1 (* Title: HOL/Tools/ATP/atp_translate.ML
2 Author: Fabian Immler, TU Muenchen
4 Author: Jasmin Blanchette, TU Muenchen
6 Translation of HOL to FOL for Sledgehammer.
9 signature ATP_TRANSLATE =
11 type ('a, 'b) ho_term = ('a, 'b) ATP_Problem.ho_term
12 type connective = ATP_Problem.connective
13 type ('a, 'b, 'c) formula = ('a, 'b, 'c) ATP_Problem.formula
14 type format = ATP_Problem.format
15 type formula_kind = ATP_Problem.formula_kind
16 type 'a problem = 'a ATP_Problem.problem
19 General | Helper | Extensionality | Intro | Elim | Simp | Local | Assum |
22 datatype order = First_Order | Higher_Order
23 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
25 All_Types | Noninf_Nonmono_Types | Fin_Nonmono_Types | Const_Arg_Types |
27 datatype type_heaviness = Heavyweight | Lightweight
30 Simple_Types of order * type_level |
31 Preds of polymorphism * type_level * type_heaviness |
32 Tags of polymorphism * type_level * type_heaviness
34 val bound_var_prefix : string
35 val schematic_var_prefix : string
36 val fixed_var_prefix : string
37 val tvar_prefix : string
38 val tfree_prefix : string
39 val const_prefix : string
40 val type_const_prefix : string
41 val class_prefix : string
42 val skolem_const_prefix : string
43 val old_skolem_const_prefix : string
44 val new_skolem_const_prefix : string
45 val type_decl_prefix : string
46 val sym_decl_prefix : string
47 val preds_sym_formula_prefix : string
48 val lightweight_tags_sym_formula_prefix : string
49 val fact_prefix : string
50 val conjecture_prefix : string
51 val helper_prefix : string
52 val class_rel_clause_prefix : string
53 val arity_clause_prefix : string
54 val tfree_clause_prefix : string
55 val typed_helper_suffix : string
56 val untyped_helper_suffix : string
57 val type_tag_idempotence_helper_name : string
58 val predicator_name : string
59 val app_op_name : string
60 val type_tag_name : string
61 val type_pred_name : string
62 val simple_type_prefix : string
63 val prefixed_predicator_name : string
64 val prefixed_app_op_name : string
65 val prefixed_type_tag_name : string
66 val ascii_of : string -> string
67 val unascii_of : string -> string
68 val strip_prefix_and_unascii : string -> string -> string option
69 val proxy_table : (string * (string * (thm * (string * string)))) list
70 val proxify_const : string -> (string * string) option
71 val invert_const : string -> string
72 val unproxify_const : string -> string
73 val new_skolem_var_name_from_const : string -> string
74 val num_type_args : theory -> string -> int
75 val atp_irrelevant_consts : string list
76 val atp_schematic_consts_of : term -> typ list Symtab.table
77 val is_locality_global : locality -> bool
78 val type_enc_from_string : string -> type_enc
79 val polymorphism_of_type_enc : type_enc -> polymorphism
80 val level_of_type_enc : type_enc -> type_level
81 val is_type_enc_virtually_sound : type_enc -> bool
82 val is_type_enc_fairly_sound : type_enc -> bool
83 val choose_format : format list -> type_enc -> format * type_enc
85 connective -> ('a, 'b, 'c) formula list -> ('a, 'b, 'c) formula
86 val unmangled_const : string -> string * (string, 'b) ho_term list
87 val unmangled_const_name : string -> string
88 val helper_table : ((string * bool) * thm list) list
90 val prepare_atp_problem :
91 Proof.context -> format -> formula_kind -> formula_kind -> type_enc -> bool
92 -> bool -> bool -> bool -> term list -> term
93 -> ((string * locality) * term) list
94 -> string problem * string Symtab.table * int * int
95 * (string * locality) list vector * int list * int Symtab.table
96 val atp_problem_weights : string problem -> (string * real) list
99 structure ATP_Translate : ATP_TRANSLATE =
105 type name = string * string
108 val generate_useful_info = false
110 fun useful_isabelle_info s =
111 if generate_useful_info then
112 SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
116 val intro_info = useful_isabelle_info "intro"
117 val elim_info = useful_isabelle_info "elim"
118 val simp_info = useful_isabelle_info "simp"
120 val bound_var_prefix = "B_"
121 val schematic_var_prefix = "V_"
122 val fixed_var_prefix = "v_"
124 val tvar_prefix = "T_"
125 val tfree_prefix = "t_"
127 val const_prefix = "c_"
128 val type_const_prefix = "tc_"
129 val class_prefix = "cl_"
131 val skolem_const_prefix = "Sledgehammer" ^ Long_Name.separator ^ "Sko"
132 val old_skolem_const_prefix = skolem_const_prefix ^ "o"
133 val new_skolem_const_prefix = skolem_const_prefix ^ "n"
135 val type_decl_prefix = "ty_"
136 val sym_decl_prefix = "sy_"
137 val preds_sym_formula_prefix = "psy_"
138 val lightweight_tags_sym_formula_prefix = "tsy_"
139 val fact_prefix = "fact_"
140 val conjecture_prefix = "conj_"
141 val helper_prefix = "help_"
142 val class_rel_clause_prefix = "clar_"
143 val arity_clause_prefix = "arity_"
144 val tfree_clause_prefix = "tfree_"
146 val typed_helper_suffix = "_T"
147 val untyped_helper_suffix = "_U"
148 val type_tag_idempotence_helper_name = helper_prefix ^ "ti_idem"
150 val predicator_name = "hBOOL"
151 val app_op_name = "hAPP"
152 val type_tag_name = "ti"
153 val type_pred_name = "is"
154 val simple_type_prefix = "ty_"
156 val prefixed_predicator_name = const_prefix ^ predicator_name
157 val prefixed_app_op_name = const_prefix ^ app_op_name
158 val prefixed_type_tag_name = const_prefix ^ type_tag_name
160 (* Freshness almost guaranteed! *)
161 val sledgehammer_weak_prefix = "Sledgehammer:"
163 (*Escaping of special characters.
164 Alphanumeric characters are left unchanged.
165 The character _ goes to __
166 Characters in the range ASCII space to / go to _A to _P, respectively.
167 Other characters go to _nnn where nnn is the decimal ASCII code.*)
168 val upper_a_minus_space = Char.ord #"A" - Char.ord #" "
170 fun stringN_of_int 0 _ = ""
171 | stringN_of_int k n =
172 stringN_of_int (k - 1) (n div 10) ^ string_of_int (n mod 10)
174 fun ascii_of_char c =
175 if Char.isAlphaNum c then
177 else if c = #"_" then
179 else if #" " <= c andalso c <= #"/" then
180 "_" ^ String.str (Char.chr (Char.ord c + upper_a_minus_space))
182 (* fixed width, in case more digits follow *)
183 "_" ^ stringN_of_int 3 (Char.ord c)
185 val ascii_of = String.translate ascii_of_char
187 (** Remove ASCII armoring from names in proof files **)
189 (* We don't raise error exceptions because this code can run inside a worker
190 thread. Also, the errors are impossible. *)
193 fun un rcs [] = String.implode(rev rcs)
194 | un rcs [#"_"] = un (#"_" :: rcs) [] (* ERROR *)
195 (* Three types of _ escapes: __, _A to _P, _nnn *)
196 | un rcs (#"_" :: #"_" :: cs) = un (#"_" :: rcs) cs
197 | un rcs (#"_" :: c :: cs) =
198 if #"A" <= c andalso c<= #"P" then
199 (* translation of #" " to #"/" *)
200 un (Char.chr (Char.ord c - upper_a_minus_space) :: rcs) cs
202 let val digits = List.take (c :: cs, 3) handle General.Subscript => [] in
203 case Int.fromString (String.implode digits) of
204 SOME n => un (Char.chr n :: rcs) (List.drop (cs, 2))
205 | NONE => un (c :: #"_" :: rcs) cs (* ERROR *)
207 | un rcs (c :: cs) = un (c :: rcs) cs
208 in un [] o String.explode end
210 (* If string s has the prefix s1, return the result of deleting it,
212 fun strip_prefix_and_unascii s1 s =
213 if String.isPrefix s1 s then
214 SOME (unascii_of (String.extract (s, size s1, NONE)))
219 [("c_False", (@{const_name False}, (@{thm fFalse_def},
220 ("fFalse", @{const_name ATP.fFalse})))),
221 ("c_True", (@{const_name True}, (@{thm fTrue_def},
222 ("fTrue", @{const_name ATP.fTrue})))),
223 ("c_Not", (@{const_name Not}, (@{thm fNot_def},
224 ("fNot", @{const_name ATP.fNot})))),
225 ("c_conj", (@{const_name conj}, (@{thm fconj_def},
226 ("fconj", @{const_name ATP.fconj})))),
227 ("c_disj", (@{const_name disj}, (@{thm fdisj_def},
228 ("fdisj", @{const_name ATP.fdisj})))),
229 ("c_implies", (@{const_name implies}, (@{thm fimplies_def},
230 ("fimplies", @{const_name ATP.fimplies})))),
231 ("equal", (@{const_name HOL.eq}, (@{thm fequal_def},
232 ("fequal", @{const_name ATP.fequal})))),
233 ("c_All", (@{const_name All}, (@{thm fAll_def},
234 ("fAll", @{const_name ATP.fAll})))),
235 ("c_Ex", (@{const_name Ex}, (@{thm fEx_def},
236 ("fEx", @{const_name ATP.fEx}))))]
238 val proxify_const = AList.lookup (op =) proxy_table #> Option.map (snd o snd)
240 (* Readable names for the more common symbolic functions. Do not mess with the
241 table unless you know what you are doing. *)
242 val const_trans_table =
243 [(@{type_name Product_Type.prod}, "prod"),
244 (@{type_name Sum_Type.sum}, "sum"),
