1(* Title: HOL/Tools/Sledgehammer/sledgehammer_mash.ML 2 Author: Jasmin Blanchette, TU Muenchen 3 Author: Cezary Kaliszyk, University of Innsbruck 4 5Sledgehammer's machine-learning-based relevance filter (MaSh). 6*) 7 8signature SLEDGEHAMMER_MASH = 9sig 10 type stature = ATP_Problem_Generate.stature 11 type raw_fact = Sledgehammer_Fact.raw_fact 12 type fact = Sledgehammer_Fact.fact 13 type fact_override = Sledgehammer_Fact.fact_override 14 type params = Sledgehammer_Prover.params 15 type prover_result = Sledgehammer_Prover.prover_result 16 17 val trace : bool Config.T 18 val duplicates : bool Config.T 19 val MePoN : string 20 val MaShN : string 21 val MeShN : string 22 val mepoN : string 23 val mashN : string 24 val meshN : string 25 val unlearnN : string 26 val learn_isarN : string 27 val learn_proverN : string 28 val relearn_isarN : string 29 val relearn_proverN : string 30 val fact_filters : string list 31 val encode_str : string -> string 32 val encode_strs : string list -> string 33 val decode_str : string -> string 34 val decode_strs : string -> string list 35 36 datatype mash_algorithm = 37 MaSh_NB 38 | MaSh_kNN 39 | MaSh_NB_kNN 40 | MaSh_NB_Ext 41 | MaSh_kNN_Ext 42 43 val is_mash_enabled : unit -> bool 44 val the_mash_algorithm : unit -> mash_algorithm 45 val str_of_mash_algorithm : mash_algorithm -> string 46 47 val mesh_facts : ('a list -> 'a list) -> ('a * 'a -> bool) -> int -> 48 (real * (('a * real) list * 'a list)) list -> 'a list 49 val nickname_of_thm : thm -> string 50 val find_suggested_facts : Proof.context -> ('b * thm) list -> string list -> ('b * thm) list 51 val crude_thm_ord : Proof.context -> thm ord 52 val thm_less : thm * thm -> bool 53 val goal_of_thm : theory -> thm -> thm 54 val run_prover_for_mash : Proof.context -> params -> string -> string -> fact list -> thm -> 55 prover_result 56 val features_of : Proof.context -> string -> stature -> term list -> string list 57 val trim_dependencies : string list -> string list option 58 val isar_dependencies_of : string Symtab.table * string Symtab.table -> thm -> string list option 59 val prover_dependencies_of : Proof.context -> params -> string -> int -> raw_fact list -> 60 string Symtab.table * string Symtab.table -> thm -> bool * string list 61 val attach_parents_to_facts : ('a * thm) list -> ('a * thm) list -> 62 (string list * ('a * thm)) list 63 val num_extra_feature_facts : int 64 val extra_feature_factor : real 65 val weight_facts_smoothly : 'a list -> ('a * real) list 66 val weight_facts_steeply : 'a list -> ('a * real) list 67 val find_mash_suggestions : Proof.context -> int -> string list -> ('a * thm) list -> 68 ('a * thm) list -> ('a * thm) list -> ('a * thm) list * ('a * thm) list 69 val mash_suggested_facts : Proof.context -> string -> params -> int -> term list -> term -> 70 raw_fact list -> fact list * fact list 71 72 val mash_unlearn : Proof.context -> unit 73 val mash_learn_proof : Proof.context -> params -> term -> thm list -> unit 74 val mash_learn_facts : Proof.context -> params -> string -> int -> bool -> Time.time -> 75 raw_fact list -> string 76 val mash_learn : Proof.context -> params -> fact_override -> thm list -> bool -> unit 77 val mash_can_suggest_facts : Proof.context -> bool 78 val mash_can_suggest_facts_fast : Proof.context -> bool 79 80 val generous_max_suggestions : int -> int 81 val mepo_weight : real 82 val mash_weight : real 83 val relevant_facts : Proof.context -> params -> string -> int -> fact_override -> term list -> 84 term -> raw_fact list -> (string * fact list) list 85end; 86 87structure Sledgehammer_MaSh : SLEDGEHAMMER_MASH = 88struct 89 90open ATP_Util 91open ATP_Problem_Generate 92open Sledgehammer_Util 93open Sledgehammer_Fact 94open Sledgehammer_Prover 95open Sledgehammer_Prover_Minimize 96open Sledgehammer_MePo 97 98val anonymous_proof_prefix = "." 99 100val trace = Attrib.setup_config_bool \<^binding>\<open>sledgehammer_mash_trace\<close> (K false) 101val duplicates = Attrib.setup_config_bool \<^binding>\<open>sledgehammer_fact_duplicates\<close> (K false) 102 103fun trace_msg ctxt msg = if Config.get ctxt trace then tracing (msg ()) else () 104 105fun gen_eq_thm ctxt = if Config.get ctxt duplicates then Thm.eq_thm_strict else Thm.eq_thm_prop 106 107val MePoN = "MePo" 108val MaShN = "MaSh" 109val MeShN = "MeSh" 110 111val mepoN = "mepo" 112val mashN = "mash" 113val meshN = "mesh" 114 115val fact_filters = [meshN, mepoN, mashN] 116 117val unlearnN = "unlearn" 118val learn_isarN = "learn_isar" 119val learn_proverN = "learn_prover" 120val relearn_isarN = "relearn_isar" 121val relearn_proverN = "relearn_prover" 122 123fun map_array_at ary f i = Array.update (ary, i, f (Array.sub (ary, i))) 124 125type xtab = int * int Symtab.table 126 127val empty_xtab = (0, Symtab.empty) 128 129fun add_to_xtab key (next, tab) = (next + 1, Symtab.update_new (key, next) tab) 130fun maybe_add_to_xtab key = perhaps (try (add_to_xtab key)) 131 132fun state_file () = Path.expand (Path.explode "$ISABELLE_HOME_USER/mash_state") 133val remove_state_file = try File.rm o state_file 134 135datatype mash_algorithm = 136 MaSh_NB 137| MaSh_kNN 138| MaSh_NB_kNN 139| MaSh_NB_Ext 140| MaSh_kNN_Ext 141 142fun mash_algorithm () = 143 (case Options.default_string \<^system_option>\<open>MaSh\<close> of 144 "yes" => SOME MaSh_NB_kNN 145 | "sml" => SOME MaSh_NB_kNN 146 | "nb" => SOME MaSh_NB 147 | "knn" => SOME MaSh_kNN 148 | "nb_knn" => SOME MaSh_NB_kNN 149 | "nb_ext" => SOME MaSh_NB_Ext 150 | "knn_ext" => SOME MaSh_kNN_Ext 151 | "none" => NONE 152 | "" => NONE 153 | algorithm => (warning ("Unknown MaSh algorithm: " ^ quote algorithm); NONE)) 154 155val is_mash_enabled = is_some o mash_algorithm 156val the_mash_algorithm = the_default MaSh_NB_kNN o mash_algorithm 157 158fun str_of_mash_algorithm MaSh_NB = "nb" 159 | str_of_mash_algorithm MaSh_kNN = "knn" 160 | str_of_mash_algorithm MaSh_NB_kNN = "nb_knn" 161 | str_of_mash_algorithm MaSh_NB_Ext = "nb_ext" 162 | str_of_mash_algorithm MaSh_kNN_Ext = "knn_ext" 163 164fun scaled_avg [] = 0 165 | scaled_avg xs = Real.ceil (100000000.0 * fold (curry (op +)) xs 0.0) div length xs 166 167fun avg [] = 0.0 168 | avg xs = fold (curry (op +)) xs 0.0 / Real.fromInt (length xs) 169 170fun normalize_scores _ [] = [] 171 | normalize_scores max_facts xs = 172 map (apsnd (curry (op *) (1.0 / avg (map snd (take max_facts xs))))) xs 173 174fun mesh_facts maybe_distinct _ max_facts [(_, (sels, unks))] = 175 map fst (take max_facts sels) @ take (max_facts - length sels) unks 176 |> maybe_distinct 177 | mesh_facts _ fact_eq max_facts mess = 178 let 179 val mess = mess |> map (apsnd (apfst (normalize_scores max_facts))) 180 181 fun score_in fact (global_weight, (sels, unks)) = 182 let val score_at = try (nth sels) #> Option.map (fn (_, score) => global_weight * score) in 183 (case find_index (curry fact_eq fact o fst) sels of 184 ~1 => if member fact_eq unks fact then NONE else SOME 0.0 185 | rank => score_at rank) 186 end 187 188 fun weight_of fact = mess |> map_filter (score_in fact) |> scaled_avg 189 in 190 fold (union fact_eq o map fst o take max_facts o fst o snd) mess [] 191 |> map (`weight_of) |> sort (int_ord o apply2 fst o swap) 192 |> map snd |> take max_facts 193 end 194 195fun smooth_weight_of_fact rank = Math.pow (1.3, 15.5 - 0.2 * Real.fromInt rank) + 15.0 (* FUDGE *) 196fun steep_weight_of_fact rank = Math.pow (0.62, log2 (Real.fromInt (rank + 1))) (* FUDGE *) 197 