handle lightweight tags sym theorems gracefully in the presence of TVars with interesting type classes
1 (* Title: HOL/Tools/Sledgehammer/sledgehammer_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
18 type name = string * string
20 datatype type_literal =
21 TyLitVar of name * name |
22 TyLitFree of name * name
24 datatype arity_literal =
25 TConsLit of name * name * name list |
26 TVarLit of name * name
30 prem_lits: arity_literal list,
31 concl_lits: arity_literal}
33 type class_rel_clause =
39 CombConst of name * typ * typ list |
40 CombVar of name * typ |
41 CombApp of combterm * combterm
43 datatype locality = General | Intro | Elim | Simp | Local | Assum | Chained
45 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
47 All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
48 datatype type_heaviness = Heavyweight | Lightweight
51 Simple_Types of type_level |
52 Preds of polymorphism * type_level * type_heaviness |
53 Tags of polymorphism * type_level * type_heaviness
55 type translated_formula
57 val bound_var_prefix : string
58 val schematic_var_prefix: string
59 val fixed_var_prefix: string
60 val tvar_prefix: string
61 val tfree_prefix: string
62 val const_prefix: string
63 val type_const_prefix: string
64 val class_prefix: string
65 val skolem_const_prefix : string
66 val old_skolem_const_prefix : string
67 val new_skolem_const_prefix : string
68 val type_decl_prefix : string
69 val sym_decl_prefix : string
70 val preds_sym_formula_prefix : string
71 val lightweight_tags_sym_formula_prefix : string
72 val fact_prefix : string
73 val conjecture_prefix : string
74 val helper_prefix : string
75 val class_rel_clause_prefix : string
76 val arity_clause_prefix : string
77 val tfree_clause_prefix : string
78 val typed_helper_suffix : string
79 val untyped_helper_suffix : string
80 val predicator_name : string
81 val app_op_name : string
82 val type_tag_name : string
83 val type_pred_name : string
84 val simple_type_prefix : string
85 val prefixed_app_op_name : string
86 val prefixed_type_tag_name : string
87 val ascii_of: string -> string
88 val unascii_of: string -> string
89 val strip_prefix_and_unascii : string -> string -> string option
90 val proxify_const : string -> (int * (string * string)) option
91 val invert_const: string -> string
92 val unproxify_const: string -> string
93 val make_bound_var : string -> string
94 val make_schematic_var : string * int -> string
95 val make_fixed_var : string -> string
96 val make_schematic_type_var : string * int -> string
97 val make_fixed_type_var : string -> string
98 val make_fixed_const : string -> string
99 val make_fixed_type_const : string -> string
100 val make_type_class : string -> string
101 val new_skolem_var_name_from_const : string -> string
102 val num_type_args : theory -> string -> int
103 val make_arity_clauses :
104 theory -> string list -> class list -> class list * arity_clause list
105 val make_class_rel_clauses :
106 theory -> class list -> class list -> class_rel_clause list
107 val combtyp_of : combterm -> typ
108 val strip_combterm_comb : combterm -> combterm * combterm list
109 val atyps_of : typ -> typ list
110 val combterm_from_term :
111 theory -> (string * typ) list -> term -> combterm * typ list
112 val is_locality_global : locality -> bool
113 val type_sys_from_string : string -> type_sys
114 val polymorphism_of_type_sys : type_sys -> polymorphism
115 val level_of_type_sys : type_sys -> type_level
116 val is_type_sys_virtually_sound : type_sys -> bool
117 val is_type_sys_fairly_sound : type_sys -> bool
118 val choose_format : format list -> type_sys -> format * type_sys
119 val raw_type_literals_for_types : typ list -> type_literal list
121 connective -> ('a, 'b, 'c) formula list -> ('a, 'b, 'c) formula
122 val unmangled_const_name : string -> string
123 val unmangled_const : string -> string * string fo_term list
124 val translate_atp_fact :
125 Proof.context -> format -> type_sys -> bool -> (string * locality) * thm
126 -> translated_formula option * ((string * locality) * thm)
127 val helper_table : (string * (bool * thm list)) list
128 val tfree_classes_of_terms : term list -> string list
129 val tvar_classes_of_terms : term list -> string list
130 val type_consts_of_terms : theory -> term list -> string list
131 val prepare_atp_problem :
132 Proof.context -> format -> formula_kind -> formula_kind -> type_sys
133 -> bool option -> bool -> bool -> term list -> term
134 -> (translated_formula option * ((string * 'a) * thm)) list
135 -> string problem * string Symtab.table * int * int
136 * (string * 'a) list vector * int list * int Symtab.table
137 val atp_problem_weights : string problem -> (string * real) list
140 structure ATP_Translate : ATP_TRANSLATE =
146 type name = string * string
149 fun union_all xss = fold (union (op =)) xss []
152 val generate_useful_info = false
154 fun useful_isabelle_info s =
155 if generate_useful_info then
156 SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
160 val intro_info = useful_isabelle_info "intro"
161 val elim_info = useful_isabelle_info "elim"
162 val simp_info = useful_isabelle_info "simp"
164 val bound_var_prefix = "B_"
165 val schematic_var_prefix = "V_"
166 val fixed_var_prefix = "v_"
168 val tvar_prefix = "T_"
169 val tfree_prefix = "t_"
171 val const_prefix = "c_"
172 val type_const_prefix = "tc_"
173 val class_prefix = "cl_"
175 val skolem_const_prefix = "Sledgehammer" ^ Long_Name.separator ^ "Sko"
176 val old_skolem_const_prefix = skolem_const_prefix ^ "o"
177 val new_skolem_const_prefix = skolem_const_prefix ^ "n"
179 val type_decl_prefix = "ty_"
180 val sym_decl_prefix = "sy_"
181 val preds_sym_formula_prefix = "psy_"
182 val lightweight_tags_sym_formula_prefix = "tsy_"
183 val fact_prefix = "fact_"
184 val conjecture_prefix = "conj_"
185 val helper_prefix = "help_"
186 val class_rel_clause_prefix = "crel_"
187 val arity_clause_prefix = "arity_"
188 val tfree_clause_prefix = "tfree_"
190 val typed_helper_suffix = "_T"
191 val untyped_helper_suffix = "_U"
193 val predicator_name = "hBOOL"
194 val app_op_name = "hAPP"
195 val type_tag_name = "ti"
196 val type_pred_name = "is"
197 val simple_type_prefix = "ty_"
199 val prefixed_app_op_name = const_prefix ^ app_op_name
200 val prefixed_type_tag_name = const_prefix ^ type_tag_name
202 (* Freshness almost guaranteed! *)
203 val sledgehammer_weak_prefix = "Sledgehammer:"
205 (*Escaping of special characters.