245 (@{const_name False}, "False"),
246 (@{const_name True}, "True"),
247 (@{const_name Not}, "Not"),
248 (@{const_name conj}, "conj"),
249 (@{const_name disj}, "disj"),
250 (@{const_name implies}, "implies"),
251 (@{const_name HOL.eq}, "equal"),
252 (@{const_name All}, "All"),
253 (@{const_name Ex}, "Ex"),
254 (@{const_name If}, "If"),
255 (@{const_name Set.member}, "member"),
256 (@{const_name Meson.COMBI}, "COMBI"),
257 (@{const_name Meson.COMBK}, "COMBK"),
258 (@{const_name Meson.COMBB}, "COMBB"),
259 (@{const_name Meson.COMBC}, "COMBC"),
260 (@{const_name Meson.COMBS}, "COMBS")]
262 |> fold (Symtab.update o swap o snd o snd o snd) proxy_table
264 (* Invert the table of translations between Isabelle and ATPs. *)
265 val const_trans_table_inv =
266 const_trans_table |> Symtab.dest |> map swap |> Symtab.make
267 val const_trans_table_unprox =
269 |> fold (fn (_, (isa, (_, (_, atp)))) => Symtab.update (atp, isa)) proxy_table
271 val invert_const = perhaps (Symtab.lookup const_trans_table_inv)
272 val unproxify_const = perhaps (Symtab.lookup const_trans_table_unprox)
275 case Symtab.lookup const_trans_table c of
279 fun ascii_of_indexname (v, 0) = ascii_of v
280 | ascii_of_indexname (v, i) = ascii_of v ^ "_" ^ string_of_int i
282 fun make_bound_var x = bound_var_prefix ^ ascii_of x
283 fun make_schematic_var v = schematic_var_prefix ^ ascii_of_indexname v
284 fun make_fixed_var x = fixed_var_prefix ^ ascii_of x
286 fun make_schematic_type_var (x, i) =
287 tvar_prefix ^ (ascii_of_indexname (unprefix "'" x, i))
288 fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (unprefix "'" x))
290 (* "HOL.eq" is mapped to the ATP's equality. *)
291 fun make_fixed_const @{const_name HOL.eq} = tptp_old_equal
292 | make_fixed_const c = const_prefix ^ lookup_const c
294 fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
296 fun make_type_class clas = class_prefix ^ ascii_of clas
298 fun new_skolem_var_name_from_const s =
299 let val ss = s |> space_explode Long_Name.separator in
300 nth ss (length ss - 2)
303 (* The number of type arguments of a constant, zero if it's monomorphic. For
304 (instances of) Skolem pseudoconstants, this information is encoded in the
306 fun num_type_args thy s =
307 if String.isPrefix skolem_const_prefix s then
308 s |> space_explode Long_Name.separator |> List.last |> Int.fromString |> the
310 (s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
312 (* These are either simplified away by "Meson.presimplify" (most of the time) or
313 handled specially via "fFalse", "fTrue", ..., "fequal". *)
314 val atp_irrelevant_consts =
315 [@{const_name False}, @{const_name True}, @{const_name Not},
316 @{const_name conj}, @{const_name disj}, @{const_name implies},
317 @{const_name HOL.eq}, @{const_name If}, @{const_name Let}]
319 val atp_monomorph_bad_consts =
320 atp_irrelevant_consts @
321 (* These are ignored anyway by the relevance filter (unless they appear in
322 higher-order places) but not by the monomorphizer. *)
323 [@{const_name all}, @{const_name "==>"}, @{const_name "=="},
324 @{const_name Trueprop}, @{const_name All}, @{const_name Ex},
325 @{const_name Ex1}, @{const_name Ball}, @{const_name Bex}]
327 fun add_schematic_const (x as (_, T)) =
328 Monomorph.typ_has_tvars T ? Symtab.insert_list (op =) x
329 val add_schematic_consts_of =
330 Term.fold_aterms (fn Const (x as (s, _)) =>
331 not (member (op =) atp_monomorph_bad_consts s)
332 ? add_schematic_const x
334 fun atp_schematic_consts_of t = add_schematic_consts_of t Symtab.empty
336 (** Definitions and functions for FOL clauses and formulas for TPTP **)
338 (* The first component is the type class; the second is a "TVar" or "TFree". *)
339 datatype type_literal =
340 TyLitVar of name * name |
341 TyLitFree of name * name
344 (** Isabelle arities **)
346 datatype arity_literal =
347 TConsLit of name * name * name list |
348 TVarLit of name * name
351 | gen_TVars n = ("T_" ^ string_of_int n) :: gen_TVars (n-1)
353 val type_class = the_single @{sort type}
355 fun add_packed_sort tvar =
356 fold (fn s => s <> type_class ? cons (`make_type_class s, `I tvar))
360 prem_lits : arity_literal list,
361 concl_lits : arity_literal}
363 (* Arity of type constructor "tcon :: (arg1, ..., argN) res" *)
364 fun make_axiom_arity_clause (tcons, name, (cls, args)) =
366 val tvars = gen_TVars (length args)
367 val tvars_srts = ListPair.zip (tvars, args)
370 prem_lits = [] |> fold (uncurry add_packed_sort) tvars_srts |> map TVarLit,
371 concl_lits = TConsLit (`make_type_class cls,
372 `make_fixed_type_const tcons,
376 fun arity_clause _ _ (_, []) = []
377 | arity_clause seen n (tcons, ("HOL.type", _) :: ars) = (* ignore *)
378 arity_clause seen n (tcons, ars)
379 | arity_clause seen n (tcons, (ar as (class, _)) :: ars) =
380 if member (op =) seen class then
381 (* multiple arities for the same (tycon, class) pair *)
382 make_axiom_arity_clause (tcons,
383 lookup_const tcons ^ "___" ^ ascii_of class ^ "_" ^ string_of_int n,
385 arity_clause seen (n + 1) (tcons, ars)
387 make_axiom_arity_clause (tcons, lookup_const tcons ^ "___" ^
388 ascii_of class, ar) ::
389 arity_clause (class :: seen) n (tcons, ars)
391 fun multi_arity_clause [] = []
392 | multi_arity_clause ((tcons, ars) :: tc_arlists) =
393 arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
395 (* Generate all pairs (tycon, class, sorts) such that tycon belongs to class in
396 theory thy provided its arguments have the corresponding sorts. *)
397 fun type_class_pairs thy tycons classes =
399 val alg = Sign.classes_of thy
400 fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
401 fun add_class tycon class =
402 cons (class, domain_sorts tycon class)
403 handle Sorts.CLASS_ERROR _ => I
404 fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
405 in map try_classes tycons end
407 (*Proving one (tycon, class) membership may require proving others, so iterate.*)
408 fun iter_type_class_pairs _ _ [] = ([], [])
409 | iter_type_class_pairs thy tycons classes =
411 fun maybe_insert_class s =
412 (s <> type_class andalso not (member (op =) classes s))
414 val cpairs = type_class_pairs thy tycons classes
416 [] |> fold (fold (fold (fold maybe_insert_class) o snd) o snd) cpairs
417 val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
418 in (classes' @ classes, union (op =) cpairs' cpairs) end
420 fun make_arity_clauses thy tycons =
421 iter_type_class_pairs thy tycons ##> multi_arity_clause
424 (** Isabelle class relations **)
426 type class_rel_clause =
431 (* Generate all pairs (sub, super) such that sub is a proper subclass of super
433 fun class_pairs _ [] _ = []
434 | class_pairs thy subs supers =
436 val class_less = Sorts.class_less (Sign.classes_of thy)
437 fun add_super sub super = class_less (sub, super) ? cons (sub, super)
438 fun add_supers sub = fold (add_super sub) supers
439 in fold add_supers subs [] end
441 fun make_class_rel_clause (sub, super) =
442 {name = sub ^ "_" ^ super, subclass = `make_type_class sub,
443 superclass = `make_type_class super}
445 fun make_class_rel_clauses thy subs supers =
446 map make_class_rel_clause (class_pairs thy subs supers)
449 CombConst of name * typ * typ list |
450 CombVar of name * typ |
451 CombApp of combterm * combterm |
452 CombAbs of (name * typ) * combterm
454 fun combtyp_of (CombConst (_, T, _)) = T
455 | combtyp_of (CombVar (_, T)) = T
456 | combtyp_of (CombApp (t1, _)) = snd (dest_funT (combtyp_of t1))
457 | combtyp_of (CombAbs ((_, T), tm)) = T --> combtyp_of tm
459 (*gets the head of a combinator application, along with the list of arguments*)
460 fun strip_combterm_comb u =
462 fun stripc (CombApp (t, u), ts) = stripc (t, u :: ts)
464 in stripc (u, []) end
466 fun atyps_of T = fold_atyps (insert (op =)) T []
468 fun new_skolem_const_name s num_T_args =
469 [new_skolem_const_prefix, s, string_of_int num_T_args]
470 |> space_implode Long_Name.separator
472 (* Converts a term (with combinators) into a combterm. Also accumulates sort
474 fun combterm_from_term thy bs (P $ Q) =
476 val (P', P_atomics_Ts) = combterm_from_term thy bs P
477 val (Q', Q_atomics_Ts) = combterm_from_term thy bs Q
478 in (CombApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
479 | combterm_from_term thy _ (Const (c, T)) =
482 (if String.isPrefix old_skolem_const_prefix c then
483 [] |> Term.add_tvarsT T |> map TVar
485 (c, T) |> Sign.const_typargs thy)
486 val c' = CombConst (`make_fixed_const c, T, tvar_list)
487 in (c', atyps_of T) end
488 | combterm_from_term _ _ (Free (v, T)) =
