(* Title: HOL/Tools/Sledgehammer/sledgehammer_compress.ML
Author: Jasmin Blanchette, TU Muenchen
Author: Steffen Juilf Smolka, TU Muenchen
Compression of reconstructed isar proofs.
*)
signature SLEDGEHAMMER_COMPRESS =
sig
type isar_proof = Sledgehammer_Proof.isar_proof
type preplay_time = Sledgehammer_Preplay.preplay_time
val compress_and_preplay_proof :
bool -> Proof.context -> string -> string -> bool -> Time.time option
-> real -> isar_proof -> isar_proof * (bool * preplay_time)
end
structure Sledgehammer_Compress : SLEDGEHAMMER_COMPRESS =
struct
open Sledgehammer_Util
open Sledgehammer_Proof
open Sledgehammer_Preplay
(* 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_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) handle Empty => raise Fail "sledgehammer_compress: pop"
fun pop_max tab = pop tab (the (Inttab.max_key tab))
handle Option => raise Fail "sledgehammer_compress: pop_max"
fun add_list tab xs = fold (Inttab.insert_list (op =)) xs tab
(* Main function for compresing proofs *)
fun compress_and_preplay_proof debug ctxt type_enc lam_trans preplay
preplay_timeout isar_compress 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 exn =>
(if Exn.is_interrupt exn orelse debug then reraise exn
else metis_fail := true; some_preplay_time)
fun get_time lazy_time =
if !metis_fail andalso not (Lazy.is_finished lazy_time)
then some_preplay_time
else Lazy.force lazy_time
val metis_fail = fn () => !metis_fail
end
(* compress top level steps - do not compress subproofs *)
fun compress_top_level on_top_level ctxt n steps =
let
(* proof step vector *)
val step_vect = steps |> map SOME |> Vector.fromList
val n_metis = add_metis_steps_top_level steps 0
val target_n_metis = Real.fromInt n_metis / isar_compress |> Real.round
(* table for mapping from (top-level-)label to step_vect position *)
fun update_table (i, Prove (_, l, _, _)) = Label_Table.update_new (l, i)
| update_table (i, Obtain (_, _, l, _, _)) = Label_Table.update_new (l, i)
| update_table _ = I
val label_index_table = fold_index update_table steps Label_Table.empty
val lookup_indices = map_filter (Label_Table.lookup label_index_table)
(* proof step references *)
fun refs step =
(case byline_of_step step of
NONE => []
| SOME (By_Metis (subproofs, (lfs, _))) =>
maps (steps_of_proof #> maps refs) subproofs @ lookup_indices lfs)
val refed_by_vect =
Vector.tabulate (Vector.length step_vect, K [])
|> fold_index (fn (i, step) => fold (update (cons i)) (refs step)) steps
|> 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 step_vect (i, [j]) =
((case (the (get i step_vect), the (get j step_vect)) of
(Prove (_, _, t, By_Metis _), Prove (_, _, _, By_Metis _)) =>
cons (Term.size_of_term t, i)
| (Prove (_, _, t, By_Metis _), Obtain (_, _, _, _, By_Metis _)) =>
cons (Term.size_of_term t, i)
| _ => I)
handle Option => raise Fail "sledgehammer_compress: add_if_cand")
| add_if_cand _ _ = I
val cand_tab =
v_fold_index (add_if_cand step_vect) refed_by_vect []
|> Inttab.make_list
(* cache metis preplay times in lazy time vector *)
val metis_time =
Vector.map
(if not preplay then K (zero_preplay_time) #> Lazy.value
else
the
#> try_metis debug type_enc lam_trans ctxt preplay_timeout
#> handle_metis_fail
#> Lazy.lazy)
step_vect
handle Option => raise Fail "sledgehammer_compress: metis_time"
fun sum_up_time lazy_time_vector =
Vector.foldl
(apfst get_time #> uncurry add_preplay_time)
zero_preplay_time lazy_time_vector
(* Merging *)
