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 is_type_enc_higher_order : type_enc -> bool
80 val polymorphism_of_type_enc : type_enc -> polymorphism
81 val level_of_type_enc : type_enc -> type_level
82 val is_type_enc_virtually_sound : type_enc -> bool
83 val is_type_enc_fairly_sound : type_enc -> bool
84 val choose_format : format list -> type_enc -> format * type_enc
86 connective -> ('a, 'b, 'c) formula list -> ('a, 'b, 'c) formula
87 val unmangled_const : string -> string * (string, 'b) ho_term list
88 val unmangled_const_name : string -> string
89 val helper_table : ((string * bool) * thm list) list
91 val conceal_lambdas : Proof.context -> term -> term
92 val introduce_combinators : Proof.context -> term -> term
93 val prepare_atp_problem :
94 Proof.context -> format -> formula_kind -> formula_kind -> type_enc -> bool
95 -> bool -> ((formula_kind * term) list -> term list) -> bool -> bool
96 -> term list -> term -> ((string * locality) * term) list
97 -> string problem * string Symtab.table * int * int
98 * (string * locality) list vector * int list * int Symtab.table
99 val atp_problem_weights : string problem -> (string * real) list
102 structure ATP_Translate : ATP_TRANSLATE =
108 type name = string * string
110 val generate_info = false (* experimental *)
112 fun isabelle_info s =
113 if generate_info then SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
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 val concealed_lambda_prefix = sledgehammer_weak_prefix ^ "lambda_"
165 (*Escaping of special characters.
166 Alphanumeric characters are left unchanged.
167 The character _ goes to __
168 Characters in the range ASCII space to / go to _A to _P, respectively.
169 Other characters go to _nnn where nnn is the decimal ASCII code.*)
170 val upper_a_minus_space = Char.ord #"A" - Char.ord #" "
172 fun stringN_of_int 0 _ = ""
173 | stringN_of_int k n =
174 stringN_of_int (k - 1) (n div 10) ^ string_of_int (n mod 10)
176 fun ascii_of_char c =
177 if Char.isAlphaNum c then
179 else if c = #"_" then
181 else if #" " <= c andalso c <= #"/" then
182 "_" ^ String.str (Char.chr (Char.ord c + upper_a_minus_space))
184 (* fixed width, in case more digits follow *)
185 "_" ^ stringN_of_int 3 (Char.ord c)
187 val ascii_of = String.translate ascii_of_char
189 (** Remove ASCII armoring from names in proof files **)
191 (* We don't raise error exceptions because this code can run inside a worker
192 thread. Also, the errors are impossible. *)
195 fun un rcs [] = String.implode(rev rcs)
196 | un rcs [#"_"] = un (#"_" :: rcs) [] (* ERROR *)
197 (* Three types of _ escapes: __, _A to _P, _nnn *)
198 | un rcs (#"_" :: #"_" :: cs) = un (#"_" :: rcs) cs
199 | un rcs (#"_" :: c :: cs) =
200 if #"A" <= c andalso c<= #"P" then
201 (* translation of #" " to #"/" *)
202 un (Char.chr (Char.ord c - upper_a_minus_space) :: rcs) cs
204 let val digits = List.take (c :: cs, 3) handle General.Subscript => [] in
205 case Int.fromString (String.implode digits) of
206 SOME n => un (Char.chr n :: rcs) (List.drop (cs, 2))
207 | NONE => un (c :: #"_" :: rcs) cs (* ERROR *)
209 | un rcs (c :: cs) = un (c :: rcs) cs
210 in un [] o String.explode end
212 (* If string s has the prefix s1, return the result of deleting it,
214 fun strip_prefix_and_unascii s1 s =
215 if String.isPrefix s1 s then
216 SOME (unascii_of (String.extract (s, size s1, NONE)))
221 [("c_False", (@{const_name False}, (@{thm fFalse_def},
222 ("fFalse", @{const_name ATP.fFalse})))),
223 ("c_True", (@{const_name True}, (@{thm fTrue_def},
224 ("fTrue", @{const_name ATP.fTrue})))),
225 ("c_Not", (@{const_name Not}, (@{thm fNot_def},
226 ("fNot", @{const_name ATP.fNot})))),
227 ("c_conj", (@{const_name conj}, (@{thm fconj_def},
228 ("fconj", @{const_name ATP.fconj})))),
229 ("c_disj", (@{const_name disj}, (@{thm fdisj_def},
230 ("fdisj", @{const_name ATP.fdisj})))),
231 ("c_implies", (@{const_name implies}, (@{thm fimplies_def},
232 ("fimplies", @{const_name ATP.fimplies})))),
233 ("equal", (@{const_name HOL.eq}, (@{thm fequal_def},
234 ("fequal", @{const_name ATP.fequal})))),
235 ("c_All", (@{const_name All}, (@{thm fAll_def},
236 ("fAll", @{const_name ATP.fAll})))),
