added Nitpick's theory and ML files to Isabelle/HOL;
the examples and the documentation are on their way.
(* 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;