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}

    19   type term_postprocessor =

    20     Proof.context -> string -> (typ -> term list) -> typ -> term -> term

    22   structure NameTable : TABLE

    24   val irrelevant : string

    25   val unknown : string

    26   val unrep : string

    27   val register_term_postprocessor :

    28     typ -> term_postprocessor -> theory -> theory

    29   val unregister_term_postprocessor : typ -> theory -> theory

    30   val tuple_list_for_name :

    31     nut NameTable.table -> Kodkod.raw_bound list -> nut -> int list list

    32   val dest_plain_fun : term -> bool * (term list * term list)

    33   val reconstruct_hol_model :

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

    35     -> nut list -> nut list -> nut NameTable.table -> Kodkod.raw_bound list

    36     -> Pretty.T * bool

    37   val prove_hol_model :

    38     scope -> Time.time option -> nut list -> nut list -> nut NameTable.table

    39     -> Kodkod.raw_bound list -> term -> bool option

    40 end;

    42 structure Nitpick_Model : NITPICK_MODEL =

    43 struct

    45 open Nitpick_Util

    46 open Nitpick_HOL

    47 open Nitpick_Scope

    48 open Nitpick_Peephole

    49 open Nitpick_Rep

    50 open Nitpick_Nut

    52 structure KK = Kodkod

    54 type params = {

    55   show_skolems: bool,

    56   show_datatypes: bool,

    57   show_consts: bool}

    59 type term_postprocessor =

    60   Proof.context -> string -> (typ -> term list) -> typ -> term -> term

    62 structure Data = Theory_Data(

    63   type T = (typ * term_postprocessor) list

    64   val empty = []

    65   val extend = I

    66   fun merge (ps1, ps2) = AList.merge (op =) (K true) (ps1, ps2))

    68 val irrelevant = "_"

    69 val unknown = "?"

    70 val unrep = "\<dots>"

    71 val maybe_mixfix = "_\<^sup>?"

    72 val base_mixfix = "_\<^bsub>base\<^esub>"

    73 val step_mixfix = "_\<^bsub>step\<^esub>"

    74 val abs_mixfix = "\<guillemotleft>_\<guillemotright>"

    75 val cyclic_co_val_name = "\<omega>"

    76 val cyclic_const_prefix = "\<xi>"

    77 val cyclic_type_name = nitpick_prefix ^ cyclic_const_prefix

    78 val opt_flag = nitpick_prefix ^ "opt"

    79 val non_opt_flag = nitpick_prefix ^ "non_opt"

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

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

    84 fun nth_atom_suffix pool s j k =

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

    86      SOME js =>

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

    88         ~1 => (Unsynchronized.change pool (cons ((s, k), j :: js));

    89                length js + 1)

    90       | n => length js - n)

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

    92   |> nat_subscript

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

    94      ? prefix "\<^isub>,"

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

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

    97     let val s' = shortest_name s in

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

    99       nth_atom_suffix pool s j k

   100     end

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

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

   103   | nth_atom_name _ _ T _ _ =

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

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

   106 fun nth_atom pool for_auto T j k =

   107   if for_auto then

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

   109   else

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

   112 (* term -> real *)

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

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

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

   116 (* term * term -> order *)

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

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

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

   120            case tp of

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

   122              (case nice_term_ord (t11, t21) of

   123                 EQUAL => nice_term_ord (t12, t22)

   124               | ord => ord)

   125            | _ => Term_Ord.fast_term_ord tp

   127 (* typ -> term_postprocessor -> theory -> theory *)

   128 fun register_term_postprocessor T p = Data.map (cons (T, p))

   129 (* typ -> theory -> theory *)

   130 fun unregister_term_postprocessor T = Data.map (AList.delete (op =) T)

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

   133 fun tuple_list_for_name rel_table bounds name =

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

   136 (* term -> term *)