237 ("c_Ex", (@{const_name Ex}, (@{thm fEx_def},
238 ("fEx", @{const_name ATP.fEx}))))]
240 val proxify_const = AList.lookup (op =) proxy_table #> Option.map (snd o snd)
242 (* Readable names for the more common symbolic functions. Do not mess with the
243 table unless you know what you are doing. *)
244 val const_trans_table =
245 [(@{type_name Product_Type.prod}, "prod"),
246 (@{type_name Sum_Type.sum}, "sum"),
247 (@{const_name False}, "False"),
248 (@{const_name True}, "True"),
249 (@{const_name Not}, "Not"),
250 (@{const_name conj}, "conj"),
251 (@{const_name disj}, "disj"),
252 (@{const_name implies}, "implies"),
253 (@{const_name HOL.eq}, "equal"),
254 (@{const_name All}, "All"),
255 (@{const_name Ex}, "Ex"),
256 (@{const_name If}, "If"),
257 (@{const_name Set.member}, "member"),
258 (@{const_name Meson.COMBI}, "COMBI"),
259 (@{const_name Meson.COMBK}, "COMBK"),
260 (@{const_name Meson.COMBB}, "COMBB"),
261 (@{const_name Meson.COMBC}, "COMBC"),
262 (@{const_name Meson.COMBS}, "COMBS")]
264 |> fold (Symtab.update o swap o snd o snd o snd) proxy_table
266 (* Invert the table of translations between Isabelle and ATPs. *)
267 val const_trans_table_inv =
268 const_trans_table |> Symtab.dest |> map swap |> Symtab.make
269 val const_trans_table_unprox =
271 |> fold (fn (_, (isa, (_, (_, atp)))) => Symtab.update (atp, isa)) proxy_table
273 val invert_const = perhaps (Symtab.lookup const_trans_table_inv)
274 val unproxify_const = perhaps (Symtab.lookup const_trans_table_unprox)
277 case Symtab.lookup const_trans_table c of
281 fun ascii_of_indexname (v, 0) = ascii_of v
282 | ascii_of_indexname (v, i) = ascii_of v ^ "_" ^ string_of_int i
284 fun make_bound_var x = bound_var_prefix ^ ascii_of x
285 fun make_schematic_var v = schematic_var_prefix ^ ascii_of_indexname v
286 fun make_fixed_var x = fixed_var_prefix ^ ascii_of x
288 fun make_schematic_type_var (x, i) =
289 tvar_prefix ^ (ascii_of_indexname (unprefix "'" x, i))
290 fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (unprefix "'" x))
292 (* "HOL.eq" is mapped to the ATP's equality. *)
293 fun make_fixed_const @{const_name HOL.eq} = tptp_old_equal
294 | make_fixed_const c = const_prefix ^ lookup_const c
296 fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
298 fun make_type_class clas = class_prefix ^ ascii_of clas
300 fun new_skolem_var_name_from_const s =
301 let val ss = s |> space_explode Long_Name.separator in
302 nth ss (length ss - 2)
305 (* The number of type arguments of a constant, zero if it's monomorphic. For
306 (instances of) Skolem pseudoconstants, this information is encoded in the
308 fun num_type_args thy s =
309 if String.isPrefix skolem_const_prefix s then
310 s |> space_explode Long_Name.separator |> List.last |> Int.fromString |> the
312 (s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
314 (* These are either simplified away by "Meson.presimplify" (most of the time) or
315 handled specially via "fFalse", "fTrue", ..., "fequal". *)
316 val atp_irrelevant_consts =
317 [@{const_name False}, @{const_name True}, @{const_name Not},
318 @{const_name conj}, @{const_name disj}, @{const_name implies},
319 @{const_name HOL.eq}, @{const_name If}, @{const_name Let}]
321 val atp_monomorph_bad_consts =
322 atp_irrelevant_consts @
323 (* These are ignored anyway by the relevance filter (unless they appear in
324 higher-order places) but not by the monomorphizer. *)
325 [@{const_name all}, @{const_name "==>"}, @{const_name "=="},
326 @{const_name Trueprop}, @{const_name All}, @{const_name Ex},
327 @{const_name Ex1}, @{const_name Ball}, @{const_name Bex}]
329 fun add_schematic_const (x as (_, T)) =
330 Monomorph.typ_has_tvars T ? Symtab.insert_list (op =) x
331 val add_schematic_consts_of =
332 Term.fold_aterms (fn Const (x as (s, _)) =>
333 not (member (op =) atp_monomorph_bad_consts s)
334 ? add_schematic_const x
336 fun atp_schematic_consts_of t = add_schematic_consts_of t Symtab.empty
338 (** Definitions and functions for FOL clauses and formulas for TPTP **)
340 (* The first component is the type class; the second is a "TVar" or "TFree". *)
341 datatype type_literal =
342 TyLitVar of name * name |
