move lambda translation option from ATP to Sledgehammer, to avoid accidentally breaking Metis (its reconstruction code can only deal with combinators)
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 concealed_lambdasN : string
35 val lambda_liftingN : string
36 val combinatorsN : string
39 val bound_var_prefix : string
40 val schematic_var_prefix : string
41 val fixed_var_prefix : string
42 val tvar_prefix : string
43 val tfree_prefix : string
44 val const_prefix : string
45 val type_const_prefix : string
46 val class_prefix : string
47 val skolem_const_prefix : string
48 val old_skolem_const_prefix : string
49 val new_skolem_const_prefix : string
50 val type_decl_prefix : string
51 val sym_decl_prefix : string
52 val preds_sym_formula_prefix : string
53 val lightweight_tags_sym_formula_prefix : string
54 val fact_prefix : string
55 val conjecture_prefix : string
56 val helper_prefix : string
57 val class_rel_clause_prefix : string
58 val arity_clause_prefix : string
59 val tfree_clause_prefix : string
60 val typed_helper_suffix : string
61 val untyped_helper_suffix : string
62 val type_tag_idempotence_helper_name : string
63 val predicator_name : string
64 val app_op_name : string
65 val type_tag_name : string
66 val type_pred_name : string
67 val simple_type_prefix : string
68 val prefixed_predicator_name : string
69 val prefixed_app_op_name : string
70 val prefixed_type_tag_name : string
71 val ascii_of : string -> string
72 val unascii_of : string -> string
73 val strip_prefix_and_unascii : string -> string -> string option
74 val proxy_table : (string * (string * (thm * (string * string)))) list
75 val proxify_const : string -> (string * string) option
76 val invert_const : string -> string
77 val unproxify_const : string -> string
78 val new_skolem_var_name_from_const : string -> string
79 val num_type_args : theory -> string -> int
80 val atp_irrelevant_consts : string list
81 val atp_schematic_consts_of : term -> typ list Symtab.table
82 val is_locality_global : locality -> bool
83 val type_enc_from_string : string -> type_enc
84 val is_type_enc_higher_order : type_enc -> bool
85 val polymorphism_of_type_enc : type_enc -> polymorphism
86 val level_of_type_enc : type_enc -> type_level
87 val is_type_enc_virtually_sound : type_enc -> bool
88 val is_type_enc_fairly_sound : type_enc -> bool
89 val choose_format : format list -> type_enc -> format * type_enc
91 connective -> ('a, 'b, 'c) formula list -> ('a, 'b, 'c) formula
92 val unmangled_const : string -> string * (string, 'b) ho_term list
93 val unmangled_const_name : string -> string
94 val helper_table : ((string * bool) * thm list) list
96 val prepare_atp_problem :
97 Proof.context -> format -> formula_kind -> formula_kind -> type_enc -> bool
98 -> bool -> string -> bool -> bool -> term list -> term
99 -> ((string * locality) * term) list
100 -> string problem * string Symtab.table * int * int
101 * (string * locality) list vector * int list * int Symtab.table
102 val atp_problem_weights : string problem -> (string * real) list
105 structure ATP_Translate : ATP_TRANSLATE =
111 type name = string * string
113 val concealed_lambdasN = "concealed_lambdas"
114 val lambda_liftingN = "lambda_lifting"
115 val combinatorsN = "combinators"
116 val lambdasN = "lambdas"
119 val generate_info = false (* experimental *)
121 fun isabelle_info s =
122 if generate_info then SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
129 val bound_var_prefix = "B_"
130 val schematic_var_prefix = "V_"
131 val fixed_var_prefix = "v_"
133 val tvar_prefix = "T_"
134 val tfree_prefix = "t_"
136 val const_prefix = "c_"
137 val type_const_prefix = "tc_"
138 val class_prefix = "cl_"
140 val skolem_const_prefix = "Sledgehammer" ^ Long_Name.separator ^ "Sko"
141 val old_skolem_const_prefix = skolem_const_prefix ^ "o"
142 val new_skolem_const_prefix = skolem_const_prefix ^ "n"
144 val type_decl_prefix = "ty_"
145 val sym_decl_prefix = "sy_"
146 val preds_sym_formula_prefix = "psy_"
147 val lightweight_tags_sym_formula_prefix = "tsy_"
148 val fact_prefix = "fact_"
149 val conjecture_prefix = "conj_"
150 val helper_prefix = "help_"
151 val class_rel_clause_prefix = "clar_"
152 val arity_clause_prefix = "arity_"
153 val tfree_clause_prefix = "tfree_"
155 val typed_helper_suffix = "_T"
156 val untyped_helper_suffix = "_U"
157 val type_tag_idempotence_helper_name = helper_prefix ^ "ti_idem"
159 val predicator_name = "hBOOL"
160 val app_op_name = "hAPP"
161 val type_tag_name = "ti"
162 val type_pred_name = "is"
163 val simple_type_prefix = "ty_"
165 val prefixed_predicator_name = const_prefix ^ predicator_name
166 val prefixed_app_op_name = const_prefix ^ app_op_name
167 val prefixed_type_tag_name = const_prefix ^ type_tag_name
169 (* Freshness almost guaranteed! *)
170 val sledgehammer_weak_prefix = "Sledgehammer:"
172 val concealed_lambda_prefix = sledgehammer_weak_prefix ^ "lambda_"
174 (*Escaping of special characters.
175 Alphanumeric characters are left unchanged.
176 The character _ goes to __
177 Characters in the range ASCII space to / go to _A to _P, respectively.
178 Other characters go to _nnn where nnn is the decimal ASCII code.*)
179 val upper_a_minus_space = Char.ord #"A" - Char.ord #" "
181 fun stringN_of_int 0 _ = ""
182 | stringN_of_int k n =
183 stringN_of_int (k - 1) (n div 10) ^ string_of_int (n mod 10)
185 fun ascii_of_char c =
186 if Char.isAlphaNum c then
188 else if c = #"_" then
190 else if #" " <= c andalso c <= #"/" then
191 "_" ^ String.str (Char.chr (Char.ord c + upper_a_minus_space))
193 (* fixed width, in case more digits follow *)
194 "_" ^ stringN_of_int 3 (Char.ord c)
196 val ascii_of = String.translate ascii_of_char
198 (** Remove ASCII armoring from names in proof files **)
200 (* We don't raise error exceptions because this code can run inside a worker
201 thread. Also, the errors are impossible. *)
204 fun un rcs [] = String.implode(rev rcs)
205 | un rcs [#"_"] = un (#"_" :: rcs) [] (* ERROR *)
206 (* Three types of _ escapes: __, _A to _P, _nnn *)
207 | un rcs (#"_" :: #"_" :: cs) = un (#"_" :: rcs) cs
208 | un rcs (#"_" :: c :: cs) =
209 if #"A" <= c andalso c<= #"P" then
210 (* translation of #" " to #"/" *)
211 un (Char.chr (Char.ord c - upper_a_minus_space) :: rcs) cs
213 let val digits = List.take (c :: cs, 3) handle General.Subscript => [] in
214 case Int.fromString (String.implode digits) of
215 SOME n => un (Char.chr n :: rcs) (List.drop (cs, 2))
216 | NONE => un (c :: #"_" :: rcs) cs (* ERROR *)
218 | un rcs (c :: cs) = un (c :: rcs) cs
219 in un [] o String.explode end
221 (* If string s has the prefix s1, return the result of deleting it,
223 fun strip_prefix_and_unascii s1 s =
224 if String.isPrefix s1 s then
225 SOME (unascii_of (String.extract (s, size s1, NONE)))
230 [("c_False", (@{const_name False}, (@{thm fFalse_def},
231 ("fFalse", @{const_name ATP.fFalse})))),
232 ("c_True", (@{const_name True}, (@{thm fTrue_def},
233 ("fTrue", @{const_name ATP.fTrue})))),
234 ("c_Not", (@{const_name Not}, (@{thm fNot_def},
235 ("fNot", @{const_name ATP.fNot})))),
236 ("c_conj", (@{const_name conj}, (@{thm fconj_def},
237 ("fconj", @{const_name ATP.fconj})))),
238 ("c_disj", (@{const_name disj}, (@{thm fdisj_def},
239 ("fdisj", @{const_name ATP.fdisj})))),
240 ("c_implies", (@{const_name implies}, (@{thm fimplies_def},
241 ("fimplies", @{const_name ATP.fimplies})))),
242 ("equal", (@{const_name HOL.eq}, (@{thm fequal_def},
243 ("fequal", @{const_name ATP.fequal})))),
244 ("c_All", (@{const_name All}, (@{thm fAll_def},
245 ("fAll", @{const_name ATP.fAll})))),
246 ("c_Ex", (@{const_name Ex}, (@{thm fEx_def},
247 ("fEx", @{const_name ATP.fEx}))))]
249 val proxify_const = AList.lookup (op =) proxy_table #> Option.map (snd o snd)
251 (* Readable names for the more common symbolic functions. Do not mess with the
252 table unless you know what you are doing. *)
253 val const_trans_table =
254 [(@{type_name Product_Type.prod}, "prod"),
255 (@{type_name Sum_Type.sum}, "sum"),
256 (@{const_name False}, "False"),
257 (@{const_name True}, "True"),
258 (@{const_name Not}, "Not"),
259 (@{const_name conj}, "conj"),
260 (@{const_name disj}, "disj"),