fun merge (Prove (_, lbl1, _, By_Metis (subproofs1, (lfs1, gfs1)))) step2 =
let
val (step_constructor, (subproofs2, (lfs2, gfs2))) =
(case step2 of
Prove (qs2, lbl2, t, By_Metis x) =>
(fn by => Prove (qs2, lbl2, t, by), x)
| Obtain (qs2, xs, lbl2, t, By_Metis x) =>
(fn by => Obtain (qs2, xs, lbl2, t, by), x)
| _ => raise Fail "sledgehammer_compress: unmergeable Isar steps" )
val lfs = remove (op =) lbl1 lfs2 |> union (op =) lfs1
val gfs = union (op =) gfs1 gfs2
val subproofs = subproofs1 @ subproofs2
in step_constructor (By_Metis (subproofs, (lfs, gfs))) end
| merge _ _ = raise Fail "sledgehammer_compress: unmergeable Isar steps"
fun try_merge metis_time (s1, i) (s2, j) =
if not preplay then (merge s1 s2 |> SOME, metis_time)
else
(case get i metis_time |> Lazy.force of
(true, _) => (NONE, metis_time)
| (_, t1) =>
(case get j metis_time |> Lazy.force of
(true, _) => (NONE, metis_time)
| (_, t2) =>
let
val s12 = merge s1 s2
val timeout = time_mult merge_timeout_slack (Time.+(t1, t2))
in
case try_metis_quietly debug type_enc lam_trans
ctxt timeout s12 () of
(true, _) => (NONE, metis_time)
| exact_time =>
(SOME s12, metis_time
|> replace (zero_preplay_time |> Lazy.value) i
|> replace (Lazy.value exact_time) j)
end))
fun merge_steps metis_time step_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, steps) => steps | (SOME s, steps) => s :: steps)
[] step_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 step_vect |> the
val s2 = get j step_vect |> the
in
case try_merge metis_time (s1, i) (s2, j) of
(NONE, metis_time) =>
merge_steps metis_time step_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 step_vect)
(map (fn i => (i, get i refed_by)) refs) []
val cand_tab = add_list cand_tab new_candidates
val step_vect = step_vect |> replace NONE i |> replace s j
in
merge_steps metis_time step_vect refed_by cand_tab (n' - 1)
(n_metis' - 1)
end
end
handle Option => raise Fail "sledgehammer_compress: merge_steps"
| List.Empty => raise Fail "sledgehammer_compress: merge_steps"
in
merge_steps metis_time step_vect refed_by_vect cand_tab n n_metis
end
fun do_proof on_top_level ctxt (Proof (Fix fix, Assume assms, steps)) =
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 (Prove (_, l, t, _)) = enrich_with_fact l t
| enrich_with_step (Obtain (_, _, l, t, _)) = enrich_with_fact l t
| enrich_with_step _ = I
val enrich_with_steps = fold enrich_with_step
val enrich_with_assms = fold (uncurry enrich_with_fact)
val rich_ctxt =
ctxt |> enrich_with_assms assms |> enrich_with_steps steps
val n = List.length fix + List.length assms + List.length steps
(* compress subproofs and top-levl steps *)
val ((steps, top_level_time), lower_level_time) =
steps |> do_subproofs rich_ctxt
|>> compress_top_level on_top_level rich_ctxt n
in
(Proof (Fix fix, Assume assms, steps),
add_preplay_time lower_level_time top_level_time)
end
and do_subproofs ctxt subproofs =
let
fun compress_each_and_collect_time compress subproofs =
let fun f_m proof time = compress proof ||> add_preplay_time time
in fold_map f_m subproofs zero_preplay_time end
val compress_subproofs =
compress_each_and_collect_time (do_proof false ctxt)
fun compress (Prove (qs, l, t, By_Metis(subproofs, facts))) =
let val (subproofs, time) = compress_subproofs subproofs
in (Prove (qs, l, t, By_Metis(subproofs, facts)), time) end
| compress atomic_step = (atomic_step, zero_preplay_time)
in
compress_each_and_collect_time compress subproofs
end
in
do_proof true ctxt proof
|> apsnd (pair (metis_fail ()))
end
end