(*  Title:      Pure/Isar/expression.ML

     Author:     Clemens Ballarin, TU Muenchen

 Locale expressions and user interface layer of locales.

 *)

 signature EXPRESSION =

 sig

   (* Locale expressions *)

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

   type 'term rewrites = (Attrib.binding * 'term) list

   type ('name, 'term) expr = ('name * ((string * bool) * ('term map * 'term rewrites))) list

   type expression_i = (string, term) expr * (binding * typ option * mixfix) list

   type expression = (xstring * Position.T, string) expr * (binding * string option * mixfix) list

   (* Processing of context statements *)

   val cert_statement: Element.context_i list -> Element.statement_i ->

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

   val read_statement: Element.context list -> Element.statement ->

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

   (* Declaring locales *)

   val cert_declaration: expression_i -> (Proof.context -> Proof.context) ->

     Element.context_i list ->

     Proof.context -> (((string * typ) * mixfix) list * (string * morphism) list

       * Element.context_i list * Proof.context) * ((string * typ) list * Proof.context)

   val cert_read_declaration: expression_i -> (Proof.context -> Proof.context) ->

     Element.context list ->

     Proof.context -> (((string * typ) * mixfix) list * (string * morphism) list

       * Element.context_i list * Proof.context) * ((string * typ) list * Proof.context)

       (*FIXME*)

   val read_declaration: expression -> (Proof.context -> Proof.context) -> Element.context list ->

     Proof.context -> (((string * typ) * mixfix) list * (string * morphism) list

       * Element.context_i list * Proof.context) * ((string * typ) list * Proof.context)

   val add_locale: binding -> binding ->

     expression_i -> Element.context_i list -> theory -> string * local_theory

   val add_locale_cmd: binding -> binding ->

     expression -> Element.context list -> theory -> string * local_theory

   (* Processing of locale expressions *)

   val cert_goal_expression: expression_i -> Proof.context ->

     (term list list * term list list * (string * morphism) list * (Attrib.binding * term) list list * morphism) * Proof.context

   val read_goal_expression: expression -> Proof.context ->

     (term list list * term list list * (string * morphism) list * (Attrib.binding * term) list list * morphism) * Proof.context

 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 rewrites = (Attrib.binding * 'term) list;

 type ('name, 'term) expr = ('name * ((string * bool) * ('term map * 'term rewrites))) list;

 type expression_i = (string, term) expr * (binding * typ option * mixfix) list;

 type expression = (xstring * Position.T, string) expr * (binding * string option * mixfix) list;

 (** Internalise locale names in expr **)

 fun check_expr thy instances = map (apfst (Locale.check 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

     val ctxt = Proof_Context.init_global thy;

     fun reject_dups message xs =

       (case duplicates (op =) xs of

         [] => ()

       | dups => error (message ^ commas dups));

     fun parm_eq ((p1, mx1), (p2, mx2)) =

       p1 = p2 andalso

         (Mixfix.equal (mx1, mx2) orelse

           error ("Conflicting syntax for parameter " ^ quote p1 ^ " in expression" ^

             Position.here_list [Mixfix.pos_of mx1, Mixfix.pos_of mx2]));

     fun params_loc loc = Locale.params_of thy loc |> map (apfst #1);

     fun params_inst (loc, (prfx, (Positional insts, eqns))) =

           let

             val ps = 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 (Locale.markup_name ctxt 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', eqns)))) end

       | params_inst (loc, (prfx, (Named insts, eqns))) =

           let

             val _ =

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

                 (map fst insts);

             val ps' = (insts, params_loc loc) |-> fold (fn (p, _) => fn ps =>

               if AList.defined (op =) ps p then AList.delete (op =) p ps

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

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

     fun params_expr is =

       let

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

           let

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

             val ps'' = distinct parm_eq (ps @ ps');

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

       in (ps', is') end;

     val (implicit, expr') = params_expr expr;

     val implicit' = map #1 implicit;

     val fixed' = map (Variable.check_name o #1) 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 (x, mx) => (Binding.name x, NONE, mx)) implicit end;

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

 (** Read instantiation **)

 (* Parse positional or named instantiation *)

