = Locale (intern sg xname)
  | intern_expr sg (Merge exprs) = Merge (map (intern_expr sg) exprs)
  | intern_expr sg (Rename (expr, xs)) = Rename (intern_expr sg expr, xs);


(* parameters *)

local

fun prep_parms prep_vars ctxt parms =
  let val vars = snd (foldl_map prep_vars (ctxt, map (fn (x, T) => ([x], T)) parms))
  in map (fn ([x'], T') => (x', T')) vars end;

in

fun read_parms x = prep_parms ProofContext.read_vars x;
fun cert_parms x = prep_parms ProofContext.cert_vars x;

end;


(* propositions and bindings *)

(* flatten ((ids, syn), expr) normalises expr (which is either a locale
   expression or a single context element) wrt.
   to the list ids of already accumulated identifiers.
   It returns (ids', syn', elemss) where ids' is an extension of ids
   with identifiers generated for expr, and elemss is the list of
   context elements generated from expr.
   syn and syn' are symtabs mapping parameter names to their syntax.  syn'
   is an extension of syn.
   For details, see flatten_expr.

   Additionally, for a locale expression, the elems are grouped into a single
   Int; individual context elements are marked Ext.  In this case, the
   identifier-like information of the element is as follows:
   - for Fixes: (("", ps), []) where the ps have type info NONE
   - for other elements: (("", []), []).
   The implementation of activate_facts relies on identifier names being
   empty strings for external elements.
*)

fun flatten (ctxt, _) ((ids, syn), Elem (Fixes fixes)) = let
	val ids' = ids @ [(("", map #1 fixes), ([], []))]
      in
	((ids',
	 merge_syntax ctxt ids'
	   (syn, Symtab.make (map (fn fx => (#1 fx, #3 fx)) fixes))
	   handle Symtab.DUPS xs => err_in_locale ctxt
	     ("Conflicting syntax for parameters: " ^ commas_quote xs)
             (map #1 ids')),
	 [((("", map (rpair NONE o #1) fixes), []), Ext (Fixes fixes))])
      end
  | flatten _ ((ids, syn), Elem elem) =
      ((ids @ [(("", []), ([], []))], syn), [((("", []), []), Ext elem)])
  | flatten (ctxt, prep_expr) ((ids, syn), Expr expr) =
      apsnd (map (apsnd Int)) (flatten_expr ctxt ((ids, syn), prep_expr expr));

local

local

fun declare_int_elem (ctxt, Fixes fixes) =
      (ctxt |> ProofContext.add_fixes (map (fn (x, T, mx) =>
        (x, Option.map (Term.map_type_tfree (TypeInfer.param 0)) T, mx)) fixes), [])
  | declare_int_elem (ctxt, _) = (ctxt, []);

fun declare_ext_elem prep_parms (ctxt, Fixes fixes) =
      let
        val parms = map (fn (x, T, _) => (x, T)) fixes;
        val parms' = prep_parms ctxt parms;
        val fixes' = map (fn ((x, T), (_, _, mx)) => (x, T, mx)) (parms' ~~ fixes);
      in (ctxt |> ProofContext.add_fixes fixes', []) end
  | declare_ext_elem prep_parms (ctxt, Constrains csts) =
      let
        val parms = map (fn (x, T) => (x, SOME T)) csts;
        val parms' = prep_parms ctxt parms;
        val ts = map (fn (x, SOME T) => Free (x, T)) parms';
      in (Library.fold ProofContext.declare_term ts ctxt, []) end
  | declare_ext_elem _ (ctxt, Assumes asms) = (ctxt, map #2 asms)
  | declare_ext_elem _ (ctxt, Defines defs) = (ctxt, map (fn (_, (t, ps)) => [(t, (ps, []))]) defs)
  | declare_ext_elem _ (ctxt, Notes facts) = (ctxt, []);

fun declare_elems prep_parms (ctxt, (((name, ps), _), elems)) =
  let val (ctxt', propps) =
    (case elems of
      Int es => foldl_map declare_int_elem (ctxt, es)
    | Ext e => foldl_map (declare_ext_elem prep_parms) (ctxt, [e]))
    handle ProofContext.CONTEXT (msg, ctxt) => err_in_locale ctxt msg [(name, map fst ps)]
  in (ctxt', propps) end;

in

(* CB: only called by prep_elemss. *)

fun declare_elemss prep_parms fixed_params raw_elemss ctxt =
  let
    (* CB: fix of type bug of goal in target with context elements.
       Parameters new in context elements must receive types that are
       distinct from types of parameters in target (fixed_params).  *)
    val ctxt_with_fixed =
      fold ProofContext.declare_term (map Free fixed_params) ctxt;
    val int_elemss =
      raw_elemss
      |> List.mapPartial (fn (id, Int es) => SOME (id, es) | _ => NONE)
      |> unify_elemss ctxt_with_fixed fixed_params;
    val (_, raw_elemss') =
      foldl_map (fn ((_, es) :: elemss, (id, Int _)) => (elemss, (id, Int es)) | x => x)
        (int_elemss, raw_elemss);
  in foldl_map (declare_elems prep_parms) (ctxt, raw_elemss') end;

end;

local

(* CB: normalise Assumes and Defines wrt. previous definitions *)

val norm_term = Envir.beta_norm oo Term.subst_atomic;

