src/HOL/Tools/Nitpick/nitpick_model.ML
author blanchet
Tue Jan 03 18:33:18 2012 +0100 (2012-01-03)
changeset 46097 0ed9365fa9d2
parent 46083 efeaa79f021b
child 46104 eb85282db54e
permissions -rw-r--r--
create consts with proper "set" types
     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 styp = Nitpick_Util.styp
    11   type scope = Nitpick_Scope.scope
    12   type rep = Nitpick_Rep.rep
    13   type nut = Nitpick_Nut.nut
    14 
    15   type params =
    16     {show_datatypes: bool,
    17      show_skolems: bool,
    18      show_consts: bool}
    19 
    20   type term_postprocessor =
    21     Proof.context -> string -> (typ -> term list) -> typ -> term -> term
    22 
    23   structure NameTable : TABLE
    24 
    25   val irrelevant : string
    26   val unknown : string
    27   val unrep : unit -> string
    28   val register_term_postprocessor :
    29     typ -> term_postprocessor -> morphism -> Context.generic -> Context.generic
    30   val register_term_postprocessor_global :
    31     typ -> term_postprocessor -> theory -> theory
    32   val unregister_term_postprocessor :
    33     typ -> morphism -> Context.generic -> Context.generic
    34   val unregister_term_postprocessor_global : typ -> theory -> theory
    35   val tuple_list_for_name :
    36     nut NameTable.table -> Kodkod.raw_bound list -> nut -> int list list
    37   val dest_plain_fun : term -> bool * (term list * term list)
    38   val reconstruct_hol_model :
    39     params -> scope -> (term option * int list) list
    40     -> (typ option * string list) list -> styp list -> styp list -> nut list
    41     -> nut list -> nut list -> nut NameTable.table -> Kodkod.raw_bound list
    42     -> Pretty.T * bool
    43   val prove_hol_model :
    44     scope -> Time.time option -> nut list -> nut list -> nut NameTable.table
    45     -> Kodkod.raw_bound list -> term -> bool option
    46 end;
    47 
    48 structure Nitpick_Model : NITPICK_MODEL =
    49 struct
    50 
    51 open Nitpick_Util
    52 open Nitpick_HOL
    53 open Nitpick_Scope
    54 open Nitpick_Peephole
    55 open Nitpick_Rep
    56 open Nitpick_Nut
    57 
    58 structure KK = Kodkod
    59 
    60 type params =
    61   {show_datatypes: bool,
    62    show_skolems: bool,
    63    show_consts: bool}
    64 
    65 type term_postprocessor =
    66   Proof.context -> string -> (typ -> term list) -> typ -> term -> term
    67 
    68 structure Data = Generic_Data
    69 (
    70   type T = (typ * term_postprocessor) list
    71   val empty = []
    72   val extend = I
    73   fun merge data = AList.merge (op =) (K true) data
    74 )
    75 
    76 fun xsym s s' () = if print_mode_active Symbol.xsymbolsN then s else s'
    77 
    78 val irrelevant = "_"
    79 val unknown = "?"
    80 val unrep = xsym "\<dots>" "..."
    81 val maybe_mixfix = xsym "_\<^sup>?" "_?"
    82 val base_mixfix = xsym "_\<^bsub>base\<^esub>" "_.base"
    83 val step_mixfix = xsym "_\<^bsub>step\<^esub>" "_.step"
    84 val abs_mixfix = xsym "\<guillemotleft>_\<guillemotright>" "\"_\""
    85 val arg_var_prefix = "x"
    86 val cyclic_co_val_name = xsym "\<omega>" "w"
    87 val cyclic_const_prefix = xsym "\<xi>" "X"
    88 fun cyclic_type_name () = nitpick_prefix ^ cyclic_const_prefix ()
    89 val opt_flag = nitpick_prefix ^ "opt"
    90 val non_opt_flag = nitpick_prefix ^ "non_opt"
    91 
    92 type atom_pool = ((string * int) * int list) list
    93 
    94 fun add_wacky_syntax ctxt =
    95   let
    96     val name_of = fst o dest_Const
    97     val thy = Proof_Context.theory_of ctxt |> Context.reject_draft
    98     val (maybe_t, thy) =
    99       Sign.declare_const_global ((@{binding nitpick_maybe}, @{typ "'a => 'a"}),
   100                           Mixfix (maybe_mixfix (), [1000], 1000)) thy
   101     val (abs_t, thy) =
   102       Sign.declare_const_global ((@{binding nitpick_abs}, @{typ "'a => 'b"}),
   103                           Mixfix (abs_mixfix (), [40], 40)) thy
   104     val (base_t, thy) =
   105       Sign.declare_const_global ((@{binding nitpick_base}, @{typ "'a => 'a"}),
   106                           Mixfix (base_mixfix (), [1000], 1000)) thy
   107     val (step_t, thy) =
   108       Sign.declare_const_global ((@{binding nitpick_step}, @{typ "'a => 'a"}),
   109                           Mixfix (step_mixfix (), [1000], 1000)) thy
   110   in
   111     (pairself (pairself name_of) ((maybe_t, abs_t), (base_t, step_t)),
   112      Proof_Context.transfer_syntax thy ctxt)
   113   end
   114 
   115 (** Term reconstruction **)
   116 
   117 fun nth_atom_number pool T j =
   118   case AList.lookup (op =) (!pool) T of
   119     SOME js =>
   120     (case find_index (curry (op =) j) js of
   121        ~1 => (Unsynchronized.change pool (cons (T, j :: js));
   122               length js + 1)
   123      | n => length js - n)
   124   | NONE => (Unsynchronized.change pool (cons (T, [j])); 1)
   125 fun atom_suffix s =
   126   nat_subscript
   127   #> (s <> "" andalso Symbol.is_ascii_digit (List.last (raw_explode s)))  (* FIXME Symbol.explode (?) *)
   128      ? prefix "\<^isub>,"
   129 fun nth_atom_name thy atomss pool prefix T j =
   130   let
   131     val ss = these (triple_lookup (type_match thy) atomss T)
   132     val m = nth_atom_number pool T j
   133   in
   134     if m <= length ss then
   135       nth ss (m - 1)
   136     else case T of
   137       Type (s, _) =>
   138       let val s' = shortest_name s in
   139         prefix ^
   140         (if T = @{typ string} then "s"
   141          else if String.isPrefix "\\" s' then s'
   142          else substring (s', 0, 1)) ^ atom_suffix s m
   143       end
   144     | TFree (s, _) => prefix ^ perhaps (try (unprefix "'")) s ^ atom_suffix s m
   145     | _ => raise TYPE ("Nitpick_Model.nth_atom_name", [T], [])
   146   end
   147 fun nth_atom thy atomss pool for_auto T j =
   148   if for_auto then
   149     Free (nth_atom_name thy atomss pool (hd (space_explode "." nitpick_prefix))
   150                         T j, T)
   151   else
   152     Const (nth_atom_name thy atomss pool "" T j, T)
   153 
   154 fun extract_real_number (Const (@{const_name divide}, _) $ t1 $ t2) =
   155     real (snd (HOLogic.dest_number t1)) / real (snd (HOLogic.dest_number t2))
   156   | extract_real_number t = real (snd (HOLogic.dest_number t))
   157 fun nice_term_ord (Abs (_, _, t1), Abs (_, _, t2)) = nice_term_ord (t1, t2)
   158   | nice_term_ord tp = Real.compare (pairself extract_real_number tp)
   159     handle TERM ("dest_number", _) =>
   160            case tp of
   161              (t11 $ t12, t21 $ t22) =>
   162              (case nice_term_ord (t11, t21) of
   163                 EQUAL => nice_term_ord (t12, t22)
