1 (* Title: HOL/Tools/Sledgehammer/sledgehammer_isar.ML
2 Author: Jasmin Blanchette, TU Muenchen
3 Author: Steffen Juilf Smolka, TU Muenchen
5 Isar proof reconstruction from ATP proofs.
8 signature SLEDGEHAMMER_ISAR =
10 type atp_step_name = ATP_Proof.atp_step_name
11 type ('a, 'b) atp_step = ('a, 'b) ATP_Proof.atp_step
12 type 'a atp_proof = 'a ATP_Proof.atp_proof
13 type stature = ATP_Problem_Generate.stature
14 type one_line_params = Sledgehammer_Reconstructor.one_line_params
16 val trace : bool Config.T
19 bool * (string option * string option) * Time.time * real * bool
20 * (term, string) atp_step list * thm
22 val proof_text : Proof.context -> bool -> bool option -> (unit -> isar_params) -> int ->
23 one_line_params -> string
26 structure Sledgehammer_Isar : SLEDGEHAMMER_ISAR =
32 open ATP_Proof_Reconstruct
33 open Sledgehammer_Util
34 open Sledgehammer_Reconstructor
35 open Sledgehammer_Isar_Proof
36 open Sledgehammer_Isar_Preplay
37 open Sledgehammer_Isar_Compress
38 open Sledgehammer_Isar_Try0
39 open Sledgehammer_Isar_Minimize
41 structure String_Redirect = ATP_Proof_Redirect(
42 type key = atp_step_name
43 val ord = fn ((s, _ : string list), (s', _)) => fast_string_ord (s, s')
48 val trace = Attrib.setup_config_bool @{binding sledgehammer_isar_trace} (K false)
50 val e_skolemize_rules = ["skolemize", "shift_quantors"]
51 val spass_pirate_datatype_rule = "DT"
52 val vampire_skolemisation_rule = "skolemisation"
53 (* TODO: Use "Z3_Proof.string_of_rule" once it is moved to Isabelle *)
54 val z3_skolemize_rule = "sk"
55 val z3_th_lemma_rule = "th-lemma"
58 e_skolemize_rules @ [spass_skolemize_rule, vampire_skolemisation_rule, z3_skolemize_rule]
60 val is_skolemize_rule = member (op =) skolemize_rules
61 val is_arith_rule = String.isPrefix z3_th_lemma_rule
62 val is_datatype_rule = String.isPrefix spass_pirate_datatype_rule
64 fun raw_label_of_num num = (num, 0)
66 fun label_of_clause [(num, _)] = raw_label_of_num num
67 | label_of_clause c = (space_implode "___" (map (fst o raw_label_of_num o fst) c), 0)
69 fun add_fact_of_dependencies [(_, ss as _ :: _)] = apsnd (union (op =) ss)
70 | add_fact_of_dependencies names = apfst (insert (op =) (label_of_clause names))
72 (* No "real" literals means only type information (tfree_tcs, clsrel, or clsarity). *)
73 fun is_only_type_information t = t aconv @{prop True}
75 (* Discard facts; consolidate adjacent lines that prove the same formula, since they differ only in
77 fun add_line_pass1 (line as (name, role, t, rule, [])) lines =
78 (* No dependencies: lemma (for Z3), fact, conjecture, or (for Vampire) internal facts or
80 if role = Lemma orelse role = Conjecture orelse role = Negated_Conjecture orelse
81 role = Hypothesis orelse is_arith_rule rule then
83 else if role = Axiom then
84 (* Facts are not proof lines. *)
85 lines |> is_only_type_information t ? map (replace_dependencies_in_line (name, []))
87 map (replace_dependencies_in_line (name, [])) lines
88 | add_line_pass1 line lines = line :: lines
90 fun add_lines_pass2 res [] = rev res
91 | add_lines_pass2 res ((name, role, t, rule, deps) :: lines) =
93 val is_last_line = null lines
95 fun looks_interesting () =
96 not (is_only_type_information t) andalso null (Term.add_tvars t [])
97 andalso length deps >= 2 andalso not (can the_single lines)
99 fun is_skolemizing_line (_, _, _, rule', deps') =
100 is_skolemize_rule rule' andalso member (op =) deps' name
101 fun is_before_skolemize_rule () = exists is_skolemizing_line lines
103 if role <> Plain orelse is_skolemize_rule rule orelse is_arith_rule rule orelse
104 is_datatype_rule rule orelse is_last_line orelse looks_interesting () orelse
105 is_before_skolemize_rule () then
106 add_lines_pass2 ((name, role, t, rule, deps) :: res) lines
108 add_lines_pass2 res (map (replace_dependencies_in_line (name, deps)) lines)
112 bool * (string option * string option) * Time.time * real * bool * (term, string) atp_step list
116 [Arith_Method, Simp_Method, Auto_Method, Fastforce_Method, Blast_Method, Force_Method,
117 Algebra_Method, Metis_Method (NONE, NONE), Meson_Method]
118 val datatype_methods = [Simp_Method, Simp_Size_Method]
119 val metislike_methods0 =
