add support for lambdas in TPTP THF generator + killed an unsound type encoding (because the monotonicity calculus assumes first-order)
1 (* Title: HOL/Tools/ATP/atp_translate.ML
2 Author: Fabian Immler, TU Muenchen
4 Author: Jasmin Blanchette, TU Muenchen
6 Translation of HOL to FOL for Sledgehammer.
9 signature ATP_TRANSLATE =
11 type ('a, 'b) ho_term = ('a, 'b) ATP_Problem.ho_term
12 type connective = ATP_Problem.connective
13 type ('a, 'b, 'c) formula = ('a, 'b, 'c) ATP_Problem.formula
14 type format = ATP_Problem.format
15 type formula_kind = ATP_Problem.formula_kind
16 type 'a problem = 'a ATP_Problem.problem
19 General | Helper | Extensionality | Intro | Elim | Simp | Local | Assum |
22 datatype order = First_Order | Higher_Order
23 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
25 All_Types | Noninf_Nonmono_Types | Fin_Nonmono_Types | Const_Arg_Types |
27 datatype type_heaviness = Heavyweight | Lightweight
30 Simple_Types of order * type_level |
31 Preds of polymorphism * type_level * type_heaviness |
32 Tags of polymorphism * type_level * type_heaviness
34 val bound_var_prefix : string
35 val schematic_var_prefix : string
36 val fixed_var_prefix : string
37 val tvar_prefix : string
38 val tfree_prefix : string
39 val const_prefix : string
40 val type_const_prefix : string
41 val class_prefix : string
42 val skolem_const_prefix : string
43 val old_skolem_const_prefix : string
44 val new_skolem_const_prefix : string
45 val type_decl_prefix : string
46 val sym_decl_prefix : string
47 val preds_sym_formula_prefix : string
48 val lightweight_tags_sym_formula_prefix : string
49 val fact_prefix : string
50 val conjecture_prefix : string
51 val helper_prefix : string
52 val class_rel_clause_prefix : string
53 val arity_clause_prefix : string
54 val tfree_clause_prefix : string
55 val typed_helper_suffix : string
56 val untyped_helper_suffix : string
57 val type_tag_idempotence_helper_name : string
58 val predicator_name : string
59 val app_op_name : string
60 val type_tag_name : string
61 val type_pred_name : string
62 val simple_type_prefix : string
63 val prefixed_predicator_name : string
64 val prefixed_app_op_name : string
65 val prefixed_type_tag_name : string
66 val ascii_of : string -> string
67 val unascii_of : string -> string
68 val strip_prefix_and_unascii : string -> string -> string option
69 val proxy_table : (string * (string * (thm * (string * string)))) list
70 val proxify_const : string -> (string * string) option
71 val invert_const : string -> string
72 val unproxify_const : string -> string
73 val new_skolem_var_name_from_const : string -> string
74 val num_type_args : theory -> string -> int
75 val atp_irrelevant_consts : string list
76 val atp_schematic_consts_of : term -> typ list Symtab.table
77 val is_locality_global : locality -> bool
78 val type_enc_from_string : string -> type_enc
79 val polymorphism_of_type_enc : type_enc -> polymorphism
80 val level_of_type_enc : type_enc -> type_level
81 val is_type_enc_virtually_sound : type_enc -> bool
82 val is_type_enc_fairly_sound : type_enc -> bool
83 val choose_format : format list -> type_enc -> format * type_enc
85 connective -> ('a, 'b, 'c) formula list -> ('a, 'b, 'c) formula
86 val unmangled_const : string -> string * (string, 'b) ho_term list
87 val unmangled_const_name : string -> string
88 val helper_table : ((string * bool) * thm list) list
90 val prepare_atp_problem :
91 Proof.context -> format -> formula_kind -> formula_kind -> type_enc -> bool
92 -> bool -> bool -> bool -> term list -> term
93 -> ((string * locality) * term) list
94 -> string problem * string Symtab.table * int * int
95 * (string * locality) list vector * int list * int Symtab.table
96 val atp_problem_weights : string problem -> (string * real) list
99 structure ATP_Translate : ATP_TRANSLATE =
105 type name = string * string
108 val generate_useful_info = false
110 fun useful_isabelle_info s =
111 if generate_useful_info then
112 SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
116 val intro_info = useful_isabelle_info "intro"
117 val elim_info = useful_isabelle_info "elim"
118 val simp_info = useful_isabelle_info "simp"
120 val bound_var_prefix = "B_"
121 val schematic_var_prefix = "V_"
122 val fixed_var_prefix = "v_"
124 val tvar_prefix = "T_"
125 val tfree_prefix = "t_"
127 val const_prefix = "c_"
128 val type_const_prefix = "tc_"
129 val class_prefix = "cl_"
131 val skolem_const_prefix = "Sledgehammer" ^ Long_Name.separator ^ "Sko"
132 val old_skolem_const_prefix = skolem_const_prefix ^ "o"
133 val new_skolem_const_prefix = skolem_const_prefix ^ "n"
135 val type_decl_prefix = "ty_"
136 val sym_decl_prefix = "sy_"
137 val preds_sym_formula_prefix = "psy_"
138 val lightweight_tags_sym_formula_prefix = "tsy_"
139 val fact_prefix = "fact_"
140 val conjecture_prefix = "conj_"
141 val helper_prefix = "help_"
142 val class_rel_clause_prefix = "clar_"
143 val arity_clause_prefix = "arity_"
144 val tfree_clause_prefix = "tfree_"
146 val typed_helper_suffix = "_T"
147 val untyped_helper_suffix = "_U"
148 val type_tag_idempotence_helper_name = helper_prefix ^ "ti_idem"
150 val predicator_name = "hBOOL"
151 val app_op_name = "hAPP"
152 val type_tag_name = "ti"
153 val type_pred_name = "is"
154 val simple_type_prefix = "ty_"
156 val prefixed_predicator_name = const_prefix ^ predicator_name
157 val prefixed_app_op_name = const_prefix ^ app_op_name
158 val prefixed_type_tag_name = const_prefix ^ type_tag_name
160 (* Freshness almost guaranteed! *)
161 val sledgehammer_weak_prefix = "Sledgehammer:"
163 (*Escaping of special characters.
164 Alphanumeric characters are left unchanged.
165 The character _ goes to __
166 Characters in the range ASCII space to / go to _A to _P, respectively.
167 Other characters go to _nnn where nnn is the decimal ASCII code.*)
168 val upper_a_minus_space = Char.ord #"A" - Char.ord #" "
170 fun stringN_of_int 0 _ = ""
171 | stringN_of_int k n =
172 stringN_of_int (k - 1) (n div 10) ^ string_of_int (n mod 10)
174 fun ascii_of_char c =
175 if Char.isAlphaNum c then
177 else if c = #"_" then
179 else if #" " <= c andalso c <= #"/" then
180 "_" ^ String.str (Char.chr (Char.ord c + upper_a_minus_space))
182 (* fixed width, in case more digits follow *)
183 "_" ^ stringN_of_int 3 (Char.ord c)
185 val ascii_of = String.translate ascii_of_char
187 (** Remove ASCII armoring from names in proof files **)
189 (* We don't raise error exceptions because this code can run inside a worker
190 thread. Also, the errors are impossible. *)
193 fun un rcs [] = String.implode(rev rcs)
194 | un rcs [#"_"] = un (#"_" :: rcs) [] (* ERROR *)
195 (* Three types of _ escapes: __, _A to _P, _nnn *)
196 | un rcs (#"_" :: #"_" :: cs) = un (#"_" :: rcs) cs
197 | un rcs (#"_" :: c :: cs) =
198 if #"A" <= c andalso c<= #"P" then
199 (* translation of #" " to #"/" *)
200 un (Char.chr (Char.ord c - upper_a_minus_space) :: rcs) cs
202 let val digits = List.take (c :: cs, 3) handle General.Subscript => [] in
203 case Int.fromString (String.implode digits) of
204 SOME n => un (Char.chr n :: rcs) (List.drop (cs, 2))
205 | NONE => un (c :: #"_" :: rcs) cs (* ERROR *)
207 | un rcs (c :: cs) = un (c :: rcs) cs
208 in un [] o String.explode end
210 (* If string s has the prefix s1, return the result of deleting it,
212 fun strip_prefix_and_unascii s1 s =
213 if String.isPrefix s1 s then
214 SOME (unascii_of (String.extract (s, size s1, NONE)))
219 [("c_False", (@{const_name False}, (@{thm fFalse_def},
220 ("fFalse", @{const_name ATP.fFalse})))),
221 ("c_True", (@{const_name True}, (@{thm fTrue_def},
222 ("fTrue", @{const_name ATP.fTrue})))),
223 ("c_Not", (@{const_name Not}, (@{thm fNot_def},
224 ("fNot", @{const_name ATP.fNot})))),
225 ("c_conj", (@{const_name conj}, (@{thm fconj_def},
226 ("fconj", @{const_name ATP.fconj})))),
227 ("c_disj", (@{const_name disj}, (@{thm fdisj_def},
228 ("fdisj", @{const_name ATP.fdisj})))),
229 ("c_implies", (@{const_name implies}, (@{thm fimplies_def},
230 ("fimplies", @{const_name ATP.fimplies})))),
231 ("equal", (@{const_name HOL.eq}, (@{thm fequal_def},
232 ("fequal", @{const_name ATP.fequal}))))]
234 val proxify_const = AList.lookup (op =) proxy_table #> Option.map (snd o snd)
236 (* Readable names for the more common symbolic functions. Do not mess with the
237 table unless you know what you are doing. *)
238 val const_trans_table =
239 [(@{type_name Product_Type.prod}, "prod"),
240 (@{type_name Sum_Type.sum}, "sum"),
241 (@{const_name False}, "False"),
242 (@{const_name True}, "True"),
243 (@{const_name Not}, "Not"),
244 (@{const_name conj}, "conj"),
245 (@{const_name disj}, "disj"),
246 (@{const_name implies}, "implies"),
