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 fo_term = 'a ATP_Problem.fo_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 fo_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 Simple_Types (Higher_Order, level)
549 | ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
550 | ("tags", (SOME Polymorphic, _, _)) =>
551 Tags (Polymorphic, level, heaviness)
552 | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
553 | ("args", (SOME poly, All_Types (* naja *), Lightweight)) =>
554 Preds (poly, Const_Arg_Types, Lightweight)
555 | ("erased", (NONE, All_Types (* naja *), Lightweight)) =>
556 Preds (Polymorphic, No_Types, Lightweight)
557 | _ => raise Same.SAME)
558 handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
560 fun is_type_enc_higher_order (Simple_Types (Higher_Order, _)) = true
561 | is_type_enc_higher_order _ = false
563 fun polymorphism_of_type_enc (Simple_Types _) = Mangled_Monomorphic
564 | polymorphism_of_type_enc (Preds (poly, _, _)) = poly
565 | polymorphism_of_type_enc (Tags (poly, _, _)) = poly
567 fun level_of_type_enc (Simple_Types (_, level)) = level
568 | level_of_type_enc (Preds (_, level, _)) = level
569 | level_of_type_enc (Tags (_, level, _)) = level
571 fun heaviness_of_type_enc (Simple_Types _) = Heavyweight
572 | heaviness_of_type_enc (Preds (_, _, heaviness)) = heaviness
573 | heaviness_of_type_enc (Tags (_, _, heaviness)) = heaviness
575 fun is_type_level_virtually_sound level =
576 level = All_Types orelse level = Noninf_Nonmono_Types
577 val is_type_enc_virtually_sound =
578 is_type_level_virtually_sound o level_of_type_enc
580 fun is_type_level_fairly_sound level =
581 is_type_level_virtually_sound level orelse level = Fin_Nonmono_Types
582 val is_type_enc_fairly_sound = is_type_level_fairly_sound o level_of_type_enc
584 fun choose_format formats (Simple_Types (order, level)) =
585 if member (op =) formats THF then
586 (THF, Simple_Types (order, level))
587 else if member (op =) formats TFF then
588 (TFF, Simple_Types (First_Order, level))
590 choose_format formats (Preds (Mangled_Monomorphic, level, Heavyweight))
591 | choose_format formats type_enc =
594 (CNF_UEQ, case type_enc of
596 (if is_type_enc_fairly_sound type_enc then Tags else Preds)
599 | format => (format, type_enc))
601 type translated_formula =
605 combformula : (name, typ, combterm) formula,
606 atomic_types : typ list}
608 fun update_combformula f ({name, locality, kind, combformula, atomic_types}
609 : translated_formula) =
610 {name = name, locality = locality, kind = kind, combformula = f combformula,
611 atomic_types = atomic_types} : translated_formula
613 fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
615 val type_instance = Sign.typ_instance o Proof_Context.theory_of
617 fun insert_type ctxt get_T x xs =
618 let val T = get_T x in
619 if exists (curry (type_instance ctxt) T o get_T) xs then xs
620 else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
623 (* The Booleans indicate whether all type arguments should be kept. *)
624 datatype type_arg_policy =
625 Explicit_Type_Args of bool |
626 Mangled_Type_Args of bool |
629 fun should_drop_arg_type_args (Simple_Types _) =
630 false (* since TFF doesn't support overloading *)
631 | should_drop_arg_type_args type_enc =
632 level_of_type_enc type_enc = All_Types andalso
633 heaviness_of_type_enc type_enc = Heavyweight
635 fun general_type_arg_policy (Tags (_, All_Types, Heavyweight)) = No_Type_Args
636 | general_type_arg_policy type_enc =
637 if level_of_type_enc type_enc = No_Types then
639 else if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
640 Mangled_Type_Args (should_drop_arg_type_args type_enc)
642 Explicit_Type_Args (should_drop_arg_type_args type_enc)
644 fun type_arg_policy type_enc s =
645 if s = @{const_name HOL.eq} orelse
646 (s = app_op_name andalso level_of_type_enc type_enc = Const_Arg_Types) then
648 else if s = type_tag_name then
649 (if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
652 Explicit_Type_Args) false
654 general_type_arg_policy type_enc
656 (*Make literals for sorted type variables*)
657 fun generic_add_sorts_on_type (_, []) = I
658 | generic_add_sorts_on_type ((x, i), s :: ss) =
659 generic_add_sorts_on_type ((x, i), ss)
660 #> (if s = the_single @{sort HOL.type} then
663 insert (op =) (TyLitFree (`make_type_class s, `make_fixed_type_var x))
665 insert (op =) (TyLitVar (`make_type_class s,
666 (make_schematic_type_var (x, i), x))))
667 fun add_sorts_on_tfree (TFree (s, S)) = generic_add_sorts_on_type ((s, ~1), S)
668 | add_sorts_on_tfree _ = I
669 fun add_sorts_on_tvar (TVar z) = generic_add_sorts_on_type z
670 | add_sorts_on_tvar _ = I
672 fun type_literals_for_types type_enc add_sorts_on_typ Ts =
673 [] |> level_of_type_enc type_enc <> No_Types ? fold add_sorts_on_typ Ts
675 fun mk_aconns c phis =
676 let val (phis', phi') = split_last phis in
677 fold_rev (mk_aconn c) phis' phi'
679 fun mk_ahorn [] phi = phi
680 | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
681 fun mk_aquant _ [] phi = phi
682 | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
683 if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
684 | mk_aquant q xs phi = AQuant (q, xs, phi)
686 fun close_universally atom_vars phi =
688 fun formula_vars bounds (AQuant (_, xs, phi)) =
689 formula_vars (map fst xs @ bounds) phi
690 | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
691 | formula_vars bounds (AAtom tm) =
692 union (op =) (atom_vars tm []
693 |> filter_out (member (op =) bounds o fst))
694 in mk_aquant AForall (formula_vars [] phi []) phi end
696 fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
697 | combterm_vars (CombConst _) = I
698 | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
699 fun close_combformula_universally phi = close_universally combterm_vars phi
701 fun term_vars (ATerm (name as (s, _), tms)) =
702 is_tptp_variable s ? insert (op =) (name, NONE) #> fold term_vars tms
703 fun close_formula_universally phi = close_universally term_vars phi
705 val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
