1 (* Title: HOL/Tools/ATP/atp_translate.ML
2 Author: Fabian Immler, TU Muenchen
4 Author: Jasmin Blanchette, TU Muenchen
6 Translation of HOL to FOL for Sledgehammer.
9 signature ATP_TRANSLATE =
11 type ('a, 'b) ho_term = ('a, 'b) ATP_Problem.ho_term
12 type connective = ATP_Problem.connective
13 type ('a, 'b, 'c) formula = ('a, 'b, 'c) ATP_Problem.formula
14 type format = ATP_Problem.format
15 type formula_kind = ATP_Problem.formula_kind
16 type 'a problem = 'a ATP_Problem.problem
19 General | Helper | Extensionality | Intro | Elim | Simp | Local | Assum |
22 datatype order = First_Order | Higher_Order
23 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
25 All_Types | Noninf_Nonmono_Types | Fin_Nonmono_Types | Const_Arg_Types |
27 datatype type_heaviness = Heavyweight | Lightweight
30 Simple_Types of order * type_level |
31 Preds of polymorphism * type_level * type_heaviness |
32 Tags of polymorphism * type_level * type_heaviness
34 val bound_var_prefix : string
35 val schematic_var_prefix : string
36 val fixed_var_prefix : string
37 val tvar_prefix : string
38 val tfree_prefix : string
39 val const_prefix : string
40 val type_const_prefix : string
41 val class_prefix : string
42 val skolem_const_prefix : string
43 val old_skolem_const_prefix : string
44 val new_skolem_const_prefix : string
45 val type_decl_prefix : string
46 val sym_decl_prefix : string
47 val preds_sym_formula_prefix : string
48 val lightweight_tags_sym_formula_prefix : string
49 val fact_prefix : string
50 val conjecture_prefix : string
51 val helper_prefix : string
52 val class_rel_clause_prefix : string
53 val arity_clause_prefix : string
54 val tfree_clause_prefix : string
55 val typed_helper_suffix : string
56 val untyped_helper_suffix : string
57 val type_tag_idempotence_helper_name : string
58 val predicator_name : string
59 val app_op_name : string
60 val type_tag_name : string
61 val type_pred_name : string
62 val simple_type_prefix : string
63 val prefixed_predicator_name : string
64 val prefixed_app_op_name : string
65 val prefixed_type_tag_name : string
66 val ascii_of : string -> string
67 val unascii_of : string -> string
68 val strip_prefix_and_unascii : string -> string -> string option
69 val proxy_table : (string * (string * (thm * (string * string)))) list
70 val proxify_const : string -> (string * string) option
71 val invert_const : string -> string
72 val unproxify_const : string -> string
73 val new_skolem_var_name_from_const : string -> string
74 val num_type_args : theory -> string -> int
75 val atp_irrelevant_consts : string list
76 val atp_schematic_consts_of : term -> typ list Symtab.table
77 val is_locality_global : locality -> bool
78 val type_enc_from_string : string -> type_enc
79 val polymorphism_of_type_enc : type_enc -> polymorphism
80 val level_of_type_enc : type_enc -> type_level
81 val is_type_enc_virtually_sound : type_enc -> bool
82 val is_type_enc_fairly_sound : type_enc -> bool
83 val choose_format : format list -> type_enc -> format * type_enc
85 connective -> ('a, 'b, 'c) formula list -> ('a, 'b, 'c) formula
86 val unmangled_const : string -> string * (string, 'b) ho_term list
87 val unmangled_const_name : string -> string
88 val helper_table : ((string * bool) * thm list) list
90 val prepare_atp_problem :
91 Proof.context -> format -> formula_kind -> formula_kind -> type_enc -> bool
92 -> bool -> bool -> bool -> term list -> term
93 -> ((string * locality) * term) list
94 -> string problem * string Symtab.table * int * int
95 * (string * locality) list vector * int list * int Symtab.table
96 val atp_problem_weights : string problem -> (string * real) list
99 structure ATP_Translate : ATP_TRANSLATE =
105 type name = string * string
108 val generate_info = false
110 fun isabelle_info s =
111 if generate_info then SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
118 val bound_var_prefix = "B_"
119 val schematic_var_prefix = "V_"
120 val fixed_var_prefix = "v_"
122 val tvar_prefix = "T_"
123 val tfree_prefix = "t_"
125 val const_prefix = "c_"
126 val type_const_prefix = "tc_"
127 val class_prefix = "cl_"
129 val skolem_const_prefix = "Sledgehammer" ^ Long_Name.separator ^ "Sko"
130 val old_skolem_const_prefix = skolem_const_prefix ^ "o"
131 val new_skolem_const_prefix = skolem_const_prefix ^ "n"
133 val type_decl_prefix = "ty_"
134 val sym_decl_prefix = "sy_"
135 val preds_sym_formula_prefix = "psy_"
136 val lightweight_tags_sym_formula_prefix = "tsy_"
137 val fact_prefix = "fact_"
138 val conjecture_prefix = "conj_"
139 val helper_prefix = "help_"
140 val class_rel_clause_prefix = "clar_"
141 val arity_clause_prefix = "arity_"
142 val tfree_clause_prefix = "tfree_"
144 val typed_helper_suffix = "_T"
145 val untyped_helper_suffix = "_U"
146 val type_tag_idempotence_helper_name = helper_prefix ^ "ti_idem"
148 val predicator_name = "hBOOL"
149 val app_op_name = "hAPP"
150 val type_tag_name = "ti"
151 val type_pred_name = "is"
152 val simple_type_prefix = "ty_"
154 val prefixed_predicator_name = const_prefix ^ predicator_name
155 val prefixed_app_op_name = const_prefix ^ app_op_name
156 val prefixed_type_tag_name = const_prefix ^ type_tag_name
158 (* Freshness almost guaranteed! *)
159 val sledgehammer_weak_prefix = "Sledgehammer:"
161 (*Escaping of special characters.
162 Alphanumeric characters are left unchanged.
163 The character _ goes to __
164 Characters in the range ASCII space to / go to _A to _P, respectively.
165 Other characters go to _nnn where nnn is the decimal ASCII code.*)
166 val upper_a_minus_space = Char.ord #"A" - Char.ord #" "
168 fun stringN_of_int 0 _ = ""
169 | stringN_of_int k n =
170 stringN_of_int (k - 1) (n div 10) ^ string_of_int (n mod 10)
172 fun ascii_of_char c =
173 if Char.isAlphaNum c then
175 else if c = #"_" then
177 else if #" " <= c andalso c <= #"/" then
178 "_" ^ String.str (Char.chr (Char.ord c + upper_a_minus_space))
180 (* fixed width, in case more digits follow *)
181 "_" ^ stringN_of_int 3 (Char.ord c)
183 val ascii_of = String.translate ascii_of_char
185 (** Remove ASCII armoring from names in proof files **)
187 (* We don't raise error exceptions because this code can run inside a worker
188 thread. Also, the errors are impossible. *)
191 fun un rcs [] = String.implode(rev rcs)
192 | un rcs [#"_"] = un (#"_" :: rcs) [] (* ERROR *)
193 (* Three types of _ escapes: __, _A to _P, _nnn *)
194 | un rcs (#"_" :: #"_" :: cs) = un (#"_" :: rcs) cs
195 | un rcs (#"_" :: c :: cs) =
196 if #"A" <= c andalso c<= #"P" then
197 (* translation of #" " to #"/" *)
198 un (Char.chr (Char.ord c - upper_a_minus_space) :: rcs) cs
200 let val digits = List.take (c :: cs, 3) handle General.Subscript => [] in
201 case Int.fromString (String.implode digits) of
202 SOME n => un (Char.chr n :: rcs) (List.drop (cs, 2))
203 | NONE => un (c :: #"_" :: rcs) cs (* ERROR *)
205 | un rcs (c :: cs) = un (c :: rcs) cs
206 in un [] o String.explode end
208 (* If string s has the prefix s1, return the result of deleting it,
210 fun strip_prefix_and_unascii s1 s =
211 if String.isPrefix s1 s then
212 SOME (unascii_of (String.extract (s, size s1, NONE)))
217 [("c_False", (@{const_name False}, (@{thm fFalse_def},
218 ("fFalse", @{const_name ATP.fFalse})))),
219 ("c_True", (@{const_name True}, (@{thm fTrue_def},
220 ("fTrue", @{const_name ATP.fTrue})))),
221 ("c_Not", (@{const_name Not}, (@{thm fNot_def},
222 ("fNot", @{const_name ATP.fNot})))),
223 ("c_conj", (@{const_name conj}, (@{thm fconj_def},
224 ("fconj", @{const_name ATP.fconj})))),
225 ("c_disj", (@{const_name disj}, (@{thm fdisj_def},
226 ("fdisj", @{const_name ATP.fdisj})))),
227 ("c_implies", (@{const_name implies}, (@{thm fimplies_def},
228 ("fimplies", @{const_name ATP.fimplies})))),
229 ("equal", (@{const_name HOL.eq}, (@{thm fequal_def},
230 ("fequal", @{const_name ATP.fequal})))),
231 ("c_All", (@{const_name All}, (@{thm fAll_def},
232 ("fAll", @{const_name ATP.fAll})))),
233 ("c_Ex", (@{const_name Ex}, (@{thm fEx_def},
234 ("fEx", @{const_name ATP.fEx}))))]
236 val proxify_const = AList.lookup (op =) proxy_table #> Option.map (snd o snd)
238 (* Readable names for the more common symbolic functions. Do not mess with the
239 table unless you know what you are doing. *)
240 val const_trans_table =
241 [(@{type_name Product_Type.prod}, "prod"),
242 (@{type_name Sum_Type.sum}, "sum"),
243 (@{const_name False}, "False"),
244 (@{const_name True}, "True"),
245 (@{const_name Not}, "Not"),
246 (@{const_name conj}, "conj"),
247 (@{const_name disj}, "disj"),
248 (@{const_name implies}, "implies"),
249 (@{const_name HOL.eq}, "equal"),
250 (@{const_name All}, "All"),
251 (@{const_name Ex}, "Ex"),
252 (@{const_name If}, "If"),
253 (@{const_name Set.member}, "member"),
254 (@{const_name Meson.COMBI}, "COMBI"),
255 (@{const_name Meson.COMBK}, "COMBK"),
256 (@{const_name Meson.COMBB}, "COMBB"),
257 (@{const_name Meson.COMBC}, "COMBC"),
258 (@{const_name Meson.COMBS}, "COMBS")]
260 |> fold (Symtab.update o swap o snd o snd o snd) proxy_table
