src/HOL/Tools/Nitpick/nitpick_model.ML
author wenzelm
Tue Jun 06 13:13:25 2017 +0200 (2017-06-06)
changeset 66020 a31760eee09d
parent 62752 d09d71223e7a
child 69593 3dda49e08b9d
permissions -rw-r--r--
discontinued obsolete print mode;
     1 (*  Title:      HOL/Tools/Nitpick/nitpick_model.ML
     2     Author:     Jasmin Blanchette, TU Muenchen
     3     Copyright   2009, 2010
     4 
     5 Model reconstruction for Nitpick.
     6 *)
     7 
     8 signature NITPICK_MODEL =
     9 sig
    10   type scope = Nitpick_Scope.scope
    11   type rep = Nitpick_Rep.rep
    12   type nut = Nitpick_Nut.nut
    13 
    14   type params =
    15     {show_types: bool,
    16      show_skolems: bool,
    17      show_consts: bool}
    18 
    19   type term_postprocessor =
    20     Proof.context -> string -> (typ -> term list) -> typ -> term -> term
    21 
    22   structure NameTable : TABLE
    23 
    24   val irrelevant : string
    25   val unknown : string
    26   val unrep_mixfix : unit -> string
    27   val register_term_postprocessor :
    28     typ -> term_postprocessor -> morphism -> Context.generic -> Context.generic
    29   val register_term_postprocessor_global :
    30     typ -> term_postprocessor -> theory -> theory
    31   val unregister_term_postprocessor :
    32     typ -> morphism -> Context.generic -> Context.generic
    33   val unregister_term_postprocessor_global : typ -> theory -> theory
    34   val tuple_list_for_name :
    35     nut NameTable.table -> Kodkod.raw_bound list -> nut -> int list list
    36   val dest_plain_fun : term -> bool * (term list * term list)
    37   val reconstruct_hol_model :
    38     params -> scope -> (term option * int list) list
    39     -> (typ option * string list) list -> (string * typ) list ->
    40     (string * typ) list -> nut list -> nut list -> nut list ->
    41     nut NameTable.table -> Kodkod.raw_bound list -> Pretty.T * bool
    42 end;
    43 
    44 structure Nitpick_Model : NITPICK_MODEL =
    45 struct
    46 
    47 open Nitpick_Util
    48 open Nitpick_HOL
    49 open Nitpick_Scope
    50 open Nitpick_Peephole
    51 open Nitpick_Rep
    52 open Nitpick_Nut
    53 
    54 structure KK = Kodkod
    55 
    56 type params =
    57   {show_types: bool,
    58    show_skolems: bool,
    59    show_consts: bool}
    60 
    61 type term_postprocessor =
    62   Proof.context -> string -> (typ -> term list) -> typ -> term -> term
    63 
    64 structure Data = Generic_Data
    65 (
    66   type T = (typ * term_postprocessor) list
    67   val empty = []
    68   val extend = I
    69   fun merge data = AList.merge (op =) (K true) data
    70 )
    71 
    72 fun xsym s s' () = if not (print_mode_active Print_Mode.ASCII) then s else s'
    73 
    74 val irrelevant = "_"
    75 val unknown = "?"
    76 val unrep_mixfix = xsym "\<dots>" "..."
    77 val maybe_mixfix = xsym "_\<^sup>?" "_?"
    78 val base_mixfix = xsym "_\<^bsub>base\<^esub>" "_.base"
    79 val step_mixfix = xsym "_\<^bsub>step\<^esub>" "_.step"
    80 val abs_mixfix = xsym "\<guillemotleft>_\<guillemotright>" "\"_\""
    81 val arg_var_prefix = "x"
    82 val cyclic_co_val_name = xsym "\<omega>" "w"
    83 val cyclic_const_prefix = xsym "\<xi>" "X"
    84 fun cyclic_type_name () = nitpick_prefix ^ cyclic_const_prefix ()
    85 val opt_flag = nitpick_prefix ^ "opt"
    86 val non_opt_flag = nitpick_prefix ^ "non_opt"
    87 
    88 type atom_pool = ((string * int) * int list) list
    89 
    90 fun mixfix (sy, ps, p) = Mixfix (Input.string sy, ps, p, Position.no_range)
    91 
    92 fun add_wacky_syntax ctxt =
    93   let
    94     val name_of = fst o dest_Const
    95     val thy = Proof_Context.theory_of ctxt
    96     val (unrep_s, thy) = thy
    97       |> Sign.declare_const_global ((@{binding nitpick_unrep}, @{typ 'a}),
    98         mixfix (unrep_mixfix (), [], 1000))
    99       |>> name_of
   100     val (maybe_s, thy) = thy
   101       |> Sign.declare_const_global ((@{binding nitpick_maybe}, @{typ "'a => 'a"}),
   102         mixfix (maybe_mixfix (), [1000], 1000))
   103       |>> name_of
   104     val (abs_s, thy) = thy
   105       |> Sign.declare_const_global ((@{binding nitpick_abs}, @{typ "'a => 'b"}),
   106         mixfix (abs_mixfix (), [40], 40))
   107       |>> name_of
   108     val (base_s, thy) = thy
   109       |> Sign.declare_const_global ((@{binding nitpick_base}, @{typ "'a => 'a"}),
   110         mixfix (base_mixfix (), [1000], 1000))
   111       |>> name_of
   112     val (step_s, thy) = thy
   113       |> Sign.declare_const_global ((@{binding nitpick_step}, @{typ "'a => 'a"}),
   114         mixfix (step_mixfix (), [1000], 1000))
   115       |>> name_of
   116   in
   117     (((unrep_s, maybe_s, abs_s), (base_s, step_s)),
   118      Proof_Context.transfer thy ctxt)
   119   end
   120 
   121 (** Term reconstruction **)
   122 
   123 fun nth_atom_number pool T j =
   124   case AList.lookup (op =) (!pool) T of
   125     SOME js =>
   126     (case find_index (curry (op =) j) js of
   127        ~1 => (Unsynchronized.change pool (cons (T, j :: js));
   128               length js + 1)
   129      | n => length js - n)
   130   | NONE => (Unsynchronized.change pool (cons (T, [j])); 1)
   131 
   132 fun atom_suffix s =
   133   nat_subscript
   134   #> (s <> "" andalso Symbol.is_ascii_digit (List.last (raw_explode s)))  (* FIXME Symbol.explode (?) *)
   135      ? prefix "\<^sub>,"
   136 
   137 fun nth_atom_name thy atomss pool prefix T j =
   138   let
   139     val ss = these (triple_lookup (type_match thy) atomss T)
   140     val m = nth_atom_number pool T j
   141   in
   142     if m <= length ss then
   143       nth ss (m - 1)
   144     else case T of
   145       Type (s, _) =>
   146       let val s' = shortest_name s in
   147         prefix ^
   148         (if T = @{typ string} then "s"
   149          else if String.isPrefix "\\" s' then s'
   150          else substring (s', 0, 1)) ^ atom_suffix s m
   151       end
   152     | TFree (s, _) => prefix ^ perhaps (try (unprefix "'")) s ^ atom_suffix s m
   153     | _ => raise TYPE ("Nitpick_Model.nth_atom_name", [T], [])
   154   end
   155 
   156 fun nth_atom thy atomss pool T j =
   157   Const (nth_atom_name thy atomss pool "" T j, T)
   158 
   159 fun extract_real_number (Const (@{const_name divide}, _) $ t1 $ t2) =