489 (CombConst (`make_fixed_var v, T, []), atyps_of T)
490 | combterm_from_term _ _ (Var (v as (s, _), T)) =
491 (if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
493 val Ts = T |> strip_type |> swap |> op ::
494 val s' = new_skolem_const_name s (length Ts)
495 in CombConst (`make_fixed_const s', T, Ts) end
497 CombVar ((make_schematic_var v, s), T), atyps_of T)
498 | combterm_from_term _ bs (Bound j) =
500 |> (fn (s, T) => (CombConst (`make_bound_var s, T, []), atyps_of T))
501 | combterm_from_term thy bs (Abs (s, T, t)) =
503 fun vary s = s |> AList.defined (op =) bs s ? vary o Symbol.bump_string
505 val (tm, atomic_Ts) = combterm_from_term thy ((s, T) :: bs) t
507 (CombAbs ((`make_bound_var s, T), tm),
508 union (op =) atomic_Ts (atyps_of T))
512 General | Helper | Extensionality | Intro | Elim | Simp | Local | Assum |
515 (* (quasi-)underapproximation of the truth *)
516 fun is_locality_global Local = false
517 | is_locality_global Assum = false
518 | is_locality_global Chained = false
519 | is_locality_global _ = true
521 datatype order = First_Order | Higher_Order
522 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
523 datatype type_level =
524 All_Types | Noninf_Nonmono_Types | Fin_Nonmono_Types | Const_Arg_Types |
526 datatype type_heaviness = Heavyweight | Lightweight
529 Simple_Types of order * type_level |
530 Preds of polymorphism * type_level * type_heaviness |
531 Tags of polymorphism * type_level * type_heaviness
533 fun try_unsuffixes ss s =
534 fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
536 fun type_enc_from_string s =
537 (case try (unprefix "poly_") s of
538 SOME s => (SOME Polymorphic, s)
540 case try (unprefix "mono_") s of
541 SOME s => (SOME Monomorphic, s)
543 case try (unprefix "mangled_") s of
544 SOME s => (SOME Mangled_Monomorphic, s)
547 (* "_query" and "_bang" are for the ASCII-challenged Metis and
549 case try_unsuffixes ["?", "_query"] s of
550 SOME s => (Noninf_Nonmono_Types, s)
552 case try_unsuffixes ["!", "_bang"] s of
553 SOME s => (Fin_Nonmono_Types, s)
554 | NONE => (All_Types, s))
556 case try (unsuffix "_heavy") s of
557 SOME s => (Heavyweight, s)
558 | NONE => (Lightweight, s))
559 |> (fn (poly, (level, (heaviness, core))) =>
560 case (core, (poly, level, heaviness)) of
561 ("simple", (NONE, _, Lightweight)) =>
562 Simple_Types (First_Order, level)
563 | ("simple_higher", (NONE, _, Lightweight)) =>
564 if level = Noninf_Nonmono_Types then raise Same.SAME
565 else Simple_Types (Higher_Order, level)
566 | ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
567 | ("tags", (SOME Polymorphic, _, _)) =>
568 Tags (Polymorphic, level, heaviness)
569 | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
570 | ("args", (SOME poly, All_Types (* naja *), Lightweight)) =>
571 Preds (poly, Const_Arg_Types, Lightweight)
572 | ("erased", (NONE, All_Types (* naja *), Lightweight)) =>
573 Preds (Polymorphic, No_Types, Lightweight)
574 | _ => raise Same.SAME)
575 handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
577 fun is_type_enc_higher_order (Simple_Types (Higher_Order, _)) = true
578 | is_type_enc_higher_order _ = false
580 fun polymorphism_of_type_enc (Simple_Types _) = Mangled_Monomorphic
581 | polymorphism_of_type_enc (Preds (poly, _, _)) = poly
582 | polymorphism_of_type_enc (Tags (poly, _, _)) = poly
584 fun level_of_type_enc (Simple_Types (_, level)) = level
585 | level_of_type_enc (Preds (_, level, _)) = level
586 | level_of_type_enc (Tags (_, level, _)) = level
588 fun heaviness_of_type_enc (Simple_Types _) = Heavyweight
589 | heaviness_of_type_enc (Preds (_, _, heaviness)) = heaviness
590 | heaviness_of_type_enc (Tags (_, _, heaviness)) = heaviness
592 fun is_type_level_virtually_sound level =
593 level = All_Types orelse level = Noninf_Nonmono_Types
594 val is_type_enc_virtually_sound =
595 is_type_level_virtually_sound o level_of_type_enc
597 fun is_type_level_fairly_sound level =
598 is_type_level_virtually_sound level orelse level = Fin_Nonmono_Types
599 val is_type_enc_fairly_sound = is_type_level_fairly_sound o level_of_type_enc
601 fun choose_format formats (Simple_Types (order, level)) =
602 if member (op =) formats THF then
603 (THF, Simple_Types (order, level))
604 else if member (op =) formats TFF then
605 (TFF, Simple_Types (First_Order, level))
607 choose_format formats (Preds (Mangled_Monomorphic, level, Heavyweight))
608 | choose_format formats type_enc =
611 (CNF_UEQ, case type_enc of
613 (if is_type_enc_fairly_sound type_enc then Tags else Preds)
616 | format => (format, type_enc))
618 type translated_formula =
622 combformula : (name, typ, combterm) formula,
623 atomic_types : typ list}
625 fun update_combformula f ({name, locality, kind, combformula, atomic_types}
626 : translated_formula) =
627 {name = name, locality = locality, kind = kind, combformula = f combformula,
628 atomic_types = atomic_types} : translated_formula
630 fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
632 val type_instance = Sign.typ_instance o Proof_Context.theory_of
634 fun insert_type ctxt get_T x xs =
635 let val T = get_T x in
636 if exists (curry (type_instance ctxt) T o get_T) xs then xs
637 else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
640 (* The Booleans indicate whether all type arguments should be kept. *)
641 datatype type_arg_policy =
642 Explicit_Type_Args of bool |
643 Mangled_Type_Args of bool |
646 fun should_drop_arg_type_args (Simple_Types _) =
647 false (* since TFF doesn't support overloading *)
648 | should_drop_arg_type_args type_enc =
649 level_of_type_enc type_enc = All_Types andalso
650 heaviness_of_type_enc type_enc = Heavyweight
652 fun type_arg_policy type_enc s =
653 if s = type_tag_name then
654 (if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
657 Explicit_Type_Args) false
658 else case type_enc of
659 Tags (_, All_Types, Heavyweight) => No_Type_Args
661 if level_of_type_enc type_enc = No_Types orelse
662 s = @{const_name HOL.eq} orelse
663 (s = app_op_name andalso
664 level_of_type_enc type_enc = Const_Arg_Types) then
667 should_drop_arg_type_args type_enc
668 |> (if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
673 (* Make literals for sorted type variables. *)
674 fun generic_add_sorts_on_type (_, []) = I
675 | generic_add_sorts_on_type ((x, i), s :: ss) =
676 generic_add_sorts_on_type ((x, i), ss)
677 #> (if s = the_single @{sort HOL.type} then
680 insert (op =) (TyLitFree (`make_type_class s, `make_fixed_type_var x))
682 insert (op =) (TyLitVar (`make_type_class s,
683 (make_schematic_type_var (x, i), x))))
684 fun add_sorts_on_tfree (TFree (s, S)) = generic_add_sorts_on_type ((s, ~1), S)
685 | add_sorts_on_tfree _ = I
686 fun add_sorts_on_tvar (TVar z) = generic_add_sorts_on_type z
687 | add_sorts_on_tvar _ = I
689 fun type_literals_for_types type_enc add_sorts_on_typ Ts =
690 [] |> level_of_type_enc type_enc <> No_Types ? fold add_sorts_on_typ Ts
692 fun mk_aconns c phis =
693 let val (phis', phi') = split_last phis in
694 fold_rev (mk_aconn c) phis' phi'
696 fun mk_ahorn [] phi = phi
697 | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
698 fun mk_aquant _ [] phi = phi
699 | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
700 if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
701 | mk_aquant q xs phi = AQuant (q, xs, phi)
703 fun close_universally atom_vars phi =
705 fun formula_vars bounds (AQuant (_, xs, phi)) =
706 formula_vars (map fst xs @ bounds) phi
707 | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
708 | formula_vars bounds (AAtom tm) =
709 union (op =) (atom_vars tm []
710 |> filter_out (member (op =) bounds o fst))
711 in mk_aquant AForall (formula_vars [] phi []) phi end
713 fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
714 | combterm_vars (CombConst _) = I
715 | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
716 | combterm_vars (CombAbs (_, tm)) = combterm_vars tm
717 fun close_combformula_universally phi = close_universally combterm_vars phi
719 fun term_vars bounds (ATerm (name as (s, _), tms)) =
720 (is_tptp_variable s andalso not (member (op =) bounds name))
721 ? insert (op =) (name, NONE) #> fold (term_vars bounds) tms
722 | term_vars bounds (AAbs ((name, _), tm)) = term_vars (name :: bounds) tm
723 fun close_formula_universally phi = close_universally (term_vars []) phi
725 val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
726 val homo_infinite_type = Type (homo_infinite_type_name, [])
728 fun ho_term_from_typ format type_enc =
730 fun term (Type (s, Ts)) =