 (*1*)local(*1*)

 fun prep_inst prep_term ctxt parms (Positional insts) =

       (insts ~~ parms) |> map

         (fn (NONE, p) => Free (p, dummyT)

           | (SOME t, _) => prep_term ctxt t)

   | prep_inst prep_term ctxt parms (Named insts) =

       parms |> map (fn p =>

         (case AList.lookup (op =) insts p of

           SOME t => prep_term ctxt t |

           NONE => Free (p, dummyT)));

 (*1*)in(*1*)

 fun parse_inst x = prep_inst Syntax.parse_term x;

 fun make_inst x = prep_inst (K I) x;

 (*1*)end;(*1*)

 (* Instantiation morphism *)

 (*val inst_morphism: (string * typ) list -> (string * bool) * term list -> Proof.context ->

         morphism * Proof.context*)

 fun inst_morphism params ((prfx, mandatory), insts') ctxt =

   let

 (** )val _ = writeln "#### Expression.inst_morphism";( **)

     (* parameters *)

     val parm_types = map #2 (params: (string * typ) list);

     val type_parms = fold Term.add_tfreesT parm_types [];

     (* type inference *)

     val parm_types' = map (Type_Infer.paramify_vars o Logic.varifyT_global) parm_types;

     val type_parms' = fold Term.add_tvarsT parm_types' [];

     val checked =

       (map (Logic.mk_type o TVar) type_parms' @ map2 Type.constraint parm_types' insts')

       |> Syntax.check_terms (Config.put Type_Infer.object_logic false ctxt)

     val (type_parms'', insts'') = chop (length type_parms') checked;

     (* context *)

     val ctxt' = fold Proof_Context.augment checked ctxt;

     val certT = Thm.trim_context_ctyp o Thm.ctyp_of ctxt';

     val cert = Thm.trim_context_cterm o Thm.cterm_of ctxt';

     (* instantiation *)

     val instT =

       (type_parms ~~ map Logic.dest_type type_parms'')

       |> map_filter (fn (v, T) => if TFree v = T then NONE else SOME (v, T));

     val cert_inst =

       ((map #1 params ~~ map (Term_Subst.instantiateT_frees instT) parm_types) ~~ insts'')

       |> map_filter (fn (v, t) => if Free v = t then NONE else SOME (v, cert t));

   in

     (Element.instantiate_normalize_morphism (map (apsnd certT) instT, cert_inst) $>

       Morphism.binding_morphism "Expression.inst" (Binding.prefix mandatory prfx), ctxt')

   end;

 (*** Locale processing ***)

 (** Parsing **)

 fun parse_elem prep_typ prep_term ctxt =

   Element.map_ctxt

    {binding = I,

     typ = prep_typ ctxt,

     term = prep_term (Proof_Context.set_mode Proof_Context.mode_schematic ctxt),

     pattern = prep_term (Proof_Context.set_mode Proof_Context.mode_pattern ctxt),

     fact = I,

     attrib = I};

 fun prepare_stmt prep_prop prep_obtains ctxt stmt =

   (case stmt of

     Element.Shows raw_shows =>

       raw_shows |> (map o apsnd o map) (fn (t, ps) =>

         (prep_prop (Proof_Context.set_mode Proof_Context.mode_schematic ctxt) t,

           map (prep_prop (Proof_Context.set_mode Proof_Context.mode_pattern ctxt)) ps))

   | Element.Obtains raw_obtains =>

       let

         val ((_, thesis), thesis_ctxt) = Obtain.obtain_thesis ctxt;

         val obtains = prep_obtains thesis_ctxt thesis raw_obtains;

       in map (fn (b, t) => ((b, []), [(t, [])])) obtains end);

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

 (*2*)local(*2*)

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

 fun mk_term t = (t, []);

 fun mk_propp (p, pats) = (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_eqns es = map (mk_term o snd) es;

 fun restore_eqns (es, cs) = map2 (fn (b, _) => fn c => (b, dest_term c)) es 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 _) = []

   | extract_elem (Lazy_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 (elem as Notes _, _) = elem

   | restore_elem (elem as Lazy_Notes _, _) = elem;

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

   let

 (** )val _ = writeln "##### Expression.prep";((**)**)

     val ctxt' = Proof_Context.augment t ctxt

   in

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

       (ctxt', ts))

   end;

