(*  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 basic ideas from Florian Kammueller's original version of

 locales, but uses the richer infrastructure of Isar instead of the raw

 meta-logic.  Furthermore, structured import of contexts (with merge

 and rename operations) are provided, 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.

 [2] Clemens Ballarin. Interpretation of Locales in Isabelle: Managing

     Dependencies between Locales. Technical Report TUM-I0607, Technische

     Universitaet Muenchen, 2006.

 [3] Clemens Ballarin. Interpretation of Locales in Isabelle: Theories and

     Proof Contexts. In J.M. Borwein and W.M. Farmer, MKM 2006, LNAI 4108,

     pages 31-43, 2006.

 *)

 (* TODO:

 - beta-eta normalisation of interpretation parameters

 - dangling type frees in locales

 - test subsumption of interpretations when merging theories

 *)

 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

   val map_elem: ('a -> 'b) -> 'a element -> 'b element

   val intern: theory -> xstring -> string

   val extern: theory -> string -> xstring

   val init: string -> theory -> Proof.context

   (* The specification of a locale *)

   val parameters_of: theory -> string ->

     ((string * typ) * mixfix) list

   val parameters_of_expr: theory -> expr ->

     ((string * typ) * mixfix) list

   val local_asms_of: theory -> string ->

     ((string * Attrib.src list) * term list) list

   val global_asms_of: theory -> string ->

     ((string * Attrib.src list) * term list) list

   (* Processing of locale statements *)

   val read_context_statement: xstring option -> Element.context element list ->

     (string * string list) list list -> Proof.context ->

     string option * Proof.context * Proof.context * (term * term list) list list

   val read_context_statement_i: string option -> Element.context element list ->

     (string * string list) list list -> Proof.context ->

     string option * Proof.context * Proof.context * (term * term list) list list

   val cert_context_statement: string option -> Element.context_i element list ->

     (term * term list) list list -> Proof.context ->

     string option * Proof.context * Proof.context * (term * term list) list list

   val read_expr: expr -> Element.context list -> Proof.context ->

     Element.context_i list * Proof.context

   val cert_expr: expr -> Element.context_i list -> Proof.context ->

     Element.context_i list * Proof.context

   (* 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 -> Proof.context -> unit

   val print_local_registrations: bool -> string -> Proof.context -> unit

   val add_locale: bool -> bstring -> expr -> Element.context list -> theory

     -> string * Proof.context

   val add_locale_i: bool -> bstring -> expr -> Element.context_i list -> theory

     -> string * Proof.context

   (* Tactics *)

   val intro_locales_tac: bool -> Proof.context -> thm list -> tactic

   (* Storing results *)

   val add_thmss: string -> string ->

     ((string * Attrib.src list) * (thm list * Attrib.src list) list) list ->

     Proof.context -> (string * thm list) list * Proof.context

   val add_term_syntax: string -> (Proof.context -> Proof.context) -> Proof.context -> Proof.context

   val interpretation: (Proof.context -> Proof.context) ->

     string * Attrib.src list -> expr -> string option list ->

     theory -> Proof.state

   val interpretation_in_locale: (Proof.context -> Proof.context) ->

     xstring * expr -> theory -> Proof.state

   val interpret: (Proof.state -> Proof.state Seq.seq) ->

     string * Attrib.src list -> expr -> string option list ->

     bool -> Proof.state -> Proof.state

 end;

 structure Locale: LOCALE =

 struct

 fun legacy_unvarifyT thm =

   let

     val cT = Thm.ctyp_of (Thm.theory_of_thm thm);

     val tvars = rev (Drule.fold_terms Term.add_tvars thm []);

     val tfrees = map (fn ((x, _), S) => SOME (cT (TFree (x, S)))) tvars;

   in Drule.instantiate' tfrees [] thm end;

 fun legacy_unvarify raw_thm =

   let

     val thm = legacy_unvarifyT raw_thm;

     val ct = Thm.cterm_of (Thm.theory_of_thm thm);

     val vars = rev (Drule.fold_terms Term.add_vars thm []);

     val frees = map (fn ((x, _), T) => SOME (ct (Free (x, T)))) vars;

   in Drule.instantiate' [] frees thm end;

 (** 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 locale =

  {axiom: Element.witness list,

     (* For locales that define predicates this is [A [A]], where A is the locale

        specification.  Otherwise [].

        Only required to generate the right witnesses for locales with predicates. *)

   import: expr,                                                     (*dynamic import*)

   elems: (Element.context_i * stamp) list,

     (* Static content, neither Fixes nor Constrains elements *)

   params: ((string * typ) * mixfix) list,                           (*all params*)

   lparams: string list,                                             (*local params*)

   term_syntax: ((Proof.context -> Proof.context) * stamp) list, (* FIXME depend on morphism *)

   regs: ((string * string list) * Element.witness list) list,

     (* Registrations: indentifiers and witnesses of locales interpreted in the locale. *)

   intros: thm list * thm list}

     (* Introduction rules: of delta predicate and locale predicate. *)

 (* 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: theory -> T ->

       (term list * ((string * Attrib.src list) * Element.witness list)) list

     val lookup: theory -> T * term list ->

       ((string * Attrib.src list) * Element.witness list) option

     val insert: theory -> term list * (string * Attrib.src list) -> T ->

       T * (term list * ((string * Attrib.src list) * Element.witness list)) list

     val add_witness: term list -> Element.witness -> T -> T

   end =

 struct

   (* a registration consists of theorems (actually, witnesses) instantiating locale

      assumptions and prefix and attributes, indexed by parameter instantiation *)

   type T = ((string * Attrib.src list) * Element.witness list) Termtab.table;

   val empty = Termtab.empty;

   (* term list represented as single term, for simultaneous matching *)

   fun termify ts =

     Term.list_comb (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, _) => reg) (r1, r2);

   fun dest_transfer thy regs =

     Termtab.dest regs |> map (apsnd (apsnd (map (Element.transfer_witness thy))));

   fun dest thy regs = dest_transfer thy regs |> map (apfst untermify);

   (* registrations that subsume t *)

   fun subsumers thy t regs =

     filter (fn (t', _) => Pattern.matches thy (t', t)) (dest_transfer thy regs);

   (* look up registration, pick one that subsumes the query *)

   fun lookup thy (regs, ts) =

     let

       val t = termify ts;

       val subs = subsumers thy t regs;

     in (case subs of

         [] => NONE

       | ((t', (attn, thms)) :: _) => let

             val (tinst, inst) = Pattern.match thy (t', t) (Vartab.empty, Vartab.empty);

             (* thms contain Frees, not Vars *)

             val tinst' = tinst |> Vartab.dest

                  |> map (fn ((x, 0), (_, T)) => (x, Logic.legacy_unvarifyT T))

                  |> Symtab.make;

             val inst' = inst |> Vartab.dest

                  |> map (fn ((x, 0), (_, t)) => (x, Logic.legacy_unvarify t))

                  |> Symtab.make;

           in

             SOME (attn, map (Element.inst_witness thy (tinst', inst')) thms)

           end)

     end;

   (* add registration if not subsumed by ones already present,

      additionally returns registrations that are strictly subsumed *)

   fun insert thy (ts, attn) regs =

     let

       val t = termify ts;

       val subs = subsumers thy t regs ;

     in (case subs of

         [] => let

                 val sups =

                   filter (fn (t', _) => Pattern.matches thy (t, t')) (dest_transfer thy 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) = the (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 _ ({axiom, import, elems, params, lparams, term_syntax, regs, intros}: locale,

       {elems = elems', term_syntax = term_syntax', regs = regs', ...}: locale) =

      {axiom = axiom,

       import = import,

       elems = gen_merge_lists (eq_snd (op =)) elems elems',

       params = params,

       lparams = lparams,

       term_syntax = Library.merge (eq_snd (op =)) (term_syntax, term_syntax'),

       regs = merge_alists regs regs',

       intros = intros};

   fun merge _ ((space1, locs1, regs1), (space2, locs2, regs2)) =

     (NameSpace.merge (space1, space2), Symtab.join join_locs (locs1, locs2),

      Symtab.join (K 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));

 fun change_locale name f thy =

   let

     val {axiom, import, elems, params, lparams, term_syntax, regs, intros} =

         the_locale thy name;

     val (axiom', import', elems', params', lparams', term_syntax', regs', intros') =

       f (axiom, import, elems, params, lparams, term_syntax, regs, intros);

   in

     put_locale name {axiom = axiom', import = import', elems = elems',

       params = params', lparams = lparams', term_syntax = term_syntax', regs = regs',

       intros = intros'} thy

   end;

