src/HOL/Tools/Nitpick/nitpick_model.ML
author blanchet
Thu May 27 17:22:16 2010 +0200 (2010-05-27)
changeset 37170 38ba15040455
parent 36607 e5f7235f39c5
child 37256 0dca1ec52999
permissions -rw-r--r--
Nitpick: show "..." in datatype values (e.g., [{0::nat, ...}]), since these are really equivalence classes
     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 : string
    27   val register_term_postprocessor :
    28     typ -> term_postprocessor -> theory -> theory
    29   val unregister_term_postprocessor : typ -> theory -> theory
    30   val tuple_list_for_name :
    31     nut NameTable.table -> Kodkod.raw_bound list -> nut -> int list list
    32   val dest_plain_fun : term -> bool * (term list * term list)
    33   val reconstruct_hol_model :
    34     params -> scope -> (term option * int list) list -> styp list -> nut list
    35     -> nut list -> nut list -> nut NameTable.table -> Kodkod.raw_bound list
    36     -> Pretty.T * bool
    37   val prove_hol_model :
    38     scope -> Time.time option -> nut list -> nut list -> nut NameTable.table
    39     -> Kodkod.raw_bound list -> term -> bool option
    40 end;
    41 
    42 structure Nitpick_Model : NITPICK_MODEL =
    43 struct
    44 
    45 open Nitpick_Util
    46 open Nitpick_HOL
    47 open Nitpick_Scope
    48 open Nitpick_Peephole
    49 open Nitpick_Rep
    50 open Nitpick_Nut
    51 
    52 structure KK = Kodkod
    53 
    54 type params =
    55   {show_datatypes: bool,
    56    show_consts: bool}
    57 
    58 type term_postprocessor =
    59   Proof.context -> string -> (typ -> term list) -> typ -> term -> term
    60 
    61 structure Data = Theory_Data(
    62   type T = (typ * term_postprocessor) list
    63   val empty = []
    64   val extend = I
    65   fun merge (x, y) = AList.merge (op =) (K true) (x, y))
    66 
    67 val irrelevant = "_"
    68 val unknown = "?"
    69 val unrep = "\<dots>"
    70 val maybe_mixfix = "_\<^sup>?"
    71 val base_mixfix = "_\<^bsub>base\<^esub>"
    72 val step_mixfix = "_\<^bsub>step\<^esub>"
    73 val abs_mixfix = "\<guillemotleft>_\<guillemotright>"
    74 val arg_var_prefix = "x"
    75 val cyclic_co_val_name = "\<omega>"
    76 val cyclic_const_prefix = "\<xi>"
    77 val cyclic_type_name = nitpick_prefix ^ cyclic_const_prefix
    78 val opt_flag = nitpick_prefix ^ "opt"
    79 val non_opt_flag = nitpick_prefix ^ "non_opt"
    80 
    81 type atom_pool = ((string * int) * int list) list
    82 
    83 fun add_wacky_syntax ctxt =
    84   let
    85     val name_of = fst o dest_Const
    86     val thy = ProofContext.theory_of ctxt |> Context.reject_draft
    87     val (maybe_t, thy) =
    88       Sign.declare_const ((@{binding nitpick_maybe}, @{typ "'a => 'a"}),
    89                           Mixfix (maybe_mixfix, [1000], 1000)) thy
    90     val (abs_t, thy) =
    91       Sign.declare_const ((@{binding nitpick_abs}, @{typ "'a => 'b"}),
    92                           Mixfix (abs_mixfix, [40], 40)) thy
    93     val (base_t, thy) =
    94       Sign.declare_const ((@{binding nitpick_base}, @{typ "'a => 'a"}),
    95                           Mixfix (base_mixfix, [1000], 1000)) thy
    96     val (step_t, thy) =
    97       Sign.declare_const ((@{binding nitpick_step}, @{typ "'a => 'a"}),
    98                           Mixfix (step_mixfix, [1000], 1000)) thy
    99   in
   100     (pairself (pairself name_of) ((maybe_t, abs_t), (base_t, step_t)),
   101      ProofContext.transfer_syntax thy ctxt)
   102   end
   103 
   104 (** Term reconstruction **)
   105 
   106 fun nth_atom_suffix pool s j k =
   107   (case AList.lookup (op =) (!pool) (s, k) of
   108      SOME js =>
   109      (case find_index (curry (op =) j) js of
   110         ~1 => (Unsynchronized.change pool (cons ((s, k), j :: js));
   111                length js + 1)
   112       | n => length js - n)
   113    | NONE => (Unsynchronized.change pool (cons ((s, k), [j])); 1))
   114   |> nat_subscript
   115   |> (s <> "" andalso Symbol.is_ascii_digit (List.last (explode s)))
   116      ? prefix "\<^isub>,"
   117 fun nth_atom_name pool prefix (Type (s, _)) j k =
   118     let val s' = shortest_name s in
   119       prefix ^ (if String.isPrefix "\\" s' then s' else substring (s', 0, 1)) ^
   120       nth_atom_suffix pool s j k
   121     end
   122   | nth_atom_name pool prefix (TFree (s, _)) j k =
   123     prefix ^ perhaps (try (unprefix "'")) s ^ nth_atom_suffix pool s j k
   124   | nth_atom_name _ _ T _ _ =
   125     raise TYPE ("Nitpick_Model.nth_atom_name", [T], [])
   126 fun nth_atom pool for_auto T j k =
   127   if for_auto then
   128     Free (nth_atom_name pool (hd (space_explode "." nitpick_prefix)) T j k, T)
   129   else
   130     Const (nth_atom_name pool "" T j k, T)
   131 
   132 fun extract_real_number (Const (@{const_name divide}, _) $ t1 $ t2) =
   133     real (snd (HOLogic.dest_number t1)) / real (snd (HOLogic.dest_number t2))
   134   | extract_real_number t = real (snd (HOLogic.dest_number t))
   135 fun nice_term_ord (Abs (_, _, t1), Abs (_, _, t2)) = nice_term_ord (t1, t2)
   136   | nice_term_ord tp = Real.compare (pairself extract_real_number tp)
   137     handle TERM ("dest_number", _) =>
   138            case tp of
   139              (t11 $ t12, t21 $ t22) =>
   140              (case nice_term_ord (t11, t21) of
   141                 EQUAL => nice_term_ord (t12, t22)
   142               | ord => ord)
   143            | _ => Term_Ord.fast_term_ord tp
   144 
   145 fun register_term_postprocessor T p = Data.map (cons (T, p))
   146 fun unregister_term_postprocessor T = Data.map (AList.delete (op =) T)
   147 
   148 fun tuple_list_for_name rel_table bounds name =
   149   the (AList.lookup (op =) bounds (the_rel rel_table name)) handle NUT _ => [[]]
   150 
   151 fun unarize_unbox_etc_term (Const (@{const_name FinFun}, _) $ t1) =
   152     unarize_unbox_etc_term t1
   153   | unarize_unbox_etc_term (Const (@{const_name FunBox}, _) $ t1) =
   154     unarize_unbox_etc_term t1
   155   | unarize_unbox_etc_term
   156         (Const (@{const_name PairBox},
   157                 Type (@{type_name fun}, [T1, Type (@{type_name fun}, [T2, _])]))
   158          $ t1 $ t2) =
   159     let val Ts = map uniterize_unarize_unbox_etc_type [T1, T2] in
   160       Const (@{const_name Pair}, Ts ---> Type (@{type_name "*"}, Ts))
   161       $ unarize_unbox_etc_term t1 $ unarize_unbox_etc_term t2
   162     end
   163   | unarize_unbox_etc_term (Const (s, T)) =