706 val homo_infinite_type = Type (homo_infinite_type_name, [])
708 fun fo_term_from_typ format type_enc =
710 fun term (Type (s, Ts)) =
711 ATerm (case (is_type_enc_higher_order type_enc, s) of
712 (true, @{type_name bool}) => `I tptp_bool_type
713 | (true, @{type_name fun}) => `I tptp_fun_type
714 | _ => if s = homo_infinite_type_name andalso
715 (format = TFF orelse format = THF) then
716 `I tptp_individual_type
718 `make_fixed_type_const s,
720 | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
721 | term (TVar ((x as (s, _)), _)) =
722 ATerm ((make_schematic_type_var x, s), [])
725 fun fo_term_for_type_arg format type_enc T =
726 if T = dummyT then NONE else SOME (fo_term_from_typ format type_enc T)
728 (* This shouldn't clash with anything else. *)
729 val mangled_type_sep = "\000"
731 fun generic_mangled_type_name f (ATerm (name, [])) = f name
732 | generic_mangled_type_name f (ATerm (name, tys)) =
733 f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
736 val bool_atype = AType (`I tptp_bool_type)
738 fun make_simple_type s =
739 if s = tptp_bool_type orelse s = tptp_fun_type orelse
740 s = tptp_individual_type then
743 simple_type_prefix ^ ascii_of s
745 fun ho_type_from_fo_term type_enc pred_sym ary =
748 AType ((make_simple_type (generic_mangled_type_name fst ty),
749 generic_mangled_type_name snd ty))
750 fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
751 fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
752 | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
753 fun to_ho (ty as ATerm ((s, _), tys)) =
754 if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
755 in if is_type_enc_higher_order type_enc then to_ho else to_fo ary end
757 fun mangled_type format type_enc pred_sym ary =
758 ho_type_from_fo_term type_enc pred_sym ary
759 o fo_term_from_typ format type_enc
761 fun mangled_const_name format type_enc T_args (s, s') =
763 val ty_args = T_args |> map_filter (fo_term_for_type_arg format type_enc)
764 fun type_suffix f g =
765 fold_rev (curry (op ^) o g o prefix mangled_type_sep
766 o generic_mangled_type_name f) ty_args ""
767 in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
769 val parse_mangled_ident =
770 Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
772 fun parse_mangled_type x =
774 -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
776 and parse_mangled_types x =
777 (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
779 fun unmangled_type s =
780 s |> suffix ")" |> raw_explode
781 |> Scan.finite Symbol.stopper
782 (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
783 quote s)) parse_mangled_type))
786 val unmangled_const_name = space_explode mangled_type_sep #> hd
787 fun unmangled_const s =
788 let val ss = space_explode mangled_type_sep s in
789 (hd ss, map unmangled_type (tl ss))
792 fun introduce_proxies type_enc =
794 fun intro top_level (CombApp (tm1, tm2)) =
795 CombApp (intro top_level tm1, intro false tm2)
796 | intro top_level (CombConst (name as (s, _), T, T_args)) =
797 (case proxify_const s of
799 if top_level orelse is_type_enc_higher_order type_enc then
800 case (top_level, s) of
801 (_, "c_False") => (`I tptp_false, [])
802 | (_, "c_True") => (`I tptp_true, [])
803 | (false, "c_Not") => (`I tptp_not, [])
804 | (false, "c_conj") => (`I tptp_and, [])
805 | (false, "c_disj") => (`I tptp_or, [])
806 | (false, "c_implies") => (`I tptp_implies, [])
808 if is_tptp_equal s then (`I tptp_equal, [])
809 else (proxy_base |>> prefix const_prefix, T_args)
812 (proxy_base |>> prefix const_prefix, T_args)
813 | NONE => (name, T_args))
814 |> (fn (name, T_args) => CombConst (name, T, T_args))
818 fun combformula_from_prop thy type_enc eq_as_iff =
820 fun do_term bs t atomic_types =
821 combterm_from_term thy bs (Envir.eta_contract t)
822 |>> (introduce_proxies type_enc #> AAtom)
823 ||> union (op =) atomic_types
824 fun do_quant bs q s T t' =
825 let val s = singleton (Name.variant_list (map fst bs)) s in
826 do_formula ((s, T) :: bs) t'
827 #>> mk_aquant q [(`make_bound_var s, SOME T)]
829 and do_conn bs c t1 t2 =
830 do_formula bs t1 ##>> do_formula bs t2 #>> uncurry (mk_aconn c)
831 and do_formula bs t =
833 @{const Trueprop} $ t1 => do_formula bs t1
834 | @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
835 | Const (@{const_name All}, _) $ Abs (s, T, t') =>
836 do_quant bs AForall s T t'
837 | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
838 do_quant bs AExists s T t'
839 | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
840 | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
841 | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
842 | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
843 if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
847 fun presimplify_term _ [] t = t
848 | presimplify_term ctxt presimp_consts t =
849 t |> exists_Const (member (op =) presimp_consts o fst) t
850 ? (Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
851 #> Meson.presimplify ctxt
854 fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
855 fun conceal_bounds Ts t =
856 subst_bounds (map (Free o apfst concealed_bound_name)
857 (0 upto length Ts - 1 ~~ Ts), t)
858 fun reveal_bounds Ts =
859 subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
860 (0 upto length Ts - 1 ~~ Ts))
862 fun is_fun_equality (@{const_name HOL.eq},
863 Type (_, [Type (@{type_name fun}, _), _])) = true
864 | is_fun_equality _ = false
866 fun extensionalize_term ctxt t =
867 if exists_Const is_fun_equality t then
868 let val thy = Proof_Context.theory_of ctxt in
869 t |> cterm_of thy |> Meson.extensionalize_conv ctxt
870 |> prop_of |> Logic.dest_equals |> snd
875 fun introduce_combinators_in_term ctxt kind t =
876 let val thy = Proof_Context.theory_of ctxt in
877 if Meson.is_fol_term thy t then
883 @{const Not} $ t1 => @{const Not} $ aux Ts t1
884 | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
885 t0 $ Abs (s, T, aux (T :: Ts) t')
886 | (t0 as Const (@{const_name All}, _)) $ t1 =>
887 aux Ts (t0 $ eta_expand Ts t1 1)
888 | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
889 t0 $ Abs (s, T, aux (T :: Ts) t')
