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

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

     2     Author:     Jasmin Blanchette, TU Muenchen

     3     Copyright   2009

     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 non_opt_name = nitpick_prefix ^ "non_opt"

    58 (* string -> int -> string *)

    59 fun atom_suffix s j =

    60   nat_subscript (j + 1)

    61   |> (s <> "" andalso Symbol.is_ascii_digit (List.last (explode s)))

    62      ? prefix "\<^isub>,"

    63 (* string -> typ -> int -> string *)

    64 fun atom_name prefix (T as Type (s, _)) j =

    65     prefix ^ substring (shortest_name s, 0, 1) ^ atom_suffix s j

    66   | atom_name prefix (T as TFree (s, _)) j =

    67     prefix ^ perhaps (try (unprefix "'")) s ^ atom_suffix s j

    68   | atom_name _ T _ = raise TYPE ("Nitpick_Model.atom_name", [T], [])

    69 (* bool -> typ -> int -> term *)

    70 fun atom for_auto T j =

    71   if for_auto then

    72     Free (atom_name (hd (space_explode "." nitpick_prefix)) T j, T)

    73   else

    74     Const (atom_name "" T j, T)

    76 (* term -> real *)

    77 fun extract_real_number (Const (@{const_name HOL.divide}, _) $ t1 $ t2) =

    78     real (snd (HOLogic.dest_number t1)) / real (snd (HOLogic.dest_number t2))

    79   | extract_real_number t = real (snd (HOLogic.dest_number t))

    80 (* term * term -> order *)

    81 fun nice_term_ord (Abs (_, _, t1), Abs (_, _, t2)) = nice_term_ord (t1, t2)

    82   | nice_term_ord tp = Real.compare (pairself extract_real_number tp)

    83     handle TERM ("dest_number", _) =>

    84            case tp of

    85              (t11 $ t12, t21 $ t22) =>

    86              (case nice_term_ord (t11, t21) of

    87                 EQUAL => nice_term_ord (t12, t22)

    88               | ord => ord)

    89            | _ => TermOrd.fast_term_ord tp

    91 (* nut NameTable.table -> KK.raw_bound list -> nut -> int list list *)

    92 fun tuple_list_for_name rel_table bounds name =

    93   the (AList.lookup (op =) bounds (the_rel rel_table name)) handle NUT _ => [[]]

    95 (* term -> term *)

    96 fun unbit_and_unbox_term (Const (@{const_name FunBox}, _) $ t1) =

    97     unbit_and_unbox_term t1

    98   | unbit_and_unbox_term (Const (@{const_name PairBox},

    99                           Type ("fun", [T1, Type ("fun", [T2, T3])]))

   100                           $ t1 $ t2) =

   101     let val Ts = map unbit_and_unbox_type [T1, T2] in

   102       Const (@{const_name Pair}, Ts ---> Type ("*", Ts))

   103       $ unbit_and_unbox_term t1 $ unbit_and_unbox_term t2

   104     end

   105   | unbit_and_unbox_term (Const (s, T)) = Const (s, unbit_and_unbox_type T)

   106   | unbit_and_unbox_term (t1 $ t2) =

   107     unbit_and_unbox_term t1 $ unbit_and_unbox_term t2

   108   | unbit_and_unbox_term (Free (s, T)) = Free (s, unbit_and_unbox_type T)

   109   | unbit_and_unbox_term (Var (x, T)) = Var (x, unbit_and_unbox_type T)

   110   | unbit_and_unbox_term (Bound j) = Bound j

   111   | unbit_and_unbox_term (Abs (s, T, t')) =

   112     Abs (s, unbit_and_unbox_type T, unbit_and_unbox_term t')

   114 (* typ -> typ -> (typ * typ) * (typ * typ) *)

   115 fun factor_out_types (T1 as Type ("*", [T11, T12]))

   116                      (T2 as Type ("*", [T21, T22])) =

   117     let val (n1, n2) = pairself num_factors_in_type (T11, T21) in

   118       if n1 = n2 then

   119         let

   120           val ((T11', opt_T12'), (T21', opt_T22')) = factor_out_types T12 T22

   121         in

   122           ((Type ("*", [T11, T11']), opt_T12'),

   123            (Type ("*", [T21, T21']), opt_T22'))

   124         end

   125       else if n1 < n2 then

   126         case factor_out_types T1 T21 of

   127           (p1, (T21', NONE)) => (p1, (T21', SOME T22))

   128         | (p1, (T21', SOME T22')) =>

   129           (p1, (T21', SOME (Type ("*", [T22', T22]))))

   130       else

   131         swap (factor_out_types T2 T1)

   132     end

   133   | factor_out_types (Type ("*", [T11, T12])) T2 = ((T11, SOME T12), (T2, NONE))

   134   | factor_out_types T1 (Type ("*", [T21, T22])) = ((T1, NONE), (T21, SOME T22))

   135   | factor_out_types T1 T2 = ((T1, NONE), (T2, NONE))

