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 |
446 CombAbs of (name * typ) * combterm
448 fun combtyp_of (CombConst (_, T, _)) = T
449 | combtyp_of (CombVar (_, T)) = T
450 | combtyp_of (CombApp (t1, _)) = snd (dest_funT (combtyp_of t1))
451 | combtyp_of (CombAbs ((_, T), tm)) = T --> combtyp_of tm
453 (*gets the head of a combinator application, along with the list of arguments*)
454 fun strip_combterm_comb u =
456 fun stripc (CombApp (t, u), ts) = stripc (t, u :: ts)
458 in stripc (u, []) end
460 fun atyps_of T = fold_atyps (insert (op =)) T []
462 fun new_skolem_const_name s num_T_args =
463 [new_skolem_const_prefix, s, string_of_int num_T_args]
464 |> space_implode Long_Name.separator
466 (* Converts a term (with combinators) into a combterm. Also accumulates sort
468 fun combterm_from_term thy bs (P $ Q) =
470 val (P', P_atomics_Ts) = combterm_from_term thy bs P
471 val (Q', Q_atomics_Ts) = combterm_from_term thy bs Q
472 in (CombApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
473 | combterm_from_term thy _ (Const (c, T)) =
476 (if String.isPrefix old_skolem_const_prefix c then
477 [] |> Term.add_tvarsT T |> map TVar
479 (c, T) |> Sign.const_typargs thy)
480 val c' = CombConst (`make_fixed_const c, T, tvar_list)
481 in (c', atyps_of T) end
482 | combterm_from_term _ _ (Free (v, T)) =
483 (CombConst (`make_fixed_var v, T, []), atyps_of T)
484 | combterm_from_term _ _ (Var (v as (s, _), T)) =
485 (if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
487 val Ts = T |> strip_type |> swap |> op ::
488 val s' = new_skolem_const_name s (length Ts)
489 in CombConst (`make_fixed_const s', T, Ts) end
491 CombVar ((make_schematic_var v, s), T), atyps_of T)
492 | combterm_from_term _ bs (Bound j) =
494 |> (fn (s, T) => (CombConst (`make_bound_var s, T, []), atyps_of T))
495 | combterm_from_term thy bs (Abs (s, T, t)) =
496 let val (tm, atomic_Ts) = combterm_from_term thy ((s, T) :: bs) t in
497 (CombAbs ((`make_bound_var s, T), tm),
498 union (op =) atomic_Ts (atyps_of T))
502 General | Helper | Extensionality | Intro | Elim | Simp | Local | Assum |
505 (* (quasi-)underapproximation of the truth *)
506 fun is_locality_global Local = false
507 | is_locality_global Assum = false
508 | is_locality_global Chained = false
509 | is_locality_global _ = true
511 datatype order = First_Order | Higher_Order
512 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
513 datatype type_level =
514 All_Types | Noninf_Nonmono_Types | Fin_Nonmono_Types | Const_Arg_Types |
516 datatype type_heaviness = Heavyweight | Lightweight
519 Simple_Types of order * type_level |
520 Preds of polymorphism * type_level * type_heaviness |
521 Tags of polymorphism * type_level * type_heaviness
523 fun try_unsuffixes ss s =
524 fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
526 fun type_enc_from_string s =
527 (case try (unprefix "poly_") s of
528 SOME s => (SOME Polymorphic, s)
530 case try (unprefix "mono_") s of
531 SOME s => (SOME Monomorphic, s)
533 case try (unprefix "mangled_") s of
534 SOME s => (SOME Mangled_Monomorphic, s)
537 (* "_query" and "_bang" are for the ASCII-challenged Metis and
539 case try_unsuffixes ["?", "_query"] s of
540 SOME s => (Noninf_Nonmono_Types, s)
542 case try_unsuffixes ["!", "_bang"] s of
543 SOME s => (Fin_Nonmono_Types, s)
544 | NONE => (All_Types, s))
546 case try (unsuffix "_heavy") s of
547 SOME s => (Heavyweight, s)
548 | NONE => (Lightweight, s))
549 |> (fn (poly, (level, (heaviness, core))) =>
550 case (core, (poly, level, heaviness)) of
551 ("simple", (NONE, _, Lightweight)) =>
552 Simple_Types (First_Order, level)
553 | ("simple_higher", (NONE, _, Lightweight)) =>
554 if level = Noninf_Nonmono_Types then raise Same.SAME
555 else Simple_Types (Higher_Order, level)
556 | ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
557 | ("tags", (SOME Polymorphic, _, _)) =>
558 Tags (Polymorphic, level, heaviness)
559 | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
560 | ("args", (SOME poly, All_Types (* naja *), Lightweight)) =>
561 Preds (poly, Const_Arg_Types, Lightweight)
562 | ("erased", (NONE, All_Types (* naja *), Lightweight)) =>
563 Preds (Polymorphic, No_Types, Lightweight)
564 | _ => raise Same.SAME)
565 handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
567 fun is_type_enc_higher_order (Simple_Types (Higher_Order, _)) = true
568 | is_type_enc_higher_order _ = false
570 fun polymorphism_of_type_enc (Simple_Types _) = Mangled_Monomorphic
571 | polymorphism_of_type_enc (Preds (poly, _, _)) = poly
572 | polymorphism_of_type_enc (Tags (poly, _, _)) = poly
574 fun level_of_type_enc (Simple_Types (_, level)) = level
575 | level_of_type_enc (Preds (_, level, _)) = level
576 | level_of_type_enc (Tags (_, level, _)) = level
578 fun heaviness_of_type_enc (Simple_Types _) = Heavyweight
579 | heaviness_of_type_enc (Preds (_, _, heaviness)) = heaviness
580 | heaviness_of_type_enc (Tags (_, _, heaviness)) = heaviness
582 fun is_type_level_virtually_sound level =
583 level = All_Types orelse level = Noninf_Nonmono_Types
584 val is_type_enc_virtually_sound =
585 is_type_level_virtually_sound o level_of_type_enc
587 fun is_type_level_fairly_sound level =
588 is_type_level_virtually_sound level orelse level = Fin_Nonmono_Types
589 val is_type_enc_fairly_sound = is_type_level_fairly_sound o level_of_type_enc
591 fun choose_format formats (Simple_Types (order, level)) =
592 if member (op =) formats THF then
593 (THF, Simple_Types (order, level))
594 else if member (op =) formats TFF then
595 (TFF, Simple_Types (First_Order, level))
597 choose_format formats (Preds (Mangled_Monomorphic, level, Heavyweight))
598 | choose_format formats type_enc =
601 (CNF_UEQ, case type_enc of
603 (if is_type_enc_fairly_sound type_enc then Tags else Preds)
606 | format => (format, type_enc))
608 type translated_formula =
612 combformula : (name, typ, combterm) formula,
613 atomic_types : typ list}
615 fun update_combformula f ({name, locality, kind, combformula, atomic_types}
616 : translated_formula) =
617 {name = name, locality = locality, kind = kind, combformula = f combformula,
618 atomic_types = atomic_types} : translated_formula
620 fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
622 val type_instance = Sign.typ_instance o Proof_Context.theory_of
624 fun insert_type ctxt get_T x xs =
625 let val T = get_T x in
626 if exists (curry (type_instance ctxt) T o get_T) xs then xs
627 else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