 (* val check: (term * term list) list -> Proof.context ->

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

 fun check cs ctxt =

   let

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

       (ctxt, Syntax.check_terms

         (Proof_Context.set_mode Proof_Context.mode_schematic ctxt) (map fst cs));

   in (cs', ctxt') end;

 (*2*)in(*2*)

 fun check_autofix insts eqnss elems concl ctxt =

   let

 (** )val _ = writeln "##### Expression.check_autofix";( **)

     val inst_cs = map extract_inst insts;

     val eqns_cs = map extract_eqns eqnss;

     val elem_css = map extract_elem elems;

     val concl_cs = (map o map) mk_propp (map snd concl);

     (* Type inference *)

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

       (fold_burrow o fold_burrow) check (inst_cs :: eqns_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_eqns (eqnss ~~ eqns_cs'),

       map restore_elem (elems ~~ elem_css'),

       map fst concl ~~ concl_cs'), ctxt')

   end;

 (*2*)end;(*2*)

 (** Prepare locale elements **)

 fun declare_elem prep_var (Fixes fixes) ctxt =

       let val (vars, _) = fold_map prep_var fixes ctxt

       in ctxt |> Proof_Context.add_fixes vars |> snd end

   | declare_elem prep_var (Constrains csts) ctxt =

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

   | declare_elem _ (Assumes _) ctxt = ctxt

   | declare_elem _ (Defines _) ctxt = ctxt

   | declare_elem _ (Notes _) ctxt = ctxt

   | declare_elem _ (Lazy_Notes _) ctxt = ctxt;

 (** Finish locale elements **)

 fun finish_inst ctxt (loc, (prfx, inst)) =

   let

     val thy = Proof_Context.theory_of ctxt;

     val (morph, _) = inst_morphism (map #1 (Locale.params_of thy loc)) (prfx, inst) ctxt;

   in (loc, morph) end;

 fun finish_fixes (parms: (string * typ) list) = map (fn (binding, _, mx) =>

   let val x = Binding.name_of binding

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

 (*3*)local(*3*)

 fun closeup _ _ false elem = elem

   | closeup (outer_ctxt, ctxt) parms true elem =

       let

         (* FIXME consider closing in syntactic phase -- before type checking *)

         fun close_frees t =

           let

             val rev_frees =

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

                 if Variable.is_fixed outer_ctxt x orelse AList.defined (op =) parms x then I

                 else insert (op =) (x, T) | _ => I) t [];

           in fold (Logic.all o Free) 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 ((name, atts), (t, ps)) =>

             let val ((c, _), t') = Local_Defs.cert_def ctxt (K []) (close_frees t)

             in ((Thm.def_binding_optional (Binding.name c) name, atts), (t', no_binds ps)) end))

         | e => e)

       end;

 (*3*)in(*3*)

 fun finish_elem _ parms _ (Fixes fixes) = Fixes (finish_fixes parms fixes)

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

   | finish_elem ctxts parms do_close (Assumes asms) = closeup ctxts parms do_close (Assumes asms)

   | finish_elem ctxts parms do_close (Defines defs) = closeup ctxts parms do_close (Defines defs)

   | finish_elem _ _ _ (elem as Notes _) = elem

   | finish_elem _ _ _ (elem as Lazy_Notes _) = elem;

 (*3*)end;(*3*)

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

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

 (*4*)local(*4*)

 fun abs_def ctxt =

   Thm.cterm_of ctxt #> Assumption.assume ctxt #> Local_Defs.abs_def_rule ctxt #> Thm.prop_of;

 fun prep_full_context_statement

     parse_typ parse_prop prep_obtains prep_var_elem prep_inst prep_eqns prep_attr prep_var_inst prep_expr

     {strict, do_close, fixed_frees} raw_import init_body raw_elems raw_stmt ctxt1 =

   let

     val thy = Proof_Context.theory_of ctxt1;