   137 (* bool -> typ -> typ -> (term * term) list -> term *)

   138 fun make_plain_fun maybe_opt T1 T2 =

   139   let

   140     (* typ -> typ -> (term * term) list -> term *)

   141     fun aux T1 T2 [] =

   142         Const (if maybe_opt orelse T2 <> bool_T then @{const_name undefined}

   143                else non_opt_name, T1 --> T2)

   144       | aux T1 T2 ((t1, t2) :: ps) =

   145         Const (@{const_name fun_upd}, (T1 --> T2) --> T1 --> T2 --> T1 --> T2)

   146         $ aux T1 T2 ps $ t1 $ t2

   147   in aux T1 T2 o rev end

   148 (* term -> bool *)

   149 fun is_plain_fun (Const (s, _)) =

   150     (s = @{const_name undefined} orelse s = non_opt_name)

   151   | is_plain_fun (Const (@{const_name fun_upd}, _) $ t0 $ _ $ _) =

   152     is_plain_fun t0

   153   | is_plain_fun _ = false

   154 (* term -> bool * (term list * term list) *)

   155 val dest_plain_fun =

   156   let

   157     (* term -> term list * term list *)

   158     fun aux (Const (s, _)) = (s <> non_opt_name, ([], []))

   159       | aux (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =

   160         let val (s, (ts1, ts2)) = aux t0 in (s, (t1 :: ts1, t2 :: ts2)) end

   161       | aux t = raise TERM ("Nitpick_Model.dest_plain_fun", [t])

   162   in apsnd (pairself rev) o aux end

   164 (* typ -> typ -> typ -> term -> term * term *)

   165 fun break_in_two T T1 T2 t =

   166   let

   167     val ps = HOLogic.flat_tupleT_paths T

   168     val cut = length (HOLogic.strip_tupleT T1)

   169     val (ps1, ps2) = pairself HOLogic.flat_tupleT_paths (T1, T2)

   170     val (ts1, ts2) = t |> HOLogic.strip_ptuple ps |> chop cut

   171   in (HOLogic.mk_ptuple ps1 T1 ts1, HOLogic.mk_ptuple ps2 T2 ts2) end

   172 (* typ -> term -> term -> term *)

   173 fun pair_up (Type ("*", [T1', T2']))

   174             (t1 as Const (@{const_name Pair},

   175                           Type ("fun", [_, Type ("fun", [_, T1])])) $ t11 $ t12)

   176             t2 =

   177     if T1 = T1' then HOLogic.mk_prod (t1, t2)

   178     else HOLogic.mk_prod (t11, pair_up T2' t12 t2)

   179   | pair_up _ t1 t2 = HOLogic.mk_prod (t1, t2)

   180 (* typ -> term -> term list * term list -> (term * term) list*)

   181 fun multi_pair_up T1 t1 (ts2, ts3) = map2 (pair o pair_up T1 t1) ts2 ts3

   183 (* typ -> typ -> typ -> term -> term *)

   184 fun typecast_fun (Type ("fun", [T1', T2'])) T1 T2 t =

   185     let

   186       (* typ -> typ -> typ -> typ -> term -> term *)

   187       fun do_curry T1 T1a T1b T2 t =

   188         let

   189           val (maybe_opt, ps) = dest_plain_fun t

   190           val ps =

   191             ps |>> map (break_in_two T1 T1a T1b)

   192                |> uncurry (map2 (fn (t1a, t1b) => fn t2 => (t1a, (t1b, t2))))

   193                |> AList.coalesce (op =)

   194                |> map (apsnd (make_plain_fun maybe_opt T1b T2))

   195         in make_plain_fun maybe_opt T1a (T1b --> T2) ps end

   196       (* typ -> typ -> term -> term *)

   197       and do_uncurry T1 T2 t =

   198         let

   199           val (maybe_opt, tsp) = dest_plain_fun t

   200           val ps =

   201             tsp |> op ~~

   202                 |> maps (fn (t1, t2) =>

   203                             multi_pair_up T1 t1 (snd (dest_plain_fun t2)))

   204         in make_plain_fun maybe_opt T1 T2 ps end

   205       (* typ -> typ -> typ -> typ -> term -> term *)

   206       and do_arrow T1' T2' _ _ (Const (s, _)) = Const (s, T1' --> T2')

   207         | do_arrow T1' T2' T1 T2

   208                    (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) =

   209           Const (@{const_name fun_upd},

   210                  (T1' --> T2') --> T1' --> T2' --> T1' --> T2')

   211           $ do_arrow T1' T2' T1 T2 t0 $ do_term T1' T1 t1 $ do_term T2' T2 t2

   212         | do_arrow _ _ _ _ t =

   213           raise TERM ("Nitpick_Model.typecast_fun.do_arrow", [t])