   164     Const (s, uniterize_unarize_unbox_etc_type T)
   165   | unarize_unbox_etc_term (t1 $ t2) =
   166     unarize_unbox_etc_term t1 $ unarize_unbox_etc_term t2
   167   | unarize_unbox_etc_term (Free (s, T)) =
   168     Free (s, uniterize_unarize_unbox_etc_type T)
   169   | unarize_unbox_etc_term (Var (x, T)) =
   170     Var (x, uniterize_unarize_unbox_etc_type T)
   171   | unarize_unbox_etc_term (Bound j) = Bound j
   172   | unarize_unbox_etc_term (Abs (s, T, t')) =
   173     Abs (s, uniterize_unarize_unbox_etc_type T, unarize_unbox_etc_term t')
   174 
   175 fun factor_out_types (T1 as Type (@{type_name "*"}, [T11, T12]))
   176                      (T2 as Type (@{type_name "*"}, [T21, T22])) =
   177     let val (n1, n2) = pairself num_factors_in_type (T11, T21) in
   178       if n1 = n2 then
   179         let
   180           val ((T11', opt_T12'), (T21', opt_T22')) = factor_out_types T12 T22
   181         in
   182           ((Type (@{type_name "*"}, [T11, T11']), opt_T12'),
   183            (Type (@{type_name "*"}, [T21, T21']), opt_T22'))
   184         end
   185       else if n1 < n2 then
   186         case factor_out_types T1 T21 of
   187           (p1, (T21', NONE)) => (p1, (T21', SOME T22))
   188         | (p1, (T21', SOME T22')) =>
   189           (p1, (T21', SOME (Type (@{type_name "*"}, [T22', T22]))))
   190       else
   191         swap (factor_out_types T2 T1)
   192     end
   193   | factor_out_types (Type (@{type_name "*"}, [T11, T12])) T2 =
   194     ((T11, SOME T12), (T2, NONE))
   195   | factor_out_types T1 (Type (@{type_name "*"}, [T21, T22])) =
   196     ((T1, NONE), (T21, SOME T22))
   197   | factor_out_types T1 T2 = ((T1, NONE), (T2, NONE))
   198 
   199 fun make_plain_fun maybe_opt T1 T2 =
   200   let
   201     fun aux T1 T2 [] =
   202         Const (if maybe_opt then opt_flag else non_opt_flag, T1 --> T2)
   203       | aux T1 T2 ((t1, t2) :: tps) =
   204         Const (@{const_name fun_upd}, (T1 --> T2) --> T1 --> T2 --> T1 --> T2)
   205         $ aux T1 T2 tps $ t1 $ t2
   206   in aux T1 T2 o rev end
   207 fun is_plain_fun (Const (s, _)) = (s = opt_flag orelse s = non_opt_flag)
   208   | is_plain_fun (Const (@{const_name fun_upd}, _) $ t0 $ _ $ _) =
   209     is_plain_fun t0
   210   | is_plain_fun _ = false
   211 val dest_plain_fun =
   212   let
   213     fun aux (Abs (_, _, Const (s, _))) = (s <> irrelevant, ([], []))
   214       | aux (Const (s, _)) = (s <> non_opt_flag, ([], []))
   215       | aux (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =
   216         let val (maybe_opt, (ts1, ts2)) = aux t0 in
   217           (maybe_opt, (t1 :: ts1, t2 :: ts2))
   218         end
   219       | aux t = raise TERM ("Nitpick_Model.dest_plain_fun", [t])
   220   in apsnd (pairself rev) o aux end
   221 
   222 fun break_in_two T T1 T2 t =
   223   let
   224     val ps = HOLogic.flat_tupleT_paths T
   225     val cut = length (HOLogic.strip_tupleT T1)
   226     val (ps1, ps2) = pairself HOLogic.flat_tupleT_paths (T1, T2)
   227     val (ts1, ts2) = t |> HOLogic.strip_ptuple ps |> chop cut
   228   in (HOLogic.mk_ptuple ps1 T1 ts1, HOLogic.mk_ptuple ps2 T2 ts2) end
   229 fun pair_up (Type (@{type_name "*"}, [T1', T2']))
   230             (t1 as Const (@{const_name Pair},
   231                           Type (@{type_name fun},
   232                                 [_, Type (@{type_name fun}, [_, T1])]))
   233              $ t11 $ t12) t2 =
   234     if T1 = T1' then HOLogic.mk_prod (t1, t2)
   235     else HOLogic.mk_prod (t11, pair_up T2' t12 t2)
   236   | pair_up _ t1 t2 = HOLogic.mk_prod (t1, t2)
   237 fun multi_pair_up T1 t1 (ts2, ts3) = map2 (pair o pair_up T1 t1) ts2 ts3
   238 
   239 fun typecast_fun (Type (@{type_name fun}, [T1', T2'])) T1 T2 t =
   240     let
   241       fun do_curry T1 T1a T1b T2 t =
   242         let
   243           val (maybe_opt, tsp) = dest_plain_fun t
   244           val tps =
   245             tsp |>> map (break_in_two T1 T1a T1b)
   246                 |> uncurry (map2 (fn (t1a, t1b) => fn t2 => (t1a, (t1b, t2))))
   247                 |> AList.coalesce (op =)
   248                 |> map (apsnd (make_plain_fun maybe_opt T1b T2))
   249         in make_plain_fun maybe_opt T1a (T1b --> T2) tps end
   250       and do_uncurry T1 T2 t =
   251         let
   252           val (maybe_opt, tsp) = dest_plain_fun t
   253           val tps =
   254             tsp |> op ~~
   255                 |> maps (fn (t1, t2) =>
   256                             multi_pair_up T1 t1 (snd (dest_plain_fun t2)))
   257         in make_plain_fun maybe_opt T1 T2 tps end
   258       and do_arrow T1' T2' _ _ (Const (s, _)) = Const (s, T1' --> T2')
   259         | do_arrow T1' T2' T1 T2
   260                    (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =
   261           Const (@{const_name fun_upd},
   262                  (T1' --> T2') --> T1' --> T2' --> T1' --> T2')
   263           $ do_arrow T1' T2' T1 T2 t0 $ do_term T1' T1 t1 $ do_term T2' T2 t2
   264         | do_arrow _ _ _ _ t =
   265           raise TERM ("Nitpick_Model.typecast_fun.do_arrow", [t])
   266       and do_fun T1' T2' T1 T2 t =
   267         case factor_out_types T1' T1 of
   268           ((_, NONE), (_, NONE)) => t |> do_arrow T1' T2' T1 T2
   269         | ((_, NONE), (T1a, SOME T1b)) =>
   270           t |> do_curry T1 T1a T1b T2 |> do_arrow T1' T2' T1a (T1b --> T2)
   271         | ((T1a', SOME T1b'), (_, NONE)) =>
   272           t |> do_arrow T1a' (T1b' --> T2') T1 T2 |> do_uncurry T1' T2'
   273         | _ => raise TYPE ("Nitpick_Model.typecast_fun.do_fun", [T1, T1'], [])
   274       and do_term (Type (@{type_name fun}, [T1', T2']))
   275                   (Type (@{type_name fun}, [T1, T2])) t =
   276           do_fun T1' T2' T1 T2 t
   277         | do_term (T' as Type (@{type_name "*"}, Ts' as [T1', T2']))
   278                   (Type (@{type_name "*"}, [T1, T2]))
   279                   (Const (@{const_name Pair}, _) $ t1 $ t2) =
   280           Const (@{const_name Pair}, Ts' ---> T')
   281           $ do_term T1' T1 t1 $ do_term T2' T2 t2
   282         | do_term T' T t =
   283           if T = T' then t
   284           else raise TYPE ("Nitpick_Model.typecast_fun.do_term", [T, T'], [])
   285     in if T1' = T1 andalso T2' = T2 then t else do_fun T1' T2' T1 T2 t end
   286   | typecast_fun T' _ _ _ =
   287     raise TYPE ("Nitpick_Model.typecast_fun", [T'], [])
   288 