890 | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
891 aux Ts (t0 $ eta_expand Ts t1 1)
892 | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
893 | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
894 | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
895 | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
897 t0 $ aux Ts t1 $ aux Ts t2
898 | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
901 t |> conceal_bounds Ts
902 |> Envir.eta_contract
904 |> Meson_Clausify.introduce_combinators_in_cterm
905 |> prop_of |> Logic.dest_equals |> snd
907 val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
908 in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
910 (* A type variable of sort "{}" will make abstraction fail. *)
911 if kind = Conjecture then HOLogic.false_const
912 else HOLogic.true_const
915 (* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
916 same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
919 fun aux (t $ u) = aux t $ aux u
920 | aux (Abs (s, T, t)) = Abs (s, T, aux t)
921 | aux (Var ((s, i), T)) =
922 Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
924 in t |> exists_subterm is_Var t ? aux end
926 fun preprocess_prop ctxt presimp_consts kind t =
928 val thy = Proof_Context.theory_of ctxt
929 val t = t |> Envir.beta_eta_contract
930 |> transform_elim_prop
931 |> Object_Logic.atomize_term thy
932 val need_trueprop = (fastype_of t = @{typ bool})
934 t |> need_trueprop ? HOLogic.mk_Trueprop
935 |> Raw_Simplifier.rewrite_term thy (Meson.unfold_set_const_simps ctxt) []
936 |> extensionalize_term ctxt
937 |> presimplify_term ctxt presimp_consts
938 |> perhaps (try (HOLogic.dest_Trueprop))
939 |> introduce_combinators_in_term ctxt kind
942 (* making fact and conjecture formulas *)
943 fun make_formula thy type_enc eq_as_iff name loc kind t =
945 val (combformula, atomic_types) =
946 combformula_from_prop thy type_enc eq_as_iff t []
948 {name = name, locality = loc, kind = kind, combformula = combformula,
949 atomic_types = atomic_types}
952 fun make_fact ctxt format type_enc eq_as_iff preproc presimp_consts
954 let val thy = Proof_Context.theory_of ctxt in
955 case t |> preproc ? preprocess_prop ctxt presimp_consts Axiom
956 |> make_formula thy type_enc (eq_as_iff andalso format <> CNF) name
958 formula as {combformula = AAtom (CombConst ((s, _), _, _)), ...} =>
959 if s = tptp_true then NONE else SOME formula
960 | formula => SOME formula
963 fun make_conjecture ctxt format prem_kind type_enc preproc presimp_consts ts =
965 val thy = Proof_Context.theory_of ctxt
966 val last = length ts - 1
968 map2 (fn j => fn t =>
970 val (kind, maybe_negate) =
975 if prem_kind = Conjecture then update_combformula mk_anot
979 (preprocess_prop ctxt presimp_consts kind #> freeze_term)
980 |> make_formula thy type_enc (format <> CNF) (string_of_int j)
987 (** Finite and infinite type inference **)
989 fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
990 | deep_freeze_atyp T = T
991 val deep_freeze_type = map_atyps deep_freeze_atyp
993 (* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
994 dangerous because their "exhaust" properties can easily lead to unsound ATP
995 proofs. On the other hand, all HOL infinite types can be given the same
996 models in first-order logic (via Löwenheim-Skolem). *)
998 fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
999 exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
1000 | should_encode_type _ _ All_Types _ = true
1001 | should_encode_type ctxt _ Fin_Nonmono_Types T =
1002 is_type_surely_finite ctxt false T
1003 | should_encode_type _ _ _ _ = false
1005 fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
1006 should_predicate_on_var T =
1007 (heaviness = Heavyweight orelse should_predicate_on_var ()) andalso
1008 should_encode_type ctxt nonmono_Ts level T
1009 | should_predicate_on_type _ _ _ _ _ = false
1011 fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
1012 String.isPrefix bound_var_prefix s
1013 | is_var_or_bound_var (CombVar _) = true
1014 | is_var_or_bound_var _ = false
1017 Top_Level of bool option |
1018 Eq_Arg of bool option |
1021 fun should_tag_with_type _ _ _ (Top_Level _) _ _ = false
1022 | should_tag_with_type ctxt nonmono_Ts (Tags (poly, level, heaviness)) site
1025 Heavyweight => should_encode_type ctxt nonmono_Ts level T
1027 case (site, is_var_or_bound_var u) of
1028 (Eq_Arg pos, true) =>
1029 (* The first disjunct prevents a subtle soundness issue explained in
1030 Blanchette's Ph.D. thesis. See also
1031 "formula_lines_for_lightweight_tags_sym_decl". *)
1032 (pos <> SOME false andalso poly = Polymorphic andalso
1033 level <> All_Types andalso heaviness = Lightweight andalso
1034 exists (fn T' => type_instance ctxt (T', T)) nonmono_Ts) orelse
1035 should_encode_type ctxt nonmono_Ts level T
1037 | should_tag_with_type _ _ _ _ _ _ = false
1039 fun homogenized_type ctxt nonmono_Ts level =
1041 val should_encode = should_encode_type ctxt nonmono_Ts level
1042 fun homo 0 T = if should_encode T then T else homo_infinite_type
1043 | homo ary (Type (@{type_name fun}, [T1, T2])) =
1044 homo 0 T1 --> homo (ary - 1) T2
1045 | homo _ _ = raise Fail "expected function type"
1048 (** "hBOOL" and "hAPP" **)
1051 {pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
1053 fun add_combterm_syms_to_table ctxt explicit_apply =
1055 fun consider_var_arity const_T var_T max_ary =
1058 if ary = max_ary orelse type_instance ctxt (var_T, T) orelse
1059 type_instance ctxt (T, var_T) then
1062 iter (ary + 1) (range_type T)
1063 in iter 0 const_T end
1064 fun add_var_or_bound_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1065 if explicit_apply = NONE andalso
1066 (can dest_funT T orelse T = @{typ bool}) then
1068 val bool_vars' = bool_vars orelse body_type T = @{typ bool}
1069 fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
1070 {pred_sym = pred_sym andalso not bool_vars',
1071 min_ary = fold (fn T' => consider_var_arity T' T) types min_ary,
1072 max_ary = max_ary, types = types}
1074 fun_var_Ts |> can dest_funT T ? insert_type ctxt I T