247 (@{const_name HOL.eq}, "equal"),
248 (@{const_name If}, "If"),
249 (@{const_name Set.member}, "member"),
250 (@{const_name Meson.COMBI}, "COMBI"),
251 (@{const_name Meson.COMBK}, "COMBK"),
252 (@{const_name Meson.COMBB}, "COMBB"),
253 (@{const_name Meson.COMBC}, "COMBC"),
254 (@{const_name Meson.COMBS}, "COMBS")]
256 |> fold (Symtab.update o swap o snd o snd o snd) proxy_table
258 (* Invert the table of translations between Isabelle and ATPs. *)
259 val const_trans_table_inv =
260 const_trans_table |> Symtab.dest |> map swap |> Symtab.make
261 val const_trans_table_unprox =
263 |> fold (fn (_, (isa, (_, (_, atp)))) => Symtab.update (atp, isa)) proxy_table
265 val invert_const = perhaps (Symtab.lookup const_trans_table_inv)
266 val unproxify_const = perhaps (Symtab.lookup const_trans_table_unprox)
269 case Symtab.lookup const_trans_table c of
273 fun ascii_of_indexname (v, 0) = ascii_of v
274 | ascii_of_indexname (v, i) = ascii_of v ^ "_" ^ string_of_int i
276 fun make_bound_var x = bound_var_prefix ^ ascii_of x
277 fun make_schematic_var v = schematic_var_prefix ^ ascii_of_indexname v
278 fun make_fixed_var x = fixed_var_prefix ^ ascii_of x
280 fun make_schematic_type_var (x, i) =
281 tvar_prefix ^ (ascii_of_indexname (unprefix "'" x, i))
282 fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (unprefix "'" x))
284 (* "HOL.eq" is mapped to the ATP's equality. *)
285 fun make_fixed_const @{const_name HOL.eq} = tptp_old_equal
286 | make_fixed_const c = const_prefix ^ lookup_const c
288 fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
290 fun make_type_class clas = class_prefix ^ ascii_of clas
292 fun new_skolem_var_name_from_const s =
293 let val ss = s |> space_explode Long_Name.separator in
294 nth ss (length ss - 2)
297 (* The number of type arguments of a constant, zero if it's monomorphic. For
298 (instances of) Skolem pseudoconstants, this information is encoded in the
300 fun num_type_args thy s =
301 if String.isPrefix skolem_const_prefix s then
302 s |> space_explode Long_Name.separator |> List.last |> Int.fromString |> the
304 (s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
306 (* These are either simplified away by "Meson.presimplify" (most of the time) or
307 handled specially via "fFalse", "fTrue", ..., "fequal". *)
308 val atp_irrelevant_consts =
309 [@{const_name False}, @{const_name True}, @{const_name Not},
310 @{const_name conj}, @{const_name disj}, @{const_name implies},
311 @{const_name HOL.eq}, @{const_name If}, @{const_name Let}]
313 val atp_monomorph_bad_consts =
314 atp_irrelevant_consts @
315 (* These are ignored anyway by the relevance filter (unless they appear in
316 higher-order places) but not by the monomorphizer. *)
317 [@{const_name all}, @{const_name "==>"}, @{const_name "=="},
318 @{const_name Trueprop}, @{const_name All}, @{const_name Ex},
319 @{const_name Ex1}, @{const_name Ball}, @{const_name Bex}]
321 fun add_schematic_const (x as (_, T)) =
322 Monomorph.typ_has_tvars T ? Symtab.insert_list (op =) x
323 val add_schematic_consts_of =
324 Term.fold_aterms (fn Const (x as (s, _)) =>
325 not (member (op =) atp_monomorph_bad_consts s)
326 ? add_schematic_const x
328 fun atp_schematic_consts_of t = add_schematic_consts_of t Symtab.empty
330 (** Definitions and functions for FOL clauses and formulas for TPTP **)
332 (* The first component is the type class; the second is a "TVar" or "TFree". *)
333 datatype type_literal =
334 TyLitVar of name * name |
335 TyLitFree of name * name
338 (** Isabelle arities **)
340 datatype arity_literal =
341 TConsLit of name * name * name list |
342 TVarLit of name * name
345 | gen_TVars n = ("T_" ^ string_of_int n) :: gen_TVars (n-1)
347 val type_class = the_single @{sort type}
349 fun add_packed_sort tvar =
350 fold (fn s => s <> type_class ? cons (`make_type_class s, `I tvar))
354 prem_lits : arity_literal list,
355 concl_lits : arity_literal}
357 (* Arity of type constructor "tcon :: (arg1, ..., argN) res" *)
358 fun make_axiom_arity_clause (tcons, name, (cls, args)) =
360 val tvars = gen_TVars (length args)
361 val tvars_srts = ListPair.zip (tvars, args)
364 prem_lits = [] |> fold (uncurry add_packed_sort) tvars_srts |> map TVarLit,
365 concl_lits = TConsLit (`make_type_class cls,
366 `make_fixed_type_const tcons,
370 fun arity_clause _ _ (_, []) = []
371 | arity_clause seen n (tcons, ("HOL.type", _) :: ars) = (* ignore *)
372 arity_clause seen n (tcons, ars)
373 | arity_clause seen n (tcons, (ar as (class, _)) :: ars) =
374 if member (op =) seen class then
375 (* multiple arities for the same (tycon, class) pair *)
376 make_axiom_arity_clause (tcons,
377 lookup_const tcons ^ "___" ^ ascii_of class ^ "_" ^ string_of_int n,
379 arity_clause seen (n + 1) (tcons, ars)
381 make_axiom_arity_clause (tcons, lookup_const tcons ^ "___" ^
382 ascii_of class, ar) ::
383 arity_clause (class :: seen) n (tcons, ars)
385 fun multi_arity_clause [] = []
386 | multi_arity_clause ((tcons, ars) :: tc_arlists) =
387 arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
389 (* Generate all pairs (tycon, class, sorts) such that tycon belongs to class in
390 theory thy provided its arguments have the corresponding sorts. *)
391 fun type_class_pairs thy tycons classes =
393 val alg = Sign.classes_of thy
394 fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
395 fun add_class tycon class =
396 cons (class, domain_sorts tycon class)
397 handle Sorts.CLASS_ERROR _ => I
398 fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
399 in map try_classes tycons end
401 (*Proving one (tycon, class) membership may require proving others, so iterate.*)
402 fun iter_type_class_pairs _ _ [] = ([], [])
403 | iter_type_class_pairs thy tycons classes =
405 fun maybe_insert_class s =
406 (s <> type_class andalso not (member (op =) classes s))
408 val cpairs = type_class_pairs thy tycons classes
410 [] |> fold (fold (fold (fold maybe_insert_class) o snd) o snd) cpairs
411 val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
412 in (classes' @ classes, union (op =) cpairs' cpairs) end
414 fun make_arity_clauses thy tycons =
415 iter_type_class_pairs thy tycons ##> multi_arity_clause
418 (** Isabelle class relations **)
420 type class_rel_clause =
425 (* Generate all pairs (sub, super) such that sub is a proper subclass of super
427 fun class_pairs _ [] _ = []
428 | class_pairs thy subs supers =
430 val class_less = Sorts.class_less (Sign.classes_of thy)
431 fun add_super sub super = class_less (sub, super) ? cons (sub, super)
432 fun add_supers sub = fold (add_super sub) supers
433 in fold add_supers subs [] end
435 fun make_class_rel_clause (sub, super) =
436 {name = sub ^ "_" ^ super, subclass = `make_type_class sub,
437 superclass = `make_type_class super}
439 fun make_class_rel_clauses thy subs supers =
440 map make_class_rel_clause (class_pairs thy subs supers)
443 CombConst of name * typ * typ list |
444 CombVar of name * typ |
445 CombApp of combterm * combterm
447 fun combtyp_of (CombConst (_, T, _)) = T
448 | combtyp_of (CombVar (_, T)) = T
449 | combtyp_of (CombApp (t1, _)) = snd (dest_funT (combtyp_of t1))
451 (*gets the head of a combinator application, along with the list of arguments*)
452 fun strip_combterm_comb u =
454 fun stripc (CombApp (t, u), ts) = stripc (t, u :: ts)
456 in stripc (u, []) end
458 fun atyps_of T = fold_atyps (insert (op =)) T []
460 fun new_skolem_const_name s num_T_args =
461 [new_skolem_const_prefix, s, string_of_int num_T_args]
462 |> space_implode Long_Name.separator
464 (* Converts a term (with combinators) into a combterm. Also accumulates sort
466 fun combterm_from_term thy bs (P $ Q) =
468 val (P', P_atomics_Ts) = combterm_from_term thy bs P
469 val (Q', Q_atomics_Ts) = combterm_from_term thy bs Q
470 in (CombApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
471 | combterm_from_term thy _ (Const (c, T)) =
474 (if String.isPrefix old_skolem_const_prefix c then
475 [] |> Term.add_tvarsT T |> map TVar
477 (c, T) |> Sign.const_typargs thy)
478 val c' = CombConst (`make_fixed_const c, T, tvar_list)
479 in (c', atyps_of T) end
480 | combterm_from_term _ _ (Free (v, T)) =
481 (CombConst (`make_fixed_var v, T, []), atyps_of T)
482 | combterm_from_term _ _ (Var (v as (s, _), T)) =
483 (if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
485 val Ts = T |> strip_type |> swap |> op ::
486 val s' = new_skolem_const_name s (length Ts)
487 in CombConst (`make_fixed_const s', T, Ts) end
489 CombVar ((make_schematic_var v, s), T), atyps_of T)
490 | combterm_from_term _ bs (Bound j) =
492 |> (fn (s, T) => (CombConst (`make_bound_var s, T, []), atyps_of T))
493 | combterm_from_term _ _ (Abs _) = raise Fail "HOL clause: Abs"