 (* 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_of thy_ctxt name =

   case Symtab.lookup (get thy_ctxt) name of

       NONE => []

     | SOME reg => Registrations.dest (thy_of thy_ctxt) reg;

 val get_global_registrations =

      gen_get_registrations (#3 o GlobalLocalesData.get) I;

 val get_local_registrations =

      gen_get_registrations LocalLocalesData.get ProofContext.theory_of;

 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 = is_some oo get_global_registration;

 val test_local_registration = is_some 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 = the_default Registrations.empty (Symtab.lookup regs name);

       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 =

   change_locale name (fn (axiom, import, elems, params, lparams, term_syntax, regs, intros) =>

     (axiom, import, elems, params, lparams, term_syntax, regs @ [(id, [])], intros));

 (* 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 =

   change_locale name (fn (axiom, import, elems, params, lparams, term_syntax, regs, intros) =>

     let

       fun add (id', thms) =

         if id = id' then (id', thm :: thms) else (id', thms);

     in (axiom, import, elems, params, lparams, term_syntax, map add regs, intros) 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 :: Attrib.pretty_attribs ctxt atts);

     fun prt_witns witns = Pretty.enclose "[" "]"

       (Pretty.breaks (map (prt_term o Element.witness_prop) witns));

     fun prt_reg (ts, (("", []), witns)) =

         if show_wits

           then Pretty.block [prt_inst ts, Pretty.fbrk, prt_witns witns]

           else prt_inst ts

       | prt_reg (ts, (attn, witns)) =

         if show_wits

           then Pretty.block ((prt_attn attn @

             [Pretty.str ":", Pretty.brk 1, prt_inst ts, Pretty.fbrk,

               prt_witns witns]))

           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 thy 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 = flat (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 error err_msg end;

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

 fun pretty_ren NONE = Pretty.str "_"

   | pretty_ren (SOME (x, NONE)) = Pretty.str x

   | pretty_ren (SOME (x, SOME syn)) =

       Pretty.block [Pretty.str x, Pretty.brk 1, Syntax.pretty_mixfix syn];

 fun pretty_expr thy (Locale name) = Pretty.str (extern thy name)

   | pretty_expr thy (Rename (expr, xs)) =

       Pretty.block [pretty_expr thy expr, Pretty.brk 1, Pretty.block (map pretty_ren xs |> Pretty.breaks)]

   | pretty_expr thy (Merge es) =

       Pretty.separate "+" (map (pretty_expr thy) es) |> Pretty.block;

 fun err_in_expr _ msg (Merge []) = error msg

   | err_in_expr ctxt msg expr =

     error (msg ^ "\n" ^ Pretty.string_of (Pretty.block

       [Pretty.str "The error(s) above occured in locale expression:", Pretty.brk 1,

        pretty_expr (ProofContext.theory_of ctxt) expr]));

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

 (* parameter types *)

 fun frozen_tvars ctxt Ts =

   #1 (Variable.importT_inst (map Logic.mk_type Ts) ctxt)

   |> map (fn ((xi, S), T) => (xi, (S, T)));

 fun unify_frozen ctxt maxidx Ts Us =

   let

     fun paramify NONE i = (NONE, i)

       | paramify (SOME T) i = apfst SOME (TypeInfer.paramify_dummies T i);

     val (Ts', maxidx') = fold_map paramify Ts maxidx;

     val (Us', maxidx'') = fold_map paramify Us maxidx';

     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 (map_filter I Vs));

   in map (Option.map (Envir.norm_type unifier')) Vs end;

 fun params_of elemss = distinct (eq_fst (op = : string * string -> bool)) (maps (snd o fst) elemss);

 fun params_of' elemss = distinct (eq_fst (op = : string * string -> bool)) (maps (snd o fst o fst) elemss);

 (* CB: param_types has the following type:

   ('a * 'b option) list -> ('a * 'b) list *)

 fun param_types ps = map_filter (fn (_, NONE) => NONE | (x, SOME T) => SOME (x, T)) ps;

 fun merge_syntax ctxt ids ss = Symtab.merge (op = : mixfix * mixfix -> bool) 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 witnesses 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 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 @ maps 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_list parms)))

       (Vartab.empty, maxidx);

     val parms' = map (apsnd (Envir.norm_type unifier)) (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 [] (map_filter snd ps)

       |> map_filter (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 (Element.instT_witness thy env)) mode),

             map (Element.instT_ctxt thy env) elems);

       in map inst (elemss ~~ envs) end;

 fun renaming xs parms = zip_options parms xs

   handle Library.UnequalLengths =>

     error ("Too many arguments in renaming: " ^

       commas (map (fn NONE => "_" | SOME x => quote (fst x)) xs));

 (* params_of_expr:

    Compute parameters (with types and syntax) of locale expression.

 *)

 fun params_of_expr ctxt fixed_params expr (prev_parms, prev_types, prev_syn) =

   let

     val thy = ProofContext.theory_of ctxt;

     fun merge_tenvs fixed tenv1 tenv2 =

         let

           val [env1, env2] = unify_parms ctxt fixed

                 [tenv1 |> Symtab.dest |> map (apsnd SOME),

                  tenv2 |> Symtab.dest |> map (apsnd SOME)]

         in

           Symtab.merge (op =) (Symtab.map (Element.instT_type env1) tenv1,

             Symtab.map (Element.instT_type env2) tenv2)

         end;

     fun merge_syn expr syn1 syn2 =

         Symtab.merge (op = : mixfix * mixfix -> bool) (syn1, syn2)

         handle Symtab.DUPS xs => err_in_expr ctxt

           ("Conflicting syntax for parameter(s): " ^ commas_quote xs) expr;

     fun params_of (expr as Locale name) =

           let

             val {import, params, ...} = the_locale thy name;

             val parms = map (fst o fst) params;

             val (parms', types', syn') = params_of import;

             val all_parms = merge_lists parms' parms;

             val all_types = merge_tenvs [] types' (params |> map fst |> Symtab.make);

             val all_syn = merge_syn expr syn' (params |> map (apfst fst) |> Symtab.make);

           in (all_parms, all_types, all_syn) end

       | params_of (expr as Rename (e, xs)) =

           let

             val (parms', types', syn') = params_of e;

             val ren = renaming xs parms';

             (* renaming may reduce number of parameters *)

             val new_parms = map (Element.rename ren) parms' |> distinct (op =);

             val ren_syn = syn' |> Symtab.dest |> map (Element.rename_var ren);

             val new_syn = fold (Symtab.insert (op =)) ren_syn Symtab.empty

                 handle Symtab.DUP x =>

                   err_in_expr ctxt ("Conflicting syntax for parameter: " ^ quote x) expr;

             val syn_types = map (apsnd (fn mx => SOME (Type.freeze_type (#1 (TypeInfer.paramify_dummies (TypeInfer.mixfixT mx) 0))))) (Symtab.dest new_syn);

             val ren_types = types' |> Symtab.dest |> map (apfst (Element.rename ren));

             val (env :: _) = unify_parms ctxt []

                 ((ren_types |> map (apsnd SOME)) :: map single syn_types);

             val new_types = fold (Symtab.insert (op =))

                 (map (apsnd (Element.instT_type env)) ren_types) Symtab.empty;

           in (new_parms, new_types, new_syn) end

       | params_of (Merge es) =

           fold (fn e => fn (parms, types, syn) =>

                    let

                      val (parms', types', syn') = params_of e

                    in

                      (merge_lists parms parms', merge_tenvs [] types types',

                       merge_syn e syn syn')

                    end)

             es ([], Symtab.empty, Symtab.empty)

       val (parms, types, syn) = params_of expr;

     in

       (merge_lists prev_parms parms, merge_tenvs fixed_params prev_types types,

        merge_syn expr prev_syn syn)

     end;

 fun make_params_ids params = [(("", params), ([], Assumed []))];

 fun make_raw_params_elemss (params, tenv, syn) =

     [((("", map (fn p => (p, Symtab.lookup tenv p)) params), Assumed []),

       Int [Fixes (map (fn p =>

         (p, Symtab.lookup tenv p, Symtab.lookup syn p |> the)) params)])];

 (* 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 rename_parms top ren ((name, ps), (parms, mode)) =

         ((name, map (Element.rename ren) ps),

          if top

          then (map (Element.rename ren) parms,

                map_mode (map (Element.rename_witness ren)) mode)

          else (parms, mode));

     (* add (name, ps) and its registrations, recursively; adjust hyps of witnesses *)

     fun add_with_regs ((name, pTs), mode) (wits, ids, visited) =

         if member (fn (a, (b, _)) => a = b) visited (name, map #1 pTs)

         then (wits, ids, visited)

         else

           let

             val {params, regs, ...} = the_locale thy name;

             val pTs' = map #1 params;

             val ren = map #1 pTs' ~~ map (fn (x, _) => (x, NONE)) pTs;

