(*  Title:      Pure/Isar/expression.ML

     Author:     Clemens Ballarin, TU Muenchen

 New locale development --- experimental.

 *)

 signature EXPRESSION =

 sig

   datatype 'term map = Positional of 'term option list | Named of (string * 'term) list;

   type 'term expr = (string * (string * 'term map)) list;

   type expression = string expr * (Binding.T * string option * mixfix) list;

   type expression_i = term expr * (Binding.T * typ option * mixfix) list;

   (* Processing of context statements *)

   val read_statement: Element.context list -> (string * string list) list list ->

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

   val cert_statement: Element.context_i list -> (term * term list) list list ->

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

   (* Declaring locales *)

   val add_locale_cmd: string -> bstring -> expression -> Element.context list -> theory ->

     string * Proof.context

   val add_locale: string -> bstring -> expression_i -> Element.context_i list -> theory ->

     string * Proof.context

   (* Interpretation *)

   val sublocale_cmd: string -> expression -> theory -> Proof.state;

   val sublocale: string -> expression_i -> theory -> Proof.state;

   val interpretation_cmd: expression -> theory -> Proof.state;

   val interpretation: expression_i -> theory -> Proof.state;

 (*

   val interpret_cmd: Morphism.morphism -> expression -> bool -> Proof.state -> Proof.state;

   val interpret: Morphism.morphism -> expression_i -> bool -> Proof.state -> Proof.state;

 *)

   (* Debugging and development *)

   val parse_expression: OuterParse.token list -> expression * OuterParse.token list

     (* FIXME to spec_parse.ML *)

 end;

 structure Expression : EXPRESSION =

 struct

 datatype ctxt = datatype Element.ctxt;

 (*** Expressions ***)

 datatype 'term map =

   Positional of 'term option list |

   Named of (string * 'term) list;

 type 'term expr = (string * (string * 'term map)) list;

 type expression = string expr * (Binding.T * string option * mixfix) list;

 type expression_i = term expr * (Binding.T * typ option * mixfix) list;

 (** Parsing and printing **)

 local

 structure P = OuterParse;

 val loc_keyword = P.$$$ "fixes" || P.$$$ "constrains" || P.$$$ "assumes" ||

    P.$$$ "defines" || P.$$$ "notes";

 fun plus1_unless test scan =

   scan ::: Scan.repeat (P.$$$ "+" |-- Scan.unless test (P.!!! scan));

 val prefix = P.name --| P.$$$ ":";

 val named = P.name -- (P.$$$ "=" |-- P.term);

 val position = P.maybe P.term;

 val instance = P.$$$ "where" |-- P.and_list1 named >> Named ||

   Scan.repeat1 position >> Positional;

 in

 val parse_expression =

   let

     fun expr2 x = P.xname x;

     fun expr1 x = (Scan.optional prefix "" -- expr2 --

       Scan.optional instance (Named []) >> (fn ((p, l), i) => (l, (p, i)))) x;

     fun expr0 x = (plus1_unless loc_keyword expr1) x;

   in expr0 -- P.for_fixes end;

 end;

 fun pretty_expr thy expr =

   let

     fun pretty_pos NONE = Pretty.str "_"

       | pretty_pos (SOME x) = Pretty.str x;

     fun pretty_named (x, y) = [Pretty.str x, Pretty.brk 1, Pretty.str "=",

           Pretty.brk 1, Pretty.str y] |> Pretty.block;

     fun pretty_ren (Positional ps) = take_suffix is_none ps |> snd |>

           map pretty_pos |> Pretty.breaks

       | pretty_ren (Named []) = []

       | pretty_ren (Named ps) = Pretty.str "where" :: Pretty.brk 1 ::