206 Alphanumeric characters are left unchanged.
207 The character _ goes to __
208 Characters in the range ASCII space to / go to _A to _P, respectively.
209 Other characters go to _nnn where nnn is the decimal ASCII code.*)
210 val upper_a_minus_space = Char.ord #"A" - Char.ord #" "
212 fun stringN_of_int 0 _ = ""
213 | stringN_of_int k n =
214 stringN_of_int (k - 1) (n div 10) ^ string_of_int (n mod 10)
216 fun ascii_of_char c =
217 if Char.isAlphaNum c then
219 else if c = #"_" then
221 else if #" " <= c andalso c <= #"/" then
222 "_" ^ String.str (Char.chr (Char.ord c + upper_a_minus_space))
224 (* fixed width, in case more digits follow *)
225 "_" ^ stringN_of_int 3 (Char.ord c)
227 val ascii_of = String.translate ascii_of_char
229 (** Remove ASCII armoring from names in proof files **)
231 (* We don't raise error exceptions because this code can run inside a worker
232 thread. Also, the errors are impossible. *)
235 fun un rcs [] = String.implode(rev rcs)
236 | un rcs [#"_"] = un (#"_" :: rcs) [] (* ERROR *)
237 (* Three types of _ escapes: __, _A to _P, _nnn *)
238 | un rcs (#"_" :: #"_" :: cs) = un (#"_"::rcs) cs
239 | un rcs (#"_" :: c :: cs) =
240 if #"A" <= c andalso c<= #"P" then
241 (* translation of #" " to #"/" *)
242 un (Char.chr (Char.ord c - upper_a_minus_space) :: rcs) cs
244 let val digits = List.take (c::cs, 3) handle Subscript => [] in
245 case Int.fromString (String.implode digits) of
246 SOME n => un (Char.chr n :: rcs) (List.drop (cs, 2))
247 | NONE => un (c:: #"_"::rcs) cs (* ERROR *)
249 | un rcs (c :: cs) = un (c :: rcs) cs
250 in un [] o String.explode end
252 (* If string s has the prefix s1, return the result of deleting it,
254 fun strip_prefix_and_unascii s1 s =
255 if String.isPrefix s1 s then
256 SOME (unascii_of (String.extract (s, size s1, NONE)))
262 (@{const_name False}, (0, ("fFalse", @{const_name ATP.fFalse})))),
263 ("c_True", (@{const_name True}, (0, ("fTrue", @{const_name ATP.fTrue})))),
264 ("c_Not", (@{const_name Not}, (1, ("fNot", @{const_name ATP.fNot})))),
265 ("c_conj", (@{const_name conj}, (2, ("fconj", @{const_name ATP.fconj})))),
266 ("c_disj", (@{const_name disj}, (2, ("fdisj", @{const_name ATP.fdisj})))),
268 (@{const_name implies}, (2, ("fimplies", @{const_name ATP.fimplies})))),
270 (@{const_name HOL.eq}, (2, ("fequal", @{const_name ATP.fequal}))))]
272 val proxify_const = AList.lookup (op =) proxies #> Option.map snd
274 (* Readable names for the more common symbolic functions. Do not mess with the
275 table unless you know what you are doing. *)
276 val const_trans_table =
277 [(@{type_name Product_Type.prod}, "prod"),
278 (@{type_name Sum_Type.sum}, "sum"),
279 (@{const_name False}, "False"),
280 (@{const_name True}, "True"),
281 (@{const_name Not}, "Not"),
282 (@{const_name conj}, "conj"),
283 (@{const_name disj}, "disj"),
284 (@{const_name implies}, "implies"),
285 (@{const_name HOL.eq}, "equal"),
286 (@{const_name If}, "If"),
287 (@{const_name Set.member}, "member"),
288 (@{const_name Meson.COMBI}, "COMBI"),
289 (@{const_name Meson.COMBK}, "COMBK"),
290 (@{const_name Meson.COMBB}, "COMBB"),
291 (@{const_name Meson.COMBC}, "COMBC"),
292 (@{const_name Meson.COMBS}, "COMBS")]
294 |> fold (Symtab.update o swap o snd o snd o snd) proxies
296 (* Invert the table of translations between Isabelle and ATPs. *)
297 val const_trans_table_inv =
298 const_trans_table |> Symtab.dest |> map swap |> Symtab.make
299 val const_trans_table_unprox =
301 |> fold (fn (_, (isa, (_, (_, metis)))) => Symtab.update (metis, isa)) proxies
303 val invert_const = perhaps (Symtab.lookup const_trans_table_inv)
304 val unproxify_const = perhaps (Symtab.lookup const_trans_table_unprox)
307 case Symtab.lookup const_trans_table c of
311 (*Remove the initial ' character from a type variable, if it is present*)
312 fun trim_type_var s =
313 if s <> "" andalso String.sub(s,0) = #"'" then String.extract(s,1,NONE)
314 else raise Fail ("trim_type: Malformed type variable encountered: " ^ s)
316 fun ascii_of_indexname (v,0) = ascii_of v
317 | ascii_of_indexname (v,i) = ascii_of v ^ "_" ^ string_of_int i
319 fun make_bound_var x = bound_var_prefix ^ ascii_of x
320 fun make_schematic_var v = schematic_var_prefix ^ ascii_of_indexname v
321 fun make_fixed_var x = fixed_var_prefix ^ ascii_of x
323 fun make_schematic_type_var (x,i) =
324 tvar_prefix ^ (ascii_of_indexname (trim_type_var x, i))
325 fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (trim_type_var x))
327 (* HOL.eq MUST BE "equal" because it's built into ATPs. *)
328 fun make_fixed_const @{const_name HOL.eq} = "equal"
329 | make_fixed_const c = const_prefix ^ lookup_const c
331 fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
333 fun make_type_class clas = class_prefix ^ ascii_of clas
335 fun new_skolem_var_name_from_const s =
336 let val ss = s |> space_explode Long_Name.separator in
337 nth ss (length ss - 2)
340 (* The number of type arguments of a constant, zero if it's monomorphic. For
341 (instances of) Skolem pseudoconstants, this information is encoded in the
343 fun num_type_args thy s =
344 if String.isPrefix skolem_const_prefix s then
345 s |> space_explode Long_Name.separator |> List.last |> Int.fromString |> the
347 (s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
349 (** Definitions and functions for FOL clauses and formulas for TPTP **)
351 (* The first component is the type class; the second is a "TVar" or "TFree". *)
352 datatype type_literal =
353 TyLitVar of name * name |
354 TyLitFree of name * name
357 (** Isabelle arities **)
359 datatype arity_literal =
360 TConsLit of name * name * name list |
361 TVarLit of name * name
364 | gen_TVars n = ("T_" ^ string_of_int n) :: gen_TVars (n-1)
366 fun pack_sort (_,[]) = []
367 | pack_sort (tvar, "HOL.type" :: srt) =
368 pack_sort (tvar, srt) (* IGNORE sort "type" *)
369 | pack_sort (tvar, cls :: srt) =
370 (`make_type_class cls, `I tvar) :: pack_sort (tvar, srt)
374 prem_lits: arity_literal list,
375 concl_lits: arity_literal}
377 (* Arity of type constructor "tcon :: (arg1, ..., argN) res" *)
378 fun make_axiom_arity_clause (tcons, name, (cls, args)) =
380 val tvars = gen_TVars (length args)
381 val tvars_srts = ListPair.zip (tvars, args)
384 prem_lits = map TVarLit (union_all (map pack_sort tvars_srts)),
385 concl_lits = TConsLit (`make_type_class cls,
386 `make_fixed_type_const tcons,
390 fun arity_clause _ _ (_, []) = []
391 | arity_clause seen n (tcons, ("HOL.type",_)::ars) = (*ignore*)
392 arity_clause seen n (tcons,ars)
393 | arity_clause seen n (tcons, (ar as (class,_)) :: ars) =
394 if member (op =) seen class then (*multiple arities for the same tycon, class pair*)
395 make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class ^ "_" ^ string_of_int n, ar) ::
396 arity_clause seen (n+1) (tcons,ars)
398 make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class, ar) ::
399 arity_clause (class::seen) n (tcons,ars)
401 fun multi_arity_clause [] = []
402 | multi_arity_clause ((tcons, ars) :: tc_arlists) =
403 arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
405 (*Generate all pairs (tycon,class,sorts) such that tycon belongs to class in theory thy
406 provided its arguments have the corresponding sorts.*)
407 fun type_class_pairs thy tycons classes =
409 val alg = Sign.classes_of thy
410 fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
411 fun add_class tycon class =
412 cons (class, domain_sorts tycon class)
413 handle Sorts.CLASS_ERROR _ => I
414 fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
415 in map try_classes tycons end
417 (*Proving one (tycon, class) membership may require proving others, so iterate.*)
418 fun iter_type_class_pairs _ _ [] = ([], [])
419 | iter_type_class_pairs thy tycons classes =
420 let val cpairs = type_class_pairs thy tycons classes
421 val newclasses = union_all (union_all (union_all (map (map #2 o #2) cpairs)))
422 |> subtract (op =) classes |> subtract (op =) HOLogic.typeS
423 val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
424 in (union (op =) classes' classes, union (op =) cpairs' cpairs) end
426 fun make_arity_clauses thy tycons =
427 iter_type_class_pairs thy tycons ##> multi_arity_clause
430 (** Isabelle class relations **)
432 type class_rel_clause =
437 (*Generate all pairs (sub,super) such that sub is a proper subclass of super in theory thy.*)
438 fun class_pairs _ [] _ = []
439 | class_pairs thy subs supers =
441 val class_less = Sorts.class_less (Sign.classes_of thy)
442 fun add_super sub super = class_less (sub, super) ? cons (sub, super)
443 fun add_supers sub = fold (add_super sub) supers
444 in fold add_supers subs [] end
446 fun make_class_rel_clause (sub,super) =
447 {name = sub ^ "_" ^ super,
448 subclass = `make_type_class sub,
449 superclass = `make_type_class super}
451 fun make_class_rel_clauses thy subs supers =
452 map make_class_rel_clause (class_pairs thy subs supers)