   160     real (snd (HOLogic.dest_number t1)) / real (snd (HOLogic.dest_number t2))
   161   | extract_real_number t = real (snd (HOLogic.dest_number t))
   162 
   163 fun nice_term_ord (Abs (_, _, t1), Abs (_, _, t2)) = nice_term_ord (t1, t2)
   164   | nice_term_ord tp = Real.compare (apply2 extract_real_number tp)
   165     handle TERM ("dest_number", _) =>
   166            case tp of
   167              (t11 $ t12, t21 $ t22) =>
   168              (case nice_term_ord (t11, t21) of
   169                 EQUAL => nice_term_ord (t12, t22)
   170               | ord => ord)
   171            | _ => Term_Ord.fast_term_ord tp
   172 
   173 fun register_term_postprocessor_generic T postproc =
   174   Data.map (cons (T, postproc))
   175 
   176 (* TODO: Consider morphism. *)
   177 fun register_term_postprocessor T postproc (_ : morphism) =
   178   register_term_postprocessor_generic T postproc
   179 
   180 val register_term_postprocessor_global =
   181   Context.theory_map oo register_term_postprocessor_generic
   182 
   183 fun unregister_term_postprocessor_generic T = Data.map (AList.delete (op =) T)
   184 (* TODO: Consider morphism. *)
   185 
   186 fun unregister_term_postprocessor T (_ : morphism) =
   187   unregister_term_postprocessor_generic T
   188 
   189 val unregister_term_postprocessor_global =
   190   Context.theory_map o unregister_term_postprocessor_generic
   191 
   192 fun tuple_list_for_name rel_table bounds name =
   193   the (AList.lookup (op =) bounds (the_rel rel_table name)) handle NUT _ => [[]]
   194 
   195 fun unarize_unbox_etc_term (Const (@{const_name FunBox}, _) $ t1) =
   196     unarize_unbox_etc_term t1
   197   | unarize_unbox_etc_term
   198         (Const (@{const_name PairBox},
   199                 Type (@{type_name fun}, [T1, Type (@{type_name fun}, [T2, _])]))
   200          $ t1 $ t2) =
   201     let val Ts = map uniterize_unarize_unbox_etc_type [T1, T2] in
   202       Const (@{const_name Pair}, Ts ---> Type (@{type_name prod}, Ts))
   203       $ unarize_unbox_etc_term t1 $ unarize_unbox_etc_term t2
   204     end
   205   | unarize_unbox_etc_term (Const (s, T)) =
   206     Const (s, uniterize_unarize_unbox_etc_type T)
   207   | unarize_unbox_etc_term (t1 $ t2) =
   208     unarize_unbox_etc_term t1 $ unarize_unbox_etc_term t2
   209   | unarize_unbox_etc_term (Free (s, T)) =
   210     Free (s, uniterize_unarize_unbox_etc_type T)
   211   | unarize_unbox_etc_term (Var (x, T)) =
   212     Var (x, uniterize_unarize_unbox_etc_type T)
   213   | unarize_unbox_etc_term (Bound j) = Bound j
   214   | unarize_unbox_etc_term (Abs (s, T, t')) =
   215     Abs (s, uniterize_unarize_unbox_etc_type T, unarize_unbox_etc_term t')
   216 
   217 fun factor_out_types (T1 as Type (@{type_name prod}, [T11, T12]))
   218                      (T2 as Type (@{type_name prod}, [T21, T22])) =
   219     let val (n1, n2) = apply2 num_factors_in_type (T11, T21) in
   220       if n1 = n2 then
   221         let
   222           val ((T11', opt_T12'), (T21', opt_T22')) = factor_out_types T12 T22
   223         in
   224           ((Type (@{type_name prod}, [T11, T11']), opt_T12'),
   225            (Type (@{type_name prod}, [T21, T21']), opt_T22'))
   226         end
   227       else if n1 < n2 then
   228         case factor_out_types T1 T21 of
   229           (p1, (T21', NONE)) => (p1, (T21', SOME T22))
   230         | (p1, (T21', SOME T22')) =>
   231           (p1, (T21', SOME (Type (@{type_name prod}, [T22', T22]))))
   232       else
   233         swap (factor_out_types T2 T1)
   234     end
   235   | factor_out_types (Type (@{type_name prod}, [T11, T12])) T2 =
   236     ((T11, SOME T12), (T2, NONE))
   237   | factor_out_types T1 (Type (@{type_name prod}, [T21, T22])) =
   238     ((T1, NONE), (T21, SOME T22))
   239   | factor_out_types T1 T2 = ((T1, NONE), (T2, NONE))
   240 
   241 (* Term-encoded data structure for holding key-value pairs as well as an "opt"
   242    flag indicating whether the function is approximated. *)
   243 fun make_plain_fun maybe_opt T1 T2 =
   244   let
   245     fun aux T1 T2 [] =
   246         Const (if maybe_opt then opt_flag else non_opt_flag, T1 --> T2)
   247       | aux T1 T2 ((t1, t2) :: tps) =
   248         Const (@{const_name fun_upd}, (T1 --> T2) --> T1 --> T2 --> T1 --> T2)
   249         $ aux T1 T2 tps $ t1 $ t2
   250   in aux T1 T2 o rev end
   251 
   252 fun is_plain_fun (Const (s, _)) = (s = opt_flag orelse s = non_opt_flag)
   253   | is_plain_fun (Const (@{const_name fun_upd}, _) $ t0 $ _ $ _) =
   254     is_plain_fun t0
   255   | is_plain_fun _ = false
   256 val dest_plain_fun =
   257   let
   258     fun aux (Abs (_, _, Const (s, _))) = (s <> irrelevant, ([], []))
   259       | aux (Const (s, _)) = (s <> non_opt_flag, ([], []))
   260       | aux (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =
   261         let val (maybe_opt, (ts1, ts2)) = aux t0 in
   262           (maybe_opt, (t1 :: ts1, t2 :: ts2))
   263         end
   264       | aux t = raise TERM ("Nitpick_Model.dest_plain_fun", [t])
   265   in apsnd (apply2 rev) o aux end
   266 
   267 fun break_in_two T T1 T2 t =
   268   let
   269     val ps = HOLogic.flat_tupleT_paths T
   270     val cut = length (HOLogic.strip_tupleT T1)
   271     val (ps1, ps2) = apply2 HOLogic.flat_tupleT_paths (T1, T2)
   272     val (ts1, ts2) = t |> HOLogic.strip_ptuple ps |> chop cut
   273   in (HOLogic.mk_ptuple ps1 T1 ts1, HOLogic.mk_ptuple ps2 T2 ts2) end
   274 
   275 fun pair_up (Type (@{type_name prod}, [T1', T2']))
   276             (t1 as Const (@{const_name Pair},
   277                           Type (@{type_name fun},
   278                                 [_, Type (@{type_name fun}, [_, T1])]))
   279              $ t11 $ t12) t2 =
   280     if T1 = T1' then HOLogic.mk_prod (t1, t2)
   281     else HOLogic.mk_prod (t11, pair_up T2' t12 t2)
   282   | pair_up _ t1 t2 = HOLogic.mk_prod (t1, t2)
   283 
   284 fun multi_pair_up T1 t1 (ts2, ts3) = map2 (pair o pair_up T1 t1) ts2 ts3
   285 
   286 fun format_fun T' T1 T2 t =
   287   let
   288     val T1' = pseudo_domain_type T'
   289     val T2' = pseudo_range_type T'
   290     fun do_curry T1 T1a T1b T2 t =
   291       let
   292         val (maybe_opt, tsp) = dest_plain_fun t
