src/HOL/Tools/Nitpick/nitpick_model.ML
author blanchet
Mon Sep 13 20:21:40 2010 +0200 (2010-09-13)
changeset 39345 062c10ff848c
parent 39118 12f3788be67b
child 39359 6f49c7fbb1b1
permissions -rw-r--r--
remove unreferenced identifiers
     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_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 : 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 -> styp list -> styp list -> nut list
    40     -> nut list -> nut list -> nut NameTable.table -> Kodkod.raw_bound list
    41     -> Pretty.T * bool
    42   val prove_hol_model :
    43     scope -> Time.time option -> nut list -> nut list -> nut NameTable.table
    44     -> Kodkod.raw_bound list -> term -> bool option
    45 end;
    46 
    47 structure Nitpick_Model : NITPICK_MODEL =
    48 struct
    49 
    50 open Nitpick_Util
    51 open Nitpick_HOL
    52 open Nitpick_Scope
    53 open Nitpick_Peephole
    54 open Nitpick_Rep
    55 open Nitpick_Nut
    56 
    57 structure KK = Kodkod
    58 
    59 type params =
    60   {show_datatypes: bool,
    61    show_consts: bool}
    62 
    63 type term_postprocessor =
    64   Proof.context -> string -> (typ -> term list) -> typ -> term -> term
    65 
    66 structure Data = Generic_Data(
    67   type T = (typ * term_postprocessor) list
    68   val empty = []
    69   val extend = I
    70   fun merge (x, y) = AList.merge (op =) (K true) (x, y))
    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 = 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 = ProofContext.theory_of ctxt |> Context.reject_draft
    94     val (maybe_t, thy) =
    95       Sign.declare_const ((@{binding nitpick_maybe}, @{typ "'a => 'a"}),
    96                           Mixfix (maybe_mixfix (), [1000], 1000)) thy
    97     val (abs_t, thy) =
    98       Sign.declare_const ((@{binding nitpick_abs}, @{typ "'a => 'b"}),
    99                           Mixfix (abs_mixfix (), [40], 40)) thy
   100     val (base_t, thy) =
   101       Sign.declare_const ((@{binding nitpick_base}, @{typ "'a => 'a"}),
   102                           Mixfix (base_mixfix (), [1000], 1000)) thy
   103     val (step_t, thy) =
   104       Sign.declare_const ((@{binding nitpick_step}, @{typ "'a => 'a"}),
   105                           Mixfix (step_mixfix (), [1000], 1000)) thy
   106   in
   107     (pairself (pairself name_of) ((maybe_t, abs_t), (base_t, step_t)),
   108      ProofContext.transfer_syntax thy ctxt)
   109   end
   110 
   111 (** Term reconstruction **)
   112 
   113 fun nth_atom_number pool T j =
   114   case AList.lookup (op =) (!pool) T of
   115     SOME js =>
   116     (case find_index (curry (op =) j) js of
   117        ~1 => (Unsynchronized.change pool (cons (T, j :: js));
   118               length js + 1)
   119      | n => length js - n)
   120   | NONE => (Unsynchronized.change pool (cons (T, [j])); 1)
   121 fun atom_suffix s =
   122   nat_subscript
   123   #> (s <> "" andalso Symbol.is_ascii_digit (List.last (explode s)))
   124      ? prefix "\<^isub>,"
   125 fun nth_atom_name thy atomss pool prefix T j =
   126   let
   127     val ss = these (triple_lookup (type_match thy) atomss T)
   128     val m = nth_atom_number pool T j
   129   in
   130     if m <= length ss then
   131       nth ss (m - 1)
   132     else case T of
   133       Type (s, _) =>
   134       let val s' = shortest_name s in
   135         prefix ^
   136         (if String.isPrefix "\\" s' then s' else substring (s', 0, 1)) ^
   137         atom_suffix s m
   138       end
   139     | TFree (s, _) => prefix ^ perhaps (try (unprefix "'")) s ^ atom_suffix s m
   140     | _ => raise TYPE ("Nitpick_Model.nth_atom_name", [T], [])
   141   end
   142 fun nth_atom thy atomss pool for_auto T j =
   143   if for_auto then
   144     Free (nth_atom_name thy atomss pool (hd (space_explode "." nitpick_prefix))
   145                         T j, T)
   146   else
   147     Const (nth_atom_name thy atomss pool "" T j, T)
   148 
   149 fun extract_real_number (Const (@{const_name divide}, _) $ t1 $ t2) =
   150     real (snd (HOLogic.dest_number t1)) / real (snd (HOLogic.dest_number t2))
   151   | extract_real_number t = real (snd (HOLogic.dest_number t))
   152 fun nice_term_ord (Abs (_, _, t1), Abs (_, _, t2)) = nice_term_ord (t1, t2)
   153   | nice_term_ord tp = Real.compare (pairself extract_real_number tp)
   154     handle TERM ("dest_number", _) =>
   155            case tp of
   156              (t11 $ t12, t21 $ t22) =>
   157              (case nice_term_ord (t11, t21) of
   158                 EQUAL => nice_term_ord (t12, t22)
   159               | ord => ord)
   160            | _ => Term_Ord.fast_term_ord tp
   161 
   162 fun register_term_postprocessor_generic T postproc =
   163   Data.map (cons (T, postproc))
   164 (* TODO: Consider morphism. *)
   165 fun register_term_postprocessor T postproc (_ : morphism) =
   166   register_term_postprocessor_generic T postproc
   167 val register_term_postprocessor_global =
   168   Context.theory_map oo register_term_postprocessor_generic
   169 
   170 fun unregister_term_postprocessor_generic T = Data.map (AList.delete (op =) T)
   171 (* TODO: Consider morphism. *)
   172 fun unregister_term_postprocessor T (_ : morphism) =
   173   unregister_term_postprocessor_generic T
   174 val unregister_term_postprocessor_global =
   175   Context.theory_map o unregister_term_postprocessor_generic
   176 
   177 fun tuple_list_for_name rel_table bounds name =
   178   the (AList.lookup (op =) bounds (the_rel rel_table name)) handle NUT _ => [[]]
   179 
   180 fun unarize_unbox_etc_term (Const (@{const_name FinFun}, _) $ t1) =
   181     unarize_unbox_etc_term t1
   182   | unarize_unbox_etc_term (Const (@{const_name FunBox}, _) $ t1) =
   183     unarize_unbox_etc_term t1
