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 type params = {

    44   show_skolems: bool,

    45   show_datatypes: bool,

    46   show_consts: bool}

    48 val unknown = "?"

    49 val unrep = "\<dots>"

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

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

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

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

    54 val non_opt_name = nitpick_prefix ^ "non_opt"

    56 (* string -> int -> string *)

    57 fun atom_suffix s j =

    58   nat_subscript (j + 1)

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

    60      ? prefix "\<^isub>,"

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

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

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

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

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

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

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

    68 fun atom for_auto T j =

    69   if for_auto then

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

    71   else

    72     Const (atom_name "" T j, T)

    74 (* nut NameTable.table -> Kodkod.raw_bound list -> nut -> int list list *)

    75 fun tuple_list_for_name rel_table bounds name =

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

    78 (* term -> term *)

    79 fun unbox_term (Const (@{const_name FunBox}, _) $ t1) = unbox_term t1

    80   | unbox_term (Const (@{const_name PairBox},

    81                        Type ("fun", [T1, Type ("fun", [T2, T3])])) $ t1 $ t2) =

    82     let val Ts = map unbox_type [T1, T2] in

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

    84       $ unbox_term t1 $ unbox_term t2

    85     end

    86   | unbox_term (Const (s, T)) = Const (s, unbox_type T)

    87   | unbox_term (t1 $ t2) = unbox_term t1 $ unbox_term t2

    88   | unbox_term (Free (s, T)) = Free (s, unbox_type T)

    89   | unbox_term (Var (x, T)) = Var (x, unbox_type T)

    90   | unbox_term (Bound j) = Bound j

    91   | unbox_term (Abs (s, T, t')) = Abs (s, unbox_type T, unbox_term t')

    93 (* typ -> typ -> (typ * typ) * (typ * typ) *)

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

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

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

    97       if n1 = n2 then

    98         let

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

   100         in

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

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

   103         end

   104       else if n1 < n2 then

   105         case factor_out_types T1 T21 of

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

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

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

   109       else

   110         swap (factor_out_types T2 T1)

   111     end

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

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

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

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

   117 fun make_plain_fun maybe_opt T1 T2 =

   118   let

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

   120     fun aux T1 T2 [] =

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

   122                else non_opt_name, T1 --> T2)

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

   124         Const (@{const_name fun_upd}, [T1 --> T2, T1, T2] ---> T1 --> T2)

   125         $ aux T1 T2 ps $ t1 $ t2

   126   in aux T1 T2 o rev end

   127 (* term -> bool *)

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

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

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

   131     is_plain_fun t0

   132   | is_plain_fun _ = false

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

   134 val dest_plain_fun =

   135   let

   136     (* term -> term list * term list *)

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

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

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

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

   141   in apsnd (pairself rev) o aux end

   143 (* typ -> typ -> typ -> term -> term * term *)

   144 fun break_in_two T T1 T2 t =

   145   let

   146     val ps = HOLogic.flat_tupleT_paths T

   147     val cut = length (HOLogic.strip_tupleT T1)

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

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

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

   151 (* typ -> term -> term -> term *)

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

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

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

   155             t2 =

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

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

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

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

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

   162 (* typ -> typ -> typ -> term -> term *)

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

   164     let

   165       (* typ -> typ -> typ -> typ -> term -> term *)

   166       fun do_curry T1 T1a T1b T2 t =

   167         let

   168           val (maybe_opt, ps) = dest_plain_fun t

   169           val ps =

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

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

   172                |> AList.coalesce (op =)

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

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

   175       (* typ -> typ -> term -> term *)

   176       and do_uncurry T1 T2 t =

   177         let

   178           val (maybe_opt, tsp) = dest_plain_fun t

   179           val ps =

   180             tsp |> op ~~

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

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

   183         in make_plain_fun maybe_opt T1 T2 ps end

   184       (* typ -> typ -> typ -> typ -> term -> term *)

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

   186         | do_arrow T1' T2' T1 T2

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

   188           Const (@{const_name fun_upd},

   189                  [T1' --> T2', T1', T2'] ---> T1' --> T2')

