src/HOL/Tools/Nitpick/nitpick_model.ML
author blanchet
Thu Feb 04 16:03:15 2010 +0100 (2010-02-04)
changeset 35070 96136eb6218f
parent 34998 5e492a862b34
child 35075 888802be2019
permissions -rw-r--r--
split "nitpick_hol.ML" into two files to make it more manageable;
more refactoring to come
     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_skolems: bool,
    17     show_datatypes: bool,
    18     show_consts: bool}
    19 
    20   structure NameTable : TABLE
    21 
    22   val tuple_list_for_name :
    23     nut NameTable.table -> Kodkod.raw_bound list -> nut -> int list list
    24   val reconstruct_hol_model :
    25     params -> scope -> (term option * int list) list -> styp list -> nut list
    26     -> nut list -> nut list -> nut NameTable.table -> Kodkod.raw_bound list
    27     -> Pretty.T * bool
    28   val prove_hol_model :
    29     scope -> Time.time option -> nut list -> nut list -> nut NameTable.table
    30     -> Kodkod.raw_bound list -> term -> bool option
    31 end;
    32 
    33 structure Nitpick_Model : NITPICK_MODEL =
    34 struct
    35 
    36 open Nitpick_Util
    37 open Nitpick_HOL
    38 open Nitpick_Scope
    39 open Nitpick_Peephole
    40 open Nitpick_Rep
    41 open Nitpick_Nut
    42 
    43 structure KK = Kodkod
    44 
    45 type params = {
    46   show_skolems: bool,
    47   show_datatypes: bool,
    48   show_consts: bool}
    49 
    50 val unknown = "?"
    51 val unrep = "\<dots>"
    52 val maybe_mixfix = "_\<^sup>?"
    53 val base_mixfix = "_\<^bsub>base\<^esub>"
    54 val step_mixfix = "_\<^bsub>step\<^esub>"
    55 val abs_mixfix = "\<guillemotleft>_\<guillemotright>"
    56 val opt_flag = nitpick_prefix ^ "opt"
    57 val non_opt_flag = nitpick_prefix ^ "non_opt"
    58 
    59 (* string -> int -> string *)
    60 fun atom_suffix s j =
    61   nat_subscript (j + 1)
    62   |> (s <> "" andalso Symbol.is_ascii_digit (List.last (explode s)))
    63      ? prefix "\<^isub>,"
    64 (* string -> typ -> int -> string *)
    65 fun atom_name prefix (T as Type (s, _)) j =
    66     let val s' = shortest_name s in
    67       prefix ^ (if String.isPrefix "\\" s' then s' else substring (s', 0, 1)) ^
    68       atom_suffix s j
    69     end
    70   | atom_name prefix (T as TFree (s, _)) j =
    71     prefix ^ perhaps (try (unprefix "'")) s ^ atom_suffix s j
    72   | atom_name _ T _ = raise TYPE ("Nitpick_Model.atom_name", [T], [])
    73 (* bool -> typ -> int -> term *)
    74 fun atom for_auto T j =
    75   if for_auto then
    76     Free (atom_name (hd (space_explode "." nitpick_prefix)) T j, T)
    77   else
    78     Const (atom_name "" T j, T)
    79 
    80 (* term -> real *)
    81 fun extract_real_number (Const (@{const_name Algebras.divide}, _) $ t1 $ t2) =
    82     real (snd (HOLogic.dest_number t1)) / real (snd (HOLogic.dest_number t2))
    83   | extract_real_number t = real (snd (HOLogic.dest_number t))
    84 (* term * term -> order *)
    85 fun nice_term_ord (Abs (_, _, t1), Abs (_, _, t2)) = nice_term_ord (t1, t2)
    86   | nice_term_ord tp = Real.compare (pairself extract_real_number tp)
    87     handle TERM ("dest_number", _) =>
    88            case tp of
    89              (t11 $ t12, t21 $ t22) =>
    90              (case nice_term_ord (t11, t21) of
    91                 EQUAL => nice_term_ord (t12, t22)
    92               | ord => ord)
    93            | _ => TermOrd.fast_term_ord tp
    94 
    95 (* nut NameTable.table -> KK.raw_bound list -> nut -> int list list *)
    96 fun tuple_list_for_name rel_table bounds name =
    97   the (AList.lookup (op =) bounds (the_rel rel_table name)) handle NUT _ => [[]]
    98 
    99 (* term -> term *)
   100 fun unbit_and_unbox_term (Const (@{const_name FunBox}, _) $ t1) =
   101     unbit_and_unbox_term t1
   102   | unbit_and_unbox_term (Const (@{const_name PairBox},
   103                           Type ("fun", [T1, Type ("fun", [T2, T3])]))
   104                           $ t1 $ t2) =
   105     let val Ts = map unbit_and_unbox_type [T1, T2] in
   106       Const (@{const_name Pair}, Ts ---> Type ("*", Ts))
   107       $ unbit_and_unbox_term t1 $ unbit_and_unbox_term t2
   108     end
   109   | unbit_and_unbox_term (Const (s, T)) = Const (s, unbit_and_unbox_type T)
   110   | unbit_and_unbox_term (t1 $ t2) =
   111     unbit_and_unbox_term t1 $ unbit_and_unbox_term t2
   112   | unbit_and_unbox_term (Free (s, T)) = Free (s, unbit_and_unbox_type T)
   113   | unbit_and_unbox_term (Var (x, T)) = Var (x, unbit_and_unbox_type T)
   114   | unbit_and_unbox_term (Bound j) = Bound j
   115   | unbit_and_unbox_term (Abs (s, T, t')) =
   116     Abs (s, unbit_and_unbox_type T, unbit_and_unbox_term t')
   117 
   118 (* typ -> typ -> (typ * typ) * (typ * typ) *)
   119 fun factor_out_types (T1 as Type ("*", [T11, T12]))
   120                      (T2 as Type ("*", [T21, T22])) =
   121     let val (n1, n2) = pairself num_factors_in_type (T11, T21) in