   214       and do_fun T1' T2' T1 T2 t =

   215         case factor_out_types T1' T1 of

   216           ((_, NONE), (_, NONE)) => t |> do_arrow T1' T2' T1 T2

   217         | ((_, NONE), (T1a, SOME T1b)) =>

   218           t |> do_curry T1 T1a T1b T2 |> do_arrow T1' T2' T1a (T1b --> T2)

   219         | ((T1a', SOME T1b'), (_, NONE)) =>

   220           t |> do_arrow T1a' (T1b' --> T2') T1 T2 |> do_uncurry T1' T2'

   221         | _ => raise TYPE ("Nitpick_Model.typecast_fun.do_fun", [T1, T1'], [])

   222       (* typ -> typ -> term -> term *)

   223       and do_term (Type ("fun", [T1', T2'])) (Type ("fun", [T1, T2])) t =

   224           do_fun T1' T2' T1 T2 t

   225         | do_term (T' as Type ("*", Ts' as [T1', T2'])) (Type ("*", [T1, T2]))

   226                   (Const (@{const_name Pair}, _) $ t1 $ t2) =

   227           Const (@{const_name Pair}, Ts' ---> T')

   228           $ do_term T1' T1 t1 $ do_term T2' T2 t2

   229         | do_term T' T t =

   230           if T = T' then t

   231           else raise TYPE ("Nitpick_Model.typecast_fun.do_term", [T, T'], [])

   232     in if T1' = T1 andalso T2' = T2 then t else do_fun T1' T2' T1 T2 t end

   233   | typecast_fun T' _ _ _ = raise TYPE ("Nitpick_Model.typecast_fun", [T'], [])

   235 (* term -> string *)

   236 fun truth_const_sort_key @{const True} = "0"

   237   | truth_const_sort_key @{const False} = "2"

   238   | truth_const_sort_key _ = "1"

   240 (* typ -> term list -> term *)

   241 fun mk_tuple (Type ("*", [T1, T2])) ts =

   242     HOLogic.mk_prod (mk_tuple T1 ts,

   243         mk_tuple T2 (List.drop (ts, length (HOLogic.flatten_tupleT T1))))

   244   | mk_tuple _ (t :: _) = t

   245   | mk_tuple T [] = raise TYPE ("Nitpick_Model.mk_tuple", [T], [])

   247 (* string * string * string * string -> scope -> nut list -> nut list

   248    -> nut list -> nut NameTable.table -> KK.raw_bound list -> typ -> typ -> rep

   249    -> int list list -> term *)

   250 fun reconstruct_term (maybe_name, base_name, step_name, abs_name)

   251         ({ext_ctxt as {thy, ctxt, ...}, card_assigns, bits, datatypes, ofs, ...}

   252          : scope) sel_names rel_table bounds =

   253   let

   254     val for_auto = (maybe_name = "")

   255     (* int list list -> int *)

   256     fun value_of_bits jss =

   257       let

   258         val j0 = offset_of_type ofs @{typ unsigned_bit}

   259         val js = map (Integer.add (~ j0) o the_single) jss

   260       in

   261         fold (fn j => Integer.add (reasonable_power 2 j |> j = bits ? op ~))

   262              js 0

   263       end

   264     (* bool -> typ -> typ -> (term * term) list -> term *)

   265     fun make_set maybe_opt T1 T2 =

   266       let

   267         val empty_const = Const (@{const_name Set.empty}, T1 --> T2)

   268         val insert_const = Const (@{const_name insert},

   269                                   T1 --> (T1 --> T2) --> T1 --> T2)

   270         (* (term * term) list -> term *)

   271         fun aux [] =

   272             if maybe_opt andalso not (is_complete_type datatypes T1) then

   273               insert_const $ Const (unrep, T1) $ empty_const

   274             else

   275               empty_const

   276           | aux ((t1, t2) :: zs) =

   277             aux zs |> t2 <> @{const False}

   278                       ? curry (op $) (insert_const

   279                                       $ (t1 |> t2 <> @{const True}

   280                                                ? curry (op $)

   281                                                        (Const (maybe_name,

   282                                                                T1 --> T1))))

   283       in aux end

   284     (* typ -> typ -> typ -> (term * term) list -> term *)

   285     fun make_map T1 T2 T2' =

   286       let

   287         val update_const = Const (@{const_name fun_upd},

   288                                   (T1 --> T2) --> T1 --> T2 --> T1 --> T2)

   289         (* (term * term) list -> term *)

   290         fun aux' [] = Const (@{const_name Map.empty}, T1 --> T2)

   291           | aux' ((t1, t2) :: ps) =

   292             (case t2 of

   293                Const (@{const_name None}, _) => aux' ps

   294              | _ => update_const $ aux' ps $ t1 $ t2)

   295         fun aux ps =

   296           if not (is_complete_type datatypes T1) then

   297             update_const $ aux' ps $ Const (unrep, T1)

   298             $ (Const (@{const_name Some}, T2' --> T2) $ Const (unknown, T2'))

