src/Pure/Isar/locale.ML

tuned Pattern.match/unify;
tuned fold;

(*  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.

Interpretation enables the reuse of theorems of locales in other
contexts, namely those defined by theories, structured proofs and
locales themselves.

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
- dangling type frees in locales
- test subsumption of interpretations when merging theories
- var vs. fixes in locale to be interpreted (interpretation in locale)
  (implicit locale expressions generated by multiple registrations)
*)

signature LOCALE =
sig
  datatype expr =
    Locale of string |
    Rename of expr * (string * mixfix option) option list |
    Merge of expr list
  val empty: expr
  datatype 'a element = Elem of 'a | Expr of expr

  (* Abstract interface to locales *)
  type locale
  val intern: theory -> xstring -> string
  val extern: theory -> string -> xstring
  val the_locale: theory -> string -> locale

  (* Processing of locale statements *)
  val read_context_statement: xstring option -> Element.context element list ->
    (string * (string list * string list)) list list -> ProofContext.context ->
    string option * (cterm list * cterm list) * ProofContext.context * ProofContext.context *
      (term * (term list * term list)) list list
  val cert_context_statement: string option -> Element.context_i element list ->
    (term * (term list * term list)) list list -> ProofContext.context ->
    string option * (cterm list * cterm list) * ProofContext.context * ProofContext.context *
      (term * (term list * term list)) list list

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

  val add_locale_context: bool -> bstring -> expr -> Element.context list -> theory
    -> (Element.context_i list * ProofContext.context) * theory
  val add_locale_context_i: bool -> bstring -> expr -> Element.context_i list -> theory
    -> (Element.context_i list * ProofContext.context) * theory
  val add_locale: bool -> bstring -> expr -> Element.context list -> theory -> theory
  val add_locale_i: bool -> bstring -> expr -> Element.context_i list -> theory -> theory

  (* Storing results *)
  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 * ProofContext.context) * (bstring * thm list) list
  val note_thmss_i: string -> string ->
    ((bstring * Attrib.src list) * (thm list * Attrib.src list) list) list ->
    theory -> (theory * ProofContext.context) * (bstring * thm list) list

  val theorem: string -> Method.text option -> (thm list list -> theory -> theory) ->
    string * Attrib.src list -> Element.context element list ->
    ((string * Attrib.src list) * (string * (string list * string list)) list) list ->
    theory -> Proof.state
  val theorem_i: string -> Method.text option -> (thm list list -> theory -> theory) ->
    string * theory attribute list -> Element.context_i element list ->
    ((string * theory attribute list) * (term * (term list * term list)) list) list ->
    theory -> Proof.state
  val theorem_in_locale: string -> Method.text option ->
    (thm list list -> thm list list -> theory -> theory) ->
    xstring -> string * Attrib.src list -> Element.context element list ->
    ((string * Attrib.src list) * (string * (string list * string list)) list) list ->
    theory -> Proof.state
  val theorem_in_locale_i: string -> Method.text option ->
    (thm list list -> thm list list -> theory -> theory) ->
    string -> string * Attrib.src list -> Element.context_i element list ->
    ((string * Attrib.src list) * (term * (term list * term list)) list) list ->
    theory -> Proof.state
  val smart_theorem: string -> xstring option ->
    string * Attrib.src list -> Element.context element list ->
    ((string * Attrib.src list) * (string * (string list * string list)) list) list ->
    theory -> Proof.state
  val interpretation: string * Attrib.src list -> expr -> string option list ->
    theory -> Proof.state
  val interpretation_in_locale: xstring * expr -> theory -> Proof.state
  val interpret: string * Attrib.src list -> expr -> string option list ->
    bool -> Proof.state -> Proof.state
end;

structure Locale: LOCALE =
struct


(** locale elements and expressions **)

datatype ctxt = datatype Element.ctxt;

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

val empty = Merge [];

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

fun map_elem f (Elem e) = Elem (f e)
  | map_elem _ (Expr e) = Expr e;

type witness = term * thm;  (*hypothesis as fact*)
type locale =
 {predicate: cterm list * witness list,
    (* CB: For 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.context_i * stamp) list,            (*static content*)
  params: ((string * typ) * mixfix option) list * string list,
                                                      (*all/local params*)
  regs: ((string * string list) * (term * thm) list) list}
    (* Registrations: indentifiers and witness theorems of locales interpreted
       in the locale.
    *)