1076 if bool_vars' = bool_vars andalso
1077 pointer_eq (fun_var_Ts', fun_var_Ts) then
1080 ((bool_vars', fun_var_Ts'), Symtab.map (K repair_min_arity) sym_tab)
1084 fun add top_level tm (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1085 let val (head, args) = strip_combterm_comb tm in
1087 CombConst ((s, _), T, _) =>
1088 if String.isPrefix bound_var_prefix s then
1089 add_var_or_bound_var T accum
1091 let val ary = length args in
1092 ((bool_vars, fun_var_Ts),
1093 case Symtab.lookup sym_tab s of
1094 SOME {pred_sym, min_ary, max_ary, types} =>
1097 pred_sym andalso top_level andalso not bool_vars
1098 val types' = types |> insert_type ctxt I T
1100 if is_some explicit_apply orelse
1101 pointer_eq (types', types) then
1104 fold (consider_var_arity T) fun_var_Ts min_ary
1106 Symtab.update (s, {pred_sym = pred_sym,
1107 min_ary = Int.min (ary, min_ary),
1108 max_ary = Int.max (ary, max_ary),
1114 val pred_sym = top_level andalso not bool_vars
1116 case explicit_apply of
1119 | NONE => fold (consider_var_arity T) fun_var_Ts ary
1121 Symtab.update_new (s, {pred_sym = pred_sym,
1122 min_ary = min_ary, max_ary = ary,
1127 | CombVar (_, T) => add_var_or_bound_var T accum
1129 |> fold (add false) args
1132 fun add_fact_syms_to_table ctxt explicit_apply =
1133 fact_lift (formula_fold NONE
1134 (K (add_combterm_syms_to_table ctxt explicit_apply)))
1136 val default_sym_tab_entries : (string * sym_info) list =
1137 (prefixed_predicator_name,
1138 {pred_sym = true, min_ary = 1, max_ary = 1, types = []}) ::
1139 ([tptp_false, tptp_true]
1140 |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []})) @
1141 ([tptp_equal, tptp_old_equal]
1142 |> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = []}))
1144 fun sym_table_for_facts ctxt explicit_apply facts =
1145 ((false, []), Symtab.empty)
1146 |> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
1147 |> fold Symtab.update default_sym_tab_entries
1149 fun min_arity_of sym_tab s =
1150 case Symtab.lookup sym_tab s of
1151 SOME ({min_ary, ...} : sym_info) => min_ary
1153 case strip_prefix_and_unascii const_prefix s of
1155 let val s = s |> unmangled_const_name |> invert_const in
1156 if s = predicator_name then 1
1157 else if s = app_op_name then 2
1158 else if s = type_pred_name then 1
1163 (* True if the constant ever appears outside of the top-level position in
1164 literals, or if it appears with different arities (e.g., because of different
1165 type instantiations). If false, the constant always receives all of its
1166 arguments and is used as a predicate. *)
1167 fun is_pred_sym sym_tab s =
1168 case Symtab.lookup sym_tab s of
1169 SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
1170 pred_sym andalso min_ary = max_ary
1173 val predicator_combconst =
1174 CombConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
1175 fun predicator tm = CombApp (predicator_combconst, tm)
1177 fun introduce_predicators_in_combterm sym_tab tm =
1178 case strip_combterm_comb tm of
1179 (CombConst ((s, _), _, _), _) =>
1180 if is_pred_sym sym_tab s then tm else predicator tm
1181 | _ => predicator tm
1183 fun list_app head args = fold (curry (CombApp o swap)) args head
1185 val app_op = `make_fixed_const app_op_name
1187 fun explicit_app arg head =
1189 val head_T = combtyp_of head
1190 val (arg_T, res_T) = dest_funT head_T
1192 CombConst (app_op, head_T --> head_T, [arg_T, res_T])
1193 in list_app explicit_app [head, arg] end
1194 fun list_explicit_app head args = fold explicit_app args head
1196 fun introduce_explicit_apps_in_combterm sym_tab =
1199 case strip_combterm_comb tm of
1200 (head as CombConst ((s, _), _, _), args) =>
1202 |> chop (min_arity_of sym_tab s)
1204 |-> list_explicit_app
1205 | (head, args) => list_explicit_app head (map aux args)
1208 fun chop_fun 0 T = ([], T)
1209 | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
1210 chop_fun (n - 1) ran_T |>> cons dom_T
1211 | chop_fun _ _ = raise Fail "unexpected non-function"
1213 fun filter_type_args _ _ _ [] = []
1214 | filter_type_args thy s arity T_args =
1216 (* will throw "TYPE" for pseudo-constants *)
1217 val U = if s = app_op_name then
1218 @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
1220 s |> Sign.the_const_type thy
1222 case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
1225 let val U_args = (s, U) |> Sign.const_typargs thy in
1227 |> map (fn (U, T) =>
1228 if member (op =) res_U_vars (dest_TVar U) then T
1232 handle TYPE _ => T_args
1234 fun enforce_type_arg_policy_in_combterm ctxt format type_enc =
1236 val thy = Proof_Context.theory_of ctxt
1237 fun aux arity (CombApp (tm1, tm2)) =
1238 CombApp (aux (arity + 1) tm1, aux 0 tm2)
1239 | aux arity (CombConst (name as (s, _), T, T_args)) =
1240 (case strip_prefix_and_unascii const_prefix s of
1241 NONE => (name, T_args)
1244 val s'' = invert_const s''
1245 fun filtered_T_args false = T_args
1246 | filtered_T_args true = filter_type_args thy s'' arity T_args
1248 case type_arg_policy type_enc s'' of
1249 Explicit_Type_Args drop_args =>
1250 (name, filtered_T_args drop_args)
1251 | Mangled_Type_Args drop_args =>
1252 (mangled_const_name format type_enc (filtered_T_args drop_args)
1254 | No_Type_Args => (name, [])
1256 |> (fn (name, T_args) => CombConst (name, T, T_args))
1260 fun repair_combterm ctxt format type_enc sym_tab =
1261 not (is_type_enc_higher_order type_enc)
1262 ? (introduce_explicit_apps_in_combterm sym_tab
1263 #> introduce_predicators_in_combterm sym_tab)
1264 #> enforce_type_arg_policy_in_combterm ctxt format type_enc
1265 fun repair_fact ctxt format type_enc sym_tab =
1266 update_combformula (formula_map
1267 (repair_combterm ctxt format type_enc sym_tab))
1269 (** Helper facts **)
1271 (* The Boolean indicates that a fairly sound type encoding is needed. *)
1273 [(("COMBI", false), @{thms Meson.COMBI_def}),
1274 (("COMBK", false), @{thms Meson.COMBK_def}),
1275 (("COMBB", false), @{thms Meson.COMBB_def}),
1276 (("COMBC", false), @{thms Meson.COMBC_def}),
1277 (("COMBS", false), @{thms Meson.COMBS_def}),
1279 (* This is a lie: Higher-order equality doesn't need a sound type encoding.