198fun weight_facts_smoothly facts = facts ~~ map smooth_weight_of_fact (0 upto length facts - 1) 199fun weight_facts_steeply facts = facts ~~ map steep_weight_of_fact (0 upto length facts - 1) 200 201fun sort_array_suffix cmp needed a = 202 let 203 exception BOTTOM of int 204 205 val al = Array.length a 206 207 fun maxson l i = 208 let val i31 = i + i + i + 1 in 209 if i31 + 2 < l then 210 let val x = Unsynchronized.ref i31 in 211 if is_less (cmp (Array.sub (a, i31), Array.sub (a, i31 + 1))) then x := i31 + 1 else (); 212 if is_less (cmp (Array.sub (a, !x), Array.sub (a, i31 + 2))) then x := i31 + 2 else (); 213 !x 214 end 215 else 216 if i31 + 1 < l andalso is_less (cmp (Array.sub (a, i31), Array.sub (a, i31 + 1))) 217 then i31 + 1 else if i31 < l then i31 else raise BOTTOM i 218 end 219 220 fun trickledown l i e = 221 let val j = maxson l i in 222 if is_greater (cmp (Array.sub (a, j), e)) then 223 (Array.update (a, i, Array.sub (a, j)); trickledown l j e) 224 else 225 Array.update (a, i, e) 226 end 227 228 fun trickle l i e = trickledown l i e handle BOTTOM i => Array.update (a, i, e) 229 230 fun bubbledown l i = 231 let val j = maxson l i in 232 Array.update (a, i, Array.sub (a, j)); 233 bubbledown l j 234 end 235 236 fun bubble l i = bubbledown l i handle BOTTOM i => i 237 238 fun trickleup i e = 239 let val father = (i - 1) div 3 in 240 if is_less (cmp (Array.sub (a, father), e)) then 241 (Array.update (a, i, Array.sub (a, father)); 242 if father > 0 then trickleup father e else Array.update (a, 0, e)) 243 else 244 Array.update (a, i, e) 245 end 246 247 fun for i = if i < 0 then () else (trickle al i (Array.sub (a, i)); for (i - 1)) 248 249 fun for2 i = 250 if i < Integer.max 2 (al - needed) then 251 () 252 else 253 let val e = Array.sub (a, i) in 254 Array.update (a, i, Array.sub (a, 0)); 255 trickleup (bubble i 0) e; 256 for2 (i - 1) 257 end 258 in 259 for (((al + 1) div 3) - 1); 260 for2 (al - 1); 261 if al > 1 then 262 let val e = Array.sub (a, 1) in 263 Array.update (a, 1, Array.sub (a, 0)); 264 Array.update (a, 0, e) 265 end 266 else 267 () 268 end 269 270fun rev_sort_list_prefix cmp needed xs = 271 let val ary = Array.fromList xs in 272 sort_array_suffix cmp needed ary; 273 Array.foldl (op ::) [] ary 274 end 275 276 277(*** Convenience functions for synchronized access ***) 278 279fun synchronized_timed_value var time_limit = 280 Synchronized.timed_access var time_limit (fn value => SOME (value, value)) 281fun synchronized_timed_change_result var time_limit f = 282 Synchronized.timed_access var time_limit (SOME o f) 283fun synchronized_timed_change var time_limit f = 284 synchronized_timed_change_result var time_limit (fn x => ((), f x)) 285 286fun mash_time_limit _ = SOME (seconds 0.1) 287 288 289(*** Isabelle-agnostic machine learning ***) 290 291structure MaSh = 292struct 293 294fun select_fact_idxs (big_number : real) recommends = 295 List.app (fn at => 296 let val (j, ov) = Array.sub (recommends, at) in 297 Array.update (recommends, at, (j, big_number + ov)) 298 end) 299 300fun wider_array_of_vector init vec = 301 let val ary = Array.array init in 302 Array.copyVec {src = vec, dst = ary, di = 0}; 303 ary 304 end 305 306val nb_def_prior_weight = 1000 (* FUDGE *) 307 308fun learn_facts (tfreq0, sfreq0, dffreq0) num_facts0 num_facts num_feats depss featss = 309 let 310 val tfreq = wider_array_of_vector (num_facts, 0) tfreq0 311 val sfreq = wider_array_of_vector (num_facts, Inttab.empty) sfreq0 312 val dffreq = wider_array_of_vector (num_feats, 0) dffreq0 313 314 fun learn_one th feats deps = 315 let 316 fun add_th weight t = 317 let 318 val im = Array.sub (sfreq, t) 319 fun fold_fn s = Inttab.map_default (s, 0) (Integer.add weight) 320 in 321 map_array_at tfreq (Integer.add weight) t; 322 Array.update (sfreq, t, fold fold_fn feats im) 323 end 324 325 val add_sym = map_array_at dffreq (Integer.add 1) 326 in 327 add_th nb_def_prior_weight th; 328 List.app (add_th 1) deps; 329 List.app add_sym feats 330 end 331 332 fun for i = 333 if i = num_facts then () 334 else (learn_one i (Vector.sub (featss, i)) (Vector.sub (depss, i)); for (i + 1)) 335 in 336 for num_facts0; 337 (Array.vector tfreq, Array.vector sfreq, Array.vector dffreq) 338 end 339 340fun naive_bayes (tfreq, sfreq, dffreq) num_facts max_suggs fact_idxs goal_feats = 341 let 342 val tau = 0.2 (* FUDGE *) 343 val pos_weight = 5.0 (* FUDGE *) 344 val def_val = ~18.0 (* FUDGE *) 345 val init_val = 30.0 (* FUDGE *) 346 347 val ln_afreq = Math.ln (Real.fromInt num_facts) 348 val idf = Vector.map (fn i => ln_afreq - Math.ln (Real.fromInt i)) dffreq 349 350 fun tfidf feat = Vector.sub (idf, feat) 351 352 fun log_posterior i = 353 let 354 val tfreq = Real.fromInt (Vector.sub (tfreq, i)) 355 356 fun add_feat (f, fw0) (res, sfh) = 357 (case Inttab.lookup sfh f of 358 SOME sf => 359 (res + fw0 * tfidf f * Math.ln (pos_weight * Real.fromInt sf / tfreq), 360 Inttab.delete f sfh) 361 | NONE => (res + fw0 * tfidf f * def_val, sfh)) 362 363 val (res, sfh) = fold add_feat goal_feats (init_val * Math.ln tfreq, Vector.sub (sfreq, i)) 364 365 fun fold_sfh (f, sf) sow = 366 sow + tfidf f * Math.ln (1.0 - Real.fromInt (sf - 1) / tfreq) 367 368 val sum_of_weights = Inttab.fold fold_sfh sfh 0.0 369 in 370 res + tau * sum_of_weights 371 end 372 373 val posterior = Array.tabulate (num_facts, (fn j => (j, log_posterior j))) 374 375 fun ret at acc = 376 if at = num_facts then acc else ret (at + 1) (Array.sub (posterior, at) :: acc) 377 in 378 select_fact_idxs 100000.0 posterior fact_idxs; 379 sort_array_suffix (Real.compare o apply2 snd) max_suggs posterior; 380 ret (Integer.max 0 (num_facts - max_suggs)) [] 381 end 382 383val initial_k = 0 384 385fun k_nearest_neighbors dffreq num_facts num_feats depss featss max_suggs fact_idxs goal_feats = 386 let 387 exception EXIT of unit 388 389 val ln_afreq = Math.ln (Real.fromInt num_facts) 390 fun tfidf feat = ln_afreq - Math.ln (Real.fromInt (Vector.sub (dffreq, feat))) 391 392 val overlaps_sqr = Array.tabulate (num_facts, rpair 0.0) 393 394 val feat_facts = Array.array (num_feats, []) 395 val _ = Vector.foldl (fn (feats, fact) => 396 (List.app (map_array_at feat_facts (cons fact)) feats; fact + 1)) 0 featss 397 398 fun do_feat (s, sw0) = 399 let 400 val sw = sw0 * tfidf s 401 val w6 = Math.pow (sw, 6.0 (* FUDGE *)) 402 403 fun inc_overlap j = 404 let val (_, ov) = Array.sub (overlaps_sqr, j) in 405 Array.update (overlaps_sqr, j, (j, w6 + ov)) 406 end 407 in 408 List.app inc_overlap (Array.sub (feat_facts, s)) 409 end 410 411 val _ = List.app do_feat goal_feats 412 val _ = sort_array_suffix (Real.compare o apply2 snd) num_facts overlaps_sqr 413 val no_recommends = Unsynchronized.ref 0 414 val recommends = Array.tabulate (num_facts, rpair 0.0) 415 val age = Unsynchronized.ref 500000000.0 416 417 fun inc_recommend v j = 418 let val (_, ov) = Array.sub (recommends, j) in 419 if ov <= 0.0 then 420 (no_recommends := !no_recommends + 1; Array.update (recommends, j, (j, !age + ov))) 421 else 422 Array.update (recommends, j, (j, v + ov)) 423 end 424 425 val k = Unsynchronized.ref 0 426 fun do_k k = 427 if k >= num_facts then 428 raise EXIT () 429 else 430 let 431 val deps_factor = 2.7 (* FUDGE *) 432 val (j, o2) = Array.sub (overlaps_sqr, num_facts - k - 1) 433 val _ = inc_recommend o2 j 434 val ds = Vector.sub (depss, j) 435 val l = Real.fromInt (length ds) 436 in 437 List.app (inc_recommend (deps_factor * o2 / l)) ds 438 end 439 440 fun while1 () = 441 if !k = initial_k + 1 then () else (do_k (!k); k := !k + 1; while1 ()) 442 handle EXIT () => () 443 444 fun while2 () = 445 if !no_recommends >= max_suggs then () 446 else (do_k (!k); k := !k + 1; age := !age - 10000.0; while2 ()) 447 handle EXIT () => () 448 449 fun ret acc at = 450 if at = num_facts then acc else ret (Array.sub (recommends, at) :: acc) (at + 1) 451 in 452 while1 (); 453 while2 (); 454 select_fact_idxs 1000000000.0 recommends fact_idxs; 455 sort_array_suffix (Real.compare o apply2 snd) max_suggs recommends; 456 ret [] (Integer.max 0 (num_facts - max_suggs)) 457 end 458 459(* experimental *) 460fun external_tool tool max_suggs learns goal_feats = 461 let 462 val ser = string_of_int (serial ()) (* poor person's attempt at thread-safety *) 463 val ocs = TextIO.openOut ("adv_syms" ^ ser) 464 val ocd = TextIO.openOut ("adv_deps" ^ ser) 465 val ocq = TextIO.openOut ("adv_seq" ^ ser) 466 val occ = TextIO.openOut ("adv_conj" ^ ser) 467 468 fun os oc s = TextIO.output (oc, s) 469 470 fun ol _ _ _ [] = () 471 | ol _ f _ [e] = f e 472 | ol oc f sep (h :: t) = (f h; os oc sep; ol oc f sep t) 473 474 fun do_learn (name, feats, deps) = 475 (os ocs name; os ocs ":"; ol ocs (os ocs o quote) ", " feats; os ocs "\n"; 476 os ocd name; os ocd ":"; ol ocd (os ocd) " " deps; os ocd "\n"; os ocq name; os ocq "\n") 477 478 fun forkexec no = 479 let 480 val cmd = 481 "~/misc/" ^ tool ^ " adv_syms" ^ ser ^ " adv_deps" ^ ser ^ " " ^ string_of_int no ^ 482 " adv_seq" ^ ser ^ " < adv_conj" ^ ser 483 in 484 fst (Isabelle_System.bash_output cmd) 485 |> space_explode " " 486 |> filter_out (curry (op =) "") 487 end 488 in 489 (List.app do_learn learns; ol occ (os occ o quote) ", " (map fst goal_feats); 490 TextIO.closeOut ocs; TextIO.closeOut ocd; TextIO.closeOut ocq; TextIO.closeOut occ; 491 forkexec max_suggs) 492 end 493 494fun k_nearest_neighbors_ext max_suggs = 495 external_tool ("newknn/knn" ^ " " ^ string_of_int initial_k) max_suggs 496fun naive_bayes_ext max_suggs = external_tool "predict/nbayes" max_suggs 497 498fun query_external ctxt algorithm max_suggs learns goal_feats = 499 (trace_msg ctxt (fn () => "MaSh query external " ^ commas (map fst goal_feats)); 500 (case algorithm of 501 MaSh_NB_Ext => naive_bayes_ext max_suggs learns goal_feats 502 | MaSh_kNN_Ext => k_nearest_neighbors_ext max_suggs learns goal_feats)) 503 504fun query_internal ctxt algorithm num_facts num_feats (fact_names, featss, depss) 505 (freqs as (_, _, dffreq)) fact_idxs max_suggs goal_feats int_goal_feats = 506 let 507 fun nb () = 508 naive_bayes freqs num_facts max_suggs fact_idxs int_goal_feats 509 |> map fst 510 fun knn () = 511 k_nearest_neighbors dffreq num_facts num_feats depss featss max_suggs fact_idxs int_goal_feats 512 |> map fst 513 in 514 (trace_msg ctxt (fn () => "MaSh query internal " ^ commas (map fst goal_feats) ^ " from {" ^ 515 elide_string 1000 (space_implode " " (Vector.foldr (op ::) [] fact_names)) ^ "}"); 516 (case algorithm of 517 MaSh_NB => nb () 518 | MaSh_kNN => knn () 519 | MaSh_NB_kNN => 520 mesh_facts I (op =) max_suggs 521 [(0.5 (* FUDGE *), (weight_facts_steeply (nb ()), [])), 522 (0.5 (* FUDGE *), (weight_facts_steeply (knn ()), []))]) 523 |> map (curry Vector.sub fact_names)) 524 end 525 526end; 527 528 529(*** Persistent, stringly-typed state ***) 530 531fun meta_char c = 532 if Char.isAlphaNum c orelse c = #"_" orelse c = #"." orelse c = #"(" orelse c = #")" orelse 533 c = #"," orelse c = #"'" then 534 String.str c 535 else 536 (* fixed width, in case more digits follow *) 537 "%" ^ stringN_of_int 3 (Char.ord c) 538 539fun unmeta_chars accum [] = String.implode (rev accum) 540 | unmeta_chars accum (#"%" :: d1 :: d2 :: d3 :: cs) = 541 (case Int.fromString (String.implode [d1, d2, d3]) of 542 SOME n => unmeta_chars (Char.chr n :: accum) cs 543 | NONE => "" (* error *)) 544 | unmeta_chars _ (#"%" :: _) = "" (* error *) 545 | unmeta_chars accum (c :: cs) = unmeta_chars (c :: accum) cs 546 547val encode_str = String.translate meta_char 548val encode_strs = map encode_str #> space_implode " " 549 550fun decode_str s = 551 if String.isSubstring "%" s then unmeta_chars [] (String.explode s) else s; 552 553fun decode_strs s = 554 space_explode " " s |> String.isSubstring "%" s ? map decode_str; 555 556datatype proof_kind = Isar_Proof | Automatic_Proof | Isar_Proof_wegen_Prover_Flop 557 558fun str_of_proof_kind Isar_Proof = "i" 559 | str_of_proof_kind Automatic_Proof = "a" 560 | str_of_proof_kind Isar_Proof_wegen_Prover_Flop = "x" 561 562fun proof_kind_of_str "a" = Automatic_Proof 563 | proof_kind_of_str "x" = Isar_Proof_wegen_Prover_Flop 564 | proof_kind_of_str _ (* "i" *) = Isar_Proof 565 566fun add_edge_to name parent = 567 Graph.default_node (parent, (Isar_Proof, [], [])) 568 #> Graph.add_edge (parent, name) 569 570fun add_node kind name parents feats deps (accum as (access_G, (fact_xtab, feat_xtab), learns)) = 571 let val fact_xtab' = add_to_xtab name fact_xtab in 572 ((Graph.new_node (name, (kind, feats, deps)) access_G 573 handle Graph.DUP _ => Graph.map_node name (K (kind, feats, deps)) access_G) 574 |> fold (add_edge_to name) parents, 575 (fact_xtab', fold maybe_add_to_xtab feats feat_xtab), 576 (name, feats, deps) :: learns) 577 end 578 handle Symtab.DUP _ => accum (* robustness (in case the state file violates the invariant) *) 579 580fun try_graph ctxt when def f = 581 f () 582 handle 583 Graph.CYCLES (cycle :: _) => 584 (trace_msg ctxt (fn () => "Cycle involving " ^ commas cycle ^ " when " ^ when); def) 585 | Graph.DUP name => 586 (trace_msg ctxt (fn () => "Duplicate fact " ^ quote name ^ " when " ^ when); def) 587 | Graph.UNDEF name => 588 (trace_msg ctxt (fn () => "Unknown fact " ^ quote name ^ " when " ^ when); def) 589 | exn => 590 if Exn.is_interrupt exn then 591 Exn.reraise exn 592 else 593 (trace_msg ctxt (fn () => "Internal error when " ^ when ^ ":\n" ^ Runtime.exn_message exn); 594 def) 595 596fun graph_info G = 597 string_of_int (length (Graph.keys G)) ^ " node(s), " ^ 598 string_of_int (fold (Integer.add o length o snd) (Graph.dest G) 0) ^ " edge(s), " ^ 599 string_of_int (length (Graph.maximals G)) ^ " maximal" 600 601type ffds = string vector * int list vector * int list vector 602type freqs = int vector * int Inttab.table vector * int vector 603 604type mash_state = 605 {access_G : (proof_kind * string list * string list) Graph.T, 606 xtabs : xtab * xtab, 607 ffds : ffds, 608 freqs : freqs, 609 dirty_facts : string list option} 610 611val empty_xtabs = (empty_xtab, empty_xtab) 612val empty_ffds = (Vector.fromList [], Vector.fromList [], Vector.fromList []) : ffds 613val empty_freqs = (Vector.fromList [], Vector.fromList [], Vector.fromList []) : freqs 614 615val empty_state = 616 {access_G = Graph.empty, 617 xtabs = empty_xtabs, 618 ffds = empty_ffds, 619 freqs = empty_freqs, 620 dirty_facts = SOME []} : mash_state 621 622fun recompute_ffds_freqs_from_learns (learns : (string * string list * string list) list) 623 ((num_facts, fact_tab), (num_feats, feat_tab)) num_facts0 (fact_names0, featss0, depss0) freqs0 = 624 let 625 val fact_names = Vector.concat [fact_names0, Vector.fromList (map #1 learns)] 626 val featss = Vector.concat [featss0, 627 Vector.fromList (map (map_filter (Symtab.lookup feat_tab) o #2) learns)] 628 val depss = Vector.concat [depss0, 629 Vector.fromList (map (map_filter (Symtab.lookup fact_tab) o #3) learns)] 