   299           else

   300             aux' ps

   301       in aux end

   302     (* typ list -> term -> term *)

   303     fun setify_mapify_funs Ts t =

   304       (case fastype_of1 (Ts, t) of

   305          Type ("fun", [T1, T2]) =>

   306          if is_plain_fun t then

   307            case T2 of

   308              @{typ bool} =>

   309              let

   310                val (maybe_opt, ts_pair) =

   311                  dest_plain_fun t ||> pairself (map (setify_mapify_funs Ts))

   312              in

   313                make_set maybe_opt T1 T2

   314                         (sort_wrt (truth_const_sort_key o snd) (op ~~ ts_pair))

   315              end

   316            | Type (@{type_name option}, [T2']) =>

   317              let

   318                val ts_pair = snd (dest_plain_fun t)

   319                              |> pairself (map (setify_mapify_funs Ts))

   320              in make_map T1 T2 T2' (rev (op ~~ ts_pair)) end

   321            | _ => raise SAME ()

   322          else

   323            raise SAME ()

   324        | _ => raise SAME ())

   325       handle SAME () =>

   326              case t of

   327                t1 $ t2 => setify_mapify_funs Ts t1 $ setify_mapify_funs Ts t2

   328              | Abs (s, T, t') => Abs (s, T, setify_mapify_funs (T :: Ts) t')

   329              | _ => t

   330     (* bool -> typ -> typ -> typ -> term list -> term list -> term *)

   331     fun make_fun maybe_opt T1 T2 T' ts1 ts2 =

   332       ts1 ~~ ts2 |> sort (nice_term_ord o pairself fst)

   333                  |> make_plain_fun (maybe_opt andalso not for_auto) T1 T2

   334                  |> unbit_and_unbox_term

   335                  |> typecast_fun (unbit_and_unbox_type T')

   336                                  (unbit_and_unbox_type T1)

   337                                  (unbit_and_unbox_type T2)

   338     (* (typ * int) list -> typ -> typ -> int -> term *)

   339     fun term_for_atom seen (T as Type ("fun", [T1, T2])) T' j =

   340         let

   341           val k1 = card_of_type card_assigns T1

   342           val k2 = card_of_type card_assigns T2

   343         in

   344           term_for_rep seen T T' (Vect (k1, Atom (k2, 0)))

   345                        [nth_combination (replicate k1 (k2, 0)) j]

   346           handle General.Subscript =>

   347                  raise ARG ("Nitpick_Model.reconstruct_term.term_for_atom",

   348                             signed_string_of_int j ^ " for " ^

   349                             string_for_rep (Vect (k1, Atom (k2, 0))))

   350         end

   351       | term_for_atom seen (Type ("*", [T1, T2])) _ j =

   352         let val k1 = card_of_type card_assigns T1 in

   353           list_comb (HOLogic.pair_const T1 T2,

   354                      map2 (fn T => term_for_atom seen T T) [T1, T2]

   355                           [j div k1, j mod k1])

   356         end

   357       | term_for_atom seen @{typ prop} _ j =

   358         HOLogic.mk_Trueprop (term_for_atom seen bool_T bool_T j)

   359       | term_for_atom _ @{typ bool} _ j =

   360         if j = 0 then @{const False} else @{const True}

   361       | term_for_atom _ @{typ unit} _ _ = @{const Unity}

   362       | term_for_atom seen T _ j =

   363         if T = nat_T then

   364           HOLogic.mk_number nat_T j

   365         else if T = int_T then

   366           HOLogic.mk_number int_T

   367               (int_for_atom (card_of_type card_assigns int_T, 0) j)

   368         else if is_fp_iterator_type T then

   369           HOLogic.mk_number nat_T (card_of_type card_assigns T - j - 1)

   370         else if T = @{typ bisim_iterator} then

   371           HOLogic.mk_number nat_T j

   372         else case datatype_spec datatypes T of

   373           NONE => atom for_auto T j

   374         | SOME {shallow = true, ...} => atom for_auto T j

   375         | SOME {co, constrs, ...} =>

   376           let

   377             (* styp -> int list *)

   378             fun tuples_for_const (s, T) =

   379               tuple_list_for_name rel_table bounds (ConstName (s, T, Any))

   380             (* unit -> indexname * typ *)

   381             fun var () = ((atom_name "" T j, 0), T)

   382             val discr_jsss = map (tuples_for_const o discr_for_constr o #const)

   383                                  constrs

   384             val real_j = j + offset_of_type ofs T

   385             val constr_x as (constr_s, constr_T) =

   386               get_first (fn (jss, {const, ...}) =>

   387                             if member (op =) jss [real_j] then SOME const

   388                             else NONE)

   389                         (discr_jsss ~~ constrs) |> the

   390             val arg_Ts = curried_binder_types constr_T

   391             val sel_xs = map (boxed_nth_sel_for_constr ext_ctxt constr_x)

   392                              (index_seq 0 (length arg_Ts))

