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 polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
24 All_Types | Noninf_Nonmono_Types | Fin_Nonmono_Types | Const_Arg_Types |
26 datatype type_heaviness = Heavyweight | Lightweight
29 Simple_Types of type_level |
30 Preds of polymorphism * type_level * type_heaviness |
31 Tags of polymorphism * type_level * type_heaviness
33 val bound_var_prefix : string
34 val schematic_var_prefix : string
35 val fixed_var_prefix : string
36 val tvar_prefix : string
37 val tfree_prefix : string
38 val const_prefix : string
39 val type_const_prefix : string
40 val class_prefix : string
41 val skolem_const_prefix : string
42 val old_skolem_const_prefix : string
43 val new_skolem_const_prefix : string
44 val type_decl_prefix : string
45 val sym_decl_prefix : string
46 val preds_sym_formula_prefix : string
47 val lightweight_tags_sym_formula_prefix : string
48 val fact_prefix : string
49 val conjecture_prefix : string
50 val helper_prefix : string
51 val class_rel_clause_prefix : string
52 val arity_clause_prefix : string
53 val tfree_clause_prefix : string
54 val typed_helper_suffix : string
55 val untyped_helper_suffix : string
56 val type_tag_idempotence_helper_name : string
57 val predicator_name : string
58 val app_op_name : string
59 val type_tag_name : string
60 val type_pred_name : string
61 val simple_type_prefix : string
62 val prefixed_predicator_name : string
63 val prefixed_app_op_name : string
64 val prefixed_type_tag_name : string
65 val ascii_of : string -> string
66 val unascii_of : string -> string
67 val strip_prefix_and_unascii : string -> string -> string option
68 val proxy_table : (string * (string * (thm * (string * string)))) list
69 val proxify_const : string -> (string * string) option
70 val invert_const : string -> string
71 val unproxify_const : string -> string
72 val new_skolem_var_name_from_const : string -> string
73 val num_type_args : theory -> string -> int
74 val atp_irrelevant_consts : string list
75 val atp_schematic_consts_of : term -> typ list Symtab.table
76 val is_locality_global : locality -> bool
77 val type_sys_from_string : string -> type_sys
78 val polymorphism_of_type_sys : type_sys -> polymorphism
79 val level_of_type_sys : type_sys -> type_level
80 val is_type_sys_virtually_sound : type_sys -> bool
81 val is_type_sys_fairly_sound : type_sys -> bool
82 val choose_format : format list -> type_sys -> format * type_sys
84 connective -> ('a, 'b, 'c) formula list -> ('a, 'b, 'c) formula
85 val unmangled_const : string -> string * string fo_term list
86 val unmangled_const_name : string -> string
87 val helper_table : ((string * bool) * thm list) list
89 val prepare_atp_problem :
90 Proof.context -> format -> formula_kind -> formula_kind -> type_sys -> bool
91 -> bool -> bool -> bool -> term list -> term
92 -> ((string * locality) * term) list
93 -> string problem * string Symtab.table * int * int
94 * (string * locality) list vector * int list * int Symtab.table
95 val atp_problem_weights : string problem -> (string * real) list
98 structure ATP_Translate : ATP_TRANSLATE =
104 type name = string * string
107 val generate_useful_info = false
109 fun useful_isabelle_info s =
110 if generate_useful_info then
111 SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
115 val intro_info = useful_isabelle_info "intro"
116 val elim_info = useful_isabelle_info "elim"
117 val simp_info = useful_isabelle_info "simp"
119 val bound_var_prefix = "B_"
120 val schematic_var_prefix = "V_"
121 val fixed_var_prefix = "v_"
123 val tvar_prefix = "T_"
124 val tfree_prefix = "t_"
126 val const_prefix = "c_"
127 val type_const_prefix = "tc_"
128 val class_prefix = "cl_"
130 val skolem_const_prefix = "Sledgehammer" ^ Long_Name.separator ^ "Sko"
131 val old_skolem_const_prefix = skolem_const_prefix ^ "o"
132 val new_skolem_const_prefix = skolem_const_prefix ^ "n"
134 val type_decl_prefix = "ty_"
135 val sym_decl_prefix = "sy_"
136 val preds_sym_formula_prefix = "psy_"
137 val lightweight_tags_sym_formula_prefix = "tsy_"
138 val fact_prefix = "fact_"
139 val conjecture_prefix = "conj_"
140 val helper_prefix = "help_"
141 val class_rel_clause_prefix = "clar_"
142 val arity_clause_prefix = "arity_"
143 val tfree_clause_prefix = "tfree_"
145 val typed_helper_suffix = "_T"
146 val untyped_helper_suffix = "_U"
147 val type_tag_idempotence_helper_name = helper_prefix ^ "ti_idem"
149 val predicator_name = "hBOOL"
150 val app_op_name = "hAPP"
151 val type_tag_name = "ti"
152 val type_pred_name = "is"
153 val simple_type_prefix = "ty_"
155 val prefixed_predicator_name = const_prefix ^ predicator_name
156 val prefixed_app_op_name = const_prefix ^ app_op_name
157 val prefixed_type_tag_name = const_prefix ^ type_tag_name
159 (* Freshness almost guaranteed! *)
160 val sledgehammer_weak_prefix = "Sledgehammer:"
162 (*Escaping of special characters.
163 Alphanumeric characters are left unchanged.
164 The character _ goes to __
165 Characters in the range ASCII space to / go to _A to _P, respectively.
166 Other characters go to _nnn where nnn is the decimal ASCII code.*)
167 val upper_a_minus_space = Char.ord #"A" - Char.ord #" "
169 fun stringN_of_int 0 _ = ""
170 | stringN_of_int k n =
171 stringN_of_int (k - 1) (n div 10) ^ string_of_int (n mod 10)
173 fun ascii_of_char c =
174 if Char.isAlphaNum c then
176 else if c = #"_" then
178 else if #" " <= c andalso c <= #"/" then
179 "_" ^ String.str (Char.chr (Char.ord c + upper_a_minus_space))
181 (* fixed width, in case more digits follow *)
182 "_" ^ stringN_of_int 3 (Char.ord c)
184 val ascii_of = String.translate ascii_of_char
186 (** Remove ASCII armoring from names in proof files **)
188 (* We don't raise error exceptions because this code can run inside a worker
189 thread. Also, the errors are impossible. *)
192 fun un rcs [] = String.implode(rev rcs)
193 | un rcs [#"_"] = un (#"_" :: rcs) [] (* ERROR *)
194 (* Three types of _ escapes: __, _A to _P, _nnn *)
195 | un rcs (#"_" :: #"_" :: cs) = un (#"_" :: rcs) cs
196 | un rcs (#"_" :: c :: cs) =
197 if #"A" <= c andalso c<= #"P" then
198 (* translation of #" " to #"/" *)
199 un (Char.chr (Char.ord c - upper_a_minus_space) :: rcs) cs
201 let val digits = List.take (c :: cs, 3) handle General.Subscript => [] in
202 case Int.fromString (String.implode digits) of
203 SOME n => un (Char.chr n :: rcs) (List.drop (cs, 2))
204 | NONE => un (c :: #"_" :: rcs) cs (* ERROR *)
206 | un rcs (c :: cs) = un (c :: rcs) cs
207 in un [] o String.explode end
209 (* If string s has the prefix s1, return the result of deleting it,
211 fun strip_prefix_and_unascii s1 s =
212 if String.isPrefix s1 s then
213 SOME (unascii_of (String.extract (s, size s1, NONE)))
218 [("c_False", (@{const_name False}, (@{thm fFalse_def},
219 ("fFalse", @{const_name ATP.fFalse})))),
220 ("c_True", (@{const_name True}, (@{thm fTrue_def},
221 ("fTrue", @{const_name ATP.fTrue})))),
222 ("c_Not", (@{const_name Not}, (@{thm fNot_def},
223 ("fNot", @{const_name ATP.fNot})))),
224 ("c_conj", (@{const_name conj}, (@{thm fconj_def},
225 ("fconj", @{const_name ATP.fconj})))),
226 ("c_disj", (@{const_name disj}, (@{thm fdisj_def},
227 ("fdisj", @{const_name ATP.fdisj})))),
228 ("c_implies", (@{const_name implies}, (@{thm fimplies_def},
229 ("fimplies", @{const_name ATP.fimplies})))),
230 ("equal", (@{const_name HOL.eq}, (@{thm fequal_def},
231 ("fequal", @{const_name ATP.fequal}))))]
233 val proxify_const = AList.lookup (op =) proxy_table #> Option.map (snd o snd)
235 (* Readable names for the more common symbolic functions. Do not mess with the
236 table unless you know what you are doing. *)
237 val const_trans_table =
238 [(@{type_name Product_Type.prod}, "prod"),
239 (@{type_name Sum_Type.sum}, "sum"),
240 (@{const_name False}, "False"),
241 (@{const_name True}, "True"),
242 (@{const_name Not}, "Not"),
243 (@{const_name conj}, "conj"),
244 (@{const_name disj}, "disj"),
245 (@{const_name implies}, "implies"),
246 (@{const_name HOL.eq}, "equal"),
247 (@{const_name If}, "If"),
248 (@{const_name Set.member}, "member"),
249 (@{const_name Meson.COMBI}, "COMBI"),
250 (@{const_name Meson.COMBK}, "COMBK"),
251 (@{const_name Meson.COMBB}, "COMBB"),
252 (@{const_name Meson.COMBC}, "COMBC"),
253 (@{const_name Meson.COMBS}, "COMBS")]
255 |> fold (Symtab.update o swap o snd o snd o snd) proxy_table
257 (* Invert the table of translations between Isabelle and ATPs. *)
258 val const_trans_table_inv =