   122       if n1 = n2 then
   123         let
   124           val ((T11', opt_T12'), (T21', opt_T22')) = factor_out_types T12 T22
   125         in
   126           ((Type ("*", [T11, T11']), opt_T12'),
   127            (Type ("*", [T21, T21']), opt_T22'))
   128         end
   129       else if n1 < n2 then
   130         case factor_out_types T1 T21 of
   131           (p1, (T21', NONE)) => (p1, (T21', SOME T22))
   132         | (p1, (T21', SOME T22')) =>
   133           (p1, (T21', SOME (Type ("*", [T22', T22]))))
   134       else
   135         swap (factor_out_types T2 T1)
   136     end
   137   | factor_out_types (Type ("*", [T11, T12])) T2 = ((T11, SOME T12), (T2, NONE))
   138   | factor_out_types T1 (Type ("*", [T21, T22])) = ((T1, NONE), (T21, SOME T22))
   139   | factor_out_types T1 T2 = ((T1, NONE), (T2, NONE))
   140 
   141 (* bool -> typ -> typ -> (term * term) list -> term *)
   142 fun make_plain_fun maybe_opt T1 T2 =
   143   let
   144     (* typ -> typ -> (term * term) list -> term *)
   145     fun aux T1 T2 [] =
   146         Const (if maybe_opt then opt_flag else non_opt_flag, T1 --> T2)
   147       | aux T1 T2 ((t1, t2) :: ps) =
   148         Const (@{const_name fun_upd}, (T1 --> T2) --> T1 --> T2 --> T1 --> T2)
   149         $ aux T1 T2 ps $ t1 $ t2
   150   in aux T1 T2 o rev end
   151 (* term -> bool *)
   152 fun is_plain_fun (Const (s, _)) = (s = opt_flag orelse s = non_opt_flag)
   153   | is_plain_fun (Const (@{const_name fun_upd}, _) $ t0 $ _ $ _) =
   154     is_plain_fun t0
   155   | is_plain_fun _ = false
   156 (* term -> bool * (term list * term list) *)
   157 val dest_plain_fun =
   158   let
   159     (* term -> bool * (term list * term list) *)
   160     fun aux (Const (s, _)) = (s <> non_opt_flag, ([], []))
   161       | aux (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =
   162         let val (s, (ts1, ts2)) = aux t0 in (s, (t1 :: ts1, t2 :: ts2)) end
   163       | aux t = raise TERM ("Nitpick_Model.dest_plain_fun", [t])
   164   in apsnd (pairself rev) o aux end
   165 
   166 (* typ -> typ -> typ -> term -> term * term *)
   167 fun break_in_two T T1 T2 t =
   168   let
   169     val ps = HOLogic.flat_tupleT_paths T
   170     val cut = length (HOLogic.strip_tupleT T1)
   171     val (ps1, ps2) = pairself HOLogic.flat_tupleT_paths (T1, T2)
   172     val (ts1, ts2) = t |> HOLogic.strip_ptuple ps |> chop cut
   173   in (HOLogic.mk_ptuple ps1 T1 ts1, HOLogic.mk_ptuple ps2 T2 ts2) end
   174 (* typ -> term -> term -> term *)
   175 fun pair_up (Type ("*", [T1', T2']))
   176             (t1 as Const (@{const_name Pair},
   177                           Type ("fun", [_, Type ("fun", [_, T1])])) $ t11 $ t12)
   178             t2 =
   179     if T1 = T1' then HOLogic.mk_prod (t1, t2)
   180     else HOLogic.mk_prod (t11, pair_up T2' t12 t2)
   181   | pair_up _ t1 t2 = HOLogic.mk_prod (t1, t2)
   182 (* typ -> term -> term list * term list -> (term * term) list*)
   183 fun multi_pair_up T1 t1 (ts2, ts3) = map2 (pair o pair_up T1 t1) ts2 ts3
   184 
   185 (* typ -> typ -> typ -> term -> term *)
   186 fun typecast_fun (Type ("fun", [T1', T2'])) T1 T2 t =
   187     let
   188       (* typ -> typ -> typ -> typ -> term -> term *)
   189       fun do_curry T1 T1a T1b T2 t =
   190         let
   191           val (maybe_opt, ps) = dest_plain_fun t
   192           val ps =
   193             ps |>> map (break_in_two T1 T1a T1b)
   194                |> uncurry (map2 (fn (t1a, t1b) => fn t2 => (t1a, (t1b, t2))))
   195                |> AList.coalesce (op =)
   196                |> map (apsnd (make_plain_fun maybe_opt T1b T2))
   197         in make_plain_fun maybe_opt T1a (T1b --> T2) ps end
   198       (* typ -> typ -> term -> term *)
   199       and do_uncurry T1 T2 t =
   200         let
   201           val (maybe_opt, tsp) = dest_plain_fun t
   202           val ps =
   203             tsp |> op ~~
   204                 |> maps (fn (t1, t2) =>
   205                             multi_pair_up T1 t1 (snd (dest_plain_fun t2)))
   206         in make_plain_fun maybe_opt T1 T2 ps end
   207       (* typ -> typ -> typ -> typ -> term -> term *)
   208       and do_arrow T1' T2' _ _ (Const (s, _)) = Const (s, T1' --> T2')
   209         | do_arrow T1' T2' T1 T2
   210                    (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =
   211           Const (@{const_name fun_upd},
   212                  (T1' --> T2') --> T1' --> T2' --> T1' --> T2')
   213           $ do_arrow T1' T2' T1 T2 t0 $ do_term T1' T1 t1 $ do_term T2' T2 t2
   214         | do_arrow _ _ _ _ t =
   215           raise TERM ("Nitpick_Model.typecast_fun.do_arrow", [t])
   216       and do_fun T1' T2' T1 T2 t =
   217         case factor_out_types T1' T1 of
   218           ((_, NONE), (_, NONE)) => t |> do_arrow T1' T2' T1 T2
   219         | ((_, NONE), (T1a, SOME T1b)) =>
   220           t |> do_curry T1 T1a T1b T2 |> do_arrow T1' T2' T1a (T1b --> T2)