           (ps |> map pretty_named |> Pretty.separate "and");

     fun pretty_rename (loc, ("", ren)) =

           Pretty.block (Pretty.str (NewLocale.extern thy loc) :: Pretty.brk 1 :: pretty_ren ren) 

       | pretty_rename (loc, (prfx, ren)) =

           Pretty.block (Pretty.str prfx :: Pretty.brk 1 :: Pretty.str (NewLocale.extern thy loc) ::

             Pretty.brk 1 :: pretty_ren ren);

   in Pretty.separate "+" (map pretty_rename expr) |> Pretty.block end;

 fun err_in_expr thy msg expr =

   let

     val err_msg =

       if null expr then msg

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

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

           pretty_expr thy expr])

   in error err_msg end;

 (** Internalise locale names in expr **)

 fun intern thy instances =  map (apfst (NewLocale.intern thy)) instances;

 (** Parameters of expression.

    Sanity check of instantiations and extraction of implicit parameters.

    The latter only occurs iff strict = false.

    Positional instantiations are extended to match full length of parameter list

    of instantiated locale. **)

 fun parameters_of thy strict (expr, fixed) =

   let

     fun reject_dups message xs =

       let val dups = duplicates (op =) xs

       in

         if null dups then () else error (message ^ commas dups)

       end;

     fun match_bind (n, b) = (n = Binding.base_name b);

     fun bind_eq (b1, b2) = (Binding.base_name b1 = Binding.base_name b2);

       (* FIXME: cannot compare bindings for equality. *)

     fun params_loc loc =

           (NewLocale.params_of thy loc |> map (fn (p, _, mx) => (p, mx)), loc);

     fun params_inst (expr as (loc, (prfx, Positional insts))) =

           let

             val (ps, loc') = params_loc loc;

 	    val d = length ps - length insts;

 	    val insts' =

 	      if d < 0 then error ("More arguments than parameters in instantiation of locale " ^

                 quote (NewLocale.extern thy loc))

 	      else insts @ replicate d NONE;

             val ps' = (ps ~~ insts') |>

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

           in (ps', (loc', (prfx, Positional insts'))) end

       | params_inst (expr as (loc, (prfx, Named insts))) =

           let

             val _ = reject_dups "Duplicate instantiation of the following parameter(s): "

               (map fst insts);

             val (ps, loc') = params_loc loc;

             val ps' = fold (fn (p, _) => fn ps =>

               if AList.defined match_bind ps p then AList.delete match_bind p ps

               else error (quote p ^" not a parameter of instantiated expression.")) insts ps;

           in (ps', (loc', (prfx, Named insts))) end;

     fun params_expr is =

           let

             val (is', ps') = fold_map (fn i => fn ps =>

               let

                 val (ps', i') = params_inst i;

                 val ps'' = AList.join bind_eq (fn p => fn (mx1, mx2) =>

                   (* FIXME: should check for bindings being the same.

                      Instead we check for equal name and syntax. *)

                   if mx1 = mx2 then mx1

                   else error ("Conflicting syntax for parameter" ^ quote (Binding.display p) ^

                     " in expression.")) (ps, ps')

               in (i', ps'') end) is []

           in (ps', is') end;

     val (implicit, expr') = params_expr expr;

     val implicit' = map (#1 #> Binding.base_name) implicit;

     val fixed' = map (#1 #> Binding.base_name) fixed;

     val _ = reject_dups "Duplicate fixed parameter(s): " fixed';

     val implicit'' = if strict then []

       else let val _ = reject_dups

           "Parameter(s) declared simultaneously in expression and for clause: " (implicit' @ fixed')

         in map (fn (b, mx) => (b, NONE, mx)) implicit end;

   in (expr', implicit'' @ fixed) end;

 (** Read instantiation **)

