author | wenzelm |
Sat, 14 Nov 2015 13:48:49 +0100 | |
changeset 61666 | f1b257607981 |
parent 61612 | 40859aa6d10c |
child 62219 | dbac573b27e7 |
permissions | -rw-r--r-- |
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(* Title: HOL/Tools/Sledgehammer/sledgehammer_isar_compress.ML |
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Author: Steffen Juilf Smolka, TU Muenchen |
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Author: Jasmin Blanchette, TU Muenchen |
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||
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Compression of Isar proofs by merging steps. |
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Only proof steps using the same proof method are merged. |
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*) |
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||
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signature SLEDGEHAMMER_ISAR_COMPRESS = |
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sig |
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type isar_proof = Sledgehammer_Isar_Proof.isar_proof |
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type isar_preplay_data = Sledgehammer_Isar_Preplay.isar_preplay_data |
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val compress_isar_proof : Proof.context -> real -> Time.time -> |
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isar_preplay_data Unsynchronized.ref -> isar_proof -> isar_proof |
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end; |
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|
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structure Sledgehammer_Isar_Compress : SLEDGEHAMMER_ISAR_COMPRESS = |
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struct |
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||
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open Sledgehammer_Util |
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open Sledgehammer_Proof_Methods |
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open Sledgehammer_Isar_Proof |
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open Sledgehammer_Isar_Preplay |
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fun collect_successors steps lbls = |
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let |
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fun collect_steps _ (accum as ([], _)) = accum |
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| collect_steps [] accum = accum |
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| collect_steps (step :: steps) accum = collect_steps steps (collect_step step accum) |
|
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and collect_step (step as Prove (_, _, l, _, subproofs, _, _, _)) x = |
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(case collect_subproofs subproofs x of |
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(accum as ([], _)) => accum |
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| accum as (l' :: lbls', accu) => if l = l' then (lbls', step :: accu) else accum) |
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| collect_step _ accum = accum |
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and collect_subproofs [] accum = accum |
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| collect_subproofs (proof :: subproofs) accum = |
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(case collect_steps (steps_of_isar_proof proof) accum of |
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accum as ([], _) => accum |
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| accum => collect_subproofs subproofs accum) |
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in |
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rev (snd (collect_steps steps (lbls, []))) |
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end |
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fun update_steps updates steps = |
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let |
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fun update_steps [] updates = ([], updates) |
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| update_steps steps [] = (steps, []) |
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| update_steps (step :: steps) updates = update_step step (update_steps steps updates) |
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and update_step step (steps, []) = (step :: steps, []) |
|
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| update_step (Prove (qs, xs, l, t, subproofs, facts, meths, comment)) |
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(steps, |
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updates as Prove (qs', xs', l', t', subproofs', facts', meths', comment') :: updates') = |
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(if l = l' then |
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update_subproofs subproofs' updates' |
|
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|>> (fn subproofs'' => Prove (qs', xs', l', t', subproofs'', facts', meths', comment')) |
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else |
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update_subproofs subproofs updates |
|
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|>> (fn subproofs' => Prove (qs, xs, l, t, subproofs', facts, meths, comment))) |
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|>> (fn step => step :: steps) |
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| update_step step (steps, updates) = (step :: steps, updates) |
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and update_subproofs [] updates = ([], updates) |
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| update_subproofs steps [] = (steps, []) |
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| update_subproofs (proof :: subproofs) updates = |
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update_proof proof (update_subproofs subproofs updates) |
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and update_proof proof (proofs, []) = (proof :: proofs, []) |
|
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| update_proof (Proof (xs, assms, steps)) (proofs, updates) = |
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let val (steps', updates') = update_steps steps updates in |
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(Proof (xs, assms, steps') :: proofs, updates') |
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end |
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in |
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fst (update_steps steps (rev updates)) |
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end |
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|
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fun merge_methods preplay_data (l1, meths1) (l2, meths2) = |
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let |
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fun is_hopeful l meth = |
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let val outcome = preplay_outcome_of_isar_step_for_method preplay_data l meth in |
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not (Lazy.is_finished outcome) orelse |
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(case Lazy.force outcome of Played _ => true | Play_Timed_Out _ => true | _ => false) |
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end |
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val (hopeful, hopeless) = |
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meths2 @ subtract (op =) meths2 meths1 |
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|> List.partition (is_hopeful l1 andf is_hopeful l2) |
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in |
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(hopeful @ hopeless, hopeless) |
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end |
