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

     Author:     Jasmin Blanchette, TU Muenchen

     Copyright   2008, 2009, 2010

 Scope enumerator for Nitpick.

 *)

 signature NITPICK_SCOPE =

 sig

   type styp = Nitpick_Util.styp

   type hol_context = Nitpick_HOL.hol_context

   type constr_spec = {

     const: styp,

     delta: int,

     epsilon: int,

     exclusive: bool,

     explicit_max: int,

     total: bool}

   type dtype_spec = {

     typ: typ,

     card: int,

     co: bool,

     complete: bool,

     concrete: bool,

     deep: bool,

     constrs: constr_spec list}

   type scope = {

     hol_ctxt: hol_context,

     card_assigns: (typ * int) list,

     bits: int,

     bisim_depth: int,

     datatypes: dtype_spec list,

     ofs: int Typtab.table}

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

   val constr_spec : dtype_spec list -> styp -> constr_spec

   val is_complete_type : dtype_spec list -> typ -> bool

   val is_concrete_type : dtype_spec list -> typ -> bool

   val is_exact_type : dtype_spec list -> typ -> bool

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

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

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

   val multiline_string_for_scope : scope -> string

   val scopes_equivalent : scope -> scope -> bool

   val scope_less_eq : scope -> scope -> bool

   val all_scopes :

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

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

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

     -> int * scope list

 end;

 structure Nitpick_Scope : NITPICK_SCOPE =

 struct

 open Nitpick_Util

 open Nitpick_HOL

 type constr_spec = {

   const: styp,

   delta: int,

   epsilon: int,

   exclusive: bool,

   explicit_max: int,

   total: bool}

 type dtype_spec = {

   typ: typ,

   card: int,

   co: bool,

   complete: bool,

   concrete: bool,

   deep: bool,

   constrs: constr_spec list}

 type scope = {

   hol_ctxt: hol_context,

   card_assigns: (typ * int) list,

   bits: int,

   bisim_depth: int,

   datatypes: dtype_spec list,

   ofs: int Typtab.table}

 datatype row_kind = Card of typ | Max of styp

 type row = row_kind * int list

 type block = row list

 (* dtype_spec list -> typ -> dtype_spec option *)

 fun datatype_spec (dtypes : dtype_spec list) T =

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

 (* dtype_spec list -> styp -> constr_spec *)

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

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

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

                    constrs of

       SOME c => c

     | NONE => constr_spec dtypes x

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

 fun is_complete_type dtypes (Type ("fun", [T1, T2])) =

     is_concrete_type dtypes T1 andalso is_complete_type dtypes T2

   | is_complete_type dtypes (Type ("*", Ts)) =

     forall (is_complete_type dtypes) Ts

   | is_complete_type dtypes T =

     not (is_integer_type T) andalso not (is_bit_type T) andalso

     #complete (the (datatype_spec dtypes T))

     handle Option.Option => true

 and is_concrete_type dtypes (Type ("fun", [T1, T2])) =

     is_complete_type dtypes T1 andalso is_concrete_type dtypes T2

   | is_concrete_type dtypes (Type ("*", Ts)) =

     forall (is_concrete_type dtypes) Ts

   | is_concrete_type dtypes T =

     #concrete (the (datatype_spec dtypes T)) handle Option.Option => true

 fun is_exact_type dtypes = is_complete_type dtypes andf is_concrete_type dtypes

 (* int Typtab.table -> typ -> int *)

 fun offset_of_type ofs T =

   case Typtab.lookup ofs T of

     SOME j0 => j0

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

 (* scope -> typ -> int * int *)