 (* Parse positional or named instantiation *)

 local

 fun prep_inst parse_term parms (Positional insts) ctxt =

       (insts ~~ parms) |> map (fn

         (NONE, p) => Syntax.parse_term ctxt p |

         (SOME t, _) => parse_term ctxt t)

   | prep_inst parse_term parms (Named insts) ctxt =

       parms |> map (fn p => case AList.lookup (op =) insts p of

         SOME t => parse_term ctxt t |

         NONE => Syntax.parse_term ctxt p);

 in

 fun parse_inst x = prep_inst Syntax.parse_term x;

 fun make_inst x = prep_inst (K I) x;

 end;

 (* Instantiation morphism *)

 fun inst_morph (parm_names, parm_types) (prfx, insts') ctxt =

   let

     (* parameters *)

     val type_parm_names = fold Term.add_tfreesT parm_types [] |> map fst;

     (* type inference and contexts *)

     val parm_types' = map (TypeInfer.paramify_vars o Logic.varifyT) parm_types;

     val type_parms = fold Term.add_tvarsT parm_types' [] |> map (Logic.mk_type o TVar);

     val arg = type_parms @ map2 TypeInfer.constrain parm_types' insts';

     val res = Syntax.check_terms ctxt arg;

     val ctxt' = ctxt |> fold Variable.auto_fixes res;

     (* instantiation *)

     val (type_parms'', res') = chop (length type_parms) res;

     val insts'' = (parm_names ~~ res') |> map_filter

       (fn (inst as (x, Free (y, _))) => if x = y then NONE else SOME inst |

         inst => SOME inst);

     val instT = Symtab.make (type_parm_names ~~ map Logic.dest_type type_parms'');

     val inst = Symtab.make insts'';

   in

     (Element.inst_morphism (ProofContext.theory_of ctxt) (instT, inst) $>

       Morphism.binding_morphism (Binding.qualify prfx), ctxt')

   end;

 (*** Locale processing ***)

 (** Parsing **)

 fun parse_elem prep_typ prep_term ctxt elem =

   Element.map_ctxt {binding = I, var = I, typ = prep_typ ctxt,

     term = prep_term ctxt, fact = I, attrib = I} elem;

 fun parse_concl prep_term ctxt concl =

   (map o map) (fn (t, ps) =>

     (prep_term ctxt, map (prep_term ctxt) ps)) concl;

 (** Simultaneous type inference: instantiations + elements + conclusion **)

 local

 fun mk_type T = (Logic.mk_type T, []);

 fun mk_term t = (t, []);

 fun mk_propp (p, pats) = (Syntax.type_constraint propT p, pats);

 fun dest_type (T, []) = Logic.dest_type T;

 fun dest_term (t, []) = t;

 fun dest_propp (p, pats) = (p, pats);

 fun extract_inst (_, (_, ts)) = map mk_term ts;

 fun restore_inst ((l, (p, _)), cs) = (l, (p, map dest_term cs));

 fun extract_elem (Fixes fixes) = map (#2 #> the_list #> map mk_type) fixes

   | extract_elem (Constrains csts) = map (#2 #> single #> map mk_type) csts

   | extract_elem (Assumes asms) = map (#2 #> map mk_propp) asms

   | extract_elem (Defines defs) = map (fn (_, (t, ps)) => [mk_propp (t, ps)]) defs

   | extract_elem (Notes _) = [];

 fun restore_elem (Fixes fixes, css) =

       (fixes ~~ css) |> map (fn ((x, _, mx), cs) =>

         (x, cs |> map dest_type |> try hd, mx)) |> Fixes

   | restore_elem (Constrains csts, css) =

       (csts ~~ css) |> map (fn ((x, _), cs) =>

         (x, cs |> map dest_type |> hd)) |> Constrains

   | restore_elem (Assumes asms, css) =

       (asms ~~ css) |> map (fn ((b, _), cs) => (b, map dest_propp cs)) |> Assumes

   | restore_elem (Defines defs, css) =

       (defs ~~ css) |> map (fn ((b, _), [c]) => (b, dest_propp c)) |> Defines

   | restore_elem (Notes notes, _) = Notes notes;

 fun check cs context =

   let

     fun prep (_, pats) (ctxt, t :: ts) =

       let val ctxt' = Variable.auto_fixes t ctxt

       in

         ((t, Syntax.check_props (ProofContext.set_mode ProofContext.mode_pattern ctxt') pats),