(* 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;



(** management of registrations in theories and proof contexts **)

structure Registrations :
  sig
    type T
    val empty: T
    val join: T * T -> T
    val dest: T -> (term list * ((string * Attrib.src list) * witness list)) list
    val lookup: theory -> T * term list ->
      ((string * Attrib.src list) * witness list) option
    val insert: theory -> term list * (string * Attrib.src list) -> T ->
      T * (term list * ((string * Attrib.src list) * witness list)) list
    val add_witness: term list -> witness -> 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) * witness 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 attributes of left theory,
     thms are equal, no attempt to subsumption testing *)
  fun join (r1, r2) = Termtab.join (fn _ => fn (reg, _) => SOME reg) (r1, r2);

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

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

  (* look up registration, pick one that subsumes the query *)
  fun lookup sign (regs, ts) =
    let
      val t = termify ts;
      val subs = subsumers sign t regs;
    in (case subs of
        [] => NONE
      | ((t', (attn, thms)) :: _) => let
            val (tinst, inst) = Pattern.match sign (t', t) (Vartab.empty, Vartab.empty);
            (* 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 (fn (t, th) =>
             (Element.inst_term (tinst', inst') t,
              Element.inst_thm sign (tinst', inst') th)) 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 t = termify ts;
      val subs = subsumers sign t regs ;
    in (case subs of
        [] => let
                val sups =
                  List.filter (fn (t', _) => Pattern.matches sign (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 GlobalLocalesData = TheoryDataFun
(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 extend = I;

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

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

val _ = Context.add_setup [GlobalLocalesData.init];



(** context data **)

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

val _ = Context.add_setup [LocalLocalesData.init];


(* access locales *)

val print_locales = GlobalLocalesData.print;

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

fun declare_locale name thy =
  thy |> GlobalLocalesData.map (fn (space, locs, regs) =>
    (Sign.declare_name 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 thy_of thy_ctxt (name, ps) =
  case Symtab.lookup (get thy_ctxt) name of
      NONE => NONE
    | SOME reg => Registrations.lookup (thy_of thy_ctxt) (reg, ps);

val get_global_registration =
     gen_get_registration (#3 o GlobalLocalesData.get) I;
val get_local_registration =
     gen_get_registration LocalLocalesData.get ProofContext.theory_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 thy_of (name, ps) attn thy_ctxt =
  map_data (fn regs =>
    let
      val thy = thy_of thy_ctxt;
      val reg = getOpt (Symtab.lookup regs name, Registrations.empty);
      val (reg', sups) = Registrations.insert thy (ps, attn) reg;
      val _ = if not (null sups) then warning
                ("Subsumed interpretation(s) of locale " ^
                 quote (extern thy 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))) I;
val put_local_registration =
     gen_put_registration LocalLocalesData.map ProofContext.theory_of;

fun put_registration_in_locale name id thy =
    let
      val {predicate, import, elems, params, regs} = the_locale thy name;
    in
      put_locale name {predicate = predicate, import = import,
        elems = elems, params = params, regs = regs @ [(id, [])]} thy
    end;


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

fun add_witness (name, ps) thm =
  Symtab.map_entry name (Registrations.add_witness ps thm);

fun add_global_witness id thm =
  GlobalLocalesData.map (fn (space, locs, regs) => (space, locs, add_witness id thm regs));

val add_local_witness = LocalLocalesData.map oo add_witness;

fun add_witness_in_locale name id thm thy =
    let
      val {predicate, import, elems, params, regs} = the_locale thy name;
      fun add (id', thms) =
          if id = id' then (id', thm :: thms) else (id', thms);
    in
      put_locale name {predicate = predicate, import = import,
        elems = elems, params = params, regs = map add regs} thy
    end;


(* printing of registrations *)

