(*  Title:      HOL/Statespace/state_space.ML

     Author:     Norbert Schirmer, TU Muenchen

 *)

 signature STATE_SPACE =

   sig

     val KN : string

     val distinct_compsN : string

     val getN : string

     val putN : string

     val injectN : string

     val namespaceN : string

     val projectN : string

     val valuetypesN : string

     val namespace_definition :

        bstring ->

        typ ->

        Expression.expression ->

        string list -> string list -> theory -> theory

     val define_statespace :

        string list ->

        string ->

        (string list * bstring * (string * string) list) list ->

        (string * string) list -> theory -> theory

     val define_statespace_i :

        string option ->

        string list ->

        string ->

        (typ list * bstring * (string * string) list) list ->

        (string * typ) list -> theory -> theory

     val statespace_decl :

        ((string list * bstring) *

          ((string list * xstring * (bstring * bstring) list) list *

           (bstring * string) list)) parser

     val neq_x_y : Proof.context -> term -> term -> thm option

     val distinctNameSolver : Simplifier.solver

     val distinctTree_tac :

        Proof.context -> term * int -> Tactical.tactic

     val distinct_simproc : Simplifier.simproc

     val get_comp : Context.generic -> string -> (typ * string) Option.option

     val get_silent : Context.generic -> bool

     val set_silent : bool -> Context.generic -> Context.generic

     val gen_lookup_tr : Proof.context -> term -> string -> term

     val lookup_swap_tr : Proof.context -> term list -> term

     val lookup_tr : Proof.context -> term list -> term

     val lookup_tr' : Proof.context -> term list -> term

     val gen_update_tr :

        bool -> Proof.context -> string -> term -> term -> term

     val update_tr : Proof.context -> term list -> term

     val update_tr' : Proof.context -> term list -> term

   end;

 structure StateSpace : STATE_SPACE =

 struct

 (* Theorems *)

 (* Names *)

 val distinct_compsN = "distinct_names"

 val namespaceN = "_namespace"

 val valuetypesN = "_valuetypes"

 val projectN = "project"

 val injectN = "inject"

 val getN = "get"

 val putN = "put"

 val project_injectL = "StateSpaceLocale.project_inject";

 val KN = "StateFun.K_statefun"

 (* Library *)

 fun fold1 f xs = fold f (tl xs) (hd xs)

 fun fold1' f [] x = x

   | fold1' f xs _ = fold1 f xs

 fun sublist_idx eq xs ys =

   let

     fun sublist n xs ys =

          if is_prefix eq xs ys then SOME n

          else (case ys of [] => NONE

                | (y::ys') => sublist (n+1) xs ys')

   in sublist 0 xs ys end;

 fun is_sublist eq xs ys = is_some (sublist_idx eq xs ys);

 fun sorted_subset eq [] ys = true

   | sorted_subset eq (x::xs) [] = false

   | sorted_subset eq (x::xs) (y::ys) = if eq (x,y) then sorted_subset eq xs ys

                                        else sorted_subset eq (x::xs) ys;

 type namespace_info =

  {declinfo: (typ*string) Termtab.table, (* type, name of statespace *)

   distinctthm: thm Symtab.table,

   silent: bool

  };

 structure NameSpaceData = Generic_Data

 (

   type T = namespace_info;

   val empty = {declinfo = Termtab.empty, distinctthm = Symtab.empty, silent = false};

   val extend = I;

   fun merge

     ({declinfo=declinfo1, distinctthm=distinctthm1, silent=silent1},

       {declinfo=declinfo2, distinctthm=distinctthm2, silent=silent2}) : T =

     {declinfo = Termtab.merge (K true) (declinfo1, declinfo2),

      distinctthm = Symtab.merge (K true) (distinctthm1, distinctthm2),

      silent = silent1 andalso silent2}

 );

 fun make_namespace_data declinfo distinctthm silent =

      {declinfo=declinfo,distinctthm=distinctthm,silent=silent};

 fun delete_declinfo n ctxt =

   let val {declinfo,distinctthm,silent} = NameSpaceData.get ctxt;