630 (* The Booleans indicate whether all type arguments should be kept. *)
631 datatype type_arg_policy =
632 Explicit_Type_Args of bool |
633 Mangled_Type_Args of bool |
636 fun should_drop_arg_type_args (Simple_Types _) =
637 false (* since TFF doesn't support overloading *)
638 | should_drop_arg_type_args type_enc =
639 level_of_type_enc type_enc = All_Types andalso
640 heaviness_of_type_enc type_enc = Heavyweight
642 fun type_arg_policy type_enc s =
643 if s = type_tag_name then
644 (if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
647 Explicit_Type_Args) false
648 else case type_enc of
649 Tags (_, All_Types, Heavyweight) => No_Type_Args
651 if level_of_type_enc type_enc = No_Types orelse
652 s = @{const_name HOL.eq} orelse
653 (s = app_op_name andalso
654 level_of_type_enc type_enc = Const_Arg_Types) then
657 should_drop_arg_type_args type_enc
658 |> (if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
663 (* Make literals for sorted type variables. *)
664 fun generic_add_sorts_on_type (_, []) = I
665 | generic_add_sorts_on_type ((x, i), s :: ss) =
666 generic_add_sorts_on_type ((x, i), ss)
667 #> (if s = the_single @{sort HOL.type} then
670 insert (op =) (TyLitFree (`make_type_class s, `make_fixed_type_var x))
672 insert (op =) (TyLitVar (`make_type_class s,
673 (make_schematic_type_var (x, i), x))))
674 fun add_sorts_on_tfree (TFree (s, S)) = generic_add_sorts_on_type ((s, ~1), S)
675 | add_sorts_on_tfree _ = I
676 fun add_sorts_on_tvar (TVar z) = generic_add_sorts_on_type z
677 | add_sorts_on_tvar _ = I
679 fun type_literals_for_types type_enc add_sorts_on_typ Ts =
680 [] |> level_of_type_enc type_enc <> No_Types ? fold add_sorts_on_typ Ts
682 fun mk_aconns c phis =
683 let val (phis', phi') = split_last phis in
684 fold_rev (mk_aconn c) phis' phi'
686 fun mk_ahorn [] phi = phi
687 | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
688 fun mk_aquant _ [] phi = phi
689 | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
690 if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
691 | mk_aquant q xs phi = AQuant (q, xs, phi)
693 fun close_universally atom_vars phi =
695 fun formula_vars bounds (AQuant (_, xs, phi)) =
696 formula_vars (map fst xs @ bounds) phi
697 | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
698 | formula_vars bounds (AAtom tm) =
699 union (op =) (atom_vars tm []
700 |> filter_out (member (op =) bounds o fst))
701 in mk_aquant AForall (formula_vars [] phi []) phi end
703 fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
704 | combterm_vars (CombConst _) = I
705 | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
706 | combterm_vars (CombAbs (_, tm)) = combterm_vars tm
707 fun close_combformula_universally phi = close_universally combterm_vars phi
709 fun term_vars bounds (ATerm (name as (s, _), tms)) =
710 (is_tptp_variable s andalso not (member (op =) bounds name))
711 ? insert (op =) (name, NONE) #> fold (term_vars bounds) tms
712 | term_vars bounds (AAbs ((name, _), tm)) = term_vars (name :: bounds) tm
713 fun close_formula_universally phi = close_universally (term_vars []) phi
715 val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
716 val homo_infinite_type = Type (homo_infinite_type_name, [])
718 fun ho_term_from_typ format type_enc =
720 fun term (Type (s, Ts)) =
721 ATerm (case (is_type_enc_higher_order type_enc, s) of
722 (true, @{type_name bool}) => `I tptp_bool_type
723 | (true, @{type_name fun}) => `I tptp_fun_type
724 | _ => if s = homo_infinite_type_name andalso
725 (format = TFF orelse format = THF) then
726 `I tptp_individual_type
728 `make_fixed_type_const s,
730 | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
731 | term (TVar ((x as (s, _)), _)) =
732 ATerm ((make_schematic_type_var x, s), [])
735 fun ho_term_for_type_arg format type_enc T =
736 if T = dummyT then NONE else SOME (ho_term_from_typ format type_enc T)
738 (* This shouldn't clash with anything else. *)
739 val mangled_type_sep = "\000"
741 fun generic_mangled_type_name f (ATerm (name, [])) = f name
742 | generic_mangled_type_name f (ATerm (name, tys)) =
743 f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
745 | generic_mangled_type_name f _ = raise Fail "unexpected type abstraction"
747 val bool_atype = AType (`I tptp_bool_type)
749 fun make_simple_type s =
750 if s = tptp_bool_type orelse s = tptp_fun_type orelse
751 s = tptp_individual_type then
754 simple_type_prefix ^ ascii_of s
756 fun ho_type_from_ho_term type_enc pred_sym ary =
759 AType ((make_simple_type (generic_mangled_type_name fst ty),
760 generic_mangled_type_name snd ty))
761 fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
762 fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
763 | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
764 | to_fo ary _ = raise Fail "unexpected type abstraction"
765 fun to_ho (ty as ATerm ((s, _), tys)) =
766 if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
767 | to_ho _ = raise Fail "unexpected type abstraction"
768 in if is_type_enc_higher_order type_enc then to_ho else to_fo ary end
770 fun ho_type_from_typ format type_enc pred_sym ary =
771 ho_type_from_ho_term type_enc pred_sym ary
772 o ho_term_from_typ format type_enc
774 fun mangled_const_name format type_enc T_args (s, s') =
776 val ty_args = T_args |> map_filter (ho_term_for_type_arg format type_enc)
777 fun type_suffix f g =
778 fold_rev (curry (op ^) o g o prefix mangled_type_sep
779 o generic_mangled_type_name f) ty_args ""
780 in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
782 val parse_mangled_ident =
783 Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
785 fun parse_mangled_type x =
787 -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
789 and parse_mangled_types x =
790 (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
792 fun unmangled_type s =
793 s |> suffix ")" |> raw_explode
794 |> Scan.finite Symbol.stopper
795 (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
796 quote s)) parse_mangled_type))
799 val unmangled_const_name = space_explode mangled_type_sep #> hd
800 fun unmangled_const s =
801 let val ss = space_explode mangled_type_sep s in
802 (hd ss, map unmangled_type (tl ss))
805 fun introduce_proxies type_enc =
807 fun intro top_level (CombApp (tm1, tm2)) =
808 CombApp (intro top_level tm1, intro false tm2)
809 | intro top_level (CombConst (name as (s, _), T, T_args)) =
810 (case proxify_const s of
812 if top_level orelse is_type_enc_higher_order type_enc then
813 case (top_level, s) of
