(* Title: HOL/Tools/Sledgehammer/sledgehammer_isar_preplay.ML
Author: Steffen Juilf Smolka, TU Muenchen
Author: Jasmin Blanchette, TU Muenchen
Preplaying of Isar proofs.
*)
signature SLEDGEHAMMER_ISAR_PREPLAY =
sig
type play_outcome = Sledgehammer_Reconstructor.play_outcome
type proof_method = Sledgehammer_Isar_Proof.proof_method
type isar_step = Sledgehammer_Isar_Proof.isar_step
type isar_proof = Sledgehammer_Isar_Proof.isar_proof
type label = Sledgehammer_Isar_Proof.label
val trace : bool Config.T
type isar_preplay_data =
{set_preplay_outcomes: label -> (proof_method * play_outcome Lazy.lazy) list -> unit,
preplay_outcome: label -> proof_method -> play_outcome Lazy.lazy,
overall_preplay_outcome: isar_proof -> play_outcome}
val enrich_context_with_local_facts : isar_proof -> Proof.context -> Proof.context
val preplay_isar_step : Proof.context -> Time.time -> proof_method -> isar_step -> play_outcome
val preplay_data_of_isar_proof : Proof.context -> Time.time -> isar_proof -> isar_preplay_data
end;
structure Sledgehammer_Isar_Preplay : SLEDGEHAMMER_ISAR_PREPLAY =
struct
open ATP_Proof_Reconstruct
open Sledgehammer_Util
open Sledgehammer_Reconstructor
open Sledgehammer_Isar_Proof
val trace = Attrib.setup_config_bool @{binding sledgehammer_preplay_trace} (K false)
fun enrich_context_with_local_facts proof ctxt =
let
val thy = Proof_Context.theory_of ctxt
fun enrich_with_fact l t =
Proof_Context.put_thms false (string_of_label l, SOME [Skip_Proof.make_thm thy t])
val enrich_with_assms = fold (uncurry enrich_with_fact)
fun enrich_with_proof (Proof (_, assms, isar_steps)) =
enrich_with_assms assms #> fold enrich_with_step isar_steps
and enrich_with_step (Let _) = I
| enrich_with_step (Prove (_, _, l, t, subproofs, _)) =
enrich_with_fact l t #> fold enrich_with_proof subproofs
in
enrich_with_proof proof ctxt
end
fun preplay_trace ctxt assmsp concl result =
let
val ctxt = ctxt |> Config.put show_markup true
val assms = op @ assmsp
val time = Pretty.str ("[" ^ string_of_play_outcome result ^ "]")
val assms = Pretty.enum " and " "using " " shows " (map (Display.pretty_thm ctxt) assms)
val concl = Syntax.pretty_term ctxt concl
in
tracing (Pretty.string_of (Pretty.blk (2, Pretty.breaks [time, assms, concl])))
end
fun take_time timeout tac arg =
let val timing = Timing.start () in
(TimeLimit.timeLimit timeout tac arg; Played (#cpu (Timing.result timing)))
handle TimeLimit.TimeOut => Play_Timed_Out timeout
end
fun resolve_fact_names ctxt names =
(names
|>> map string_of_label
|> pairself (maps (thms_of_name ctxt)))
handle ERROR msg => error ("preplay error: " ^ msg)
fun thm_of_proof ctxt (Proof (fixed_frees, assms, steps)) =
let
val thy = Proof_Context.theory_of ctxt
val concl =
(case try List.last steps of
SOME (Prove (_, [], _, t, _, _)) => t
| _ => raise Fail "preplay error: malformed subproof")
val var_idx = maxidx_of_term concl + 1
fun var_of_free (x, T) = Var ((x, var_idx), T)
val subst = map (`var_of_free #> swap #> apfst Free) fixed_frees
in
Logic.list_implies (assms |> map snd, concl)
|> subst_free subst
|> Skip_Proof.make_thm thy
end
fun tac_of_method ctxt (local_facts, global_facts) meth =
Method.insert_tac local_facts THEN'
(case meth of
Meson_Method => Meson.meson_tac ctxt global_facts
| Metis_Method (type_enc_opt, lam_trans_opt) =>
Metis_Tactic.metis_tac [type_enc_opt |> the_default partial_type_enc]
(the_default default_metis_lam_trans lam_trans_opt) ctxt global_facts
| _ =>
Method.insert_tac global_facts THEN'
(case meth of
Simp_Method => Simplifier.asm_full_simp_tac ctxt
| Simp_Size_Method =>
Simplifier.asm_full_simp_tac (Simplifier.add_simp @{thm size_ne_size_imp_ne} ctxt)
| Auto_Method => K (Clasimp.auto_tac ctxt)
