signature SLEDGEHAMMER_SHRINK =
sig
type isar_step = Sledgehammer_Isar_Reconstruct.isar_step
val shrink_proof :
bool -> Proof.context -> string -> string -> bool -> Time.time -> real
-> isar_step list -> isar_step list * (bool * Time.time)
end
structure Sledgehammer_Shrink (* : SLEDGEHAMMER_SHRINK *) =
struct
open Sledgehammer_Isar_Reconstruct
(* 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)
(* Timing *)
type ext_time = bool * Time.time
fun ext_time_add (b1, t1) (b2, t2) : ext_time = (b1 orelse b2, t1+t2)
val no_time = (false, seconds 0.0)
fun take_time timeout tac arg =
let val timing = Timing.start () in
(TimeLimit.timeLimit timeout tac arg;
Timing.result timing |> #cpu |> SOME)
handle _ => NONE
end
fun sum_up_time timeout =
Vector.foldl
((fn (SOME t, (b, ts)) => (b, t+ts)
| (NONE, (_, ts)) => (true, ts+timeout)) o apfst Lazy.force)
no_time
(* 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_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
(* Main function for shrinking proofs *)
fun shrink_proof debug ctxt type_enc lam_trans preplay preplay_timeout
isar_shrink proof =
let
fun shrink_top_level 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 (label, _)) =
Label_Table.update_new (label, i)
| update_table (i, Prove (_, label, _, _)) =
Label_Table.update_new (label, i)
| update_table _ = I
val label_index_table = fold_index update_table proof Label_Table.empty
(* proof references *)
fun refs (Prove (_, _, _, By_Metis (lfs, _))) =
maps (the_list o Label_Table.lookup label_index_table) lfs
| refs (Prove (_, _, _, Case_Split (cases, (lfs, _)))) =
maps (the_list o Label_Table.lookup label_index_table) 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) *)
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 try_metis timeout (Prove (_, _, t, By_Metis fact_names)) =
if not preplay then (fn () => SOME (seconds 0.0)) else
let
val facts =
fact_names
|>> map string_for_label
|> op @
|> map (the_single o thms_of_name ctxt) (* FIXME: maps (the o thms_of_name ctxt) *)
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
| try_metis _ _ = (fn () => SOME (seconds 0.0) )
(* Lazy metis time vector, cache *)
val metis_time =
Vector.map (Lazy.lazy o try_metis preplay_timeout o the) proof_vect
(* Merging *)
fun merge (Prove (_, label1, _, By_Metis (lfs1, gfs1)))
(Prove (qs2, label2 , t, By_Metis (lfs2, gfs2))) =
let
val ls = remove (op =) label1 lfs2 |> union (op =) lfs1
val ss = union (op =) gfs1 gfs2
in Prove (qs2, label2, t, By_Metis (ls, ss)) end
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.+ (t1, t2) |> Time.toReal |> curry Real.* merge_timeout_slack
|> Time.fromReal
in
case try_metis timeout s12 () of
NONE => (NONE, metis_time)
| some_t12 =>
(SOME s12, metis_time
|> replace (seconds 0.0 |> 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 (top_level andalso n'<3)
then
(Vector.foldr
(fn (NONE, proof) => proof | (SOME s, proof) => s :: proof)
[] proof_vect,
sum_up_time preplay_timeout 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 shrink_proof' top_level ctxt proof =
let
(* Enrich context with top-level facts *)
val thy = Proof_Context.theory_of ctxt
fun enrich_ctxt (Assume (label, t)) ctxt =
Proof_Context.put_thms false
(string_for_label label, SOME [Skip_Proof.make_thm thy t]) ctxt
| enrich_ctxt (Prove (_, label, t, _)) ctxt =
Proof_Context.put_thms false
(string_for_label label, SOME [Skip_Proof.make_thm thy t]) ctxt
| enrich_ctxt _ ctxt = ctxt
val rich_ctxt = fold enrich_ctxt proof ctxt
(* Shrink case_splits and top-levl *)
val ((proof, top_level_time), lower_level_time) =
proof |> shrink_case_splits rich_ctxt
|>> shrink_top_level top_level rich_ctxt
in
(proof, ext_time_add lower_level_time top_level_time)
end
and shrink_case_splits ctxt proof =
let
fun shrink_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_and_collect_time (shrink_proof' false ctxt)
fun shrink (Prove (qs, lbl, t, Case_Split (cases, facts))) =
let val (cases, time) = shrink_case_split cases
in (Prove (qs, lbl, t, Case_Split (cases, facts)), time) end
| shrink step = (step, no_time)
in
shrink_and_collect_time shrink proof
end
in
shrink_proof' true ctxt proof
end
end