src/HOL/Tools/Nitpick/nitpick_model.ML
author blanchet
Sat Feb 13 15:04:09 2010 +0100 (2010-02-13)
changeset 35180 c57dba973391
parent 35179 4b198af5beb5
child 35188 8c70a34931b1
permissions -rw-r--r--
more work on Nitpick's support for nonstandard models + fix in model reconstruction
     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 cyclic_co_val_name = "\<omega>"
    57 val cyclic_type_name = "\<xi>"
    58 val opt_flag = nitpick_prefix ^ "opt"
    59 val non_opt_flag = nitpick_prefix ^ "non_opt"
    60 
    61 type atom_pool = ((string * int) * int list) list
    62 
    63 (* atom_pool Unsynchronized.ref -> string -> int -> int -> string *)
    64 fun nth_atom_suffix pool s j k =
    65   (case AList.lookup (op =) (!pool) (s, k) of
    66      SOME js =>
    67      (case find_index (curry (op =) j) js of
    68         ~1 => (Unsynchronized.change pool (cons ((s, k), j :: js));
    69                length js + 1)
    70       | n => length js - n)
    71    | NONE => (Unsynchronized.change pool (cons ((s, k), [j])); 1))
    72   |> nat_subscript
    73   |> (s <> "" andalso Symbol.is_ascii_digit (List.last (explode s)))
    74      ? prefix "\<^isub>,"
    75 (* atom_pool Unsynchronized.ref -> string -> typ -> int -> int -> string *)
    76 fun nth_atom_name pool prefix (T as Type (s, _)) j k =
    77     let val s' = shortest_name s in
    78       prefix ^ (if String.isPrefix "\\" s' then s' else substring (s', 0, 1)) ^
    79       nth_atom_suffix pool s j k
    80     end
    81   | nth_atom_name pool prefix (T as TFree (s, _)) j k =
    82     prefix ^ perhaps (try (unprefix "'")) s ^ nth_atom_suffix pool s j k
    83   | nth_atom_name _ _ T _ _ =
    84     raise TYPE ("Nitpick_Model.nth_atom_name", [T], [])
    85 (* atom_pool Unsynchronized.ref -> bool -> typ -> int -> int -> term *)
    86 fun nth_atom pool for_auto T j k =
    87   if for_auto then
    88     Free (nth_atom_name pool (hd (space_explode "." nitpick_prefix)) T j k, T)
    89   else
    90     Const (nth_atom_name pool "" T j k, T)
    91 
    92 (* term -> real *)
    93 fun extract_real_number (Const (@{const_name divide}, _) $ t1 $ t2) =
    94     real (snd (HOLogic.dest_number t1)) / real (snd (HOLogic.dest_number t2))
    95   | extract_real_number t = real (snd (HOLogic.dest_number t))
    96 (* term * term -> order *)
    97 fun nice_term_ord (Abs (_, _, t1), Abs (_, _, t2)) = nice_term_ord (t1, t2)
    98   | nice_term_ord tp = Real.compare (pairself extract_real_number tp)
    99     handle TERM ("dest_number", _) =>
   100            case tp of
   101              (t11 $ t12, t21 $ t22) =>
   102              (case nice_term_ord (t11, t21) of
   103                 EQUAL => nice_term_ord (t12, t22)
   104               | ord => ord)
   105            | _ => TermOrd.fast_term_ord tp
   106 
   107 (* nut NameTable.table -> KK.raw_bound list -> nut -> int list list *)
   108 fun tuple_list_for_name rel_table bounds name =
   109   the (AList.lookup (op =) bounds (the_rel rel_table name)) handle NUT _ => [[]]
   110 
   111 (* term -> term *)
   112 fun unbit_and_unbox_term (Const (@{const_name FunBox}, _) $ t1) =
   113     unbit_and_unbox_term t1
   114   | unbit_and_unbox_term (Const (@{const_name PairBox},
   115                           Type ("fun", [T1, Type ("fun", [T2, T3])]))
   116                           $ t1 $ t2) =
   117     let val Ts = map unbit_and_unbox_type [T1, T2] in
   118       Const (@{const_name Pair}, Ts ---> Type ("*", Ts))
   119       $ unbit_and_unbox_term t1 $ unbit_and_unbox_term t2
   120     end
   121   | unbit_and_unbox_term (Const (s, T)) = Const (s, unbit_and_unbox_type T)
   122   | unbit_and_unbox_term (t1 $ t2) =
   123     unbit_and_unbox_term t1 $ unbit_and_unbox_term t2
   124   | unbit_and_unbox_term (Free (s, T)) = Free (s, unbit_and_unbox_type T)
   125   | unbit_and_unbox_term (Var (x, T)) = Var (x, unbit_and_unbox_type T)
   126   | unbit_and_unbox_term (Bound j) = Bound j
   127   | unbit_and_unbox_term (Abs (s, T, t')) =
   128     Abs (s, unbit_and_unbox_type T, unbit_and_unbox_term t')
   129 
   130 (* typ -> typ -> (typ * typ) * (typ * typ) *)
   131 fun factor_out_types (T1 as Type ("*", [T11, T12]))
   132                      (T2 as Type ("*", [T21, T22])) =
   133     let val (n1, n2) = pairself num_factors_in_type (T11, T21) in
   134       if n1 = n2 then
   135         let
   136           val ((T11', opt_T12'), (T21', opt_T22')) = factor_out_types T12 T22
   137         in
   138           ((Type ("*", [T11, T11']), opt_T12'),
   139            (Type ("*", [T21, T21']), opt_T22'))
   140         end
   141       else if n1 < n2 then
   142         case factor_out_types T1 T21 of
   143           (p1, (T21', NONE)) => (p1, (T21', SOME T22))
   144         | (p1, (T21', SOME T22')) =>
   145           (p1, (T21', SOME (Type ("*", [T22', T22]))))
   146       else
   147         swap (factor_out_types T2 T1)
   148     end
   149   | factor_out_types (Type ("*", [T11, T12])) T2 = ((T11, SOME T12), (T2, NONE))
