src/HOL/Tools/Nitpick/nitpick_model.ML
author blanchet
Wed Oct 07 15:31:47 2015 +0200 (2015-10-07)
changeset 61357 25ca76cfa9ce
parent 61333 24b5e7579fdd
child 61358 131fc8c10402
permissions -rw-r--r--
removed dead code
     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 print_mode_active Symbol.xsymbolsN 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 add_wacky_syntax ctxt =
    91   let
    92     val name_of = fst o dest_Const
    93     val thy = Proof_Context.theory_of ctxt
    94     val (unrep_s, thy) = thy
    95       |> Sign.declare_const_global ((@{binding nitpick_unrep}, @{typ 'a}),
    96         Mixfix (unrep_mixfix (), [], 1000))
    97       |>> name_of
    98     val (maybe_s, thy) = thy
    99       |> Sign.declare_const_global ((@{binding nitpick_maybe}, @{typ "'a => 'a"}),
   100         Mixfix (maybe_mixfix (), [1000], 1000))
   101       |>> name_of
   102     val (abs_s, thy) = thy
   103       |> Sign.declare_const_global ((@{binding nitpick_abs}, @{typ "'a => 'b"}),
   104         Mixfix (abs_mixfix (), [40], 40))
   105       |>> name_of
   106     val (base_s, thy) = thy
   107       |> Sign.declare_const_global ((@{binding nitpick_base}, @{typ "'a => 'a"}),
   108         Mixfix (base_mixfix (), [1000], 1000))
   109       |>> name_of
   110     val (step_s, thy) = thy
   111       |> Sign.declare_const_global ((@{binding nitpick_step}, @{typ "'a => 'a"}),
   112         Mixfix (step_mixfix (), [1000], 1000))
   113       |>> name_of
   114   in
   115     (((unrep_s, maybe_s, abs_s), (base_s, step_s)),
   116      Proof_Context.transfer thy ctxt)
   117   end
   118 
   119 (** Term reconstruction **)
   120 
   121 fun nth_atom_number pool T j =
   122   case AList.lookup (op =) (!pool) T of
   123     SOME js =>
   124     (case find_index (curry (op =) j) js of
   125        ~1 => (Unsynchronized.change pool (cons (T, j :: js));
   126               length js + 1)
   127      | n => length js - n)
   128   | NONE => (Unsynchronized.change pool (cons (T, [j])); 1)
   129 
   130 fun atom_suffix s =
   131   nat_subscript
   132   #> (s <> "" andalso Symbol.is_ascii_digit (List.last (raw_explode s)))  (* FIXME Symbol.explode (?) *)
   133      ? prefix "\<^sub>,"
   134 
   135 fun nth_atom_name thy atomss pool prefix T j =
   136   let
   137     val ss = these (triple_lookup (type_match thy) atomss T)
   138     val m = nth_atom_number pool T j
   139   in
   140     if m <= length ss then
   141       nth ss (m - 1)
   142     else case T of
   143       Type (s, _) =>
   144       let val s' = shortest_name s in
   145         prefix ^
   146         (if T = @{typ string} then "s"
   147          else if String.isPrefix "\\" s' then s'
   148          else substring (s', 0, 1)) ^ atom_suffix s m
   149       end
   150     | TFree (s, _) => prefix ^ perhaps (try (unprefix "'")) s ^ atom_suffix s m
   151     | _ => raise TYPE ("Nitpick_Model.nth_atom_name", [T], [])
   152   end
   153 
   154 fun nth_atom thy atomss pool T j =
   155   Const (nth_atom_name thy atomss pool "" T j, T)
   156 
   157 fun extract_real_number (Const (@{const_name divide}, _) $ t1 $ t2) =
   158     real (snd (HOLogic.dest_number t1)) / real (snd (HOLogic.dest_number t2))
   159   | extract_real_number t = real (snd (HOLogic.dest_number t))
   160 
   161 fun nice_term_ord (Abs (_, _, t1), Abs (_, _, t2)) = nice_term_ord (t1, t2)
   162   | nice_term_ord tp = Real.compare (apply2 extract_real_number tp)
   163     handle TERM ("dest_number", _) =>
   164            case tp of
   165              (t11 $ t12, t21 $ t22) =>
   166              (case nice_term_ord (t11, t21) of
   167                 EQUAL => nice_term_ord (t12, t22)
   168               | ord => ord)
   169            | _ => Term_Ord.fast_term_ord tp
   170 
   171 fun register_term_postprocessor_generic T postproc =
   172   Data.map (cons (T, postproc))
   173 
   174 (* TODO: Consider morphism. *)
   175 fun register_term_postprocessor T postproc (_ : morphism) =
   176   register_term_postprocessor_generic T postproc
   177 
   178 val register_term_postprocessor_global =
   179   Context.theory_map oo register_term_postprocessor_generic
   180 
   181 fun unregister_term_postprocessor_generic T = Data.map (AList.delete (op =) T)
   182 (* TODO: Consider morphism. *)
   183 
   184 fun unregister_term_postprocessor T (_ : morphism) =
   185   unregister_term_postprocessor_generic T
   186 
   187 val unregister_term_postprocessor_global =
   188   Context.theory_map o unregister_term_postprocessor_generic
   189 
   190 fun tuple_list_for_name rel_table bounds name =
   191   the (AList.lookup (op =) bounds (the_rel rel_table name)) handle NUT _ => [[]]
   192 
   193 fun unarize_unbox_etc_term (Const (@{const_name FunBox}, _) $ t1) =
   194     unarize_unbox_etc_term t1
   195   | unarize_unbox_etc_term
   196         (Const (@{const_name PairBox},
   197                 Type (@{type_name fun}, [T1, Type (@{type_name fun}, [T2, _])]))
   198          $ t1 $ t2) =
   199     let val Ts = map uniterize_unarize_unbox_etc_type [T1, T2] in
   200       Const (@{const_name Pair}, Ts ---> Type (@{type_name prod}, Ts))
   201       $ unarize_unbox_etc_term t1 $ unarize_unbox_etc_term t2
   202     end
   203   | unarize_unbox_etc_term (Const (s, T)) =
   204     Const (s, uniterize_unarize_unbox_etc_type T)
   205   | unarize_unbox_etc_term (t1 $ t2) =
   206     unarize_unbox_etc_term t1 $ unarize_unbox_etc_term t2
   207   | unarize_unbox_etc_term (Free (s, T)) =
   208     Free (s, uniterize_unarize_unbox_etc_type T)
   209   | unarize_unbox_etc_term (Var (x, T)) =
   210     Var (x, uniterize_unarize_unbox_etc_type T)
   211   | unarize_unbox_etc_term (Bound j) = Bound j
   212   | unarize_unbox_etc_term (Abs (s, T, t')) =
   213     Abs (s, uniterize_unarize_unbox_etc_type T, unarize_unbox_etc_term t')
   214 
   215 fun factor_out_types (T1 as Type (@{type_name prod}, [T11, T12]))