   137 fun unarize_unbox_etc_term (Const (@{const_name FinFun}, _) $ t1) =

   138     unarize_unbox_etc_term t1

   139   | unarize_unbox_etc_term (Const (@{const_name FunBox}, _) $ t1) =

   140     unarize_unbox_etc_term t1

   141   | unarize_unbox_etc_term

   142         (Const (@{const_name PairBox},

   143                 Type (@{type_name fun}, [T1, Type (@{type_name fun}, [T2, _])]))

   144          $ t1 $ t2) =

   145     let val Ts = map uniterize_unarize_unbox_etc_type [T1, T2] in

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

   147       $ unarize_unbox_etc_term t1 $ unarize_unbox_etc_term t2

   148     end

   149   | unarize_unbox_etc_term (Const (s, T)) =

   150     Const (s, uniterize_unarize_unbox_etc_type T)

   151   | unarize_unbox_etc_term (t1 $ t2) =

   152     unarize_unbox_etc_term t1 $ unarize_unbox_etc_term t2

   153   | unarize_unbox_etc_term (Free (s, T)) =

   154     Free (s, uniterize_unarize_unbox_etc_type T)

   155   | unarize_unbox_etc_term (Var (x, T)) =

   156     Var (x, uniterize_unarize_unbox_etc_type T)

   157   | unarize_unbox_etc_term (Bound j) = Bound j

   158   | unarize_unbox_etc_term (Abs (s, T, t')) =

   159     Abs (s, uniterize_unarize_unbox_etc_type T, unarize_unbox_etc_term t')

   161 (* typ -> typ -> (typ * typ) * (typ * typ) *)

   162 fun factor_out_types (T1 as Type (@{type_name "*"}, [T11, T12]))

   163                      (T2 as Type (@{type_name "*"}, [T21, T22])) =

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

   165       if n1 = n2 then

   166         let

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

   168         in

   169           ((Type (@{type_name "*"}, [T11, T11']), opt_T12'),

   170            (Type (@{type_name "*"}, [T21, T21']), opt_T22'))

   171         end

   172       else if n1 < n2 then

   173         case factor_out_types T1 T21 of

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

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

   176           (p1, (T21', SOME (Type (@{type_name "*"}, [T22', T22]))))

   177       else

   178         swap (factor_out_types T2 T1)

   179     end

   180   | factor_out_types (Type (@{type_name "*"}, [T11, T12])) T2 =

   181     ((T11, SOME T12), (T2, NONE))

   182   | factor_out_types T1 (Type (@{type_name "*"}, [T21, T22])) =

   183     ((T1, NONE), (T21, SOME T22))

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

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

   187 fun make_plain_fun maybe_opt T1 T2 =

   188   let

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

   190     fun aux T1 T2 [] =

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

   192       | aux T1 T2 ((t1, t2) :: tps) =

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

   194         $ aux T1 T2 tps $ t1 $ t2

   195   in aux T1 T2 o rev end

   196 (* term -> bool *)

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

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

   199     is_plain_fun t0

   200   | is_plain_fun _ = false

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

   202 val dest_plain_fun =

   203   let

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

   205     fun aux (Abs (_, _, Const (s, _))) = (s <> irrelevant, ([], []))

   206       | aux (Const (s, _)) = (s <> non_opt_flag, ([], []))

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

   208         let val (maybe_opt, (ts1, ts2)) = aux t0 in

   209           (maybe_opt, (t1 :: ts1, t2 :: ts2))

   210         end

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

   212   in apsnd (pairself rev) o aux end

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

   215 fun break_in_two T T1 T2 t =

   216   let

   217     val ps = HOLogic.flat_tupleT_paths T

   218     val cut = length (HOLogic.strip_tupleT T1)

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

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

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

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

   223 fun pair_up (Type (@{type_name "*"}, [T1', T2']))

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

   225                           Type (@{type_name fun},

   226                                 [_, Type (@{type_name fun}, [_, T1])]))

