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

    Author:     Jasmin Blanchette, TU Muenchen

    Copyright   2008, 2009

Scope enumerator for Nitpick.

*)

signature NITPICK_SCOPE =

sig

  type styp = Nitpick_Util.styp

  type extended_context = Nitpick_HOL.extended_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,

    precise: bool,

    shallow: bool,

    constrs: constr_spec list}

  type scope = {

    ext_ctxt: extended_context,

    card_assigns: (typ * int) list,

    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_precise_type : dtype_spec list -> typ -> bool

  val is_fully_comparable_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 :

    extended_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

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,

  precise: bool,

  shallow: bool,

  constrs: constr_spec list}

type scope = {

  ext_ctxt: extended_context,

  card_assigns: (typ * int) list,

  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 (equal 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 (equal (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_precise_type dtypes (Type ("fun", Ts)) =

    forall (is_precise_type dtypes) Ts

  | is_precise_type dtypes (Type ("*", Ts)) = forall (is_precise_type dtypes) Ts

  | is_precise_type dtypes T =

    not (is_integer_type T) andalso #precise (the (datatype_spec dtypes T))

    handle Option.Option => true

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

    is_precise_type dtypes T1 andalso is_fully_comparable_type dtypes T2

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

    forall (is_fully_comparable_type dtypes) Ts

  | is_fully_comparable_type _ _ = true

(* 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 ({ext_ctxt as {thy, ctxt, ...}, card_assigns,

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

  let

    val (iter_asgns, card_asgns) =

      card_assigns |> filter_out (equal @{typ bisim_iterator} o fst)

                   |> List.partition (is_fp_iterator_type o fst)

    val (unimportant_card_asgns, important_card_asgns) =

      card_asgns |> 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_asgns

    fun bisims () =

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

      else ["bisim_depth = " ^ string_of_int bisim_depth]

  in

    setmp_show_all_types

        (fn () => (cards important_card_asgns, cards unimportant_card_asgns,

                   maxes (), iters (), bisims ())) ()

  end

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

fun pretties_for_scope scope verbose =

  let

    val (important_cards, unimportant_cards, maxes, iters, bisim_depths) =

      quintuple_for_scope maybe_quote scope

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

             (if verbose then

                map (prefix "card ") unimportant_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 (important_cards, unimportant_cards, maxes, iters, bisim_depths) =

      quintuple_for_scope I scope

    val cards = important_cards @ unimportant_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 asgns key =

  case triple_lookup eq asgns 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 asgns T =

  map (curry Int.max 1) (lookup_ints_assign (type_match thy) asgns 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 asgns x =

  lookup_ints_assign (const_match thy) asgns 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_asgns constr =

  SOME (Max constr, lookup_const_ints_assign thy maxes_asgns constr)

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

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

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

   -> typ -> block *)

fun block_for_type (ext_ctxt as {thy, ...}) cards_asgns maxes_asgns iters_asgns

                   bisim_depths T =

  if T = @{typ bisim_iterator} then

    [(Card T, map (fn k => Int.max (0, k) + 1) bisim_depths)]

  else if is_fp_iterator_type T then

    [(Card T, map (fn k => Int.max (0, k) + 1)

                  (lookup_const_ints_assign thy iters_asgns

                                            (const_for_iterator_type T)))]

  else

    (Card T, lookup_type_ints_assign thy cards_asgns T) ::

    (case datatype_constrs ext_ctxt T of

       [_] => []

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

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

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

   -> typ list -> typ list -> block list *)

fun blocks_for_types ext_ctxt cards_asgns maxes_asgns iters_asgns bisim_depths

                     mono_Ts nonmono_Ts =

  let

    (* typ -> block *)

    val block_for = block_for_type ext_ctxt cards_asgns maxes_asgns iters_asgns

                                   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 (equal 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 (equal 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 (equal (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

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

fun is_surely_inconsistent_card_assign ext_ctxt (card_asgns, max_asgns) (T, k) =

  case datatype_constrs ext_ctxt T of

    [] => false

  | xs =>

    let

      val precise_cards =

        map (Integer.prod

             o map (bounded_precise_card_of_type ext_ctxt k 0 card_asgns)

             o binder_types o snd) xs

      val maxes = map (constr_max max_asgns) xs

      (* int -> int -> int *)

      fun effective_max 0 ~1 = k

        | effective_max 0 max = max

        | effective_max card ~1 = card

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

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

      (* unit -> int *)

      fun doms_card () =

        xs |> map (Integer.prod o map (bounded_card_of_type k ~1 card_asgns)

                   o binder_types o snd)

           |> Integer.sum

    in

      max < k

      orelse (forall (not_equal 0) precise_cards andalso doms_card () < k)

    end

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

(* extended_context -> scope_desc -> bool *)

fun is_surely_inconsistent_scope_description ext_ctxt

                                             (desc as (card_asgns, _)) =

  exists (is_surely_inconsistent_card_assign ext_ctxt desc) card_asgns

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

fun repair_card_assigns ext_ctxt (card_asgns, max_asgns) =

  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) :: asgns) =

        (if is_surely_inconsistent_scope_description ext_ctxt

                ((T, k) :: seen, max_asgns) then

           raise SAME ()

         else

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

             SOME asgns => SOME asgns

           | NONE => raise SAME ())

