src/HOL/Tools/Nitpick/nitpick_model.ML
author blanchet
Thu Dec 17 15:22:11 2009 +0100 (2009-12-17)
changeset 34124 c4628a1dcf75
parent 34123 c4988215a691
child 34126 8a2c5d7aff51
permissions -rw-r--r--
added support for binary nat/int representation to Nitpick
     1 (*  Title:      HOL/Tools/Nitpick/nitpick_model.ML
     2     Author:     Jasmin Blanchette, TU Muenchen
     3     Copyright   2009
     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 type params = {
    44   show_skolems: bool,
    45   show_datatypes: bool,
    46   show_consts: bool}
    47 
    48 val unknown = "?"
    49 val unrep = "\<dots>"
    50 val maybe_mixfix = "_\<^sup>?"
    51 val base_mixfix = "_\<^bsub>base\<^esub>"
    52 val step_mixfix = "_\<^bsub>step\<^esub>"
    53 val abs_mixfix = "\<guillemotleft>_\<guillemotright>"
    54 val non_opt_name = nitpick_prefix ^ "non_opt"
    55 
    56 (* string -> int -> string *)
    57 fun atom_suffix s j =
    58   nat_subscript (j + 1)
    59   |> (s <> "" andalso Symbol.is_ascii_digit (List.last (explode s)))
    60      ? prefix "\<^isub>,"
    61 (* string -> typ -> int -> string *)
    62 fun atom_name prefix (T as Type (s, _)) j =
    63     prefix ^ substring (shortest_name s, 0, 1) ^ atom_suffix s j
    64   | atom_name prefix (T as TFree (s, _)) j =
    65     prefix ^ perhaps (try (unprefix "'")) s ^ atom_suffix s j
    66   | atom_name _ T _ = raise TYPE ("Nitpick_Model.atom_name", [T], [])
    67 (* bool -> typ -> int -> term *)
    68 fun atom for_auto T j =
    69   if for_auto then
    70     Free (atom_name (hd (space_explode "." nitpick_prefix)) T j, T)
    71   else
    72     Const (atom_name "" T j, T)
    73 
    74 (* term * term -> order *)
    75 fun nice_term_ord (Abs (_, _, t1), Abs (_, _, t2)) = nice_term_ord (t1, t2)
    76   | nice_term_ord (t1, t2) =
    77     int_ord (snd (HOLogic.dest_number t1), snd (HOLogic.dest_number t2))
    78     handle TERM ("dest_number", _) =>
    79            case (t1, t2) of
    80              (t11 $ t12, t21 $ t22) =>
    81              (case nice_term_ord (t11, t21) of
    82                 EQUAL => nice_term_ord (t12, t22)
    83               | ord => ord)
    84            | _ => TermOrd.term_ord (t1, t2)
    85 
    86 (* nut NameTable.table -> Kodkod.raw_bound list -> nut -> int list list *)
    87 fun tuple_list_for_name rel_table bounds name =
    88   the (AList.lookup (op =) bounds (the_rel rel_table name)) handle NUT _ => [[]]
    89 
    90 (* term -> term *)
    91 fun unbit_and_unbox_term (Const (@{const_name FunBox}, _) $ t1) =
    92     unbit_and_unbox_term t1
    93   | unbit_and_unbox_term (Const (@{const_name PairBox},
    94                           Type ("fun", [T1, Type ("fun", [T2, T3])]))
    95                           $ t1 $ t2) =
    96     let val Ts = map unbit_and_unbox_type [T1, T2] in
    97       Const (@{const_name Pair}, Ts ---> Type ("*", Ts))
    98       $ unbit_and_unbox_term t1 $ unbit_and_unbox_term t2
    99     end
   100   | unbit_and_unbox_term (Const (s, T)) = Const (s, unbit_and_unbox_type T)
   101   | unbit_and_unbox_term (t1 $ t2) =
   102     unbit_and_unbox_term t1 $ unbit_and_unbox_term t2
   103   | unbit_and_unbox_term (Free (s, T)) = Free (s, unbit_and_unbox_type T)
   104   | unbit_and_unbox_term (Var (x, T)) = Var (x, unbit_and_unbox_type T)
   105   | unbit_and_unbox_term (Bound j) = Bound j
   106   | unbit_and_unbox_term (Abs (s, T, t')) =
   107     Abs (s, unbit_and_unbox_type T, unbit_and_unbox_term t')
   108 
   109 (* typ -> typ -> (typ * typ) * (typ * typ) *)
   110 fun factor_out_types (T1 as Type ("*", [T11, T12]))
   111                      (T2 as Type ("*", [T21, T22])) =
   112     let val (n1, n2) = pairself num_factors_in_type (T11, T21) in
   113       if n1 = n2 then
   114         let
   115           val ((T11', opt_T12'), (T21', opt_T22')) = factor_out_types T12 T22
   116         in
   117           ((Type ("*", [T11, T11']), opt_T12'),
   118            (Type ("*", [T21, T21']), opt_T22'))
   119         end
   120       else if n1 < n2 then
   121         case factor_out_types T1 T21 of
   122           (p1, (T21', NONE)) => (p1, (T21', SOME T22))
   123         | (p1, (T21', SOME T22')) =>
   124           (p1, (T21', SOME (Type ("*", [T22', T22]))))
   125       else
   126         swap (factor_out_types T2 T1)
   127     end
   128   | factor_out_types (Type ("*", [T11, T12])) T2 = ((T11, SOME T12), (T2, NONE))
   129   | factor_out_types T1 (Type ("*", [T21, T22])) = ((T1, NONE), (T21, SOME T22))
   130   | factor_out_types T1 T2 = ((T1, NONE), (T2, NONE))
   131 
   132 (* bool -> typ -> typ -> (term * term) list -> term *)
   133 fun make_plain_fun maybe_opt T1 T2 =