   227              $ t11 $ t12) t2 =

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

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

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

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

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

   234 (* typ -> typ -> typ -> term -> term *)

   235 fun typecast_fun (Type (@{type_name fun}, [T1', T2'])) T1 T2 t =

   236     let

   237       (* typ -> typ -> typ -> typ -> term -> term *)

   238       fun do_curry T1 T1a T1b T2 t =

   239         let

   240           val (maybe_opt, tsp) = dest_plain_fun t

   241           val tps =

   242             tsp |>> map (break_in_two T1 T1a T1b)

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

   244                 |> AList.coalesce (op =)

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

   246         in make_plain_fun maybe_opt T1a (T1b --> T2) tps end

   247       (* typ -> typ -> term -> term *)

   248       and do_uncurry T1 T2 t =

   249         let

   250           val (maybe_opt, tsp) = dest_plain_fun t

   251           val tps =

   252             tsp |> op ~~

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

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

   255         in make_plain_fun maybe_opt T1 T2 tps end

   256       (* typ -> typ -> typ -> typ -> term -> term *)

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

   258         | do_arrow T1' T2' T1 T2

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

   260           Const (@{const_name fun_upd},

   261                  (T1' --> T2') --> T1' --> T2' --> T1' --> T2')

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

   263         | do_arrow _ _ _ _ t =

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

   265       and do_fun T1' T2' T1 T2 t =

   266         case factor_out_types T1' T1 of

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

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

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

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

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

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

   273       (* typ -> typ -> term -> term *)

   274       and do_term (Type (@{type_name fun}, [T1', T2']))

   275                   (Type (@{type_name fun}, [T1, T2])) t =

   276           do_fun T1' T2' T1 T2 t

   277         | do_term (T' as Type (@{type_name "*"}, Ts' as [T1', T2']))

   278                   (Type (@{type_name "*"}, [T1, T2]))

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

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

   281           $ do_term T1' T1 t1 $ do_term T2' T2 t2

   282         | do_term T' T t =

   283           if T = T' then t

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

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

   286   | typecast_fun T' _ _ _ =

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

   289 (* term -> string *)

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

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

   292   | truth_const_sort_key _ = "1"

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

   295 fun mk_tuple (Type (@{type_name "*"}, [T1, T2])) ts =

   296     HOLogic.mk_prod (mk_tuple T1 ts,

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

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

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

   301 (* theory -> typ * typ -> bool *)

   302 fun varified_type_match thy (candid_T, pat_T) =

   303   strict_type_match thy (candid_T, Logic.varifyT pat_T)

   305 (* atom_pool -> (string * string) * (string * string) -> scope -> nut list

   306    -> nut list -> nut list -> nut NameTable.table -> KK.raw_bound list -> typ

   307    -> term list *)

   308 fun all_values_of_type pool wacky_names (scope as {card_assigns, ...} : scope)

   309                        sel_names rel_table bounds card T =

   310   let

   311     val card = if card = 0 then card_of_type card_assigns T else card

   312     (* nat -> term *)

   313     fun nth_value_of_type n =

   314       let

   315         (* bool -> term *)

   316         fun term unfold =

   317           reconstruct_term unfold pool wacky_names scope sel_names rel_table

   318                            bounds T T (Atom (card, 0)) [[n]]

   319       in

   320         case term false of

   321           t as Const (s, _) =>

   322           if String.isPrefix cyclic_const_prefix s then

   323             HOLogic.mk_eq (t, term true)

   324           else

   325             t

   326         | t => t

   327       end

   328   in index_seq 0 card |> map nth_value_of_type |> sort nice_term_ord end

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

   330    -> nut list -> nut list -> nut list -> nut NameTable.table

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

   332 and reconstruct_term unfold pool (wacky_names as ((maybe_name, abs_name), _))

   333         (scope as {hol_ctxt as {ctxt, thy, stds, ...}, binarize, card_assigns,