   289 fun truth_const_sort_key @{const True} = "0"
   290   | truth_const_sort_key @{const False} = "2"
   291   | truth_const_sort_key _ = "1"
   292 
   293 fun mk_tuple (Type (@{type_name "*"}, [T1, T2])) ts =
   294     HOLogic.mk_prod (mk_tuple T1 ts,
   295         mk_tuple T2 (List.drop (ts, length (HOLogic.flatten_tupleT T1))))
   296   | mk_tuple _ (t :: _) = t
   297   | mk_tuple T [] = raise TYPE ("Nitpick_Model.mk_tuple", [T], [])
   298 
   299 fun varified_type_match thy (candid_T, pat_T) =
   300   strict_type_match thy (candid_T, Logic.varifyT_global pat_T)
   301 
   302 fun all_values_of_type pool wacky_names (scope as {card_assigns, ...} : scope)
   303                        sel_names rel_table bounds card T =
   304   let
   305     val card = if card = 0 then card_of_type card_assigns T else card
   306     fun nth_value_of_type n =
   307       let
   308         fun term unfold =
   309           reconstruct_term unfold pool wacky_names scope sel_names rel_table
   310                            bounds T T (Atom (card, 0)) [[n]]
   311       in
   312         case term false of
   313           t as Const (s, _) =>
   314           if String.isPrefix cyclic_const_prefix s then
   315             HOLogic.mk_eq (t, term true)
   316           else
   317             t
   318         | t => t
   319       end
   320   in index_seq 0 card |> map nth_value_of_type |> sort nice_term_ord end
   321 and reconstruct_term unfold pool (wacky_names as ((maybe_name, abs_name), _))
   322         (scope as {hol_ctxt as {ctxt, thy, stds, ...}, binarize, card_assigns,
   323                    bits, datatypes, ofs, ...}) sel_names rel_table bounds =
   324   let
   325     val for_auto = (maybe_name = "")
   326     fun value_of_bits jss =
   327       let
   328         val j0 = offset_of_type ofs @{typ unsigned_bit}
   329         val js = map (Integer.add (~ j0) o the_single) jss
   330       in
   331         fold (fn j => Integer.add (reasonable_power 2 j |> j = bits ? op ~))
   332              js 0
   333       end
   334     val all_values =
   335       all_values_of_type pool wacky_names scope sel_names rel_table bounds 0
   336     fun postprocess_term (Type (@{type_name fun}, _)) = I
   337       | postprocess_term T =
   338         if null (Data.get thy) then
   339           I
   340         else case AList.lookup (varified_type_match thy) (Data.get thy) T of
   341           SOME postproc => postproc ctxt maybe_name all_values T
   342         | NONE => I
   343     fun postprocess_subterms Ts (t1 $ t2) =
   344         let val t = postprocess_subterms Ts t1 $ postprocess_subterms Ts t2 in
   345           postprocess_term (fastype_of1 (Ts, t)) t
   346         end
   347       | postprocess_subterms Ts (Abs (s, T, t')) =
   348         Abs (s, T, postprocess_subterms (T :: Ts) t')
   349       | postprocess_subterms Ts t = postprocess_term (fastype_of1 (Ts, t)) t
   350     fun make_set maybe_opt T1 T2 tps =
   351       let
   352         val empty_const = Const (@{const_abbrev Set.empty}, T1 --> T2)
   353         val insert_const = Const (@{const_name insert},
   354                                   T1 --> (T1 --> T2) --> T1 --> T2)
   355         fun aux [] =
   356             if maybe_opt andalso not (is_complete_type datatypes false T1) then
   357               insert_const $ Const (unrep, T1) $ empty_const
   358             else
   359               empty_const
   360           | aux ((t1, t2) :: zs) =
   361             aux zs
   362             |> t2 <> @{const False}
   363                ? curry (op $)
   364                        (insert_const
   365                         $ (t1 |> t2 <> @{const True}
   366                                  ? curry (op $)
   367                                          (Const (maybe_name, T1 --> T1))))
   368       in
   369         if forall (fn (_, t) => t <> @{const True} andalso t <> @{const False})
   370                   tps then
   371           Const (unknown, T1 --> T2)
   372         else
   373           aux tps
   374       end
   375     fun make_map maybe_opt T1 T2 T2' =
   376       let
   377         val update_const = Const (@{const_name fun_upd},
   378                                   (T1 --> T2) --> T1 --> T2 --> T1 --> T2)
   379         fun aux' [] = Const (@{const_abbrev Map.empty}, T1 --> T2)
   380           | aux' ((t1, t2) :: tps) =
   381             (case t2 of
   382                Const (@{const_name None}, _) => aux' tps
   383              | _ => update_const $ aux' tps $ t1 $ t2)
   384         fun aux tps =
   385           if maybe_opt andalso not (is_complete_type datatypes false T1) then
   386             update_const $ aux' tps $ Const (unrep, T1)
   387             $ (Const (@{const_name Some}, T2' --> T2) $ Const (unknown, T2'))
   388           else
   389             aux' tps
   390       in aux end
   391     fun polish_funs Ts t =
   392       (case fastype_of1 (Ts, t) of
   393          Type (@{type_name fun}, [T1, T2]) =>
   394          if is_plain_fun t then
   395            case T2 of
   396              @{typ bool} =>
   397              let
   398                val (maybe_opt, ts_pair) =
   399                  dest_plain_fun t ||> pairself (map (polish_funs Ts))
   400              in
   401                make_set maybe_opt T1 T2
   402                         (sort_wrt (truth_const_sort_key o snd) (op ~~ ts_pair))
   403              end
   404            | Type (@{type_name option}, [T2']) =>
   405              let
   406                val (maybe_opt, ts_pair) =
   407                  dest_plain_fun t ||> pairself (map (polish_funs Ts))
   408              in make_map maybe_opt T1 T2 T2' (rev (op ~~ ts_pair)) end
   409            | _ => raise SAME ()
   410          else
   411            raise SAME ()
   412        | _ => raise SAME ())
   413       handle SAME () =>
   414              case t of
   415                (t1 as Const (@{const_name fun_upd}, _) $ t11 $ _)
   416                $ (t2 as Const (s, _)) =>
   417                if s = unknown then polish_funs Ts t11
   418                else polish_funs Ts t1 $ polish_funs Ts t2
   419              | t1 $ t2 => polish_funs Ts t1 $ polish_funs Ts t2
   420              | Abs (s, T, t') => Abs (s, T, polish_funs (T :: Ts) t')
   421              | Const (s, Type (@{type_name fun}, [T1, T2])) =>
   422                if s = opt_flag orelse s = non_opt_flag then
   423                  Abs ("x", T1,