   221         | ((T1a', SOME T1b'), (_, NONE)) =>
   222           t |> do_arrow T1a' (T1b' --> T2') T1 T2 |> do_uncurry T1' T2'
   223         | _ => raise TYPE ("Nitpick_Model.typecast_fun.do_fun", [T1, T1'], [])
   224       (* typ -> typ -> term -> term *)
   225       and do_term (Type ("fun", [T1', T2'])) (Type ("fun", [T1, T2])) t =
   226           do_fun T1' T2' T1 T2 t
   227         | do_term (T' as Type ("*", Ts' as [T1', T2'])) (Type ("*", [T1, T2]))
   228                   (Const (@{const_name Pair}, _) $ t1 $ t2) =
   229           Const (@{const_name Pair}, Ts' ---> T')
   230           $ do_term T1' T1 t1 $ do_term T2' T2 t2
   231         | do_term T' T t =
   232           if T = T' then t
   233           else raise TYPE ("Nitpick_Model.typecast_fun.do_term", [T, T'], [])
   234     in if T1' = T1 andalso T2' = T2 then t else do_fun T1' T2' T1 T2 t end
   235   | typecast_fun T' _ _ _ =
   236     raise TYPE ("Nitpick_Model.typecast_fun", [T'], [])
   237 
   238 (* term -> string *)
   239 fun truth_const_sort_key @{const True} = "0"
   240   | truth_const_sort_key @{const False} = "2"
   241   | truth_const_sort_key _ = "1"
   242 
   243 (* typ -> term list -> term *)
   244 fun mk_tuple (Type ("*", [T1, T2])) ts =
   245     HOLogic.mk_prod (mk_tuple T1 ts,
   246         mk_tuple T2 (List.drop (ts, length (HOLogic.flatten_tupleT T1))))
   247   | mk_tuple _ (t :: _) = t
   248   | mk_tuple T [] = raise TYPE ("Nitpick_Model.mk_tuple", [T], [])
   249 
   250 (* string * string * string * string -> scope -> nut list -> nut list
   251    -> nut list -> nut NameTable.table -> KK.raw_bound list -> typ -> typ -> rep
   252    -> int list list -> term *)
   253 fun reconstruct_term (maybe_name, base_name, step_name, abs_name)
   254         ({hol_ctxt as {thy, ctxt, ...}, card_assigns, bits, datatypes, ofs, ...}
   255          : scope) sel_names rel_table bounds =
   256   let
   257     val for_auto = (maybe_name = "")
   258     (* int list list -> int *)
   259     fun value_of_bits jss =
   260       let
   261         val j0 = offset_of_type ofs @{typ unsigned_bit}
   262         val js = map (Integer.add (~ j0) o the_single) jss
   263       in
   264         fold (fn j => Integer.add (reasonable_power 2 j |> j = bits ? op ~))
   265              js 0
   266       end
   267     (* bool -> typ -> typ -> (term * term) list -> term *)
   268     fun make_set maybe_opt T1 T2 =
   269       let
   270         val empty_const = Const (@{const_name Set.empty}, T1 --> T2)
   271         val insert_const = Const (@{const_name insert},
   272                                   T1 --> (T1 --> T2) --> T1 --> T2)
   273         (* (term * term) list -> term *)
   274         fun aux [] =
   275             if maybe_opt andalso not (is_complete_type datatypes T1) then
   276               insert_const $ Const (unrep, T1) $ empty_const
   277             else
   278               empty_const
   279           | aux ((t1, t2) :: zs) =
   280             aux zs |> t2 <> @{const False}
   281                       ? curry (op $) (insert_const
   282                                       $ (t1 |> t2 <> @{const True}
   283                                                ? curry (op $)
   284                                                        (Const (maybe_name,
   285                                                                T1 --> T1))))
   286       in aux end
   287     (* typ -> typ -> typ -> (term * term) list -> term *)
   288     fun make_map T1 T2 T2' =
   289       let
   290         val update_const = Const (@{const_name fun_upd},
   291                                   (T1 --> T2) --> T1 --> T2 --> T1 --> T2)
   292         (* (term * term) list -> term *)
   293         fun aux' [] = Const (@{const_name Map.empty}, T1 --> T2)
   294           | aux' ((t1, t2) :: ps) =
   295             (case t2 of
   296                Const (@{const_name None}, _) => aux' ps
   297              | _ => update_const $ aux' ps $ t1 $ t2)
   298         fun aux ps =
   299           if not (is_complete_type datatypes T1) then
   300             update_const $ aux' ps $ Const (unrep, T1)
   301             $ (Const (@{const_name Some}, T2' --> T2) $ Const (unknown, T2'))
   302           else
   303             aux' ps
   304       in aux end
   305     (* typ list -> term -> term *)
   306     fun polish_funs Ts t =
   307       (case fastype_of1 (Ts, t) of
   308          Type ("fun", [T1, T2]) =>
   309          if is_plain_fun t then
   310            case T2 of
   311              @{typ bool} =>
   312              let
   313                val (maybe_opt, ts_pair) =
   314                  dest_plain_fun t ||> pairself (map (polish_funs Ts))
   315              in
   316                make_set maybe_opt T1 T2
   317                         (sort_wrt (truth_const_sort_key o snd) (op ~~ ts_pair))
   318              end