   334                    bits, datatypes, ofs, ...}) sel_names rel_table bounds =

   335   let

   336     val for_auto = (maybe_name = "")

   337     (* int list list -> int *)

   338     fun value_of_bits jss =

   339       let

   340         val j0 = offset_of_type ofs @{typ unsigned_bit}

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

   342       in

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

   344              js 0

   345       end

   346     (* typ -> term list *)

   347     val all_values =

   348       all_values_of_type pool wacky_names scope sel_names rel_table bounds 0

   349     (* typ -> term -> term *)

   350     fun postprocess_term (Type (@{type_name fun}, _)) = I

   351       | postprocess_term T =

   352         if null (Data.get thy) then

   353           I

   354         else case AList.lookup (varified_type_match thy) (Data.get thy) T of

   355           SOME postproc => postproc ctxt maybe_name all_values T

   356         | NONE => I

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

   358     fun postprocess_subterms Ts (t1 $ t2) =

   359         let val t = postprocess_subterms Ts t1 $ postprocess_subterms Ts t2 in

   360           postprocess_term (fastype_of1 (Ts, t)) t

   361         end

   362       | postprocess_subterms Ts (Abs (s, T, t')) =

   363         Abs (s, T, postprocess_subterms (T :: Ts) t')

   364       | postprocess_subterms Ts t = postprocess_term (fastype_of1 (Ts, t)) t

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

   366     fun make_set maybe_opt T1 T2 tps =

   367       let

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

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

   370                                   T1 --> (T1 --> T2) --> T1 --> T2)

   371         (* (term * term) list -> term *)

   372         fun aux [] =

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

   374               insert_const $ Const (unrep, T1) $ empty_const

   375             else

   376               empty_const

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

   378             aux zs

   379             |> t2 <> @{const False}

   380                ? curry (op $)

   381                        (insert_const

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

   383                                  ? curry (op $)

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

   385       in

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

   387                   tps then

   388           Const (unknown, T1 --> T2)

   389         else

   390           aux tps

   391       end

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

   393     fun make_map maybe_opt T1 T2 T2' =

   394       let

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

   396                                   (T1 --> T2) --> T1 --> T2 --> T1 --> T2)

   397         (* (term * term) list -> term *)

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

   399           | aux' ((t1, t2) :: tps) =

   400             (case t2 of

   401                Const (@{const_name None}, _) => aux' tps

   402              | _ => update_const $ aux' tps $ t1 $ t2)

   403         fun aux tps =

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

   405             update_const $ aux' tps $ Const (unrep, T1)

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

   407           else

   408             aux' tps

   409       in aux end

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

   411     fun polish_funs Ts t =

   412       (case fastype_of1 (Ts, t) of

   413          Type (@{type_name fun}, [T1, T2]) =>

   414          if is_plain_fun t then

   415            case T2 of

   416              @{typ bool} =>

   417              let

   418                val (maybe_opt, ts_pair) =

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

   420              in

   421                make_set maybe_opt T1 T2

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

   423              end

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

   425              let

   426                val (maybe_opt, ts_pair) =

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

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

   429            | _ => raise SAME ()

   430          else

   431            raise SAME ()

   432        | _ => raise SAME ())

   433       handle SAME () =>

   434              case t of

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

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

   437                if s = unknown then polish_funs Ts t11

   438                else polish_funs Ts t1 $ polish_funs Ts t2

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

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

   441              | Const (s, Type (@{type_name fun}, [T1, T2])) =>

   442                if s = opt_flag orelse s = non_opt_flag then

   443                  Abs ("x", T1,

   444                       Const (if is_complete_type datatypes false T1 then

   445                                irrelevant

   446                              else

   447                                unknown, T2))

   448                else

   449                  t

   450              | t => t

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

   452     fun make_fun maybe_opt T1 T2 T' ts1 ts2 =

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

   454                  |> make_plain_fun maybe_opt T1 T2

   455                  |> unarize_unbox_etc_term

   456                  |> typecast_fun (uniterize_unarize_unbox_etc_type T')