630 in 631 ((fact_names, featss, depss), 632 MaSh.learn_facts freqs0 num_facts0 num_facts num_feats depss featss) 633 end 634 635fun reorder_learns (num_facts, fact_tab) learns = 636 let val ary = Array.array (num_facts, ("", [], [])) in 637 List.app (fn learn as (fact, _, _) => 638 Array.update (ary, the (Symtab.lookup fact_tab fact), learn)) 639 learns; 640 Array.foldr (op ::) [] ary 641 end 642 643fun recompute_ffds_freqs_from_access_G access_G (xtabs as (fact_xtab, _)) = 644 let 645 val learns = 646 Graph.schedule (fn _ => fn (fact, (_, feats, deps)) => (fact, feats, deps)) access_G 647 |> reorder_learns fact_xtab 648 in 649 recompute_ffds_freqs_from_learns learns xtabs 0 empty_ffds empty_freqs 650 end 651 652local 653 654val version = "*** MaSh version 20190121 ***" 655 656exception FILE_VERSION_TOO_NEW of unit 657 658fun extract_node line = 659 (case space_explode ":" line of 660 [head, tail] => 661 (case (space_explode " " head, map (unprefix " ") (space_explode ";" tail)) of 662 ([kind, name], [parents, feats, deps]) => 663 SOME (proof_kind_of_str kind, decode_str name, decode_strs parents, decode_strs feats, 664 decode_strs deps) 665 | _ => NONE) 666 | _ => NONE) 667 668fun would_load_state (memory_time, _) = 669 let val path = state_file () in 670 (case try OS.FileSys.modTime (File.platform_path path) of 671 NONE => false 672 | SOME disk_time => memory_time < disk_time) 673 end; 674 675fun load_state ctxt (time_state as (memory_time, _)) = 676 let val path = state_file () in 677 (case try OS.FileSys.modTime (File.platform_path path) of 678 NONE => time_state 679 | SOME disk_time => 680 if memory_time >= disk_time then 681 time_state 682 else 683 (disk_time, 684 (case try File.read_lines path of 685 SOME (version' :: node_lines) => 686 let 687 fun extract_line_and_add_node line = 688 (case extract_node line of 689 NONE => I (* should not happen *) 690 | SOME (kind, name, parents, feats, deps) => add_node kind name parents feats deps) 691 692 val empty_G_etc = (Graph.empty, empty_xtabs, []) 693 694 val (access_G, xtabs, rev_learns) = 695 (case string_ord (version', version) of 696 EQUAL => 697 try_graph ctxt "loading state" empty_G_etc 698 (fn () => fold extract_line_and_add_node node_lines empty_G_etc) 699 | LESS => (remove_state_file (); empty_G_etc) (* cannot parse old file *) 700 | GREATER => raise FILE_VERSION_TOO_NEW ()) 701 702 val (ffds, freqs) = 703 recompute_ffds_freqs_from_learns (rev rev_learns) xtabs 0 empty_ffds empty_freqs 704 in 705 trace_msg ctxt (fn () => "Loaded fact graph (" ^ graph_info access_G ^ ")"); 706 {access_G = access_G, xtabs = xtabs, ffds = ffds, freqs = freqs, dirty_facts = SOME []} 707 end 708 | _ => empty_state))) 709 end 710 711fun str_of_entry (kind, name, parents, feats, deps) = 712 str_of_proof_kind kind ^ " " ^ encode_str name ^ ": " ^ encode_strs parents ^ "; " ^ 713 encode_strs feats ^ "; " ^ encode_strs deps ^ "\n" 714 715fun save_state _ (time_state as (_, {dirty_facts = SOME [], ...})) = time_state 716 | save_state ctxt (memory_time, {access_G, xtabs, ffds, freqs, dirty_facts}) = 717 let 718 fun append_entry (name, ((kind, feats, deps), (parents, _))) = 719 cons (kind, name, Graph.Keys.dest parents, feats, deps) 720 721 val path = state_file () 722 val dirty_facts' = 723 (case try OS.FileSys.modTime (File.platform_path path) of 724 NONE => NONE 725 | SOME disk_time => if disk_time <= memory_time then dirty_facts else NONE) 726 val (banner, entries) = 727 (case dirty_facts' of 728 SOME names => (NONE, fold (append_entry o Graph.get_entry access_G) names []) 729 | NONE => (SOME (version ^ "\n"), Graph.fold append_entry access_G [])) 730 in 731 (case banner of SOME s => File.write path s | NONE => (); 732 entries |> chunk_list 500 |> List.app (File.append path o implode o map str_of_entry)) 733 handle IO.Io _ => (); 734 trace_msg ctxt (fn () => 735 "Saved fact graph (" ^ graph_info access_G ^ 736 (case dirty_facts of 737 SOME dirty_facts => "; " ^ string_of_int (length dirty_facts) ^ " dirty fact(s)" 738 | _ => "") ^ ")"); 739 (Time.now (), 740 {access_G = access_G, xtabs = xtabs, ffds = ffds, freqs = freqs, dirty_facts = SOME []}) 741 end 742 743val global_state = Synchronized.var "Sledgehammer_MaSh.global_state" (Time.zeroTime, empty_state) 744 745in 746 747fun map_state ctxt f = 748 (trace_msg ctxt (fn () => "Changing MaSh state"); 749 synchronized_timed_change global_state mash_time_limit 750 (load_state ctxt ##> f #> save_state ctxt)) 751 |> ignore 752 handle FILE_VERSION_TOO_NEW () => () 753 754fun peek_state ctxt = 755 (trace_msg ctxt (fn () => "Peeking at MaSh state"); 756 (case synchronized_timed_value global_state mash_time_limit of 757 NONE => NONE 758 | SOME state => if would_load_state state then NONE else SOME state)) 759 760fun get_state ctxt = 761 (trace_msg ctxt (fn () => "Retrieving MaSh state"); 762 synchronized_timed_change_result global_state mash_time_limit 763 (perhaps (try (load_state ctxt)) #> `snd)) 764 765fun clear_state ctxt = 766 (trace_msg ctxt (fn () => "Clearing MaSh state"); 767 Synchronized.change global_state (fn _ => (remove_state_file (); (Time.zeroTime, empty_state)))) 768 769end 770 771 772(*** Isabelle helpers ***) 773 774fun crude_printed_term size t = 775 let 776 fun term _ (res, 0) = (res, 0) 777 | term (t $ u) (res, size) = 778 let 779 val (res, size) = term t (res ^ "(", size) 780 val (res, size) = term u (res ^ " ", size) 781 in 782 (res ^ ")", size) 783 end 784 | term (Abs (s, _, t)) (res, size) = term t (res ^ "%" ^ s ^ ".", size - 1) 785 | term (Bound n) (res, size) = (res ^ "#" ^ string_of_int n, size - 1) 786 | term (Const (s, _)) (res, size) = (res ^ Long_Name.base_name s, size - 1) 787 | term (Free (s, _)) (res, size) = (res ^ s, size - 1) 788 | term (Var ((s, _), _)) (res, size) = (res ^ s, size - 1) 789 in 790 fst (term t ("", size)) 791 end 792 793fun nickname_of_thm th = 794 if Thm.has_name_hint th then 795 let val hint = Thm.get_name_hint th in 796 (* There must be a better way to detect local facts. *) 797 (case Long_Name.dest_local hint of 798 SOME suf => 799 Long_Name.implode [Thm.theory_name th, suf, crude_printed_term 25 (Thm.prop_of th)] 800 | NONE => hint) 801 end 802 else 803 crude_printed_term 50 (Thm.prop_of th) 804 805fun find_suggested_facts ctxt facts = 806 let 807 fun add (fact as (_, th)) = Symtab.default (nickname_of_thm th, fact) 808 val tab = fold add facts Symtab.empty 809 fun lookup nick = 810 Symtab.lookup tab nick 811 |> tap (fn NONE => trace_msg ctxt (fn () => "Cannot find " ^ quote nick) | _ => ()) 812 in map_filter lookup end 813 814fun free_feature_of s = "f" ^ s 815fun thy_feature_of s = "y" ^ s 816fun type_feature_of s = "t" ^ s 817fun class_feature_of s = "s" ^ s 818val local_feature = "local" 819 820fun crude_thm_ord ctxt = 821 let 822 val ancestor_lengths = 823 fold (fn thy => Symtab.update (Context.theory_name thy, length (Context.ancestors_of thy))) 824 (Theory.nodes_of (Proof_Context.theory_of ctxt)) Symtab.empty 825 val ancestor_length = Symtab.lookup ancestor_lengths o Context.theory_id_name 826 827 fun crude_theory_ord p = 828 if Context.eq_thy_id p then EQUAL 829 else if Context.proper_subthy_id p then LESS 830 else if Context.proper_subthy_id (swap p) then GREATER 831 else 832 (case apply2 ancestor_length p of 833 (SOME m, SOME n) => 834 (case int_ord (m, n) of 835 EQUAL => string_ord (apply2 Context.theory_id_name p) 836 | ord => ord) 837 | _ => string_ord (apply2 Context.theory_id_name p)) 838 in 839 fn p => 840 (case crude_theory_ord (apply2 Thm.theory_id p) of 841 EQUAL => 842 (* The hack below is necessary because of odd dependencies that are not reflected in the theory 843 comparison. *) 844 let val q = apply2 nickname_of_thm p in 845 (* Hack to put "xxx_def" before "xxxI" and "xxxE" *) 846 (case bool_ord (apply2 (String.isSuffix "_def") (swap q)) of 847 EQUAL => string_ord q 848 | ord => ord) 849 end 850 | ord => ord) 851 end; 852 853val thm_less_eq = Context.subthy_id o apply2 Thm.theory_id 854fun thm_less p = thm_less_eq p andalso not (thm_less_eq (swap p)) 855 856val freezeT = Type.legacy_freeze_type 857 858fun freeze (t $ u) = freeze t $ freeze u 859 | freeze (Abs (s, T, t)) = Abs (s, freezeT T, freeze t) 860 | freeze (Var ((s, _), T)) = Free (s, freezeT T) 861 | freeze (Const (s, T)) = Const (s, freezeT T) 862 | freeze (Free (s, T)) = Free (s, freezeT T) 863 | freeze t = t 864 865fun goal_of_thm thy = Thm.prop_of #> freeze #> Thm.global_cterm_of thy #> Goal.init 866 867fun run_prover_for_mash ctxt params prover goal_name facts goal = 868 let 869 val problem = 870 {comment = "Goal: " ^ goal_name, state = Proof.init ctxt, goal = goal, subgoal = 1, 871 subgoal_count = 1, factss = [("", facts)], found_proof = I} 872 in 873 get_minimizing_prover ctxt MaSh (K ()) prover params problem 874 end 875 876val bad_types = [\<^type_name>\<open>prop\<close>, \<^type_name>\<open>bool\<close>, \<^type_name>\<open>fun\<close>] 877 878val crude_str_of_sort = space_implode "," o map Long_Name.base_name o subtract (op =) \<^sort>\<open>type\<close> 879 880fun crude_str_of_typ (Type (s, [])) = Long_Name.base_name s 881 | crude_str_of_typ (Type (s, Ts)) = Long_Name.base_name s ^ implode (map crude_str_of_typ Ts) 882 | crude_str_of_typ (TFree (_, S)) = crude_str_of_sort S 883 | crude_str_of_typ (TVar (_, S)) = crude_str_of_sort S 884 885fun maybe_singleton_str "" = [] 886 | maybe_singleton_str s = [s] 887 888val max_pat_breadth = 5 (* FUDGE *) 889 890fun term_features_of ctxt thy_name term_max_depth type_max_depth ts = 891 let 892 val thy = Proof_Context.theory_of ctxt 893 894 val fixes = map snd (Variable.dest_fixes ctxt) 895 val classes = Sign.classes_of thy 896 897 fun add_classes \<^sort>\<open>type\<close> = I 898 | add_classes S = 899 fold (`(Sorts.super_classes classes) 900 #> swap #> op :: 901 #> subtract (op =) \<^sort>\<open>type\<close> 902 #> map class_feature_of 903 #> union (op =)) S 904 905 fun pattify_type 0 _ = [] 906 | pattify_type _ (Type (s, [])) = if member (op =) bad_types s then [] else [s] 907 | pattify_type depth (Type (s, U :: Ts)) = 908 let 909 val T = Type (s, Ts) 910 val ps = take max_pat_breadth (pattify_type depth T) 911 val qs = take max_pat_breadth ("" :: pattify_type (depth - 1) U) 912 in 913 map_product (fn p => fn "" => p | q => p ^ "(" ^ q ^ ")") ps qs 914 end 915 | pattify_type _ (TFree (_, S)) = maybe_singleton_str (crude_str_of_sort S) 916 | pattify_type _ (TVar (_, S)) = maybe_singleton_str (crude_str_of_sort S) 917 918 fun add_type_pat depth T = 919 union (op =) (map type_feature_of (pattify_type depth T)) 920 921 fun add_type_pats 0 _ = I 922 | add_type_pats depth t = add_type_pat depth t #> add_type_pats (depth - 1) t 923 924 fun add_type T = 925 add_type_pats type_max_depth T 926 #> fold_atyps_sorts (add_classes o snd) T 927 928 fun add_subtypes (T as Type (_, Ts)) = add_type T #> fold add_subtypes Ts 929 | add_subtypes T = add_type T 930 931 fun pattify_term _ 0 _ = [] 932 | pattify_term _ _ (Const (s, _)) = 933 if is_widely_irrelevant_const s then [] else [s] 934 | pattify_term _ _ (Free (s, T)) = 935 maybe_singleton_str (crude_str_of_typ T) 936 |> (if member (op =) fixes s then cons (free_feature_of (Long_Name.append thy_name s)) 937 else I) 938 | pattify_term _ _ (Var (_, T)) = 939 maybe_singleton_str (crude_str_of_typ T) 940 | pattify_term Ts _ (Bound j) = 941 maybe_singleton_str (crude_str_of_typ (nth Ts j)) 942 | pattify_term Ts depth (t $ u) = 943 let 944 val ps = take max_pat_breadth (pattify_term Ts depth t) 945 val qs = take max_pat_breadth ("" :: pattify_term Ts (depth - 1) u) 946 in 947 map_product (fn p => fn "" => p | q => p ^ "(" ^ q ^ ")") ps qs 948 end 949 | pattify_term _ _ _ = [] 950 951 fun add_term_pat Ts = union (op =) oo pattify_term Ts 952 953 fun add_term_pats _ 0 _ = I 954 | add_term_pats Ts depth t = add_term_pat Ts depth t #> add_term_pats Ts (depth - 1) t 955 956 fun add_term Ts = add_term_pats Ts term_max_depth 957 958 fun add_subterms Ts t = 959 (case strip_comb t of 960 (Const (s, T), args) => 961 (not (is_widely_irrelevant_const s) ? add_term Ts t) 962 #> add_subtypes T #> fold (add_subterms Ts) args 963 | (head, args) => 964 (case head of 965 Free (_, T) => add_term Ts t #> add_subtypes T 966 | Var (_, T) => add_subtypes T 967 | Abs (_, T, body) => add_subtypes T #> add_subterms (T :: Ts) body 968 | _ => I) 969 #> fold (add_subterms Ts) args) 970 in 971 fold (add_subterms []) ts [] 972 end 973 974val term_max_depth = 2 975val type_max_depth = 1 976 977(* TODO: Generate type classes for types? *) 978fun features_of ctxt thy_name (scope, _) ts = 979 thy_feature_of thy_name :: 980 term_features_of ctxt thy_name term_max_depth type_max_depth ts 981 |> scope <> Global ? cons local_feature 982 983(* Too many dependencies is a sign that a decision procedure is at work. There is not much to learn 984 from such proofs. *) 985val max_dependencies = 20 (* FUDGE *) 986 987val prover_default_max_facts = 25 (* FUDGE *) 988 989(* "type_definition_xxx" facts are characterized by their use of "CollectI". *) 990val typedef_dep = nickname_of_thm @{thm CollectI} 991(* Mysterious parts of the class machinery create lots of proofs that refer exclusively to 992 "someI_ex" (and to some internal constructions). *) 993val class_some_dep = nickname_of_thm @{thm someI_ex} 994 995val fundef_ths = 996 @{thms fundef_ex1_existence fundef_ex1_uniqueness fundef_ex1_iff fundef_default_value} 997 |> map nickname_of_thm 998 999(* "Rep_xxx_inject", "Abs_xxx_inverse", etc., are derived using these facts. *) 1000val typedef_ths = 1001 @{thms type_definition.Abs_inverse type_definition.Rep_inverse type_definition.Rep 1002 type_definition.Rep_inject type_definition.Abs_inject type_definition.Rep_cases 1003 type_definition.Abs_cases type_definition.Rep_induct type_definition.Abs_induct 1004 type_definition.Rep_range type_definition.Abs_image} 1005 |> map nickname_of_thm 1006 1007fun is_size_def [dep] th = 1008 (case first_field ".rec" dep of 1009 SOME (pref, _) => 1010 (case first_field ".size" (nickname_of_thm th) of 1011 SOME (pref', _) => pref = pref' 1012 | NONE => false) 1013 | NONE => false) 1014 | is_size_def _ _ = false 1015 1016fun trim_dependencies deps = 1017 if length deps > max_dependencies then NONE else SOME deps 1018 1019fun isar_dependencies_of name_tabs th = 1020 thms_in_proof max_dependencies (SOME name_tabs) th 1021 |> Option.map (fn deps => 1022 if deps = [typedef_dep] orelse deps = [class_some_dep] orelse 1023 exists (member (op =) fundef_ths) deps orelse exists (member (op =) typedef_ths) deps orelse 1024 is_size_def deps th then 1025 [] 1026 else 1027 deps) 1028 1029fun prover_dependencies_of ctxt (params as {verbose, max_facts, ...