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_const_prefix = "\<xi>"

    58 val cyclic_type_name = nitpick_prefix ^ cyclic_const_prefix

    59 val opt_flag = nitpick_prefix ^ "opt"

    60 val non_opt_flag = nitpick_prefix ^ "non_opt"

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

    64 (* atom_pool Unsynchronized.ref -> string -> int -> int -> string *)

    65 fun nth_atom_suffix pool s j k =

    66   (case AList.lookup (op =) (!pool) (s, k) of

    67      SOME js =>

    68      (case find_index (curry (op =) j) js of

    69         ~1 => (Unsynchronized.change pool (cons ((s, k), j :: js));

    70                length js + 1)

    71       | n => length js - n)

    72    | NONE => (Unsynchronized.change pool (cons ((s, k), [j])); 1))

    73   |> nat_subscript

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

    75      ? prefix "\<^isub>,"

    76 (* atom_pool Unsynchronized.ref -> string -> typ -> int -> int -> string *)

    77 fun nth_atom_name pool prefix (Type (s, _)) j k =

    78     let val s' = shortest_name s in

    79       prefix ^ (if String.isPrefix "\\" s' then s' else substring (s', 0, 1)) ^

    80       nth_atom_suffix pool s j k

    81     end

    82   | nth_atom_name pool prefix (TFree (s, _)) j k =

    83     prefix ^ perhaps (try (unprefix "'")) s ^ nth_atom_suffix pool s j k

    84   | nth_atom_name _ _ T _ _ =

    85     raise TYPE ("Nitpick_Model.nth_atom_name", [T], [])

    86 (* atom_pool Unsynchronized.ref -> bool -> typ -> int -> int -> term *)

    87 fun nth_atom pool for_auto T j k =

    88   if for_auto then

    89     Free (nth_atom_name pool (hd (space_explode "." nitpick_prefix)) T j k, T)

    90   else

    91     Const (nth_atom_name pool "" T j k, T)

    93 (* term -> real *)

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

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

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

    97 (* term * term -> order *)

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

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

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

   101            case tp of

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

   103              (case nice_term_ord (t11, t21) of

   104                 EQUAL => nice_term_ord (t12, t22)

   105               | ord => ord)

   106            | _ => Term_Ord.fast_term_ord tp

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

   109 fun tuple_list_for_name rel_table bounds name =

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

   112 (* term -> term *)

   113 fun unarize_and_unbox_term (Const (@{const_name FunBox}, _) $ t1) =

   114     unarize_and_unbox_term t1

   115   | unarize_and_unbox_term (Const (@{const_name PairBox},

   116                                    Type ("fun", [T1, Type ("fun", [T2, _])]))

   117                             $ t1 $ t2) =

   118     let val Ts = map unarize_unbox_and_uniterize_type [T1, T2] in

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

   120       $ unarize_and_unbox_term t1 $ unarize_and_unbox_term t2

   121     end

   122   | unarize_and_unbox_term (Const (s, T)) =

   123     Const (s, unarize_unbox_and_uniterize_type T)

   124   | unarize_and_unbox_term (t1 $ t2) =

   125     unarize_and_unbox_term t1 $ unarize_and_unbox_term t2

   126   | unarize_and_unbox_term (Free (s, T)) =

   127     Free (s, unarize_unbox_and_uniterize_type T)

   128   | unarize_and_unbox_term (Var (x, T)) =

   129     Var (x, unarize_unbox_and_uniterize_type T)

   130   | unarize_and_unbox_term (Bound j) = Bound j

   131   | unarize_and_unbox_term (Abs (s, T, t')) =

   132     Abs (s, unarize_unbox_and_uniterize_type T, unarize_and_unbox_term t')

   134 (* typ -> typ -> (typ * typ) * (typ * typ) *)

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

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

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

   138       if n1 = n2 then

   139         let

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

   141         in

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

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

   144         end

   145       else if n1 < n2 then

   146         case factor_out_types T1 T21 of

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

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

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

   150       else

   151         swap (factor_out_types T2 T1)