   457                                  (uniterize_unarize_unbox_etc_type T1)

   458                                  (uniterize_unarize_unbox_etc_type T2)

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

   460     fun term_for_atom seen (T as Type (@{type_name fun}, [T1, T2])) T' j _ =

   461         let

   462           val k1 = card_of_type card_assigns T1

   463           val k2 = card_of_type card_assigns T2

   464         in

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

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

   467           handle General.Subscript =>

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

   469                             signed_string_of_int j ^ " for " ^

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

   471         end

   472       | term_for_atom seen (Type (@{type_name "*"}, [T1, T2])) _ j k =

   473         let

   474           val k1 = card_of_type card_assigns T1

   475           val k2 = k div k1

   476         in

   477           list_comb (HOLogic.pair_const T1 T2,

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

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

   480         end

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

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

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

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

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

   486       | term_for_atom seen T _ j k =

   487         if T = nat_T andalso is_standard_datatype thy stds nat_T then

   488           HOLogic.mk_number nat_T j

   489         else if T = int_T then

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

   491         else if is_fp_iterator_type T then

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

   493         else if T = @{typ bisim_iterator} then

   494           HOLogic.mk_number nat_T j

   495         else case datatype_spec datatypes T of

   496           NONE => nth_atom pool for_auto T j k

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

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

   499           let

   500             (* styp -> int list *)

   501             fun tuples_for_const (s, T) =

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

   503             (* unit -> term *)

   504             fun cyclic_atom () =

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

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

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

   509                                  constrs

   510             val real_j = j + offset_of_type ofs T

   511             val constr_x as (constr_s, constr_T) =

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

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

   514                             else NONE)

   515                         (discr_jsss ~~ constrs) |> the

   516             val arg_Ts = curried_binder_types constr_T

   517             val sel_xs =

   518               map (binarized_and_boxed_nth_sel_for_constr hol_ctxt binarize

   519                                                           constr_x)

   520                   (index_seq 0 (length arg_Ts))

   521             val sel_Rs =

   522               map (fn x => get_first

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

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

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

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

   527                                sel_names |> the) sel_xs

   528             val arg_Rs = map (snd o dest_Func) sel_Rs

   529             val sel_jsss = map tuples_for_const sel_xs

   530             val arg_jsss =

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

   532                                         else NONE)) sel_jsss

   533             val uncur_arg_Ts = binder_types constr_T

   534             val maybe_cyclic = co orelse not standard

   535           in

   536             if maybe_cyclic andalso not (null seen) andalso

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

   538               cyclic_var ()

   539             else if constr_s = @{const_name Word} then

   540               HOLogic.mk_number

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

   542                   (value_of_bits (the_single arg_jsss))

   543             else

   544               let

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

   546                 val ts =

   547                   if length arg_Ts = 0 then

   548                     []

   549                   else

   550                     map3 (fn Ts =>

   551                              term_for_rep (constr_s <> @{const_name FinFun})

   552                                           seen Ts Ts) arg_Ts arg_Rs arg_jsss

   553                     |> mk_tuple (HOLogic.mk_tupleT uncur_arg_Ts)

   554                     |> dest_n_tuple (length uncur_arg_Ts)

   555                 val t =

   556                   if constr_s = @{const_name Abs_Frac} then

   557                     case ts of

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

   559                       frac_from_term_pair (body_type T) t1 t2

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

   561                                        \term_for_atom (Abs_Frac)", ts)

   562                   else if not for_auto andalso

   563                           (is_abs_fun thy constr_x orelse

   564                            constr_s = @{const_name Quot}) then

   565                     Const (abs_name, constr_T) $ the_single ts

   566                   else

   567                     list_comb (Const constr_x, ts)