1280 However, this is done so for backward compatibility: Including the
1281 equality helpers by default in Metis breaks a few existing proofs. *)
1282 @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1283 fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1284 (("fFalse", false), [@{lemma "~ fFalse" by (unfold fFalse_def) fast}]),
1285 (("fFalse", true), @{thms True_or_False}),
1286 (("fTrue", false), [@{lemma "fTrue" by (unfold fTrue_def) fast}]),
1287 (("fTrue", true), @{thms True_or_False}),
1289 @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1290 fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1292 @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
1293 by (unfold fconj_def) fast+}),
1295 @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
1296 by (unfold fdisj_def) fast+}),
1297 (("fimplies", false),
1298 @{lemma "P | fimplies P Q" "~ Q | fimplies P Q" "~ fimplies P Q | ~ P | Q"
1299 by (unfold fimplies_def) fast+}),
1300 (("If", true), @{thms if_True if_False True_or_False})]
1301 |> map (apsnd (map zero_var_indexes))
1303 val type_tag = `make_fixed_const type_tag_name
1305 fun type_tag_idempotence_fact () =
1307 fun var s = ATerm (`I s, [])
1308 fun tag tm = ATerm (type_tag, [var "T", tm])
1309 val tagged_a = tag (var "A")
1311 Formula (type_tag_idempotence_helper_name, Axiom,
1312 AAtom (ATerm (`I tptp_equal, [tag tagged_a, tagged_a]))
1313 |> close_formula_universally, simp_info, NONE)
1316 fun should_specialize_helper type_enc t =
1317 case general_type_arg_policy type_enc of
1318 Mangled_Type_Args _ => not (null (Term.hidden_polymorphism t))
1321 fun helper_facts_for_sym ctxt format type_enc (s, {types, ...} : sym_info) =
1322 case strip_prefix_and_unascii const_prefix s of
1325 val thy = Proof_Context.theory_of ctxt
1326 val unmangled_s = mangled_s |> unmangled_const_name
1327 fun dub_and_inst needs_fairly_sound (th, j) =
1328 ((unmangled_s ^ "_" ^ string_of_int j ^
1329 (if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^
1330 (if needs_fairly_sound then typed_helper_suffix
1331 else untyped_helper_suffix),
1333 let val t = th |> prop_of in
1334 t |> should_specialize_helper type_enc t
1336 [T] => specialize_type thy (invert_const unmangled_s, T)
1340 map_filter (make_fact ctxt format type_enc false false [])
1341 val fairly_sound = is_type_enc_fairly_sound type_enc
1344 |> maps (fn ((helper_s, needs_fairly_sound), ths) =>
1345 if helper_s <> unmangled_s orelse
1346 (needs_fairly_sound andalso not fairly_sound) then
1349 ths ~~ (1 upto length ths)
1350 |> map (dub_and_inst needs_fairly_sound)
1354 fun helper_facts_for_sym_table ctxt format type_enc sym_tab =
1355 Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_enc) sym_tab
1358 (***************************************************************)
1359 (* Type Classes Present in the Axiom or Conjecture Clauses *)
1360 (***************************************************************)
1362 fun set_insert (x, s) = Symtab.update (x, ()) s
1364 fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
1366 (* Remove this trivial type class (FIXME: similar code elsewhere) *)
1367 fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
1369 fun classes_of_terms get_Ts =
1370 map (map snd o get_Ts)
1371 #> List.foldl add_classes Symtab.empty
1372 #> delete_type #> Symtab.keys
1374 val tfree_classes_of_terms = classes_of_terms OldTerm.term_tfrees
1375 val tvar_classes_of_terms = classes_of_terms OldTerm.term_tvars
1377 fun fold_type_constrs f (Type (s, Ts)) x =
1378 fold (fold_type_constrs f) Ts (f (s, x))
1379 | fold_type_constrs _ _ x = x
1381 (*Type constructors used to instantiate overloaded constants are the only ones needed.*)
1382 fun add_type_constrs_in_term thy =
1384 fun add (Const (@{const_name Meson.skolem}, _) $ _) = I
1385 | add (t $ u) = add t #> add u
1386 | add (Const (x as (s, _))) =
1387 if String.isPrefix skolem_const_prefix s then I
1388 else x |> Sign.const_typargs thy |> fold (fold_type_constrs set_insert)
1389 | add (Abs (_, _, u)) = add u
1393 fun type_constrs_of_terms thy ts =
1394 Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty)
1396 fun translate_formulas ctxt format prem_kind type_enc preproc hyp_ts concl_t
1399 val thy = Proof_Context.theory_of ctxt
1400 val fact_ts = facts |> map snd
1401 val presimp_consts = Meson.presimplified_consts ctxt
1402 val make_fact = make_fact ctxt format type_enc true preproc presimp_consts
1403 val (facts, fact_names) =
1404 facts |> map (fn (name, t) => (name, t) |> make_fact |> rpair name)
1405 |> map_filter (try (apfst the))
1407 (* Remove existing facts from the conjecture, as this can dramatically
1408 boost an ATP's performance (for some reason). *)
1411 |> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t)
1412 val goal_t = Logic.list_implies (hyp_ts, concl_t)
1413 val all_ts = goal_t :: fact_ts
1414 val subs = tfree_classes_of_terms all_ts
1415 val supers = tvar_classes_of_terms all_ts
1416 val tycons = type_constrs_of_terms thy all_ts
1419 |> make_conjecture ctxt format prem_kind type_enc preproc presimp_consts
1420 val (supers', arity_clauses) =
1421 if level_of_type_enc type_enc = No_Types then ([], [])
1422 else make_arity_clauses thy tycons supers
1423 val class_rel_clauses = make_class_rel_clauses thy subs supers'
1425 (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
1428 fun fo_literal_from_type_literal (TyLitVar (class, name)) =
1429 (true, ATerm (class, [ATerm (name, [])]))
1430 | fo_literal_from_type_literal (TyLitFree (class, name)) =
1431 (true, ATerm (class, [ATerm (name, [])]))
1433 fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
1435 val type_pred = `make_fixed_const type_pred_name
1437 fun type_pred_combterm ctxt format type_enc T tm =
1438 CombApp (CombConst (type_pred, T --> @{typ bool}, [T])