261 (@{const_name implies}, "implies"),
262 (@{const_name HOL.eq}, "equal"),
263 (@{const_name All}, "All"),
264 (@{const_name Ex}, "Ex"),
265 (@{const_name If}, "If"),
266 (@{const_name Set.member}, "member"),
267 (@{const_name Meson.COMBI}, "COMBI"),
268 (@{const_name Meson.COMBK}, "COMBK"),
269 (@{const_name Meson.COMBB}, "COMBB"),
270 (@{const_name Meson.COMBC}, "COMBC"),
271 (@{const_name Meson.COMBS}, "COMBS")]
273 |> fold (Symtab.update o swap o snd o snd o snd) proxy_table
275 (* Invert the table of translations between Isabelle and ATPs. *)
276 val const_trans_table_inv =
277 const_trans_table |> Symtab.dest |> map swap |> Symtab.make
278 val const_trans_table_unprox =
280 |> fold (fn (_, (isa, (_, (_, atp)))) => Symtab.update (atp, isa)) proxy_table
282 val invert_const = perhaps (Symtab.lookup const_trans_table_inv)
283 val unproxify_const = perhaps (Symtab.lookup const_trans_table_unprox)
286 case Symtab.lookup const_trans_table c of
290 fun ascii_of_indexname (v, 0) = ascii_of v
291 | ascii_of_indexname (v, i) = ascii_of v ^ "_" ^ string_of_int i
293 fun make_bound_var x = bound_var_prefix ^ ascii_of x
294 fun make_schematic_var v = schematic_var_prefix ^ ascii_of_indexname v
295 fun make_fixed_var x = fixed_var_prefix ^ ascii_of x
297 fun make_schematic_type_var (x, i) =
298 tvar_prefix ^ (ascii_of_indexname (unprefix "'" x, i))
299 fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (unprefix "'" x))
301 (* "HOL.eq" is mapped to the ATP's equality. *)
302 fun make_fixed_const @{const_name HOL.eq} = tptp_old_equal
303 | make_fixed_const c = const_prefix ^ lookup_const c
305 fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
307 fun make_type_class clas = class_prefix ^ ascii_of clas
309 fun new_skolem_var_name_from_const s =
310 let val ss = s |> space_explode Long_Name.separator in
311 nth ss (length ss - 2)
314 (* The number of type arguments of a constant, zero if it's monomorphic. For
315 (instances of) Skolem pseudoconstants, this information is encoded in the
317 fun num_type_args thy s =
318 if String.isPrefix skolem_const_prefix s then
319 s |> space_explode Long_Name.separator |> List.last |> Int.fromString |> the
321 (s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
323 (* These are either simplified away by "Meson.presimplify" (most of the time) or
324 handled specially via "fFalse", "fTrue", ..., "fequal". *)
325 val atp_irrelevant_consts =
326 [@{const_name False}, @{const_name True}, @{const_name Not},
327 @{const_name conj}, @{const_name disj}, @{const_name implies},
328 @{const_name HOL.eq}, @{const_name If}, @{const_name Let}]
330 val atp_monomorph_bad_consts =
331 atp_irrelevant_consts @
332 (* These are ignored anyway by the relevance filter (unless they appear in
333 higher-order places) but not by the monomorphizer. *)
334 [@{const_name all}, @{const_name "==>"}, @{const_name "=="},
335 @{const_name Trueprop}, @{const_name All}, @{const_name Ex},
336 @{const_name Ex1}, @{const_name Ball}, @{const_name Bex}]
338 fun add_schematic_const (x as (_, T)) =
339 Monomorph.typ_has_tvars T ? Symtab.insert_list (op =) x
340 val add_schematic_consts_of =
341 Term.fold_aterms (fn Const (x as (s, _)) =>
342 not (member (op =) atp_monomorph_bad_consts s)
343 ? add_schematic_const x
345 fun atp_schematic_consts_of t = add_schematic_consts_of t Symtab.empty
347 (** Definitions and functions for FOL clauses and formulas for TPTP **)
349 (* The first component is the type class; the second is a "TVar" or "TFree". *)
350 datatype type_literal =
351 TyLitVar of name * name |
352 TyLitFree of name * name
355 (** Isabelle arities **)
357 datatype arity_literal =
358 TConsLit of name * name * name list |
359 TVarLit of name * name
362 | gen_TVars n = ("T_" ^ string_of_int n) :: gen_TVars (n-1)
364 val type_class = the_single @{sort type}
366 fun add_packed_sort tvar =
367 fold (fn s => s <> type_class ? cons (`make_type_class s, `I tvar))
371 prem_lits : arity_literal list,
372 concl_lits : arity_literal}
374 (* Arity of type constructor "tcon :: (arg1, ..., argN) res" *)
375 fun make_axiom_arity_clause (tcons, name, (cls, args)) =
377 val tvars = gen_TVars (length args)
378 val tvars_srts = ListPair.zip (tvars, args)
381 prem_lits = [] |> fold (uncurry add_packed_sort) tvars_srts |> map TVarLit,
382 concl_lits = TConsLit (`make_type_class cls,
383 `make_fixed_type_const tcons,
387 fun arity_clause _ _ (_, []) = []
388 | arity_clause seen n (tcons, ("HOL.type", _) :: ars) = (* ignore *)
389 arity_clause seen n (tcons, ars)
390 | arity_clause seen n (tcons, (ar as (class, _)) :: ars) =
391 if member (op =) seen class then
392 (* multiple arities for the same (tycon, class) pair *)
393 make_axiom_arity_clause (tcons,
394 lookup_const tcons ^ "___" ^ ascii_of class ^ "_" ^ string_of_int n,
396 arity_clause seen (n + 1) (tcons, ars)
398 make_axiom_arity_clause (tcons, lookup_const tcons ^ "___" ^
399 ascii_of class, ar) ::
400 arity_clause (class :: seen) n (tcons, ars)
402 fun multi_arity_clause [] = []
403 | multi_arity_clause ((tcons, ars) :: tc_arlists) =
404 arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
406 (* Generate all pairs (tycon, class, sorts) such that tycon belongs to class in
407 theory thy provided its arguments have the corresponding sorts. *)
408 fun type_class_pairs thy tycons classes =
410 val alg = Sign.classes_of thy
411 fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
412 fun add_class tycon class =
413 cons (class, domain_sorts tycon class)
414 handle Sorts.CLASS_ERROR _ => I
415 fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
416 in map try_classes tycons end
418 (*Proving one (tycon, class) membership may require proving others, so iterate.*)
419 fun iter_type_class_pairs _ _ [] = ([], [])
420 | iter_type_class_pairs thy tycons classes =
422 fun maybe_insert_class s =
423 (s <> type_class andalso not (member (op =) classes s))
425 val cpairs = type_class_pairs thy tycons classes
427 [] |> fold (fold (fold (fold maybe_insert_class) o snd) o snd) cpairs
428 val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
429 in (classes' @ classes, union (op =) cpairs' cpairs) end
431 fun make_arity_clauses thy tycons =
432 iter_type_class_pairs thy tycons ##> multi_arity_clause
435 (** Isabelle class relations **)
437 type class_rel_clause =
442 (* Generate all pairs (sub, super) such that sub is a proper subclass of super
444 fun class_pairs _ [] _ = []
445 | class_pairs thy subs supers =
447 val class_less = Sorts.class_less (Sign.classes_of thy)
448 fun add_super sub super = class_less (sub, super) ? cons (sub, super)
449 fun add_supers sub = fold (add_super sub) supers
450 in fold add_supers subs [] end
452 fun make_class_rel_clause (sub, super) =
453 {name = sub ^ "_" ^ super, subclass = `make_type_class sub,
454 superclass = `make_type_class super}
456 fun make_class_rel_clauses thy subs supers =
457 map make_class_rel_clause (class_pairs thy subs supers)
460 CombConst of name * typ * typ list |
461 CombVar of name * typ |
462 CombApp of combterm * combterm |
463 CombAbs of (name * typ) * combterm
465 fun combtyp_of (CombConst (_, T, _)) = T
466 | combtyp_of (CombVar (_, T)) = T
467 | combtyp_of (CombApp (t1, _)) = snd (dest_funT (combtyp_of t1))
468 | combtyp_of (CombAbs ((_, T), tm)) = T --> combtyp_of tm
470 (*gets the head of a combinator application, along with the list of arguments*)
471 fun strip_combterm_comb u =
473 fun stripc (CombApp (t, u), ts) = stripc (t, u :: ts)
475 in stripc (u, []) end
477 fun atyps_of T = fold_atyps (insert (op =)) T []
479 fun new_skolem_const_name s num_T_args =
480 [new_skolem_const_prefix, s, string_of_int num_T_args]
481 |> space_implode Long_Name.separator
483 (* Converts a term (with combinators) into a combterm. Also accumulates sort
485 fun combterm_from_term thy bs (P $ Q) =
487 val (P', P_atomics_Ts) = combterm_from_term thy bs P
488 val (Q', Q_atomics_Ts) = combterm_from_term thy bs Q
489 in (CombApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
490 | combterm_from_term thy _ (Const (c, T)) =
493 (if String.isPrefix old_skolem_const_prefix c then