   164               | ord => ord)
   165            | _ => Term_Ord.fast_term_ord tp
   166 
   167 fun register_term_postprocessor_generic T postproc =
   168   Data.map (cons (T, postproc))
   169 (* TODO: Consider morphism. *)
   170 fun register_term_postprocessor T postproc (_ : morphism) =
   171   register_term_postprocessor_generic T postproc
   172 val register_term_postprocessor_global =
   173   Context.theory_map oo register_term_postprocessor_generic
   174 
   175 fun unregister_term_postprocessor_generic T = Data.map (AList.delete (op =) T)
   176 (* TODO: Consider morphism. *)
   177 fun unregister_term_postprocessor T (_ : morphism) =
   178   unregister_term_postprocessor_generic T
   179 val unregister_term_postprocessor_global =
   180   Context.theory_map o unregister_term_postprocessor_generic
   181 
   182 fun tuple_list_for_name rel_table bounds name =
   183   the (AList.lookup (op =) bounds (the_rel rel_table name)) handle NUT _ => [[]]
   184 
   185 fun unarize_unbox_etc_term (Const (@{const_name FunBox}, _) $ t1) =
   186     unarize_unbox_etc_term t1
   187   | unarize_unbox_etc_term
   188         (Const (@{const_name PairBox},
   189                 Type (@{type_name fun}, [T1, Type (@{type_name fun}, [T2, _])]))
   190          $ t1 $ t2) =
   191     let val Ts = map uniterize_unarize_unbox_etc_type [T1, T2] in
   192       Const (@{const_name Pair}, Ts ---> Type (@{type_name prod}, Ts))
   193       $ unarize_unbox_etc_term t1 $ unarize_unbox_etc_term t2
   194     end
   195   | unarize_unbox_etc_term (Const (s, T)) =
   196     Const (s, uniterize_unarize_unbox_etc_type T)
   197   | unarize_unbox_etc_term (t1 $ t2) =
   198     unarize_unbox_etc_term t1 $ unarize_unbox_etc_term t2
   199   | unarize_unbox_etc_term (Free (s, T)) =
   200     Free (s, uniterize_unarize_unbox_etc_type T)
   201   | unarize_unbox_etc_term (Var (x, T)) =
   202     Var (x, uniterize_unarize_unbox_etc_type T)
   203   | unarize_unbox_etc_term (Bound j) = Bound j
   204   | unarize_unbox_etc_term (Abs (s, T, t')) =
   205     Abs (s, uniterize_unarize_unbox_etc_type T, unarize_unbox_etc_term t')
   206 
   207 fun factor_out_types (T1 as Type (@{type_name prod}, [T11, T12]))
   208                      (T2 as Type (@{type_name prod}, [T21, T22])) =
   209     let val (n1, n2) = pairself num_factors_in_type (T11, T21) in
   210       if n1 = n2 then
   211         let
   212           val ((T11', opt_T12'), (T21', opt_T22')) = factor_out_types T12 T22
   213         in
   214           ((Type (@{type_name prod}, [T11, T11']), opt_T12'),
   215            (Type (@{type_name prod}, [T21, T21']), opt_T22'))
   216         end
   217       else if n1 < n2 then
   218         case factor_out_types T1 T21 of
   219           (p1, (T21', NONE)) => (p1, (T21', SOME T22))
   220         | (p1, (T21', SOME T22')) =>
   221           (p1, (T21', SOME (Type (@{type_name prod}, [T22', T22]))))
   222       else
   223         swap (factor_out_types T2 T1)
   224     end
   225   | factor_out_types (Type (@{type_name prod}, [T11, T12])) T2 =
   226     ((T11, SOME T12), (T2, NONE))
   227   | factor_out_types T1 (Type (@{type_name prod}, [T21, T22])) =
   228     ((T1, NONE), (T21, SOME T22))
   229   | factor_out_types T1 T2 = ((T1, NONE), (T2, NONE))
   230 
   231 (* Term-encoded data structure for holding key-value pairs as well as an "opt"
   232    flag indicating whether the function is approximated. *)
   233 fun make_plain_fun maybe_opt T1 T2 =
   234   let
   235     fun aux T1 T2 [] =
   236         Const (if maybe_opt then opt_flag else non_opt_flag, T1 --> T2)
   237       | aux T1 T2 ((t1, t2) :: tps) =
   238         Const (@{const_name fun_upd}, (T1 --> T2) --> T1 --> T2 --> T1 --> T2)
   239         $ aux T1 T2 tps $ t1 $ t2
   240   in aux T1 T2 o rev end
   241 fun is_plain_fun (Const (s, _)) = (s = opt_flag orelse s = non_opt_flag)
   242   | is_plain_fun (Const (@{const_name fun_upd}, _) $ t0 $ _ $ _) =
   243     is_plain_fun t0
   244   | is_plain_fun _ = false
   245 val dest_plain_fun =
   246   let
   247     fun aux (Abs (_, _, Const (s, _))) = (s <> irrelevant, ([], []))
   248       | aux (Const (s, _)) = (s <> non_opt_flag, ([], []))
   249       | aux (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =
   250         let val (maybe_opt, (ts1, ts2)) = aux t0 in
   251           (maybe_opt, (t1 :: ts1, t2 :: ts2))
   252         end
   253       | aux t = raise TERM ("Nitpick_Model.dest_plain_fun", [t])
   254   in apsnd (pairself rev) o aux end
   255 
   256 fun break_in_two T T1 T2 t =
   257   let
   258     val ps = HOLogic.flat_tupleT_paths T
   259     val cut = length (HOLogic.strip_tupleT T1)
   260     val (ps1, ps2) = pairself HOLogic.flat_tupleT_paths (T1, T2)
   261     val (ts1, ts2) = t |> HOLogic.strip_ptuple ps |> chop cut
   262   in (HOLogic.mk_ptuple ps1 T1 ts1, HOLogic.mk_ptuple ps2 T2 ts2) end
   263 fun pair_up (Type (@{type_name prod}, [T1', T2']))
   264             (t1 as Const (@{const_name Pair},
   265                           Type (@{type_name fun},
   266                                 [_, Type (@{type_name fun}, [_, T1])]))
   267              $ t11 $ t12) t2 =
   268     if T1 = T1' then HOLogic.mk_prod (t1, t2)
   269     else HOLogic.mk_prod (t11, pair_up T2' t12 t2)
   270   | pair_up _ t1 t2 = HOLogic.mk_prod (t1, t2)
   271 fun multi_pair_up T1 t1 (ts2, ts3) = map2 (pair o pair_up T1 t1) ts2 ts3
   272 
   273 fun format_fun T' T1 T2 t =
   274   let
   275     val T1' = pseudo_domain_type T'
   276     val T2' = pseudo_range_type T'
   277     fun do_curry T1 T1a T1b T2 t =
   278       let
   279         val (maybe_opt, tsp) = dest_plain_fun t
   280         val tps =
   281           tsp |>> map (break_in_two T1 T1a T1b)
   282               |> uncurry (map2 (fn (t1a, t1b) => fn t2 => (t1a, (t1b, t2))))
   283               |> AList.coalesce (op =)
   284               |> map (apsnd (make_plain_fun maybe_opt T1b T2))
   285       in make_plain_fun maybe_opt T1a (T1b --> T2) tps end
   286     and do_uncurry T1 T2 t =
   287       let
   288         val (maybe_opt, tsp) = dest_plain_fun t
   289         val tps =
   290           tsp |> op ~~
   291               |> maps (fn (t1, t2) =>
   292                           multi_pair_up T1 t1 (snd (dest_plain_fun t2)))
   293       in make_plain_fun maybe_opt T1 T2 tps end
   294     and do_arrow T1' T2' _ _ (Const (s, _)) = Const (s, T1' --> T2')
   295       | do_arrow T1' T2' T1 T2
   296                  (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =
   297         Const (@{const_name fun_upd},
   298                (T1' --> T2') --> T1' --> T2' --> T1' --> T2')