   150   | factor_out_types T1 (Type ("*", [T21, T22])) = ((T1, NONE), (T21, SOME T22))
   151   | factor_out_types T1 T2 = ((T1, NONE), (T2, NONE))
   152 
   153 (* bool -> typ -> typ -> (term * term) list -> term *)
   154 fun make_plain_fun maybe_opt T1 T2 =
   155   let
   156     (* typ -> typ -> (term * term) list -> term *)
   157     fun aux T1 T2 [] =
   158         Const (if maybe_opt then opt_flag else non_opt_flag, T1 --> T2)
   159       | aux T1 T2 ((t1, t2) :: ps) =
   160         Const (@{const_name fun_upd}, (T1 --> T2) --> T1 --> T2 --> T1 --> T2)
   161         $ aux T1 T2 ps $ t1 $ t2
   162   in aux T1 T2 o rev end
   163 (* term -> bool *)
   164 fun is_plain_fun (Const (s, _)) = (s = opt_flag orelse s = non_opt_flag)
   165   | is_plain_fun (Const (@{const_name fun_upd}, _) $ t0 $ _ $ _) =
   166     is_plain_fun t0
   167   | is_plain_fun _ = false
   168 (* term -> bool * (term list * term list) *)
   169 val dest_plain_fun =
   170   let
   171     (* term -> bool * (term list * term list) *)
   172     fun aux (Const (s, _)) = (s <> non_opt_flag, ([], []))
   173       | aux (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =
   174         let val (s, (ts1, ts2)) = aux t0 in (s, (t1 :: ts1, t2 :: ts2)) end
   175       | aux t = raise TERM ("Nitpick_Model.dest_plain_fun", [t])
   176   in apsnd (pairself rev) o aux end
   177 
   178 (* typ -> typ -> typ -> term -> term * term *)
   179 fun break_in_two T T1 T2 t =
   180   let
   181     val ps = HOLogic.flat_tupleT_paths T
   182     val cut = length (HOLogic.strip_tupleT T1)
   183     val (ps1, ps2) = pairself HOLogic.flat_tupleT_paths (T1, T2)
   184     val (ts1, ts2) = t |> HOLogic.strip_ptuple ps |> chop cut
   185   in (HOLogic.mk_ptuple ps1 T1 ts1, HOLogic.mk_ptuple ps2 T2 ts2) end
   186 (* typ -> term -> term -> term *)
   187 fun pair_up (Type ("*", [T1', T2']))
   188             (t1 as Const (@{const_name Pair},
   189                           Type ("fun", [_, Type ("fun", [_, T1])])) $ t11 $ t12)
   190             t2 =
   191     if T1 = T1' then HOLogic.mk_prod (t1, t2)
   192     else HOLogic.mk_prod (t11, pair_up T2' t12 t2)
   193   | pair_up _ t1 t2 = HOLogic.mk_prod (t1, t2)
   194 (* typ -> term -> term list * term list -> (term * term) list*)
   195 fun multi_pair_up T1 t1 (ts2, ts3) = map2 (pair o pair_up T1 t1) ts2 ts3
   196 
   197 (* typ -> typ -> typ -> term -> term *)
   198 fun typecast_fun (Type ("fun", [T1', T2'])) T1 T2 t =
   199     let
   200       (* typ -> typ -> typ -> typ -> term -> term *)
   201       fun do_curry T1 T1a T1b T2 t =
   202         let
   203           val (maybe_opt, ps) = dest_plain_fun t
   204           val ps =
   205             ps |>> map (break_in_two T1 T1a T1b)
   206                |> uncurry (map2 (fn (t1a, t1b) => fn t2 => (t1a, (t1b, t2))))
   207                |> AList.coalesce (op =)
   208                |> map (apsnd (make_plain_fun maybe_opt T1b T2))
   209         in make_plain_fun maybe_opt T1a (T1b --> T2) ps end
   210       (* typ -> typ -> term -> term *)
   211       and do_uncurry T1 T2 t =
   212         let
   213           val (maybe_opt, tsp) = dest_plain_fun t
   214           val ps =
   215             tsp |> op ~~
   216                 |> maps (fn (t1, t2) =>
   217                             multi_pair_up T1 t1 (snd (dest_plain_fun t2)))
   218         in make_plain_fun maybe_opt T1 T2 ps end
   219       (* typ -> typ -> typ -> typ -> term -> term *)
   220       and do_arrow T1' T2' _ _ (Const (s, _)) = Const (s, T1' --> T2')
   221         | do_arrow T1' T2' T1 T2
   222                    (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =
   223           Const (@{const_name fun_upd},
   224                  (T1' --> T2') --> T1' --> T2' --> T1' --> T2')
   225           $ do_arrow T1' T2' T1 T2 t0 $ do_term T1' T1 t1 $ do_term T2' T2 t2
   226         | do_arrow _ _ _ _ t =
   227           raise TERM ("Nitpick_Model.typecast_fun.do_arrow", [t])
   228       and do_fun T1' T2' T1 T2 t =
   229         case factor_out_types T1' T1 of
   230           ((_, NONE), (_, NONE)) => t |> do_arrow T1' T2' T1 T2
   231         | ((_, NONE), (T1a, SOME T1b)) =>
   232           t |> do_curry T1 T1a T1b T2 |> do_arrow T1' T2' T1a (T1b --> T2)
   233         | ((T1a', SOME T1b'), (_, NONE)) =>
   234           t |> do_arrow T1a' (T1b' --> T2') T1 T2 |> do_uncurry T1' T2'
   235         | _ => raise TYPE ("Nitpick_Model.typecast_fun.do_fun", [T1, T1'], [])
   236       (* typ -> typ -> term -> term *)
   237       and do_term (Type ("fun", [T1', T2'])) (Type ("fun", [T1, T2])) t =
   238           do_fun T1' T2' T1 T2 t
   239         | do_term (T' as Type ("*", Ts' as [T1', T2'])) (Type ("*", [T1, T2]))
   240                   (Const (@{const_name Pair}, _) $ t1 $ t2) =
   241           Const (@{const_name Pair}, Ts' ---> T')
   242           $ do_term T1' T1 t1 $ do_term T2' T2 t2
   243         | do_term T' T t =
   244           if T = T' then t