814 (_, "c_False") => (`I tptp_false, [])
815 | (_, "c_True") => (`I tptp_true, [])
816 | (false, "c_Not") => (`I tptp_not, [])
817 | (false, "c_conj") => (`I tptp_and, [])
818 | (false, "c_disj") => (`I tptp_or, [])
819 | (false, "c_implies") => (`I tptp_implies, [])
821 if is_tptp_equal s then (`I tptp_equal, [])
822 else (proxy_base |>> prefix const_prefix, T_args)
825 (proxy_base |>> prefix const_prefix, T_args)
826 | NONE => (name, T_args))
827 |> (fn (name, T_args) => CombConst (name, T, T_args))
828 | intro _ (CombAbs (bound, tm)) = CombAbs (bound, intro false tm)
832 fun combformula_from_prop thy type_enc eq_as_iff =
834 fun do_term bs t atomic_types =
835 combterm_from_term thy bs (Envir.eta_contract t)
836 |>> (introduce_proxies type_enc #> AAtom)
837 ||> union (op =) atomic_types
838 fun do_quant bs q s T t' =
839 let val s = singleton (Name.variant_list (map fst bs)) s in
840 do_formula ((s, T) :: bs) t'
841 #>> mk_aquant q [(`make_bound_var s, SOME T)]
843 and do_conn bs c t1 t2 =
844 do_formula bs t1 ##>> do_formula bs t2 #>> uncurry (mk_aconn c)
845 and do_formula bs t =
847 @{const Trueprop} $ t1 => do_formula bs t1
848 | @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
849 | Const (@{const_name All}, _) $ Abs (s, T, t') =>
850 do_quant bs AForall s T t'
851 | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
852 do_quant bs AExists s T t'
853 | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
854 | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
855 | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
856 | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
857 if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
861 fun presimplify_term _ [] t = t
862 | presimplify_term ctxt presimp_consts t =
863 t |> exists_Const (member (op =) presimp_consts o fst) t
864 ? (Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
865 #> Meson.presimplify ctxt
868 fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
869 fun conceal_bounds Ts t =
870 subst_bounds (map (Free o apfst concealed_bound_name)
871 (0 upto length Ts - 1 ~~ Ts), t)
872 fun reveal_bounds Ts =
873 subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
874 (0 upto length Ts - 1 ~~ Ts))
876 fun is_fun_equality (@{const_name HOL.eq},
877 Type (_, [Type (@{type_name fun}, _), _])) = true
878 | is_fun_equality _ = false
880 fun extensionalize_term ctxt t =
881 if exists_Const is_fun_equality t then
882 let val thy = Proof_Context.theory_of ctxt in
883 t |> cterm_of thy |> Meson.extensionalize_conv ctxt
884 |> prop_of |> Logic.dest_equals |> snd
889 fun introduce_combinators_in_term ctxt kind t =
890 let val thy = Proof_Context.theory_of ctxt in
891 if Meson.is_fol_term thy t then
897 @{const Not} $ t1 => @{const Not} $ aux Ts t1
898 | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
899 t0 $ Abs (s, T, aux (T :: Ts) t')
900 | (t0 as Const (@{const_name All}, _)) $ t1 =>
901 aux Ts (t0 $ eta_expand Ts t1 1)
902 | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
903 t0 $ Abs (s, T, aux (T :: Ts) t')
904 | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
905 aux Ts (t0 $ eta_expand Ts t1 1)
906 | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
907 | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
908 | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
909 | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
911 t0 $ aux Ts t1 $ aux Ts t2
912 | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
915 t |> conceal_bounds Ts
916 |> Envir.eta_contract
918 |> Meson_Clausify.introduce_combinators_in_cterm
919 |> prop_of |> Logic.dest_equals |> snd
921 val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
922 in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
924 (* A type variable of sort "{}" will make abstraction fail. *)
925 if kind = Conjecture then HOLogic.false_const
926 else HOLogic.true_const
929 (* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
930 same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
933 fun aux (t $ u) = aux t $ aux u
934 | aux (Abs (s, T, t)) = Abs (s, T, aux t)
935 | aux (Var ((s, i), T)) =
936 Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
938 in t |> exists_subterm is_Var t ? aux end
940 fun preprocess_prop ctxt type_enc presimp_consts kind t =
942 val thy = Proof_Context.theory_of ctxt
943 val t = t |> Envir.beta_eta_contract
944 |> transform_elim_prop
945 |> Object_Logic.atomize_term thy
946 val need_trueprop = (fastype_of t = @{typ bool})
948 t |> need_trueprop ? HOLogic.mk_Trueprop
949 |> Raw_Simplifier.rewrite_term thy (Meson.unfold_set_const_simps ctxt) []
950 |> extensionalize_term ctxt
951 |> presimplify_term ctxt presimp_consts
952 |> perhaps (try (HOLogic.dest_Trueprop))
953 |> not (is_type_enc_higher_order type_enc)
954 ? introduce_combinators_in_term ctxt kind
957 (* making fact and conjecture formulas *)
958 fun make_formula thy type_enc eq_as_iff name loc kind t =
960 val (combformula, atomic_types) =
961 combformula_from_prop thy type_enc eq_as_iff t []
963 {name = name, locality = loc, kind = kind, combformula = combformula,
964 atomic_types = atomic_types}
967 fun make_fact ctxt format type_enc eq_as_iff preproc presimp_consts
969 let val thy = Proof_Context.theory_of ctxt in
970 case t |> preproc ? preprocess_prop ctxt type_enc presimp_consts Axiom
971 |> make_formula thy type_enc (eq_as_iff andalso format <> CNF) name
973 formula as {combformula = AAtom (CombConst ((s, _), _, _)), ...} =>
974 if s = tptp_true then NONE else SOME formula
975 | formula => SOME formula
978 fun make_conjecture ctxt format prem_kind type_enc preproc presimp_consts ts =
980 val thy = Proof_Context.theory_of ctxt
981 val last = length ts - 1
983 map2 (fn j => fn t =>
985 val (kind, maybe_negate) =
990 if prem_kind = Conjecture then update_combformula mk_anot
994 (preprocess_prop ctxt type_enc presimp_consts kind #> freeze_term)
995 |> make_formula thy type_enc (format <> CNF) (string_of_int j)
1002 (** Finite and infinite type inference **)
1004 fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
1005 | deep_freeze_atyp T = T
1006 val deep_freeze_type = map_atyps deep_freeze_atyp
1008 (* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
1009 dangerous because their "exhaust" properties can easily lead to unsound ATP
1010 proofs. On the other hand, all HOL infinite types can be given the same
1011 models in first-order logic (via Löwenheim-Skolem). *)
1013 fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