   299         $ do_arrow T1' T2' T1 T2 t0 $ do_term T1' T1 t1 $ do_term T2' T2 t2
   300       | do_arrow _ _ _ _ t =
   301         raise TERM ("Nitpick_Model.format_fun.do_arrow", [t])
   302     and do_fun T1' T2' T1 T2 t =
   303       case factor_out_types T1' T1 of
   304         ((_, NONE), (_, NONE)) => t |> do_arrow T1' T2' T1 T2
   305       | ((_, NONE), (T1a, SOME T1b)) =>
   306         t |> do_curry T1 T1a T1b T2 |> do_arrow T1' T2' T1a (T1b --> T2)
   307       | ((T1a', SOME T1b'), (_, NONE)) =>
   308         t |> do_arrow T1a' (T1b' --> T2') T1 T2 |> do_uncurry T1' T2'
   309       | _ => raise TYPE ("Nitpick_Model.format_fun.do_fun", [T1, T1'], [])
   310     and do_term (Type (@{type_name fun}, [T1', T2']))
   311                 (Type (@{type_name fun}, [T1, T2])) t =
   312         do_fun T1' T2' T1 T2 t
   313       | do_term (T' as Type (@{type_name prod}, Ts' as [T1', T2']))
   314                 (Type (@{type_name prod}, [T1, T2]))
   315                 (Const (@{const_name Pair}, _) $ t1 $ t2) =
   316         Const (@{const_name Pair}, Ts' ---> T')
   317         $ do_term T1' T1 t1 $ do_term T2' T2 t2
   318       | do_term T' T t =
   319         if T = T' then t
   320         else raise TYPE ("Nitpick_Model.format_fun.do_term", [T, T'], [])
   321   in if T1' = T1 andalso T2' = T2 then t else do_fun T1' T2' T1 T2 t end
   322 
   323 fun truth_const_sort_key @{const True} = "0"
   324   | truth_const_sort_key @{const False} = "2"
   325   | truth_const_sort_key _ = "1"
   326 
   327 fun mk_tuple (Type (@{type_name prod}, [T1, T2])) ts =
   328     HOLogic.mk_prod (mk_tuple T1 ts,
   329         mk_tuple T2 (List.drop (ts, length (HOLogic.flatten_tupleT T1))))
   330   | mk_tuple _ (t :: _) = t
   331   | mk_tuple T [] = raise TYPE ("Nitpick_Model.mk_tuple", [T], [])
   332 
   333 fun varified_type_match ctxt (candid_T, pat_T) =
   334   let val thy = Proof_Context.theory_of ctxt in
   335     strict_type_match thy (candid_T, varify_type ctxt pat_T)
   336   end
   337 
   338 fun all_values_of_type pool wacky_names (scope as {card_assigns, ...} : scope)
   339                        atomss sel_names rel_table bounds card T =
   340   let
   341     val card = if card = 0 then card_of_type card_assigns T else card
   342     fun nth_value_of_type n =
   343       let
   344         fun term unfold =
   345           reconstruct_term true unfold pool wacky_names scope atomss sel_names
   346                            rel_table bounds T T (Atom (card, 0)) [[n]]
   347       in
   348         case term false of
   349           t as Const (s, _) =>
   350           if String.isPrefix (cyclic_const_prefix ()) s then
   351             HOLogic.mk_eq (t, term true)
   352           else
   353             t
   354         | t => t
   355       end
   356   in index_seq 0 card |> map nth_value_of_type |> sort nice_term_ord end
   357 and reconstruct_term maybe_opt unfold pool
   358         (wacky_names as ((maybe_name, abs_name), _))
   359         (scope as {hol_ctxt as {thy, ctxt, stds, ...}, binarize, card_assigns,
   360                    bits, datatypes, ofs, ...})
   361         atomss sel_names rel_table bounds =
   362   let
   363     val for_auto = (maybe_name = "")
   364     fun value_of_bits jss =
   365       let
   366         val j0 = offset_of_type ofs @{typ unsigned_bit}
   367         val js = map (Integer.add (~ j0) o the_single) jss
   368       in
   369         fold (fn j => Integer.add (reasonable_power 2 j |> j = bits ? op ~))
   370              js 0
   371       end
   372     val all_values =
   373       all_values_of_type pool wacky_names scope atomss sel_names rel_table
   374                          bounds 0
   375     fun postprocess_term (Type (@{type_name fun}, _)) = I
   376       | postprocess_term T =
   377         case Data.get (Context.Proof ctxt) of
   378           [] => I
   379         | postprocs =>
   380           case AList.lookup (varified_type_match ctxt) postprocs T of
   381             SOME postproc => postproc ctxt maybe_name all_values T
   382           | NONE => I
   383     fun postprocess_subterms Ts (t1 $ t2) =
   384         let val t = postprocess_subterms Ts t1 $ postprocess_subterms Ts t2 in
   385           postprocess_term (fastype_of1 (Ts, t)) t
   386         end
   387       | postprocess_subterms Ts (Abs (s, T, t')) =
   388         Abs (s, T, postprocess_subterms (T :: Ts) t')
   389       | postprocess_subterms Ts t = postprocess_term (fastype_of1 (Ts, t)) t
   390     fun make_set maybe_opt T tps =
   391       let
   392         val set_T = HOLogic.mk_setT T
   393         val empty_const = Const (@{const_abbrev Set.empty}, set_T)
   394         val insert_const = Const (@{const_name insert}, T --> set_T --> set_T)
   395         fun aux [] =
   396             if maybe_opt andalso not (is_complete_type datatypes false T) then
   397               insert_const $ Const (unrep (), T) $ empty_const
   398             else
   399               empty_const
   400           | aux ((t1, t2) :: zs) =
   401             aux zs
   402             |> t2 <> @{const False}
   403                ? curry (op $)
   404                        (insert_const
   405                         $ (t1 |> t2 <> @{const True}
   406                                  ? curry (op $)
   407                                          (Const (maybe_name, T --> T))))
   408       in
   409         if forall (fn (_, t) => t <> @{const True} andalso t <> @{const False})
   410                   tps then
   411           Const (unknown, set_T)
   412         else
   413           aux tps
   414       end
   415     fun make_map maybe_opt T1 T2 T2' =
   416       let
   417         val update_const = Const (@{const_name fun_upd},
   418                                   (T1 --> T2) --> T1 --> T2 --> T1 --> T2)
   419         fun aux' [] = Const (@{const_abbrev Map.empty}, T1 --> T2)
   420           | aux' ((t1, t2) :: tps) =
   421             (case t2 of
   422                Const (@{const_name None}, _) => aux' tps
   423              | _ => update_const $ aux' tps $ t1 $ t2)
   424         fun aux tps =
   425           if maybe_opt andalso not (is_complete_type datatypes false T1) then
   426             update_const $ aux' tps $ Const (unrep (), T1)
   427             $ (Const (@{const_name Some}, T2' --> T2) $ Const (unknown, T2'))
   428           else
   429             aux' tps
   430       in aux end
   431     fun polish_funs Ts t =
   432       (case fastype_of1 (Ts, t) of
   433          Type (@{type_name fun}, [T1, T2]) =>
   434          if is_plain_fun t then
   435            case T2 of
   436              Type (@{type_name option}, [T2']) =>
   437              let
   438                val (maybe_opt, ts_pair) =