   216                      (T2 as Type (@{type_name prod}, [T21, T22])) =
   217     let val (n1, n2) = apply2 num_factors_in_type (T11, T21) in
   218       if n1 = n2 then
   219         let
   220           val ((T11', opt_T12'), (T21', opt_T22')) = factor_out_types T12 T22
   221         in
   222           ((Type (@{type_name prod}, [T11, T11']), opt_T12'),
   223            (Type (@{type_name prod}, [T21, T21']), opt_T22'))
   224         end
   225       else if n1 < n2 then
   226         case factor_out_types T1 T21 of
   227           (p1, (T21', NONE)) => (p1, (T21', SOME T22))
   228         | (p1, (T21', SOME T22')) =>
   229           (p1, (T21', SOME (Type (@{type_name prod}, [T22', T22]))))
   230       else
   231         swap (factor_out_types T2 T1)
   232     end
   233   | factor_out_types (Type (@{type_name prod}, [T11, T12])) T2 =
   234     ((T11, SOME T12), (T2, NONE))
   235   | factor_out_types T1 (Type (@{type_name prod}, [T21, T22])) =
   236     ((T1, NONE), (T21, SOME T22))
   237   | factor_out_types T1 T2 = ((T1, NONE), (T2, NONE))
   238 
   239 (* Term-encoded data structure for holding key-value pairs as well as an "opt"
   240    flag indicating whether the function is approximated. *)
   241 fun make_plain_fun maybe_opt T1 T2 =
   242   let
   243     fun aux T1 T2 [] =
   244         Const (if maybe_opt then opt_flag else non_opt_flag, T1 --> T2)
   245       | aux T1 T2 ((t1, t2) :: tps) =
   246         Const (@{const_name fun_upd}, (T1 --> T2) --> T1 --> T2 --> T1 --> T2)
   247         $ aux T1 T2 tps $ t1 $ t2
   248   in aux T1 T2 o rev end
   249 
   250 fun is_plain_fun (Const (s, _)) = (s = opt_flag orelse s = non_opt_flag)
   251   | is_plain_fun (Const (@{const_name fun_upd}, _) $ t0 $ _ $ _) =
   252     is_plain_fun t0
   253   | is_plain_fun _ = false
   254 val dest_plain_fun =
   255   let
   256     fun aux (Abs (_, _, Const (s, _))) = (s <> irrelevant, ([], []))
   257       | aux (Const (s, _)) = (s <> non_opt_flag, ([], []))
   258       | aux (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =
   259         let val (maybe_opt, (ts1, ts2)) = aux t0 in
   260           (maybe_opt, (t1 :: ts1, t2 :: ts2))
   261         end
   262       | aux t = raise TERM ("Nitpick_Model.dest_plain_fun", [t])
   263   in apsnd (apply2 rev) o aux end
   264 
   265 fun break_in_two T T1 T2 t =
   266   let
   267     val ps = HOLogic.flat_tupleT_paths T
   268     val cut = length (HOLogic.strip_tupleT T1)
   269     val (ps1, ps2) = apply2 HOLogic.flat_tupleT_paths (T1, T2)
   270     val (ts1, ts2) = t |> HOLogic.strip_ptuple ps |> chop cut
   271   in (HOLogic.mk_ptuple ps1 T1 ts1, HOLogic.mk_ptuple ps2 T2 ts2) end
   272 
   273 fun pair_up (Type (@{type_name prod}, [T1', T2']))
   274             (t1 as Const (@{const_name Pair},
   275                           Type (@{type_name fun},
   276                                 [_, Type (@{type_name fun}, [_, T1])]))
   277              $ t11 $ t12) t2 =
   278     if T1 = T1' then HOLogic.mk_prod (t1, t2)
   279     else HOLogic.mk_prod (t11, pair_up T2' t12 t2)
   280   | pair_up _ t1 t2 = HOLogic.mk_prod (t1, t2)
   281 
   282 fun multi_pair_up T1 t1 (ts2, ts3) = map2 (pair o pair_up T1 t1) ts2 ts3
   283 
   284 fun format_fun T' T1 T2 t =
   285   let
   286     val T1' = pseudo_domain_type T'
   287     val T2' = pseudo_range_type T'
   288     fun do_curry T1 T1a T1b T2 t =
   289       let
   290         val (maybe_opt, tsp) = dest_plain_fun t
   291         val tps =
   292           tsp |>> map (break_in_two T1 T1a T1b)
   293               |> uncurry (map2 (fn (t1a, t1b) => fn t2 => (t1a, (t1b, t2))))
   294               |> AList.coalesce (op =)
   295               |> map (apsnd (make_plain_fun maybe_opt T1b T2))
   296       in make_plain_fun maybe_opt T1a (T1b --> T2) tps end
   297     and do_uncurry T1 T2 t =
   298       let
   299         val (maybe_opt, tsp) = dest_plain_fun t
   300         val tps =
   301           tsp |> op ~~
   302               |> maps (fn (t1, t2) =>
   303                           multi_pair_up T1 t1 (snd (dest_plain_fun t2)))
   304       in make_plain_fun maybe_opt T1 T2 tps end
   305     and do_arrow T1' T2' _ _ (Const (s, _)) = Const (s, T1' --> T2')
   306       | do_arrow T1' T2' T1 T2
   307                  (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =
   308         Const (@{const_name fun_upd},
   309                (T1' --> T2') --> T1' --> T2' --> T1' --> T2')
   310         $ do_arrow T1' T2' T1 T2 t0 $ do_term T1' T1 t1 $ do_term T2' T2 t2
   311       | do_arrow _ _ _ _ t =
   312         raise TERM ("Nitpick_Model.format_fun.do_arrow", [t])
   313     and do_fun T1' T2' T1 T2 t =
   314       case factor_out_types T1' T1 of
   315         ((_, NONE), (_, NONE)) => t |> do_arrow T1' T2' T1 T2
   316       | ((_, NONE), (T1a, SOME T1b)) =>
   317         t |> do_curry T1 T1a T1b T2 |> do_arrow T1' T2' T1a (T1b --> T2)
   318       | ((T1a', SOME T1b'), (_, NONE)) =>
   319         t |> do_arrow T1a' (T1b' --> T2') T1 T2 |> do_uncurry T1' T2'
   320       | _ => raise TYPE ("Nitpick_Model.format_fun.do_fun", [T1, T1'], [])
   321     and do_term (Type (@{type_name fun}, [T1', T2']))
   322                 (Type (@{type_name fun}, [T1, T2])) t =
   323         do_fun T1' T2' T1 T2 t
   324       | do_term (T' as Type (@{type_name prod}, Ts' as [T1', T2']))
   325                 (Type (@{type_name prod}, [T1, T2]))
   326                 (Const (@{const_name Pair}, _) $ t1 $ t2) =
   327         Const (@{const_name Pair}, Ts' ---> T')
   328         $ do_term T1' T1 t1 $ do_term T2' T2 t2
   329       | do_term T' T t =
   330         if T = T' then t
   331         else raise TYPE ("Nitpick_Model.format_fun.do_term", [T, T'], [])
   332   in if T1' = T1 andalso T2' = T2 then t else do_fun T1' T2' T1 T2 t end
   333 
   334 fun truth_const_sort_key @{const True} = "0"
