src/HOL/Statespace/state_space.ML

tuned signature: more position information;

(*  Title:      HOL/Statespace/state_space.ML
    Author:     Norbert Schirmer, TU Muenchen, 2007
    Author:     Norbert Schirmer, Apple, 2021
*)

signature STATE_SPACE =
sig
  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 ->
     (xstring, string) Expression.expr * (binding * string option * mixfix) list ->
     string list -> string list -> theory -> theory

  val define_statespace :
     string list ->
     string ->
     ((string * bool) * (string list * bstring * (string * string) list)) list ->
     (string * string) list -> theory -> theory
  val define_statespace_i :
     string option ->
     string list ->
     string ->
     ((string * bool) * (typ list * bstring * (string * string) list)) list ->
     (string * typ) list -> theory -> theory

  val statespace_decl :
     ((string list * bstring) *
       (((string * bool) * (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 is_statespace : Context.generic -> xstring -> bool

  val get_comp' : Context.generic -> string -> (typ * string list) option
  val get_comp : Context.generic -> string -> (typ * string) option (* legacy wrapper, eventually replace by primed version *)
  val get_comps : Context.generic -> (typ * string list) Termtab.table

  val silent : bool Config.T

  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 -> bool -> Proof.context -> string -> term -> term -> term
  val gen_update_tr : (* legacy wrapper, eventually replace by primed version *)
     bool ->  Proof.context -> string -> term -> term -> term

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

  val trace_data: Context.generic -> unit
end;

structure StateSpace : STATE_SPACE =
struct

(* 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";


(* Library *)

fun fold1 f xs = fold f (tl xs) (hd xs)
fun fold1' f [] x = x
  | fold1' f xs _ = fold1 f xs

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;

fun comps_of_distinct_thm thm = Thm.prop_of thm
  |> (fn (_$(_$t)) => DistinctTreeProver.dest_tree t) |> map (fst o dest_Free) |> sort_strings;

fun insert_tagged_distinct_thms tagged_thm tagged_thms =
 let
   fun ins t1 [] = [t1]
     | ins (t1 as (names1, _)) ((t2 as (names2, _))::thms) =
         if Ord_List.subset string_ord (names1, names2) then t2::thms
         else if Ord_List.subset string_ord (names2, names1) then ins t1 thms
         else t2 :: ins t1 thms
 in
   ins tagged_thm tagged_thms
 end

fun join_tagged_distinct_thms tagged_thms1 tagged_thms2 =
  tagged_thms1 |> fold insert_tagged_distinct_thms tagged_thms2

fun tag_distinct_thm thm = (comps_of_distinct_thm thm, thm)
val tag_distinct_thms = map tag_distinct_thm

fun join_distinct_thms (thms1, thms2) =
  if pointer_eq (thms1, thms2) then thms1
  else join_tagged_distinct_thms (tag_distinct_thms thms1) (tag_distinct_thms thms2) |> map snd

fun insert_distinct_thm thm thms = join_distinct_thms (thms, [thm])


fun join_declinfo_entry name (T1:typ, names1:string list) (T2, names2) =
  let
    fun typ_info T names = @{make_string} T ^ " "  ^ Pretty.string_of (Pretty.str_list "(" ")" names);
  in
    if T1 = T2 then (T1, distinct (op =) (names1 @ names2))
    else error ("statespace component '" ^ name ^ "' disagrees on type:\n " ^
       typ_info T1 names1 ^ " vs. "  ^ typ_info T2 names2
     )
  end
fun guess_name (Free (x,_)) = x
  | guess_name _ = "unknown"

val join_declinfo = Termtab.join (fn t => uncurry (join_declinfo_entry (guess_name t)))


(*
  A component might appear in *different* statespaces within the same context. However, it must
  be mapped to the same type. Note that this information is currently only properly maintained
  within contexts where all components are actually "fixes" and not arbitrary terms. Moreover, on
  the theory level the info stays empty.