   134   let
   135     (* typ -> typ -> (term * term) list -> term *)
   136     fun aux T1 T2 [] =
   137         Const (if maybe_opt orelse T2 <> bool_T then @{const_name undefined}
   138                else non_opt_name, T1 --> T2)
   139       | aux T1 T2 ((t1, t2) :: ps) =
   140         Const (@{const_name fun_upd}, (T1 --> T2) --> T1 --> T2 --> T1 --> T2)
   141         $ aux T1 T2 ps $ t1 $ t2
   142   in aux T1 T2 o rev end
   143 (* term -> bool *)
   144 fun is_plain_fun (Const (s, _)) =
   145     (s = @{const_name undefined} orelse s = non_opt_name)
   146   | is_plain_fun (Const (@{const_name fun_upd}, _) $ t0 $ _ $ _) =
   147     is_plain_fun t0
   148   | is_plain_fun _ = false
   149 (* term -> bool * (term list * term list) *)
   150 val dest_plain_fun =
   151   let
   152     (* term -> term list * term list *)
   153     fun aux (Const (s, _)) = (s <> non_opt_name, ([], []))
   154       | aux (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =
   155         let val (s, (ts1, ts2)) = aux t0 in (s, (t1 :: ts1, t2 :: ts2)) end
   156       | aux t = raise TERM ("Nitpick_Model.dest_plain_fun", [t])
   157   in apsnd (pairself rev) o aux end
   158 
   159 (* typ -> typ -> typ -> term -> term * term *)
   160 fun break_in_two T T1 T2 t =
   161   let
   162     val ps = HOLogic.flat_tupleT_paths T
   163     val cut = length (HOLogic.strip_tupleT T1)
   164     val (ps1, ps2) = pairself HOLogic.flat_tupleT_paths (T1, T2)
   165     val (ts1, ts2) = t |> HOLogic.strip_ptuple ps |> chop cut
   166   in (HOLogic.mk_ptuple ps1 T1 ts1, HOLogic.mk_ptuple ps2 T2 ts2) end
   167 (* typ -> term -> term -> term *)
   168 fun pair_up (Type ("*", [T1', T2']))
   169             (t1 as Const (@{const_name Pair},
   170                           Type ("fun", [_, Type ("fun", [_, T1])])) $ t11 $ t12)
   171             t2 =
   172     if T1 = T1' then HOLogic.mk_prod (t1, t2)
   173     else HOLogic.mk_prod (t11, pair_up T2' t12 t2)
   174   | pair_up _ t1 t2 = HOLogic.mk_prod (t1, t2)
   175 (* typ -> term -> term list * term list -> (term * term) list*)
   176 fun multi_pair_up T1 t1 (ts2, ts3) = map2 (pair o pair_up T1 t1) ts2 ts3
   177 
   178 (* typ -> typ -> typ -> term -> term *)
   179 fun typecast_fun (Type ("fun", [T1', T2'])) T1 T2 t =
   180     let
   181       (* typ -> typ -> typ -> typ -> term -> term *)
   182       fun do_curry T1 T1a T1b T2 t =
   183         let
   184           val (maybe_opt, ps) = dest_plain_fun t
   185           val ps =
   186             ps |>> map (break_in_two T1 T1a T1b)
   187                |> uncurry (map2 (fn (t1a, t1b) => fn t2 => (t1a, (t1b, t2))))
   188                |> AList.coalesce (op =)
   189                |> map (apsnd (make_plain_fun maybe_opt T1b T2))
   190         in make_plain_fun maybe_opt T1a (T1b --> T2) ps end
   191       (* typ -> typ -> term -> term *)
   192       and do_uncurry T1 T2 t =
   193         let
   194           val (maybe_opt, tsp) = dest_plain_fun t
   195           val ps =
   196             tsp |> op ~~
   197                 |> maps (fn (t1, t2) =>
   198                             multi_pair_up T1 t1 (snd (dest_plain_fun t2)))
   199         in make_plain_fun maybe_opt T1 T2 ps end
   200       (* typ -> typ -> typ -> typ -> term -> term *)
   201       and do_arrow T1' T2' _ _ (Const (s, _)) = Const (s, T1' --> T2')
   202         | do_arrow T1' T2' T1 T2
   203                    (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =
   204           Const (@{const_name fun_upd},
   205                  (T1' --> T2') --> T1' --> T2' --> T1' --> T2')
   206           $ do_arrow T1' T2' T1 T2 t0 $ do_term T1' T1 t1 $ do_term T2' T2 t2
   207         | do_arrow _ _ _ _ t =
   208           raise TERM ("Nitpick_Model.typecast_fun.do_arrow", [t])
   209       and do_fun T1' T2' T1 T2 t =
   210         case factor_out_types T1' T1 of
   211           ((_, NONE), (_, NONE)) => t |> do_arrow T1' T2' T1 T2
   212         | ((_, NONE), (T1a, SOME T1b)) =>
   213           t |> do_curry T1 T1a T1b T2 |> do_arrow T1' T2' T1a (T1b --> T2)
   214         | ((T1a', SOME T1b'), (_, NONE)) =>
   215           t |> do_arrow T1a' (T1b' --> T2') T1 T2 |> do_uncurry T1' T2'
   216         | _ => raise TYPE ("Nitpick_Model.typecast_fun.do_fun", [T1, T1'], [])
   217       (* typ -> typ -> term -> term *)
   218       and do_term (Type ("fun", [T1', T2'])) (Type ("fun", [T1, T2])) t =
   219           do_fun T1' T2' T1 T2 t
   220         | do_term (T' as Type ("*", Ts' as [T1', T2'])) (Type ("*", [T1, T2]))
   221                   (Const (@{const_name Pair}, _) $ t1 $ t2) =
   222           Const (@{const_name Pair}, Ts' ---> T')