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

    val prt_term = Pretty.quote o ProofContext.pretty_term ctxt;
    fun prt_inst ts =
        Pretty.enclose "(" ")" (Pretty.breaks (map prt_term ts));
    fun prt_attn (prfx, atts) =
        Pretty.breaks (Pretty.str prfx :: Args.pretty_attribs ctxt atts);
    fun prt_thm (_, th) = Pretty.quote (ProofContext.pretty_thm ctxt th);
    fun prt_thms thms =
        Pretty.enclose "[" "]" (Pretty.breaks (map prt_thm thms));
    fun prt_reg (ts, (("", []), thms)) =
        if show_wits
          then Pretty.block [prt_inst ts, Pretty.fbrk, prt_thms thms]
          else prt_inst ts
      | prt_reg (ts, (attn, thms)) =
        if show_wits
          then Pretty.block ((prt_attn attn @
            [Pretty.str ":", Pretty.brk 1, prt_inst ts, Pretty.fbrk,
              prt_thms thms]))
          else Pretty.block ((prt_attn attn @
            [Pretty.str ":", Pretty.brk 1, prt_inst ts]));

    val loc_int = intern thy 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_reg 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 show_wits loc ctxt =
  (print_global_registrations show_wits loc (ProofContext.theory_of ctxt);
   print_local_registrations' show_wits loc ctxt);


(* diagnostics *)

fun err_in_locale ctxt msg ids =
  let
    val thy = ProofContext.theory_of ctxt;
    fun prt_id (name, parms) =
      [Pretty.block (Pretty.breaks (map Pretty.str (extern thy 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;

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



(** witnesses -- protected facts **)

fun assume_protected thy t =
  (t, Goal.protect (Thm.assume (Thm.cterm_of thy t)));

fun prove_protected thy t tac =
  (t, Goal.prove thy [] [] (Logic.protect t) (fn _ =>
    Tactic.rtac Drule.protectI 1 THEN tac));

val conclude_protected = Goal.conclude #> Goal.norm_hhf;

fun satisfy_protected pths thm =
  let
    fun satisfy chyp =
      (case find_first (fn (t, _) => Thm.term_of chyp aconv t) pths of
        NONE => I
      | SOME (_, th) => Drule.implies_intr_protected [chyp] #> Goal.comp_hhf th);
  in fold satisfy (#hyps (Thm.crep_thm thm)) thm end;



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

(* parameter types *)

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

fun frozen_tvars ctxt Ts =
  let
    val tvars = rev (fold 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 thy = ProofContext.theory_of ctxt;

    fun unify (SOME T, SOME U) env = (Sign.typ_unify thy (U, T) env
          handle Type.TUNIFY => raise TYPE ("unify_frozen: failed to unify types", [U, T], []))
      | unify _ env = env;
    val (unifier, _) = fold unify (Ts' ~~ Us') (Vartab.empty, maxidx'');
    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 (op =)) (List.concat (map (snd o fst) elemss));
fun params_of' elemss = gen_distinct (eq_fst (op =)) (List.concat (map (snd o fst o fst) elemss));
fun params_syn_of syn elemss =
  gen_distinct (eq_fst (op =)) (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);


(* Distinction of assumed vs. derived identifiers.
   The former may have axioms relating assumptions of the context to
   assumptions of the specification fragment (for locales with
   predicates).  The latter have witness theorems relating assumptions of the
   specification fragment to assumptions of other (assumed) specification
   fragments. *)

datatype 'a mode = Assumed of 'a | Derived of 'a;

fun map_mode f (Assumed x) = Assumed (f x)
  | map_mode f (Derived x) = Derived (f x);


(* flatten expressions *)

local

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 raw_parmss =
  let
    val thy = ProofContext.theory_of ctxt;
    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 U envir = Sign.typ_unify thy (U, T) envir
      handle Type.TUNIFY =>
        let val prt = Sign.string_of_typ thy in
          raise TYPE ("unify_parms: failed to unify types " ^
            prt U ^ " and " ^ prt T, [U, T], [])
        end;
    fun unify_list (T :: Us) = fold (unify T) Us
      | unify_list [] = I;
    val (unifier, _) = fold unify_list (map #2 (Symtab.dest (Symtab.make_multi parms)))
      (Vartab.empty, maxidx);

    val parms' = map (apsnd (Envir.norm_type unifier)) (gen_distinct (eq_fst (op =)) 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, T) end)
      |> Symtab.make;
  in map inst_parms idx_parmss end;