   245           else raise TYPE ("Nitpick_Model.typecast_fun.do_term", [T, T'], [])
   246     in if T1' = T1 andalso T2' = T2 then t else do_fun T1' T2' T1 T2 t end
   247   | typecast_fun T' _ _ _ =
   248     raise TYPE ("Nitpick_Model.typecast_fun", [T'], [])
   249 
   250 (* term -> string *)
   251 fun truth_const_sort_key @{const True} = "0"
   252   | truth_const_sort_key @{const False} = "2"
   253   | truth_const_sort_key _ = "1"
   254 
   255 (* typ -> term list -> term *)
   256 fun mk_tuple (Type ("*", [T1, T2])) ts =
   257     HOLogic.mk_prod (mk_tuple T1 ts,
   258         mk_tuple T2 (List.drop (ts, length (HOLogic.flatten_tupleT T1))))
   259   | mk_tuple _ (t :: _) = t
   260   | mk_tuple T [] = raise TYPE ("Nitpick_Model.mk_tuple", [T], [])
   261 
   262 (* bool -> atom_pool -> string * string * string * string -> scope -> nut list
   263    -> nut list -> nut list -> nut NameTable.table -> KK.raw_bound list -> typ
   264    -> typ -> rep -> int list list -> term *)
   265 fun reconstruct_term elaborate pool (maybe_name, base_name, step_name, abs_name)
   266         ({hol_ctxt as {thy, ctxt, ...}, card_assigns, bits, datatypes, ofs, ...}
   267          : scope) sel_names rel_table bounds =
   268   let
   269     val for_auto = (maybe_name = "")
   270     (* int list list -> int *)
   271     fun value_of_bits jss =
   272       let
   273         val j0 = offset_of_type ofs @{typ unsigned_bit}
   274         val js = map (Integer.add (~ j0) o the_single) jss
   275       in
   276         fold (fn j => Integer.add (reasonable_power 2 j |> j = bits ? op ~))
   277              js 0
   278       end
   279     (* bool -> typ -> typ -> (term * term) list -> term *)
   280     fun make_set maybe_opt T1 T2 =
   281       let
   282         val empty_const = Const (@{const_name Set.empty}, T1 --> T2)
   283         val insert_const = Const (@{const_name insert},
   284                                   T1 --> (T1 --> T2) --> T1 --> T2)
   285         (* (term * term) list -> term *)
   286         fun aux [] =
   287             if maybe_opt andalso not (is_complete_type datatypes T1) then
   288               insert_const $ Const (unrep, T1) $ empty_const
   289             else
   290               empty_const
   291           | aux ((t1, t2) :: zs) =
   292             aux zs |> t2 <> @{const False}
   293                       ? curry (op $) (insert_const
   294                                       $ (t1 |> t2 <> @{const True}
   295                                                ? curry (op $)
   296                                                        (Const (maybe_name,
   297                                                                T1 --> T1))))
   298       in aux end
   299     (* typ -> typ -> typ -> (term * term) list -> term *)
   300     fun make_map T1 T2 T2' =
   301       let
   302         val update_const = Const (@{const_name fun_upd},
   303                                   (T1 --> T2) --> T1 --> T2 --> T1 --> T2)
   304         (* (term * term) list -> term *)
   305         fun aux' [] = Const (@{const_name Map.empty}, T1 --> T2)
   306           | aux' ((t1, t2) :: ps) =
   307             (case t2 of
   308                Const (@{const_name None}, _) => aux' ps
   309              | _ => update_const $ aux' ps $ t1 $ t2)
   310         fun aux ps =
   311           if not (is_complete_type datatypes T1) then
   312             update_const $ aux' ps $ Const (unrep, T1)
   313             $ (Const (@{const_name Some}, T2' --> T2) $ Const (unknown, T2'))
   314           else
   315             aux' ps
   316       in aux end
   317     (* typ list -> term -> term *)
   318     fun polish_funs Ts t =
   319       (case fastype_of1 (Ts, t) of
   320          Type ("fun", [T1, T2]) =>
   321          if is_plain_fun t then
   322            case T2 of
   323              @{typ bool} =>
   324              let
   325                val (maybe_opt, ts_pair) =
   326                  dest_plain_fun t ||> pairself (map (polish_funs Ts))
   327              in
   328                make_set maybe_opt T1 T2
   329                         (sort_wrt (truth_const_sort_key o snd) (op ~~ ts_pair))
   330              end
   331            | Type (@{type_name option}, [T2']) =>
   332              let
   333                val ts_pair = snd (dest_plain_fun t)
   334                              |> pairself (map (polish_funs Ts))
   335              in make_map T1 T2 T2' (rev (op ~~ ts_pair)) end
   336            | _ => raise SAME ()
   337          else
   338            raise SAME ()
   339        | _ => raise SAME ())
   340       handle SAME () =>
   341              case t of
   342                (t1 as Const (@{const_name fun_upd}, _) $ t11 $ _)
   343                $ (t2 as Const (s, _)) =>
   344                if s = unknown then polish_funs Ts t11
   345                else polish_funs Ts t1 $ polish_funs Ts t2
   346              | t1 $ t2 => polish_funs Ts t1 $ polish_funs Ts t2
