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

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

     2     Author:     Jasmin Blanchette, TU Muenchen

     3     Copyright   2008, 2009, 2010

     5 Scope enumerator for Nitpick.

     6 *)

     8 signature NITPICK_SCOPE =

     9 sig

    10   type styp = Nitpick_Util.styp

    11   type hol_context = Nitpick_HOL.hol_context

    13   type constr_spec = {

    14     const: styp,

    15     delta: int,

    16     epsilon: int,

    17     exclusive: bool,

    18     explicit_max: int,

    19     total: bool}

    21   type dtype_spec = {

    22     typ: typ,

    23     card: int,

    24     co: bool,

    25     standard: bool,

    26     complete: bool * bool,

    27     concrete: bool * bool,

    28     deep: bool,

    29     constrs: constr_spec list}

    31   type scope = {

    32     hol_ctxt: hol_context,

    33     binarize: bool,

    34     card_assigns: (typ * int) list,

    35     bits: int,

    36     bisim_depth: int,

    37     datatypes: dtype_spec list,

    38     ofs: int Typtab.table}

    40   val datatype_spec : dtype_spec list -> typ -> dtype_spec option

    41   val constr_spec : dtype_spec list -> styp -> constr_spec

    42   val is_complete_type : dtype_spec list -> bool -> typ -> bool

    43   val is_concrete_type : dtype_spec list -> bool -> typ -> bool

    44   val is_exact_type : dtype_spec list -> bool -> typ -> bool

    45   val offset_of_type : int Typtab.table -> typ -> int

    46   val spec_of_type : scope -> typ -> int * int

    47   val pretties_for_scope : scope -> bool -> Pretty.T list

    48   val multiline_string_for_scope : scope -> string

    49   val scopes_equivalent : scope * scope -> bool

    50   val scope_less_eq : scope -> scope -> bool

    51   val all_scopes :

    52     hol_context -> bool -> (typ option * int list) list

    53     -> (styp option * int list) list -> (styp option * int list) list

    54     -> int list -> int list -> typ list -> typ list -> typ list -> typ list

    55     -> int * scope list

    56 end;

    58 structure Nitpick_Scope : NITPICK_SCOPE =

    59 struct

    61 open Nitpick_Util

    62 open Nitpick_HOL

    64 type constr_spec = {

    65   const: styp,

    66   delta: int,

    67   epsilon: int,

    68   exclusive: bool,

    69   explicit_max: int,

    70   total: bool}

    72 type dtype_spec = {

    73   typ: typ,

    74   card: int,

    75   co: bool,

    76   standard: bool,

    77   complete: bool * bool,

    78   concrete: bool * bool,

    79   deep: bool,

    80   constrs: constr_spec list}

    82 type scope = {

    83   hol_ctxt: hol_context,

    84   binarize: bool,

    85   card_assigns: (typ * int) list,

    86   bits: int,

    87   bisim_depth: int,

    88   datatypes: dtype_spec list,

    89   ofs: int Typtab.table}

    91 datatype row_kind = Card of typ | Max of styp

    93 type row = row_kind * int list

    94 type block = row list

    96 fun datatype_spec (dtypes : dtype_spec list) T =

    97   List.find (curry (op =) T o #typ) dtypes

    99 fun constr_spec [] x = raise TERM ("Nitpick_Scope.constr_spec", [Const x])

   100   | constr_spec ({constrs, ...} :: dtypes : dtype_spec list) (x as (s, T)) =

   101     case List.find (curry (op =) (s, body_type T) o (apsnd body_type o #const))

   102                    constrs of

   103       SOME c => c

   104     | NONE => constr_spec dtypes x

   106 fun is_complete_type dtypes facto (Type (@{type_name fun}, [T1, T2])) =

   107     is_concrete_type dtypes facto T1 andalso is_complete_type dtypes facto T2