262 (* Invert the table of translations between Isabelle and ATPs. *)
263 val const_trans_table_inv =
264 const_trans_table |> Symtab.dest |> map swap |> Symtab.make
265 val const_trans_table_unprox =
267 |> fold (fn (_, (isa, (_, (_, atp)))) => Symtab.update (atp, isa)) proxy_table
269 val invert_const = perhaps (Symtab.lookup const_trans_table_inv)
270 val unproxify_const = perhaps (Symtab.lookup const_trans_table_unprox)
273 case Symtab.lookup const_trans_table c of
277 fun ascii_of_indexname (v, 0) = ascii_of v
278 | ascii_of_indexname (v, i) = ascii_of v ^ "_" ^ string_of_int i
280 fun make_bound_var x = bound_var_prefix ^ ascii_of x
281 fun make_schematic_var v = schematic_var_prefix ^ ascii_of_indexname v
282 fun make_fixed_var x = fixed_var_prefix ^ ascii_of x
284 fun make_schematic_type_var (x, i) =
285 tvar_prefix ^ (ascii_of_indexname (unprefix "'" x, i))
286 fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (unprefix "'" x))
288 (* "HOL.eq" is mapped to the ATP's equality. *)
289 fun make_fixed_const @{const_name HOL.eq} = tptp_old_equal
290 | make_fixed_const c = const_prefix ^ lookup_const c
292 fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
294 fun make_type_class clas = class_prefix ^ ascii_of clas
296 fun new_skolem_var_name_from_const s =
297 let val ss = s |> space_explode Long_Name.separator in
298 nth ss (length ss - 2)
301 (* The number of type arguments of a constant, zero if it's monomorphic. For
302 (instances of) Skolem pseudoconstants, this information is encoded in the
304 fun num_type_args thy s =
305 if String.isPrefix skolem_const_prefix s then
306 s |> space_explode Long_Name.separator |> List.last |> Int.fromString |> the
308 (s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
310 (* These are either simplified away by "Meson.presimplify" (most of the time) or
311 handled specially via "fFalse", "fTrue", ..., "fequal". *)
312 val atp_irrelevant_consts =
313 [@{const_name False}, @{const_name True}, @{const_name Not},
314 @{const_name conj}, @{const_name disj}, @{const_name implies},
315 @{const_name HOL.eq}, @{const_name If}, @{const_name Let}]
317 val atp_monomorph_bad_consts =
318 atp_irrelevant_consts @
319 (* These are ignored anyway by the relevance filter (unless they appear in
320 higher-order places) but not by the monomorphizer. *)
321 [@{const_name all}, @{const_name "==>"}, @{const_name "=="},
322 @{const_name Trueprop}, @{const_name All}, @{const_name Ex},
323 @{const_name Ex1}, @{const_name Ball}, @{const_name Bex}]
325 fun add_schematic_const (x as (_, T)) =
326 Monomorph.typ_has_tvars T ? Symtab.insert_list (op =) x
327 val add_schematic_consts_of =
328 Term.fold_aterms (fn Const (x as (s, _)) =>
329 not (member (op =) atp_monomorph_bad_consts s)
330 ? add_schematic_const x
332 fun atp_schematic_consts_of t = add_schematic_consts_of t Symtab.empty
334 (** Definitions and functions for FOL clauses and formulas for TPTP **)
336 (* The first component is the type class; the second is a "TVar" or "TFree". *)
337 datatype type_literal =
338 TyLitVar of name * name |
339 TyLitFree of name * name
342 (** Isabelle arities **)
344 datatype arity_literal =
345 TConsLit of name * name * name list |
346 TVarLit of name * name
349 | gen_TVars n = ("T_" ^ string_of_int n) :: gen_TVars (n-1)
351 val type_class = the_single @{sort type}
353 fun add_packed_sort tvar =
354 fold (fn s => s <> type_class ? cons (`make_type_class s, `I tvar))
358 prem_lits : arity_literal list,
359 concl_lits : arity_literal}
361 (* Arity of type constructor "tcon :: (arg1, ..., argN) res" *)
362 fun make_axiom_arity_clause (tcons, name, (cls, args)) =
364 val tvars = gen_TVars (length args)
365 val tvars_srts = ListPair.zip (tvars, args)
368 prem_lits = [] |> fold (uncurry add_packed_sort) tvars_srts |> map TVarLit,
369 concl_lits = TConsLit (`make_type_class cls,
370 `make_fixed_type_const tcons,
374 fun arity_clause _ _ (_, []) = []
375 | arity_clause seen n (tcons, ("HOL.type", _) :: ars) = (* ignore *)
376 arity_clause seen n (tcons, ars)
377 | arity_clause seen n (tcons, (ar as (class, _)) :: ars) =
378 if member (op =) seen class then
379 (* multiple arities for the same (tycon, class) pair *)
380 make_axiom_arity_clause (tcons,
381 lookup_const tcons ^ "___" ^ ascii_of class ^ "_" ^ string_of_int n,
383 arity_clause seen (n + 1) (tcons, ars)
385 make_axiom_arity_clause (tcons, lookup_const tcons ^ "___" ^
386 ascii_of class, ar) ::
387 arity_clause (class :: seen) n (tcons, ars)
389 fun multi_arity_clause [] = []
390 | multi_arity_clause ((tcons, ars) :: tc_arlists) =
391 arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
393 (* Generate all pairs (tycon, class, sorts) such that tycon belongs to class in
394 theory thy provided its arguments have the corresponding sorts. *)
395 fun type_class_pairs thy tycons classes =
397 val alg = Sign.classes_of thy
398 fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
399 fun add_class tycon class =
400 cons (class, domain_sorts tycon class)
401 handle Sorts.CLASS_ERROR _ => I
402 fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
403 in map try_classes tycons end
405 (*Proving one (tycon, class) membership may require proving others, so iterate.*)
406 fun iter_type_class_pairs _ _ [] = ([], [])
407 | iter_type_class_pairs thy tycons classes =
409 fun maybe_insert_class s =
410 (s <> type_class andalso not (member (op =) classes s))
412 val cpairs = type_class_pairs thy tycons classes
414 [] |> fold (fold (fold (fold maybe_insert_class) o snd) o snd) cpairs
415 val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
416 in (classes' @ classes, union (op =) cpairs' cpairs) end
418 fun make_arity_clauses thy tycons =
419 iter_type_class_pairs thy tycons ##> multi_arity_clause
422 (** Isabelle class relations **)
424 type class_rel_clause =
429 (* Generate all pairs (sub, super) such that sub is a proper subclass of super
431 fun class_pairs _ [] _ = []
432 | class_pairs thy subs supers =
434 val class_less = Sorts.class_less (Sign.classes_of thy)
435 fun add_super sub super = class_less (sub, super) ? cons (sub, super)
436 fun add_supers sub = fold (add_super sub) supers
437 in fold add_supers subs [] end
439 fun make_class_rel_clause (sub, super) =
440 {name = sub ^ "_" ^ super, subclass = `make_type_class sub,
441 superclass = `make_type_class super}
443 fun make_class_rel_clauses thy subs supers =
444 map make_class_rel_clause (class_pairs thy subs supers)
447 CombConst of name * typ * typ list |
448 CombVar of name * typ |
449 CombApp of combterm * combterm |
450 CombAbs of (name * typ) * combterm
452 fun combtyp_of (CombConst (_, T, _)) = T
453 | combtyp_of (CombVar (_, T)) = T
454 | combtyp_of (CombApp (t1, _)) = snd (dest_funT (combtyp_of t1))
455 | combtyp_of (CombAbs ((_, T), tm)) = T --> combtyp_of tm
457 (*gets the head of a combinator application, along with the list of arguments*)
458 fun strip_combterm_comb u =
460 fun stripc (CombApp (t, u), ts) = stripc (t, u :: ts)
462 in stripc (u, []) end
464 fun atyps_of T = fold_atyps (insert (op =)) T []
466 fun new_skolem_const_name s num_T_args =
467 [new_skolem_const_prefix, s, string_of_int num_T_args]
468 |> space_implode Long_Name.separator
470 (* Converts a term (with combinators) into a combterm. Also accumulates sort
472 fun combterm_from_term thy bs (P $ Q) =
474 val (P', P_atomics_Ts) = combterm_from_term thy bs P
475 val (Q', Q_atomics_Ts) = combterm_from_term thy bs Q
476 in (CombApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
477 | combterm_from_term thy _ (Const (c, T)) =
480 (if String.isPrefix old_skolem_const_prefix c then
481 [] |> Term.add_tvarsT T |> map TVar
483 (c, T) |> Sign.const_typargs thy)
484 val c' = CombConst (`make_fixed_const c, T, tvar_list)
485 in (c', atyps_of T) end
486 | combterm_from_term _ _ (Free (v, T)) =
487 (CombConst (`make_fixed_var v, T, []), atyps_of T)
488 | combterm_from_term _ _ (Var (v as (s, _), T)) =
489 (if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
491 val Ts = T |> strip_type |> swap |> op ::
492 val s' = new_skolem_const_name s (length Ts)
493 in CombConst (`make_fixed_const s', T, Ts) end
495 CombVar ((make_schematic_var v, s), T), atyps_of T)
496 | combterm_from_term _ bs (Bound j) =
498 |> (fn (s, T) => (CombConst (`make_bound_var s, T, []), atyps_of T))
499 | combterm_from_term thy bs (Abs (s, T, t)) =
501 fun vary s = s |> AList.defined (op =) bs s ? vary o Symbol.bump_string
503 val (tm, atomic_Ts) = combterm_from_term thy ((s, T) :: bs) t
505 (CombAbs ((`make_bound_var s, T), tm),
506 union (op =) atomic_Ts (atyps_of T))
510 General | Helper | Extensionality | Intro | Elim | Simp | Local | Assum |
513 (* (quasi-)underapproximation of the truth *)
514 fun is_locality_global Local = false
515 | is_locality_global Assum = false
516 | is_locality_global Chained = false
517 | is_locality_global _ = true
519 datatype order = First_Order | Higher_Order
