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_Proof_Methods.one_line_params
16 val trace : bool Config.T
19 bool * (string option * string option) * Time.time * real * bool * bool
20 * (term, string) atp_step list * thm
22 val proof_text : Proof.context -> bool -> bool option -> bool option -> (unit -> isar_params) ->
23 int -> one_line_params -> string
26 structure Sledgehammer_Isar : SLEDGEHAMMER_ISAR =
32 open ATP_Proof_Reconstruct
33 open Sledgehammer_Util
34 open Sledgehammer_Proof_Methods
35 open Sledgehammer_Isar_Proof
36 open Sledgehammer_Isar_Preplay
37 open Sledgehammer_Isar_Compress
38 open Sledgehammer_Isar_Minimize
40 structure String_Redirect = ATP_Proof_Redirect(
41 type key = atp_step_name
42 val ord = fn ((s, _ : string list), (s', _)) => fast_string_ord (s, s')
47 val trace = Attrib.setup_config_bool @{binding sledgehammer_isar_trace} (K false)
49 val e_skolemize_rules = ["skolemize", "shift_quantors"]
50 val spass_pirate_datatype_rule = "DT"
51 val vampire_skolemisation_rule = "skolemisation"
52 (* TODO: Use "Z3_Proof.string_of_rule" once it is moved to Isabelle *)
53 val z3_skolemize_rule = "sk"
54 val z3_th_lemma_rule = "th-lemma"
57 e_skolemize_rules @ [spass_skolemize_rule, vampire_skolemisation_rule, z3_skolemize_rule]
59 val is_skolemize_rule = member (op =) skolemize_rules
60 val is_arith_rule = String.isPrefix z3_th_lemma_rule
61 val is_datatype_rule = String.isPrefix spass_pirate_datatype_rule
63 fun raw_label_of_num num = (num, 0)
65 fun label_of_clause [(num, _)] = raw_label_of_num num
66 | label_of_clause c = (space_implode "___" (map (fst o raw_label_of_num o fst) c), 0)
68 fun add_fact_of_dependencies [(_, ss as _ :: _)] = apsnd (union (op =) ss)
69 | add_fact_of_dependencies names = apfst (insert (op =) (label_of_clause names))
71 (* No "real" literals means only type information (tfree_tcs, clsrel, or clsarity). *)
72 fun is_only_type_information t = t aconv @{prop True}
74 (* Discard facts; consolidate adjacent lines that prove the same formula, since they differ only in
76 fun add_line_pass1 (line as (name, role, t, rule, [])) lines =
77 (* No dependencies: lemma (for Z3), fact, conjecture, or (for Vampire) internal facts or
79 if role = Lemma orelse role = Conjecture orelse role = Negated_Conjecture orelse
80 role = Hypothesis orelse is_arith_rule rule then
82 else if role = Axiom then
83 (* Facts are not proof lines. *)
84 lines |> is_only_type_information t ? map (replace_dependencies_in_line (name, []))
86 map (replace_dependencies_in_line (name, [])) lines
87 | add_line_pass1 line lines = line :: lines
89 fun add_lines_pass2 res [] = rev res
90 | add_lines_pass2 res ((name, role, t, rule, deps) :: lines) =
92 val is_last_line = null lines
94 fun looks_interesting () =
95 not (is_only_type_information t) andalso null (Term.add_tvars t [])
96 andalso length deps >= 2 andalso not (can the_single lines)
98 fun is_skolemizing_line (_, _, _, rule', deps') =
99 is_skolemize_rule rule' andalso member (op =) deps' name
100 fun is_before_skolemize_rule () = exists is_skolemizing_line lines
102 if role <> Plain orelse is_skolemize_rule rule orelse is_arith_rule rule orelse
103 is_datatype_rule rule orelse is_last_line orelse looks_interesting () orelse
104 is_before_skolemize_rule () then
105 add_lines_pass2 ((name, role, t, rule, deps) :: res) lines
107 add_lines_pass2 res (map (replace_dependencies_in_line (name, deps)) lines)
111 bool * (string option * string option) * Time.time * real * bool * bool
112 * (term, string) atp_step list * thm
114 val basic_systematic_methods = [Metis_Method (NONE, NONE), Meson_Method, Blast_Method]
115 val simp_based_methods = [Simp_Method, Auto_Method, Fastforce_Method, Force_Method]
116 val basic_arith_methods = [Linarith_Method, Presburger_Method, Algebra_Method]
118 val arith_methods = basic_arith_methods @ simp_based_methods @ basic_systematic_methods
