wneuper/isa: src/HOL/Tools/Nitpick/nitpick

     1 (*  Title:      HOL/Tools/Nitpick/nitpick_model.ML

     2     Author:     Jasmin Blanchette, TU Muenchen

     3     Copyright   2009, 2010

     5 Model reconstruction for Nitpick.

     6 *)

     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

    15   type params = {

    16     show_skolems: bool,

    17     show_datatypes: bool,

    18     show_consts: bool}

    20   structure NameTable : TABLE

    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;

    33 structure Nitpick_Model : NITPICK_MODEL =

    34 struct

    36 open Nitpick_Util

    37 open Nitpick_HOL

    38 open Nitpick_Scope

    39 open Nitpick_Peephole

    40 open Nitpick_Rep

    41 open Nitpick_Nut

    43 structure KK = Kodkod

    45 type params = {

    46   show_skolems: bool,

    47   show_datatypes: bool,

    48   show_consts: bool}

    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"

    61 type atom_pool = ((string * int) * int list) list

    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)

    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

   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 _ => [[]]

   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')

   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))

   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

   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

   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'], [])

   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"

   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], [])

   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)

   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

   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

   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

   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

   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

   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

   809 end;

author	blanchet
	Sat, 13 Feb 2010 15:04:09 +0100
changeset 35180	c57dba973391
parent 35179	4b198af5beb5
child 35188	8c70a34931b1
permissions	-rw-r--r--