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

     fun prep_insts_cumulative (loc, (prfx, (inst, eqns))) (i, insts, eqnss, ctxt) =

       let

         val params = map #1 (Locale.params_of thy loc);

         val inst' = prep_inst ctxt (map #1 params) inst;

         val parm_types' =

           params |> map (#2 #> Logic.varifyT_global #>

               Term.map_type_tvar (fn ((x, _), S) => TVar ((x, i), S)) #>

               Type_Infer.paramify_vars);

         val inst'' = map2 Type.constraint parm_types' inst';

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

         val ((insts'', _, _, _), ctxt2) = check_autofix insts' [] [] [] ctxt;

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

         val (inst_morph, _) = inst_morphism params (prfx, inst''') ctxt;

         val ctxt' = Locale.activate_declarations (loc, inst_morph) ctxt2

           handle ERROR msg => if null eqns then error msg else

             (Locale.tracing ctxt1

              (msg ^ "\nFalling back to reading rewrites clause before activation.");

              ctxt2);

         val attrss = map (apsnd (map (prep_attr ctxt)) o fst) eqns;

         val eqns' = (prep_eqns ctxt' o map snd) eqns;

         val eqnss' = [attrss ~~ eqns'];

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

         val rewrite_morph = eqns'

           |> map (abs_def ctxt')

           |> Variable.export_terms ctxt' ctxt

           |> Element.eq_term_morphism (Proof_Context.theory_of ctxt)

           |> the_default Morphism.identity;

        val ctxt'' = Locale.activate_declarations (loc, inst_morph $> rewrite_morph) ctxt;

        val eqnss' = eqnss @ [attrss ~~ Variable.export_terms ctxt' ctxt eqns'];

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

     fun prep_elem raw_elem ctxt =

       let

         val ctxt' = ctxt

           |> Context_Position.set_visible false

           |> declare_elem prep_var_elem raw_elem

           |> Context_Position.restore_visible ctxt;

         val elems' = parse_elem parse_typ parse_prop ctxt' raw_elem;

       in (elems', ctxt') end;

     val fors = fold_map prep_var_inst fixed ctxt1 |> fst;

     val ctxt2 = ctxt1 |> Proof_Context.add_fixes fors |> snd;

     val (_, insts', eqnss', ctxt3) = fold prep_insts_cumulative raw_insts (0, [], [], ctxt2);

     fun prep_stmt elems ctxt =

       check_autofix insts' [] elems (prepare_stmt parse_prop prep_obtains ctxt raw_stmt) ctxt;

     val _ =

       if fixed_frees then ()

       else

         (case fold (fold (Variable.add_frees ctxt3) o snd o snd) insts' [] of

           [] => ()

         | frees => error ("Illegal free variables in expression: " ^

             commas_quote (map (Syntax.string_of_term ctxt3 o Free) (rev frees))));

     val ((insts, _, elems', concl), ctxt4) = ctxt3

       |> init_body

       |> fold_map prep_elem raw_elems

       |-> prep_stmt;

     (* parameters from expression and elements *)

     val xs = maps (fn Fixes fixes => map (Variable.check_name o #1) fixes | _ => [])

       (Fixes fors :: elems');

     val (parms, ctxt5) = fold_map Proof_Context.inferred_param xs ctxt4;

     val fors' = finish_fixes parms fors;

     val fixed = map (fn (b, SOME T, mx) => ((Binding.name_of b, T), mx)) fors';

     val deps = map (finish_inst ctxt5) insts;

     val elems'' = map (finish_elem (ctxt1, ctxt5) parms do_close) elems';

   in ((fixed, deps, eqnss', elems'', concl), (parms, ctxt5)) end;

 (*4*)in(*4*)

 fun cert_full_context_statement x =

 ((** )writeln "##### Expression.cert_full_context_statement";( **)

   prep_full_context_statement (K I) (K I) Obtain.cert_obtains

     Proof_Context.cert_var make_inst Syntax.check_props (K I) Proof_Context.cert_var (K I) x);

 fun cert_read_full_context_statement x =

 ((** )writeln "##### Expression.cert_read_full_context_statement";( **)

   prep_full_context_statement Syntax.parse_typ Syntax.parse_prop Obtain.parse_obtains

     Proof_Context.read_var make_inst Syntax.check_props (K I) Proof_Context.cert_var (K I) x);

 fun read_full_context_statement x =

 ((**)writeln "##### Expression.read_full_context_statement";(**)

   prep_full_context_statement Syntax.parse_typ Syntax.parse_prop Obtain.parse_obtains

