--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_reconstruct.ML Tue Oct 16 20:31:08 2012 +0200
@@ -0,0 +1,414 @@
+(* Title: HOL/Tools/Sledgehammer/sledgehammer_reconstruct.ML
+ Author: Jasmin Blanchette, TU Muenchen
+ Author: Steffen Juilf Smolka, TU Muenchen
+
+*)
+
+signature SLEDGEHAMMER_PROOF_RECONSTRUCT =
+sig
+ type isar_params = ATP_Proof_Reconstruct.isar_params
+ type one_line_params = ATP_Proof_Reconstruct.one_line_params
+ val isar_proof_text :
+ Proof.context -> bool -> isar_params ->
+ one_line_params -> string
+ val proof_text :
+ Proof.context -> bool -> isar_params ->
+ int -> one_line_params -> string
+end;
+
+structure Sledgehammer_Reconstruct : SLEDGEHAMMER_PROOF_RECONSTRUCT =
+struct
+
+open ATP_Util
+open ATP_Proof
+open ATP_Problem_Generate
+open ATP_Proof_Reconstruct
+open String_Redirect
+
+(** Type annotations **)
+
+fun post_traverse_term_type' f _ (t as Const (_, T)) s = f t T s
+ | post_traverse_term_type' f _ (t as Free (_, T)) s = f t T s
+ | post_traverse_term_type' f _ (t as Var (_, T)) s = f t T s
+ | post_traverse_term_type' f env (t as Bound i) s = f t (nth env i) s
+ | post_traverse_term_type' f env (Abs (x, T1, b)) s =
+ let
+ val ((b', s'), T2) = post_traverse_term_type' f (T1 :: env) b s
+ in f (Abs (x, T1, b')) (T1 --> T2) s' end
+ | post_traverse_term_type' f env (u $ v) s =
+ let
+ val ((u', s'), Type (_, [_, T])) = post_traverse_term_type' f env u s
+ val ((v', s''), _) = post_traverse_term_type' f env v s'
+ in f (u' $ v') T s'' end
+
+fun post_traverse_term_type f s t =
+ post_traverse_term_type' (fn t => fn T => fn s => (f t T s, T)) [] t s |> fst
+fun post_fold_term_type f s t =
+ post_traverse_term_type (fn t => fn T => fn s => (t, f t T s)) s t |> snd
+
+(* Data structures, orders *)
+val cost_ord = prod_ord int_ord (prod_ord int_ord int_ord)
+
+structure Var_Set_Tab = Table(
+ type key = indexname list
+ val ord = list_ord Term_Ord.fast_indexname_ord)
+
+(* (1) Generalize Types *)
+fun generalize_types ctxt t =
+ t |> map_types (fn _ => dummyT)
+ |> Syntax.check_term
+ (Proof_Context.set_mode Proof_Context.mode_pattern ctxt)
+
+(* (2) Typing-spot Table *)
+local
+fun key_of_atype (TVar (idxn, _)) =
+ Ord_List.insert Term_Ord.fast_indexname_ord idxn
+ | key_of_atype _ = I
+fun key_of_type T = fold_atyps key_of_atype T []
+fun update_tab t T (tab, pos) =
+ (case key_of_type T of
+ [] => tab
+ | key =>
+ let val cost = (size_of_typ T, (size_of_term t, pos)) in
+ case Var_Set_Tab.lookup tab key of
+ NONE => Var_Set_Tab.update_new (key, cost) tab
+ | SOME old_cost =>
+ (case cost_ord (cost, old_cost) of
+ LESS => Var_Set_Tab.update (key, cost) tab
+ | _ => tab)
+ end,
+ pos + 1)
+in
+val typing_spot_table =
+ post_fold_term_type update_tab (Var_Set_Tab.empty, 0) #> fst
+end
+
+(* (3) Reverse-Greedy *)
+fun reverse_greedy typing_spot_tab =
+ let
+ fun update_count z =
+ fold (fn tvar => fn tab =>
+ let val c = Vartab.lookup tab tvar |> the_default 0 in