in

fun unify_elemss _ _ [] = []
  | unify_elemss _ [] [elems] = [elems]
  | unify_elemss ctxt fixed_parms elemss =
      let
        val thy = ProofContext.theory_of ctxt;
        val envs = unify_parms ctxt fixed_parms (map (snd o fst o fst) elemss);
        fun inst ((((name, ps), mode), elems), env) =
          (((name, map (apsnd (Option.map (Element.instT_type env))) ps),
              map_mode (map (fn (t, th) =>
                (Element.instT_term env t, Element.instT_thm thy env th))) mode),
            map (Element.instT_ctxt thy env) elems);
      in map inst (elemss ~~ envs) end;

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

fun unify_elemss' _ _ [] [] = []
  | unify_elemss' _ [] [elems] [] = [elems]
  | unify_elemss' ctxt fixed_parms elemss c_parms =
      let
        val thy = ProofContext.theory_of ctxt;
        val envs =
          unify_parms ctxt fixed_parms (map (snd o fst o fst) elemss @ map single c_parms);
        fun inst ((((name, ps), (ps', mode)), elems), env) =
          (((name, map (apsnd (Option.map (Element.instT_type env))) ps), (ps', mode)),
           map (Element.instT_ctxt thy 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;

    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, mode)) =
      let val ps' = map (Element.rename ren) ps in
        (case duplicates ps' of
          [] => ((name, ps'),
                 if top then (map (Element.rename ren) parms,
                   map_mode (map (fn (t, th) =>
                     (Element.rename_term ren t, Element.rename_thm ren th))) mode)
                 else (parms, mode))
        | dups => err_in_locale ctxt ("Duplicate parameters: " ^ commas_quote dups) [(name, ps')])
      end;

    (* add registrations of (name, ps), recursively;
       adjust hyps of witness theorems *)

    fun add_regs (name, ps) (ths, ids) =
        let
          val {params, regs, ...} = the_locale thy name;
          val ps' = map #1 (#1 params);
          val ren = map #1 ps' ~~ map (fn (x, _) => (x, NONE)) ps;
            (* dummy syntax, since required by rename *)
          val ps'' = map (fn ((p, _), (_, T)) => (p, T)) (ps ~~ ps');
          val [env] = unify_parms ctxt ps [map (apsnd SOME) ps''];
            (* propagate parameter types, to keep them consistent *)
          val regs' = map (fn ((name, ps), ths) =>
              ((name, map (Element.rename ren) ps), ths)) regs;
          val new_regs = gen_rems (eq_fst (op =)) (regs', ids);
          val new_ids = map fst new_regs;
          val new_idTs = map (apsnd (map (fn p => (p, (the o AList.lookup (op =) ps) p)))) new_ids;

          val new_ths = new_regs |> map (fn (_, ths') => ths' |> map (fn (t, th) =>
           (t |> Element.instT_term env |> Element.rename_term ren,
            th |> Element.instT_thm thy env |> Element.rename_thm ren |> satisfy_protected ths)));
          val new_ids' = map (fn (id, ths) =>
              (id, ([], Derived ths))) (new_ids ~~ new_ths);
        in
          fold add_regs new_idTs (ths @ List.concat new_ths, ids @ new_ids')
        end;

    (* distribute top-level axioms over assumed ids *)

    fun axiomify all_ps ((name, parms), (_, Assumed _)) axioms =
        let
          val {elems, ...} = the_locale thy name;
          val ts = List.concat (map
            (fn (Assumes asms, _) => List.concat (map (map #1 o #2) asms)
              | _ => [])
            elems);
          val (axs1, axs2) = splitAt (length ts, axioms);
        in (((name, parms), (all_ps, Assumed axs1)), axs2) end
      | axiomify all_ps (id, (_, Derived ths)) axioms =
          ((id, (all_ps, Derived ths)), axioms);

    (* identifiers of an expression *)