520 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
521 datatype type_level =
522 All_Types | Noninf_Nonmono_Types | Fin_Nonmono_Types | Const_Arg_Types |
524 datatype type_heaviness = Heavyweight | Lightweight
527 Simple_Types of order * type_level |
528 Preds of polymorphism * type_level * type_heaviness |
529 Tags of polymorphism * type_level * type_heaviness
531 fun try_unsuffixes ss s =
532 fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
534 fun type_enc_from_string s =
535 (case try (unprefix "poly_") s of
536 SOME s => (SOME Polymorphic, s)
538 case try (unprefix "mono_") s of
539 SOME s => (SOME Monomorphic, s)
541 case try (unprefix "mangled_") s of
542 SOME s => (SOME Mangled_Monomorphic, s)
545 (* "_query" and "_bang" are for the ASCII-challenged Metis and
547 case try_unsuffixes ["?", "_query"] s of
548 SOME s => (Noninf_Nonmono_Types, s)
550 case try_unsuffixes ["!", "_bang"] s of
551 SOME s => (Fin_Nonmono_Types, s)
552 | NONE => (All_Types, s))
554 case try (unsuffix "_heavy") s of
555 SOME s => (Heavyweight, s)
556 | NONE => (Lightweight, s))
557 |> (fn (poly, (level, (heaviness, core))) =>
558 case (core, (poly, level, heaviness)) of
559 ("simple", (NONE, _, Lightweight)) =>
560 Simple_Types (First_Order, level)
561 | ("simple_higher", (NONE, _, Lightweight)) =>
562 if level = Noninf_Nonmono_Types then raise Same.SAME
563 else Simple_Types (Higher_Order, level)
564 | ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
565 | ("tags", (SOME Polymorphic, _, _)) =>
566 Tags (Polymorphic, level, heaviness)
567 | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
568 | ("args", (SOME poly, All_Types (* naja *), Lightweight)) =>
569 Preds (poly, Const_Arg_Types, Lightweight)
570 | ("erased", (NONE, All_Types (* naja *), Lightweight)) =>
571 Preds (Polymorphic, No_Types, Lightweight)
572 | _ => raise Same.SAME)
573 handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
575 fun is_type_enc_higher_order (Simple_Types (Higher_Order, _)) = true
576 | is_type_enc_higher_order _ = false
578 fun polymorphism_of_type_enc (Simple_Types _) = Mangled_Monomorphic
579 | polymorphism_of_type_enc (Preds (poly, _, _)) = poly
580 | polymorphism_of_type_enc (Tags (poly, _, _)) = poly
582 fun level_of_type_enc (Simple_Types (_, level)) = level
583 | level_of_type_enc (Preds (_, level, _)) = level
584 | level_of_type_enc (Tags (_, level, _)) = level
586 fun heaviness_of_type_enc (Simple_Types _) = Heavyweight
587 | heaviness_of_type_enc (Preds (_, _, heaviness)) = heaviness
588 | heaviness_of_type_enc (Tags (_, _, heaviness)) = heaviness
590 fun is_type_level_virtually_sound level =
591 level = All_Types orelse level = Noninf_Nonmono_Types
592 val is_type_enc_virtually_sound =
593 is_type_level_virtually_sound o level_of_type_enc
595 fun is_type_level_fairly_sound level =
596 is_type_level_virtually_sound level orelse level = Fin_Nonmono_Types
597 val is_type_enc_fairly_sound = is_type_level_fairly_sound o level_of_type_enc
599 fun choose_format formats (Simple_Types (order, level)) =
600 if member (op =) formats THF then
601 (THF, Simple_Types (order, level))
602 else if member (op =) formats TFF then
603 (TFF, Simple_Types (First_Order, level))
605 choose_format formats (Preds (Mangled_Monomorphic, level, Heavyweight))
606 | choose_format formats type_enc =
609 (CNF_UEQ, case type_enc of
611 (if is_type_enc_fairly_sound type_enc then Tags else Preds)
614 | format => (format, type_enc))
616 type translated_formula =
620 combformula : (name, typ, combterm) formula,
621 atomic_types : typ list}
623 fun update_combformula f ({name, locality, kind, combformula, atomic_types}
624 : translated_formula) =
625 {name = name, locality = locality, kind = kind, combformula = f combformula,
626 atomic_types = atomic_types} : translated_formula
628 fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
630 val type_instance = Sign.typ_instance o Proof_Context.theory_of
632 fun insert_type ctxt get_T x xs =
633 let val T = get_T x in
634 if exists (curry (type_instance ctxt) T o get_T) xs then xs
635 else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
638 (* The Booleans indicate whether all type arguments should be kept. *)
639 datatype type_arg_policy =
640 Explicit_Type_Args of bool |
641 Mangled_Type_Args of bool |
644 fun should_drop_arg_type_args (Simple_Types _) =
645 false (* since TFF doesn't support overloading *)
646 | should_drop_arg_type_args type_enc =
647 level_of_type_enc type_enc = All_Types andalso
648 heaviness_of_type_enc type_enc = Heavyweight
650 fun type_arg_policy type_enc s =
651 if s = type_tag_name then
652 (if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
655 Explicit_Type_Args) false
656 else case type_enc of
657 Tags (_, All_Types, Heavyweight) => No_Type_Args
659 if level_of_type_enc type_enc = No_Types orelse
660 s = @{const_name HOL.eq} orelse
661 (s = app_op_name andalso
662 level_of_type_enc type_enc = Const_Arg_Types) then
665 should_drop_arg_type_args type_enc
666 |> (if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
671 (* Make literals for sorted type variables. *)
672 fun generic_add_sorts_on_type (_, []) = I
673 | generic_add_sorts_on_type ((x, i), s :: ss) =
674 generic_add_sorts_on_type ((x, i), ss)
675 #> (if s = the_single @{sort HOL.type} then
678 insert (op =) (TyLitFree (`make_type_class s, `make_fixed_type_var x))
680 insert (op =) (TyLitVar (`make_type_class s,
681 (make_schematic_type_var (x, i), x))))
682 fun add_sorts_on_tfree (TFree (s, S)) = generic_add_sorts_on_type ((s, ~1), S)
683 | add_sorts_on_tfree _ = I
684 fun add_sorts_on_tvar (TVar z) = generic_add_sorts_on_type z
685 | add_sorts_on_tvar _ = I
687 fun type_literals_for_types type_enc add_sorts_on_typ Ts =
688 [] |> level_of_type_enc type_enc <> No_Types ? fold add_sorts_on_typ Ts
690 fun mk_aconns c phis =
691 let val (phis', phi') = split_last phis in
692 fold_rev (mk_aconn c) phis' phi'
694 fun mk_ahorn [] phi = phi
695 | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
696 fun mk_aquant _ [] phi = phi
697 | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
698 if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
699 | mk_aquant q xs phi = AQuant (q, xs, phi)
701 fun close_universally atom_vars phi =
703 fun formula_vars bounds (AQuant (_, xs, phi)) =
704 formula_vars (map fst xs @ bounds) phi
705 | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
706 | formula_vars bounds (AAtom tm) =
707 union (op =) (atom_vars tm []
708 |> filter_out (member (op =) bounds o fst))
709 in mk_aquant AForall (formula_vars [] phi []) phi end
711 fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
712 | combterm_vars (CombConst _) = I
713 | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
714 | combterm_vars (CombAbs (_, tm)) = combterm_vars tm
715 fun close_combformula_universally phi = close_universally combterm_vars phi
717 fun term_vars bounds (ATerm (name as (s, _), tms)) =
718 (is_tptp_variable s andalso not (member (op =) bounds name))
719 ? insert (op =) (name, NONE) #> fold (term_vars bounds) tms
720 | term_vars bounds (AAbs ((name, _), tm)) = term_vars (name :: bounds) tm
721 fun close_formula_universally phi = close_universally (term_vars []) phi
723 val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
724 val homo_infinite_type = Type (homo_infinite_type_name, [])
726 fun ho_term_from_typ format type_enc =
728 fun term (Type (s, Ts)) =
729 ATerm (case (is_type_enc_higher_order type_enc, s) of
730 (true, @{type_name bool}) => `I tptp_bool_type
731 | (true, @{type_name fun}) => `I tptp_fun_type
732 | _ => if s = homo_infinite_type_name andalso
733 (format = TFF orelse format = THF) then
734 `I tptp_individual_type
736 `make_fixed_type_const s,
738 | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
739 | term (TVar ((x as (s, _)), _)) =
740 ATerm ((make_schematic_type_var x, s), [])
743 fun ho_term_for_type_arg format type_enc T =
744 if T = dummyT then NONE else SOME (ho_term_from_typ format type_enc T)
746 (* This shouldn't clash with anything else. *)
747 val mangled_type_sep = "\000"
749 fun generic_mangled_type_name f (ATerm (name, [])) = f name
750 | generic_mangled_type_name f (ATerm (name, tys)) =
751 f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
753 | generic_mangled_type_name _ _ = raise Fail "unexpected type abstraction"
755 val bool_atype = AType (`I tptp_bool_type)
757 fun make_simple_type s =
758 if s = tptp_bool_type orelse s = tptp_fun_type orelse
759 s = tptp_individual_type then
762 simple_type_prefix ^ ascii_of s
764 fun ho_type_from_ho_term type_enc pred_sym ary =
767 AType ((make_simple_type (generic_mangled_type_name fst ty),
768 generic_mangled_type_name snd ty))
769 fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
770 fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
771 | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
772 | to_fo _ _ = raise Fail "unexpected type abstraction"
773 fun to_ho (ty as ATerm ((s, _), tys)) =