   424                       Const (if is_complete_type datatypes false T1 then
   425                                irrelevant
   426                              else
   427                                unknown, T2))
   428                else
   429                  t
   430              | t => t
   431     fun make_fun maybe_opt T1 T2 T' ts1 ts2 =
   432       ts1 ~~ ts2 |> sort (nice_term_ord o pairself fst)
   433                  |> make_plain_fun maybe_opt T1 T2
   434                  |> unarize_unbox_etc_term
   435                  |> typecast_fun (uniterize_unarize_unbox_etc_type T')
   436                                  (uniterize_unarize_unbox_etc_type T1)
   437                                  (uniterize_unarize_unbox_etc_type T2)
   438     fun term_for_atom seen (T as Type (@{type_name fun}, [T1, T2])) T' j _ =
   439         let
   440           val k1 = card_of_type card_assigns T1
   441           val k2 = card_of_type card_assigns T2
   442         in
   443           term_for_rep true seen T T' (Vect (k1, Atom (k2, 0)))
   444                        [nth_combination (replicate k1 (k2, 0)) j]
   445           handle General.Subscript =>
   446                  raise ARG ("Nitpick_Model.reconstruct_term.term_for_atom",
   447                             signed_string_of_int j ^ " for " ^
   448                             string_for_rep (Vect (k1, Atom (k2, 0))))
   449         end
   450       | term_for_atom seen (Type (@{type_name "*"}, [T1, T2])) _ j k =
   451         let
   452           val k1 = card_of_type card_assigns T1
   453           val k2 = k div k1
   454         in
   455           list_comb (HOLogic.pair_const T1 T2,
   456                      map3 (fn T => term_for_atom seen T T) [T1, T2]
   457                           [j div k2, j mod k2] [k1, k2]) (* ### k2 or k1? FIXME *)
   458         end
   459       | term_for_atom seen @{typ prop} _ j k =
   460         HOLogic.mk_Trueprop (term_for_atom seen bool_T bool_T j k)
   461       | term_for_atom _ @{typ bool} _ j _ =
   462         if j = 0 then @{const False} else @{const True}
   463       | term_for_atom _ @{typ unit} _ _ _ = @{const Unity}
   464       | term_for_atom seen T _ j k =
   465         if T = nat_T andalso is_standard_datatype thy stds nat_T then
   466           HOLogic.mk_number nat_T j
   467         else if T = int_T then
   468           HOLogic.mk_number int_T (int_for_atom (k, 0) j)
   469         else if is_fp_iterator_type T then
   470           HOLogic.mk_number nat_T (k - j - 1)
   471         else if T = @{typ bisim_iterator} then
   472           HOLogic.mk_number nat_T j
   473         else case datatype_spec datatypes T of
   474           NONE => nth_atom pool for_auto T j k
   475         | SOME {deep = false, ...} => nth_atom pool for_auto T j k
   476         | SOME {co, standard, constrs, ...} =>
   477           let
   478             fun tuples_for_const (s, T) =
   479               tuple_list_for_name rel_table bounds (ConstName (s, T, Any))
   480             fun cyclic_atom () =
   481               nth_atom pool for_auto (Type (cyclic_type_name, [])) j k
   482             fun cyclic_var () = Var ((nth_atom_name pool "" T j k, 0), T)
   483 
   484             val discr_jsss = map (tuples_for_const o discr_for_constr o #const)
   485                                  constrs
   486             val real_j = j + offset_of_type ofs T
   487             val constr_x as (constr_s, constr_T) =
   488               get_first (fn (jss, {const, ...}) =>
   489                             if member (op =) jss [real_j] then SOME const
   490                             else NONE)
   491                         (discr_jsss ~~ constrs) |> the
   492             val arg_Ts = curried_binder_types constr_T
   493             val sel_xs =
   494               map (binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize
   495                                                           constr_x)
   496                   (index_seq 0 (length arg_Ts))
   497             val sel_Rs =
   498               map (fn x => get_first
   499                                (fn ConstName (s', T', R) =>
   500                                    if (s', T') = x then SOME R else NONE
   501                                  | u => raise NUT ("Nitpick_Model.reconstruct_\
   502                                                    \term.term_for_atom", [u]))
   503                                sel_names |> the) sel_xs
   504             val arg_Rs = map (snd o dest_Func) sel_Rs
   505             val sel_jsss = map tuples_for_const sel_xs
   506             val arg_jsss =
   507               map (map_filter (fn js => if hd js = real_j then SOME (tl js)
   508                                         else NONE)) sel_jsss
   509             val uncur_arg_Ts = binder_types constr_T
   510             val maybe_cyclic = co orelse not standard
   511           in
   512             if maybe_cyclic andalso not (null seen) andalso
   513                member (op =) (seen |> unfold ? (fst o split_last)) (T, j) then
   514               cyclic_var ()
   515             else if constr_s = @{const_name Word} then
   516               HOLogic.mk_number
   517                   (if T = @{typ "unsigned_bit word"} then nat_T else int_T)
   518                   (value_of_bits (the_single arg_jsss))
   519             else
   520               let
   521                 val seen = seen |> maybe_cyclic ? cons (T, j)
   522                 val ts =
   523                   if length arg_Ts = 0 then
   524                     []
   525                   else
   526                     map3 (fn Ts =>
   527                              term_for_rep (constr_s <> @{const_name FinFun})
   528                                           seen Ts Ts) arg_Ts arg_Rs arg_jsss
   529                     |> mk_tuple (HOLogic.mk_tupleT uncur_arg_Ts)
   530                     |> dest_n_tuple (length uncur_arg_Ts)
   531                 val t =
   532                   if constr_s = @{const_name Abs_Frac} then
   533                     case ts of
   534                       [Const (@{const_name Pair}, _) $ t1 $ t2] =>
   535                       frac_from_term_pair (body_type T) t1 t2
   536                     | _ => raise TERM ("Nitpick_Model.reconstruct_term.\
   537                                        \term_for_atom (Abs_Frac)", ts)
   538                   else if not for_auto andalso
   539                           (is_abs_fun thy constr_x orelse