           (ctxt', ts))

       end

     val (cs', (context', _)) = fold_map prep cs

       (context, Syntax.check_terms

         (ProofContext.set_mode ProofContext.mode_schematic context) (map fst cs));

   in (cs', context') end;

 in

 fun check_autofix insts elems concl ctxt =

   let

     val inst_cs = map extract_inst insts;

     val elem_css = map extract_elem elems;

     val concl_cs = (map o map) mk_propp concl;

     (* Type inference *)

     val (inst_cs' :: css', ctxt') =

       (fold_burrow o fold_burrow) check (inst_cs :: elem_css @ [concl_cs]) ctxt;

     val (elem_css', [concl_cs']) = chop (length elem_css) css';

   in

     (map restore_inst (insts ~~ inst_cs'), map restore_elem (elems ~~ elem_css'),

       concl_cs', ctxt')

   end;

 end;

 (** Prepare locale elements **)

 fun declare_elem prep_vars (Fixes fixes) ctxt =

       let val (vars, _) = prep_vars fixes ctxt

       in ctxt |> ProofContext.add_fixes_i vars |> snd end

   | declare_elem prep_vars (Constrains csts) ctxt =

       ctxt |> prep_vars (map (fn (x, T) => (Binding.name x, SOME T, NoSyn)) csts) |> snd

   | declare_elem _ (Assumes _) ctxt = ctxt

   | declare_elem _ (Defines _) ctxt = ctxt

   | declare_elem _ (Notes _) ctxt = ctxt;

 (** Finish locale elements, extract specification text **)

 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 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 = error (msg ^ ": " ^ quote y);

   in

     exists (fn (x, _) => x = y) xs andalso

       err "Attempt to define previously specified variable";

     exists (fn (Free (y', _), _) => y = y' | _ => false) env andalso

       err "Attempt to redefine variable";

     (Term.add_frees b' xs, (Free (y, T), b') :: env, th :: ths)

   end;

 fun eval_text _ _ (Fixes _) text = text

   | eval_text _ _ (Constrains _) text = text

   | eval_text _ 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 ctxt _ (Defines defs) (spec, binds) =

       (spec, fold (bind_def ctxt o #1 o #2) defs binds)

   | eval_text _ _ (Notes _) text = text;

 fun closeup _ _ false elem = elem

   | closeup ctxt parms true elem =

       let

         fun close_frees t =

           let

             val rev_frees =

               Term.fold_aterms (fn Free (x, T) =>

                 if AList.defined (op =) parms x then I else insert (op =) (x, T) | _ => I) t [];

           in Term.list_all_free (rev rev_frees, t) end;

         fun no_binds [] = []

           | no_binds _ = error "Illegal term bindings in context 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_primitive parms _ (Fixes fixes) = Fixes (map (fn (binding, _, mx) =>

       let val x = Binding.base_name binding

       in (binding, AList.lookup (op =) parms x, mx) end) fixes)

   | finish_primitive _ _ (Constrains _) = Constrains []

   | finish_primitive _ close (Assumes asms) = close (Assumes asms)

   | finish_primitive _ close (Defines defs) = close (Defines defs)

   | finish_primitive _ _ (Notes facts) = Notes facts;

 fun finish_inst ctxt parms do_close (loc, (prfx, inst)) text =

   let

     val thy = ProofContext.theory_of ctxt;

     val (parm_names, parm_types) = NewLocale.params_of thy loc |>

       map (fn (b, SOME T, _) => (Binding.base_name b, T)) |> split_list;

     val (asm, defs) = NewLocale.specification_of thy loc;

     val (morph, _) = inst_morph (parm_names, parm_types) (prfx, inst) ctxt;

     val asm' = Option.map (Morphism.term morph) asm;

     val defs' = map (Morphism.term morph) defs;

     val text' = text |>

       (if is_some asm

         then eval_text ctxt false (Assumes [(Attrib.empty_binding, [(the asm', [])])])

         else I) |>

       (if not (null defs)

         then eval_text ctxt false (Defines (map (fn def => (Attrib.empty_binding, (def, []))) defs'))

         else I)