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

   (card_of_type card_assigns T

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

 (* (string -> string) -> scope

    -> string list * string list * string list * string list * string list *)

 fun quintuple_for_scope quote ({hol_ctxt as {thy, ctxt, ...}, card_assigns,

                                 bits, bisim_depth, datatypes, ...} : scope) =

   let

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

                      @{typ bisim_iterator}]

     val (iter_assigns, card_assigns) =

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

                    |> List.partition (is_fp_iterator_type o fst)

     val (secondary_card_assigns, primary_card_assigns) =

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

                                       o fst)

     val cards =

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

                         string_of_int k)

     fun maxes () =

       maps (map_filter

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

                     if explicit_max < 0 then

                       NONE

                     else

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

                             string_of_int explicit_max))

                  o #constrs) datatypes

     fun iters () =

       map (fn (T, k) =>

               quote (Syntax.string_of_term ctxt

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

               string_of_int (k - 1)) iter_assigns

     fun miscs () =

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

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

        else ["bisim_depth = " ^ signed_string_of_int bisim_depth])

   in

     setmp_show_all_types

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

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

   end

 (* scope -> bool -> Pretty.T list *)

 fun pretties_for_scope scope verbose =

   let

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

       quintuple_for_scope maybe_quote scope

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

              (if verbose then

                 map (prefix "card ") secondary_cards @

                 map (prefix "max ") maxes @

                 map (prefix "iter ") iters @

                 bisim_depths

               else

                 [])

   in

     if null ss then []

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

   end

 (* scope -> string *)

 fun multiline_string_for_scope scope =

   let

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

       quintuple_for_scope I scope

     val cards = primary_cards @ secondary_cards

   in

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

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

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

          bisim_depths of

       [] => "empty"

     | lines => space_implode "\n" lines

   end

 (* scope -> scope -> bool *)

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

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

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

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

 (* row -> int *)

 fun rank_of_row (_, ks) = length ks

 (* block -> int *)

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

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

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

 (* int -> block -> block *)

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

 (* (''a * ''a -> bool) -> (''a option * int list) list -> ''a -> int list *)

 fun lookup_ints_assign eq assigns key =

   case triple_lookup eq assigns key of

     SOME ks => ks

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

 (* theory -> (typ option * int list) list -> typ -> int list *)

 fun lookup_type_ints_assign thy assigns T =

   map (curry Int.max 1) (lookup_ints_assign (type_match thy) assigns T)

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

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

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

 fun lookup_const_ints_assign thy assigns x =

   lookup_ints_assign (const_match thy) assigns x

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

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

 (* theory -> (styp option * int list) list -> styp -> row option *)

 fun row_for_constr thy maxes_assigns constr =

   SOME (Max constr, lookup_const_ints_assign thy maxes_assigns constr)

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

 val max_bits = 31 (* Kodkod limit *)

 (* hol_context -> (typ option * int list) list -> (styp option * int list) list

    -> (styp option * int list) list -> int list -> int list -> typ -> block *)

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

                    iters_assigns bitss bisim_depths T =

   if T = @{typ unsigned_bit} then

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

   else if T = @{typ signed_bit} then

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

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

     [(Card T, lookup_type_ints_assign thy cards_assigns nat_T)]

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

     [(Card T, lookup_type_ints_assign thy cards_assigns int_T)]

   else if T = @{typ bisim_iterator} then

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

   else if is_fp_iterator_type T then

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

                   (lookup_const_ints_assign thy iters_assigns

                                             (const_for_iterator_type T)))]

   else

     (Card T, lookup_type_ints_assign thy cards_assigns T) ::

     (case datatype_constrs hol_ctxt T of

        [_] => []

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

 (* hol_context -> (typ option * int list) list -> (styp option * int list) list

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

    -> typ list -> block list *)

 fun blocks_for_types hol_ctxt cards_assigns maxes_assigns iters_assigns bitss

                      bisim_depths mono_Ts nonmono_Ts =

   let

     (* typ -> block *)

     val block_for = block_for_type hol_ctxt cards_assigns maxes_assigns

                                    iters_assigns bitss bisim_depths

     val mono_block = maps block_for mono_Ts

     val nonmono_blocks = map block_for nonmono_Ts

   in mono_block :: nonmono_blocks end

 val sync_threshold = 5

 (* int list -> int list list *)

 fun all_combinations_ordered_smartly ks =

   let

     (* int list -> int *)

     fun cost_with_monos [] = 0

       | cost_with_monos (k :: ks) =

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

           k - sync_threshold

         else

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

     fun cost_without_monos [] = 0

       | cost_without_monos [k] = k

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

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

           k - sync_threshold

         else

           Integer.sum (k :: ks)

   in

     ks |> all_combinations

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

                  else cost_without_monos))