259 const_trans_table |> Symtab.dest |> map swap |> Symtab.make
260 val const_trans_table_unprox =
262 |> fold (fn (_, (isa, (_, (_, atp)))) => Symtab.update (atp, isa)) proxy_table
264 val invert_const = perhaps (Symtab.lookup const_trans_table_inv)
265 val unproxify_const = perhaps (Symtab.lookup const_trans_table_unprox)
268 case Symtab.lookup const_trans_table c of
272 fun ascii_of_indexname (v, 0) = ascii_of v
273 | ascii_of_indexname (v, i) = ascii_of v ^ "_" ^ string_of_int i
275 fun make_bound_var x = bound_var_prefix ^ ascii_of x
276 fun make_schematic_var v = schematic_var_prefix ^ ascii_of_indexname v
277 fun make_fixed_var x = fixed_var_prefix ^ ascii_of x
279 fun make_schematic_type_var (x, i) =
280 tvar_prefix ^ (ascii_of_indexname (unprefix "'" x, i))
281 fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (unprefix "'" x))
283 (* "HOL.eq" is mapped to the ATP's equality. *)
284 fun make_fixed_const @{const_name HOL.eq} = tptp_old_equal
285 | make_fixed_const c = const_prefix ^ lookup_const c
287 fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
289 fun make_type_class clas = class_prefix ^ ascii_of clas
291 fun new_skolem_var_name_from_const s =
292 let val ss = s |> space_explode Long_Name.separator in
293 nth ss (length ss - 2)
296 (* The number of type arguments of a constant, zero if it's monomorphic. For
297 (instances of) Skolem pseudoconstants, this information is encoded in the
299 fun num_type_args thy s =
300 if String.isPrefix skolem_const_prefix s then
301 s |> space_explode Long_Name.separator |> List.last |> Int.fromString |> the
303 (s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
305 (* These are either simplified away by "Meson.presimplify" (most of the time) or
306 handled specially via "fFalse", "fTrue", ..., "fequal". *)
307 val atp_irrelevant_consts =
308 [@{const_name False}, @{const_name True}, @{const_name Not},
309 @{const_name conj}, @{const_name disj}, @{const_name implies},
310 @{const_name HOL.eq}, @{const_name If}, @{const_name Let}]
312 val atp_monomorph_bad_consts =
313 atp_irrelevant_consts @
314 (* These are ignored anyway by the relevance filter (unless they appear in
315 higher-order places) but not by the monomorphizer. *)
316 [@{const_name all}, @{const_name "==>"}, @{const_name "=="},
317 @{const_name Trueprop}, @{const_name All}, @{const_name Ex},
318 @{const_name Ex1}, @{const_name Ball}, @{const_name Bex}]
320 fun add_schematic_const (x as (_, T)) =
321 Monomorph.typ_has_tvars T ? Symtab.insert_list (op =) x
322 val add_schematic_consts_of =
323 Term.fold_aterms (fn Const (x as (s, _)) =>
324 not (member (op =) atp_monomorph_bad_consts s)
325 ? add_schematic_const x
327 fun atp_schematic_consts_of t = add_schematic_consts_of t Symtab.empty
329 (** Definitions and functions for FOL clauses and formulas for TPTP **)
331 (* The first component is the type class; the second is a "TVar" or "TFree". *)
332 datatype type_literal =
333 TyLitVar of name * name |
334 TyLitFree of name * name
337 (** Isabelle arities **)
339 datatype arity_literal =
340 TConsLit of name * name * name list |
341 TVarLit of name * name
344 | gen_TVars n = ("T_" ^ string_of_int n) :: gen_TVars (n-1)
346 val type_class = the_single @{sort type}
348 fun add_packed_sort tvar =
349 fold (fn s => s <> type_class ? cons (`make_type_class s, `I tvar))
353 prem_lits : arity_literal list,
354 concl_lits : arity_literal}
356 (* Arity of type constructor "tcon :: (arg1, ..., argN) res" *)
357 fun make_axiom_arity_clause (tcons, name, (cls, args)) =
359 val tvars = gen_TVars (length args)
360 val tvars_srts = ListPair.zip (tvars, args)
363 prem_lits = [] |> fold (uncurry add_packed_sort) tvars_srts |> map TVarLit,
364 concl_lits = TConsLit (`make_type_class cls,
365 `make_fixed_type_const tcons,
369 fun arity_clause _ _ (_, []) = []
370 | arity_clause seen n (tcons, ("HOL.type", _) :: ars) = (* ignore *)
371 arity_clause seen n (tcons, ars)
372 | arity_clause seen n (tcons, (ar as (class, _)) :: ars) =
373 if member (op =) seen class then
374 (* multiple arities for the same (tycon, class) pair *)
375 make_axiom_arity_clause (tcons,
376 lookup_const tcons ^ "___" ^ ascii_of class ^ "_" ^ string_of_int n,
378 arity_clause seen (n + 1) (tcons, ars)
380 make_axiom_arity_clause (tcons, lookup_const tcons ^ "___" ^
381 ascii_of class, ar) ::
382 arity_clause (class :: seen) n (tcons, ars)
384 fun multi_arity_clause [] = []
385 | multi_arity_clause ((tcons, ars) :: tc_arlists) =
386 arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
388 (* Generate all pairs (tycon, class, sorts) such that tycon belongs to class in
389 theory thy provided its arguments have the corresponding sorts. *)
390 fun type_class_pairs thy tycons classes =
392 val alg = Sign.classes_of thy
393 fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
394 fun add_class tycon class =
395 cons (class, domain_sorts tycon class)
396 handle Sorts.CLASS_ERROR _ => I
397 fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
398 in map try_classes tycons end
400 (*Proving one (tycon, class) membership may require proving others, so iterate.*)
401 fun iter_type_class_pairs _ _ [] = ([], [])
402 | iter_type_class_pairs thy tycons classes =
404 fun maybe_insert_class s =
405 (s <> type_class andalso not (member (op =) classes s))
407 val cpairs = type_class_pairs thy tycons classes
409 [] |> fold (fold (fold (fold maybe_insert_class) o snd) o snd) cpairs
410 val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
411 in (classes' @ classes, union (op =) cpairs' cpairs) end
413 fun make_arity_clauses thy tycons =
414 iter_type_class_pairs thy tycons ##> multi_arity_clause
417 (** Isabelle class relations **)
419 type class_rel_clause =
424 (* Generate all pairs (sub, super) such that sub is a proper subclass of super
426 fun class_pairs _ [] _ = []
427 | class_pairs thy subs supers =
429 val class_less = Sorts.class_less (Sign.classes_of thy)
430 fun add_super sub super = class_less (sub, super) ? cons (sub, super)
431 fun add_supers sub = fold (add_super sub) supers
432 in fold add_supers subs [] end
434 fun make_class_rel_clause (sub, super) =
435 {name = sub ^ "_" ^ super, subclass = `make_type_class sub,
436 superclass = `make_type_class super}
438 fun make_class_rel_clauses thy subs supers =
439 map make_class_rel_clause (class_pairs thy subs supers)
442 CombConst of name * typ * typ list |
443 CombVar of name * typ |
444 CombApp of combterm * combterm
446 fun combtyp_of (CombConst (_, T, _)) = T
447 | combtyp_of (CombVar (_, T)) = T
448 | combtyp_of (CombApp (t1, _)) = snd (dest_funT (combtyp_of t1))
450 (*gets the head of a combinator application, along with the list of arguments*)
451 fun strip_combterm_comb u =
453 fun stripc (CombApp (t, u), ts) = stripc (t, u :: ts)
455 in stripc (u, []) end
457 fun atyps_of T = fold_atyps (insert (op =)) T []
459 fun new_skolem_const_name s num_T_args =
460 [new_skolem_const_prefix, s, string_of_int num_T_args]
461 |> space_implode Long_Name.separator
463 (* Converts a term (with combinators) into a combterm. Also accumulates sort
465 fun combterm_from_term thy bs (P $ Q) =
467 val (P', P_atomics_Ts) = combterm_from_term thy bs P
468 val (Q', Q_atomics_Ts) = combterm_from_term thy bs Q
469 in (CombApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
470 | combterm_from_term thy _ (Const (c, T)) =
473 (if String.isPrefix old_skolem_const_prefix c then
474 [] |> Term.add_tvarsT T |> map TVar
476 (c, T) |> Sign.const_typargs thy)
477 val c' = CombConst (`make_fixed_const c, T, tvar_list)
478 in (c', atyps_of T) end
479 | combterm_from_term _ _ (Free (v, T)) =
480 (CombConst (`make_fixed_var v, T, []), atyps_of T)
481 | combterm_from_term _ _ (Var (v as (s, _), T)) =
482 (if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
484 val Ts = T |> strip_type |> swap |> op ::
485 val s' = new_skolem_const_name s (length Ts)
486 in CombConst (`make_fixed_const s', T, Ts) end
488 CombVar ((make_schematic_var v, s), T), atyps_of T)
489 | combterm_from_term _ bs (Bound j) =
491 |> (fn (s, T) => (CombConst (`make_bound_var s, T, []), atyps_of T))
492 | combterm_from_term _ _ (Abs _) = raise Fail "HOL clause: Abs"
495 General | Helper | Extensionality | Intro | Elim | Simp | Local | Assum |
498 (* (quasi-)underapproximation of the truth *)
499 fun is_locality_global Local = false
500 | is_locality_global Assum = false
501 | is_locality_global Chained = false