774 if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
775 | to_ho _ = raise Fail "unexpected type abstraction"
776 in if is_type_enc_higher_order type_enc then to_ho else to_fo ary end
778 fun ho_type_from_typ format type_enc pred_sym ary =
779 ho_type_from_ho_term type_enc pred_sym ary
780 o ho_term_from_typ format type_enc
782 fun mangled_const_name format type_enc T_args (s, s') =
784 val ty_args = T_args |> map_filter (ho_term_for_type_arg format type_enc)
785 fun type_suffix f g =
786 fold_rev (curry (op ^) o g o prefix mangled_type_sep
787 o generic_mangled_type_name f) ty_args ""
788 in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
790 val parse_mangled_ident =
791 Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
793 fun parse_mangled_type x =
795 -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
797 and parse_mangled_types x =
798 (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
800 fun unmangled_type s =
801 s |> suffix ")" |> raw_explode
802 |> Scan.finite Symbol.stopper
803 (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
804 quote s)) parse_mangled_type))
807 val unmangled_const_name = space_explode mangled_type_sep #> hd
808 fun unmangled_const s =
809 let val ss = space_explode mangled_type_sep s in
810 (hd ss, map unmangled_type (tl ss))
813 fun introduce_proxies type_enc =
815 fun intro top_level (CombApp (tm1, tm2)) =
816 CombApp (intro top_level tm1, intro false tm2)
817 | intro top_level (CombConst (name as (s, _), T, T_args)) =
818 (case proxify_const s of
820 if top_level orelse is_type_enc_higher_order type_enc then
821 case (top_level, s) of
822 (_, "c_False") => (`I tptp_false, [])
823 | (_, "c_True") => (`I tptp_true, [])
824 | (false, "c_Not") => (`I tptp_not, [])
825 | (false, "c_conj") => (`I tptp_and, [])
826 | (false, "c_disj") => (`I tptp_or, [])
827 | (false, "c_implies") => (`I tptp_implies, [])
828 | (false, "c_All") => (`I tptp_ho_forall, [])
829 | (false, "c_Ex") => (`I tptp_ho_exists, [])
831 if is_tptp_equal s then (`I tptp_equal, [])
832 else (proxy_base |>> prefix const_prefix, T_args)
835 (proxy_base |>> prefix const_prefix, T_args)
836 | NONE => (name, T_args))
837 |> (fn (name, T_args) => CombConst (name, T, T_args))
838 | intro _ (CombAbs (bound, tm)) = CombAbs (bound, intro false tm)
842 fun combformula_from_prop thy type_enc eq_as_iff =
844 fun do_term bs t atomic_types =
845 combterm_from_term thy bs (Envir.eta_contract t)
846 |>> (introduce_proxies type_enc #> AAtom)
847 ||> union (op =) atomic_types
848 fun do_quant bs q s T t' =
849 let val s = singleton (Name.variant_list (map fst bs)) s in
850 do_formula ((s, T) :: bs) t'
851 #>> mk_aquant q [(`make_bound_var s, SOME T)]
853 and do_conn bs c t1 t2 =
854 do_formula bs t1 ##>> do_formula bs t2 #>> uncurry (mk_aconn c)
855 and do_formula bs t =
857 @{const Trueprop} $ t1 => do_formula bs t1
858 | @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
859 | Const (@{const_name All}, _) $ Abs (s, T, t') =>
860 do_quant bs AForall s T t'
861 | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
862 do_quant bs AExists s T t'
863 | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
864 | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
865 | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
866 | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
867 if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
871 fun presimplify_term _ [] t = t
872 | presimplify_term ctxt presimp_consts t =
873 t |> exists_Const (member (op =) presimp_consts o fst) t
874 ? (Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
875 #> Meson.presimplify ctxt
878 fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
879 fun conceal_bounds Ts t =
880 subst_bounds (map (Free o apfst concealed_bound_name)
881 (0 upto length Ts - 1 ~~ Ts), t)
882 fun reveal_bounds Ts =
883 subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
884 (0 upto length Ts - 1 ~~ Ts))
886 fun is_fun_equality (@{const_name HOL.eq},
887 Type (_, [Type (@{type_name fun}, _), _])) = true
888 | is_fun_equality _ = false
890 fun extensionalize_term ctxt t =
891 if exists_Const is_fun_equality t then
892 let val thy = Proof_Context.theory_of ctxt in
893 t |> cterm_of thy |> Meson.extensionalize_conv ctxt
894 |> prop_of |> Logic.dest_equals |> snd
899 fun process_abstractions_in_term ctxt type_enc kind t =
900 let val thy = Proof_Context.theory_of ctxt in
901 if Meson.is_fol_term thy t then
907 @{const Not} $ t1 => @{const Not} $ aux Ts t1
908 | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
909 t0 $ Abs (s, T, aux (T :: Ts) t')
910 | (t0 as Const (@{const_name All}, _)) $ t1 =>
911 aux Ts (t0 $ eta_expand Ts t1 1)
912 | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
913 t0 $ Abs (s, T, aux (T :: Ts) t')
914 | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
915 aux Ts (t0 $ eta_expand Ts t1 1)
916 | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
917 | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
918 | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
919 | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
921 t0 $ aux Ts t1 $ aux Ts t2
922 | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
924 else if is_type_enc_higher_order type_enc then
925 t |> Envir.eta_contract
927 t |> conceal_bounds Ts
928 |> Envir.eta_contract
930 |> Meson_Clausify.introduce_combinators_in_cterm
931 |> prop_of |> Logic.dest_equals |> snd
933 val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
934 in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
936 (* A type variable of sort "{}" will make abstraction fail. *)
937 if kind = Conjecture then HOLogic.false_const
938 else HOLogic.true_const
941 (* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
942 same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
945 fun aux (t $ u) = aux t $ aux u
946 | aux (Abs (s, T, t)) = Abs (s, T, aux t)
947 | aux (Var ((s, i), T)) =
948 Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
950 in t |> exists_subterm is_Var t ? aux end
952 fun preprocess_prop ctxt type_enc presimp_consts kind t =
954 val thy = Proof_Context.theory_of ctxt
955 val t = t |> Envir.beta_eta_contract
956 |> transform_elim_prop
957 |> Object_Logic.atomize_term thy
958 val need_trueprop = (fastype_of t = @{typ bool})
960 t |> need_trueprop ? HOLogic.mk_Trueprop
961 |> Raw_Simplifier.rewrite_term thy (Meson.unfold_set_const_simps ctxt) []
962 |> extensionalize_term ctxt
963 |> presimplify_term ctxt presimp_consts
964 |> perhaps (try (HOLogic.dest_Trueprop))
965 |> process_abstractions_in_term ctxt type_enc kind
968 (* making fact and conjecture formulas *)
969 fun make_formula thy type_enc eq_as_iff name loc kind t =
971 val (combformula, atomic_types) =
972 combformula_from_prop thy type_enc eq_as_iff t []
974 {name = name, locality = loc, kind = kind, combformula = combformula,
975 atomic_types = atomic_types}
978 fun make_fact ctxt format type_enc eq_as_iff preproc presimp_consts
980 let val thy = Proof_Context.theory_of ctxt in
981 case t |> preproc ? preprocess_prop ctxt type_enc presimp_consts Axiom
982 |> make_formula thy type_enc (eq_as_iff andalso format <> CNF) name
984 formula as {combformula = AAtom (CombConst ((s, _), _, _)), ...} =>
985 if s = tptp_true then NONE else SOME formula
986 | formula => SOME formula
989 fun make_conjecture ctxt format prem_kind type_enc preproc presimp_consts ts =
991 val thy = Proof_Context.theory_of ctxt
992 val last = length ts - 1
994 map2 (fn j => fn t =>
996 val (kind, maybe_negate) =
1001 if prem_kind = Conjecture then update_combformula mk_anot
1005 (preprocess_prop ctxt type_enc presimp_consts kind #> freeze_term)
1006 |> make_formula thy type_enc (format <> CNF) (string_of_int j)
1013 (** Finite and infinite type inference **)
1015 fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
1016 | deep_freeze_atyp T = T
1017 val deep_freeze_type = map_atyps deep_freeze_atyp
1019 (* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
1020 dangerous because their "exhaust" properties can easily lead to unsound ATP
1021 proofs. On the other hand, all HOL infinite types can be given the same
1022 models in first-order logic (via Löwenheim-Skolem). *)
1024 fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
1025 exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
1026 | should_encode_type _ _ All_Types _ = true
1027 | should_encode_type ctxt _ Fin_Nonmono_Types T =
1028 is_type_surely_finite ctxt false T
1029 | should_encode_type _ _ _ _ = false
1031 fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
1032 should_predicate_on_var T =
1033 (heaviness = Heavyweight orelse should_predicate_on_var ()) andalso
1034 should_encode_type ctxt nonmono_Ts level T
1035 | should_predicate_on_type _ _ _ _ _ = false
1037 fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
1038 String.isPrefix bound_var_prefix s
1039 | is_var_or_bound_var (CombVar _) = true
1040 | is_var_or_bound_var _ = false