455 CombConst of name * typ * typ list |
456 CombVar of name * typ |
457 CombApp of combterm * combterm
459 fun combtyp_of (CombConst (_, T, _)) = T
460 | combtyp_of (CombVar (_, T)) = T
461 | combtyp_of (CombApp (t1, _)) = snd (dest_funT (combtyp_of t1))
463 (*gets the head of a combinator application, along with the list of arguments*)
464 fun strip_combterm_comb u =
465 let fun stripc (CombApp(t,u), ts) = stripc (t, u::ts)
469 fun atyps_of T = fold_atyps (insert (op =)) T []
471 fun new_skolem_const_name s num_T_args =
472 [new_skolem_const_prefix, s, string_of_int num_T_args]
473 |> space_implode Long_Name.separator
475 (* Converts a term (with combinators) into a combterm. Also accumulates sort
477 fun combterm_from_term thy bs (P $ Q) =
479 val (P', P_atomics_Ts) = combterm_from_term thy bs P
480 val (Q', Q_atomics_Ts) = combterm_from_term thy bs Q
481 in (CombApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
482 | combterm_from_term thy _ (Const (c, T)) =
485 (if String.isPrefix old_skolem_const_prefix c then
486 [] |> Term.add_tvarsT T |> map TVar
488 (c, T) |> Sign.const_typargs thy)
489 val c' = CombConst (`make_fixed_const c, T, tvar_list)
490 in (c', atyps_of T) end
491 | combterm_from_term _ _ (Free (v, T)) =
492 (CombConst (`make_fixed_var v, T, []), atyps_of T)
493 | combterm_from_term _ _ (Var (v as (s, _), T)) =
494 (if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
496 val Ts = T |> strip_type |> swap |> op ::
497 val s' = new_skolem_const_name s (length Ts)
498 in CombConst (`make_fixed_const s', T, Ts) end
500 CombVar ((make_schematic_var v, s), T), atyps_of T)
501 | combterm_from_term _ bs (Bound j) =
503 |> (fn (s, T) => (CombConst (`make_bound_var s, T, []), atyps_of T))
504 | combterm_from_term _ _ (Abs _) = raise Fail "HOL clause: Abs"
506 datatype locality = General | Intro | Elim | Simp | Local | Assum | Chained
508 (* (quasi-)underapproximation of the truth *)
509 fun is_locality_global Local = false
510 | is_locality_global Assum = false
511 | is_locality_global Chained = false
512 | is_locality_global _ = true
514 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
515 datatype type_level =
516 All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
517 datatype type_heaviness = Heavyweight | Lightweight
520 Simple_Types of type_level |
521 Preds of polymorphism * type_level * type_heaviness |
522 Tags of polymorphism * type_level * type_heaviness
524 fun try_unsuffixes ss s =
525 fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
527 fun type_sys_from_string s =
528 (case try (unprefix "poly_") s of
529 SOME s => (SOME Polymorphic, s)
531 case try (unprefix "mono_") s of
532 SOME s => (SOME Monomorphic, s)
534 case try (unprefix "mangled_") s of
535 SOME s => (SOME Mangled_Monomorphic, s)
538 (* "_query" and "_bang" are for the ASCII-challenged Mirabelle. *)
539 case try_unsuffixes ["?", "_query"] s of
540 SOME s => (Nonmonotonic_Types, s)
542 case try_unsuffixes ["!", "_bang"] s of
543 SOME s => (Finite_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)) => Simple_Types level
552 | ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
553 | ("tags", (SOME Polymorphic, All_Types, _)) =>
554 Tags (Polymorphic, All_Types, heaviness)
555 | ("tags", (SOME Polymorphic, _, _)) =>
556 (* The actual light encoding is very unsound. *)
557 Tags (Polymorphic, level, Heavyweight)
558 | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
559 | ("args", (SOME poly, All_Types (* naja *), Lightweight)) =>
560 Preds (poly, Const_Arg_Types, Lightweight)
561 | ("erased", (NONE, All_Types (* naja *), Lightweight)) =>
562 Preds (Polymorphic, No_Types, Lightweight)
563 | _ => raise Same.SAME)
564 handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
566 fun polymorphism_of_type_sys (Simple_Types _) = Mangled_Monomorphic
567 | polymorphism_of_type_sys (Preds (poly, _, _)) = poly
568 | polymorphism_of_type_sys (Tags (poly, _, _)) = poly
570 fun level_of_type_sys (Simple_Types level) = level
571 | level_of_type_sys (Preds (_, level, _)) = level
572 | level_of_type_sys (Tags (_, level, _)) = level
574 fun heaviness_of_type_sys (Simple_Types _) = Heavyweight
575 | heaviness_of_type_sys (Preds (_, _, heaviness)) = heaviness
576 | heaviness_of_type_sys (Tags (_, _, heaviness)) = heaviness
578 fun is_type_level_virtually_sound level =
579 level = All_Types orelse level = Nonmonotonic_Types
580 val is_type_sys_virtually_sound =
581 is_type_level_virtually_sound o level_of_type_sys
583 fun is_type_level_fairly_sound level =
584 is_type_level_virtually_sound level orelse level = Finite_Types
585 val is_type_sys_fairly_sound = is_type_level_fairly_sound o level_of_type_sys
587 fun is_setting_higher_order THF (Simple_Types _) = true
588 | is_setting_higher_order _ _ = false
590 fun choose_format formats (Simple_Types level) =
591 if member (op =) formats THF then (THF, Simple_Types level)
592 else if member (op =) formats TFF then (TFF, Simple_Types level)
593 else choose_format formats (Preds (Mangled_Monomorphic, level, Heavyweight))
594 | choose_format formats type_sys =
597 (CNF_UEQ, case type_sys of
599 (if is_type_sys_fairly_sound type_sys then Preds else Tags)
602 | format => (format, type_sys))
604 type translated_formula =
608 combformula: (name, typ, combterm) formula,
609 atomic_types: typ list}
611 fun update_combformula f ({name, locality, kind, combformula, atomic_types}
612 : translated_formula) =
613 {name = name, locality = locality, kind = kind, combformula = f combformula,
614 atomic_types = atomic_types} : translated_formula
616 fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
618 val type_instance = Sign.typ_instance o Proof_Context.theory_of
620 fun insert_type ctxt get_T x xs =
621 let val T = get_T x in
622 if exists (curry (type_instance ctxt) T o get_T) xs then xs
623 else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
626 (* The Booleans indicate whether all type arguments should be kept. *)
627 datatype type_arg_policy =
628 Explicit_Type_Args of bool |
629 Mangled_Type_Args of bool |
632 fun should_drop_arg_type_args (Simple_Types _) =
633 false (* since TFF doesn't support overloading *)
634 | should_drop_arg_type_args type_sys =
635 level_of_type_sys type_sys = All_Types andalso
636 heaviness_of_type_sys type_sys = Heavyweight
638 fun general_type_arg_policy (Tags (_, All_Types, Heavyweight)) = No_Type_Args
639 | general_type_arg_policy type_sys =
640 if level_of_type_sys type_sys = No_Types then
642 else if polymorphism_of_type_sys type_sys = Mangled_Monomorphic then
643 Mangled_Type_Args (should_drop_arg_type_args type_sys)
645 Explicit_Type_Args (should_drop_arg_type_args type_sys)
647 fun type_arg_policy type_sys s =
648 if s = @{const_name HOL.eq} orelse
649 (s = app_op_name andalso level_of_type_sys type_sys = Const_Arg_Types) then
651 else if s = type_tag_name then
652 Explicit_Type_Args false
654 general_type_arg_policy type_sys
656 (*Make literals for sorted type variables*)
657 fun generic_sorts_on_type (_, []) = []
658 | generic_sorts_on_type ((x, i), s :: ss) =
659 generic_sorts_on_type ((x, i), ss)
660 |> (if s = the_single @{sort HOL.type} then
663 cons (TyLitFree (`make_type_class s, `make_fixed_type_var x))
665 cons (TyLitVar (`make_type_class s,
666 (make_schematic_type_var (x, i), x))))
667 fun sorts_on_tfree (TFree (s, S)) = generic_sorts_on_type ((s, ~1), S)
668 | sorts_on_tfree _ = []
669 fun sorts_on_tvar (TVar z) = generic_sorts_on_type z
670 | sorts_on_tvar _ = []
672 (* Given a list of sorted type variables, return a list of type literals. *)
673 fun raw_type_literals_for_types Ts =
674 union_all (map sorts_on_tfree Ts @ map sorts_on_tvar Ts)
676 fun type_literals_for_types type_sys sorts_on_typ Ts =
677 if level_of_type_sys type_sys = No_Types then []
678 else union_all (map sorts_on_typ Ts)
680 fun mk_aconns c phis =
681 let val (phis', phi') = split_last phis in
682 fold_rev (mk_aconn c) phis' phi'
684 fun mk_ahorn [] phi = phi
685 | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
686 fun mk_aquant _ [] phi = phi
687 | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
688 if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
689 | mk_aquant q xs phi = AQuant (q, xs, phi)
691 fun close_universally atom_vars phi =
693 fun formula_vars bounds (AQuant (_, xs, phi)) =
694 formula_vars (map fst xs @ bounds) phi
695 | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
696 | formula_vars bounds (AAtom tm) =
697 union (op =) (atom_vars tm []
698 |> filter_out (member (op =) bounds o fst))
699 in mk_aquant AForall (formula_vars [] phi []) phi end
701 fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
702 | combterm_vars (CombConst _) = I
703 | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
704 fun close_combformula_universally phi = close_universally combterm_vars phi