119 val datatype_methods = [Simp_Method, Simp_Size_Method]
120 val systematic_methods0 = basic_systematic_methods @ basic_arith_methods @ simp_based_methods @
121 [Metis_Method (SOME no_typesN, NONE)]
122 val rewrite_methods = simp_based_methods @ basic_systematic_methods @ basic_arith_methods
123 val skolem_methods = basic_systematic_methods
125 fun isar_proof_text ctxt debug isar_proofs smt_proofs isar_params
126 (one_line_params as (_, _, _, _, subgoal, subgoal_count)) =
128 fun isar_proof_of () =
130 val SOME (verbose, alt_metis_args, preplay_timeout, compress_isar, try0_isar, minimize,
131 atp_proof, goal) = try isar_params ()
133 val systematic_methods = insert (op =) (Metis_Method alt_metis_args) systematic_methods0
135 fun massage_methods (meths as meth :: _) =
136 if not try0_isar then [meth]
137 else if smt_proofs = SOME true then SMT_Method :: meths
140 val (params, _, concl_t) = strip_subgoal goal subgoal ctxt
141 val fixes = map (fn (s, T) => (Binding.name s, SOME T, NoSyn)) params
142 val ctxt = ctxt |> Variable.set_body false |> Proof_Context.add_fixes fixes |> snd
144 val do_preplay = preplay_timeout <> Time.zeroTime
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))
173 Prove ([], skos, l, t, [], ([], []), meths, "")
176 val bot = atp_proof |> List.last |> #1
180 |> map (fn (name, _, _, _, from) => (from, name))
181 |> make_refute_graph bot
182 |> fold (Atom_Graph.default_node o rpair ()) conjs
184 val axioms = axioms_of_refute_graph refute_graph conjs
186 val tainted = tainted_atoms_of_refute_graph refute_graph conjs
187 val is_clause_tainted = exists (member (op =) tainted)
190 |> fold (fn (name as (s, _), role, t, rule, _) =>
191 Symtab.update_new (s, (rule, t
192 |> (if is_clause_tainted [name] then
193 HOLogic.dest_Trueprop
194 #> role <> Conjecture ? s_not
195 #> fold exists_of (map Var (Term.add_vars t []))
196 #> HOLogic.mk_Trueprop
201 val rule_of_clause_id = fst o the o Symtab.lookup steps o fst
203 fun prop_of_clause [(num, _)] = Symtab.lookup steps num |> the |> snd |> close_form
204 | prop_of_clause names =
206 val lits = map (HOLogic.dest_Trueprop o snd)
207 (map_filter (Symtab.lookup steps o fst) names)
209 (case List.partition (can HOLogic.dest_not) lits of
210 (negs as _ :: _, pos as _ :: _) =>
211 s_imp (Library.foldr1 s_conj (map HOLogic.dest_not negs), Library.foldr1 s_disj pos)
212 | _ => fold (curry s_disj) lits @{term False})
214 |> HOLogic.mk_Trueprop |> close_form
216 fun maybe_show outer c = (outer andalso eq_set (op =) (c, conjs)) ? cons Show
218 fun isar_steps outer predecessor accum [] =
220 |> (if tainted = [] then
221 cons (Prove (if outer then [Show] else [], [], no_label, concl_t, [],
222 (the_list predecessor, []), massage_methods systematic_methods, ""))
226 | isar_steps outer _ accum (Have (id, (gamma, c)) :: infs) =
228 val l = label_of_clause c
229 val t = prop_of_clause c
230 val rule = rule_of_clause_id id
231 val skolem = is_skolemize_rule rule
233 val deps = fold add_fact_of_dependencies gamma ([], [])
235 (if skolem then skolem_methods
236 else if is_arith_rule rule then arith_methods
237 else if is_datatype_rule rule then datatype_methods
238 else systematic_methods)
241 fun prove sub facts = Prove (maybe_show outer c [], [], l, t, sub, facts, meths, "")
242 fun steps_of_rest step = isar_steps outer (SOME l) (step :: accum) infs
244 if is_clause_tainted c then
247 if skolem andalso is_clause_tainted g then
248 let val subproof = Proof (skolems_of (prop_of_clause g), [], rev accum) in
249 isar_steps outer (SOME l) [prove [subproof] ([], [])] infs
252 steps_of_rest (prove [] deps)
253 | _ => steps_of_rest (prove [] deps))
255 steps_of_rest (if skolem then Prove ([], skolems_of t, l, t, [], deps, meths, "")
258 | isar_steps outer predecessor accum (Cases cases :: infs) =
260 fun isar_case (c, subinfs) =
261 isar_proof false [] [(label_of_clause c, prop_of_clause c)] [] subinfs