   in NameSpaceData.put

        (make_namespace_data (Termtab.delete_safe n declinfo) distinctthm silent) ctxt

   end;

 fun update_declinfo (n,v) ctxt =

   let val {declinfo,distinctthm,silent} = NameSpaceData.get ctxt;

   in NameSpaceData.put

       (make_namespace_data (Termtab.update (n,v) declinfo) distinctthm silent) ctxt

   end;

 fun set_silent silent ctxt =

   let val {declinfo,distinctthm,...} = NameSpaceData.get ctxt;

   in NameSpaceData.put

       (make_namespace_data declinfo distinctthm silent) ctxt

   end;

 val get_silent = #silent o NameSpaceData.get;

 fun prove_interpretation_in ctxt_tac (name, expr) thy =

    thy

    |> Expression.sublocale_cmd name expr

    |> Proof.global_terminal_proof

          (Method.Basic (fn ctxt => SIMPLE_METHOD (ctxt_tac ctxt)), NONE)

    |> ProofContext.theory_of

 fun add_locale name expr elems thy =

   thy 

   |> Expression.add_locale (Binding.name name) (Binding.name name) expr elems

   |> snd

   |> Local_Theory.exit;

 fun add_locale_cmd name expr elems thy =

   thy 

   |> Expression.add_locale_cmd (Binding.name name) Binding.empty expr elems

   |> snd

   |> Local_Theory.exit;

 type statespace_info =

  {args: (string * sort) list, (* type arguments *)

   parents: (typ list * string * string option list) list,

              (* type instantiation, state-space name, component renamings *)

   components: (string * typ) list,

   types: typ list (* range types of state space *)

  };

 structure StateSpaceData = Generic_Data

 (

   type T = statespace_info Symtab.table;

   val empty = Symtab.empty;

   val extend = I;

   fun merge data : T = Symtab.merge (K true) data;

 );

 fun add_statespace name args parents components types ctxt =

      StateSpaceData.put

       (Symtab.update_new (name, {args=args,parents=parents,

                                 components=components,types=types}) (StateSpaceData.get ctxt))

       ctxt;

 fun get_statespace ctxt name =

       Symtab.lookup (StateSpaceData.get ctxt) name;

 fun lookupI eq xs n =

   (case AList.lookup eq xs n of

      SOME v => v

    | NONE => n);

 fun mk_free ctxt name =

   if Variable.is_fixed ctxt name orelse Variable.is_declared ctxt name

   then

     let val n' = lookupI (op =) (Variable.fixes_of ctxt) name

     in SOME (Free (n',ProofContext.infer_type ctxt (n', dummyT))) end

   else NONE

 fun get_dist_thm ctxt name = Symtab.lookup (#distinctthm (NameSpaceData.get ctxt)) name;

 fun get_comp ctxt name =

      Option.mapPartial

        (Termtab.lookup (#declinfo (NameSpaceData.get ctxt)))

        (mk_free (Context.proof_of ctxt) name);

 (*** Tactics ***)

 fun neq_x_y ctxt x y =

   (let

     val dist_thm = the (get_dist_thm (Context.Proof ctxt) (#1 (dest_Free x)));

     val ctree = cprop_of dist_thm |> Thm.dest_comb |> #2 |> Thm.dest_comb |> #2;

     val tree = term_of ctree;

     val x_path = the (DistinctTreeProver.find_tree x tree);

     val y_path = the (DistinctTreeProver.find_tree y tree);

     val thm = DistinctTreeProver.distinctTreeProver dist_thm x_path y_path;

   in SOME thm

   end handle Option => NONE)

 fun distinctTree_tac ctxt

       (Const ("Trueprop",_) $

         (Const ("Not", _) $ (Const ("op =", _) $ (x as Free _)$ (y as Free _))), i) =

   (case (neq_x_y ctxt x y) of

      SOME neq => rtac neq i

    | NONE => no_tac)

   | distinctTree_tac _ _ = no_tac;

 val distinctNameSolver = mk_solver' "distinctNameSolver"