1439 |> enforce_type_arg_policy_in_combterm ctxt format type_enc, tm)
1441 fun is_var_positively_naked_in_term _ (SOME false) _ accum = accum
1442 | is_var_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
1443 accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
1444 fun should_predicate_on_var_in_formula pos phi (SOME true) name =
1445 formula_fold pos (is_var_positively_naked_in_term name) phi false
1446 | should_predicate_on_var_in_formula _ _ _ _ = true
1448 fun mk_const_aterm format type_enc x T_args args =
1449 ATerm (x, map_filter (fo_term_for_type_arg format type_enc) T_args @ args)
1451 fun tag_with_type ctxt format nonmono_Ts type_enc pos T tm =
1452 CombConst (type_tag, T --> T, [T])
1453 |> enforce_type_arg_policy_in_combterm ctxt format type_enc
1454 |> term_from_combterm ctxt format nonmono_Ts type_enc (Top_Level pos)
1455 |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
1456 and term_from_combterm ctxt format nonmono_Ts type_enc =
1460 val (head, args) = strip_combterm_comb u
1461 val (x as (s, _), T_args) =
1463 CombConst (name, _, T_args) => (name, T_args)
1464 | CombVar (name, _) => (name, [])
1465 | CombApp _ => raise Fail "impossible \"CombApp\""
1466 val (pos, arg_site) =
1469 (pos, if is_tptp_equal s then Eq_Arg pos else Elsewhere)
1470 | Eq_Arg pos => (pos, Elsewhere)
1471 | Elsewhere => (NONE, Elsewhere)
1472 val t = mk_const_aterm format type_enc x T_args
1473 (map (aux arg_site) args)
1474 val T = combtyp_of u
1476 t |> (if should_tag_with_type ctxt nonmono_Ts type_enc site u T then
1477 tag_with_type ctxt format nonmono_Ts type_enc pos T
1482 and formula_from_combformula ctxt format nonmono_Ts type_enc
1483 should_predicate_on_var =
1486 term_from_combterm ctxt format nonmono_Ts type_enc (Top_Level pos)
1489 Simple_Types (_, level) =>
1490 homogenized_type ctxt nonmono_Ts level 0
1491 #> mangled_type format type_enc false 0 #> SOME
1493 fun do_out_of_bound_type pos phi universal (name, T) =
1494 if should_predicate_on_type ctxt nonmono_Ts type_enc
1495 (fn () => should_predicate_on_var pos phi universal name) T then
1497 |> type_pred_combterm ctxt format type_enc T
1498 |> do_term pos |> AAtom |> SOME
1501 fun do_formula pos (AQuant (q, xs, phi)) =
1503 val phi = phi |> do_formula pos
1504 val universal = Option.map (q = AExists ? not) pos
1506 AQuant (q, xs |> map (apsnd (fn NONE => NONE
1507 | SOME T => do_bound_type T)),
1508 (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
1510 (fn (_, NONE) => NONE
1512 do_out_of_bound_type pos phi universal (s, T))
1516 | do_formula pos (AConn conn) = aconn_map pos do_formula conn
1517 | do_formula pos (AAtom tm) = AAtom (do_term pos tm)
1520 fun bound_tvars type_enc Ts =
1521 mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
1522 (type_literals_for_types type_enc add_sorts_on_tvar Ts))
1524 (* Each fact is given a unique fact number to avoid name clashes (e.g., because
1525 of monomorphization). The TPTP explicitly forbids name clashes, and some of
1526 the remote provers might care. *)
1527 fun formula_line_for_fact ctxt format prefix encode freshen pos nonmono_Ts
1528 type_enc (j, {name, locality, kind, combformula, atomic_types}) =
1529 (prefix ^ (if freshen then string_of_int j ^ "_" else "") ^ encode name,
1532 |> close_combformula_universally
1533 |> formula_from_combformula ctxt format nonmono_Ts type_enc
1534 should_predicate_on_var_in_formula
1535 (if pos then SOME true else NONE)
1536 |> bound_tvars type_enc atomic_types
1537 |> close_formula_universally,
1546 fun formula_line_for_class_rel_clause ({name, subclass, superclass, ...}
1547 : class_rel_clause) =
1548 let val ty_arg = ATerm (`I "T", []) in
1549 Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
1550 AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
1551 AAtom (ATerm (superclass, [ty_arg]))])
1552 |> close_formula_universally, intro_info, NONE)
1555 fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
1556 (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
1557 | fo_literal_from_arity_literal (TVarLit (c, sort)) =
1558 (false, ATerm (c, [ATerm (sort, [])]))
1560 fun formula_line_for_arity_clause ({name, prem_lits, concl_lits, ...}
1562 Formula (arity_clause_prefix ^ name, Axiom,
1563 mk_ahorn (map (formula_from_fo_literal o apfst not
1564 o fo_literal_from_arity_literal) prem_lits)
1565 (formula_from_fo_literal
1566 (fo_literal_from_arity_literal concl_lits))
1567 |> close_formula_universally, intro_info, NONE)
1569 fun formula_line_for_conjecture ctxt format nonmono_Ts type_enc
1570 ({name, kind, combformula, atomic_types, ...} : translated_formula) =
1571 Formula (conjecture_prefix ^ name, kind,
1572 formula_from_combformula ctxt format nonmono_Ts type_enc
1573 should_predicate_on_var_in_formula (SOME false)
1574 (close_combformula_universally combformula)
1575 |> bound_tvars type_enc atomic_types
1576 |> close_formula_universally, NONE, NONE)
1578 fun free_type_literals type_enc ({atomic_types, ...} : translated_formula) =
1579 atomic_types |> type_literals_for_types type_enc add_sorts_on_tfree
1580 |> map fo_literal_from_type_literal
1582 fun formula_line_for_free_type j lit =
1583 Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis,
1584 formula_from_fo_literal lit, NONE, NONE)
1585 fun formula_lines_for_free_types type_enc facts =
1587 val litss = map (free_type_literals type_enc) facts
1588 val lits = fold (union (op =)) litss []
1589 in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
1591 (** Symbol declarations **)
1593 fun should_declare_sym type_enc pred_sym s =
1594 is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
1596 Simple_Types _ => true
1597 | Tags (_, _, Lightweight) => true
1598 | _ => not pred_sym)
1600 fun sym_decl_table_for_facts ctxt type_enc repaired_sym_tab (conjs, facts) =