   319            | Type (@{type_name option}, [T2']) =>
   320              let
   321                val ts_pair = snd (dest_plain_fun t)
   322                              |> pairself (map (polish_funs Ts))
   323              in make_map T1 T2 T2' (rev (op ~~ ts_pair)) end
   324            | _ => raise SAME ()
   325          else
   326            raise SAME ()
   327        | _ => raise SAME ())
   328       handle SAME () =>
   329              case t of
   330                (t1 as Const (@{const_name fun_upd}, _) $ t11 $ _)
   331                $ (t2 as Const (s, _)) =>
   332                if s = unknown then polish_funs Ts t11
   333                else polish_funs Ts t1 $ polish_funs Ts t2
   334              | t1 $ t2 => polish_funs Ts t1 $ polish_funs Ts t2
   335              | Abs (s, T, t') => Abs (s, T, polish_funs (T :: Ts) t')
   336              | Const (s, Type ("fun", [T1, T2])) =>
   337                if s = opt_flag orelse s = non_opt_flag then
   338                  Abs ("x", T1, Const (unknown, T2))
   339                else
   340                  t
   341              | t => t
   342     (* bool -> typ -> typ -> typ -> term list -> term list -> term *)
   343     fun make_fun maybe_opt T1 T2 T' ts1 ts2 =
   344       ts1 ~~ ts2 |> sort (nice_term_ord o pairself fst)
   345                  |> make_plain_fun maybe_opt T1 T2
   346                  |> unbit_and_unbox_term
   347                  |> typecast_fun (unbit_and_unbox_type T')
   348                                  (unbit_and_unbox_type T1)
   349                                  (unbit_and_unbox_type T2)
   350     (* (typ * int) list -> typ -> typ -> int -> term *)
   351     fun term_for_atom seen (T as Type ("fun", [T1, T2])) T' j =
   352         let
   353           val k1 = card_of_type card_assigns T1
   354           val k2 = card_of_type card_assigns T2
   355         in
   356           term_for_rep seen T T' (Vect (k1, Atom (k2, 0)))
   357                        [nth_combination (replicate k1 (k2, 0)) j]
   358           handle General.Subscript =>
   359                  raise ARG ("Nitpick_Model.reconstruct_term.term_for_atom",
   360                             signed_string_of_int j ^ " for " ^
   361                             string_for_rep (Vect (k1, Atom (k2, 0))))
   362         end
   363       | term_for_atom seen (Type ("*", [T1, T2])) _ j =
   364         let val k1 = card_of_type card_assigns T1 in
   365           list_comb (HOLogic.pair_const T1 T2,
   366                      map2 (fn T => term_for_atom seen T T) [T1, T2]
   367                           [j div k1, j mod k1])
   368         end
   369       | term_for_atom seen @{typ prop} _ j =
   370         HOLogic.mk_Trueprop (term_for_atom seen bool_T bool_T j)
   371       | term_for_atom _ @{typ bool} _ j =
   372         if j = 0 then @{const False} else @{const True}
   373       | term_for_atom _ @{typ unit} _ _ = @{const Unity}
   374       | term_for_atom seen T _ j =
   375         if T = nat_T then
   376           HOLogic.mk_number nat_T j
   377         else if T = int_T then
   378           HOLogic.mk_number int_T
   379               (int_for_atom (card_of_type card_assigns int_T, 0) j)
   380         else if is_fp_iterator_type T then
   381           HOLogic.mk_number nat_T (card_of_type card_assigns T - j - 1)
   382         else if T = @{typ bisim_iterator} then
   383           HOLogic.mk_number nat_T j
   384         else case datatype_spec datatypes T of
   385           NONE => atom for_auto T j
   386         | SOME {deep = false, ...} => atom for_auto T j
   387         | SOME {co, constrs, ...} =>
   388           let
   389             (* styp -> int list *)
   390             fun tuples_for_const (s, T) =
   391               tuple_list_for_name rel_table bounds (ConstName (s, T, Any))
   392             (* unit -> indexname * typ *)
   393             fun var () = ((atom_name "" T j, 0), T)
   394             val discr_jsss = map (tuples_for_const o discr_for_constr o #const)
   395                                  constrs
   396             val real_j = j + offset_of_type ofs T
   397             val constr_x as (constr_s, constr_T) =
   398               get_first (fn (jss, {const, ...}) =>
   399                             if member (op =) jss [real_j] then SOME const
   400                             else NONE)
   401                         (discr_jsss ~~ constrs) |> the
   402             val arg_Ts = curried_binder_types constr_T
   403             val sel_xs = map (boxed_nth_sel_for_constr hol_ctxt constr_x)
   404                              (index_seq 0 (length arg_Ts))
   405             val sel_Rs =
   406               map (fn x => get_first
   407                                (fn ConstName (s', T', R) =>
   408                                    if (s', T') = x then SOME R else NONE
   409                                  | u => raise NUT ("Nitpick_Model.reconstruct_\