343 TyLitFree of name * name
346 (** Isabelle arities **)
348 datatype arity_literal =
349 TConsLit of name * name * name list |
350 TVarLit of name * name
353 | gen_TVars n = ("T_" ^ string_of_int n) :: gen_TVars (n-1)
355 val type_class = the_single @{sort type}
357 fun add_packed_sort tvar =
358 fold (fn s => s <> type_class ? cons (`make_type_class s, `I tvar))
362 prem_lits : arity_literal list,
363 concl_lits : arity_literal}
365 (* Arity of type constructor "tcon :: (arg1, ..., argN) res" *)
366 fun make_axiom_arity_clause (tcons, name, (cls, args)) =
368 val tvars = gen_TVars (length args)
369 val tvars_srts = ListPair.zip (tvars, args)
372 prem_lits = [] |> fold (uncurry add_packed_sort) tvars_srts |> map TVarLit,
373 concl_lits = TConsLit (`make_type_class cls,
374 `make_fixed_type_const tcons,
378 fun arity_clause _ _ (_, []) = []
379 | arity_clause seen n (tcons, ("HOL.type", _) :: ars) = (* ignore *)
380 arity_clause seen n (tcons, ars)
381 | arity_clause seen n (tcons, (ar as (class, _)) :: ars) =
382 if member (op =) seen class then
383 (* multiple arities for the same (tycon, class) pair *)
384 make_axiom_arity_clause (tcons,
385 lookup_const tcons ^ "___" ^ ascii_of class ^ "_" ^ string_of_int n,
387 arity_clause seen (n + 1) (tcons, ars)
389 make_axiom_arity_clause (tcons, lookup_const tcons ^ "___" ^
390 ascii_of class, ar) ::
391 arity_clause (class :: seen) n (tcons, ars)
393 fun multi_arity_clause [] = []
394 | multi_arity_clause ((tcons, ars) :: tc_arlists) =
395 arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
397 (* Generate all pairs (tycon, class, sorts) such that tycon belongs to class in
398 theory thy provided its arguments have the corresponding sorts. *)
399 fun type_class_pairs thy tycons classes =
401 val alg = Sign.classes_of thy
402 fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
403 fun add_class tycon class =
404 cons (class, domain_sorts tycon class)
405 handle Sorts.CLASS_ERROR _ => I
406 fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
407 in map try_classes tycons end
409 (*Proving one (tycon, class) membership may require proving others, so iterate.*)
410 fun iter_type_class_pairs _ _ [] = ([], [])
411 | iter_type_class_pairs thy tycons classes =
413 fun maybe_insert_class s =
414 (s <> type_class andalso not (member (op =) classes s))
416 val cpairs = type_class_pairs thy tycons classes
418 [] |> fold (fold (fold (fold maybe_insert_class) o snd) o snd) cpairs
419 val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
420 in (classes' @ classes, union (op =) cpairs' cpairs) end
422 fun make_arity_clauses thy tycons =
423 iter_type_class_pairs thy tycons ##> multi_arity_clause
426 (** Isabelle class relations **)
428 type class_rel_clause =
433 (* Generate all pairs (sub, super) such that sub is a proper subclass of super
435 fun class_pairs _ [] _ = []
436 | class_pairs thy subs supers =
438 val class_less = Sorts.class_less (Sign.classes_of thy)
439 fun add_super sub super = class_less (sub, super) ? cons (sub, super)
440 fun add_supers sub = fold (add_super sub) supers
441 in fold add_supers subs [] end
443 fun make_class_rel_clause (sub, super) =
444 {name = sub ^ "_" ^ super, subclass = `make_type_class sub,
445 superclass = `make_type_class super}
447 fun make_class_rel_clauses thy subs supers =
448 map make_class_rel_clause (class_pairs thy subs supers)
450 (* intermediate terms *)
452 IConst of name * typ * typ list |
454 IApp of iterm * iterm |
455 IAbs of (name * typ) * iterm
457 fun ityp_of (IConst (_, T, _)) = T
458 | ityp_of (IVar (_, T)) = T
459 | ityp_of (IApp (t1, _)) = snd (dest_funT (ityp_of t1))
460 | ityp_of (IAbs ((_, T), tm)) = T --> ityp_of tm
462 (*gets the head of a combinator application, along with the list of arguments*)
463 fun strip_iterm_comb u =
465 fun stripc (IApp (t, u), ts) = stripc (t, u :: ts)
467 in stripc (u, []) end
469 fun atyps_of T = fold_atyps (insert (op =)) T []
471 fun new_skolem_const_name s num_T_args =
472 [new_skolem_const_prefix, s, string_of_int num_T_args]
473 |> space_implode Long_Name.separator
475 (* Converts an Isabelle/HOL term (with combinators) into an intermediate term.