   184   | unarize_unbox_etc_term
   185         (Const (@{const_name PairBox},
   186                 Type (@{type_name fun}, [T1, Type (@{type_name fun}, [T2, _])]))
   187          $ t1 $ t2) =
   188     let val Ts = map uniterize_unarize_unbox_etc_type [T1, T2] in
   189       Const (@{const_name Pair}, Ts ---> Type (@{type_name prod}, Ts))
   190       $ unarize_unbox_etc_term t1 $ unarize_unbox_etc_term t2
   191     end
   192   | unarize_unbox_etc_term (Const (s, T)) =
   193     Const (s, uniterize_unarize_unbox_etc_type T)
   194   | unarize_unbox_etc_term (t1 $ t2) =
   195     unarize_unbox_etc_term t1 $ unarize_unbox_etc_term t2
   196   | unarize_unbox_etc_term (Free (s, T)) =
   197     Free (s, uniterize_unarize_unbox_etc_type T)
   198   | unarize_unbox_etc_term (Var (x, T)) =
   199     Var (x, uniterize_unarize_unbox_etc_type T)
   200   | unarize_unbox_etc_term (Bound j) = Bound j
   201   | unarize_unbox_etc_term (Abs (s, T, t')) =
   202     Abs (s, uniterize_unarize_unbox_etc_type T, unarize_unbox_etc_term t')
   203 
   204 fun factor_out_types (T1 as Type (@{type_name prod}, [T11, T12]))
   205                      (T2 as Type (@{type_name prod}, [T21, T22])) =
   206     let val (n1, n2) = pairself num_factors_in_type (T11, T21) in
   207       if n1 = n2 then
   208         let
   209           val ((T11', opt_T12'), (T21', opt_T22')) = factor_out_types T12 T22
   210         in
   211           ((Type (@{type_name prod}, [T11, T11']), opt_T12'),
   212            (Type (@{type_name prod}, [T21, T21']), opt_T22'))
   213         end
   214       else if n1 < n2 then
   215         case factor_out_types T1 T21 of
   216           (p1, (T21', NONE)) => (p1, (T21', SOME T22))
   217         | (p1, (T21', SOME T22')) =>
   218           (p1, (T21', SOME (Type (@{type_name prod}, [T22', T22]))))
   219       else
   220         swap (factor_out_types T2 T1)
   221     end
   222   | factor_out_types (Type (@{type_name prod}, [T11, T12])) T2 =
   223     ((T11, SOME T12), (T2, NONE))
   224   | factor_out_types T1 (Type (@{type_name prod}, [T21, T22])) =
   225     ((T1, NONE), (T21, SOME T22))
   226   | factor_out_types T1 T2 = ((T1, NONE), (T2, NONE))
   227 
   228 fun make_plain_fun maybe_opt T1 T2 =
   229   let
   230     fun aux T1 T2 [] =
   231         Const (if maybe_opt then opt_flag else non_opt_flag, T1 --> T2)
   232       | aux T1 T2 ((t1, t2) :: tps) =
   233         Const (@{const_name fun_upd}, (T1 --> T2) --> T1 --> T2 --> T1 --> T2)
   234         $ aux T1 T2 tps $ t1 $ t2
   235   in aux T1 T2 o rev end
   236 fun is_plain_fun (Const (s, _)) = (s = opt_flag orelse s = non_opt_flag)
   237   | is_plain_fun (Const (@{const_name fun_upd}, _) $ t0 $ _ $ _) =
   238     is_plain_fun t0
   239   | is_plain_fun _ = false
   240 val dest_plain_fun =
   241   let
   242     fun aux (Abs (_, _, Const (s, _))) = (s <> irrelevant, ([], []))
   243       | aux (Const (s, _)) = (s <> non_opt_flag, ([], []))
   244       | aux (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =
   245         let val (maybe_opt, (ts1, ts2)) = aux t0 in
   246           (maybe_opt, (t1 :: ts1, t2 :: ts2))
   247         end
   248       | aux t = raise TERM ("Nitpick_Model.dest_plain_fun", [t])
   249   in apsnd (pairself rev) o aux end
   250 
   251 fun break_in_two T T1 T2 t =
   252   let
   253     val ps = HOLogic.flat_tupleT_paths T
   254     val cut = length (HOLogic.strip_tupleT T1)
   255     val (ps1, ps2) = pairself HOLogic.flat_tupleT_paths (T1, T2)
   256     val (ts1, ts2) = t |> HOLogic.strip_ptuple ps |> chop cut
   257   in (HOLogic.mk_ptuple ps1 T1 ts1, HOLogic.mk_ptuple ps2 T2 ts2) end
   258 fun pair_up (Type (@{type_name prod}, [T1', T2']))
   259             (t1 as Const (@{const_name Pair},
   260                           Type (@{type_name fun},
   261                                 [_, Type (@{type_name fun}, [_, T1])]))
   262              $ t11 $ t12) t2 =
   263     if T1 = T1' then HOLogic.mk_prod (t1, t2)
   264     else HOLogic.mk_prod (t11, pair_up T2' t12 t2)
   265   | pair_up _ t1 t2 = HOLogic.mk_prod (t1, t2)
   266 fun multi_pair_up T1 t1 (ts2, ts3) = map2 (pair o pair_up T1 t1) ts2 ts3
   267 
   268 fun typecast_fun (Type (@{type_name fun}, [T1', T2'])) T1 T2 t =
   269     let
   270       fun do_curry T1 T1a T1b T2 t =
   271         let
   272           val (maybe_opt, tsp) = dest_plain_fun t
   273           val tps =
   274             tsp |>> map (break_in_two T1 T1a T1b)
   275                 |> uncurry (map2 (fn (t1a, t1b) => fn t2 => (t1a, (t1b, t2))))
   276                 |> AList.coalesce (op =)
   277                 |> map (apsnd (make_plain_fun maybe_opt T1b T2))
   278         in make_plain_fun maybe_opt T1a (T1b --> T2) tps end
   279       and do_uncurry T1 T2 t =
   280         let
   281           val (maybe_opt, tsp) = dest_plain_fun t
   282           val tps =
   283             tsp |> op ~~
   284                 |> maps (fn (t1, t2) =>
   285                             multi_pair_up T1 t1 (snd (dest_plain_fun t2)))
   286         in make_plain_fun maybe_opt T1 T2 tps end
   287       and do_arrow T1' T2' _ _ (Const (s, _)) = Const (s, T1' --> T2')
   288         | do_arrow T1' T2' T1 T2
   289                    (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =
   290           Const (@{const_name fun_upd},
   291                  (T1' --> T2') --> T1' --> T2' --> T1' --> T2')
   292           $ do_arrow T1' T2' T1 T2 t0 $ do_term T1' T1 t1 $ do_term T2' T2 t2
   293         | do_arrow _ _ _ _ t =
   294           raise TERM ("Nitpick_Model.typecast_fun.do_arrow", [t])
   295       and do_fun T1' T2' T1 T2 t =
   296         case factor_out_types T1' T1 of
   297           ((_, NONE), (_, NONE)) => t |> do_arrow T1' T2' T1 T2