494 [] |> Term.add_tvarsT T |> map TVar
496 (c, T) |> Sign.const_typargs thy)
497 val c' = CombConst (`make_fixed_const c, T, tvar_list)
498 in (c', atyps_of T) end
499 | combterm_from_term _ _ (Free (v, T)) =
500 (CombConst (`make_fixed_var v, T, []), atyps_of T)
501 | combterm_from_term _ _ (Var (v as (s, _), T)) =
502 (if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
504 val Ts = T |> strip_type |> swap |> op ::
505 val s' = new_skolem_const_name s (length Ts)
506 in CombConst (`make_fixed_const s', T, Ts) end
508 CombVar ((make_schematic_var v, s), T), atyps_of T)
509 | combterm_from_term _ bs (Bound j) =
511 |> (fn (s, T) => (CombConst (`make_bound_var s, T, []), atyps_of T))
512 | combterm_from_term thy bs (Abs (s, T, t)) =
514 fun vary s = s |> AList.defined (op =) bs s ? vary o Symbol.bump_string
516 val (tm, atomic_Ts) = combterm_from_term thy ((s, T) :: bs) t
518 (CombAbs ((`make_bound_var s, T), tm),
519 union (op =) atomic_Ts (atyps_of T))
523 General | Helper | Extensionality | Intro | Elim | Simp | Local | Assum |
526 (* (quasi-)underapproximation of the truth *)
527 fun is_locality_global Local = false
528 | is_locality_global Assum = false
529 | is_locality_global Chained = false
530 | is_locality_global _ = true
532 datatype order = First_Order | Higher_Order
533 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
534 datatype type_level =
535 All_Types | Noninf_Nonmono_Types | Fin_Nonmono_Types | Const_Arg_Types |
537 datatype type_heaviness = Heavyweight | Lightweight
540 Simple_Types of order * type_level |
541 Preds of polymorphism * type_level * type_heaviness |
542 Tags of polymorphism * type_level * type_heaviness
544 fun try_unsuffixes ss s =
545 fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
547 fun type_enc_from_string s =
548 (case try (unprefix "poly_") s of
549 SOME s => (SOME Polymorphic, s)
551 case try (unprefix "mono_") s of
552 SOME s => (SOME Monomorphic, s)
554 case try (unprefix "mangled_") s of
555 SOME s => (SOME Mangled_Monomorphic, s)
558 (* "_query" and "_bang" are for the ASCII-challenged Metis and
560 case try_unsuffixes ["?", "_query"] s of
561 SOME s => (Noninf_Nonmono_Types, s)
563 case try_unsuffixes ["!", "_bang"] s of
564 SOME s => (Fin_Nonmono_Types, s)
565 | NONE => (All_Types, s))
567 case try (unsuffix "_heavy") s of
568 SOME s => (Heavyweight, s)
569 | NONE => (Lightweight, s))
570 |> (fn (poly, (level, (heaviness, core))) =>
571 case (core, (poly, level, heaviness)) of
572 ("simple", (NONE, _, Lightweight)) =>
573 Simple_Types (First_Order, level)
574 | ("simple_higher", (NONE, _, Lightweight)) =>
575 if level = Noninf_Nonmono_Types then raise Same.SAME
576 else Simple_Types (Higher_Order, level)
577 | ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
578 | ("tags", (SOME Polymorphic, _, _)) =>
579 Tags (Polymorphic, level, heaviness)
580 | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
581 | ("args", (SOME poly, All_Types (* naja *), Lightweight)) =>
582 Preds (poly, Const_Arg_Types, Lightweight)
583 | ("erased", (NONE, All_Types (* naja *), Lightweight)) =>
584 Preds (Polymorphic, No_Types, Lightweight)
585 | _ => raise Same.SAME)
586 handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
588 fun is_type_enc_higher_order (Simple_Types (Higher_Order, _)) = true
589 | is_type_enc_higher_order _ = false
591 fun polymorphism_of_type_enc (Simple_Types _) = Mangled_Monomorphic
592 | polymorphism_of_type_enc (Preds (poly, _, _)) = poly
593 | polymorphism_of_type_enc (Tags (poly, _, _)) = poly
595 fun level_of_type_enc (Simple_Types (_, level)) = level
596 | level_of_type_enc (Preds (_, level, _)) = level
597 | level_of_type_enc (Tags (_, level, _)) = level
599 fun heaviness_of_type_enc (Simple_Types _) = Heavyweight
600 | heaviness_of_type_enc (Preds (_, _, heaviness)) = heaviness
601 | heaviness_of_type_enc (Tags (_, _, heaviness)) = heaviness
603 fun is_type_level_virtually_sound level =
604 level = All_Types orelse level = Noninf_Nonmono_Types
605 val is_type_enc_virtually_sound =
606 is_type_level_virtually_sound o level_of_type_enc
608 fun is_type_level_fairly_sound level =
609 is_type_level_virtually_sound level orelse level = Fin_Nonmono_Types
610 val is_type_enc_fairly_sound = is_type_level_fairly_sound o level_of_type_enc
612 fun choose_format formats (Simple_Types (order, level)) =
613 if member (op =) formats THF then
614 (THF, Simple_Types (order, level))
615 else if member (op =) formats TFF then
616 (TFF, Simple_Types (First_Order, level))
618 choose_format formats (Preds (Mangled_Monomorphic, level, Heavyweight))
619 | choose_format formats type_enc =
622 (CNF_UEQ, case type_enc of
624 (if is_type_enc_fairly_sound type_enc then Tags else Preds)
627 | format => (format, type_enc))
629 type translated_formula =
633 combformula : (name, typ, combterm) formula,
634 atomic_types : typ list}
636 fun update_combformula f ({name, locality, kind, combformula, atomic_types}
637 : translated_formula) =
638 {name = name, locality = locality, kind = kind, combformula = f combformula,
639 atomic_types = atomic_types} : translated_formula
641 fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
643 val type_instance = Sign.typ_instance o Proof_Context.theory_of
645 fun insert_type ctxt get_T x xs =
646 let val T = get_T x in
647 if exists (curry (type_instance ctxt) T o get_T) xs then xs
648 else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
651 (* The Booleans indicate whether all type arguments should be kept. *)
652 datatype type_arg_policy =
653 Explicit_Type_Args of bool |
654 Mangled_Type_Args of bool |
657 fun should_drop_arg_type_args (Simple_Types _) =
658 false (* since TFF doesn't support overloading *)
659 | should_drop_arg_type_args type_enc =
660 level_of_type_enc type_enc = All_Types andalso
661 heaviness_of_type_enc type_enc = Heavyweight
663 fun type_arg_policy type_enc s =
664 if s = type_tag_name then
665 (if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
668 Explicit_Type_Args) false
669 else case type_enc of
670 Tags (_, All_Types, Heavyweight) => No_Type_Args
672 if level_of_type_enc type_enc = No_Types orelse
673 s = @{const_name HOL.eq} orelse
674 (s = app_op_name andalso
675 level_of_type_enc type_enc = Const_Arg_Types) then
678 should_drop_arg_type_args type_enc
679 |> (if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
684 (* Make literals for sorted type variables. *)
685 fun generic_add_sorts_on_type (_, []) = I
686 | generic_add_sorts_on_type ((x, i), s :: ss) =
687 generic_add_sorts_on_type ((x, i), ss)
688 #> (if s = the_single @{sort HOL.type} then
691 insert (op =) (TyLitFree (`make_type_class s, `make_fixed_type_var x))
693 insert (op =) (TyLitVar (`make_type_class s,
694 (make_schematic_type_var (x, i), x))))
695 fun add_sorts_on_tfree (TFree (s, S)) = generic_add_sorts_on_type ((s, ~1), S)
696 | add_sorts_on_tfree _ = I
697 fun add_sorts_on_tvar (TVar z) = generic_add_sorts_on_type z
698 | add_sorts_on_tvar _ = I
700 fun type_literals_for_types type_enc add_sorts_on_typ Ts =
701 [] |> level_of_type_enc type_enc <> No_Types ? fold add_sorts_on_typ Ts
703 fun mk_aconns c phis =
704 let val (phis', phi') = split_last phis in
705 fold_rev (mk_aconn c) phis' phi'
707 fun mk_ahorn [] phi = phi
708 | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
709 fun mk_aquant _ [] phi = phi
710 | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
711 if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
712 | mk_aquant q xs phi = AQuant (q, xs, phi)
714 fun close_universally atom_vars phi =
716 fun formula_vars bounds (AQuant (_, xs, phi)) =
717 formula_vars (map fst xs @ bounds) phi
718 | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
719 | formula_vars bounds (AAtom tm) =
720 union (op =) (atom_vars tm []
721 |> filter_out (member (op =) bounds o fst))
722 in mk_aquant AForall (formula_vars [] phi []) phi end
724 fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
725 | combterm_vars (CombConst _) = I
726 | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
727 | combterm_vars (CombAbs (_, tm)) = combterm_vars tm
728 fun close_combformula_universally phi = close_universally combterm_vars phi