   108   | is_complete_type dtypes facto (Type (@{type_name fin_fun}, [T1, T2])) =

   109     is_exact_type dtypes facto T1 andalso is_complete_type dtypes facto T2

   110   | is_complete_type dtypes facto (Type (@{type_name "*"}, Ts)) =

   111     forall (is_complete_type dtypes facto) Ts

   112   | is_complete_type dtypes facto T =

   113     not (is_integer_like_type T) andalso not (is_bit_type T) andalso

   114     fun_from_pair (#complete (the (datatype_spec dtypes T))) facto

   115     handle Option.Option => true

   116 and is_concrete_type dtypes facto (Type (@{type_name fun}, [T1, T2])) =

   117     is_complete_type dtypes facto T1 andalso is_concrete_type dtypes facto T2

   118   | is_concrete_type dtypes facto (Type (@{type_name fin_fun}, [_, T2])) =

   119     is_concrete_type dtypes facto T2

   120   | is_concrete_type dtypes facto (Type (@{type_name "*"}, Ts)) =

   121     forall (is_concrete_type dtypes facto) Ts

   122   | is_concrete_type dtypes facto T =

   123     fun_from_pair (#concrete (the (datatype_spec dtypes T))) facto

   124     handle Option.Option => true

   125 and is_exact_type dtypes facto =

   126   is_complete_type dtypes facto andf is_concrete_type dtypes facto

   128 fun offset_of_type ofs T =

   129   case Typtab.lookup ofs T of

   130     SOME j0 => j0

   131   | NONE => Typtab.lookup ofs dummyT |> the_default 0

   133 fun spec_of_type ({card_assigns, ofs, ...} : scope) T =

   134   (card_of_type card_assigns T

   135    handle TYPE ("Nitpick_HOL.card_of_type", _, _) => ~1, offset_of_type ofs T)

   137 fun quintuple_for_scope quote

   138         ({hol_ctxt = {thy, ctxt, stds, ...}, card_assigns, bits, bisim_depth,

   139          datatypes, ...} : scope) =

   140   let

   141     val boring_Ts = [@{typ unsigned_bit}, @{typ signed_bit},

   142                      @{typ bisim_iterator}]

   143     val (iter_assigns, card_assigns) =

   144       card_assigns |> filter_out (member (op =) boring_Ts o fst)

   145                    |> List.partition (is_fp_iterator_type o fst)

   146     val (secondary_card_assigns, primary_card_assigns) =

   147       card_assigns |> List.partition ((is_integer_type orf is_datatype thy stds)

   148                                       o fst)

   149     val cards =

   150       map (fn (T, k) => quote (string_for_type ctxt T) ^ " = " ^

   151                         string_of_int k)

   152     fun maxes () =

   153       maps (map_filter

   154                 (fn {const, explicit_max, ...} =>

   155                     if explicit_max < 0 then

   156                       NONE

   157                     else

   158                       SOME (Syntax.string_of_term ctxt (Const const) ^ " = " ^

   159                             string_of_int explicit_max))

   160                  o #constrs) datatypes

   161     fun iters () =

   162       map (fn (T, k) =>

   163               quote (Syntax.string_of_term ctxt

   164                          (Const (const_for_iterator_type T))) ^ " = " ^

   165               string_of_int (k - 1)) iter_assigns

   166     fun miscs () =

   167       (if bits = 0 then [] else ["bits = " ^ string_of_int bits]) @

   168       (if bisim_depth < 0 andalso forall (not o #co) datatypes then []

   169        else ["bisim_depth = " ^ signed_string_of_int bisim_depth])

   170   in

   171     setmp_show_all_types

   172         (fn () => (cards primary_card_assigns, cards secondary_card_assigns,

   173                    maxes (), iters (), miscs ())) ()

   174   end

   176 fun pretties_for_scope scope verbose =

   177   let

   178     val (primary_cards, secondary_cards, maxes, iters, bisim_depths) =

   179       quintuple_for_scope maybe_quote scope

   180     val ss = map (prefix "card ") primary_cards @

   181              (if verbose then

   182                 map (prefix "card ") secondary_cards @

   183                 map (prefix "max ") maxes @

   184                 map (prefix "iter ") iters @

   185                 bisim_depths

   186               else

   187                 [])

   188   in

   189     if null ss then []