476 Also accumulates sort infomation. *)
477 fun iterm_from_term thy bs (P $ Q) =
479 val (P', P_atomics_Ts) = iterm_from_term thy bs P
480 val (Q', Q_atomics_Ts) = iterm_from_term thy bs Q
481 in (IApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
482 | iterm_from_term thy _ (Const (c, T)) =
485 (if String.isPrefix old_skolem_const_prefix c then
486 [] |> Term.add_tvarsT T |> map TVar
488 (c, T) |> Sign.const_typargs thy)
489 val c' = IConst (`make_fixed_const c, T, tvar_list)
490 in (c', atyps_of T) end
491 | iterm_from_term _ _ (Free (v, T)) =
492 (IConst (`make_fixed_var v, T, []), atyps_of T)
493 | iterm_from_term _ _ (Var (v as (s, _), T)) =
494 (if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
496 val Ts = T |> strip_type |> swap |> op ::
497 val s' = new_skolem_const_name s (length Ts)
498 in IConst (`make_fixed_const s', T, Ts) end
500 IVar ((make_schematic_var v, s), T), atyps_of T)
501 | iterm_from_term _ bs (Bound j) =
502 nth bs j |> (fn (s, T) => (IConst (`make_bound_var s, T, []), atyps_of T))
503 | iterm_from_term thy bs (Abs (s, T, t)) =
505 fun vary s = s |> AList.defined (op =) bs s ? vary o Symbol.bump_string
507 val (tm, atomic_Ts) = iterm_from_term thy ((s, T) :: bs) t
509 (IAbs ((`make_bound_var s, T), tm),
510 union (op =) atomic_Ts (atyps_of T))
514 General | Helper | Extensionality | Intro | Elim | Simp | Local | Assum |
517 (* (quasi-)underapproximation of the truth *)
518 fun is_locality_global Local = false
519 | is_locality_global Assum = false
520 | is_locality_global Chained = false
521 | is_locality_global _ = true
523 datatype order = First_Order | Higher_Order
524 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
525 datatype type_level =
526 All_Types | Noninf_Nonmono_Types | Fin_Nonmono_Types | Const_Arg_Types |
528 datatype type_heaviness = Heavyweight | Lightweight
531 Simple_Types of order * type_level |
532 Preds of polymorphism * type_level * type_heaviness |
533 Tags of polymorphism * type_level * type_heaviness
535 fun try_unsuffixes ss s =
536 fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
538 fun type_enc_from_string s =
539 (case try (unprefix "poly_") s of
540 SOME s => (SOME Polymorphic, s)
542 case try (unprefix "mono_") s of
543 SOME s => (SOME Monomorphic, s)
545 case try (unprefix "mangled_") s of
546 SOME s => (SOME Mangled_Monomorphic, s)
549 (* "_query" and "_bang" are for the ASCII-challenged Metis and
551 case try_unsuffixes ["?", "_query"] s of
552 SOME s => (Noninf_Nonmono_Types, s)
554 case try_unsuffixes ["!", "_bang"] s of
555 SOME s => (Fin_Nonmono_Types, s)
556 | NONE => (All_Types, s))
558 case try (unsuffix "_heavy") s of
559 SOME s => (Heavyweight, s)
560 | NONE => (Lightweight, s))
561 |> (fn (poly, (level, (heaviness, core))) =>
562 case (core, (poly, level, heaviness)) of
563 ("simple", (NONE, _, Lightweight)) =>
564 Simple_Types (First_Order, level)
565 | ("simple_higher", (NONE, _, Lightweight)) =>
566 if level = Noninf_Nonmono_Types then raise Same.SAME
567 else Simple_Types (Higher_Order, level)
568 | ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
569 | ("tags", (SOME Polymorphic, _, _)) =>
570 Tags (Polymorphic, level, heaviness)
571 | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
572 | ("args", (SOME poly, All_Types (* naja *), Lightweight)) =>
573 Preds (poly, Const_Arg_Types, Lightweight)
574 | ("erased", (NONE, All_Types (* naja *), Lightweight)) =>
575 Preds (Polymorphic, No_Types, Lightweight)
576 | _ => raise Same.SAME)
577 handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
579 fun is_type_enc_higher_order (Simple_Types (Higher_Order, _)) = true
580 | is_type_enc_higher_order _ = false
582 fun polymorphism_of_type_enc (Simple_Types _) = Mangled_Monomorphic
583 | polymorphism_of_type_enc (Preds (poly, _, _)) = poly
584 | polymorphism_of_type_enc (Tags (poly, _, _)) = poly
586 fun level_of_type_enc (Simple_Types (_, level)) = level
587 | level_of_type_enc (Preds (_, level, _)) = level
588 | level_of_type_enc (Tags (_, level, _)) = level
590 fun heaviness_of_type_enc (Simple_Types _) = Heavyweight
591 | heaviness_of_type_enc (Preds (_, _, heaviness)) = heaviness