   568               in

   569                 if maybe_cyclic then

   570                   let val var = cyclic_var () in

   571                     if unfold andalso not standard andalso

   572                        length seen = 1 andalso

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

   574                                           String.isPrefix cyclic_const_prefix s

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

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

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

   578                       if co then

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

   580                         $ Abs (cyclic_co_val_name, T,

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

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

   583                       else

   584                         cyclic_atom ()

   585                     else

   586                       t

   587                   end

   588                 else

   589                   t

   590               end

   591           end

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

   593        -> term *)

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

   595       make_fun true T1 T2 T'

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

   597                (map (term_for_rep true seen T2 T2 R o single)

   598                     (batch_list (arity_of_rep R) js))

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

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

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

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

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

   604       | term_for_rep _ seen (Type (@{type_name "*"}, [T1, T2])) _

   605                      (Struct [R1, R2]) [js] =

   606         let

   607           val arity1 = arity_of_rep R1

   608           val (js1, js2) = chop arity1 js

   609         in

   610           list_comb (HOLogic.pair_const T1 T2,

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

   612                           [[js1], [js2]])

   613         end

   614       | term_for_rep _ seen (Type (@{type_name fun}, [T1, T2])) T'

   615                      (Vect (k, R')) [js] =

   616         term_for_vect seen k R' T1 T2 T' js

   617       | term_for_rep _ seen (Type (@{type_name fun}, [T1, T2])) T'

   618                      (Func (R1, Formula Neut)) jss =

   619         let

   620           val jss1 = all_combinations_for_rep R1

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

   622           val ts2 =

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

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

   625                 jss1

   626         in make_fun false T1 T2 T' ts1 ts2 end

   627       | term_for_rep maybe_opt seen (Type (@{type_name fun}, [T1, T2])) T'

   628                      (Func (R1, R2)) jss =

   629         let

   630           val arity1 = arity_of_rep R1

   631           val jss1 = all_combinations_for_rep R1

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

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

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

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

   636         in make_fun maybe_opt T1 T2 T' ts1 ts2 end

   637       | term_for_rep _ seen T T' (Opt R) jss =

   638         if null jss then Const (unknown, T)

   639         else term_for_rep true seen T T' R jss

   640       | term_for_rep _ _ T _ R jss =

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

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

   643                    string_of_int (length jss))

   644   in

   645     postprocess_subterms [] o polish_funs [] o unarize_unbox_etc_term

   646     oooo term_for_rep true []

   647   end

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

   650    -> nut -> term *)

   651 fun term_for_name pool scope sel_names rel_table bounds name =

   652   let val T = type_of name in

   653     tuple_list_for_name rel_table bounds name

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

   655                         rel_table bounds T T (rep_of name)

   656   end

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

   659 fun add_wacky_syntax ctxt =

   660   let

   661     (* term -> string *)

   662     val name_of = fst o dest_Const

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

   664     val (maybe_t, thy) =

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

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

   667     val (abs_t, thy) =

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

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

   670     val (base_t, thy) =

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

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

   673     val (step_t, thy) =

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

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

   676   in

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

   678      ProofContext.transfer_syntax thy ctxt)

   679   end

   681 (* term -> term *)

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

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

   684                                                 $ Bound 0 $ t')) =

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

   686   | unfold_outer_the_binders t = t

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

   688 fun bisimilar_values _ 0 _ = true

   689   | bisimilar_values coTs max_depth (t1, t2) =

   690     let val T = fastype_of t1 in

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

   692         let

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

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

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

   696         in

   697           head1 = head2 andalso

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

   699         end

   700       else

   701         t1 = t2

   702     end

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

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

   706   -> Pretty.T * bool *)

   707 fun reconstruct_hol_model {show_skolems, show_datatypes, show_consts}

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

   709                       debug, binary_ints, destroy_constrs, specialize,

   710                       skolemize, star_linear_preds, uncurry, fast_descrs,

   711                       tac_timeout, evals, case_names, def_table, nondef_table,