   298         | ((_, NONE), (T1a, SOME T1b)) =>
   299           t |> do_curry T1 T1a T1b T2 |> do_arrow T1' T2' T1a (T1b --> T2)
   300         | ((T1a', SOME T1b'), (_, NONE)) =>
   301           t |> do_arrow T1a' (T1b' --> T2') T1 T2 |> do_uncurry T1' T2'
   302         | _ => raise TYPE ("Nitpick_Model.typecast_fun.do_fun", [T1, T1'], [])
   303       and do_term (Type (@{type_name fun}, [T1', T2']))
   304                   (Type (@{type_name fun}, [T1, T2])) t =
   305           do_fun T1' T2' T1 T2 t
   306         | do_term (T' as Type (@{type_name prod}, Ts' as [T1', T2']))
   307                   (Type (@{type_name prod}, [T1, T2]))
   308                   (Const (@{const_name Pair}, _) $ t1 $ t2) =
   309           Const (@{const_name Pair}, Ts' ---> T')
   310           $ do_term T1' T1 t1 $ do_term T2' T2 t2
   311         | do_term T' T t =
   312           if T = T' then t
   313           else raise TYPE ("Nitpick_Model.typecast_fun.do_term", [T, T'], [])
   314     in if T1' = T1 andalso T2' = T2 then t else do_fun T1' T2' T1 T2 t end
   315   | typecast_fun T' _ _ _ =
   316     raise TYPE ("Nitpick_Model.typecast_fun", [T'], [])
   317 
   318 fun truth_const_sort_key @{const True} = "0"
   319   | truth_const_sort_key @{const False} = "2"
   320   | truth_const_sort_key _ = "1"
   321 
   322 fun mk_tuple (Type (@{type_name prod}, [T1, T2])) ts =
   323     HOLogic.mk_prod (mk_tuple T1 ts,
   324         mk_tuple T2 (List.drop (ts, length (HOLogic.flatten_tupleT T1))))
   325   | mk_tuple _ (t :: _) = t
   326   | mk_tuple T [] = raise TYPE ("Nitpick_Model.mk_tuple", [T], [])
   327 
   328 fun varified_type_match ctxt (candid_T, pat_T) =
   329   let val thy = ProofContext.theory_of ctxt in
   330     strict_type_match thy (candid_T, varify_type ctxt pat_T)
   331   end
   332 
   333 fun all_values_of_type pool wacky_names (scope as {card_assigns, ...} : scope)
   334                        atomss sel_names rel_table bounds card T =
   335   let
   336     val card = if card = 0 then card_of_type card_assigns T else card
   337     fun nth_value_of_type n =
   338       let
   339         fun term unfold =
   340           reconstruct_term true unfold pool wacky_names scope atomss sel_names
   341                            rel_table bounds T T (Atom (card, 0)) [[n]]
   342       in
   343         case term false of
   344           t as Const (s, _) =>
   345           if String.isPrefix (cyclic_const_prefix ()) s then
   346             HOLogic.mk_eq (t, term true)
   347           else
   348             t
   349         | t => t
   350       end
   351   in index_seq 0 card |> map nth_value_of_type |> sort nice_term_ord end
   352 and reconstruct_term maybe_opt unfold pool
   353         (wacky_names as ((maybe_name, abs_name), _))
   354         (scope as {hol_ctxt as {thy, ctxt, stds, ...}, binarize, card_assigns,
   355                    bits, datatypes, ofs, ...})
   356         atomss sel_names rel_table bounds =
   357   let
   358     val for_auto = (maybe_name = "")
   359     fun value_of_bits jss =
   360       let
   361         val j0 = offset_of_type ofs @{typ unsigned_bit}
   362         val js = map (Integer.add (~ j0) o the_single) jss
   363       in
   364         fold (fn j => Integer.add (reasonable_power 2 j |> j = bits ? op ~))
   365              js 0
   366       end
   367     val all_values =
   368       all_values_of_type pool wacky_names scope atomss sel_names rel_table
   369                          bounds 0
   370     fun postprocess_term (Type (@{type_name fun}, _)) = I
   371       | postprocess_term T =
   372         case Data.get (Context.Proof ctxt) of
   373           [] => I
   374         | postprocs =>
   375           case AList.lookup (varified_type_match ctxt) postprocs T of
   376             SOME postproc => postproc ctxt maybe_name all_values T
   377           | NONE => I
   378     fun postprocess_subterms Ts (t1 $ t2) =
   379         let val t = postprocess_subterms Ts t1 $ postprocess_subterms Ts t2 in
   380           postprocess_term (fastype_of1 (Ts, t)) t
   381         end
   382       | postprocess_subterms Ts (Abs (s, T, t')) =
   383         Abs (s, T, postprocess_subterms (T :: Ts) t')
   384       | postprocess_subterms Ts t = postprocess_term (fastype_of1 (Ts, t)) t
   385     fun make_set maybe_opt T1 T2 tps =
   386       let
   387         val empty_const = Const (@{const_abbrev Set.empty}, T1 --> T2)
   388         val insert_const = Const (@{const_name insert},
   389                                   T1 --> (T1 --> T2) --> T1 --> T2)
   390         fun aux [] =
   391             if maybe_opt andalso not (is_complete_type datatypes false T1) then
   392               insert_const $ Const (unrep (), T1) $ empty_const
   393             else
   394               empty_const
   395           | aux ((t1, t2) :: zs) =
   396             aux zs
   397             |> t2 <> @{const False}
   398                ? curry (op $)
   399                        (insert_const
   400                         $ (t1 |> t2 <> @{const True}
   401                                  ? curry (op $)
   402                                          (Const (maybe_name, T1 --> T1))))
   403       in
   404         if forall (fn (_, t) => t <> @{const True} andalso t <> @{const False})
   405                   tps then
   406           Const (unknown, T1 --> T2)
   407         else
   408           aux tps
   409       end
   410     fun make_map maybe_opt T1 T2 T2' =
   411       let
   412         val update_const = Const (@{const_name fun_upd},
   413                                   (T1 --> T2) --> T1 --> T2 --> T1 --> T2)
   414         fun aux' [] = Const (@{const_abbrev Map.empty}, T1 --> T2)
   415           | aux' ((t1, t2) :: tps) =