(* CB: following code (abstract_term, abstract_thm, bind_def)
   used in eval_text for Defines elements. *)

fun abstract_term eq =    (*assumes well-formedness according to ProofContext.cert_def*)
  let
    val body = Term.strip_all_body eq;
    val vars = map Free (Term.rename_wrt_term body (Term.strip_all_vars eq));
    val (lhs, rhs) = Logic.dest_equals (Term.subst_bounds (vars, body));
    val (f, xs) = Term.strip_comb lhs;
    val eq' = Term.list_abs_free (map Term.dest_Free xs, rhs);
  in (Term.dest_Free f, eq') end;

fun abstract_thm sign eq =
  Thm.assume (Thm.cterm_of sign eq) |> Drule.gen_all |> Drule.abs_def;

fun bind_def ctxt (name, ps) ((xs, env, ths), eq) =
  let
    val ((y, T), b) = abstract_term eq;
    val b' = norm_term env b;
    val th = abstract_thm (ProofContext.sign_of ctxt) eq;
    fun err msg = err_in_locale ctxt (msg ^ ": " ^ quote y) [(name, map fst ps)];
  in
    conditional (exists (equal y o #1) xs) (fn () =>
      err "Attempt to define previously specified variable");
    conditional (exists (fn (Free (y', _), _) => y = y' | _ => false) env) (fn () =>
      err "Attempt to redefine variable");
    (Term.add_frees (xs, b'), (Free (y, T), b') :: env, th :: ths)
  end;

(* CB: for finish_elems (Int and Ext) *)

fun eval_text _ _ _ (text, Fixes _) = text
  | eval_text _ _ _ (text, Constrains _) = text
  | eval_text _ _ is_ext ((((exts, exts'), (ints, ints')), (xs, env, defs)), Assumes asms) =
      let
        val ts = List.concat (map (map #1 o #2) asms);
        val ts' = map (norm_term env) ts;
        val spec' =
          if is_ext then ((exts @ ts, exts' @ ts'), (ints, ints'))
          else ((exts, exts'), (ints @ ts, ints' @ ts'));
      in (spec', (Library.foldl Term.add_frees (xs, ts'), env, defs)) end
  | eval_text ctxt (id, _) _ ((spec, binds), Defines defs) =
      (spec, Library.foldl (bind_def ctxt id) (binds, map (#1 o #2) defs))
  | eval_text _ _ _ (text, Notes _) = text;

(* CB: for finish_elems (Ext) *)

fun closeup _ false elem = elem
  | closeup ctxt true elem =
      let
        fun close_frees t =
          let val frees = rev (filter_out (ProofContext.is_fixed ctxt o #1)
            (Term.add_frees ([], t)))
          in Term.list_all_free (frees, t) end;

        fun no_binds [] = []
          | no_binds _ =
              raise ProofContext.CONTEXT ("Illegal term bindings in locale element", ctxt);
      in
        (case elem of
          Assumes asms => Assumes (asms |> map (fn (a, propps) =>
            (a, map (fn (t, (ps, qs)) => (close_frees t, (no_binds ps, no_binds qs))) propps)))
        | Defines defs => Defines (defs |> map (fn (a, (t, ps)) =>
            (a, (close_frees (#2 (ProofContext.cert_def ctxt t)), no_binds ps))))
        | e => e)
      end;


fun finish_ext_elem parms _ (Fixes fixes, _) = Fixes (map (fn (x, _, mx) =>
      (x, assoc_string (parms, x), mx)) fixes)
  | finish_ext_elem parms _ (Constrains csts, _) =
      Constrains (map (fn (x, _) => (x, valOf (assoc_string (parms, x)))) csts)
  | finish_ext_elem _ close (Assumes asms, propp) =
      close (Assumes (map #1 asms ~~ propp))
  | finish_ext_elem _ close (Defines defs, propp) =
      close (Defines (map #1 defs ~~ map (fn [(t, (ps, []))] => (t, ps)) propp))
  | finish_ext_elem _ _ (Notes facts, _) = Notes facts;

(* CB: finish_parms introduces type info from parms to identifiers *)
(* CB: only needed for types that have been NONE so far???
   If so, which are these??? *)

fun finish_parms parms (((name, ps), axs), elems) =
  (((name, map (fn (x, _) => (x, assoc (parms, x))) ps), axs), elems);