   335   | truth_const_sort_key @{const False} = "2"
   336   | truth_const_sort_key _ = "1"
   337 
   338 fun mk_tuple (Type (@{type_name prod}, [T1, T2])) ts =
   339     HOLogic.mk_prod (mk_tuple T1 ts,
   340         mk_tuple T2 (List.drop (ts, length (HOLogic.flatten_tupleT T1))))
   341   | mk_tuple _ (t :: _) = t
   342   | mk_tuple T [] = raise TYPE ("Nitpick_Model.mk_tuple", [T], [])
   343 
   344 fun varified_type_match ctxt (candid_T, pat_T) =
   345   let val thy = Proof_Context.theory_of ctxt in
   346     strict_type_match thy (candid_T, varify_type ctxt pat_T)
   347   end
   348 
   349 fun all_values_of_type pool wacky_names (scope as {card_assigns, ...} : scope)
   350                        atomss sel_names rel_table bounds card T =
   351   let
   352     val card = if card = 0 then card_of_type card_assigns T else card
   353     fun nth_value_of_type n =
   354       let
   355         fun term unfold =
   356           reconstruct_term true unfold pool wacky_names scope atomss sel_names
   357                            rel_table bounds T T (Atom (card, 0)) [[n]]
   358       in
   359         case term false of
   360           t as Const (s, _) =>
   361           if String.isPrefix (cyclic_const_prefix ()) s then
   362             HOLogic.mk_eq (t, term true)
   363           else
   364             t
   365         | t => t
   366       end
   367   in index_seq 0 card |> map nth_value_of_type |> sort nice_term_ord end
   368 and reconstruct_term maybe_opt unfold pool
   369         (wacky_names as ((unrep_name, maybe_name, abs_name), _))
   370         (scope as {hol_ctxt as {thy, ctxt, ...}, binarize, card_assigns, bits,
   371                    data_types, ofs, ...})
   372         atomss sel_names rel_table bounds =
   373   let
   374     fun value_of_bits jss =
   375       let
   376         val j0 = offset_of_type ofs @{typ unsigned_bit}
   377         val js = map (Integer.add (~ j0) o the_single) jss
   378       in
   379         fold (fn j => Integer.add (reasonable_power 2 j |> j = bits ? op ~))
   380              js 0
   381       end
   382     val all_values =
   383       all_values_of_type pool wacky_names scope atomss sel_names rel_table
   384                          bounds 0
   385     fun postprocess_term (Type (@{type_name fun}, _)) = I
   386       | postprocess_term T =
   387         case Data.get (Context.Proof ctxt) of
   388           [] => I
   389         | postprocs =>
   390           case AList.lookup (varified_type_match ctxt) postprocs T of
   391             SOME postproc => postproc ctxt maybe_name all_values T
   392           | NONE => I
   393     fun postprocess_subterms Ts (t1 $ t2) =
   394         let val t = postprocess_subterms Ts t1 $ postprocess_subterms Ts t2 in
   395           postprocess_term (fastype_of1 (Ts, t)) t
   396         end
   397       | postprocess_subterms Ts (Abs (s, T, t')) =
   398         Abs (s, T, postprocess_subterms (T :: Ts) t')
   399       | postprocess_subterms Ts t = postprocess_term (fastype_of1 (Ts, t)) t
   400     fun make_set maybe_opt T tps =
   401       let
   402         val set_T = HOLogic.mk_setT T
   403         val empty_const = Const (@{const_abbrev Set.empty}, set_T)
   404         val insert_const = Const (@{const_name insert}, T --> set_T --> set_T)
   405         fun aux [] =
   406             if maybe_opt andalso not (is_complete_type data_types false T) then
   407               insert_const $ Const (unrep_name, T) $ empty_const
   408             else
   409               empty_const
   410           | aux ((t1, t2) :: zs) =
   411             aux zs
   412             |> t2 <> @{const False}
   413                ? curry (op $)
   414                        (insert_const
   415                         $ (t1 |> t2 <> @{const True}
   416                                  ? curry (op $)
   417                                          (Const (maybe_name, T --> T))))
   418       in
   419         if forall (fn (_, t) => t <> @{const True} andalso t <> @{const False})
   420                   tps then
   421           Const (unknown, set_T)
   422         else
   423           aux tps
   424       end
   425     fun make_map maybe_opt T1 T2 T2' =
   426       let
   427         val update_const = Const (@{const_name fun_upd},
   428                                   (T1 --> T2) --> T1 --> T2 --> T1 --> T2)
   429         fun aux' [] = Const (@{const_abbrev Map.empty}, T1 --> T2)
   430           | aux' ((t1, t2) :: tps) =
   431             (case t2 of
   432                Const (@{const_name None}, _) => aux' tps
   433              | _ => update_const $ aux' tps $ t1 $ t2)
   434         fun aux tps =
   435           if maybe_opt andalso not (is_complete_type data_types false T1) then
   436             update_const $ aux' tps $ Const (unrep_name, T1)
   437             $ (Const (@{const_name Some}, T2' --> T2) $ Const (unknown, T2'))
   438           else
   439             aux' tps
   440       in aux end
   441     fun polish_funs Ts t =
   442       (case fastype_of1 (Ts, t) of
   443          Type (@{type_name fun}, [T1, T2]) =>
   444          if is_plain_fun t then
   445            case T2 of
   446              Type (@{type_name option}, [T2']) =>
   447              let
   448                val (maybe_opt, ts_pair) =
   449                  dest_plain_fun t ||> apply2 (map (polish_funs Ts))
   450              in make_map maybe_opt T1 T2 T2' (rev (op ~~ ts_pair)) end
   451            | _ => raise SAME ()
   452          else
   453            raise SAME ()
   454        | _ => raise SAME ())
   455       handle SAME () =>
   456              case t of
   457                (t1 as Const (@{const_name fun_upd}, _) $ t11 $ _)
   458                $ (t2 as Const (s, _)) =>
   459                if s = unknown then polish_funs Ts t11
   460                else polish_funs Ts t1 $ polish_funs Ts t2