502 | is_locality_global _ = true
504 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
505 datatype type_level =
506 All_Types | Noninf_Nonmono_Types | Fin_Nonmono_Types | Const_Arg_Types |
508 datatype type_heaviness = Heavyweight | Lightweight
511 Simple_Types of type_level |
512 Preds of polymorphism * type_level * type_heaviness |
513 Tags of polymorphism * type_level * type_heaviness
515 fun try_unsuffixes ss s =
516 fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
518 fun type_sys_from_string s =
519 (case try (unprefix "poly_") s of
520 SOME s => (SOME Polymorphic, s)
522 case try (unprefix "mono_") s of
523 SOME s => (SOME Monomorphic, s)
525 case try (unprefix "mangled_") s of
526 SOME s => (SOME Mangled_Monomorphic, s)
529 (* "_query" and "_bang" are for the ASCII-challenged Mirabelle. *)
530 case try_unsuffixes ["?", "_query"] s of
531 SOME s => (Noninf_Nonmono_Types, s)
533 case try_unsuffixes ["!", "_bang"] s of
534 SOME s => (Fin_Nonmono_Types, s)
535 | NONE => (All_Types, s))
537 case try (unsuffix "_heavy") s of
538 SOME s => (Heavyweight, s)
539 | NONE => (Lightweight, s))
540 |> (fn (poly, (level, (heaviness, core))) =>
541 case (core, (poly, level, heaviness)) of
542 ("simple", (NONE, _, Lightweight)) => Simple_Types level
543 | ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
544 | ("tags", (SOME Polymorphic, _, _)) =>
545 Tags (Polymorphic, level, heaviness)
546 | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
547 | ("args", (SOME poly, All_Types (* naja *), Lightweight)) =>
548 Preds (poly, Const_Arg_Types, Lightweight)
549 | ("erased", (NONE, All_Types (* naja *), Lightweight)) =>
550 Preds (Polymorphic, No_Types, Lightweight)
551 | _ => raise Same.SAME)
552 handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
554 fun polymorphism_of_type_sys (Simple_Types _) = Mangled_Monomorphic
555 | polymorphism_of_type_sys (Preds (poly, _, _)) = poly
556 | polymorphism_of_type_sys (Tags (poly, _, _)) = poly
558 fun level_of_type_sys (Simple_Types level) = level
559 | level_of_type_sys (Preds (_, level, _)) = level
560 | level_of_type_sys (Tags (_, level, _)) = level
562 fun heaviness_of_type_sys (Simple_Types _) = Heavyweight
563 | heaviness_of_type_sys (Preds (_, _, heaviness)) = heaviness
564 | heaviness_of_type_sys (Tags (_, _, heaviness)) = heaviness
566 fun is_type_level_virtually_sound level =
567 level = All_Types orelse level = Noninf_Nonmono_Types
568 val is_type_sys_virtually_sound =
569 is_type_level_virtually_sound o level_of_type_sys
571 fun is_type_level_fairly_sound level =
572 is_type_level_virtually_sound level orelse level = Fin_Nonmono_Types
573 val is_type_sys_fairly_sound = is_type_level_fairly_sound o level_of_type_sys
575 fun is_setting_higher_order THF (Simple_Types _) = true
576 | is_setting_higher_order _ _ = false
578 fun choose_format formats (Simple_Types level) =
579 if member (op =) formats THF then (THF, Simple_Types level)
580 else if member (op =) formats TFF then (TFF, Simple_Types level)
581 else choose_format formats (Preds (Mangled_Monomorphic, level, Heavyweight))
582 | choose_format formats type_sys =
585 (CNF_UEQ, case type_sys of
587 (if is_type_sys_fairly_sound type_sys then Tags else Preds)
590 | format => (format, type_sys))
592 type translated_formula =
596 combformula : (name, typ, combterm) formula,
597 atomic_types : typ list}
599 fun update_combformula f ({name, locality, kind, combformula, atomic_types}
600 : translated_formula) =
601 {name = name, locality = locality, kind = kind, combformula = f combformula,
602 atomic_types = atomic_types} : translated_formula
604 fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
606 val type_instance = Sign.typ_instance o Proof_Context.theory_of
608 fun insert_type ctxt get_T x xs =
609 let val T = get_T x in
610 if exists (curry (type_instance ctxt) T o get_T) xs then xs
611 else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
614 (* The Booleans indicate whether all type arguments should be kept. *)
615 datatype type_arg_policy =
616 Explicit_Type_Args of bool |
617 Mangled_Type_Args of bool |
620 fun should_drop_arg_type_args (Simple_Types _) =
621 false (* since TFF doesn't support overloading *)
622 | should_drop_arg_type_args type_sys =
623 level_of_type_sys type_sys = All_Types andalso
624 heaviness_of_type_sys type_sys = Heavyweight
626 fun general_type_arg_policy (Tags (_, All_Types, Heavyweight)) = No_Type_Args
627 | general_type_arg_policy type_sys =
628 if level_of_type_sys type_sys = No_Types then
630 else if polymorphism_of_type_sys type_sys = Mangled_Monomorphic then
631 Mangled_Type_Args (should_drop_arg_type_args type_sys)
633 Explicit_Type_Args (should_drop_arg_type_args type_sys)
635 fun type_arg_policy type_sys s =
636 if s = @{const_name HOL.eq} orelse
637 (s = app_op_name andalso level_of_type_sys type_sys = Const_Arg_Types) then
639 else if s = type_tag_name then
640 Explicit_Type_Args false
642 general_type_arg_policy type_sys
644 (*Make literals for sorted type variables*)
645 fun generic_add_sorts_on_type (_, []) = I
646 | generic_add_sorts_on_type ((x, i), s :: ss) =
647 generic_add_sorts_on_type ((x, i), ss)
648 #> (if s = the_single @{sort HOL.type} then
651 insert (op =) (TyLitFree (`make_type_class s, `make_fixed_type_var x))
653 insert (op =) (TyLitVar (`make_type_class s,
654 (make_schematic_type_var (x, i), x))))
655 fun add_sorts_on_tfree (TFree (s, S)) = generic_add_sorts_on_type ((s, ~1), S)
656 | add_sorts_on_tfree _ = I
657 fun add_sorts_on_tvar (TVar z) = generic_add_sorts_on_type z
658 | add_sorts_on_tvar _ = I
660 fun type_literals_for_types type_sys add_sorts_on_typ Ts =
661 [] |> level_of_type_sys type_sys <> No_Types ? fold add_sorts_on_typ Ts
663 fun mk_aconns c phis =
664 let val (phis', phi') = split_last phis in
665 fold_rev (mk_aconn c) phis' phi'
667 fun mk_ahorn [] phi = phi
668 | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
669 fun mk_aquant _ [] phi = phi
670 | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
671 if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
672 | mk_aquant q xs phi = AQuant (q, xs, phi)
674 fun close_universally atom_vars phi =
676 fun formula_vars bounds (AQuant (_, xs, phi)) =
677 formula_vars (map fst xs @ bounds) phi
678 | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
679 | formula_vars bounds (AAtom tm) =
680 union (op =) (atom_vars tm []
681 |> filter_out (member (op =) bounds o fst))
682 in mk_aquant AForall (formula_vars [] phi []) phi end
684 fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
685 | combterm_vars (CombConst _) = I
686 | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
687 fun close_combformula_universally phi = close_universally combterm_vars phi
689 fun term_vars (ATerm (name as (s, _), tms)) =
690 is_tptp_variable s ? insert (op =) (name, NONE) #> fold term_vars tms
691 fun close_formula_universally phi = close_universally term_vars phi
693 val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
694 val homo_infinite_type = Type (homo_infinite_type_name, [])
696 fun fo_term_from_typ format type_sys =
698 fun term (Type (s, Ts)) =
699 ATerm (case (is_setting_higher_order format type_sys, s) of
700 (true, @{type_name bool}) => `I tptp_bool_type
701 | (true, @{type_name fun}) => `I tptp_fun_type
702 | _ => if s = homo_infinite_type_name andalso
703 (format = TFF orelse format = THF) then
704 `I tptp_individual_type
706 `make_fixed_type_const s,
708 | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
709 | term (TVar ((x as (s, _)), _)) =
710 ATerm ((make_schematic_type_var x, s), [])
713 fun fo_term_for_type_arg format type_sys T =
714 if T = dummyT then NONE else SOME (fo_term_from_typ format type_sys T)
716 (* This shouldn't clash with anything else. *)
717 val mangled_type_sep = "\000"
719 fun generic_mangled_type_name f (ATerm (name, [])) = f name
720 | generic_mangled_type_name f (ATerm (name, tys)) =
721 f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
724 val bool_atype = AType (`I tptp_bool_type)
726 fun make_simple_type s =
727 if s = tptp_bool_type orelse s = tptp_fun_type orelse
728 s = tptp_individual_type then
731 simple_type_prefix ^ ascii_of s
733 fun ho_type_from_fo_term format type_sys pred_sym ary =
736 AType ((make_simple_type (generic_mangled_type_name fst ty),
737 generic_mangled_type_name snd ty))
738 fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
739 fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