               (* dummy syntax, since required by rename *)

             val pTs'' = map (fn ((p, _), (_, T)) => (p, T)) (pTs ~~ pTs');

             val [env] = unify_parms ctxt pTs [map (apsnd SOME) pTs''];

               (* propagate parameter types, to keep them consistent *)

             val regs' = map (fn ((name, ps), wits) =>

                 ((name, map (Element.rename ren) ps),

                  map (Element.transfer_witness thy) wits)) regs;

             val new_regs = regs';

             val new_ids = map fst new_regs;

             val new_idTs = map (apsnd (map (fn p => (p, (the o AList.lookup (op =) pTs) p)))) new_ids;

             val new_wits = new_regs |> map (#2 #> map

               (Element.instT_witness thy env #> Element.rename_witness ren #>

                 Element.satisfy_witness wits));

             val new_ids' = map (fn (id, wits) =>

                 (id, ([], Derived wits))) (new_ids ~~ new_wits);

             val new_idTs' = map (fn ((n, pTs), (_, ([], mode))) =>

                 ((n, pTs), mode)) (new_idTs ~~ new_ids');

             val new_id = ((name, map #1 pTs), ([], mode));

             val (wits', ids', visited') = fold add_with_regs new_idTs'

               (wits @ flat new_wits, ids, visited @ [new_id]);

           in

             (wits', ids' @ [new_id], visited')

           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 = maps

             (fn (Assumes asms, _) => maps (map #1 o #2) asms

               | _ => [])

             elems;

           val (axs1, axs2) = chop (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 {axiom, import, params, ...} = the_locale thy name;

             val ps = map (#1 o #1) params;

             val (ids', parms') = identify false import;

                 (* acyclic import dependencies *)

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

             val ids_ax = if top then fst (fold_map (axiomify ps) ids'' axiom) else ids'';

             in (ids_ax, merge_lists parms' ps) end

       | identify top (Rename (e, xs)) =

           let

             val (ids', parms') = identify top e;

             val ren = renaming xs parms'

               handle ERROR msg => err_in_locale' ctxt msg ids';

             val ids'' = distinct (eq_fst (op =)) (map (rename_parms top ren) ids');

             val parms'' = distinct (op =) (maps (#2 o #1) ids'');

           in (ids'', parms'') end

       | identify top (Merge es) =

           fold (fn e => fn (ids, parms) =>

                    let

                      val (ids', parms') = identify top e

                    in

                      (merge_alists ids ids', merge_lists parms parms')

                    end)

             es ([], []);

     fun inst_wit all_params (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;

     fun eval all_params tenv syn ((name, params), (locale_params, mode)) =

       let

         val {params = ps_mx, elems = elems_stamped, ...} = the_locale thy name;

         val elems = map fst elems_stamped;

         val ps = map fst ps_mx;

         fun lookup_syn x = (case Symtab.lookup syn x of SOME Structure => NONE | opt => opt);

         val locale_params' = map (fn p => (p, Symtab.lookup tenv p |> the)) locale_params;

         val mode' = map_mode (map (Element.map_witness (inst_wit all_params))) mode;

         val ren = map fst ps ~~ map (fn p => (p, lookup_syn p)) params;

         val [env] = unify_parms ctxt all_params [map (apfst (Element.rename ren) o apsnd SOME) ps];

         val elems' = elems

               |> map (Element.rename_ctxt ren)

               |> map (Element.map_ctxt {var = I, typ = I, term = I, fact = I, attrib = I,

                    name = NameSpace.qualified (space_implode "_" params)})

               |> map (Element.instT_ctxt thy env)

       in (((name, map (apsnd SOME) locale_params'), mode'), elems') end;

     (* parameters, their types and syntax *)

     val (all_params', tenv, syn) = params_of_expr ctxt [] expr ([], Symtab.empty, Symtab.empty);

     val all_params = map (fn p => (p, Symtab.lookup tenv p |> the)) all_params';

     (* compute identifiers and syntax, merge with previous ones *)

     val (ids, _) = identify true expr;

     val idents = subtract (eq_fst (op =)) prev_idents ids;

     val syntax = merge_syntax ctxt ids (syn, prev_syntax);

     (* type-instantiate elements *)

     val final_elemss = map (eval all_params tenv syntax) idents;

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

 end;

 (* activate elements *)

 local

 fun axioms_export axs _ hyps =

   Element.satisfy_thm axs

   #> Drule.implies_intr_list (Library.drop (length axs, hyps));

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

 fun activate_elem _ _ ((ctxt, mode), Fixes fixes) =

       ((ctxt |> ProofContext.add_fixes_i fixes |> snd, mode), [])

   | activate_elem _ _ ((ctxt, mode), Constrains _) =

       ((ctxt, mode), [])

   | activate_elem ax_in_ctxt _ ((ctxt, Assumed axs), Assumes asms) =

       let

         val asms' = Attrib.map_specs (Attrib.attribute_i (ProofContext.theory_of ctxt)) asms;

         val ts = maps (map #1 o #2) asms';

         val (ps, qs) = chop (length ts) axs;

         val (_, ctxt') =

           ctxt |> fold Variable.fix_frees ts

           |> ProofContext.add_assms_i (axioms_export (if ax_in_ctxt then ps else [])) 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.attribute_i (ProofContext.theory_of ctxt)) defs;

         val asms = defs' |> map (fn ((name, atts), (t, ps)) =>

             let val ((c, _), t') = LocalDefs.cert_def ctxt t

             in (t', ((Thm.def_name_optional c name, atts), [(t', ps)])) end);

         val (_, ctxt') =

           ctxt |> fold (Variable.fix_frees o #1) asms

           |> ProofContext.add_assms_i LocalDefs.def_export (map #2 asms);

       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.attribute_i (ProofContext.theory_of ctxt)) facts;

         val (res, ctxt') = ctxt |> ProofContext.note_thmss_i facts';

       in ((ctxt', mode), if is_ext then res else []) end;

 fun activate_elems ax_in_ctxt (((name, ps), mode), elems) ctxt =

   let

     val thy = ProofContext.theory_of ctxt;

     val ((ctxt', _), res) =

         foldl_map (activate_elem ax_in_ctxt (name = "")) ((ProofContext.qualified_names ctxt, mode), elems)

       handle ERROR msg => 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

                     Element.assume_witness thy o Element.witness_prop) axs ctxt''

               | Derived ths => fold (add_local_witness (name, ps')) ths ctxt''

             end

   in (ProofContext.restore_naming ctxt ctxt'', res) end;

 fun activate_elemss ax_in_ctxt 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 flat

             (activate_elems ax_in_ctxt (((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), mode), 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 ax_in_ctxt prep_facts (ctxt, args) =

   let val ((elemss, factss), ctxt') = activate_elemss ax_in_ctxt prep_facts args ctxt |>> split_list

   in (ctxt', (elemss, flat factss)) 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);

 (* 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_i (map (fn (x, T, mx) =>

         (x, Option.map (Term.map_type_tfree (TypeInfer.param 0)) T, mx)) fixes) |> snd, [])

   | declare_int_elem (ctxt, _) = (ctxt, []);

 fun declare_ext_elem prep_vars (ctxt, Fixes fixes) =

       let val (vars, _) = prep_vars fixes ctxt

       in (ctxt |> ProofContext.add_fixes_i vars |> snd, []) end

   | declare_ext_elem prep_vars (ctxt, Constrains csts) =

       let val (_, ctxt') = prep_vars (map (fn (x, T) => (x, SOME T, NoSyn)) csts) ctxt

       in (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_vars (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_vars) (ctxt, [e]))

       handle ERROR msg => err_in_locale ctxt msg [(name, map fst ps)]

     in (ctxt', propps) end

   | declare_elems _ (ctxt, ((_, Derived _), elems)) = (ctxt, []);

 in

 fun declare_elemss prep_vars 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 Variable.declare_term (map Free fixed_params) ctxt;

     val int_elemss =

       raw_elemss

       |> map_filter (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_vars) (ctxt, raw_elemss') end;

 end;

 local

 val norm_term = Envir.beta_norm oo Term.subst_atomic;

 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) = LocalDefs.abs_def 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 = maps (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 witnesses *)

 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 (Element.satisfy_thm 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 (Element.satisfy_thm wits) |> SOME

   | finish_derived _ wits _ (Notes facts) = (Notes facts)

       |> Element.map_ctxt_values I I (Element.satisfy_thm 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 (Variable.is_fixed ctxt o #1) (Term.add_frees t []))

           in Term.list_all_free (frees, t) end;

         fun no_binds [] = []

           | no_binds _ = error "Illegal term bindings in locale element";

       in

         (case elem of

           Assumes asms => Assumes (asms |> map (fn (a, propps) =>

             (a, map (fn (t, ps) => (close_frees t, no_binds ps)) propps)))

         | Defines defs => Defines (defs |> map (fn (a, (t, ps)) =>

             (a, (close_frees (#2 (LocalDefs.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 _, _) = Constrains []

   | 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 = : string * string -> bool) 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' = map_filter