    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), ([], Assumed []))];
            val (_, ids''') = add_regs (name, map #1 (#1 params)) ([], ids'');

            val ids_ax = if top then fst
                 (fold_map (axiomify ps) ids''' axioms)
              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 (op =)) (map (rename_parms top ren) ids');
            val parms'' = distinct (List.concat (map (#2 o #1) ids''));
            val syn'' = syn' |> Symtab.dest |> map (Element.rename_var ren) |> Symtab.make;
            (* check for conflicting syntax? *)
          in (ids'', parms'', syn'') end
      | identify top (Merge es) =
          fold (fn e => fn (ids, parms, syn) =>
                   let
                     val (ids', parms', syn') = identify top e
                   in
                     (merge_alists ids ids',
                      merge_lists parms parms',
                      merge_syntax ctxt ids' (syn, syn'))
                   end)
            es ([], [], Symtab.empty);


    (* 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 (apsnd SOME o #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 (Element.rename ren)) ps', map (Element.rename ren) qs),
            map (Element.rename_ctxt ren o #1) elems);
        val elems'' = elems' |> map (Element.map_ctxt
          {var = I, typ = I, term = I, fact = I, attrib = I,
            name = NameSpace.qualified (space_implode "_" xs)});
      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 (op =)) (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 mode *)
    val all_params' = params_of' elemss;
    val all_params = param_types all_params';
    val elemss' = map (fn (((name, _), (ps, mode)), elems) =>
         (((name, map (fn p => (p, AList.lookup (op =) all_params p)) ps), mode), elems))
         elemss;
    fun inst_th (t, th) = let
         val {hyps, prop, ...} = Thm.rep_thm th;
         val ps = map (apsnd SOME) (fold Term.add_frees (prop :: hyps) []);
         val [env] = unify_parms ctxt all_params [ps];
         val t' = Element.instT_term env t;
         val th' = Element.instT_thm thy env th;
       in (t', th') end;
    val final_elemss = map (fn ((id, mode), elems) =>
         ((id, map_mode (map inst_th) mode), elems)) elemss';

  in ((prev_idents @ idents, syntax), final_elemss) end;

end;


(* activate elements *)

local

fun export_axioms axs _ hyps =
  satisfy_protected axs
  #> Drule.implies_intr_list (Library.drop (length axs, hyps))
  #> Seq.single;


(* NB: derived ids contain only facts at this stage *)

fun activate_elem _ ((ctxt, mode), Fixes fixes) =
      ((ctxt |> ProofContext.add_fixes fixes, mode), [])
  | activate_elem _ ((ctxt, mode), Constrains _) =
      ((ctxt, mode), [])
  | activate_elem _ ((ctxt, Assumed axs), Assumes asms) =
      let
        val asms' = Attrib.map_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', Assumed qs), []) end
  | activate_elem _ ((ctxt, Derived ths), Assumes asms) =
      ((ctxt, Derived ths), [])
  | activate_elem _ ((ctxt, Assumed axs), Defines defs) =
      let
        val defs' = Attrib.map_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', Assumed axs), []) end
  | activate_elem _ ((ctxt, Derived ths), Defines defs) =
      ((ctxt, Derived ths), [])
  | activate_elem is_ext ((ctxt, mode), Notes facts) =
      let
        val facts' = Attrib.map_facts (Attrib.context_attribute_i ctxt) facts;
        val (res, ctxt') = ctxt |> ProofContext.note_thmss_i facts';
      in ((ctxt', mode), if is_ext then res else []) end;

fun activate_elems (((name, ps), mode), elems) ctxt =
  let
    val thy = ProofContext.theory_of ctxt;
    val ((ctxt', _), res) =
        foldl_map (activate_elem (name = "")) ((ProofContext.qualified_names ctxt, mode), 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 case mode of
                Assumed axs =>
                  fold (add_local_witness (name, ps') o assume_protected thy o #1) axs ctxt''
              | Derived ths => fold (add_local_witness (name, ps')) ths ctxt''
            end
  in (ProofContext.restore_naming ctxt ctxt'', res) end;

fun activate_elemss prep_facts =
    fold_map (fn (((name, ps), mode), raw_elems) => fn ctxt =>
      let
        val elems = map (prep_facts ctxt) raw_elems;
        val (ctxt', res) = apsnd List.concat
            (activate_elems (((name, ps), mode), elems) ctxt);
        val elems' = elems |> map (Element.map_ctxt
          {name = I, var = I, typ = I, term = I, fact = I, attrib = Args.closure});
      in ((((name, ps), elems'), res), ctxt') 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 (ctxt, args) =
    let
      val (res, ctxt') = activate_elemss prep_facts args ctxt;
    in
      (ctxt', apsnd List.concat (split_list res))
    end;