706 fun term_vars (ATerm (name as (s, _), tms)) =
707 is_tptp_variable s ? insert (op =) (name, NONE) #> fold term_vars tms
708 fun close_formula_universally phi = close_universally term_vars phi
710 val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
711 val homo_infinite_type = Type (homo_infinite_type_name, [])
713 fun fo_term_from_typ higher_order =
715 fun term (Type (s, Ts)) =
716 ATerm (case (higher_order, s) of
717 (true, @{type_name bool}) => `I tptp_bool_type
718 | (true, @{type_name fun}) => `I tptp_fun_type
719 | _ => if s = homo_infinite_type_name then `I tptp_individual_type
720 else `make_fixed_type_const s,
722 | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
723 | term (TVar ((x as (s, _)), _)) =
724 ATerm ((make_schematic_type_var x, s), [])
727 (* This shouldn't clash with anything else. *)
728 val mangled_type_sep = "\000"
730 fun generic_mangled_type_name f (ATerm (name, [])) = f name
731 | generic_mangled_type_name f (ATerm (name, tys)) =
732 f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
735 val bool_atype = AType (`I tptp_bool_type)
737 fun make_simple_type s =
738 if s = tptp_bool_type orelse s = tptp_fun_type orelse
739 s = tptp_individual_type then
742 simple_type_prefix ^ ascii_of s
744 fun ho_type_from_fo_term higher_order pred_sym ary =
747 AType ((make_simple_type (generic_mangled_type_name fst ty),
748 generic_mangled_type_name snd ty))
749 fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
750 fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
751 | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
752 fun to_ho (ty as ATerm ((s, _), tys)) =
753 if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
754 in if higher_order then to_ho else to_fo ary end
756 fun mangled_type higher_order pred_sym ary =
757 ho_type_from_fo_term higher_order pred_sym ary o fo_term_from_typ higher_order
759 fun mangled_const_name T_args (s, s') =
761 val ty_args = map (fo_term_from_typ false) T_args
762 fun type_suffix f g =
763 fold_rev (curry (op ^) o g o prefix mangled_type_sep
764 o generic_mangled_type_name f) ty_args ""
765 in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
767 val parse_mangled_ident =
768 Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
770 fun parse_mangled_type x =
772 -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
774 and parse_mangled_types x =
775 (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
777 fun unmangled_type s =
778 s |> suffix ")" |> raw_explode
779 |> Scan.finite Symbol.stopper
780 (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
781 quote s)) parse_mangled_type))
784 val unmangled_const_name = space_explode mangled_type_sep #> hd
785 fun unmangled_const s =
786 let val ss = space_explode mangled_type_sep s in
787 (hd ss, map unmangled_type (tl ss))
790 fun introduce_proxies format type_sys =
792 fun intro top_level (CombApp (tm1, tm2)) =
793 CombApp (intro top_level tm1, intro false tm2)
794 | intro top_level (CombConst (name as (s, _), T, T_args)) =
795 (case proxify_const s of
796 SOME (_, proxy_base) =>
797 if top_level orelse is_setting_higher_order format type_sys then
798 case (top_level, s) of
799 (_, "c_False") => (`I tptp_false, [])
800 | (_, "c_True") => (`I tptp_true, [])
801 | (false, "c_Not") => (`I tptp_not, [])
802 | (false, "c_conj") => (`I tptp_and, [])
803 | (false, "c_disj") => (`I tptp_or, [])
804 | (false, "c_implies") => (`I tptp_implies, [])
806 if is_tptp_equal s then (`I tptp_equal, [])
807 else (proxy_base |>> prefix const_prefix, T_args)
810 (proxy_base |>> prefix const_prefix, T_args)
811 | NONE => (name, T_args))
812 |> (fn (name, T_args) => CombConst (name, T, T_args))
816 fun combformula_from_prop thy format type_sys eq_as_iff =
818 fun do_term bs t atomic_types =
819 combterm_from_term thy bs (Envir.eta_contract t)
820 |>> (introduce_proxies format type_sys #> AAtom)
821 ||> union (op =) atomic_types
822 fun do_quant bs q s T t' =
823 let val s = Name.variant (map fst bs) s in
824 do_formula ((s, T) :: bs) t'
825 #>> mk_aquant q [(`make_bound_var s, SOME T)]
827 and do_conn bs c t1 t2 =
828 do_formula bs t1 ##>> do_formula bs t2
829 #>> uncurry (mk_aconn c)
830 and do_formula bs t =
832 @{const Trueprop} $ t1 => do_formula bs t1
833 | @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
834 | Const (@{const_name All}, _) $ Abs (s, T, t') =>
835 do_quant bs AForall s T t'
836 | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
837 do_quant bs AExists s T t'
838 | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
839 | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
840 | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
841 | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
842 if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
846 fun presimplify_term ctxt =
847 Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
848 #> Meson.presimplify ctxt
851 fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
852 fun conceal_bounds Ts t =
853 subst_bounds (map (Free o apfst concealed_bound_name)
854 (0 upto length Ts - 1 ~~ Ts), t)
855 fun reveal_bounds Ts =
856 subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
857 (0 upto length Ts - 1 ~~ Ts))
859 fun extensionalize_term ctxt t =
860 let val thy = Proof_Context.theory_of ctxt in
861 t |> cterm_of thy |> Meson.extensionalize_conv ctxt
862 |> prop_of |> Logic.dest_equals |> snd
865 fun introduce_combinators_in_term ctxt kind t =
866 let val thy = Proof_Context.theory_of ctxt in
867 if Meson.is_fol_term thy t then
873 @{const Not} $ t1 => @{const Not} $ aux Ts t1
874 | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
875 t0 $ Abs (s, T, aux (T :: Ts) t')
876 | (t0 as Const (@{const_name All}, _)) $ t1 =>
877 aux Ts (t0 $ eta_expand Ts t1 1)
878 | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
879 t0 $ Abs (s, T, aux (T :: Ts) t')
880 | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
881 aux Ts (t0 $ eta_expand Ts t1 1)
882 | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
883 | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
884 | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
885 | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
887 t0 $ aux Ts t1 $ aux Ts t2
888 | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
891 t |> conceal_bounds Ts
892 |> Envir.eta_contract
894 |> Meson_Clausify.introduce_combinators_in_cterm
895 |> prop_of |> Logic.dest_equals |> snd
897 val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
898 in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
900 (* A type variable of sort "{}" will make abstraction fail. *)
901 if kind = Conjecture then HOLogic.false_const
902 else HOLogic.true_const
905 (* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
906 same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
909 fun aux (t $ u) = aux t $ aux u
910 | aux (Abs (s, T, t)) = Abs (s, T, aux t)
911 | aux (Var ((s, i), T)) =
912 Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
914 in t |> exists_subterm is_Var t ? aux end
916 fun preprocess_prop ctxt presimp kind t =
918 val thy = Proof_Context.theory_of ctxt
919 val t = t |> Envir.beta_eta_contract
920 |> transform_elim_prop
921 |> Object_Logic.atomize_term thy
922 val need_trueprop = (fastype_of t = @{typ bool})
924 t |> need_trueprop ? HOLogic.mk_Trueprop
925 |> Raw_Simplifier.rewrite_term thy (Meson.unfold_set_const_simps ctxt) []
926 |> extensionalize_term ctxt
927 |> presimp ? presimplify_term ctxt
928 |> perhaps (try (HOLogic.dest_Trueprop))
929 |> introduce_combinators_in_term ctxt kind
932 (* making fact and conjecture formulas *)
933 fun make_formula thy format type_sys eq_as_iff name loc kind t =
935 val (combformula, atomic_types) =
936 combformula_from_prop thy format type_sys eq_as_iff t []
938 {name = name, locality = loc, kind = kind, combformula = combformula,
939 atomic_types = atomic_types}
942 fun make_fact ctxt format type_sys keep_trivial eq_as_iff preproc presimp
944 let val thy = Proof_Context.theory_of ctxt in
946 t |> preproc ? preprocess_prop ctxt presimp Axiom
947 |> make_formula thy format type_sys eq_as_iff name loc Axiom) of
949 formula as {combformula = AAtom (CombConst ((s, _), _, _)), ...}) =>
950 if s = tptp_true then NONE else SOME formula
951 | (_, formula) => SOME formula
954 fun make_conjecture ctxt format prem_kind type_sys preproc ts =
956 val thy = Proof_Context.theory_of ctxt
957 val last = length ts - 1
959 map2 (fn j => fn t =>
961 val (kind, maybe_negate) =
966 if prem_kind = Conjecture then update_combformula mk_anot
969 t |> preproc ? (preprocess_prop ctxt true kind #> freeze_term)
970 |> make_formula thy format type_sys true (string_of_int j)
977 (** Finite and infinite type inference **)
979 fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
980 | deep_freeze_atyp T = T
981 val deep_freeze_type = map_atyps deep_freeze_atyp