               (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;

 (* Remove duplicate Defines elements: temporary workaround to fix Afp/Category. *)

 fun defs_ord (defs1, defs2) =

     list_ord (fn ((_, (d1, _)), (_, (d2, _))) =>

       Term.fast_term_ord (d1, d2)) (defs1, defs2);

 structure Defstab =

     TableFun(type key = ((string * Attrib.src list) * (term * term list)) list

         val ord = defs_ord);

 fun rem_dup_defs es ds =

     fold_map (fn e as (Defines defs) => (fn ds =>

                  if Defstab.defined ds defs

                  then (Defines [], ds)

                  else (e, Defstab.update (defs, ()) ds))

                | e => (fn ds => (e, ds))) es ds;

 fun rem_dup_elemss (Int es) ds = apfst Int (rem_dup_defs es ds)

   | rem_dup_elemss (Ext e) ds = (Ext e, ds);

 fun rem_dup_defines raw_elemss =

     fold_map (fn (id as (_, (Assumed _)), es) => (fn ds =>

                      apfst (pair id) (rem_dup_elemss es ds))

                | (id as (_, (Derived _)), es) => (fn ds =>

                      ((id, es), ds))) raw_elemss Defstab.empty |> #1;

 (* 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_vars 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_elemss = rem_dup_defines raw_elemss;

     val (raw_ctxt, raw_proppss) = declare_elemss prep_vars 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. *)

     fun prep_prop raw_propp (raw_ctxt, raw_concl)  =

       let

         (* 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 Variable.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 Variable.declare_term (maps (map fst) all_propp) ctxt;

         (* CB: resolve schematic variables (patterns) in conclusion and external elements. *)

         val all_propp' = map2 (curry (op ~~))

           (#1 (#2 (ProofContext.bind_propp_schematic_i (ctxt, all_propp)))) (map (map snd) all_propp);

         val (concl, propp) = chop (length raw_concl) all_propp';

       in (propp, (ctxt, concl)) end

     val (proppss, (ctxt, concl)) =

       (fold_burrow o fold_burrow) prep_prop raw_proppss (raw_ctxt, raw_concl);

     (* 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 (Variable.default_type raw_ctxt) xs)

       (map (Variable.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

            is a free variable; substitutions represent defines elements and

            the rhs is normalised wrt. the previous env

          defs: theorems representing the substitutions from defines elements

            (thms are normalised wrt. env).

        elemss is an updated version of raw_elemss:

          - type info added to Fixes and modified in Constrains

          - axiom and definition statement replaced by corresponding one

            from proppss in Assumes and Defines

          - Facts unchanged

        *)

   in ((parms, elemss, concl), text) end;

 in

 fun read_elemss x = prep_elemss ProofContext.read_vars ProofContext.read_propp_schematic x;

 fun cert_elemss x = prep_elemss ProofContext.cert_vars ProofContext.cert_propp_schematic x;

 end;

 (* facts and attributes *)

 local

 fun check_name name =

   if NameSpace.is_qualified name then error ("Illegal qualified name: " ^ quote name)

   else name;

 fun prep_facts _ _ _ ctxt (Int elem) =

       Element.map_ctxt_values I I (Thm.transfer (ProofContext.theory_of ctxt)) elem

   | prep_facts prep_name get intern ctxt (Ext elem) = elem |> Element.map_ctxt

      {var = I, typ = I, term = I,

       name = prep_name,

       fact = get ctxt,

       attrib = Args.assignable o intern (ProofContext.theory_of ctxt)};

 in

 fun read_facts x = prep_facts check_name ProofContext.get_thms Attrib.intern_src x;

 fun cert_facts x = prep_facts I (K I) (K I) x;

 end;

 (* Get the specification of a locale *)

 (*The global specification is made from the parameters and global

   assumptions, the local specification from the parameters and the

   local assumptions.*)

 local

 fun gen_asms_of get thy name =

   let

     val ctxt = ProofContext.init thy;

     val (_, raw_elemss) = flatten (ctxt, I) (([], Symtab.empty), Expr (Locale name));

     val ((_, elemss, _), _) = read_elemss false ctxt [] raw_elemss [];

   in

     elemss |> get

       |> maps (fn (_, es) => map (fn Int e => e) es)

       |> maps (fn Assumes asms => asms | _ => [])

       |> map (apsnd (map fst))

   end;

 in

 fun parameters_of thy name =

   the_locale thy name |> #params;

 fun parameters_of_expr thy expr =

   let

     val ctxt = ProofContext.init thy;

     val pts = params_of_expr ctxt [] (intern_expr thy expr)

         ([], Symtab.empty, Symtab.empty);

     val raw_params_elemss = make_raw_params_elemss pts;

     val ((_, syn), raw_elemss) = flatten (ctxt, intern_expr thy)

         (([], Symtab.empty), Expr expr);

     val ((parms, _, _), _) =

         read_elemss false ctxt [] (raw_params_elemss @ raw_elemss) [];

   in map (fn p as (n, _) => (p, Symtab.lookup syn n |> the)) parms end;

 fun local_asms_of thy name =

   gen_asms_of (single o Library.last_elem) thy name;

 fun global_asms_of thy name =

   gen_asms_of I thy name;

 end;

 (* full context statements: import + elements + conclusion *)

 local

 fun prep_context_statement prep_expr prep_elemss prep_facts

     do_close fixed_params import elements raw_concl context =

   let

     val thy = ProofContext.theory_of context;

     val (import_params, import_tenv, import_syn) =

       params_of_expr context fixed_params (prep_expr thy import)

         ([], Symtab.empty, Symtab.empty);

     val includes = map_filter (fn Expr e => SOME e | Elem _ => NONE) elements;

     val (incl_params, incl_tenv, incl_syn) = fold (params_of_expr context fixed_params)

       (map (prep_expr thy) includes) (import_params, import_tenv, import_syn);

     val ((import_ids, _), raw_import_elemss) =

       flatten (context, prep_expr thy) (([], Symtab.empty), Expr import);

     (* CB: normalise "includes" among elements *)

     val ((ids, syn), raw_elemsss) = foldl_map (flatten (context, prep_expr thy))

       ((import_ids, incl_syn), elements);

     val raw_elemss = flat raw_elemsss;

     (* CB: raw_import_elemss @ raw_elemss is the normalised list of

        context elements obtained from import and elements. *)

     (* Now additional elements for parameters are inserted. *)

     val import_params_ids = make_params_ids import_params;

     val incl_params_ids =

         make_params_ids (incl_params \\ import_params);

     val raw_import_params_elemss =

         make_raw_params_elemss (import_params, incl_tenv, incl_syn);

     val raw_incl_params_elemss =

         make_raw_params_elemss (incl_params \\ import_params, incl_tenv, incl_syn);

     val ((parms, all_elemss, concl), (spec, (_, _, defs))) = prep_elemss do_close

       context fixed_params

       (raw_import_params_elemss @ raw_import_elemss @ raw_incl_params_elemss @ raw_elemss) raw_concl;

     (* replace extended ids (for axioms) by ids *)

     val (import_ids', incl_ids) = chop (length import_ids) ids;

     val all_ids = import_params_ids @ import_ids' @ incl_params_ids @ incl_ids;

     val all_elemss' = map (fn (((_, ps), _), (((n, ps'), mode), elems)) =>

         (((n, map (fn p => (p, (the o AList.lookup (op =) ps') p)) ps), mode), elems))

       (all_ids ~~ all_elemss);

