(*  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 -> int -> 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 (* FIXME odd merge *)}

);

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 I name expr []

   |> Proof.global_terminal_proof

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

   |> Proof_Context.theory_of

fun add_locale name expr elems thy =

  thy 

  |> Expression.add_locale I (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 I (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 mk_free ctxt name =

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

  then

    let val n' = Variable.intern_fixed ctxt name

    in SOME (Free (n', Proof_Context.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 = SUBGOAL (fn (goal, i) =>

  (case goal of

    Const (@{const_name Trueprop}, _) $

      (Const (@{const_name Not}, _) $

        (Const (@{const_name HOL.eq}, _) $ (x as Free _) $ (y as Free _))) =>

      (case neq_x_y ctxt x y of

        SOME neq => rtac neq i

      | NONE => no_tac)

  | _ => no_tac));

val distinctNameSolver = mk_solver' "distinctNameSolver"

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

                 SOME ctxt => distinctTree_tac ctxt

                | NONE => K no_tac)

val distinct_simproc =

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

    (fn thy => fn ss => (fn (Const (@{const_name HOL.eq},_)$(x as Free _)$(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 = CSUBGOAL (fn (goal, i) =>

      let

        val distinct_thm = Proof_Context.get_thm ctxt dist_thm_name;

        val rule = DistinctTreeProver.distinct_implProver distinct_thm goal;

      in rtac rule i end);

    fun tac ctxt =

      Locale.intro_locales_tac true ctxt [] THEN ALLGOALS (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 = Thm.declaration_attribute (fn thm => fn context =>

      (case context of

        Context.Theory _ => context

      | Context.Proof ctxt =>

        let

          val {declinfo,distinctthm=tt,silent} = NameSpaceData.get context;

          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 =

            Simplifier.map_ss

              (Simplifier.with_context (Context_Position.set_visible false ctxt)

                (fn ss => ss addsimprocs [distinct_simproc]));

          val context' =

              context

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

              |> activate_simproc;

        in context' 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]

     |> Proof_Context.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);

fun add_declaration name decl thy =

  thy

  |> Named_Target.init I 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 General.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 = Proof_Context.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 =

      Print_Mode.setmp []

        (Syntax.string_of_typ (Config.put show_sorts true (Syntax.init_pretty_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) []

     |> Proof_Context.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

     |> Proof_Context.theory_of 

     |> fold interprete_parent parents

     |> add_declaration full_name (declare_declinfo components')

  end;

(* prepare arguments *)

fun read_raw_parent ctxt raw_T =

  (case Proof_Context.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 = Proof_Context.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 = Proof_Context.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, x] =

  (case Term_Position.strip_positions x of

    Free (n,_) => gen_lookup_tr ctxt s n

  | _ => raise Match);

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, x, v] =

  (case Term_Position.strip_positions x of

    Free (n, _) => gen_update_tr false ctxt n v s

  | _ => raise Match);

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;