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

   end

 (* typ -> bool *)

 fun is_self_recursive_constr_type T =

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

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

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

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

 (* hol_context -> scope_desc -> typ * int -> bool *)

 fun is_surely_inconsistent_card_assign hol_ctxt (card_assigns, max_assigns)

                                        (T, k) =

   case datatype_constrs hol_ctxt T of

     [] => false

   | xs =>

     let

       val dom_cards =

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

              o binder_types o snd) xs

       val maxes = map (constr_max max_assigns) xs

       (* int -> int -> int *)

       fun effective_max card ~1 = card

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

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

     in max < k end

 (* hol_context -> (typ * int) list -> (typ * int) list -> (styp * int) list

    -> bool *)

 fun is_surely_inconsistent_scope_description hol_ctxt seen rest max_assigns =

   exists (is_surely_inconsistent_card_assign hol_ctxt

                                              (seen @ rest, max_assigns)) seen

 (* hol_context -> scope_desc -> (typ * int) list option *)

 fun repair_card_assigns hol_ctxt (card_assigns, max_assigns) =

   let

     (* (typ * int) list -> (typ * int) list -> (typ * int) list option *)

     fun aux seen [] = SOME seen

       | aux seen ((T, 0) :: _) = NONE

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

         (if is_surely_inconsistent_scope_description hol_ctxt ((T, k) :: seen)

                                                      rest max_assigns then

            raise SAME ()

          else

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

              SOME assigns => SOME assigns

            | NONE => raise SAME ())

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

   in aux [] (rev card_assigns) end

 (* theory -> (typ * int) list -> typ * int -> typ * int *)

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

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

           let

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

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

         else if is_fp_iterator_type T then

           case Ts of

             [] => 1

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

         else

           k)

   | repair_iterator_assign _ _ assign = assign

 (* row -> scope_desc -> scope_desc *)

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

   case kind of

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

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

 (* block -> scope_desc *)

 fun scope_descriptor_from_block block =

   fold_rev add_row_to_scope_descriptor block ([], [])

 (* hol_context -> block list -> int list -> scope_desc option *)

 fun scope_descriptor_from_combination (hol_ctxt as {thy, ...}) blocks columns =

   let

     val (card_assigns, max_assigns) =

       maps project_block (columns ~~ blocks) |> scope_descriptor_from_block

     val card_assigns = repair_card_assigns hol_ctxt (card_assigns, max_assigns)

                        |> the

   in

     SOME (map (repair_iterator_assign thy card_assigns) card_assigns,

           max_assigns)

   end

   handle Option.Option => NONE

 (* theory -> (typ * int) list -> dtype_spec list -> int Typtab.table *)

 fun offset_table_for_card_assigns thy assigns dtypes =

   let

     (* int -> (int * int) list -> (typ * int) list -> int Typtab.table

        -> int Typtab.table *)

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

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

         if k = 1 orelse is_integer_type T orelse is_bit_type T then

           aux next reusable assigns

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

                 > 1 then

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

         else

           case AList.lookup (op =) reusable k of

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

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

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

   in aux 0 [] assigns Typtab.empty end

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

 fun domain_card max card_assigns =

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

 (* scope_desc -> bool -> int -> (int -> int) -> int -> int -> bool * styp

    -> constr_spec list -> constr_spec list *)

 fun add_constr_spec (card_assigns, max_assigns) co card sum_dom_cards

                     num_self_recs num_non_self_recs (self_rec, x as (s, T))

                     constrs =

   let

     val max = constr_max max_assigns x

     (* int -> int *)

     fun bound k = Int.min (card, (max >= 0 ? curry Int.min max) k)

     (* unit -> int *)