     (* CB: all_elemss and parms contain the correct parameter types *)

     val (ps, qs) = chop (length raw_import_params_elemss + length raw_import_elemss) all_elemss';

     val (import_ctxt, (import_elemss, _)) =

       activate_facts false prep_facts (context, ps);

     val (ctxt, (elemss, _)) =

       activate_facts false prep_facts (import_ctxt, qs);

   in

     ((((import_ctxt, import_elemss), (ctxt, elemss, syn)),

       (parms, spec, defs)), concl)

   end;

 fun prep_statement prep_locale prep_ctxt raw_locale elems concl ctxt =

   let

     val thy = ProofContext.theory_of ctxt;

     val locale = Option.map (prep_locale thy) raw_locale;

     val (fixed_params, import) =

       (case locale of

         NONE => ([], empty)

       | SOME name =>

           let val {params = ps, ...} = the_locale thy name

           in (map fst ps, Locale name) end);

     val ((((locale_ctxt, _), (elems_ctxt, _, _)), _), concl') =

       prep_ctxt false fixed_params import elems concl ctxt;

   in (locale, locale_ctxt, elems_ctxt, concl') end;

 fun prep_expr prep import body ctxt =

   let

     val (((_, import_elemss), (ctxt', elemss, _)), _) = prep import body ctxt;

     val all_elems = maps snd (import_elemss @ elemss);

   in (all_elems, ctxt') end;

 in

 val read_ctxt = prep_context_statement intern_expr read_elemss read_facts;

 val cert_ctxt = prep_context_statement (K I) cert_elemss cert_facts;

 fun read_context import body ctxt = #1 (read_ctxt true [] import (map Elem body) [] ctxt);

 fun cert_context import body ctxt = #1 (cert_ctxt true [] import (map Elem body) [] ctxt);

 val read_expr = prep_expr read_context;

 val cert_expr = prep_expr cert_context;

 fun read_context_statement loc = prep_statement intern read_ctxt loc;

 fun read_context_statement_i loc = prep_statement (K I) read_ctxt loc;

 fun cert_context_statement loc = prep_statement (K I) cert_ctxt loc;

 end;

 (* print locale *)

 fun print_locale thy show_facts import body =

   let val (all_elems, ctxt) = read_expr import body (ProofContext.init thy) in

     Pretty.big_list "locale elements:" (all_elems

       |> (if show_facts then I else filter (fn Notes _ => false | _ => true))

       |> map (Pretty.chunks o Element.pretty_ctxt ctxt))

     |> Pretty.writeln

   end;

 (** store results **)

 (* naming of interpreted theorems *)

 fun global_note_prefix_i kind prfx args thy =

   thy

   |> Theory.qualified_names

   |> Theory.sticky_prefix prfx

   |> PureThy.note_thmss_i kind args

   ||> Theory.restore_naming thy;

 fun local_note_prefix_i prfx args ctxt =

   ctxt

   |> ProofContext.qualified_names

   |> ProofContext.sticky_prefix prfx

   |> ProofContext.note_thmss_i args

   ||> ProofContext.restore_naming ctxt;

 (* collect witnesses for global registration;

    requires parameters and flattened list of (assumed!) identifiers

    instead of recomputing it from the target *)

 fun collect_global_witnesses thy parms ids vts = let

     val ts = map Logic.unvarify vts;

     val (parms, parmTs) = split_list parms;

     val parmvTs = map Logic.varifyT parmTs;

     val vtinst = fold (Sign.typ_match thy) (parmvTs ~~ map Term.fastype_of ts) Vartab.empty;

     val tinst = Vartab.dest vtinst |> map (fn ((x, 0), (_, T)) => (x, T))

         |> Symtab.make;

     (* replace parameter names in ids by instantiations *)

     val vinst = Symtab.make (parms ~~ vts);

     fun vinst_names ps = map (the o Symtab.lookup vinst) ps;

     val inst = Symtab.make (parms ~~ ts);

     val ids' = map (apsnd vinst_names) ids;

     val wits = maps (snd o the o get_global_registration thy) ids';

   in ((tinst, inst), wits) end;

 (* store instantiations of args for all registered interpretations

    of the theory *)

 fun note_thmss_registrations kind target args thy =

   let

     val parms = the_locale thy target |> #params |> map fst;

     val ids = flatten (ProofContext.init thy, intern_expr thy)

       (([], Symtab.empty), Expr (Locale target)) |> fst |> fst

       |> map_filter (fn (id, (_, Assumed _)) => SOME id | _ => NONE)

     val regs = get_global_registrations thy target;

     (* add args to thy for all registrations *)

     fun activate (vts, ((prfx, atts2), _)) thy =

       let

         val (insts, prems) = collect_global_witnesses thy parms ids vts;

         val attrib = Attrib.attribute_i thy;

         val inst_atts =

           Args.map_values I (Element.instT_type (#1 insts))

             (Element.inst_term insts) (Element.inst_thm thy insts);

         val inst_thm =

           Drule.standard o Element.satisfy_thm prems o Element.inst_thm thy insts;

         val args' = args |> map (fn ((name, atts), bs) =>

             ((name, map (attrib o inst_atts) atts),

               bs |> map (fn (ths, more_atts) =>

                 (map inst_thm ths, map attrib (map inst_atts more_atts @ atts2)))));

       in global_note_prefix_i kind prfx args' thy |> snd end;

   in fold activate regs thy end;

 (* term syntax *)

 fun add_term_syntax loc syn =

   syn #> ProofContext.theory (change_locale loc

     (fn (axiom, import, elems, params, lparams, term_syntax, regs, intros) =>

       (axiom, import, elems, params, lparams, (syn, stamp ()) :: term_syntax, regs, intros)));

 fun init_term_syntax loc ctxt =

   fold_rev (fn (f, _) => fn ctxt' => f ctxt')

     (#term_syntax (the_locale (ProofContext.theory_of ctxt) loc)) ctxt;

 fun init loc =

   ProofContext.init

   #> init_term_syntax loc

   #> (#2 o cert_context_statement (SOME loc) [] []);

 (* locale results *)

 fun add_thmss kind loc args ctxt =

   let

     val (ctxt', ([(_, [Notes args'])], facts)) =

       activate_facts true cert_facts (ctxt, [((("", []), Assumed []), [Ext (Notes args)])]);

     val ctxt'' = ctxt' |> ProofContext.theory

       (change_locale loc

         (fn (axiom, import, elems, params, lparams, term_syntax, regs, intros) =>

           (axiom, import, elems @ [(Notes args', stamp ())],

             params, lparams, term_syntax, regs, intros))

       #> note_thmss_registrations kind loc args');

   in (facts, ctxt'') end;

 fun locale_results kind loc args = add_thmss kind loc (map (apsnd Thm.simple_fact) args);

 (** define locales **)

 (* predicate text *)

 (* CB: generate locale predicates and delta predicates *)

 local

 (* introN: name of theorems for introduction rules of locale and

      delta predicates;

    axiomsN: name of theorem set with destruct rules for locale predicates,

      also name suffix of delta predicates. *)

 val introN = "intro";

 val axiomsN = "axioms";

 fun atomize_spec thy ts =

   let

     val t = Logic.mk_conjunction_list ts;

     val body = ObjectLogic.atomize_term thy t;

     val bodyT = Term.fastype_of body;

   in

     if bodyT = propT then (t, propT, Thm.reflexive (Thm.cterm_of thy t))

     else (body, bodyT, ObjectLogic.atomize_cterm (Thm.cterm_of thy t))

   end;

 fun aprop_tr' n c = (c, fn args =>

   if length args = n then Syntax.const "_aprop" $ Term.list_comb (Syntax.free c, args)

   else raise Match);

 (* CB: define one predicate including its intro rule and axioms

    - bname: predicate name

    - parms: locale parameters

    - defs: thms representing substitutions from defines elements

    - ts: terms representing locale assumptions (not normalised wrt. defs)

    - norm_ts: terms representing locale assumptions (normalised wrt. defs)

    - thy: the theory

 *)

 fun def_pred bname parms defs ts norm_ts thy =

   let

     val name = Sign.full_name thy bname;

     val (body, bodyT, body_eq) = atomize_spec thy norm_ts;

     val env = Term.add_term_free_names (body, []);

     val xs = filter (member (op =) env o #1) parms;

     val Ts = map #2 xs;

     val extraTs = (Term.term_tfrees body \\ foldr Term.add_typ_tfrees [] Ts)

       |> Library.sort_wrt #1 |> map TFree;

     val predT = map Term.itselfT extraTs ---> Ts ---> bodyT;

     val args = map Logic.mk_type extraTs @ map Free xs;

     val head = Term.list_comb (Const (name, predT), args);

     val statement = ObjectLogic.ensure_propT thy head;

     val ([pred_def], defs_thy) =

       thy

       |> (if bodyT <> propT then I else

         Theory.add_trfuns ([], [], map (aprop_tr' (length args)) (NameSpace.accesses' name), []))

       |> Theory.add_consts_i [(bname, predT, NoSyn)]

       |> PureThy.add_defs_i false [((Thm.def_name bname, Logic.mk_equals (head, body)), [])];

     val defs_ctxt = ProofContext.init defs_thy |> Variable.declare_term head;

     val cert = Thm.cterm_of defs_thy;

     val intro = Goal.prove_global defs_thy [] norm_ts statement (fn _ =>

       Tactic.rewrite_goals_tac [pred_def] THEN

       Tactic.compose_tac (false, body_eq RS Drule.equal_elim_rule1, 1) 1 THEN

       Tactic.compose_tac (false, Conjunction.intr_list (map (Thm.assume o cert) norm_ts), 0) 1);

     val conjuncts =

       (Drule.equal_elim_rule2 OF [body_eq,

         Tactic.rewrite_rule [pred_def] (Thm.assume (cert statement))])

       |> Conjunction.elim_precise [length ts] |> hd;

     val axioms = ts ~~ conjuncts |> map (fn (t, ax) =>

       Element.prove_witness defs_ctxt t

        (Tactic.rewrite_goals_tac defs THEN

         Tactic.compose_tac (false, ax, 0) 1));

   in ((statement, intro, axioms), defs_thy) end;

 fun assumes_to_notes (Assumes asms) axms =

     fold_map (fn (a, spec) => fn axs =>

        let val (ps, qs) = chop (length spec) axs

        in ((a, [(ps, [])]), qs) end) asms axms

     |> apfst Notes

   | assumes_to_notes e axms = (e, axms);