   152     end

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

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

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

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

   158 fun make_plain_fun maybe_opt T1 T2 =

   159   let

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

   161     fun aux T1 T2 [] =

   162         Const (if maybe_opt then opt_flag else non_opt_flag, T1 --> T2)

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

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

   165         $ aux T1 T2 ps $ t1 $ t2

   166   in aux T1 T2 o rev end

   167 (* term -> bool *)

   168 fun is_plain_fun (Const (s, _)) = (s = opt_flag orelse s = non_opt_flag)

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

   170     is_plain_fun t0

   171   | is_plain_fun _ = false

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

   173 val dest_plain_fun =

   174   let

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

   176     fun aux (Const (s, _)) = (s <> non_opt_flag, ([], []))

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

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

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

   180   in apsnd (pairself rev) o aux end

   182 (* typ -> typ -> typ -> term -> term * term *)

   183 fun break_in_two T T1 T2 t =

   184   let

   185     val ps = HOLogic.flat_tupleT_paths T

   186     val cut = length (HOLogic.strip_tupleT T1)

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

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

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

   190 (* typ -> term -> term -> term *)

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

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

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

   194             t2 =

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

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

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

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

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

   201 (* typ -> typ -> typ -> term -> term *)

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

   203     let

   204       (* typ -> typ -> typ -> typ -> term -> term *)

   205       fun do_curry T1 T1a T1b T2 t =

   206         let

   207           val (maybe_opt, ps) = dest_plain_fun t

   208           val ps =

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

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

   211                |> AList.coalesce (op =)

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

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

   214       (* typ -> typ -> term -> term *)

   215       and do_uncurry T1 T2 t =

   216         let

   217           val (maybe_opt, tsp) = dest_plain_fun t

   218           val ps =

   219             tsp |> op ~~

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

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

   222         in make_plain_fun maybe_opt T1 T2 ps end

   223       (* typ -> typ -> typ -> typ -> term -> term *)

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

   225         | do_arrow T1' T2' T1 T2

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

   227           Const (@{const_name fun_upd},

   228                  (T1' --> T2') --> T1' --> T2' --> T1' --> T2')

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

   230         | do_arrow _ _ _ _ t =

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

   232       and do_fun T1' T2' T1 T2 t =

   233         case factor_out_types T1' T1 of

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

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

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

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

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

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

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

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

   242           do_fun T1' T2' T1 T2 t

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

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

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

   246           $ do_term T1' T1 t1 $ do_term T2' T2 t2

   247         | do_term T' T t =

   248           if T = T' then t

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

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

   251   | typecast_fun T' _ _ _ =

   252     raise TYPE ("Nitpick_Model.typecast_fun", [T'], [])

   254 (* term -> string *)

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

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

   257   | truth_const_sort_key _ = "1"

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

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

   261     HOLogic.mk_prod (mk_tuple T1 ts,

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

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

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

   266 (* bool -> atom_pool -> (string * string) * (string * string) -> scope

   267    -> nut list -> nut list -> nut list -> nut NameTable.table

   268    -> KK.raw_bound list -> typ -> typ -> rep -> int list list -> term *)

   269 fun reconstruct_term unfold pool ((maybe_name, abs_name), _)

   270         ({hol_ctxt as {thy, stds, ...}, binarize, card_assigns, bits, datatypes,

   271           ofs, ...} : scope) sel_names rel_table bounds =

   272   let

   273     val for_auto = (maybe_name = "")

   274     (* int list list -> int *)

   275     fun value_of_bits jss =

   276       let

   277         val j0 = offset_of_type ofs @{typ unsigned_bit}

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

   279       in

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

   281              js 0

   282       end

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

   284     fun make_set maybe_opt T1 T2 tps =

   285       let

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

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

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

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

   290         fun aux [] =

   291             if maybe_opt andalso not (is_complete_type datatypes false T1) then