740 | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
741 fun to_ho (ty as ATerm ((s, _), tys)) =
742 if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
743 in if is_setting_higher_order format type_sys then to_ho else to_fo ary end
745 fun mangled_type format type_sys pred_sym ary =
746 ho_type_from_fo_term format type_sys pred_sym ary
747 o fo_term_from_typ format type_sys
749 fun mangled_const_name format type_sys T_args (s, s') =
751 val ty_args = T_args |> map_filter (fo_term_for_type_arg format type_sys)
752 fun type_suffix f g =
753 fold_rev (curry (op ^) o g o prefix mangled_type_sep
754 o generic_mangled_type_name f) ty_args ""
755 in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
757 val parse_mangled_ident =
758 Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
760 fun parse_mangled_type x =
762 -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
764 and parse_mangled_types x =
765 (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
767 fun unmangled_type s =
768 s |> suffix ")" |> raw_explode
769 |> Scan.finite Symbol.stopper
770 (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
771 quote s)) parse_mangled_type))
774 val unmangled_const_name = space_explode mangled_type_sep #> hd
775 fun unmangled_const s =
776 let val ss = space_explode mangled_type_sep s in
777 (hd ss, map unmangled_type (tl ss))
780 fun introduce_proxies format type_sys =
782 fun intro top_level (CombApp (tm1, tm2)) =
783 CombApp (intro top_level tm1, intro false tm2)
784 | intro top_level (CombConst (name as (s, _), T, T_args)) =
785 (case proxify_const s of
787 if top_level orelse is_setting_higher_order format type_sys then
788 case (top_level, s) of
789 (_, "c_False") => (`I tptp_false, [])
790 | (_, "c_True") => (`I tptp_true, [])
791 | (false, "c_Not") => (`I tptp_not, [])
792 | (false, "c_conj") => (`I tptp_and, [])
793 | (false, "c_disj") => (`I tptp_or, [])
794 | (false, "c_implies") => (`I tptp_implies, [])
796 if is_tptp_equal s then (`I tptp_equal, [])
797 else (proxy_base |>> prefix const_prefix, T_args)
800 (proxy_base |>> prefix const_prefix, T_args)
801 | NONE => (name, T_args))
802 |> (fn (name, T_args) => CombConst (name, T, T_args))
806 fun combformula_from_prop thy format type_sys eq_as_iff =
808 fun do_term bs t atomic_types =
809 combterm_from_term thy bs (Envir.eta_contract t)
810 |>> (introduce_proxies format type_sys #> AAtom)
811 ||> union (op =) atomic_types
812 fun do_quant bs q s T t' =
813 let val s = singleton (Name.variant_list (map fst bs)) s in
814 do_formula ((s, T) :: bs) t'
815 #>> mk_aquant q [(`make_bound_var s, SOME T)]
817 and do_conn bs c t1 t2 =
818 do_formula bs t1 ##>> do_formula bs t2 #>> uncurry (mk_aconn c)
819 and do_formula bs t =
821 @{const Trueprop} $ t1 => do_formula bs t1
822 | @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
823 | Const (@{const_name All}, _) $ Abs (s, T, t') =>
824 do_quant bs AForall s T t'
825 | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
826 do_quant bs AExists s T t'
827 | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
828 | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
829 | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
830 | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
831 if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
835 fun presimplify_term _ [] t = t
836 | presimplify_term ctxt presimp_consts t =
837 t |> exists_Const (member (op =) presimp_consts o fst) t
838 ? (Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
839 #> Meson.presimplify ctxt
842 fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
843 fun conceal_bounds Ts t =
844 subst_bounds (map (Free o apfst concealed_bound_name)
845 (0 upto length Ts - 1 ~~ Ts), t)
846 fun reveal_bounds Ts =
847 subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
848 (0 upto length Ts - 1 ~~ Ts))
850 fun is_fun_equality (@{const_name HOL.eq},
851 Type (_, [Type (@{type_name fun}, _), _])) = true
852 | is_fun_equality _ = false
854 fun extensionalize_term ctxt t =
855 if exists_Const is_fun_equality t then
856 let val thy = Proof_Context.theory_of ctxt in
857 t |> cterm_of thy |> Meson.extensionalize_conv ctxt
858 |> prop_of |> Logic.dest_equals |> snd
863 fun introduce_combinators_in_term ctxt kind t =
864 let val thy = Proof_Context.theory_of ctxt in
865 if Meson.is_fol_term thy t then
871 @{const Not} $ t1 => @{const Not} $ aux Ts t1
872 | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
873 t0 $ Abs (s, T, aux (T :: Ts) t')
874 | (t0 as Const (@{const_name All}, _)) $ t1 =>
875 aux Ts (t0 $ eta_expand Ts t1 1)
876 | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
877 t0 $ Abs (s, T, aux (T :: Ts) t')
878 | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
879 aux Ts (t0 $ eta_expand Ts t1 1)
880 | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
881 | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
882 | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
883 | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
885 t0 $ aux Ts t1 $ aux Ts t2
886 | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
889 t |> conceal_bounds Ts
890 |> Envir.eta_contract
892 |> Meson_Clausify.introduce_combinators_in_cterm
893 |> prop_of |> Logic.dest_equals |> snd
895 val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
896 in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
898 (* A type variable of sort "{}" will make abstraction fail. *)
899 if kind = Conjecture then HOLogic.false_const
900 else HOLogic.true_const
903 (* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
904 same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
907 fun aux (t $ u) = aux t $ aux u
908 | aux (Abs (s, T, t)) = Abs (s, T, aux t)
909 | aux (Var ((s, i), T)) =
910 Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
912 in t |> exists_subterm is_Var t ? aux end
914 fun preprocess_prop ctxt presimp_consts kind t =
916 val thy = Proof_Context.theory_of ctxt
917 val t = t |> Envir.beta_eta_contract
918 |> transform_elim_prop
919 |> Object_Logic.atomize_term thy
920 val need_trueprop = (fastype_of t = @{typ bool})
922 t |> need_trueprop ? HOLogic.mk_Trueprop
923 |> Raw_Simplifier.rewrite_term thy (Meson.unfold_set_const_simps ctxt) []
924 |> extensionalize_term ctxt
925 |> presimplify_term ctxt presimp_consts
926 |> perhaps (try (HOLogic.dest_Trueprop))
927 |> introduce_combinators_in_term ctxt kind
930 (* making fact and conjecture formulas *)
931 fun make_formula thy format type_sys eq_as_iff name loc kind t =
933 val (combformula, atomic_types) =
934 combformula_from_prop thy format type_sys eq_as_iff t []
936 {name = name, locality = loc, kind = kind, combformula = combformula,
937 atomic_types = atomic_types}
940 fun make_fact ctxt format type_sys eq_as_iff preproc presimp_consts
942 let val thy = Proof_Context.theory_of ctxt in
943 case t |> preproc ? preprocess_prop ctxt presimp_consts Axiom
944 |> make_formula thy format type_sys (eq_as_iff andalso format <> CNF)
946 formula as {combformula = AAtom (CombConst ((s, _), _, _)), ...} =>
947 if s = tptp_true then NONE else SOME formula
948 | formula => SOME formula
951 fun make_conjecture ctxt format prem_kind type_sys preproc presimp_consts ts =
953 val thy = Proof_Context.theory_of ctxt
954 val last = length ts - 1
956 map2 (fn j => fn t =>
958 val (kind, maybe_negate) =
963 if prem_kind = Conjecture then update_combformula mk_anot
967 (preprocess_prop ctxt presimp_consts kind #> freeze_term)
968 |> make_formula thy format type_sys (format <> CNF)
969 (string_of_int j) Local kind
975 (** Finite and infinite type inference **)
977 fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
978 | deep_freeze_atyp T = T
979 val deep_freeze_type = map_atyps deep_freeze_atyp
981 (* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
982 dangerous because their "exhaust" properties can easily lead to unsound ATP
983 proofs. On the other hand, all HOL infinite types can be given the same
984 models in first-order logic (via Löwenheim-Skolem). *)
986 fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
987 exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
988 | should_encode_type _ _ All_Types _ = true
989 | should_encode_type ctxt _ Fin_Nonmono_Types T =
990 is_type_surely_finite ctxt false T
991 | should_encode_type _ _ _ _ = false
993 fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
994 should_predicate_on_var T =