+ Vartab.update (tvar, c + z) tab
+ end)
+ fun superfluous tcount =
+ forall (fn tvar => the (Vartab.lookup tcount tvar) > 1)
+ fun drop_superfluous (tvars, (_, (_, spot))) (spots, tcount) =
+ if superfluous tcount tvars then (spots, update_count ~1 tvars tcount)
+ else (spot :: spots, tcount)
+ val (typing_spots, tvar_count_tab) =
+ Var_Set_Tab.fold
+ (fn kv as (k, _) => apfst (cons kv) #> apsnd (update_count 1 k))
+ typing_spot_tab ([], Vartab.empty)
+ |>> sort_distinct (rev_order o cost_ord o pairself snd)
+ in fold drop_superfluous typing_spots ([], tvar_count_tab) |> fst end
+
+(* (4) Introduce Annotations *)
+fun introduce_annotations thy spots t t' =
+ let
+ val get_types = post_fold_term_type (K cons) []
+ fun match_types tp =
+ fold (Sign.typ_match thy) (op ~~ (pairself get_types tp)) Vartab.empty
+ fun unica' b x [] = if b then [x] else []
+ | unica' b x (y :: ys) =
+ if x = y then unica' false x ys
+ else unica' true y ys |> b ? cons x
+ fun unica ord xs =
+ case sort ord xs of x :: ys => unica' true x ys | [] => []
+ val add_all_tfree_namesT = fold_atyps (fn TFree (x, _) => cons x | _ => I)
+ fun erase_unica_tfrees env =
+ let
+ val unica =
+ Vartab.fold (add_all_tfree_namesT o snd o snd) env []
+ |> unica fast_string_ord
+ val erase_unica = map_atyps
+ (fn T as TFree (s, _) =>
+ if Ord_List.member fast_string_ord unica s then dummyT else T
+ | T => T)
+ in Vartab.map (K (apsnd erase_unica)) env end
+ val env = match_types (t', t) |> erase_unica_tfrees
+ fun get_annot env (TFree _) = (false, (env, dummyT))
+ | get_annot env (T as TVar (v, S)) =
+ let val T' = Envir.subst_type env T in
+ if T' = dummyT then (false, (env, dummyT))
+ else (true, (Vartab.update (v, (S, dummyT)) env, T'))
+ end
+ | get_annot env (Type (S, Ts)) =
+ (case fold_rev (fn T => fn (b, (env, Ts)) =>
+ let
+ val (b', (env', T)) = get_annot env T
+ in (b orelse b', (env', T :: Ts)) end)
+ Ts (false, (env, [])) of
+ (true, (env', Ts)) => (true, (env', Type (S, Ts)))
+ | (false, (env', _)) => (false, (env', dummyT)))
+ fun post1 _ T (env, cp, ps as p :: ps', annots) =
+ if p <> cp then
+ (env, cp + 1, ps, annots)
+ else
+ let val (_, (env', T')) = get_annot env T in
+ (env', cp + 1, ps', (p, T') :: annots)
+ end
+ | post1 _ _ accum = accum
+ val (_, _, _, annots) = post_fold_term_type post1 (env, 0, spots, []) t'
+ fun post2 t _ (cp, annots as (p, T) :: annots') =
+ if p <> cp then (t, (cp + 1, annots))
+ else (Type.constraint T t, (cp + 1, annots'))
+ | post2 t _ x = (t, x)
+ in post_traverse_term_type post2 (0, rev annots) t |> fst end
+
+(* (5) Annotate *)
+fun annotate_types ctxt t =
+ let
+ val thy = Proof_Context.theory_of ctxt
+ val t' = generalize_types ctxt t
+ val typing_spots =
+ t' |> typing_spot_table
+ |> reverse_greedy
+ |> sort int_ord
+ in introduce_annotations thy typing_spots t t' end
+
+fun string_for_proof ctxt type_enc lam_trans i n =
+ let
+ fun fix_print_mode f x =
+ Print_Mode.setmp (filter (curry (op =) Symbol.xsymbolsN)