}) prover auto_level facts 1030 name_tabs th = 1031 (case isar_dependencies_of name_tabs th of 1032 SOME [] => (false, []) 1033 | isar_deps0 => 1034 let 1035 val isar_deps = these isar_deps0 1036 val thy = Proof_Context.theory_of ctxt 1037 val goal = goal_of_thm thy th 1038 val name = nickname_of_thm th 1039 val (_, hyp_ts, concl_t) = ATP_Util.strip_subgoal goal 1 ctxt 1040 val facts = facts |> filter (fn (_, th') => thm_less (th', th)) 1041 1042 fun nickify ((_, stature), th) = ((nickname_of_thm th, stature), th) 1043 1044 fun is_dep dep (_, th) = (nickname_of_thm th = dep) 1045 1046 fun add_isar_dep facts dep accum = 1047 if exists (is_dep dep) accum then 1048 accum 1049 else 1050 (case find_first (is_dep dep) facts of 1051 SOME ((_, status), th) => accum @ [(("", status), th)] 1052 | NONE => accum (* should not happen *)) 1053 1054 val mepo_facts = 1055 facts 1056 |> mepo_suggested_facts ctxt params (max_facts |> the_default prover_default_max_facts) NONE 1057 hyp_ts concl_t 1058 val facts = 1059 mepo_facts 1060 |> fold (add_isar_dep facts) isar_deps 1061 |> map nickify 1062 val num_isar_deps = length isar_deps 1063 in 1064 if verbose andalso auto_level = 0 then 1065 writeln ("MaSh: " ^ quote prover ^ " on " ^ quote name ^ " with " ^ 1066 string_of_int num_isar_deps ^ " + " ^ string_of_int (length facts - num_isar_deps) ^ 1067 " facts") 1068 else 1069 (); 1070 (case run_prover_for_mash ctxt params prover name facts goal of 1071 {outcome = NONE, used_facts, ...} => 1072 (if verbose andalso auto_level = 0 then 1073 let val num_facts = length used_facts in 1074 writeln ("Found proof with " ^ string_of_int num_facts ^ " fact" ^ 1075 plural_s num_facts) 1076 end 1077 else 1078 (); 1079 (true, map fst used_facts)) 1080 | _ => (false, isar_deps)) 1081 end) 1082 1083 1084(*** High-level communication with MaSh ***) 1085 1086(* In the following functions, chunks are risers w.r.t. "thm_less_eq". *) 1087 1088fun chunks_and_parents_for chunks th = 1089 let 1090 fun insert_parent new parents = 1091 let val parents = parents |> filter_out (fn p => thm_less_eq (p, new)) in 1092 parents |> forall (fn p => not (thm_less_eq (new, p))) parents ? cons new 1093 end 1094 1095 fun rechunk seen (rest as th' :: ths) = 1096 if thm_less_eq (th', th) then (rev seen, rest) 1097 else rechunk (th' :: seen) ths 1098 1099 fun do_chunk [] accum = accum 1100 | do_chunk (chunk as hd_chunk :: _) (chunks, parents) = 1101 if thm_less_eq (hd_chunk, th) then 1102 (chunk :: chunks, insert_parent hd_chunk parents) 1103 else if thm_less_eq (List.last chunk, th) then 1104 let val (front, back as hd_back :: _) = rechunk [] chunk in 1105 (front :: back :: chunks, insert_parent hd_back parents) 1106 end 1107 else 1108 (chunk :: chunks, parents) 1109 in 1110 fold_rev do_chunk chunks ([], []) 1111 |>> cons [] 1112 ||> map nickname_of_thm 1113 end 1114 1115fun attach_parents_to_facts _ [] = [] 1116 | attach_parents_to_facts old_facts (facts as (_, th) :: _) = 1117 let 1118 fun do_facts _ [] = [] 1119 | do_facts (_, parents) [fact] = [(parents, fact)] 1120 | do_facts (chunks, parents) 1121 ((fact as (_, th)) :: (facts as (_, th') :: _)) = 1122 let 1123 val chunks = app_hd (cons th) chunks 1124 val chunks_and_parents' = 1125 if thm_less_eq (th, th') andalso 1126 Thm.theory_name th = Thm.theory_name th' 1127 then (chunks, [nickname_of_thm th]) 1128 else chunks_and_parents_for chunks th' 1129 in 1130 (parents, fact) :: do_facts chunks_and_parents' facts 1131 end 1132 in 1133 old_facts @ facts 1134 |> do_facts (chunks_and_parents_for [[]] th) 1135 |> drop (length old_facts) 1136 end 1137 1138fun is_fact_in_graph access_G = can (Graph.get_node access_G) o nickname_of_thm 1139 1140val chained_feature_factor = 0.5 (* FUDGE *) 1141val extra_feature_factor = 0.1 (* FUDGE *) 1142val num_extra_feature_facts = 10 (* FUDGE *) 1143 1144val max_proximity_facts = 100 (* FUDGE *) 1145 1146fun find_mash_suggestions ctxt max_facts suggs facts chained raw_unknown = 1147 let 1148 val inter_fact = inter (eq_snd Thm.eq_thm_prop) 1149 val raw_mash = find_suggested_facts ctxt facts suggs 1150 val proximate = take max_proximity_facts facts 1151 val unknown_chained = inter_fact raw_unknown chained 1152 val unknown_proximate = inter_fact raw_unknown proximate 1153 val mess = 1154 [(0.9 (* FUDGE *), (map (rpair 1.0) unknown_chained, [])), 1155 (0.4 (* FUDGE *), (weight_facts_smoothly unknown_proximate, [])), 1156 (0.1 (* FUDGE *), (weight_facts_steeply raw_mash, raw_unknown))] 1157 val unknown = raw_unknown 1158 |> fold (subtract (eq_snd Thm.eq_thm_prop)) [unknown_chained, unknown_proximate] 1159 in 1160 (mesh_facts (fact_distinct (op aconv)) (eq_snd (gen_eq_thm ctxt)) max_facts mess, unknown) 1161 end 1162 1163fun mash_suggested_facts ctxt thy_name ({debug, ...} : params) max_suggs hyp_ts concl_t facts = 1164 let 1165 val algorithm = the_mash_algorithm () 1166 1167 val facts = facts 1168 |> rev_sort_list_prefix (crude_thm_ord ctxt o apply2 snd) 1169 (Int.max (num_extra_feature_facts, max_proximity_facts)) 1170 1171 val chained = filter (fn ((_, (scope, _)), _) => scope = Chained) facts 1172 1173 fun fact_has_right_theory (_, th) = thy_name = Thm.theory_name th 1174 1175 fun chained_or_extra_features_of factor (((_, stature), th), weight) = 1176 [Thm.prop_of th] 1177 |> features_of ctxt (Thm.theory_name th) stature 1178 |> map (rpair (weight * factor)) 1179 in 1180 (case get_state ctxt of 1181 NONE => ([], []) 1182 | SOME {access_G, xtabs = ((num_facts, fact_tab), (num_feats, feat_tab)), ffds, freqs, ...} => 1183 let 1184 val goal_feats0 = 1185 features_of ctxt thy_name (Local, General) (concl_t :: hyp_ts) 1186 val chained_feats = chained 1187 |> map (rpair 1.0) 1188 |> map (chained_or_extra_features_of chained_feature_factor) 1189 |> rpair [] |-> fold (union (eq_fst (op =))) 1190 val extra_feats = facts 1191 |> take (Int.max (0, num_extra_feature_facts - length chained)) 1192 |> filter fact_has_right_theory 1193 |> weight_facts_steeply 1194 |> map (chained_or_extra_features_of extra_feature_factor) 1195 |> rpair [] |-> fold (union (eq_fst (op =))) 1196 1197 val goal_feats = 1198 fold (union (eq_fst (op =))) [chained_feats, extra_feats] (map (rpair 1.0) goal_feats0) 1199 |> debug ? sort (Real.compare o swap o apply2 snd) 1200 1201 val fact_idxs = map_filter (Symtab.lookup fact_tab o nickname_of_thm o snd) facts 1202 1203 val suggs = 1204 if algorithm = MaSh_NB_Ext orelse algorithm = MaSh_kNN_Ext then 1205 let 1206 val learns = 1207 Graph.schedule (fn _ => fn (fact, (_, feats, deps)) => (fact, feats, deps)) 1208 access_G 1209 in 1210 MaSh.query_external ctxt algorithm max_suggs learns goal_feats 1211 end 1212 else 1213 let 1214 val int_goal_feats = 1215 map_filter (fn (s, w) => Option.map (rpair w) (Symtab.lookup feat_tab s)) goal_feats 1216 in 1217 MaSh.query_internal ctxt algorithm num_facts num_feats ffds freqs fact_idxs max_suggs 1218 goal_feats int_goal_feats 1219 end 1220 1221 val unknown = filter_out (is_fact_in_graph access_G o snd) facts 1222 in 1223 find_mash_suggestions ctxt max_suggs suggs facts chained unknown 1224 |> apply2 (map fact_of_raw_fact) 1225 end) 1226 end 1227 1228fun mash_unlearn ctxt = (clear_state ctxt; writeln "Reset MaSh") 1229 1230fun learn_wrt_access_graph ctxt (name, parents, feats, deps) 1231 (accum as (access_G, (fact_xtab, feat_xtab))) = 1232 let 1233 fun maybe_learn_from from (accum as (parents, access_G)) = 1234 try_graph ctxt "updating graph" accum (fn () => 1235 (from :: parents, Graph.add_edge_acyclic (from, name) access_G)) 1236 1237 val access_G = access_G |> Graph.default_node (name, (Isar_Proof, feats, deps)) 1238 val (parents, access_G) = ([], access_G) |> fold maybe_learn_from parents 1239 val (deps, _) = ([], access_G) |> fold maybe_learn_from deps 1240 1241 val fact_xtab = add_to_xtab name fact_xtab 1242 val feat_xtab = fold maybe_add_to_xtab feats feat_xtab 1243 in 1244 (SOME (name, parents, feats, deps), (access_G, (fact_xtab, feat_xtab))) 1245 end 1246 handle Symtab.DUP _ => (NONE, accum) (* facts sometimes have the same name, confusingly *) 1247 1248fun relearn_wrt_access_graph ctxt (name, deps) access_G = 1249 let 1250 fun maybe_relearn_from from (accum as (parents, access_G)) = 1251 try_graph ctxt "updating graph" accum (fn () => 1252 (from :: parents, Graph.add_edge_acyclic (from, name) access_G)) 1253 val access_G = 1254 access_G |> Graph.map_node name (fn (_, feats, _) => (Automatic_Proof, feats, deps)) 1255 val (deps, _) = ([], access_G) |> fold maybe_relearn_from deps 1256 in 1257 ((name, deps), access_G) 1258 end 1259 1260fun flop_wrt_access_graph name = 1261 Graph.map_node name (fn (_, feats, deps) => (Isar_Proof_wegen_Prover_Flop, feats, deps)) 1262 1263val learn_timeout_slack = 20.0 1264 1265fun launch_thread timeout task = 1266 let 1267 val hard_timeout = time_mult learn_timeout_slack timeout 1268 val birth_time = Time.now () 1269 val death_time = birth_time + hard_timeout 1270 val desc = ("Machine learner for Sledgehammer", "") 1271 in 1272 Async_Manager_Legacy.thread MaShN birth_time death_time desc task 1273 end 1274 1275fun anonymous_proof_name () = 1276 Date.fmt (anonymous_proof_prefix ^ "%Y%m%d.%H%M%S.") (Date.fromTimeLocal (Time.now ())) ^ 1277 serial_string () 1278 1279fun mash_learn_proof ctxt ({timeout, ...} : params) t used_ths = 1280 if not (null used_ths) andalso is_mash_enabled () then 1281 launch_thread timeout (fn () => 1282 let 1283 val thy = Proof_Context.theory_of ctxt 1284 val feats = features_of ctxt (Context.theory_name thy) (Local, General) [t] 1285 in 1286 map_state ctxt 1287 (fn {access_G, xtabs as ((num_facts0, _), _), ffds, freqs, dirty_facts} => 1288 let 1289 val deps = used_ths 1290 |> filter (is_fact_in_graph access_G) 1291 |> map nickname_of_thm 1292 1293 val name = anonymous_proof_name () 1294 val (access_G', xtabs', rev_learns) = 1295 add_node Automatic_Proof name [] (* ignore parents *) feats deps 1296 (access_G, xtabs, []) 1297 1298 val (ffds', freqs') = 1299 recompute_ffds_freqs_from_learns (rev rev_learns) xtabs' num_facts0 ffds freqs 1300 in 1301 {access_G = access_G', xtabs = xtabs', ffds = ffds', freqs = freqs', 1302 dirty_facts = Option.map (cons name) dirty_facts} 1303 end); 1304 (true, "") 1305 end) 1306 else 1307 () 1308 1309fun sendback sub = Active.sendback_markup_command (sledgehammerN ^ " " ^ sub) 1310 1311val commit_timeout = seconds 30.0 1312 1313(* The timeout is understood in a very relaxed fashion. *) 1314fun mash_learn_facts ctxt (params as {debug, verbose, ...}) prover auto_level run_prover 1315 learn_timeout facts = 1316 let 1317 val timer = Timer.startRealTimer () 1318 fun next_commit_time () = Timer.checkRealTimer timer + commit_timeout 1319 in 1320 (case get_state ctxt of 1321 NONE => "MaSh is busy\nPlease try again later" 1322 | SOME {access_G, ...} => 1323 let 1324 val is_in_access_G = is_fact_in_graph access_G o snd 1325 val no_new_facts = forall is_in_access_G facts 1326 in 1327 if no_new_facts andalso not run_prover then 1328 if auto_level < 2 then 1329 "No new " ^ (if run_prover then "automatic" else "Isar") ^ " proofs to learn" ^ 1330 (if auto_level = 0 andalso not run_prover then 1331 "\n\nHint: Try " ^ sendback learn_proverN ^ " to learn from an automatic prover" 1332 else 1333 "") 1334 else 1335 "" 1336 else 1337 let 1338 val name_tabs = build_name_tables nickname_of_thm facts 1339 1340 fun deps_of status th = 1341 if status = Non_Rec_Def orelse status = Rec_Def then 1342 SOME [] 1343 else if run_prover then 1344 prover_dependencies_of ctxt params prover auto_level facts name_tabs th 1345 |> (fn (false, _) => NONE | (true, deps) => trim_dependencies deps) 1346 else 1347 isar_dependencies_of name_tabs th 1348 1349 fun do_commit [] [] [] state = state 1350 | do_commit learns relearns flops 1351 {access_G, xtabs as ((num_facts0, _), _), ffds, freqs, dirty_facts} = 1352 let 1353 val was_empty = Graph.is_empty access_G 1354 1355 val (learns, (access_G', xtabs')) = 1356 fold_map (learn_wrt_access_graph ctxt) learns (access_G, xtabs) 1357 |>> map_filter I 1358 val (relearns, access_G'') = 1359 fold_map (relearn_wrt_access_graph ctxt) relearns access_G' 1360 1361 val access_G''' = access_G'' |> fold flop_wrt_access_graph flops 1362 val dirty_facts' = 1363 (case (was_empty, dirty_facts) of 1364 (false, SOME names) => SOME (map #1 learns @ map #1 relearns @ names) 1365 | _ => NONE) 1366 1367 val (ffds', freqs') = 1368 if null relearns then 1369 recompute_ffds_freqs_from_learns 1370 (map (fn (name, _, feats, deps) => (name, feats, deps)) learns) xtabs' 1371 num_facts0 ffds freqs 1372 else 1373 recompute_ffds_freqs_from_access_G access_G''' xtabs' 1374 in 1375 {access_G = access_G''', xtabs = xtabs', ffds = ffds', freqs = freqs', 1376 dirty_facts = dirty_facts'} 1377 end 1378 1379 fun commit last learns relearns flops = 1380 (if debug andalso auto_level = 0 then writeln "Committing..." else (); 1381 map_state ctxt (do_commit (rev learns) relearns flops); 1382 if not last andalso auto_level = 0 then 1383 let val num_proofs = length learns + length relearns in 1384 writeln ("Learned " ^ string_of_int num_proofs ^ " " ^ 1385 (if run_prover then "automatic" else "Isar") ^ " proof" ^ 1386 plural_s num_proofs ^ " in the last " ^ string_of_time commit_timeout) 1387 end 1388 else 1389 ()) 1390 1391 fun learn_new_fact _ (accum as (_, (_, _, true))) = accum 1392 | learn_new_fact (parents, ((_, stature as (_, status)), th)) 1393 (learns, (num_nontrivial, next_commit, _)) = 1394 let 1395 val name = nickname_of_thm th 1396 val feats = features_of ctxt (Thm.theory_name th) stature [Thm.prop_of th] 1397 val deps = these (deps_of status th) 1398 val num_nontrivial = num_nontrivial |> not (null deps) ? Integer.add 1 1399 val learns = (name, parents, feats, deps) :: learns 1400 val (learns, next_commit) = 1401 if Timer.checkRealTimer timer > next_commit then 1402 (commit false learns [] []; ([], next_commit_time ())) 1403 else 1404 (learns, next_commit) 1405 val timed_out = Timer.checkRealTimer timer > learn_timeout 1406 in 1407 (learns, (num_nontrivial, next_commit, timed_out)) 1408 end 1409 1410 val (num_new_facts, num_nontrivial) = 1411 if no_new_facts then 1412 (0, 0) 1413 else 1414 let 1415 val new_facts = facts 1416 |> sort (crude_thm_ord ctxt o apply2 snd) 1417 |> map (pair []) (* ignore parents *) 1418 |> filter_out (is_in_access_G o snd) 1419 val (learns, (num_nontrivial, _, _)) = 1420 ([], (0, next_commit_time (), false)) 1421 |> fold learn_new_fact new_facts 1422 in 1423 commit true learns [] []; (length new_facts, num_nontrivial) 1424 end 1425 1426 fun relearn_old_fact _ (accum as (_, (_, _, true))) = accum 1427 | relearn_old_fact ((_, (_, status)), th) 1428 ((relearns, flops), (num_nontrivial, next_commit, _)) = 1429 let 1430 val name = nickname_of_thm th 1431 val (num_nontrivial, relearns, flops) = 1432 (case deps_of status th of 1433 SOME deps => (num_nontrivial + 1, (name, deps) :: relearns, flops) 1434 | NONE => (num_nontrivial, relearns, name :: flops)) 1435 val (relearns, flops, next_commit) = 1436 if Timer.checkRealTimer timer > next_commit then 1437 (commit false [] relearns flops; ([], [], next_commit_time ())) 1438 else 1439 (relearns, flops, next_commit) 1440 val timed_out = Timer.checkRealTimer timer > learn_timeout 1441 in 1442 ((relearns, flops), (num_nontrivial, next_commit, timed_out)) 1443 end 1444 1445 val num_nontrivial = 1446 if not run_prover then 1447 num_nontrivial 1448 else 1449 let 1450 val max_isar = 1000 * max_dependencies 1451 1452 fun priority_of th = 1453 Random.random_range 0 max_isar + 1454 (case try (Graph.get_node access_G) (nickname_of_thm th) of 1455 SOME (Isar_Proof, _, deps) => ~100 * length deps 1456 | SOME (Automatic_Proof, _, _) => 2 * max_isar 1457 | SOME (Isar_Proof_wegen_Prover_Flop, _, _) => max_isar 1458 | NONE => 0) 1459 1460 val old_facts = facts 1461 |> filter is_in_access_G 1462 |> map (`(priority_of o snd)) 1463 |> sort (int_ord o apply2 fst) 1464 |> map snd 1465 val ((relearns, flops), (num_nontrivial, _, _)) = 1466 (([], []), (num_nontrivial, next_commit_time (), false)) 1467 |> fold relearn_old_fact old_facts 1468 in 1469 commit true [] relearns flops; num_nontrivial 1470 end 1471 in 1472 if verbose orelse auto_level < 2 then 1473 "Learned " ^ string_of_int num_new_facts ^ " fact" ^ plural_s num_new_facts ^ 1474 " and " ^ string_of_int num_nontrivial ^ " nontrivial " ^ 1475 (if run_prover then "automatic and " else "") ^ "Isar proof" ^ 1476 plural_s num_nontrivial ^ 1477 (if verbose then " in " ^ string_of_time (Timer.checkRealTimer timer) else "") 1478 else 1479 "" 1480 end 1481 end) 1482 end 1483 1484fun mash_learn ctxt (params as {provers, timeout, ...}) fact_override chained run_prover = 1485 let 1486 val css = Sledgehammer_Fact.clasimpset_rule_table_of ctxt 1487 val ctxt = ctxt |> Config.put instantiate_inducts false 1488 val facts = 1489 nearly_all_facts ctxt false fact_override Keyword.empty_keywords css chained [] \<^prop>\<open>True\<close> 1490 |> sort (crude_thm_ord ctxt o apply2 snd o swap) 1491 val num_facts = length facts 1492 val prover = hd provers 1493 1494 fun learn auto_level run_prover = 1495 mash_learn_facts ctxt params prover auto_level run_prover one_year facts 1496 |> writeln 1497 in 1498 if run_prover then 1499 (writeln ("MaShing through " ^ string_of_int num_facts ^ " fact" ^ 1500 plural_s num_facts ^ " for automatic proofs (" ^ quote prover ^ " timeout: " ^ 1501 string_of_time timeout ^ ").\n\nCollecting Isar proofs first..."); 1502 learn 1 false; 1503 writeln "Now collecting automatic proofs\n\ 1504 \This may take several hours; you can safely stop the learning process at any point"; 1505 learn 0 true) 1506 else 1507 (writeln ("MaShing through " ^ string_of_int num_facts ^ " fact" ^ 1508 plural_s num_facts ^ " for Isar proofs..."); 1509 learn 0 false) 1510 end 1511 1512fun mash_can_suggest_facts ctxt = 1513 (case get_state ctxt of 1514 NONE => false 1515 | SOME {access_G, ...} => not (Graph.is_empty access_G)) 1516 1517fun mash_can_suggest_facts_fast ctxt = 1518 (case peek_state ctxt of 1519 NONE => false 1520 | SOME (_, {access_G, ...}) => not (Graph.is_empty access_G)) 1521 1522(* Generate more suggestions than requested, because some might be thrown out later for various 1523 reasons (e.g., duplicates). *) 1524fun generous_max_suggestions max_facts = 2 * max_facts + 25 (* FUDGE *) 1525 1526val mepo_weight = 0.5 (* FUDGE *) 1527val mash_weight = 0.5 (* FUDGE *) 1528 1529val max_facts_to_learn_before_query = 100 (* FUDGE *) 1530 1531(* The threshold should be large enough so that MaSh does not get activated for Auto Sledgehammer. *) 1532val min_secs_for_learning = 10 1533 1534fun relevant_facts ctxt (params as {verbose, learn, fact_filter, timeout, ...}) prover 1535 max_facts ({add, only, ...} : fact_override) hyp_ts concl_t facts = 1536 if not (subset (op =) (the_list fact_filter, fact_filters)) then 1537 error ("Unknown fact filter: " ^ quote (the fact_filter)) 1538 else if only then 1539 [("", map fact_of_raw_fact facts)] 1540 else if max_facts <= 0 orelse null facts then 1541 [("", [])] 1542 else 1543 let 1544 val thy_name = Context.theory_name (Proof_Context.theory_of ctxt) 1545 1546 fun maybe_launch_thread exact min_num_facts_to_learn = 1547 if not (Async_Manager_Legacy.has_running_threads MaShN) andalso 1548 Time.toSeconds timeout >= min_secs_for_learning then 1549 let val timeout = time_mult learn_timeout_slack timeout in 1550 (if verbose then 1551 writeln ("Started MaShing through " ^ 1552 (if exact then "" else "up to ") ^ string_of_int min_num_facts_to_learn ^ 1553 " fact" ^ plural_s min_num_facts_to_learn ^ " in the background") 1554 else 1555 ()); 1556 launch_thread timeout 1557 (fn () => (true, mash_learn_facts ctxt params prover 2 false timeout facts)) 1558 end 1559 else 1560 () 1561 1562 val mash_enabled = is_mash_enabled () 1563 val mash_fast = mash_can_suggest_facts_fast ctxt 1564 1565 fun please_learn () = 1566 if mash_fast then 1567 (case get_state ctxt of 1568 NONE => maybe_launch_thread false (length facts) 1569 | SOME {access_G, xtabs = ((num_facts0, _), _), ...} => 1570 let 1571 val is_in_access_G = is_fact_in_graph access_G o snd 1572 val min_num_facts_to_learn = length facts - num_facts0 1573 in 1574 if min_num_facts_to_learn <= max_facts_to_learn_before_query then 1575 (case length (filter_out is_in_access_G facts) of 1576 0 => () 1577 | num_facts_to_learn => 1578 if num_facts_to_learn <= max_facts_to_learn_before_query then 1579 mash_learn_facts ctxt params prover 2 false timeout facts 1580 |> (fn "" => () | s => writeln (MaShN ^ ": " ^ s)) 1581 else 1582 maybe_launch_thread true num_facts_to_learn) 1583 else 1584 maybe_launch_thread false min_num_facts_to_learn 1585 end) 1586 else 1587 maybe_launch_thread false (length facts) 1588 1589 val _ = 1590 if learn andalso mash_enabled andalso fact_filter <> SOME mepoN then please_learn () else () 1591 1592 val effective_fact_filter = 1593 (case fact_filter of 1594 SOME ff => ff 1595 | NONE => if mash_enabled andalso mash_fast then meshN else mepoN) 1596 1597 val unique_facts = drop_duplicate_facts facts 1598 val add_ths = Attrib.eval_thms ctxt add 1599 1600 fun in_add (_, th) = member Thm.eq_thm_prop add_ths th 1601 1602 fun add_and_take accepts = 1603 (case add_ths of 1604 [] => accepts 1605 | _ => 1606 (unique_facts |> filter in_add |> map fact_of_raw_fact) @ (accepts |> filter_out in_add)) 1607 |> take max_facts 1608 1609 fun mepo () = 1610 (mepo_suggested_facts ctxt params max_facts NONE hyp_ts concl_t unique_facts 1611 |> weight_facts_steeply, []) 1612 1613 fun mash () = 1614 mash_suggested_facts ctxt thy_name params (generous_max_suggestions max_facts) hyp_ts 1615 concl_t facts 1616 |>> weight_facts_steeply 1617 1618 val mess = 1619 (* the order is important for the "case" expression below *) 1620 [] |> effective_fact_filter <> mepoN ? cons (mash_weight, mash) 1621 |> effective_fact_filter <> mashN ? cons (mepo_weight, mepo) 1622 |> Par_List.map (apsnd (fn f => f ())) 1623 val mesh = 1624 mesh_facts (fact_distinct (op aconv)) (eq_snd (gen_eq_thm ctxt)) max_facts mess 1625 |> add_and_take 1626 in 1627 (case (fact_filter, mess) of 1628 (NONE, [(_, (mepo, _)), (_, (mash, _))]) => 1629 [(meshN, mesh), 1630 (mepoN, mepo |> map fst |> add_and_take), 1631 (mashN, mash |> map fst |> add_and_take)] 1632 | _ => [(effective_fact_filter, mesh)]) 1633 end 1634 1635end; 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