496 General | Helper | Extensionality | Intro | Elim | Simp | Local | Assum |
499 (* (quasi-)underapproximation of the truth *)
500 fun is_locality_global Local = false
501 | is_locality_global Assum = false
502 | is_locality_global Chained = false
503 | is_locality_global _ = true
505 datatype order = First_Order | Higher_Order
506 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
507 datatype type_level =
508 All_Types | Noninf_Nonmono_Types | Fin_Nonmono_Types | Const_Arg_Types |
510 datatype type_heaviness = Heavyweight | Lightweight
513 Simple_Types of order * type_level |
514 Preds of polymorphism * type_level * type_heaviness |
515 Tags of polymorphism * type_level * type_heaviness
517 fun try_unsuffixes ss s =
518 fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
520 fun type_enc_from_string s =
521 (case try (unprefix "poly_") s of
522 SOME s => (SOME Polymorphic, s)
524 case try (unprefix "mono_") s of
525 SOME s => (SOME Monomorphic, s)
527 case try (unprefix "mangled_") s of
528 SOME s => (SOME Mangled_Monomorphic, s)
531 (* "_query" and "_bang" are for the ASCII-challenged Metis and
533 case try_unsuffixes ["?", "_query"] s of
534 SOME s => (Noninf_Nonmono_Types, s)
536 case try_unsuffixes ["!", "_bang"] s of
537 SOME s => (Fin_Nonmono_Types, s)
538 | NONE => (All_Types, s))
540 case try (unsuffix "_heavy") s of
541 SOME s => (Heavyweight, s)
542 | NONE => (Lightweight, s))
543 |> (fn (poly, (level, (heaviness, core))) =>
544 case (core, (poly, level, heaviness)) of
545 ("simple", (NONE, _, Lightweight)) =>
546 Simple_Types (First_Order, level)
547 | ("simple_higher", (NONE, _, Lightweight)) =>
548 if level = Noninf_Nonmono_Types then raise Same.SAME
549 else Simple_Types (Higher_Order, level)
550 | ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
551 | ("tags", (SOME Polymorphic, _, _)) =>
552 Tags (Polymorphic, level, heaviness)
553 | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
554 | ("args", (SOME poly, All_Types (* naja *), Lightweight)) =>
555 Preds (poly, Const_Arg_Types, Lightweight)
556 | ("erased", (NONE, All_Types (* naja *), Lightweight)) =>
557 Preds (Polymorphic, No_Types, Lightweight)
558 | _ => raise Same.SAME)
559 handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
561 fun is_type_enc_higher_order (Simple_Types (Higher_Order, _)) = true
562 | is_type_enc_higher_order _ = false
564 fun polymorphism_of_type_enc (Simple_Types _) = Mangled_Monomorphic
565 | polymorphism_of_type_enc (Preds (poly, _, _)) = poly
566 | polymorphism_of_type_enc (Tags (poly, _, _)) = poly
568 fun level_of_type_enc (Simple_Types (_, level)) = level
569 | level_of_type_enc (Preds (_, level, _)) = level
570 | level_of_type_enc (Tags (_, level, _)) = level
572 fun heaviness_of_type_enc (Simple_Types _) = Heavyweight
573 | heaviness_of_type_enc (Preds (_, _, heaviness)) = heaviness
574 | heaviness_of_type_enc (Tags (_, _, heaviness)) = heaviness
576 fun is_type_level_virtually_sound level =
577 level = All_Types orelse level = Noninf_Nonmono_Types
578 val is_type_enc_virtually_sound =
579 is_type_level_virtually_sound o level_of_type_enc
581 fun is_type_level_fairly_sound level =
582 is_type_level_virtually_sound level orelse level = Fin_Nonmono_Types
583 val is_type_enc_fairly_sound = is_type_level_fairly_sound o level_of_type_enc
585 fun choose_format formats (Simple_Types (order, level)) =
586 if member (op =) formats THF then
587 (THF, Simple_Types (order, level))
588 else if member (op =) formats TFF then
589 (TFF, Simple_Types (First_Order, level))
591 choose_format formats (Preds (Mangled_Monomorphic, level, Heavyweight))
592 | choose_format formats type_enc =
595 (CNF_UEQ, case type_enc of
597 (if is_type_enc_fairly_sound type_enc then Tags else Preds)
600 | format => (format, type_enc))
602 type translated_formula =
606 combformula : (name, typ, combterm) formula,
607 atomic_types : typ list}
609 fun update_combformula f ({name, locality, kind, combformula, atomic_types}
610 : translated_formula) =
611 {name = name, locality = locality, kind = kind, combformula = f combformula,
612 atomic_types = atomic_types} : translated_formula
614 fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
616 val type_instance = Sign.typ_instance o Proof_Context.theory_of
618 fun insert_type ctxt get_T x xs =
619 let val T = get_T x in
620 if exists (curry (type_instance ctxt) T o get_T) xs then xs
621 else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
624 (* The Booleans indicate whether all type arguments should be kept. *)
625 datatype type_arg_policy =
626 Explicit_Type_Args of bool |
627 Mangled_Type_Args of bool |
630 fun should_drop_arg_type_args (Simple_Types _) =
631 false (* since TFF doesn't support overloading *)
632 | should_drop_arg_type_args type_enc =
633 level_of_type_enc type_enc = All_Types andalso
634 heaviness_of_type_enc type_enc = Heavyweight
636 fun type_arg_policy type_enc s =
637 if s = type_tag_name then
638 (if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
641 Explicit_Type_Args) false
642 else case type_enc of
643 Tags (_, All_Types, Heavyweight) => No_Type_Args
645 if level_of_type_enc type_enc = No_Types orelse
646 s = @{const_name HOL.eq} orelse
647 (s = app_op_name andalso
648 level_of_type_enc type_enc = Const_Arg_Types) then
651 should_drop_arg_type_args type_enc
652 |> (if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
657 (* Make literals for sorted type variables. *)
658 fun generic_add_sorts_on_type (_, []) = I
659 | generic_add_sorts_on_type ((x, i), s :: ss) =
660 generic_add_sorts_on_type ((x, i), ss)
661 #> (if s = the_single @{sort HOL.type} then
664 insert (op =) (TyLitFree (`make_type_class s, `make_fixed_type_var x))
666 insert (op =) (TyLitVar (`make_type_class s,
667 (make_schematic_type_var (x, i), x))))
668 fun add_sorts_on_tfree (TFree (s, S)) = generic_add_sorts_on_type ((s, ~1), S)
669 | add_sorts_on_tfree _ = I
670 fun add_sorts_on_tvar (TVar z) = generic_add_sorts_on_type z
671 | add_sorts_on_tvar _ = I
673 fun type_literals_for_types type_enc add_sorts_on_typ Ts =
674 [] |> level_of_type_enc type_enc <> No_Types ? fold add_sorts_on_typ Ts
676 fun mk_aconns c phis =
677 let val (phis', phi') = split_last phis in
678 fold_rev (mk_aconn c) phis' phi'
680 fun mk_ahorn [] phi = phi
681 | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
682 fun mk_aquant _ [] phi = phi
683 | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
684 if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
685 | mk_aquant q xs phi = AQuant (q, xs, phi)
687 fun close_universally atom_vars phi =
689 fun formula_vars bounds (AQuant (_, xs, phi)) =
690 formula_vars (map fst xs @ bounds) phi
691 | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
692 | formula_vars bounds (AAtom tm) =
693 union (op =) (atom_vars tm []
694 |> filter_out (member (op =) bounds o fst))
695 in mk_aquant AForall (formula_vars [] phi []) phi end
697 fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
698 | combterm_vars (CombConst _) = I
699 | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
700 fun close_combformula_universally phi = close_universally combterm_vars phi
702 fun term_vars bounds (ATerm (name as (s, _), tms)) =
703 (is_tptp_variable s andalso not (member (op =) bounds name))
704 ? insert (op =) (name, NONE) #> fold (term_vars bounds) tms
705 | term_vars bounds (AAbs ((name, _), tm)) = term_vars (name :: bounds) tm
706 fun close_formula_universally phi = close_universally (term_vars []) phi
708 val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
709 val homo_infinite_type = Type (homo_infinite_type_name, [])
711 fun ho_term_from_typ format type_enc =
713 fun term (Type (s, Ts)) =
714 ATerm (case (is_type_enc_higher_order type_enc, s) of
715 (true, @{type_name bool}) => `I tptp_bool_type
716 | (true, @{type_name fun}) => `I tptp_fun_type
717 | _ => if s = homo_infinite_type_name andalso
718 (format = TFF orelse format = THF) then
719 `I tptp_individual_type
721 `make_fixed_type_const s,
723 | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
724 | term (TVar ((x as (s, _)), _)) =
725 ATerm ((make_schematic_type_var x, s), [])
728 fun ho_term_for_type_arg format type_enc T =
729 if T = dummyT then NONE else SOME (ho_term_from_typ format type_enc T)
731 (* This shouldn't clash with anything else. *)
732 val mangled_type_sep = "\000"
734 fun generic_mangled_type_name f (ATerm (name, [])) = f name
735 | generic_mangled_type_name f (ATerm (name, tys)) =
736 f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
738 | generic_mangled_type_name f _ = raise Fail "unexpected type abstraction"
740 val bool_atype = AType (`I tptp_bool_type)
742 fun make_simple_type s =