   461              | t1 $ t2 => polish_funs Ts t1 $ polish_funs Ts t2
   462              | Abs (s, T, t') => Abs (s, T, polish_funs (T :: Ts) t')
   463              | Const (s, Type (@{type_name fun}, [T1, T2])) =>
   464                if s = opt_flag orelse s = non_opt_flag then
   465                  Abs ("x", T1,
   466                       Const (if is_complete_type data_types false T1 then
   467                                irrelevant
   468                              else
   469                                unknown, T2))
   470                else
   471                  t
   472              | t => t
   473     fun make_fun_or_set maybe_opt T T1 T2 T' ts1 ts2 =
   474       ts1 ~~ ts2
   475       |> sort (nice_term_ord o apply2 fst)
   476       |> (case T of
   477             Type (@{type_name set}, _) =>
   478             sort_by (truth_const_sort_key o snd)
   479             #> make_set maybe_opt T'
   480           | _ =>
   481             make_plain_fun maybe_opt T1 T2
   482             #> unarize_unbox_etc_term
   483             #> format_fun (uniterize_unarize_unbox_etc_type T')
   484                           (uniterize_unarize_unbox_etc_type T1)
   485                           (uniterize_unarize_unbox_etc_type T2))
   486 
   487     fun term_for_fun_or_set seen T T' j =
   488         let
   489           val k1 = card_of_type card_assigns (pseudo_domain_type T)
   490           val k2 = card_of_type card_assigns (pseudo_range_type T)
   491         in
   492           term_for_rep true seen T T' (Vect (k1, Atom (k2, 0)))
   493                        [nth_combination (replicate k1 (k2, 0)) j]
   494           handle General.Subscript =>
   495                  raise ARG ("Nitpick_Model.reconstruct_term.\
   496                             \term_for_fun_or_set",
   497                             signed_string_of_int j ^ " for " ^
   498                             string_for_rep (Vect (k1, Atom (k2, 0))))
   499         end
   500     and term_for_atom seen (T as Type (@{type_name fun}, _)) T' j _ =
   501         term_for_fun_or_set seen T T' j
   502       | term_for_atom seen (T as Type (@{type_name set}, _)) T' j _ =
   503         term_for_fun_or_set seen T T' j
   504       | term_for_atom seen (Type (@{type_name prod}, [T1, T2])) _ j k =
   505         let
   506           val k1 = card_of_type card_assigns T1
   507           val k2 = k div k1
   508         in
   509           list_comb (HOLogic.pair_const T1 T2,
   510                      @{map 3} (fn T => term_for_atom seen T T) [T1, T2]
   511                           (* ### k2 or k1? FIXME *)
   512                           [j div k2, j mod k2] [k1, k2])
   513         end
   514       | term_for_atom seen @{typ prop} _ j k =
   515         HOLogic.mk_Trueprop (term_for_atom seen bool_T bool_T j k)
   516       | term_for_atom _ @{typ bool} _ j _ =
   517         if j = 0 then @{const False} else @{const True}
   518       | term_for_atom seen T _ j k =
   519         if T = nat_T then
   520           HOLogic.mk_number nat_T j
   521         else if T = int_T then
   522           HOLogic.mk_number int_T (int_for_atom (k, 0) j)
   523         else if is_fp_iterator_type T then
   524           HOLogic.mk_number nat_T (k - j - 1)
   525         else if T = @{typ bisim_iterator} then
   526           HOLogic.mk_number nat_T j
   527         else case data_type_spec data_types T of
   528           NONE => nth_atom thy atomss pool T j
   529         | SOME {deep = false, ...} => nth_atom thy atomss pool T j
   530         | SOME {co, constrs, ...} =>
   531           let
   532             fun tuples_for_const (s, T) =
   533               tuple_list_for_name rel_table bounds (ConstName (s, T, Any))
   534             fun cyclic_atom () =
   535               nth_atom thy atomss pool (Type (cyclic_type_name (), [])) j
   536             fun cyclic_var () =
   537               Var ((nth_atom_name thy atomss pool "" T j, 0), T)
   538             val discr_jsss = map (tuples_for_const o discr_for_constr o #const)
   539                                  constrs
   540             val real_j = j + offset_of_type ofs T
   541             val constr_x as (constr_s, constr_T) =
   542               get_first (fn (jss, {const, ...}) =>
   543                             if member (op =) jss [real_j] then SOME const
   544                             else NONE)
   545                         (discr_jsss ~~ constrs) |> the
   546             val arg_Ts = curried_binder_types constr_T
   547             val sel_xs =
   548               map (binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize
   549                                                           constr_x)
   550                   (index_seq 0 (length arg_Ts))
   551             val sel_Rs =
   552               map (fn x => get_first
   553                                (fn ConstName (s', T', R) =>
   554                                    if (s', T') = x then SOME R else NONE
   555                                  | u => raise NUT ("Nitpick_Model.reconstruct_\
   556                                                    \term.term_for_atom", [u]))
   557                                sel_names |> the) sel_xs
   558             val arg_Rs = map (snd o dest_Func) sel_Rs
   559             val sel_jsss = map tuples_for_const sel_xs
   560             val arg_jsss =
   561               map (map_filter (fn js => if hd js = real_j then SOME (tl js)
   562                                         else NONE)) sel_jsss
   563             val uncur_arg_Ts = binder_types constr_T
   564           in
   565             if co andalso not (null seen) andalso
   566                member (op =) (seen |> unfold ? (fst o split_last)) (T, j) then
   567               cyclic_var ()
   568             else if constr_s = @{const_name Word} then
   569               HOLogic.mk_number
