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 fun is_True_prop t = t aconv @{prop True}
73 fun add_line_pass1 (line as (name, role, t, rule, [])) lines =
74 (* No dependencies: lemma (for Z3), fact, conjecture, or (for Vampire) internal facts or
76 if role = Conjecture orelse role = Negated_Conjecture then
78 else if is_True_prop t then
79 map (replace_dependencies_in_line (name, [])) lines
80 else if role = Lemma orelse role = Hypothesis orelse is_arith_rule rule then
82 else if role = Axiom then
83 lines (* axioms (facts) need no proof lines *)
85 map (replace_dependencies_in_line (name, [])) lines
86 | add_line_pass1 line lines = line :: lines
88 fun add_lines_pass2 res _ [] = rev res
89 | add_lines_pass2 res prev_t ((line as (name, role, t, rule, deps)) :: lines) =
91 val is_last_line = null lines
93 fun looks_interesting () =
94 not (is_True_prop t) andalso not (t aconv prev_t) andalso null (Term.add_tvars t []) andalso
95 length deps >= 2 andalso not (can the_single lines)
97 fun is_skolemizing_line (_, _, _, rule', deps') =
98 is_skolemize_rule rule' andalso member (op =) deps' name
99 fun is_before_skolemize_rule () = exists is_skolemizing_line lines
101 if role <> Plain orelse is_skolemize_rule rule orelse is_arith_rule rule orelse
102 is_datatype_rule rule orelse is_last_line orelse looks_interesting () orelse
103 is_before_skolemize_rule () then
104 add_lines_pass2 (line :: res) t lines
106 add_lines_pass2 res t (map (replace_dependencies_in_line (name, deps)) lines)
110 bool * (string option * string option) * Time.time * real * bool * bool
111 * (term, string) atp_step list * thm
113 val basic_systematic_methods = [Metis_Method (NONE, NONE), Meson_Method, Blast_Method, SATx_Method]
114 val simp_based_methods = [Auto_Method, Simp_Method, Fastforce_Method, Force_Method]
115 val basic_arith_methods = [Linarith_Method, Presburger_Method, Algebra_Method]
117 val arith_methods = basic_arith_methods @ simp_based_methods @ basic_systematic_methods
118 val datatype_methods = [Simp_Method, Simp_Size_Method]
119 val systematic_methods0 = basic_systematic_methods @ basic_arith_methods @ simp_based_methods @
120 [Metis_Method (SOME no_typesN, NONE)]
121 val rewrite_methods = simp_based_methods @ basic_systematic_methods @ basic_arith_methods
122 val skolem_methods = basic_systematic_methods
124 fun isar_proof_text ctxt debug isar_proofs smt_proofs isar_params
125 (one_line_params as (_, _, _, _, subgoal, subgoal_count)) =
127 val _ = if debug then Output.urgent_message "Constructing Isar proof..." else ()
129 fun isar_proof_of () =
131 val SOME (verbose, alt_metis_args, preplay_timeout, compress_isar, try0_isar, minimize,
132 atp_proof, goal) = try isar_params ()
134 val systematic_methods = insert (op =) (Metis_Method alt_metis_args) systematic_methods0
136 fun massage_methods (meths as meth :: _) =
137 if not try0_isar then [meth]
138 else if smt_proofs = SOME true then SMT2_Method :: meths
141 val (params, _, concl_t) = strip_subgoal goal subgoal ctxt
142 val fixes = map (fn (s, T) => (Binding.name s, SOME T, NoSyn)) params
143 val ctxt = ctxt |> Variable.set_body false |> Proof_Context.add_fixes fixes |> snd
145 val do_preplay = preplay_timeout <> Time.zeroTime
146 val compress_isar = if isar_proofs = NONE andalso do_preplay then 1000.0 else compress_isar
148 val is_fixed = Variable.is_declared ctxt orf Name.is_skolem
149 fun skolems_of t = Term.add_frees t [] |> filter_out (is_fixed o fst) |> rev