743 if s = tptp_bool_type orelse s = tptp_fun_type orelse
744 s = tptp_individual_type then
747 simple_type_prefix ^ ascii_of s
749 fun ho_type_from_ho_term type_enc pred_sym ary =
752 AType ((make_simple_type (generic_mangled_type_name fst ty),
753 generic_mangled_type_name snd ty))
754 fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
755 fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
756 | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
757 | to_fo ary _ = raise Fail "unexpected type abstraction"
758 fun to_ho (ty as ATerm ((s, _), tys)) =
759 if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
760 | to_ho _ = raise Fail "unexpected type abstraction"
761 in if is_type_enc_higher_order type_enc then to_ho else to_fo ary end
763 fun mangled_type format type_enc pred_sym ary =
764 ho_type_from_ho_term type_enc pred_sym ary
765 o ho_term_from_typ format type_enc
767 fun mangled_const_name format type_enc T_args (s, s') =
769 val ty_args = T_args |> map_filter (ho_term_for_type_arg format type_enc)
770 fun type_suffix f g =
771 fold_rev (curry (op ^) o g o prefix mangled_type_sep
772 o generic_mangled_type_name f) ty_args ""
773 in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
775 val parse_mangled_ident =
776 Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
778 fun parse_mangled_type x =
780 -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
782 and parse_mangled_types x =
783 (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
785 fun unmangled_type s =
786 s |> suffix ")" |> raw_explode
787 |> Scan.finite Symbol.stopper
788 (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
789 quote s)) parse_mangled_type))
792 val unmangled_const_name = space_explode mangled_type_sep #> hd
793 fun unmangled_const s =
794 let val ss = space_explode mangled_type_sep s in
795 (hd ss, map unmangled_type (tl ss))
798 fun introduce_proxies type_enc =
800 fun intro top_level (CombApp (tm1, tm2)) =
801 CombApp (intro top_level tm1, intro false tm2)
802 | intro top_level (CombConst (name as (s, _), T, T_args)) =
803 (case proxify_const s of
805 if top_level orelse is_type_enc_higher_order type_enc then
806 case (top_level, s) of
807 (_, "c_False") => (`I tptp_false, [])
808 | (_, "c_True") => (`I tptp_true, [])
809 | (false, "c_Not") => (`I tptp_not, [])
810 | (false, "c_conj") => (`I tptp_and, [])
811 | (false, "c_disj") => (`I tptp_or, [])
812 | (false, "c_implies") => (`I tptp_implies, [])
814 if is_tptp_equal s then (`I tptp_equal, [])
815 else (proxy_base |>> prefix const_prefix, T_args)
818 (proxy_base |>> prefix const_prefix, T_args)
819 | NONE => (name, T_args))
820 |> (fn (name, T_args) => CombConst (name, T, T_args))
824 fun combformula_from_prop thy type_enc eq_as_iff =
826 fun do_term bs t atomic_types =
827 combterm_from_term thy bs (Envir.eta_contract t)
828 |>> (introduce_proxies type_enc #> AAtom)
829 ||> union (op =) atomic_types
830 fun do_quant bs q s T t' =
831 let val s = singleton (Name.variant_list (map fst bs)) s in
832 do_formula ((s, T) :: bs) t'
833 #>> mk_aquant q [(`make_bound_var s, SOME T)]
835 and do_conn bs c t1 t2 =
836 do_formula bs t1 ##>> do_formula bs t2 #>> uncurry (mk_aconn c)
837 and do_formula bs t =
839 @{const Trueprop} $ t1 => do_formula bs t1
840 | @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
841 | Const (@{const_name All}, _) $ Abs (s, T, t') =>
842 do_quant bs AForall s T t'
843 | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
844 do_quant bs AExists s T t'
845 | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
846 | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
847 | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
848 | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
849 if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
853 fun presimplify_term _ [] t = t
854 | presimplify_term ctxt presimp_consts t =
855 t |> exists_Const (member (op =) presimp_consts o fst) t
856 ? (Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
857 #> Meson.presimplify ctxt
860 fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
861 fun conceal_bounds Ts t =
862 subst_bounds (map (Free o apfst concealed_bound_name)
863 (0 upto length Ts - 1 ~~ Ts), t)
864 fun reveal_bounds Ts =
865 subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
866 (0 upto length Ts - 1 ~~ Ts))
868 fun is_fun_equality (@{const_name HOL.eq},
869 Type (_, [Type (@{type_name fun}, _), _])) = true
870 | is_fun_equality _ = false
872 fun extensionalize_term ctxt t =
873 if exists_Const is_fun_equality t then
874 let val thy = Proof_Context.theory_of ctxt in
875 t |> cterm_of thy |> Meson.extensionalize_conv ctxt
876 |> prop_of |> Logic.dest_equals |> snd
881 fun introduce_combinators_in_term ctxt kind t =
882 let val thy = Proof_Context.theory_of ctxt in
883 if Meson.is_fol_term thy t then
889 @{const Not} $ t1 => @{const Not} $ aux Ts t1
890 | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
891 t0 $ Abs (s, T, aux (T :: Ts) t')
892 | (t0 as Const (@{const_name All}, _)) $ t1 =>
893 aux Ts (t0 $ eta_expand Ts t1 1)
894 | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
895 t0 $ Abs (s, T, aux (T :: Ts) t')
896 | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
897 aux Ts (t0 $ eta_expand Ts t1 1)
898 | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
899 | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
900 | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
901 | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
903 t0 $ aux Ts t1 $ aux Ts t2
904 | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
907 t |> conceal_bounds Ts
908 |> Envir.eta_contract
910 |> Meson_Clausify.introduce_combinators_in_cterm
911 |> prop_of |> Logic.dest_equals |> snd
913 val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
914 in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
916 (* A type variable of sort "{}" will make abstraction fail. *)
917 if kind = Conjecture then HOLogic.false_const
918 else HOLogic.true_const
921 (* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
922 same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
925 fun aux (t $ u) = aux t $ aux u
926 | aux (Abs (s, T, t)) = Abs (s, T, aux t)
927 | aux (Var ((s, i), T)) =
928 Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
930 in t |> exists_subterm is_Var t ? aux end
932 fun preprocess_prop ctxt presimp_consts kind t =
934 val thy = Proof_Context.theory_of ctxt
935 val t = t |> Envir.beta_eta_contract
936 |> transform_elim_prop
937 |> Object_Logic.atomize_term thy
938 val need_trueprop = (fastype_of t = @{typ bool})
940 t |> need_trueprop ? HOLogic.mk_Trueprop
941 |> Raw_Simplifier.rewrite_term thy (Meson.unfold_set_const_simps ctxt) []
942 |> extensionalize_term ctxt
943 |> presimplify_term ctxt presimp_consts
944 |> perhaps (try (HOLogic.dest_Trueprop))
945 |> introduce_combinators_in_term ctxt kind
948 (* making fact and conjecture formulas *)
949 fun make_formula thy type_enc eq_as_iff name loc kind t =
951 val (combformula, atomic_types) =
952 combformula_from_prop thy type_enc eq_as_iff t []
954 {name = name, locality = loc, kind = kind, combformula = combformula,
955 atomic_types = atomic_types}
958 fun make_fact ctxt format type_enc eq_as_iff preproc presimp_consts
960 let val thy = Proof_Context.theory_of ctxt in
961 case t |> preproc ? preprocess_prop ctxt presimp_consts Axiom
962 |> make_formula thy type_enc (eq_as_iff andalso format <> CNF) name
964 formula as {combformula = AAtom (CombConst ((s, _), _, _)), ...} =>
965 if s = tptp_true then NONE else SOME formula
966 | formula => SOME formula
969 fun make_conjecture ctxt format prem_kind type_enc preproc presimp_consts ts =
971 val thy = Proof_Context.theory_of ctxt
972 val last = length ts - 1
974 map2 (fn j => fn t =>
976 val (kind, maybe_negate) =
981 if prem_kind = Conjecture then update_combformula mk_anot
985 (preprocess_prop ctxt presimp_consts kind #> freeze_term)
986 |> make_formula thy type_enc (format <> CNF) (string_of_int j)
993 (** Finite and infinite type inference **)
995 fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
996 | deep_freeze_atyp T = T
997 val deep_freeze_type = map_atyps deep_freeze_atyp
999 (* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
1000 dangerous because their "exhaust" properties can easily lead to unsound ATP
1001 proofs. On the other hand, all HOL infinite types can be given the same
1002 models in first-order logic (via Löwenheim-Skolem). *)
1004 fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
1005 exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
1006 | should_encode_type _ _ All_Types _ = true