1014 exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
1015 | should_encode_type _ _ All_Types _ = true
1016 | should_encode_type ctxt _ Fin_Nonmono_Types T =
1017 is_type_surely_finite ctxt false T
1018 | should_encode_type _ _ _ _ = false
1020 fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
1021 should_predicate_on_var T =
1022 (heaviness = Heavyweight orelse should_predicate_on_var ()) andalso
1023 should_encode_type ctxt nonmono_Ts level T
1024 | should_predicate_on_type _ _ _ _ _ = false
1026 fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
1027 String.isPrefix bound_var_prefix s
1028 | is_var_or_bound_var (CombVar _) = true
1029 | is_var_or_bound_var _ = false
1032 Top_Level of bool option |
1033 Eq_Arg of bool option |
1036 fun should_tag_with_type _ _ _ (Top_Level _) _ _ = false
1037 | should_tag_with_type ctxt nonmono_Ts (Tags (poly, level, heaviness)) site
1040 Heavyweight => should_encode_type ctxt nonmono_Ts level T
1042 case (site, is_var_or_bound_var u) of
1043 (Eq_Arg pos, true) =>
1044 (* The first disjunct prevents a subtle soundness issue explained in
1045 Blanchette's Ph.D. thesis. See also
1046 "formula_lines_for_lightweight_tags_sym_decl". *)
1047 (pos <> SOME false andalso poly = Polymorphic andalso
1048 level <> All_Types andalso heaviness = Lightweight andalso
1049 exists (fn T' => type_instance ctxt (T', T)) nonmono_Ts) orelse
1050 should_encode_type ctxt nonmono_Ts level T
1052 | should_tag_with_type _ _ _ _ _ _ = false
1054 fun homogenized_type ctxt nonmono_Ts level =
1056 val should_encode = should_encode_type ctxt nonmono_Ts level
1057 fun homo 0 T = if should_encode T then T else homo_infinite_type
1058 | homo ary (Type (@{type_name fun}, [T1, T2])) =
1059 homo 0 T1 --> homo (ary - 1) T2
1060 | homo _ _ = raise Fail "expected function type"
1063 (** "hBOOL" and "hAPP" **)
1066 {pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
1068 fun add_combterm_syms_to_table ctxt explicit_apply =
1070 fun consider_var_arity const_T var_T max_ary =
1073 if ary = max_ary orelse type_instance ctxt (var_T, T) orelse
1074 type_instance ctxt (T, var_T) then
1077 iter (ary + 1) (range_type T)
1078 in iter 0 const_T end
1079 fun add_var_or_bound_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1080 if explicit_apply = NONE andalso
1081 (can dest_funT T orelse T = @{typ bool}) then
1083 val bool_vars' = bool_vars orelse body_type T = @{typ bool}
1084 fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
1085 {pred_sym = pred_sym andalso not bool_vars',
1086 min_ary = fold (fn T' => consider_var_arity T' T) types min_ary,
1087 max_ary = max_ary, types = types}
1089 fun_var_Ts |> can dest_funT T ? insert_type ctxt I T
1091 if bool_vars' = bool_vars andalso
1092 pointer_eq (fun_var_Ts', fun_var_Ts) then
1095 ((bool_vars', fun_var_Ts'), Symtab.map (K repair_min_arity) sym_tab)
1099 fun add top_level tm (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1100 let val (head, args) = strip_combterm_comb tm in
1102 CombConst ((s, _), T, _) =>
1103 if String.isPrefix bound_var_prefix s then
1104 add_var_or_bound_var T accum
1106 let val ary = length args in
1107 ((bool_vars, fun_var_Ts),
1108 case Symtab.lookup sym_tab s of
1109 SOME {pred_sym, min_ary, max_ary, types} =>
1112 pred_sym andalso top_level andalso not bool_vars
1113 val types' = types |> insert_type ctxt I T
1115 if is_some explicit_apply orelse
1116 pointer_eq (types', types) then
1119 fold (consider_var_arity T) fun_var_Ts min_ary
1121 Symtab.update (s, {pred_sym = pred_sym,
1122 min_ary = Int.min (ary, min_ary),
1123 max_ary = Int.max (ary, max_ary),
1129 val pred_sym = top_level andalso not bool_vars
1131 case explicit_apply of
1134 | NONE => fold (consider_var_arity T) fun_var_Ts ary
1136 Symtab.update_new (s, {pred_sym = pred_sym,
1137 min_ary = min_ary, max_ary = ary,
1142 | CombVar (_, T) => add_var_or_bound_var T accum
1144 |> fold (add false) args
1147 fun add_fact_syms_to_table ctxt explicit_apply =
1148 fact_lift (formula_fold NONE
1149 (K (add_combterm_syms_to_table ctxt explicit_apply)))
1151 val default_sym_tab_entries : (string * sym_info) list =
1152 (prefixed_predicator_name,
1153 {pred_sym = true, min_ary = 1, max_ary = 1, types = []}) ::
1154 ([tptp_false, tptp_true]
1155 |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []})) @
1156 ([tptp_equal, tptp_old_equal]
1157 |> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = []}))
1159 fun sym_table_for_facts ctxt explicit_apply facts =
1160 ((false, []), Symtab.empty)
1161 |> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
1162 |> fold Symtab.update default_sym_tab_entries
1164 fun min_arity_of sym_tab s =
1165 case Symtab.lookup sym_tab s of
1166 SOME ({min_ary, ...} : sym_info) => min_ary
1168 case strip_prefix_and_unascii const_prefix s of
1170 let val s = s |> unmangled_const_name |> invert_const in
1171 if s = predicator_name then 1
1172 else if s = app_op_name then 2
1173 else if s = type_pred_name then 1
1178 (* True if the constant ever appears outside of the top-level position in
1179 literals, or if it appears with different arities (e.g., because of different
1180 type instantiations). If false, the constant always receives all of its
1181 arguments and is used as a predicate. *)
1182 fun is_pred_sym sym_tab s =
1183 case Symtab.lookup sym_tab s of
1184 SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
1185 pred_sym andalso min_ary = max_ary
1188 val predicator_combconst =
1189 CombConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
1190 fun predicator tm = CombApp (predicator_combconst, tm)
1192 fun introduce_predicators_in_combterm sym_tab tm =
1193 case strip_combterm_comb tm of
1194 (CombConst ((s, _), _, _), _) =>
1195 if is_pred_sym sym_tab s then tm else predicator tm
1196 | _ => predicator tm
1198 fun list_app head args = fold (curry (CombApp o swap)) args head
1200 val app_op = `make_fixed_const app_op_name
1202 fun explicit_app arg head =
1204 val head_T = combtyp_of head
1205 val (arg_T, res_T) = dest_funT head_T
1207 CombConst (app_op, head_T --> head_T, [arg_T, res_T])
1208 in list_app explicit_app [head, arg] end
1209 fun list_explicit_app head args = fold explicit_app args head
1211 fun introduce_explicit_apps_in_combterm sym_tab =
1214 case strip_combterm_comb tm of
1215 (head as CombConst ((s, _), _, _), args) =>
1217 |> chop (min_arity_of sym_tab s)
1219 |-> list_explicit_app
1220 | (head, args) => list_explicit_app head (map aux args)