731 ATerm (case (is_type_enc_higher_order type_enc, s) of
732 (true, @{type_name bool}) => `I tptp_bool_type
733 | (true, @{type_name fun}) => `I tptp_fun_type
734 | _ => if s = homo_infinite_type_name andalso
735 (format = TFF orelse format = THF) then
736 `I tptp_individual_type
738 `make_fixed_type_const s,
740 | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
741 | term (TVar ((x as (s, _)), _)) =
742 ATerm ((make_schematic_type_var x, s), [])
745 fun ho_term_for_type_arg format type_enc T =
746 if T = dummyT then NONE else SOME (ho_term_from_typ format type_enc T)
748 (* This shouldn't clash with anything else. *)
749 val mangled_type_sep = "\000"
751 fun generic_mangled_type_name f (ATerm (name, [])) = f name
752 | generic_mangled_type_name f (ATerm (name, tys)) =
753 f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
755 | generic_mangled_type_name _ _ = raise Fail "unexpected type abstraction"
757 val bool_atype = AType (`I tptp_bool_type)
759 fun make_simple_type s =
760 if s = tptp_bool_type orelse s = tptp_fun_type orelse
761 s = tptp_individual_type then
764 simple_type_prefix ^ ascii_of s
766 fun ho_type_from_ho_term type_enc pred_sym ary =
769 AType ((make_simple_type (generic_mangled_type_name fst ty),
770 generic_mangled_type_name snd ty))
771 fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
772 fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
773 | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
774 | to_fo _ _ = raise Fail "unexpected type abstraction"
775 fun to_ho (ty as ATerm ((s, _), tys)) =
776 if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
777 | to_ho _ = raise Fail "unexpected type abstraction"
778 in if is_type_enc_higher_order type_enc then to_ho else to_fo ary end
780 fun ho_type_from_typ format type_enc pred_sym ary =
781 ho_type_from_ho_term type_enc pred_sym ary
782 o ho_term_from_typ format type_enc
784 fun mangled_const_name format type_enc T_args (s, s') =
786 val ty_args = T_args |> map_filter (ho_term_for_type_arg format type_enc)
787 fun type_suffix f g =
788 fold_rev (curry (op ^) o g o prefix mangled_type_sep
789 o generic_mangled_type_name f) ty_args ""
790 in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
792 val parse_mangled_ident =
793 Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
795 fun parse_mangled_type x =
797 -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
799 and parse_mangled_types x =
800 (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
802 fun unmangled_type s =
803 s |> suffix ")" |> raw_explode
804 |> Scan.finite Symbol.stopper
805 (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
806 quote s)) parse_mangled_type))
809 val unmangled_const_name = space_explode mangled_type_sep #> hd
810 fun unmangled_const s =
811 let val ss = space_explode mangled_type_sep s in
812 (hd ss, map unmangled_type (tl ss))
815 fun introduce_proxies type_enc =
817 fun intro top_level (CombApp (tm1, tm2)) =
818 CombApp (intro top_level tm1, intro false tm2)
819 | intro top_level (CombConst (name as (s, _), T, T_args)) =
820 (case proxify_const s of
822 if top_level orelse is_type_enc_higher_order type_enc then
823 case (top_level, s) of
824 (_, "c_False") => (`I tptp_false, [])
825 | (_, "c_True") => (`I tptp_true, [])
826 | (false, "c_Not") => (`I tptp_not, [])
827 | (false, "c_conj") => (`I tptp_and, [])
828 | (false, "c_disj") => (`I tptp_or, [])
829 | (false, "c_implies") => (`I tptp_implies, [])
830 | (false, "c_All") => (`I tptp_ho_forall, [])
831 | (false, "c_Ex") => (`I tptp_ho_exists, [])
833 if is_tptp_equal s then (`I tptp_equal, [])
834 else (proxy_base |>> prefix const_prefix, T_args)
837 (proxy_base |>> prefix const_prefix, T_args)
838 | NONE => (name, T_args))
839 |> (fn (name, T_args) => CombConst (name, T, T_args))
840 | intro _ (CombAbs (bound, tm)) = CombAbs (bound, intro false tm)
844 fun combformula_from_prop thy type_enc eq_as_iff =
846 fun do_term bs t atomic_types =
847 combterm_from_term thy bs (Envir.eta_contract t)
848 |>> (introduce_proxies type_enc #> AAtom)
849 ||> union (op =) atomic_types
850 fun do_quant bs q s T t' =
851 let val s = singleton (Name.variant_list (map fst bs)) s in
852 do_formula ((s, T) :: bs) t'
853 #>> mk_aquant q [(`make_bound_var s, SOME T)]
855 and do_conn bs c t1 t2 =
856 do_formula bs t1 ##>> do_formula bs t2 #>> uncurry (mk_aconn c)
857 and do_formula bs t =
859 @{const Trueprop} $ t1 => do_formula bs t1
860 | @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
861 | Const (@{const_name All}, _) $ Abs (s, T, t') =>
862 do_quant bs AForall s T t'
863 | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
864 do_quant bs AExists s T t'
865 | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
866 | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
867 | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
868 | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
869 if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
873 fun presimplify_term _ [] t = t
874 | presimplify_term ctxt presimp_consts t =
875 t |> exists_Const (member (op =) presimp_consts o fst) t
876 ? (Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
877 #> Meson.presimplify ctxt
880 fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
881 fun conceal_bounds Ts t =
882 subst_bounds (map (Free o apfst concealed_bound_name)
883 (0 upto length Ts - 1 ~~ Ts), t)
884 fun reveal_bounds Ts =
885 subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
886 (0 upto length Ts - 1 ~~ Ts))
888 fun is_fun_equality (@{const_name HOL.eq},
889 Type (_, [Type (@{type_name fun}, _), _])) = true
890 | is_fun_equality _ = false
892 fun extensionalize_term ctxt t =
893 if exists_Const is_fun_equality t then
894 let val thy = Proof_Context.theory_of ctxt in
895 t |> cterm_of thy |> Meson.extensionalize_conv ctxt
896 |> prop_of |> Logic.dest_equals |> snd
901 fun process_abstractions_in_term ctxt type_enc kind t =
902 let val thy = Proof_Context.theory_of ctxt in
903 if Meson.is_fol_term thy t then
909 @{const Not} $ t1 => @{const Not} $ aux Ts t1
910 | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
911 t0 $ Abs (s, T, aux (T :: Ts) t')
912 | (t0 as Const (@{const_name All}, _)) $ t1 =>
913 aux Ts (t0 $ eta_expand Ts t1 1)
914 | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
915 t0 $ Abs (s, T, aux (T :: Ts) t')
916 | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
917 aux Ts (t0 $ eta_expand Ts t1 1)
918 | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
919 | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
920 | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
921 | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
923 t0 $ aux Ts t1 $ aux Ts t2
924 | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
926 else if is_type_enc_higher_order type_enc then
927 t |> Envir.eta_contract
929 t |> conceal_bounds Ts
930 |> Envir.eta_contract
932 |> Meson_Clausify.introduce_combinators_in_cterm
933 |> prop_of |> Logic.dest_equals |> snd
935 val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
936 in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
938 (* A type variable of sort "{}" will make abstraction fail. *)
939 if kind = Conjecture then HOLogic.false_const
940 else HOLogic.true_const
943 (* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
944 same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
947 fun aux (t $ u) = aux t $ aux u
948 | aux (Abs (s, T, t)) = Abs (s, T, aux t)
949 | aux (Var ((s, i), T)) =
950 Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
952 in t |> exists_subterm is_Var t ? aux end
954 fun preprocess_prop ctxt type_enc presimp_consts kind t =
956 val thy = Proof_Context.theory_of ctxt
957 val t = t |> Envir.beta_eta_contract
958 |> transform_elim_prop
959 |> Object_Logic.atomize_term thy
960 val need_trueprop = (fastype_of t = @{typ bool})
962 t |> need_trueprop ? HOLogic.mk_Trueprop
963 |> Raw_Simplifier.rewrite_term thy (Meson.unfold_set_const_simps ctxt) []
964 |> extensionalize_term ctxt
965 |> presimplify_term ctxt presimp_consts
966 |> perhaps (try (HOLogic.dest_Trueprop))
967 |> process_abstractions_in_term ctxt type_enc kind
970 (* making fact and conjecture formulas *)
971 fun make_formula thy type_enc eq_as_iff name loc kind t =
973 val (combformula, atomic_types) =
974 combformula_from_prop thy type_enc eq_as_iff t []
976 {name = name, locality = loc, kind = kind, combformula = combformula,
977 atomic_types = atomic_types}
980 fun make_fact ctxt format type_enc eq_as_iff preproc presimp_consts