   347              | Abs (s, T, t') => Abs (s, T, polish_funs (T :: Ts) t')
   348              | Const (s, Type ("fun", [T1, T2])) =>
   349                if s = opt_flag orelse s = non_opt_flag then
   350                  Abs ("x", T1, Const (unknown, T2))
   351                else
   352                  t
   353              | t => t
   354     (* bool -> typ -> typ -> typ -> term list -> term list -> term *)
   355     fun make_fun maybe_opt T1 T2 T' ts1 ts2 =
   356       ts1 ~~ ts2 |> sort (nice_term_ord o pairself fst)
   357                  |> make_plain_fun maybe_opt T1 T2
   358                  |> unbit_and_unbox_term
   359                  |> typecast_fun (unbit_and_unbox_type T')
   360                                  (unbit_and_unbox_type T1)
   361                                  (unbit_and_unbox_type T2)
   362     (* (typ * int) list -> typ -> typ -> int -> term *)
   363     fun term_for_atom seen (T as Type ("fun", [T1, T2])) T' j k =
   364         let
   365           val k1 = card_of_type card_assigns T1
   366           val k2 = card_of_type card_assigns T2
   367         in
   368           term_for_rep seen T T' (Vect (k1, Atom (k2, 0)))
   369                        [nth_combination (replicate k1 (k2, 0)) j]
   370           handle General.Subscript =>
   371                  raise ARG ("Nitpick_Model.reconstruct_term.term_for_atom",
   372                             signed_string_of_int j ^ " for " ^
   373                             string_for_rep (Vect (k1, Atom (k2, 0))))
   374         end
   375       | term_for_atom seen (Type ("*", [T1, T2])) _ j k =
   376         let
   377           val k1 = card_of_type card_assigns T1
   378           val k2 = k div k1
   379         in
   380           list_comb (HOLogic.pair_const T1 T2,
   381                      map3 (fn T => term_for_atom seen T T) [T1, T2]
   382                           [j div k2, j mod k2] [k1, k2]) (* ### k2 or k1? FIXME *)
   383         end
   384       | term_for_atom seen @{typ prop} _ j k =
   385         HOLogic.mk_Trueprop (term_for_atom seen bool_T bool_T j k)
   386       | term_for_atom _ @{typ bool} _ j _ =
   387         if j = 0 then @{const False} else @{const True}
   388       | term_for_atom _ @{typ unit} _ _ _ = @{const Unity}
   389       | term_for_atom seen T _ j k =
   390         if T = nat_T then
   391           HOLogic.mk_number nat_T j
   392         else if T = int_T then
   393           HOLogic.mk_number int_T (int_for_atom (k, 0) j)
   394         else if is_fp_iterator_type T then
   395           HOLogic.mk_number nat_T (k - j - 1)
   396         else if T = @{typ bisim_iterator} then
   397           HOLogic.mk_number nat_T j
   398         else case datatype_spec datatypes T of
   399           NONE => nth_atom pool for_auto T j k
   400         | SOME {deep = false, ...} => nth_atom pool for_auto T j k
   401         | SOME {co, standard, constrs, ...} =>
   402           let
   403             (* styp -> int list *)
   404             fun tuples_for_const (s, T) =
   405               tuple_list_for_name rel_table bounds (ConstName (s, T, Any))
   406             (* unit -> term *)
   407             fun cyclic_atom () =
   408               nth_atom pool for_auto (Type (cyclic_type_name, [])) j k
   409             fun cyclic_var () = Var ((nth_atom_name pool "" T j k, 0), T)
   410 
   411             val discr_jsss = map (tuples_for_const o discr_for_constr o #const)
   412                                  constrs
   413             val real_j = j + offset_of_type ofs T
   414             val constr_x as (constr_s, constr_T) =
   415               get_first (fn (jss, {const, ...}) =>
   416                             if member (op =) jss [real_j] then SOME const
   417                             else NONE)
   418                         (discr_jsss ~~ constrs) |> the
   419             val arg_Ts = curried_binder_types constr_T
   420             val sel_xs = map (boxed_nth_sel_for_constr hol_ctxt constr_x)
   421                              (index_seq 0 (length arg_Ts))
   422             val sel_Rs =
   423               map (fn x => get_first
   424                                (fn ConstName (s', T', R) =>
   425                                    if (s', T') = x then SOME R else NONE
   426                                  | u => raise NUT ("Nitpick_Model.reconstruct_\
   427                                                    \term.term_for_atom", [u]))
   428                                sel_names |> the) sel_xs
   429             val arg_Rs = map (snd o dest_Func) sel_Rs
   430             val sel_jsss = map tuples_for_const sel_xs
   431             val arg_jsss =
   432               map (map_filter (fn js => if hd js = real_j then SOME (tl js)
   433                                         else NONE)) sel_jsss
   434             val uncur_arg_Ts = binder_types constr_T
   435             val maybe_cyclic = co orelse not standard
   436           in