120 [Metis_Method (NONE, NONE), Simp_Method, Auto_Method, Arith_Method, Blast_Method,
121 Fastforce_Method, Force_Method, Algebra_Method, Meson_Method]
122 val rewrite_methods =
123 [Auto_Method, Simp_Method, Fastforce_Method, Force_Method, Metis_Method (NONE, NONE),
125 val skolem_methods = [Metis_Method (NONE, NONE), Blast_Method, Meson_Method]
127 fun isar_proof_text ctxt debug isar_proofs isar_params
128 (one_line_params as (_, _, _, _, subgoal, subgoal_count)) =
130 fun isar_proof_of () =
132 val SOME (verbose, alt_metis_args, preplay_timeout, compress_isar, try0_isar, atp_proof,
133 goal) = try isar_params ()
135 val metislike_methods = insert (op =) (Metis_Method alt_metis_args) metislike_methods0
137 val (params, _, concl_t) = strip_subgoal goal subgoal ctxt
140 |> map (fn (s, T) => (Binding.name s, SOME T, NoSyn))
141 |> (fn fixes => ctxt |> Variable.set_body false |> Proof_Context.add_fixes fixes)
143 val do_preplay = preplay_timeout <> Time.zeroTime
144 val try0_isar = try0_isar andalso do_preplay
145 val compress_isar = if isar_proofs = NONE andalso do_preplay then 1000.0 else compress_isar
147 val is_fixed = Variable.is_declared ctxt orf can Name.dest_skolem
148 fun skolems_of t = Term.add_frees t [] |> filter_out (is_fixed o fst) |> rev
150 fun get_role keep_role ((num, _), role, t, rule, _) =
151 if keep_role role then SOME ((raw_label_of_num num, t), rule) else NONE
155 |> rpair [] |-> fold_rev add_line_pass1
156 |> add_lines_pass2 []
159 map_filter (fn (name, role, _, _, _) =>
160 if member (op =) [Conjecture, Negated_Conjecture] role then SOME name else NONE)
162 val assms = map_filter (Option.map fst o get_role (curry (op =) Hypothesis)) atp_proof
164 map_filter (get_role (curry (op =) Lemma)) atp_proof
165 |> map (fn ((l, t), rule) =>
168 if is_skolemize_rule rule then (skolems_of t, skolem_methods)
169 else if is_arith_rule rule then ([], arith_methods)
170 else ([], rewrite_methods)
172 Prove ([], skos, l, t, [], (([], []), meths))
175 val bot = atp_proof |> List.last |> #1
179 |> map (fn (name, _, _, _, from) => (from, name))
180 |> make_refute_graph bot
181 |> fold (Atom_Graph.default_node o rpair ()) conjs
183 val axioms = axioms_of_refute_graph refute_graph conjs
185 val tainted = tainted_atoms_of_refute_graph refute_graph conjs
186 val is_clause_tainted = exists (member (op =) tainted)
189 |> fold (fn (name as (s, _), role, t, rule, _) =>
190 Symtab.update_new (s, (rule, t
191 |> (if is_clause_tainted [name] then
192 HOLogic.dest_Trueprop
193 #> role <> Conjecture ? s_not
194 #> fold exists_of (map Var (Term.add_vars t []))
195 #> HOLogic.mk_Trueprop
200 val rule_of_clause_id = fst o the o Symtab.lookup steps o fst
202 fun prop_of_clause [(num, _)] = Symtab.lookup steps num |> the |> snd |> close_form
203 | prop_of_clause names =
205 val lits = map (HOLogic.dest_Trueprop o snd)
206 (map_filter (Symtab.lookup steps o fst) names)
208 (case List.partition (can HOLogic.dest_not) lits of
209 (negs as _ :: _, pos as _ :: _) =>
210 s_imp (Library.foldr1 s_conj (map HOLogic.dest_not negs), Library.foldr1 s_disj pos)
211 | _ => fold (curry s_disj) lits @{term False})
213 |> HOLogic.mk_Trueprop |> close_form
215 fun maybe_show outer c = (outer andalso eq_set (op =) (c, conjs)) ? cons Show
217 fun isar_steps outer predecessor accum [] =
219 |> (if tainted = [] then
220 cons (Prove (if outer then [Show] else [], [], no_label, concl_t, [],
221 ((the_list predecessor, []), metislike_methods)))
225 | isar_steps outer _ accum (Have (id, (gamma, c)) :: infs) =
227 val l = label_of_clause c
228 val t = prop_of_clause c
229 val rule = rule_of_clause_id id
230 val skolem = is_skolemize_rule rule
232 fun prove sub by = Prove (maybe_show outer c [], [], l, t, sub, by)
233 fun do_rest l step = isar_steps outer (SOME l) (step :: accum) infs
235 val deps = fold add_fact_of_dependencies gamma no_facts
237 if skolem then skolem_methods
238 else if is_arith_rule rule then arith_methods
239 else if is_datatype_rule rule then datatype_methods
240 else metislike_methods
241 val by = (deps, meths)
243 if is_clause_tainted c then
246 if skolem andalso is_clause_tainted g then
247 let val subproof = Proof (skolems_of (prop_of_clause g), [], rev accum) in