982 let val thy = Proof_Context.theory_of ctxt in
983 case t |> preproc ? preprocess_prop ctxt type_enc presimp_consts Axiom
984 |> make_formula thy type_enc (eq_as_iff andalso format <> CNF) name
986 formula as {combformula = AAtom (CombConst ((s, _), _, _)), ...} =>
987 if s = tptp_true then NONE else SOME formula
988 | formula => SOME formula
991 fun make_conjecture ctxt format prem_kind type_enc preproc presimp_consts ts =
993 val thy = Proof_Context.theory_of ctxt
994 val last = length ts - 1
996 map2 (fn j => fn t =>
998 val (kind, maybe_negate) =
1003 if prem_kind = Conjecture then update_combformula mk_anot
1007 (preprocess_prop ctxt type_enc presimp_consts kind #> freeze_term)
1008 |> make_formula thy type_enc (format <> CNF) (string_of_int j)
1015 (** Finite and infinite type inference **)
1017 fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
1018 | deep_freeze_atyp T = T
1019 val deep_freeze_type = map_atyps deep_freeze_atyp
1021 (* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
1022 dangerous because their "exhaust" properties can easily lead to unsound ATP
1023 proofs. On the other hand, all HOL infinite types can be given the same
1024 models in first-order logic (via Löwenheim-Skolem). *)
1026 fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
1027 exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
1028 | should_encode_type _ _ All_Types _ = true
1029 | should_encode_type ctxt _ Fin_Nonmono_Types T =
1030 is_type_surely_finite ctxt false T
1031 | should_encode_type _ _ _ _ = false
1033 fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
1034 should_predicate_on_var T =
1035 (heaviness = Heavyweight orelse should_predicate_on_var ()) andalso
1036 should_encode_type ctxt nonmono_Ts level T
1037 | should_predicate_on_type _ _ _ _ _ = false
1039 fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
1040 String.isPrefix bound_var_prefix s
1041 | is_var_or_bound_var (CombVar _) = true
1042 | is_var_or_bound_var _ = false
1045 Top_Level of bool option |
1046 Eq_Arg of bool option |
1049 fun should_tag_with_type _ _ _ (Top_Level _) _ _ = false
1050 | should_tag_with_type ctxt nonmono_Ts (Tags (poly, level, heaviness)) site
1053 Heavyweight => should_encode_type ctxt nonmono_Ts level T
1055 case (site, is_var_or_bound_var u) of
1056 (Eq_Arg pos, true) =>
1057 (* The first disjunct prevents a subtle soundness issue explained in
1058 Blanchette's Ph.D. thesis. See also
1059 "formula_lines_for_lightweight_tags_sym_decl". *)
1060 (pos <> SOME false andalso poly = Polymorphic andalso
1061 level <> All_Types andalso heaviness = Lightweight andalso
1062 exists (fn T' => type_instance ctxt (T', T)) nonmono_Ts) orelse
1063 should_encode_type ctxt nonmono_Ts level T
1065 | should_tag_with_type _ _ _ _ _ _ = false
1067 fun homogenized_type ctxt nonmono_Ts level =
1069 val should_encode = should_encode_type ctxt nonmono_Ts level
1070 fun homo 0 T = if should_encode T then T else homo_infinite_type
1071 | homo ary (Type (@{type_name fun}, [T1, T2])) =
1072 homo 0 T1 --> homo (ary - 1) T2
1073 | homo _ _ = raise Fail "expected function type"
1076 (** "hBOOL" and "hAPP" **)
1079 {pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
1081 fun add_combterm_syms_to_table ctxt explicit_apply =
1083 fun consider_var_arity const_T var_T max_ary =
1086 if ary = max_ary orelse type_instance ctxt (var_T, T) orelse
1087 type_instance ctxt (T, var_T) then
1090 iter (ary + 1) (range_type T)
1091 in iter 0 const_T end
1092 fun add_var_or_bound_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1093 if explicit_apply = NONE andalso
1094 (can dest_funT T orelse T = @{typ bool}) then
1096 val bool_vars' = bool_vars orelse body_type T = @{typ bool}
1097 fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
1098 {pred_sym = pred_sym andalso not bool_vars',
1099 min_ary = fold (fn T' => consider_var_arity T' T) types min_ary,
1100 max_ary = max_ary, types = types}
1102 fun_var_Ts |> can dest_funT T ? insert_type ctxt I T
1104 if bool_vars' = bool_vars andalso
1105 pointer_eq (fun_var_Ts', fun_var_Ts) then
1108 ((bool_vars', fun_var_Ts'), Symtab.map (K repair_min_arity) sym_tab)
1112 fun add top_level tm (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1113 let val (head, args) = strip_combterm_comb tm in
1115 CombConst ((s, _), T, _) =>
1116 if String.isPrefix bound_var_prefix s then
1117 add_var_or_bound_var T accum
1119 let val ary = length args in
1120 ((bool_vars, fun_var_Ts),
1121 case Symtab.lookup sym_tab s of
1122 SOME {pred_sym, min_ary, max_ary, types} =>
1125 pred_sym andalso top_level andalso not bool_vars
1126 val types' = types |> insert_type ctxt I T
1128 if is_some explicit_apply orelse
1129 pointer_eq (types', types) then
1132 fold (consider_var_arity T) fun_var_Ts min_ary
1134 Symtab.update (s, {pred_sym = pred_sym,
1135 min_ary = Int.min (ary, min_ary),
1136 max_ary = Int.max (ary, max_ary),
1142 val pred_sym = top_level andalso not bool_vars
1144 case explicit_apply of
1147 | NONE => fold (consider_var_arity T) fun_var_Ts ary
1149 Symtab.update_new (s, {pred_sym = pred_sym,
1150 min_ary = min_ary, max_ary = ary,
1155 | CombVar (_, T) => add_var_or_bound_var T accum
1156 | CombAbs ((_, T), tm) =>
1157 accum |> add_var_or_bound_var T |> add false tm
1159 |> fold (add false) args
1162 fun add_fact_syms_to_table ctxt explicit_apply =
1163 fact_lift (formula_fold NONE
1164 (K (add_combterm_syms_to_table ctxt explicit_apply)))
1166 val default_sym_tab_entries : (string * sym_info) list =
1167 (prefixed_predicator_name,
1168 {pred_sym = true, min_ary = 1, max_ary = 1, types = []}) ::
1169 ([tptp_false, tptp_true]
1170 |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []})) @
1171 ([tptp_equal, tptp_old_equal]
1172 |> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = []}))
1174 fun sym_table_for_facts ctxt explicit_apply facts =
1175 ((false, []), Symtab.empty)
1176 |> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
1177 |> fold Symtab.update default_sym_tab_entries
1179 fun min_arity_of sym_tab s =
1180 case Symtab.lookup sym_tab s of
1181 SOME ({min_ary, ...} : sym_info) => min_ary
1183 case strip_prefix_and_unascii const_prefix s of
1185 let val s = s |> unmangled_const_name |> invert_const in
1186 if s = predicator_name then 1
1187 else if s = app_op_name then 2
1188 else if s = type_pred_name then 1
1193 (* True if the constant ever appears outside of the top-level position in
1194 literals, or if it appears with different arities (e.g., because of different
1195 type instantiations). If false, the constant always receives all of its
1196 arguments and is used as a predicate. *)
1197 fun is_pred_sym sym_tab s =
1198 case Symtab.lookup sym_tab s of
1199 SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
1200 pred_sym andalso min_ary = max_ary
1203 val predicator_combconst =
1204 CombConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
1205 fun predicator tm = CombApp (predicator_combconst, tm)
1207 fun introduce_predicators_in_combterm sym_tab tm =
1208 case strip_combterm_comb tm of
1209 (CombConst ((s, _), _, _), _) =>
1210 if is_pred_sym sym_tab s then tm else predicator tm
1211 | _ => predicator tm
1213 fun list_app head args = fold (curry (CombApp o swap)) args head
1215 val app_op = `make_fixed_const app_op_name
1217 fun explicit_app arg head =
1219 val head_T = combtyp_of head
1220 val (arg_T, res_T) = dest_funT head_T
1222 CombConst (app_op, head_T --> head_T, [arg_T, res_T])
1223 in list_app explicit_app [head, arg] end
1224 fun list_explicit_app head args = fold explicit_app args head
1226 fun introduce_explicit_apps_in_combterm sym_tab =
1229 case strip_combterm_comb tm of
1230 (head as CombConst ((s, _), _, _), args) =>
1232 |> chop (min_arity_of sym_tab s)
1234 |-> list_explicit_app
1235 | (head, args) => list_explicit_app head (map aux args)
1238 fun chop_fun 0 T = ([], T)
1239 | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
1240 chop_fun (n - 1) ran_T |>> cons dom_T
1241 | chop_fun _ _ = raise Fail "unexpected non-function"
1243 fun filter_type_args _ _ _ [] = []
1244 | filter_type_args thy s arity T_args =
1246 (* will throw "TYPE" for pseudo-constants *)
1247 val U = if s = app_op_name then
1248 @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
1250 s |> Sign.the_const_type thy
1252 case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
1255 let val U_args = (s, U) |> Sign.const_typargs thy in
1257 |> map (fn (U, T) =>