   437             if maybe_cyclic andalso not (null seen) andalso
   438                member (op =) (seen |> elaborate ? (fst o split_last)) (T, j) then
   439               cyclic_var ()
   440             else if constr_s = @{const_name Word} then
   441               HOLogic.mk_number
   442                   (if T = @{typ "unsigned_bit word"} then nat_T else int_T)
   443                   (value_of_bits (the_single arg_jsss))
   444             else
   445               let
   446                 val seen = seen |> maybe_cyclic ? cons (T, j)
   447                 val ts =
   448                   if length arg_Ts = 0 then
   449                     []
   450                   else
   451                     map3 (fn Ts => term_for_rep seen Ts Ts) arg_Ts arg_Rs
   452                          arg_jsss
   453                     |> mk_tuple (HOLogic.mk_tupleT uncur_arg_Ts)
   454                     |> dest_n_tuple (length uncur_arg_Ts)
   455                 val t =
   456                   if constr_s = @{const_name Abs_Frac} then
   457                     let
   458                       val num_T = body_type T
   459                       (* int -> term *)
   460                       val mk_num = HOLogic.mk_number num_T
   461                     in
   462                       case ts of
   463                         [Const (@{const_name Pair}, _) $ t1 $ t2] =>
   464                         (case snd (HOLogic.dest_number t1) of
   465                            0 => mk_num 0
   466                          | n1 => case HOLogic.dest_number t2 |> snd of
   467                                    1 => mk_num n1
   468                                  | n2 => Const (@{const_name divide},
   469                                                 num_T --> num_T --> num_T)
   470                                          $ mk_num n1 $ mk_num n2)
   471                       | _ => raise TERM ("Nitpick_Model.reconstruct_term.\
   472                                          \term_for_atom (Abs_Frac)", ts)
   473                     end
   474                   else if not for_auto andalso
   475                           (is_abs_fun thy constr_x orelse
   476                            constr_s = @{const_name Quot}) then
   477                     Const (abs_name, constr_T) $ the_single ts
   478                   else
   479                     list_comb (Const constr_x, ts)
   480               in
   481                 if maybe_cyclic then
   482                   let val var = cyclic_var () in
   483                     if elaborate andalso not standard andalso
   484                        length seen = 1 andalso
   485                        exists_subterm (fn Const (s, _) =>
   486                                           String.isPrefix cyclic_type_name s
   487                                         | t' => t' = var) t then
   488                       let val atom = cyclic_atom () in
   489                         HOLogic.mk_eq (atom, subst_atomic [(var, atom)] t)
   490                       end
   491                     else if exists_subterm (curry (op =) var) t then
   492                       if co then
   493                         Const (@{const_name The}, (T --> bool_T) --> T)
   494                         $ Abs (cyclic_co_val_name, T,
   495                                Const (@{const_name "op ="}, T --> T --> bool_T)
   496                                $ Bound 0 $ abstract_over (var, t))
   497                       else
   498                         cyclic_atom ()
   499                     else
   500                       t
   501                   end
   502                 else
   503                   t
   504               end
   505           end
   506     (* (typ * int) list -> int -> rep -> typ -> typ -> typ -> int list
   507        -> term *)
   508     and term_for_vect seen k R T1 T2 T' js =
   509       make_fun true T1 T2 T'
   510                (map (fn j => term_for_atom seen T1 T1 j k) (index_seq 0 k))
   511                (map (term_for_rep seen T2 T2 R o single)
   512                     (batch_list (arity_of_rep R) js))
   513     (* (typ * int) list -> typ -> typ -> rep -> int list list -> term *)
   514     and term_for_rep seen T T' Unit [[]] = term_for_atom seen T T' 0 1
   515       | term_for_rep seen T T' (R as Atom (k, j0)) [[j]] =
   516         if j >= j0 andalso j < j0 + k then term_for_atom seen T T' (j - j0) k
   517         else raise REP ("Nitpick_Model.reconstruct_term.term_for_rep", [R])
   518       | term_for_rep seen (Type ("*", [T1, T2])) _ (Struct [R1, R2]) [js] =
   519         let
   520           val arity1 = arity_of_rep R1
   521           val (js1, js2) = chop arity1 js
   522         in
   523           list_comb (HOLogic.pair_const T1 T2,
   524                      map3 (fn T => term_for_rep seen T T) [T1, T2] [R1, R2]
   525                           [[js1], [js2]])
   526         end
   527       | term_for_rep seen (Type ("fun", [T1, T2])) T' (R as Vect (k, R')) [js] =