   223           $ do_term T1' T1 t1 $ do_term T2' T2 t2
   224         | do_term T' T t =
   225           if T = T' then t
   226           else raise TYPE ("Nitpick_Model.typecast_fun.do_term", [T, T'], [])
   227     in if T1' = T1 andalso T2' = T2 then t else do_fun T1' T2' T1 T2 t end
   228   | typecast_fun T' _ _ _ = raise TYPE ("Nitpick_Model.typecast_fun", [T'], [])
   229 
   230 (* term -> string *)
   231 fun truth_const_sort_key @{const True} = "0"
   232   | truth_const_sort_key @{const False} = "2"
   233   | truth_const_sort_key _ = "1"
   234 
   235 (* typ -> term list -> term *)
   236 fun mk_tuple (Type ("*", [T1, T2])) ts =
   237     HOLogic.mk_prod (mk_tuple T1 ts,
   238         mk_tuple T2 (List.drop (ts, length (HOLogic.flatten_tupleT T1))))
   239   | mk_tuple _ (t :: _) = t
   240   | mk_tuple T [] = raise TYPE ("Nitpick_Model.mk_tuple", [T], [])
   241 
   242 (* string * string * string * string -> scope -> nut list -> nut list
   243    -> nut list -> nut NameTable.table -> Kodkod.raw_bound list -> typ -> typ
   244    -> rep -> int list list -> term *)
   245 fun reconstruct_term (maybe_name, base_name, step_name, abs_name)
   246         ({ext_ctxt as {thy, ctxt, ...}, card_assigns, bits, datatypes, ofs, ...}
   247          : scope) sel_names rel_table bounds =
   248   let
   249     val for_auto = (maybe_name = "")
   250     (* int list list -> int *)
   251     fun value_of_bits jss =
   252       let
   253         val j0 = offset_of_type ofs @{typ unsigned_bit}
   254         val js = map (Integer.add (~ j0) o the_single) jss
   255       in
   256         fold (fn j => Integer.add (reasonable_power 2 j |> j = bits ? op ~))
   257              js 0
   258       end
   259     (* bool -> typ -> typ -> (term * term) list -> term *)
   260     fun make_set maybe_opt T1 T2 =
   261       let
   262         val empty_const = Const (@{const_name Set.empty}, T1 --> T2)
   263         val insert_const = Const (@{const_name insert},
   264                                   T1 --> (T1 --> T2) --> T1 --> T2)
   265         (* (term * term) list -> term *)
   266         fun aux [] =
   267             if maybe_opt andalso not (is_complete_type datatypes T1) then
   268               insert_const $ Const (unrep, T1) $ empty_const
   269             else
   270               empty_const
   271           | aux ((t1, t2) :: zs) =
   272             aux zs |> t2 <> @{const False}
   273                       ? curry (op $) (insert_const
   274                                       $ (t1 |> t2 <> @{const True}
   275                                                ? curry (op $)
   276                                                        (Const (maybe_name,
   277                                                                T1 --> T1))))
   278       in aux end
   279     (* typ -> typ -> typ -> (term * term) list -> term *)
   280     fun make_map T1 T2 T2' =
   281       let
   282         val update_const = Const (@{const_name fun_upd},
   283                                   (T1 --> T2) --> T1 --> T2 --> T1 --> T2)
   284         (* (term * term) list -> term *)
   285         fun aux' [] = Const (@{const_name Map.empty}, T1 --> T2)
   286           | aux' ((t1, t2) :: ps) =
   287             (case t2 of
   288                Const (@{const_name None}, _) => aux' ps
   289              | _ => update_const $ aux' ps $ t1 $ t2)
   290         fun aux ps =
   291           if not (is_complete_type datatypes T1) then
   292             update_const $ aux' ps $ Const (unrep, T1)
   293             $ (Const (@{const_name Some}, T2' --> T2) $ Const (unknown, T2'))
   294           else
   295             aux' ps
   296       in aux end
   297     (* typ list -> term -> term *)
   298     fun setify_mapify_funs Ts t =
   299       (case fastype_of1 (Ts, t) of
   300          Type ("fun", [T1, T2]) =>
   301          if is_plain_fun t then
   302            case T2 of
   303              @{typ bool} =>
   304              let
   305                val (maybe_opt, ts_pair) =
   306                  dest_plain_fun t ||> pairself (map (setify_mapify_funs Ts))
   307              in
   308                make_set maybe_opt T1 T2
   309                         (sort_wrt (truth_const_sort_key o snd) (op ~~ ts_pair))
   310              end
   311            | Type (@{type_name option}, [T2']) =>
   312              let
   313                val ts_pair = snd (dest_plain_fun t)
   314                              |> pairself (map (setify_mapify_funs Ts))
   315              in make_map T1 T2 T2' (rev (op ~~ ts_pair)) end
   316            | _ => raise SAME ()
   317          else
   318            raise SAME ()