1258 if member (op =) res_U_vars (dest_TVar U) then T
1262 handle TYPE _ => T_args
1264 fun enforce_type_arg_policy_in_combterm ctxt format type_enc =
1266 val thy = Proof_Context.theory_of ctxt
1267 fun aux arity (CombApp (tm1, tm2)) =
1268 CombApp (aux (arity + 1) tm1, aux 0 tm2)
1269 | aux arity (CombConst (name as (s, _), T, T_args)) =
1270 (case strip_prefix_and_unascii const_prefix s of
1271 NONE => (name, T_args)
1274 val s'' = invert_const s''
1275 fun filtered_T_args false = T_args
1276 | filtered_T_args true = filter_type_args thy s'' arity T_args
1278 case type_arg_policy type_enc s'' of
1279 Explicit_Type_Args drop_args =>
1280 (name, filtered_T_args drop_args)
1281 | Mangled_Type_Args drop_args =>
1282 (mangled_const_name format type_enc (filtered_T_args drop_args)
1284 | No_Type_Args => (name, [])
1286 |> (fn (name, T_args) => CombConst (name, T, T_args))
1287 | aux _ (CombAbs (bound, tm)) = CombAbs (bound, aux 0 tm)
1291 fun repair_combterm ctxt format type_enc sym_tab =
1292 not (is_type_enc_higher_order type_enc)
1293 ? (introduce_explicit_apps_in_combterm sym_tab
1294 #> introduce_predicators_in_combterm sym_tab)
1295 #> enforce_type_arg_policy_in_combterm ctxt format type_enc
1296 fun repair_fact ctxt format type_enc sym_tab =
1297 update_combformula (formula_map
1298 (repair_combterm ctxt format type_enc sym_tab))
1300 (** Helper facts **)
1302 (* The Boolean indicates that a fairly sound type encoding is needed. *)
1304 [(("COMBI", false), @{thms Meson.COMBI_def}),
1305 (("COMBK", false), @{thms Meson.COMBK_def}),
1306 (("COMBB", false), @{thms Meson.COMBB_def}),
1307 (("COMBC", false), @{thms Meson.COMBC_def}),
1308 (("COMBS", false), @{thms Meson.COMBS_def}),
1309 (("fFalse", false), [@{lemma "~ fFalse" by (unfold fFalse_def) fast}]),
1310 (("fFalse", true), @{thms True_or_False}),
1311 (("fTrue", false), [@{lemma "fTrue" by (unfold fTrue_def) fast}]),
1312 (("fTrue", true), @{thms True_or_False}),
1314 @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1315 fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1317 @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
1318 by (unfold fconj_def) fast+}),
1320 @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
1321 by (unfold fdisj_def) fast+}),
1322 (("fimplies", false),
1323 @{lemma "P | fimplies P Q" "~ Q | fimplies P Q" "~ fimplies P Q | ~ P | Q"
1324 by (unfold fimplies_def) fast+}),
1326 (* This is a lie: Higher-order equality doesn't need a sound type encoding.
1327 However, this is done so for backward compatibility: Including the
1328 equality helpers by default in Metis breaks a few existing proofs. *)
1329 @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1330 fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1331 (("fAll", false), []), (*TODO: add helpers*)
1332 (("fEx", false), []), (*TODO: add helpers*)
1333 (("If", true), @{thms if_True if_False True_or_False})]
1334 |> map (apsnd (map zero_var_indexes))
1336 val type_tag = `make_fixed_const type_tag_name
1338 fun type_tag_idempotence_fact () =
1340 fun var s = ATerm (`I s, [])
1341 fun tag tm = ATerm (type_tag, [var "T", tm])
1342 val tagged_a = tag (var "A")
1344 Formula (type_tag_idempotence_helper_name, Axiom,
1345 AAtom (ATerm (`I tptp_equal, [tag tagged_a, tagged_a]))
1346 |> close_formula_universally, simp_info, NONE)
1349 fun should_specialize_helper type_enc t =
1350 polymorphism_of_type_enc type_enc = Mangled_Monomorphic andalso
1351 level_of_type_enc type_enc <> No_Types andalso
1352 not (null (Term.hidden_polymorphism t))
1354 fun helper_facts_for_sym ctxt format type_enc (s, {types, ...} : sym_info) =
1355 case strip_prefix_and_unascii const_prefix s of
1358 val thy = Proof_Context.theory_of ctxt
1359 val unmangled_s = mangled_s |> unmangled_const_name
1360 fun dub needs_fairly_sound j k =
1361 (unmangled_s ^ "_" ^ string_of_int j ^ "_" ^ string_of_int k ^
1362 (if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^
1363 (if needs_fairly_sound then typed_helper_suffix
1364 else untyped_helper_suffix),
1366 fun dub_and_inst needs_fairly_sound (th, j) =
1367 let val t = prop_of th in
1368 if should_specialize_helper type_enc t then
1369 map (fn T => specialize_type thy (invert_const unmangled_s, T) t)
1374 |> map (fn (k, t) => (dub needs_fairly_sound j k, t)) o tag_list 1
1376 map_filter (make_fact ctxt format type_enc false false [])
1377 val fairly_sound = is_type_enc_fairly_sound type_enc
1380 |> maps (fn ((helper_s, needs_fairly_sound), ths) =>
1381 if helper_s <> unmangled_s orelse
1382 (needs_fairly_sound andalso not fairly_sound) then
1385 ths ~~ (1 upto length ths)
1386 |> maps (dub_and_inst needs_fairly_sound)
1390 fun helper_facts_for_sym_table ctxt format type_enc sym_tab =
1391 Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_enc) sym_tab
1394 (***************************************************************)
1395 (* Type Classes Present in the Axiom or Conjecture Clauses *)
1396 (***************************************************************)
1398 fun set_insert (x, s) = Symtab.update (x, ()) s
1400 fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
1402 (* Remove this trivial type class (FIXME: similar code elsewhere) *)
1403 fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
1405 fun classes_of_terms get_Ts =
1406 map (map snd o get_Ts)
1407 #> List.foldl add_classes Symtab.empty
1408 #> delete_type #> Symtab.keys
1410 val tfree_classes_of_terms = classes_of_terms OldTerm.term_tfrees
1411 val tvar_classes_of_terms = classes_of_terms OldTerm.term_tvars
1413 fun fold_type_constrs f (Type (s, Ts)) x =
1414 fold (fold_type_constrs f) Ts (f (s, x))
1415 | fold_type_constrs _ _ x = x
1417 (*Type constructors used to instantiate overloaded constants are the only ones needed.*)
1418 fun add_type_constrs_in_term thy =
1420 fun add (Const (@{const_name Meson.skolem}, _) $ _) = I
1421 | add (t $ u) = add t #> add u
1422 | add (Const (x as (s, _))) =
1423 if String.isPrefix skolem_const_prefix s then I
1424 else x |> Sign.const_typargs thy |> fold (fold_type_constrs set_insert)
1425 | add (Abs (_, _, u)) = add u
1429 fun type_constrs_of_terms thy ts =
1430 Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty)
1432 fun translate_formulas ctxt format prem_kind type_enc preproc hyp_ts concl_t
1435 val thy = Proof_Context.theory_of ctxt
1436 val fact_ts = facts |> map snd
1437 val presimp_consts = Meson.presimplified_consts ctxt
1438 val make_fact = make_fact ctxt format type_enc true preproc presimp_consts
1439 val (facts, fact_names) =
1440 facts |> map (fn (name, t) => (name, t) |> make_fact |> rpair name)
1441 |> map_filter (try (apfst the))
1443 (* Remove existing facts from the conjecture, as this can dramatically
1444 boost an ATP's performance (for some reason). *)
1447 |> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t)
1448 val goal_t = Logic.list_implies (hyp_ts, concl_t)
1449 val all_ts = goal_t :: fact_ts
1450 val subs = tfree_classes_of_terms all_ts
1451 val supers = tvar_classes_of_terms all_ts
1452 val tycons = type_constrs_of_terms thy all_ts
1455 |> make_conjecture ctxt format prem_kind type_enc preproc presimp_consts
1456 val (supers', arity_clauses) =
1457 if level_of_type_enc type_enc = No_Types then ([], [])
1458 else make_arity_clauses thy tycons supers
1459 val class_rel_clauses = make_class_rel_clauses thy subs supers'
1461 (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
1464 fun fo_literal_from_type_literal (TyLitVar (class, name)) =
1465 (true, ATerm (class, [ATerm (name, [])]))
1466 | fo_literal_from_type_literal (TyLitFree (class, name)) =
1467 (true, ATerm (class, [ATerm (name, [])]))
1469 fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
1471 val type_pred = `make_fixed_const type_pred_name
1473 fun type_pred_combterm ctxt format type_enc T tm =
1474 CombApp (CombConst (type_pred, T --> @{typ bool}, [T])
1475 |> enforce_type_arg_policy_in_combterm ctxt format type_enc, tm)
1477 fun is_var_positively_naked_in_term _ (SOME false) _ accum = accum
1478 | is_var_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
1479 accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
1480 | is_var_positively_naked_in_term _ _ _ _ = true
1481 fun should_predicate_on_var_in_formula pos phi (SOME true) name =
1482 formula_fold pos (is_var_positively_naked_in_term name) phi false
1483 | should_predicate_on_var_in_formula _ _ _ _ = true
1485 fun mk_aterm format type_enc name T_args args =
1486 ATerm (name, map_filter (ho_term_for_type_arg format type_enc) T_args @ args)