 (* FIXME clone from new_locale.ML *)

   in ((loc, morph), text') end;

 fun finish_elem ctxt parms do_close elem text =

   let

     val elem' = finish_primitive parms (closeup ctxt parms do_close) elem;

     val text' = eval_text ctxt true elem' text;

   in (elem', text') end

 fun finish ctxt parms do_close insts elems text =

   let

     val (deps, text') = fold_map (finish_inst ctxt parms do_close) insts text;

     val (elems', text'') = fold_map (finish_elem ctxt parms do_close) elems text';

   in (deps, elems', text'') end;

 (** Process full context statement: instantiations + elements + conclusion **)

 (* Interleave incremental parsing and type inference over entire parsed stretch. *)

 local

 fun prep_full_context_statement parse_typ parse_prop parse_inst prep_vars prep_expr

     strict do_close context raw_import raw_elems raw_concl =

   let

     val thy = ProofContext.theory_of context;

     val (raw_insts, fixed) = parameters_of thy strict (apfst (prep_expr thy) raw_import);

     fun prep_inst (loc, (prfx, inst)) (i, insts, ctxt) =

       let

         val (parm_names, parm_types) = NewLocale.params_of thy loc |>

           map (fn (b, SOME T, _) => (Binding.base_name b, T)) |> split_list;

         val inst' = parse_inst parm_names inst ctxt;

         val parm_types' = map (TypeInfer.paramify_vars o

           Term.map_type_tvar (fn ((x, _), S) => TVar ((x, i), S)) o Logic.varifyT) parm_types;

         val inst'' = map2 TypeInfer.constrain parm_types' inst';

         val insts' = insts @ [(loc, (prfx, inst''))];

         val (insts'', _, _, ctxt' (* FIXME not used *) ) = check_autofix insts' [] [] ctxt;

         val inst''' = insts'' |> List.last |> snd |> snd;

         val (morph, _) = inst_morph (parm_names, parm_types) (prfx, inst''') ctxt;

         val ctxt'' = NewLocale.activate_declarations thy (loc, morph) ctxt;

       in (i+1, insts', ctxt'') end;

     fun prep_elem raw_elem (insts, elems, ctxt) =

       let

         val ctxt' = declare_elem prep_vars raw_elem ctxt;

         val elems' = elems @ [parse_elem parse_typ parse_prop ctxt' raw_elem];

         (* FIXME term bindings *)

         val (_, _, _, ctxt'') = check_autofix insts elems' [] ctxt';

       in (insts, elems', ctxt') end;

     fun prep_concl raw_concl (insts, elems, ctxt) =

       let

         val concl = (map o map) (fn (t, ps) =>

           (parse_prop ctxt t, map (parse_prop ctxt) ps)) raw_concl;

       in check_autofix insts elems concl ctxt end;

     val fors = prep_vars fixed context |> fst;

     val ctxt = context |> ProofContext.add_fixes_i fors |> snd;

     val (_, insts', ctxt') = fold prep_inst raw_insts (0, [], NewLocale.clear_local_idents ctxt);

     val (_, elems'', ctxt'') = fold prep_elem raw_elems (insts', [], ctxt');

     val (insts, elems, concl, ctxt) = prep_concl raw_concl (insts', elems'', ctxt'');

     (* Retrieve parameter types *)

     val xs = fold (fn Fixes fixes => (fn ps => ps @ map (Binding.base_name o #1) fixes) |