   319        | _ => raise SAME ())
   320       handle SAME () =>
   321              case t of
   322                t1 $ t2 => setify_mapify_funs Ts t1 $ setify_mapify_funs Ts t2
   323              | Abs (s, T, t') => Abs (s, T, setify_mapify_funs (T :: Ts) t')
   324              | _ => t
   325     (* bool -> typ -> typ -> typ -> term list -> term list -> term *)
   326     fun make_fun maybe_opt T1 T2 T' ts1 ts2 =
   327       ts1 ~~ ts2 |> T1 = @{typ bisim_iterator} ? rev
   328                  |> make_plain_fun (maybe_opt andalso not for_auto) T1 T2
   329                  |> unbit_and_unbox_term
   330                  |> typecast_fun (unbit_and_unbox_type T')
   331                                  (unbit_and_unbox_type T1)
   332                                  (unbit_and_unbox_type T2)
   333     (* (typ * int) list -> typ -> typ -> int -> term *)
   334     fun term_for_atom seen (T as Type ("fun", [T1, T2])) T' j =
   335         let
   336           val k1 = card_of_type card_assigns T1
   337           val k2 = card_of_type card_assigns T2
   338         in
   339           term_for_rep seen T T' (Vect (k1, Atom (k2, 0)))
   340                        [nth_combination (replicate k1 (k2, 0)) j]
   341           handle General.Subscript =>
   342                  raise ARG ("Nitpick_Model.reconstruct_term.term_for_atom",
   343                             signed_string_of_int j ^ " for " ^
   344                             string_for_rep (Vect (k1, Atom (k2, 0))))
   345         end
   346       | term_for_atom seen (Type ("*", [T1, T2])) _ j =
   347         let val k1 = card_of_type card_assigns T1 in
   348           list_comb (HOLogic.pair_const T1 T2,
   349                      map2 (fn T => term_for_atom seen T T) [T1, T2]
   350                           [j div k1, j mod k1])
   351         end
   352       | term_for_atom seen @{typ prop} _ j =
   353         HOLogic.mk_Trueprop (term_for_atom seen bool_T bool_T j)
   354       | term_for_atom _ @{typ bool} _ j =
   355         if j = 0 then @{const False} else @{const True}
   356       | term_for_atom _ @{typ unit} _ _ = @{const Unity}
   357       | term_for_atom seen T _ j =
   358         if T = nat_T then
   359           HOLogic.mk_number nat_T j
   360         else if T = int_T then
   361           HOLogic.mk_number int_T
   362               (int_for_atom (card_of_type card_assigns int_T, 0) j)
   363         else if is_fp_iterator_type T then
   364           HOLogic.mk_number nat_T (card_of_type card_assigns T - j - 1)
   365         else if T = @{typ bisim_iterator} then
   366           HOLogic.mk_number nat_T j
   367         else case datatype_spec datatypes T of
   368           NONE => atom for_auto T j
   369         | SOME {shallow = true, ...} => atom for_auto T j
   370         | SOME {co, constrs, ...} =>
   371           let
   372             (* styp -> int list *)
   373             fun tuples_for_const (s, T) =
   374               tuple_list_for_name rel_table bounds (ConstName (s, T, Any))
   375             (* unit -> indexname * typ *)
   376             fun var () = ((atom_name "" T j, 0), T)
   377             val discr_jsss = map (tuples_for_const o discr_for_constr o #const)
   378                                  constrs
   379             val real_j = j + offset_of_type ofs T
   380             val constr_x as (constr_s, constr_T) =
   381               get_first (fn (jss, {const, ...}) =>
   382                             if member (op =) jss [real_j] then SOME const
   383                             else NONE)
   384                         (discr_jsss ~~ constrs) |> the
   385             val arg_Ts = curried_binder_types constr_T
   386             val sel_xs = map (boxed_nth_sel_for_constr ext_ctxt constr_x)
   387                              (index_seq 0 (length arg_Ts))
   388             val sel_Rs =
   389               map (fn x => get_first
   390                                (fn ConstName (s', T', R) =>
   391                                    if (s', T') = x then SOME R else NONE
   392                                  | u => raise NUT ("Nitpick_Model.reconstruct_\
   393                                                    \term.term_for_atom", [u]))
   394                                sel_names |> the) sel_xs
   395             val arg_Rs = map (snd o dest_Func) sel_Rs
   396             val sel_jsss = map tuples_for_const sel_xs
   397             val arg_jsss =
   398               map (map_filter (fn js => if hd js = real_j then SOME (tl js)
   399                                         else NONE)) sel_jsss
   400             val uncur_arg_Ts = binder_types constr_T
   401           in