1488 fun tag_with_type ctxt format nonmono_Ts type_enc pos T tm =
1489 CombConst (type_tag, T --> T, [T])
1490 |> enforce_type_arg_policy_in_combterm ctxt format type_enc
1491 |> ho_term_from_combterm ctxt format nonmono_Ts type_enc (Top_Level pos)
1492 |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm])
1493 | _ => raise Fail "unexpected lambda-abstraction")
1494 and ho_term_from_combterm ctxt format nonmono_Ts type_enc =
1498 val (head, args) = strip_combterm_comb u
1501 Top_Level pos => pos
1506 CombConst (name as (s, _), _, T_args) =>
1508 val arg_site = if is_tptp_equal s then Eq_Arg pos else Elsewhere
1510 mk_aterm format type_enc name T_args (map (aux arg_site) args)
1512 | CombVar (name, _) => mk_aterm format type_enc name [] (map (aux Elsewhere) args)
1513 | CombAbs ((name, T), tm) =>
1514 AAbs ((name, ho_type_from_typ format type_enc true 0 T), aux Elsewhere tm)
1515 | CombApp _ => raise Fail "impossible \"CombApp\""
1516 val T = combtyp_of u
1518 t |> (if should_tag_with_type ctxt nonmono_Ts type_enc site u T then
1519 tag_with_type ctxt format nonmono_Ts type_enc pos T
1524 and formula_from_combformula ctxt format nonmono_Ts type_enc
1525 should_predicate_on_var =
1528 ho_term_from_combterm ctxt format nonmono_Ts type_enc (Top_Level pos)
1531 Simple_Types (_, level) =>
1532 homogenized_type ctxt nonmono_Ts level 0
1533 #> ho_type_from_typ format type_enc false 0 #> SOME
1535 fun do_out_of_bound_type pos phi universal (name, T) =
1536 if should_predicate_on_type ctxt nonmono_Ts type_enc
1537 (fn () => should_predicate_on_var pos phi universal name) T then
1539 |> type_pred_combterm ctxt format type_enc T
1540 |> do_term pos |> AAtom |> SOME
1543 fun do_formula pos (AQuant (q, xs, phi)) =
1545 val phi = phi |> do_formula pos
1546 val universal = Option.map (q = AExists ? not) pos
1548 AQuant (q, xs |> map (apsnd (fn NONE => NONE
1549 | SOME T => do_bound_type T)),
1550 (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
1552 (fn (_, NONE) => NONE
1554 do_out_of_bound_type pos phi universal (s, T))
1558 | do_formula pos (AConn conn) = aconn_map pos do_formula conn
1559 | do_formula pos (AAtom tm) = AAtom (do_term pos tm)
1562 fun bound_tvars type_enc Ts =
1563 mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
1564 (type_literals_for_types type_enc add_sorts_on_tvar Ts))
1566 (* Each fact is given a unique fact number to avoid name clashes (e.g., because
1567 of monomorphization). The TPTP explicitly forbids name clashes, and some of
1568 the remote provers might care. *)
1569 fun formula_line_for_fact ctxt format prefix encode freshen pos nonmono_Ts
1570 type_enc (j, {name, locality, kind, combformula, atomic_types}) =
1571 (prefix ^ (if freshen then string_of_int j ^ "_" else "") ^ encode name,
1574 |> close_combformula_universally
1575 |> formula_from_combformula ctxt format nonmono_Ts type_enc
1576 should_predicate_on_var_in_formula
1577 (if pos then SOME true else NONE)
1578 |> bound_tvars type_enc atomic_types
1579 |> close_formula_universally,
1588 fun formula_line_for_class_rel_clause ({name, subclass, superclass, ...}
1589 : class_rel_clause) =
1590 let val ty_arg = ATerm (`I "T", []) in
1591 Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
1592 AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
1593 AAtom (ATerm (superclass, [ty_arg]))])
1594 |> close_formula_universally, intro_info, NONE)
1597 fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
1598 (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
1599 | fo_literal_from_arity_literal (TVarLit (c, sort)) =
1600 (false, ATerm (c, [ATerm (sort, [])]))
1602 fun formula_line_for_arity_clause ({name, prem_lits, concl_lits, ...}
1604 Formula (arity_clause_prefix ^ name, Axiom,
1605 mk_ahorn (map (formula_from_fo_literal o apfst not
1606 o fo_literal_from_arity_literal) prem_lits)
1607 (formula_from_fo_literal
1608 (fo_literal_from_arity_literal concl_lits))
1609 |> close_formula_universally, intro_info, NONE)
1611 fun formula_line_for_conjecture ctxt format nonmono_Ts type_enc
1612 ({name, kind, combformula, atomic_types, ...} : translated_formula) =
1613 Formula (conjecture_prefix ^ name, kind,
1614 formula_from_combformula ctxt format nonmono_Ts type_enc
1615 should_predicate_on_var_in_formula (SOME false)
1616 (close_combformula_universally combformula)
1617 |> bound_tvars type_enc atomic_types
1618 |> close_formula_universally, NONE, NONE)
1620 fun free_type_literals type_enc ({atomic_types, ...} : translated_formula) =
1621 atomic_types |> type_literals_for_types type_enc add_sorts_on_tfree
1622 |> map fo_literal_from_type_literal
1624 fun formula_line_for_free_type j lit =
1625 Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis,
1626 formula_from_fo_literal lit, NONE, NONE)
1627 fun formula_lines_for_free_types type_enc facts =
1629 val litss = map (free_type_literals type_enc) facts
1630 val lits = fold (union (op =)) litss []
1631 in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
1633 (** Symbol declarations **)
1635 fun should_declare_sym type_enc pred_sym s =
1636 is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
1638 Simple_Types _ => true
1639 | Tags (_, _, Lightweight) => true
1640 | _ => not pred_sym)
1642 fun sym_decl_table_for_facts ctxt type_enc repaired_sym_tab (conjs, facts) =
1644 fun add_combterm in_conj tm =
1645 let val (head, args) = strip_combterm_comb tm in
1647 CombConst ((s, s'), T, T_args) =>
1648 let val pred_sym = is_pred_sym repaired_sym_tab s in
1649 if should_declare_sym type_enc pred_sym s then
1650 Symtab.map_default (s, [])
1651 (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
1656 | CombAbs (_, tm) => add_combterm in_conj tm
1658 #> fold (add_combterm in_conj) args
1660 fun add_fact in_conj =
1661 fact_lift (formula_fold NONE (K (add_combterm in_conj)))
1664 |> is_type_enc_fairly_sound type_enc
1665 ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
1668 (* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
1669 out with monotonicity" paper presented at CADE 2011. *)
1670 fun add_combterm_nonmonotonic_types _ _ _ _ (SOME false) _ = I
1671 | add_combterm_nonmonotonic_types ctxt level sound locality _
1672 (CombApp (CombApp (CombConst ((s, _), Type (_, [T, _]), _), tm1),
1674 (is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
1676 Noninf_Nonmono_Types =>
1677 not (is_locality_global locality) orelse
1678 not (is_type_surely_infinite ctxt sound T)
1679 | Fin_Nonmono_Types => is_type_surely_finite ctxt false T
1680 | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
1681 | add_combterm_nonmonotonic_types _ _ _ _ _ _ = I
1682 fun add_fact_nonmonotonic_types ctxt level sound
1683 ({kind, locality, combformula, ...} : translated_formula) =
1684 formula_fold (SOME (kind <> Conjecture))
1685 (add_combterm_nonmonotonic_types ctxt level sound locality)
1687 fun nonmonotonic_types_for_facts ctxt type_enc sound facts =
1688 let val level = level_of_type_enc type_enc in
1689 if level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types then
1690 [] |> fold (add_fact_nonmonotonic_types ctxt level sound) facts
1691 (* We must add "bool" in case the helper "True_or_False" is added
1692 later. In addition, several places in the code rely on the list of
1693 nonmonotonic types not being empty. *)
1694 |> insert_type ctxt I @{typ bool}
1699 fun decl_line_for_sym ctxt format nonmono_Ts type_enc s
1700 (s', T_args, T, pred_sym, ary, _) =
1702 val (T_arg_Ts, level) =
1704 Simple_Types (_, level) => ([], level)
1705 | _ => (replicate (length T_args) homo_infinite_type, No_Types)
1707 Decl (sym_decl_prefix ^ s, (s, s'),
1708 (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
1709 |> ho_type_from_typ format type_enc pred_sym (length T_arg_Ts + ary))
1712 fun formula_line_for_preds_sym_decl ctxt format conj_sym_kind nonmono_Ts
1713 poly_nonmono_Ts type_enc n s j (s', T_args, T, _, ary, in_conj) =
1715 val (kind, maybe_negate) =
1716 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1718 val (arg_Ts, res_T) = chop_fun ary T
1719 val num_args = length arg_Ts
1721 1 upto num_args |> map (`I o make_bound_var o string_of_int)
1723 bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
1724 val sym_needs_arg_types = n > 1 orelse exists (curry (op =) dummyT) T_args
1725 fun should_keep_arg_type T =
1726 sym_needs_arg_types orelse
1727 not (should_predicate_on_type ctxt nonmono_Ts type_enc (K false) T)
1729 arg_Ts |> map (fn T => if should_keep_arg_type T then SOME T else NONE)