      (fn ss => case try Simplifier.the_context ss of

                  SOME ctxt => SUBGOAL (distinctTree_tac ctxt)

                 | NONE => fn i => no_tac)

 val distinct_simproc =

   Simplifier.simproc @{theory HOL} "StateSpace.distinct_simproc" ["x = y"]

     (fn thy => fn ss => (fn (Const ("op =",_)$(x as Free _)$(y as Free _)) =>

         (case try Simplifier.the_context ss of

           SOME ctxt => Option.map (fn neq => DistinctTreeProver.neq_to_eq_False OF [neq])

                        (neq_x_y ctxt x y)

         | NONE => NONE)

       | _ => NONE))

 local

   val ss = HOL_basic_ss

 in

 fun interprete_parent name dist_thm_name parent_expr thy =

   let

     fun solve_tac ctxt (_,i) st =

       let

         val distinct_thm = ProofContext.get_thm ctxt dist_thm_name;

         val goal = List.nth (cprems_of st,i-1);

         val rule = DistinctTreeProver.distinct_implProver distinct_thm goal;

       in EVERY [rtac rule i] st

       end

     fun tac ctxt = EVERY [Locale.intro_locales_tac true ctxt [],

                           ALLGOALS (SUBGOAL (solve_tac ctxt))]

   in thy

      |> prove_interpretation_in tac (name,parent_expr)

   end;

 end;

 fun namespace_definition name nameT parent_expr parent_comps new_comps thy =

   let

     val all_comps = parent_comps @ new_comps;

     val vars = (map (fn n => (Binding.name n, NONE, NoSyn)) all_comps);

     val full_name = Sign.full_bname thy name;

     val dist_thm_name = distinct_compsN;

     val dist_thm_full_name = dist_thm_name;

     fun comps_of_thm thm = prop_of thm

              |> (fn (_$(_$t)) => DistinctTreeProver.dest_tree t) |> map (fst o dest_Free);

     fun type_attr phi (ctxt,thm) =

       (case ctxt of Context.Theory _ => (ctxt,thm)

        | _ =>

         let

           val {declinfo,distinctthm=tt,silent} = (NameSpaceData.get ctxt);

           val all_names = comps_of_thm thm;

           fun upd name tt =

                (case (Symtab.lookup tt name) of

                  SOME dthm => if sorted_subset (op =) (comps_of_thm dthm) all_names

                               then Symtab.update (name,thm) tt else tt

                 | NONE => Symtab.update (name,thm) tt)

           val tt' = tt |> fold upd all_names;

           val activate_simproc =

               Output.no_warnings_CRITICAL   (* FIXME !?! *)

                (Simplifier.map_ss (fn ss => ss addsimprocs [distinct_simproc]));

           val ctxt' =

               ctxt

               |> NameSpaceData.put {declinfo=declinfo,distinctthm=tt',silent=silent}

               |> activate_simproc

         in (ctxt',thm)

         end)

     val attr = Attrib.internal type_attr;

     val assumes = Element.Assumes [((Binding.name dist_thm_name,[attr]),

                     [(HOLogic.Trueprop $

                       (Const ("DistinctTreeProver.all_distinct",

                                  Type ("DistinctTreeProver.tree",[nameT]) --> HOLogic.boolT) $

                       DistinctTreeProver.mk_tree (fn n => Free (n,nameT)) nameT

                                 (sort fast_string_ord all_comps)),

                       ([]))])];

   in thy

      |> add_locale name ([],vars) [assumes]

      |> ProofContext.theory_of

      |> interprete_parent name dist_thm_full_name parent_expr

   end;

 fun encode_dot x = if x= #"." then #"_" else x;

 fun encode_type (TFree (s, _)) = s

   | encode_type (TVar ((s,i),_)) = "?" ^ s ^ string_of_int i

   | encode_type (Type (n,Ts)) =

       let

         val Ts' = fold1' (fn x => fn y => x ^ "_" ^ y) (map encode_type Ts) "";