592 | heaviness_of_type_enc (Tags (_, _, heaviness)) = heaviness
594 fun is_type_level_virtually_sound level =
595 level = All_Types orelse level = Noninf_Nonmono_Types
596 val is_type_enc_virtually_sound =
597 is_type_level_virtually_sound o level_of_type_enc
599 fun is_type_level_fairly_sound level =
600 is_type_level_virtually_sound level orelse level = Fin_Nonmono_Types
601 val is_type_enc_fairly_sound = is_type_level_fairly_sound o level_of_type_enc
603 fun choose_format formats (Simple_Types (order, level)) =
604 if member (op =) formats THF then
605 (THF, Simple_Types (order, level))
606 else if member (op =) formats TFF then
607 (TFF, Simple_Types (First_Order, level))
609 choose_format formats (Preds (Mangled_Monomorphic, level, Heavyweight))
610 | choose_format formats type_enc =
613 (CNF_UEQ, case type_enc of
615 (if is_type_enc_fairly_sound type_enc then Tags else Preds)
618 | format => (format, type_enc))
620 type translated_formula =
624 iformula : (name, typ, iterm) formula,
625 atomic_types : typ list}
627 fun update_iformula f ({name, locality, kind, iformula, atomic_types}
628 : translated_formula) =
629 {name = name, locality = locality, kind = kind, iformula = f iformula,
630 atomic_types = atomic_types} : translated_formula
632 fun fact_lift f ({iformula, ...} : translated_formula) = f iformula
634 val type_instance = Sign.typ_instance o Proof_Context.theory_of
636 fun insert_type ctxt get_T x xs =
637 let val T = get_T x in
638 if exists (curry (type_instance ctxt) T o get_T) xs then xs
639 else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
642 (* The Booleans indicate whether all type arguments should be kept. *)
643 datatype type_arg_policy =
644 Explicit_Type_Args of bool |
645 Mangled_Type_Args of bool |
648 fun should_drop_arg_type_args (Simple_Types _) =
649 false (* since TFF doesn't support overloading *)
650 | should_drop_arg_type_args type_enc =
651 level_of_type_enc type_enc = All_Types andalso
652 heaviness_of_type_enc type_enc = Heavyweight
654 fun type_arg_policy type_enc s =
655 if s = type_tag_name then
656 (if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
659 Explicit_Type_Args) false
660 else case type_enc of
661 Tags (_, All_Types, Heavyweight) => No_Type_Args
663 if level_of_type_enc type_enc = No_Types orelse
664 s = @{const_name HOL.eq} orelse
665 (s = app_op_name andalso
666 level_of_type_enc type_enc = Const_Arg_Types) then
669 should_drop_arg_type_args type_enc
670 |> (if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
675 (* Make literals for sorted type variables. *)
676 fun generic_add_sorts_on_type (_, []) = I
677 | generic_add_sorts_on_type ((x, i), s :: ss) =
678 generic_add_sorts_on_type ((x, i), ss)
679 #> (if s = the_single @{sort HOL.type} then
682 insert (op =) (TyLitFree (`make_type_class s, `make_fixed_type_var x))
684 insert (op =) (TyLitVar (`make_type_class s,
685 (make_schematic_type_var (x, i), x))))
686 fun add_sorts_on_tfree (TFree (s, S)) = generic_add_sorts_on_type ((s, ~1), S)
687 | add_sorts_on_tfree _ = I
688 fun add_sorts_on_tvar (TVar z) = generic_add_sorts_on_type z
689 | add_sorts_on_tvar _ = I
691 fun type_literals_for_types type_enc add_sorts_on_typ Ts =
692 [] |> level_of_type_enc type_enc <> No_Types ? fold add_sorts_on_typ Ts
694 fun mk_aconns c phis =
695 let val (phis', phi') = split_last phis in
696 fold_rev (mk_aconn c) phis' phi'
698 fun mk_ahorn [] phi = phi
699 | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
700 fun mk_aquant _ [] phi = phi
701 | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
702 if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
703 | mk_aquant q xs phi = AQuant (q, xs, phi)
705 fun close_universally atom_vars phi =
707 fun formula_vars bounds (AQuant (_, xs, phi)) =
708 formula_vars (map fst xs @ bounds) phi
709 | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
710 | formula_vars bounds (AAtom tm) =
711 union (op =) (atom_vars tm []
712 |> filter_out (member (op =) bounds o fst))
713 in mk_aquant AForall (formula_vars [] phi []) phi end
715 fun iterm_vars (IApp (tm1, tm2)) = fold iterm_vars [tm1, tm2]
716 | iterm_vars (IConst _) = I
717 | iterm_vars (IVar (name, T)) = insert (op =) (name, SOME T)