       _ => fn ps => ps) (Fixes fors :: elems) [];

     val (Ts, ctxt') = fold_map ProofContext.inferred_param xs ctxt; 

     val parms = xs ~~ Ts;  (* params from expression and elements *)

     val Fixes fors' = finish_primitive parms I (Fixes fors);

     val (deps, elems', text) = finish ctxt' parms do_close insts elems ((([], []), ([], [])), ([], [], []));

     (* text has the following structure:

            (((exts, exts'), (ints, ints')), (xs, env, defs))

        where

          exts: external assumptions (terms in assumes elements)

          exts': dito, normalised wrt. env

          ints: internal assumptions (terms in assumptions from insts)

          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).

        elems is an updated version of raw_elems:

          - 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 ((fors', deps, elems', concl), (parms, text)) end

 in

 fun read_full_context_statement x =

   prep_full_context_statement Syntax.parse_typ Syntax.parse_prop parse_inst

   ProofContext.read_vars intern x;

 fun cert_full_context_statement x =

   prep_full_context_statement (K I) (K I) make_inst ProofContext.cert_vars (K I) x;

 end;

 (* Context statement: elements + conclusion *)

 local

 fun prep_statement prep activate raw_elems raw_concl context =

   let

      val ((_, _, elems, concl), _) = prep true false context ([], []) raw_elems raw_concl;

      val (_, context') = activate elems (ProofContext.set_stmt true context);

   in (concl, context') end;

 in

 fun read_statement x = prep_statement read_full_context_statement Element.activate x;

 fun cert_statement x = prep_statement cert_full_context_statement Element.activate_i x;

 end;

 (* Locale declaration: import + elements *)

 local

 fun prep_declaration prep activate raw_import raw_elems context =

   let

     val thy = ProofContext.theory_of context;

     val ((fixed, deps, elems, _), (parms, (spec, (_, _, defs)))) =

       prep false true context raw_import raw_elems [];

     (* Declare parameters and imported facts *)

     val context' = context |>

       ProofContext.add_fixes_i fixed |> snd |>

       NewLocale.clear_local_idents |> fold (NewLocale.activate_local_facts thy) deps;

     val ((elems', _), _) = activate elems (ProofContext.set_stmt true context');

   in ((fixed, deps, elems'), (parms, spec, defs)) end;

 in

 fun read_declaration x = prep_declaration read_full_context_statement Element.activate x;

 fun cert_declaration x = prep_declaration cert_full_context_statement Element.activate_i x;

 end;

 (* Locale expression to set up a goal *)

 local

 fun props_of thy (name, morph) =

   let

     val (asm, defs) = NewLocale.specification_of thy name;

   in

     (case asm of NONE => defs | SOME asm => asm :: defs) |> map (Morphism.term morph)

   end;

 fun prep_goal_expression prep expression context =

   let

     val thy = ProofContext.theory_of context;

     val ((fixed, deps, _, _), _) = prep true true context expression [] [];

     (* proof obligations *)

     val propss = map (props_of thy) deps;

     val goal_ctxt = context |>

       ProofContext.add_fixes_i fixed |> snd |>

       (fold o fold) Variable.auto_fixes propss;

     val export = Variable.export_morphism goal_ctxt context;

     val exp_fact = Drule.zero_var_indexes_list o map Thm.strip_shyps o Morphism.fact export;

 (*    val exp_term = TermSubst.zero_var_indexes o Morphism.term export; *)

     val exp_term = Drule.term_rule thy (singleton exp_fact);

     val exp_typ = Logic.type_map exp_term;

     val export' =

       Morphism.morphism {binding = I, var = I, typ = exp_typ, term = exp_term, fact = exp_fact};

   in ((propss, deps, export'), goal_ctxt) end;

 in

 fun read_goal_expression x = prep_goal_expression read_full_context_statement x;

 fun cert_goal_expression x = prep_goal_expression cert_full_context_statement x;

 end;