730 fun term_vars bounds (ATerm (name as (s, _), tms)) =
731 (is_tptp_variable s andalso not (member (op =) bounds name))
732 ? insert (op =) (name, NONE) #> fold (term_vars bounds) tms
733 | term_vars bounds (AAbs ((name, _), tm)) = term_vars (name :: bounds) tm
734 fun close_formula_universally phi = close_universally (term_vars []) phi
736 val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
737 val homo_infinite_type = Type (homo_infinite_type_name, [])
739 fun ho_term_from_typ format type_enc =
741 fun term (Type (s, Ts)) =
742 ATerm (case (is_type_enc_higher_order type_enc, s) of
743 (true, @{type_name bool}) => `I tptp_bool_type
744 | (true, @{type_name fun}) => `I tptp_fun_type
745 | _ => if s = homo_infinite_type_name andalso
746 (format = TFF orelse format = THF) then
747 `I tptp_individual_type
749 `make_fixed_type_const s,
751 | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
752 | term (TVar ((x as (s, _)), _)) =
753 ATerm ((make_schematic_type_var x, s), [])
756 fun ho_term_for_type_arg format type_enc T =
757 if T = dummyT then NONE else SOME (ho_term_from_typ format type_enc T)
759 (* This shouldn't clash with anything else. *)
760 val mangled_type_sep = "\000"
762 fun generic_mangled_type_name f (ATerm (name, [])) = f name
763 | generic_mangled_type_name f (ATerm (name, tys)) =
764 f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
766 | generic_mangled_type_name _ _ = raise Fail "unexpected type abstraction"
768 val bool_atype = AType (`I tptp_bool_type)
770 fun make_simple_type s =
771 if s = tptp_bool_type orelse s = tptp_fun_type orelse
772 s = tptp_individual_type then
775 simple_type_prefix ^ ascii_of s
777 fun ho_type_from_ho_term type_enc pred_sym ary =
780 AType ((make_simple_type (generic_mangled_type_name fst ty),
781 generic_mangled_type_name snd ty))
782 fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
783 fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
784 | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
785 | to_fo _ _ = raise Fail "unexpected type abstraction"
786 fun to_ho (ty as ATerm ((s, _), tys)) =
787 if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
788 | to_ho _ = raise Fail "unexpected type abstraction"
789 in if is_type_enc_higher_order type_enc then to_ho else to_fo ary end
791 fun ho_type_from_typ format type_enc pred_sym ary =
792 ho_type_from_ho_term type_enc pred_sym ary
793 o ho_term_from_typ format type_enc
795 fun mangled_const_name format type_enc T_args (s, s') =
797 val ty_args = T_args |> map_filter (ho_term_for_type_arg format type_enc)
798 fun type_suffix f g =
799 fold_rev (curry (op ^) o g o prefix mangled_type_sep
800 o generic_mangled_type_name f) ty_args ""
801 in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
803 val parse_mangled_ident =
804 Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
806 fun parse_mangled_type x =
808 -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
810 and parse_mangled_types x =
811 (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
813 fun unmangled_type s =
814 s |> suffix ")" |> raw_explode
815 |> Scan.finite Symbol.stopper
816 (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
817 quote s)) parse_mangled_type))
820 val unmangled_const_name = space_explode mangled_type_sep #> hd
821 fun unmangled_const s =
822 let val ss = space_explode mangled_type_sep s in
823 (hd ss, map unmangled_type (tl ss))
826 fun introduce_proxies type_enc =
828 fun intro top_level (CombApp (tm1, tm2)) =
829 CombApp (intro top_level tm1, intro false tm2)
830 | intro top_level (CombConst (name as (s, _), T, T_args)) =
831 (case proxify_const s of
833 if top_level orelse is_type_enc_higher_order type_enc then
834 case (top_level, s) of
835 (_, "c_False") => (`I tptp_false, [])
836 | (_, "c_True") => (`I tptp_true, [])
837 | (false, "c_Not") => (`I tptp_not, [])
838 | (false, "c_conj") => (`I tptp_and, [])
839 | (false, "c_disj") => (`I tptp_or, [])
840 | (false, "c_implies") => (`I tptp_implies, [])
841 | (false, "c_All") => (`I tptp_ho_forall, [])
842 | (false, "c_Ex") => (`I tptp_ho_exists, [])
844 if is_tptp_equal s then (`I tptp_equal, [])
845 else (proxy_base |>> prefix const_prefix, T_args)
848 (proxy_base |>> prefix const_prefix, T_args)
849 | NONE => (name, T_args))
850 |> (fn (name, T_args) => CombConst (name, T, T_args))
851 | intro _ (CombAbs (bound, tm)) = CombAbs (bound, intro false tm)
855 fun combformula_from_prop thy type_enc eq_as_iff =
857 fun do_term bs t atomic_types =
858 combterm_from_term thy bs (Envir.eta_contract t)
859 |>> (introduce_proxies type_enc #> AAtom)
860 ||> union (op =) atomic_types
861 fun do_quant bs q s T t' =
862 let val s = singleton (Name.variant_list (map fst bs)) s in
863 do_formula ((s, T) :: bs) t'
864 #>> mk_aquant q [(`make_bound_var s, SOME T)]
866 and do_conn bs c t1 t2 =
867 do_formula bs t1 ##>> do_formula bs t2 #>> uncurry (mk_aconn c)
868 and do_formula bs t =
870 @{const Trueprop} $ t1 => do_formula bs t1
871 | @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
872 | Const (@{const_name All}, _) $ Abs (s, T, t') =>
873 do_quant bs AForall s T t'
874 | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
875 do_quant bs AExists s T t'
876 | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
877 | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
878 | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
879 | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
880 if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
884 fun presimplify_term _ [] t = t
885 | presimplify_term ctxt presimp_consts t =
886 t |> exists_Const (member (op =) presimp_consts o fst) t
887 ? (Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
888 #> Meson.presimplify ctxt
891 fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
892 fun conceal_bounds Ts t =
893 subst_bounds (map (Free o apfst concealed_bound_name)
894 (0 upto length Ts - 1 ~~ Ts), t)
895 fun reveal_bounds Ts =
896 subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
897 (0 upto length Ts - 1 ~~ Ts))
899 fun is_fun_equality (@{const_name HOL.eq},
900 Type (_, [Type (@{type_name fun}, _), _])) = true
901 | is_fun_equality _ = false
903 fun extensionalize_term ctxt t =
904 if exists_Const is_fun_equality t then
905 let val thy = Proof_Context.theory_of ctxt in
906 t |> cterm_of thy |> Meson.extensionalize_conv ctxt
907 |> prop_of |> Logic.dest_equals |> snd
912 fun conceal_lambdas Ts (t1 $ t2) = conceal_lambdas Ts t1 $ conceal_lambdas Ts t2
913 | conceal_lambdas Ts (Abs (_, T, t)) =
914 (* slightly unsound because of hash collisions *)
915 Free (concealed_lambda_prefix ^ string_of_int (hash_term t),
916 T --> fastype_of1 (Ts, t))
917 | conceal_lambdas _ t = t
919 fun process_abstractions_in_term ctxt lambda_trans kind t =
920 let val thy = Proof_Context.theory_of ctxt in
921 if Meson.is_fol_term thy t then
927 @{const Not} $ t1 => @{const Not} $ aux Ts t1
928 | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
929 t0 $ Abs (s, T, aux (T :: Ts) t')
930 | (t0 as Const (@{const_name All}, _)) $ t1 =>
931 aux Ts (t0 $ eta_expand Ts t1 1)
932 | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
933 t0 $ Abs (s, T, aux (T :: Ts) t')
934 | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
935 aux Ts (t0 $ eta_expand Ts t1 1)
936 | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
937 | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
938 | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
939 | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
941 t0 $ aux Ts t1 $ aux Ts t2
943 if not (exists_subterm (fn Abs _ => true | _ => false) t) then
946 let val t = t |> Envir.eta_contract in
947 if lambda_trans = concealed_lambdasN then
948 t |> conceal_lambdas []
949 else if lambda_trans = lambda_liftingN then
950 t (* TODO: implement *)
951 else if lambda_trans = combinatorsN then
952 t |> conceal_bounds Ts
954 |> Meson_Clausify.introduce_combinators_in_cterm
955 |> prop_of |> Logic.dest_equals |> snd
957 else if lambda_trans = lambdasN then
960 error ("Unknown lambda translation method: " ^
961 quote lambda_trans ^ ".")