   570                   (if T = @{typ "unsigned_bit word"} then nat_T else int_T)
   571                   (value_of_bits (the_single arg_jsss))
   572             else
   573               let
   574                 val seen = seen |> co ? cons (T, j)
   575                 val ts =
   576                   if length arg_Ts = 0 then
   577                     []
   578                   else
   579                     @{map 3} (fn Ts => term_for_rep true seen Ts Ts) arg_Ts arg_Rs
   580                          arg_jsss
   581                     |> mk_tuple (HOLogic.mk_tupleT uncur_arg_Ts)
   582                     |> dest_n_tuple (length uncur_arg_Ts)
   583                 val t =
   584                   if constr_s = @{const_name Abs_Frac} then
   585                     case ts of
   586                       [Const (@{const_name Pair}, _) $ t1 $ t2] =>
   587                       frac_from_term_pair (body_type T) t1 t2
   588                     | _ => raise TERM ("Nitpick_Model.reconstruct_term.\
   589                                        \term_for_atom (Abs_Frac)", ts)
   590                   else if is_abs_fun ctxt constr_x orelse
   591                           constr_s = @{const_name Quot} then
   592                     Const (abs_name, constr_T) $ the_single ts
   593                   else
   594                     list_comb (Const constr_x, ts)
   595               in
   596                 if co then
   597                   let val var = cyclic_var () in
   598                     if exists_subterm (curry (op =) var) t then
   599                       if co then
   600                         Const (@{const_name The}, (T --> bool_T) --> T)
   601                         $ Abs (cyclic_co_val_name (), T,
   602                                Const (@{const_name HOL.eq}, T --> T --> bool_T)
   603                                $ Bound 0 $ abstract_over (var, t))
   604                       else
   605                         cyclic_atom ()
   606                     else
   607                       t
   608                   end
   609                 else
   610                   t
   611               end
   612           end
   613     and term_for_vect seen k R T T' js =
   614       let
   615         val T1 = pseudo_domain_type T
   616         val T2 = pseudo_range_type T
   617       in
   618         make_fun_or_set true T T1 T2 T'
   619             (map (fn j => term_for_atom seen T1 T1 j k) (index_seq 0 k))
   620             (map (term_for_rep true seen T2 T2 R o single)
   621                  (chunk_list (arity_of_rep R) js))
   622       end
   623     and term_for_rep _ seen T T' (R as Atom (k, j0)) [[j]] =
   624         if j >= j0 andalso j < j0 + k then term_for_atom seen T T' (j - j0) k
   625         else raise REP ("Nitpick_Model.reconstruct_term.term_for_rep", [R])
   626       | term_for_rep _ seen (Type (@{type_name prod}, [T1, T2])) _
   627                      (Struct [R1, R2]) [js] =
   628         let
   629           val arity1 = arity_of_rep R1
   630           val (js1, js2) = chop arity1 js
   631         in
   632           list_comb (HOLogic.pair_const T1 T2,
   633                      @{map 3} (fn T => term_for_rep true seen T T) [T1, T2] [R1, R2]
   634                           [[js1], [js2]])
   635         end
   636       | term_for_rep _ seen T T' (Vect (k, R')) [js] =
   637         term_for_vect seen k R' T T' js
   638       | term_for_rep maybe_opt seen T T' (Func (R1, Formula Neut)) jss =
   639         let
   640           val T1 = pseudo_domain_type T
   641           val T2 = pseudo_range_type T
   642           val jss1 = all_combinations_for_rep R1
   643           val ts1 = map (term_for_rep true seen T1 T1 R1 o single) jss1
   644           val ts2 =
   645             map (fn js => term_for_rep true seen T2 T2 (Atom (2, 0))
   646                                        [[int_from_bool (member (op =) jss js)]])
   647                 jss1
   648         in make_fun_or_set maybe_opt T T1 T2 T' ts1 ts2 end
   649       | term_for_rep maybe_opt seen T T' (Func (R1, R2)) jss =
   650         let
   651           val T1 = pseudo_domain_type T
   652           val T2 = pseudo_range_type T
   653           val arity1 = arity_of_rep R1
   654           val jss1 = all_combinations_for_rep R1
   655           val ts1 = map (term_for_rep false seen T1 T1 R1 o single) jss1
   656           val grouped_jss2 = AList.group (op =) (map (chop arity1) jss)
   657           val ts2 = map (term_for_rep false seen T2 T2 R2 o the_default []
   658                          o AList.lookup (op =) grouped_jss2) jss1
   659         in make_fun_or_set maybe_opt T T1 T2 T' ts1 ts2 end
   660       | term_for_rep _ seen T T' (Opt R) jss =
   661         if null jss then Const (unknown, T)
   662         else term_for_rep true seen T T' R jss
   663       | term_for_rep _ _ T _ R jss =
   664         raise ARG ("Nitpick_Model.reconstruct_term.term_for_rep",
   665                    Syntax.string_of_typ ctxt T ^ " " ^ string_for_rep R ^ " " ^
   666                    string_of_int (length jss))
   667   in
   668     postprocess_subterms [] o polish_funs [] o unarize_unbox_etc_term
   669     oooo term_for_rep maybe_opt []
   670   end
   671 
   672 (** Constant postprocessing **)
   673 
   674 fun dest_n_tuple_type 1 T = [T]
   675   | dest_n_tuple_type n (Type (_, [T1, T2])) =
   676     T1 :: dest_n_tuple_type (n - 1) T2
   677   | dest_n_tuple_type _ T =
   678     raise TYPE ("Nitpick_Model.dest_n_tuple_type", [T], [])
   679 
   680 fun const_format thy def_tables (x as (s, T)) =
   681   if String.isPrefix unrolled_prefix s then
   682     const_format thy def_tables (original_name s, range_type T)
   683   else if String.isPrefix skolem_prefix s then
   684     let
   685       val k = unprefix skolem_prefix s
   686               |> strip_first_name_sep |> fst |> space_explode "@"