         val n' = String.map encode_dot n;

       in if Ts'="" then n' else Ts' ^ "_" ^ n' end;

 fun project_name T = projectN ^"_"^encode_type T;

 fun inject_name T = injectN ^"_"^encode_type T;

 fun project_free T pT V = Free (project_name T, V --> pT);

 fun inject_free T pT V = Free (inject_name T, pT --> V);

 fun get_name n = getN ^ "_" ^ n;

 fun put_name n = putN ^ "_" ^ n;

 fun get_const n T nT V = Free (get_name n, (nT --> V) --> T);

 fun put_const n T nT V = Free (put_name n, T --> (nT --> V) --> (nT --> V));

 fun lookup_const T nT V = Const ("StateFun.lookup",(V --> T) --> nT --> (nT --> V) --> T);

 fun update_const T nT V =

  Const ("StateFun.update",

           (V --> T) --> (T --> V) --> nT --> (T --> T) --> (nT --> V) --> (nT --> V));

 fun K_const T = Const ("StateFun.K_statefun",T --> T --> T);

 val no_syn = #3 (Syntax.no_syn ((),()));

 fun add_declaration name decl thy =

   thy

   |> Named_Target.init name

   |> (fn lthy => Local_Theory.declaration false (decl lthy) lthy)

   |> Local_Theory.exit_global;

 fun parent_components thy (Ts, pname, renaming) =

   let

     val ctxt = Context.Theory thy;

     fun rename [] xs = xs

       | rename (NONE::rs)  (x::xs) = x::rename rs xs

       | rename (SOME r::rs) ((x,T)::xs) = (r,T)::rename rs xs;

     val {args,parents,components,...} =

               the (Symtab.lookup (StateSpaceData.get ctxt) pname);

     val inst = map fst args ~~ Ts;

     val subst = Term.map_type_tfree (the o AList.lookup (op =) inst o fst);

     val parent_comps =

       maps (fn (Ts',n,rs) => parent_components thy (map subst Ts',n,rs)) parents;

     val all_comps = rename renaming (parent_comps @ map (apsnd subst) components);

   in all_comps end;

 fun take_upto i xs = List.take(xs,i) handle Subscript => xs;

 fun statespace_definition state_type args name parents parent_comps components thy =

   let

     val full_name = Sign.full_bname thy name;

     val all_comps = parent_comps @ components;

     val components' = map (fn (n,T) => (n,(T,full_name))) components;

     val all_comps' = map (fn (n,T) => (n,(T,full_name))) all_comps;

     fun parent_expr (_,n,rs) = (suffix namespaceN n,((n,false),Expression.Positional rs));

         (* FIXME: a more specific renaming-prefix (including parameter names) may be nicer *)

     val parents_expr = map parent_expr parents;

     fun distinct_types Ts =

       let val tab = fold (fn T => fn tab => Typtab.update (T,()) tab) Ts Typtab.empty;

       in map fst (Typtab.dest tab) end;

     val Ts = distinct_types (map snd all_comps);

     val arg_names = map fst args;

     val valueN = Name.variant arg_names "'value";

     val nameN = Name.variant (valueN::arg_names) "'name";

     val valueT = TFree (valueN, Sign.defaultS thy);

     val nameT = TFree (nameN, Sign.defaultS thy);

     val stateT = nameT --> valueT;

     fun projectT T = valueT --> T;

     fun injectT T = T --> valueT;

     val locinsts = map (fn T => (project_injectL,

                     (("",false),Expression.Positional 

                              [SOME (Free (project_name T,projectT T)), 

                               SOME (Free ((inject_name T,injectT T)))]))) Ts;

     val locs = maps (fn T => [(Binding.name (project_name T),NONE,NoSyn),

                                      (Binding.name (inject_name T),NONE,NoSyn)]) Ts;

     val constrains = maps (fn T => [(project_name T,projectT T),(inject_name T,injectT T)]) Ts;

     fun interprete_parent_valuetypes (Ts, pname, _) thy =

       let

         val {args,types,...} =

              the (Symtab.lookup (StateSpaceData.get (Context.Theory thy)) pname);

         val inst = map fst args ~~ Ts;

         val subst = Term.map_type_tfree (the o AList.lookup (op =) inst o fst);

         val pars = maps ((fn T => [project_name T,inject_name T]) o subst) types;

         val expr = ([(suffix valuetypesN name, 

                      (("",false),Expression.Positional (map SOME pars)))],[]);

       in

         prove_interpretation_in (ALLGOALS o solve_tac o Assumption.all_prems_of)