151 fun get_role keep_role ((num, _), role, t, rule, _) =
152 if keep_role role then SOME ((raw_label_of_num num, t), rule) else NONE
156 |> rpair [] |-> fold_rev add_line_pass1
157 |> add_lines_pass2 [] Term.dummy
160 map_filter (fn (name, role, _, _, _) =>
161 if member (op =) [Conjecture, Negated_Conjecture] role then SOME name else NONE)
163 val assms = map_filter (Option.map fst o get_role (curry (op =) Hypothesis)) atp_proof
165 map_filter (get_role (curry (op =) Lemma)) atp_proof
166 |> map (fn ((l, t), rule) =>
169 (if is_skolemize_rule rule then (skolems_of t, skolem_methods)
170 else if is_arith_rule rule then ([], arith_methods)
171 else ([], rewrite_methods))
174 Prove ([], skos, l, t, [], ([], []), meths, "")
177 val bot = atp_proof |> List.last |> #1
181 |> map (fn (name, _, _, _, from) => (from, name))
182 |> make_refute_graph bot
183 |> fold (Atom_Graph.default_node o rpair ()) conjs
185 val axioms = axioms_of_refute_graph refute_graph conjs
187 val tainted = tainted_atoms_of_refute_graph refute_graph conjs
188 val is_clause_tainted = exists (member (op =) tainted)
191 |> fold (fn (name as (s, _), role, t, rule, _) =>
192 Symtab.update_new (s, (rule, t
193 |> (if is_clause_tainted [name] then
194 HOLogic.dest_Trueprop
195 #> role <> Conjecture ? s_not
196 #> fold exists_of (map Var (Term.add_vars t []))
197 #> HOLogic.mk_Trueprop
202 val rule_of_clause_id = fst o the o Symtab.lookup steps o fst
204 fun prop_of_clause [(num, _)] = Symtab.lookup steps num |> the |> snd |> close_form
205 | prop_of_clause names =
207 val lits = map (HOLogic.dest_Trueprop o snd)
208 (map_filter (Symtab.lookup steps o fst) names)
210 (case List.partition (can HOLogic.dest_not) lits of
211 (negs as _ :: _, pos as _ :: _) =>
212 s_imp (Library.foldr1 s_conj (map HOLogic.dest_not negs), Library.foldr1 s_disj pos)
213 | _ => fold (curry s_disj) lits @{term False})
215 |> HOLogic.mk_Trueprop |> close_form
217 fun maybe_show outer c = (outer andalso eq_set (op =) (c, conjs)) ? cons Show
219 fun isar_steps outer predecessor accum [] =
221 |> (if tainted = [] then
222 cons (Prove (if outer then [Show] else [], [], no_label, concl_t, [],
223 (the_list predecessor, []), massage_methods systematic_methods, ""))
227 | isar_steps outer _ accum (Have (id, (gamma, c)) :: infs) =
229 val l = label_of_clause c
230 val t = prop_of_clause c
231 val rule = rule_of_clause_id id
232 val skolem = is_skolemize_rule rule
234 val deps = fold add_fact_of_dependencies gamma ([], [])
236 (if skolem then skolem_methods
237 else if is_arith_rule rule then arith_methods
238 else if is_datatype_rule rule then datatype_methods
239 else systematic_methods)
242 fun prove sub facts = Prove (maybe_show outer c [], [], l, t, sub, facts, meths, "")
243 fun steps_of_rest step = isar_steps outer (SOME l) (step :: accum) infs
245 if is_clause_tainted c then
248 if skolem andalso is_clause_tainted g then
249 let val subproof = Proof (skolems_of (prop_of_clause g), [], rev accum) in
250 isar_steps outer (SOME l) [prove [subproof] ([], [])] infs
253 steps_of_rest (prove [] deps)
254 | _ => steps_of_rest (prove [] deps))
256 steps_of_rest (if skolem then Prove ([], skolems_of t, l, t, [], deps, meths, "")
259 | isar_steps outer predecessor accum (Cases cases :: infs) =
261 fun isar_case (c, subinfs) =
262 isar_proof false [] [(label_of_clause c, prop_of_clause c)] [] subinfs
263 val c = succedent_of_cases cases
264 val l = label_of_clause c
265 val t = prop_of_clause c
267 Prove (maybe_show outer c [], [], l, t,