   439                  dest_plain_fun t ||> pairself (map (polish_funs Ts))
   440              in make_map maybe_opt T1 T2 T2' (rev (op ~~ ts_pair)) end
   441            | _ => raise SAME ()
   442          else
   443            raise SAME ()
   444        | _ => raise SAME ())
   445       handle SAME () =>
   446              case t of
   447                (t1 as Const (@{const_name fun_upd}, _) $ t11 $ _)
   448                $ (t2 as Const (s, _)) =>
   449                if s = unknown then polish_funs Ts t11
   450                else polish_funs Ts t1 $ polish_funs Ts t2
   451              | t1 $ t2 => polish_funs Ts t1 $ polish_funs Ts t2
   452              | Abs (s, T, t') => Abs (s, T, polish_funs (T :: Ts) t')
   453              | Const (s, Type (@{type_name fun}, [T1, T2])) =>
   454                if s = opt_flag orelse s = non_opt_flag then
   455                  Abs ("x", T1,
   456                       Const (if is_complete_type datatypes false T1 then
   457                                irrelevant
   458                              else
   459                                unknown, T2))
   460                else
   461                  t
   462              | t => t
   463     fun make_fun_or_set maybe_opt T T1 T2 T' ts1 ts2 =
   464       ts1 ~~ ts2
   465       |> sort (nice_term_ord o pairself fst)
   466       |> (case T of
   467             Type (@{type_name set}, _) =>
   468             sort_wrt (truth_const_sort_key o snd)
   469             #> make_set maybe_opt T'
   470           | _ =>
   471             make_plain_fun maybe_opt T1 T2
   472             #> unarize_unbox_etc_term
   473             #> format_fun (uniterize_unarize_unbox_etc_type T')
   474                           (uniterize_unarize_unbox_etc_type T1)
   475                           (uniterize_unarize_unbox_etc_type T2))
   476     fun term_for_atom seen (T as Type (@{type_name fun}, [T1, T2])) T' j _ =
   477         let
   478           val k1 = card_of_type card_assigns T1
   479           val k2 = card_of_type card_assigns T2
   480         in
   481           term_for_rep true seen T T' (Vect (k1, Atom (k2, 0)))
   482                        [nth_combination (replicate k1 (k2, 0)) j]
   483           handle General.Subscript =>
   484                  raise ARG ("Nitpick_Model.reconstruct_term.term_for_atom",
   485                             signed_string_of_int j ^ " for " ^
   486                             string_for_rep (Vect (k1, Atom (k2, 0))))
   487         end
   488       | term_for_atom seen (Type (@{type_name prod}, [T1, T2])) _ j k =
   489         let
   490           val k1 = card_of_type card_assigns T1
   491           val k2 = k div k1
   492         in
   493           list_comb (HOLogic.pair_const T1 T2,
   494                      map3 (fn T => term_for_atom seen T T) [T1, T2]
   495                           [j div k2, j mod k2] [k1, k2]) (* ### k2 or k1? FIXME *)
   496         end
   497       | term_for_atom seen @{typ prop} _ j k =
   498         HOLogic.mk_Trueprop (term_for_atom seen bool_T bool_T j k)
   499       | term_for_atom _ @{typ bool} _ j _ =
   500         if j = 0 then @{const False} else @{const True}
   501       | term_for_atom seen T _ j k =
   502         if T = nat_T andalso is_standard_datatype thy stds nat_T then
   503           HOLogic.mk_number nat_T j
   504         else if T = int_T then
   505           HOLogic.mk_number int_T (int_for_atom (k, 0) j)
   506         else if is_fp_iterator_type T then
   507           HOLogic.mk_number nat_T (k - j - 1)
   508         else if T = @{typ bisim_iterator} then
   509           HOLogic.mk_number nat_T j
   510         else case datatype_spec datatypes T of
   511           NONE => nth_atom thy atomss pool for_auto T j
   512         | SOME {deep = false, ...} => nth_atom thy atomss pool for_auto T j
   513         | SOME {co, standard, constrs, ...} =>
   514           let
   515             fun tuples_for_const (s, T) =
   516               tuple_list_for_name rel_table bounds (ConstName (s, T, Any))
   517             fun cyclic_atom () =
   518               nth_atom thy atomss pool for_auto (Type (cyclic_type_name (), []))
   519                        j
   520             fun cyclic_var () =
   521               Var ((nth_atom_name thy atomss pool "" T j, 0), T)
   522             val discr_jsss = map (tuples_for_const o discr_for_constr o #const)
   523                                  constrs
   524             val real_j = j + offset_of_type ofs T
   525             val constr_x as (constr_s, constr_T) =
   526               get_first (fn (jss, {const, ...}) =>
   527                             if member (op =) jss [real_j] then SOME const
   528                             else NONE)
   529                         (discr_jsss ~~ constrs) |> the
   530             val arg_Ts = curried_binder_types constr_T
   531             val sel_xs =
   532               map (binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize
   533                                                           constr_x)
   534                   (index_seq 0 (length arg_Ts))
   535             val sel_Rs =
   536               map (fn x => get_first
   537                                (fn ConstName (s', T', R) =>
   538                                    if (s', T') = x then SOME R else NONE
   539                                  | u => raise NUT ("Nitpick_Model.reconstruct_\
   540                                                    \term.term_for_atom", [u]))
   541                                sel_names |> the) sel_xs
   542             val arg_Rs = map (snd o dest_Func) sel_Rs
   543             val sel_jsss = map tuples_for_const sel_xs
   544             val arg_jsss =
   545               map (map_filter (fn js => if hd js = real_j then SOME (tl js)
   546                                         else NONE)) sel_jsss
   547             val uncur_arg_Ts = binder_types constr_T
   548             val maybe_cyclic = co orelse not standard
   549           in
   550             if maybe_cyclic andalso not (null seen) andalso
   551                member (op =) (seen |> unfold ? (fst o split_last)) (T, j) then
   552               cyclic_var ()
   553             else if constr_s = @{const_name Word} then
   554               HOLogic.mk_number
   555                   (if T = @{typ "unsigned_bit word"} then nat_T else int_T)
   556                   (value_of_bits (the_single arg_jsss))
   557             else
   558               let
   559                 val seen = seen |> maybe_cyclic ? cons (T, j)
   560                 val ts =
   561                   if length arg_Ts = 0 then
   562                     []
   563                   else