   402             if co andalso member (op =) seen (T, j) then
   403               Var (var ())
   404             else if constr_s = @{const_name Word} then
   405               HOLogic.mk_number
   406                   (if T = @{typ "unsigned_bit word"} then nat_T else int_T)
   407                   (value_of_bits (the_single arg_jsss))
   408             else
   409               let
   410                 val seen = seen |> co ? cons (T, j)
   411                 val ts =
   412                   if length arg_Ts = 0 then
   413                     []
   414                   else
   415                     map3 (fn Ts => term_for_rep seen Ts Ts) arg_Ts arg_Rs
   416                          arg_jsss
   417                     |> mk_tuple (HOLogic.mk_tupleT uncur_arg_Ts)
   418                     |> dest_n_tuple (length uncur_arg_Ts)
   419                 val t =
   420                   if constr_s = @{const_name Abs_Frac} then
   421                     let
   422                       val num_T = body_type T
   423                       (* int -> term *)
   424                       val mk_num = HOLogic.mk_number num_T
   425                     in
   426                       case ts of
   427                         [Const (@{const_name Pair}, _) $ t1 $ t2] =>
   428                         (case snd (HOLogic.dest_number t1) of
   429                            0 => mk_num 0
   430                          | n1 => case HOLogic.dest_number t2 |> snd of
   431                                    1 => mk_num n1
   432                                  | n2 => Const (@{const_name HOL.divide},
   433                                                 num_T --> num_T --> num_T)
   434                                          $ mk_num n1 $ mk_num n2)
   435                       | _ => raise TERM ("Nitpick_Model.reconstruct_term.term_\
   436                                          \for_atom (Abs_Frac)", ts)
   437                     end
   438                   else if not for_auto andalso is_abs_fun thy constr_x then
   439                     Const (abs_name, constr_T) $ the_single ts
   440                   else
   441                     list_comb (Const constr_x, ts)
   442               in
   443                 if co then
   444                   let val var = var () in
   445                     if exists_subterm (curry (op =) (Var var)) t then
   446                       Const (@{const_name The}, (T --> bool_T) --> T)
   447                       $ Abs ("\<omega>", T,
   448                              Const (@{const_name "op ="}, T --> T --> bool_T)
   449                              $ Bound 0 $ abstract_over (Var var, t))
   450                     else
   451                       t
   452                   end
   453                 else
   454                   t
   455               end
   456           end
   457     (* (typ * int) list -> int -> rep -> typ -> typ -> typ -> int list
   458        -> term *)
   459     and term_for_vect seen k R T1 T2 T' js =
   460       make_fun true T1 T2 T' (map (term_for_atom seen T1 T1) (index_seq 0 k))
   461                (map (term_for_rep seen T2 T2 R o single)
   462                     (batch_list (arity_of_rep R) js))
   463     (* (typ * int) list -> typ -> typ -> rep -> int list list -> term *)
   464     and term_for_rep seen T T' Unit [[]] = term_for_atom seen T T' 0
   465       | term_for_rep seen T T' (R as Atom (k, j0)) [[j]] =
   466         if j >= j0 andalso j < j0 + k then term_for_atom seen T T' (j - j0)
   467         else raise REP ("Nitpick_Model.reconstruct_term.term_for_rep", [R])
   468       | term_for_rep seen (Type ("*", [T1, T2])) _ (Struct [R1, R2]) [js] =
   469         let
   470           val arity1 = arity_of_rep R1
   471           val (js1, js2) = chop arity1 js
   472         in
   473           list_comb (HOLogic.pair_const T1 T2,
   474                      map3 (fn T => term_for_rep seen T T) [T1, T2] [R1, R2]
   475                           [[js1], [js2]])
   476         end
   477       | term_for_rep seen (Type ("fun", [T1, T2])) T' (R as Vect (k, R')) [js] =
   478         term_for_vect seen k R' T1 T2 T' js
   479       | term_for_rep seen (Type ("fun", [T1, T2])) T' (Func (R1, Formula Neut))
   480                      jss =
   481         let
   482           val jss1 = all_combinations_for_rep R1
   483           val ts1 = map (term_for_rep seen T1 T1 R1 o single) jss1
   484           val ts2 =
   485             map (fn js => term_for_rep seen T2 T2 (Atom (2, 0))
   486                                        [[int_for_bool (member (op =) jss js)]])
   487                 jss1
   488         in make_fun false T1 T2 T' ts1 ts2 end