  This means that on the theory level we do not make use of the syntax and the tree-based distinct simprocs.
  N.B: It might still make sense (from a performance perspective) to overcome this limitation
  and even use the simprocs when a statespace is interpreted for concrete names like HOL-strings.
  Once the distinct-theorem is proven by the interpretation the simproc can use the positions in
  the tree to derive distinctness of two strings vs. HOL-string comparison.
 *)

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 Data = Generic_Data
(
  type T =
    (typ * string list) Termtab.table * (*declinfo: type, names of statespaces of component*)
    thm list Symtab.table * (*distinctthm: minimal list of maximal distinctness-assumptions for a component name*)
    statespace_info Symtab.table;
  val empty = (Termtab.empty, Symtab.empty, Symtab.empty);
  fun merge ((declinfo1, distinctthm1, statespaces1), (declinfo2, distinctthm2, statespaces2)) =
   (join_declinfo (declinfo1, declinfo2),
    Symtab.join (K join_distinct_thms) (distinctthm1, distinctthm2),
    Symtab.merge (K true) (statespaces1, statespaces2));
);

val get_declinfo = #1 o Data.get
val get_distinctthm = #2 o Data.get
val get_statespaces = #3 o Data.get

val map_declinfo = Data.map o @{apply 3(1)}
val map_distinctthm = Data.map o @{apply 3(2)}
val map_statespaces = Data.map o @{apply 3(3)}

fun trace_data context =
  tracing ("StateSpace.Data: " ^ @{make_string}
   {declinfo = get_declinfo context,
    distinctthm = get_distinctthm context,
    statespaces = get_statespaces context})

fun update_declinfo (n,v) = map_declinfo (fn declinfo =>
  let val vs = apsnd single v
  in Termtab.map_default (n, vs) (join_declinfo_entry (guess_name n) vs) declinfo end);

fun expression_no_pos (expr, fixes) : Expression.expression =
  (map (fn (name, inst) => ((name, Position.none), inst)) expr, fixes);

fun prove_interpretation_in ctxt_tac (name, expr) thy =
   thy
   |> Interpretation.global_sublocale_cmd (name, Position.none) (expression_no_pos expr) []
   |> Proof.global_terminal_proof
         ((Method.Basic (fn ctxt => SIMPLE_METHOD (ctxt_tac ctxt)), Position.no_range), NONE)
   |> Proof_Context.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 [] (expression_no_pos expr) elems
  |> snd
  |> Local_Theory.exit;

fun is_statespace context name =
  Symtab.defined (get_statespaces context) (Locale.intern (Context.theory_of context) name)

fun add_statespace name args parents components types =
  map_statespaces (Symtab.update_new (name, {args=args,parents=parents, components=components,types=types}))

val get_statespace = Symtab.lookup o get_statespaces
val the_statespace = the oo get_statespace


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 |> perhaps Long_Name.dest_hidden;
      val free = Free (n', Proof_Context.infer_type ctxt (n', dummyT))
    in SOME (free) end
  else (tracing ("variable not fixed or declared: " ^ name); NONE)


fun get_dist_thm context name =
  Symtab.lookup_list (get_distinctthm context) name
  |> map (Thm.transfer'' context)

fun get_dist_thm2 ctxt x y =
 (let
    val dist_thms = [x, y] |> map (#1 o dest_Free)
      |> maps (get_dist_thm (Context.Proof ctxt));

    fun get_paths dist_thm =
      let
        val ctree = Thm.cprop_of dist_thm |> Thm.dest_comb |> #2 |> Thm.dest_comb |> #2;
        val tree = Thm.term_of ctree;
        val x_path = the (DistinctTreeProver.find_tree x tree);
        val y_path = the (DistinctTreeProver.find_tree y tree);
      in SOME (dist_thm, x_path, y_path) end
      handle Option.Option => NONE

    val result = get_first get_paths dist_thms
  in
    result
  end)


fun get_comp' context name =
  mk_free (Context.proof_of context) name
  |> Option.mapPartial (fn t =>
       let
         val declinfo = get_declinfo context
       in
         case Termtab.lookup declinfo t of
           NONE => (* during syntax phase, types of fixes might not yet be constrained completely *)
             AList.lookup (fn (x, Free (n,_)) => n = x | _ => false) (Termtab.dest declinfo) name
         | some => some
       end)