   712                       user_nondefs, simp_table, psimp_table, intro_table,

   713                       ground_thm_table, ersatz_table, skolems, special_funs,

   714                       unrolled_preds, wf_cache, constr_cache},

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

   716         formats all_frees free_names sel_names nonsel_names rel_table bounds =

   717   let

   718     val pool = Unsynchronized.ref []

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

   720       add_wacky_syntax ctxt

   721     val hol_ctxt =

   722       {thy = thy, ctxt = ctxt, max_bisim_depth = max_bisim_depth, boxes = boxes,

   723        stds = stds, wfs = wfs, user_axioms = user_axioms, debug = debug,

   724        binary_ints = binary_ints, destroy_constrs = destroy_constrs,

   725        specialize = specialize, skolemize = skolemize,

   726        star_linear_preds = star_linear_preds, uncurry = uncurry,

   727        fast_descrs = fast_descrs, tac_timeout = tac_timeout, evals = evals,

   728        case_names = case_names, def_table = def_table,

   729        nondef_table = nondef_table, user_nondefs = user_nondefs,

   730        simp_table = simp_table, psimp_table = psimp_table,

   731        intro_table = intro_table, ground_thm_table = ground_thm_table,

   732        ersatz_table = ersatz_table, skolems = skolems,

   733        special_funs = special_funs, unrolled_preds = unrolled_preds,

   734        wf_cache = wf_cache, constr_cache = constr_cache}

   735     val scope = {hol_ctxt = hol_ctxt, binarize = binarize,

   736                  card_assigns = card_assigns, bits = bits,

   737                  bisim_depth = bisim_depth, datatypes = datatypes, ofs = ofs}

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

   739     fun term_for_rep unfold =

   740       reconstruct_term unfold pool wacky_names scope sel_names rel_table bounds

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

   742     fun nth_value_of_type card T n =

   743       let

   744         (* bool -> term *)

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

   746       in

   747         case aux false of

   748           t as Const (s, _) =>

   749           if String.isPrefix cyclic_const_prefix s then

   750             HOLogic.mk_eq (t, aux true)

   751           else

   752             t

   753         | t => t

   754       end

   755     (* nat -> typ -> term list *)

   756     val all_values =

   757       all_values_of_type pool wacky_names scope sel_names rel_table bounds

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

   759     fun is_codatatype_wellformed (cos : dtype_spec list)

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

   761       let

   762         val ts = all_values card typ

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

   764       in

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

   766                (all_distinct_unordered_pairs_of ts)

   767       end

   768     (* string -> Pretty.T *)

   769     fun pretty_for_assign name =

   770       let

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

   772           case name of

   773             FreeName (s, T, _) =>

   774             let val t = Free (s, uniterize_unarize_unbox_etc_type T) in

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

   776             end

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

   778             (assign_operator_for_const (s, T),

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

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

   781                             \pretty_for_assign", [name])

   782         val t2 = if rep_of name = Any then

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

   784                  else

   785                    tuple_list_for_name rel_table bounds name

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

   787       in

   788         Pretty.block (Pretty.breaks

   789             [setmp_show_all_types (Syntax.pretty_term ctxt) t1,

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

   791       end

   792     (* dtype_spec -> Pretty.T *)

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

   794       Pretty.block (Pretty.breaks

   795           (Syntax.pretty_typ ctxt (uniterize_unarize_unbox_etc_type typ) ::

   796            (case typ of

   797               Type (@{type_name fin_fun}, _) => [Pretty.str "[finite]"]

   798             | Type (@{type_name fun_box}, _) => [Pretty.str "[boxed]"]

   799             | Type (@{type_name pair_box}, _) => [Pretty.str "[boxed]"]

   800             | _ => []) @

   801            [Pretty.str "=",

   802             Pretty.enum "," "{" "}"

   803                 (map (Syntax.pretty_term ctxt) (all_values card typ) @

   804                  (if fun_from_pair complete false then []