   416             (case t2 of
   417                Const (@{const_name None}, _) => aux' tps
   418              | _ => update_const $ aux' tps $ t1 $ t2)
   419         fun aux tps =
   420           if maybe_opt andalso not (is_complete_type datatypes false T1) then
   421             update_const $ aux' tps $ Const (unrep (), T1)
   422             $ (Const (@{const_name Some}, T2' --> T2) $ Const (unknown, T2'))
   423           else
   424             aux' tps
   425       in aux end
   426     fun polish_funs Ts t =
   427       (case fastype_of1 (Ts, t) of
   428          Type (@{type_name fun}, [T1, T2]) =>
   429          if is_plain_fun t then
   430            case T2 of
   431              @{typ bool} =>
   432              let
   433                val (maybe_opt, ts_pair) =
   434                  dest_plain_fun t ||> pairself (map (polish_funs Ts))
   435              in
   436                make_set maybe_opt T1 T2
   437                         (sort_wrt (truth_const_sort_key o snd) (op ~~ ts_pair))
   438              end
   439            | Type (@{type_name option}, [T2']) =>
   440              let
   441                val (maybe_opt, ts_pair) =
   442                  dest_plain_fun t ||> pairself (map (polish_funs Ts))
   443              in make_map maybe_opt T1 T2 T2' (rev (op ~~ ts_pair)) end
   444            | _ => raise SAME ()
   445          else
   446            raise SAME ()
   447        | _ => raise SAME ())
   448       handle SAME () =>
   449              case t of
   450                (t1 as Const (@{const_name fun_upd}, _) $ t11 $ _)
   451                $ (t2 as Const (s, _)) =>
   452                if s = unknown then polish_funs Ts t11
   453                else polish_funs Ts t1 $ polish_funs Ts t2
   454              | t1 $ t2 => polish_funs Ts t1 $ polish_funs Ts t2
   455              | Abs (s, T, t') => Abs (s, T, polish_funs (T :: Ts) t')
   456              | Const (s, Type (@{type_name fun}, [T1, T2])) =>
   457                if s = opt_flag orelse s = non_opt_flag then
   458                  Abs ("x", T1,
   459                       Const (if is_complete_type datatypes false T1 then
   460                                irrelevant
   461                              else
   462                                unknown, T2))
   463                else
   464                  t
   465              | t => t
   466     fun make_fun maybe_opt T1 T2 T' ts1 ts2 =
   467       ts1 ~~ ts2 |> sort (nice_term_ord o pairself fst)
   468                  |> make_plain_fun maybe_opt T1 T2
   469                  |> unarize_unbox_etc_term
   470                  |> typecast_fun (uniterize_unarize_unbox_etc_type T')
   471                                  (uniterize_unarize_unbox_etc_type T1)
   472                                  (uniterize_unarize_unbox_etc_type T2)
   473     fun term_for_atom seen (T as Type (@{type_name fun}, [T1, T2])) T' j _ =
   474         let
   475           val k1 = card_of_type card_assigns T1
   476           val k2 = card_of_type card_assigns T2
   477         in
   478           term_for_rep true seen T T' (Vect (k1, Atom (k2, 0)))
   479                        [nth_combination (replicate k1 (k2, 0)) j]
   480           handle General.Subscript =>
   481                  raise ARG ("Nitpick_Model.reconstruct_term.term_for_atom",
   482                             signed_string_of_int j ^ " for " ^
   483                             string_for_rep (Vect (k1, Atom (k2, 0))))
   484         end
   485       | term_for_atom seen (Type (@{type_name prod}, [T1, T2])) _ j k =
   486         let
   487           val k1 = card_of_type card_assigns T1
   488           val k2 = k div k1
   489         in
   490           list_comb (HOLogic.pair_const T1 T2,
   491                      map3 (fn T => term_for_atom seen T T) [T1, T2]
   492                           [j div k2, j mod k2] [k1, k2]) (* ### k2 or k1? FIXME *)
   493         end
   494       | term_for_atom seen @{typ prop} _ j k =
   495         HOLogic.mk_Trueprop (term_for_atom seen bool_T bool_T j k)
   496       | term_for_atom _ @{typ bool} _ j _ =
   497         if j = 0 then @{const False} else @{const True}
   498       | term_for_atom seen T _ j k =
   499         if T = nat_T andalso is_standard_datatype thy stds nat_T then
   500           HOLogic.mk_number nat_T j
   501         else if T = int_T then
   502           HOLogic.mk_number int_T (int_for_atom (k, 0) j)
   503         else if is_fp_iterator_type T then
   504           HOLogic.mk_number nat_T (k - j - 1)
   505         else if T = @{typ bisim_iterator} then
   506           HOLogic.mk_number nat_T j
   507         else case datatype_spec datatypes T of
   508           NONE => nth_atom thy atomss pool for_auto T j
   509         | SOME {deep = false, ...} => nth_atom thy atomss pool for_auto T j
   510         | SOME {co, standard, constrs, ...} =>
   511           let
   512             fun tuples_for_const (s, T) =
   513               tuple_list_for_name rel_table bounds (ConstName (s, T, Any))
   514             fun cyclic_atom () =
   515               nth_atom thy atomss pool for_auto (Type (cyclic_type_name (), []))
   516                        j
   517             fun cyclic_var () =
   518               Var ((nth_atom_name thy atomss pool "" T j, 0), T)
   519             val discr_jsss = map (tuples_for_const o discr_for_constr o #const)
   520                                  constrs
   521             val real_j = j + offset_of_type ofs T
   522             val constr_x as (constr_s, constr_T) =
   523               get_first (fn (jss, {const, ...}) =>
   524                             if member (op =) jss [real_j] then SOME const
   525                             else NONE)
   526                         (discr_jsss ~~ constrs) |> the