   293         val tps =
   294           tsp |>> map (break_in_two T1 T1a T1b)
   295               |> uncurry (map2 (fn (t1a, t1b) => fn t2 => (t1a, (t1b, t2))))
   296               |> AList.coalesce (op =)
   297               |> map (apsnd (make_plain_fun maybe_opt T1b T2))
   298       in make_plain_fun maybe_opt T1a (T1b --> T2) tps end
   299     and do_uncurry T1 T2 t =
   300       let
   301         val (maybe_opt, tsp) = dest_plain_fun t
   302         val tps =
   303           tsp |> op ~~
   304               |> maps (fn (t1, t2) =>
   305                           multi_pair_up T1 t1 (snd (dest_plain_fun t2)))
   306       in make_plain_fun maybe_opt T1 T2 tps end
   307     and do_arrow T1' T2' _ _ (Const (s, _)) = Const (s, T1' --> T2')
   308       | do_arrow T1' T2' T1 T2
   309                  (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =
   310         Const (@{const_name fun_upd},
   311                (T1' --> T2') --> T1' --> T2' --> T1' --> T2')
   312         $ do_arrow T1' T2' T1 T2 t0 $ do_term T1' T1 t1 $ do_term T2' T2 t2
   313       | do_arrow _ _ _ _ t =
   314         raise TERM ("Nitpick_Model.format_fun.do_arrow", [t])
   315     and do_fun T1' T2' T1 T2 t =
   316       case factor_out_types T1' T1 of
   317         ((_, NONE), (_, NONE)) => t |> do_arrow T1' T2' T1 T2
   318       | ((_, NONE), (T1a, SOME T1b)) =>
   319         t |> do_curry T1 T1a T1b T2 |> do_arrow T1' T2' T1a (T1b --> T2)
   320       | ((T1a', SOME T1b'), (_, NONE)) =>
   321         t |> do_arrow T1a' (T1b' --> T2') T1 T2 |> do_uncurry T1' T2'
   322       | _ => raise TYPE ("Nitpick_Model.format_fun.do_fun", [T1, T1'], [])
   323     and do_term (Type (@{type_name fun}, [T1', T2']))
   324                 (Type (@{type_name fun}, [T1, T2])) t =
   325         do_fun T1' T2' T1 T2 t
   326       | do_term (T' as Type (@{type_name prod}, Ts' as [T1', T2']))
   327                 (Type (@{type_name prod}, [T1, T2]))
   328                 (Const (@{const_name Pair}, _) $ t1 $ t2) =
   329         Const (@{const_name Pair}, Ts' ---> T')
   330         $ do_term T1' T1 t1 $ do_term T2' T2 t2
   331       | do_term T' T t =
   332         if T = T' then t
   333         else raise TYPE ("Nitpick_Model.format_fun.do_term", [T, T'], [])
   334   in if T1' = T1 andalso T2' = T2 then t else do_fun T1' T2' T1 T2 t end
   335 
   336 fun truth_const_sort_key @{const True} = "0"
   337   | truth_const_sort_key @{const False} = "2"
   338   | truth_const_sort_key _ = "1"
   339 
   340 fun mk_tuple (Type (@{type_name prod}, [T1, T2])) ts =
   341     HOLogic.mk_prod (mk_tuple T1 ts,
   342         mk_tuple T2 (List.drop (ts, length (HOLogic.flatten_tupleT T1))))
   343   | mk_tuple _ (t :: _) = t
   344   | mk_tuple T [] = raise TYPE ("Nitpick_Model.mk_tuple", [T], [])
   345 
   346 fun varified_type_match ctxt (candid_T, pat_T) =
   347   let val thy = Proof_Context.theory_of ctxt in
   348     strict_type_match thy (candid_T, varify_type ctxt pat_T)
   349   end
   350 
   351 fun all_values_of_type pool wacky_names (scope as {card_assigns, ...} : scope)
   352                        atomss sel_names rel_table bounds card T =
   353   let
   354     val card = if card = 0 then card_of_type card_assigns T else card
   355     fun nth_value_of_type n =
   356       let
   357         fun term unfold =
   358           reconstruct_term true unfold pool wacky_names scope atomss sel_names
   359                            rel_table bounds T T (Atom (card, 0)) [[n]]
   360       in
   361         case term false of
   362           t as Const (s, _) =>
   363           if String.isPrefix (cyclic_const_prefix ()) s then
   364             HOLogic.mk_eq (t, term true)
   365           else
   366             t
   367         | t => t
   368       end
   369   in index_seq 0 card |> map nth_value_of_type |> sort nice_term_ord end
   370 and reconstruct_term maybe_opt unfold pool
   371         (wacky_names as ((unrep_name, maybe_name, abs_name), _))
   372         (scope as {hol_ctxt as {thy, ctxt, ...}, binarize, card_assigns, bits,
   373                    data_types, ofs, ...})
   374         atomss sel_names rel_table bounds =
   375   let
   376     fun value_of_bits jss =
   377       let
   378         val j0 = offset_of_type ofs @{typ unsigned_bit}
   379         val js = map (Integer.add (~ j0) o the_single) jss
   380       in
   381         fold (fn j => Integer.add (reasonable_power 2 j |> j = bits ? op ~))
   382              js 0
   383       end
   384     val all_values =
   385       all_values_of_type pool wacky_names scope atomss sel_names rel_table
   386                          bounds 0
   387     fun postprocess_term (Type (@{type_name fun}, _)) = I
   388       | postprocess_term T =
   389         case Data.get (Context.Proof ctxt) of
   390           [] => I
   391         | postprocs =>
   392           case AList.lookup (varified_type_match ctxt) postprocs T of
   393             SOME postproc => postproc ctxt maybe_name all_values T
   394           | NONE => I
   395     fun postprocess_subterms Ts (t1 $ t2) =
   396         let val t = postprocess_subterms Ts t1 $ postprocess_subterms Ts t2 in
   397           postprocess_term (fastype_of1 (Ts, t)) t
   398         end
   399       | postprocess_subterms Ts (Abs (s, T, t')) =
   400         Abs (s, T, postprocess_subterms (T :: Ts) t')
   401       | postprocess_subterms Ts t = postprocess_term (fastype_of1 (Ts, t)) t
   402     fun make_set maybe_opt T tps =
   403       let
   404         val set_T = HOLogic.mk_setT T
   405         val empty_const = Const (@{const_abbrev Set.empty}, set_T)
   406         val insert_const = Const (@{const_name insert}, T --> set_T --> set_T)
   407         fun aux [] =
   408             if maybe_opt andalso not (is_complete_type data_types false T) then
   409               insert_const $ Const (unrep_name, T) $ empty_const
   410             else
   411               empty_const
   412           | aux ((t1, t2) :: zs) =
   413             aux zs
   414             |> t2 <> @{const False}
   415                ? curry (op $)
   416                        (insert_const
   417                         $ (t1 |> t2 <> @{const True}
   418                                  ? curry (op $)
   419                                          (Const (maybe_name, T --> T))))