   489       | term_for_rep seen (Type ("fun", [T1, T2])) T' (Func (R1, R2)) jss =
   490         let
   491           val arity1 = arity_of_rep R1
   492           val jss1 = all_combinations_for_rep R1
   493           val ts1 = map (term_for_rep seen T1 T1 R1 o single) jss1
   494           val grouped_jss2 = AList.group (op =) (map (chop arity1) jss)
   495           val ts2 = map (term_for_rep seen T2 T2 R2 o the_default []
   496                          o AList.lookup (op =) grouped_jss2) jss1
   497         in make_fun true T1 T2 T' ts1 ts2 end
   498       | term_for_rep seen T T' (Opt R) jss =
   499         if null jss then Const (unknown, T) else term_for_rep seen T T' R jss
   500       | term_for_rep seen T _ R jss =
   501         raise ARG ("Nitpick_Model.reconstruct_term.term_for_rep",
   502                    Refute.string_of_typ T ^ " " ^ string_for_rep R ^ " " ^
   503                    string_of_int (length jss))
   504   in
   505     (not for_auto ? setify_mapify_funs []) o unbit_and_unbox_term
   506     oooo term_for_rep []
   507   end
   508 
   509 (* scope -> nut list -> nut NameTable.table -> Kodkod.raw_bound list -> nut
   510    -> term *)
   511 fun term_for_name scope sel_names rel_table bounds name =
   512   let val T = type_of name in
   513     tuple_list_for_name rel_table bounds name
   514     |> reconstruct_term ("", "", "", "") scope sel_names rel_table bounds T T
   515                         (rep_of name)
   516   end
   517 
   518 (* Proof.context
   519    -> (string * string * string * string * string) * Proof.context *)
   520 fun add_wacky_syntax ctxt =
   521   let
   522     (* term -> string *)
   523     val name_of = fst o dest_Const
   524     val thy = ProofContext.theory_of ctxt |> Context.reject_draft
   525     val (maybe_t, thy) =
   526       Sign.declare_const ((@{binding nitpick_maybe}, @{typ "'a => 'a"}),
   527                           Mixfix (maybe_mixfix, [1000], 1000)) thy
   528     val (base_t, thy) =
   529       Sign.declare_const ((@{binding nitpick_base}, @{typ "'a => 'a"}),
   530                           Mixfix (base_mixfix, [1000], 1000)) thy
   531     val (step_t, thy) =
   532       Sign.declare_const ((@{binding nitpick_step}, @{typ "'a => 'a"}),
   533                           Mixfix (step_mixfix, [1000], 1000)) thy
   534     val (abs_t, thy) =
   535       Sign.declare_const ((@{binding nitpick_abs}, @{typ "'a => 'b"}),
   536                           Mixfix (abs_mixfix, [40], 40)) thy
   537   in
   538     ((name_of maybe_t, name_of base_t, name_of step_t, name_of abs_t),
   539      ProofContext.transfer_syntax thy ctxt)
   540   end
   541 
   542 (* term -> term *)
   543 fun unfold_outer_the_binders (t as Const (@{const_name The}, _)
   544                                    $ Abs (s, T, Const (@{const_name "op ="}, _)
   545                                                 $ Bound 0 $ t')) =
   546     betapply (Abs (s, T, t'), t) |> unfold_outer_the_binders
   547   | unfold_outer_the_binders t = t
   548 (* typ list -> int -> term * term -> bool *)
   549 fun bisimilar_values _ 0 _ = true
   550   | bisimilar_values coTs max_depth (t1, t2) =
   551     let val T = fastype_of t1 in
   552       if exists_subtype (member (op =) coTs) T then
   553         let
   554           val ((head1, args1), (head2, args2)) =
   555             pairself (strip_comb o unfold_outer_the_binders) (t1, t2)
   556           val max_depth = max_depth - (if member (op =) coTs T then 1 else 0)
   557         in
   558           head1 = head2
   559           andalso forall (bisimilar_values coTs max_depth) (args1 ~~ args2)
   560         end
   561       else
   562         t1 = t2
   563     end
   564 
   565 (* params -> scope -> (term option * int list) list -> styp list -> nut list
   566   -> nut list -> nut list -> nut NameTable.table -> Kodkod.raw_bound list
   567   -> Pretty.T * bool *)
   568 fun reconstruct_hol_model {show_skolems, show_datatypes, show_consts}
   569         ({ext_ctxt as {thy, ctxt, max_bisim_depth, boxes, wfs, user_axioms,
   570                        debug, binary_ints, destroy_constrs, specialize,
   571                        skolemize, star_linear_preds, uncurry, fast_descrs,
   572                        tac_timeout, evals, case_names, def_table, nondef_table,
   573                        user_nondefs, simp_table, psimp_table, intro_table,
   574                        ground_thm_table, ersatz_table, skolems, special_funs,
   575                        unrolled_preds, wf_cache, constr_cache},
   576          card_assigns, bits, bisim_depth, datatypes, ofs} : scope)
   577         formats all_frees free_names sel_names nonsel_names rel_table bounds =