   527             val arg_Ts = curried_binder_types constr_T
   528             val sel_xs =
   529               map (binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize
   530                                                           constr_x)
   531                   (index_seq 0 (length arg_Ts))
   532             val sel_Rs =
   533               map (fn x => get_first
   534                                (fn ConstName (s', T', R) =>
   535                                    if (s', T') = x then SOME R else NONE
   536                                  | u => raise NUT ("Nitpick_Model.reconstruct_\
   537                                                    \term.term_for_atom", [u]))
   538                                sel_names |> the) sel_xs
   539             val arg_Rs = map (snd o dest_Func) sel_Rs
   540             val sel_jsss = map tuples_for_const sel_xs
   541             val arg_jsss =
   542               map (map_filter (fn js => if hd js = real_j then SOME (tl js)
   543                                         else NONE)) sel_jsss
   544             val uncur_arg_Ts = binder_types constr_T
   545             val maybe_cyclic = co orelse not standard
   546           in
   547             if maybe_cyclic andalso not (null seen) andalso
   548                member (op =) (seen |> unfold ? (fst o split_last)) (T, j) then
   549               cyclic_var ()
   550             else if constr_s = @{const_name Word} then
   551               HOLogic.mk_number
   552                   (if T = @{typ "unsigned_bit word"} then nat_T else int_T)
   553                   (value_of_bits (the_single arg_jsss))
   554             else
   555               let
   556                 val seen = seen |> maybe_cyclic ? cons (T, j)
   557                 val ts =
   558                   if length arg_Ts = 0 then
   559                     []
   560                   else
   561                     map3 (fn Ts =>
   562                              term_for_rep (constr_s <> @{const_name FinFun})
   563                                           seen Ts Ts) arg_Ts arg_Rs arg_jsss
   564                     |> mk_tuple (HOLogic.mk_tupleT uncur_arg_Ts)
   565                     |> dest_n_tuple (length uncur_arg_Ts)
   566                 val t =
   567                   if constr_s = @{const_name Abs_Frac} then
   568                     case ts of
   569                       [Const (@{const_name Pair}, _) $ t1 $ t2] =>
   570                       frac_from_term_pair (body_type T) t1 t2
   571                     | _ => raise TERM ("Nitpick_Model.reconstruct_term.\
   572                                        \term_for_atom (Abs_Frac)", ts)
   573                   else if not for_auto andalso
   574                           (is_abs_fun ctxt constr_x orelse
   575                            constr_s = @{const_name Quot}) then
   576                     Const (abs_name, constr_T) $ the_single ts
   577                   else
   578                     list_comb (Const constr_x, ts)
   579               in
   580                 if maybe_cyclic then
   581                   let val var = cyclic_var () in
   582                     if unfold andalso not standard andalso
   583                        length seen = 1 andalso
   584                        exists_subterm
   585                            (fn Const (s, _) =>
   586                                String.isPrefix (cyclic_const_prefix ()) s
   587                              | t' => t' = var) t then
   588                       subst_atomic [(var, cyclic_atom ())] t
   589                     else if exists_subterm (curry (op =) var) t then
   590                       if co then
   591                         Const (@{const_name The}, (T --> bool_T) --> T)
   592                         $ Abs (cyclic_co_val_name (), T,
   593                                Const (@{const_name HOL.eq}, T --> T --> bool_T)
   594                                $ Bound 0 $ abstract_over (var, t))
   595                       else
   596                         cyclic_atom ()
   597                     else
   598                       t
   599                   end
   600                 else
   601                   t
   602               end
   603           end
   604     and term_for_vect seen k R T1 T2 T' js =
   605       make_fun true T1 T2 T'
   606                (map (fn j => term_for_atom seen T1 T1 j k) (index_seq 0 k))
   607                (map (term_for_rep true seen T2 T2 R o single)
   608                     (batch_list (arity_of_rep R) js))
   609     and term_for_rep _ seen T T' (R as Atom (k, j0)) [[j]] =
   610         if j >= j0 andalso j < j0 + k then term_for_atom seen T T' (j - j0) k
   611         else raise REP ("Nitpick_Model.reconstruct_term.term_for_rep", [R])
   612       | term_for_rep _ seen (Type (@{type_name prod}, [T1, T2])) _
   613                      (Struct [R1, R2]) [js] =
   614         let
   615           val arity1 = arity_of_rep R1
   616           val (js1, js2) = chop arity1 js
   617         in
   618           list_comb (HOLogic.pair_const T1 T2,
   619                      map3 (fn T => term_for_rep true seen T T) [T1, T2] [R1, R2]
   620                           [[js1], [js2]])
   621         end
   622       | term_for_rep _ seen (Type (@{type_name fun}, [T1, T2])) T'
   623                      (Vect (k, R')) [js] =
   624         term_for_vect seen k R' T1 T2 T' js
   625       | term_for_rep maybe_opt seen (Type (@{type_name fun}, [T1, T2])) T'
   626                      (Func (R1, Formula Neut)) jss =
   627         let
   628           val jss1 = all_combinations_for_rep R1
   629           val ts1 = map (term_for_rep true seen T1 T1 R1 o single) jss1
   630           val ts2 =