   393             val sel_Rs =

   394               map (fn x => get_first

   395                                (fn ConstName (s', T', R) =>

   396                                    if (s', T') = x then SOME R else NONE

   397                                  | u => raise NUT ("Nitpick_Model.reconstruct_\

   398                                                    \term.term_for_atom", [u]))

   399                                sel_names |> the) sel_xs

   400             val arg_Rs = map (snd o dest_Func) sel_Rs

   401             val sel_jsss = map tuples_for_const sel_xs

   402             val arg_jsss =

   403               map (map_filter (fn js => if hd js = real_j then SOME (tl js)

   404                                         else NONE)) sel_jsss

   405             val uncur_arg_Ts = binder_types constr_T

   406           in

   407             if co andalso member (op =) seen (T, j) then

   408               Var (var ())

   409             else if constr_s = @{const_name Word} then

   410               HOLogic.mk_number

   411                   (if T = @{typ "unsigned_bit word"} then nat_T else int_T)

   412                   (value_of_bits (the_single arg_jsss))

   413             else

   414               let

   415                 val seen = seen |> co ? cons (T, j)

   416                 val ts =

   417                   if length arg_Ts = 0 then

   418                     []

   419                   else

   420                     map3 (fn Ts => term_for_rep seen Ts Ts) arg_Ts arg_Rs

   421                          arg_jsss

   422                     |> mk_tuple (HOLogic.mk_tupleT uncur_arg_Ts)

   423                     |> dest_n_tuple (length uncur_arg_Ts)

   424                 val t =

   425                   if constr_s = @{const_name Abs_Frac} then

   426                     let

   427                       val num_T = body_type T

   428                       (* int -> term *)

   429                       val mk_num = HOLogic.mk_number num_T

   430                     in

   431                       case ts of

   432                         [Const (@{const_name Pair}, _) $ t1 $ t2] =>

   433                         (case snd (HOLogic.dest_number t1) of

   434                            0 => mk_num 0

   435                          | n1 => case HOLogic.dest_number t2 |> snd of

   436                                    1 => mk_num n1

   437                                  | n2 => Const (@{const_name HOL.divide},

   438                                                 num_T --> num_T --> num_T)

   439                                          $ mk_num n1 $ mk_num n2)

   440                       | _ => raise TERM ("Nitpick_Model.reconstruct_term.term_\

   441                                          \for_atom (Abs_Frac)", ts)

   442                     end

   443                   else if not for_auto andalso is_abs_fun thy constr_x then

   444                     Const (abs_name, constr_T) $ the_single ts

   445                   else

   446                     list_comb (Const constr_x, ts)

   447               in

   448                 if co then

   449                   let val var = var () in

   450                     if exists_subterm (curry (op =) (Var var)) t then

   451                       Const (@{const_name The}, (T --> bool_T) --> T)

   452                       $ Abs ("\<omega>", T,

   453                              Const (@{const_name "op ="}, T --> T --> bool_T)

   454                              $ Bound 0 $ abstract_over (Var var, t))

   455                     else

   456                       t

   457                   end

   458                 else

   459                   t

   460               end

   461           end

   462     (* (typ * int) list -> int -> rep -> typ -> typ -> typ -> int list

   463        -> term *)

   464     and term_for_vect seen k R T1 T2 T' js =

   465       make_fun true T1 T2 T' (map (term_for_atom seen T1 T1) (index_seq 0 k))

   466                (map (term_for_rep seen T2 T2 R o single)

   467                     (batch_list (arity_of_rep R) js))

   468     (* (typ * int) list -> typ -> typ -> rep -> int list list -> term *)

   469     and term_for_rep seen T T' Unit [[]] = term_for_atom seen T T' 0

   470       | term_for_rep seen T T' (R as Atom (k, j0)) [[j]] =

   471         if j >= j0 andalso j < j0 + k then term_for_atom seen T T' (j - j0)

   472         else raise REP ("Nitpick_Model.reconstruct_term.term_for_rep", [R])

   473       | term_for_rep seen (Type ("*", [T1, T2])) _ (Struct [R1, R2]) [js] =

   474         let

   475           val arity1 = arity_of_rep R1

   476           val (js1, js2) = chop arity1 js

   477         in

   478           list_comb (HOLogic.pair_const T1 T2,

   479                      map3 (fn T => term_for_rep seen T T) [T1, T2] [R1, R2]

   480                           [[js1], [js2]])

   481         end

   482       | term_for_rep seen (Type ("fun", [T1, T2])) T' (R as Vect (k, R')) [js] =

   483         term_for_vect seen k R' T1 T2 T' js

   484       | term_for_rep seen (Type ("fun", [T1, T2])) T' (Func (R1, Formula Neut))

   485                      jss =

   486         let

   487           val jss1 = all_combinations_for_rep R1

   488           val ts1 = map (term_for_rep seen T1 T1 R1 o single) jss1

   489           val ts2 =

   490             map (fn js => term_for_rep seen T2 T2 (Atom (2, 0))