+ (print_mode_value ())) f x
+ fun do_indent ind = replicate_string (ind * indent_size) " "
+ fun do_free (s, T) =
+ maybe_quote s ^ " :: " ^
+ maybe_quote (fix_print_mode (Syntax.string_of_typ ctxt) T)
+ fun do_label l = if l = no_label then "" else string_for_label l ^ ": "
+ fun do_have qs =
+ (if member (op =) qs Moreover then "moreover " else "") ^
+ (if member (op =) qs Ultimately then "ultimately " else "") ^
+ (if member (op =) qs Then then
+ if member (op =) qs Show then "thus" else "hence"
+ else
+ if member (op =) qs Show then "show" else "have")
+ val do_term =
+ maybe_quote o fix_print_mode (Syntax.string_of_term ctxt)
+ o annotate_types ctxt
+ val reconstr = Metis (type_enc, lam_trans)
+ fun do_facts (ls, ss) =
+ reconstructor_command reconstr 1 1 [] 0
+ (ls |> sort_distinct (prod_ord string_ord int_ord),
+ ss |> sort_distinct string_ord)
+ and do_step ind (Fix xs) =
+ do_indent ind ^ "fix " ^ space_implode " and " (map do_free xs) ^ "\n"
+ | do_step ind (Let (t1, t2)) =
+ do_indent ind ^ "let " ^ do_term t1 ^ " = " ^ do_term t2 ^ "\n"
+ | do_step ind (Assume (l, t)) =
+ do_indent ind ^ "assume " ^ do_label l ^ do_term t ^ "\n"
+ | do_step ind (Prove (qs, l, t, By_Metis facts)) =
+ do_indent ind ^ do_have qs ^ " " ^
+ do_label l ^ do_term t ^ " " ^ do_facts facts ^ "\n"
+ | do_step ind (Prove (qs, l, t, Case_Split (proofs, facts))) =
+ implode (map (prefix (do_indent ind ^ "moreover\n") o do_block ind)
+ proofs) ^
+ do_indent ind ^ do_have qs ^ " " ^ do_label l ^ do_term t ^ " " ^
+ do_facts facts ^ "\n"
+ and do_steps prefix suffix ind steps =
+ let val s = implode (map (do_step ind) steps) in
+ replicate_string (ind * indent_size - size prefix) " " ^ prefix ^
+ String.extract (s, ind * indent_size,
+ SOME (size s - ind * indent_size - 1)) ^
+ suffix ^ "\n"
+ end
+ and do_block ind proof = do_steps "{ " " }" (ind + 1) proof
+ (* One-step proofs are pointless; better use the Metis one-liner
+ directly. *)
+ and do_proof [Prove (_, _, _, By_Metis _)] = ""
+ | do_proof proof =
+ (if i <> 1 then "prefer " ^ string_of_int i ^ "\n" else "") ^
+ do_indent 0 ^ "proof -\n" ^ do_steps "" "" 1 proof ^ do_indent 0 ^
+ (if n <> 1 then "next" else "qed")
+ in do_proof end
+
+fun min_local ctxt type_enc lam_trans proof =
+ let
+ (* Merging spots, greedy algorithm *)
+ fun cost (Prove (_, _ , t, _)) = Term.size_of_term t
+ | cost _ = ~1
+ fun can_merge (Prove (_, lbl, _, By_Metis _)) (Prove (_, _, _, By_Metis _)) =
+ (lbl = no_label)
+ | can_merge _ _ = false
+ val merge_spots =
+ fold_index
+ (fn (i, s2) => fn (s1, pile) => (s2, pile |> can_merge s1 s2 ? cons (i, cost s1)))
+ (tl proof) (hd proof, [])
+ |> snd |> sort (rev_order o int_ord o pairself snd) |> map fst
+
+ (* Enrich context with facts *)
+ val thy = Proof_Context.theory_of ctxt
+ fun sorry t = Skip_Proof.make_thm thy (HOLogic.mk_Trueprop t) (* FIXME: mk_Trueprop always ok? *)
+ fun enrich_ctxt' (Prove (_, lbl, t, _)) ctxt =