   631             map (fn js => term_for_rep true seen T2 T2 (Atom (2, 0))
   632                                        [[int_from_bool (member (op =) jss js)]])
   633                 jss1
   634         in make_fun maybe_opt T1 T2 T' ts1 ts2 end
   635       | term_for_rep maybe_opt seen (Type (@{type_name fun}, [T1, T2])) T'
   636                      (Func (R1, R2)) jss =
   637         let
   638           val arity1 = arity_of_rep R1
   639           val jss1 = all_combinations_for_rep R1
   640           val ts1 = map (term_for_rep false seen T1 T1 R1 o single) jss1
   641           val grouped_jss2 = AList.group (op =) (map (chop arity1) jss)
   642           val ts2 = map (term_for_rep false seen T2 T2 R2 o the_default []
   643                          o AList.lookup (op =) grouped_jss2) jss1
   644         in make_fun maybe_opt T1 T2 T' ts1 ts2 end
   645       | term_for_rep _ seen T T' (Opt R) jss =
   646         if null jss then Const (unknown, T)
   647         else term_for_rep true seen T T' R jss
   648       | term_for_rep _ _ T _ R jss =
   649         raise ARG ("Nitpick_Model.reconstruct_term.term_for_rep",
   650                    Syntax.string_of_typ ctxt T ^ " " ^ string_for_rep R ^ " " ^
   651                    string_of_int (length jss))
   652   in
   653     postprocess_subterms [] o polish_funs [] o unarize_unbox_etc_term
   654     oooo term_for_rep maybe_opt []
   655   end
   656 
   657 (** Constant postprocessing **)
   658 
   659 fun dest_n_tuple_type 1 T = [T]
   660   | dest_n_tuple_type n (Type (_, [T1, T2])) =
   661     T1 :: dest_n_tuple_type (n - 1) T2
   662   | dest_n_tuple_type _ T =
   663     raise TYPE ("Nitpick_Model.dest_n_tuple_type", [T], [])
   664 
   665 fun const_format thy def_table (x as (s, T)) =
   666   if String.isPrefix unrolled_prefix s then
   667     const_format thy def_table (original_name s, range_type T)
   668   else if String.isPrefix skolem_prefix s then
   669     let
   670       val k = unprefix skolem_prefix s
   671               |> strip_first_name_sep |> fst |> space_explode "@"
   672               |> hd |> Int.fromString |> the
   673     in [k, num_binder_types T - k] end
   674   else if original_name s <> s then
   675     [num_binder_types T]
   676   else case def_of_const thy def_table x of
   677     SOME t' => if fixpoint_kind_of_rhs t' <> NoFp then
   678                  let val k = length (strip_abs_vars t') in
   679                    [k, num_binder_types T - k]
   680                  end
   681                else
   682                  [num_binder_types T]
   683   | NONE => [num_binder_types T]
   684 fun intersect_formats _ [] = []
   685   | intersect_formats [] _ = []
   686   | intersect_formats ks1 ks2 =
   687     let val ((ks1', k1), (ks2', k2)) = pairself split_last (ks1, ks2) in
   688       intersect_formats (ks1' @ (if k1 > k2 then [k1 - k2] else []))
   689                         (ks2' @ (if k2 > k1 then [k2 - k1] else [])) @
   690       [Int.min (k1, k2)]
   691     end
   692 
   693 fun lookup_format thy def_table formats t =
   694   case AList.lookup (fn (SOME x, SOME y) =>
   695                         (term_match thy) (x, y) | _ => false)
   696                     formats (SOME t) of
   697     SOME format => format
   698   | NONE => let val format = the (AList.lookup (op =) formats NONE) in
   699               case t of
   700                 Const x => intersect_formats format
   701                                              (const_format thy def_table x)
   702               | _ => format
   703             end
   704 
   705 fun format_type default_format format T =
   706   let
   707     val T = uniterize_unarize_unbox_etc_type T
   708     val format = format |> filter (curry (op <) 0)
   709   in
   710     if forall (curry (op =) 1) format then
   711       T
   712     else
   713       let
   714         val (binder_Ts, body_T) = strip_type T
   715         val batched =
   716           binder_Ts
   717           |> map (format_type default_format default_format)
   718           |> rev |> chunk_list_unevenly (rev format)
   719           |> map (HOLogic.mk_tupleT o rev)
   720       in List.foldl (op -->) body_T batched end
   721   end
   722 fun format_term_type thy def_table formats t =
   723   format_type (the (AList.lookup (op =) formats NONE))
   724               (lookup_format thy def_table formats t) (fastype_of t)
   725 
   726 fun repair_special_format js m format =
   727   m - 1 downto 0 |> chunk_list_unevenly (rev format)
   728                  |> map (rev o filter_out (member (op =) js))
   729                  |> filter_out null |> map length |> rev
   730 
   731 fun user_friendly_const ({thy, evals, def_table, skolems, special_funs, ...}
   732                          : hol_context) (base_name, step_name) formats =
   733   let
   734     val default_format = the (AList.lookup (op =) formats NONE)
   735     fun do_const (x as (s, T)) =
   736       (if String.isPrefix special_prefix s then
   737          let
   738            val do_term = map_aterms (fn Const x => fst (do_const x) | t' => t')
   739            val (x' as (_, T'), js, ts) =
   740              AList.find (op =) (!special_funs) (s, unarize_unbox_etc_type T)
   741              |> the_single
   742            val max_j = List.last js
   743            val Ts = List.take (binder_types T', max_j + 1)
   744            val missing_js = filter_out (member (op =) js) (0 upto max_j)
   745            val missing_Ts = filter_indices missing_js Ts
   746            fun nth_missing_var n =
   747              ((arg_var_prefix ^ nat_subscript (n + 1), 0), nth missing_Ts n)
   748            val missing_vars = map nth_missing_var (0 upto length missing_js - 1)
   749            val vars = special_bounds ts @ missing_vars