   491                                        [[int_for_bool (member (op =) jss js)]])

   492                 jss1

   493         in make_fun false T1 T2 T' ts1 ts2 end

   494       | term_for_rep seen (Type ("fun", [T1, T2])) T' (Func (R1, R2)) jss =

   495         let

   496           val arity1 = arity_of_rep R1

   497           val jss1 = all_combinations_for_rep R1

   498           val ts1 = map (term_for_rep seen T1 T1 R1 o single) jss1

   499           val grouped_jss2 = AList.group (op =) (map (chop arity1) jss)

   500           val ts2 = map (term_for_rep seen T2 T2 R2 o the_default []

   501                          o AList.lookup (op =) grouped_jss2) jss1

   502         in make_fun true T1 T2 T' ts1 ts2 end

   503       | term_for_rep seen T T' (Opt R) jss =

   504         if null jss then Const (unknown, T) else term_for_rep seen T T' R jss

   505       | term_for_rep seen T _ R jss =

   506         raise ARG ("Nitpick_Model.reconstruct_term.term_for_rep",

   507                    Refute.string_of_typ T ^ " " ^ string_for_rep R ^ " " ^

   508                    string_of_int (length jss))

   509   in

   510     (not for_auto ? setify_mapify_funs []) o unbit_and_unbox_term

   511     oooo term_for_rep []

   512   end

   514 (* scope -> nut list -> nut NameTable.table -> KK.raw_bound list -> nut

   515    -> term *)

   516 fun term_for_name scope sel_names rel_table bounds name =

   517   let val T = type_of name in

   518     tuple_list_for_name rel_table bounds name

   519     |> reconstruct_term ("", "", "", "") scope sel_names rel_table bounds T T

   520                         (rep_of name)

   521   end

   523 (* Proof.context

   524    -> (string * string * string * string * string) * Proof.context *)

   525 fun add_wacky_syntax ctxt =

   526   let

   527     (* term -> string *)

   528     val name_of = fst o dest_Const

   529     val thy = ProofContext.theory_of ctxt |> Context.reject_draft

   530     val (maybe_t, thy) =

   531       Sign.declare_const ((@{binding nitpick_maybe}, @{typ "'a => 'a"}),

   532                           Mixfix (maybe_mixfix, [1000], 1000)) thy

   533     val (base_t, thy) =

   534       Sign.declare_const ((@{binding nitpick_base}, @{typ "'a => 'a"}),

   535                           Mixfix (base_mixfix, [1000], 1000)) thy

   536     val (step_t, thy) =

   537       Sign.declare_const ((@{binding nitpick_step}, @{typ "'a => 'a"}),

   538                           Mixfix (step_mixfix, [1000], 1000)) thy

   539     val (abs_t, thy) =

   540       Sign.declare_const ((@{binding nitpick_abs}, @{typ "'a => 'b"}),

   541                           Mixfix (abs_mixfix, [40], 40)) thy

   542   in

   543     ((name_of maybe_t, name_of base_t, name_of step_t, name_of abs_t),

   544      ProofContext.transfer_syntax thy ctxt)

   545   end

   547 (* term -> term *)

   548 fun unfold_outer_the_binders (t as Const (@{const_name The}, _)

   549                                    $ Abs (s, T, Const (@{const_name "op ="}, _)

   550                                                 $ Bound 0 $ t')) =

   551     betapply (Abs (s, T, t'), t) |> unfold_outer_the_binders

   552   | unfold_outer_the_binders t = t

   553 (* typ list -> int -> term * term -> bool *)

   554 fun bisimilar_values _ 0 _ = true

   555   | bisimilar_values coTs max_depth (t1, t2) =

   556     let val T = fastype_of t1 in

   557       if exists_subtype (member (op =) coTs) T then

   558         let

   559           val ((head1, args1), (head2, args2)) =

   560             pairself (strip_comb o unfold_outer_the_binders) (t1, t2)

   561           val max_depth = max_depth - (if member (op =) coTs T then 1 else 0)

   562         in

   563           head1 = head2

   564           andalso forall (bisimilar_values coTs max_depth) (args1 ~~ args2)

   565         end

   566       else

   567         t1 = t2

   568     end

   570 (* params -> scope -> (term option * int list) list -> styp list -> nut list

   571   -> nut list -> nut list -> nut NameTable.table -> KK.raw_bound list

   572   -> Pretty.T * bool *)

   573 fun reconstruct_hol_model {show_skolems, show_datatypes, show_consts}

   574         ({ext_ctxt as {thy, ctxt, max_bisim_depth, boxes, wfs, user_axioms,

   575                        debug, binary_ints, destroy_constrs, specialize,

   576                        skolemize, star_linear_preds, uncurry, fast_descrs,

   577                        tac_timeout, evals, case_names, def_table, nondef_table,

   578                        user_nondefs, simp_table, psimp_table, intro_table,

   579                        ground_thm_table, ersatz_table, skolems, special_funs,