   410                                                    \term.term_for_atom", [u]))
   411                                sel_names |> the) sel_xs
   412             val arg_Rs = map (snd o dest_Func) sel_Rs
   413             val sel_jsss = map tuples_for_const sel_xs
   414             val arg_jsss =
   415               map (map_filter (fn js => if hd js = real_j then SOME (tl js)
   416                                         else NONE)) sel_jsss
   417             val uncur_arg_Ts = binder_types constr_T
   418           in
   419             if co andalso member (op =) seen (T, j) then
   420               Var (var ())
   421             else if constr_s = @{const_name Word} then
   422               HOLogic.mk_number
   423                   (if T = @{typ "unsigned_bit word"} then nat_T else int_T)
   424                   (value_of_bits (the_single arg_jsss))
   425             else
   426               let
   427                 val seen = seen |> co ? cons (T, j)
   428                 val ts =
   429                   if length arg_Ts = 0 then
   430                     []
   431                   else
   432                     map3 (fn Ts => term_for_rep seen Ts Ts) arg_Ts arg_Rs
   433                          arg_jsss
   434                     |> mk_tuple (HOLogic.mk_tupleT uncur_arg_Ts)
   435                     |> dest_n_tuple (length uncur_arg_Ts)
   436                 val t =
   437                   if constr_s = @{const_name Abs_Frac} then
   438                     let
   439                       val num_T = body_type T
   440                       (* int -> term *)
   441                       val mk_num = HOLogic.mk_number num_T
   442                     in
   443                       case ts of
   444                         [Const (@{const_name Pair}, _) $ t1 $ t2] =>
   445                         (case snd (HOLogic.dest_number t1) of
   446                            0 => mk_num 0
   447                          | n1 => case HOLogic.dest_number t2 |> snd of
   448                                    1 => mk_num n1
   449                                  | n2 => Const (@{const_name Algebras.divide},
   450                                                 num_T --> num_T --> num_T)
   451                                          $ mk_num n1 $ mk_num n2)
   452                       | _ => raise TERM ("Nitpick_Model.reconstruct_term.\
   453                                          \term_for_atom (Abs_Frac)", ts)
   454                     end
   455                   else if not for_auto andalso
   456                           (is_abs_fun thy constr_x orelse
   457                            constr_s = @{const_name Quot}) then
   458                     Const (abs_name, constr_T) $ the_single ts
   459                   else if not for_auto andalso
   460                           constr_s = @{const_name NonStd} then
   461                     Const (fst (dest_Const (the_single ts)), T)
   462                   else
   463                     list_comb (Const constr_x, ts)
   464               in
   465                 if co then
   466                   let val var = var () in
   467                     if exists_subterm (curry (op =) (Var var)) t then
   468                       Const (@{const_name The}, (T --> bool_T) --> T)
   469                       $ Abs ("\<omega>", T,
   470                              Const (@{const_name "op ="}, T --> T --> bool_T)
   471                              $ Bound 0 $ abstract_over (Var var, t))
   472                     else
   473                       t
   474                   end
   475                 else
   476                   t
   477               end
   478           end
   479     (* (typ * int) list -> int -> rep -> typ -> typ -> typ -> int list
   480        -> term *)
   481     and term_for_vect seen k R T1 T2 T' js =
   482       make_fun true T1 T2 T' (map (term_for_atom seen T1 T1) (index_seq 0 k))
   483                (map (term_for_rep seen T2 T2 R o single)
   484                     (batch_list (arity_of_rep R) js))
   485     (* (typ * int) list -> typ -> typ -> rep -> int list list -> term *)
   486     and term_for_rep seen T T' Unit [[]] = term_for_atom seen T T' 0
   487       | term_for_rep seen T T' (R as Atom (k, j0)) [[j]] =
   488         if j >= j0 andalso j < j0 + k then term_for_atom seen T T' (j - j0)
   489         else raise REP ("Nitpick_Model.reconstruct_term.term_for_rep", [R])
   490       | term_for_rep seen (Type ("*", [T1, T2])) _ (Struct [R1, R2]) [js] =
   491         let
   492           val arity1 = arity_of_rep R1
   493           val (js1, js2) = chop arity1 js
   494         in
   495           list_comb (HOLogic.pair_const T1 T2,
   496                      map3 (fn T => term_for_rep seen T T) [T1, T2] [R1, R2]
   497                           [[js1], [js2]])
   498         end
   499       | term_for_rep seen (Type ("fun", [T1, T2])) T' (R as Vect (k, R')) [js] =