   190     else serial_commas "and" ss |> map Pretty.str |> Pretty.breaks

   191   end

   193 fun multiline_string_for_scope scope =

   194   let

   195     val (primary_cards, secondary_cards, maxes, iters, bisim_depths) =

   196       quintuple_for_scope I scope

   197     val cards = primary_cards @ secondary_cards

   198   in

   199     case (if null cards then [] else ["card: " ^ commas cards]) @

   200          (if null maxes then [] else ["max: " ^ commas maxes]) @

   201          (if null iters then [] else ["iter: " ^ commas iters]) @

   202          bisim_depths of

   203       [] => "empty"

   204     | lines => space_implode "\n" lines

   205   end

   207 fun scopes_equivalent (s1 : scope, s2 : scope) =

   208   #datatypes s1 = #datatypes s2 andalso #card_assigns s1 = #card_assigns s2

   209 fun scope_less_eq (s1 : scope) (s2 : scope) =

   210   (s1, s2) |> pairself (map snd o #card_assigns) |> op ~~ |> forall (op <=)

   212 fun rank_of_row (_, ks) = length ks

   213 fun rank_of_block block = fold Integer.max (map rank_of_row block) 1

   214 fun project_row column (y, ks) = (y, [nth ks (Int.min (column, length ks - 1))])

   215 fun project_block (column, block) = map (project_row column) block

   217 fun lookup_ints_assign eq assigns key =

   218   case triple_lookup eq assigns key of

   219     SOME ks => ks

   220   | NONE => raise ARG ("Nitpick_Scope.lookup_ints_assign", "")

   221 fun lookup_type_ints_assign thy assigns T =

   222   map (Integer.max 1) (lookup_ints_assign (type_match thy) assigns T)

   223   handle ARG ("Nitpick_Scope.lookup_ints_assign", _) =>

   224          raise TYPE ("Nitpick_Scope.lookup_type_ints_assign", [T], [])

   225 fun lookup_const_ints_assign thy assigns x =

   226   lookup_ints_assign (const_match thy) assigns x

   227   handle ARG ("Nitpick_Scope.lookup_ints_assign", _) =>

   228          raise TERM ("Nitpick_Scope.lookup_const_ints_assign", [Const x])

   230 fun row_for_constr thy maxes_assigns constr =

   231   SOME (Max constr, lookup_const_ints_assign thy maxes_assigns constr)

   232   handle TERM ("lookup_const_ints_assign", _) => NONE

   234 val max_bits = 31 (* Kodkod limit *)

   236 fun block_for_type (hol_ctxt as {thy, ...}) binarize cards_assigns maxes_assigns

   237                    iters_assigns bitss bisim_depths T =

   238   if T = @{typ unsigned_bit} then

   239     [(Card T, map (Integer.min max_bits o Integer.max 1) bitss)]

   240   else if T = @{typ signed_bit} then

   241     [(Card T, map (Integer.add 1 o Integer.min max_bits o Integer.max 1) bitss)]

   242   else if T = @{typ "unsigned_bit word"} then

   243     [(Card T, lookup_type_ints_assign thy cards_assigns nat_T)]

   244   else if T = @{typ "signed_bit word"} then

   245     [(Card T, lookup_type_ints_assign thy cards_assigns int_T)]

   246   else if T = @{typ bisim_iterator} then

   247     [(Card T, map (Integer.add 1 o Integer.max 0) bisim_depths)]

   248   else if is_fp_iterator_type T then

   249     [(Card T, map (Integer.add 1 o Integer.max 0)

   250                   (lookup_const_ints_assign thy iters_assigns

   251                                             (const_for_iterator_type T)))]

   252   else

   253     (Card T, lookup_type_ints_assign thy cards_assigns T) ::

   254     (case binarized_and_boxed_datatype_constrs hol_ctxt binarize T of

   255        [_] => []

   256      | constrs => map_filter (row_for_constr thy maxes_assigns) constrs)

   258 fun blocks_for_types hol_ctxt binarize cards_assigns maxes_assigns iters_assigns

   259                      bitss bisim_depths mono_Ts nonmono_Ts =

   260   let

   261     val block_for = block_for_type hol_ctxt binarize cards_assigns maxes_assigns