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

   191         | do_arrow _ _ _ _ t =

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

   193       and do_fun T1' T2' T1 T2 t =

   194         case factor_out_types T1' T1 of

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

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

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

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

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

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

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

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

   203           do_fun T1' T2' T1 T2 t

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

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

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

   207           $ do_term T1' T1 t1 $ do_term T2' T2 t2

   208         | do_term T' T t =

   209           if T = T' then t

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

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

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

   214 (* term -> string *)

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

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

   217   | truth_const_sort_key _ = "1"

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

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

   221     HOLogic.mk_prod (mk_tuple T1 ts,

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

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

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

   226    -> nut list -> nut NameTable.table -> Kodkod.raw_bound list -> typ -> typ

   227    -> rep -> int list list -> term *)

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

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

   230          : scope) sel_names rel_table bounds =

   231   let

   232     val for_auto = (maybe_name = "")

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

   234     fun make_set maybe_opt T1 T2 =

   235       let

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

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

   238                                   [T1, T1 --> T2] ---> T1 --> T2)

   239         (* (term * term) list -> term *)

   240         fun aux [] =

   241             if maybe_opt andalso not (is_precise_type datatypes T1) then

   242               insert_const $ Const (unrep, T1) $ empty_const

   243             else

   244               empty_const

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

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

   247                       ? curry (op $) (insert_const

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

   249                                                ? curry (op $)

   250                                                        (Const (maybe_name,

   251                                                                T1 --> T1))))

   252       in aux end

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

   254     fun make_map T1 T2 T2' =

   255       let

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

   257                                   [T1 --> T2, T1, T2] ---> T1 --> T2)

   258         (* (term * term) list -> term *)

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

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

   261             (case t2 of

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

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

   264         fun aux ps =

   265           if not (is_precise_type datatypes T1) then

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

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

   268           else

   269             aux' ps

   270       in aux end

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

   272     fun setify_mapify_funs Ts t =

   273       (case fastype_of1 (Ts, t) of

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

   275          if is_plain_fun t then

   276            case T2 of

   277              @{typ bool} =>

   278              let

   279                val (maybe_opt, ts_pair) =

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

   281              in

   282                make_set maybe_opt T1 T2

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

   284              end

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

   286              let

   287                val ts_pair = snd (dest_plain_fun t)

   288                              |> pairself (map (setify_mapify_funs Ts))

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

   290            | _ => raise SAME ()

   291          else

   292            raise SAME ()

   293        | _ => raise SAME ())

   294       handle SAME () =>

   295              case t of

   296                t1 $ t2 => setify_mapify_funs Ts t1 $ setify_mapify_funs Ts t2

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

   298              | _ => t

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

   300     fun make_fun maybe_opt T1 T2 T' ts1 ts2 =

   301       ts1 ~~ ts2 |> T1 = @{typ bisim_iterator} ? rev

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

   303                  |> unbox_term

   304                  |> typecast_fun (unbox_type T') (unbox_type T1) (unbox_type T2)

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

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

   307         let

   308           val k1 = card_of_type card_assigns T1

   309           val k2 = card_of_type card_assigns T2

   310         in

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

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

   313           handle General.Subscript =>

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

   315                             signed_string_of_int j ^ " for " ^

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

   317         end

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

   319         let val k1 = card_of_type card_assigns T1 in

   320           list_comb (HOLogic.pair_const T1 T2,

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

   322                           [j div k1, j mod k1])

   323         end

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

   325         HOLogic.mk_Trueprop (term_for_atom seen bool_T bool_T j)

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

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

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

   329       | term_for_atom seen T _ j =

   330         if T = nat_T then

   331           HOLogic.mk_number nat_T j

   332         else if T = int_T then

   333           HOLogic.mk_number int_T

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

   335         else if is_fp_iterator_type T then

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

   337         else if T = @{typ bisim_iterator} then

   338           HOLogic.mk_number nat_T j

   339         else case datatype_spec datatypes T of

   340           NONE => atom for_auto T j

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

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

   343           let

   344             (* styp -> int list *)

