(* 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,
standard: bool,
complete: bool * bool,
concrete: bool * bool,
deep: bool,
constrs: constr_spec list}
type scope = {
hol_ctxt: hol_context,
binarize: bool,
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 -> bool -> typ -> bool
val is_concrete_type : dtype_spec list -> bool -> typ -> bool
val is_exact_type : dtype_spec list -> bool -> 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 -> bool -> 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 -> 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,
standard: bool,
complete: bool * bool,
concrete: bool * bool,
deep: bool,
constrs: constr_spec list}
type scope = {
hol_ctxt: hol_context,
binarize: bool,
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 -> bool -> typ -> bool *)
fun is_complete_type dtypes facto (Type (@{type_name fun}, [T1, T2])) =
is_concrete_type dtypes facto T1 andalso is_complete_type dtypes facto T2
| is_complete_type dtypes facto (Type (@{type_name fin_fun}, [T1, T2])) =
is_exact_type dtypes facto T1 andalso is_complete_type dtypes facto T2
| is_complete_type dtypes facto (Type (@{type_name "*"}, Ts)) =
forall (is_complete_type dtypes facto) Ts
| is_complete_type dtypes facto T =
not (is_integer_like_type T) andalso not (is_bit_type T) andalso
fun_from_pair (#complete (the (datatype_spec dtypes T))) facto
handle Option.Option => true
and is_concrete_type dtypes facto (Type (@{type_name fun}, [T1, T2])) =
is_complete_type dtypes facto T1 andalso is_concrete_type dtypes facto T2
| is_concrete_type dtypes facto (Type (@{type_name fin_fun}, [_, T2])) =
is_concrete_type dtypes facto T2
| is_concrete_type dtypes facto (Type (@{type_name "*"}, Ts)) =
forall (is_concrete_type dtypes facto) Ts
| is_concrete_type dtypes facto T =
fun_from_pair (#concrete (the (datatype_spec dtypes T))) facto
handle Option.Option => true
and is_exact_type dtypes facto =
is_complete_type dtypes facto andf is_concrete_type dtypes facto
(* 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 = {thy, ctxt, stds, ...}, 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 stds)
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 -> bool -> (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, ...}) binarize 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 binarized_and_boxed_datatype_constrs hol_ctxt binarize T of
[_] => []
| constrs => map_filter (row_for_constr thy maxes_assigns) constrs)
(* hol_context -> bool -> (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 binarize cards_assigns maxes_assigns iters_assigns
bitss bisim_depths mono_Ts nonmono_Ts =
let
(* typ -> block *)
val block_for = block_for_type hol_ctxt binarize 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 -> bool -> scope_desc -> typ * int -> bool *)
fun is_surely_inconsistent_card_assign hol_ctxt binarize
(card_assigns, max_assigns) (T, k) =
case binarized_and_boxed_datatype_constrs hol_ctxt binarize 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 -> bool -> (typ * int) list -> (typ * int) list
-> (styp * int) list -> bool *)
fun is_surely_inconsistent_scope_description hol_ctxt binarize seen rest
max_assigns =
exists (is_surely_inconsistent_card_assign hol_ctxt binarize
(seen @ rest, max_assigns)) seen
(* hol_context -> bool -> scope_desc -> (typ * int) list option *)
fun repair_card_assigns hol_ctxt binarize (card_assigns, max_assigns) =
let
(* (typ * int) list -> (typ * int) list -> (typ * int) list option *)
fun aux seen [] = SOME seen
| aux _ ((_, 0) :: _) = NONE
| aux seen ((T, k) :: rest) =
(if is_surely_inconsistent_scope_description hol_ctxt binarize
((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 (_, 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 -> bool -> block list -> int list -> scope_desc option *)
fun scope_descriptor_from_combination (hol_ctxt as {thy, ...}) binarize 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 binarize (card_assigns, max_assigns) |> the
in
SOME (map (repair_iterator_assign thy card_assigns) card_assigns,
max_assigns)
end
handle Option.Option => NONE
(* (typ * int) list -> dtype_spec list -> int Typtab.table *)
fun offset_table_for_card_assigns 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_iterator_type T 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 (_, T))
constrs =
let
val max = constr_max max_assigns x
(* 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 -> bool -> typ list -> (typ * int) list -> typ -> bool *)
fun has_exact_card hol_ctxt facto finitizable_dataTs card_assigns T =
let val card = card_of_type card_assigns T in
card = bounded_exact_card_of_type hol_ctxt
(if facto then finitizable_dataTs else []) (card + 1) 0
card_assigns T
end
(* hol_context -> bool -> typ list -> typ list -> scope_desc -> typ * int
-> dtype_spec *)
fun datatype_spec_from_scope_descriptor (hol_ctxt as {thy, stds, ...}) binarize
deep_dataTs finitizable_dataTs (desc as (card_assigns, _)) (T, card) =
let
val deep = member (op =) deep_dataTs T
val co = is_codatatype thy T
val standard = is_standard_datatype thy stds T
val xs = binarized_and_boxed_datatype_constrs hol_ctxt binarize 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
(* bool -> bool *)
fun is_complete facto =
has_exact_card hol_ctxt facto finitizable_dataTs card_assigns T
fun is_concrete facto =
is_word_type T orelse
xs |> maps (binder_types o snd) |> maps binder_types
|> forall (has_exact_card hol_ctxt facto finitizable_dataTs
card_assigns)
val complete = pair_from_fun is_complete
val concrete = pair_from_fun is_concrete
(* 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, standard = standard, complete = complete,
concrete = concrete, deep = deep, constrs = constrs}
end
(* hol_context -> bool -> int -> typ list -> typ list -> scope_desc -> scope *)
fun scope_from_descriptor (hol_ctxt as {thy, stds, ...}) binarize sym_break
deep_dataTs finitizable_dataTs
(desc as (card_assigns, _)) =
let
val datatypes =
map (datatype_spec_from_scope_descriptor hol_ctxt binarize deep_dataTs
finitizable_dataTs desc)
(filter (is_datatype thy stds 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, binarize = binarize, 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 card_assigns datatypes}
end
(* theory -> typ list -> (typ option * int list) list
-> (typ option * int list) list *)
fun repair_cards_assigns_wrt_boxing_etc _ _ [] = []
| repair_cards_assigns_wrt_boxing_etc 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) |> map (rpair ks o SOME)
else
[(SOME T, ks)]) @
repair_cards_assigns_wrt_boxing_etc thy Ts cards_assigns
| repair_cards_assigns_wrt_boxing_etc thy Ts ((NONE, ks) :: cards_assigns) =
(NONE, ks) :: repair_cards_assigns_wrt_boxing_etc thy Ts cards_assigns
val max_scopes = 4096
val distinct_threshold = 512
(* hol_context -> bool -> int -> (typ option * int list) list
-> (styp option * int list) list -> (styp option * int list) list -> int list
-> typ list -> typ list -> typ list ->typ list -> int * scope list *)
fun all_scopes (hol_ctxt as {thy, ...}) binarize sym_break cards_assigns
maxes_assigns iters_assigns bitss bisim_depths mono_Ts nonmono_Ts
deep_dataTs finitizable_dataTs =
let
val cards_assigns = repair_cards_assigns_wrt_boxing_etc thy mono_Ts
cards_assigns
val blocks = blocks_for_types hol_ctxt binarize 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 binarize blocks)
head
in
(length all - length head,
descs |> length descs <= distinct_threshold ? distinct (op =)
|> map (scope_from_descriptor hol_ctxt binarize sym_break
deep_dataTs finitizable_dataTs))
end
end;