1043 Top_Level of bool option |
1044 Eq_Arg of bool option |
1047 fun should_tag_with_type _ _ _ (Top_Level _) _ _ = false
1048 | should_tag_with_type ctxt nonmono_Ts (Tags (poly, level, heaviness)) site
1051 Heavyweight => should_encode_type ctxt nonmono_Ts level T
1053 case (site, is_var_or_bound_var u) of
1054 (Eq_Arg pos, true) =>
1055 (* The first disjunct prevents a subtle soundness issue explained in
1056 Blanchette's Ph.D. thesis. See also
1057 "formula_lines_for_lightweight_tags_sym_decl". *)
1058 (pos <> SOME false andalso poly = Polymorphic andalso
1059 level <> All_Types andalso heaviness = Lightweight andalso
1060 exists (fn T' => type_instance ctxt (T', T)) nonmono_Ts) orelse
1061 should_encode_type ctxt nonmono_Ts level T
1063 | should_tag_with_type _ _ _ _ _ _ = false
1065 fun homogenized_type ctxt nonmono_Ts level =
1067 val should_encode = should_encode_type ctxt nonmono_Ts level
1068 fun homo 0 T = if should_encode T then T else homo_infinite_type
1069 | homo ary (Type (@{type_name fun}, [T1, T2])) =
1070 homo 0 T1 --> homo (ary - 1) T2
1071 | homo _ _ = raise Fail "expected function type"
1074 (** "hBOOL" and "hAPP" **)
1077 {pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
1079 fun add_combterm_syms_to_table ctxt explicit_apply =
1081 fun consider_var_arity const_T var_T max_ary =
1084 if ary = max_ary orelse type_instance ctxt (var_T, T) orelse
1085 type_instance ctxt (T, var_T) then
1088 iter (ary + 1) (range_type T)
1089 in iter 0 const_T end
1090 fun add_var_or_bound_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1091 if explicit_apply = NONE andalso
1092 (can dest_funT T orelse T = @{typ bool}) then
1094 val bool_vars' = bool_vars orelse body_type T = @{typ bool}
1095 fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
1096 {pred_sym = pred_sym andalso not bool_vars',
1097 min_ary = fold (fn T' => consider_var_arity T' T) types min_ary,
1098 max_ary = max_ary, types = types}
1100 fun_var_Ts |> can dest_funT T ? insert_type ctxt I T
1102 if bool_vars' = bool_vars andalso
1103 pointer_eq (fun_var_Ts', fun_var_Ts) then
1106 ((bool_vars', fun_var_Ts'), Symtab.map (K repair_min_arity) sym_tab)
1110 fun add top_level tm (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1111 let val (head, args) = strip_combterm_comb tm in
1113 CombConst ((s, _), T, _) =>
1114 if String.isPrefix bound_var_prefix s then
1115 add_var_or_bound_var T accum
1117 let val ary = length args in
1118 ((bool_vars, fun_var_Ts),
1119 case Symtab.lookup sym_tab s of
1120 SOME {pred_sym, min_ary, max_ary, types} =>
1123 pred_sym andalso top_level andalso not bool_vars
1124 val types' = types |> insert_type ctxt I T
1126 if is_some explicit_apply orelse
1127 pointer_eq (types', types) then
1130 fold (consider_var_arity T) fun_var_Ts min_ary
1132 Symtab.update (s, {pred_sym = pred_sym,
1133 min_ary = Int.min (ary, min_ary),
1134 max_ary = Int.max (ary, max_ary),
1140 val pred_sym = top_level andalso not bool_vars
1142 case explicit_apply of
1145 | NONE => fold (consider_var_arity T) fun_var_Ts ary
1147 Symtab.update_new (s, {pred_sym = pred_sym,
1148 min_ary = min_ary, max_ary = ary,
1153 | CombVar (_, T) => add_var_or_bound_var T accum
1154 | CombAbs ((_, T), tm) =>
1155 accum |> add_var_or_bound_var T |> add false tm
1157 |> fold (add false) args
1160 fun add_fact_syms_to_table ctxt explicit_apply =
1161 fact_lift (formula_fold NONE
1162 (K (add_combterm_syms_to_table ctxt explicit_apply)))
1164 val default_sym_tab_entries : (string * sym_info) list =
1165 (prefixed_predicator_name,
1166 {pred_sym = true, min_ary = 1, max_ary = 1, types = []}) ::
1167 ([tptp_false, tptp_true]
1168 |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []})) @
1169 ([tptp_equal, tptp_old_equal]
1170 |> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = []}))
1172 fun sym_table_for_facts ctxt explicit_apply facts =
1173 ((false, []), Symtab.empty)
1174 |> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
1175 |> fold Symtab.update default_sym_tab_entries
1177 fun min_arity_of sym_tab s =
1178 case Symtab.lookup sym_tab s of
1179 SOME ({min_ary, ...} : sym_info) => min_ary
1181 case strip_prefix_and_unascii const_prefix s of
1183 let val s = s |> unmangled_const_name |> invert_const in
1184 if s = predicator_name then 1
1185 else if s = app_op_name then 2
1186 else if s = type_pred_name then 1
1191 (* True if the constant ever appears outside of the top-level position in
1192 literals, or if it appears with different arities (e.g., because of different
1193 type instantiations). If false, the constant always receives all of its
1194 arguments and is used as a predicate. *)
1195 fun is_pred_sym sym_tab s =
1196 case Symtab.lookup sym_tab s of
1197 SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
1198 pred_sym andalso min_ary = max_ary
1201 val predicator_combconst =
1202 CombConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
1203 fun predicator tm = CombApp (predicator_combconst, tm)
1205 fun introduce_predicators_in_combterm sym_tab tm =
1206 case strip_combterm_comb tm of
1207 (CombConst ((s, _), _, _), _) =>
1208 if is_pred_sym sym_tab s then tm else predicator tm
1209 | _ => predicator tm
1211 fun list_app head args = fold (curry (CombApp o swap)) args head
1213 val app_op = `make_fixed_const app_op_name
1215 fun explicit_app arg head =
1217 val head_T = combtyp_of head
1218 val (arg_T, res_T) = dest_funT head_T
1220 CombConst (app_op, head_T --> head_T, [arg_T, res_T])
1221 in list_app explicit_app [head, arg] end
1222 fun list_explicit_app head args = fold explicit_app args head
1224 fun introduce_explicit_apps_in_combterm sym_tab =
1227 case strip_combterm_comb tm of
1228 (head as CombConst ((s, _), _, _), args) =>
1230 |> chop (min_arity_of sym_tab s)
1232 |-> list_explicit_app
1233 | (head, args) => list_explicit_app head (map aux args)
1236 fun chop_fun 0 T = ([], T)
1237 | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
1238 chop_fun (n - 1) ran_T |>> cons dom_T
1239 | chop_fun _ _ = raise Fail "unexpected non-function"
1241 fun filter_type_args _ _ _ [] = []
1242 | filter_type_args thy s arity T_args =
1244 (* will throw "TYPE" for pseudo-constants *)
1245 val U = if s = app_op_name then
1246 @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
1248 s |> Sign.the_const_type thy
1250 case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
1253 let val U_args = (s, U) |> Sign.const_typargs thy in
1255 |> map (fn (U, T) =>
1256 if member (op =) res_U_vars (dest_TVar U) then T
1260 handle TYPE _ => T_args
1262 fun enforce_type_arg_policy_in_combterm ctxt format type_enc =
1264 val thy = Proof_Context.theory_of ctxt
1265 fun aux arity (CombApp (tm1, tm2)) =
1266 CombApp (aux (arity + 1) tm1, aux 0 tm2)
1267 | aux arity (CombConst (name as (s, _), T, T_args)) =
1268 (case strip_prefix_and_unascii const_prefix s of
1269 NONE => (name, T_args)
1272 val s'' = invert_const s''
1273 fun filtered_T_args false = T_args
1274 | filtered_T_args true = filter_type_args thy s'' arity T_args
1276 case type_arg_policy type_enc s'' of
1277 Explicit_Type_Args drop_args =>
1278 (name, filtered_T_args drop_args)
1279 | Mangled_Type_Args drop_args =>
1280 (mangled_const_name format type_enc (filtered_T_args drop_args)
1282 | No_Type_Args => (name, [])
1284 |> (fn (name, T_args) => CombConst (name, T, T_args))
1285 | aux _ (CombAbs (bound, tm)) = CombAbs (bound, aux 0 tm)
1289 fun repair_combterm ctxt format type_enc sym_tab =
1290 not (is_type_enc_higher_order type_enc)
1291 ? (introduce_explicit_apps_in_combterm sym_tab
1292 #> introduce_predicators_in_combterm sym_tab)
1293 #> enforce_type_arg_policy_in_combterm ctxt format type_enc
1294 fun repair_fact ctxt format type_enc sym_tab =
1295 update_combformula (formula_map
1296 (repair_combterm ctxt format type_enc sym_tab))
1298 (** Helper facts **)
1300 (* The Boolean indicates that a fairly sound type encoding is needed. *)
1302 [(("COMBI", false), @{thms Meson.COMBI_def}),
1303 (("COMBK", false), @{thms Meson.COMBK_def}),
1304 (("COMBB", false), @{thms Meson.COMBB_def}),
1305 (("COMBC", false), @{thms Meson.COMBC_def}),
1306 (("COMBS", false), @{thms Meson.COMBS_def}),
1307 (("fFalse", false), [@{lemma "~ fFalse" by (unfold fFalse_def) fast}]),
1308 (("fFalse", true), @{thms True_or_False}),
1309 (("fTrue", false), [@{lemma "fTrue" by (unfold fTrue_def) fast}]),
1310 (("fTrue", true), @{thms True_or_False}),
1312 @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1313 fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1315 @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
1316 by (unfold fconj_def) fast+}),
1318 @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
1319 by (unfold fdisj_def) fast+}),
1320 (("fimplies", false),
1321 @{lemma "P | fimplies P Q" "~ Q | fimplies P Q" "~ fimplies P Q | ~ P | Q"
1322 by (unfold fimplies_def) fast+}),
1324 (* This is a lie: Higher-order equality doesn't need a sound type encoding.