   564                     map3 (fn Ts => term_for_rep true seen Ts Ts) arg_Ts arg_Rs
   565                          arg_jsss
   566                     |> mk_tuple (HOLogic.mk_tupleT uncur_arg_Ts)
   567                     |> dest_n_tuple (length uncur_arg_Ts)
   568                 val t =
   569                   if constr_s = @{const_name Abs_Frac} then
   570                     case ts of
   571                       [Const (@{const_name Pair}, _) $ t1 $ t2] =>
   572                       frac_from_term_pair (body_type T) t1 t2
   573                     | _ => raise TERM ("Nitpick_Model.reconstruct_term.\
   574                                        \term_for_atom (Abs_Frac)", ts)
   575                   else if not for_auto andalso
   576                           (is_abs_fun ctxt constr_x orelse
   577                            constr_s = @{const_name Quot}) then
   578                     Const (abs_name, constr_T) $ the_single ts
   579                   else
   580                     list_comb (Const constr_x, ts)
   581               in
   582                 if maybe_cyclic then
   583                   let val var = cyclic_var () in
   584                     if unfold andalso not standard andalso
   585                        length seen = 1 andalso
   586                        exists_subterm
   587                            (fn Const (s, _) =>
   588                                String.isPrefix (cyclic_const_prefix ()) s
   589                              | t' => t' = var) t then
   590                       subst_atomic [(var, cyclic_atom ())] t
   591                     else if exists_subterm (curry (op =) var) t then
   592                       if co then
   593                         Const (@{const_name The}, (T --> bool_T) --> T)
   594                         $ Abs (cyclic_co_val_name (), T,
   595                                Const (@{const_name HOL.eq}, T --> T --> bool_T)
   596                                $ Bound 0 $ abstract_over (var, t))
   597                       else
   598                         cyclic_atom ()
   599                     else
   600                       t
   601                   end
   602                 else
   603                   t
   604               end
   605           end
   606     and term_for_vect seen k R T T' js =
   607       let
   608         val T1 = pseudo_domain_type T
   609         val T2 = pseudo_range_type T
   610       in
   611         make_fun_or_set true T T1 T2 T'
   612             (map (fn j => term_for_atom seen T1 T1 j k) (index_seq 0 k))
   613             (map (term_for_rep true seen T2 T2 R o single)
   614                  (batch_list (arity_of_rep R) js))
   615       end
   616     and term_for_rep _ seen T T' (R as Atom (k, j0)) [[j]] =
   617         if j >= j0 andalso j < j0 + k then term_for_atom seen T T' (j - j0) k
   618         else raise REP ("Nitpick_Model.reconstruct_term.term_for_rep", [R])
   619       | term_for_rep _ seen (Type (@{type_name prod}, [T1, T2])) _
   620                      (Struct [R1, R2]) [js] =
   621         let
   622           val arity1 = arity_of_rep R1
   623           val (js1, js2) = chop arity1 js
   624         in
   625           list_comb (HOLogic.pair_const T1 T2,
   626                      map3 (fn T => term_for_rep true seen T T) [T1, T2] [R1, R2]
   627                           [[js1], [js2]])
   628         end
   629       | term_for_rep _ seen T T' (Vect (k, R')) [js] =
   630         term_for_vect seen k R' T T' js
   631       | term_for_rep maybe_opt seen T T' (Func (R1, Formula Neut)) jss =
   632         let
   633           val T1 = pseudo_domain_type T
   634           val T2 = pseudo_range_type T
   635           val jss1 = all_combinations_for_rep R1
   636           val ts1 = map (term_for_rep true seen T1 T1 R1 o single) jss1
   637           val ts2 =
   638             map (fn js => term_for_rep true seen T2 T2 (Atom (2, 0))
   639                                        [[int_from_bool (member (op =) jss js)]])
   640                 jss1
   641         in make_fun_or_set maybe_opt T T1 T2 T' ts1 ts2 end
   642       | term_for_rep maybe_opt seen T T' (Func (R1, R2)) jss =
   643         let
   644           val T1 = pseudo_domain_type T
   645           val T2 = pseudo_range_type T
   646           val arity1 = arity_of_rep R1
   647           val jss1 = all_combinations_for_rep R1
   648           val ts1 = map (term_for_rep false seen T1 T1 R1 o single) jss1
   649           val grouped_jss2 = AList.group (op =) (map (chop arity1) jss)
   650           val ts2 = map (term_for_rep false seen T2 T2 R2 o the_default []
   651                          o AList.lookup (op =) grouped_jss2) jss1
   652         in make_fun_or_set maybe_opt T T1 T2 T' ts1 ts2 end
   653       | term_for_rep _ seen T T' (Opt R) jss =
   654         if null jss then Const (unknown, T)
   655         else term_for_rep true seen T T' R jss
   656       | term_for_rep _ _ T _ R jss =
   657         raise ARG ("Nitpick_Model.reconstruct_term.term_for_rep",
   658                    Syntax.string_of_typ ctxt T ^ " " ^ string_for_rep R ^ " " ^
   659                    string_of_int (length jss))
   660   in
   661     postprocess_subterms [] o polish_funs [] o unarize_unbox_etc_term
   662     oooo term_for_rep maybe_opt []
   663   end
   664 
   665 (** Constant postprocessing **)
   666 
   667 fun dest_n_tuple_type 1 T = [T]
   668   | dest_n_tuple_type n (Type (_, [T1, T2])) =
   669     T1 :: dest_n_tuple_type (n - 1) T2
   670   | dest_n_tuple_type _ T =
   671     raise TYPE ("Nitpick_Model.dest_n_tuple_type", [T], [])
   672 
   673 fun const_format thy def_tables (x as (s, T)) =
   674   if String.isPrefix unrolled_prefix s then
   675     const_format thy def_tables (original_name s, range_type T)
   676   else if String.isPrefix skolem_prefix s then
   677     let
   678       val k = unprefix skolem_prefix s
   679               |> strip_first_name_sep |> fst |> space_explode "@"
   680               |> hd |> Int.fromString |> the
   681     in [k, num_binder_types T - k] end
   682   else if original_name s <> s then
   683     [num_binder_types T]
   684   else case def_of_const thy def_tables x of
   685     SOME t' => if fixpoint_kind_of_rhs t' <> NoFp then
   686                  let val k = length (strip_abs_vars t') in
   687                    [k, num_binder_types T - k]
   688                  end
   689                else
   690                  [num_binder_types T]
   691   | NONE => [num_binder_types T]
   692 fun intersect_formats _ [] = []
   693   | intersect_formats [] _ = []
   694   | intersect_formats ks1 ks2 =
   695     let val ((ks1', k1), (ks2', k2)) = pairself split_last (ks1, ks2) in
