(* Title: HOL/Tools/Sledgehammer/sledgehammer_shrink.ML
Author: Jasmin Blanchette, TU Muenchen
Author: Steffen Juilf Smolka, TU Muenchen
Shrinking and preplaying of reconstructed isar proofs.
*)
signature SLEDGEHAMMER_SHRINK =
sig
type isar_step = Sledgehammer_Proof.isar_step
val shrink_proof :
bool -> Proof.context -> string -> string -> bool -> Time.time option
-> real -> isar_step list -> isar_step list * (bool * (bool * Time.time))
end
structure Sledgehammer_Shrink : SLEDGEHAMMER_SHRINK =
struct
open Sledgehammer_Util
open Sledgehammer_Proof
(* Parameters *)
val merge_timeout_slack = 1.2
(* Data structures, orders *)
val label_ord = prod_ord int_ord fast_string_ord o pairself swap
structure Label_Table = Table(
type key = label
val ord = label_ord)
(* clean vector interface *)
fun get i v = Vector.sub (v, i)
fun replace x i v = Vector.update (v, i, x)
fun update f i v = replace (get i v |> f) i v
fun v_map_index f v = Vector.foldr (op::) nil v |> map_index f |> Vector.fromList
fun v_fold_index f v s =
Vector.foldl (fn (x, (i, s)) => (i+1, f (i, x) s)) (0, s) v |> snd
(* Queue interface to table *)
fun pop tab key =
let val v = hd (Inttab.lookup_list tab key) in
(v, Inttab.remove_list (op =) (key, v) tab)
end
fun pop_max tab = pop tab (the (Inttab.max_key tab))
fun add_list tab xs = fold (Inttab.insert_list (op =)) xs tab
(* Timing *)
fun ext_time_add (b1, t1) (b2, t2) = (b1 orelse b2, Time.+(t1,t2))
val no_time = (false, Time.zeroTime)
fun take_time timeout tac arg =
let val timing = Timing.start () in
(TimeLimit.timeLimit timeout tac arg;
Timing.result timing |> #cpu |> SOME)
handle TimeLimit.TimeOut => NONE
end
(* Main function for shrinking proofs *)
fun shrink_proof debug ctxt type_enc lam_trans preplay preplay_timeout
isar_shrink proof =
let
(* 60 seconds seems like a good interpreation of "no timeout" *)
val preplay_timeout = preplay_timeout |> the_default (seconds 60.0)
(* handle metis preplay fail *)
local
open Unsynchronized
val metis_fail = ref false
in
fun handle_metis_fail try_metis () =
try_metis () handle exp =>
(if debug then raise exp else metis_fail := true; SOME Time.zeroTime)
fun get_time lazy_time =
if !metis_fail then SOME Time.zeroTime else Lazy.force lazy_time
val metis_fail = fn () => !metis_fail
end
(* Shrink proof on top level - do not shrink case splits *)
fun shrink_top_level on_top_level ctxt proof =
let
(* proof vector *)
val proof_vect = proof |> map SOME |> Vector.fromList
val n = Vector.length proof_vect
val n_metis = metis_steps_top_level proof
val target_n_metis = Real.fromInt n_metis / isar_shrink |> Real.round
(* table for mapping from (top-level-)label to proof position *)
fun update_table (i, Assume (l, _)) = Label_Table.update_new (l, i)
| update_table (i, Obtain (_, _, l, _, _)) = Label_Table.update_new (l, i)
| update_table (i, Prove (_, l, _, _)) = Label_Table.update_new (l, i)
| update_table _ = I
val label_index_table = fold_index update_table proof Label_Table.empty
val lookup_indices = map_filter (Label_Table.lookup label_index_table)
(* proof references *)
fun refs (Obtain (_, _, _, _, By_Metis (lfs, _))) = lookup_indices lfs
| refs (Prove (_, _, _, By_Metis (lfs, _))) = lookup_indices lfs
| refs (Prove (_, _, _, Case_Split (cases, (lfs, _)))) =