1602 fun add_combterm in_conj tm =
1603 let val (head, args) = strip_combterm_comb tm in
1605 CombConst ((s, s'), T, T_args) =>
1606 let val pred_sym = is_pred_sym repaired_sym_tab s in
1607 if should_declare_sym type_enc pred_sym s then
1608 Symtab.map_default (s, [])
1609 (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
1615 #> fold (add_combterm in_conj) args
1617 fun add_fact in_conj =
1618 fact_lift (formula_fold NONE (K (add_combterm in_conj)))
1621 |> is_type_enc_fairly_sound type_enc
1622 ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
1625 (* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
1626 out with monotonicity" paper presented at CADE 2011. *)
1627 fun add_combterm_nonmonotonic_types _ _ _ _ (SOME false) _ = I
1628 | add_combterm_nonmonotonic_types ctxt level sound locality _
1629 (CombApp (CombApp (CombConst ((s, _), Type (_, [T, _]), _), tm1),
1631 (is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
1633 Noninf_Nonmono_Types =>
1634 not (is_locality_global locality) orelse
1635 not (is_type_surely_infinite ctxt sound T)
1636 | Fin_Nonmono_Types => is_type_surely_finite ctxt false T
1637 | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
1638 | add_combterm_nonmonotonic_types _ _ _ _ _ _ = I
1639 fun add_fact_nonmonotonic_types ctxt level sound
1640 ({kind, locality, combformula, ...} : translated_formula) =
1641 formula_fold (SOME (kind <> Conjecture))
1642 (add_combterm_nonmonotonic_types ctxt level sound locality)
1644 fun nonmonotonic_types_for_facts ctxt type_enc sound facts =
1645 let val level = level_of_type_enc type_enc in
1646 if level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types then
1647 [] |> fold (add_fact_nonmonotonic_types ctxt level sound) facts
1648 (* We must add "bool" in case the helper "True_or_False" is added
1649 later. In addition, several places in the code rely on the list of
1650 nonmonotonic types not being empty. *)
1651 |> insert_type ctxt I @{typ bool}
1656 fun decl_line_for_sym ctxt format nonmono_Ts type_enc s
1657 (s', T_args, T, pred_sym, ary, _) =
1659 val (T_arg_Ts, level) =
1661 Simple_Types (_, level) => ([], level)
1662 | _ => (replicate (length T_args) homo_infinite_type, No_Types)
1664 Decl (sym_decl_prefix ^ s, (s, s'),
1665 (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
1666 |> mangled_type format type_enc pred_sym (length T_arg_Ts + ary))
1669 fun formula_line_for_preds_sym_decl ctxt format conj_sym_kind nonmono_Ts
1670 poly_nonmono_Ts type_enc n s j (s', T_args, T, _, ary, in_conj) =
1672 val (kind, maybe_negate) =
1673 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1675 val (arg_Ts, res_T) = chop_fun ary T
1676 val num_args = length arg_Ts
1678 1 upto num_args |> map (`I o make_bound_var o string_of_int)
1680 bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
1681 val sym_needs_arg_types = n > 1 orelse exists (curry (op =) dummyT) T_args
1682 fun should_keep_arg_type T =
1683 sym_needs_arg_types orelse
1684 not (should_predicate_on_type ctxt nonmono_Ts type_enc (K false) T)
1686 arg_Ts |> map (fn T => if should_keep_arg_type T then SOME T else NONE)
1688 Formula (preds_sym_formula_prefix ^ s ^
1689 (if n > 1 then "_" ^ string_of_int j else ""), kind,
1690 CombConst ((s, s'), T, T_args)
1691 |> fold (curry (CombApp o swap)) bounds
1692 |> type_pred_combterm ctxt format type_enc res_T
1693 |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
1694 |> formula_from_combformula ctxt format poly_nonmono_Ts type_enc
1695 (K (K (K (K true)))) (SOME true)
1696 |> n > 1 ? bound_tvars type_enc (atyps_of T)
1697 |> close_formula_universally
1702 fun formula_lines_for_lightweight_tags_sym_decl ctxt format conj_sym_kind
1703 poly_nonmono_Ts type_enc n s
1704 (j, (s', T_args, T, pred_sym, ary, in_conj)) =
1707 lightweight_tags_sym_formula_prefix ^ s ^
1708 (if n > 1 then "_" ^ string_of_int j else "")
1709 val (kind, maybe_negate) =
1710 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1712 val (arg_Ts, res_T) = chop_fun ary T
1714 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
1715 val bounds = bound_names |> map (fn name => ATerm (name, []))
1716 val cst = mk_const_aterm format type_enc (s, s') T_args
1717 val atomic_Ts = atyps_of T
1719 (if pred_sym then AConn (AIff, map AAtom tms)
1720 else AAtom (ATerm (`I tptp_equal, tms)))
1721 |> bound_tvars type_enc atomic_Ts
1722 |> close_formula_universally
1724 (* See also "should_tag_with_type". *)
1725 fun should_encode T =
1726 should_encode_type ctxt poly_nonmono_Ts All_Types T orelse
1728 Tags (Polymorphic, level, Lightweight) =>
1729 level <> All_Types andalso Monomorph.typ_has_tvars T
1731 val tag_with = tag_with_type ctxt format poly_nonmono_Ts type_enc NONE
1732 val add_formula_for_res =
1733 if should_encode res_T then
1734 cons (Formula (ident_base ^ "_res", kind,
1735 eq [tag_with res_T (cst bounds), cst bounds],
1739 fun add_formula_for_arg k =
1740 let val arg_T = nth arg_Ts k in
1741 if should_encode arg_T then
1742 case chop k bounds of
1743 (bounds1, bound :: bounds2) =>
1744 cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
1745 eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
1748 | _ => raise Fail "expected nonempty tail"
1753 [] |> not pred_sym ? add_formula_for_res
1754 |> fold add_formula_for_arg (ary - 1 downto 0)
1757 fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
1759 fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts
1760 poly_nonmono_Ts type_enc (s, decls) =
1763 decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_enc s)
1768 decl :: (decls' as _ :: _) =>
1769 let val T = result_type_of_decl decl in
1770 if forall (curry (type_instance ctxt o swap) T
1771 o result_type_of_decl) decls' then
1777 val n = length decls
1779 decls |> filter (should_predicate_on_type ctxt poly_nonmono_Ts type_enc