     Proof_Context.read_var parse_inst Syntax.read_props Attrib.check_src

       Proof_Context.read_var check_expr x);

 (*4*)end;(*4*)

 (* Context statement: elements + statement *)

 (*5*)local(*5*)

 fun prep_statement prep activate raw_elems raw_stmt ctxt =

   let

     val ((_, _, _, elems, concl), _) =

       prep {strict = true, do_close = false, fixed_frees = true}

         ([], []) I raw_elems raw_stmt ctxt;

     val ctxt' = ctxt

       |> Proof_Context.set_stmt true

       |> fold_map activate elems |> #2

       |> Proof_Context.restore_stmt ctxt;

   in (concl, ctxt') end;

 (*5*)in(*5*)

 fun cert_statement x = prep_statement cert_full_context_statement Element.activate_i x;

 fun read_statement x = prep_statement read_full_context_statement Element.activate x;

 (*5*)end;(*5*)

 (* Locale declaration: import + elements *)

 fun fix_params params =

   Proof_Context.add_fixes (map (fn ((x, T), mx) => (Binding.name x, SOME T, mx)) params) #> snd;

 (*6*)local(*6*)

 fun prep_declaration prep activate raw_import init_body raw_elems ctxt =

   let

     val ((fixed, deps, eqnss, elems, _), (parms, ctxt0)) =

       prep {strict = false, do_close = true, fixed_frees = false}

         raw_import init_body raw_elems (Element.Shows []) ctxt;

     val _ = null (flat eqnss) orelse error "Illegal rewrites clause(s) in declaration of locale";

     (* Declare parameters and imported facts *)

     val ctxt' = ctxt

       |> fix_params fixed

       |> fold (Context.proof_map o Locale.activate_facts NONE) deps;

     val (elems', ctxt'') = ctxt'

       |> Proof_Context.set_stmt true

       |> fold_map activate elems

       ||> Proof_Context.restore_stmt ctxt';

   in ((fixed, deps, elems', ctxt''), (parms, ctxt0)) end;

 (*6*)in(*6*)

 fun cert_declaration x = prep_declaration cert_full_context_statement Element.activate_i x;

 fun cert_read_declaration x = prep_declaration cert_read_full_context_statement Element.activate x;

 fun read_declaration x = prep_declaration read_full_context_statement Element.activate x;

 (*6*)end;(*6*)

 (* Locale expression to set up a goal *)

 (*7*)local(*7*)

 fun props_of thy (name, morph) =

   let val (asm, defs) = Locale.specification_of thy name

   in map (Morphism.term morph) (the_list asm @ defs) end;

 fun prep_goal_expression prep expression ctxt =

   let

     val thy = Proof_Context.theory_of ctxt;

     val ((fixed, deps, eqnss, _, _), _) =

       prep {strict = true, do_close = true, fixed_frees = true} expression I []

         (Element.Shows []) ctxt;

     (* proof obligations *)

     val propss = map (props_of thy) deps;

     val eq_propss = (map o map) snd eqnss;

     val goal_ctxt = ctxt

       |> fix_params fixed

       |> (fold o fold) Proof_Context.augment (propss @ eq_propss);

     val export = Proof_Context.export_morphism goal_ctxt ctxt;

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

     val exp_term = Term_Subst.zero_var_indexes o Morphism.term export;

     val exp_typ = Logic.type_map exp_term;

     val export' =

       Morphism.morphism "Expression.prep_goal"

         {binding = [], typ = [exp_typ], term = [exp_term], fact = [exp_fact]};

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

 (*7*)in(*7*)

 fun cert_goal_expression x = prep_goal_expression cert_full_context_statement x;

 fun read_goal_expression x = prep_goal_expression read_full_context_statement x;

 (*7*)end;(*7*)

 (*** Locale declarations ***)

 (* extract specification text *)

 val norm_term = Envir.beta_norm oo Term.subst_atomic;

 fun bind_def ctxt eq (xs, env, eqs) =

   let

     val _ = Local_Defs.cert_def ctxt (K []) eq;

     val ((y, T), b) = Local_Defs.abs_def eq;

     val b' = norm_term env b;