lookup_indices lfs @ maps (maps refs) cases
| refs _ = []
val refed_by_vect =
Vector.tabulate (n, (fn _ => []))
|> fold_index (fn (i, step) => fold (update (cons i)) (refs step)) proof
|> Vector.map rev (* after rev, indices are sorted in ascending order *)
(* candidates for elimination, use table as priority queue (greedy
algorithm) *)
(* TODO: consider adding "Obtain" cases *)
fun add_if_cand proof_vect (i, [j]) =
(case (the (get i proof_vect), the (get j proof_vect)) of
(Prove (_, _, t, By_Metis _), Prove (_, _, _, By_Metis _)) =>
cons (Term.size_of_term t, i)
| _ => I)
| add_if_cand _ _ = I
val cand_tab =
v_fold_index (add_if_cand proof_vect) refed_by_vect []
|> Inttab.make_list
(* Metis Preplaying *)
fun resolve_fact_names names =
names
|>> map string_for_label
|> op @
|> maps (thms_of_name ctxt)
(* TODO: add "Obtain" case *)
exception ZeroTime
fun try_metis timeout (succedent, step) =
(if not preplay then K (SOME Time.zeroTime) else
let
val (t, byline, obtain) =
(case step of
Prove (_, _, t, byline) => (t, byline, false)
| Obtain (_, xs, _, t, byline) =>
(* proof obligation: !!thesis. (!!x. A x ==> thesis) ==> thesis
(see ~~/src/Pure/Isar/obtain.ML) *)
let
(*val thesis = Term.Free ("thesis", HOLogic.boolT)
|> HOLogic.mk_Trueprop
val frees = map Term.Free xs
(* !!x1..xn. t ==> thesis (xs = [x1, .., xn]) *)
val inner_prop = fold_rev Logic.all frees (Logic.mk_implies (t, thesis))
(* !!thesis. (!!x1..xn. t ==> thesis) ==> thesis *)
val prop = Logic.all thesis (Logic.mk_implies (inner_prop, thesis))*)
val thesis = Term.Free ("thesis", HOLogic.boolT)
val prop =
HOLogic.mk_imp (HOLogic.dest_Trueprop t, thesis)
|> fold_rev (fn (x, T) => fn t => HOLogic.mk_all (x, T, t)) xs
|> rpair thesis
|> HOLogic.mk_imp
|> (fn t => HOLogic.mk_all ("thesis", HOLogic.boolT, t))
|> HOLogic.mk_Trueprop
in
(prop, byline, true)
end
| _ => raise ZeroTime)
val make_thm = Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
val facts =
(case byline of
By_Metis fact_names => resolve_fact_names fact_names
| Case_Split (cases, fact_names) =>
resolve_fact_names fact_names
@ (case the succedent of
Assume (_, t) => make_thm t
| Obtain (_, _, _, t, _) => make_thm t
| Prove (_, _, t, _) => make_thm t
| _ => error "Internal error: unexpected succedent of case split")
:: map (hd #> (fn Assume (_, a) => Logic.mk_implies (a, t)
| _ => error "Internal error: malformed case split")
#> make_thm)
cases)
val ctxt = ctxt |> Config.put Metis_Tactic.verbose debug
|> obtain ? Config.put Metis_Tactic.new_skolem true
val goal =
Goal.prove (Config.put Metis_Tactic.verbose debug ctxt) [] [] t
fun tac {context = ctxt, prems = _} =
Metis_Tactic.metis_tac [type_enc] lam_trans ctxt facts 1
in
take_time timeout (fn () => goal tac)
end)
handle ZeroTime => K (SOME Time.zeroTime)
val try_metis_quietly = the_default NONE oo try oo try_metis
(* cache metis preplay times in lazy time vector *)
val metis_time =
v_map_index
(Lazy.lazy o handle_metis_fail o try_metis preplay_timeout
o apfst (fn i => try (the o get (i-1)) proof_vect) o apsnd the)
proof_vect
fun sum_up_time lazy_time_vector =
Vector.foldl
((fn (SOME t, (b, ts)) => (b, Time.+(t, ts))
| (NONE, (_, ts)) => (true, Time.+(ts, preplay_timeout)))
o apfst get_time)
no_time lazy_time_vector
(* Merging *)