   687               |> hd |> Int.fromString |> the
   688     in [k, num_binder_types T - k] end
   689   else if original_name s <> s then
   690     [num_binder_types T]
   691   else case def_of_const thy def_tables x of
   692     SOME t' => if fixpoint_kind_of_rhs t' <> NoFp then
   693                  let val k = length (strip_abs_vars t') in
   694                    [k, num_binder_types T - k]
   695                  end
   696                else
   697                  [num_binder_types T]
   698   | NONE => [num_binder_types T]
   699 
   700 fun intersect_formats _ [] = []
   701   | intersect_formats [] _ = []
   702   | intersect_formats ks1 ks2 =
   703     let val ((ks1', k1), (ks2', k2)) = apply2 split_last (ks1, ks2) in
   704       intersect_formats (ks1' @ (if k1 > k2 then [k1 - k2] else []))
   705                         (ks2' @ (if k2 > k1 then [k2 - k1] else [])) @
   706       [Int.min (k1, k2)]
   707     end
   708 
   709 fun lookup_format thy def_tables formats t =
   710   case AList.lookup (fn (SOME x, SOME y) =>
   711                         (term_match thy) (x, y) | _ => false)
   712                     formats (SOME t) of
   713     SOME format => format
   714   | NONE => let val format = the (AList.lookup (op =) formats NONE) in
   715               case t of
   716                 Const x => intersect_formats format
   717                                              (const_format thy def_tables x)
   718               | _ => format
   719             end
   720 
   721 fun format_type default_format format T =
   722   let
   723     val T = uniterize_unarize_unbox_etc_type T
   724     val format = format |> filter (curry (op <) 0)
   725   in
   726     if forall (curry (op =) 1) format then
   727       T
   728     else
   729       let
   730         val (binder_Ts, body_T) = strip_type T
   731         val batched =
   732           binder_Ts
   733           |> map (format_type default_format default_format)
   734           |> rev |> chunk_list_unevenly (rev format)
   735           |> map (HOLogic.mk_tupleT o rev)
   736       in List.foldl (op -->) body_T batched end
   737   end
   738 
   739 fun format_term_type thy def_tables formats t =
   740   format_type (the (AList.lookup (op =) formats NONE))
   741               (lookup_format thy def_tables formats t) (fastype_of t)
   742 
   743 fun repair_special_format js m format =
   744   m - 1 downto 0 |> chunk_list_unevenly (rev format)
   745                  |> map (rev o filter_out (member (op =) js))
   746                  |> filter_out null |> map length |> rev
   747 
   748 fun user_friendly_const ({thy, evals, def_tables, skolems, special_funs, ...}
   749                          : hol_context) (base_name, step_name) formats =
   750   let
   751     val default_format = the (AList.lookup (op =) formats NONE)
   752     fun do_const (x as (s, T)) =
   753       (if String.isPrefix special_prefix s then
   754          let
   755            val do_term = map_aterms (fn Const x => fst (do_const x) | t' => t')
   756            val (x' as (_, T'), js, ts) =
   757              AList.find (op =) (!special_funs) (s, unarize_unbox_etc_type T)
   758              |> the_single
   759            val max_j = List.last js
   760            val Ts = List.take (binder_types T', max_j + 1)
   761            val missing_js = filter_out (member (op =) js) (0 upto max_j)
   762            val missing_Ts = filter_indices missing_js Ts
   763            fun nth_missing_var n =
   764              ((arg_var_prefix ^ nat_subscript (n + 1), 0), nth missing_Ts n)
   765            val missing_vars = map nth_missing_var (0 upto length missing_js - 1)
   766            val vars = special_bounds ts @ missing_vars
   767            val ts' =
   768              map (fn j =>
   769                      case AList.lookup (op =) (js ~~ ts) j of
   770                        SOME t => do_term t
   771                      | NONE =>
   772                        Var (nth missing_vars
   773                                 (find_index (curry (op =) j) missing_js)))
   774                  (0 upto max_j)
   775            val t = do_const x' |> fst
   776            val format =
   777              case AList.lookup (fn (SOME t1, SOME t2) => term_match thy (t1, t2)
   778                                  | _ => false) formats (SOME t) of
   779                SOME format =>
   780                repair_special_format js (num_binder_types T') format
   781              | NONE =>
   782                const_format thy def_tables x'
   783                |> repair_special_format js (num_binder_types T')
   784                |> intersect_formats default_format
   785          in
   786            (list_comb (t, ts') |> fold_rev abs_var vars,
   787             format_type default_format format T)
   788          end
   789        else if String.isPrefix uncurry_prefix s then
   790          let
   791            val (ss, s') = unprefix uncurry_prefix s
   792                           |> strip_first_name_sep |>> space_explode "@"
   793          in
   794            if String.isPrefix step_prefix s' then
   795              do_const (s', T)
   796            else
   797              let
   798                val k = the (Int.fromString (hd ss))
   799                val j = the (Int.fromString (List.last ss))
   800                val (before_Ts, (tuple_T, rest_T)) =
   801                  strip_n_binders j T ||> (strip_n_binders 1 #>> hd)
   802                val T' = before_Ts ---> dest_n_tuple_type k tuple_T ---> rest_T
   803              in do_const (s', T') end
   804          end
   805        else if String.isPrefix unrolled_prefix s then
   806          let val t = Const (original_name s, range_type T) in
   807            (lambda (Free (iter_var_prefix, nat_T)) t,
   808             format_type default_format
   809                         (lookup_format thy def_tables formats t) T)