   696       intersect_formats (ks1' @ (if k1 > k2 then [k1 - k2] else []))
   697                         (ks2' @ (if k2 > k1 then [k2 - k1] else [])) @
   698       [Int.min (k1, k2)]
   699     end
   700 
   701 fun lookup_format thy def_tables formats t =
   702   case AList.lookup (fn (SOME x, SOME y) =>
   703                         (term_match thy) (x, y) | _ => false)
   704                     formats (SOME t) of
   705     SOME format => format
   706   | NONE => let val format = the (AList.lookup (op =) formats NONE) in
   707               case t of
   708                 Const x => intersect_formats format
   709                                              (const_format thy def_tables x)
   710               | _ => format
   711             end
   712 
   713 fun format_type default_format format T =
   714   let
   715     val T = uniterize_unarize_unbox_etc_type T
   716     val format = format |> filter (curry (op <) 0)
   717   in
   718     if forall (curry (op =) 1) format then
   719       T
   720     else
   721       let
   722         val (binder_Ts, body_T) = strip_type T
   723         val batched =
   724           binder_Ts
   725           |> map (format_type default_format default_format)
   726           |> rev |> chunk_list_unevenly (rev format)
   727           |> map (HOLogic.mk_tupleT o rev)
   728       in List.foldl (op -->) body_T batched end
   729   end
   730 fun format_term_type thy def_tables formats t =
   731   format_type (the (AList.lookup (op =) formats NONE))
   732               (lookup_format thy def_tables formats t) (fastype_of t)
   733 
   734 fun repair_special_format js m format =
   735   m - 1 downto 0 |> chunk_list_unevenly (rev format)
   736                  |> map (rev o filter_out (member (op =) js))
   737                  |> filter_out null |> map length |> rev
   738 
   739 fun user_friendly_const ({thy, evals, def_tables, skolems, special_funs, ...}
   740                          : hol_context) (base_name, step_name) formats =
   741   let
   742     val default_format = the (AList.lookup (op =) formats NONE)
   743     fun do_const (x as (s, T)) =
   744       (if String.isPrefix special_prefix s then
   745          let
   746            val do_term = map_aterms (fn Const x => fst (do_const x) | t' => t')
   747            val (x' as (_, T'), js, ts) =
   748              AList.find (op =) (!special_funs) (s, unarize_unbox_etc_type T)
   749              |> the_single
   750            val max_j = List.last js
   751            val Ts = List.take (binder_types T', max_j + 1)
   752            val missing_js = filter_out (member (op =) js) (0 upto max_j)
   753            val missing_Ts = filter_indices missing_js Ts
   754            fun nth_missing_var n =
   755              ((arg_var_prefix ^ nat_subscript (n + 1), 0), nth missing_Ts n)
   756            val missing_vars = map nth_missing_var (0 upto length missing_js - 1)
   757            val vars = special_bounds ts @ missing_vars
   758            val ts' =
   759              map (fn j =>
   760                      case AList.lookup (op =) (js ~~ ts) j of
   761                        SOME t => do_term t
   762                      | NONE =>
   763                        Var (nth missing_vars
   764                                 (find_index (curry (op =) j) missing_js)))
   765                  (0 upto max_j)
   766            val t = do_const x' |> fst
   767            val format =
   768              case AList.lookup (fn (SOME t1, SOME t2) => term_match thy (t1, t2)
   769                                  | _ => false) formats (SOME t) of
   770                SOME format =>
   771                repair_special_format js (num_binder_types T') format
   772              | NONE =>
   773                const_format thy def_tables x'
   774                |> repair_special_format js (num_binder_types T')
   775                |> intersect_formats default_format
   776          in
   777            (list_comb (t, ts') |> fold_rev abs_var vars,
   778             format_type default_format format T)
   779          end
   780        else if String.isPrefix uncurry_prefix s then
   781          let
   782            val (ss, s') = unprefix uncurry_prefix s
   783                           |> strip_first_name_sep |>> space_explode "@"
   784          in
   785            if String.isPrefix step_prefix s' then
   786              do_const (s', T)
   787            else
   788              let
   789                val k = the (Int.fromString (hd ss))
   790                val j = the (Int.fromString (List.last ss))
   791                val (before_Ts, (tuple_T, rest_T)) =
   792                  strip_n_binders j T ||> (strip_n_binders 1 #>> hd)
   793                val T' = before_Ts ---> dest_n_tuple_type k tuple_T ---> rest_T
   794              in do_const (s', T') end
   795          end
   796        else if String.isPrefix unrolled_prefix s then
   797          let val t = Const (original_name s, range_type T) in
   798            (lambda (Free (iter_var_prefix, nat_T)) t,
   799             format_type default_format
   800                         (lookup_format thy def_tables formats t) T)
   801          end
   802        else if String.isPrefix base_prefix s then
   803          (Const (base_name, T --> T) $ Const (unprefix base_prefix s, T),
   804           format_type default_format default_format T)
   805        else if String.isPrefix step_prefix s then
   806          (Const (step_name, T --> T) $ Const (unprefix step_prefix s, T),
   807           format_type default_format default_format T)
   808        else if String.isPrefix quot_normal_prefix s then
   809          let val t = Const (nitpick_prefix ^ "quotient normal form", T) in
   810            (t, format_term_type thy def_tables formats t)
   811          end
   812        else if String.isPrefix skolem_prefix s then
   813          let
   814            val ss = the (AList.lookup (op =) (!skolems) s)
   815            val (Ts, Ts') = chop (length ss) (binder_types T)
   816            val frees = map Free (ss ~~ Ts)
   817            val s' = original_name s
   818          in
   819            (fold lambda frees (Const (s', Ts' ---> T)),
   820             format_type default_format
   821                         (lookup_format thy def_tables formats (Const x)) T)
   822          end
   823        else if String.isPrefix eval_prefix s then
   824          let
   825            val t = nth evals (the (Int.fromString (unprefix eval_prefix s)))
   826          in (t, format_term_type thy def_tables formats t) end
   827        else
   828          (* The selector case can occur in conjunction with fractional types.
