src/HOL/Tools/Nitpick/nitpick_scope.ML

+(*  Title:      HOL/Nitpick/Tools/nitpick_scope.ML
+    Author:     Jasmin Blanchette, TU Muenchen
+    Copyright   2008, 2009
+
+Scope enumerator for Nitpick.
+*)
+
+signature NITPICK_SCOPE =
+sig
+  type extended_context = NitpickHOL.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,
+    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 -> scope list
+end;
+
+structure NitpickScope : NITPICK_SCOPE =
+struct
+
+open NitpickUtil
+open NitpickHOL
+
+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,
+  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 ("NitpickScope.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 =
+    T <> nat_T andalso T <> int_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 ("NitpickHOL.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_datatype thy orf is_integer_type) 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 ("NitpickScope.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 ("NitpickScope.lookup_ints_assign", _) =>
+         raise TYPE ("NitpickScope.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 ("NitpickScope.lookup_ints_assign", _) =>
+         raise TERM ("NitpickScope.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
+
+(* Proof.context -> (typ option * int list) list
+   -> (styp option * int list) list -> (styp option * int list) list -> int list
+   -> typ -> block *)
+fun block_for_type ctxt cards_asgns maxes_asgns iters_asgns bisim_depths T =
+  let val thy = ProofContext.theory_of ctxt in
+    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 thy T of
+         [_] => []
+       | constrs => map_filter (row_for_constr thy maxes_asgns) constrs)
+  end
+
+(* Proof.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 ctxt cards_asgns maxes_asgns iters_asgns bisim_depths
+                     mono_Ts nonmono_Ts =
+  let
+    val thy = ProofContext.theory_of ctxt
+    (* typ -> block *)
+    val block_for = block_for_type 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
+
+(* theory -> scope_desc -> typ * int -> bool *)
+fun is_surely_inconsistent_card_assign thy (card_asgns, max_asgns) (T, k) =
+  case datatype_constrs thy T of
+    [] => false
+  | xs =>
+    let
+      val precise_cards =
+        map (Integer.prod
+             o map (bounded_precise_card_of_type thy 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 ("NitpickHOL.card_of_type", _, _) => false
+
+(* theory -> scope_desc -> bool *)
+fun is_surely_inconsistent_scope_description thy (desc as (card_asgns, _)) =
+  exists (is_surely_inconsistent_card_assign thy desc) card_asgns
+
+(* theory -> scope_desc -> (typ * int) list option *)
+fun repair_card_assigns thy (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 thy
+                ((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 ([], [])
+(* theory -> block list -> int list -> scope_desc option *)
+fun scope_descriptor_from_combination thy blocks columns =
+  let
+    val (card_asgns, max_asgns) =
+      maps project_block (columns ~~ blocks) |> scope_descriptor_from_block
+    val card_asgns = repair_card_assigns thy (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 -> scope_desc -> typ * int -> dtype_spec *)
+fun datatype_spec_from_scope_descriptor (ext_ctxt as {thy, ...})
+                                        (desc as (card_asgns, _)) (T, card) =
+  let
+    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 thy (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, constrs = constrs} end
+
+(* extended_context -> int -> scope_desc -> scope *)
+fun scope_from_descriptor (ext_ctxt as {thy, ...}) sym_break
+                          (desc as (card_asgns, _)) =
+  let
+    val datatypes = map (datatype_spec_from_scope_descriptor ext_ctxt 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 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 -> scope list *)
+fun all_scopes (ext_ctxt as {thy, ctxt, ...}) sym_break cards_asgns maxes_asgns
+               iters_asgns bisim_depths mono_Ts nonmono_Ts =
+  let
+    val cards_asgns = fix_cards_assigns_wrt_boxing thy mono_Ts cards_asgns
+    val blocks = blocks_for_types ctxt cards_asgns maxes_asgns iters_asgns
+                                  bisim_depths mono_Ts nonmono_Ts
+    val ranks = map rank_of_block blocks
+    val descs = all_combinations_ordered_smartly (map (rpair 0) ranks)
+                |> map_filter (scope_descriptor_from_combination thy blocks)
+  in
+    descs |> length descs <= distinct_threshold ? distinct (op =)
+          |> map (scope_from_descriptor ext_ctxt sym_break)
+  end
+
+end;