   810          end
   811        else if String.isPrefix base_prefix s then
   812          (Const (base_name, T --> T) $ Const (unprefix base_prefix s, T),
   813           format_type default_format default_format T)
   814        else if String.isPrefix step_prefix s then
   815          (Const (step_name, T --> T) $ Const (unprefix step_prefix s, T),
   816           format_type default_format default_format T)
   817        else if String.isPrefix quot_normal_prefix s then
   818          let val t = Const (nitpick_prefix ^ "quotient normal form", T) in
   819            (t, format_term_type thy def_tables formats t)
   820          end
   821        else if String.isPrefix skolem_prefix s then
   822          let
   823            val ss = the (AList.lookup (op =) (!skolems) s)
   824            val (Ts, Ts') = chop (length ss) (binder_types T)
   825            val frees = map Free (ss ~~ Ts)
   826            val s' = original_name s
   827          in
   828            (fold lambda frees (Const (s', Ts' ---> T)),
   829             format_type default_format
   830                         (lookup_format thy def_tables formats (Const x)) T)
   831          end
   832        else if String.isPrefix eval_prefix s then
   833          let
   834            val t = nth evals (the (Int.fromString (unprefix eval_prefix s)))
   835          in (t, format_term_type thy def_tables formats t) end
   836        else
   837          (* The selector case can occur in conjunction with fractional types.
   838             It's not pretty. *)
   839          let val t = Const (s |> not (is_sel s) ? original_name, T) in
   840            (t, format_term_type thy def_tables formats t)
   841          end)
   842       |>> map_types uniterize_unarize_unbox_etc_type
   843       |>> shorten_names_in_term |>> Term.map_abs_vars shortest_name
   844   in do_const end
   845 
   846 fun assign_operator_for_const (s, T) =
   847   if String.isPrefix ubfp_prefix s then
   848     xsym "\<le>" "<=" ()
   849   else if String.isPrefix lbfp_prefix s then
   850     xsym "\<ge>" ">=" ()
   851   else if original_name s <> s then
   852     assign_operator_for_const (strip_first_name_sep s |> snd, T)
   853   else
   854     "="
   855 
   856 (** Model reconstruction **)
   857 
   858 fun unfold_outer_the_binders (t as Const (@{const_name The}, _)
   859                                    $ Abs (s, T, Const (@{const_name HOL.eq}, _)
   860                                                 $ Bound 0 $ t')) =
   861     betapply (Abs (s, T, t'), t) |> unfold_outer_the_binders
   862   | unfold_outer_the_binders t = t
   863 
   864 fun bisimilar_values _ 0 _ = true
   865   | bisimilar_values coTs max_depth (t1, t2) =
   866     let val T = fastype_of t1 in
   867       if exists_subtype (member (op =) coTs) T then
   868         let
   869           val ((head1, args1), (head2, args2)) =
   870             apply2 (strip_comb o unfold_outer_the_binders) (t1, t2)
   871           val max_depth = max_depth - (if member (op =) coTs T then 1 else 0)
   872         in
   873           head1 = head2 andalso
   874           forall (bisimilar_values coTs max_depth) (args1 ~~ args2)
   875         end
   876       else
   877         t1 = t2
   878     end
   879 
   880 fun pretty_term_auto_global ctxt t0 =
   881   let
   882     val t = map_aterms (fn t as Const (s, _) =>
   883       if s = irrelevant orelse s = unknown then Term.dummy else t | t => t) t0
   884 
   885     fun add_fake_const s =
   886       Sign.declare_const_global ((Binding.name s, @{typ 'a}), NoSyn)
   887       #> #2
   888 
   889     val globals = Term.add_const_names t []
   890       |> filter_out (String.isSubstring Long_Name.separator)
   891 
   892     val fake_ctxt =
   893       ctxt |> Proof_Context.background_theory (fn thy =>
   894         thy
   895         |> Sign.map_naming (K Name_Space.global_naming)
   896         |> fold (perhaps o try o add_fake_const) globals
   897         |> Sign.restore_naming thy)
   898   in
   899     Syntax.pretty_term fake_ctxt t
   900   end
   901 
   902 fun reconstruct_hol_model {show_types, show_skolems, show_consts}
   903         ({hol_ctxt = {thy, ctxt, max_bisim_depth, boxes, wfs, user_axioms,
   904                       debug, whacks, binary_ints, destroy_constrs, specialize,
   905                       star_linear_preds, total_consts, needs, tac_timeout,
   906                       evals, case_names, def_tables, nondef_table, nondefs,
   907                       simp_table, psimp_table, choice_spec_table, intro_table,
   908                       ground_thm_table, ersatz_table, skolems, special_funs,
   909                       unrolled_preds, wf_cache, constr_cache}, binarize,
   910                       card_assigns, bits, bisim_depth, data_types, ofs} : scope)
   911         formats atomss real_frees pseudo_frees free_names sel_names nonsel_names
   912         rel_table bounds =
   913   let
   914     val pool = Unsynchronized.ref []
   915     val (wacky_names as (_, base_step_names), ctxt) = add_wacky_syntax ctxt
   916     val hol_ctxt =
   917       {thy = thy, ctxt = ctxt, max_bisim_depth = max_bisim_depth, boxes = boxes,
   918        wfs = wfs, user_axioms = user_axioms, debug = debug, whacks = whacks,
   919        binary_ints = binary_ints, destroy_constrs = destroy_constrs,
   920        specialize = specialize, star_linear_preds = star_linear_preds,
   921        total_consts = total_consts, needs = needs, tac_timeout = tac_timeout,
   922        evals = evals, case_names = case_names, def_tables = def_tables,
   923        nondef_table = nondef_table, nondefs = nondefs, simp_table = simp_table,
   924        psimp_table = psimp_table, choice_spec_table = choice_spec_table,
   925        intro_table = intro_table, ground_thm_table = ground_thm_table,
   926        ersatz_table = ersatz_table, skolems = skolems,
