--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_shrink.ML Wed Nov 28 12:22:17 2012 +0100
@@ -0,0 +1,226 @@
+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 = metis_steps_top_level proof
+ val n_target = Real.fromInt n / 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 (Vector.length proof_vect, (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 (qs1, label1, _, By_Metis (lfs1, gfs1)))
+ (Prove (qs2, label2 , t, By_Metis (lfs2, gfs2))) =
+ let
+ val qs = inter (op =) qs1 qs2 (* FIXME: Is this correct? *)
+ |> member (op =) (union (op =) qs1 qs2) Ultimately ? cons Ultimately
+ |> member (op =) qs2 Show ? cons Show
+ val ls = remove (op =) label1 lfs2 |> union (op =) lfs1
+ val ss = union (op =) gfs1 gfs2
+ in Prove (qs, 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' =
+ if Inttab.is_empty cand_tab
+ orelse n' <= n_target
+ orelse (top_level andalso Vector.length proof_vect<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'
+ | (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)
+ end
+ end
+ in
+ merge_steps metis_time proof_vect refed_by_vect cand_tab n
+ 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