(* legacy wrapper *)
fun get_comp ctxt name =
 get_comp' ctxt name |> Option.map (apsnd (fn ns => if null ns then "" else hd ns))

val get_comps = get_declinfo


(*** Tactics ***)

fun neq_x_y ctxt x y =
  (let
    val (dist_thm, x_path, y_path) = the (get_dist_thm2 ctxt x y);
    val thm = DistinctTreeProver.distinctTreeProver ctxt dist_thm x_path y_path;
  in SOME thm
  end handle Option.Option => NONE)

fun distinctTree_tac ctxt = SUBGOAL (fn (goal, i) =>
  (case goal of
    Const (\<^const_name>\<open>Trueprop\<close>, _) $
      (Const (\<^const_name>\<open>Not\<close>, _) $
        (Const (\<^const_name>\<open>HOL.eq\<close>, _) $ (x as Free _) $ (y as Free _))) =>
      (case neq_x_y ctxt x y of
        SOME neq => resolve_tac ctxt [neq] i
      | NONE => no_tac)
  | _ => no_tac));

val distinctNameSolver = mk_solver "distinctNameSolver" distinctTree_tac;

val distinct_simproc =
  Simplifier.make_simproc \<^context> "StateSpace.distinct_simproc"
   {lhss = [\<^term>\<open>x = y\<close>],
    proc = fn _ => fn ctxt => fn ct =>
      (case Thm.term_of ct of
        Const (\<^const_name>\<open>HOL.eq\<close>,_) $ (x as Free _) $ (y as Free _) =>
          Option.map (fn neq => DistinctTreeProver.neq_to_eq_False OF [neq])
            (neq_x_y ctxt x y)
      | _ => NONE)};

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 ctxt distinct_thm goal;
      in resolve_tac ctxt [rule] i end);

    fun tac ctxt =
      Locale.intro_locales_tac {strict = true, eager = true} ctxt [] THEN ALLGOALS (solve_tac ctxt);

  in
    thy |> prove_interpretation_in tac (name, parent_expr)
  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 dist_thm_name = distinct_compsN;

    val dist_thm_full_name = dist_thm_name;

    fun type_attr phi = Thm.declaration_attribute (fn thm => fn context =>
      (case context of
        Context.Theory _ => context
      | Context.Proof ctxt =>
        let
          val declinfo = get_declinfo context
          val tt = get_distinctthm context;
          val all_names = comps_of_distinct_thm thm;
          val thm0 = Thm.trim_context thm;
          fun upd name = Symtab.map_default (name, [thm0]) (insert_distinct_thm thm0)

          val tt' = tt |> fold upd all_names;
          val context' =
              Context_Position.set_visible false ctxt
              addsimprocs [distinct_simproc]
              |> Context_Position.restore_visible ctxt
              |> Context.Proof
              |> map_declinfo (K declinfo)
              |> map_distinctthm (K tt');
        in context' end));

    val attr = Attrib.internal \<^here> type_attr;

    val assume =
      ((Binding.name dist_thm_name, [attr]),
        [(HOLogic.Trueprop $
          (Const (\<^const_name>\<open>all_distinct\<close>, Type (\<^type_name>\<open>tree\<close>, [nameT]) --> HOLogic.boolT) $
            DistinctTreeProver.mk_tree (fn n => Free (n, nameT)) nameT
              (sort fast_string_ord all_comps)), [])]);
  in
    thy
    |> add_locale name ([], vars) [Element.Assumes [assume]]
    |> 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 add_declaration name decl thy =
  thy
  |> Named_Target.init [] name
  |> (fn lthy =>
    Local_Theory.declaration {syntax = true, pervasive = false, pos = Position.thread_data ()}
      (decl lthy) lthy)
  |> Local_Theory.exit_global;

fun parent_components thy (Ts, pname, renaming) =
  let
    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_statespace (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 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 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;

    fun parent_expr (prefix, (_, n, rs)) =
      (suffix namespaceN n, (prefix, (Expression.Positional rs,[])));
    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 = singleton (Name.variant_list arg_names) "'value";
    val nameN = singleton (Name.variant_list (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,
                    ((encode_type T,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 (prefix, (Ts, pname, _)) thy =
      let
        val {args,types,...} = the_statespace (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,
                     (prefix, (Expression.Positional (map SOME pars),[])))],[]);
      in
        prove_interpretation_in (fn ctxt => ALLGOALS (solve_tac ctxt (Assumption.all_prems_of ctxt)))
          (suffix valuetypesN name, expr) thy
      end;

    fun interprete_parent (prefix, (_, pname, rs)) =
      let
        val expr = ([(pname, (prefix, (Expression.Positional rs,[])))],[])
      in prove_interpretation_in
           (fn ctxt => Locale.intro_locales_tac {strict = true, eager = 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;
            val ctxt' = ctxt |> fold upd updates
          in ctxt' 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 (map snd 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_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' = Term.add_tfreesT 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' = Term.add_tfreesT 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 (prefix, (Ts, pname, rs)) env =
      let
        val prefix' =
          (case prefix of
            ("", mandatory) => (pname, mandatory)
          | _ => prefix);