   829             It's not pretty. *)
   830          let val t = Const (s |> not (is_sel s) ? original_name, T) in
   831            (t, format_term_type thy def_tables formats t)
   832          end)
   833       |>> map_types uniterize_unarize_unbox_etc_type
   834       |>> shorten_names_in_term |>> Term.map_abs_vars shortest_name
   835   in do_const end
   836 
   837 fun assign_operator_for_const (s, T) =
   838   if String.isPrefix ubfp_prefix s then
   839     if is_fun_type T then xsym "\<subseteq>" "<=" ()
   840     else xsym "\<le>" "<=" ()
   841   else if String.isPrefix lbfp_prefix s then
   842     if is_fun_type T then xsym "\<supseteq>" ">=" ()
   843     else xsym "\<ge>" ">=" ()
   844   else if original_name s <> s then
   845     assign_operator_for_const (strip_first_name_sep s |> snd, T)
   846   else
   847     "="
   848 
   849 (** Model reconstruction **)
   850 
   851 fun unfold_outer_the_binders (t as Const (@{const_name The}, _)
   852                                    $ Abs (s, T, Const (@{const_name HOL.eq}, _)
   853                                                 $ Bound 0 $ t')) =
   854     betapply (Abs (s, T, t'), t) |> unfold_outer_the_binders
   855   | unfold_outer_the_binders t = t
   856 fun bisimilar_values _ 0 _ = true
   857   | bisimilar_values coTs max_depth (t1, t2) =
   858     let val T = fastype_of t1 in
   859       if exists_subtype (member (op =) coTs) T then
   860         let
   861           val ((head1, args1), (head2, args2)) =
   862             pairself (strip_comb o unfold_outer_the_binders) (t1, t2)
   863           val max_depth = max_depth - (if member (op =) coTs T then 1 else 0)
   864         in
   865           head1 = head2 andalso
   866           forall (bisimilar_values coTs max_depth) (args1 ~~ args2)
   867         end
   868       else
   869         t1 = t2
   870     end
   871 
   872 fun reconstruct_hol_model {show_datatypes, show_skolems, show_consts}
   873         ({hol_ctxt = {thy, ctxt, max_bisim_depth, boxes, stds, wfs, user_axioms,
   874                       debug, whacks, binary_ints, destroy_constrs, specialize,
   875                       star_linear_preds, total_consts, needs, tac_timeout,
   876                       evals, case_names, def_tables, nondef_table, nondefs,
   877                       simp_table, psimp_table, choice_spec_table, intro_table,
   878                       ground_thm_table, ersatz_table, skolems, special_funs,
   879                       unrolled_preds, wf_cache, constr_cache}, binarize,
   880                       card_assigns, bits, bisim_depth, datatypes, ofs} : scope)
   881         formats atomss real_frees pseudo_frees free_names sel_names nonsel_names
   882         rel_table bounds =
   883   let
   884     val pool = Unsynchronized.ref []
   885     val (wacky_names as (_, base_step_names), ctxt) =
   886       add_wacky_syntax ctxt
   887     val hol_ctxt =
   888       {thy = thy, ctxt = ctxt, max_bisim_depth = max_bisim_depth, boxes = boxes,
   889        stds = stds, wfs = wfs, user_axioms = user_axioms, debug = debug,
   890        whacks = whacks, binary_ints = binary_ints,
   891        destroy_constrs = destroy_constrs, specialize = specialize,
   892        star_linear_preds = star_linear_preds, total_consts = total_consts,
   893        needs = needs, tac_timeout = tac_timeout, evals = evals,
   894        case_names = case_names, def_tables = def_tables,
   895        nondef_table = nondef_table, nondefs = nondefs, simp_table = simp_table,
   896        psimp_table = psimp_table, choice_spec_table = choice_spec_table,
   897        intro_table = intro_table, ground_thm_table = ground_thm_table,
   898        ersatz_table = ersatz_table, skolems = skolems,
   899        special_funs = special_funs, unrolled_preds = unrolled_preds,
   900        wf_cache = wf_cache, constr_cache = constr_cache}
   901     val scope =
   902       {hol_ctxt = hol_ctxt, binarize = binarize, card_assigns = card_assigns,
   903        bits = bits, bisim_depth = bisim_depth, datatypes = datatypes, ofs = ofs}
   904     fun term_for_rep maybe_opt unfold =
   905       reconstruct_term maybe_opt unfold pool wacky_names scope atomss
   906                        sel_names rel_table bounds
   907     val all_values =
   908       all_values_of_type pool wacky_names scope atomss sel_names rel_table
   909                          bounds
   910     fun is_codatatype_wellformed (cos : datatype_spec list)
   911                                  ({typ, card, ...} : datatype_spec) =
   912       let
   913         val ts = all_values card typ
   914         val max_depth = Integer.sum (map #card cos)
   915       in
   916         forall (not o bisimilar_values (map #typ cos) max_depth)
   917                (all_distinct_unordered_pairs_of ts)
   918       end
   919     fun pretty_for_assign name =
   920       let
   921         val (oper, (t1, T'), T) =
   922           case name of
   923             FreeName (s, T, _) =>
   924             let val t = Free (s, uniterize_unarize_unbox_etc_type T) in
   925               ("=", (t, format_term_type thy def_tables formats t), T)
   926             end
   927           | ConstName (s, T, _) =>
   928             (assign_operator_for_const (s, T),
   929              user_friendly_const hol_ctxt base_step_names formats (s, T), T)
   930           | _ => raise NUT ("Nitpick_Model.reconstruct_hol_model.\
   931                             \pretty_for_assign", [name])
   932         val t2 = if rep_of name = Any then
   933                    Const (@{const_name undefined}, T')
   934                  else
   935                    tuple_list_for_name rel_table bounds name
   936                    |> term_for_rep (not (is_fully_representable_set name)) false
   937                                    T T' (rep_of name)
   938       in
   939         Pretty.block (Pretty.breaks
   940             [Syntax.pretty_term (set_show_all_types ctxt) t1,
   941              Pretty.str oper, Syntax.pretty_term ctxt t2])
   942       end
   943     fun pretty_for_datatype ({typ, card, complete, ...} : datatype_spec) =
   944       Pretty.block (Pretty.breaks
   945           (pretty_for_type ctxt typ ::
   946            (case typ of
   947               Type (@{type_name fun_box}, _) => [Pretty.str "[boxed]"]
   948             | Type (@{type_name pair_box}, _) => [Pretty.str "[boxed]"]
   949             | _ => []) @
   950            [Pretty.str "=",
   951             Pretty.enum "," "{" "}"