   540                            constr_s = @{const_name Quot}) then
   541                     Const (abs_name, constr_T) $ the_single ts
   542                   else
   543                     list_comb (Const constr_x, ts)
   544               in
   545                 if maybe_cyclic then
   546                   let val var = cyclic_var () in
   547                     if unfold andalso not standard andalso
   548                        length seen = 1 andalso
   549                        exists_subterm (fn Const (s, _) =>
   550                                           String.isPrefix cyclic_const_prefix s
   551                                         | t' => t' = var) t then
   552                       subst_atomic [(var, cyclic_atom ())] t
   553                     else if exists_subterm (curry (op =) var) t then
   554                       if co then
   555                         Const (@{const_name The}, (T --> bool_T) --> T)
   556                         $ Abs (cyclic_co_val_name, T,
   557                                Const (@{const_name "op ="}, T --> T --> bool_T)
   558                                $ Bound 0 $ abstract_over (var, t))
   559                       else
   560                         cyclic_atom ()
   561                     else
   562                       t
   563                   end
   564                 else
   565                   t
   566               end
   567           end
   568     and term_for_vect seen k R T1 T2 T' js =
   569       make_fun true T1 T2 T'
   570                (map (fn j => term_for_atom seen T1 T1 j k) (index_seq 0 k))
   571                (map (term_for_rep true seen T2 T2 R o single)
   572                     (batch_list (arity_of_rep R) js))
   573     and term_for_rep _ seen T T' Unit [[]] = term_for_atom seen T T' 0 1
   574       | term_for_rep _ seen T T' (R as Atom (k, j0)) [[j]] =
   575         if j >= j0 andalso j < j0 + k then term_for_atom seen T T' (j - j0) k
   576         else raise REP ("Nitpick_Model.reconstruct_term.term_for_rep", [R])
   577       | term_for_rep _ seen (Type (@{type_name "*"}, [T1, T2])) _
   578                      (Struct [R1, R2]) [js] =
   579         let
   580           val arity1 = arity_of_rep R1
   581           val (js1, js2) = chop arity1 js
   582         in
   583           list_comb (HOLogic.pair_const T1 T2,
   584                      map3 (fn T => term_for_rep true seen T T) [T1, T2] [R1, R2]
   585                           [[js1], [js2]])
   586         end
   587       | term_for_rep _ seen (Type (@{type_name fun}, [T1, T2])) T'
   588                      (Vect (k, R')) [js] =
   589         term_for_vect seen k R' T1 T2 T' js
   590       | term_for_rep maybe_opt seen (Type (@{type_name fun}, [T1, T2])) T'
   591                      (Func (R1, Formula Neut)) jss =
   592         let
   593           val jss1 = all_combinations_for_rep R1
   594           val ts1 = map (term_for_rep true seen T1 T1 R1 o single) jss1
   595           val ts2 =
   596             map (fn js => term_for_rep true seen T2 T2 (Atom (2, 0))
   597                                        [[int_from_bool (member (op =) jss js)]])
   598                 jss1
   599         in make_fun maybe_opt T1 T2 T' ts1 ts2 end
   600       | term_for_rep maybe_opt seen (Type (@{type_name fun}, [T1, T2])) T'
   601                      (Func (R1, R2)) jss =
   602         let
   603           val arity1 = arity_of_rep R1
   604           val jss1 = all_combinations_for_rep R1
   605           val ts1 = map (term_for_rep false seen T1 T1 R1 o single) jss1
   606           val grouped_jss2 = AList.group (op =) (map (chop arity1) jss)
   607           val ts2 = map (term_for_rep false seen T2 T2 R2 o the_default []
   608                          o AList.lookup (op =) grouped_jss2) jss1
   609         in make_fun maybe_opt T1 T2 T' ts1 ts2 end
   610       | term_for_rep _ seen T T' (Opt R) jss =
   611         if null jss then Const (unknown, T)
   612         else term_for_rep true seen T T' R jss
   613       | term_for_rep _ _ T _ R jss =
   614         raise ARG ("Nitpick_Model.reconstruct_term.term_for_rep",
   615                    Refute.string_of_typ T ^ " " ^ string_for_rep R ^ " " ^
   616                    string_of_int (length jss))
   617   in
   618     postprocess_subterms [] o polish_funs [] o unarize_unbox_etc_term
   619     oooo term_for_rep true []
   620   end
   621 
   622 (** Constant postprocessing **)
   623 
   624 fun dest_n_tuple_type 1 T = [T]
   625   | dest_n_tuple_type n (Type (_, [T1, T2])) =
   626     T1 :: dest_n_tuple_type (n - 1) T2
   627   | dest_n_tuple_type _ T =
   628     raise TYPE ("Nitpick_Model.dest_n_tuple_type", [T], [])
   629 
   630 fun const_format thy def_table (x as (s, T)) =
   631   if String.isPrefix unrolled_prefix s then
   632     const_format thy def_table (original_name s, range_type T)
   633   else if String.isPrefix skolem_prefix s then
   634     let
   635       val k = unprefix skolem_prefix s
   636               |> strip_first_name_sep |> fst |> space_explode "@"
   637               |> hd |> Int.fromString |> the
   638     in [k, num_binder_types T - k] end
   639   else if original_name s <> s then
   640     [num_binder_types T]
   641   else case def_of_const thy def_table x of
   642     SOME t' => if fixpoint_kind_of_rhs t' <> NoFp then
   643                  let val k = length (strip_abs_vars t') in
   644                    [k, num_binder_types T - k]
   645                  end
   646                else
   647                  [num_binder_types T]
   648   | NONE => [num_binder_types T]
   649 fun intersect_formats _ [] = []
   650   | intersect_formats [] _ = []
   651   | intersect_formats ks1 ks2 =
   652     let val ((ks1', k1), (ks2', k2)) = pairself split_last (ks1, ks2) in
   653       intersect_formats (ks1' @ (if k1 > k2 then [k1 - k2] else []))
   654                         (ks2' @ (if k2 > k1 then [k2 - k1] else [])) @
   655       [Int.min (k1, k2)]
   656     end
   657 
   658 fun lookup_format thy def_table formats t =
   659   case AList.lookup (fn (SOME x, SOME y) =>
   660                         (term_match thy) (x, y) | _ => false)
   661                     formats (SOME t) of
   662     SOME format => format
   663   | NONE => let val format = the (AList.lookup (op =) formats NONE) in
   664               case t of
   665                 Const x => intersect_formats format