1223 fun chop_fun 0 T = ([], T)
1224 | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
1225 chop_fun (n - 1) ran_T |>> cons dom_T
1226 | chop_fun _ _ = raise Fail "unexpected non-function"
1228 fun filter_type_args _ _ _ [] = []
1229 | filter_type_args thy s arity T_args =
1231 (* will throw "TYPE" for pseudo-constants *)
1232 val U = if s = app_op_name then
1233 @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
1235 s |> Sign.the_const_type thy
1237 case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
1240 let val U_args = (s, U) |> Sign.const_typargs thy in
1242 |> map (fn (U, T) =>
1243 if member (op =) res_U_vars (dest_TVar U) then T
1247 handle TYPE _ => T_args
1249 fun enforce_type_arg_policy_in_combterm ctxt format type_enc =
1251 val thy = Proof_Context.theory_of ctxt
1252 fun aux arity (CombApp (tm1, tm2)) =
1253 CombApp (aux (arity + 1) tm1, aux 0 tm2)
1254 | aux arity (CombConst (name as (s, _), T, T_args)) =
1255 (case strip_prefix_and_unascii const_prefix s of
1256 NONE => (name, T_args)
1259 val s'' = invert_const s''
1260 fun filtered_T_args false = T_args
1261 | filtered_T_args true = filter_type_args thy s'' arity T_args
1263 case type_arg_policy type_enc s'' of
1264 Explicit_Type_Args drop_args =>
1265 (name, filtered_T_args drop_args)
1266 | Mangled_Type_Args drop_args =>
1267 (mangled_const_name format type_enc (filtered_T_args drop_args)
1269 | No_Type_Args => (name, [])
1271 |> (fn (name, T_args) => CombConst (name, T, T_args))
1272 | aux _ (CombAbs (bound, tm)) = CombAbs (bound, aux 0 tm)
1276 fun repair_combterm ctxt format type_enc sym_tab =
1277 not (is_type_enc_higher_order type_enc)
1278 ? (introduce_explicit_apps_in_combterm sym_tab
1279 #> introduce_predicators_in_combterm sym_tab)
1280 #> enforce_type_arg_policy_in_combterm ctxt format type_enc
1281 fun repair_fact ctxt format type_enc sym_tab =
1282 update_combformula (formula_map
1283 (repair_combterm ctxt format type_enc sym_tab))
1285 (** Helper facts **)
1287 (* The Boolean indicates that a fairly sound type encoding is needed. *)
1289 [(("COMBI", false), @{thms Meson.COMBI_def}),
1290 (("COMBK", false), @{thms Meson.COMBK_def}),
1291 (("COMBB", false), @{thms Meson.COMBB_def}),
1292 (("COMBC", false), @{thms Meson.COMBC_def}),
1293 (("COMBS", false), @{thms Meson.COMBS_def}),
1295 (* This is a lie: Higher-order equality doesn't need a sound type encoding.
1296 However, this is done so for backward compatibility: Including the
1297 equality helpers by default in Metis breaks a few existing proofs. *)
1298 @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1299 fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1300 (("fFalse", false), [@{lemma "~ fFalse" by (unfold fFalse_def) fast}]),
1301 (("fFalse", true), @{thms True_or_False}),
1302 (("fTrue", false), [@{lemma "fTrue" by (unfold fTrue_def) fast}]),
1303 (("fTrue", true), @{thms True_or_False}),
1305 @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1306 fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1308 @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
1309 by (unfold fconj_def) fast+}),
1311 @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
1312 by (unfold fdisj_def) fast+}),
1313 (("fimplies", false),
1314 @{lemma "P | fimplies P Q" "~ Q | fimplies P Q" "~ fimplies P Q | ~ P | Q"
1315 by (unfold fimplies_def) fast+}),
1316 (("If", true), @{thms if_True if_False True_or_False})]
1317 |> map (apsnd (map zero_var_indexes))
1319 val type_tag = `make_fixed_const type_tag_name
1321 fun type_tag_idempotence_fact () =
1323 fun var s = ATerm (`I s, [])
1324 fun tag tm = ATerm (type_tag, [var "T", tm])
1325 val tagged_a = tag (var "A")
1327 Formula (type_tag_idempotence_helper_name, Axiom,
1328 AAtom (ATerm (`I tptp_equal, [tag tagged_a, tagged_a]))
1329 |> close_formula_universally, simp_info, NONE)
1332 fun should_specialize_helper type_enc t =
1333 polymorphism_of_type_enc type_enc = Mangled_Monomorphic andalso
1334 level_of_type_enc type_enc <> No_Types andalso
1335 not (null (Term.hidden_polymorphism t))
1337 fun helper_facts_for_sym ctxt format type_enc (s, {types, ...} : sym_info) =
1338 case strip_prefix_and_unascii const_prefix s of
1341 val thy = Proof_Context.theory_of ctxt
1342 val unmangled_s = mangled_s |> unmangled_const_name
1343 fun dub needs_fairly_sound j k =
1344 (unmangled_s ^ "_" ^ string_of_int j ^ "_" ^ string_of_int k ^
1345 (if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^
1346 (if needs_fairly_sound then typed_helper_suffix
1347 else untyped_helper_suffix),
1349 fun dub_and_inst needs_fairly_sound (th, j) =
1350 let val t = prop_of th in
1351 if should_specialize_helper type_enc t then
1352 map (fn T => specialize_type thy (invert_const unmangled_s, T) t)
1357 |> map (fn (k, t) => (dub needs_fairly_sound j k, t)) o tag_list 1
1359 map_filter (make_fact ctxt format type_enc false false [])
1360 val fairly_sound = is_type_enc_fairly_sound type_enc
1363 |> maps (fn ((helper_s, needs_fairly_sound), ths) =>
1364 if helper_s <> unmangled_s orelse
1365 (needs_fairly_sound andalso not fairly_sound) then
1368 ths ~~ (1 upto length ths)
1369 |> maps (dub_and_inst needs_fairly_sound)
1373 fun helper_facts_for_sym_table ctxt format type_enc sym_tab =
1374 Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_enc) sym_tab
1377 (***************************************************************)
1378 (* Type Classes Present in the Axiom or Conjecture Clauses *)
1379 (***************************************************************)
1381 fun set_insert (x, s) = Symtab.update (x, ()) s
1383 fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
1385 (* Remove this trivial type class (FIXME: similar code elsewhere) *)
1386 fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
1388 fun classes_of_terms get_Ts =
1389 map (map snd o get_Ts)
1390 #> List.foldl add_classes Symtab.empty
1391 #> delete_type #> Symtab.keys
1393 val tfree_classes_of_terms = classes_of_terms OldTerm.term_tfrees
1394 val tvar_classes_of_terms = classes_of_terms OldTerm.term_tvars
1396 fun fold_type_constrs f (Type (s, Ts)) x =
1397 fold (fold_type_constrs f) Ts (f (s, x))
1398 | fold_type_constrs _ _ x = x
1400 (*Type constructors used to instantiate overloaded constants are the only ones needed.*)
1401 fun add_type_constrs_in_term thy =
1403 fun add (Const (@{const_name Meson.skolem}, _) $ _) = I
1404 | add (t $ u) = add t #> add u
1405 | add (Const (x as (s, _))) =
1406 if String.isPrefix skolem_const_prefix s then I