   345             fun tuples_for_const (s, T) =

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

   347             (* unit -> indexname * typ *)

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

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

   350                                  constrs

   351             val real_j = j + offset_of_type ofs T

   352             val constr_x as (constr_s, constr_T) =

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

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

   355                             else NONE)

   356                         (discr_jsss ~~ constrs) |> the

   357             val arg_Ts = curried_binder_types constr_T

   358             val sel_xs = map (boxed_nth_sel_for_constr ext_ctxt constr_x)

   359                              (index_seq 0 (length arg_Ts))

   360             val sel_Rs =

   361               map (fn x => get_first

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

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

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

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

   366                                sel_names |> the) sel_xs

   367             val arg_Rs = map (snd o dest_Func) sel_Rs

   368             val sel_jsss = map tuples_for_const sel_xs

   369             val arg_jsss =

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

   371                                         else NONE)) sel_jsss

   372             val uncur_arg_Ts = binder_types constr_T

   373           in

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

   375               Var (var ())

   376             else

   377               let

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

   379                 val ts =

   380                   if length arg_Ts = 0 then

   381                     []

   382                   else

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

   384                          arg_jsss

   385                     |> mk_tuple (HOLogic.mk_tupleT uncur_arg_Ts)

   386                     |> dest_n_tuple (length uncur_arg_Ts)

   387                 val t =

   388                   if constr_s = @{const_name Abs_Frac} then

   389                     let

   390                       val num_T = body_type T

   391                       (* int -> term *)

   392                       val mk_num = HOLogic.mk_number num_T

   393                     in

   394                       case ts of

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

   396                         (case snd (HOLogic.dest_number t1) of

   397                            0 => mk_num 0

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

   399                                    1 => mk_num n1

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

   401                                                 [num_T, num_T] ---> num_T)

   402                                          $ mk_num n1 $ mk_num n2)

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

   404                                          \for_atom (Abs_Frac)", ts)

   405                     end

   406                   else if not for_auto andalso is_abs_fun thy constr_x then

   407                     Const (abs_name, constr_T) $ the_single ts

   408                   else

   409                     list_comb (Const constr_x, ts)

   410               in

   411                 if co then

   412                   let val var = var () in

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

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

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

   416                              Const (@{const_name "op ="}, [T, T] ---> bool_T)

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

   418                     else

   419                       t

   420                   end

   421                 else

   422                   t

   423               end

   424           end

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

   426        -> term *)

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

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

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

   430                     (batch_list (arity_of_rep R) js))

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

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

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

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

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

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

   437         let

   438           val arity1 = arity_of_rep R1

   439           val (js1, js2) = chop arity1 js

   440         in

   441           list_comb (HOLogic.pair_const T1 T2,

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

   443                           [[js1], [js2]])

   444         end

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

   446         term_for_vect seen k R' T1 T2 T' js

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

   448                      jss =

   449         let

   450           val jss1 = all_combinations_for_rep R1

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

   452           val ts2 =

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

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

   455                 jss1

   456         in make_fun false T1 T2 T' ts1 ts2 end

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

   458         let

   459           val arity1 = arity_of_rep R1

   460           val jss1 = all_combinations_for_rep R1

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

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

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

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

   465         in make_fun true T1 T2 T' ts1 ts2 end

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

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

   468       | term_for_rep seen T _ R jss =

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

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

   471                    string_of_int (length jss))

   472   in

   473     (not for_auto ? setify_mapify_funs []) o unbox_term oooo term_for_rep []

   474   end

   476 (* scope -> nut list -> nut NameTable.table -> Kodkod.raw_bound list -> nut

   477    -> term *)

   478 fun term_for_name scope sel_names rel_table bounds name =

   479   let val T = type_of name in

   480     tuple_list_for_name rel_table bounds name

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

   482                         (rep_of name)