963 val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
964 in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
966 (* A type variable of sort "{}" will make abstraction fail. *)
967 if kind = Conjecture then HOLogic.false_const
968 else HOLogic.true_const
971 (* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
972 same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
975 fun aux (t $ u) = aux t $ aux u
976 | aux (Abs (s, T, t)) = Abs (s, T, aux t)
977 | aux (Var ((s, i), T)) =
978 Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
980 in t |> exists_subterm is_Var t ? aux end
982 fun preprocess_prop ctxt lambda_trans presimp_consts kind t =
984 val thy = Proof_Context.theory_of ctxt
985 val t = t |> Envir.beta_eta_contract
986 |> transform_elim_prop
987 |> Object_Logic.atomize_term thy
988 val need_trueprop = (fastype_of t = @{typ bool})
990 t |> need_trueprop ? HOLogic.mk_Trueprop
991 |> Raw_Simplifier.rewrite_term thy (Meson.unfold_set_const_simps ctxt) []
992 |> extensionalize_term ctxt
993 |> presimplify_term ctxt presimp_consts
994 |> perhaps (try (HOLogic.dest_Trueprop))
995 |> process_abstractions_in_term ctxt lambda_trans kind
998 (* making fact and conjecture formulas *)
999 fun make_formula thy type_enc eq_as_iff name loc kind t =
1001 val (combformula, atomic_types) =
1002 combformula_from_prop thy type_enc eq_as_iff t []
1004 {name = name, locality = loc, kind = kind, combformula = combformula,
1005 atomic_types = atomic_types}
1008 fun make_fact ctxt format type_enc lambda_trans eq_as_iff preproc presimp_consts
1010 let val thy = Proof_Context.theory_of ctxt in
1011 case t |> preproc ? preprocess_prop ctxt lambda_trans presimp_consts Axiom
1012 |> make_formula thy type_enc (eq_as_iff andalso format <> CNF) name
1014 formula as {combformula = AAtom (CombConst ((s, _), _, _)), ...} =>
1015 if s = tptp_true then NONE else SOME formula
1016 | formula => SOME formula
1019 fun make_conjecture ctxt format prem_kind type_enc lambda_trans preproc
1022 val thy = Proof_Context.theory_of ctxt
1023 val last = length ts - 1
1025 map2 (fn j => fn t =>
1027 val (kind, maybe_negate) =
1032 if prem_kind = Conjecture then update_combformula mk_anot
1036 (preprocess_prop ctxt lambda_trans presimp_consts kind
1038 |> make_formula thy type_enc (format <> CNF) (string_of_int j)
1045 (** Finite and infinite type inference **)
1047 fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
1048 | deep_freeze_atyp T = T
1049 val deep_freeze_type = map_atyps deep_freeze_atyp
1051 (* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
1052 dangerous because their "exhaust" properties can easily lead to unsound ATP
1053 proofs. On the other hand, all HOL infinite types can be given the same
1054 models in first-order logic (via Löwenheim-Skolem). *)
1056 fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
1057 exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
1058 | should_encode_type _ _ All_Types _ = true
1059 | should_encode_type ctxt _ Fin_Nonmono_Types T =
1060 is_type_surely_finite ctxt false T
1061 | should_encode_type _ _ _ _ = false
1063 fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
1064 should_predicate_on_var T =
1065 (heaviness = Heavyweight orelse should_predicate_on_var ()) andalso
1066 should_encode_type ctxt nonmono_Ts level T
1067 | should_predicate_on_type _ _ _ _ _ = false
1069 fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
1070 String.isPrefix bound_var_prefix s
1071 | is_var_or_bound_var (CombVar _) = true
1072 | is_var_or_bound_var _ = false
1075 Top_Level of bool option |
1076 Eq_Arg of bool option |
1079 fun should_tag_with_type _ _ _ (Top_Level _) _ _ = false
1080 | should_tag_with_type ctxt nonmono_Ts (Tags (poly, level, heaviness)) site
1083 Heavyweight => should_encode_type ctxt nonmono_Ts level T
1085 case (site, is_var_or_bound_var u) of
1086 (Eq_Arg pos, true) =>
1087 (* The first disjunct prevents a subtle soundness issue explained in
1088 Blanchette's Ph.D. thesis. See also
1089 "formula_lines_for_lightweight_tags_sym_decl". *)
1090 (pos <> SOME false andalso poly = Polymorphic andalso
1091 level <> All_Types andalso heaviness = Lightweight andalso
1092 exists (fn T' => type_instance ctxt (T', T)) nonmono_Ts) orelse
1093 should_encode_type ctxt nonmono_Ts level T
1095 | should_tag_with_type _ _ _ _ _ _ = false
1097 fun homogenized_type ctxt nonmono_Ts level =
1099 val should_encode = should_encode_type ctxt nonmono_Ts level
1100 fun homo 0 T = if should_encode T then T else homo_infinite_type
1101 | homo ary (Type (@{type_name fun}, [T1, T2])) =
1102 homo 0 T1 --> homo (ary - 1) T2
1103 | homo _ _ = raise Fail "expected function type"
1106 (** "hBOOL" and "hAPP" **)
1109 {pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
1111 fun add_combterm_syms_to_table ctxt explicit_apply =
1113 fun consider_var_arity const_T var_T max_ary =
1116 if ary = max_ary orelse type_instance ctxt (var_T, T) orelse
1117 type_instance ctxt (T, var_T) then
1120 iter (ary + 1) (range_type T)
1121 in iter 0 const_T end
1122 fun add_var_or_bound_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1123 if explicit_apply = NONE andalso
1124 (can dest_funT T orelse T = @{typ bool}) then
1126 val bool_vars' = bool_vars orelse body_type T = @{typ bool}
1127 fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
1128 {pred_sym = pred_sym andalso not bool_vars',
1129 min_ary = fold (fn T' => consider_var_arity T' T) types min_ary,
1130 max_ary = max_ary, types = types}
1132 fun_var_Ts |> can dest_funT T ? insert_type ctxt I T
1134 if bool_vars' = bool_vars andalso
1135 pointer_eq (fun_var_Ts', fun_var_Ts) then
1138 ((bool_vars', fun_var_Ts'), Symtab.map (K repair_min_arity) sym_tab)
1142 fun add top_level tm (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1143 let val (head, args) = strip_combterm_comb tm in
1145 CombConst ((s, _), T, _) =>
1146 if String.isPrefix bound_var_prefix s then
1147 add_var_or_bound_var T accum
1149 let val ary = length args in
1150 ((bool_vars, fun_var_Ts),
1151 case Symtab.lookup sym_tab s of
1152 SOME {pred_sym, min_ary, max_ary, types} =>
1155 pred_sym andalso top_level andalso not bool_vars
1156 val types' = types |> insert_type ctxt I T
1158 if is_some explicit_apply orelse
1159 pointer_eq (types', types) then
1162 fold (consider_var_arity T) fun_var_Ts min_ary
1164 Symtab.update (s, {pred_sym = pred_sym,
1165 min_ary = Int.min (ary, min_ary),
1166 max_ary = Int.max (ary, max_ary),
1172 val pred_sym = top_level andalso not bool_vars
1174 case explicit_apply of
1177 | NONE => fold (consider_var_arity T) fun_var_Ts ary
1179 Symtab.update_new (s, {pred_sym = pred_sym,
1180 min_ary = min_ary, max_ary = ary,
1185 | CombVar (_, T) => add_var_or_bound_var T accum
1186 | CombAbs ((_, T), tm) =>
1187 accum |> add_var_or_bound_var T |> add false tm
1189 |> fold (add false) args
1192 fun add_fact_syms_to_table ctxt explicit_apply =
1193 fact_lift (formula_fold NONE
1194 (K (add_combterm_syms_to_table ctxt explicit_apply)))
1196 val default_sym_tab_entries : (string * sym_info) list =
1197 (prefixed_predicator_name,
1198 {pred_sym = true, min_ary = 1, max_ary = 1, types = []}) ::
1199 ([tptp_false, tptp_true]
1200 |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []})) @
1201 ([tptp_equal, tptp_old_equal]
1202 |> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = []}))
1204 fun sym_table_for_facts ctxt explicit_apply facts =
1205 ((false, []), Symtab.empty)
1206 |> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
1207 |> fold Symtab.update default_sym_tab_entries
1209 fun min_arity_of sym_tab s =
1210 case Symtab.lookup sym_tab s of
1211 SOME ({min_ary, ...} : sym_info) => min_ary
1213 case strip_prefix_and_unascii const_prefix s of
1215 let val s = s |> unmangled_const_name |> invert_const in
1216 if s = predicator_name then 1
1217 else if s = app_op_name then 2
1218 else if s = type_pred_name then 1
1223 (* True if the constant ever appears outside of the top-level position in
1224 literals, or if it appears with different arities (e.g., because of different
1225 type instantiations). If false, the constant always receives all of its
1226 arguments and is used as a predicate. *)
1227 fun is_pred_sym sym_tab s =
1228 case Symtab.lookup sym_tab s of
1229 SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
1230 pred_sym andalso min_ary = max_ary
1233 val predicator_combconst =
1234 CombConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
1235 fun predicator tm = CombApp (predicator_combconst, tm)
1237 fun introduce_predicators_in_combterm sym_tab tm =
1238 case strip_combterm_comb tm of
1239 (CombConst ((s, _), _, _), _) =>
1240 if is_pred_sym sym_tab s then tm else predicator tm
1241 | _ => predicator tm
1243 fun list_app head args = fold (curry (CombApp o swap)) args head
1245 val app_op = `make_fixed_const app_op_name
1247 fun explicit_app arg head =
1249 val head_T = combtyp_of head
1250 val (arg_T, res_T) = dest_funT head_T
1252 CombConst (app_op, head_T --> head_T, [arg_T, res_T])
1253 in list_app explicit_app [head, arg] end
1254 fun list_explicit_app head args = fold explicit_app args head
1256 fun introduce_explicit_apps_in_combterm sym_tab =
1259 case strip_combterm_comb tm of
1260 (head as CombConst ((s, _), _, _), args) =>
1262 |> chop (min_arity_of sym_tab s)
1264 |-> list_explicit_app
1265 | (head, args) => list_explicit_app head (map aux args)
1268 fun chop_fun 0 T = ([], T)
1269 | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
1270 chop_fun (n - 1) ran_T |>> cons dom_T
1271 | chop_fun _ _ = raise Fail "unexpected non-function"
1273 fun filter_type_args _ _ _ [] = []
1274 | filter_type_args thy s arity T_args =
1276 (* will throw "TYPE" for pseudo-constants *)
1277 val U = if s = app_op_name then
1278 @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
1280 s |> Sign.the_const_type thy
1282 case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
1285 let val U_args = (s, U) |> Sign.const_typargs thy in
1287 |> map (fn (U, T) =>
1288 if member (op =) res_U_vars (dest_TVar U) then T
1292 handle TYPE _ => T_args
1294 fun enforce_type_arg_policy_in_combterm ctxt format type_enc =
1296 val thy = Proof_Context.theory_of ctxt
1297 fun aux arity (CombApp (tm1, tm2)) =
1298 CombApp (aux (arity + 1) tm1, aux 0 tm2)
1299 | aux arity (CombConst (name as (s, _), T, T_args)) =
1300 (case strip_prefix_and_unascii const_prefix s of
1301 NONE => (name, T_args)
1304 val s'' = invert_const s''
1305 fun filtered_T_args false = T_args
1306 | filtered_T_args true = filter_type_args thy s'' arity T_args
1308 case type_arg_policy type_enc s'' of
1309 Explicit_Type_Args drop_args =>
1310 (name, filtered_T_args drop_args)
1311 | Mangled_Type_Args drop_args =>
1312 (mangled_const_name format type_enc (filtered_T_args drop_args)
1314 | No_Type_Args => (name, [])
1316 |> (fn (name, T_args) => CombConst (name, T, T_args))
1317 | aux _ (CombAbs (bound, tm)) = CombAbs (bound, aux 0 tm)
1321 fun repair_combterm ctxt format type_enc sym_tab =
1322 not (is_type_enc_higher_order type_enc)
1323 ? (introduce_explicit_apps_in_combterm sym_tab
1324 #> introduce_predicators_in_combterm sym_tab)
1325 #> enforce_type_arg_policy_in_combterm ctxt format type_enc
1326 fun repair_fact ctxt format type_enc sym_tab =
1327 update_combformula (formula_map
1328 (repair_combterm ctxt format type_enc sym_tab))
1330 (** Helper facts **)
1332 (* The Boolean indicates that a fairly sound type encoding is needed. *)
1334 [(("COMBI", false), @{thms Meson.COMBI_def}),
1335 (("COMBK", false), @{thms Meson.COMBK_def}),
1336 (("COMBB", false), @{thms Meson.COMBB_def}),
1337 (("COMBC", false), @{thms Meson.COMBC_def}),
1338 (("COMBS", false), @{thms Meson.COMBS_def}),
1339 (("fFalse", false), [@{lemma "~ fFalse" by (unfold fFalse_def) fast}]),
1340 (("fFalse", true), @{thms True_or_False}),
1341 (("fTrue", false), [@{lemma "fTrue" by (unfold fTrue_def) fast}]),
1342 (("fTrue", true), @{thms True_or_False}),
1344 @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1345 fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1347 @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
1348 by (unfold fconj_def) fast+}),
1350 @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
1351 by (unfold fdisj_def) fast+}),
1352 (("fimplies", false),
1353 @{lemma "P | fimplies P Q" "~ Q | fimplies P Q" "~ fimplies P Q | ~ P | Q"
1354 by (unfold fimplies_def) fast+}),
1356 (* This is a lie: Higher-order equality doesn't need a sound type encoding.