268 map isar_case (filter_out (null o snd) cases),
269 (the_list predecessor, []), massage_methods systematic_methods, "")
271 isar_steps outer (SOME l) (step :: accum) infs
273 and isar_proof outer fix assms lems infs =
274 Proof (fix, assms, lems @ isar_steps outer NONE [] infs)
276 val trace = Config.get ctxt trace
278 val canonical_isar_proof =
280 |> trace ? tap (tracing o prefix "Refute graph: " o string_of_refute_graph)
281 |> redirect_graph axioms tainted bot
282 |> trace ? tap (tracing o prefix "Direct proof: " o string_of_direct_proof)
283 |> isar_proof true params assms lems
284 |> postprocess_isar_proof_remove_unreferenced_steps I
285 |> relabel_isar_proof_canonically
287 val ctxt = ctxt |> enrich_context_with_local_facts canonical_isar_proof
289 val preplay_data = Unsynchronized.ref Canonical_Label_Tab.empty
291 val _ = fold_isar_steps (fn meth =>
292 K (set_preplay_outcomes_of_isar_step ctxt debug preplay_timeout preplay_data meth []))
293 (steps_of_isar_proof canonical_isar_proof) ()
295 fun str_of_preplay_outcome outcome =
296 if Lazy.is_finished outcome then string_of_play_outcome (Lazy.force outcome) else "?"
297 fun str_of_meth l meth =
298 string_of_proof_method [] meth ^ " " ^
299 str_of_preplay_outcome (preplay_outcome_of_isar_step_for_method (!preplay_data) l meth)
300 fun comment_of l = map (str_of_meth l) #> commas
302 fun trace_isar_proof label proof =
304 tracing (timestamp () ^ "\n" ^ label ^ ":\n\n" ^
305 string_of_isar_proof ctxt subgoal subgoal_count
306 (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 debug compress_isar preplay_timeout 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 debug preplay_data)
324 |> tap (trace_isar_proof "Minimized")
325 (* It's not clear whether this is worth the trouble (and if so, "isar_compress" has an
326 unnatural semantics): *)
329 ? (compress_isar_proof ctxt compress_isar preplay_timeout preplay_data
330 #> tap (trace_isar_proof "Compressed again"))
332 |> `(preplay_outcome_of_isar_proof (!preplay_data))
333 ||> (comment_isar_proof comment_of
335 #> kill_useless_labels_in_isar_proof
336 #> relabel_isar_proof_nicely)
338 (case string_of_isar_proof ctxt subgoal subgoal_count isar_proof of
340 if isar_proofs = SOME true then "\nNo structured proof available (proof too simple)."
346 let val num_steps = add_isar_steps (steps_of_isar_proof isar_proof) 0 in
347 [string_of_int num_steps ^ " step" ^ plural_s num_steps]
351 (if do_preplay then [string_of_play_outcome play_outcome] else [])
353 "\n\nStructured proof" ^ (commas msg |> not (null msg) ? enclose " (" ")") ^ ":\n" ^
354 Active.sendback_markup [Markup.padding_command] isar_text
358 val one_line_proof = one_line_proof_text 0 one_line_params
363 (case try isar_proof_of () of
366 if isar_proofs = SOME true then "\nWarning: Isar proof construction failed." else "")
367 in one_line_proof ^ isar_proof end
369 fun isar_proof_would_be_a_good_idea smt_proofs (meth, play) =
371 Played _ => meth = SMT2_Method andalso smt_proofs <> SOME true
372 | Play_Timed_Out time => Time.> (time, Time.zeroTime)
373 | Play_Failed => true)
375 fun proof_text ctxt debug isar_proofs smt_proofs isar_params num_chained
376 (one_line_params as (preplay, _, _, _, _, _)) =
377 (if isar_proofs = SOME true orelse
378 (isar_proofs = NONE andalso isar_proof_would_be_a_good_idea smt_proofs preplay) then
379 isar_proof_text ctxt debug isar_proofs smt_proofs isar_params
381 one_line_proof_text num_chained) one_line_params