1781 o result_type_of_decl)
1783 (0 upto length decls - 1, decls)
1784 |-> map2 (formula_line_for_preds_sym_decl ctxt format conj_sym_kind
1785 nonmono_Ts poly_nonmono_Ts type_enc n s)
1787 | Tags (_, _, heaviness) =>
1791 let val n = length decls in
1792 (0 upto n - 1 ~~ decls)
1793 |> maps (formula_lines_for_lightweight_tags_sym_decl ctxt format
1794 conj_sym_kind poly_nonmono_Ts type_enc n s)
1797 fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1798 poly_nonmono_Ts type_enc sym_decl_tab =
1803 |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
1804 nonmono_Ts poly_nonmono_Ts type_enc)
1806 fun needs_type_tag_idempotence (Tags (poly, level, heaviness)) =
1807 poly <> Mangled_Monomorphic andalso
1808 ((level = All_Types andalso heaviness = Lightweight) orelse
1809 level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types)
1810 | needs_type_tag_idempotence _ = false
1812 fun offset_of_heading_in_problem _ [] j = j
1813 | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
1814 if heading = needle then j
1815 else offset_of_heading_in_problem needle problem (j + length lines)
1817 val implicit_declsN = "Should-be-implicit typings"
1818 val explicit_declsN = "Explicit typings"
1819 val factsN = "Relevant facts"
1820 val class_relsN = "Class relationships"
1821 val aritiesN = "Arities"
1822 val helpersN = "Helper facts"
1823 val conjsN = "Conjectures"
1824 val free_typesN = "Type variables"
1826 val explicit_apply = NONE (* for experimental purposes *)
1828 fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_enc sound
1829 exporter readable_names preproc hyp_ts concl_t facts =
1831 val (format, type_enc) = choose_format [format] type_enc
1832 val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
1833 translate_formulas ctxt format prem_kind type_enc preproc hyp_ts concl_t
1835 val sym_tab = conjs @ facts |> sym_table_for_facts ctxt explicit_apply
1837 conjs @ facts |> nonmonotonic_types_for_facts ctxt type_enc sound
1838 val repair = repair_fact ctxt format type_enc sym_tab
1839 val (conjs, facts) = (conjs, facts) |> pairself (map repair)
1840 val repaired_sym_tab =
1841 conjs @ facts |> sym_table_for_facts ctxt (SOME false)
1843 repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_enc
1845 val poly_nonmono_Ts =
1846 if null nonmono_Ts orelse nonmono_Ts = [@{typ bool}] orelse
1847 polymorphism_of_type_enc type_enc <> Polymorphic then
1850 [TVar (("'a", 0), HOLogic.typeS)]
1851 val sym_decl_lines =
1852 (conjs, helpers @ facts)
1853 |> sym_decl_table_for_facts ctxt type_enc repaired_sym_tab
1854 |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1855 poly_nonmono_Ts type_enc
1857 0 upto length helpers - 1 ~~ helpers
1858 |> map (formula_line_for_fact ctxt format helper_prefix I false true
1859 poly_nonmono_Ts type_enc)
1860 |> (if needs_type_tag_idempotence type_enc then
1861 cons (type_tag_idempotence_fact ())
1864 (* Reordering these might confuse the proof reconstruction code or the SPASS
1867 [(explicit_declsN, sym_decl_lines),
1869 map (formula_line_for_fact ctxt format fact_prefix ascii_of
1870 (not exporter) (not exporter) nonmono_Ts
1872 (0 upto length facts - 1 ~~ facts)),
1873 (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
1874 (aritiesN, map formula_line_for_arity_clause arity_clauses),
1875 (helpersN, helper_lines),
1877 map (formula_line_for_conjecture ctxt format nonmono_Ts type_enc)
1879 (free_typesN, formula_lines_for_free_types type_enc (facts @ conjs))]
1883 CNF => ensure_cnf_problem
1884 | CNF_UEQ => filter_cnf_ueq_problem
1886 |> (if is_format_typed format then
1887 declare_undeclared_syms_in_atp_problem type_decl_prefix
1891 val (problem, pool) = problem |> nice_atp_problem readable_names
1892 val helpers_offset = offset_of_heading_in_problem helpersN problem 0
1894 map_filter (fn (j, {name, ...}) =>
1895 if String.isSuffix typed_helper_suffix name then SOME j
1897 ((helpers_offset + 1 upto helpers_offset + length helpers)
1899 fun add_sym_arity (s, {min_ary, ...} : sym_info) =
1901 case strip_prefix_and_unascii const_prefix s of
1902 SOME s => Symtab.insert (op =) (s, min_ary)
1908 case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
1909 offset_of_heading_in_problem conjsN problem 0,
1910 offset_of_heading_in_problem factsN problem 0,
1911 fact_names |> Vector.fromList,
1913 Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
1917 val conj_weight = 0.0
1918 val hyp_weight = 0.1
1919 val fact_min_weight = 0.2
1920 val fact_max_weight = 1.0
1921 val type_info_default_weight = 0.8
1923 fun add_term_weights weight (ATerm (s, tms)) =
1924 is_tptp_user_symbol s ? Symtab.default (s, weight)
1925 #> fold (add_term_weights weight) tms
1926 fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
1927 formula_fold NONE (K (add_term_weights weight)) phi
1928 | add_problem_line_weights _ _ = I
1930 fun add_conjectures_weights [] = I
1931 | add_conjectures_weights conjs =
1932 let val (hyps, conj) = split_last conjs in
1933 add_problem_line_weights conj_weight conj
1934 #> fold (add_problem_line_weights hyp_weight) hyps
1937 fun add_facts_weights facts =
1939 val num_facts = length facts
1941 fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
1942 / Real.fromInt num_facts
1944 map weight_of (0 upto num_facts - 1) ~~ facts
1945 |> fold (uncurry add_problem_line_weights)
1948 (* Weights are from 0.0 (most important) to 1.0 (least important). *)
1949 fun atp_problem_weights problem =
1950 let val get = these o AList.lookup (op =) problem in
1952 |> add_conjectures_weights (get free_typesN @ get conjsN)
1953 |> add_facts_weights (get factsN)
1954 |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
1955 [explicit_declsN, class_relsN, aritiesN]
1957 |> sort (prod_ord Real.compare string_ord o pairself swap)