   500         term_for_vect seen k R' T1 T2 T' js
   501       | term_for_rep seen (Type ("fun", [T1, T2])) T' (Func (R1, Formula Neut))
   502                      jss =
   503         let
   504           val jss1 = all_combinations_for_rep R1
   505           val ts1 = map (term_for_rep seen T1 T1 R1 o single) jss1
   506           val ts2 =
   507             map (fn js => term_for_rep seen T2 T2 (Atom (2, 0))
   508                                        [[int_for_bool (member (op =) jss js)]])
   509                 jss1
   510         in make_fun false T1 T2 T' ts1 ts2 end
   511       | term_for_rep seen (Type ("fun", [T1, T2])) T' (Func (R1, R2)) jss =
   512         let
   513           val arity1 = arity_of_rep R1
   514           val jss1 = all_combinations_for_rep R1
   515           val ts1 = map (term_for_rep seen T1 T1 R1 o single) jss1
   516           val grouped_jss2 = AList.group (op =) (map (chop arity1) jss)
   517           val ts2 = map (term_for_rep seen T2 T2 R2 o the_default []
   518                          o AList.lookup (op =) grouped_jss2) jss1
   519         in make_fun true T1 T2 T' ts1 ts2 end
   520       | term_for_rep seen T T' (Opt R) jss =
   521         if null jss then Const (unknown, T) else term_for_rep seen T T' R jss
   522       | term_for_rep seen T _ R jss =
   523         raise ARG ("Nitpick_Model.reconstruct_term.term_for_rep",
   524                    Refute.string_of_typ T ^ " " ^ string_for_rep R ^ " " ^
   525                    string_of_int (length jss))
   526   in
   527     polish_funs [] o unbit_and_unbox_term oooo term_for_rep []
   528   end
   529 
   530 (* scope -> nut list -> nut NameTable.table -> KK.raw_bound list -> nut
   531    -> term *)
   532 fun term_for_name scope sel_names rel_table bounds name =
   533   let val T = type_of name in
   534     tuple_list_for_name rel_table bounds name
   535     |> reconstruct_term ("", "", "", "") scope sel_names rel_table bounds T T
   536                         (rep_of name)
   537   end
   538 
   539 (* Proof.context -> (string * string * string * string) * Proof.context *)
   540 fun add_wacky_syntax ctxt =
   541   let
   542     (* term -> string *)
   543     val name_of = fst o dest_Const
   544     val thy = ProofContext.theory_of ctxt |> Context.reject_draft
   545     val (maybe_t, thy) =
   546       Sign.declare_const ((@{binding nitpick_maybe}, @{typ "'a => 'a"}),
   547                           Mixfix (maybe_mixfix, [1000], 1000)) thy
   548     val (base_t, thy) =
   549       Sign.declare_const ((@{binding nitpick_base}, @{typ "'a => 'a"}),
   550                           Mixfix (base_mixfix, [1000], 1000)) thy
   551     val (step_t, thy) =
   552       Sign.declare_const ((@{binding nitpick_step}, @{typ "'a => 'a"}),
   553                           Mixfix (step_mixfix, [1000], 1000)) thy
   554     val (abs_t, thy) =
   555       Sign.declare_const ((@{binding nitpick_abs}, @{typ "'a => 'b"}),
   556                           Mixfix (abs_mixfix, [40], 40)) thy
   557   in
   558     ((name_of maybe_t, name_of base_t, name_of step_t, name_of abs_t),
   559      ProofContext.transfer_syntax thy ctxt)
   560   end
   561 
   562 (* term -> term *)
   563 fun unfold_outer_the_binders (t as Const (@{const_name The}, _)
   564                                    $ Abs (s, T, Const (@{const_name "op ="}, _)
   565                                                 $ Bound 0 $ t')) =
   566     betapply (Abs (s, T, t'), t) |> unfold_outer_the_binders
   567   | unfold_outer_the_binders t = t
   568 (* typ list -> int -> term * term -> bool *)
   569 fun bisimilar_values _ 0 _ = true
   570   | bisimilar_values coTs max_depth (t1, t2) =
   571     let val T = fastype_of t1 in
   572       if exists_subtype (member (op =) coTs) T then
   573         let
   574           val ((head1, args1), (head2, args2)) =
   575             pairself (strip_comb o unfold_outer_the_binders) (t1, t2)
   576           val max_depth = max_depth - (if member (op =) coTs T then 1 else 0)
   577         in
   578           head1 = head2 andalso
   579           forall (bisimilar_values coTs max_depth) (args1 ~~ args2)
   580         end
   581       else
   582         t1 = t2
   583     end
   584 
   585 (* params -> scope -> (term option * int list) list -> styp list -> nut list
   586   -> nut list -> nut list -> nut NameTable.table -> KK.raw_bound list
   587   -> Pretty.T * bool *)
   588 fun reconstruct_hol_model {show_skolems, show_datatypes, show_consts}
   589         ({hol_ctxt as {thy, ctxt, max_bisim_depth, boxes, stds, wfs,
   590                        user_axioms, debug, binary_ints, destroy_constrs,
   591                        specialize, skolemize, star_linear_preds, uncurry,
   592                        fast_descrs, tac_timeout, evals, case_names, def_table,
   593                        nondef_table, user_nondefs, simp_table, psimp_table,