           (suffix valuetypesN name, expr) thy

       end;

     fun interprete_parent (_, pname, rs) =

       let

         val expr = ([(pname, (("",false), Expression.Positional rs))],[])

       in prove_interpretation_in

            (fn ctxt => Locale.intro_locales_tac false ctxt [])

            (full_name, expr) end;

     fun declare_declinfo updates lthy phi ctxt =

       let

         fun upd_prf ctxt =

           let

             fun upd (n,v) =

               let

                 val nT = ProofContext.infer_type (Local_Theory.target_of lthy) (n, dummyT)

               in Context.proof_map

                   (update_declinfo (Morphism.term phi (Free (n,nT)),v))

               end;

           in ctxt |> fold upd updates end;

       in Context.mapping I upd_prf ctxt end;

    fun string_of_typ T =

       setmp_CRITICAL show_sorts true

        (Print_Mode.setmp [] (Syntax.string_of_typ (ProofContext.init_global thy))) T;

    val fixestate = (case state_type of

          NONE => []

        | SOME s =>

           let

             val fx = Element.Fixes [(Binding.name s,SOME (string_of_typ stateT),NoSyn)];

             val cs = Element.Constrains

                        (map (fn (n,T) =>  (n,string_of_typ T))

                          ((map (fn (n,_) => (n,nameT)) all_comps) @

                           constrains))

           in [fx,cs] end

        )

   in thy

      |> namespace_definition

            (suffix namespaceN name) nameT (parents_expr,[])

            (map fst parent_comps) (map fst components)

      |> Context.theory_map (add_statespace full_name args parents components [])

      |> add_locale (suffix valuetypesN name) (locinsts,locs) []

      |> ProofContext.theory_of 

      |> fold interprete_parent_valuetypes parents

      |> add_locale_cmd name

               ([(suffix namespaceN full_name ,(("",false),Expression.Named [])),

                 (suffix valuetypesN full_name,(("",false),Expression.Named  []))],[]) fixestate

      |> ProofContext.theory_of 

      |> fold interprete_parent parents

      |> add_declaration (SOME full_name) (declare_declinfo components')

   end;

 (* prepare arguments *)

 fun read_raw_parent ctxt raw_T =

   (case ProofContext.read_typ_abbrev ctxt raw_T of

     Type (name, Ts) => (Ts, name)

   | T => error ("Bad parent statespace specification: " ^ Syntax.string_of_typ ctxt T));

 fun read_typ ctxt raw_T env =

   let

     val ctxt' = fold (Variable.declare_typ o TFree) env ctxt;

     val T = Syntax.read_typ ctxt' raw_T;

     val env' = OldTerm.add_typ_tfrees (T, env);

   in (T, env') end;

 fun cert_typ ctxt raw_T env =

   let

     val thy = ProofContext.theory_of ctxt;

     val T = Type.no_tvars (Sign.certify_typ thy raw_T)

       handle TYPE (msg, _, _) => error msg;

     val env' = OldTerm.add_typ_tfrees (T, env);

   in (T, env') end;

 fun gen_define_statespace prep_typ state_space args name parents comps thy =

   let (* - args distinct

          - only args may occur in comps and parent-instantiations

          - number of insts must match parent args

          - no duplicate renamings

          - renaming should occur in namespace

       *)

     val _ = writeln ("Defining statespace " ^ quote name ^ " ...");

     val ctxt = ProofContext.init_global thy;

     fun add_parent (Ts,pname,rs) env =

       let

         val full_pname = Sign.full_bname thy pname;

         val {args,components,...} =

               (case get_statespace (Context.Theory thy) full_pname of

                 SOME r => r

                | NONE => error ("Undefined statespace " ^ quote pname));

         val (Ts',env') = fold_map (prep_typ ctxt) Ts env

             handle ERROR msg => cat_error msg

                     ("The error(s) above occurred in parent statespace specification "