   666                                              (const_format thy def_table x)
   667               | _ => format
   668             end
   669 
   670 fun format_type default_format format T =
   671   let
   672     val T = uniterize_unarize_unbox_etc_type T
   673     val format = format |> filter (curry (op <) 0)
   674   in
   675     if forall (curry (op =) 1) format then
   676       T
   677     else
   678       let
   679         val (binder_Ts, body_T) = strip_type T
   680         val batched =
   681           binder_Ts
   682           |> map (format_type default_format default_format)
   683           |> rev |> chunk_list_unevenly (rev format)
   684           |> map (HOLogic.mk_tupleT o rev)
   685       in List.foldl (op -->) body_T batched end
   686   end
   687 fun format_term_type thy def_table formats t =
   688   format_type (the (AList.lookup (op =) formats NONE))
   689               (lookup_format thy def_table formats t) (fastype_of t)
   690 
   691 fun repair_special_format js m format =
   692   m - 1 downto 0 |> chunk_list_unevenly (rev format)
   693                  |> map (rev o filter_out (member (op =) js))
   694                  |> filter_out null |> map length |> rev
   695 
   696 fun user_friendly_const ({thy, evals, def_table, skolems, special_funs, ...}
   697                          : hol_context) (base_name, step_name) formats =
   698   let
   699     val default_format = the (AList.lookup (op =) formats NONE)
   700     fun do_const (x as (s, T)) =
   701       (if String.isPrefix special_prefix s then
   702          let
   703            val do_term = map_aterms (fn Const x => fst (do_const x) | t' => t')
   704            val (x' as (_, T'), js, ts) =
   705              AList.find (op =) (!special_funs) (s, unarize_unbox_etc_type T)
   706              |> the_single
   707            val max_j = List.last js
   708            val Ts = List.take (binder_types T', max_j + 1)
   709            val missing_js = filter_out (member (op =) js) (0 upto max_j)
   710            val missing_Ts = filter_indices missing_js Ts
   711            fun nth_missing_var n =
   712              ((arg_var_prefix ^ nat_subscript (n + 1), 0), nth missing_Ts n)
   713            val missing_vars = map nth_missing_var (0 upto length missing_js - 1)
   714            val vars = special_bounds ts @ missing_vars
   715            val ts' =
   716              map (fn j =>
   717                      case AList.lookup (op =) (js ~~ ts) j of
   718                        SOME t => do_term t
   719                      | NONE =>
   720                        Var (nth missing_vars
   721                                 (find_index (curry (op =) j) missing_js)))
   722                  (0 upto max_j)
   723            val t = do_const x' |> fst
   724            val format =
   725              case AList.lookup (fn (SOME t1, SOME t2) => term_match thy (t1, t2)
   726                                  | _ => false) formats (SOME t) of
   727                SOME format =>
   728                repair_special_format js (num_binder_types T') format
   729              | NONE =>
   730                const_format thy def_table x'
   731                |> repair_special_format js (num_binder_types T')
   732                |> intersect_formats default_format
   733          in
   734            (list_comb (t, ts') |> fold_rev abs_var vars,
   735             format_type default_format format T)
   736          end
   737        else if String.isPrefix uncurry_prefix s then
   738          let
   739            val (ss, s') = unprefix uncurry_prefix s
   740                           |> strip_first_name_sep |>> space_explode "@"
   741          in
   742            if String.isPrefix step_prefix s' then
   743              do_const (s', T)
   744            else
   745              let
   746                val k = the (Int.fromString (hd ss))
   747                val j = the (Int.fromString (List.last ss))
   748                val (before_Ts, (tuple_T, rest_T)) =
   749                  strip_n_binders j T ||> (strip_n_binders 1 #>> hd)
   750                val T' = before_Ts ---> dest_n_tuple_type k tuple_T ---> rest_T
   751              in do_const (s', T') end
   752          end
   753        else if String.isPrefix unrolled_prefix s then
   754          let val t = Const (original_name s, range_type T) in
   755            (lambda (Free (iter_var_prefix, nat_T)) t,
   756             format_type default_format
   757                         (lookup_format thy def_table formats t) T)
   758          end
   759        else if String.isPrefix base_prefix s then
   760          (Const (base_name, T --> T) $ Const (unprefix base_prefix s, T),
   761           format_type default_format default_format T)
   762        else if String.isPrefix step_prefix s then
   763          (Const (step_name, T --> T) $ Const (unprefix step_prefix s, T),
   764           format_type default_format default_format T)
   765        else if String.isPrefix quot_normal_prefix s then
   766          let val t = Const (nitpick_prefix ^ "normalize quotient type", T) in
   767            (t, format_term_type thy def_table formats t)
   768          end
   769        else if String.isPrefix skolem_prefix s then
   770          let
   771            val ss = the (AList.lookup (op =) (!skolems) s)
   772            val (Ts, Ts') = chop (length ss) (binder_types T)
   773            val frees = map Free (ss ~~ Ts)
   774            val s' = original_name s
   775          in
   776            (fold lambda frees (Const (s', Ts' ---> T)),
   777             format_type default_format
   778                         (lookup_format thy def_table formats (Const x)) T)
   779          end
   780        else if String.isPrefix eval_prefix s then
   781          let
   782            val t = nth evals (the (Int.fromString (unprefix eval_prefix s)))
   783          in (t, format_term_type thy def_table formats t) end
   784        else if s = @{const_name undefined_fast_The} then
   785          (Const (nitpick_prefix ^ "The fallback", T),
   786           format_type default_format
   787                       (lookup_format thy def_table formats
   788                            (Const (@{const_name The}, (T --> bool_T) --> T))) T)
   789        else if s = @{const_name undefined_fast_Eps} then
   790          (Const (nitpick_prefix ^ "Eps fallback", T),
   791           format_type default_format
   792                       (lookup_format thy def_table formats