995 (heaviness = Heavyweight orelse should_predicate_on_var ()) andalso
996 should_encode_type ctxt nonmono_Ts level T
997 | should_predicate_on_type _ _ _ _ _ = false
999 fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
1000 String.isPrefix bound_var_prefix s
1001 | is_var_or_bound_var (CombVar _) = true
1002 | is_var_or_bound_var _ = false
1005 Top_Level of bool option |
1006 Eq_Arg of bool option |
1009 fun should_tag_with_type _ _ _ (Top_Level _) _ _ = false
1010 | should_tag_with_type ctxt nonmono_Ts (Tags (poly, level, heaviness)) site
1013 Heavyweight => should_encode_type ctxt nonmono_Ts level T
1015 case (site, is_var_or_bound_var u) of
1016 (Eq_Arg pos, true) =>
1017 (* The first disjunct prevents a subtle soundness issue explained in
1018 Blanchette's Ph.D. thesis. See also
1019 "formula_lines_for_lightweight_tags_sym_decl". *)
1020 (pos <> SOME false andalso poly = Polymorphic andalso
1021 level <> All_Types andalso heaviness = Lightweight andalso
1022 exists (fn T' => type_instance ctxt (T', T)) nonmono_Ts) orelse
1023 should_encode_type ctxt nonmono_Ts level T
1025 | should_tag_with_type _ _ _ _ _ _ = false
1027 fun homogenized_type ctxt nonmono_Ts level =
1029 val should_encode = should_encode_type ctxt nonmono_Ts level
1030 fun homo 0 T = if should_encode T then T else homo_infinite_type
1031 | homo ary (Type (@{type_name fun}, [T1, T2])) =
1032 homo 0 T1 --> homo (ary - 1) T2
1033 | homo _ _ = raise Fail "expected function type"
1036 (** "hBOOL" and "hAPP" **)
1039 {pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
1041 fun add_combterm_syms_to_table ctxt explicit_apply =
1043 fun consider_var_arity const_T var_T max_ary =
1046 if ary = max_ary orelse type_instance ctxt (var_T, T) orelse
1047 type_instance ctxt (T, var_T) then
1050 iter (ary + 1) (range_type T)
1051 in iter 0 const_T end
1052 fun add_var_or_bound_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1053 if explicit_apply = NONE andalso
1054 (can dest_funT T orelse T = @{typ bool}) then
1056 val bool_vars' = bool_vars orelse body_type T = @{typ bool}
1057 fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
1058 {pred_sym = pred_sym andalso not bool_vars',
1059 min_ary = fold (fn T' => consider_var_arity T' T) types min_ary,
1060 max_ary = max_ary, types = types}
1062 fun_var_Ts |> can dest_funT T ? insert_type ctxt I T
1064 if bool_vars' = bool_vars andalso
1065 pointer_eq (fun_var_Ts', fun_var_Ts) then
1068 ((bool_vars', fun_var_Ts'), Symtab.map (K repair_min_arity) sym_tab)
1072 fun add top_level tm (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1073 let val (head, args) = strip_combterm_comb tm in
1075 CombConst ((s, _), T, _) =>
1076 if String.isPrefix bound_var_prefix s then
1077 add_var_or_bound_var T accum
1079 let val ary = length args in
1080 ((bool_vars, fun_var_Ts),
1081 case Symtab.lookup sym_tab s of
1082 SOME {pred_sym, min_ary, max_ary, types} =>
1085 pred_sym andalso top_level andalso not bool_vars
1086 val types' = types |> insert_type ctxt I T
1088 if is_some explicit_apply orelse
1089 pointer_eq (types', types) then
1092 fold (consider_var_arity T) fun_var_Ts min_ary
1094 Symtab.update (s, {pred_sym = pred_sym,
1095 min_ary = Int.min (ary, min_ary),
1096 max_ary = Int.max (ary, max_ary),
1102 val pred_sym = top_level andalso not bool_vars
1104 case explicit_apply of
1107 | NONE => fold (consider_var_arity T) fun_var_Ts ary
1109 Symtab.update_new (s, {pred_sym = pred_sym,
1110 min_ary = min_ary, max_ary = ary,
1115 | CombVar (_, T) => add_var_or_bound_var T accum
1117 |> fold (add false) args
1120 fun add_fact_syms_to_table ctxt explicit_apply =
1121 fact_lift (formula_fold NONE
1122 (K (add_combterm_syms_to_table ctxt explicit_apply)))
1124 val default_sym_tab_entries : (string * sym_info) list =
1125 (prefixed_predicator_name,
1126 {pred_sym = true, min_ary = 1, max_ary = 1, types = []}) ::
1127 ([tptp_false, tptp_true]
1128 |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []})) @
1129 ([tptp_equal, tptp_old_equal]
1130 |> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = []}))
1132 fun sym_table_for_facts ctxt explicit_apply facts =
1133 ((false, []), Symtab.empty)
1134 |> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
1135 |> fold Symtab.update default_sym_tab_entries
1137 fun min_arity_of sym_tab s =
1138 case Symtab.lookup sym_tab s of
1139 SOME ({min_ary, ...} : sym_info) => min_ary
1141 case strip_prefix_and_unascii const_prefix s of
1143 let val s = s |> unmangled_const_name |> invert_const in
1144 if s = predicator_name then 1
1145 else if s = app_op_name then 2
1146 else if s = type_pred_name then 1
1151 (* True if the constant ever appears outside of the top-level position in
1152 literals, or if it appears with different arities (e.g., because of different
1153 type instantiations). If false, the constant always receives all of its
1154 arguments and is used as a predicate. *)
1155 fun is_pred_sym sym_tab s =
1156 case Symtab.lookup sym_tab s of
1157 SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
1158 pred_sym andalso min_ary = max_ary
1161 val predicator_combconst =
1162 CombConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
1163 fun predicator tm = CombApp (predicator_combconst, tm)
1165 fun introduce_predicators_in_combterm sym_tab tm =
1166 case strip_combterm_comb tm of
1167 (CombConst ((s, _), _, _), _) =>
1168 if is_pred_sym sym_tab s then tm else predicator tm
1169 | _ => predicator tm
1171 fun list_app head args = fold (curry (CombApp o swap)) args head
1173 val app_op = `make_fixed_const app_op_name
1175 fun explicit_app arg head =
1177 val head_T = combtyp_of head
1178 val (arg_T, res_T) = dest_funT head_T
1180 CombConst (app_op, head_T --> head_T, [arg_T, res_T])
1181 in list_app explicit_app [head, arg] end
1182 fun list_explicit_app head args = fold explicit_app args head
1184 fun introduce_explicit_apps_in_combterm sym_tab =
1187 case strip_combterm_comb tm of
1188 (head as CombConst ((s, _), _, _), args) =>
1190 |> chop (min_arity_of sym_tab s)
1192 |-> list_explicit_app
1193 | (head, args) => list_explicit_app head (map aux args)
1196 fun chop_fun 0 T = ([], T)
1197 | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
1198 chop_fun (n - 1) ran_T |>> cons dom_T
1199 | chop_fun _ _ = raise Fail "unexpected non-function"
1201 fun filter_type_args _ _ _ [] = []
1202 | filter_type_args thy s arity T_args =
1204 (* will throw "TYPE" for pseudo-constants *)
1205 val U = if s = app_op_name then
1206 @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
1208 s |> Sign.the_const_type thy
1210 case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
1213 let val U_args = (s, U) |> Sign.const_typargs thy in
1215 |> map (fn (U, T) =>
1216 if member (op =) res_U_vars (dest_TVar U) then T
1220 handle TYPE _ => T_args
1222 fun enforce_type_arg_policy_in_combterm ctxt format type_sys =
1224 val thy = Proof_Context.theory_of ctxt
1225 fun aux arity (CombApp (tm1, tm2)) =
1226 CombApp (aux (arity + 1) tm1, aux 0 tm2)
1227 | aux arity (CombConst (name as (s, _), T, T_args)) =
1228 (case strip_prefix_and_unascii const_prefix s of
1229 NONE => (name, T_args)
1232 val s'' = invert_const s''
1233 fun filtered_T_args false = T_args
1234 | filtered_T_args true = filter_type_args thy s'' arity T_args
1236 case type_arg_policy type_sys s'' of
1237 Explicit_Type_Args drop_args =>
1238 (name, filtered_T_args drop_args)
1239 | Mangled_Type_Args drop_args =>
1240 (mangled_const_name format type_sys (filtered_T_args drop_args)
1242 | No_Type_Args => (name, [])
1244 |> (fn (name, T_args) => CombConst (name, T, T_args))
1248 fun repair_combterm ctxt format type_sys sym_tab =
1249 not (is_setting_higher_order format type_sys)
1250 ? (introduce_explicit_apps_in_combterm sym_tab
1251 #> introduce_predicators_in_combterm sym_tab)
1252 #> enforce_type_arg_policy_in_combterm ctxt format type_sys
1253 fun repair_fact ctxt format type_sys sym_tab =
1254 update_combformula (formula_map
1255 (repair_combterm ctxt format type_sys sym_tab))
1257 (** Helper facts **)
1259 (* The Boolean indicates that a fairly sound type encoding is needed. *)
1261 [(("COMBI", false), @{thms Meson.COMBI_def}),
1262 (("COMBK", false), @{thms Meson.COMBK_def}),
1263 (("COMBB", false), @{thms Meson.COMBB_def}),
1264 (("COMBC", false), @{thms Meson.COMBC_def}),
1265 (("COMBS", false), @{thms Meson.COMBS_def}),
1267 (* This is a lie: Higher-order equality doesn't need a sound type encoding.