   420       in
   421         if forall (fn (_, t) => t <> @{const True} andalso t <> @{const False})
   422                   tps then
   423           Const (unknown, set_T)
   424         else
   425           aux tps
   426       end
   427     fun make_map maybe_opt T1 T2 T2' =
   428       let
   429         val update_const = Const (@{const_name fun_upd},
   430                                   (T1 --> T2) --> T1 --> T2 --> T1 --> T2)
   431         fun aux' [] = Const (@{const_abbrev Map.empty}, T1 --> T2)
   432           | aux' ((t1, t2) :: tps) =
   433             (case t2 of
   434                Const (@{const_name None}, _) => aux' tps
   435              | _ => update_const $ aux' tps $ t1 $ t2)
   436         fun aux tps =
   437           if maybe_opt andalso not (is_complete_type data_types false T1) then
   438             update_const $ aux' tps $ Const (unrep_name, T1)
   439             $ (Const (@{const_name Some}, T2' --> T2) $ Const (unknown, T2'))
   440           else
   441             aux' tps
   442       in aux end
   443     fun polish_funs Ts t =
   444       (case fastype_of1 (Ts, t) of
   445          Type (@{type_name fun}, [T1, T2]) =>
   446          if is_plain_fun t then
   447            case T2 of
   448              Type (@{type_name option}, [T2']) =>
   449              let
   450                val (maybe_opt, ts_pair) =
   451                  dest_plain_fun t ||> apply2 (map (polish_funs Ts))
   452              in make_map maybe_opt T1 T2 T2' (rev (op ~~ ts_pair)) end
   453            | _ => raise SAME ()
   454          else
   455            raise SAME ()
   456        | _ => raise SAME ())
   457       handle SAME () =>
   458              case t of
   459                (t1 as Const (@{const_name fun_upd}, _) $ t11 $ _)
   460                $ (t2 as Const (s, _)) =>
   461                if s = unknown then polish_funs Ts t11
   462                else polish_funs Ts t1 $ polish_funs Ts t2
   463              | t1 $ t2 => polish_funs Ts t1 $ polish_funs Ts t2
   464              | Abs (s, T, t') => Abs (s, T, polish_funs (T :: Ts) t')
   465              | Const (s, Type (@{type_name fun}, [T1, T2])) =>
   466                if s = opt_flag orelse s = non_opt_flag then
   467                  Abs ("x", T1,
   468                       Const (if is_complete_type data_types false T1 then
   469                                irrelevant
   470                              else
   471                                unknown, T2))
   472                else
   473                  t
   474              | t => t
   475     fun make_fun_or_set maybe_opt T T1 T2 T' ts1 ts2 =
   476       ts1 ~~ ts2
   477       |> sort (nice_term_ord o apply2 fst)
   478       |> (case T of
   479             Type (@{type_name set}, _) =>
   480             sort_by (truth_const_sort_key o snd)
   481             #> make_set maybe_opt T'
   482           | _ =>
   483             make_plain_fun maybe_opt T1 T2
   484             #> unarize_unbox_etc_term
   485             #> format_fun (uniterize_unarize_unbox_etc_type T')
   486                           (uniterize_unarize_unbox_etc_type T1)
   487                           (uniterize_unarize_unbox_etc_type T2))
   488 
   489     fun term_for_fun_or_set seen T T' j =
   490         let
   491           val k1 = card_of_type card_assigns (pseudo_domain_type T)
   492           val k2 = card_of_type card_assigns (pseudo_range_type T)
   493         in
   494           term_for_rep true seen T T' (Vect (k1, Atom (k2, 0)))
   495                        [nth_combination (replicate k1 (k2, 0)) j]
   496           handle General.Subscript =>
   497                  raise ARG ("Nitpick_Model.reconstruct_term.\
   498                             \term_for_fun_or_set",
   499                             signed_string_of_int j ^ " for " ^
   500                             string_for_rep (Vect (k1, Atom (k2, 0))))
   501         end
   502     and term_for_atom seen (T as Type (@{type_name fun}, _)) T' j _ =
   503         term_for_fun_or_set seen T T' j
   504       | term_for_atom seen (T as Type (@{type_name set}, _)) T' j _ =
   505         term_for_fun_or_set seen T T' j
   506       | term_for_atom seen (Type (@{type_name prod}, [T1, T2])) _ j k =
   507         let
   508           val k1 = card_of_type card_assigns T1
   509           val k2 = k div k1
   510         in
   511           list_comb (HOLogic.pair_const T1 T2,
   512                      @{map 3} (fn T => term_for_atom seen T T) [T1, T2]
   513                           (* ### k2 or k1? FIXME *)
   514                           [j div k2, j mod k2] [k1, k2])
   515         end
   516       | term_for_atom seen @{typ prop} _ j k =
   517         HOLogic.mk_Trueprop (term_for_atom seen bool_T bool_T j k)
   518       | term_for_atom _ @{typ bool} _ j _ =
   519         if j = 0 then @{const False} else @{const True}
   520       | term_for_atom seen T _ j k =
   521         if T = nat_T then
   522           HOLogic.mk_number nat_T j
   523         else if T = int_T then
   524           HOLogic.mk_number int_T (int_for_atom (k, 0) j)
   525         else if is_fp_iterator_type T then
   526           HOLogic.mk_number nat_T (k - j - 1)
   527         else if T = @{typ bisim_iterator} then
   528           HOLogic.mk_number nat_T j
   529         else case data_type_spec data_types T of
   530           NONE => nth_atom thy atomss pool T j
   531         | SOME {deep = false, ...} => nth_atom thy atomss pool T j
   532         | SOME {co, constrs, ...} =>
   533           let
   534             fun tuples_for_const (s, T) =
   535               tuple_list_for_name rel_table bounds (ConstName (s, T, Any))
   536             fun cyclic_atom () =
   537               nth_atom thy atomss pool (Type (cyclic_type_name (), [])) j
   538             fun cyclic_var () =
   539               Var ((nth_atom_name thy atomss pool "" T j, 0), T)
   540             val discr_jsss = map (tuples_for_const o discr_for_constr o #const)
   541                                  constrs
   542             val real_j = j + offset_of_type ofs T
   543             val constr_x as (constr_s, constr_T) =
   544               get_first (fn (jss, {const, ...}) =>
   545                             if member (op =) jss [real_j] then SOME const