   594                        intro_table, ground_thm_table, ersatz_table, skolems,
   595                        special_funs, unrolled_preds, wf_cache, constr_cache},
   596          card_assigns, bits, bisim_depth, datatypes, ofs} : scope)
   597         formats all_frees free_names sel_names nonsel_names rel_table bounds =
   598   let
   599     val (wacky_names as (_, base_name, step_name, _), ctxt) =
   600       add_wacky_syntax ctxt
   601     val hol_ctxt =
   602       {thy = thy, ctxt = ctxt, max_bisim_depth = max_bisim_depth, boxes = boxes,
   603        stds = stds, wfs = wfs, user_axioms = user_axioms, debug = debug,
   604        binary_ints = binary_ints, destroy_constrs = destroy_constrs,
   605        specialize = specialize, skolemize = skolemize,
   606        star_linear_preds = star_linear_preds, uncurry = uncurry,
   607        fast_descrs = fast_descrs, tac_timeout = tac_timeout, evals = evals,
   608        case_names = case_names, def_table = def_table,
   609        nondef_table = nondef_table, user_nondefs = user_nondefs,
   610        simp_table = simp_table, psimp_table = psimp_table,
   611        intro_table = intro_table, ground_thm_table = ground_thm_table,
   612        ersatz_table = ersatz_table, skolems = skolems,
   613        special_funs = special_funs, unrolled_preds = unrolled_preds,
   614        wf_cache = wf_cache, constr_cache = constr_cache}
   615     val scope = {hol_ctxt = hol_ctxt, card_assigns = card_assigns,
   616                  bits = bits, bisim_depth = bisim_depth, datatypes = datatypes,
   617                  ofs = ofs}
   618     (* typ -> typ -> rep -> int list list -> term *)
   619     val term_for_rep = reconstruct_term wacky_names scope sel_names rel_table
   620                                         bounds
   621     (* nat -> typ -> nat -> typ *)
   622     fun nth_value_of_type card T n = term_for_rep T T (Atom (card, 0)) [[n]]
   623     (* nat -> typ -> typ list *)
   624     fun all_values_of_type card T =
   625       index_seq 0 card |> map (nth_value_of_type card T) |> sort nice_term_ord
   626     (* dtype_spec list -> dtype_spec -> bool *)
   627     fun is_codatatype_wellformed (cos : dtype_spec list)
   628                                  ({typ, card, ...} : dtype_spec) =
   629       let
   630         val ts = all_values_of_type card typ
   631         val max_depth = Integer.sum (map #card cos)
   632       in
   633         forall (not o bisimilar_values (map #typ cos) max_depth)
   634                (all_distinct_unordered_pairs_of ts)
   635       end
   636     (* string -> Pretty.T *)
   637     fun pretty_for_assign name =
   638       let
   639         val (oper, (t1, T'), T) =
   640           case name of
   641             FreeName (s, T, _) =>
   642             let val t = Free (s, unbit_and_unbox_type T) in
   643               ("=", (t, format_term_type thy def_table formats t), T)
   644             end
   645           | ConstName (s, T, _) =>
   646             (assign_operator_for_const (s, T),
   647              user_friendly_const hol_ctxt (base_name, step_name) formats (s, T),
   648              T)
   649           | _ => raise NUT ("Nitpick_Model.reconstruct_hol_model.\
   650                             \pretty_for_assign", [name])
   651         val t2 = if rep_of name = Any then
   652                    Const (@{const_name undefined}, T')
   653                  else
   654                    tuple_list_for_name rel_table bounds name
   655                    |> term_for_rep T T' (rep_of name)
   656       in
   657         Pretty.block (Pretty.breaks
   658             [setmp_show_all_types (Syntax.pretty_term ctxt) t1,
   659              Pretty.str oper, Syntax.pretty_term ctxt t2])
   660       end
   661     (* dtype_spec -> Pretty.T *)
   662     fun pretty_for_datatype ({typ, card, complete, ...} : dtype_spec) =
   663       Pretty.block (Pretty.breaks
   664           [Syntax.pretty_typ ctxt (unbit_and_unbox_type typ), Pretty.str "=",
   665            Pretty.enum "," "{" "}"
   666                (map (Syntax.pretty_term ctxt) (all_values_of_type card typ) @
   667                 (if complete then [] else [Pretty.str unrep]))])
   668     (* typ -> dtype_spec list *)
   669     fun integer_datatype T =
   670       [{typ = T, card = card_of_type card_assigns T, co = false,
   671         complete = false, concrete = true, deep = true, constrs = []}]
   672       handle TYPE ("Nitpick_HOL.card_of_type", _, _) => []
   673     val (codatatypes, datatypes) =
   674       datatypes |> filter #deep |> List.partition #co
   675                 ||> append (integer_datatype nat_T @ integer_datatype int_T)
   676     val block_of_datatypes =
   677       if show_datatypes andalso not (null datatypes) then
   678         [Pretty.big_list ("Datatype" ^ plural_s_for_list datatypes ^ ":")
   679                          (map pretty_for_datatype datatypes)]
   680       else
   681         []