1407 else x |> Sign.const_typargs thy |> fold (fold_type_constrs set_insert)
1408 | add (Abs (_, _, u)) = add u
1412 fun type_constrs_of_terms thy ts =
1413 Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty)
1415 fun translate_formulas ctxt format prem_kind type_enc preproc hyp_ts concl_t
1418 val thy = Proof_Context.theory_of ctxt
1419 val fact_ts = facts |> map snd
1420 val presimp_consts = Meson.presimplified_consts ctxt
1421 val make_fact = make_fact ctxt format type_enc true preproc presimp_consts
1422 val (facts, fact_names) =
1423 facts |> map (fn (name, t) => (name, t) |> make_fact |> rpair name)
1424 |> map_filter (try (apfst the))
1426 (* Remove existing facts from the conjecture, as this can dramatically
1427 boost an ATP's performance (for some reason). *)
1430 |> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t)
1431 val goal_t = Logic.list_implies (hyp_ts, concl_t)
1432 val all_ts = goal_t :: fact_ts
1433 val subs = tfree_classes_of_terms all_ts
1434 val supers = tvar_classes_of_terms all_ts
1435 val tycons = type_constrs_of_terms thy all_ts
1438 |> make_conjecture ctxt format prem_kind type_enc preproc presimp_consts
1439 val (supers', arity_clauses) =
1440 if level_of_type_enc type_enc = No_Types then ([], [])
1441 else make_arity_clauses thy tycons supers
1442 val class_rel_clauses = make_class_rel_clauses thy subs supers'
1444 (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
1447 fun fo_literal_from_type_literal (TyLitVar (class, name)) =
1448 (true, ATerm (class, [ATerm (name, [])]))
1449 | fo_literal_from_type_literal (TyLitFree (class, name)) =
1450 (true, ATerm (class, [ATerm (name, [])]))
1452 fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
1454 val type_pred = `make_fixed_const type_pred_name
1456 fun type_pred_combterm ctxt format type_enc T tm =
1457 CombApp (CombConst (type_pred, T --> @{typ bool}, [T])
1458 |> enforce_type_arg_policy_in_combterm ctxt format type_enc, tm)
1460 fun is_var_positively_naked_in_term _ (SOME false) _ accum = accum
1461 | is_var_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
1462 accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
1463 | is_var_positively_naked_in_term name _ _ _ = true
1464 fun should_predicate_on_var_in_formula pos phi (SOME true) name =
1465 formula_fold pos (is_var_positively_naked_in_term name) phi false
1466 | should_predicate_on_var_in_formula _ _ _ _ = true
1468 fun mk_aterm format type_enc name T_args args =
1469 ATerm (name, map_filter (ho_term_for_type_arg format type_enc) T_args @ args)
1471 fun tag_with_type ctxt format nonmono_Ts type_enc pos T tm =
1472 CombConst (type_tag, T --> T, [T])
1473 |> enforce_type_arg_policy_in_combterm ctxt format type_enc
1474 |> ho_term_from_combterm ctxt format nonmono_Ts type_enc (Top_Level pos)
1475 |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
1476 and ho_term_from_combterm ctxt format nonmono_Ts type_enc =
1480 val (head, args) = strip_combterm_comb u
1483 Top_Level pos => pos
1488 CombConst (name as (s, _), _, T_args) =>
1490 val arg_site = if is_tptp_equal s then Eq_Arg pos else Elsewhere
1492 mk_aterm format type_enc name T_args (map (aux arg_site) args)
1494 | CombVar (name, _) => mk_aterm format type_enc name [] []
1495 | CombAbs ((name, T), tm) =>
1496 AAbs ((name, ho_type_from_typ format type_enc true 0 T), aux Elsewhere tm)
1497 | CombApp _ => raise Fail "impossible \"CombApp\""
1498 val T = combtyp_of u
1500 t |> (if should_tag_with_type ctxt nonmono_Ts type_enc site u T then
1501 tag_with_type ctxt format nonmono_Ts type_enc pos T
1506 and formula_from_combformula ctxt format nonmono_Ts type_enc
1507 should_predicate_on_var =
1510 ho_term_from_combterm ctxt format nonmono_Ts type_enc (Top_Level pos)
1513 Simple_Types (_, level) =>
1514 homogenized_type ctxt nonmono_Ts level 0
1515 #> ho_type_from_typ format type_enc false 0 #> SOME
1517 fun do_out_of_bound_type pos phi universal (name, T) =
1518 if should_predicate_on_type ctxt nonmono_Ts type_enc
1519 (fn () => should_predicate_on_var pos phi universal name) T then
1521 |> type_pred_combterm ctxt format type_enc T
1522 |> do_term pos |> AAtom |> SOME
1525 fun do_formula pos (AQuant (q, xs, phi)) =
1527 val phi = phi |> do_formula pos
1528 val universal = Option.map (q = AExists ? not) pos
1530 AQuant (q, xs |> map (apsnd (fn NONE => NONE
1531 | SOME T => do_bound_type T)),
1532 (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
1534 (fn (_, NONE) => NONE
1536 do_out_of_bound_type pos phi universal (s, T))
1540 | do_formula pos (AConn conn) = aconn_map pos do_formula conn
1541 | do_formula pos (AAtom tm) = AAtom (do_term pos tm)
1544 fun bound_tvars type_enc Ts =
1545 mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
1546 (type_literals_for_types type_enc add_sorts_on_tvar Ts))
1548 (* Each fact is given a unique fact number to avoid name clashes (e.g., because
1549 of monomorphization). The TPTP explicitly forbids name clashes, and some of
1550 the remote provers might care. *)
1551 fun formula_line_for_fact ctxt format prefix encode freshen pos nonmono_Ts
1552 type_enc (j, {name, locality, kind, combformula, atomic_types}) =
1553 (prefix ^ (if freshen then string_of_int j ^ "_" else "") ^ encode name,
1556 |> close_combformula_universally
1557 |> formula_from_combformula ctxt format nonmono_Ts type_enc
1558 should_predicate_on_var_in_formula
1559 (if pos then SOME true else NONE)
1560 |> bound_tvars type_enc atomic_types
1561 |> close_formula_universally,
1570 fun formula_line_for_class_rel_clause ({name, subclass, superclass, ...}
1571 : class_rel_clause) =
1572 let val ty_arg = ATerm (`I "T", []) in
1573 Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
1574 AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
1575 AAtom (ATerm (superclass, [ty_arg]))])
1576 |> close_formula_universally, intro_info, NONE)
1579 fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
1580 (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
1581 | fo_literal_from_arity_literal (TVarLit (c, sort)) =
1582 (false, ATerm (c, [ATerm (sort, [])]))
1584 fun formula_line_for_arity_clause ({name, prem_lits, concl_lits, ...}
1586 Formula (arity_clause_prefix ^ name, Axiom,
1587 mk_ahorn (map (formula_from_fo_literal o apfst not
1588 o fo_literal_from_arity_literal) prem_lits)
1589 (formula_from_fo_literal
1590 (fo_literal_from_arity_literal concl_lits))
1591 |> close_formula_universally, intro_info, NONE)