   292               insert_const $ Const (unrep, T1) $ empty_const

   293             else

   294               empty_const

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

   296             aux zs

   297             |> t2 <> @{const False}

   298                ? curry (op $)

   299                        (insert_const

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

   301                                  ? curry (op $)

   302                                          (Const (maybe_name, T1 --> T1))))

   303       in

   304         if forall (fn (_, t) => t <> @{const True} andalso t <> @{const False})

   305                   tps then

   306           Const (unknown, T1 --> T2)

   307         else

   308           aux tps

   309       end

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

   311     fun make_map T1 T2 T2' =

   312       let

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

   314                                   (T1 --> T2) --> T1 --> T2 --> T1 --> T2)

   315         (* (term * term) list -> term *)

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

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

   318             (case t2 of

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

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

   321         fun aux ps =

   322           if not (is_complete_type datatypes false T1) then

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

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

   325           else

   326             aux' ps

   327       in aux end

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

   329     fun polish_funs Ts t =

   330       (case fastype_of1 (Ts, t) of

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

   332          if is_plain_fun t then

   333            case T2 of

   334              @{typ bool} =>

   335              let

   336                val (maybe_opt, ts_pair) =

   337                  dest_plain_fun t ||> pairself (map (polish_funs Ts))

   338              in

   339                make_set maybe_opt T1 T2

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

   341              end

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

   343              let

   344                val ts_pair = snd (dest_plain_fun t)

   345                              |> pairself (map (polish_funs Ts))

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

   347            | _ => raise SAME ()

   348          else

   349            raise SAME ()

   350        | _ => raise SAME ())

   351       handle SAME () =>

   352              case t of

   353                (t1 as Const (@{const_name fun_upd}, _) $ t11 $ _)

   354                $ (t2 as Const (s, _)) =>

   355                if s = unknown then polish_funs Ts t11

   356                else polish_funs Ts t1 $ polish_funs Ts t2

   357              | t1 $ t2 => polish_funs Ts t1 $ polish_funs Ts t2

   358              | Abs (s, T, t') => Abs (s, T, polish_funs (T :: Ts) t')

   359              | Const (s, Type ("fun", [T1, T2])) =>

   360                if s = opt_flag orelse s = non_opt_flag then

   361                  Abs ("x", T1, Const (unknown, T2))

   362                else

   363                  t

   364              | t => t

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

   366     fun make_fun maybe_opt T1 T2 T' ts1 ts2 =

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

   368                  |> make_plain_fun maybe_opt T1 T2

   369                  |> unarize_and_unbox_term

   370                  |> typecast_fun (unarize_unbox_and_uniterize_type T')

   371                                  (unarize_unbox_and_uniterize_type T1)

   372                                  (unarize_unbox_and_uniterize_type T2)

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

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

   375         let

   376           val k1 = card_of_type card_assigns T1

   377           val k2 = card_of_type card_assigns T2

   378         in

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

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

   381           handle General.Subscript =>

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

   383                             signed_string_of_int j ^ " for " ^

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

   385         end

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

   387         let

   388           val k1 = card_of_type card_assigns T1

   389           val k2 = k div k1

   390         in

   391           list_comb (HOLogic.pair_const T1 T2,

   392                      map3 (fn T => term_for_atom seen T T) [T1, T2]

   393                           [j div k2, j mod k2] [k1, k2]) (* ### k2 or k1? FIXME *)