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

   in

     (case filter (fn (Free (y', _), _) => y = y' | _ => false) env of

       [] => (Term.add_frees b' xs, (Free (y, T), b') :: env, eq :: eqs)

     | dups =>

         if forall (fn (_, b'') => b' aconv b'') dups then (xs, env, eqs)

         else err "Attempt to redefine variable")

   end;

 (* 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: the equations from the defines elements

    *)

 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

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

 fun eval_inst ctxt (loc, morph) text =

   let

     val thy = Proof_Context.theory_of ctxt;

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

     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 [(Binding.empty_atts, [(the asm', [])])])

         else I) |>

        (if not (null defs) then

           eval_text ctxt false (Defines (map (fn def => (Binding.empty_atts, (def, []))) defs'))

         else I)

 (* FIXME clone from locale.ML *)

   in text' end;

 fun eval_elem ctxt elem text =

   eval_text ctxt true elem text;

 fun eval ctxt deps elems =

   let

     val text' = fold (eval_inst ctxt) deps ((([], []), ([], [])), ([], [], []));

     val ((spec, (_, _, defs))) = fold (eval_elem ctxt) elems text';

   in (spec, defs) end;

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

      also name suffix of delta predicates and assumptions. *)

 val axiomsN = "axioms";

 (*8*)local(*8*)

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

      delta predicates *)

 val introN = "intro";

 fun atomize_spec ctxt ts =

   let

     val t = Logic.mk_conjunction_balanced ts;

     val body = Object_Logic.atomize_term ctxt t;

     val bodyT = Term.fastype_of body;

   in

     if bodyT = propT

     then (t, propT, Thm.reflexive (Thm.cterm_of ctxt t))

     else (body, bodyT, Object_Logic.atomize ctxt (Thm.cterm_of ctxt t))

   end;

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

 fun aprop_tr' n c =

   let

     val c' = Lexicon.mark_const c;

     fun tr' (_: Proof.context) T args =

       if T <> dummyT andalso length args = n

       then Syntax.const "_aprop" $ Term.list_comb (Syntax.const c', args)

       else raise Match;

   in (c', tr') end;

 (* define one predicate including its intro rule and axioms

    - binding: 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 binding parms defs ts norm_ts thy =

   let

     val name = Sign.full_name thy binding;

     val thy_ctxt = Proof_Context.init_global thy;

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

     val env = Term.add_free_names body [];

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

     val Ts = map #2 xs;

     val extraTs =

       (subtract (op =) (fold Term.add_tfreesT Ts []) (Term.add_tfrees body []))

       |> sort_by #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 = Object_Logic.ensure_propT thy_ctxt head;

     val ([pred_def], defs_thy) =

       thy

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

       |> Sign.declare_const_global ((binding, predT), NoSyn) |> snd

       |> Global_Theory.add_defs false [((Thm.def_binding binding, Logic.mk_equals (head, body)), [])];

     val defs_ctxt = Proof_Context.init_global defs_thy |> Variable.declare_term head;

     val intro = Goal.prove_global defs_thy [] norm_ts statement

       (fn {context = ctxt, ...} =>

         rewrite_goals_tac ctxt [pred_def] THEN

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

         compose_tac defs_ctxt

           (false,

             Conjunction.intr_balanced (map (Thm.assume o Thm.cterm_of defs_ctxt) norm_ts), 0) 1);

     val conjuncts =

       (Drule.equal_elim_rule2 OF

         [body_eq, rewrite_rule defs_ctxt [pred_def] (Thm.assume (Thm.cterm_of defs_ctxt statement))])

       |> Conjunction.elim_balanced (length ts);

     val (_, axioms_ctxt) = defs_ctxt

       |> Assumption.add_assumes (maps Thm.chyps_of (defs @ conjuncts));

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

       Element.prove_witness axioms_ctxt t

        (rewrite_goals_tac axioms_ctxt defs THEN compose_tac axioms_ctxt (false, ax, 0) 1));

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

 (*8*)in(*8*)

 (* main predicate definition function *)

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

   let

     val ctxt = Proof_Context.init_global thy;

     val defs' = map (Thm.cterm_of ctxt #> Assumption.assume ctxt #> Drule.abs_def) defs;