718 | iterm_vars (IAbs (_, tm)) = iterm_vars tm
719 fun close_iformula_universally phi = close_universally iterm_vars phi
721 fun term_vars bounds (ATerm (name as (s, _), tms)) =
722 (is_tptp_variable s andalso not (member (op =) bounds name))
723 ? insert (op =) (name, NONE) #> fold (term_vars bounds) tms
724 | term_vars bounds (AAbs ((name, _), tm)) = term_vars (name :: bounds) tm
725 fun close_formula_universally phi = close_universally (term_vars []) phi
727 val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
728 val homo_infinite_type = Type (homo_infinite_type_name, [])
730 fun ho_term_from_typ format type_enc =
732 fun term (Type (s, Ts)) =
733 ATerm (case (is_type_enc_higher_order type_enc, s) of
734 (true, @{type_name bool}) => `I tptp_bool_type
735 | (true, @{type_name fun}) => `I tptp_fun_type
736 | _ => if s = homo_infinite_type_name andalso
737 (format = TFF orelse format = THF) then
738 `I tptp_individual_type
740 `make_fixed_type_const s,
742 | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
743 | term (TVar ((x as (s, _)), _)) =
744 ATerm ((make_schematic_type_var x, s), [])
747 fun ho_term_for_type_arg format type_enc T =
748 if T = dummyT then NONE else SOME (ho_term_from_typ format type_enc T)
750 (* This shouldn't clash with anything else. *)
751 val mangled_type_sep = "\000"
753 fun generic_mangled_type_name f (ATerm (name, [])) = f name
754 | generic_mangled_type_name f (ATerm (name, tys)) =
755 f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
757 | generic_mangled_type_name _ _ = raise Fail "unexpected type abstraction"
759 val bool_atype = AType (`I tptp_bool_type)
761 fun make_simple_type s =
762 if s = tptp_bool_type orelse s = tptp_fun_type orelse
763 s = tptp_individual_type then
766 simple_type_prefix ^ ascii_of s
768 fun ho_type_from_ho_term type_enc pred_sym ary =
771 AType ((make_simple_type (generic_mangled_type_name fst ty),
772 generic_mangled_type_name snd ty))
773 fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
774 fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
775 | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
776 | to_fo _ _ = raise Fail "unexpected type abstraction"
777 fun to_ho (ty as ATerm ((s, _), tys)) =
778 if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
779 | to_ho _ = raise Fail "unexpected type abstraction"
780 in if is_type_enc_higher_order type_enc then to_ho else to_fo ary end
782 fun ho_type_from_typ format type_enc pred_sym ary =
783 ho_type_from_ho_term type_enc pred_sym ary
784 o ho_term_from_typ format type_enc
786 fun mangled_const_name format type_enc T_args (s, s') =
788 val ty_args = T_args |> map_filter (ho_term_for_type_arg format type_enc)
789 fun type_suffix f g =
790 fold_rev (curry (op ^) o g o prefix mangled_type_sep
791 o generic_mangled_type_name f) ty_args ""
792 in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
794 val parse_mangled_ident =
795 Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
797 fun parse_mangled_type x =
799 -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
801 and parse_mangled_types x =
802 (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
804 fun unmangled_type s =
805 s |> suffix ")" |> raw_explode
806 |> Scan.finite Symbol.stopper
807 (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
808 quote s)) parse_mangled_type))
811 val unmangled_const_name = space_explode mangled_type_sep #> hd
812 fun unmangled_const s =
813 let val ss = space_explode mangled_type_sep s in
814 (hd ss, map unmangled_type (tl ss))
817 fun introduce_proxies type_enc =
819 fun intro top_level (IApp (tm1, tm2)) =
820 IApp (intro top_level tm1, intro false tm2)
821 | intro top_level (IConst (name as (s, _), T, T_args)) =
822 (case proxify_const s of
824 if top_level orelse is_type_enc_higher_order type_enc then
825 case (top_level, s) of
826 (_, "c_False") => (`I tptp_false, [])
827 | (_, "c_True") => (`I tptp_true, [])
828 | (false, "c_Not") => (`I tptp_not, [])
829 | (false, "c_conj") => (`I tptp_and, [])
830 | (false, "c_disj") => (`I tptp_or, [])
831 | (false, "c_implies") => (`I tptp_implies, [])
832 | (false, "c_All") => (`I tptp_ho_forall, [])
833 | (false, "c_Ex") => (`I tptp_ho_exists, [])