1593 fun formula_line_for_conjecture ctxt format nonmono_Ts type_enc
1594 ({name, kind, combformula, atomic_types, ...} : translated_formula) =
1595 Formula (conjecture_prefix ^ name, kind,
1596 formula_from_combformula ctxt format nonmono_Ts type_enc
1597 should_predicate_on_var_in_formula (SOME false)
1598 (close_combformula_universally combformula)
1599 |> bound_tvars type_enc atomic_types
1600 |> close_formula_universally, NONE, NONE)
1602 fun free_type_literals type_enc ({atomic_types, ...} : translated_formula) =
1603 atomic_types |> type_literals_for_types type_enc add_sorts_on_tfree
1604 |> map fo_literal_from_type_literal
1606 fun formula_line_for_free_type j lit =
1607 Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis,
1608 formula_from_fo_literal lit, NONE, NONE)
1609 fun formula_lines_for_free_types type_enc facts =
1611 val litss = map (free_type_literals type_enc) facts
1612 val lits = fold (union (op =)) litss []
1613 in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
1615 (** Symbol declarations **)
1617 fun should_declare_sym type_enc pred_sym s =
1618 is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
1620 Simple_Types _ => true
1621 | Tags (_, _, Lightweight) => true
1622 | _ => not pred_sym)
1624 fun sym_decl_table_for_facts ctxt type_enc repaired_sym_tab (conjs, facts) =
1626 fun add_combterm in_conj tm =
1627 let val (head, args) = strip_combterm_comb tm in
1629 CombConst ((s, s'), T, T_args) =>
1630 let val pred_sym = is_pred_sym repaired_sym_tab s in
1631 if should_declare_sym type_enc pred_sym s then
1632 Symtab.map_default (s, [])
1633 (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
1639 #> fold (add_combterm in_conj) args
1641 fun add_fact in_conj =
1642 fact_lift (formula_fold NONE (K (add_combterm in_conj)))
1645 |> is_type_enc_fairly_sound type_enc
1646 ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
1649 (* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
1650 out with monotonicity" paper presented at CADE 2011. *)
1651 fun add_combterm_nonmonotonic_types _ _ _ _ (SOME false) _ = I
1652 | add_combterm_nonmonotonic_types ctxt level sound locality _
1653 (CombApp (CombApp (CombConst ((s, _), Type (_, [T, _]), _), tm1),
1655 (is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
1657 Noninf_Nonmono_Types =>
1658 not (is_locality_global locality) orelse
1659 not (is_type_surely_infinite ctxt sound T)
1660 | Fin_Nonmono_Types => is_type_surely_finite ctxt false T
1661 | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
1662 | add_combterm_nonmonotonic_types _ _ _ _ _ _ = I
1663 fun add_fact_nonmonotonic_types ctxt level sound
1664 ({kind, locality, combformula, ...} : translated_formula) =
1665 formula_fold (SOME (kind <> Conjecture))
1666 (add_combterm_nonmonotonic_types ctxt level sound locality)
1668 fun nonmonotonic_types_for_facts ctxt type_enc sound facts =
1669 let val level = level_of_type_enc type_enc in
1670 if level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types then
1671 [] |> fold (add_fact_nonmonotonic_types ctxt level sound) facts
1672 (* We must add "bool" in case the helper "True_or_False" is added
1673 later. In addition, several places in the code rely on the list of
1674 nonmonotonic types not being empty. *)
1675 |> insert_type ctxt I @{typ bool}
1680 fun decl_line_for_sym ctxt format nonmono_Ts type_enc s
1681 (s', T_args, T, pred_sym, ary, _) =
1683 val (T_arg_Ts, level) =
1685 Simple_Types (_, level) => ([], level)
1686 | _ => (replicate (length T_args) homo_infinite_type, No_Types)
1688 Decl (sym_decl_prefix ^ s, (s, s'),
1689 (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
1690 |> ho_type_from_typ format type_enc pred_sym (length T_arg_Ts + ary))
1693 fun formula_line_for_preds_sym_decl ctxt format conj_sym_kind nonmono_Ts
1694 poly_nonmono_Ts type_enc n s j (s', T_args, T, _, ary, in_conj) =
1696 val (kind, maybe_negate) =
1697 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1699 val (arg_Ts, res_T) = chop_fun ary T
1700 val num_args = length arg_Ts
1702 1 upto num_args |> map (`I o make_bound_var o string_of_int)
1704 bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
1705 val sym_needs_arg_types = n > 1 orelse exists (curry (op =) dummyT) T_args
1706 fun should_keep_arg_type T =
1707 sym_needs_arg_types orelse
1708 not (should_predicate_on_type ctxt nonmono_Ts type_enc (K false) T)
1710 arg_Ts |> map (fn T => if should_keep_arg_type T then SOME T else NONE)
1712 Formula (preds_sym_formula_prefix ^ s ^
1713 (if n > 1 then "_" ^ string_of_int j else ""), kind,
1714 CombConst ((s, s'), T, T_args)
1715 |> fold (curry (CombApp o swap)) bounds
1716 |> type_pred_combterm ctxt format type_enc res_T
1717 |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
1718 |> formula_from_combformula ctxt format poly_nonmono_Ts type_enc
1719 (K (K (K (K true)))) (SOME true)
1720 |> n > 1 ? bound_tvars type_enc (atyps_of T)
1721 |> close_formula_universally
1726 fun formula_lines_for_lightweight_tags_sym_decl ctxt format conj_sym_kind
1727 poly_nonmono_Ts type_enc n s
1728 (j, (s', T_args, T, pred_sym, ary, in_conj)) =
1731 lightweight_tags_sym_formula_prefix ^ s ^
1732 (if n > 1 then "_" ^ string_of_int j else "")
1733 val (kind, maybe_negate) =
1734 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1736 val (arg_Ts, res_T) = chop_fun ary T
1738 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
1739 val bounds = bound_names |> map (fn name => ATerm (name, []))
1740 val cst = mk_aterm format type_enc (s, s') T_args
1741 val atomic_Ts = atyps_of T
1743 (if pred_sym then AConn (AIff, map AAtom tms)
1744 else AAtom (ATerm (`I tptp_equal, tms)))
1745 |> bound_tvars type_enc atomic_Ts
1746 |> close_formula_universally
1748 (* See also "should_tag_with_type". *)
1749 fun should_encode T =
1750 should_encode_type ctxt poly_nonmono_Ts All_Types T orelse
1752 Tags (Polymorphic, level, Lightweight) =>
1753 level <> All_Types andalso Monomorph.typ_has_tvars T
1755 val tag_with = tag_with_type ctxt format poly_nonmono_Ts type_enc NONE
1756 val add_formula_for_res =
1757 if should_encode res_T then
1758 cons (Formula (ident_base ^ "_res", kind,
1759 eq [tag_with res_T (cst bounds), cst bounds],
1763 fun add_formula_for_arg k =
1764 let val arg_T = nth arg_Ts k in
1765 if should_encode arg_T then
1766 case chop k bounds of
1767 (bounds1, bound :: bounds2) =>
1768 cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
1769 eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