   483   end

   485 (* Proof.context

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

   487 fun add_wacky_syntax ctxt =

   488   let

   489     (* term -> string *)

   490     val name_of = fst o dest_Const

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

   492     val (maybe_t, thy) =

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

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

   495     val (base_t, thy) =

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

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

   498     val (step_t, thy) =

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

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

   501     val (abs_t, thy) =

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

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

   504   in

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

   506      ProofContext.transfer_syntax thy ctxt)

   507   end

   509 (* term -> term *)

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

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

   512                                                 $ Bound 0 $ t')) =

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

   514   | unfold_outer_the_binders t = t

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

   516 fun bisimilar_values _ 0 _ = true

   517   | bisimilar_values coTs max_depth (t1, t2) =

   518     let val T = fastype_of t1 in

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

   520         let

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

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

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

   524         in

   525           head1 = head2

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

   527         end

   528       else

   529         t1 = t2

   530     end

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

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

   534   -> Pretty.T * bool *)

   535 fun reconstruct_hol_model {show_skolems, show_datatypes, show_consts}

   536         ({ext_ctxt as {thy, ctxt, max_bisim_depth, boxes, user_axioms, debug,

   537                        wfs, destroy_constrs, specialize, skolemize,

   538                        star_linear_preds, uncurry, fast_descrs, tac_timeout,

   539                        evals, case_names, def_table, nondef_table, user_nondefs,

   540                        simp_table, psimp_table, intro_table, ground_thm_table,

   541                        ersatz_table, skolems, special_funs, unrolled_preds,

   542                        wf_cache, constr_cache},

   543          card_assigns, bisim_depth, datatypes, ofs} : scope) formats all_frees

   544         free_names sel_names nonsel_names rel_table bounds =

   545   let

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

   547       add_wacky_syntax ctxt

   548     val ext_ctxt =

   549       {thy = thy, ctxt = ctxt, max_bisim_depth = max_bisim_depth, boxes = boxes,

   550        wfs = wfs, user_axioms = user_axioms, debug = debug,

   551        destroy_constrs = destroy_constrs, specialize = specialize,

   552        skolemize = skolemize, star_linear_preds = star_linear_preds,

   553        uncurry = uncurry, fast_descrs = fast_descrs, tac_timeout = tac_timeout,

   554        evals = evals, case_names = case_names, def_table = def_table,

   555        nondef_table = nondef_table, user_nondefs = user_nondefs,

   556        simp_table = simp_table, psimp_table = psimp_table,

   557        intro_table = intro_table, ground_thm_table = ground_thm_table,

   558        ersatz_table = ersatz_table, skolems = skolems,

   559        special_funs = special_funs, unrolled_preds = unrolled_preds,

   560        wf_cache = wf_cache, constr_cache = constr_cache}

   561     val scope = {ext_ctxt = ext_ctxt, card_assigns = card_assigns,

   562                  bisim_depth = bisim_depth, datatypes = datatypes, ofs = ofs}

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

   564     val term_for_rep = reconstruct_term wacky_names scope sel_names rel_table

   565                                         bounds

   566     (* typ -> typ -> typ *)

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

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

   569     fun is_codatatype_wellformed (cos : dtype_spec list)

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

   571       let

   572         val ts = map (nth_value_of_type typ card) (index_seq 0 card)

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

   574       in

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

   576                (all_distinct_unordered_pairs_of ts)

   577       end

   578     (* string -> Pretty.T *)

   579     fun pretty_for_assign name =

   580       let

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

   582           case name of

   583             FreeName (s, T, _) =>

   584             let val t = Free (s, unbox_type T) in

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

   586             end

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

   588             (assign_operator_for_const (s, T),

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

   590              T)

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

   592                             \pretty_for_assign", [name])

   593         val t2 = if rep_of name = Any then

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

   595                  else

   596                    tuple_list_for_name rel_table bounds name

   597                    |> term_for_rep T T' (rep_of name)

   598       in

   599         Pretty.block (Pretty.breaks

   600             [setmp_show_all_types (Syntax.pretty_term ctxt) t1,

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

   602       end

   603     (* dtype_spec -> Pretty.T *)