   952                 (map (Syntax.pretty_term ctxt) (all_values card typ) @
   953                  (if fun_from_pair complete false then []
   954                   else [Pretty.str (unrep ())]))]))
   955     fun integer_datatype T =
   956       [{typ = T, card = card_of_type card_assigns T, co = false,
   957         standard = true, self_rec = true, complete = (false, false),
   958         concrete = (true, true), deep = true, constrs = []}]
   959       handle TYPE ("Nitpick_HOL.card_of_type", _, _) => []
   960     val (codatatypes, datatypes) =
   961       datatypes |> filter #deep |> List.partition #co
   962                 ||> append (integer_datatype int_T
   963                             |> is_standard_datatype thy stds nat_T
   964                                ? append (integer_datatype nat_T))
   965     val block_of_datatypes =
   966       if show_datatypes andalso not (null datatypes) then
   967         [Pretty.big_list ("Datatype" ^ plural_s_for_list datatypes ^ ":")
   968                          (map pretty_for_datatype datatypes)]
   969       else
   970         []
   971     val block_of_codatatypes =
   972       if show_datatypes andalso not (null codatatypes) then
   973         [Pretty.big_list ("Codatatype" ^ plural_s_for_list codatatypes ^ ":")
   974                          (map pretty_for_datatype codatatypes)]
   975       else
   976         []
   977     fun block_of_names show title names =
   978       if show andalso not (null names) then
   979         Pretty.str (title ^ plural_s_for_list names ^ ":")
   980         :: map (Pretty.indent indent_size o pretty_for_assign)
   981                (sort_wrt (original_name o nickname_of) names)
   982       else
   983         []
   984     fun free_name_for_term keep_all (x as (s, T)) =
   985       case filter (curry (op =) x
   986                    o pairf nickname_of (uniterize_unarize_unbox_etc_type
   987                                         o type_of)) free_names of
   988         [name] => SOME name
   989       | [] => if keep_all then SOME (FreeName (s, T, Any)) else NONE
   990       | _ => raise TERM ("Nitpick_Model.reconstruct_hol_model.\
   991                          \free_name_for_term", [Const x])
   992     val (skolem_names, nonskolem_nonsel_names) =
   993       List.partition is_skolem_name nonsel_names
   994     val (eval_names, noneval_nonskolem_nonsel_names) =
   995       List.partition (String.isPrefix eval_prefix o nickname_of)
   996                      nonskolem_nonsel_names
   997       ||> filter_out (member (op =) [@{const_name bisim},
   998                                      @{const_name bisim_iterator_max}]
   999                       o nickname_of)
  1000       ||> append (map_filter (free_name_for_term false) pseudo_frees)
  1001     val real_free_names = map_filter (free_name_for_term true) real_frees
  1002     val chunks = block_of_names true "Free variable" real_free_names @
  1003                  block_of_names show_skolems "Skolem constant" skolem_names @
  1004                  block_of_names true "Evaluated term" eval_names @
  1005                  block_of_datatypes @ block_of_codatatypes @
  1006                  block_of_names show_consts "Constant"
  1007                                 noneval_nonskolem_nonsel_names
  1008   in
  1009     (Pretty.chunks (if null chunks then [Pretty.str "Empty assignment"]
  1010                     else chunks),
  1011      bisim_depth >= 0 orelse
  1012      forall (is_codatatype_wellformed codatatypes) codatatypes)
  1013   end
  1014 
  1015 fun term_for_name pool scope atomss sel_names rel_table bounds name =
  1016   let val T = type_of name in
  1017     tuple_list_for_name rel_table bounds name
  1018     |> reconstruct_term (not (is_fully_representable_set name)) false pool
  1019                         (("", ""), ("", "")) scope atomss sel_names rel_table
  1020                         bounds T T (rep_of name)
  1021   end
  1022 
  1023 fun prove_hol_model (scope as {hol_ctxt = {thy, ctxt, debug, ...},
  1024                                card_assigns, ...})
  1025                     auto_timeout free_names sel_names rel_table bounds prop =
  1026   let
  1027     val pool = Unsynchronized.ref []
  1028     val atomss = [(NONE, [])]
  1029     fun free_type_assm (T, k) =
  1030       let
  1031         fun atom j = nth_atom thy atomss pool true T j
  1032         fun equation_for_atom j = HOLogic.eq_const T $ Bound 0 $ atom j
  1033         val eqs = map equation_for_atom (index_seq 0 k)
  1034         val compreh_assm =
  1035           Const (@{const_name All}, (T --> bool_T) --> bool_T)
  1036               $ Abs ("x", T, foldl1 HOLogic.mk_disj eqs)
  1037         val distinct_assm = distinctness_formula T (map atom (index_seq 0 k))
  1038       in s_conj (compreh_assm, distinct_assm) end
  1039     fun free_name_assm name =
  1040       HOLogic.mk_eq (Free (nickname_of name, type_of name),
  1041                      term_for_name pool scope atomss sel_names rel_table bounds
  1042                                    name)
  1043     val freeT_assms = map free_type_assm (filter (is_TFree o fst) card_assigns)
  1044     val model_assms = map free_name_assm free_names
  1045     val assm = foldr1 s_conj (freeT_assms @ model_assms)
  1046     fun try_out negate =
  1047       let
  1048         val concl = (negate ? curry (op $) @{const Not})
  1049                     (Object_Logic.atomize_term thy prop)
  1050         val prop = HOLogic.mk_Trueprop (HOLogic.mk_imp (assm, concl))
  1051                    |> map_types (map_type_tfree
  1052                                      (fn (s, []) => TFree (s, HOLogic.typeS)
  1053                                        | x => TFree x))
  1054         val _ =
  1055           if debug then
  1056             (if negate then "Genuineness" else "Spuriousness") ^ " goal: " ^
  1057             Syntax.string_of_term ctxt prop ^ "."
  1058             |> Output.urgent_message
  1059           else
  1060             ()
  1061         val goal = prop |> cterm_of thy |> Goal.init
  1062       in
  1063         (goal |> SINGLE (DETERM_TIMEOUT auto_timeout (auto_tac ctxt))
  1064               |> the |> Goal.finish ctxt; true)
  1065         handle THM _ => false
  1066              | TimeLimit.TimeOut => false
  1067       end
  1068   in
  1069     if try_out false then SOME true
  1070     else if try_out true then SOME false
  1071     else NONE
  1072   end
  1073 
  1074 end;