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|
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fun merge_steps preplay_data (Prove ([], xs1, l1, _, subproofs1, (lfs1, gfs1), meths1, comment1)) |
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(Prove (qs2, xs2, l2, t, subproofs2, (lfs2, gfs2), meths2, comment2)) = |
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let |
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val (meths, hopeless) = merge_methods preplay_data (l1, meths1) (l2, meths2) |
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val lfs = union (op =) lfs1 (remove (op =) l1 lfs2) |
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val gfs = union (op =) gfs1 gfs2 |
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in |
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(Prove (qs2, inter (op =) (Term.add_frees t []) (xs1 @ xs2), l2, t, |
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subproofs1 @ subproofs2, sort_facts (lfs, gfs), meths, comment1 ^ comment2), |
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hopeless) |
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end |
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val merge_slack_time = seconds 0.01 |
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val merge_slack_factor = 1.5 |
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fun adjust_merge_timeout max time = |
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let val timeout = time_mult merge_slack_factor (Time.+ (merge_slack_time, time)) in |
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if Time.< (max, timeout) then max else timeout |
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end |
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val compress_degree = 2 |
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(* Precondition: The proof must be labeled canonically. *) |
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fun compress_isar_proof ctxt compress preplay_timeout preplay_data proof = |
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if compress <= 1.0 then |
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proof |
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else |
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let |
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val (compress_further, decrement_step_count) = |
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let |
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val number_of_steps = add_isar_steps (steps_of_isar_proof proof) 0 |
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val target_number_of_steps = Real.ceil (Real.fromInt number_of_steps / compress) |
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val delta = Unsynchronized.ref (number_of_steps - target_number_of_steps) |
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in |
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(fn () => !delta > 0, fn () => delta := !delta - 1) |
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end |
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|
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val (get_successors, replace_successor) = |
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let |
|
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fun add_refs (Prove (_, _, l, _, _, (lfs, _), _, _)) = |
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fold (fn key => Canonical_Label_Tab.cons_list (key, l)) lfs |
|
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| add_refs _ = I |
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|
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val tab = |
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Canonical_Label_Tab.empty |
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|> fold_isar_steps add_refs (steps_of_isar_proof proof) |
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(* "rev" should have the same effect as "sort canonical_label_ord" *) |
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|> Canonical_Label_Tab.map (K rev) |
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|> Unsynchronized.ref |
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|
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fun get_successors l = Canonical_Label_Tab.lookup_list (!tab) l |
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fun set_successors l refs = tab := Canonical_Label_Tab.update (l, refs) (!tab) |
|
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fun replace_successor old new dest = |
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get_successors dest |
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|> Ord_List.remove canonical_label_ord old |
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|> Ord_List.union canonical_label_ord new |
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|> set_successors dest |
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in |
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(get_successors, replace_successor) |
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end |
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fun reference_time l = |
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(case forced_intermediate_preplay_outcome_of_isar_step (!preplay_data) l of |
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Played time => time |
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| _ => preplay_timeout) |
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|
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(* elimination of trivial, one-step subproofs *) |
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fun elim_one_subproof time (step as Prove (qs, xs, l, t, _, (lfs, gfs), meths, comment)) subs |
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nontriv_subs = |
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if null subs orelse not (compress_further ()) then |
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Prove (qs, xs, l, t, List.revAppend (nontriv_subs, subs), (lfs, gfs), meths, comment) |
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else |
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(case subs of |
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(sub as Proof (_, assms, [Prove (_, _, l', _, [], (lfs', gfs'), meths', _)])) :: subs => |
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let |
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(* merge steps *) |
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val subs'' = subs @ nontriv_subs |
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val lfs'' = union (op =) lfs (subtract (op =) (map fst assms) lfs') |
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val gfs'' = union (op =) gfs' gfs |
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val (meths'' as _ :: _, hopeless) = |
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merge_methods (!preplay_data) (l', meths') (l, meths) |
|
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val step'' = Prove (qs, xs, l, t, subs'', (lfs'', gfs''), meths'', comment) |
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(* check if the modified step can be preplayed fast enough *) |
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val timeout = adjust_merge_timeout preplay_timeout (Time.+ (time, reference_time l')) |
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175 |
in |
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(case preplay_isar_step ctxt timeout hopeless step'' of |
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meths_outcomes as (_, Played time'') :: _ => |
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(* "l'" successfully eliminated *) |
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(decrement_step_count (); |
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set_preplay_outcomes_of_isar_step ctxt time'' preplay_data step'' meths_outcomes; |