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

  in aux [] (rev card_asgns) end

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

fun repair_iterator_assign thy asgns (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) asgns) 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 asgns (foldr1 HOLogic.mk_prodT Ts)

        else

          k)

  | repair_iterator_assign _ _ asgn = asgn

(* row -> scope_desc -> scope_desc *)

fun add_row_to_scope_descriptor (kind, ks) (card_asgns, max_asgns) =

  case kind of

    Card T => ((T, the_single ks) :: card_asgns, max_asgns)

  | Max x => (card_asgns, (x, the_single ks) :: max_asgns)

(* block -> scope_desc *)

fun scope_descriptor_from_block block =

  fold_rev add_row_to_scope_descriptor block ([], [])

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

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

  let

    val (card_asgns, max_asgns) =

      maps project_block (columns ~~ blocks) |> scope_descriptor_from_block

    val card_asgns = repair_card_assigns ext_ctxt (card_asgns, max_asgns) |> the

  in

    SOME (map (repair_iterator_assign thy card_asgns) card_asgns, max_asgns)

  end

  handle Option.Option => NONE

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

fun offset_table_for_card_assigns thy asgns 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) :: asgns) =

        if k = 1 orelse is_integer_type T then

          aux next reusable asgns

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

                > 1 then

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

        else

          case AList.lookup (op =) reusable k of

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

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

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

  in aux 0 [] asgns Typtab.empty end

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

fun domain_card max card_asgns =

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

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

   -> constr_spec list -> constr_spec list *)

fun add_constr_spec (card_asgns, max_asgns) 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_asgns 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 not self_rec andalso num_non_self_recs = 1

           andalso domain_card 2 card_asgns T = 1 then

          {delta = 0, epsilon = 1, exclusive = (s = @{const_name Nil}),

           total = true}

        else if s = @{const_name Cons} then

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

        else

          {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_asgns 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

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

fun datatype_spec_from_scope_descriptor (ext_ctxt as {thy, ...}) shallow_dataTs

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

  let

    val shallow = T mem shallow_dataTs

    val co = is_codatatype thy T

    val xs = boxed_datatype_constrs ext_ctxt T

    val self_recs = map (is_self_recursive_constr_type o snd) xs

    val (num_self_recs, num_non_self_recs) =

      List.partition (equal true) self_recs |> pairself length

    val precise = (card = bounded_precise_card_of_type ext_ctxt (card + 1) 0

                                                       card_asgns T)

    (* int -> int *)

    fun sum_dom_cards max =

      map (domain_card max card_asgns 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) (self_recs ~~ xs) []

  in

    {typ = T, card = card, co = co, precise = precise, shallow = shallow,

     constrs = constrs}

  end

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

fun scope_from_descriptor (ext_ctxt as {thy, ...}) sym_break shallow_dataTs

                          (desc as (card_asgns, _)) =

  let

    val datatypes =

      map (datatype_spec_from_scope_descriptor ext_ctxt shallow_dataTs desc)

          (filter (is_datatype thy o fst) card_asgns)

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

  in

    {ext_ctxt = ext_ctxt, card_assigns = card_asgns, datatypes = datatypes,

     bisim_depth = bisim_depth,

     ofs = if sym_break <= 0 then Typtab.empty

           else offset_table_for_card_assigns thy card_asgns datatypes}

  end

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

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

fun fix_cards_assigns_wrt_boxing _ _ [] = []

  | fix_cards_assigns_wrt_boxing thy Ts ((SOME T, ks) :: cards_asgns) =

    (if is_fun_type T orelse is_pair_type T then

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

          |> map (rpair ks o SOME)

     else

       [(SOME T, ks)]) @ fix_cards_assigns_wrt_boxing thy Ts cards_asgns

  | fix_cards_assigns_wrt_boxing thy Ts ((NONE, ks) :: cards_asgns) =

    (NONE, ks) :: fix_cards_assigns_wrt_boxing thy Ts cards_asgns

val max_scopes = 4096

val distinct_threshold = 512

(* extended_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 (ext_ctxt as {thy, ...}) sym_break cards_asgns maxes_asgns

               iters_asgns bisim_depths mono_Ts nonmono_Ts shallow_dataTs =

  let

    val cards_asgns = fix_cards_assigns_wrt_boxing thy mono_Ts cards_asgns

    val blocks = blocks_for_types ext_ctxt cards_asgns maxes_asgns iters_asgns

                                  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 ext_ctxt blocks)

                           head

  in

    (length all - length head,

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

           |> map (scope_from_descriptor ext_ctxt sym_break shallow_dataTs))

  end

end;