        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 ((prefix', (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 o snd) 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 " ^ quote 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_quote 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 ***)

val silent = Attrib.setup_config_bool \<^binding>\<open>statespace_silent\<close> (K false);

fun gen_lookup_tr ctxt s n =
  (case get_comp' (Context.Proof ctxt) n of
    SOME (T, _) =>
      Syntax.const \<^const_name>\<open>StateFun.lookup\<close> $
        Syntax.free (project_name T) $ Syntax.free n $ s
  | NONE =>
      if Config.get ctxt silent
      then Syntax.const \<^const_name>\<open>StateFun.lookup\<close> $
        Syntax.const \<^const_syntax>\<open>undefined\<close> $ Syntax.free n $ s
      else raise TERM ("StateSpace.gen_lookup_tr: component " ^ quote 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' _ _ = raise Match;

fun gen'_update_tr const_val id ctxt n v s =
  let
    fun pname T = if id then \<^const_name>\<open>Fun.id\<close> else project_name T;
    fun iname T = if id then \<^const_name>\<open>Fun.id\<close> else inject_name T;
    val v = if const_val then (Syntax.const \<^const_name>\<open>K_statefun\<close> $ v) else v
  in
    (case get_comp' (Context.Proof ctxt) n of
      SOME (T, _) =>
        Syntax.const \<^const_name>\<open>StateFun.update\<close> $
          Syntax.free (pname T) $ Syntax.free (iname T) $
          Syntax.free n $ v $ s
    | NONE =>
        if Config.get ctxt silent then
          Syntax.const \<^const_name>\<open>StateFun.update\<close> $
            Syntax.const \<^const_syntax>\<open>undefined\<close> $ Syntax.const \<^const_syntax>\<open>undefined\<close> $
            Syntax.free n $ v $ s
       else raise TERM ("StateSpace.gen_update_tr: component " ^ n ^ " not defined", []))
   end;

val gen_update_tr = gen'_update_tr true

fun update_tr ctxt [s, x, v] =
  (case Term_Position.strip_positions x of
    Free (n, _) => gen'_update_tr true 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 \<^const_name>\<open>K_statefun\<close> 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;




(*** outer syntax *)

local

val type_insts =
  Parse.typ >> single ||
  \<^keyword>\<open>(\<close> |-- Parse.!!! (Parse.list1 Parse.typ --| \<^keyword>\<open>)\<close>)

val comp = Parse.name -- (\<^keyword>\<open>::\<close> |-- Parse.!!! Parse.typ);
fun plus1_unless test scan =
  scan ::: Scan.repeat (\<^keyword>\<open>+\<close> |-- Scan.unless test (Parse.!!! scan));

val mapsto = \<^keyword>\<open>=\<close>;
val rename = Parse.name -- (mapsto |-- Parse.name);
val renames = Scan.optional (\<^keyword>\<open>[\<close> |-- Parse.!!! (Parse.list1 rename --| \<^keyword>\<open>]\<close>)) [];

val parent =
  Parse_Spec.locale_prefix --
  ((type_insts -- Parse.name) || (Parse.name >> pair [])) -- renames
    >> (fn ((prefix, (insts, name)), renames) => (prefix, (insts, name, renames)));

in

val statespace_decl =
  Parse.type_args -- Parse.name --
    (\<^keyword>\<open>=\<close> |--
      ((Scan.repeat1 comp >> pair []) ||
        (plus1_unless comp parent --
          Scan.optional (\<^keyword>\<open>+\<close> |-- Parse.!!! (Scan.repeat1 comp)) [])));
val _ =
  Outer_Syntax.command \<^command_keyword>\<open>statespace\<close> "define state-space as locale context"
    (statespace_decl >> (fn ((args, name), (parents, comps)) =>
      Toplevel.theory (define_statespace args name parents comps)));

end;

end;