| Fastforce_Method => Clasimp.fast_force_tac ctxt
| Force_Method => Clasimp.force_tac ctxt
| Arith_Method => Arith_Data.arith_tac ctxt
| Blast_Method => blast_tac ctxt
| Algebra_Method => Groebner.algebra_tac [] [] ctxt
| _ => raise Fail "Sledgehammer_Isar_Preplay: tac_of_method"))
(* main function for preplaying Isar steps; may throw exceptions *)
fun raw_preplay_step ctxt timeout meth (Prove (_, xs, _, t, subproofs, (fact_names, _))) =
let
val goal =
(case xs of
[] => t
| _ =>
(* proof obligation: !!thesis. (!!x. A x ==> thesis) ==> thesis
(cf. "~~/src/Pure/Isar/obtain.ML") *)
let
(* FIXME: generate fresh name *)
val thesis = Free ("thesis_preplay", HOLogic.boolT)
val thesis_prop = HOLogic.mk_Trueprop thesis
val frees = map Free xs
(* !!x1..xn. t ==> thesis (xs = [x1, .., xn]) *)
val inner_prop = fold_rev Logic.all frees (Logic.mk_implies (t, thesis_prop))
in
(* !!thesis. (!!x1..xn. t ==> thesis) ==> thesis *)
Logic.all thesis (Logic.mk_implies (inner_prop, thesis_prop))
end)
val facts =
resolve_fact_names ctxt fact_names
|>> append (map (thm_of_proof ctxt) subproofs)
fun prove () =
Goal.prove ctxt [] [] goal (fn {context = ctxt, ...} =>
HEADGOAL (tac_of_method ctxt facts meth))
handle ERROR msg => error ("Preplay error: " ^ msg)
val play_outcome = take_time timeout prove ()
in
(if Config.get ctxt trace then preplay_trace ctxt facts goal play_outcome else ();
play_outcome)
end
fun preplay_isar_step ctxt timeout meth =
try (raw_preplay_step ctxt timeout meth)
#> the_default Play_Failed
type isar_preplay_data =
{set_preplay_outcomes: label -> (proof_method * play_outcome Lazy.lazy) list -> unit,
preplay_outcome: label -> proof_method -> play_outcome Lazy.lazy,
overall_preplay_outcome: isar_proof -> play_outcome}
fun time_of_play (Played time) = time
| time_of_play (Play_Timed_Out time) = time
fun merge_preplay_outcomes Play_Failed _ = Play_Failed
| merge_preplay_outcomes _ Play_Failed = Play_Failed
| merge_preplay_outcomes (Played time1) (Played time2) = Played (Time.+ (time1, time2))
| merge_preplay_outcomes play1 play2 =
Play_Timed_Out (Time.+ (pairself time_of_play (play1, play2)))
(* Given a (canonically labeled) proof, produces an imperative preplay interface with a shared table
mapping from labels to preplay results. The preplay results are caluclated lazily and cached to
avoid repeated calculation. *)
fun preplay_data_of_isar_proof ctxt preplay_timeout proof =
let
val preplay_tab = Unsynchronized.ref Canonical_Label_Tab.empty
fun set_preplay_outcomes l meths_outcomes =
preplay_tab := Canonical_Label_Tab.map_entry l (fold (AList.update (op =)) meths_outcomes)
(!preplay_tab)
fun preplay_outcome l meth =
(case Canonical_Label_Tab.lookup (!preplay_tab) l of
SOME meths_outcomes =>
(case AList.lookup (op =) meths_outcomes meth of
SOME outcome => outcome
| NONE => raise Fail "Sledgehammer_Isar_Preplay: missing method")
| NONE => raise Fail "Sledgehammer_Isar_Preplay: missing label")
fun result_of_step (Prove (_, _, l, _, _, (_, meth :: _))) =
Lazy.force (preplay_outcome l meth)
| result_of_step _ = Played Time.zeroTime
fun overall_preplay_outcome (Proof (_, _, steps)) =
fold_isar_steps (merge_preplay_outcomes o result_of_step) steps (Played Time.zeroTime)
fun reset_preplay_outcomes (step as Prove (_, _, l, _, _, (_, meths))) =
preplay_tab := Canonical_Label_Tab.update (l, map (fn meth =>
(meth, Lazy.lazy (fn () => preplay_isar_step ctxt preplay_timeout meth step))) meths)
(!preplay_tab)
| reset_preplay_outcomes _ = ()
val _ = fold_isar_steps (K o reset_preplay_outcomes) (steps_of_proof proof) ()
in
{set_preplay_outcomes = set_preplay_outcomes,
preplay_outcome = preplay_outcome,
overall_preplay_outcome = overall_preplay_outcome}
end
end;