   394         end

   395       | term_for_atom seen @{typ prop} _ j k =

   396         HOLogic.mk_Trueprop (term_for_atom seen bool_T bool_T j k)

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

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

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

   400       | term_for_atom seen T _ j k =

   401         if T = nat_T andalso is_standard_datatype thy stds nat_T then

   402           HOLogic.mk_number nat_T j

   403         else if T = int_T then

   404           HOLogic.mk_number int_T (int_for_atom (k, 0) j)

   405         else if is_fp_iterator_type T then

   406           HOLogic.mk_number nat_T (k - j - 1)

   407         else if T = @{typ bisim_iterator} then

   408           HOLogic.mk_number nat_T j

   409         else case datatype_spec datatypes T of

   410           NONE => nth_atom pool for_auto T j k

   411         | SOME {deep = false, ...} => nth_atom pool for_auto T j k

   412         | SOME {co, standard, constrs, ...} =>

   413           let

   414             (* styp -> int list *)

   415             fun tuples_for_const (s, T) =

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

   417             (* unit -> term *)

   418             fun cyclic_atom () =

   419               nth_atom pool for_auto (Type (cyclic_type_name, [])) j k

   420             fun cyclic_var () = Var ((nth_atom_name pool "" T j k, 0), T)

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

   423                                  constrs

   424             val real_j = j + offset_of_type ofs T

   425             val constr_x as (constr_s, constr_T) =

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

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

   428                             else NONE)

   429                         (discr_jsss ~~ constrs) |> the

   430             val arg_Ts = curried_binder_types constr_T

   431             val sel_xs =

   432               map (binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize

   433                                                           constr_x)

   434                   (index_seq 0 (length arg_Ts))

   435             val sel_Rs =

   436               map (fn x => get_first

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

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

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

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

   441                                sel_names |> the) sel_xs

   442             val arg_Rs = map (snd o dest_Func) sel_Rs

   443             val sel_jsss = map tuples_for_const sel_xs

   444             val arg_jsss =

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

   446                                         else NONE)) sel_jsss

   447             val uncur_arg_Ts = binder_types constr_T

   448             val maybe_cyclic = co orelse not standard

   449           in

   450             if maybe_cyclic andalso not (null seen) andalso

   451                member (op =) (seen |> unfold ? (fst o split_last)) (T, j) then

   452               cyclic_var ()

   453             else if constr_s = @{const_name Word} then

   454               HOLogic.mk_number

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

   456                   (value_of_bits (the_single arg_jsss))

   457             else

   458               let

   459                 val seen = seen |> maybe_cyclic ? cons (T, j)

   460                 val ts =

   461                   if length arg_Ts = 0 then

   462                     []

   463                   else

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

   465                          arg_jsss

   466                     |> mk_tuple (HOLogic.mk_tupleT uncur_arg_Ts)

   467                     |> dest_n_tuple (length uncur_arg_Ts)

   468                 val t =

   469                   if constr_s = @{const_name Abs_Frac} then

   470                     let

   471                       val num_T = body_type T

   472                       (* int -> term *)

   473                       val mk_num = HOLogic.mk_number num_T

   474                     in

   475                       case ts of

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

   477                         (case snd (HOLogic.dest_number t1) of

   478                            0 => mk_num 0

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

   480                                    1 => mk_num n1

   481                                  | n2 => Const (@{const_name divide},

   482                                                 num_T --> num_T --> num_T)

   483                                          $ mk_num n1 $ mk_num n2)

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

   485                                          \term_for_atom (Abs_Frac)", ts)

   486                     end

   487                   else if not for_auto andalso

   488                           (is_abs_fun thy constr_x orelse

   489                            constr_s = @{const_name Quot}) then

   490                     Const (abs_name, constr_T) $ the_single ts

   491                   else

   492                     list_comb (Const constr_x, ts)

   493               in

   494                 if maybe_cyclic then

   495                   let val var = cyclic_var () in

   496                     if unfold andalso not standard andalso

   497                        length seen = 1 andalso

   498                        exists_subterm (fn Const (s, _) =>

   499                                           String.isPrefix cyclic_const_prefix s

   500                                         | t' => t' = var) t then

   501                       subst_atomic [(var, cyclic_atom ())] t

   502                     else if exists_subterm (curry (op =) var) t then

   503                       if co then

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

   505                         $ Abs (cyclic_co_val_name, T,

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

   507                                $ Bound 0 $ abstract_over (var, t))