983 (* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
984 dangerous because their "exhaust" properties can easily lead to unsound ATP
985 proofs. On the other hand, all HOL infinite types can be given the same
986 models in first-order logic (via Löwenheim-Skolem). *)
988 fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
989 exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
990 | should_encode_type _ _ All_Types _ = true
991 | should_encode_type ctxt _ Finite_Types T = is_type_surely_finite ctxt T
992 | should_encode_type _ _ _ _ = false
994 fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
995 should_predicate_on_var T =
996 (heaviness = Heavyweight orelse should_predicate_on_var ()) andalso
997 should_encode_type ctxt nonmono_Ts level T
998 | should_predicate_on_type _ _ _ _ _ = false
1000 fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
1001 String.isPrefix bound_var_prefix s
1002 | is_var_or_bound_var (CombVar _) = true
1003 | is_var_or_bound_var _ = false
1005 datatype tag_site = Top_Level | Eq_Arg | Elsewhere
1007 fun should_tag_with_type _ _ _ Top_Level _ _ = false
1008 | should_tag_with_type ctxt nonmono_Ts (Tags (_, level, heaviness)) site u T =
1010 Heavyweight => should_encode_type ctxt nonmono_Ts level T
1012 case (site, is_var_or_bound_var u) of
1013 (Eq_Arg, true) => should_encode_type ctxt nonmono_Ts level T
1015 | should_tag_with_type _ _ _ _ _ _ = false
1017 fun homogenized_type ctxt nonmono_Ts level =
1019 val should_encode = should_encode_type ctxt nonmono_Ts level
1020 fun homo 0 T = if should_encode T then T else homo_infinite_type
1021 | homo ary (Type (@{type_name fun}, [T1, T2])) =
1022 homo 0 T1 --> homo (ary - 1) T2
1023 | homo _ _ = raise Fail "expected function type"
1026 (** "hBOOL" and "hAPP" **)
1029 {pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
1031 fun add_combterm_syms_to_table ctxt explicit_apply =
1033 fun consider_var_arity const_T var_T max_ary =
1036 if ary = max_ary orelse type_instance ctxt (var_T, T) then ary
1037 else iter (ary + 1) (range_type T)
1038 in iter 0 const_T end
1039 fun add top_level tm (accum as (ho_var_Ts, sym_tab)) =
1040 let val (head, args) = strip_combterm_comb tm in
1042 CombConst ((s, _), T, _) =>
1043 if String.isPrefix bound_var_prefix s then
1044 if explicit_apply = NONE andalso can dest_funT T then
1046 fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
1047 {pred_sym = pred_sym,
1049 fold (fn T' => consider_var_arity T' T) types min_ary,
1050 max_ary = max_ary, types = types}
1051 val ho_var_Ts' = ho_var_Ts |> insert_type ctxt I T
1053 if pointer_eq (ho_var_Ts', ho_var_Ts) then accum
1054 else (ho_var_Ts', Symtab.map (K repair_min_arity) sym_tab)
1060 val ary = length args
1063 case Symtab.lookup sym_tab s of
1064 SOME {pred_sym, min_ary, max_ary, types} =>
1066 val types' = types |> insert_type ctxt I T
1068 if is_some explicit_apply orelse
1069 pointer_eq (types', types) then
1072 fold (consider_var_arity T) ho_var_Ts min_ary
1074 Symtab.update (s, {pred_sym = pred_sym andalso top_level,
1075 min_ary = Int.min (ary, min_ary),
1076 max_ary = Int.max (ary, max_ary),
1083 case explicit_apply of
1086 | NONE => fold (consider_var_arity T) ho_var_Ts ary
1088 Symtab.update_new (s, {pred_sym = top_level,
1089 min_ary = min_ary, max_ary = ary,
1095 |> fold (add false) args
1098 fun add_fact_syms_to_table ctxt explicit_apply =
1099 fact_lift (formula_fold NONE
1100 (K (add_combterm_syms_to_table ctxt explicit_apply)))
1102 val default_sym_table_entries : (string * sym_info) list =
1103 [(tptp_equal, {pred_sym = true, min_ary = 2, max_ary = 2, types = []}),
1104 (tptp_old_equal, {pred_sym = true, min_ary = 2, max_ary = 2, types = []}),
1105 (make_fixed_const predicator_name,
1106 {pred_sym = true, min_ary = 1, max_ary = 1, types = []})] @
1107 ([tptp_false, tptp_true]
1108 |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []}))
1110 fun sym_table_for_facts ctxt explicit_apply facts =
1112 |> fold Symtab.default default_sym_table_entries
1113 |> pair [] |> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
1115 fun min_arity_of sym_tab s =
1116 case Symtab.lookup sym_tab s of
1117 SOME ({min_ary, ...} : sym_info) => min_ary
1119 case strip_prefix_and_unascii const_prefix s of
1121 let val s = s |> unmangled_const_name |> invert_const in
1122 if s = predicator_name then 1
1123 else if s = app_op_name then 2
1124 else if s = type_pred_name then 1
1129 (* True if the constant ever appears outside of the top-level position in
1130 literals, or if it appears with different arities (e.g., because of different
1131 type instantiations). If false, the constant always receives all of its
1132 arguments and is used as a predicate. *)
1133 fun is_pred_sym sym_tab s =
1134 case Symtab.lookup sym_tab s of
1135 SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
1136 pred_sym andalso min_ary = max_ary
1139 val predicator_combconst =
1140 CombConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
1141 fun predicator tm = CombApp (predicator_combconst, tm)
1143 fun introduce_predicators_in_combterm sym_tab tm =
1144 case strip_combterm_comb tm of
1145 (CombConst ((s, _), _, _), _) =>
1146 if is_pred_sym sym_tab s then tm else predicator tm
1147 | _ => predicator tm
1149 fun list_app head args = fold (curry (CombApp o swap)) args head
1151 val app_op = `make_fixed_const app_op_name
1153 fun explicit_app arg head =
1155 val head_T = combtyp_of head
1156 val (arg_T, res_T) = dest_funT head_T
1158 CombConst (app_op, head_T --> head_T, [arg_T, res_T])
1159 in list_app explicit_app [head, arg] end
1160 fun list_explicit_app head args = fold explicit_app args head
1162 fun introduce_explicit_apps_in_combterm sym_tab =
1165 case strip_combterm_comb tm of
1166 (head as CombConst ((s, _), _, _), args) =>
1168 |> chop (min_arity_of sym_tab s)
1170 |-> list_explicit_app
1171 | (head, args) => list_explicit_app head (map aux args)
1174 fun chop_fun 0 T = ([], T)
1175 | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
1176 chop_fun (n - 1) ran_T |>> cons dom_T
1177 | chop_fun _ _ = raise Fail "unexpected non-function"
1179 fun filter_type_args _ _ _ [] = []
1180 | filter_type_args thy s arity T_args =
1182 (* will throw "TYPE" for pseudo-constants *)
1183 val U = if s = app_op_name then
1184 @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
1186 s |> Sign.the_const_type thy
1188 case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
1191 let val U_args = (s, U) |> Sign.const_typargs thy in
1193 |> map_filter (fn (U, T) =>
1194 if member (op =) res_U_vars (dest_TVar U) then
1200 handle TYPE _ => T_args
1202 fun enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys =
1204 val thy = Proof_Context.theory_of ctxt
1205 fun aux arity (CombApp (tm1, tm2)) =
1206 CombApp (aux (arity + 1) tm1, aux 0 tm2)
1207 | aux arity (CombConst (name as (s, _), T, T_args)) =
1209 val level = level_of_type_sys type_sys
1211 (* Aggressively merge most "hAPPs" if the type system is unsound
1212 anyway, by distinguishing overloads only on the homogenized
1213 result type. Don't do it for lightweight type systems, though,
1214 since it leads to too many unsound proofs. *)
1215 if s = prefixed_app_op_name andalso length T_args = 2 andalso
1216 not (is_type_sys_virtually_sound type_sys) andalso
1217 heaviness_of_type_sys type_sys = Heavyweight then
1218 T_args |> map (homogenized_type ctxt nonmono_Ts level 0)
1219 |> (fn Ts => let val T = hd Ts --> nth Ts 1 in
1225 (case strip_prefix_and_unascii const_prefix s of
1226 NONE => (name, T_args)
1229 val s'' = invert_const s''
1230 fun filtered_T_args false = T_args
1231 | filtered_T_args true = filter_type_args thy s'' arity T_args
1233 case type_arg_policy type_sys s'' of
1234 Explicit_Type_Args drop_args =>
1235 (name, filtered_T_args drop_args)
1236 | Mangled_Type_Args drop_args =>
1237 (mangled_const_name (filtered_T_args drop_args) name, [])
1238 | No_Type_Args => (name, [])
1240 |> (fn (name, T_args) => CombConst (name, T, T_args))
1245 fun repair_combterm ctxt format nonmono_Ts type_sys sym_tab =
1246 not (is_setting_higher_order format type_sys)
1247 ? (introduce_explicit_apps_in_combterm sym_tab
1248 #> introduce_predicators_in_combterm sym_tab)
1249 #> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
1250 fun repair_fact ctxt format nonmono_Ts type_sys sym_tab =
1251 update_combformula (formula_map
1252 (repair_combterm ctxt format nonmono_Ts type_sys sym_tab))
1254 (** Helper facts **)
1256 (* The Boolean indicates that a fairly sound type encoding is needed. *)
1258 [("COMBI", (false, @{thms Meson.COMBI_def})),
1259 ("COMBK", (false, @{thms Meson.COMBK_def})),
1260 ("COMBB", (false, @{thms Meson.COMBB_def})),
1261 ("COMBC", (false, @{thms Meson.COMBC_def})),
1262 ("COMBS", (false, @{thms Meson.COMBS_def})),
1264 (* This is a lie: Higher-order equality doesn't need a sound type encoding.