   578   let
   579     val (wacky_names as (_, base_name, step_name, _), ctxt) =
   580       add_wacky_syntax ctxt
   581     val ext_ctxt =
   582       {thy = thy, ctxt = ctxt, max_bisim_depth = max_bisim_depth, boxes = boxes,
   583        wfs = wfs, user_axioms = user_axioms, debug = debug,
   584        binary_ints = binary_ints, destroy_constrs = destroy_constrs,
   585        specialize = specialize, skolemize = skolemize,
   586        star_linear_preds = star_linear_preds, uncurry = uncurry,
   587        fast_descrs = fast_descrs, tac_timeout = tac_timeout, evals = evals,
   588        case_names = case_names, def_table = def_table,
   589        nondef_table = nondef_table, user_nondefs = user_nondefs,
   590        simp_table = simp_table, psimp_table = psimp_table,
   591        intro_table = intro_table, ground_thm_table = ground_thm_table,
   592        ersatz_table = ersatz_table, skolems = skolems,
   593        special_funs = special_funs, unrolled_preds = unrolled_preds,
   594        wf_cache = wf_cache, constr_cache = constr_cache}
   595     val scope = {ext_ctxt = ext_ctxt, card_assigns = card_assigns,
   596                  bits = bits, bisim_depth = bisim_depth, datatypes = datatypes,
   597                  ofs = ofs}
   598     (* typ -> typ -> rep -> int list list -> term *)
   599     val term_for_rep = reconstruct_term wacky_names scope sel_names rel_table
   600                                         bounds
   601     (* nat -> typ -> nat -> typ *)
   602     fun nth_value_of_type card T n = term_for_rep T T (Atom (card, 0)) [[n]]
   603     (* nat -> typ -> typ list *)
   604     fun all_values_of_type card T =
   605       index_seq 0 card |> map (nth_value_of_type card T) |> sort nice_term_ord
   606     (* dtype_spec list -> dtype_spec -> bool *)
   607     fun is_codatatype_wellformed (cos : dtype_spec list)
   608                                  ({typ, card, ...} : dtype_spec) =
   609       let
   610         val ts = all_values_of_type card typ
   611         val max_depth = Integer.sum (map #card cos)
   612       in
   613         forall (not o bisimilar_values (map #typ cos) max_depth)
   614                (all_distinct_unordered_pairs_of ts)
   615       end
   616     (* string -> Pretty.T *)
   617     fun pretty_for_assign name =
   618       let
   619         val (oper, (t1, T'), T) =
   620           case name of
   621             FreeName (s, T, _) =>
   622             let val t = Free (s, unbit_and_unbox_type T) in
   623               ("=", (t, format_term_type thy def_table formats t), T)
   624             end
   625           | ConstName (s, T, _) =>
   626             (assign_operator_for_const (s, T),
   627              user_friendly_const ext_ctxt (base_name, step_name) formats (s, T),
   628              T)
   629           | _ => raise NUT ("Nitpick_Model.reconstruct_hol_model.\
   630                             \pretty_for_assign", [name])
   631         val t2 = if rep_of name = Any then
   632                    Const (@{const_name undefined}, T')
   633                  else
   634                    tuple_list_for_name rel_table bounds name
   635                    |> term_for_rep T T' (rep_of name)
   636       in
   637         Pretty.block (Pretty.breaks
   638             [setmp_show_all_types (Syntax.pretty_term ctxt) t1,
   639              Pretty.str oper, Syntax.pretty_term ctxt t2])
   640       end
   641     (* dtype_spec -> Pretty.T *)
   642     fun pretty_for_datatype ({typ, card, complete, ...} : dtype_spec) =
   643       Pretty.block (Pretty.breaks
   644           [Syntax.pretty_typ ctxt (unbit_and_unbox_type typ), Pretty.str "=",
   645            Pretty.enum "," "{" "}"
   646                (map (Syntax.pretty_term ctxt) (all_values_of_type card typ)
   647                 @ (if complete then [] else [Pretty.str unrep]))])
   648     (* typ -> dtype_spec list *)
   649     fun integer_datatype T =
   650       [{typ = T, card = card_of_type card_assigns T, co = false,
   651         complete = false, concrete = true, shallow = false, constrs = []}]
   652       handle TYPE ("Nitpick_HOL.card_of_type", _, _) => []
   653     val (codatatypes, datatypes) =
   654       datatypes |> filter_out #shallow
   655                 |> List.partition #co
   656                 ||> append (integer_datatype nat_T @ integer_datatype int_T)
   657     val block_of_datatypes =
   658       if show_datatypes andalso not (null datatypes) then
   659         [Pretty.big_list ("Datatype" ^ plural_s_for_list datatypes ^ ":")
   660                          (map pretty_for_datatype datatypes)]
   661       else
