(*  Title:      Pure/Isar/expression.ML

     Author:     Clemens Ballarin, TU Muenchen

 Locale expressions.

 *)

 signature EXPRESSION =

 sig

   (* Locale expressions *)

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

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

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

   type expression = string expr * (binding * string option * mixfix) list

   (* Processing of context statements *)

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

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

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

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

   (* Declaring locales *)

   val cert_declaration: expression_i -> (Proof.context -> Proof.context) -> Element.context_i list ->

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

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

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

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

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

       (*FIXME*)

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

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

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

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

     theory -> string * local_theory

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

     theory -> string * local_theory

   (* Interpretation *)

   val cert_goal_expression: expression_i -> Proof.context ->

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

   val read_goal_expression: expression -> Proof.context ->

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

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

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

   val interpretation: expression_i -> (Attrib.binding * term) list ->

     theory -> Proof.state

   val interpretation_cmd: expression -> (Attrib.binding * string) list ->

     theory -> Proof.state

   val interpret: expression_i -> bool -> Proof.state -> Proof.state

   val interpret_cmd: expression -> bool -> Proof.state -> Proof.state

 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 * bool) * 'term map)) list;

 type expression = string expr * (binding * string option * mixfix) list;

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

 (** Internalise locale names in expr **)

 fun intern thy instances =  map (apfst (Locale.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.name_of b);

     fun parm_eq ((b1, mx1: mixfix), (b2, mx2)) =

       (* FIXME: cannot compare bindings for equality, instead check for equal name and syntax *)

       Binding.name_of b1 = Binding.name_of b2 andalso

         (mx1 = mx2 orelse

           error ("Conflicting syntax for parameter " ^ quote (Binding.str_of b1) ^ " in expression"));

     fun params_loc loc =

       (Locale.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 (Locale.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'' = distinct parm_eq (ps @ ps');

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

           in (ps', is') end;

     val (implicit, expr') = params_expr expr;

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

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

 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, strict), 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.add_prefix strict 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 (ProofContext.set_mode ProofContext.mode_schematic ctxt),

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

     fact = I,

     attrib = I};

 fun parse_concl prep_term ctxt concl =

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

     (prep_term (ProofContext.set_mode ProofContext.mode_schematic ctxt) t, (* FIXME ?? *)

       map (prep_term (ProofContext.set_mode ProofContext.mode_pattern 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 **)

 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; (* FIXME use fold Logic.all *)

   (* FIXME consider closing in syntactic phase *)

         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') = LocalDefs.cert_def ctxt (close_frees t)

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

         | e => e)

       end;

 fun finish_primitive parms _ (Fixes fixes) = Fixes (map (fn (binding, _, mx) =>

       let val x = Binding.name_of 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)) =

   let

     val thy = ProofContext.theory_of ctxt;

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

       map_split (fn (b, SOME T, _) => (Binding.name_of b, T));

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

   in (loc, morph) end;

 fun finish_elem ctxt parms do_close elem =

   let

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

   in elem' end

 fun finish ctxt parms do_close insts elems =

   let

     val deps = map (finish_inst ctxt parms do_close) insts;

     val elems' = map (finish_elem ctxt parms do_close) elems;

   in (deps, elems') 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 prep_vars_elem prep_inst prep_vars_inst prep_expr

     strict do_close raw_import init_body raw_elems raw_concl ctxt1 =

   let

     val thy = ProofContext.theory_of ctxt1;

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

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

       let

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

           map_split (fn (b, SOME T, _) => (Binding.name_of b, T))

             (*FIXME return value of Locale.params_of has strange type*)

         val inst' = prep_inst ctxt parm_names inst;

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

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

     fun prep_elem insts raw_elem (elems, ctxt) =

       let

         val ctxt' = declare_elem prep_vars_elem raw_elem ctxt;

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

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

       in (elems', ctxt') end;

     fun prep_concl raw_concl (insts, elems, ctxt) =

       let

         val concl = parse_concl parse_prop ctxt raw_concl;

       in check_autofix insts elems concl ctxt end;

     val fors = prep_vars_inst fixed ctxt1 |> fst;

     val ctxt2 = ctxt1 |> ProofContext.add_fixes_i fors |> snd;