   528         term_for_vect seen k R' T1 T2 T' js
   529       | term_for_rep seen (Type ("fun", [T1, T2])) T' (Func (R1, Formula Neut))
   530                      jss =
   531         let
   532           val jss1 = all_combinations_for_rep R1
   533           val ts1 = map (term_for_rep seen T1 T1 R1 o single) jss1
   534           val ts2 =
   535             map (fn js => term_for_rep seen T2 T2 (Atom (2, 0))
   536                                        [[int_for_bool (member (op =) jss js)]])
   537                 jss1
   538         in make_fun false T1 T2 T' ts1 ts2 end
   539       | term_for_rep seen (Type ("fun", [T1, T2])) T' (Func (R1, R2)) jss =
   540         let
   541           val arity1 = arity_of_rep R1
   542           val jss1 = all_combinations_for_rep R1
   543           val ts1 = map (term_for_rep seen T1 T1 R1 o single) jss1
   544           val grouped_jss2 = AList.group (op =) (map (chop arity1) jss)
   545           val ts2 = map (term_for_rep seen T2 T2 R2 o the_default []
   546                          o AList.lookup (op =) grouped_jss2) jss1
   547         in make_fun true T1 T2 T' ts1 ts2 end
   548       | term_for_rep seen T T' (Opt R) jss =
   549         if null jss then Const (unknown, T) else term_for_rep seen T T' R jss
   550       | term_for_rep seen T _ R jss =
   551         raise ARG ("Nitpick_Model.reconstruct_term.term_for_rep",
   552                    Refute.string_of_typ T ^ " " ^ string_for_rep R ^ " " ^
   553                    string_of_int (length jss))
   554   in polish_funs [] o unbit_and_unbox_term oooo term_for_rep [] end
   555 
   556 (* atom_pool -> scope -> nut list -> nut NameTable.table -> KK.raw_bound list
   557    -> nut -> term *)
   558 fun term_for_name pool scope sel_names rel_table bounds name =
   559   let val T = type_of name in
   560     tuple_list_for_name rel_table bounds name
   561     |> reconstruct_term false pool ("", "", "", "") scope sel_names rel_table
   562                         bounds T T (rep_of name)
   563   end
   564 
   565 (* Proof.context -> (string * string * string * string) * Proof.context *)
   566 fun add_wacky_syntax ctxt =
   567   let
   568     (* term -> string *)
   569     val name_of = fst o dest_Const
   570     val thy = ProofContext.theory_of ctxt |> Context.reject_draft
   571     val (maybe_t, thy) =
   572       Sign.declare_const ((@{binding nitpick_maybe}, @{typ "'a => 'a"}),
   573                           Mixfix (maybe_mixfix, [1000], 1000)) thy
   574     val (base_t, thy) =
   575       Sign.declare_const ((@{binding nitpick_base}, @{typ "'a => 'a"}),
   576                           Mixfix (base_mixfix, [1000], 1000)) thy
   577     val (step_t, thy) =
   578       Sign.declare_const ((@{binding nitpick_step}, @{typ "'a => 'a"}),
   579                           Mixfix (step_mixfix, [1000], 1000)) thy
   580     val (abs_t, thy) =
   581       Sign.declare_const ((@{binding nitpick_abs}, @{typ "'a => 'b"}),
   582                           Mixfix (abs_mixfix, [40], 40)) thy
   583   in
   584     ((name_of maybe_t, name_of base_t, name_of step_t, name_of abs_t),
   585      ProofContext.transfer_syntax thy ctxt)
   586   end
   587 
   588 (* term -> term *)
   589 fun unfold_outer_the_binders (t as Const (@{const_name The}, _)
   590                                    $ Abs (s, T, Const (@{const_name "op ="}, _)
   591                                                 $ Bound 0 $ t')) =
   592     betapply (Abs (s, T, t'), t) |> unfold_outer_the_binders
   593   | unfold_outer_the_binders t = t
   594 (* typ list -> int -> term * term -> bool *)
   595 fun bisimilar_values _ 0 _ = true
   596   | bisimilar_values coTs max_depth (t1, t2) =
   597     let val T = fastype_of t1 in
   598       if exists_subtype (member (op =) coTs) T then
   599         let
   600           val ((head1, args1), (head2, args2)) =
   601             pairself (strip_comb o unfold_outer_the_binders) (t1, t2)
   602           val max_depth = max_depth - (if member (op =) coTs T then 1 else 0)
   603         in
   604           head1 = head2 andalso
   605           forall (bisimilar_values coTs max_depth) (args1 ~~ args2)
   606         end
   607       else
   608         t1 = t2
   609     end
   610 
   611 (* params -> scope -> (term option * int list) list -> styp list -> nut list
   612   -> nut list -> nut list -> nut NameTable.table -> KK.raw_bound list
   613   -> Pretty.T * bool *)
   614 fun reconstruct_hol_model {show_skolems, show_datatypes, show_consts}
   615         ({hol_ctxt as {thy, ctxt, max_bisim_depth, boxes, stds, wfs,
   616                        user_axioms, debug, binary_ints, destroy_constrs,
   617                        specialize, skolemize, star_linear_preds, uncurry,
   618                        fast_descrs, tac_timeout, evals, case_names, def_table,
   619                        nondef_table, user_nondefs, simp_table, psimp_table,
   620                        intro_table, ground_thm_table, ersatz_table, skolems,