   927        special_funs = special_funs, unrolled_preds = unrolled_preds,
   928        wf_cache = wf_cache, constr_cache = constr_cache}
   929     val scope =
   930       {hol_ctxt = hol_ctxt, binarize = binarize, card_assigns = card_assigns,
   931        bits = bits, bisim_depth = bisim_depth, data_types = data_types,
   932        ofs = ofs}
   933     fun term_for_rep maybe_opt unfold =
   934       reconstruct_term maybe_opt unfold pool wacky_names scope atomss
   935                        sel_names rel_table bounds
   936     val all_values =
   937       all_values_of_type pool wacky_names scope atomss sel_names rel_table
   938                          bounds
   939     fun is_codatatype_wellformed (cos : data_type_spec list)
   940                                  ({typ, card, ...} : data_type_spec) =
   941       let
   942         val ts = all_values card typ
   943         val max_depth = Integer.sum (map #card cos)
   944       in
   945         forall (not o bisimilar_values (map #typ cos) max_depth)
   946                (all_distinct_unordered_pairs_of ts)
   947       end
   948     fun pretty_for_assign name =
   949       let
   950         val (oper, (t1, T'), T) =
   951           case name of
   952             FreeName (s, T, _) =>
   953             let val t = Free (s, uniterize_unarize_unbox_etc_type T) in
   954               ("=", (t, format_term_type thy def_tables formats t), T)
   955             end
   956           | ConstName (s, T, _) =>
   957             (assign_operator_for_const (s, T),
   958              user_friendly_const hol_ctxt base_step_names formats (s, T), T)
   959           | _ => raise NUT ("Nitpick_Model.reconstruct_hol_model.\
   960                             \pretty_for_assign", [name])
   961         val t2 = if rep_of name = Any then
   962                    Const (@{const_name undefined}, T')
   963                  else
   964                    tuple_list_for_name rel_table bounds name
   965                    |> term_for_rep (not (is_fully_representable_set name)) false
   966                                    T T' (rep_of name)
   967       in
   968         Pretty.block (Pretty.breaks
   969             [pretty_term_auto_global ctxt t1, Pretty.str oper,
   970              pretty_term_auto_global ctxt t2])
   971       end
   972     fun pretty_for_data_type ({typ, card, complete, ...} : data_type_spec) =
   973       Pretty.block (Pretty.breaks
   974           (pretty_for_type ctxt typ ::
   975            (case typ of
   976               Type (@{type_name fun_box}, _) => [Pretty.str "[boxed]"]
   977             | Type (@{type_name pair_box}, _) => [Pretty.str "[boxed]"]
   978             | _ => []) @
   979            [Pretty.str "=",
   980             Pretty.enum "," "{" "}"
   981                 (map (pretty_term_auto_global ctxt) (all_values card typ) @
   982                  (if fun_from_pair complete false then []
   983                   else [Pretty.str (unrep_mixfix ())]))]))
   984     fun integer_data_type T =
   985       [{typ = T, card = card_of_type card_assigns T, co = false,
   986         self_rec = true, complete = (false, false), concrete = (true, true),
   987         deep = true, constrs = []}]
   988       handle TYPE ("Nitpick_HOL.card_of_type", _, _) => []
   989     val data_types =
   990       data_types |> filter #deep
   991                  |> append (maps integer_data_type [nat_T, int_T])
   992     val block_of_data_types =
   993       if show_types andalso not (null data_types) then
   994         [Pretty.big_list ("Type" ^ plural_s_for_list data_types ^ ":")
   995                          (map pretty_for_data_type data_types)]
   996       else
   997         []
   998     fun block_of_names show title names =
   999       if show andalso not (null names) then
  1000         Pretty.str (title ^ plural_s_for_list names ^ ":")
  1001         :: map (Pretty.indent indent_size o pretty_for_assign)
  1002                (sort_by (original_name o nickname_of) names)
  1003       else
  1004         []
  1005     fun free_name_for_term keep_all (x as (s, T)) =
  1006       case filter (curry (op =) x
  1007                    o pairf nickname_of (uniterize_unarize_unbox_etc_type
  1008                                         o type_of)) free_names of
  1009         [name] => SOME name
  1010       | [] => if keep_all then SOME (FreeName (s, T, Any)) else NONE
  1011       | _ => raise TERM ("Nitpick_Model.reconstruct_hol_model.\
  1012                          \free_name_for_term", [Const x])
  1013     val (skolem_names, nonskolem_nonsel_names) =
  1014       List.partition is_skolem_name nonsel_names
  1015     val (eval_names, noneval_nonskolem_nonsel_names) =
  1016       List.partition (String.isPrefix eval_prefix o nickname_of)
  1017                      nonskolem_nonsel_names
  1018       ||> filter_out (member (op =) [@{const_name bisim},
  1019                                      @{const_name bisim_iterator_max}]
  1020                       o nickname_of)
  1021       ||> append (map_filter (free_name_for_term false) pseudo_frees)
  1022     val real_free_names = map_filter (free_name_for_term true) real_frees
  1023     val chunks = block_of_names true "Free variable" real_free_names @
  1024                  block_of_names show_skolems "Skolem constant" skolem_names @
  1025                  block_of_names true "Evaluated term" eval_names @
  1026                  block_of_data_types @
  1027                  block_of_names show_consts "Constant"
  1028                                 noneval_nonskolem_nonsel_names
  1029     val codatatypes = filter #co data_types;
  1030   in
  1031     (Pretty.chunks (if null chunks then [Pretty.str "Empty assignment"]
  1032                     else chunks),
  1033      bisim_depth >= 0 orelse
  1034      forall (is_codatatype_wellformed codatatypes) codatatypes)
  1035   end
  1036 
  1037 end;