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

end;



(** prepare locale elements **)

(* expressions *)

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


(* parameters *)

local

fun prep_parms prep_vars ctxt parms =
  let val vars = fst (fold_map prep_vars (map (fn (x, T) => ([x], T)) parms) ctxt)
  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 (ctxt, prep_expr) ((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), ([], Assumed []))]
      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), Assumed []), Ext (Fixes fixes))])
      end
  | flatten _ ((ids, syn), Elem elem) =
      ((ids @ [(("", []), ([], Assumed []))], syn), [((("", []), Assumed []), 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), Assumed _), 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
  | declare_elems _ (ctxt, ((_, Derived _), elems)) = (ctxt, []);

in

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

val norm_term = Envir.beta_norm oo Term.subst_atomic;

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 thy eq =
  Thm.assume (Thm.cterm_of thy eq) |> Drule.gen_all |> Drule.abs_def;

fun bind_def ctxt (name, ps) eq (xs, env, ths) =
  let
    val ((y, T), b) = abstract_term eq;
    val b' = norm_term env b;
    val th = abstract_thm (ProofContext.theory_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 b' xs, (Free (y, T), b') :: env, th :: ths)
  end;


(* CB: for finish_elems (Int and Ext),
   extracts specification, only of assumed elements *)

fun eval_text _ _ _ (Fixes _) text = text
  | eval_text _ _ _ (Constrains _) text = text
  | eval_text _ (_, Assumed _) is_ext (Assumes asms)
        (((exts, exts'), (ints, ints')), (xs, env, defs)) =
      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', (fold Term.add_frees ts' xs, env, defs)) end
  | eval_text _ (_, Derived _) _ (Assumes _) text = text
  | eval_text ctxt (id, Assumed _) _ (Defines defs) (spec, binds) =
      (spec, fold (bind_def ctxt id o #1 o #2) defs binds)
  | eval_text _ (_, Derived _) _ (Defines _) text = text
  | eval_text _ _ _ (Notes _) text = text;


(* for finish_elems (Int),
   remove redundant elements of derived identifiers,
   turn assumptions and definitions into facts,
   adjust hypotheses of facts using witness theorems *)

fun finish_derived _ _ (Assumed _) (Fixes fixes) = SOME (Fixes fixes)
  | finish_derived _ _ (Assumed _) (Constrains csts) = SOME (Constrains csts)
  | finish_derived _ _ (Assumed _) (Assumes asms) = SOME (Assumes asms)
  | finish_derived _ _ (Assumed _) (Defines defs) = SOME (Defines defs)

  | finish_derived _ _ (Derived _) (Fixes _) = NONE
  | finish_derived _ _ (Derived _) (Constrains _) = NONE
  | finish_derived sign wits (Derived _) (Assumes asms) = asms
      |> map (apsnd (map (fn (a, _) => ([Thm.assume (cterm_of sign a)], []))))
      |> Notes |> Element.map_ctxt_values I I (satisfy_protected wits) |> SOME
  | finish_derived sign wits (Derived _) (Defines defs) = defs
      |> map (apsnd (fn (d, _) => [([Thm.assume (cterm_of sign d)], [])]))
      |> Notes |> Element.map_ctxt_values I I (satisfy_protected wits) |> SOME

  | finish_derived _ wits _ (Notes facts) = (Notes facts)
      |> Element.map_ctxt_values I I (satisfy_protected wits) |> SOME;