 (*** Locale declarations ***)

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

      also name suffix of delta predicates and assumptions. *)

 val axiomsN = "axioms";

 local

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

      delta predicates *)

 val introN = "intro";

 fun atomize_spec thy ts =

   let

     val t = Logic.mk_conjunction_balanced 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 (Thm.cterm_of thy t))

   end;

 (* achieve plain syntax for locale predicates (without "PROP") *)

 fun aprop_tr' n c = (Syntax.constN ^ c, fn ctxt => fn args =>

   if length args = n then

     Syntax.const "_aprop" $

       Term.list_comb (Syntax.free (Consts.extern (ProofContext.consts_of ctxt) c), args)

   else raise Match);

 (* 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_bname 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 \\ fold Term.add_tfreesT 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

       |> bodyT = propT ? Sign.add_advanced_trfuns ([], [], [aprop_tr' (length args) name], [])

       |> Sign.declare_const [] ((Binding.name bname, predT), NoSyn) |> snd

       |> PureThy.add_defs false

         [((Thm.def_name bname, Logic.mk_equals (head, body)), [Thm.kind_internal])];

     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 _ =>

       MetaSimplifier.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_balanced (map (Thm.assume o cert) norm_ts), 0) 1);

     val conjuncts =

       (Drule.equal_elim_rule2 OF [body_eq,

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

       |> Conjunction.elim_balanced (length ts);

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

       Element.prove_witness defs_ctxt t

        (MetaSimplifier.rewrite_goals_tac defs THEN

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

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

 in

 (* CB: main predicate definition function *)

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

   let

     val (a_pred, a_intro, a_axioms, thy'') =

       if null exts then (NONE, NONE, [], thy)

       else

         let

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

           val ((statement, intro, axioms), thy') =

             thy

             |> def_pred aname parms defs exts exts';

           val (_, thy'') =

             thy'

             |> Sign.add_path aname

             |> Sign.no_base_names

             |> PureThy.note_thmss Thm.internalK

               [((Binding.name introN, []), [([intro], [NewLocale.unfold_attrib])])]

             ||> Sign.restore_naming thy';

           in (SOME statement, SOME intro, axioms, thy'') end;

     val (b_pred, b_intro, b_axioms, thy'''') =

       if null ints then (NONE, NONE, [], thy'')

       else

         let

           val ((statement, intro, axioms), thy''') =

             thy''

             |> def_pred pname parms defs (ints @ the_list a_pred) (ints' @ the_list a_pred);

           val (_, thy'''') =

             thy'''

             |> Sign.add_path pname

             |> Sign.no_base_names

             |> PureThy.note_thmss Thm.internalK

                  [((Binding.name introN, []), [([intro], [NewLocale.intro_attrib])]),

                   ((Binding.name axiomsN, []),

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

             ||> Sign.restore_naming thy''';

         in (SOME statement, SOME intro, axioms, thy'''') end;

   in ((a_pred, a_intro, a_axioms), (b_pred, b_intro, b_axioms), thy'''') end;

 end;

 local

 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 (curry Notes Thm.assumptionK)

   | assumes_to_notes e axms = (e, axms);

 fun defines_to_notes 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

       (Notes (Thm.definitionK, notes), defns @ defs')

     end

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

 fun gen_add_locale prep_decl

     bname predicate_name raw_imprt raw_body thy =

   let

     val thy_ctxt = ProofContext.init thy;

     val name = Sign.full_bname thy bname;

     val _ = NewLocale.test_locale thy name andalso

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

     val ((fixed, deps, body_elems), text as (parms, ((_, exts'), _), defs)) =

       prep_decl raw_imprt raw_body thy_ctxt;

     val ((a_statement, a_intro, a_axioms), (b_statement, b_intro, b_axioms), thy') =

       define_preds predicate_name text thy;

     val extraTs = fold Term.add_tfrees exts' [] \\ fold Term.add_tfreesT (map snd parms) [];

     val _ = if null extraTs then ()