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

     val ctxt4 = init_body ctxt3;

     val (elems, ctxt5) = fold (prep_elem insts') raw_elems ([], ctxt4);

     val (insts, elems', concl, ctxt6) =

       prep_concl raw_concl (insts', elems, ctxt5);

     (* Retrieve parameter types *)

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

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

     val (Ts, ctxt7) = fold_map ProofContext.inferred_param xs ctxt6; 

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

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

     val (deps, elems'') = finish ctxt6 parms do_close insts elems';

   in ((fors', deps, elems'', concl), (parms, ctxt7)) end

 in

 fun cert_full_context_statement x =

   prep_full_context_statement (K I) (K I) ProofContext.cert_vars

   make_inst ProofContext.cert_vars (K I) x;

 fun cert_read_full_context_statement x =

   prep_full_context_statement Syntax.parse_typ Syntax.parse_prop ProofContext.read_vars

   make_inst ProofContext.cert_vars (K I) x;

 fun read_full_context_statement x =

   prep_full_context_statement Syntax.parse_typ Syntax.parse_prop ProofContext.read_vars

   parse_inst ProofContext.read_vars intern x;

 end;

 (* Context statement: elements + conclusion *)

 local

 fun prep_statement prep activate raw_elems raw_concl context =

   let

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

        prep true false ([], []) I raw_elems raw_concl context;

      val (_, context') = context |>

        ProofContext.set_stmt true |>

        activate elems;

   in (concl, context') end;

 in

 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;

 end;

 (* Locale declaration: import + elements *)

 local

 fun prep_declaration prep activate raw_import init_body raw_elems context =

   let

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

       prep false true raw_import init_body raw_elems [] context ;

     (* Declare parameters and imported facts *)

     val context' = context |>

       ProofContext.add_fixes_i fixed |> snd |>

       fold Locale.activate_local_facts deps;

     val (elems', _) = context' |>

       ProofContext.set_stmt true |>

       activate elems;

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

 in

 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;

 end;

 (* Locale expression to set up a goal *)

 local

 fun props_of thy (name, morph) =

   let

     val (asm, defs) = Locale.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 expression I [] [] context;

     (* 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_typ = Logic.type_map exp_term;

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

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

 in

 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;

 end;

 (*** 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 _ = LocalDefs.cert_def ctxt eq;

     val ((y, T), b) = LocalDefs.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;

 fun eval_inst ctxt (loc, morph) text =

   let

     val thy = ProofContext.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 [(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 locale.ML *)

   in text' end;

 fun eval_elem ctxt elem text =

   let

     val text' = eval_text ctxt true elem text;

   in text' end;

 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";

 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_free_names body [];

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

     val Ts = map #2 xs;

     val extraTs =

       (Term.add_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

         [((Binding.name (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 defs' = map (cterm_of thy #> Assumption.assume #> Drule.gen_all #> Drule.abs_def) defs;

     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], [Locale.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], [Locale.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) =

       Notes (Thm.definitionK, map (fn (a, (def, _)) =>

         (a, [([Assumption.assume (cterm_of thy def)],

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

   | defines_to_notes _ e = e;

 fun gen_add_locale prep_decl

     bname raw_predicate_bname raw_import raw_body thy =

   let

     val name = Sign.full_bname thy bname;

     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 (ProofContext.init thy);

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

     val predicate_bname = if raw_predicate_bname = "" then bname

       else raw_predicate_bname;

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

       define_preds predicate_bname parms 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 a_satisfy = Element.satisfy_morphism a_axioms;

     val b_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 notes =

         if is_some asm

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

           [([Assumption.assume (cterm_of thy' (the asm))],

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

         else [];

     val notes' = body_elems |>

       map (defines_to_notes thy') |>

       map (Element.morph_ctxt a_satisfy) |>

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

       fst |>

       map (Element.morph_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 b_axioms;

     val loc_ctxt = thy'

       |> Locale.register_locale bname (extraTs, params)