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

   806     (* typ -> dtype_spec list *)

   807     fun integer_datatype T =

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

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

   810         deep = true, constrs = []}]

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

   812     val (codatatypes, datatypes) =

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

   814                 ||> append (integer_datatype int_T

   815                             |> is_standard_datatype thy stds nat_T

   816                                ? append (integer_datatype nat_T))

   817     val block_of_datatypes =

   818       if show_datatypes andalso not (null datatypes) then

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

   820                          (map pretty_for_datatype datatypes)]

   821       else

   822         []

   823     val block_of_codatatypes =

   824       if show_datatypes andalso not (null codatatypes) then

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

   826                          (map pretty_for_datatype codatatypes)]

   827       else

   828         []

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

   830     fun block_of_names show title names =

   831       if show andalso not (null names) then

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

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

   834                (sort_wrt (original_name o nickname_of) names)

   835       else

   836         []

   837     val (skolem_names, nonskolem_nonsel_names) =

   838       List.partition is_skolem_name nonsel_names

   839     val (eval_names, noneval_nonskolem_nonsel_names) =

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

   841                      nonskolem_nonsel_names

   842       ||> filter_out (member (op =) [@{const_name bisim},

   843                                      @{const_name bisim_iterator_max}]

   844                       o nickname_of)

   845     val free_names =

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

   847               case filter (curry (op =) x

   848                        o pairf nickname_of

   849                                (uniterize_unarize_unbox_etc_type o type_of))

   850                        free_names of

   851                 [name] => name

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

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

   854                                  [Const x])) all_frees

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

   856                  block_of_names show_skolems "Skolem constant" skolem_names @

   857                  block_of_names true "Evaluated term" eval_names @

   858                  block_of_datatypes @ block_of_codatatypes @

   859                  block_of_names show_consts "Constant"

   860                                 noneval_nonskolem_nonsel_names

   861   in

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

   863                     else chunks),

   864      bisim_depth >= 0 orelse

   865      forall (is_codatatype_wellformed codatatypes) codatatypes)

   866   end

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

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

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

   871                                card_assigns, ...})

   872                     auto_timeout free_names sel_names rel_table bounds prop =

   873   let

   874     val pool = Unsynchronized.ref []

   875     (* typ * int -> term *)

   876     fun free_type_assm (T, k) =

   877       let

   878         (* int -> term *)

   879         fun atom j = nth_atom pool true T j k

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

   881         val eqs = map equation_for_atom (index_seq 0 k)

   882         val compreh_assm =

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

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

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

   886       in s_conj (compreh_assm, distinct_assm) end

   887     (* nut -> term *)

   888     fun free_name_assm name =

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

   890                      term_for_name pool scope sel_names rel_table bounds name)

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

   892     val model_assms = map free_name_assm free_names

   893     val assm = foldr1 s_conj (freeT_assms @ model_assms)

   894     (* bool -> bool *)

   895     fun try_out negate =

   896       let

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

   898                     (Object_Logic.atomize_term thy prop)

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

   900                    |> map_types (map_type_tfree

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

   902                                        | x => TFree x))

   903        val _ = if debug then

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

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

   906                else

   907                  ()

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

   909       in

   910         (goal |> SINGLE (DETERM_TIMEOUT auto_timeout

   911                                         (auto_tac (clasimpset_of ctxt)))

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

   913         handle THM _ => false

   914              | TimeLimit.TimeOut => false

   915       end

   916   in

   917     if try_out false then SOME true

   918     else if try_out true then SOME false

   919     else NONE

   920   end

   922 end;

author	blanchet
	Thu, 11 Mar 2010 15:33:45 +0100
changeset 35712	77aa29bf14ee
parent 35711	548d3f16404b
child 35714	eee1a5e0d334
permissions	-rw-r--r--