   546                             else NONE)
   547                         (discr_jsss ~~ constrs) |> the
   548             val arg_Ts = curried_binder_types constr_T
   549             val sel_xs =
   550               map (binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize
   551                                                           constr_x)
   552                   (index_seq 0 (length arg_Ts))
   553             val sel_Rs =
   554               map (fn x => get_first
   555                                (fn ConstName (s', T', R) =>
   556                                    if (s', T') = x then SOME R else NONE
   557                                  | u => raise NUT ("Nitpick_Model.reconstruct_\
   558                                                    \term.term_for_atom", [u]))
   559                                sel_names |> the) sel_xs
   560             val arg_Rs = map (snd o dest_Func) sel_Rs
   561             val sel_jsss = map tuples_for_const sel_xs
   562             val arg_jsss =
   563               map (map_filter (fn js => if hd js = real_j then SOME (tl js)
   564                                         else NONE)) sel_jsss
   565             val uncur_arg_Ts = binder_types constr_T
   566           in
   567             if co andalso not (null seen) andalso
   568                member (op =) (seen |> unfold ? (fst o split_last)) (T, j) then
   569               cyclic_var ()
   570             else if constr_s = @{const_name Word} then
   571               HOLogic.mk_number
   572                   (if T = @{typ "unsigned_bit word"} then nat_T else int_T)
   573                   (value_of_bits (the_single arg_jsss))
   574             else
   575               let
   576                 val seen = seen |> co ? cons (T, j)
   577                 val ts =
   578                   if length arg_Ts = 0 then
   579                     []
   580                   else
   581                     @{map 3} (fn Ts => term_for_rep true seen Ts Ts) arg_Ts arg_Rs
   582                          arg_jsss
   583                     |> mk_tuple (HOLogic.mk_tupleT uncur_arg_Ts)
   584                     |> dest_n_tuple (length uncur_arg_Ts)
   585                 val t =
   586                   if constr_s = @{const_name Abs_Frac} then
   587                     case ts of
   588                       [Const (@{const_name Pair}, _) $ t1 $ t2] =>
   589                       frac_from_term_pair (body_type T) t1 t2
   590                     | _ => raise TERM ("Nitpick_Model.reconstruct_term.\
   591                                        \term_for_atom (Abs_Frac)", ts)
   592                   else if is_abs_fun ctxt constr_x orelse
   593                           constr_s = @{const_name Quot} then
   594                     Const (abs_name, constr_T) $ the_single ts
   595                   else
   596                     list_comb (Const constr_x, ts)
   597               in
   598                 if co then
   599                   let val var = cyclic_var () in
   600                     if exists_subterm (curry (op =) var) t then
   601                       if co then
   602                         Const (@{const_name The}, (T --> bool_T) --> T)
   603                         $ Abs (cyclic_co_val_name (), T,
   604                                Const (@{const_name HOL.eq}, T --> T --> bool_T)
   605                                $ Bound 0 $ abstract_over (var, t))
   606                       else
   607                         cyclic_atom ()
   608                     else
   609                       t
   610                   end
   611                 else
   612                   t
   613               end
   614           end
   615     and term_for_vect seen k R T T' js =
   616       let
   617         val T1 = pseudo_domain_type T
   618         val T2 = pseudo_range_type T
   619       in
   620         make_fun_or_set true T T1 T2 T'
   621             (map (fn j => term_for_atom seen T1 T1 j k) (index_seq 0 k))
   622             (map (term_for_rep true seen T2 T2 R o single)
   623                  (chunk_list (arity_of_rep R) js))
   624       end
   625     and term_for_rep _ seen T T' (R as Atom (k, j0)) [[j]] =
   626         if j >= j0 andalso j < j0 + k then term_for_atom seen T T' (j - j0) k
   627         else raise REP ("Nitpick_Model.reconstruct_term.term_for_rep", [R])
   628       | term_for_rep _ seen (Type (@{type_name prod}, [T1, T2])) _
   629                      (Struct [R1, R2]) [js] =
   630         let
   631           val arity1 = arity_of_rep R1
   632           val (js1, js2) = chop arity1 js
   633         in
   634           list_comb (HOLogic.pair_const T1 T2,
   635                      @{map 3} (fn T => term_for_rep true seen T T) [T1, T2] [R1, R2]
   636                           [[js1], [js2]])
   637         end
   638       | term_for_rep _ seen T T' (Vect (k, R')) [js] =
   639         term_for_vect seen k R' T T' js
   640       | term_for_rep maybe_opt seen T T' (Func (R1, Formula Neut)) jss =
   641         let
   642           val T1 = pseudo_domain_type T
   643           val T2 = pseudo_range_type T
   644           val jss1 = all_combinations_for_rep R1
   645           val ts1 = map (term_for_rep true seen T1 T1 R1 o single) jss1
   646           val ts2 =
   647             map (fn js => term_for_rep true seen T2 T2 (Atom (2, 0))
   648                                        [[int_from_bool (member (op =) jss js)]])
   649                 jss1
   650         in make_fun_or_set maybe_opt T T1 T2 T' ts1 ts2 end
   651       | term_for_rep maybe_opt seen T T' (Func (R1, R2)) jss =
   652         let
   653           val T1 = pseudo_domain_type T
   654           val T2 = pseudo_range_type T
   655           val arity1 = arity_of_rep R1
   656           val jss1 = all_combinations_for_rep R1
   657           val ts1 = map (term_for_rep false seen T1 T1 R1 o single) jss1
   658           val grouped_jss2 = AList.group (op =) (map (chop arity1) jss)
   659           val ts2 = map (term_for_rep false seen T2 T2 R2 o the_default []
   660                          o AList.lookup (op =) grouped_jss2) jss1
   661         in make_fun_or_set maybe_opt T T1 T2 T' ts1 ts2 end
   662       | term_for_rep _ seen T T' (Opt R) jss =