1325 However, this is done so for backward compatibility: Including the
1326 equality helpers by default in Metis breaks a few existing proofs. *)
1327 @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1328 fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1329 (("fAll", false), []), (*TODO: add helpers*)
1330 (("fEx", false), []), (*TODO: add helpers*)
1331 (("If", true), @{thms if_True if_False True_or_False})]
1332 |> map (apsnd (map zero_var_indexes))
1334 val type_tag = `make_fixed_const type_tag_name
1336 fun type_tag_idempotence_fact () =
1338 fun var s = ATerm (`I s, [])
1339 fun tag tm = ATerm (type_tag, [var "T", tm])
1340 val tagged_a = tag (var "A")
1342 Formula (type_tag_idempotence_helper_name, Axiom,
1343 AAtom (ATerm (`I tptp_equal, [tag tagged_a, tagged_a]))
1344 |> close_formula_universally, isabelle_info simpN, NONE)
1347 fun should_specialize_helper type_enc t =
1348 polymorphism_of_type_enc type_enc = Mangled_Monomorphic andalso
1349 level_of_type_enc type_enc <> No_Types andalso
1350 not (null (Term.hidden_polymorphism t))
1352 fun helper_facts_for_sym ctxt format type_enc (s, {types, ...} : sym_info) =
1353 case strip_prefix_and_unascii const_prefix s of
1356 val thy = Proof_Context.theory_of ctxt
1357 val unmangled_s = mangled_s |> unmangled_const_name
1358 fun dub needs_fairly_sound j k =
1359 (unmangled_s ^ "_" ^ string_of_int j ^ "_" ^ string_of_int k ^
1360 (if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^
1361 (if needs_fairly_sound then typed_helper_suffix
1362 else untyped_helper_suffix),
1364 fun dub_and_inst needs_fairly_sound (th, j) =
1365 let val t = prop_of th in
1366 if should_specialize_helper type_enc t then
1367 map (fn T => specialize_type thy (invert_const unmangled_s, T) t)
1372 |> map (fn (k, t) => (dub needs_fairly_sound j k, t)) o tag_list 1
1374 map_filter (make_fact ctxt format type_enc false false [])
1375 val fairly_sound = is_type_enc_fairly_sound type_enc
1378 |> maps (fn ((helper_s, needs_fairly_sound), ths) =>
1379 if helper_s <> unmangled_s orelse
1380 (needs_fairly_sound andalso not fairly_sound) then
1383 ths ~~ (1 upto length ths)
1384 |> maps (dub_and_inst needs_fairly_sound)
1388 fun helper_facts_for_sym_table ctxt format type_enc sym_tab =
1389 Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_enc) sym_tab
1392 (***************************************************************)
1393 (* Type Classes Present in the Axiom or Conjecture Clauses *)
1394 (***************************************************************)
1396 fun set_insert (x, s) = Symtab.update (x, ()) s
1398 fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
1400 (* Remove this trivial type class (FIXME: similar code elsewhere) *)
1401 fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
1403 fun classes_of_terms get_Ts =
1404 map (map snd o get_Ts)
1405 #> List.foldl add_classes Symtab.empty
1406 #> delete_type #> Symtab.keys
1408 val tfree_classes_of_terms = classes_of_terms OldTerm.term_tfrees
1409 val tvar_classes_of_terms = classes_of_terms OldTerm.term_tvars
1411 fun fold_type_constrs f (Type (s, Ts)) x =
1412 fold (fold_type_constrs f) Ts (f (s, x))
1413 | fold_type_constrs _ _ x = x
1415 (*Type constructors used to instantiate overloaded constants are the only ones needed.*)
1416 fun add_type_constrs_in_term thy =
1418 fun add (Const (@{const_name Meson.skolem}, _) $ _) = I
1419 | add (t $ u) = add t #> add u
1420 | add (Const (x as (s, _))) =
1421 if String.isPrefix skolem_const_prefix s then I
1422 else x |> Sign.const_typargs thy |> fold (fold_type_constrs set_insert)
1423 | add (Abs (_, _, u)) = add u
1427 fun type_constrs_of_terms thy ts =
1428 Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty)
1430 fun translate_formulas ctxt format prem_kind type_enc preproc hyp_ts concl_t
1433 val thy = Proof_Context.theory_of ctxt
1434 val fact_ts = facts |> map snd
1435 val presimp_consts = Meson.presimplified_consts ctxt
1436 val make_fact = make_fact ctxt format type_enc true preproc presimp_consts
1437 val (facts, fact_names) =
1438 facts |> map (fn (name, t) => (name, t) |> make_fact |> rpair name)
1439 |> map_filter (try (apfst the))
1441 (* Remove existing facts from the conjecture, as this can dramatically
1442 boost an ATP's performance (for some reason). *)
1445 |> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t)
1446 val goal_t = Logic.list_implies (hyp_ts, concl_t)
1447 val all_ts = goal_t :: fact_ts
1448 val subs = tfree_classes_of_terms all_ts
1449 val supers = tvar_classes_of_terms all_ts
1450 val tycons = type_constrs_of_terms thy all_ts
1453 |> make_conjecture ctxt format prem_kind type_enc preproc presimp_consts
1454 val (supers', arity_clauses) =
1455 if level_of_type_enc type_enc = No_Types then ([], [])
1456 else make_arity_clauses thy tycons supers
1457 val class_rel_clauses = make_class_rel_clauses thy subs supers'
1459 (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
1462 fun fo_literal_from_type_literal (TyLitVar (class, name)) =
1463 (true, ATerm (class, [ATerm (name, [])]))
1464 | fo_literal_from_type_literal (TyLitFree (class, name)) =
1465 (true, ATerm (class, [ATerm (name, [])]))
1467 fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
1469 val type_pred = `make_fixed_const type_pred_name
1471 fun type_pred_combterm ctxt format type_enc T tm =
1472 CombApp (CombConst (type_pred, T --> @{typ bool}, [T])
1473 |> enforce_type_arg_policy_in_combterm ctxt format type_enc, tm)
1475 fun is_var_positively_naked_in_term _ (SOME false) _ accum = accum
1476 | is_var_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
1477 accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
1478 | is_var_positively_naked_in_term _ _ _ _ = true
1479 fun should_predicate_on_var_in_formula pos phi (SOME true) name =
1480 formula_fold pos (is_var_positively_naked_in_term name) phi false
1481 | should_predicate_on_var_in_formula _ _ _ _ = true
1483 fun mk_aterm format type_enc name T_args args =
1484 ATerm (name, map_filter (ho_term_for_type_arg format type_enc) T_args @ args)
1486 fun tag_with_type ctxt format nonmono_Ts type_enc pos T tm =
1487 CombConst (type_tag, T --> T, [T])
1488 |> enforce_type_arg_policy_in_combterm ctxt format type_enc
1489 |> ho_term_from_combterm ctxt format nonmono_Ts type_enc (Top_Level pos)
1490 |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm])
1491 | _ => raise Fail "unexpected lambda-abstraction")
1492 and ho_term_from_combterm ctxt format nonmono_Ts type_enc =
1496 val (head, args) = strip_combterm_comb u
1499 Top_Level pos => pos
1504 CombConst (name as (s, _), _, T_args) =>
1506 val arg_site = if is_tptp_equal s then Eq_Arg pos else Elsewhere
1508 mk_aterm format type_enc name T_args (map (aux arg_site) args)
1510 | CombVar (name, _) => mk_aterm format type_enc name [] (map (aux Elsewhere) args)
1511 | CombAbs ((name, T), tm) =>
1512 AAbs ((name, ho_type_from_typ format type_enc true 0 T), aux Elsewhere tm)
1513 | CombApp _ => raise Fail "impossible \"CombApp\""
1514 val T = combtyp_of u
1516 t |> (if should_tag_with_type ctxt nonmono_Ts type_enc site u T then
1517 tag_with_type ctxt format nonmono_Ts type_enc pos T
1522 and formula_from_combformula ctxt format nonmono_Ts type_enc
1523 should_predicate_on_var =
1526 ho_term_from_combterm ctxt format nonmono_Ts type_enc (Top_Level pos)
1529 Simple_Types (_, level) =>
1530 homogenized_type ctxt nonmono_Ts level 0
1531 #> ho_type_from_typ format type_enc false 0 #> SOME
1533 fun do_out_of_bound_type pos phi universal (name, T) =
1534 if should_predicate_on_type ctxt nonmono_Ts type_enc
1535 (fn () => should_predicate_on_var pos phi universal name) T then
1537 |> type_pred_combterm ctxt format type_enc T
1538 |> do_term pos |> AAtom |> SOME