   662         []
   663     val block_of_codatatypes =
   664       if show_datatypes andalso not (null codatatypes) then
   665         [Pretty.big_list ("Codatatype" ^ plural_s_for_list codatatypes ^ ":")
   666                          (map pretty_for_datatype codatatypes)]
   667       else
   668         []
   669     (* bool -> string -> nut list -> Pretty.T list *)
   670     fun block_of_names show title names =
   671       if show andalso not (null names) then
   672         Pretty.str (title ^ plural_s_for_list names ^ ":")
   673         :: map (Pretty.indent indent_size o pretty_for_assign)
   674                (sort_wrt (original_name o nickname_of) names)
   675       else
   676         []
   677     val (skolem_names, nonskolem_nonsel_names) =
   678       List.partition is_skolem_name nonsel_names
   679     val (eval_names, noneval_nonskolem_nonsel_names) =
   680       List.partition (String.isPrefix eval_prefix o nickname_of)
   681                      nonskolem_nonsel_names
   682       ||> filter_out (curry (op =) @{const_name bisim_iterator_max}
   683                       o nickname_of)
   684     val free_names =
   685       map (fn x as (s, T) =>
   686               case filter (curry (op =) x
   687                            o pairf nickname_of (unbit_and_unbox_type o type_of))
   688                           free_names of
   689                 [name] => name
   690               | [] => FreeName (s, T, Any)
   691               | _ => raise TERM ("Nitpick_Model.reconstruct_hol_model",
   692                                  [Const x])) all_frees
   693     val chunks = block_of_names true "Free variable" free_names @
   694                  block_of_names show_skolems "Skolem constant" skolem_names @
   695                  block_of_names true "Evaluated term" eval_names @
   696                  block_of_datatypes @ block_of_codatatypes @
   697                  block_of_names show_consts "Constant"
   698                                 noneval_nonskolem_nonsel_names
   699   in
   700     (Pretty.chunks (if null chunks then [Pretty.str "Empty assignment"]
   701                     else chunks),
   702      bisim_depth >= 0
   703      orelse forall (is_codatatype_wellformed codatatypes) codatatypes)
   704   end
   705 
   706 (* scope -> Time.time option -> nut list -> nut list -> nut NameTable.table
   707    -> Kodkod.raw_bound list -> term -> bool option *)
   708 fun prove_hol_model (scope as {ext_ctxt as {thy, ctxt, ...}, card_assigns, ...})
   709                     auto_timeout free_names sel_names rel_table bounds prop =
   710   let
   711     (* typ * int -> term *)
   712     fun free_type_assm (T, k) =
   713       let
   714         (* int -> term *)
   715         val atom = atom true T
   716         fun equation_for_atom j = HOLogic.eq_const T $ Bound 0 $ atom j
   717         val eqs = map equation_for_atom (index_seq 0 k)
   718         val compreh_assm =
   719           Const (@{const_name All}, (T --> bool_T) --> bool_T)
   720               $ Abs ("x", T, foldl1 HOLogic.mk_disj eqs)
   721         val distinct_assm = distinctness_formula T (map atom (index_seq 0 k))
   722       in HOLogic.mk_conj (compreh_assm, distinct_assm) end
   723     (* nut -> term *)
   724     fun free_name_assm name =
   725       HOLogic.mk_eq (Free (nickname_of name, type_of name),
   726                      term_for_name scope sel_names rel_table bounds name)
   727     val freeT_assms = map free_type_assm (filter (is_TFree o fst) card_assigns)
   728     val model_assms = map free_name_assm free_names
   729     val assm = List.foldr HOLogic.mk_conj @{const True}
   730                           (freeT_assms @ model_assms)
   731     (* bool -> bool *)
   732     fun try_out negate =
   733       let
   734         val concl = (negate ? curry (op $) @{const Not})
   735                     (ObjectLogic.atomize_term thy prop)
   736         val goal = HOLogic.mk_Trueprop (HOLogic.mk_imp (assm, concl))
   737                    |> map_types (map_type_tfree
   738                           (fn (s, []) => TFree (s, HOLogic.typeS)
   739                             | x => TFree x))
   740                    |> cterm_of thy |> Goal.init
   741       in
   742         (goal |> SINGLE (DETERM_TIMEOUT auto_timeout
   743                                         (auto_tac (clasimpset_of ctxt)))
   744               |> the |> Goal.finish ctxt; true)
   745         handle THM _ => false
   746              | TimeLimit.TimeOut => false
   747       end
   748   in
   749     if try_out false then SOME true
   750     else if try_out true then SOME false
   751     else NONE
   752   end
   753 
   754 end;