   508                       else

   509                         cyclic_atom ()

   510                     else

   511                       t

   512                   end

   513                 else

   514                   t

   515               end

   516           end

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

   518        -> term *)

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

   520       make_fun true T1 T2 T'

   521                (map (fn j => term_for_atom seen T1 T1 j k) (index_seq 0 k))

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

   523                     (batch_list (arity_of_rep R) js))

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

   525     and term_for_rep seen T T' Unit [[]] = term_for_atom seen T T' 0 1

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

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

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

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

   530         let

   531           val arity1 = arity_of_rep R1

   532           val (js1, js2) = chop arity1 js

   533         in

   534           list_comb (HOLogic.pair_const T1 T2,

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

   536                           [[js1], [js2]])

   537         end

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

   539         term_for_vect seen k R' T1 T2 T' js

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

   541                      jss =

   542         let

   543           val jss1 = all_combinations_for_rep R1

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

   545           val ts2 =

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

   547                                        [[int_from_bool (member (op =) jss js)]])

   548                 jss1

   549         in make_fun false T1 T2 T' ts1 ts2 end

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

   551         let

   552           val arity1 = arity_of_rep R1

   553           val jss1 = all_combinations_for_rep R1

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

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

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

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

   558         in make_fun true T1 T2 T' ts1 ts2 end

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

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

   561       | term_for_rep _ T _ R jss =

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

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

   564                    string_of_int (length jss))

   565   in polish_funs [] o unarize_and_unbox_term oooo term_for_rep [] end

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

   568    -> nut -> term *)

   569 fun term_for_name pool scope sel_names rel_table bounds name =

   570   let val T = type_of name in

   571     tuple_list_for_name rel_table bounds name

   572     |> reconstruct_term false pool (("", ""), ("", "")) scope sel_names

   573                         rel_table bounds T T (rep_of name)

   574   end

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

   577 fun add_wacky_syntax ctxt =

   578   let

   579     (* term -> string *)

   580     val name_of = fst o dest_Const

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

   582     val (maybe_t, thy) =

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

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

   585     val (abs_t, thy) =

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

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

   588     val (base_t, thy) =

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

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

   591     val (step_t, thy) =

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

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

   594   in

   595     (pairself (pairself name_of) ((maybe_t, abs_t), (base_t, step_t)),

   596      ProofContext.transfer_syntax thy ctxt)

   597   end

   599 (* term -> term *)

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

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

   602                                                 $ Bound 0 $ t')) =

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

   604   | unfold_outer_the_binders t = t

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

   606 fun bisimilar_values _ 0 _ = true

   607   | bisimilar_values coTs max_depth (t1, t2) =

   608     let val T = fastype_of t1 in

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

   610         let

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

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

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

   614         in

   615           head1 = head2 andalso

   616           forall (bisimilar_values coTs max_depth) (args1 ~~ args2)

   617         end

   618       else

   619         t1 = t2

   620     end

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

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

   624   -> Pretty.T * bool *)

   625 fun reconstruct_hol_model {show_skolems, show_datatypes, show_consts}

   626         ({hol_ctxt = {thy, ctxt, max_bisim_depth, boxes, stds, wfs, user_axioms,

   627                       debug, binary_ints, destroy_constrs, specialize,

   628                       skolemize, star_linear_preds, uncurry, fast_descrs,

   629                       tac_timeout, evals, case_names, def_table, nondef_table,

   630                       user_nondefs, simp_table, psimp_table, intro_table,

   631                       ground_thm_table, ersatz_table, skolems, special_funs,

   632                       unrolled_preds, wf_cache, constr_cache},

   633          binarize, card_assigns, bits, bisim_depth, datatypes, ofs} : scope)

   634         formats all_frees free_names sel_names nonsel_names rel_table bounds =

   635   let

   636     val pool = Unsynchronized.ref []