(* 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, AList.lookup (op =) parms x, mx)) fixes)
  | finish_ext_elem parms _ (Constrains csts, _) =
      Constrains (map (fn (x, _) => (x, (the o AList.lookup (op =) 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), mode), elems) =
  (((name, map (fn (x, _) => (x, AList.lookup (op =) parms x)) ps), mode), elems);

fun finish_elems ctxt parms _ ((text, wits), ((id, Int e), _)) =
      let
        val [(id' as (_, mode), es)] = unify_elemss ctxt parms [(id, e)];
        val wits' = case mode of Assumed _ => wits | Derived ths => wits @ ths;
        val text' = fold (eval_text ctxt id' false) es text;
        val es' = List.mapPartial
              (finish_derived (ProofContext.theory_of ctxt) wits' mode) es;
      in ((text', wits'), (id', map Int es')) end
  | finish_elems ctxt parms do_close ((text, wits), ((id, Ext e), [propp])) =
      let
        val e' = finish_ext_elem parms (closeup ctxt do_close) (e, propp);
        val text' = eval_text ctxt id true e' text;
      in ((text', wits), (id, [Ext e'])) end

in

(* CB: only called by prep_elemss *)

fun finish_elemss ctxt parms do_close =
  foldl_map (apsnd (finish_parms parms) o finish_elems ctxt parms do_close);

end;


(* CB: type inference and consistency checks for locales.

   Works by building a context (through declare_elemss), extracting the
   required information and adjusting the context elements (finish_elemss).
   Can also universally close free vars in assms and defs.  This is only
   needed for Ext elements and controlled by parameter do_close.

   Only elements of assumed identifiers are considered.
*)

fun prep_elemss prep_parms prepp do_close context fixed_params raw_elemss raw_concl =
  let
    (* CB: contexts computed in the course of this function are discarded.
       They are used for type inference and consistency checks only. *)
    (* CB: fixed_params are the parameters (with types) of the target locale,
       empty list if there is no target. *)
    (* CB: raw_elemss are list of pairs consisting of identifiers and
       context elements, the latter marked as internal or external. *)
    val (raw_ctxt, raw_proppss) = declare_elemss prep_parms fixed_params raw_elemss context;
    (* CB: raw_ctxt is context with additional fixed variables derived from
       the fixes elements in raw_elemss,
       raw_proppss contains assumptions and definitions from the
       external elements in raw_elemss. *)
    val raw_propps = map List.concat raw_proppss;
    val raw_propp = List.concat raw_propps;

    (* CB: add type information from fixed_params to context (declare_term) *)
    (* CB: process patterns (conclusion and external elements only) *)
    val (ctxt, all_propp) =
      prepp (fold ProofContext.declare_term (map Free fixed_params) raw_ctxt, raw_concl @ raw_propp);
    (* CB: add type information from conclusion and external elements
       to context *)
    val ctxt = fold ProofContext.declare_term (List.concat (map (map fst) all_propp)) ctxt;

    (* CB: resolve schematic variables (patterns) in conclusion and external
       elements. *)
    val all_propp' = map2 (op ~~)
      (#1 (#2 (ProofContext.bind_propp_schematic_i (ctxt, all_propp))), map (map snd) all_propp);
    val (concl, propp) = splitAt(length raw_concl, all_propp');
    val propps = unflat raw_propps propp;
    val proppss = map (uncurry unflat) (raw_proppss ~~ propps);

    (* CB: obtain all parameters from identifier part of raw_elemss *)
    val xs = map #1 (params_of' raw_elemss);
    val typing = unify_frozen ctxt 0
      (map (ProofContext.default_type raw_ctxt) xs)
      (map (ProofContext.default_type ctxt) xs);
    val parms = param_types (xs ~~ typing);
    (* CB: parms are the parameters from raw_elemss, with correct typing. *)

    (* CB: extract information from assumes and defines elements
       (fixes, constrains and notes in raw_elemss don't have an effect on
       text and elemss), compute final form of context elements. *)
    val ((text, _), elemss) = finish_elemss ctxt parms do_close
      ((((([], []), ([], [])), ([], [], [])), []), raw_elemss ~~ proppss);
    (* CB: text has the following structure:
           (((exts, exts'), (ints, ints')), (xs, env, defs))
       where
         exts: external assumptions (terms in external assumes elements)
         exts': dito, normalised wrt. env
         ints: internal assumptions (terms in internal assumes elements)
         ints': dito, normalised wrt. env
         xs: the free variables in exts' and ints' and rhss of definitions,
           this includes parameters except defined parameters
         env: list of term pairs encoding substitutions, where the first term