   580                        unrolled_preds, wf_cache, constr_cache},

   581          card_assigns, bits, bisim_depth, datatypes, ofs} : scope)

   582         formats all_frees free_names sel_names nonsel_names rel_table bounds =

   583   let

   584     val (wacky_names as (_, base_name, step_name, _), ctxt) =

   585       add_wacky_syntax ctxt

   586     val ext_ctxt =

   587       {thy = thy, ctxt = ctxt, max_bisim_depth = max_bisim_depth, boxes = boxes,

   588        wfs = wfs, user_axioms = user_axioms, debug = debug,

   589        binary_ints = binary_ints, destroy_constrs = destroy_constrs,

   590        specialize = specialize, skolemize = skolemize,

   591        star_linear_preds = star_linear_preds, uncurry = uncurry,

   592        fast_descrs = fast_descrs, tac_timeout = tac_timeout, evals = evals,

   593        case_names = case_names, def_table = def_table,

   594        nondef_table = nondef_table, user_nondefs = user_nondefs,

   595        simp_table = simp_table, psimp_table = psimp_table,

   596        intro_table = intro_table, ground_thm_table = ground_thm_table,

   597        ersatz_table = ersatz_table, skolems = skolems,

   598        special_funs = special_funs, unrolled_preds = unrolled_preds,

   599        wf_cache = wf_cache, constr_cache = constr_cache}

   600     val scope = {ext_ctxt = ext_ctxt, card_assigns = card_assigns,

   601                  bits = bits, bisim_depth = bisim_depth, datatypes = datatypes,

   602                  ofs = ofs}

   603     (* typ -> typ -> rep -> int list list -> term *)

   604     val term_for_rep = reconstruct_term wacky_names scope sel_names rel_table

   605                                         bounds

   606     (* nat -> typ -> nat -> typ *)

   607     fun nth_value_of_type card T n = term_for_rep T T (Atom (card, 0)) [[n]]

   608     (* nat -> typ -> typ list *)

   609     fun all_values_of_type card T =

   610       index_seq 0 card |> map (nth_value_of_type card T) |> sort nice_term_ord

   611     (* dtype_spec list -> dtype_spec -> bool *)

   612     fun is_codatatype_wellformed (cos : dtype_spec list)

   613                                  ({typ, card, ...} : dtype_spec) =

   614       let

   615         val ts = all_values_of_type card typ

   616         val max_depth = Integer.sum (map #card cos)

   617       in

   618         forall (not o bisimilar_values (map #typ cos) max_depth)

   619                (all_distinct_unordered_pairs_of ts)

   620       end

   621     (* string -> Pretty.T *)

   622     fun pretty_for_assign name =

   623       let

   624         val (oper, (t1, T'), T) =

   625           case name of

   626             FreeName (s, T, _) =>

   627             let val t = Free (s, unbit_and_unbox_type T) in

   628               ("=", (t, format_term_type thy def_table formats t), T)

   629             end

   630           | ConstName (s, T, _) =>

   631             (assign_operator_for_const (s, T),

   632              user_friendly_const ext_ctxt (base_name, step_name) formats (s, T),

   633              T)

   634           | _ => raise NUT ("Nitpick_Model.reconstruct_hol_model.\

   635                             \pretty_for_assign", [name])

   636         val t2 = if rep_of name = Any then

   637                    Const (@{const_name undefined}, T')

   638                  else

   639                    tuple_list_for_name rel_table bounds name

   640                    |> term_for_rep T T' (rep_of name)

   641       in

   642         Pretty.block (Pretty.breaks

   643             [setmp_show_all_types (Syntax.pretty_term ctxt) t1,

   644              Pretty.str oper, Syntax.pretty_term ctxt t2])

   645       end

   646     (* dtype_spec -> Pretty.T *)

   647     fun pretty_for_datatype ({typ, card, complete, ...} : dtype_spec) =

   648       Pretty.block (Pretty.breaks

   649           [Syntax.pretty_typ ctxt (unbit_and_unbox_type typ), Pretty.str "=",

   650            Pretty.enum "," "{" "}"

   651                (map (Syntax.pretty_term ctxt) (all_values_of_type card typ)

   652                 @ (if complete then [] else [Pretty.str unrep]))])

   653     (* typ -> dtype_spec list *)

   654     fun integer_datatype T =

   655       [{typ = T, card = card_of_type card_assigns T, co = false,

   656         complete = false, concrete = true, shallow = false, constrs = []}]

   657       handle TYPE ("Nitpick_HOL.card_of_type", _, _) => []

   658     val (codatatypes, datatypes) =

   659       datatypes |> filter_out #shallow

   660                 |> List.partition #co

   661                 ||> append (integer_datatype nat_T @ integer_datatype int_T)

   662     val block_of_datatypes =

   663       if show_datatypes andalso not (null datatypes) then

   664         [Pretty.big_list ("Datatype" ^ plural_s_for_list datatypes ^ ":")