1268 However, this is done so for backward compatibility: Including the
1269 equality helpers by default in Metis breaks a few existing proofs. *)
1270 @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1271 fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1272 (("fFalse", false), [@{lemma "~ fFalse" by (unfold fFalse_def) fast}]),
1273 (("fFalse", true), @{thms True_or_False}),
1274 (("fTrue", false), [@{lemma "fTrue" by (unfold fTrue_def) fast}]),
1275 (("fTrue", true), @{thms True_or_False}),
1277 @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1278 fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1280 @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
1281 by (unfold fconj_def) fast+}),
1283 @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
1284 by (unfold fdisj_def) fast+}),
1285 (("fimplies", false),
1286 @{lemma "P | fimplies P Q" "~ Q | fimplies P Q" "~ fimplies P Q | ~ P | Q"
1287 by (unfold fimplies_def) fast+}),
1288 (("If", true), @{thms if_True if_False True_or_False})]
1289 |> map (apsnd (map zero_var_indexes))
1291 val type_tag = `make_fixed_const type_tag_name
1293 fun type_tag_idempotence_fact () =
1295 fun var s = ATerm (`I s, [])
1296 fun tag tm = ATerm (type_tag, [var "T", tm])
1297 val tagged_a = tag (var "A")
1299 Formula (type_tag_idempotence_helper_name, Axiom,
1300 AAtom (ATerm (`I tptp_equal, [tag tagged_a, tagged_a]))
1301 |> close_formula_universally, simp_info, NONE)
1304 fun should_specialize_helper type_sys t =
1305 case general_type_arg_policy type_sys of
1306 Mangled_Type_Args _ => not (null (Term.hidden_polymorphism t))
1309 fun helper_facts_for_sym ctxt format type_sys (s, {types, ...} : sym_info) =
1310 case strip_prefix_and_unascii const_prefix s of
1313 val thy = Proof_Context.theory_of ctxt
1314 val unmangled_s = mangled_s |> unmangled_const_name
1315 fun dub_and_inst needs_fairly_sound (th, j) =
1316 ((unmangled_s ^ "_" ^ string_of_int j ^
1317 (if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^
1318 (if needs_fairly_sound then typed_helper_suffix
1319 else untyped_helper_suffix),
1321 let val t = th |> prop_of in
1322 t |> should_specialize_helper type_sys t
1324 [T] => specialize_type thy (invert_const unmangled_s, T)
1328 map_filter (make_fact ctxt format type_sys false false [])
1329 val fairly_sound = is_type_sys_fairly_sound type_sys
1332 |> maps (fn ((helper_s, needs_fairly_sound), ths) =>
1333 if helper_s <> unmangled_s orelse
1334 (needs_fairly_sound andalso not fairly_sound) then
1337 ths ~~ (1 upto length ths)
1338 |> map (dub_and_inst needs_fairly_sound)
1342 fun helper_facts_for_sym_table ctxt format type_sys sym_tab =
1343 Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_sys) sym_tab
1346 (***************************************************************)
1347 (* Type Classes Present in the Axiom or Conjecture Clauses *)
1348 (***************************************************************)
1350 fun set_insert (x, s) = Symtab.update (x, ()) s
1352 fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
1354 (* Remove this trivial type class (FIXME: similar code elsewhere) *)
1355 fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
1357 fun classes_of_terms get_Ts =
1358 map (map snd o get_Ts)
1359 #> List.foldl add_classes Symtab.empty
1360 #> delete_type #> Symtab.keys
1362 val tfree_classes_of_terms = classes_of_terms OldTerm.term_tfrees
1363 val tvar_classes_of_terms = classes_of_terms OldTerm.term_tvars
1365 fun fold_type_constrs f (Type (s, Ts)) x =
1366 fold (fold_type_constrs f) Ts (f (s, x))
1367 | fold_type_constrs _ _ x = x
1369 (*Type constructors used to instantiate overloaded constants are the only ones needed.*)
1370 fun add_type_constrs_in_term thy =
1372 fun add (Const (@{const_name Meson.skolem}, _) $ _) = I
1373 | add (t $ u) = add t #> add u
1374 | add (Const (x as (s, _))) =
1375 if String.isPrefix skolem_const_prefix s then I
1376 else x |> Sign.const_typargs thy |> fold (fold_type_constrs set_insert)
1377 | add (Abs (_, _, u)) = add u
1381 fun type_constrs_of_terms thy ts =
1382 Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty)
1384 fun translate_formulas ctxt format prem_kind type_sys preproc hyp_ts concl_t
1387 val thy = Proof_Context.theory_of ctxt
1388 val fact_ts = facts |> map snd
1389 val presimp_consts = Meson.presimplified_consts ctxt
1390 val make_fact = make_fact ctxt format type_sys true preproc presimp_consts
1391 val (facts, fact_names) =
1392 facts |> map (fn (name, t) => (name, t) |> make_fact |> rpair name)
1393 |> map_filter (try (apfst the))
1395 (* Remove existing facts from the conjecture, as this can dramatically
1396 boost an ATP's performance (for some reason). *)
1399 |> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t)
1400 val goal_t = Logic.list_implies (hyp_ts, concl_t)
1401 val all_ts = goal_t :: fact_ts
1402 val subs = tfree_classes_of_terms all_ts
1403 val supers = tvar_classes_of_terms all_ts
1404 val tycons = type_constrs_of_terms thy all_ts
1407 |> make_conjecture ctxt format prem_kind type_sys preproc presimp_consts
1408 val (supers', arity_clauses) =
1409 if level_of_type_sys type_sys = No_Types then ([], [])
1410 else make_arity_clauses thy tycons supers
1411 val class_rel_clauses = make_class_rel_clauses thy subs supers'
1413 (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
1416 fun fo_literal_from_type_literal (TyLitVar (class, name)) =
1417 (true, ATerm (class, [ATerm (name, [])]))
1418 | fo_literal_from_type_literal (TyLitFree (class, name)) =
1419 (true, ATerm (class, [ATerm (name, [])]))
1421 fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
1423 val type_pred = `make_fixed_const type_pred_name
1425 fun type_pred_combterm ctxt format type_sys T tm =
1426 CombApp (CombConst (type_pred, T --> @{typ bool}, [T])
1427 |> enforce_type_arg_policy_in_combterm ctxt format type_sys, tm)
1429 fun is_var_positively_naked_in_term _ (SOME false) _ accum = accum
1430 | is_var_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
1431 accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
1432 fun should_predicate_on_var_in_formula pos phi (SOME true) name =
1433 formula_fold pos (is_var_positively_naked_in_term name) phi false
1434 | should_predicate_on_var_in_formula _ _ _ _ = true
1436 fun mk_const_aterm format type_sys x T_args args =
1437 ATerm (x, map_filter (fo_term_for_type_arg format type_sys) T_args @ args)
1439 fun tag_with_type ctxt format nonmono_Ts type_sys pos T tm =
1440 CombConst (type_tag, T --> T, [T])
1441 |> enforce_type_arg_policy_in_combterm ctxt format type_sys
1442 |> term_from_combterm ctxt format nonmono_Ts type_sys (Top_Level pos)
1443 |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
1444 and term_from_combterm ctxt format nonmono_Ts type_sys =
1448 val (head, args) = strip_combterm_comb u
1449 val (x as (s, _), T_args) =
1451 CombConst (name, _, T_args) => (name, T_args)
1452 | CombVar (name, _) => (name, [])
1453 | CombApp _ => raise Fail "impossible \"CombApp\""
1454 val (pos, arg_site) =
1457 (pos, if is_tptp_equal s then Eq_Arg pos else Elsewhere)
1458 | Eq_Arg pos => (pos, Elsewhere)
1459 | Elsewhere => (NONE, Elsewhere)
1460 val t = mk_const_aterm format type_sys x T_args
1461 (map (aux arg_site) args)
1462 val T = combtyp_of u
1464 t |> (if should_tag_with_type ctxt nonmono_Ts type_sys site u T then
1465 tag_with_type ctxt format nonmono_Ts type_sys pos T
1470 and formula_from_combformula ctxt format nonmono_Ts type_sys
1471 should_predicate_on_var =
1474 term_from_combterm ctxt format nonmono_Ts type_sys (Top_Level pos)
1477 Simple_Types level =>
1478 homogenized_type ctxt nonmono_Ts level 0
1479 #> mangled_type format type_sys false 0 #> SOME