   793                            (Const (@{const_name Eps}, (T --> bool_T) --> T))) T)
   794        else
   795          let val t = Const (original_name s, T) in
   796            (t, format_term_type thy def_table formats t)
   797          end)
   798       |>> map_types uniterize_unarize_unbox_etc_type
   799       |>> shorten_names_in_term |>> Term.map_abs_vars shortest_name
   800   in do_const end
   801 
   802 fun assign_operator_for_const (s, T) =
   803   if String.isPrefix ubfp_prefix s then
   804     if is_fun_type T then "\<subseteq>" else "\<le>"
   805   else if String.isPrefix lbfp_prefix s then
   806     if is_fun_type T then "\<supseteq>" else "\<ge>"
   807   else if original_name s <> s then
   808     assign_operator_for_const (strip_first_name_sep s |> snd, T)
   809   else
   810     "="
   811 
   812 (** Model reconstruction **)
   813 
   814 fun term_for_name pool scope sel_names rel_table bounds name =
   815   let val T = type_of name in
   816     tuple_list_for_name rel_table bounds name
   817     |> reconstruct_term false pool (("", ""), ("", "")) scope sel_names
   818                         rel_table bounds T T (rep_of name)
   819   end
   820 
   821 fun unfold_outer_the_binders (t as Const (@{const_name The}, _)
   822                                    $ Abs (s, T, Const (@{const_name "op ="}, _)
   823                                                 $ Bound 0 $ t')) =
   824     betapply (Abs (s, T, t'), t) |> unfold_outer_the_binders
   825   | unfold_outer_the_binders t = t
   826 fun bisimilar_values _ 0 _ = true
   827   | bisimilar_values coTs max_depth (t1, t2) =
   828     let val T = fastype_of t1 in
   829       if exists_subtype (member (op =) coTs) T then
   830         let
   831           val ((head1, args1), (head2, args2)) =
   832             pairself (strip_comb o unfold_outer_the_binders) (t1, t2)
   833           val max_depth = max_depth - (if member (op =) coTs T then 1 else 0)
   834         in
   835           head1 = head2 andalso
   836           forall (bisimilar_values coTs max_depth) (args1 ~~ args2)
   837         end
   838       else
   839         t1 = t2
   840     end
   841 
   842 fun reconstruct_hol_model {show_datatypes, show_consts}
   843         ({hol_ctxt = {thy, ctxt, max_bisim_depth, boxes, stds, wfs, user_axioms,
   844                       debug, binary_ints, destroy_constrs, specialize,
   845                       star_linear_preds, fast_descrs, tac_timeout, evals,
   846                       case_names, def_table, nondef_table, user_nondefs,
   847                       simp_table, psimp_table, choice_spec_table, intro_table,
   848                       ground_thm_table, ersatz_table, skolems, special_funs,
   849                       unrolled_preds, wf_cache, constr_cache},
   850          binarize, card_assigns, bits, bisim_depth, datatypes, ofs} : scope)
   851         formats all_frees free_names sel_names nonsel_names rel_table bounds =
   852   let
   853     val pool = Unsynchronized.ref []
   854     val (wacky_names as (_, base_step_names), ctxt) =
   855       add_wacky_syntax ctxt
   856     val hol_ctxt =
   857       {thy = thy, ctxt = ctxt, max_bisim_depth = max_bisim_depth, boxes = boxes,
   858        stds = stds, wfs = wfs, user_axioms = user_axioms, debug = debug,
   859        binary_ints = binary_ints, destroy_constrs = destroy_constrs,
   860        specialize = specialize, star_linear_preds = star_linear_preds,
   861        fast_descrs = fast_descrs, tac_timeout = tac_timeout, evals = evals,
   862        case_names = case_names, def_table = def_table,
   863        nondef_table = nondef_table, user_nondefs = user_nondefs,
   864        simp_table = simp_table, psimp_table = psimp_table,
   865        choice_spec_table = choice_spec_table, intro_table = intro_table,
   866        ground_thm_table = ground_thm_table, ersatz_table = ersatz_table,
   867        skolems = skolems, special_funs = special_funs,
   868        unrolled_preds = unrolled_preds, wf_cache = wf_cache,
   869        constr_cache = constr_cache}
   870     val scope =
   871       {hol_ctxt = hol_ctxt, binarize = binarize, card_assigns = card_assigns,
   872        bits = bits, bisim_depth = bisim_depth, datatypes = datatypes, ofs = ofs}
   873     fun term_for_rep unfold =
   874       reconstruct_term unfold pool wacky_names scope sel_names rel_table bounds
   875     fun nth_value_of_type card T n =
   876       let
   877         fun aux unfold = term_for_rep unfold T T (Atom (card, 0)) [[n]]
   878       in
   879         case aux false of
   880           t as Const (s, _) =>
   881           if String.isPrefix cyclic_const_prefix s then
   882             HOLogic.mk_eq (t, aux true)
   883           else
   884             t
   885         | t => t
   886       end
   887     val all_values =
   888       all_values_of_type pool wacky_names scope sel_names rel_table bounds
   889     fun is_codatatype_wellformed (cos : dtype_spec list)
   890                                  ({typ, card, ...} : dtype_spec) =
   891       let
   892         val ts = all_values card typ
   893         val max_depth = Integer.sum (map #card cos)
   894       in
   895         forall (not o bisimilar_values (map #typ cos) max_depth)
   896                (all_distinct_unordered_pairs_of ts)
   897       end
   898     fun pretty_for_assign name =
   899       let
   900         val (oper, (t1, T'), T) =
   901           case name of
   902             FreeName (s, T, _) =>
   903             let val t = Free (s, uniterize_unarize_unbox_etc_type T) in
   904               ("=", (t, format_term_type thy def_table formats t), T)
   905             end
   906           | ConstName (s, T, _) =>
   907             (assign_operator_for_const (s, T),
   908              user_friendly_const hol_ctxt base_step_names formats (s, T), T)
   909           | _ => raise NUT ("Nitpick_Model.reconstruct_hol_model.\
   910                             \pretty_for_assign", [name])
   911         val t2 = if rep_of name = Any then
   912                    Const (@{const_name undefined}, T')
   913                  else
   914                    tuple_list_for_name rel_table bounds name
   915                    |> term_for_rep false T T' (rep_of name)
   916       in
   917         Pretty.block (Pretty.breaks
   918             [setmp_show_all_types (Syntax.pretty_term ctxt) t1,
   919              Pretty.str oper, Syntax.pretty_term ctxt t2])