   665                          (map pretty_for_datatype datatypes)]

   666       else

   667         []

   668     val block_of_codatatypes =

   669       if show_datatypes andalso not (null codatatypes) then

   670         [Pretty.big_list ("Codatatype" ^ plural_s_for_list codatatypes ^ ":")

   671                          (map pretty_for_datatype codatatypes)]

   672       else

   673         []

   674     (* bool -> string -> nut list -> Pretty.T list *)

   675     fun block_of_names show title names =

   676       if show andalso not (null names) then

   677         Pretty.str (title ^ plural_s_for_list names ^ ":")

   678         :: map (Pretty.indent indent_size o pretty_for_assign)

   679                (sort_wrt (original_name o nickname_of) names)

   680       else

   681         []

   682     val (skolem_names, nonskolem_nonsel_names) =

   683       List.partition is_skolem_name nonsel_names

   684     val (eval_names, noneval_nonskolem_nonsel_names) =

   685       List.partition (String.isPrefix eval_prefix o nickname_of)

   686                      nonskolem_nonsel_names

   687       ||> filter_out (curry (op =) @{const_name bisim_iterator_max}

   688                       o nickname_of)

   689     val free_names =

   690       map (fn x as (s, T) =>

   691               case filter (curry (op =) x

   692                            o pairf nickname_of (unbit_and_unbox_type o type_of))

   693                           free_names of

   694                 [name] => name

   695               | [] => FreeName (s, T, Any)

   696               | _ => raise TERM ("Nitpick_Model.reconstruct_hol_model",

   697                                  [Const x])) all_frees

   698     val chunks = block_of_names true "Free variable" free_names @

   699                  block_of_names show_skolems "Skolem constant" skolem_names @

   700                  block_of_names true "Evaluated term" eval_names @

   701                  block_of_datatypes @ block_of_codatatypes @

   702                  block_of_names show_consts "Constant"

   703                                 noneval_nonskolem_nonsel_names

   704   in

   705     (Pretty.chunks (if null chunks then [Pretty.str "Empty assignment"]

   706                     else chunks),

   707      bisim_depth >= 0

   708      orelse forall (is_codatatype_wellformed codatatypes) codatatypes)

   709   end

   711 (* scope -> Time.time option -> nut list -> nut list -> nut NameTable.table

   712    -> KK.raw_bound list -> term -> bool option *)

   713 fun prove_hol_model (scope as {ext_ctxt as {thy, ctxt, ...}, card_assigns, ...})

   714                     auto_timeout free_names sel_names rel_table bounds prop =

   715   let

   716     (* typ * int -> term *)

   717     fun free_type_assm (T, k) =

   718       let

   719         (* int -> term *)

   720         val atom = atom true T

   721         fun equation_for_atom j = HOLogic.eq_const T $ Bound 0 $ atom j

   722         val eqs = map equation_for_atom (index_seq 0 k)

   723         val compreh_assm =

   724           Const (@{const_name All}, (T --> bool_T) --> bool_T)

   725               $ Abs ("x", T, foldl1 HOLogic.mk_disj eqs)

   726         val distinct_assm = distinctness_formula T (map atom (index_seq 0 k))

   727       in HOLogic.mk_conj (compreh_assm, distinct_assm) end

   728     (* nut -> term *)

   729     fun free_name_assm name =

   730       HOLogic.mk_eq (Free (nickname_of name, type_of name),

   731                      term_for_name scope sel_names rel_table bounds name)

   732     val freeT_assms = map free_type_assm (filter (is_TFree o fst) card_assigns)

   733     val model_assms = map free_name_assm free_names

   734     val assm = List.foldr HOLogic.mk_conj @{const True}

   735                           (freeT_assms @ model_assms)

   736     (* bool -> bool *)

   737     fun try_out negate =

   738       let

   739         val concl = (negate ? curry (op $) @{const Not})

   740                     (ObjectLogic.atomize_term thy prop)

   741         val goal = HOLogic.mk_Trueprop (HOLogic.mk_imp (assm, concl))

   742                    |> map_types (map_type_tfree

   743                           (fn (s, []) => TFree (s, HOLogic.typeS)

   744                             | x => TFree x))

   745                    |> cterm_of thy |> Goal.init

   746       in

   747         (goal |> SINGLE (DETERM_TIMEOUT auto_timeout

   748                                         (auto_tac (clasimpset_of ctxt)))

   749               |> the |> Goal.finish ctxt; true)

   750         handle THM _ => false

   751              | TimeLimit.TimeOut => false

   752       end

   753   in

   754     if try_out false then SOME true

   755     else if try_out true then SOME false

   756     else NONE

   757   end

   759 end;

author	blanchet
	Fri, 18 Dec 2009 12:00:29 +0100
changeset 34123	8a2c5d7aff51
parent 34121	c4628a1dcf75
child 34923	c4f04bee79f3
permissions	-rw-r--r--