   750            val ts' =
   751              map (fn j =>
   752                      case AList.lookup (op =) (js ~~ ts) j of
   753                        SOME t => do_term t
   754                      | NONE =>
   755                        Var (nth missing_vars
   756                                 (find_index (curry (op =) j) missing_js)))
   757                  (0 upto max_j)
   758            val t = do_const x' |> fst
   759            val format =
   760              case AList.lookup (fn (SOME t1, SOME t2) => term_match thy (t1, t2)
   761                                  | _ => false) formats (SOME t) of
   762                SOME format =>
   763                repair_special_format js (num_binder_types T') format
   764              | NONE =>
   765                const_format thy def_table x'
   766                |> repair_special_format js (num_binder_types T')
   767                |> intersect_formats default_format
   768          in
   769            (list_comb (t, ts') |> fold_rev abs_var vars,
   770             format_type default_format format T)
   771          end
   772        else if String.isPrefix uncurry_prefix s then
   773          let
   774            val (ss, s') = unprefix uncurry_prefix s
   775                           |> strip_first_name_sep |>> space_explode "@"
   776          in
   777            if String.isPrefix step_prefix s' then
   778              do_const (s', T)
   779            else
   780              let
   781                val k = the (Int.fromString (hd ss))
   782                val j = the (Int.fromString (List.last ss))
   783                val (before_Ts, (tuple_T, rest_T)) =
   784                  strip_n_binders j T ||> (strip_n_binders 1 #>> hd)
   785                val T' = before_Ts ---> dest_n_tuple_type k tuple_T ---> rest_T
   786              in do_const (s', T') end
   787          end
   788        else if String.isPrefix unrolled_prefix s then
   789          let val t = Const (original_name s, range_type T) in
   790            (lambda (Free (iter_var_prefix, nat_T)) t,
   791             format_type default_format
   792                         (lookup_format thy def_table formats t) T)
   793          end
   794        else if String.isPrefix base_prefix s then
   795          (Const (base_name, T --> T) $ Const (unprefix base_prefix s, T),
   796           format_type default_format default_format T)
   797        else if String.isPrefix step_prefix s then
   798          (Const (step_name, T --> T) $ Const (unprefix step_prefix s, T),
   799           format_type default_format default_format T)
   800        else if String.isPrefix quot_normal_prefix s then
   801          let val t = Const (nitpick_prefix ^ "quotient normal form", T) in
   802            (t, format_term_type thy def_table formats t)
   803          end
   804        else if String.isPrefix skolem_prefix s then
   805          let
   806            val ss = the (AList.lookup (op =) (!skolems) s)
   807            val (Ts, Ts') = chop (length ss) (binder_types T)
   808            val frees = map Free (ss ~~ Ts)
   809            val s' = original_name s
   810          in
   811            (fold lambda frees (Const (s', Ts' ---> T)),
   812             format_type default_format
   813                         (lookup_format thy def_table formats (Const x)) T)
   814          end
   815        else if String.isPrefix eval_prefix s then
   816          let
   817            val t = nth evals (the (Int.fromString (unprefix eval_prefix s)))
   818          in (t, format_term_type thy def_table formats t) end
   819        else if s = @{const_name undefined_fast_The} then
   820          (Const (nitpick_prefix ^ "The fallback", T),
   821           format_type default_format
   822                       (lookup_format thy def_table formats
   823                            (Const (@{const_name The}, (T --> bool_T) --> T))) T)
   824        else if s = @{const_name undefined_fast_Eps} then
   825          (Const (nitpick_prefix ^ "Eps fallback", T),
   826           format_type default_format
   827                       (lookup_format thy def_table formats
   828                            (Const (@{const_name Eps}, (T --> bool_T) --> T))) T)
   829        else
   830          let val t = Const (original_name s, T) in
   831            (t, format_term_type thy def_table 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_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, fast_descrs, tac_timeout, evals,
   876                       case_names, def_table, nondef_table, user_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},
   880          binarize, 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, fast_descrs = fast_descrs,
   893        tac_timeout = tac_timeout, evals = evals, case_names = case_names,
   894        def_table = def_table, nondef_table = nondef_table,
   895        user_nondefs = user_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_table 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 fin_fun}, _) => [Pretty.str "[finite]"]
   948             | Type (@{type_name fun_box}, _) => [Pretty.str "[boxed]"]
   949             | Type (@{type_name pair_box}, _) => [Pretty.str "[boxed]"]
   950             | _ => []) @
   951            [Pretty.str "=",
   952             Pretty.enum "," "{" "}"
   953                 (map (Syntax.pretty_term ctxt) (all_values card typ) @
   954                  (if fun_from_pair complete false then []
   955                   else [Pretty.str (unrep ())]))]))
   956     fun integer_datatype T =
   957       [{typ = T, card = card_of_type card_assigns T, co = false,
   958         standard = true, self_rec = true, complete = (false, false),
   959         concrete = (true, true), deep = true, constrs = []}]