   637     val (wacky_names as (_, base_step_names), ctxt) =

   638       add_wacky_syntax ctxt

   639     val hol_ctxt =

   640       {thy = thy, ctxt = ctxt, max_bisim_depth = max_bisim_depth, boxes = boxes,

   641        stds = stds, wfs = wfs, user_axioms = user_axioms, debug = debug,

   642        binary_ints = binary_ints, destroy_constrs = destroy_constrs,

   643        specialize = specialize, skolemize = skolemize,

   644        star_linear_preds = star_linear_preds, uncurry = uncurry,

   645        fast_descrs = fast_descrs, tac_timeout = tac_timeout, evals = evals,

   646        case_names = case_names, def_table = def_table,

   647        nondef_table = nondef_table, user_nondefs = user_nondefs,

   648        simp_table = simp_table, psimp_table = psimp_table,

   649        intro_table = intro_table, ground_thm_table = ground_thm_table,

   650        ersatz_table = ersatz_table, skolems = skolems,

   651        special_funs = special_funs, unrolled_preds = unrolled_preds,

   652        wf_cache = wf_cache, constr_cache = constr_cache}

   653     val scope = {hol_ctxt = hol_ctxt, binarize = binarize,

   654                  card_assigns = card_assigns, bits = bits,

   655                  bisim_depth = bisim_depth, datatypes = datatypes, ofs = ofs}

   656     (* bool -> typ -> typ -> rep -> int list list -> term *)

   657     fun term_for_rep unfold =

   658       reconstruct_term unfold pool wacky_names scope sel_names rel_table bounds

   659     (* nat -> typ -> nat -> term *)

   660     fun nth_value_of_type card T n =

   661       let

   662         (* bool -> term *)

   663         fun aux unfold = term_for_rep unfold T T (Atom (card, 0)) [[n]]

   664       in

   665         case aux false of

   666           t as Const (s, _) =>

   667           if String.isPrefix cyclic_const_prefix s then

   668             HOLogic.mk_eq (t, aux true)

   669           else

   670             t

   671         | t => t

   672       end

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

   674     fun all_values_of_type card T =

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

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

   677     fun is_codatatype_wellformed (cos : dtype_spec list)

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

   679       let

   680         val ts = all_values_of_type card typ

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

   682       in

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

   684                (all_distinct_unordered_pairs_of ts)

   685       end

   686     (* string -> Pretty.T *)

   687     fun pretty_for_assign name =

   688       let

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

   690           case name of

   691             FreeName (s, T, _) =>

   692             let val t = Free (s, unarize_unbox_and_uniterize_type T) in

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

   694             end

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

   696             (assign_operator_for_const (s, T),

   697              user_friendly_const hol_ctxt base_step_names formats (s, T), T)

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

   699                             \pretty_for_assign", [name])

   700         val t2 = if rep_of name = Any then

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

   702                  else

   703                    tuple_list_for_name rel_table bounds name

   704                    |> term_for_rep false T T' (rep_of name)

   705       in

   706         Pretty.block (Pretty.breaks

   707             [setmp_show_all_types (Syntax.pretty_term ctxt) t1,

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

   709       end

   710     (* dtype_spec -> Pretty.T *)

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

   712       Pretty.block (Pretty.breaks

   713           [Syntax.pretty_typ ctxt (unarize_unbox_and_uniterize_type typ),

   714            Pretty.str "=",

   715            Pretty.enum "," "{" "}"

   716                (map (Syntax.pretty_term ctxt) (all_values_of_type card typ) @

   717                 (if fun_from_pair complete false then []

   718                  else [Pretty.str unrep]))])

   719     (* typ -> dtype_spec list *)

   720     fun integer_datatype T =

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

   722         standard = true, complete = (false, false), concrete = (true, true),

   723         deep = true, constrs = []}]