1731 Formula (preds_sym_formula_prefix ^ s ^
1732 (if n > 1 then "_" ^ string_of_int j else ""), kind,
1733 CombConst ((s, s'), T, T_args)
1734 |> fold (curry (CombApp o swap)) bounds
1735 |> type_pred_combterm ctxt format type_enc res_T
1736 |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
1737 |> formula_from_combformula ctxt format poly_nonmono_Ts type_enc
1738 (K (K (K (K true)))) (SOME true)
1739 |> n > 1 ? bound_tvars type_enc (atyps_of T)
1740 |> close_formula_universally
1745 fun formula_lines_for_lightweight_tags_sym_decl ctxt format conj_sym_kind
1746 poly_nonmono_Ts type_enc n s
1747 (j, (s', T_args, T, pred_sym, ary, in_conj)) =
1750 lightweight_tags_sym_formula_prefix ^ s ^
1751 (if n > 1 then "_" ^ string_of_int j else "")
1752 val (kind, maybe_negate) =
1753 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1755 val (arg_Ts, res_T) = chop_fun ary T
1757 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
1758 val bounds = bound_names |> map (fn name => ATerm (name, []))
1759 val cst = mk_aterm format type_enc (s, s') T_args
1760 val atomic_Ts = atyps_of T
1762 (if pred_sym then AConn (AIff, map AAtom tms)
1763 else AAtom (ATerm (`I tptp_equal, tms)))
1764 |> bound_tvars type_enc atomic_Ts
1765 |> close_formula_universally
1767 (* See also "should_tag_with_type". *)
1768 fun should_encode T =
1769 should_encode_type ctxt poly_nonmono_Ts All_Types T orelse
1771 Tags (Polymorphic, level, Lightweight) =>
1772 level <> All_Types andalso Monomorph.typ_has_tvars T
1774 val tag_with = tag_with_type ctxt format poly_nonmono_Ts type_enc NONE
1775 val add_formula_for_res =
1776 if should_encode res_T then
1777 cons (Formula (ident_base ^ "_res", kind,
1778 eq [tag_with res_T (cst bounds), cst bounds],
1782 fun add_formula_for_arg k =
1783 let val arg_T = nth arg_Ts k in
1784 if should_encode arg_T then
1785 case chop k bounds of
1786 (bounds1, bound :: bounds2) =>
1787 cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
1788 eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
1791 | _ => raise Fail "expected nonempty tail"
1796 [] |> not pred_sym ? add_formula_for_res
1797 |> fold add_formula_for_arg (ary - 1 downto 0)
1800 fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
1802 fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts
1803 poly_nonmono_Ts type_enc (s, decls) =
1806 decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_enc s)
1811 decl :: (decls' as _ :: _) =>
1812 let val T = result_type_of_decl decl in
1813 if forall (curry (type_instance ctxt o swap) T
1814 o result_type_of_decl) decls' then
1820 val n = length decls
1822 decls |> filter (should_predicate_on_type ctxt poly_nonmono_Ts type_enc
1824 o result_type_of_decl)
1826 (0 upto length decls - 1, decls)
1827 |-> map2 (formula_line_for_preds_sym_decl ctxt format conj_sym_kind
1828 nonmono_Ts poly_nonmono_Ts type_enc n s)
1830 | Tags (_, _, heaviness) =>
1834 let val n = length decls in
1835 (0 upto n - 1 ~~ decls)
1836 |> maps (formula_lines_for_lightweight_tags_sym_decl ctxt format
1837 conj_sym_kind poly_nonmono_Ts type_enc n s)
1840 fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1841 poly_nonmono_Ts type_enc sym_decl_tab =
1846 |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
1847 nonmono_Ts poly_nonmono_Ts type_enc)
1849 fun needs_type_tag_idempotence (Tags (poly, level, heaviness)) =
1850 poly <> Mangled_Monomorphic andalso
1851 ((level = All_Types andalso heaviness = Lightweight) orelse
1852 level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types)
1853 | needs_type_tag_idempotence _ = false
1855 fun offset_of_heading_in_problem _ [] j = j
1856 | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
1857 if heading = needle then j
1858 else offset_of_heading_in_problem needle problem (j + length lines)
1860 val implicit_declsN = "Should-be-implicit typings"
1861 val explicit_declsN = "Explicit typings"
1862 val factsN = "Relevant facts"
1863 val class_relsN = "Class relationships"
1864 val aritiesN = "Arities"
1865 val helpersN = "Helper facts"
1866 val conjsN = "Conjectures"
1867 val free_typesN = "Type variables"
1869 val explicit_apply = NONE (* for experimental purposes *)
1871 fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_enc sound
1872 exporter readable_names preproc hyp_ts concl_t facts =
1874 val (format, type_enc) = choose_format [format] type_enc
1875 val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
1876 translate_formulas ctxt format prem_kind type_enc preproc hyp_ts concl_t
1878 val sym_tab = conjs @ facts |> sym_table_for_facts ctxt explicit_apply
1880 conjs @ facts |> nonmonotonic_types_for_facts ctxt type_enc sound
1881 val repair = repair_fact ctxt format type_enc sym_tab
1882 val (conjs, facts) = (conjs, facts) |> pairself (map repair)
1883 val repaired_sym_tab =
1884 conjs @ facts |> sym_table_for_facts ctxt (SOME false)
1886 repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_enc
1888 val poly_nonmono_Ts =
1889 if null nonmono_Ts orelse nonmono_Ts = [@{typ bool}] orelse
1890 polymorphism_of_type_enc type_enc <> Polymorphic then
1893 [TVar (("'a", 0), HOLogic.typeS)]
1894 val sym_decl_lines =
1895 (conjs, helpers @ facts)
1896 |> sym_decl_table_for_facts ctxt type_enc repaired_sym_tab
1897 |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1898 poly_nonmono_Ts type_enc
1900 0 upto length helpers - 1 ~~ helpers
1901 |> map (formula_line_for_fact ctxt format helper_prefix I false true
1902 poly_nonmono_Ts type_enc)
1903 |> (if needs_type_tag_idempotence type_enc then
1904 cons (type_tag_idempotence_fact ())
1907 (* Reordering these might confuse the proof reconstruction code or the SPASS
1910 [(explicit_declsN, sym_decl_lines),
1912 map (formula_line_for_fact ctxt format fact_prefix ascii_of
1913 (not exporter) (not exporter) nonmono_Ts
1915 (0 upto length facts - 1 ~~ facts)),
1916 (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
1917 (aritiesN, map formula_line_for_arity_clause arity_clauses),
1918 (helpersN, helper_lines),
1920 map (formula_line_for_conjecture ctxt format nonmono_Ts type_enc)
1922 (free_typesN, formula_lines_for_free_types type_enc (facts @ conjs))]
1926 CNF => ensure_cnf_problem
1927 | CNF_UEQ => filter_cnf_ueq_problem
1929 |> (if is_format_typed format then
1930 declare_undeclared_syms_in_atp_problem type_decl_prefix
1934 val (problem, pool) = problem |> nice_atp_problem readable_names
1935 val helpers_offset = offset_of_heading_in_problem helpersN problem 0
1937 map_filter (fn (j, {name, ...}) =>
1938 if String.isSuffix typed_helper_suffix name then SOME j
1940 ((helpers_offset + 1 upto helpers_offset + length helpers)
1942 fun add_sym_arity (s, {min_ary, ...} : sym_info) =
1944 case strip_prefix_and_unascii const_prefix s of
1945 SOME s => Symtab.insert (op =) (s, min_ary)
1951 case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
1952 offset_of_heading_in_problem conjsN problem 0,
1953 offset_of_heading_in_problem factsN problem 0,
1954 fact_names |> Vector.fromList,
1956 Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
1960 val conj_weight = 0.0
1961 val hyp_weight = 0.1
1962 val fact_min_weight = 0.2
1963 val fact_max_weight = 1.0
1964 val type_info_default_weight = 0.8
1966 fun add_term_weights weight (ATerm (s, tms)) =
1967 is_tptp_user_symbol s ? Symtab.default (s, weight)
1968 #> fold (add_term_weights weight) tms
1969 | add_term_weights weight (AAbs (_, tm)) = add_term_weights weight tm
1970 fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
1971 formula_fold NONE (K (add_term_weights weight)) phi
1972 | add_problem_line_weights _ _ = I
1974 fun add_conjectures_weights [] = I
1975 | add_conjectures_weights conjs =
1976 let val (hyps, conj) = split_last conjs in
1977 add_problem_line_weights conj_weight conj
1978 #> fold (add_problem_line_weights hyp_weight) hyps
1981 fun add_facts_weights facts =
1983 val num_facts = length facts
1985 fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
1986 / Real.fromInt num_facts
1988 map weight_of (0 upto num_facts - 1) ~~ facts
1989 |> fold (uncurry add_problem_line_weights)
1992 (* Weights are from 0.0 (most important) to 1.0 (least important). *)
1993 fun atp_problem_weights problem =
1994 let val get = these o AList.lookup (op =) problem in
1996 |> add_conjectures_weights (get free_typesN @ get conjsN)
1997 |> add_facts_weights (get factsN)
1998 |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
1999 [explicit_declsN, class_relsN, aritiesN]
2001 |> sort (prod_ord Real.compare string_ord o pairself swap)