   663         if null jss then Const (unknown, T)
   664         else term_for_rep true seen T T' R jss
   665       | term_for_rep _ _ T _ R jss =
   666         raise ARG ("Nitpick_Model.reconstruct_term.term_for_rep",
   667                    Syntax.string_of_typ ctxt T ^ " " ^ string_for_rep R ^ " " ^
   668                    string_of_int (length jss))
   669   in
   670     postprocess_subterms [] o polish_funs [] o unarize_unbox_etc_term
   671     oooo term_for_rep maybe_opt []
   672   end
   673 
   674 (** Constant postprocessing **)
   675 
   676 fun dest_n_tuple_type 1 T = [T]
   677   | dest_n_tuple_type n (Type (_, [T1, T2])) =
   678     T1 :: dest_n_tuple_type (n - 1) T2
   679   | dest_n_tuple_type _ T =
   680     raise TYPE ("Nitpick_Model.dest_n_tuple_type", [T], [])
   681 
   682 fun const_format thy def_tables (x as (s, T)) =
   683   if String.isPrefix unrolled_prefix s then
   684     const_format thy def_tables (original_name s, range_type T)
   685   else if String.isPrefix skolem_prefix s then
   686     let
   687       val k = unprefix skolem_prefix s
   688               |> strip_first_name_sep |> fst |> space_explode "@"
   689               |> hd |> Int.fromString |> the
   690     in [k, num_binder_types T - k] end
   691   else if original_name s <> s then
   692     [num_binder_types T]
   693   else case def_of_const thy def_tables x of
   694     SOME t' => if fixpoint_kind_of_rhs t' <> NoFp then
   695                  let val k = length (strip_abs_vars t') in
   696                    [k, num_binder_types T - k]
   697                  end
   698                else
   699                  [num_binder_types T]
   700   | NONE => [num_binder_types T]
   701 
   702 fun intersect_formats _ [] = []
   703   | intersect_formats [] _ = []
   704   | intersect_formats ks1 ks2 =
   705     let val ((ks1', k1), (ks2', k2)) = apply2 split_last (ks1, ks2) in
   706       intersect_formats (ks1' @ (if k1 > k2 then [k1 - k2] else []))
   707                         (ks2' @ (if k2 > k1 then [k2 - k1] else [])) @
   708       [Int.min (k1, k2)]
   709     end
   710 
   711 fun lookup_format thy def_tables formats t =
   712   case AList.lookup (fn (SOME x, SOME y) =>
   713                         (term_match thy) (x, y) | _ => false)
   714                     formats (SOME t) of
   715     SOME format => format
   716   | NONE => let val format = the (AList.lookup (op =) formats NONE) in
   717               case t of
   718                 Const x => intersect_formats format
   719                                              (const_format thy def_tables x)
   720               | _ => format
   721             end
   722 
   723 fun format_type default_format format T =
   724   let
   725     val T = uniterize_unarize_unbox_etc_type T
   726     val format = format |> filter (curry (op <) 0)
   727   in
   728     if forall (curry (op =) 1) format then
   729       T
   730     else
   731       let
   732         val (binder_Ts, body_T) = strip_type T
   733         val batched =
   734           binder_Ts
   735           |> map (format_type default_format default_format)
   736           |> rev |> chunk_list_unevenly (rev format)
   737           |> map (HOLogic.mk_tupleT o rev)
   738       in List.foldl (op -->) body_T batched end
   739   end
   740 
   741 fun format_term_type thy def_tables formats t =
   742   format_type (the (AList.lookup (op =) formats NONE))
   743               (lookup_format thy def_tables formats t) (fastype_of t)
   744 
   745 fun repair_special_format js m format =
   746   m - 1 downto 0 |> chunk_list_unevenly (rev format)
   747                  |> map (rev o filter_out (member (op =) js))
   748                  |> filter_out null |> map length |> rev
   749 
   750 fun user_friendly_const ({thy, evals, def_tables, skolems, special_funs, ...}
   751                          : hol_context) (base_name, step_name) formats =
   752   let
   753     val default_format = the (AList.lookup (op =) formats NONE)
   754     fun do_const (x as (s, T)) =
   755       (if String.isPrefix special_prefix s then
   756          let
   757            val do_term = map_aterms (fn Const x => fst (do_const x) | t' => t')
   758            val (x' as (_, T'), js, ts) =
   759              AList.find (op =) (!special_funs) (s, unarize_unbox_etc_type T)
   760              |> the_single
   761            val max_j = List.last js
   762            val Ts = List.take (binder_types T', max_j + 1)
   763            val missing_js = filter_out (member (op =) js) (0 upto max_j)
   764            val missing_Ts = filter_indices missing_js Ts
   765            fun nth_missing_var n =
   766              ((arg_var_prefix ^ nat_subscript (n + 1), 0), nth missing_Ts n)
   767            val missing_vars = map nth_missing_var (0 upto length missing_js - 1)
   768            val vars = special_bounds ts @ missing_vars
   769            val ts' =
   770              map (fn j =>
   771                      case AList.lookup (op =) (js ~~ ts) j of
   772                        SOME t => do_term t
   773                      | NONE =>
   774                        Var (nth missing_vars
   775                                 (find_index (curry (op =) j) missing_js)))
   776                  (0 upto max_j)
   777            val t = do_const x' |> fst
   778            val format =
   779              case AList.lookup (fn (SOME t1, SOME t2) => term_match thy (t1, t2)
   780                                  | _ => false) formats (SOME t) of
   781                SOME format =>
   782                repair_special_format js (num_binder_types T') format
   783              | NONE =>
   784                const_format thy def_tables x'
   785                |> repair_special_format js (num_binder_types T')
   786                |> intersect_formats default_format
   787          in
   788            (list_comb (t, ts') |> fold_rev abs_var vars,
   789             format_type default_format format T)
   790          end
   791        else if String.isPrefix uncurry_prefix s then
   792          let
   793            val (ss, s') = unprefix uncurry_prefix s
   794                           |> strip_first_name_sep |>> space_explode "@"
   795          in
   796            if String.isPrefix step_prefix s' then