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

     val satisfy = Element.satisfy_morphism b_axioms;

     val params = fixed @

       (body_elems |> map_filter (fn Fixes fixes => SOME fixes | _ => NONE) |> flat);

     val asm = if is_some b_statement then b_statement else a_statement;

     val (body_elems', defns) = fold_map (defines_to_notes thy') body_elems [];

     val notes = body_elems' |>

       (fn elems => fold_map assumes_to_notes elems (map Element.conclude_witness a_axioms)) |>

       fst |> map (Element.morph_ctxt satisfy) |>

       map_filter (fn Notes notes => SOME notes | _ => NONE) |>

       (if is_some asm

         then cons (Thm.internalK, [((Binding.name (bname ^ "_" ^ axiomsN), []),

           [([assume (cterm_of thy' (the asm))], [(Attrib.internal o K) NewLocale.witness_attrib])])])

         else I);

     val deps' = map (fn (l, morph) => (l, morph $> satisfy)) deps;

     val loc_ctxt = thy' |>

       NewLocale.register_locale bname (extraTs, params)

         (asm, map prop_of defs) ([], [])

         (map (fn n => (n, stamp ())) notes |> rev) (map (fn d => (d, stamp ())) deps' |> rev) |>

       NewLocale.init name

   in (name, loc_ctxt) end;

 in

 val add_locale_cmd = gen_add_locale read_declaration;

 val add_locale = gen_add_locale cert_declaration;

 end;

 (*** Interpretation ***)

 (** Witnesses and goals **)

 fun prep_propp propss = propss |> map (map (rpair [] o Element.mark_witness));

 fun prep_result propps thmss =

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

 (** Interpretation between locales: declaring sublocale relationships **)

 local

 fun gen_sublocale prep_expr intern

     raw_target expression thy =

   let

     val target = intern thy raw_target;

     val target_ctxt = NewLocale.init target thy;

     val ((propss, deps, export), goal_ctxt) = prep_expr expression target_ctxt;

     fun store_dep ((name, morph), thms) =

       NewLocale.add_dependency target (name, morph $> Element.satisfy_morphism thms $> export);

     fun after_qed results =

       ProofContext.theory (

         (* store dependencies *)

         fold store_dep (deps ~~ prep_result propss results) #>

         (* propagate registrations *)

         (fn thy => fold_rev (fn reg => NewLocale.activate_global_facts reg)

           (NewLocale.get_global_registrations thy) thy));

   in

     goal_ctxt |>

       Proof.theorem_i NONE after_qed (prep_propp propss) |>

       Element.refine_witness |> Seq.hd

   end;

 in

 fun sublocale_cmd x = gen_sublocale read_goal_expression NewLocale.intern x;

 fun sublocale x = gen_sublocale cert_goal_expression (K I) x;

 end;

 (** Interpretation in theories **)

 local

 fun gen_interpretation prep_expr

     expression thy =

   let

     val ctxt = ProofContext.init thy;

     val ((propss, deps, export), goal_ctxt) = prep_expr expression ctxt;

     fun store_reg ((name, morph), thms) =

       let

         val morph' = morph $> Element.satisfy_morphism thms $> export;

       in

         NewLocale.add_global_registration (name, morph') #>

         NewLocale.activate_global_facts (name, morph')

       end;

     fun after_qed results =

       ProofContext.theory (fold store_reg (deps ~~ prep_result propss results));

   in

     goal_ctxt |>

       Proof.theorem_i NONE after_qed (prep_propp propss) |>

       Element.refine_witness |> Seq.hd

   end;

 in

 fun interpretation_cmd x = gen_interpretation read_goal_expression x;

 fun interpretation x = gen_interpretation cert_goal_expression x;

 end;

 end;