1772 | _ => raise Fail "expected nonempty tail"
1777 [] |> not pred_sym ? add_formula_for_res
1778 |> fold add_formula_for_arg (ary - 1 downto 0)
1781 fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
1783 fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts
1784 poly_nonmono_Ts type_enc (s, decls) =
1787 decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_enc s)
1792 decl :: (decls' as _ :: _) =>
1793 let val T = result_type_of_decl decl in
1794 if forall (curry (type_instance ctxt o swap) T
1795 o result_type_of_decl) decls' then
1801 val n = length decls
1803 decls |> filter (should_predicate_on_type ctxt poly_nonmono_Ts type_enc
1805 o result_type_of_decl)
1807 (0 upto length decls - 1, decls)
1808 |-> map2 (formula_line_for_preds_sym_decl ctxt format conj_sym_kind
1809 nonmono_Ts poly_nonmono_Ts type_enc n s)
1811 | Tags (_, _, heaviness) =>
1815 let val n = length decls in
1816 (0 upto n - 1 ~~ decls)
1817 |> maps (formula_lines_for_lightweight_tags_sym_decl ctxt format
1818 conj_sym_kind poly_nonmono_Ts type_enc n s)
1821 fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1822 poly_nonmono_Ts type_enc sym_decl_tab =
1827 |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
1828 nonmono_Ts poly_nonmono_Ts type_enc)
1830 fun needs_type_tag_idempotence (Tags (poly, level, heaviness)) =
1831 poly <> Mangled_Monomorphic andalso
1832 ((level = All_Types andalso heaviness = Lightweight) orelse
1833 level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types)
1834 | needs_type_tag_idempotence _ = false
1836 fun offset_of_heading_in_problem _ [] j = j
1837 | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
1838 if heading = needle then j
1839 else offset_of_heading_in_problem needle problem (j + length lines)
1841 val implicit_declsN = "Should-be-implicit typings"
1842 val explicit_declsN = "Explicit typings"
1843 val factsN = "Relevant facts"
1844 val class_relsN = "Class relationships"
1845 val aritiesN = "Arities"
1846 val helpersN = "Helper facts"
1847 val conjsN = "Conjectures"
1848 val free_typesN = "Type variables"
1850 val explicit_apply = NONE (* for experimental purposes *)
1852 fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_enc sound
1853 exporter readable_names preproc hyp_ts concl_t facts =
1855 val (format, type_enc) = choose_format [format] type_enc
1856 val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
1857 translate_formulas ctxt format prem_kind type_enc preproc hyp_ts concl_t
1859 val sym_tab = conjs @ facts |> sym_table_for_facts ctxt explicit_apply
1861 conjs @ facts |> nonmonotonic_types_for_facts ctxt type_enc sound
1862 val repair = repair_fact ctxt format type_enc sym_tab
1863 val (conjs, facts) = (conjs, facts) |> pairself (map repair)
1864 val repaired_sym_tab =
1865 conjs @ facts |> sym_table_for_facts ctxt (SOME false)
1867 repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_enc
1869 val poly_nonmono_Ts =
1870 if null nonmono_Ts orelse nonmono_Ts = [@{typ bool}] orelse
1871 polymorphism_of_type_enc type_enc <> Polymorphic then
1874 [TVar (("'a", 0), HOLogic.typeS)]
1875 val sym_decl_lines =
1876 (conjs, helpers @ facts)
1877 |> sym_decl_table_for_facts ctxt type_enc repaired_sym_tab
1878 |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1879 poly_nonmono_Ts type_enc
1881 0 upto length helpers - 1 ~~ helpers
1882 |> map (formula_line_for_fact ctxt format helper_prefix I false true
1883 poly_nonmono_Ts type_enc)
1884 |> (if needs_type_tag_idempotence type_enc then
1885 cons (type_tag_idempotence_fact ())
1888 (* Reordering these might confuse the proof reconstruction code or the SPASS
1891 [(explicit_declsN, sym_decl_lines),
1893 map (formula_line_for_fact ctxt format fact_prefix ascii_of
1894 (not exporter) (not exporter) nonmono_Ts
1896 (0 upto length facts - 1 ~~ facts)),
1897 (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
1898 (aritiesN, map formula_line_for_arity_clause arity_clauses),
1899 (helpersN, helper_lines),
1901 map (formula_line_for_conjecture ctxt format nonmono_Ts type_enc)
1903 (free_typesN, formula_lines_for_free_types type_enc (facts @ conjs))]
1907 CNF => ensure_cnf_problem
1908 | CNF_UEQ => filter_cnf_ueq_problem
1910 |> (if is_format_typed format then
1911 declare_undeclared_syms_in_atp_problem type_decl_prefix
1915 val (problem, pool) = problem |> nice_atp_problem readable_names
1916 val helpers_offset = offset_of_heading_in_problem helpersN problem 0
1918 map_filter (fn (j, {name, ...}) =>
1919 if String.isSuffix typed_helper_suffix name then SOME j
1921 ((helpers_offset + 1 upto helpers_offset + length helpers)
1923 fun add_sym_arity (s, {min_ary, ...} : sym_info) =
1925 case strip_prefix_and_unascii const_prefix s of
1926 SOME s => Symtab.insert (op =) (s, min_ary)
1932 case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
1933 offset_of_heading_in_problem conjsN problem 0,
1934 offset_of_heading_in_problem factsN problem 0,
1935 fact_names |> Vector.fromList,
1937 Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
1941 val conj_weight = 0.0
1942 val hyp_weight = 0.1
1943 val fact_min_weight = 0.2
1944 val fact_max_weight = 1.0
1945 val type_info_default_weight = 0.8
1947 fun add_term_weights weight (ATerm (s, tms)) =
1948 is_tptp_user_symbol s ? Symtab.default (s, weight)
1949 #> fold (add_term_weights weight) tms
1950 | add_term_weights weight (AAbs (_, tm)) = add_term_weights weight tm
1951 fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
1952 formula_fold NONE (K (add_term_weights weight)) phi
1953 | add_problem_line_weights _ _ = I
1955 fun add_conjectures_weights [] = I
1956 | add_conjectures_weights conjs =
1957 let val (hyps, conj) = split_last conjs in
1958 add_problem_line_weights conj_weight conj
1959 #> fold (add_problem_line_weights hyp_weight) hyps
1962 fun add_facts_weights facts =
1964 val num_facts = length facts
1966 fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
1967 / Real.fromInt num_facts
1969 map weight_of (0 upto num_facts - 1) ~~ facts
1970 |> fold (uncurry add_problem_line_weights)
1973 (* Weights are from 0.0 (most important) to 1.0 (least important). *)
1974 fun atp_problem_weights problem =
1975 let val get = these o AList.lookup (op =) problem in
1977 |> add_conjectures_weights (get free_typesN @ get conjsN)
1978 |> add_facts_weights (get factsN)
1979 |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
1980 [explicit_declsN, class_relsN, aritiesN]
1982 |> sort (prod_ord Real.compare string_ord o pairself swap)