   621                        special_funs, unrolled_preds, wf_cache, constr_cache},
   622          card_assigns, bits, bisim_depth, datatypes, ofs} : scope)
   623         formats all_frees free_names sel_names nonsel_names rel_table bounds =
   624   let
   625     val pool = Unsynchronized.ref []
   626     val (wacky_names as (_, base_name, step_name, _), ctxt) =
   627       add_wacky_syntax ctxt
   628     val hol_ctxt =
   629       {thy = thy, ctxt = ctxt, max_bisim_depth = max_bisim_depth, boxes = boxes,
   630        stds = stds, wfs = wfs, user_axioms = user_axioms, debug = debug,
   631        binary_ints = binary_ints, destroy_constrs = destroy_constrs,
   632        specialize = specialize, skolemize = skolemize,
   633        star_linear_preds = star_linear_preds, uncurry = uncurry,
   634        fast_descrs = fast_descrs, tac_timeout = tac_timeout, evals = evals,
   635        case_names = case_names, def_table = def_table,
   636        nondef_table = nondef_table, user_nondefs = user_nondefs,
   637        simp_table = simp_table, psimp_table = psimp_table,
   638        intro_table = intro_table, ground_thm_table = ground_thm_table,
   639        ersatz_table = ersatz_table, skolems = skolems,
   640        special_funs = special_funs, unrolled_preds = unrolled_preds,
   641        wf_cache = wf_cache, constr_cache = constr_cache}
   642     val scope = {hol_ctxt = hol_ctxt, card_assigns = card_assigns,
   643                  bits = bits, bisim_depth = bisim_depth, datatypes = datatypes,
   644                  ofs = ofs}
   645     (* bool -> typ -> typ -> rep -> int list list -> term *)
   646     fun term_for_rep elaborate =
   647       reconstruct_term elaborate pool wacky_names scope sel_names rel_table
   648                        bounds
   649     (* nat -> typ -> nat -> typ *)
   650     fun nth_value_of_type card T n =
   651       term_for_rep true T T (Atom (card, 0)) [[n]]
   652     (* nat -> typ -> typ list *)
   653     fun all_values_of_type card T =
   654       index_seq 0 card |> map (nth_value_of_type card T) |> sort nice_term_ord
   655     (* dtype_spec list -> dtype_spec -> bool *)
   656     fun is_codatatype_wellformed (cos : dtype_spec list)
   657                                  ({typ, card, ...} : dtype_spec) =
   658       let
   659         val ts = all_values_of_type card typ
   660         val max_depth = Integer.sum (map #card cos)
   661       in
   662         forall (not o bisimilar_values (map #typ cos) max_depth)
   663                (all_distinct_unordered_pairs_of ts)
   664       end
   665     (* string -> Pretty.T *)
   666     fun pretty_for_assign name =
   667       let
   668         val (oper, (t1, T'), T) =
   669           case name of
   670             FreeName (s, T, _) =>
   671             let val t = Free (s, unbit_and_unbox_type T) in
   672               ("=", (t, format_term_type thy def_table formats t), T)
   673             end
   674           | ConstName (s, T, _) =>
   675             (assign_operator_for_const (s, T),
   676              user_friendly_const hol_ctxt (base_name, step_name) formats (s, T),
   677              T)
   678           | _ => raise NUT ("Nitpick_Model.reconstruct_hol_model.\
   679                             \pretty_for_assign", [name])
   680         val t2 = if rep_of name = Any then
   681                    Const (@{const_name undefined}, T')
   682                  else
   683                    tuple_list_for_name rel_table bounds name
   684                    |> term_for_rep false T T' (rep_of name)
   685       in
   686         Pretty.block (Pretty.breaks
   687             [setmp_show_all_types (Syntax.pretty_term ctxt) t1,
   688              Pretty.str oper, Syntax.pretty_term ctxt t2])
   689       end
   690     (* dtype_spec -> Pretty.T *)
   691     fun pretty_for_datatype ({typ, card, complete, ...} : dtype_spec) =
   692       Pretty.block (Pretty.breaks
   693           [Syntax.pretty_typ ctxt (unbit_and_unbox_type typ), Pretty.str "=",
   694            Pretty.enum "," "{" "}"
   695                (map (Syntax.pretty_term ctxt) (all_values_of_type card typ) @
   696                 (if complete then [] else [Pretty.str unrep]))])
   697     (* typ -> dtype_spec list *)
   698     fun integer_datatype T =
   699       [{typ = T, card = card_of_type card_assigns T, co = false,
   700         standard = true, complete = false, concrete = true, deep = true,
   701         constrs = []}]
   702       handle TYPE ("Nitpick_HOL.card_of_type", _, _) => []
   703     val (codatatypes, datatypes) =
   704       datatypes |> filter #deep |> List.partition #co
   705                 ||> append (integer_datatype nat_T @ integer_datatype int_T)
   706     val block_of_datatypes =
   707       if show_datatypes andalso not (null datatypes) then
   708         [Pretty.big_list ("Datatype" ^ plural_s_for_list datatypes ^ ":")
   709                          (map pretty_for_datatype datatypes)]
   710       else
   711         []