1265 However, this is done so for backward compatibility: Including the
1266 equality helpers by default in Metis breaks a few existing proofs. *)
1267 (true, @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1268 fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]})),
1269 ("fFalse", (true, @{thms True_or_False})),
1270 ("fFalse", (false, [@{lemma "~ fFalse" by (unfold fFalse_def) fast}])),
1271 ("fTrue", (true, @{thms True_or_False})),
1272 ("fTrue", (false, [@{lemma "fTrue" by (unfold fTrue_def) fast}])),
1274 (false, @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1275 fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]})),
1278 @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
1279 by (unfold fconj_def) fast+})),
1282 @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
1283 by (unfold fdisj_def) fast+})),
1285 (false, @{lemma "P | fimplies P Q" "~ Q | fimplies P Q"
1286 "~ fimplies P Q | ~ P | Q"
1287 by (unfold fimplies_def) fast+})),
1288 ("If", (true, @{thms if_True if_False True_or_False}))]
1290 val type_tag = `make_fixed_const type_tag_name
1292 fun ti_ti_helper_fact () =
1294 fun var s = ATerm (`I s, [])
1295 fun tag tm = ATerm (type_tag, [var "X", tm])
1297 Formula (helper_prefix ^ "ti_ti", Axiom,
1298 AAtom (ATerm (`I tptp_equal, [tag (tag (var "Y")), tag (var "Y")]))
1299 |> close_formula_universally, simp_info, NONE)
1302 fun helper_facts_for_sym ctxt format type_sys (s, {types, ...} : sym_info) =
1303 case strip_prefix_and_unascii const_prefix s of
1306 val thy = Proof_Context.theory_of ctxt
1307 val unmangled_s = mangled_s |> unmangled_const_name
1308 fun dub_and_inst c needs_fairly_sound (th, j) =
1309 ((c ^ "_" ^ string_of_int j ^
1310 (if needs_fairly_sound then typed_helper_suffix
1311 else untyped_helper_suffix),
1313 let val t = th |> prop_of in
1314 t |> ((case general_type_arg_policy type_sys of
1315 Mangled_Type_Args _ => true
1316 | _ => false) andalso
1317 not (null (Term.hidden_polymorphism t)))
1319 [T] => specialize_type thy (invert_const unmangled_s, T)
1322 fun make_facts eq_as_iff =
1323 map_filter (make_fact ctxt format type_sys true false eq_as_iff false)
1324 val fairly_sound = is_type_sys_fairly_sound type_sys
1327 |> maps (fn (metis_s, (needs_fairly_sound, ths)) =>
1328 if metis_s <> unmangled_s orelse
1329 (needs_fairly_sound andalso not fairly_sound) then
1332 ths ~~ (1 upto length ths)
1333 |> map (dub_and_inst mangled_s needs_fairly_sound)
1334 |> make_facts (not needs_fairly_sound))
1337 fun helper_facts_for_sym_table ctxt format type_sys sym_tab =
1338 Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_sys) sym_tab
1341 fun translate_atp_fact ctxt format type_sys keep_trivial =
1342 `(make_fact ctxt format type_sys keep_trivial true true true o apsnd prop_of)
1344 (***************************************************************)
1345 (* Type Classes Present in the Axiom or Conjecture Clauses *)
1346 (***************************************************************)
1348 fun set_insert (x, s) = Symtab.update (x, ()) s
1350 fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
1352 (* Remove this trivial type class (FIXME: similar code elsewhere) *)
1353 fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
1355 fun classes_of_terms get_Ts =
1356 map (map snd o get_Ts)
1357 #> List.foldl add_classes Symtab.empty
1358 #> delete_type #> Symtab.keys
1360 val tfree_classes_of_terms = classes_of_terms OldTerm.term_tfrees
1361 val tvar_classes_of_terms = classes_of_terms OldTerm.term_tvars
1363 (*fold type constructors*)
1364 fun fold_type_consts f (Type (a, Ts)) x = fold (fold_type_consts f) Ts (f (a,x))
1365 | fold_type_consts _ _ x = x
1367 (*Type constructors used to instantiate overloaded constants are the only ones needed.*)
1368 fun add_type_consts_in_term thy =
1370 fun aux (Const (@{const_name Meson.skolem}, _) $ _) = I
1371 | aux (t $ u) = aux t #> aux u
1373 fold (fold_type_consts set_insert) (Sign.const_typargs thy x)
1374 | aux (Abs (_, _, u)) = aux u
1378 fun type_consts_of_terms thy ts =
1379 Symtab.keys (fold (add_type_consts_in_term thy) ts Symtab.empty)
1381 fun translate_formulas ctxt format prem_kind type_sys preproc hyp_ts concl_t
1384 val thy = Proof_Context.theory_of ctxt
1385 val fact_ts = map (prop_of o snd o snd) rich_facts
1386 val (facts, fact_names) =
1388 |> map_filter (fn (NONE, _) => NONE
1389 | (SOME fact, (name, _)) => SOME (fact, name))
1391 (* Remove existing facts from the conjecture, as this can dramatically
1392 boost an ATP's performance (for some reason). *)
1393 val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
1394 val goal_t = Logic.list_implies (hyp_ts, concl_t)
1395 val all_ts = goal_t :: fact_ts
1396 val subs = tfree_classes_of_terms all_ts
1397 val supers = tvar_classes_of_terms all_ts
1398 val tycons = type_consts_of_terms thy all_ts
1401 |> make_conjecture ctxt format prem_kind type_sys preproc
1402 val (supers', arity_clauses) =
1403 if level_of_type_sys type_sys = No_Types then ([], [])
1404 else make_arity_clauses thy tycons supers
1405 val class_rel_clauses = make_class_rel_clauses thy subs supers'
1407 (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
1410 fun fo_literal_from_type_literal (TyLitVar (class, name)) =
1411 (true, ATerm (class, [ATerm (name, [])]))
1412 | fo_literal_from_type_literal (TyLitFree (class, name)) =
1413 (true, ATerm (class, [ATerm (name, [])]))
1415 fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
1417 val type_pred = `make_fixed_const type_pred_name
1419 fun type_pred_combterm ctxt nonmono_Ts type_sys T tm =
1420 CombApp (CombConst (type_pred, T --> @{typ bool}, [T])
1421 |> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys,
1424 fun var_occurs_positively_naked_in_term _ (SOME false) _ accum = accum
1425 | var_occurs_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
1426 accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
1427 fun is_var_nonmonotonic_in_formula _ _ (SOME false) _ = false
1428 | is_var_nonmonotonic_in_formula pos phi _ name =
1429 formula_fold pos (var_occurs_positively_naked_in_term name) phi false
1431 fun mk_const_aterm x T_args args =
1432 ATerm (x, map (fo_term_from_typ false) T_args @ args)
1434 fun tag_with_type ctxt format nonmono_Ts type_sys T tm =
1435 CombConst (type_tag, T --> T, [T])
1436 |> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
1437 |> term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
1438 |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
1439 and term_from_combterm ctxt format nonmono_Ts type_sys =
1443 val (head, args) = strip_combterm_comb u
1444 val (x as (s, _), T_args) =
1446 CombConst (name, _, T_args) => (name, T_args)
1447 | CombVar (name, _) => (name, [])
1448 | CombApp _ => raise Fail "impossible \"CombApp\""
1449 val arg_site = if site = Top_Level andalso is_tptp_equal s then Eq_Arg
1451 val t = mk_const_aterm x T_args (map (aux arg_site) args)
1452 val T = combtyp_of u
1454 t |> (if should_tag_with_type ctxt nonmono_Ts type_sys site u T then
1455 tag_with_type ctxt format nonmono_Ts type_sys T
1460 and formula_from_combformula ctxt format nonmono_Ts type_sys
1461 should_predicate_on_var =
1463 val higher_order = is_setting_higher_order format type_sys
1464 val do_term = term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
1467 Simple_Types level =>
1468 homogenized_type ctxt nonmono_Ts level 0
1469 #> mangled_type higher_order false 0 #> SOME
1471 fun do_out_of_bound_type pos phi universal (name, T) =