1357 However, this is done so for backward compatibility: Including the
1358 equality helpers by default in Metis breaks a few existing proofs. *)
1359 @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1360 fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1361 (("fAll", false), []), (*TODO: add helpers*)
1362 (("fEx", false), []), (*TODO: add helpers*)
1363 (("If", true), @{thms if_True if_False True_or_False})]
1364 |> map (apsnd (map zero_var_indexes))
1366 val type_tag = `make_fixed_const type_tag_name
1368 fun type_tag_idempotence_fact () =
1370 fun var s = ATerm (`I s, [])
1371 fun tag tm = ATerm (type_tag, [var "T", tm])
1372 val tagged_a = tag (var "A")
1374 Formula (type_tag_idempotence_helper_name, Axiom,
1375 AAtom (ATerm (`I tptp_equal, [tag tagged_a, tagged_a]))
1376 |> close_formula_universally, isabelle_info simpN, NONE)
1379 fun should_specialize_helper type_enc t =
1380 polymorphism_of_type_enc type_enc = Mangled_Monomorphic andalso
1381 level_of_type_enc type_enc <> No_Types andalso
1382 not (null (Term.hidden_polymorphism t))
1384 fun helper_facts_for_sym ctxt format type_enc lambda_trans
1385 (s, {types, ...} : sym_info) =
1386 case strip_prefix_and_unascii const_prefix s of
1389 val thy = Proof_Context.theory_of ctxt
1390 val unmangled_s = mangled_s |> unmangled_const_name
1391 fun dub needs_fairly_sound j k =
1392 (unmangled_s ^ "_" ^ string_of_int j ^ "_" ^ string_of_int k ^
1393 (if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^
1394 (if needs_fairly_sound then typed_helper_suffix
1395 else untyped_helper_suffix),
1397 fun dub_and_inst needs_fairly_sound (th, j) =
1398 let val t = prop_of th in
1399 if should_specialize_helper type_enc t then
1400 map (fn T => specialize_type thy (invert_const unmangled_s, T) t)
1405 |> map (fn (k, t) => (dub needs_fairly_sound j k, t)) o tag_list 1
1407 map_filter (make_fact ctxt format type_enc lambda_trans false false [])
1408 val fairly_sound = is_type_enc_fairly_sound type_enc
1411 |> maps (fn ((helper_s, needs_fairly_sound), ths) =>
1412 if helper_s <> unmangled_s orelse
1413 (needs_fairly_sound andalso not fairly_sound) then
1416 ths ~~ (1 upto length ths)
1417 |> maps (dub_and_inst needs_fairly_sound)
1421 fun helper_facts_for_sym_table ctxt format type_enc lambda_trans sym_tab =
1422 Symtab.fold_rev (append
1423 o helper_facts_for_sym ctxt format type_enc lambda_trans)
1426 (***************************************************************)
1427 (* Type Classes Present in the Axiom or Conjecture Clauses *)
1428 (***************************************************************)
1430 fun set_insert (x, s) = Symtab.update (x, ()) s
1432 fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
1434 (* Remove this trivial type class (FIXME: similar code elsewhere) *)
1435 fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
1437 fun classes_of_terms get_Ts =
1438 map (map snd o get_Ts)
1439 #> List.foldl add_classes Symtab.empty
1440 #> delete_type #> Symtab.keys
1442 val tfree_classes_of_terms = classes_of_terms OldTerm.term_tfrees
1443 val tvar_classes_of_terms = classes_of_terms OldTerm.term_tvars
1445 fun fold_type_constrs f (Type (s, Ts)) x =
1446 fold (fold_type_constrs f) Ts (f (s, x))
1447 | fold_type_constrs _ _ x = x
1449 (*Type constructors used to instantiate overloaded constants are the only ones needed.*)
1450 fun add_type_constrs_in_term thy =
1452 fun add (Const (@{const_name Meson.skolem}, _) $ _) = I
1453 | add (t $ u) = add t #> add u
1454 | add (Const (x as (s, _))) =
1455 if String.isPrefix skolem_const_prefix s then I
1456 else x |> Sign.const_typargs thy |> fold (fold_type_constrs set_insert)
1457 | add (Abs (_, _, u)) = add u
1461 fun type_constrs_of_terms thy ts =
1462 Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty)
1464 fun translate_formulas ctxt format prem_kind type_enc lambda_trans preproc
1465 hyp_ts concl_t facts =
1467 val thy = Proof_Context.theory_of ctxt
1468 val fact_ts = facts |> map snd
1469 val presimp_consts = Meson.presimplified_consts ctxt
1471 make_fact ctxt format type_enc lambda_trans true preproc presimp_consts
1472 val (facts, fact_names) =
1473 facts |> map (fn (name, t) => (name, t) |> make_fact |> rpair name)
1474 |> map_filter (try (apfst the))
1476 (* Remove existing facts from the conjecture, as this can dramatically
1477 boost an ATP's performance (for some reason). *)
1480 |> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t)
1481 val goal_t = Logic.list_implies (hyp_ts, concl_t)
1482 val all_ts = goal_t :: fact_ts
1483 val subs = tfree_classes_of_terms all_ts
1484 val supers = tvar_classes_of_terms all_ts
1485 val tycons = type_constrs_of_terms thy all_ts
1488 |> make_conjecture ctxt format prem_kind type_enc lambda_trans preproc
1490 val (supers', arity_clauses) =
1491 if level_of_type_enc type_enc = No_Types then ([], [])
1492 else make_arity_clauses thy tycons supers
1493 val class_rel_clauses = make_class_rel_clauses thy subs supers'
1495 (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
1498 fun fo_literal_from_type_literal (TyLitVar (class, name)) =
1499 (true, ATerm (class, [ATerm (name, [])]))
1500 | fo_literal_from_type_literal (TyLitFree (class, name)) =
1501 (true, ATerm (class, [ATerm (name, [])]))
1503 fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
1505 val type_pred = `make_fixed_const type_pred_name
1507 fun type_pred_combterm ctxt format type_enc T tm =
1508 CombApp (CombConst (type_pred, T --> @{typ bool}, [T])
1509 |> enforce_type_arg_policy_in_combterm ctxt format type_enc, tm)
1511 fun is_var_positively_naked_in_term _ (SOME false) _ accum = accum
1512 | is_var_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
1513 accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
1514 | is_var_positively_naked_in_term _ _ _ _ = true
1515 fun should_predicate_on_var_in_formula pos phi (SOME true) name =
1516 formula_fold pos (is_var_positively_naked_in_term name) phi false
1517 | should_predicate_on_var_in_formula _ _ _ _ = true
1519 fun mk_aterm format type_enc name T_args args =
1520 ATerm (name, map_filter (ho_term_for_type_arg format type_enc) T_args @ args)
1522 fun tag_with_type ctxt format nonmono_Ts type_enc pos T tm =
1523 CombConst (type_tag, T --> T, [T])
1524 |> enforce_type_arg_policy_in_combterm ctxt format type_enc
1525 |> ho_term_from_combterm ctxt format nonmono_Ts type_enc (Top_Level pos)
1526 |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm])
1527 | _ => raise Fail "unexpected lambda-abstraction")
1528 and ho_term_from_combterm ctxt format nonmono_Ts type_enc =
1532 val (head, args) = strip_combterm_comb u
1535 Top_Level pos => pos
1540 CombConst (name as (s, _), _, T_args) =>
1542 val arg_site = if is_tptp_equal s then Eq_Arg pos else Elsewhere
1544 mk_aterm format type_enc name T_args (map (aux arg_site) args)
1546 | CombVar (name, _) => mk_aterm format type_enc name [] (map (aux Elsewhere) args)
1547 | CombAbs ((name, T), tm) =>
1548 AAbs ((name, ho_type_from_typ format type_enc true 0 T), aux Elsewhere tm)
1549 | CombApp _ => raise Fail "impossible \"CombApp\""
1550 val T = combtyp_of u
1552 t |> (if should_tag_with_type ctxt nonmono_Ts type_enc site u T then
1553 tag_with_type ctxt format nonmono_Ts type_enc pos T
1558 and formula_from_combformula ctxt format nonmono_Ts type_enc
1559 should_predicate_on_var =
1562 ho_term_from_combterm ctxt format nonmono_Ts type_enc (Top_Level pos)
1565 Simple_Types (_, level) =>
1566 homogenized_type ctxt nonmono_Ts level 0
1567 #> ho_type_from_typ format type_enc false 0 #> SOME
1569 fun do_out_of_bound_type pos phi universal (name, T) =
1570 if should_predicate_on_type ctxt nonmono_Ts type_enc
1571 (fn () => should_predicate_on_var pos phi universal name) T then
1573 |> type_pred_combterm ctxt format type_enc T
1574 |> do_term pos |> AAtom |> SOME
1577 fun do_formula pos (AQuant (q, xs, phi)) =