   920       end
   921     fun pretty_for_datatype ({typ, card, complete, ...} : dtype_spec) =
   922       Pretty.block (Pretty.breaks
   923           (Syntax.pretty_typ ctxt (uniterize_unarize_unbox_etc_type typ) ::
   924            (case typ of
   925               Type (@{type_name fin_fun}, _) => [Pretty.str "[finite]"]
   926             | Type (@{type_name fun_box}, _) => [Pretty.str "[boxed]"]
   927             | Type (@{type_name pair_box}, _) => [Pretty.str "[boxed]"]
   928             | _ => []) @
   929            [Pretty.str "=",
   930             Pretty.enum "," "{" "}"
   931                 (map (Syntax.pretty_term ctxt) (all_values card typ) @
   932                  (if fun_from_pair complete false then []
   933                   else [Pretty.str unrep]))]))
   934     fun integer_datatype T =
   935       [{typ = T, card = card_of_type card_assigns T, co = false,
   936         standard = true, complete = (false, false), concrete = (true, true),
   937         deep = true, constrs = []}]
   938       handle TYPE ("Nitpick_HOL.card_of_type", _, _) => []
   939     val (codatatypes, datatypes) =
   940       datatypes |> filter #deep |> List.partition #co
   941                 ||> append (integer_datatype int_T
   942                             |> is_standard_datatype thy stds nat_T
   943                                ? append (integer_datatype nat_T))
   944     val block_of_datatypes =
   945       if show_datatypes andalso not (null datatypes) then
   946         [Pretty.big_list ("Datatype" ^ plural_s_for_list datatypes ^ ":")
   947                          (map pretty_for_datatype datatypes)]
   948       else
   949         []
   950     val block_of_codatatypes =
   951       if show_datatypes andalso not (null codatatypes) then
   952         [Pretty.big_list ("Codatatype" ^ plural_s_for_list codatatypes ^ ":")
   953                          (map pretty_for_datatype codatatypes)]
   954       else
   955         []
   956     fun block_of_names show title names =
   957       if show andalso not (null names) then
   958         Pretty.str (title ^ plural_s_for_list names ^ ":")
   959         :: map (Pretty.indent indent_size o pretty_for_assign)
   960                (sort_wrt (original_name o nickname_of) names)
   961       else
   962         []
   963     val (skolem_names, nonskolem_nonsel_names) =
   964       List.partition is_skolem_name nonsel_names
   965     val (eval_names, noneval_nonskolem_nonsel_names) =
   966       List.partition (String.isPrefix eval_prefix o nickname_of)
   967                      nonskolem_nonsel_names
   968       ||> filter_out (member (op =) [@{const_name bisim},
   969                                      @{const_name bisim_iterator_max}]
   970                       o nickname_of)
   971     val free_names =
   972       map (fn x as (s, T) =>
   973               case filter (curry (op =) x
   974                        o pairf nickname_of
   975                                (uniterize_unarize_unbox_etc_type o type_of))
   976                        free_names of
   977                 [name] => name
   978               | [] => FreeName (s, T, Any)
   979               | _ => raise TERM ("Nitpick_Model.reconstruct_hol_model",
   980                                  [Const x])) all_frees
   981     val chunks = block_of_names true "Free variable" free_names @
   982                  block_of_names true "Skolem constant" skolem_names @
   983                  block_of_names true "Evaluated term" eval_names @
   984                  block_of_datatypes @ block_of_codatatypes @
   985                  block_of_names show_consts "Constant"
   986                                 noneval_nonskolem_nonsel_names
   987   in
   988     (Pretty.chunks (if null chunks then [Pretty.str "Empty assignment"]
   989                     else chunks),
   990      bisim_depth >= 0 orelse
   991      forall (is_codatatype_wellformed codatatypes) codatatypes)
   992   end
   993 
   994 fun prove_hol_model (scope as {hol_ctxt = {thy, ctxt, debug, ...},
   995                                card_assigns, ...})
   996                     auto_timeout free_names sel_names rel_table bounds prop =
   997   let
   998     val pool = Unsynchronized.ref []
   999     fun free_type_assm (T, k) =
  1000       let
  1001         fun atom j = nth_atom pool true T j k
  1002         fun equation_for_atom j = HOLogic.eq_const T $ Bound 0 $ atom j
  1003         val eqs = map equation_for_atom (index_seq 0 k)
  1004         val compreh_assm =
  1005           Const (@{const_name All}, (T --> bool_T) --> bool_T)
  1006               $ Abs ("x", T, foldl1 HOLogic.mk_disj eqs)
  1007         val distinct_assm = distinctness_formula T (map atom (index_seq 0 k))
  1008       in s_conj (compreh_assm, distinct_assm) end
  1009     fun free_name_assm name =
  1010       HOLogic.mk_eq (Free (nickname_of name, type_of name),
  1011                      term_for_name pool scope sel_names rel_table bounds name)
  1012     val freeT_assms = map free_type_assm (filter (is_TFree o fst) card_assigns)
  1013     val model_assms = map free_name_assm free_names
  1014     val assm = foldr1 s_conj (freeT_assms @ model_assms)
  1015     fun try_out negate =
  1016       let
  1017         val concl = (negate ? curry (op $) @{const Not})
  1018                     (Object_Logic.atomize_term thy prop)
  1019         val prop = HOLogic.mk_Trueprop (HOLogic.mk_imp (assm, concl))
  1020                    |> map_types (map_type_tfree
  1021                                      (fn (s, []) => TFree (s, HOLogic.typeS)
  1022                                        | x => TFree x))
  1023        val _ = if debug then
  1024                  priority ((if negate then "Genuineness" else "Spuriousness") ^
  1025                            " goal: " ^ Syntax.string_of_term ctxt prop ^ ".")
  1026                else
  1027                  ()
  1028         val goal = prop |> cterm_of thy |> Goal.init
  1029       in
  1030         (goal |> SINGLE (DETERM_TIMEOUT auto_timeout
  1031                                         (auto_tac (clasimpset_of ctxt)))
  1032               |> the |> Goal.finish ctxt; true)
  1033         handle THM _ => false
  1034              | TimeLimit.TimeOut => false
  1035       end
  1036   in
  1037     if try_out false then SOME true
  1038     else if try_out true then SOME false
  1039     else NONE
  1040   end
  1041 
  1042 end;