                     ^ quote pname);

         val err_insts = if length args <> length Ts' then

             ["number of type instantiation(s) does not match arguments of parent statespace "

               ^ quote pname]

             else [];

         val rnames = map fst rs

         val err_dup_renamings = (case duplicates (op =) rnames of

              [] => []

             | dups => ["Duplicate renaming(s) for " ^ commas dups])

         val cnames = map fst components;

         val err_rename_unknowns = (case subtract (op =) cnames rnames of

               [] => []

              | rs => ["Unknown components " ^ commas rs]);

         val rs' = map (AList.lookup (op =) rs o fst) components;

         val errs =err_insts @ err_dup_renamings @ err_rename_unknowns

       in if null errs then ((Ts',full_pname,rs'),env')

          else error (cat_lines (errs @ ["in parent statespace " ^ quote pname]))

       end;

     val (parents',env) = fold_map add_parent parents [];

     val err_dup_args =

          (case duplicates (op =) args of

             [] => []

           | dups => ["Duplicate type argument(s) " ^ commas dups]);

     val err_dup_components =

          (case duplicates (op =) (map fst comps) of

            [] => []

           | dups => ["Duplicate state-space components " ^ commas dups]);

     fun prep_comp (n,T) env =

       let val (T', env') = prep_typ ctxt T env handle ERROR msg =>

        cat_error msg ("The error(s) above occurred in component " ^ quote n)

       in ((n,T'), env') end;

     val (comps',env') = fold_map prep_comp comps env;

     val err_extra_frees =

       (case subtract (op =) args (map fst env') of

         [] => []

       | extras => ["Extra free type variable(s) " ^ commas extras]);

     val defaultS = Sign.defaultS thy;

     val args' = map (fn x => (x, AList.lookup (op =) env x |> the_default defaultS)) args;

     fun fst_eq ((x:string,_),(y,_)) = x = y;

     fun snd_eq ((_,t:typ),(_,u)) = t = u;

     val raw_parent_comps = maps (parent_components thy) parents';

     fun check_type (n,T) =

           (case distinct (snd_eq) (filter (curry fst_eq (n,T)) raw_parent_comps) of

              []  => []

            | [_] => []

            | rs  => ["Different types for component " ^ n ^": " ^

                 commas (map (Syntax.string_of_typ ctxt o snd) rs)])

     val err_dup_types = maps check_type (duplicates fst_eq raw_parent_comps)

     val parent_comps = distinct (fst_eq) raw_parent_comps;

     val all_comps = parent_comps @ comps';

     val err_comp_in_parent = (case duplicates (op =) (map fst all_comps) of

                [] => []

              | xs => ["Components already defined in parents: " ^ commas xs]);

     val errs = err_dup_args @ err_dup_components @ err_extra_frees @

                err_dup_types @ err_comp_in_parent;

   in if null errs

      then thy |> statespace_definition state_space args' name parents' parent_comps comps'

      else error (cat_lines errs)

   end

   handle ERROR msg => cat_error msg ("Failed to define statespace " ^ quote name);

 val define_statespace = gen_define_statespace read_typ NONE;

 val define_statespace_i = gen_define_statespace cert_typ;