1481 fun do_out_of_bound_type pos phi universal (name, T) =
1482 if should_predicate_on_type ctxt nonmono_Ts type_sys
1483 (fn () => should_predicate_on_var pos phi universal name) T then
1485 |> type_pred_combterm ctxt format type_sys T
1486 |> do_term pos |> AAtom |> SOME
1489 fun do_formula pos (AQuant (q, xs, phi)) =
1491 val phi = phi |> do_formula pos
1492 val universal = Option.map (q = AExists ? not) pos
1494 AQuant (q, xs |> map (apsnd (fn NONE => NONE
1495 | SOME T => do_bound_type T)),
1496 (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
1498 (fn (_, NONE) => NONE
1500 do_out_of_bound_type pos phi universal (s, T))
1504 | do_formula pos (AConn conn) = aconn_map pos do_formula conn
1505 | do_formula pos (AAtom tm) = AAtom (do_term pos tm)
1508 fun bound_tvars type_sys Ts =
1509 mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
1510 (type_literals_for_types type_sys add_sorts_on_tvar Ts))
1512 (* Each fact is given a unique fact number to avoid name clashes (e.g., because
1513 of monomorphization). The TPTP explicitly forbids name clashes, and some of
1514 the remote provers might care. *)
1515 fun formula_line_for_fact ctxt format prefix encode freshen pos nonmono_Ts
1516 type_sys (j, {name, locality, kind, combformula, atomic_types}) =
1517 (prefix ^ (if freshen then string_of_int j ^ "_" else "") ^ encode name,
1520 |> close_combformula_universally
1521 |> formula_from_combformula ctxt format nonmono_Ts type_sys
1522 should_predicate_on_var_in_formula
1523 (if pos then SOME true else NONE)
1524 |> bound_tvars type_sys atomic_types
1525 |> close_formula_universally,
1534 fun formula_line_for_class_rel_clause ({name, subclass, superclass, ...}
1535 : class_rel_clause) =
1536 let val ty_arg = ATerm (`I "T", []) in
1537 Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
1538 AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
1539 AAtom (ATerm (superclass, [ty_arg]))])
1540 |> close_formula_universally, intro_info, NONE)
1543 fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
1544 (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
1545 | fo_literal_from_arity_literal (TVarLit (c, sort)) =
1546 (false, ATerm (c, [ATerm (sort, [])]))
1548 fun formula_line_for_arity_clause ({name, prem_lits, concl_lits, ...}
1550 Formula (arity_clause_prefix ^ name, Axiom,
1551 mk_ahorn (map (formula_from_fo_literal o apfst not
1552 o fo_literal_from_arity_literal) prem_lits)
1553 (formula_from_fo_literal
1554 (fo_literal_from_arity_literal concl_lits))
1555 |> close_formula_universally, intro_info, NONE)
1557 fun formula_line_for_conjecture ctxt format nonmono_Ts type_sys
1558 ({name, kind, combformula, atomic_types, ...} : translated_formula) =
1559 Formula (conjecture_prefix ^ name, kind,
1560 formula_from_combformula ctxt format nonmono_Ts type_sys
1561 should_predicate_on_var_in_formula (SOME false)
1562 (close_combformula_universally combformula)
1563 |> bound_tvars type_sys atomic_types
1564 |> close_formula_universally, NONE, NONE)
1566 fun free_type_literals type_sys ({atomic_types, ...} : translated_formula) =
1567 atomic_types |> type_literals_for_types type_sys add_sorts_on_tfree
1568 |> map fo_literal_from_type_literal
1570 fun formula_line_for_free_type j lit =
1571 Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis,
1572 formula_from_fo_literal lit, NONE, NONE)
1573 fun formula_lines_for_free_types type_sys facts =
1575 val litss = map (free_type_literals type_sys) facts
1576 val lits = fold (union (op =)) litss []
1577 in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
1579 (** Symbol declarations **)
1581 fun should_declare_sym type_sys pred_sym s =
1582 is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
1584 Simple_Types _ => true
1585 | Tags (_, _, Lightweight) => true
1586 | _ => not pred_sym)
1588 fun sym_decl_table_for_facts ctxt type_sys repaired_sym_tab (conjs, facts) =
1590 fun add_combterm in_conj tm =
1591 let val (head, args) = strip_combterm_comb tm in
1593 CombConst ((s, s'), T, T_args) =>
1594 let val pred_sym = is_pred_sym repaired_sym_tab s in
1595 if should_declare_sym type_sys pred_sym s then
1596 Symtab.map_default (s, [])
1597 (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
1603 #> fold (add_combterm in_conj) args
1605 fun add_fact in_conj =
1606 fact_lift (formula_fold NONE (K (add_combterm in_conj)))
1609 |> is_type_sys_fairly_sound type_sys
1610 ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
1613 (* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
1614 out with monotonicity" paper presented at CADE 2011. *)
1615 fun add_combterm_nonmonotonic_types _ _ _ _ (SOME false) _ = I
1616 | add_combterm_nonmonotonic_types ctxt level sound locality _
1617 (CombApp (CombApp (CombConst ((s, _), Type (_, [T, _]), _), tm1),
1619 (is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
1621 Noninf_Nonmono_Types =>
1622 not (is_locality_global locality) orelse
1623 not (is_type_surely_infinite ctxt sound T)
1624 | Fin_Nonmono_Types => is_type_surely_finite ctxt false T
1625 | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
1626 | add_combterm_nonmonotonic_types _ _ _ _ _ _ = I
1627 fun add_fact_nonmonotonic_types ctxt level sound
1628 ({kind, locality, combformula, ...} : translated_formula) =
1629 formula_fold (SOME (kind <> Conjecture))
1630 (add_combterm_nonmonotonic_types ctxt level sound locality)
1632 fun nonmonotonic_types_for_facts ctxt type_sys sound facts =
1633 let val level = level_of_type_sys type_sys in
1634 if level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types then
1635 [] |> fold (add_fact_nonmonotonic_types ctxt level sound) facts
1636 (* We must add "bool" in case the helper "True_or_False" is added
1637 later. In addition, several places in the code rely on the list of
1638 nonmonotonic types not being empty. *)
1639 |> insert_type ctxt I @{typ bool}
1644 fun decl_line_for_sym ctxt format nonmono_Ts type_sys s
1645 (s', T_args, T, pred_sym, ary, _) =
1647 val (T_arg_Ts, level) =
1649 Simple_Types level => ([], level)
1650 | _ => (replicate (length T_args) homo_infinite_type, No_Types)
1652 Decl (sym_decl_prefix ^ s, (s, s'),
1653 (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
1654 |> mangled_type format type_sys pred_sym (length T_arg_Ts + ary))
1657 fun formula_line_for_preds_sym_decl ctxt format conj_sym_kind nonmono_Ts
1658 poly_nonmono_Ts type_sys n s j (s', T_args, T, _, ary, in_conj) =
1660 val (kind, maybe_negate) =
1661 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1663 val (arg_Ts, res_T) = chop_fun ary T
1664 val num_args = length arg_Ts
1666 1 upto num_args |> map (`I o make_bound_var o string_of_int)
1668 bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
1669 val sym_needs_arg_types = n > 1 orelse exists (curry (op =) dummyT) T_args
1670 fun should_keep_arg_type T =
1671 sym_needs_arg_types orelse
1672 not (should_predicate_on_type ctxt nonmono_Ts type_sys (K false) T)
1674 arg_Ts |> map (fn T => if should_keep_arg_type T then SOME T else NONE)
1676 Formula (preds_sym_formula_prefix ^ s ^
1677 (if n > 1 then "_" ^ string_of_int j else ""), kind,
1678 CombConst ((s, s'), T, T_args)
1679 |> fold (curry (CombApp o swap)) bounds
1680 |> type_pred_combterm ctxt format type_sys res_T
1681 |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
1682 |> formula_from_combformula ctxt format poly_nonmono_Ts type_sys
1683 (K (K (K (K true)))) (SOME true)
1684 |> n > 1 ? bound_tvars type_sys (atyps_of T)
1685 |> close_formula_universally
1690 fun formula_lines_for_lightweight_tags_sym_decl ctxt format conj_sym_kind
1691 poly_nonmono_Ts type_sys n s
1692 (j, (s', T_args, T, pred_sym, ary, in_conj)) =
1695 lightweight_tags_sym_formula_prefix ^ s ^
1696 (if n > 1 then "_" ^ string_of_int j else "")