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map (replace_successor l' [l]) lfs'; |
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elim_one_subproof time'' step'' subs nontriv_subs) |
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| _ => elim_one_subproof time step subs (sub :: nontriv_subs)) |
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184 |
end |
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| sub :: subs => elim_one_subproof time step subs (sub :: nontriv_subs)) |
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186 |
|
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fun elim_subproofs (step as Prove (_, _, l, _, subproofs, _, _, _)) = |
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if exists (null o tl o steps_of_isar_proof) subproofs then |
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elim_one_subproof (reference_time l) step subproofs [] |
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else |
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step |
55299 | 192 |
| elim_subproofs step = step |
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193 |
|
54712 | 194 |
fun compress_top_level steps = |
195 |
let |
|
57764 | 196 |
val cand_key = apfst (length o get_successors) |
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val cand_ord = |
|
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prod_ord int_ord (prod_ord (int_ord o swap) (int_ord o swap)) o apply2 cand_key |
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199 |
|
55298 | 200 |
fun pop_next_candidate [] = (NONE, []) |
201 |
| pop_next_candidate (cands as (cand :: cands')) = |
|
55331 | 202 |
fold (fn x => fn y => if cand_ord (x, y) = LESS then x else y) cands' cand |
55325 | 203 |
|> (fn best => (SOME best, remove (op =) best cands)) |
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204 |
|
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fun try_eliminate i l labels steps = |
54712 | 206 |
let |
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val (steps_before, (cand as Prove (_, _, _, _, _, (lfs, _), _, _)) :: steps_after) = |
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chop i steps |
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val succs = collect_successors steps_after labels |
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val (succs', hopelesses) = split_list (map (merge_steps (!preplay_data) cand) succs) |
54712 | 211 |
in |
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(case try (map ((fn Played time => time) o |
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forced_intermediate_preplay_outcome_of_isar_step (!preplay_data))) labels of |
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NONE => steps |
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| SOME times0 => |
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let |
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val n = length labels |
61666 | 218 |
val total_time = Library.foldl Time.+ (reference_time l, times0) |
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val timeout = adjust_merge_timeout preplay_timeout |
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(Time.fromReal (Time.toReal total_time / Real.fromInt n)) |
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val meths_outcomess = @{map 2} (preplay_isar_step ctxt timeout) hopelesses succs' |
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|
222 |
in |
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(case try (map (fn (_, Played time) :: _ => time)) meths_outcomess of |
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224 |
NONE => steps |
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225 |
| SOME times => |
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226 |
(* "l" successfully eliminated *) |
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227 |
(decrement_step_count (); |
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@{map 3} (fn time => set_preplay_outcomes_of_isar_step ctxt time preplay_data) |
55332
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|
229 |
times succs' meths_outcomess; |
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|
230 |
map (replace_successor l labels) lfs; |
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|
231 |
steps_before @ update_steps succs' steps_after)) |
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|
232 |
end) |
54712 | 233 |
end |
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diff
changeset
|
234 |
|
54712 | 235 |
fun compression_loop candidates steps = |
236 |
if not (compress_further ()) then |
|
237 |
steps |
|
238 |
else |
|
55298 | 239 |
(case pop_next_candidate candidates of |
54712 | 240 |
(NONE, _) => steps (* no more candidates for elimination *) |
57766 | 241 |
| (SOME (l, (num_xs, _)), candidates') => |
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|
242 |
(case find_index (curry (op =) (SOME l) o label_of_isar_step) steps of |
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|
243 |
~1 => steps |
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|
244 |
| i => |
57766 | 245 |
let |
246 |
val successors = get_successors l |
|
247 |
val num_successors = length successors |
|
248 |
in |
|
249 |
(* Careful with "obtain", so we don't "obtain" twice the same variable after a |
|
250 |
merge. *) |
|
251 |
if num_successors > (if num_xs > 0 then 1 else compress_degree) then |
|
57162 | 252 |
steps |
253 |
else |
|
254 |
steps |
|
255 |
|> not (null successors) ? try_eliminate i l successors |
|
256 |
|> compression_loop candidates' |
|
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|
257 |
end)) |
55331 | 258 |
|
57764 | 259 |
fun add_cand (Prove (_, xs, l, t, _, _, _, _)) = cons (l, (length xs, size_of_term t)) |
55331 | 260 |
| add_cand _ = I |
261 |
||
262 |
(* the very last step is not a candidate *) |
|
263 |
val candidates = fold add_cand (fst (split_last steps)) [] |
|
54712 | 264 |
in |
265 |
compression_loop candidates steps |
|
266 |
end |
|
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diff
changeset
|
267 |
|
55268 | 268 |
(* Proofs are compressed bottom-up, beginning with the innermost subproofs. On the innermost |
269 |
proof level, the proof steps have no subproofs. In the best case, these steps can be merged |
|
270 |
into just one step, resulting in a trivial subproof. Going one level up, trivial subproofs |
|
271 |
can be eliminated. In the best case, this once again leads to a proof whose proof steps do |
|
272 |
not have subproofs. Applying this approach recursively will result in a flat proof in the |
|
273 |
best cast. *) |
|
57760 | 274 |
fun compress_proof (proof as (Proof (xs, assms, steps))) = |
275 |
if compress_further () then Proof (xs, assms, compress_steps steps) else proof |
|
55263 | 276 |
and compress_steps steps = |
54712 | 277 |
(* bottom-up: compress innermost proofs first *) |
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|
278 |
steps |
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279 |
|> map (fn step => step |> compress_further () ? compress_sub_levels) |
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|
280 |
|> compress_further () ? compress_top_level |
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diff
changeset
|
281 |
and compress_sub_levels (Prove (qs, xs, l, t, subproofs, facts, meths, comment)) = |
52556
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|
282 |
(* compress subproofs *) |
55299 | 283 |
Prove (qs, xs, l, t, map compress_proof subproofs, facts, meths, comment) |
54712 | 284 |
(* eliminate trivial subproofs *) |
285 |
|> compress_further () ? elim_subproofs |
|
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changeset
|
286 |
| compress_sub_levels step = step |
54712 | 287 |
in |
55263 | 288 |
compress_proof proof |
54712 | 289 |
end |
50259 | 290 |
|
54504 | 291 |
end; |