248 isar_steps outer (SOME l) [prove [subproof] (no_facts, meths)] infs
251 do_rest l (prove [] by)
252 | _ => do_rest l (prove [] by))
254 do_rest l (if skolem then Prove ([], skolems_of t, l, t, [], by) else prove [] by)
256 | isar_steps outer predecessor accum (Cases cases :: infs) =
258 fun isar_case (c, subinfs) =
259 isar_proof false [] [(label_of_clause c, prop_of_clause c)] [] subinfs
260 val c = succedent_of_cases cases
261 val l = label_of_clause c
262 val t = prop_of_clause c
264 Prove (maybe_show outer c [], [], l, t,
265 map isar_case (filter_out (null o snd) cases),
266 ((the_list predecessor, []), metislike_methods))
268 isar_steps outer (SOME l) (step :: accum) infs
270 and isar_proof outer fix assms lems infs =
271 Proof (fix, assms, lems @ isar_steps outer NONE [] infs)
273 val string_of_isar_proof = string_of_isar_proof ctxt subgoal subgoal_count
275 val trace = Config.get ctxt trace
277 val canonical_isar_proof =
279 |> trace ? tap (tracing o prefix "Refute graph: " o string_of_refute_graph)
280 |> redirect_graph axioms tainted bot
281 |> trace ? tap (tracing o prefix "Direct proof: " o string_of_direct_proof)
282 |> isar_proof true params assms lems
283 |> postprocess_isar_proof_remove_unreferenced_steps I
284 |> relabel_isar_proof_canonically
286 val preplay_ctxt = ctxt
287 |> enrich_context_with_local_facts canonical_isar_proof
288 |> silence_reconstructors debug
290 val preplay_data = Unsynchronized.ref Canonical_Label_Tab.empty
292 fun reset_preplay_outcomes (step as Prove (_, _, l, _, _, (_, meths))) =
293 set_preplay_outcomes_of_isar_step preplay_data l (map (fn meth => (meth,
294 Lazy.lazy (fn () => preplay_isar_step preplay_ctxt preplay_timeout meth step)))
296 | reset_preplay_outcomes _ = ()
298 val _ = fold_isar_steps (K o reset_preplay_outcomes)
299 (steps_of_isar_proof canonical_isar_proof) ()
301 fun str_of_preplay_outcome outcome =
302 if Lazy.is_finished outcome then string_of_play_outcome (Lazy.force outcome) else "?"
304 fun str_of_meth l meth =
305 string_of_proof_method meth ^ " " ^
306 str_of_preplay_outcome (preplay_outcome_of_isar_step (!preplay_data) l meth)
307 fun comment_of l = map (str_of_meth l) #> commas
309 fun trace_isar_proof label proof =
311 tracing (timestamp () ^ "\n" ^ label ^ ":\n\n" ^ string_of_isar_proof comment_of proof ^
316 val (play_outcome, isar_proof) =
318 |> tap (trace_isar_proof "Original")
319 |> compress_isar_proof preplay_ctxt compress_isar preplay_data
320 |> tap (trace_isar_proof "Compressed")
321 |> try0_isar ? try0_isar_proof preplay_ctxt preplay_timeout preplay_data
322 |> tap (trace_isar_proof "Tried0")
323 |> postprocess_isar_proof_remove_unreferenced_steps
324 (try0_isar ? minimize_isar_step_dependencies preplay_ctxt preplay_data)
325 |> tap (trace_isar_proof "Minimized")
326 |> `(preplay_outcome_of_isar_proof (!preplay_data))
328 ||> kill_useless_labels_in_isar_proof
329 ||> relabel_isar_proof_finally
331 (case string_of_isar_proof (K (K "")) isar_proof of
333 if isar_proofs = SOME true then "\nNo structured proof available (proof too simple)."
339 let val num_steps = add_isar_steps (steps_of_isar_proof isar_proof) 0 in
340 [string_of_int num_steps ^ " step" ^ plural_s num_steps]
344 (if do_preplay then [string_of_play_outcome play_outcome] else [])
346 "\n\nStructured proof" ^ (commas msg |> not (null msg) ? enclose " (" ")") ^ ":\n" ^
347 Active.sendback_markup [Markup.padding_command] isar_text
351 val one_line_proof = one_line_proof_text 0 one_line_params
356 (case try isar_proof_of () of
359 if isar_proofs = SOME true then "\nWarning: The Isar proof construction failed." else "")
360 in one_line_proof ^ isar_proof end
362 fun isar_proof_would_be_a_good_idea (reconstr, play) =
364 Played _ => reconstr = SMT
365 | Play_Timed_Out _ => true
366 | Play_Failed => true
367 | Not_Played => false)
369 fun proof_text ctxt debug isar_proofs isar_params num_chained
370 (one_line_params as (preplay, _, _, _, _, _)) =
371 (if isar_proofs = SOME true orelse
372 (isar_proofs = NONE andalso isar_proof_would_be_a_good_idea preplay) then
373 isar_proof_text ctxt debug isar_proofs isar_params
375 one_line_proof_text num_chained) one_line_params