1697 val (kind, maybe_negate) =
1698 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1700 val (arg_Ts, res_T) = chop_fun ary T
1702 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
1703 val bounds = bound_names |> map (fn name => ATerm (name, []))
1704 val cst = mk_const_aterm format type_sys (s, s') T_args
1705 val atomic_Ts = atyps_of T
1707 (if pred_sym then AConn (AIff, map AAtom tms)
1708 else AAtom (ATerm (`I tptp_equal, tms)))
1709 |> bound_tvars type_sys atomic_Ts
1710 |> close_formula_universally
1712 (* See also "should_tag_with_type". *)
1713 fun should_encode T =
1714 should_encode_type ctxt poly_nonmono_Ts All_Types T orelse
1716 Tags (Polymorphic, level, Lightweight) =>
1717 level <> All_Types andalso Monomorph.typ_has_tvars T
1719 val tag_with = tag_with_type ctxt format poly_nonmono_Ts type_sys NONE
1720 val add_formula_for_res =
1721 if should_encode res_T then
1722 cons (Formula (ident_base ^ "_res", kind,
1723 eq [tag_with res_T (cst bounds), cst bounds],
1727 fun add_formula_for_arg k =
1728 let val arg_T = nth arg_Ts k in
1729 if should_encode arg_T then
1730 case chop k bounds of
1731 (bounds1, bound :: bounds2) =>
1732 cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
1733 eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
1736 | _ => raise Fail "expected nonempty tail"
1741 [] |> not pred_sym ? add_formula_for_res
1742 |> fold add_formula_for_arg (ary - 1 downto 0)
1745 fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
1747 fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts
1748 poly_nonmono_Ts type_sys (s, decls) =
1751 decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_sys s)
1756 decl :: (decls' as _ :: _) =>
1757 let val T = result_type_of_decl decl in
1758 if forall (curry (type_instance ctxt o swap) T
1759 o result_type_of_decl) decls' then
1765 val n = length decls
1767 decls |> filter (should_predicate_on_type ctxt poly_nonmono_Ts type_sys
1769 o result_type_of_decl)
1771 (0 upto length decls - 1, decls)
1772 |-> map2 (formula_line_for_preds_sym_decl ctxt format conj_sym_kind
1773 nonmono_Ts poly_nonmono_Ts type_sys n s)
1775 | Tags (_, _, heaviness) =>
1779 let val n = length decls in
1780 (0 upto n - 1 ~~ decls)
1781 |> maps (formula_lines_for_lightweight_tags_sym_decl ctxt format
1782 conj_sym_kind poly_nonmono_Ts type_sys n s)
1785 fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1786 poly_nonmono_Ts type_sys sym_decl_tab =
1791 |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
1792 nonmono_Ts poly_nonmono_Ts type_sys)
1794 fun needs_type_tag_idempotence (Tags (poly, level, heaviness)) =
1795 poly <> Mangled_Monomorphic andalso
1796 ((level = All_Types andalso heaviness = Lightweight) orelse
1797 level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types)
1798 | needs_type_tag_idempotence _ = false
1800 fun offset_of_heading_in_problem _ [] j = j
1801 | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
1802 if heading = needle then j
1803 else offset_of_heading_in_problem needle problem (j + length lines)
1805 val implicit_declsN = "Should-be-implicit typings"
1806 val explicit_declsN = "Explicit typings"
1807 val factsN = "Relevant facts"
1808 val class_relsN = "Class relationships"
1809 val aritiesN = "Arities"
1810 val helpersN = "Helper facts"
1811 val conjsN = "Conjectures"
1812 val free_typesN = "Type variables"
1814 val explicit_apply = NONE (* for experimental purposes *)
1816 fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_sys sound
1817 exporter readable_names preproc hyp_ts concl_t facts =
1819 val (format, type_sys) = choose_format [format] type_sys
1820 val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
1821 translate_formulas ctxt format prem_kind type_sys preproc hyp_ts concl_t
1823 val sym_tab = conjs @ facts |> sym_table_for_facts ctxt explicit_apply
1825 conjs @ facts |> nonmonotonic_types_for_facts ctxt type_sys sound
1826 val repair = repair_fact ctxt format type_sys sym_tab
1827 val (conjs, facts) = (conjs, facts) |> pairself (map repair)
1828 val repaired_sym_tab =
1829 conjs @ facts |> sym_table_for_facts ctxt (SOME false)
1831 repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_sys
1833 val poly_nonmono_Ts =
1834 if null nonmono_Ts orelse nonmono_Ts = [@{typ bool}] orelse
1835 polymorphism_of_type_sys type_sys <> Polymorphic then
1838 [TVar (("'a", 0), HOLogic.typeS)]
1839 val sym_decl_lines =
1840 (conjs, helpers @ facts)
1841 |> sym_decl_table_for_facts ctxt type_sys repaired_sym_tab
1842 |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1843 poly_nonmono_Ts type_sys
1845 0 upto length helpers - 1 ~~ helpers
1846 |> map (formula_line_for_fact ctxt format helper_prefix I false true
1847 poly_nonmono_Ts type_sys)
1848 |> (if needs_type_tag_idempotence type_sys then
1849 cons (type_tag_idempotence_fact ())
1852 (* Reordering these might confuse the proof reconstruction code or the SPASS
1855 [(explicit_declsN, sym_decl_lines),
1857 map (formula_line_for_fact ctxt format fact_prefix ascii_of
1858 (not exporter) (not exporter) nonmono_Ts
1860 (0 upto length facts - 1 ~~ facts)),
1861 (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
1862 (aritiesN, map formula_line_for_arity_clause arity_clauses),
1863 (helpersN, helper_lines),
1865 map (formula_line_for_conjecture ctxt format nonmono_Ts type_sys)
1867 (free_typesN, formula_lines_for_free_types type_sys (facts @ conjs))]
1871 CNF => ensure_cnf_problem
1872 | CNF_UEQ => filter_cnf_ueq_problem
1874 |> (if is_format_typed format then
1875 declare_undeclared_syms_in_atp_problem type_decl_prefix
1879 val (problem, pool) = problem |> nice_atp_problem readable_names
1880 val helpers_offset = offset_of_heading_in_problem helpersN problem 0
1882 map_filter (fn (j, {name, ...}) =>
1883 if String.isSuffix typed_helper_suffix name then SOME j
1885 ((helpers_offset + 1 upto helpers_offset + length helpers)
1887 fun add_sym_arity (s, {min_ary, ...} : sym_info) =
1889 case strip_prefix_and_unascii const_prefix s of
1890 SOME s => Symtab.insert (op =) (s, min_ary)
1896 case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
1897 offset_of_heading_in_problem conjsN problem 0,
1898 offset_of_heading_in_problem factsN problem 0,
1899 fact_names |> Vector.fromList,
1901 Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
1905 val conj_weight = 0.0
1906 val hyp_weight = 0.1
1907 val fact_min_weight = 0.2
1908 val fact_max_weight = 1.0
1909 val type_info_default_weight = 0.8
1911 fun add_term_weights weight (ATerm (s, tms)) =
1912 is_tptp_user_symbol s ? Symtab.default (s, weight)
1913 #> fold (add_term_weights weight) tms
1914 fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
1915 formula_fold NONE (K (add_term_weights weight)) phi
1916 | add_problem_line_weights _ _ = I
1918 fun add_conjectures_weights [] = I
1919 | add_conjectures_weights conjs =
1920 let val (hyps, conj) = split_last conjs in
1921 add_problem_line_weights conj_weight conj
1922 #> fold (add_problem_line_weights hyp_weight) hyps
1925 fun add_facts_weights facts =
1927 val num_facts = length facts
1929 fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
1930 / Real.fromInt num_facts
1932 map weight_of (0 upto num_facts - 1) ~~ facts
1933 |> fold (uncurry add_problem_line_weights)
1936 (* Weights are from 0.0 (most important) to 1.0 (least important). *)
1937 fun atp_problem_weights problem =
1938 let val get = these o AList.lookup (op =) problem in
1940 |> add_conjectures_weights (get free_typesN @ get conjsN)
1941 |> add_facts_weights (get factsN)
1942 |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
1943 [explicit_declsN, class_relsN, aritiesN]
1945 |> sort (prod_ord Real.compare string_ord o pairself swap)