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

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

       else

         let

           val abinding =

             if null ints then binding else Binding.suffix_name ("_" ^ axiomsN) binding;

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

             thy

             |> def_pred abinding parms defs' exts exts';

           val ((_, [intro']), thy'') =

             thy'

             |> Sign.qualified_path true abinding

             |> Global_Theory.note_thms ""

               ((Binding.name introN, []), [([intro], [Locale.unfold_add])])

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

           val ctxt''' = Proof_Context.init_global thy''';

           val ([(_, [intro']), _], thy'''') =

             thy'''

             |> Sign.qualified_path true binding

             |> Global_Theory.note_thmss ""

                  [((Binding.name introN, []), [([intro], [Locale.intro_add])]),

                   ((Binding.name axiomsN, []),

                     [(map (Drule.export_without_context o Element.conclude_witness ctxt''') 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;

 (*8*)end;(*8*)

 (*9*)local(*9*)

 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 "")

   | assumes_to_notes e axms = (e, axms);

 fun defines_to_notes ctxt (Defines defs) =

       Notes ("", map (fn (a, (def, _)) =>

         (a, [([Assumption.assume ctxt (Thm.cterm_of ctxt def)],

           [(Attrib.internal o K) Locale.witness_add])])) defs)

   | defines_to_notes _ e = e;

 val is_hyp = fn Assumes _ => true | Defines _ => true | _ => false;

 fun gen_add_locale prep_decl

     binding raw_predicate_binding raw_import raw_body thy =

   let

     val name = Sign.full_name thy binding;

     val _ = Locale.defined thy name andalso

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

     val ((fixed, deps, body_elems, _), (parms, ctxt')) =

       prep_decl raw_import I raw_body (Proof_Context.init_global thy);

     val text as (((_, exts'), _), defs) = eval ctxt' deps body_elems;

     val extraTs =

       subtract (op =)

         (fold Term.add_tfreesT (map snd parms) [])

         (fold Term.add_tfrees exts' []);

     val _ =

       if null extraTs then ()

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

           Binding.print binding ^ ": " ^

           commas (map (Syntax.string_of_typ ctxt' o TFree) (sort_by #1 extraTs)));

     val predicate_binding =

       if Binding.is_empty raw_predicate_binding then binding

       else raw_predicate_binding;

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

       define_preds predicate_binding parms text thy;

     val pred_ctxt = Proof_Context.init_global thy';

     val a_satisfy = Element.satisfy_morphism a_axioms;

     val b_satisfy = Element.satisfy_morphism b_axioms;

     val params = fixed @

       maps (fn Fixes fixes =>

         map (fn (b, SOME T, mx) => ((Binding.name_of b, T), mx)) fixes | _ => []) body_elems;

     val asm = if is_some b_statement then b_statement else a_statement;

     val hyp_spec = filter is_hyp body_elems;

     val notes =

       if is_some asm then

         [("", [((Binding.suffix_name ("_" ^ axiomsN) binding, []),

           [([Assumption.assume pred_ctxt (Thm.cterm_of pred_ctxt (the asm))],

             [(Attrib.internal o K) Locale.witness_add])])])]

       else [];

     val notes' =

       body_elems

       |> map (defines_to_notes pred_ctxt)

       |> map (Element.transform_ctxt a_satisfy)

       |> (fn elems =>

         fold_map assumes_to_notes elems (map (Element.conclude_witness pred_ctxt) a_axioms))

       |> fst

       |> map (Element.transform_ctxt b_satisfy)

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

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

     val axioms = map (Element.conclude_witness pred_ctxt) b_axioms;

     val loc_ctxt = thy'

       |> Locale.register_locale binding (extraTs, params)

           (asm, rev defs) (a_intro, b_intro) axioms hyp_spec [] (rev notes) (rev deps')

       |> Named_Target.init name

       |> fold (fn (kind, facts) => Local_Theory.notes_kind kind facts #> snd) notes';

   in (name, loc_ctxt) end;

 (*9*)in(*9*)

 val add_locale = gen_add_locale cert_declaration;

 val add_locale_cmd = gen_add_locale read_declaration;

 (*9*)end;(*9*)

 end;