           (asm, rev defs) (a_intro, b_intro) axioms ([], []) 

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

       |> TheoryTarget.init (SOME name)

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

   in (name, loc_ctxt) end;

 in

 val add_locale = gen_add_locale cert_declaration;

 val add_locale_cmd = gen_add_locale read_declaration;

 end;

 (*** Interpretation ***)

 (** 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 = Locale.init target thy;

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

     fun after_qed witss = ProofContext.theory (

       fold2 (fn (name, morph) => fn wits => Locale.add_dependency target

         (name, morph $> Element.satisfy_morphism wits $> export)) deps witss #>

       (fn thy => fold_rev Locale.activate_global_facts

           (Locale.get_registrations thy) thy));

   in Element.witness_proof after_qed propss goal_ctxt end;

 in

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

 fun sublocale_cmd x = gen_sublocale read_goal_expression Locale.intern x;

 end;

 (** Interpretation in theories **)

 local

 fun gen_interpretation prep_expr parse_prop prep_attr

     expression equations theory =

   let

     val ((propss, regs, export), expr_ctxt) = ProofContext.init theory

       |> prep_expr expression;

     val eqns = map (parse_prop expr_ctxt o snd) equations |> Syntax.check_terms expr_ctxt;

     val eq_attns = map ((apsnd o map) (prep_attr theory) o fst) equations;

     val goal_ctxt = fold Variable.auto_fixes eqns expr_ctxt;

     val export' = Variable.export_morphism goal_ctxt expr_ctxt;

     fun store_reg ((name, morph), wits) thy =

       let

         val wits' = map (Element.morph_witness export') wits;

         val morph' = morph $> Element.satisfy_morphism wits';

       in

         thy

         |> Locale.add_registration (name, (morph', export))

         |> pair (name, morph')

       end;

     fun store_eqns_activate regs [] thy =

           thy

           |> fold (fn (name, morph) =>

                Locale.activate_global_facts (name, morph $> export)) regs

       | store_eqns_activate regs eqs thy =

           let

             val eqs' = eqs |> map (Morphism.thm (export' $> export) #>

               LocalDefs.meta_rewrite_rule (ProofContext.init thy) #>

               Drule.abs_def);

             val eq_morph = Element.eq_morphism thy eqs';

             val eq_attns' = map ((apsnd o map) (Attrib.attribute_i thy)) eq_attns;

           in

             thy

             |> fold (fn (name, morph) =>

                 Locale.amend_registration eq_morph (name, morph) #>

                 Locale.activate_global_facts (name, morph $> eq_morph $> export)) regs

             |> PureThy.note_thmss Thm.lemmaK (eq_attns' ~~ map (fn eq => [([eq], [])]) eqs')

             |> snd

           end;

     fun after_qed wits eqs = ProofContext.theory (fold_map store_reg (regs ~~ wits)

         #-> (fn regs => store_eqns_activate regs eqs));

   in Element.witness_proof_eqs after_qed propss eqns goal_ctxt end;

 in

 fun interpretation x = gen_interpretation cert_goal_expression (K I) (K I) x;

 fun interpretation_cmd x = gen_interpretation read_goal_expression

   Syntax.parse_prop Attrib.intern_src x;

 end;

 (** Interpretation in proof contexts **)

 local

 fun gen_interpret prep_expr

     expression int state =

   let

     val _ = Proof.assert_forward_or_chain state;

     val ctxt = Proof.context_of state;

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

     fun store_reg (name, morph) thms =

       let

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

       in Locale.activate_local_facts (name, morph') end;

     fun after_qed wits =

       Proof.map_context (fold2 store_reg regs wits);

   in

     state

     |> Element.witness_local_proof after_qed "interpret" propss goal_ctxt int

   end;

 in

 fun interpret x = gen_interpret cert_goal_expression x;

 fun interpret_cmd x = gen_interpret read_goal_expression x;

 end;

 end;