1541 fun do_formula pos (AQuant (q, xs, phi)) =
1543 val phi = phi |> do_formula pos
1544 val universal = Option.map (q = AExists ? not) pos
1546 AQuant (q, xs |> map (apsnd (fn NONE => NONE
1547 | SOME T => do_bound_type T)),
1548 (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
1550 (fn (_, NONE) => NONE
1552 do_out_of_bound_type pos phi universal (s, T))
1556 | do_formula pos (AConn conn) = aconn_map pos do_formula conn
1557 | do_formula pos (AAtom tm) = AAtom (do_term pos tm)
1560 fun bound_tvars type_enc Ts =
1561 mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
1562 (type_literals_for_types type_enc add_sorts_on_tvar Ts))
1564 (* Each fact is given a unique fact number to avoid name clashes (e.g., because
1565 of monomorphization). The TPTP explicitly forbids name clashes, and some of
1566 the remote provers might care. *)
1567 fun formula_line_for_fact ctxt format prefix encode freshen pos nonmono_Ts
1568 type_enc (j, {name, locality, kind, combformula, atomic_types}) =
1569 (prefix ^ (if freshen then string_of_int j ^ "_" else "") ^ encode name,
1572 |> close_combformula_universally
1573 |> formula_from_combformula ctxt format nonmono_Ts type_enc
1574 should_predicate_on_var_in_formula
1575 (if pos then SOME true else NONE)
1576 |> bound_tvars type_enc atomic_types
1577 |> close_formula_universally,
1580 Intro => isabelle_info introN
1581 | Elim => isabelle_info elimN
1582 | Simp => isabelle_info simpN
1586 fun formula_line_for_class_rel_clause ({name, subclass, superclass, ...}
1587 : class_rel_clause) =
1588 let val ty_arg = ATerm (`I "T", []) in
1589 Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
1590 AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
1591 AAtom (ATerm (superclass, [ty_arg]))])
1592 |> close_formula_universally, isabelle_info introN, NONE)
1595 fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
1596 (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
1597 | fo_literal_from_arity_literal (TVarLit (c, sort)) =
1598 (false, ATerm (c, [ATerm (sort, [])]))
1600 fun formula_line_for_arity_clause ({name, prem_lits, concl_lits, ...}
1602 Formula (arity_clause_prefix ^ name, Axiom,
1603 mk_ahorn (map (formula_from_fo_literal o apfst not
1604 o fo_literal_from_arity_literal) prem_lits)
1605 (formula_from_fo_literal
1606 (fo_literal_from_arity_literal concl_lits))
1607 |> close_formula_universally, isabelle_info introN, NONE)
1609 fun formula_line_for_conjecture ctxt format nonmono_Ts type_enc
1610 ({name, kind, combformula, atomic_types, ...} : translated_formula) =
1611 Formula (conjecture_prefix ^ name, kind,
1612 formula_from_combformula ctxt format nonmono_Ts type_enc
1613 should_predicate_on_var_in_formula (SOME false)
1614 (close_combformula_universally combformula)
1615 |> bound_tvars type_enc atomic_types
1616 |> close_formula_universally, NONE, NONE)
1618 fun free_type_literals type_enc ({atomic_types, ...} : translated_formula) =
1619 atomic_types |> type_literals_for_types type_enc add_sorts_on_tfree
1620 |> map fo_literal_from_type_literal
1622 fun formula_line_for_free_type j lit =
1623 Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis,
1624 formula_from_fo_literal lit, NONE, NONE)
1625 fun formula_lines_for_free_types type_enc facts =
1627 val litss = map (free_type_literals type_enc) facts
1628 val lits = fold (union (op =)) litss []
1629 in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
1631 (** Symbol declarations **)
1633 fun should_declare_sym type_enc pred_sym s =
1634 is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
1636 Simple_Types _ => true
1637 | Tags (_, _, Lightweight) => true
1638 | _ => not pred_sym)
1640 fun sym_decl_table_for_facts ctxt type_enc repaired_sym_tab (conjs, facts) =
1642 fun add_combterm in_conj tm =
1643 let val (head, args) = strip_combterm_comb tm in
1645 CombConst ((s, s'), T, T_args) =>
1646 let val pred_sym = is_pred_sym repaired_sym_tab s in
1647 if should_declare_sym type_enc pred_sym s then
1648 Symtab.map_default (s, [])
1649 (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
1654 | CombAbs (_, tm) => add_combterm in_conj tm
1656 #> fold (add_combterm in_conj) args
1658 fun add_fact in_conj =
1659 fact_lift (formula_fold NONE (K (add_combterm in_conj)))
1662 |> is_type_enc_fairly_sound type_enc
1663 ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
1666 (* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
1667 out with monotonicity" paper presented at CADE 2011. *)
1668 fun add_combterm_nonmonotonic_types _ _ _ _ (SOME false) _ = I
1669 | add_combterm_nonmonotonic_types ctxt level sound locality _
1670 (CombApp (CombApp (CombConst ((s, _), Type (_, [T, _]), _), tm1),
1672 (is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
1674 Noninf_Nonmono_Types =>
1675 not (is_locality_global locality) orelse
1676 not (is_type_surely_infinite ctxt sound T)
1677 | Fin_Nonmono_Types => is_type_surely_finite ctxt false T
1678 | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
1679 | add_combterm_nonmonotonic_types _ _ _ _ _ _ = I
1680 fun add_fact_nonmonotonic_types ctxt level sound
1681 ({kind, locality, combformula, ...} : translated_formula) =
1682 formula_fold (SOME (kind <> Conjecture))
1683 (add_combterm_nonmonotonic_types ctxt level sound locality)
1685 fun nonmonotonic_types_for_facts ctxt type_enc sound facts =
1686 let val level = level_of_type_enc type_enc in
1687 if level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types then
1688 [] |> fold (add_fact_nonmonotonic_types ctxt level sound) facts
1689 (* We must add "bool" in case the helper "True_or_False" is added
1690 later. In addition, several places in the code rely on the list of
1691 nonmonotonic types not being empty. *)
1692 |> insert_type ctxt I @{typ bool}
1697 fun decl_line_for_sym ctxt format nonmono_Ts type_enc s
1698 (s', T_args, T, pred_sym, ary, _) =
1700 val (T_arg_Ts, level) =
1702 Simple_Types (_, level) => ([], level)
1703 | _ => (replicate (length T_args) homo_infinite_type, No_Types)
1705 Decl (sym_decl_prefix ^ s, (s, s'),
1706 (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
1707 |> ho_type_from_typ format type_enc pred_sym (length T_arg_Ts + ary))
1710 fun formula_line_for_preds_sym_decl ctxt format conj_sym_kind nonmono_Ts
1711 poly_nonmono_Ts type_enc n s j (s', T_args, T, _, ary, in_conj) =
1713 val (kind, maybe_negate) =
1714 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1716 val (arg_Ts, res_T) = chop_fun ary T
1717 val num_args = length arg_Ts
1719 1 upto num_args |> map (`I o make_bound_var o string_of_int)
1721 bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
1722 val sym_needs_arg_types = n > 1 orelse exists (curry (op =) dummyT) T_args
1723 fun should_keep_arg_type T =
1724 sym_needs_arg_types orelse
1725 not (should_predicate_on_type ctxt nonmono_Ts type_enc (K false) T)
1727 arg_Ts |> map (fn T => if should_keep_arg_type T then SOME T else NONE)
1729 Formula (preds_sym_formula_prefix ^ s ^
1730 (if n > 1 then "_" ^ string_of_int j else ""), kind,
1731 CombConst ((s, s'), T, T_args)
1732 |> fold (curry (CombApp o swap)) bounds
1733 |> type_pred_combterm ctxt format type_enc res_T
1734 |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
1735 |> formula_from_combformula ctxt format poly_nonmono_Ts type_enc
1736 (K (K (K (K true)))) (SOME true)
1737 |> n > 1 ? bound_tvars type_enc (atyps_of T)
1738 |> close_formula_universally
1740 isabelle_info introN, NONE)
1743 fun formula_lines_for_lightweight_tags_sym_decl ctxt format conj_sym_kind
1744 poly_nonmono_Ts type_enc n s
1745 (j, (s', T_args, T, pred_sym, ary, in_conj)) =
1748 lightweight_tags_sym_formula_prefix ^ s ^
1749 (if n > 1 then "_" ^ string_of_int j else "")
1750 val (kind, maybe_negate) =