+ if lbl = no_label then ctxt
+ else Proof_Context.put_thms false (string_for_label lbl, SOME [sorry t]) ctxt
+ | enrich_ctxt' _ ctxt = ctxt
+ val rich_ctxt = fold enrich_ctxt' proof ctxt
+
+ (* Timing *)
+ fun take_time tac arg =
+ let
+ val t_start = Timing.start ()
+ in
+ (tac arg ; Timing.result t_start |> #cpu)
+ end
+ fun try_metis (Prove (qs, _, t, By_Metis fact_names)) s0 =
+ let
+ fun thmify (Prove (_, _, t, _)) = sorry t
+ val facts = fact_names |>> map string_for_label
+ |> op@
+ |> map (Proof_Context.get_thm rich_ctxt)
+ |> (if member op= qs Then
+ then cons (the s0 |> thmify)
+ else I)
+ val goal = Goal.prove ctxt [] [] (HOLogic.mk_Trueprop t) (* FIXME: mk_Trueprop always ok? *)
+ fun tac {context = ctxt, prems = _} =
+ Metis_Tactic.metis_tac [type_enc] lam_trans ctxt facts 1
+ in
+ take_time (fn () => goal tac)
+ end
+
+ (* Merging *)
+ fun merge (Prove (qs1, _, _, By_Metis (ls1, ss1)))
+ (Prove (qs2, lbl , t, By_Metis (ls2, ss2))) =
+ 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
+ in Prove (qs, lbl, t, By_Metis (ls1@ls2, ss1@ss2)) end
+ fun try_merge proof i =
+ let
+ val (front, s0, s1, s2, tail) =
+ case (proof, i) of
+ ((s1::s2::proof), 0) => ([], NONE, s1, s2, proof)
+ | _ => let val (front, s0::s1::s2::tail) = chop (i-1) proof
+ in (front, SOME s0, s1, s2, tail) end
+ val s12 = merge s1 s2
+ val t1 = try_metis s1 s0 ()
+ val t2 = try_metis s2 (SOME s1) ()
+ val tlimit = t1 + t2 |> Time.toReal |> curry Real.* 1.2 |> Time.fromReal
+ in
+ (TimeLimit.timeLimit tlimit (try_metis s12 s0) ();
+ SOME (front @ (case s0 of NONE => s12::tail | SOME s => s::s12::tail)))
+ handle _ => NONE
+ end
+ fun merge_steps proof [] = proof
+ | merge_steps proof (i::is) =
+ case try_merge proof i of
+ NONE => merge_steps proof is
+ | SOME proof' => merge_steps proof' (map (fn j => if j>i then j-1 else j) is)
+ in merge_steps proof merge_spots end
+
+fun isar_proof_text ctxt isar_proof_requested
+ (debug, isar_shrink_factor, pool, fact_names, sym_tab, atp_proof, goal)
+ (one_line_params as (_, _, _, _, subgoal, subgoal_count)) =
+ let
+ val isar_shrink_factor =
+ (if isar_proof_requested then 1 else 2) * isar_shrink_factor
+ val (params, hyp_ts, concl_t) = strip_subgoal ctxt goal subgoal
+ val frees = fold Term.add_frees (concl_t :: hyp_ts) []
+ val one_line_proof = one_line_proof_text 0 one_line_params
+ val type_enc =
+ if is_typed_helper_used_in_atp_proof atp_proof then full_typesN
+ else partial_typesN
+ val lam_trans = lam_trans_from_atp_proof atp_proof metis_default_lam_trans
+
+ fun isar_proof_of () =
+ let
+ val atp_proof =
+ atp_proof
+ |> clean_up_atp_proof_dependencies
+ |> nasty_atp_proof pool
+ |> map_term_names_in_atp_proof repair_name
+ |> decode_lines ctxt sym_tab
+ |> rpair [] |-> fold_rev (add_line fact_names)
+ |> repair_waldmeister_endgame
+ |> rpair [] |-> fold_rev add_nontrivial_line
+ |> rpair (0, [])
+ |-> fold_rev (add_desired_line isar_shrink_factor fact_names frees)