   262                                    iters_assigns bitss bisim_depths

   263     val mono_block = maps block_for mono_Ts

   264     val nonmono_blocks = map block_for nonmono_Ts

   265   in mono_block :: nonmono_blocks end

   267 val sync_threshold = 5

   269 fun all_combinations_ordered_smartly ks =

   270   let

   271     fun cost_with_monos [] = 0

   272       | cost_with_monos (k :: ks) =

   273         if k < sync_threshold andalso forall (curry (op =) k) ks then

   274           k - sync_threshold

   275         else

   276           k * (k + 1) div 2 + Integer.sum ks

   277     fun cost_without_monos [] = 0

   278       | cost_without_monos [k] = k

   279       | cost_without_monos (_ :: k :: ks) =

   280         if k < sync_threshold andalso forall (curry (op =) k) ks then

   281           k - sync_threshold

   282         else

   283           Integer.sum (k :: ks)

   284   in

   285     ks |> all_combinations

   286        |> map (`(if fst (hd ks) > 1 then cost_with_monos

   287                  else cost_without_monos))

   288        |> sort (int_ord o pairself fst) |> map snd

   289   end

   291 fun is_self_recursive_constr_type T =

   292   exists (exists_subtype (curry (op =) (body_type T))) (binder_types T)

   294 fun constr_max maxes x = the_default ~1 (AList.lookup (op =) maxes x)

   296 type scope_desc = (typ * int) list * (styp * int) list

   298 fun is_surely_inconsistent_card_assign hol_ctxt binarize

   299                                        (card_assigns, max_assigns) (T, k) =

   300   case binarized_and_boxed_datatype_constrs hol_ctxt binarize T of

   301     [] => false

   302   | xs =>

   303     let

   304       val dom_cards =

   305         map (Integer.prod o map (bounded_card_of_type k ~1 card_assigns)

   306              o binder_types o snd) xs

   307       val maxes = map (constr_max max_assigns) xs

   308       fun effective_max card ~1 = card

   309         | effective_max card max = Int.min (card, max)

   310       val max = map2 effective_max dom_cards maxes |> Integer.sum

   311     in max < k end

   312 fun is_surely_inconsistent_scope_description hol_ctxt binarize seen rest

   313                                              max_assigns =

   314   exists (is_surely_inconsistent_card_assign hol_ctxt binarize

   315                                              (seen @ rest, max_assigns)) seen

   317 fun repair_card_assigns hol_ctxt binarize (card_assigns, max_assigns) =

   318   let

   319     fun aux seen [] = SOME seen

   320       | aux _ ((_, 0) :: _) = NONE

   321       | aux seen ((T, k) :: rest) =

   322         (if is_surely_inconsistent_scope_description hol_ctxt binarize

   323                 ((T, k) :: seen) rest max_assigns then

   324            raise SAME ()

   325          else

   326            case aux ((T, k) :: seen) rest of

   327              SOME assigns => SOME assigns

   328            | NONE => raise SAME ())

   329         handle SAME () => aux seen ((T, k - 1) :: rest)

   330   in aux [] (rev card_assigns) end

   332 fun repair_iterator_assign thy assigns (T as Type (_, Ts), k) =

   333     (T, if T = @{typ bisim_iterator} then

   334           let

   335             val co_cards = map snd (filter (is_codatatype thy o fst) assigns)

   336           in Int.min (k, Integer.sum co_cards) end

   337         else if is_fp_iterator_type T then

   338           case Ts of

   339             [] => 1

   340           | _ => bounded_card_of_type k ~1 assigns (foldr1 HOLogic.mk_prodT Ts)

   341         else

   342           k)

   343   | repair_iterator_assign _ _ assign = assign

   345 fun add_row_to_scope_descriptor (kind, ks) (card_assigns, max_assigns) =

   346   case kind of

   347     Card T => ((T, the_single ks) :: card_assigns, max_assigns)

   348   | Max x => (card_assigns, (x, the_single ks) :: max_assigns)

   349 fun scope_descriptor_from_block block =

   350   fold_rev add_row_to_scope_descriptor block ([], [])

   351 fun scope_descriptor_from_combination (hol_ctxt as {thy, ...}) binarize blocks

   352                                       columns =

   353   let

   354     val (card_assigns, max_assigns) =

   355       maps project_block (columns ~~ blocks) |> scope_descriptor_from_block

   356     val card_assigns =

   357       repair_card_assigns hol_ctxt binarize (card_assigns, max_assigns) |> the