835 if is_tptp_equal s then (`I tptp_equal, [])
836 else (proxy_base |>> prefix const_prefix, T_args)
839 (proxy_base |>> prefix const_prefix, T_args)
840 | NONE => (name, T_args))
841 |> (fn (name, T_args) => IConst (name, T, T_args))
842 | intro _ (IAbs (bound, tm)) = IAbs (bound, intro false tm)
846 fun iformula_from_prop thy type_enc eq_as_iff =
848 fun do_term bs t atomic_types =
849 iterm_from_term thy bs (Envir.eta_contract t)
850 |>> (introduce_proxies type_enc #> AAtom)
851 ||> union (op =) atomic_types
852 fun do_quant bs q s T t' =
853 let val s = singleton (Name.variant_list (map fst bs)) s in
854 do_formula ((s, T) :: bs) t'
855 #>> mk_aquant q [(`make_bound_var s, SOME T)]
857 and do_conn bs c t1 t2 =
858 do_formula bs t1 ##>> do_formula bs t2 #>> uncurry (mk_aconn c)
859 and do_formula bs t =
861 @{const Trueprop} $ t1 => do_formula bs t1
862 | @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
863 | Const (@{const_name All}, _) $ Abs (s, T, t') =>
864 do_quant bs AForall s T t'
865 | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
866 do_quant bs AExists s T t'
867 | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
868 | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
869 | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
870 | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
871 if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
875 fun presimplify_term _ [] t = t
876 | presimplify_term ctxt presimp_consts t =
877 t |> exists_Const (member (op =) presimp_consts o fst) t
878 ? (Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
879 #> Meson.presimplify ctxt
882 fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
883 fun conceal_bounds Ts t =
884 subst_bounds (map (Free o apfst concealed_bound_name)
885 (0 upto length Ts - 1 ~~ Ts), t)
886 fun reveal_bounds Ts =
887 subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
888 (0 upto length Ts - 1 ~~ Ts))
890 fun is_fun_equality (@{const_name HOL.eq},
891 Type (_, [Type (@{type_name fun}, _), _])) = true
892 | is_fun_equality _ = false
894 fun extensionalize_term ctxt t =
895 if exists_Const is_fun_equality t then
896 let val thy = Proof_Context.theory_of ctxt in
897 t |> cterm_of thy |> Meson.extensionalize_conv ctxt
898 |> prop_of |> Logic.dest_equals |> snd
903 fun simple_translate_lambdas do_lambdas ctxt t =
907 @{const Not} $ t1 => @{const Not} $ aux Ts t1
908 | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
909 t0 $ Abs (s, T, aux (T :: Ts) t')
910 | (t0 as Const (@{const_name All}, _)) $ t1 =>
911 aux Ts (t0 $ eta_expand Ts t1 1)
912 | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
913 t0 $ Abs (s, T, aux (T :: Ts) t')
914 | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
915 aux Ts (t0 $ eta_expand Ts t1 1)
916 | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
917 | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
918 | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
919 | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
921 t0 $ aux Ts t1 $ aux Ts t2
923 if not (exists_subterm (fn Abs _ => true | _ => false) t) then t
924 else t |> Envir.eta_contract |> do_lambdas ctxt Ts
925 val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
926 in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
928 fun do_conceal_lambdas Ts (t1 $ t2) =
929 do_conceal_lambdas Ts t1 $ do_conceal_lambdas Ts t2
930 | do_conceal_lambdas Ts (Abs (_, T, t)) =
931 (* slightly unsound because of hash collisions *)
932 Free (concealed_lambda_prefix ^ string_of_int (hash_term t),
933 T --> fastype_of1 (Ts, t))
934 | do_conceal_lambdas _ t = t
935 val conceal_lambdas = simple_translate_lambdas (K do_conceal_lambdas)
937 fun do_introduce_combinators ctxt Ts t =
938 let val thy = Proof_Context.theory_of ctxt in
939 t |> conceal_bounds Ts
941 |> Meson_Clausify.introduce_combinators_in_cterm
942 |> prop_of |> Logic.dest_equals |> snd
945 (* A type variable of sort "{}" will make abstraction fail. *)
946 handle THM _ => do_conceal_lambdas Ts t
947 val introduce_combinators = simple_translate_lambdas do_introduce_combinators
949 fun process_abstractions_in_terms ctxt trans_lambdas ps =