 (*** parse/print - translations ***)

 local

 fun map_get_comp f ctxt (Free (name,_)) =

       (case (get_comp ctxt name) of

         SOME (T,_) => f T T dummyT

       | NONE => (Syntax.free "arbitrary"(*; error "context not ready"*)))

   | map_get_comp _ _ _ = Syntax.free "arbitrary";

 val get_comp_projection = map_get_comp project_free;

 val get_comp_injection  = map_get_comp inject_free;

 fun name_of (Free (n,_)) = n;

 in

 fun gen_lookup_tr ctxt s n =

       (case get_comp (Context.Proof ctxt) n of

         SOME (T,_) =>

            Syntax.const "StateFun.lookup"$Syntax.free (project_name T)$Syntax.free n$s

        | NONE =>

            if get_silent (Context.Proof ctxt)

            then Syntax.const "StateFun.lookup" $ Syntax.const "undefined" $ Syntax.free n $ s

            else raise TERM ("StateSpace.gen_lookup_tr: component " ^ n ^ " not defined",[]));

 fun lookup_tr ctxt [s,Free (n,_)] = gen_lookup_tr ctxt s n;

 fun lookup_swap_tr ctxt [Free (n,_),s] = gen_lookup_tr ctxt s n;

 fun lookup_tr' ctxt [_$Free (prj,_),n as (_$Free (name,_)),s] =

      ( case get_comp (Context.Proof ctxt) name of

          SOME (T,_) =>  if prj=project_name T then

                            Syntax.const "_statespace_lookup" $ s $ n

                         else raise Match

       | NONE => raise Match)

   | lookup_tr' _ ts = raise Match;

 fun gen_update_tr id ctxt n v s =

   let

     fun pname T = if id then "Fun.id" else project_name T

     fun iname T = if id then "Fun.id" else inject_name T

    in

      (case get_comp (Context.Proof ctxt) n of

        SOME (T,_) => Syntax.const "StateFun.update"$

                    Syntax.free (pname T)$Syntax.free (iname T)$

                    Syntax.free n$(Syntax.const KN $ v)$s

       | NONE =>

          if get_silent (Context.Proof ctxt)

          then Syntax.const "StateFun.update"$

                    Syntax.const "undefined" $ Syntax.const "undefined" $

                    Syntax.free n $ (Syntax.const KN $ v) $ s

          else raise TERM ("StateSpace.gen_update_tr: component " ^ n ^ " not defined",[]))

    end;

 fun update_tr ctxt [s,Free (n,_),v] = gen_update_tr false ctxt n v s;

 fun update_tr' ctxt [_$Free (prj,_),_$Free (inj,_),n as (_$Free (name,_)),(Const (k,_)$v),s] =

      if Long_Name.base_name k = Long_Name.base_name KN then

         (case get_comp (Context.Proof ctxt) name of

           SOME (T,_) => if inj=inject_name T andalso prj=project_name T then

                            Syntax.const "_statespace_update" $ s $ n $ v

                         else raise Match

          | NONE => raise Match)

      else raise Match

   | update_tr' _ _ = raise Match;

 end;

 (*** outer syntax *)

 val type_insts =

   Parse.typ >> single ||

   Parse.$$$ "(" |-- Parse.!!! (Parse.list1 Parse.typ --| Parse.$$$ ")")

 val comp = Parse.name -- (Parse.$$$ "::" |-- Parse.!!! Parse.typ);

 fun plus1_unless test scan =

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

 val mapsto = Parse.$$$ "=";

 val rename = Parse.name -- (mapsto |-- Parse.name);

 val renames = Scan.optional (Parse.$$$ "[" |-- Parse.!!! (Parse.list1 rename --| Parse.$$$ "]")) [];

 val parent = ((type_insts -- Parse.xname) || (Parse.xname >> pair [])) -- renames

              >> (fn ((insts,name),renames) => (insts,name,renames))

 val statespace_decl =

    Parse.type_args -- Parse.name --

     (Parse.$$$ "=" |--

      ((Scan.repeat1 comp >> pair []) ||

       (plus1_unless comp parent --

         Scan.optional (Parse.$$$ "+" |-- Parse.!!! (Scan.repeat1 comp)) [])))

 val statespace_command =

   Outer_Syntax.command "statespace" "define state space" Keyword.thy_decl

   (statespace_decl >> (fn ((args,name),(parents,comps)) =>

                            Toplevel.theory (define_statespace args name parents comps)))

 end;