(* TODO: consider adding "Obtain" cases *)
fun merge (Prove (_, label1, _, By_Metis (lfs1, gfs1)))
(Prove (qs2, label2, t, By_Metis (lfs2, gfs2))) =
let
val lfs = remove (op =) label1 lfs2 |> union (op =) lfs1
val gfs = union (op =) gfs1 gfs2
in Prove (qs2, label2, t, By_Metis (lfs, gfs)) end
| merge _ _ = error "Internal error: Unmergeable Isar steps"
fun try_merge metis_time (s1, i) (s2, j) =
(case get i metis_time |> Lazy.force of
NONE => (NONE, metis_time)
| SOME t1 =>
(case get j metis_time |> Lazy.force of
NONE => (NONE, metis_time)
| SOME t2 =>
let
val s12 = merge s1 s2
val timeout = time_mult merge_timeout_slack (Time.+(t1, t2))
in
case try_metis_quietly timeout (NONE, s12) () of
NONE => (NONE, metis_time)
| some_t12 =>
(SOME s12, metis_time
|> replace (Time.zeroTime |> SOME |> Lazy.value) i
|> replace (Lazy.value some_t12) j)
end))
fun merge_steps metis_time proof_vect refed_by cand_tab n' n_metis' =
if Inttab.is_empty cand_tab
orelse n_metis' <= target_n_metis
orelse (on_top_level andalso n'<3)
then
(Vector.foldr
(fn (NONE, proof) => proof | (SOME s, proof) => s :: proof)
[] proof_vect,
sum_up_time metis_time)
else
let
val (i, cand_tab) = pop_max cand_tab
val j = get i refed_by |> the_single
val s1 = get i proof_vect |> the
val s2 = get j proof_vect |> the
in
case try_merge metis_time (s1, i) (s2, j) of
(NONE, metis_time) =>
merge_steps metis_time proof_vect refed_by cand_tab n' n_metis'
| (s, metis_time) =>
let
val refs = refs s1
val refed_by = refed_by |> fold
(update (Ord_List.remove int_ord i #> Ord_List.insert int_ord j)) refs
val new_candidates =
fold (add_if_cand proof_vect)
(map (fn i => (i, get i refed_by)) refs) []
val cand_tab = add_list cand_tab new_candidates
val proof_vect = proof_vect |> replace NONE i |> replace s j
in
merge_steps metis_time proof_vect refed_by cand_tab (n' - 1)
(n_metis' - 1)
end
end
in
merge_steps metis_time proof_vect refed_by_vect cand_tab n n_metis
end
fun do_proof on_top_level ctxt proof =
let
(* Enrich context with top-level facts *)
val thy = Proof_Context.theory_of ctxt
(* TODO: add Skolem variables to context? *)
fun enrich_with_fact l t =
Proof_Context.put_thms false
(string_for_label l, SOME [Skip_Proof.make_thm thy t])
fun enrich_with_step (Assume (l, t)) = enrich_with_fact l t
| enrich_with_step (Obtain (_, _, l, t, _)) = enrich_with_fact l t
| enrich_with_step (Prove (_, l, t, _)) = enrich_with_fact l t
| enrich_with_step _ = I
val rich_ctxt = fold enrich_with_step proof ctxt
(* Shrink case_splits and top-levl *)
val ((proof, top_level_time), lower_level_time) =
proof |> do_case_splits rich_ctxt
|>> shrink_top_level on_top_level rich_ctxt
in
(proof, ext_time_add lower_level_time top_level_time)
end
and do_case_splits ctxt proof =
let
fun shrink_each_and_collect_time shrink candidates =
let fun f_m cand time = shrink cand ||> ext_time_add time
in fold_map f_m candidates no_time end
val shrink_case_split =
shrink_each_and_collect_time (do_proof false ctxt)
fun shrink (Prove (qs, l, t, Case_Split (cases, facts))) =
let val (cases, time) = shrink_case_split cases
in (Prove (qs, l, t, Case_Split (cases, facts)), time) end
| shrink step = (step, no_time)
in
shrink_each_and_collect_time shrink proof
end
in
do_proof true ctxt proof
|> apsnd (pair (metis_fail ()))
end
end