 (* CB: the following two change only "new" elems, these have identifier ("", _). *)

 (* turn Assumes into Notes elements *)

 fun change_assumes_elemss axioms elemss =

   let

     fun change (id as ("", _), es) =

           fold_map assumes_to_notes

             (map (Element.map_ctxt_values I I (Element.satisfy_thm axioms)) es)

           #-> (fn es' => pair (id, es'))

       | change e = pair e;

   in

     fst (fold_map change elemss (map Element.conclude_witness axioms))

   end;

 (* adjust hyps of Notes elements *)

 fun change_elemss_hyps axioms elemss =

   let

     fun change (id as ("", _), es) =

         (id, map (fn e as (Notes _) => Element.map_ctxt_values I I (Element.satisfy_thm axioms) e

                    | e => e) es)

       | change e = e;

   in map change elemss end;

 in

 (* CB: main predicate definition function *)

 fun define_preds bname (parms, ((exts, exts'), (ints, ints')), defs) elemss thy =

   let

     val ((elemss', more_ts), a_elem, a_intro, thy') =

       if null exts then ((elemss, []), [], [], thy)

       else

         let

           val aname = if null ints then bname else bname ^ "_" ^ axiomsN;

           val ((statement, intro, axioms), def_thy) =

             thy |> def_pred aname parms defs exts exts';

           val elemss' = change_assumes_elemss axioms elemss;

           val def_thy' = def_thy

             |> PureThy.note_thmss_qualified "" aname [((introN, []), [([intro], [])])]

             |> snd;

           val a_elem = [(("", []), [Assumes [((bname ^ "_" ^ axiomsN, []), [(statement, [])])]])];

         in ((elemss', [statement]), a_elem, [intro], def_thy') end;

     val (predicate, stmt', elemss'', b_intro, thy'') =

       if null ints then (([], []), more_ts, elemss' @ a_elem, [], thy')

       else

         let

           val ((statement, intro, axioms), def_thy) =

             thy' |> def_pred bname parms defs (ints @ more_ts) (ints' @ more_ts);

           val cstatement = Thm.cterm_of def_thy statement;

           val elemss'' = change_elemss_hyps axioms elemss';

           val def_thy' =

           def_thy

           |> PureThy.note_thmss_qualified "" bname

                [((introN, []), [([intro], [])]),

                 ((axiomsN, []), [(map (Drule.standard o Element.conclude_witness) axioms, [])])]

           |> snd;

           val b_elem = [(("", []),

                [Assumes [((bname ^ "_" ^ axiomsN, []), [(statement, [])])]])];

         in (([cstatement], axioms), [statement], elemss'' @ b_elem, [intro], def_thy') end;

   in (((elemss'', predicate, stmt'), (a_intro, b_intro)), thy'') end;

 end;

 (* add_locale(_i) *)

 local

 (* turn Defines into Notes elements, accumulate definition terms *)

 fun defines_to_notes is_ext thy (Defines defs) defns =

     let

       val defs' = map (fn (_, (def, _)) => (("", []), (def, []))) defs

       val notes = map (fn (a, (def, _)) =>

         (a, [([assume (cterm_of thy def)], [])])) defs

     in (if is_ext then SOME (Notes notes) else NONE, defns @ [Defines defs']) end

   | defines_to_notes _ _ e defns = (SOME e, defns);

 fun change_defines_elemss thy elemss defns =

   let

     fun change (id as (n, _), es) defns =

         let

           val (es', defns') = fold_map (defines_to_notes (n="") thy) es defns

         in ((id, map_filter I es'), defns') end

   in fold_map change elemss defns end;

 fun gen_add_locale prep_ctxt prep_expr

     do_predicate bname raw_import raw_body thy =

   let

     val name = Sign.full_name thy bname;

     val _ = conditional (is_some (get_locale thy name)) (fn () =>

       error ("Duplicate definition of locale " ^ quote name));

     val thy_ctxt = ProofContext.init thy;

     val (((import_ctxt, import_elemss), (body_ctxt, body_elemss, syn)),

       text as (parms, ((_, exts'), _), defs)) =

       prep_ctxt raw_import raw_body thy_ctxt;

     val elemss = import_elemss @ body_elemss |>

         map_filter (fn ((id, Assumed axs), elems) => SOME (id, elems) | _ => NONE);

     val import = prep_expr thy raw_import;

     val extraTs = foldr Term.add_term_tfrees [] exts' \\

       foldr Term.add_typ_tfrees [] (map snd parms);

     val _ = if null extraTs then ()

       else warning ("Additional type variable(s) in locale specification " ^ quote bname);

     val ((((elemss', predicate as (predicate_statement, predicate_axioms), stmt'), intros),

           pred_thy), (import, regs)) =

       if do_predicate then

         let

           val (elemss', defns) = change_defines_elemss thy elemss [];

           val elemss'' = elemss' @ [(("", []), defns)];

           val (((elemss''', predicate as (_, axioms), stmt'), intros), thy') =

             define_preds bname text elemss'' thy;

           fun mk_regs elemss wits =

             fold_map (fn (id, elems) => fn wts => let

                 val ts = List.concat (List.mapPartial (fn (Assumes asms) =>

                   SOME (List.concat (map (map #1 o #2) asms)) | _ => NONE) elems);

                 val (wts1, wts2) = chop (length ts) wts

               in ((apsnd (map fst) id, wts1), wts2) end) elemss wits |> fst;

           val regs = mk_regs elemss''' axioms |>

                 map_filter (fn (("", _), _) => NONE | e => SOME e);

         in ((((elemss''', predicate, stmt'), intros), thy'), (empty, regs)) end

       else ((((elemss, ([], []), []), ([], [])), thy), (import, []));

     fun axiomify axioms elemss =

       (axioms, elemss) |> foldl_map (fn (axs, (id, elems)) => let

                    val ts = flat (map_filter (fn (Assumes asms) =>

                      SOME (maps (map #1 o #2) asms) | _ => NONE) elems);

                    val (axs1, axs2) = chop (length ts) axs;

                  in (axs2, ((id, Assumed axs1), elems)) end)

         |> snd;

     val (ctxt, (_, facts)) = activate_facts true (K I)

       (ProofContext.init pred_thy, axiomify predicate_axioms elemss');

     val export = singleton (ProofContext.export_standard

         (Assumption.add_view thy_ctxt predicate_statement ctxt) thy_ctxt);

     val facts' = facts |> map (fn (a, ths) => ((a, []), [(map export ths, [])]));

     val elems' = maps #2 (filter (equal "" o #1 o #1) elemss');

     val elems'' = map_filter (fn (Fixes _) => NONE | e => SOME e) elems';

     val axs' = map (Element.assume_witness pred_thy) stmt';

     val ctxt' = ctxt |> ProofContext.theory (fn pred_thy => pred_thy

       |> PureThy.note_thmss_qualified "" bname facts' |> snd

       |> declare_locale name

       |> put_locale name

        {axiom = axs',

         import = import,

         elems = map (fn e => (e, stamp ())) elems'',

         params = params_of elemss' |> map (fn (x, SOME T) => ((x, T), the (Symtab.lookup syn x))),

         lparams = map #1 (params_of' body_elemss),

         term_syntax = [],

         regs = regs,

         intros = intros});

   in (name, ctxt') end;

 in

 val add_locale = gen_add_locale read_context intern_expr;

 val add_locale_i = gen_add_locale cert_context (K I);

 end;

 val _ = Context.add_setup

  (add_locale_i true "var" empty [Fixes [(Name.internal "x", NONE, NoSyn)]] #>

   snd #> ProofContext.theory_of #>

   add_locale_i true "struct" empty [Fixes [(Name.internal "S", NONE, Structure)]] #>

   snd #> ProofContext.theory_of);