1472 if should_predicate_on_type ctxt nonmono_Ts type_sys
1473 (fn () => should_predicate_on_var pos phi universal name) T then
1475 |> type_pred_combterm ctxt nonmono_Ts type_sys T
1476 |> do_term |> AAtom |> SOME
1479 fun do_formula pos (AQuant (q, xs, phi)) =
1481 val phi = phi |> do_formula pos
1482 val universal = Option.map (q = AExists ? not) pos
1484 AQuant (q, xs |> map (apsnd (fn NONE => NONE
1485 | SOME T => do_bound_type T)),
1486 (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
1488 (fn (_, NONE) => NONE
1490 do_out_of_bound_type pos phi universal (s, T))
1494 | do_formula pos (AConn conn) = aconn_map pos do_formula conn
1495 | do_formula _ (AAtom tm) = AAtom (do_term tm)
1496 in do_formula o SOME end
1498 fun bound_tvars type_sys Ts =
1499 mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
1500 (type_literals_for_types type_sys sorts_on_tvar Ts))
1502 fun formula_for_fact ctxt format nonmono_Ts type_sys
1503 ({combformula, atomic_types, ...} : translated_formula) =
1505 |> close_combformula_universally
1506 |> formula_from_combformula ctxt format nonmono_Ts type_sys
1507 is_var_nonmonotonic_in_formula true
1508 |> bound_tvars type_sys atomic_types
1509 |> close_formula_universally
1511 (* Each fact is given a unique fact number to avoid name clashes (e.g., because
1512 of monomorphization). The TPTP explicitly forbids name clashes, and some of
1513 the remote provers might care. *)
1514 fun formula_line_for_fact ctxt format prefix nonmono_Ts type_sys
1515 (j, formula as {name, locality, kind, ...}) =
1516 Formula (prefix ^ (if polymorphism_of_type_sys type_sys = Polymorphic then ""
1517 else string_of_int j ^ "_") ^
1519 kind, formula_for_fact ctxt format nonmono_Ts type_sys formula, NONE,
1526 fun formula_line_for_class_rel_clause ({name, subclass, superclass, ...}
1527 : class_rel_clause) =
1528 let val ty_arg = ATerm (`I "T", []) in
1529 Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
1530 AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
1531 AAtom (ATerm (superclass, [ty_arg]))])
1532 |> close_formula_universally, intro_info, NONE)
1535 fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
1536 (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
1537 | fo_literal_from_arity_literal (TVarLit (c, sort)) =
1538 (false, ATerm (c, [ATerm (sort, [])]))
1540 fun formula_line_for_arity_clause ({name, prem_lits, concl_lits, ...}
1542 Formula (arity_clause_prefix ^ ascii_of name, Axiom,
1543 mk_ahorn (map (formula_from_fo_literal o apfst not
1544 o fo_literal_from_arity_literal) prem_lits)
1545 (formula_from_fo_literal
1546 (fo_literal_from_arity_literal concl_lits))
1547 |> close_formula_universally, intro_info, NONE)
1549 fun formula_line_for_conjecture ctxt format nonmono_Ts type_sys
1550 ({name, kind, combformula, atomic_types, ...} : translated_formula) =
1551 Formula (conjecture_prefix ^ name, kind,
1552 formula_from_combformula ctxt format nonmono_Ts type_sys
1553 is_var_nonmonotonic_in_formula false
1554 (close_combformula_universally combformula)
1555 |> bound_tvars type_sys atomic_types
1556 |> close_formula_universally, NONE, NONE)
1558 fun free_type_literals type_sys ({atomic_types, ...} : translated_formula) =
1559 atomic_types |> type_literals_for_types type_sys sorts_on_tfree
1560 |> map fo_literal_from_type_literal
1562 fun formula_line_for_free_type j lit =
1563 Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis,
1564 formula_from_fo_literal lit, NONE, NONE)
1565 fun formula_lines_for_free_types type_sys facts =
1567 val litss = map (free_type_literals type_sys) facts
1568 val lits = fold (union (op =)) litss []
1569 in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
1571 (** Symbol declarations **)
1573 fun should_declare_sym type_sys pred_sym s =
1574 is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
1576 Simple_Types _ => true
1577 | Tags (_, _, Lightweight) => true
1578 | _ => not pred_sym)
1580 fun sym_decl_table_for_facts ctxt type_sys repaired_sym_tab (conjs, facts) =
1582 fun add_combterm in_conj tm =
1583 let val (head, args) = strip_combterm_comb tm in
1585 CombConst ((s, s'), T, T_args) =>
1586 let val pred_sym = is_pred_sym repaired_sym_tab s in
1587 if should_declare_sym type_sys pred_sym s then
1588 Symtab.map_default (s, [])
1589 (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
1595 #> fold (add_combterm in_conj) args
1597 fun add_fact in_conj =
1598 fact_lift (formula_fold NONE (K (add_combterm in_conj)))
1601 |> is_type_sys_fairly_sound type_sys
1602 ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
1605 (* These types witness that the type classes they belong to allow infinite
1606 models and hence that any types with these type classes is monotonic. *)
1607 val known_infinite_types =
1608 [@{typ nat}, Type ("Int.int", []), @{typ "nat => bool"}]
1610 (* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
1611 out with monotonicity" paper presented at CADE 2011. *)
1612 fun add_combterm_nonmonotonic_types _ _ (SOME false) _ = I
1613 | add_combterm_nonmonotonic_types ctxt level _
1614 (CombApp (CombApp (CombConst ((s, _), Type (_, [T, _]), _), tm1), tm2)) =
1615 (is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
1617 Nonmonotonic_Types =>
1618 not (is_type_surely_infinite ctxt known_infinite_types T)
1619 | Finite_Types => is_type_surely_finite ctxt T
1620 | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
1621 | add_combterm_nonmonotonic_types _ _ _ _ = I
1622 fun add_fact_nonmonotonic_types ctxt level ({kind, combformula, ...}
1623 : translated_formula) =
1624 formula_fold (SOME (kind <> Conjecture))
1625 (add_combterm_nonmonotonic_types ctxt level) combformula
1626 fun nonmonotonic_types_for_facts ctxt type_sys facts =
1627 let val level = level_of_type_sys type_sys in
1628 if level = Nonmonotonic_Types orelse level = Finite_Types then
1629 [] |> fold (add_fact_nonmonotonic_types ctxt level) facts
1630 (* We must add "bool" in case the helper "True_or_False" is added
1631 later. In addition, several places in the code rely on the list of
1632 nonmonotonic types not being empty. *)
1633 |> insert_type ctxt I @{typ bool}
1638 fun decl_line_for_sym ctxt format nonmono_Ts type_sys s
1639 (s', T_args, T, pred_sym, ary, _) =
1641 val (higher_order, T_arg_Ts, level) =
1643 Simple_Types level => (format = THF, [], level)
1644 | _ => (false, replicate (length T_args) homo_infinite_type, No_Types)
1646 Decl (sym_decl_prefix ^ s, (s, s'),
1647 (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
1648 |> mangled_type higher_order pred_sym (length T_arg_Ts + ary))
1651 fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
1653 fun formula_line_for_preds_sym_decl ctxt format conj_sym_kind nonmono_Ts
1654 type_sys n s j (s', T_args, T, _, ary, in_conj) =
1656 val (kind, maybe_negate) =
1657 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1659 val (arg_Ts, res_T) = chop_fun ary T
1661 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
1663 bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
1665 arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
1668 Formula (preds_sym_formula_prefix ^ s ^
1669 (if n > 1 then "_" ^ string_of_int j else ""), kind,
1670 CombConst ((s, s'), T, T_args)
1671 |> fold (curry (CombApp o swap)) bounds
1672 |> type_pred_combterm ctxt nonmono_Ts type_sys res_T
1673 |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
1674 |> formula_from_combformula ctxt format nonmono_Ts type_sys
1675 (K (K (K (K true)))) true