1007 | should_encode_type ctxt _ Fin_Nonmono_Types T =
1008 is_type_surely_finite ctxt false T
1009 | should_encode_type _ _ _ _ = false
1011 fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
1012 should_predicate_on_var T =
1013 (heaviness = Heavyweight orelse should_predicate_on_var ()) andalso
1014 should_encode_type ctxt nonmono_Ts level T
1015 | should_predicate_on_type _ _ _ _ _ = false
1017 fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
1018 String.isPrefix bound_var_prefix s
1019 | is_var_or_bound_var (CombVar _) = true
1020 | is_var_or_bound_var _ = false
1023 Top_Level of bool option |
1024 Eq_Arg of bool option |
1027 fun should_tag_with_type _ _ _ (Top_Level _) _ _ = false
1028 | should_tag_with_type ctxt nonmono_Ts (Tags (poly, level, heaviness)) site
1031 Heavyweight => should_encode_type ctxt nonmono_Ts level T
1033 case (site, is_var_or_bound_var u) of
1034 (Eq_Arg pos, true) =>
1035 (* The first disjunct prevents a subtle soundness issue explained in
1036 Blanchette's Ph.D. thesis. See also
1037 "formula_lines_for_lightweight_tags_sym_decl". *)
1038 (pos <> SOME false andalso poly = Polymorphic andalso
1039 level <> All_Types andalso heaviness = Lightweight andalso
1040 exists (fn T' => type_instance ctxt (T', T)) nonmono_Ts) orelse
1041 should_encode_type ctxt nonmono_Ts level T
1043 | should_tag_with_type _ _ _ _ _ _ = false
1045 fun homogenized_type ctxt nonmono_Ts level =
1047 val should_encode = should_encode_type ctxt nonmono_Ts level
1048 fun homo 0 T = if should_encode T then T else homo_infinite_type
1049 | homo ary (Type (@{type_name fun}, [T1, T2])) =
1050 homo 0 T1 --> homo (ary - 1) T2
1051 | homo _ _ = raise Fail "expected function type"
1054 (** "hBOOL" and "hAPP" **)
1057 {pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
1059 fun add_combterm_syms_to_table ctxt explicit_apply =
1061 fun consider_var_arity const_T var_T max_ary =
1064 if ary = max_ary orelse type_instance ctxt (var_T, T) orelse
1065 type_instance ctxt (T, var_T) then
1068 iter (ary + 1) (range_type T)
1069 in iter 0 const_T end
1070 fun add_var_or_bound_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1071 if explicit_apply = NONE andalso
1072 (can dest_funT T orelse T = @{typ bool}) then
1074 val bool_vars' = bool_vars orelse body_type T = @{typ bool}
1075 fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
1076 {pred_sym = pred_sym andalso not bool_vars',
1077 min_ary = fold (fn T' => consider_var_arity T' T) types min_ary,
1078 max_ary = max_ary, types = types}
1080 fun_var_Ts |> can dest_funT T ? insert_type ctxt I T
1082 if bool_vars' = bool_vars andalso
1083 pointer_eq (fun_var_Ts', fun_var_Ts) then
1086 ((bool_vars', fun_var_Ts'), Symtab.map (K repair_min_arity) sym_tab)
1090 fun add top_level tm (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1091 let val (head, args) = strip_combterm_comb tm in
1093 CombConst ((s, _), T, _) =>
1094 if String.isPrefix bound_var_prefix s then
1095 add_var_or_bound_var T accum
1097 let val ary = length args in
1098 ((bool_vars, fun_var_Ts),
1099 case Symtab.lookup sym_tab s of
1100 SOME {pred_sym, min_ary, max_ary, types} =>
1103 pred_sym andalso top_level andalso not bool_vars
1104 val types' = types |> insert_type ctxt I T
1106 if is_some explicit_apply orelse
1107 pointer_eq (types', types) then
1110 fold (consider_var_arity T) fun_var_Ts min_ary
1112 Symtab.update (s, {pred_sym = pred_sym,
1113 min_ary = Int.min (ary, min_ary),
1114 max_ary = Int.max (ary, max_ary),
1120 val pred_sym = top_level andalso not bool_vars
1122 case explicit_apply of
1125 | NONE => fold (consider_var_arity T) fun_var_Ts ary
1127 Symtab.update_new (s, {pred_sym = pred_sym,
1128 min_ary = min_ary, max_ary = ary,
1133 | CombVar (_, T) => add_var_or_bound_var T accum
1135 |> fold (add false) args
1138 fun add_fact_syms_to_table ctxt explicit_apply =
1139 fact_lift (formula_fold NONE
1140 (K (add_combterm_syms_to_table ctxt explicit_apply)))
1142 val default_sym_tab_entries : (string * sym_info) list =
1143 (prefixed_predicator_name,
1144 {pred_sym = true, min_ary = 1, max_ary = 1, types = []}) ::
1145 ([tptp_false, tptp_true]
1146 |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []})) @
1147 ([tptp_equal, tptp_old_equal]
1148 |> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = []}))
1150 fun sym_table_for_facts ctxt explicit_apply facts =
1151 ((false, []), Symtab.empty)
1152 |> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
1153 |> fold Symtab.update default_sym_tab_entries
1155 fun min_arity_of sym_tab s =
1156 case Symtab.lookup sym_tab s of
1157 SOME ({min_ary, ...} : sym_info) => min_ary
1159 case strip_prefix_and_unascii const_prefix s of
1161 let val s = s |> unmangled_const_name |> invert_const in
1162 if s = predicator_name then 1
1163 else if s = app_op_name then 2
1164 else if s = type_pred_name then 1
1169 (* True if the constant ever appears outside of the top-level position in
1170 literals, or if it appears with different arities (e.g., because of different
1171 type instantiations). If false, the constant always receives all of its
1172 arguments and is used as a predicate. *)
1173 fun is_pred_sym sym_tab s =
1174 case Symtab.lookup sym_tab s of
1175 SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
1176 pred_sym andalso min_ary = max_ary
1179 val predicator_combconst =
1180 CombConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
1181 fun predicator tm = CombApp (predicator_combconst, tm)
1183 fun introduce_predicators_in_combterm sym_tab tm =
1184 case strip_combterm_comb tm of
1185 (CombConst ((s, _), _, _), _) =>
1186 if is_pred_sym sym_tab s then tm else predicator tm
1187 | _ => predicator tm
1189 fun list_app head args = fold (curry (CombApp o swap)) args head
1191 val app_op = `make_fixed_const app_op_name
1193 fun explicit_app arg head =
1195 val head_T = combtyp_of head
1196 val (arg_T, res_T) = dest_funT head_T
1198 CombConst (app_op, head_T --> head_T, [arg_T, res_T])
1199 in list_app explicit_app [head, arg] end
1200 fun list_explicit_app head args = fold explicit_app args head
1202 fun introduce_explicit_apps_in_combterm sym_tab =
1205 case strip_combterm_comb tm of
1206 (head as CombConst ((s, _), _, _), args) =>
1208 |> chop (min_arity_of sym_tab s)
1210 |-> list_explicit_app
1211 | (head, args) => list_explicit_app head (map aux args)
1214 fun chop_fun 0 T = ([], T)
1215 | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
1216 chop_fun (n - 1) ran_T |>> cons dom_T
1217 | chop_fun _ _ = raise Fail "unexpected non-function"
1219 fun filter_type_args _ _ _ [] = []
1220 | filter_type_args thy s arity T_args =
1222 (* will throw "TYPE" for pseudo-constants *)
1223 val U = if s = app_op_name then
1224 @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
1226 s |> Sign.the_const_type thy
1228 case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
1231 let val U_args = (s, U) |> Sign.const_typargs thy in
1233 |> map (fn (U, T) =>
1234 if member (op =) res_U_vars (dest_TVar U) then T
1238 handle TYPE _ => T_args
1240 fun enforce_type_arg_policy_in_combterm ctxt format type_enc =
1242 val thy = Proof_Context.theory_of ctxt
1243 fun aux arity (CombApp (tm1, tm2)) =
1244 CombApp (aux (arity + 1) tm1, aux 0 tm2)
1245 | aux arity (CombConst (name as (s, _), T, T_args)) =
1246 (case strip_prefix_and_unascii const_prefix s of
1247 NONE => (name, T_args)
1250 val s'' = invert_const s''
1251 fun filtered_T_args false = T_args
1252 | filtered_T_args true = filter_type_args thy s'' arity T_args
1254 case type_arg_policy type_enc s'' of
1255 Explicit_Type_Args drop_args =>
1256 (name, filtered_T_args drop_args)
1257 | Mangled_Type_Args drop_args =>
1258 (mangled_const_name format type_enc (filtered_T_args drop_args)
1260 | No_Type_Args => (name, [])
1262 |> (fn (name, T_args) => CombConst (name, T, T_args))
1266 fun repair_combterm ctxt format type_enc sym_tab =
1267 not (is_type_enc_higher_order type_enc)
1268 ? (introduce_explicit_apps_in_combterm sym_tab
1269 #> introduce_predicators_in_combterm sym_tab)
1270 #> enforce_type_arg_policy_in_combterm ctxt format type_enc
1271 fun repair_fact ctxt format type_enc sym_tab =
1272 update_combformula (formula_map
1273 (repair_combterm ctxt format type_enc sym_tab))
1275 (** Helper facts **)
1277 (* The Boolean indicates that a fairly sound type encoding is needed. *)
1279 [(("COMBI", false), @{thms Meson.COMBI_def}),
1280 (("COMBK", false), @{thms Meson.COMBK_def}),
1281 (("COMBB", false), @{thms Meson.COMBB_def}),
1282 (("COMBC", false), @{thms Meson.COMBC_def}),
1283 (("COMBS", false), @{thms Meson.COMBS_def}),
1285 (* This is a lie: Higher-order equality doesn't need a sound type encoding.