   358   in

   359     SOME (map (repair_iterator_assign thy card_assigns) card_assigns,

   360           max_assigns)

   361   end

   362   handle Option.Option => NONE

   364 fun offset_table_for_card_assigns assigns dtypes =

   365   let

   366     fun aux next _ [] = Typtab.update_new (dummyT, next)

   367       | aux next reusable ((T, k) :: assigns) =

   368         if k = 1 orelse is_iterator_type T orelse is_integer_type T

   369            orelse is_bit_type T then

   370           aux next reusable assigns

   371         else if length (these (Option.map #constrs (datatype_spec dtypes T)))

   372                 > 1 then

   373           Typtab.update_new (T, next) #> aux (next + k) reusable assigns

   374         else

   375           case AList.lookup (op =) reusable k of

   376             SOME j0 => Typtab.update_new (T, j0) #> aux next reusable assigns

   377           | NONE => Typtab.update_new (T, next)

   378                     #> aux (next + k) ((k, next) :: reusable) assigns

   379   in aux 0 [] assigns Typtab.empty end

   381 fun domain_card max card_assigns =

   382   Integer.prod o map (bounded_card_of_type max max card_assigns) o binder_types

   384 fun add_constr_spec (card_assigns, max_assigns) co card sum_dom_cards

   385                     num_self_recs num_non_self_recs (self_rec, x as (_, T))

   386                     constrs =

   387   let

   388     val max = constr_max max_assigns x

   389     fun next_delta () = if null constrs then 0 else #epsilon (hd constrs)

   390     val {delta, epsilon, exclusive, total} =

   391       if max = 0 then

   392         let val delta = next_delta () in

   393           {delta = delta, epsilon = delta, exclusive = true, total = false}

   394         end

   395       else if not co andalso num_self_recs > 0 then

   396         (if num_self_recs = 1 andalso num_non_self_recs = 1 then

   397            if self_rec then

   398              case constrs of

   399                [{delta = 0, epsilon = 1, exclusive = true, ...}] =>

   400                {delta = 1, epsilon = card, exclusive = true, total = false}

   401              | _ => raise SAME ()

   402            else

   403              if domain_card 2 card_assigns T = 1 then

   404                {delta = 0, epsilon = 1, exclusive = true, total = true}

   405              else

   406                raise SAME ()

   407          else

   408            raise SAME ())

   409         handle SAME () =>

   410                {delta = 0, epsilon = card, exclusive = false, total = false}

   411       else if card = sum_dom_cards (card + 1) then

   412         let val delta = next_delta () in

   413           {delta = delta, epsilon = delta + domain_card card card_assigns T,

   414            exclusive = true, total = true}

   415         end

   416       else

   417         {delta = 0, epsilon = card,

   418          exclusive = (num_self_recs + num_non_self_recs = 1), total = false}

   419   in

   420     {const = x, delta = delta, epsilon = epsilon, exclusive = exclusive,

   421      explicit_max = max, total = total} :: constrs

   422   end

   424 fun has_exact_card hol_ctxt facto finitizable_dataTs card_assigns T =

   425   let val card = card_of_type card_assigns T in

   426     card = bounded_exact_card_of_type hol_ctxt

   427                (if facto then finitizable_dataTs else []) (card + 1) 0

   428                card_assigns T

   429   end

   431 fun datatype_spec_from_scope_descriptor (hol_ctxt as {thy, stds, ...}) binarize

   432         deep_dataTs finitizable_dataTs (desc as (card_assigns, _)) (T, card) =

   433   let

   434     val deep = member (op =) deep_dataTs T

   435     val co = is_codatatype thy T

   436     val standard = is_standard_datatype thy stds T

   437     val xs = binarized_and_boxed_datatype_constrs hol_ctxt binarize T

   438     val self_recs = map (is_self_recursive_constr_type o snd) xs

   439     val (num_self_recs, num_non_self_recs) =

   440       List.partition I self_recs |> pairself length

   441     fun is_complete facto =

   442       has_exact_card hol_ctxt facto finitizable_dataTs card_assigns T

   443     fun is_concrete facto =

   444       is_word_type T orelse

   445       xs |> maps (binder_types o snd) |> maps binder_types

   446          |> forall (has_exact_card hol_ctxt facto finitizable_dataTs

   447                                    card_assigns)