 (** Normalisation of locale statements ---

     discharges goals implied by interpretations **)

 local

 fun locale_assm_intros thy =

   Symtab.fold (fn (_, {intros = (a, _), ...}) => fn intros => (a @ intros))

     (#2 (GlobalLocalesData.get thy)) [];

 fun locale_base_intros thy =

   Symtab.fold (fn (_, {intros = (_, b), ...}) => fn intros => (b @ intros))

     (#2 (GlobalLocalesData.get thy)) [];

 fun all_witnesses ctxt =

   let

     val thy = ProofContext.theory_of ctxt;

     fun get registrations = Symtab.fold (fn (_, regs) => fn thms =>

         (Registrations.dest thy regs |> map (fn (_, (_, wits)) =>

           map Element.conclude_witness wits) |> flat) @ thms)

       registrations [];

     val globals = get (#3 (GlobalLocalesData.get thy));

     val locals = get (LocalLocalesData.get ctxt);

   in globals @ locals end;

 (* FIXME: proper varification *)

 in

 fun intro_locales_tac eager ctxt facts st =

   let

     val wits = all_witnesses ctxt |> map Thm.varifyT;

     val thy = ProofContext.theory_of ctxt;

     val intros = locale_base_intros thy @ (if eager then locale_assm_intros thy else []);

   in

     (ALLGOALS (Method.insert_tac facts THEN'

         REPEAT_ALL_NEW (resolve_tac (wits @ intros)))

       THEN Tactic.distinct_subgoals_tac) st

   end;

 val _ = Context.add_setup (Method.add_methods

   [("intro_locales",

     Method.ctxt_args (fn ctxt => Method.METHOD (intro_locales_tac false ctxt)),

     "back-chain introduction rules of locales without unfolding predicates"),

    ("unfold_locales",

     Method.ctxt_args (fn ctxt => Method.METHOD (intro_locales_tac true ctxt)),

     "back-chain all introduction rules of locales")]);

 end;

 (** Interpretation commands **)

 local

 (* extract proof obligations (assms and defs) from elements *)

 fun extract_asms_elems ((id, Assumed _), elems) = (id, maps Element.prems_of elems)

   | extract_asms_elems ((id, Derived _), _) = (id, []);

 (* activate instantiated facts in theory or context *)

 fun gen_activate_facts_elemss get_reg note attrib std put_reg add_wit

         attn all_elemss new_elemss propss thmss thy_ctxt =

     let

       fun activate_elem disch (prfx, atts) (Notes facts) thy_ctxt =

           let

             val facts' = facts

               (* discharge hyps in attributes *)

               |> Attrib.map_facts (attrib thy_ctxt o Args.map_values I I I disch)

               (* insert interpretation attributes *)

               |> map (apfst (apsnd (fn a => a @ map (attrib thy_ctxt) atts)))

               (* discharge hyps *)

               |> map (apsnd (map (apfst (map disch))));

           in snd (note prfx facts' thy_ctxt) end

         | activate_elem _ _ _ thy_ctxt = thy_ctxt;

       fun activate_elems disch ((id, _), elems) thy_ctxt =

           let

             val ((prfx, atts2), _) = the (get_reg thy_ctxt id)

                 handle Option => sys_error ("Unknown registration of " ^

                   quote (fst id) ^ " while activating facts.");

           in

             fold (activate_elem disch (prfx, atts2)) elems thy_ctxt

           end;

       val thy_ctxt' = thy_ctxt

         (* add registrations *)

         |> fold (fn ((id, _), _) => put_reg id attn) new_elemss

         (* add witnesses of Assumed elements *)

         |> fold (fn (id, thms) => fold (add_wit id) thms) (map fst propss ~~ thmss);

       val prems = flat (map_filter

             (fn ((id, Assumed _), _) => Option.map snd (get_reg thy_ctxt' id)

               | ((_, Derived _), _) => NONE) all_elemss);

       val thy_ctxt'' = thy_ctxt'

         (* add witnesses of Derived elements *)

         |> fold (fn (id, thms) => fold (add_wit id o Element.satisfy_witness prems) thms)

            (map_filter (fn ((_, Assumed _), _) => NONE

               | ((id, Derived thms), _) => SOME (id, thms)) new_elemss)

       val disch' = std o Element.satisfy_thm prems;  (* FIXME *)

     in

       thy_ctxt''

         (* add facts to theory or context *)

         |> fold (activate_elems disch') new_elemss

     end;

 fun global_activate_facts_elemss x = gen_activate_facts_elemss

       (fn thy => fn (name, ps) =>

         get_global_registration thy (name, map Logic.varify ps))

       (global_note_prefix_i "")

       Attrib.attribute_i Drule.standard

       (fn (name, ps) => put_global_registration (name, map Logic.varify ps))

       (fn (n, ps) => add_global_witness (n, map Logic.varify ps) o

         Element.map_witness (fn (t, th) => (Logic.legacy_unvarify t, legacy_unvarify th))

         (* FIXME *)) x;

 fun local_activate_facts_elemss x = gen_activate_facts_elemss

       get_local_registration

       local_note_prefix_i

       (Attrib.attribute_i o ProofContext.theory_of) I

       put_local_registration

       add_local_witness x;

 fun gen_prep_registration mk_ctxt is_local read_terms test_reg activate

     attn expr insts thy_ctxt =

   let

     val ctxt = mk_ctxt thy_ctxt;

     val thy = ProofContext.theory_of ctxt;

     val ctxt' = ctxt |> ProofContext.theory_of |> ProofContext.init;

     val pts = params_of_expr ctxt' [] (intern_expr thy expr)

           ([], Symtab.empty, Symtab.empty);

     val params_ids = make_params_ids (#1 pts);

     val raw_params_elemss = make_raw_params_elemss pts;

     val ((ids, _), raw_elemss) = flatten (ctxt', intern_expr thy)

           (([], Symtab.empty), Expr expr);

     val ((parms, all_elemss, _), (_, (_, defs, _))) =

           read_elemss false ctxt' [] (raw_params_elemss @ raw_elemss) [];

     (** compute instantiation **)

     (* user input *)

     val insts = if length parms < length insts

          then error "More arguments than parameters in instantiation."

          else insts @ replicate (length parms - length insts) NONE;

     val (ps, pTs) = split_list parms;

     val pvTs = map Logic.legacy_varifyT pTs;

     (* instantiations given by user *)

     val given = map_filter (fn (_, (NONE, _)) => NONE

          | (x, (SOME inst, T)) => SOME (x, (inst, T))) (ps ~~ (insts ~~ pvTs));

     val (given_ps, given_insts) = split_list given;

     val tvars = foldr Term.add_typ_tvars [] pvTs;

     val used = foldr Term.add_typ_varnames [] pvTs;

     fun sorts (a, i) = AList.lookup (op =) tvars (a, i);

     val (vs, vinst) = read_terms thy_ctxt sorts used given_insts;

     val vars = foldl Term.add_term_tvar_ixns [] vs \\ map fst tvars;

     val vars' = fold Term.add_varnames vs vars;

     val _ = if null vars' then ()

          else error ("Illegal schematic variable(s) in instantiation: " ^

            commas_quote (map Syntax.string_of_vname vars'));

     (* replace new types (which are TFrees) by ones with new names *)

     val new_Tnames = foldr Term.add_term_tfree_names [] vs;

     val new_Tnames' = Name.invent_list used "'a" (length new_Tnames);

     val renameT =

           if is_local then I

           else Logic.legacy_unvarifyT o Term.map_type_tfree (fn (a, s) =>

             TFree ((the o AList.lookup (op =) (new_Tnames ~~ new_Tnames')) a, s));

     val rename =

           if is_local then I

           else Term.map_types renameT;

     val tinst = Symtab.make (map

                 (fn ((x, 0), T) => (x, T |> renameT)

                   | ((_, n), _) => sys_error "Internal error var in prep_registration") vinst);

     val inst = Symtab.make (given_ps ~~ map rename vs);

     (* defined params without user input *)

     val not_given = map_filter (fn (x, (NONE, T)) => SOME (x, T)

          | (_, (SOME _, _)) => NONE) (ps ~~ (insts ~~ pTs));

     fun add_def (p, pT) inst =

       let

         val (t, T) = case find_first (fn (Free (a, _), _) => a = p) defs of

                NONE => error ("Instance missing for parameter " ^ quote p)

              | SOME (Free (_, T), t) => (t, T);

         val d = Element.inst_term (tinst, inst) t;

       in Symtab.update_new (p, d) inst end;

     val inst = fold add_def not_given inst;

     val insts = (tinst, inst);

     (* Note: insts contain no vars. *)

     (** compute proof obligations **)