   682     val block_of_codatatypes =
   683       if show_datatypes andalso not (null codatatypes) then
   684         [Pretty.big_list ("Codatatype" ^ plural_s_for_list codatatypes ^ ":")
   685                          (map pretty_for_datatype codatatypes)]
   686       else
   687         []
   688     (* bool -> string -> nut list -> Pretty.T list *)
   689     fun block_of_names show title names =
   690       if show andalso not (null names) then
   691         Pretty.str (title ^ plural_s_for_list names ^ ":")
   692         :: map (Pretty.indent indent_size o pretty_for_assign)
   693                (sort_wrt (original_name o nickname_of) names)
   694       else
   695         []
   696     val (skolem_names, nonskolem_nonsel_names) =
   697       List.partition is_skolem_name nonsel_names
   698     val (eval_names, noneval_nonskolem_nonsel_names) =
   699       List.partition (String.isPrefix eval_prefix o nickname_of)
   700                      nonskolem_nonsel_names
   701       ||> filter_out (curry (op =) @{const_name bisim_iterator_max}
   702                       o nickname_of)
   703     val free_names =
   704       map (fn x as (s, T) =>
   705               case filter (curry (op =) x
   706                            o pairf nickname_of (unbit_and_unbox_type o type_of))
   707                           free_names of
   708                 [name] => name
   709               | [] => FreeName (s, T, Any)
   710               | _ => raise TERM ("Nitpick_Model.reconstruct_hol_model",
   711                                  [Const x])) all_frees
   712     val chunks = block_of_names true "Free variable" free_names @
   713                  block_of_names show_skolems "Skolem constant" skolem_names @
   714                  block_of_names true "Evaluated term" eval_names @
   715                  block_of_datatypes @ block_of_codatatypes @
   716                  block_of_names show_consts "Constant"
   717                                 noneval_nonskolem_nonsel_names
   718   in
   719     (Pretty.chunks (if null chunks then [Pretty.str "Empty assignment"]
   720                     else chunks),
   721      bisim_depth >= 0 orelse
   722      forall (is_codatatype_wellformed codatatypes) codatatypes)
   723   end
   724 
   725 (* scope -> Time.time option -> nut list -> nut list -> nut NameTable.table
   726    -> KK.raw_bound list -> term -> bool option *)
   727 fun prove_hol_model (scope as {hol_ctxt as {thy, ctxt, debug, ...},
   728                                card_assigns, ...})
   729                     auto_timeout free_names sel_names rel_table bounds prop =
   730   let
   731     (* typ * int -> term *)
   732     fun free_type_assm (T, k) =
   733       let
   734         (* int -> term *)
   735         val atom = atom true T
   736         fun equation_for_atom j = HOLogic.eq_const T $ Bound 0 $ atom j
   737         val eqs = map equation_for_atom (index_seq 0 k)
   738         val compreh_assm =
   739           Const (@{const_name All}, (T --> bool_T) --> bool_T)
   740               $ Abs ("x", T, foldl1 HOLogic.mk_disj eqs)
   741         val distinct_assm = distinctness_formula T (map atom (index_seq 0 k))
   742       in s_conj (compreh_assm, distinct_assm) end
   743     (* nut -> term *)
   744     fun free_name_assm name =
   745       HOLogic.mk_eq (Free (nickname_of name, type_of name),
   746                      term_for_name scope sel_names rel_table bounds name)
   747     val freeT_assms = map free_type_assm (filter (is_TFree o fst) card_assigns)
   748     val model_assms = map free_name_assm free_names
   749     val assm = foldr1 s_conj (freeT_assms @ model_assms)
   750     (* bool -> bool *)
   751     fun try_out negate =
   752       let
   753         val concl = (negate ? curry (op $) @{const Not})
   754                     (ObjectLogic.atomize_term thy prop)
   755         val prop = HOLogic.mk_Trueprop (HOLogic.mk_imp (assm, concl))
   756                    |> map_types (map_type_tfree
   757                                      (fn (s, []) => TFree (s, HOLogic.typeS)
   758                                        | x => TFree x))
   759        val _ = if debug then
   760                  priority ((if negate then "Genuineness" else "Spuriousness") ^
   761                            " goal: " ^ Syntax.string_of_term ctxt prop ^ ".")
   762                else
   763                  ()
   764         val goal = prop |> cterm_of thy |> Goal.init
   765       in
   766         (goal |> SINGLE (DETERM_TIMEOUT auto_timeout
   767                                         (auto_tac (clasimpset_of ctxt)))
   768               |> the |> Goal.finish ctxt; true)
   769         handle THM _ => false
   770              | TimeLimit.TimeOut => false
   771       end
   772   in
   773     if try_out false then SOME true
   774     else if try_out true then SOME false
   775     else NONE
   776   end
   777 
   778 end;