   797              do_const (s', T)
   798            else
   799              let
   800                val k = the (Int.fromString (hd ss))
   801                val j = the (Int.fromString (List.last ss))
   802                val (before_Ts, (tuple_T, rest_T)) =
   803                  strip_n_binders j T ||> (strip_n_binders 1 #>> hd)
   804                val T' = before_Ts ---> dest_n_tuple_type k tuple_T ---> rest_T
   805              in do_const (s', T') end
   806          end
   807        else if String.isPrefix unrolled_prefix s then
   808          let val t = Const (original_name s, range_type T) in
   809            (lambda (Free (iter_var_prefix, nat_T)) t,
   810             format_type default_format
   811                         (lookup_format thy def_tables formats t) T)
   812          end
   813        else if String.isPrefix base_prefix s then
   814          (Const (base_name, T --> T) $ Const (unprefix base_prefix s, T),
   815           format_type default_format default_format T)
   816        else if String.isPrefix step_prefix s then
   817          (Const (step_name, T --> T) $ Const (unprefix step_prefix s, T),
   818           format_type default_format default_format T)
   819        else if String.isPrefix quot_normal_prefix s then
   820          let val t = Const (nitpick_prefix ^ "quotient normal form", T) in
   821            (t, format_term_type thy def_tables formats t)
   822          end
   823        else if String.isPrefix skolem_prefix s then
   824          let
   825            val ss = the (AList.lookup (op =) (!skolems) s)
   826            val (Ts, Ts') = chop (length ss) (binder_types T)
   827            val frees = map Free (ss ~~ Ts)
   828            val s' = original_name s
   829          in
   830            (fold lambda frees (Const (s', Ts' ---> T)),
   831             format_type default_format
   832                         (lookup_format thy def_tables formats (Const x)) T)
   833          end
   834        else if String.isPrefix eval_prefix s then
   835          let
   836            val t = nth evals (the (Int.fromString (unprefix eval_prefix s)))
   837          in (t, format_term_type thy def_tables formats t) end
   838        else
   839          (* The selector case can occur in conjunction with fractional types.
   840             It's not pretty. *)
   841          let val t = Const (s |> not (is_sel s) ? original_name, T) in
   842            (t, format_term_type thy def_tables formats t)
   843          end)
   844       |>> map_types uniterize_unarize_unbox_etc_type
   845       |>> shorten_names_in_term |>> Term.map_abs_vars shortest_name
   846   in do_const end
   847 
   848 fun assign_operator_for_const (s, T) =
   849   if String.isPrefix ubfp_prefix s then
   850     xsym "\<le>" "<=" ()
   851   else if String.isPrefix lbfp_prefix s then
   852     xsym "\<ge>" ">=" ()
   853   else if original_name s <> s then
   854     assign_operator_for_const (strip_first_name_sep s |> snd, T)
   855   else
   856     "="
   857 
   858 (** Model reconstruction **)
   859 
   860 fun unfold_outer_the_binders (t as Const (@{const_name The}, _)
   861                                    $ Abs (s, T, Const (@{const_name HOL.eq}, _)
   862                                                 $ Bound 0 $ t')) =
   863     betapply (Abs (s, T, t'), t) |> unfold_outer_the_binders
   864   | unfold_outer_the_binders t = t
   865 
   866 fun bisimilar_values _ 0 _ = true
   867   | bisimilar_values coTs max_depth (t1, t2) =
   868     let val T = fastype_of t1 in
   869       if exists_subtype (member (op =) coTs) T then
   870         let
   871           val ((head1, args1), (head2, args2)) =
   872             apply2 (strip_comb o unfold_outer_the_binders) (t1, t2)
   873           val max_depth = max_depth - (if member (op =) coTs T then 1 else 0)
   874         in
   875           head1 = head2 andalso
   876           forall (bisimilar_values coTs max_depth) (args1 ~~ args2)
   877         end
   878       else
   879         t1 = t2
   880     end
   881 
   882 fun pretty_term_auto_global ctxt t0 =
   883   let
   884     val t = map_aterms (fn t as Const (s, _) =>
   885       if s = irrelevant orelse s = unknown then Term.dummy else t | t => t) t0
   886 
   887     fun add_fake_const s =
   888       Symbol_Pos.is_identifier s
   889       ? (#2 o Sign.declare_const_global ((Binding.name s, @{typ 'a}), NoSyn))
   890 
   891     val globals = Term.add_const_names t []
   892       |> filter_out (String.isSubstring Long_Name.separator)
   893 
   894     val fake_ctxt =
   895       ctxt |> Proof_Context.background_theory (fn thy =>
   896         thy
   897         |> Sign.map_naming (K Name_Space.global_naming)
   898         |> fold (perhaps o try o add_fake_const) globals
   899         |> Sign.restore_naming thy)
   900   in
   901     Syntax.pretty_term fake_ctxt t
   902   end
   903 
   904 fun reconstruct_hol_model {show_types, show_skolems, show_consts}
   905         ({hol_ctxt = {thy, ctxt, max_bisim_depth, boxes, wfs, user_axioms,
   906                       debug, whacks, binary_ints, destroy_constrs, specialize,
   907                       star_linear_preds, total_consts, needs, tac_timeout,
   908                       evals, case_names, def_tables, nondef_table, nondefs,
   909                       simp_table, psimp_table, choice_spec_table, intro_table,
   910                       ground_thm_table, ersatz_table, skolems, special_funs,
   911                       unrolled_preds, wf_cache, constr_cache}, binarize,
   912                       card_assigns, bits, bisim_depth, data_types, ofs} : scope)
   913         formats atomss real_frees pseudo_frees free_names sel_names nonsel_names
   914         rel_table bounds =
   915   let
   916     val pool = Unsynchronized.ref []
   917     val (wacky_names as (_, base_step_names), ctxt) = add_wacky_syntax ctxt
   918     val hol_ctxt =
   919       {thy = thy, ctxt = ctxt, max_bisim_depth = max_bisim_depth, boxes = boxes,
   920        wfs = wfs, user_axioms = user_axioms, debug = debug, whacks = whacks,
   921        binary_ints = binary_ints, destroy_constrs = destroy_constrs,
   922        specialize = specialize, star_linear_preds = star_linear_preds,
   923        total_consts = total_consts, needs = needs, tac_timeout = tac_timeout,