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

     val {delta, epsilon, exclusive, total} =

       if max = 0 then

         let val delta = next_delta () in

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

         end

       else if not co andalso num_self_recs > 0 then

         (if num_self_recs = 1 andalso num_non_self_recs = 1 then

            if self_rec then

              case constrs of

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

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

              | _ => raise SAME ()

            else

              if domain_card 2 card_assigns T = 1 then

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

              else

                raise SAME ()

          else

            raise SAME ())

         handle SAME () =>

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

       else if card = sum_dom_cards (card + 1) then

         let val delta = next_delta () in

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

            exclusive = true, total = true}

         end

       else

         {delta = 0, epsilon = card,

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

   in

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

      explicit_max = max, total = total} :: constrs

   end

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

 fun has_exact_card hol_ctxt card_assigns T =

   let val card = card_of_type card_assigns T in

     card = bounded_exact_card_of_type hol_ctxt (card + 1) 0 card_assigns T

   end

 (* hol_context -> typ list -> scope_desc -> typ * int -> dtype_spec *)

 fun datatype_spec_from_scope_descriptor (hol_ctxt as {thy, ...}) deep_dataTs

                                         (desc as (card_assigns, _)) (T, card) =

   let

     val deep = member (op =) deep_dataTs T

     val co = is_codatatype thy T

     val xs = boxed_datatype_constrs hol_ctxt T

     val self_recs = map (is_self_recursive_constr_type o snd) xs

     val (num_self_recs, num_non_self_recs) =

       List.partition I self_recs |> pairself length

     val complete = has_exact_card hol_ctxt card_assigns T

     val concrete = xs |> maps (binder_types o snd) |> maps binder_types

                       |> forall (has_exact_card hol_ctxt card_assigns)

     (* int -> int *)

     fun sum_dom_cards max =

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

     val constrs =

       fold_rev (add_constr_spec desc co card sum_dom_cards num_self_recs

                                 num_non_self_recs)

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

   in

     {typ = T, card = card, co = co, complete = complete, concrete = concrete,

      deep = deep, constrs = constrs}

   end

 (* int -> int *)

 fun min_bits_for_nat_value n = if n <= 0 then 0 else IntInf.log2 n + 1

 (* scope_desc -> int *)

 fun min_bits_for_max_assigns (_, []) = 0

   | min_bits_for_max_assigns (card_assigns, max_assigns) =

     min_bits_for_nat_value (fold Integer.max

         (map snd card_assigns @ map snd max_assigns) 0)

 (* hol_context -> int -> typ list -> scope_desc -> scope *)

 fun scope_from_descriptor (hol_ctxt as {thy, ...}) sym_break deep_dataTs

                           (desc as (card_assigns, _)) =

   let

     val datatypes =

       map (datatype_spec_from_scope_descriptor hol_ctxt deep_dataTs desc)

           (filter (is_datatype thy o fst) card_assigns)

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

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

                       card_of_type card_assigns @{typ unsigned_bit}

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

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

   in

     {hol_ctxt = hol_ctxt, card_assigns = card_assigns, datatypes = datatypes,

      bits = bits, bisim_depth = bisim_depth,

      ofs = if sym_break <= 0 then Typtab.empty

            else offset_table_for_card_assigns thy card_assigns datatypes}

   end

 (* theory -> typ list -> (typ option * int list) list

    -> (typ option * int list) list *)

 fun repair_cards_assigns_wrt_boxing _ _ [] = []

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

     (if is_fun_type T orelse is_pair_type T then

        Ts |> filter (curry (type_match thy o swap) T o unbit_and_unbox_type)

           |> map (rpair ks o SOME)

      else

        [(SOME T, ks)]) @ repair_cards_assigns_wrt_boxing thy Ts cards_assigns

   | repair_cards_assigns_wrt_boxing thy Ts ((NONE, ks) :: cards_assigns) =

     (NONE, ks) :: repair_cards_assigns_wrt_boxing thy Ts cards_assigns

 val max_scopes = 4096

 val distinct_threshold = 512

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

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

    -> typ list -> typ list -> typ list -> int * scope list *)

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

                iters_assigns bitss bisim_depths mono_Ts nonmono_Ts deep_dataTs =

   let

     val cards_assigns = repair_cards_assigns_wrt_boxing thy mono_Ts

                                                         cards_assigns

     val blocks = blocks_for_types hol_ctxt cards_assigns maxes_assigns

                                   iters_assigns bitss bisim_depths mono_Ts

                                   nonmono_Ts

     val ranks = map rank_of_block blocks

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

     val head = take max_scopes all

     val descs = map_filter (scope_descriptor_from_combination hol_ctxt blocks)

                            head

   in

     (length all - length head,

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

            |> map (scope_from_descriptor hol_ctxt sym_break deep_dataTs))

   end

 end;