1579 val phi = phi |> do_formula pos
1580 val universal = Option.map (q = AExists ? not) pos
1582 AQuant (q, xs |> map (apsnd (fn NONE => NONE
1583 | SOME T => do_bound_type T)),
1584 (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
1586 (fn (_, NONE) => NONE
1588 do_out_of_bound_type pos phi universal (s, T))
1592 | do_formula pos (AConn conn) = aconn_map pos do_formula conn
1593 | do_formula pos (AAtom tm) = AAtom (do_term pos tm)
1596 fun bound_tvars type_enc Ts =
1597 mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
1598 (type_literals_for_types type_enc add_sorts_on_tvar Ts))
1600 (* Each fact is given a unique fact number to avoid name clashes (e.g., because
1601 of monomorphization). The TPTP explicitly forbids name clashes, and some of
1602 the remote provers might care. *)
1603 fun formula_line_for_fact ctxt format prefix encode freshen pos nonmono_Ts
1604 type_enc (j, {name, locality, kind, combformula, atomic_types}) =
1605 (prefix ^ (if freshen then string_of_int j ^ "_" else "") ^ encode name,
1608 |> close_combformula_universally
1609 |> formula_from_combformula ctxt format nonmono_Ts type_enc
1610 should_predicate_on_var_in_formula
1611 (if pos then SOME true else NONE)
1612 |> bound_tvars type_enc atomic_types
1613 |> close_formula_universally,
1616 Intro => isabelle_info introN
1617 | Elim => isabelle_info elimN
1618 | Simp => isabelle_info simpN
1622 fun formula_line_for_class_rel_clause ({name, subclass, superclass, ...}
1623 : class_rel_clause) =
1624 let val ty_arg = ATerm (`I "T", []) in
1625 Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
1626 AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
1627 AAtom (ATerm (superclass, [ty_arg]))])
1628 |> close_formula_universally, isabelle_info introN, NONE)
1631 fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
1632 (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
1633 | fo_literal_from_arity_literal (TVarLit (c, sort)) =
1634 (false, ATerm (c, [ATerm (sort, [])]))
1636 fun formula_line_for_arity_clause ({name, prem_lits, concl_lits, ...}
1638 Formula (arity_clause_prefix ^ name, Axiom,
1639 mk_ahorn (map (formula_from_fo_literal o apfst not
1640 o fo_literal_from_arity_literal) prem_lits)
1641 (formula_from_fo_literal
1642 (fo_literal_from_arity_literal concl_lits))
1643 |> close_formula_universally, isabelle_info introN, NONE)
1645 fun formula_line_for_conjecture ctxt format nonmono_Ts type_enc
1646 ({name, kind, combformula, atomic_types, ...} : translated_formula) =
1647 Formula (conjecture_prefix ^ name, kind,
1648 formula_from_combformula ctxt format nonmono_Ts type_enc
1649 should_predicate_on_var_in_formula (SOME false)
1650 (close_combformula_universally combformula)
1651 |> bound_tvars type_enc atomic_types
1652 |> close_formula_universally, NONE, NONE)
1654 fun free_type_literals type_enc ({atomic_types, ...} : translated_formula) =
1655 atomic_types |> type_literals_for_types type_enc add_sorts_on_tfree
1656 |> map fo_literal_from_type_literal
1658 fun formula_line_for_free_type j lit =
1659 Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis,
1660 formula_from_fo_literal lit, NONE, NONE)
1661 fun formula_lines_for_free_types type_enc facts =
1663 val litss = map (free_type_literals type_enc) facts
1664 val lits = fold (union (op =)) litss []
1665 in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
1667 (** Symbol declarations **)
1669 fun should_declare_sym type_enc pred_sym s =
1670 is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
1672 Simple_Types _ => true
1673 | Tags (_, _, Lightweight) => true
1674 | _ => not pred_sym)
1676 fun sym_decl_table_for_facts ctxt type_enc repaired_sym_tab (conjs, facts) =
1678 fun add_combterm in_conj tm =
1679 let val (head, args) = strip_combterm_comb tm in
1681 CombConst ((s, s'), T, T_args) =>
1682 let val pred_sym = is_pred_sym repaired_sym_tab s in
1683 if should_declare_sym type_enc pred_sym s then
1684 Symtab.map_default (s, [])
1685 (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
1690 | CombAbs (_, tm) => add_combterm in_conj tm
1692 #> fold (add_combterm in_conj) args
1694 fun add_fact in_conj =
1695 fact_lift (formula_fold NONE (K (add_combterm in_conj)))
1698 |> is_type_enc_fairly_sound type_enc
1699 ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
1702 (* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
1703 out with monotonicity" paper presented at CADE 2011. *)
1704 fun add_combterm_nonmonotonic_types _ _ _ _ (SOME false) _ = I
1705 | add_combterm_nonmonotonic_types ctxt level sound locality _
1706 (CombApp (CombApp (CombConst ((s, _), Type (_, [T, _]), _), tm1),
1708 (is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
1710 Noninf_Nonmono_Types =>
1711 not (is_locality_global locality) orelse
1712 not (is_type_surely_infinite ctxt sound T)
1713 | Fin_Nonmono_Types => is_type_surely_finite ctxt false T
1714 | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
1715 | add_combterm_nonmonotonic_types _ _ _ _ _ _ = I
1716 fun add_fact_nonmonotonic_types ctxt level sound
1717 ({kind, locality, combformula, ...} : translated_formula) =
1718 formula_fold (SOME (kind <> Conjecture))
1719 (add_combterm_nonmonotonic_types ctxt level sound locality)
1721 fun nonmonotonic_types_for_facts ctxt type_enc sound facts =
1722 let val level = level_of_type_enc type_enc in
1723 if level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types then
1724 [] |> fold (add_fact_nonmonotonic_types ctxt level sound) facts
1725 (* We must add "bool" in case the helper "True_or_False" is added
1726 later. In addition, several places in the code rely on the list of
1727 nonmonotonic types not being empty. *)
1728 |> insert_type ctxt I @{typ bool}
1733 fun decl_line_for_sym ctxt format nonmono_Ts type_enc s
1734 (s', T_args, T, pred_sym, ary, _) =
1736 val (T_arg_Ts, level) =
1738 Simple_Types (_, level) => ([], level)
1739 | _ => (replicate (length T_args) homo_infinite_type, No_Types)
1741 Decl (sym_decl_prefix ^ s, (s, s'),
1742 (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
1743 |> ho_type_from_typ format type_enc pred_sym (length T_arg_Ts + ary))
1746 fun formula_line_for_preds_sym_decl ctxt format conj_sym_kind nonmono_Ts
1747 poly_nonmono_Ts type_enc n s j (s', T_args, T, _, ary, in_conj) =
1749 val (kind, maybe_negate) =
1750 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1752 val (arg_Ts, res_T) = chop_fun ary T
1753 val num_args = length arg_Ts
1755 1 upto num_args |> map (`I o make_bound_var o string_of_int)
1757 bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
1758 val sym_needs_arg_types = n > 1 orelse exists (curry (op =) dummyT) T_args
1759 fun should_keep_arg_type T =
1760 sym_needs_arg_types orelse
1761 not (should_predicate_on_type ctxt nonmono_Ts type_enc (K false) T)
1763 arg_Ts |> map (fn T => if should_keep_arg_type T then SOME T else NONE)
1765 Formula (preds_sym_formula_prefix ^ s ^
1766 (if n > 1 then "_" ^ string_of_int j else ""), kind,
1767 CombConst ((s, s'), T, T_args)
1768 |> fold (curry (CombApp o swap)) bounds
1769 |> type_pred_combterm ctxt format type_enc res_T
1770 |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
1771 |> formula_from_combformula ctxt format poly_nonmono_Ts type_enc
1772 (K (K (K (K true)))) (SOME true)
1773 |> n > 1 ? bound_tvars type_enc (atyps_of T)
1774 |> close_formula_universally
1776 isabelle_info introN, NONE)
1779 fun formula_lines_for_lightweight_tags_sym_decl ctxt format conj_sym_kind
1780 poly_nonmono_Ts type_enc n s
1781 (j, (s', T_args, T, pred_sym, ary, in_conj)) =
1784 lightweight_tags_sym_formula_prefix ^ s ^
1785 (if n > 1 then "_" ^ string_of_int j else "")
1786 val (kind, maybe_negate) =
1787 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1789 val (arg_Ts, res_T) = chop_fun ary T
1791 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