     (* restore "small" ids *)

     val ids' = map (fn ((n, ps), (_, mode)) =>

           ((n, map (fn p => Free (p, (the o AList.lookup (op =) parms) p)) ps), mode))

         ids;

     val (_, all_elemss') = chop (length raw_params_elemss) all_elemss

     (* instantiate ids and elements *)

     val inst_elemss = (ids' ~~ all_elemss') |> map (fn (((n, ps), _), ((_, mode), elems)) =>

       ((n, map (Element.inst_term insts) ps),

         map (fn Int e => Element.inst_ctxt thy insts e) elems)

       |> apfst (fn id => (id, map_mode (map (Element.inst_witness thy insts)) mode)));

     (* remove fragments already registered with theory or context *)

     val new_inst_elemss = filter (fn ((id, _), _) =>

           not (test_reg thy_ctxt id)) inst_elemss;

     val new_ids = map #1 new_inst_elemss;

     val propss = map extract_asms_elems new_inst_elemss;

     val bind_attrib = Attrib.crude_closure ctxt o Args.assignable;

     val attn' = apsnd (map (bind_attrib o Attrib.intern_src thy)) attn;

   in (propss, activate attn' inst_elemss new_inst_elemss propss) end;

 val prep_global_registration = gen_prep_registration

      ProofContext.init false

      (fn thy => fn sorts => fn used =>

        Sign.read_def_terms (thy, K NONE, sorts) used true)

      (fn thy => fn (name, ps) =>

        test_global_registration thy (name, map Logic.varify ps))

      global_activate_facts_elemss;

 val prep_local_registration = gen_prep_registration

      I true

      (fn ctxt => ProofContext.read_termTs ctxt (K false) (K NONE))

      smart_test_registration

      local_activate_facts_elemss;

 fun prep_registration_in_locale target expr thy =

   (* target already in internal form *)

   let

     val ctxt = ProofContext.init thy;

     val ((raw_target_ids, target_syn), _) = flatten (ctxt, I)

         (([], Symtab.empty), Expr (Locale target));

     val fixed = the_locale thy target |> #params |> map #1;

     val ((all_ids, syn), raw_elemss) = flatten (ctxt, intern_expr thy)

         ((raw_target_ids, target_syn), Expr expr);

     val (target_ids, ids) = chop (length raw_target_ids) all_ids;

     val ((parms, elemss, _), _) = read_elemss false ctxt fixed raw_elemss [];

     (** compute proof obligations **)

     (* restore "small" ids, with mode *)

     val ids' = map (apsnd snd) ids;

     (* remove Int markers *)

     val elemss' = map (fn (_, es) =>

         map (fn Int e => e) es) elemss

     (* extract assumptions and defs *)

     val ids_elemss = ids' ~~ elemss';

     val propss = map extract_asms_elems ids_elemss;

     (** activation function:

         - add registrations to the target locale

         - add induced registrations for all global registrations of

           the target, unless already present

         - add facts of induced registrations to theory **)

     val t_ids = map_filter

         (fn (id, (_, Assumed _)) => SOME id | _ => NONE) target_ids;

     fun activate thmss thy = let

         val satisfy = Element.satisfy_thm (flat thmss);

         val ids_elemss_thmss = ids_elemss ~~ thmss;

         val regs = get_global_registrations thy target;

         fun activate_id (((id, Assumed _), _), thms) thy =

             thy |> put_registration_in_locale target id

                 |> fold (add_witness_in_locale target id) thms

           | activate_id _ thy = thy;

         fun activate_reg (vts, ((prfx, atts2), _)) thy = let

             val (insts, wits) = collect_global_witnesses thy fixed t_ids vts;

             fun inst_parms ps = map

                   (the o AList.lookup (op =) (map #1 fixed ~~ vts)) ps;

             val disch = Element.satisfy_thm wits;

             val new_elemss = filter (fn (((name, ps), _), _) =>

                 not (test_global_registration thy (name, inst_parms ps))) (ids_elemss);

             fun activate_assumed_id (((_, Derived _), _), _) thy = thy

               | activate_assumed_id ((((name, ps), Assumed _), _), thms) thy = let

                 val ps' = inst_parms ps;

               in

                 if test_global_registration thy (name, ps')

                 then thy

                 else thy

                   |> put_global_registration (name, ps') (prfx, atts2)

                   |> fold (fn witn => fn thy => add_global_witness (name, ps')

                      (Element.inst_witness thy insts witn) thy) thms

               end;

             fun activate_derived_id ((_, Assumed _), _) thy = thy

               | activate_derived_id (((name, ps), Derived ths), _) thy = let

                 val ps' = inst_parms ps;

               in

                 if test_global_registration thy (name, ps')

                 then thy

                 else thy

                   |> put_global_registration (name, ps') (prfx, atts2)

                   |> fold (fn witn => fn thy => add_global_witness (name, ps')

                        (witn |> Element.map_witness (fn (t, th) =>  (* FIXME *)

                        (Element.inst_term insts t,

                         disch (Element.inst_thm thy insts (satisfy th))))) thy) ths

               end;

             fun activate_elem (Notes facts) thy =

                 let

                   val facts' = facts

                       |> Attrib.map_facts (Attrib.attribute_i thy o

                          Args.map_values I (Element.instT_type (#1 insts))

                            (Element.inst_term insts)

                            (disch o Element.inst_thm thy insts o satisfy))

                       |> map (apfst (apsnd (fn a => a @ map (Attrib.attribute thy) atts2)))

                       |> map (apsnd (map (apfst (map (disch o Element.inst_thm thy insts o satisfy)))))

                 in

                   thy

                   |> global_note_prefix_i "" prfx facts'

                   |> snd

                 end

               | activate_elem _ thy = thy;

             fun activate_elems (_, elems) thy = fold activate_elem elems thy;

           in thy |> fold activate_assumed_id ids_elemss_thmss

                  |> fold activate_derived_id ids_elemss

                  |> fold activate_elems new_elemss end;

       in

         thy |> fold activate_id ids_elemss_thmss

             |> fold activate_reg regs

       end;

   in (propss, activate) end;

 fun prep_propp propss = propss |> map (fn (_, props) =>

   (("", []), map (rpair [] o Element.mark_witness) props));

 fun prep_result propps thmss =

   ListPair.map (fn ((_, props), thms) => map2 Element.make_witness props thms) (propps, thmss);

 fun goal_name thy kind target propss =

     kind ^ Proof.goal_names (Option.map (extern thy) target) ""

       (propss |> map (fn ((name, _), _) => extern thy name));

 val global_goal = Proof.global_goal ProofDisplay.present_results

   Attrib.attribute_i ProofContext.bind_propp_schematic_i;

 in

 fun interpretation after_qed (prfx, atts) expr insts thy =

   let

     val (propss, activate) = prep_global_registration (prfx, atts) expr insts thy;

     val kind = goal_name thy "interpretation" NONE propss;

     fun after_qed' results =

       ProofContext.theory (activate (prep_result propss results))

       #> after_qed;

   in

     ProofContext.init thy

     |> Proof.theorem_i kind NONE after_qed' NONE ("", []) (prep_propp propss)

     |> Element.refine_witness |> Seq.hd

   end;

 fun interpretation_in_locale after_qed (raw_target, expr) thy =

   let

     val target = intern thy raw_target;

     val (propss, activate) = prep_registration_in_locale target expr thy;

     val kind = goal_name thy "interpretation" (SOME target) propss;

     val raw_stmt = prep_propp propss;

     val (_, _, goal_ctxt, propp) = thy

       |> ProofContext.init |> init_term_syntax target

       |> cert_context_statement (SOME target) [] (map snd raw_stmt)

     fun after_qed' results =

       ProofContext.theory (activate (prep_result propss results))

       #> after_qed;

   in

     goal_ctxt

     |> global_goal kind NONE after_qed' NONE ("", []) (map fst raw_stmt ~~ propp)

     |> Element.refine_witness |> Seq.hd

   end;

 fun interpret after_qed (prfx, atts) expr insts int state =

   let

     val _ = Proof.assert_forward_or_chain state;

     val ctxt = Proof.context_of state;

     val (propss, activate) = prep_local_registration (prfx, atts) expr insts ctxt;

     val kind = goal_name (Proof.theory_of state) "interpret" NONE propss;

     fun after_qed' results =

       Proof.map_context (K (ctxt |> activate (prep_result propss results)))

       #> Proof.put_facts NONE

       #> after_qed;

   in

     state

     |> Proof.local_goal (ProofDisplay.print_results int) (K I) ProofContext.bind_propp_i

       kind NONE after_qed' (prep_propp propss)

     |> Element.refine_witness |> Seq.hd

   end;

 end;

 end;