1286 However, this is done so for backward compatibility: Including the
1287 equality helpers by default in Metis breaks a few existing proofs. *)
1288 @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1289 fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1290 (("fFalse", false), [@{lemma "~ fFalse" by (unfold fFalse_def) fast}]),
1291 (("fFalse", true), @{thms True_or_False}),
1292 (("fTrue", false), [@{lemma "fTrue" by (unfold fTrue_def) fast}]),
1293 (("fTrue", true), @{thms True_or_False}),
1295 @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1296 fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1298 @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
1299 by (unfold fconj_def) fast+}),
1301 @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
1302 by (unfold fdisj_def) fast+}),
1303 (("fimplies", false),
1304 @{lemma "P | fimplies P Q" "~ Q | fimplies P Q" "~ fimplies P Q | ~ P | Q"
1305 by (unfold fimplies_def) fast+}),
1306 (("If", true), @{thms if_True if_False True_or_False})]
1307 |> map (apsnd (map zero_var_indexes))
1309 val type_tag = `make_fixed_const type_tag_name
1311 fun type_tag_idempotence_fact () =
1313 fun var s = ATerm (`I s, [])
1314 fun tag tm = ATerm (type_tag, [var "T", tm])
1315 val tagged_a = tag (var "A")
1317 Formula (type_tag_idempotence_helper_name, Axiom,
1318 AAtom (ATerm (`I tptp_equal, [tag tagged_a, tagged_a]))
1319 |> close_formula_universally, simp_info, NONE)
1322 fun should_specialize_helper type_enc t =
1323 polymorphism_of_type_enc type_enc = Mangled_Monomorphic andalso
1324 level_of_type_enc type_enc <> No_Types andalso
1325 not (null (Term.hidden_polymorphism t))
1327 fun helper_facts_for_sym ctxt format type_enc (s, {types, ...} : sym_info) =
1328 case strip_prefix_and_unascii const_prefix s of
1331 val thy = Proof_Context.theory_of ctxt
1332 val unmangled_s = mangled_s |> unmangled_const_name
1333 fun dub needs_fairly_sound j k =
1334 (unmangled_s ^ "_" ^ string_of_int j ^ "_" ^ string_of_int k ^
1335 (if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^
1336 (if needs_fairly_sound then typed_helper_suffix
1337 else untyped_helper_suffix),
1339 fun dub_and_inst needs_fairly_sound (th, j) =
1340 let val t = prop_of th in
1341 if should_specialize_helper type_enc t then
1342 map (fn T => specialize_type thy (invert_const unmangled_s, T) t)
1347 |> map (fn (k, t) => (dub needs_fairly_sound j k, t)) o tag_list 1
1349 map_filter (make_fact ctxt format type_enc false false [])
1350 val fairly_sound = is_type_enc_fairly_sound type_enc
1353 |> maps (fn ((helper_s, needs_fairly_sound), ths) =>
1354 if helper_s <> unmangled_s orelse
1355 (needs_fairly_sound andalso not fairly_sound) then
1358 ths ~~ (1 upto length ths)
1359 |> maps (dub_and_inst needs_fairly_sound)
1363 fun helper_facts_for_sym_table ctxt format type_enc sym_tab =
1364 Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_enc) sym_tab
1367 (***************************************************************)
1368 (* Type Classes Present in the Axiom or Conjecture Clauses *)
1369 (***************************************************************)
1371 fun set_insert (x, s) = Symtab.update (x, ()) s
1373 fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
1375 (* Remove this trivial type class (FIXME: similar code elsewhere) *)
1376 fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
1378 fun classes_of_terms get_Ts =
1379 map (map snd o get_Ts)
1380 #> List.foldl add_classes Symtab.empty
1381 #> delete_type #> Symtab.keys
1383 val tfree_classes_of_terms = classes_of_terms OldTerm.term_tfrees
1384 val tvar_classes_of_terms = classes_of_terms OldTerm.term_tvars
1386 fun fold_type_constrs f (Type (s, Ts)) x =
1387 fold (fold_type_constrs f) Ts (f (s, x))
1388 | fold_type_constrs _ _ x = x
1390 (*Type constructors used to instantiate overloaded constants are the only ones needed.*)
1391 fun add_type_constrs_in_term thy =
1393 fun add (Const (@{const_name Meson.skolem}, _) $ _) = I
1394 | add (t $ u) = add t #> add u
1395 | add (Const (x as (s, _))) =
1396 if String.isPrefix skolem_const_prefix s then I
1397 else x |> Sign.const_typargs thy |> fold (fold_type_constrs set_insert)
1398 | add (Abs (_, _, u)) = add u
1402 fun type_constrs_of_terms thy ts =
1403 Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty)
1405 fun translate_formulas ctxt format prem_kind type_enc preproc hyp_ts concl_t
1408 val thy = Proof_Context.theory_of ctxt
1409 val fact_ts = facts |> map snd
1410 val presimp_consts = Meson.presimplified_consts ctxt
1411 val make_fact = make_fact ctxt format type_enc true preproc presimp_consts
1412 val (facts, fact_names) =
1413 facts |> map (fn (name, t) => (name, t) |> make_fact |> rpair name)
1414 |> map_filter (try (apfst the))
1416 (* Remove existing facts from the conjecture, as this can dramatically
1417 boost an ATP's performance (for some reason). *)
1420 |> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t)
1421 val goal_t = Logic.list_implies (hyp_ts, concl_t)
1422 val all_ts = goal_t :: fact_ts
1423 val subs = tfree_classes_of_terms all_ts
1424 val supers = tvar_classes_of_terms all_ts
1425 val tycons = type_constrs_of_terms thy all_ts
1428 |> make_conjecture ctxt format prem_kind type_enc preproc presimp_consts
1429 val (supers', arity_clauses) =
1430 if level_of_type_enc type_enc = No_Types then ([], [])
1431 else make_arity_clauses thy tycons supers
1432 val class_rel_clauses = make_class_rel_clauses thy subs supers'
1434 (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
1437 fun fo_literal_from_type_literal (TyLitVar (class, name)) =
1438 (true, ATerm (class, [ATerm (name, [])]))
1439 | fo_literal_from_type_literal (TyLitFree (class, name)) =
1440 (true, ATerm (class, [ATerm (name, [])]))
1442 fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
1444 val type_pred = `make_fixed_const type_pred_name
1446 fun type_pred_combterm ctxt format type_enc T tm =
1447 CombApp (CombConst (type_pred, T --> @{typ bool}, [T])
1448 |> enforce_type_arg_policy_in_combterm ctxt format type_enc, tm)
1450 fun is_var_positively_naked_in_term _ (SOME false) _ accum = accum
1451 | is_var_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
1452 accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
1453 | is_var_positively_naked_in_term name _ _ _ = true
1454 fun should_predicate_on_var_in_formula pos phi (SOME true) name =
1455 formula_fold pos (is_var_positively_naked_in_term name) phi false
1456 | should_predicate_on_var_in_formula _ _ _ _ = true
1458 fun mk_const_aterm format type_enc x T_args args =
1459 ATerm (x, map_filter (ho_term_for_type_arg format type_enc) T_args @ args)
1461 fun tag_with_type ctxt format nonmono_Ts type_enc pos T tm =
1462 CombConst (type_tag, T --> T, [T])
1463 |> enforce_type_arg_policy_in_combterm ctxt format type_enc
1464 |> term_from_combterm ctxt format nonmono_Ts type_enc (Top_Level pos)
1465 |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
1466 and term_from_combterm ctxt format nonmono_Ts type_enc =
1470 val (head, args) = strip_combterm_comb u
1471 val (x as (s, _), T_args) =
1473 CombConst (name, _, T_args) => (name, T_args)
1474 | CombVar (name, _) => (name, [])
1475 | CombApp _ => raise Fail "impossible \"CombApp\""
1476 val (pos, arg_site) =
1479 (pos, if is_tptp_equal s then Eq_Arg pos else Elsewhere)
1480 | Eq_Arg pos => (pos, Elsewhere)
1481 | Elsewhere => (NONE, Elsewhere)
1482 val t = mk_const_aterm format type_enc x T_args
1483 (map (aux arg_site) args)
1484 val T = combtyp_of u
1486 t |> (if should_tag_with_type ctxt nonmono_Ts type_enc site u T then
1487 tag_with_type ctxt format nonmono_Ts type_enc pos T
1492 and formula_from_combformula ctxt format nonmono_Ts type_enc
1493 should_predicate_on_var =
1496 term_from_combterm ctxt format nonmono_Ts type_enc (Top_Level pos)