1792 val bounds = bound_names |> map (fn name => ATerm (name, []))
1793 val cst = mk_aterm format type_enc (s, s') T_args
1794 val atomic_Ts = atyps_of T
1796 (if pred_sym then AConn (AIff, map AAtom tms)
1797 else AAtom (ATerm (`I tptp_equal, tms)))
1798 |> bound_tvars type_enc atomic_Ts
1799 |> close_formula_universally
1801 (* See also "should_tag_with_type". *)
1802 fun should_encode T =
1803 should_encode_type ctxt poly_nonmono_Ts All_Types T orelse
1805 Tags (Polymorphic, level, Lightweight) =>
1806 level <> All_Types andalso Monomorph.typ_has_tvars T
1808 val tag_with = tag_with_type ctxt format poly_nonmono_Ts type_enc NONE
1809 val add_formula_for_res =
1810 if should_encode res_T then
1811 cons (Formula (ident_base ^ "_res", kind,
1812 eq [tag_with res_T (cst bounds), cst bounds],
1813 isabelle_info simpN, NONE))
1816 fun add_formula_for_arg k =
1817 let val arg_T = nth arg_Ts k in
1818 if should_encode arg_T then
1819 case chop k bounds of
1820 (bounds1, bound :: bounds2) =>
1821 cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
1822 eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
1824 isabelle_info simpN, NONE))
1825 | _ => raise Fail "expected nonempty tail"
1830 [] |> not pred_sym ? add_formula_for_res
1831 |> fold add_formula_for_arg (ary - 1 downto 0)
1834 fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
1836 fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts
1837 poly_nonmono_Ts type_enc (s, decls) =
1840 decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_enc s)
1845 decl :: (decls' as _ :: _) =>
1846 let val T = result_type_of_decl decl in
1847 if forall (curry (type_instance ctxt o swap) T
1848 o result_type_of_decl) decls' then
1854 val n = length decls
1856 decls |> filter (should_predicate_on_type ctxt poly_nonmono_Ts type_enc
1858 o result_type_of_decl)
1860 (0 upto length decls - 1, decls)
1861 |-> map2 (formula_line_for_preds_sym_decl ctxt format conj_sym_kind
1862 nonmono_Ts poly_nonmono_Ts type_enc n s)
1864 | Tags (_, _, heaviness) =>
1868 let val n = length decls in
1869 (0 upto n - 1 ~~ decls)
1870 |> maps (formula_lines_for_lightweight_tags_sym_decl ctxt format
1871 conj_sym_kind poly_nonmono_Ts type_enc n s)
1874 fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1875 poly_nonmono_Ts type_enc sym_decl_tab =
1880 |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
1881 nonmono_Ts poly_nonmono_Ts type_enc)
1883 fun needs_type_tag_idempotence (Tags (poly, level, heaviness)) =
1884 poly <> Mangled_Monomorphic andalso
1885 ((level = All_Types andalso heaviness = Lightweight) orelse
1886 level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types)
1887 | needs_type_tag_idempotence _ = false
1889 fun offset_of_heading_in_problem _ [] j = j
1890 | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
1891 if heading = needle then j
1892 else offset_of_heading_in_problem needle problem (j + length lines)
1894 val implicit_declsN = "Should-be-implicit typings"
1895 val explicit_declsN = "Explicit typings"
1896 val factsN = "Relevant facts"
1897 val class_relsN = "Class relationships"
1898 val aritiesN = "Arities"
1899 val helpersN = "Helper facts"
1900 val conjsN = "Conjectures"
1901 val free_typesN = "Type variables"
1903 val explicit_apply = NONE (* for experiments *)
1905 fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_enc sound
1906 exporter lambda_trans readable_names preproc hyp_ts concl_t facts =
1908 val (format, type_enc) = choose_format [format] type_enc
1910 if lambda_trans = lambdasN andalso
1911 not (is_type_enc_higher_order type_enc) then
1912 error ("Lambda translation method incompatible with \
1913 \first-order encoding.")
1916 val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
1917 translate_formulas ctxt format prem_kind type_enc lambda_trans preproc
1918 hyp_ts concl_t facts
1919 val sym_tab = conjs @ facts |> sym_table_for_facts ctxt explicit_apply
1921 conjs @ facts |> nonmonotonic_types_for_facts ctxt type_enc sound
1922 val repair = repair_fact ctxt format type_enc sym_tab
1923 val (conjs, facts) = (conjs, facts) |> pairself (map repair)
1924 val repaired_sym_tab =
1925 conjs @ facts |> sym_table_for_facts ctxt (SOME false)
1928 |> helper_facts_for_sym_table ctxt format type_enc lambda_trans
1930 val poly_nonmono_Ts =
1931 if null nonmono_Ts orelse nonmono_Ts = [@{typ bool}] orelse
1932 polymorphism_of_type_enc type_enc <> Polymorphic then
1935 [TVar (("'a", 0), HOLogic.typeS)]
1936 val sym_decl_lines =
1937 (conjs, helpers @ facts)
1938 |> sym_decl_table_for_facts ctxt type_enc repaired_sym_tab
1939 |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1940 poly_nonmono_Ts type_enc
1942 0 upto length helpers - 1 ~~ helpers
1943 |> map (formula_line_for_fact ctxt format helper_prefix I false true
1944 poly_nonmono_Ts type_enc)
1945 |> (if needs_type_tag_idempotence type_enc then
1946 cons (type_tag_idempotence_fact ())
1949 (* Reordering these might confuse the proof reconstruction code or the SPASS
1952 [(explicit_declsN, sym_decl_lines),
1954 map (formula_line_for_fact ctxt format fact_prefix ascii_of
1955 (not exporter) (not exporter) nonmono_Ts
1957 (0 upto length facts - 1 ~~ facts)),
1958 (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
1959 (aritiesN, map formula_line_for_arity_clause arity_clauses),
1960 (helpersN, helper_lines),
1962 map (formula_line_for_conjecture ctxt format nonmono_Ts type_enc)
1964 (free_typesN, formula_lines_for_free_types type_enc (facts @ conjs))]
1968 CNF => ensure_cnf_problem
1969 | CNF_UEQ => filter_cnf_ueq_problem
1971 |> (if is_format_typed format then
1972 declare_undeclared_syms_in_atp_problem type_decl_prefix
1976 val (problem, pool) = problem |> nice_atp_problem readable_names
1977 val helpers_offset = offset_of_heading_in_problem helpersN problem 0
1979 map_filter (fn (j, {name, ...}) =>
1980 if String.isSuffix typed_helper_suffix name then SOME j
1982 ((helpers_offset + 1 upto helpers_offset + length helpers)
1984 fun add_sym_arity (s, {min_ary, ...} : sym_info) =
1986 case strip_prefix_and_unascii const_prefix s of
1987 SOME s => Symtab.insert (op =) (s, min_ary)
1993 case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
1994 offset_of_heading_in_problem conjsN problem 0,
1995 offset_of_heading_in_problem factsN problem 0,
1996 fact_names |> Vector.fromList,
1998 Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
2002 val conj_weight = 0.0
2003 val hyp_weight = 0.1
2004 val fact_min_weight = 0.2
2005 val fact_max_weight = 1.0
2006 val type_info_default_weight = 0.8
2008 fun add_term_weights weight (ATerm (s, tms)) =
2009 is_tptp_user_symbol s ? Symtab.default (s, weight)
2010 #> fold (add_term_weights weight) tms
2011 | add_term_weights weight (AAbs (_, tm)) = add_term_weights weight tm
2012 fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
2013 formula_fold NONE (K (add_term_weights weight)) phi
2014 | add_problem_line_weights _ _ = I
2016 fun add_conjectures_weights [] = I
2017 | add_conjectures_weights conjs =
2018 let val (hyps, conj) = split_last conjs in
2019 add_problem_line_weights conj_weight conj
2020 #> fold (add_problem_line_weights hyp_weight) hyps
2023 fun add_facts_weights facts =
2025 val num_facts = length facts
2027 fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
2028 / Real.fromInt num_facts
2030 map weight_of (0 upto num_facts - 1) ~~ facts
2031 |> fold (uncurry add_problem_line_weights)
2034 (* Weights are from 0.0 (most important) to 1.0 (least important). *)
2035 fun atp_problem_weights problem =
2036 let val get = these o AList.lookup (op =) problem in
2038 |> add_conjectures_weights (get free_typesN @ get conjsN)
2039 |> add_facts_weights (get factsN)
2040 |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
2041 [explicit_declsN, class_relsN, aritiesN]
2043 |> sort (prod_ord Real.compare string_ord o pairself swap)