1751 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1753 val (arg_Ts, res_T) = chop_fun ary T
1755 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
1756 val bounds = bound_names |> map (fn name => ATerm (name, []))
1757 val cst = mk_aterm format type_enc (s, s') T_args
1758 val atomic_Ts = atyps_of T
1760 (if pred_sym then AConn (AIff, map AAtom tms)
1761 else AAtom (ATerm (`I tptp_equal, tms)))
1762 |> bound_tvars type_enc atomic_Ts
1763 |> close_formula_universally
1765 (* See also "should_tag_with_type". *)
1766 fun should_encode T =
1767 should_encode_type ctxt poly_nonmono_Ts All_Types T orelse
1769 Tags (Polymorphic, level, Lightweight) =>
1770 level <> All_Types andalso Monomorph.typ_has_tvars T
1772 val tag_with = tag_with_type ctxt format poly_nonmono_Ts type_enc NONE
1773 val add_formula_for_res =
1774 if should_encode res_T then
1775 cons (Formula (ident_base ^ "_res", kind,
1776 eq [tag_with res_T (cst bounds), cst bounds],
1777 isabelle_info simpN, NONE))
1780 fun add_formula_for_arg k =
1781 let val arg_T = nth arg_Ts k in
1782 if should_encode arg_T then
1783 case chop k bounds of
1784 (bounds1, bound :: bounds2) =>
1785 cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
1786 eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
1788 isabelle_info simpN, NONE))
1789 | _ => raise Fail "expected nonempty tail"
1794 [] |> not pred_sym ? add_formula_for_res
1795 |> fold add_formula_for_arg (ary - 1 downto 0)
1798 fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
1800 fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts
1801 poly_nonmono_Ts type_enc (s, decls) =
1804 decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_enc s)
1809 decl :: (decls' as _ :: _) =>
1810 let val T = result_type_of_decl decl in
1811 if forall (curry (type_instance ctxt o swap) T
1812 o result_type_of_decl) decls' then
1818 val n = length decls
1820 decls |> filter (should_predicate_on_type ctxt poly_nonmono_Ts type_enc
1822 o result_type_of_decl)
1824 (0 upto length decls - 1, decls)
1825 |-> map2 (formula_line_for_preds_sym_decl ctxt format conj_sym_kind
1826 nonmono_Ts poly_nonmono_Ts type_enc n s)
1828 | Tags (_, _, heaviness) =>
1832 let val n = length decls in
1833 (0 upto n - 1 ~~ decls)
1834 |> maps (formula_lines_for_lightweight_tags_sym_decl ctxt format
1835 conj_sym_kind poly_nonmono_Ts type_enc n s)
1838 fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1839 poly_nonmono_Ts type_enc sym_decl_tab =
1844 |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
1845 nonmono_Ts poly_nonmono_Ts type_enc)
1847 fun needs_type_tag_idempotence (Tags (poly, level, heaviness)) =
1848 poly <> Mangled_Monomorphic andalso
1849 ((level = All_Types andalso heaviness = Lightweight) orelse
1850 level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types)
1851 | needs_type_tag_idempotence _ = false
1853 fun offset_of_heading_in_problem _ [] j = j
1854 | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
1855 if heading = needle then j
1856 else offset_of_heading_in_problem needle problem (j + length lines)
1858 val implicit_declsN = "Should-be-implicit typings"
1859 val explicit_declsN = "Explicit typings"
1860 val factsN = "Relevant facts"
1861 val class_relsN = "Class relationships"
1862 val aritiesN = "Arities"
1863 val helpersN = "Helper facts"
1864 val conjsN = "Conjectures"
1865 val free_typesN = "Type variables"
1867 val explicit_apply = NONE (* for experimental purposes *)
1869 fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_enc sound
1870 exporter readable_names preproc hyp_ts concl_t facts =
1872 val (format, type_enc) = choose_format [format] type_enc
1873 val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
1874 translate_formulas ctxt format prem_kind type_enc preproc hyp_ts concl_t
1876 val sym_tab = conjs @ facts |> sym_table_for_facts ctxt explicit_apply
1878 conjs @ facts |> nonmonotonic_types_for_facts ctxt type_enc sound
1879 val repair = repair_fact ctxt format type_enc sym_tab
1880 val (conjs, facts) = (conjs, facts) |> pairself (map repair)
1881 val repaired_sym_tab =
1882 conjs @ facts |> sym_table_for_facts ctxt (SOME false)
1884 repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_enc
1886 val poly_nonmono_Ts =
1887 if null nonmono_Ts orelse nonmono_Ts = [@{typ bool}] orelse
1888 polymorphism_of_type_enc type_enc <> Polymorphic then
1891 [TVar (("'a", 0), HOLogic.typeS)]
1892 val sym_decl_lines =
1893 (conjs, helpers @ facts)
1894 |> sym_decl_table_for_facts ctxt type_enc repaired_sym_tab
1895 |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1896 poly_nonmono_Ts type_enc
1898 0 upto length helpers - 1 ~~ helpers
1899 |> map (formula_line_for_fact ctxt format helper_prefix I false true
1900 poly_nonmono_Ts type_enc)
1901 |> (if needs_type_tag_idempotence type_enc then
1902 cons (type_tag_idempotence_fact ())
1905 (* Reordering these might confuse the proof reconstruction code or the SPASS
1908 [(explicit_declsN, sym_decl_lines),
1910 map (formula_line_for_fact ctxt format fact_prefix ascii_of
1911 (not exporter) (not exporter) nonmono_Ts
1913 (0 upto length facts - 1 ~~ facts)),
1914 (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
1915 (aritiesN, map formula_line_for_arity_clause arity_clauses),
1916 (helpersN, helper_lines),
1918 map (formula_line_for_conjecture ctxt format nonmono_Ts type_enc)
1920 (free_typesN, formula_lines_for_free_types type_enc (facts @ conjs))]
1924 CNF => ensure_cnf_problem
1925 | CNF_UEQ => filter_cnf_ueq_problem
1927 |> (if is_format_typed format then
1928 declare_undeclared_syms_in_atp_problem type_decl_prefix
1932 val (problem, pool) = problem |> nice_atp_problem readable_names
1933 val helpers_offset = offset_of_heading_in_problem helpersN problem 0
1935 map_filter (fn (j, {name, ...}) =>
1936 if String.isSuffix typed_helper_suffix name then SOME j
1938 ((helpers_offset + 1 upto helpers_offset + length helpers)
1940 fun add_sym_arity (s, {min_ary, ...} : sym_info) =
1942 case strip_prefix_and_unascii const_prefix s of
1943 SOME s => Symtab.insert (op =) (s, min_ary)
1949 case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
1950 offset_of_heading_in_problem conjsN problem 0,
1951 offset_of_heading_in_problem factsN problem 0,
1952 fact_names |> Vector.fromList,
1954 Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
1958 val conj_weight = 0.0
1959 val hyp_weight = 0.1
1960 val fact_min_weight = 0.2
1961 val fact_max_weight = 1.0
1962 val type_info_default_weight = 0.8
1964 fun add_term_weights weight (ATerm (s, tms)) =
1965 is_tptp_user_symbol s ? Symtab.default (s, weight)
1966 #> fold (add_term_weights weight) tms
1967 | add_term_weights weight (AAbs (_, tm)) = add_term_weights weight tm
1968 fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
1969 formula_fold NONE (K (add_term_weights weight)) phi
1970 | add_problem_line_weights _ _ = I
1972 fun add_conjectures_weights [] = I
1973 | add_conjectures_weights conjs =
1974 let val (hyps, conj) = split_last conjs in
1975 add_problem_line_weights conj_weight conj
1976 #> fold (add_problem_line_weights hyp_weight) hyps
1979 fun add_facts_weights facts =
1981 val num_facts = length facts
1983 fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
1984 / Real.fromInt num_facts
1986 map weight_of (0 upto num_facts - 1) ~~ facts
1987 |> fold (uncurry add_problem_line_weights)
1990 (* Weights are from 0.0 (most important) to 1.0 (least important). *)
1991 fun atp_problem_weights problem =
1992 let val get = these o AList.lookup (op =) problem in
1994 |> add_conjectures_weights (get free_typesN @ get conjsN)
1995 |> add_facts_weights (get factsN)
1996 |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
1997 [explicit_declsN, class_relsN, aritiesN]
1999 |> sort (prod_ord Real.compare string_ord o pairself swap)