   448     val complete = pair_from_fun is_complete

   449     val concrete = pair_from_fun is_concrete

   450     fun sum_dom_cards max =

   451       map (domain_card max card_assigns o snd) xs |> Integer.sum

   452     val constrs =

   453       fold_rev (add_constr_spec desc co card sum_dom_cards num_self_recs

   454                                 num_non_self_recs)

   455                (sort (bool_ord o swap o pairself fst) (self_recs ~~ xs)) []

   456   in

   457     {typ = T, card = card, co = co, standard = standard, complete = complete,

   458      concrete = concrete, deep = deep, constrs = constrs}

   459   end

   461 fun scope_from_descriptor (hol_ctxt as {thy, stds, ...}) binarize deep_dataTs

   462                           finitizable_dataTs (desc as (card_assigns, _)) =

   463   let

   464     val datatypes =

   465       map (datatype_spec_from_scope_descriptor hol_ctxt binarize deep_dataTs

   466                                                finitizable_dataTs desc)

   467           (filter (is_datatype thy stds o fst) card_assigns)

   468     val bits = card_of_type card_assigns @{typ signed_bit} - 1

   469                handle TYPE ("Nitpick_HOL.card_of_type", _, _) =>

   470                       card_of_type card_assigns @{typ unsigned_bit}

   471                       handle TYPE ("Nitpick_HOL.card_of_type", _, _) => 0

   472     val bisim_depth = card_of_type card_assigns @{typ bisim_iterator} - 1

   473   in

   474     {hol_ctxt = hol_ctxt, binarize = binarize, card_assigns = card_assigns,

   475      datatypes = datatypes, bits = bits, bisim_depth = bisim_depth,

   476      ofs = offset_table_for_card_assigns card_assigns datatypes}

   477   end

   479 fun repair_cards_assigns_wrt_boxing_etc _ _ [] = []

   480   | repair_cards_assigns_wrt_boxing_etc thy Ts ((SOME T, ks) :: cards_assigns) =

   481     (if is_fun_type T orelse is_pair_type T then

   482        Ts |> filter (curry (type_match thy o swap) T) |> map (rpair ks o SOME)

   483      else

   484        [(SOME T, ks)]) @

   485        repair_cards_assigns_wrt_boxing_etc thy Ts cards_assigns

   486   | repair_cards_assigns_wrt_boxing_etc thy Ts ((NONE, ks) :: cards_assigns) =

   487     (NONE, ks) :: repair_cards_assigns_wrt_boxing_etc thy Ts cards_assigns

   489 val max_scopes = 4096

   490 val distinct_threshold = 512

   492 fun all_scopes (hol_ctxt as {thy, ...}) binarize cards_assigns maxes_assigns

   493                iters_assigns bitss bisim_depths mono_Ts nonmono_Ts deep_dataTs

   494                finitizable_dataTs =

   495   let

   496     val cards_assigns = repair_cards_assigns_wrt_boxing_etc thy mono_Ts

   497                                                             cards_assigns

   498     val blocks = blocks_for_types hol_ctxt binarize cards_assigns maxes_assigns

   499                                   iters_assigns bitss bisim_depths mono_Ts

   500                                   nonmono_Ts

   501     val ranks = map rank_of_block blocks

   502     val all = all_combinations_ordered_smartly (map (rpair 0) ranks)

   503     val head = take max_scopes all

   504     val descs =

   505       map_filter (scope_descriptor_from_combination hol_ctxt binarize blocks)

   506                  head

   507   in

   508     (length all - length head,

   509      descs |> length descs <= distinct_threshold ? distinct (op =)

   510            |> map (scope_from_descriptor hol_ctxt binarize deep_dataTs

   511                                          finitizable_dataTs))

   512   end

   514 end;

author	blanchet
	Sat, 24 Apr 2010 16:43:03 +0200
changeset 36386	2132f15b366f
parent 36385	ff5f88702590
child 36390	eee4ee6a5cbe
permissions	-rw-r--r--