262 val c = succedent_of_cases cases
263 val l = label_of_clause c
264 val t = prop_of_clause c
266 Prove (maybe_show outer c [], [], l, t,
267 map isar_case (filter_out (null o snd) cases),
268 (the_list predecessor, []), massage_methods systematic_methods, "")
270 isar_steps outer (SOME l) (step :: accum) infs
272 and isar_proof outer fix assms lems infs =
273 Proof (fix, assms, lems @ isar_steps outer NONE [] infs)
275 val string_of_isar_proof = string_of_isar_proof ctxt subgoal subgoal_count
277 val trace = Config.get ctxt trace
279 val canonical_isar_proof =
281 |> trace ? tap (tracing o prefix "Refute graph: " o string_of_refute_graph)
282 |> redirect_graph axioms tainted bot
283 |> trace ? tap (tracing o prefix "Direct proof: " o string_of_direct_proof)
284 |> isar_proof true params assms lems
285 |> postprocess_isar_proof_remove_unreferenced_steps I
286 |> relabel_isar_proof_canonically
288 val ctxt = ctxt |> enrich_context_with_local_facts canonical_isar_proof
290 val preplay_data = Unsynchronized.ref Canonical_Label_Tab.empty
292 val _ = fold_isar_steps (fn meth =>
293 K (set_preplay_outcomes_of_isar_step ctxt preplay_timeout preplay_data meth []))
294 (steps_of_isar_proof canonical_isar_proof) ()
296 fun str_of_preplay_outcome outcome =
297 if Lazy.is_finished outcome then string_of_play_outcome (Lazy.force outcome) else "?"
298 fun str_of_meth l meth =
299 string_of_proof_method meth ^ " " ^
300 str_of_preplay_outcome (preplay_outcome_of_isar_step_for_method (!preplay_data) l meth)
301 fun comment_of l = map (str_of_meth l) #> commas
303 fun trace_isar_proof label proof =
305 tracing (timestamp () ^ "\n" ^ label ^ ":\n\n" ^
306 string_of_isar_proof (comment_isar_proof comment_of proof) ^ "\n")
310 fun comment_of l (meth :: _) =
312 Lazy.force (preplay_outcome_of_isar_step_for_method (!preplay_data) l meth)) of
313 (false, Played _) => ""
314 | (_, outcome) => string_of_play_outcome outcome)
316 val (play_outcome, isar_proof) =
318 |> tap (trace_isar_proof "Original")
319 |> compress_isar_proof ctxt compress_isar preplay_data
320 |> tap (trace_isar_proof "Compressed")
321 |> postprocess_isar_proof_remove_unreferenced_steps
322 (keep_fastest_method_of_isar_step (!preplay_data)
323 #> minimize ? minimize_isar_step_dependencies ctxt preplay_data)
324 |> tap (trace_isar_proof "Minimized")
326 ? (compress_isar_proof ctxt compress_isar preplay_data
327 #> tap (trace_isar_proof "Compressed again"))
328 |> `(preplay_outcome_of_isar_proof (!preplay_data))
329 ||> (comment_isar_proof comment_of
331 #> kill_useless_labels_in_isar_proof
332 #> relabel_isar_proof_nicely)
334 (case string_of_isar_proof isar_proof of
336 if isar_proofs = SOME true then "\nNo structured proof available (proof too simple)."
342 let val num_steps = add_isar_steps (steps_of_isar_proof isar_proof) 0 in
343 [string_of_int num_steps ^ " step" ^ plural_s num_steps]
347 (if do_preplay then [string_of_play_outcome play_outcome] else [])
349 "\n\nStructured proof" ^ (commas msg |> not (null msg) ? enclose " (" ")") ^ ":\n" ^
350 Active.sendback_markup [Markup.padding_command] isar_text
354 val one_line_proof = one_line_proof_text 0 one_line_params
359 (case try isar_proof_of () of
362 if isar_proofs = SOME true then "\nWarning: The Isar proof construction failed." else "")
363 in one_line_proof ^ isar_proof end
365 fun isar_proof_would_be_a_good_idea smt_proofs (meth, play) =
367 Played _ => meth = SMT_Method andalso smt_proofs <> SOME true
368 | Play_Timed_Out _ => true
369 | Play_Failed => true
370 | Not_Played => false)
372 fun proof_text ctxt debug isar_proofs smt_proofs isar_params num_chained
373 (one_line_params as (preplay, _, _, _, _, _)) =
374 (if isar_proofs = SOME true orelse
375 (isar_proofs = NONE andalso isar_proof_would_be_a_good_idea smt_proofs preplay) then
376 isar_proof_text ctxt debug isar_proofs smt_proofs isar_params
378 one_line_proof_text num_chained) one_line_params