1499 Simple_Types (_, level) =>
1500 homogenized_type ctxt nonmono_Ts level 0
1501 #> mangled_type format type_enc false 0 #> SOME
1503 fun do_out_of_bound_type pos phi universal (name, T) =
1504 if should_predicate_on_type ctxt nonmono_Ts type_enc
1505 (fn () => should_predicate_on_var pos phi universal name) T then
1507 |> type_pred_combterm ctxt format type_enc T
1508 |> do_term pos |> AAtom |> SOME
1511 fun do_formula pos (AQuant (q, xs, phi)) =
1513 val phi = phi |> do_formula pos
1514 val universal = Option.map (q = AExists ? not) pos
1516 AQuant (q, xs |> map (apsnd (fn NONE => NONE
1517 | SOME T => do_bound_type T)),
1518 (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
1520 (fn (_, NONE) => NONE
1522 do_out_of_bound_type pos phi universal (s, T))
1526 | do_formula pos (AConn conn) = aconn_map pos do_formula conn
1527 | do_formula pos (AAtom tm) = AAtom (do_term pos tm)
1530 fun bound_tvars type_enc Ts =
1531 mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
1532 (type_literals_for_types type_enc add_sorts_on_tvar Ts))
1534 (* Each fact is given a unique fact number to avoid name clashes (e.g., because
1535 of monomorphization). The TPTP explicitly forbids name clashes, and some of
1536 the remote provers might care. *)
1537 fun formula_line_for_fact ctxt format prefix encode freshen pos nonmono_Ts
1538 type_enc (j, {name, locality, kind, combformula, atomic_types}) =
1539 (prefix ^ (if freshen then string_of_int j ^ "_" else "") ^ encode name,
1542 |> close_combformula_universally
1543 |> formula_from_combformula ctxt format nonmono_Ts type_enc
1544 should_predicate_on_var_in_formula
1545 (if pos then SOME true else NONE)
1546 |> bound_tvars type_enc atomic_types
1547 |> close_formula_universally,
1556 fun formula_line_for_class_rel_clause ({name, subclass, superclass, ...}
1557 : class_rel_clause) =
1558 let val ty_arg = ATerm (`I "T", []) in
1559 Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
1560 AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
1561 AAtom (ATerm (superclass, [ty_arg]))])
1562 |> close_formula_universally, intro_info, NONE)
1565 fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
1566 (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
1567 | fo_literal_from_arity_literal (TVarLit (c, sort)) =
1568 (false, ATerm (c, [ATerm (sort, [])]))
1570 fun formula_line_for_arity_clause ({name, prem_lits, concl_lits, ...}
1572 Formula (arity_clause_prefix ^ name, Axiom,
1573 mk_ahorn (map (formula_from_fo_literal o apfst not
1574 o fo_literal_from_arity_literal) prem_lits)
1575 (formula_from_fo_literal
1576 (fo_literal_from_arity_literal concl_lits))
1577 |> close_formula_universally, intro_info, NONE)
1579 fun formula_line_for_conjecture ctxt format nonmono_Ts type_enc
1580 ({name, kind, combformula, atomic_types, ...} : translated_formula) =
1581 Formula (conjecture_prefix ^ name, kind,
1582 formula_from_combformula ctxt format nonmono_Ts type_enc
1583 should_predicate_on_var_in_formula (SOME false)
1584 (close_combformula_universally combformula)
1585 |> bound_tvars type_enc atomic_types
1586 |> close_formula_universally, NONE, NONE)
1588 fun free_type_literals type_enc ({atomic_types, ...} : translated_formula) =
1589 atomic_types |> type_literals_for_types type_enc add_sorts_on_tfree
1590 |> map fo_literal_from_type_literal
1592 fun formula_line_for_free_type j lit =
1593 Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis,
1594 formula_from_fo_literal lit, NONE, NONE)
1595 fun formula_lines_for_free_types type_enc facts =
1597 val litss = map (free_type_literals type_enc) facts
1598 val lits = fold (union (op =)) litss []
1599 in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
1601 (** Symbol declarations **)
1603 fun should_declare_sym type_enc pred_sym s =
1604 is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
1606 Simple_Types _ => true
1607 | Tags (_, _, Lightweight) => true
1608 | _ => not pred_sym)
1610 fun sym_decl_table_for_facts ctxt type_enc repaired_sym_tab (conjs, facts) =
1612 fun add_combterm in_conj tm =
1613 let val (head, args) = strip_combterm_comb tm in
1615 CombConst ((s, s'), T, T_args) =>
1616 let val pred_sym = is_pred_sym repaired_sym_tab s in
1617 if should_declare_sym type_enc pred_sym s then
1618 Symtab.map_default (s, [])
1619 (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
1625 #> fold (add_combterm in_conj) args
1627 fun add_fact in_conj =
1628 fact_lift (formula_fold NONE (K (add_combterm in_conj)))
1631 |> is_type_enc_fairly_sound type_enc
1632 ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
1635 (* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
1636 out with monotonicity" paper presented at CADE 2011. *)
1637 fun add_combterm_nonmonotonic_types _ _ _ _ (SOME false) _ = I
1638 | add_combterm_nonmonotonic_types ctxt level sound locality _
1639 (CombApp (CombApp (CombConst ((s, _), Type (_, [T, _]), _), tm1),
1641 (is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
1643 Noninf_Nonmono_Types =>
1644 not (is_locality_global locality) orelse
1645 not (is_type_surely_infinite ctxt sound T)
1646 | Fin_Nonmono_Types => is_type_surely_finite ctxt false T
1647 | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
1648 | add_combterm_nonmonotonic_types _ _ _ _ _ _ = I
1649 fun add_fact_nonmonotonic_types ctxt level sound
1650 ({kind, locality, combformula, ...} : translated_formula) =
1651 formula_fold (SOME (kind <> Conjecture))
1652 (add_combterm_nonmonotonic_types ctxt level sound locality)
1654 fun nonmonotonic_types_for_facts ctxt type_enc sound facts =
1655 let val level = level_of_type_enc type_enc in
1656 if level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types then
1657 [] |> fold (add_fact_nonmonotonic_types ctxt level sound) facts
1658 (* We must add "bool" in case the helper "True_or_False" is added
1659 later. In addition, several places in the code rely on the list of
1660 nonmonotonic types not being empty. *)
1661 |> insert_type ctxt I @{typ bool}
1666 fun decl_line_for_sym ctxt format nonmono_Ts type_enc s
1667 (s', T_args, T, pred_sym, ary, _) =
1669 val (T_arg_Ts, level) =
1671 Simple_Types (_, level) => ([], level)
1672 | _ => (replicate (length T_args) homo_infinite_type, No_Types)
1674 Decl (sym_decl_prefix ^ s, (s, s'),
1675 (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
1676 |> mangled_type format type_enc pred_sym (length T_arg_Ts + ary))
1679 fun formula_line_for_preds_sym_decl ctxt format conj_sym_kind nonmono_Ts
1680 poly_nonmono_Ts type_enc n s j (s', T_args, T, _, ary, in_conj) =
1682 val (kind, maybe_negate) =
1683 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1685 val (arg_Ts, res_T) = chop_fun ary T
1686 val num_args = length arg_Ts
1688 1 upto num_args |> map (`I o make_bound_var o string_of_int)
1690 bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
1691 val sym_needs_arg_types = n > 1 orelse exists (curry (op =) dummyT) T_args
1692 fun should_keep_arg_type T =
1693 sym_needs_arg_types orelse
1694 not (should_predicate_on_type ctxt nonmono_Ts type_enc (K false) T)
1696 arg_Ts |> map (fn T => if should_keep_arg_type T then SOME T else NONE)
1698 Formula (preds_sym_formula_prefix ^ s ^
1699 (if n > 1 then "_" ^ string_of_int j else ""), kind,
1700 CombConst ((s, s'), T, T_args)
1701 |> fold (curry (CombApp o swap)) bounds
1702 |> type_pred_combterm ctxt format type_enc res_T
1703 |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
1704 |> formula_from_combformula ctxt format poly_nonmono_Ts type_enc
1705 (K (K (K (K true)))) (SOME true)
1706 |> n > 1 ? bound_tvars type_enc (atyps_of T)
1707 |> close_formula_universally
1712 fun formula_lines_for_lightweight_tags_sym_decl ctxt format conj_sym_kind
1713 poly_nonmono_Ts type_enc n s
1714 (j, (s', T_args, T, pred_sym, ary, in_conj)) =
1717 lightweight_tags_sym_formula_prefix ^ s ^