   960       handle TYPE ("Nitpick_HOL.card_of_type", _, _) => []
   961     val (codatatypes, datatypes) =
   962       datatypes |> filter #deep |> List.partition #co
   963                 ||> append (integer_datatype int_T
   964                             |> is_standard_datatype thy stds nat_T
   965                                ? append (integer_datatype nat_T))
   966     val block_of_datatypes =
   967       if show_datatypes andalso not (null datatypes) then
   968         [Pretty.big_list ("Datatype" ^ plural_s_for_list datatypes ^ ":")
   969                          (map pretty_for_datatype datatypes)]
   970       else
   971         []
   972     val block_of_codatatypes =
   973       if show_datatypes andalso not (null codatatypes) then
   974         [Pretty.big_list ("Codatatype" ^ plural_s_for_list codatatypes ^ ":")
   975                          (map pretty_for_datatype codatatypes)]
   976       else
   977         []
   978     fun block_of_names show title names =
   979       if show andalso not (null names) then
   980         Pretty.str (title ^ plural_s_for_list names ^ ":")
   981         :: map (Pretty.indent indent_size o pretty_for_assign)
   982                (sort_wrt (original_name o nickname_of) names)
   983       else
   984         []
   985     fun free_name_for_term keep_all (x as (s, T)) =
   986       case filter (curry (op =) x
   987                    o pairf nickname_of (uniterize_unarize_unbox_etc_type
   988                                         o type_of)) free_names of
   989         [name] => SOME name
   990       | [] => if keep_all then SOME (FreeName (s, T, Any)) else NONE
   991       | _ => raise TERM ("Nitpick_Model.reconstruct_hol_model.\
   992                          \free_name_for_term", [Const x])
   993     val (skolem_names, nonskolem_nonsel_names) =
   994       List.partition is_skolem_name nonsel_names
   995     val (eval_names, noneval_nonskolem_nonsel_names) =
   996       List.partition (String.isPrefix eval_prefix o nickname_of)
   997                      nonskolem_nonsel_names
   998       ||> filter_out (member (op =) [@{const_name bisim},
   999                                      @{const_name bisim_iterator_max}]
  1000                       o nickname_of)
  1001       ||> append (map_filter (free_name_for_term false) pseudo_frees)
  1002     val real_free_names = map_filter (free_name_for_term true) real_frees
  1003     val chunks = block_of_names true "Free variable" real_free_names @
  1004                  block_of_names true "Skolem constant" skolem_names @
  1005                  block_of_names true "Evaluated term" eval_names @
  1006                  block_of_datatypes @ block_of_codatatypes @
  1007                  block_of_names show_consts "Constant"
  1008                                 noneval_nonskolem_nonsel_names
  1009   in
  1010     (Pretty.chunks (if null chunks then [Pretty.str "Empty assignment"]
  1011                     else chunks),
  1012      bisim_depth >= 0 orelse
  1013      forall (is_codatatype_wellformed codatatypes) codatatypes)
  1014   end
  1015 
  1016 fun term_for_name pool scope atomss sel_names rel_table bounds name =
  1017   let val T = type_of name in
  1018     tuple_list_for_name rel_table bounds name
  1019     |> reconstruct_term (not (is_fully_representable_set name)) false pool
  1020                         (("", ""), ("", "")) scope atomss sel_names rel_table
  1021                         bounds T T (rep_of name)
  1022   end
  1023 
  1024 fun prove_hol_model (scope as {hol_ctxt = {thy, ctxt, debug, ...},
  1025                                card_assigns, ...})
  1026                     auto_timeout free_names sel_names rel_table bounds prop =
  1027   let
  1028     val pool = Unsynchronized.ref []
  1029     val atomss = [(NONE, [])]
  1030     fun free_type_assm (T, k) =
  1031       let
  1032         fun atom j = nth_atom thy atomss pool true T j
  1033         fun equation_for_atom j = HOLogic.eq_const T $ Bound 0 $ atom j
  1034         val eqs = map equation_for_atom (index_seq 0 k)
  1035         val compreh_assm =
  1036           Const (@{const_name All}, (T --> bool_T) --> bool_T)
  1037               $ Abs ("x", T, foldl1 HOLogic.mk_disj eqs)
  1038         val distinct_assm = distinctness_formula T (map atom (index_seq 0 k))
  1039       in s_conj (compreh_assm, distinct_assm) end
  1040     fun free_name_assm name =
  1041       HOLogic.mk_eq (Free (nickname_of name, type_of name),
  1042                      term_for_name pool scope atomss sel_names rel_table bounds
  1043                                    name)
  1044     val freeT_assms = map free_type_assm (filter (is_TFree o fst) card_assigns)
  1045     val model_assms = map free_name_assm free_names
  1046     val assm = foldr1 s_conj (freeT_assms @ model_assms)
  1047     fun try_out negate =
  1048       let
  1049         val concl = (negate ? curry (op $) @{const Not})
  1050                     (Object_Logic.atomize_term thy prop)
  1051         val prop = HOLogic.mk_Trueprop (HOLogic.mk_imp (assm, concl))
  1052                    |> map_types (map_type_tfree
  1053                                      (fn (s, []) => TFree (s, HOLogic.typeS)
  1054                                        | x => TFree x))
  1055        val _ = if debug then
  1056                  priority ((if negate then "Genuineness" else "Spuriousness") ^
  1057                            " goal: " ^ Syntax.string_of_term ctxt prop ^ ".")
  1058                else
  1059                  ()
  1060         val goal = prop |> cterm_of thy |> Goal.init
  1061       in
  1062         (goal |> SINGLE (DETERM_TIMEOUT auto_timeout
  1063                                         (auto_tac (clasimpset_of 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;