   604     fun pretty_for_datatype ({typ, card, precise, ...} : dtype_spec) =

   605       Pretty.block (Pretty.breaks

   606           [Syntax.pretty_typ ctxt (unbox_type typ), Pretty.str "=",

   607            Pretty.enum "," "{" "}"

   608                (map (Syntax.pretty_term ctxt o nth_value_of_type typ card)

   609                     (index_seq 0 card) @

   610                 (if precise then [] else [Pretty.str unrep]))])

   611     (* typ -> dtype_spec list *)

   612     fun integer_datatype T =

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

   614         precise = false, shallow = false, constrs = []}]

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

   616     val (codatatypes, datatypes) =

   617       datatypes |> filter_out #shallow

   618                 |> List.partition #co

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

   620     val block_of_datatypes =

   621       if show_datatypes andalso not (null datatypes) then

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

   623                          (map pretty_for_datatype datatypes)]

   624       else

   625         []

   626     val block_of_codatatypes =

   627       if show_datatypes andalso not (null codatatypes) then

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

   629                          (map pretty_for_datatype codatatypes)]

   630       else

   631         []

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

   633     fun block_of_names show title names =

   634       if show andalso not (null names) then

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

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

   637                (sort_wrt (original_name o nickname_of) names)

   638       else

   639         []

   640     val (skolem_names, nonskolem_nonsel_names) =

   641       List.partition is_skolem_name nonsel_names

   642     val (eval_names, noneval_nonskolem_nonsel_names) =

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

   644                      nonskolem_nonsel_names

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

   646                       o nickname_of)

   647     val free_names =

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

   649               case filter (curry (op =) x

   650                            o pairf nickname_of (unbox_type o type_of))

   651                           free_names of

   652                 [name] => name

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

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

   655                                  [Const x])) all_frees

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

   657                  block_of_names show_skolems "Skolem constant" skolem_names @

   658                  block_of_names true "Evaluated term" eval_names @

   659                  block_of_datatypes @ block_of_codatatypes @

   660                  block_of_names show_consts "Constant"

   661                                 noneval_nonskolem_nonsel_names

   662   in

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

   664                     else chunks),

   665      bisim_depth >= 0

   666      orelse forall (is_codatatype_wellformed codatatypes) codatatypes)

   667   end

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

   670    -> Kodkod.raw_bound list -> term -> bool option *)

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

   672                     auto_timeout free_names sel_names rel_table bounds prop =

   673   let

   674     (* typ * int -> term *)

   675     fun free_type_assm (T, k) =

   676       let

   677         (* int -> term *)

   678         val atom = atom true T

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

   680         val eqs = map equation_for_atom (index_seq 0 k)

   681         val compreh_assm =

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

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

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

   685       in HOLogic.mk_conj (compreh_assm, distinct_assm) end

   686     (* nut -> term *)

   687     fun free_name_assm name =

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

   689                      term_for_name scope sel_names rel_table bounds name)

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

   691     val model_assms = map free_name_assm free_names

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

   693                           (freeT_assms @ model_assms)

   694     (* bool -> bool *)

   695     fun try_out negate =

   696       let

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

   698                     (ObjectLogic.atomize_term thy prop)

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

   700                    |> map_types (map_type_tfree

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

   702                             | x => TFree x))

   703                    |> cterm_of thy |> Goal.init

   704       in

   705         (goal |> SINGLE (DETERM_TIMEOUT auto_timeout

   706                                         (auto_tac (clasimpset_of ctxt)))

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

   708         handle THM _ => false

   709              | TimeLimit.TimeOut => false

   710       end

   711   in

   712     if try_out false then SOME true

   713     else if try_out true then SOME false

   714     else NONE

   715   end

   717 end;

author	blanchet
	Mon, 14 Dec 2009 12:30:26 +0100
changeset 34118	5e831d805118
parent 33982	1ae222745c4a
child 34120	c4988215a691
permissions	-rw-r--r--