   712     val block_of_codatatypes =
   713       if show_datatypes andalso not (null codatatypes) then
   714         [Pretty.big_list ("Codatatype" ^ plural_s_for_list codatatypes ^ ":")
   715                          (map pretty_for_datatype codatatypes)]
   716       else
   717         []
   718     (* bool -> string -> nut list -> Pretty.T list *)
   719     fun block_of_names show title names =
   720       if show andalso not (null names) then
   721         Pretty.str (title ^ plural_s_for_list names ^ ":")
   722         :: map (Pretty.indent indent_size o pretty_for_assign)
   723                (sort_wrt (original_name o nickname_of) names)
   724       else
   725         []
   726     val (skolem_names, nonskolem_nonsel_names) =
   727       List.partition is_skolem_name nonsel_names
   728     val (eval_names, noneval_nonskolem_nonsel_names) =
   729       List.partition (String.isPrefix eval_prefix o nickname_of)
   730                      nonskolem_nonsel_names
   731       ||> filter_out (curry (op =) @{const_name bisim_iterator_max}
   732                       o nickname_of)
   733     val free_names =
   734       map (fn x as (s, T) =>
   735               case filter (curry (op =) x
   736                            o pairf nickname_of (unbit_and_unbox_type o type_of))
   737                           free_names of
   738                 [name] => name
   739               | [] => FreeName (s, T, Any)
   740               | _ => raise TERM ("Nitpick_Model.reconstruct_hol_model",
   741                                  [Const x])) all_frees
   742     val chunks = block_of_names true "Free variable" free_names @
   743                  block_of_names show_skolems "Skolem constant" skolem_names @
   744                  block_of_names true "Evaluated term" eval_names @
   745                  block_of_datatypes @ block_of_codatatypes @
   746                  block_of_names show_consts "Constant"
   747                                 noneval_nonskolem_nonsel_names
   748   in
   749     (Pretty.chunks (if null chunks then [Pretty.str "Empty assignment"]
   750                     else chunks),
   751      bisim_depth >= 0 orelse
   752      forall (is_codatatype_wellformed codatatypes) codatatypes)
   753   end
   754 
   755 (* scope -> Time.time option -> nut list -> nut list -> nut NameTable.table
   756    -> KK.raw_bound list -> term -> bool option *)
   757 fun prove_hol_model (scope as {hol_ctxt as {thy, ctxt, debug, ...},
   758                                card_assigns, ...})
   759                     auto_timeout free_names sel_names rel_table bounds prop =
   760   let
   761     val pool = Unsynchronized.ref []
   762     (* typ * int -> term *)
   763     fun free_type_assm (T, k) =
   764       let
   765         (* int -> term *)
   766         fun atom j = nth_atom pool true T j k
   767         fun equation_for_atom j = HOLogic.eq_const T $ Bound 0 $ atom j
   768         val eqs = map equation_for_atom (index_seq 0 k)
   769         val compreh_assm =
   770           Const (@{const_name All}, (T --> bool_T) --> bool_T)
   771               $ Abs ("x", T, foldl1 HOLogic.mk_disj eqs)
   772         val distinct_assm = distinctness_formula T (map atom (index_seq 0 k))
   773       in s_conj (compreh_assm, distinct_assm) end
   774     (* nut -> term *)
   775     fun free_name_assm name =
   776       HOLogic.mk_eq (Free (nickname_of name, type_of name),
   777                      term_for_name pool scope sel_names rel_table bounds name)
   778     val freeT_assms = map free_type_assm (filter (is_TFree o fst) card_assigns)
   779     val model_assms = map free_name_assm free_names
   780     val assm = foldr1 s_conj (freeT_assms @ model_assms)
   781     (* bool -> bool *)
   782     fun try_out negate =
   783       let
   784         val concl = (negate ? curry (op $) @{const Not})
   785                     (ObjectLogic.atomize_term thy prop)
   786         val prop = HOLogic.mk_Trueprop (HOLogic.mk_imp (assm, concl))
   787                    |> map_types (map_type_tfree
   788                                      (fn (s, []) => TFree (s, HOLogic.typeS)
   789                                        | x => TFree x))
   790        val _ = if debug then
   791                  priority ((if negate then "Genuineness" else "Spuriousness") ^
   792                            " goal: " ^ Syntax.string_of_term ctxt prop ^ ".")
   793                else
   794                  ()
   795         val goal = prop |> cterm_of thy |> Goal.init
   796       in
   797         (goal |> SINGLE (DETERM_TIMEOUT auto_timeout
   798                                         (auto_tac (clasimpset_of ctxt)))
   799               |> the |> Goal.finish ctxt; true)
   800         handle THM _ => false
   801              | TimeLimit.TimeOut => false
   802       end
   803   in
   804     if try_out false then SOME true
   805     else if try_out true then SOME false
   806     else NONE
   807   end
   808 
   809 end;