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

   725     val (codatatypes, datatypes) =

   726       datatypes |> filter #deep |> List.partition #co

   727                 ||> append (integer_datatype int_T

   728                             |> is_standard_datatype thy stds nat_T

   729                                ? append (integer_datatype nat_T))

   730     val block_of_datatypes =

   731       if show_datatypes andalso not (null datatypes) then

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

   733                          (map pretty_for_datatype datatypes)]

   734       else

   735         []

   736     val block_of_codatatypes =

   737       if show_datatypes andalso not (null codatatypes) then

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

   739                          (map pretty_for_datatype codatatypes)]

   740       else

   741         []

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

   743     fun block_of_names show title names =

   744       if show andalso not (null names) then

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

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

   747                (sort_wrt (original_name o nickname_of) names)

   748       else

   749         []

   750     val (skolem_names, nonskolem_nonsel_names) =

   751       List.partition is_skolem_name nonsel_names

   752     val (eval_names, noneval_nonskolem_nonsel_names) =

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

   754                      nonskolem_nonsel_names

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

   756                       o nickname_of)

   757     val free_names =

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

   759               case filter (curry (op =) x

   760                        o pairf nickname_of

   761                                (unarize_unbox_and_uniterize_type o type_of))

   762                        free_names of

   763                 [name] => name

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

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

   766                                  [Const x])) all_frees

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

   768                  block_of_names show_skolems "Skolem constant" skolem_names @

   769                  block_of_names true "Evaluated term" eval_names @

   770                  block_of_datatypes @ block_of_codatatypes @

   771                  block_of_names show_consts "Constant"

   772                                 noneval_nonskolem_nonsel_names

   773   in

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

   775                     else chunks),

   776      bisim_depth >= 0 orelse

   777      forall (is_codatatype_wellformed codatatypes) codatatypes)

   778   end

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

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

   782 fun prove_hol_model (scope as {hol_ctxt = {thy, ctxt, debug, ...},

   783                                card_assigns, ...})

   784                     auto_timeout free_names sel_names rel_table bounds prop =

   785   let

   786     val pool = Unsynchronized.ref []

   787     (* typ * int -> term *)

   788     fun free_type_assm (T, k) =

   789       let

   790         (* int -> term *)

   791         fun atom j = nth_atom pool true T j k

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

   793         val eqs = map equation_for_atom (index_seq 0 k)

   794         val compreh_assm =

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

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

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

   798       in s_conj (compreh_assm, distinct_assm) end

   799     (* nut -> term *)

   800     fun free_name_assm name =

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

   802                      term_for_name pool scope sel_names rel_table bounds name)

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

   804     val model_assms = map free_name_assm free_names

   805     val assm = foldr1 s_conj (freeT_assms @ model_assms)

   806     (* bool -> bool *)

   807     fun try_out negate =

   808       let

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

   810                     (Object_Logic.atomize_term thy prop)

   811         val prop = HOLogic.mk_Trueprop (HOLogic.mk_imp (assm, concl))

   812                    |> map_types (map_type_tfree

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

   814                                        | x => TFree x))

   815        val _ = if debug then

   816                  priority ((if negate then "Genuineness" else "Spuriousness") ^

   817                            " goal: " ^ Syntax.string_of_term ctxt prop ^ ".")

   818                else

   819                  ()

   820         val goal = prop |> cterm_of thy |> Goal.init

   821       in

   822         (goal |> SINGLE (DETERM_TIMEOUT auto_timeout

   823                                         (auto_tac (clasimpset_of ctxt)))

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

   825         handle THM _ => false

   826              | TimeLimit.TimeOut => false

   827       end

   828   in

   829     if try_out false then SOME true

   830     else if try_out true then SOME false

   831     else NONE

   832   end

   834 end;

author	wenzelm
	Sun, 07 Mar 2010 12:19:47 +0100
changeset 35625	9c818cab0dd0
parent 35408	b48ab741683b
child 35665	ff2bf50505ab
permissions	-rw-r--r--