1676 |> n > 1 ? bound_tvars type_sys (atyps_of T)
1677 |> close_formula_universally
1682 fun formula_lines_for_lightweight_tags_sym_decl ctxt format conj_sym_kind
1683 nonmono_Ts type_sys n s (j, (s', T_args, T, pred_sym, ary, in_conj)) =
1686 lightweight_tags_sym_formula_prefix ^ s ^
1687 (if n > 1 then "_" ^ string_of_int j else "")
1688 val (kind, maybe_negate) =
1689 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1691 val (arg_Ts, res_T) = chop_fun ary T
1693 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
1694 val bounds = bound_names |> map (fn name => ATerm (name, []))
1695 val cst = mk_const_aterm (s, s') T_args
1696 val atomic_Ts = atyps_of T
1698 (if pred_sym then AConn (AIff, map AAtom tms)
1699 else AAtom (ATerm (`I tptp_equal, tms)))
1700 |> bound_tvars type_sys atomic_Ts
1701 |> close_formula_universally
1703 val should_encode = should_encode_type ctxt nonmono_Ts All_Types
1704 val tag_with = tag_with_type ctxt format nonmono_Ts type_sys
1705 val add_formula_for_res =
1706 if should_encode res_T then
1707 cons (Formula (ident_base ^ "_res", kind,
1708 eq [tag_with res_T (cst bounds), cst bounds],
1712 fun add_formula_for_arg k =
1713 let val arg_T = nth arg_Ts k in
1714 if should_encode arg_T then
1715 case chop k bounds of
1716 (bounds1, bound :: bounds2) =>
1717 cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
1718 eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
1721 | _ => raise Fail "expected nonempty tail"
1726 [] |> not pred_sym ? add_formula_for_res
1727 |> fold add_formula_for_arg (ary - 1 downto 0)
1730 fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
1732 fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts type_sys
1736 decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_sys s)
1741 decl :: (decls' as _ :: _) =>
1742 let val T = result_type_of_decl decl in
1743 if forall (curry (type_instance ctxt o swap) T
1744 o result_type_of_decl) decls' then
1750 val n = length decls
1753 |> filter (should_predicate_on_type ctxt nonmono_Ts type_sys (K true)
1754 o result_type_of_decl)
1756 (0 upto length decls - 1, decls)
1757 |-> map2 (formula_line_for_preds_sym_decl ctxt format conj_sym_kind
1758 nonmono_Ts type_sys n s)
1760 | Tags (_, _, heaviness) =>
1764 let val n = length decls in
1765 (0 upto n - 1 ~~ decls)
1766 |> maps (formula_lines_for_lightweight_tags_sym_decl ctxt format
1767 conj_sym_kind nonmono_Ts type_sys n s)
1770 fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1771 type_sys sym_decl_tab =
1776 |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
1777 nonmono_Ts type_sys)
1779 fun should_add_ti_ti_helper (Tags (Polymorphic, level, Heavyweight)) =
1780 level = Nonmonotonic_Types orelse level = Finite_Types
1781 | should_add_ti_ti_helper _ = false
1783 fun offset_of_heading_in_problem _ [] j = j
1784 | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
1785 if heading = needle then j
1786 else offset_of_heading_in_problem needle problem (j + length lines)
1788 val implicit_declsN = "Should-be-implicit typings"
1789 val explicit_declsN = "Explicit typings"
1790 val factsN = "Relevant facts"
1791 val class_relsN = "Class relationships"
1792 val aritiesN = "Arities"
1793 val helpersN = "Helper facts"
1794 val conjsN = "Conjectures"
1795 val free_typesN = "Type variables"
1797 fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_sys
1798 explicit_apply readable_names preproc hyp_ts concl_t
1801 val (format, type_sys) = choose_format [format] type_sys
1802 val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
1803 translate_formulas ctxt format prem_kind type_sys preproc hyp_ts concl_t
1805 val sym_tab = conjs @ facts |> sym_table_for_facts ctxt explicit_apply
1806 val nonmono_Ts = conjs @ facts |> nonmonotonic_types_for_facts ctxt type_sys
1807 val repair = repair_fact ctxt format nonmono_Ts type_sys sym_tab
1808 val (conjs, facts) = (conjs, facts) |> pairself (map repair)
1809 val repaired_sym_tab =
1810 conjs @ facts |> sym_table_for_facts ctxt (SOME false)
1812 repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_sys
1814 val lavish_nonmono_Ts =
1815 if null nonmono_Ts orelse
1816 polymorphism_of_type_sys type_sys <> Polymorphic then
1819 [TVar (("'a", 0), HOLogic.typeS)]
1820 val sym_decl_lines =
1821 (conjs, helpers @ facts)
1822 |> sym_decl_table_for_facts ctxt type_sys repaired_sym_tab
1823 |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind
1824 lavish_nonmono_Ts type_sys
1826 0 upto length helpers - 1 ~~ helpers
1827 |> map (formula_line_for_fact ctxt format helper_prefix lavish_nonmono_Ts
1829 |> (if should_add_ti_ti_helper type_sys then cons (ti_ti_helper_fact ())
1831 (* Reordering these might confuse the proof reconstruction code or the SPASS
1834 [(explicit_declsN, sym_decl_lines),
1836 map (formula_line_for_fact ctxt format fact_prefix nonmono_Ts type_sys)
1837 (0 upto length facts - 1 ~~ facts)),
1838 (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
1839 (aritiesN, map formula_line_for_arity_clause arity_clauses),
1840 (helpersN, helper_lines),
1842 map (formula_line_for_conjecture ctxt format nonmono_Ts type_sys)
1844 (free_typesN, formula_lines_for_free_types type_sys (facts @ conjs))]
1848 CNF => ensure_cnf_problem
1849 | CNF_UEQ => filter_cnf_ueq_problem
1851 |> (if is_format_typed format then
1852 declare_undeclared_syms_in_atp_problem type_decl_prefix
1856 val (problem, pool) = problem |> nice_atp_problem readable_names
1857 val helpers_offset = offset_of_heading_in_problem helpersN problem 0
1859 map_filter (fn (j, {name, ...}) =>
1860 if String.isSuffix typed_helper_suffix name then SOME j
1862 ((helpers_offset + 1 upto helpers_offset + length helpers)
1864 fun add_sym_arity (s, {min_ary, ...} : sym_info) =
1866 case strip_prefix_and_unascii const_prefix s of
1867 SOME s => Symtab.insert (op =) (s, min_ary)
1873 case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
1874 offset_of_heading_in_problem conjsN problem 0,
1875 offset_of_heading_in_problem factsN problem 0,
1876 fact_names |> Vector.fromList,
1878 Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
1882 val conj_weight = 0.0
1883 val hyp_weight = 0.1
1884 val fact_min_weight = 0.2
1885 val fact_max_weight = 1.0
1886 val type_info_default_weight = 0.8
1888 fun add_term_weights weight (ATerm (s, tms)) =
1889 is_tptp_user_symbol s ? Symtab.default (s, weight)
1890 #> fold (add_term_weights weight) tms
1891 fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
1892 formula_fold NONE (K (add_term_weights weight)) phi
1893 | add_problem_line_weights _ _ = I
1895 fun add_conjectures_weights [] = I
1896 | add_conjectures_weights conjs =
1897 let val (hyps, conj) = split_last conjs in
1898 add_problem_line_weights conj_weight conj
1899 #> fold (add_problem_line_weights hyp_weight) hyps
1902 fun add_facts_weights facts =
1904 val num_facts = length facts
1906 fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
1907 / Real.fromInt num_facts
1909 map weight_of (0 upto num_facts - 1) ~~ facts
1910 |> fold (uncurry add_problem_line_weights)
1913 (* Weights are from 0.0 (most important) to 1.0 (least important). *)
1914 fun atp_problem_weights problem =
1915 let val get = these o AList.lookup (op =) problem in
1917 |> add_conjectures_weights (get free_typesN @ get conjsN)
1918 |> add_facts_weights (get factsN)
1919 |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
1920 [explicit_declsN, class_relsN, aritiesN]
1922 |> sort (prod_ord Real.compare string_ord o pairself swap)