1718 (if n > 1 then "_" ^ string_of_int j else "")
1719 val (kind, maybe_negate) =
1720 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1722 val (arg_Ts, res_T) = chop_fun ary T
1724 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
1725 val bounds = bound_names |> map (fn name => ATerm (name, []))
1726 val cst = mk_const_aterm format type_enc (s, s') T_args
1727 val atomic_Ts = atyps_of T
1729 (if pred_sym then AConn (AIff, map AAtom tms)
1730 else AAtom (ATerm (`I tptp_equal, tms)))
1731 |> bound_tvars type_enc atomic_Ts
1732 |> close_formula_universally
1734 (* See also "should_tag_with_type". *)
1735 fun should_encode T =
1736 should_encode_type ctxt poly_nonmono_Ts All_Types T orelse
1738 Tags (Polymorphic, level, Lightweight) =>
1739 level <> All_Types andalso Monomorph.typ_has_tvars T
1741 val tag_with = tag_with_type ctxt format poly_nonmono_Ts type_enc NONE
1742 val add_formula_for_res =
1743 if should_encode res_T then
1744 cons (Formula (ident_base ^ "_res", kind,
1745 eq [tag_with res_T (cst bounds), cst bounds],
1749 fun add_formula_for_arg k =
1750 let val arg_T = nth arg_Ts k in
1751 if should_encode arg_T then
1752 case chop k bounds of
1753 (bounds1, bound :: bounds2) =>
1754 cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
1755 eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
1758 | _ => raise Fail "expected nonempty tail"
1763 [] |> not pred_sym ? add_formula_for_res
1764 |> fold add_formula_for_arg (ary - 1 downto 0)
1767 fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
1769 fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts
1770 poly_nonmono_Ts type_enc (s, decls) =
1773 decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_enc s)
1778 decl :: (decls' as _ :: _) =>
1779 let val T = result_type_of_decl decl in
1780 if forall (curry (type_instance ctxt o swap) T
1781 o result_type_of_decl) decls' then
1787 val n = length decls
1789 decls |> filter (should_predicate_on_type ctxt poly_nonmono_Ts type_enc
1791 o result_type_of_decl)
1793 (0 upto length decls - 1, decls)
1794 |-> map2 (formula_line_for_preds_sym_decl ctxt format conj_sym_kind
1795 nonmono_Ts poly_nonmono_Ts type_enc n s)
1797 | Tags (_, _, heaviness) =>
1801 let val n = length decls in
1802 (0 upto n - 1 ~~ decls)
1803 |> maps (formula_lines_for_lightweight_tags_sym_decl ctxt format
1804 conj_sym_kind poly_nonmono_Ts type_enc n s)
1807 fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1808 poly_nonmono_Ts type_enc sym_decl_tab =
1813 |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
1814 nonmono_Ts poly_nonmono_Ts type_enc)
1816 fun needs_type_tag_idempotence (Tags (poly, level, heaviness)) =
1817 poly <> Mangled_Monomorphic andalso
1818 ((level = All_Types andalso heaviness = Lightweight) orelse
1819 level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types)
1820 | needs_type_tag_idempotence _ = false
1822 fun offset_of_heading_in_problem _ [] j = j
1823 | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
1824 if heading = needle then j
1825 else offset_of_heading_in_problem needle problem (j + length lines)
1827 val implicit_declsN = "Should-be-implicit typings"
1828 val explicit_declsN = "Explicit typings"
1829 val factsN = "Relevant facts"
1830 val class_relsN = "Class relationships"
1831 val aritiesN = "Arities"
1832 val helpersN = "Helper facts"
1833 val conjsN = "Conjectures"
1834 val free_typesN = "Type variables"
1836 val explicit_apply = NONE (* for experimental purposes *)
1838 fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_enc sound
1839 exporter readable_names preproc hyp_ts concl_t facts =
1841 val (format, type_enc) = choose_format [format] type_enc
1842 val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
1843 translate_formulas ctxt format prem_kind type_enc preproc hyp_ts concl_t
1845 val sym_tab = conjs @ facts |> sym_table_for_facts ctxt explicit_apply
1847 conjs @ facts |> nonmonotonic_types_for_facts ctxt type_enc sound
1848 val repair = repair_fact ctxt format type_enc sym_tab
1849 val (conjs, facts) = (conjs, facts) |> pairself (map repair)
1850 val repaired_sym_tab =
1851 conjs @ facts |> sym_table_for_facts ctxt (SOME false)
1853 repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_enc
1855 val poly_nonmono_Ts =
1856 if null nonmono_Ts orelse nonmono_Ts = [@{typ bool}] orelse
1857 polymorphism_of_type_enc type_enc <> Polymorphic then
1860 [TVar (("'a", 0), HOLogic.typeS)]
1861 val sym_decl_lines =
1862 (conjs, helpers @ facts)
1863 |> sym_decl_table_for_facts ctxt type_enc repaired_sym_tab
1864 |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1865 poly_nonmono_Ts type_enc
1867 0 upto length helpers - 1 ~~ helpers
1868 |> map (formula_line_for_fact ctxt format helper_prefix I false true
1869 poly_nonmono_Ts type_enc)
1870 |> (if needs_type_tag_idempotence type_enc then
1871 cons (type_tag_idempotence_fact ())
1874 (* Reordering these might confuse the proof reconstruction code or the SPASS
1877 [(explicit_declsN, sym_decl_lines),
1879 map (formula_line_for_fact ctxt format fact_prefix ascii_of
1880 (not exporter) (not exporter) nonmono_Ts
1882 (0 upto length facts - 1 ~~ facts)),
1883 (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
1884 (aritiesN, map formula_line_for_arity_clause arity_clauses),
1885 (helpersN, helper_lines),
1887 map (formula_line_for_conjecture ctxt format nonmono_Ts type_enc)
1889 (free_typesN, formula_lines_for_free_types type_enc (facts @ conjs))]
1893 CNF => ensure_cnf_problem
1894 | CNF_UEQ => filter_cnf_ueq_problem
1896 |> (if is_format_typed format then
1897 declare_undeclared_syms_in_atp_problem type_decl_prefix
1901 val (problem, pool) = problem |> nice_atp_problem readable_names
1902 val helpers_offset = offset_of_heading_in_problem helpersN problem 0
1904 map_filter (fn (j, {name, ...}) =>
1905 if String.isSuffix typed_helper_suffix name then SOME j
1907 ((helpers_offset + 1 upto helpers_offset + length helpers)
1909 fun add_sym_arity (s, {min_ary, ...} : sym_info) =
1911 case strip_prefix_and_unascii const_prefix s of
1912 SOME s => Symtab.insert (op =) (s, min_ary)
1918 case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
1919 offset_of_heading_in_problem conjsN problem 0,
1920 offset_of_heading_in_problem factsN problem 0,
1921 fact_names |> Vector.fromList,
1923 Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
1927 val conj_weight = 0.0
1928 val hyp_weight = 0.1
1929 val fact_min_weight = 0.2
1930 val fact_max_weight = 1.0
1931 val type_info_default_weight = 0.8
1933 fun add_term_weights weight (ATerm (s, tms)) =
1934 is_tptp_user_symbol s ? Symtab.default (s, weight)
1935 #> fold (add_term_weights weight) tms
1936 | add_term_weights weight (AAbs (_, tm)) = add_term_weights weight tm
1937 fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
1938 formula_fold NONE (K (add_term_weights weight)) phi
1939 | add_problem_line_weights _ _ = I
1941 fun add_conjectures_weights [] = I
1942 | add_conjectures_weights conjs =
1943 let val (hyps, conj) = split_last conjs in
1944 add_problem_line_weights conj_weight conj
1945 #> fold (add_problem_line_weights hyp_weight) hyps
1948 fun add_facts_weights facts =
1950 val num_facts = length facts
1952 fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
1953 / Real.fromInt num_facts
1955 map weight_of (0 upto num_facts - 1) ~~ facts
1956 |> fold (uncurry add_problem_line_weights)
1959 (* Weights are from 0.0 (most important) to 1.0 (least important). *)
1960 fun atp_problem_weights problem =
1961 let val get = these o AList.lookup (op =) problem in
1963 |> add_conjectures_weights (get free_typesN @ get conjsN)
1964 |> add_facts_weights (get factsN)
1965 |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
1966 [explicit_declsN, class_relsN, aritiesN]
1968 |> sort (prod_ord Real.compare string_ord o pairself swap)