   924        evals = evals, case_names = case_names, def_tables = def_tables,
   925        nondef_table = nondef_table, nondefs = nondefs, simp_table = simp_table,
   926        psimp_table = psimp_table, choice_spec_table = choice_spec_table,
   927        intro_table = intro_table, ground_thm_table = ground_thm_table,
   928        ersatz_table = ersatz_table, skolems = skolems,
   929        special_funs = special_funs, unrolled_preds = unrolled_preds,
   930        wf_cache = wf_cache, constr_cache = constr_cache}
   931     val scope =
   932       {hol_ctxt = hol_ctxt, binarize = binarize, card_assigns = card_assigns,
   933        bits = bits, bisim_depth = bisim_depth, data_types = data_types,
   934        ofs = ofs}
   935     fun term_for_rep maybe_opt unfold =
   936       reconstruct_term maybe_opt unfold pool wacky_names scope atomss
   937                        sel_names rel_table bounds
   938     val all_values =
   939       all_values_of_type pool wacky_names scope atomss sel_names rel_table
   940                          bounds
   941     fun is_codatatype_wellformed (cos : data_type_spec list)
   942                                  ({typ, card, ...} : data_type_spec) =
   943       let
   944         val ts = all_values card typ
   945         val max_depth = Integer.sum (map #card cos)
   946       in
   947         forall (not o bisimilar_values (map #typ cos) max_depth)
   948                (all_distinct_unordered_pairs_of ts)
   949       end
   950     fun pretty_for_assign name =
   951       let
   952         val (oper, (t1, T'), T) =
   953           case name of
   954             FreeName (s, T, _) =>
   955             let val t = Free (s, uniterize_unarize_unbox_etc_type T) in
   956               ("=", (t, format_term_type thy def_tables formats t), T)
   957             end
   958           | ConstName (s, T, _) =>
   959             (assign_operator_for_const (s, T),
   960              user_friendly_const hol_ctxt base_step_names formats (s, T), T)
   961           | _ => raise NUT ("Nitpick_Model.reconstruct_hol_model.\
   962                             \pretty_for_assign", [name])
   963         val t2 = if rep_of name = Any then
   964                    Const (@{const_name undefined}, T')
   965                  else
   966                    tuple_list_for_name rel_table bounds name
   967                    |> term_for_rep (not (is_fully_representable_set name)) false
   968                                    T T' (rep_of name)
   969       in
   970         Pretty.block (Pretty.breaks
   971             [pretty_term_auto_global ctxt t1, Pretty.str oper,
   972              pretty_term_auto_global ctxt t2])
   973       end
   974     fun pretty_for_data_type ({typ, card, complete, ...} : data_type_spec) =
   975       Pretty.block (Pretty.breaks
   976           (pretty_for_type ctxt typ ::
   977            (case typ of
   978               Type (@{type_name fun_box}, _) => [Pretty.str "[boxed]"]
   979             | Type (@{type_name pair_box}, _) => [Pretty.str "[boxed]"]
   980             | _ => []) @
   981            [Pretty.str "=",
   982             Pretty.enum "," "{" "}"
   983                 (map (pretty_term_auto_global ctxt) (all_values card typ) @
   984                  (if fun_from_pair complete false then []
   985                   else [Pretty.str (unrep_mixfix ())]))]))
   986     fun integer_data_type T =
   987       [{typ = T, card = card_of_type card_assigns T, co = false,
   988         self_rec = true, complete = (false, false), concrete = (true, true),
   989         deep = true, constrs = []}]
   990       handle TYPE ("Nitpick_HOL.card_of_type", _, _) => []
   991     val data_types =
   992       data_types |> filter #deep
   993                  |> append (maps integer_data_type [nat_T, int_T])
   994     val block_of_data_types =
   995       if show_types andalso not (null data_types) then
   996         [Pretty.big_list ("Type" ^ plural_s_for_list data_types ^ ":")
   997                          (map pretty_for_data_type data_types)]
   998       else
   999         []
  1000     fun block_of_names show title names =
  1001       if show andalso not (null names) then
  1002         Pretty.str (title ^ plural_s_for_list names ^ ":")
  1003         :: map (Pretty.indent indent_size o pretty_for_assign)
  1004                (sort_by (original_name o nickname_of) names)
  1005       else
  1006         []
  1007     fun free_name_for_term keep_all (x as (s, T)) =
  1008       case filter (curry (op =) x
  1009                    o pairf nickname_of (uniterize_unarize_unbox_etc_type
  1010                                         o type_of)) free_names of
  1011         [name] => SOME name
  1012       | [] => if keep_all then SOME (FreeName (s, T, Any)) else NONE
  1013       | _ => raise TERM ("Nitpick_Model.reconstruct_hol_model.\
  1014                          \free_name_for_term", [Const x])
  1015     val (skolem_names, nonskolem_nonsel_names) =
  1016       List.partition is_skolem_name nonsel_names
  1017     val (eval_names, noneval_nonskolem_nonsel_names) =
  1018       List.partition (String.isPrefix eval_prefix o nickname_of)
  1019                      nonskolem_nonsel_names
  1020       ||> filter_out (member (op =) [@{const_name bisim},
  1021                                      @{const_name bisim_iterator_max}]
  1022                       o nickname_of)
  1023       ||> append (map_filter (free_name_for_term false) pseudo_frees)
  1024     val real_free_names = map_filter (free_name_for_term true) real_frees
  1025     val chunks = block_of_names true "Free variable" real_free_names @
  1026                  block_of_names show_skolems "Skolem constant" skolem_names @
  1027                  block_of_names true "Evaluated term" eval_names @
  1028                  block_of_data_types @
  1029                  block_of_names show_consts "Constant"
  1030                                 noneval_nonskolem_nonsel_names
  1031     val codatatypes = filter #co data_types;
  1032   in
  1033     (Pretty.chunks (if null chunks then [Pretty.str "Empty assignment"]
  1034                     else chunks),
  1035      bisim_depth >= 0 orelse
  1036      forall (is_codatatype_wellformed codatatypes) codatatypes)
  1037   end
  1038 
  1039 end;