+ |> snd
+ val conj_name = conjecture_prefix ^ string_of_int (length hyp_ts)
+ val conjs =
+ atp_proof
+ |> map_filter (fn Inference_Step (name as (_, ss), _, _, []) =>
+ if member (op =) ss conj_name then SOME name else NONE
+ | _ => NONE)
+ fun dep_of_step (Definition_Step _) = NONE
+ | dep_of_step (Inference_Step (name, _, _, from)) = SOME (from, name)
+ val ref_graph = atp_proof |> map_filter dep_of_step |> make_ref_graph
+ val axioms = axioms_of_ref_graph ref_graph conjs
+ val tainted = tainted_atoms_of_ref_graph ref_graph conjs
+ val props =
+ Symtab.empty
+ |> fold (fn Definition_Step _ => I (* FIXME *)
+ | Inference_Step ((s, _), t, _, _) =>
+ Symtab.update_new (s,
+ t |> fold forall_of (map Var (Term.add_vars t []))
+ |> member (op = o apsnd fst) tainted s ? s_not))
+ atp_proof
+ fun prop_of_clause c =
+ fold (curry s_disj) (map_filter (Symtab.lookup props o fst) c)
+ @{term False}
+ fun label_of_clause [name] = raw_label_for_name name
+ | label_of_clause c = (space_implode "___" (map fst c), 0)
+ fun maybe_show outer c =
+ (outer andalso length c = 1 andalso subset (op =) (c, conjs))
+ ? cons Show
+ fun do_have outer qs (gamma, c) =
+ Prove (maybe_show outer c qs, label_of_clause c, prop_of_clause c,
+ By_Metis (fold (add_fact_from_dependency fact_names
+ o the_single) gamma ([], [])))
+ fun do_inf outer (Have z) = do_have outer [] z
+ | do_inf outer (Hence z) = do_have outer [Then] z
+ | do_inf outer (Cases cases) =
+ let val c = succedent_of_cases cases in
+ Prove (maybe_show outer c [Ultimately], label_of_clause c,
+ prop_of_clause c,
+ Case_Split (map (do_case false) cases, ([], [])))
+ end
+ and do_case outer (c, infs) =
+ Assume (label_of_clause c, prop_of_clause c) ::
+ map (do_inf outer) infs
+ val isar_proof =
+ (if null params then [] else [Fix params]) @
+ (ref_graph
+ |> redirect_graph axioms tainted
+ |> chain_direct_proof
+ |> map (do_inf true)
+ |> kill_duplicate_assumptions_in_proof
+ |> kill_useless_labels_in_proof
+ |> relabel_proof
+ |> min_local ctxt type_enc lam_trans)
+ |> string_for_proof ctxt type_enc lam_trans subgoal subgoal_count
+ in
+ case isar_proof of
+ "" =>
+ if isar_proof_requested then
+ "\nNo structured proof available (proof too short)."
+ else
+ ""
+ | _ =>
+ "\n\n" ^ (if isar_proof_requested then "Structured proof"
+ else "Perhaps this will work") ^
+ ":\n" ^ Markup.markup Isabelle_Markup.sendback isar_proof
+ end
+ val isar_proof =
+ if debug then
+ isar_proof_of ()
+ else case try isar_proof_of () of
+ SOME s => s
+ | NONE => if isar_proof_requested then
+ "\nWarning: The Isar proof construction failed."
+ else
+ ""
+ in one_line_proof ^ isar_proof end
+
+fun proof_text ctxt isar_proof isar_params num_chained
+ (one_line_params as (preplay, _, _, _, _, _)) =
+ (if case preplay of Failed_to_Play _ => true | _ => isar_proof then
+ isar_proof_text ctxt isar_proof isar_params
+ else
+ one_line_proof_text num_chained) one_line_params
+
+end;