951 val thy = Proof_Context.theory_of ctxt
952 val (fo_ps, ho_ps) = ps |> List.partition (Meson.is_fol_term thy o snd)
953 in map snd fo_ps @ trans_lambdas ho_ps end
955 (* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
956 same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
959 fun aux (t $ u) = aux t $ aux u
960 | aux (Abs (s, T, t)) = Abs (s, T, aux t)
961 | aux (Var ((s, i), T)) =
962 Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
964 in t |> exists_subterm is_Var t ? aux end
966 fun preprocess_prop ctxt presimp_consts t =
968 val thy = Proof_Context.theory_of ctxt
969 val t = t |> Envir.beta_eta_contract
970 |> transform_elim_prop
971 |> Object_Logic.atomize_term thy
972 val need_trueprop = (fastype_of t = @{typ bool})
974 t |> need_trueprop ? HOLogic.mk_Trueprop
975 |> Raw_Simplifier.rewrite_term thy (Meson.unfold_set_const_simps ctxt) []
976 |> extensionalize_term ctxt
977 |> presimplify_term ctxt presimp_consts
978 |> perhaps (try (HOLogic.dest_Trueprop))
981 (* making fact and conjecture formulas *)
982 fun make_formula thy type_enc eq_as_iff name loc kind t =
984 val (iformula, atomic_types) =
985 iformula_from_prop thy type_enc eq_as_iff t []
987 {name = name, locality = loc, kind = kind, iformula = iformula,
988 atomic_types = atomic_types}
991 fun make_fact ctxt format type_enc eq_as_iff ((name, loc), t) =
992 let val thy = Proof_Context.theory_of ctxt in
993 case t |> make_formula thy type_enc (eq_as_iff andalso format <> CNF) name
995 formula as {iformula = AAtom (IConst ((s, _), _, _)), ...} =>
996 if s = tptp_true then NONE else SOME formula
997 | formula => SOME formula
1000 fun make_conjecture ctxt format type_enc ps =
1002 val thy = Proof_Context.theory_of ctxt
1003 val last = length ps - 1
1005 map2 (fn j => fn (kind, t) =>
1006 t |> make_formula thy type_enc (format <> CNF) (string_of_int j)
1008 |> (j <> last) = (kind = Conjecture) ? update_iformula mk_anot)
1012 (** Finite and infinite type inference **)
1014 fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
1015 | deep_freeze_atyp T = T
1016 val deep_freeze_type = map_atyps deep_freeze_atyp
1018 (* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
1019 dangerous because their "exhaust" properties can easily lead to unsound ATP
1020 proofs. On the other hand, all HOL infinite types can be given the same
1021 models in first-order logic (via Löwenheim-Skolem). *)
1023 fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
1024 exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
1025 | should_encode_type _ _ All_Types _ = true
1026 | should_encode_type ctxt _ Fin_Nonmono_Types T =
1027 is_type_surely_finite ctxt false T
1028 | should_encode_type _ _ _ _ = false
1030 fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
1031 should_predicate_on_var T =
1032 (heaviness = Heavyweight orelse should_predicate_on_var ()) andalso
1033 should_encode_type ctxt nonmono_Ts level T
1034 | should_predicate_on_type _ _ _ _ _ = false
1036 fun is_var_or_bound_var (IConst ((s, _), _, _)) =
1037 String.isPrefix bound_var_prefix s
1038 | is_var_or_bound_var (IVar _) = true
1039 | is_var_or_bound_var _ = false
1042 Top_Level of bool option |
1043 Eq_Arg of bool option |
1046 fun should_tag_with_type _ _ _ (Top_Level _) _ _ = false
1047 | should_tag_with_type ctxt nonmono_Ts (Tags (poly, level, heaviness)) site
1050 Heavyweight => should_encode_type ctxt nonmono_Ts level T
1052 case (site, is_var_or_bound_var u) of
1053 (Eq_Arg pos, true) =>
1054 (* The first disjunct prevents a subtle soundness issue explained in
1055 Blanchette's Ph.D. thesis. See also
1056 "formula_lines_for_lightweight_tags_sym_decl". *)
1057 (pos <> SOME false andalso poly = Polymorphic andalso
1058 level <> All_Types andalso heaviness = Lightweight andalso
1059 exists (fn T' => type_instance ctxt (T', T)) nonmono_Ts) orelse
1060 should_encode_type ctxt nonmono_Ts level T
1062 | should_tag_with_type _ _ _ _ _ _ = false
1064 fun homogenized_type ctxt nonmono_Ts level =
1066 val should_encode = should_encode_type ctxt nonmono_Ts level
1067 fun homo 0 T = if should_encode T then T else homo_infinite_type
1068 | homo ary (Type (@{type_name fun}, [T1, T2])) =
1069 homo 0 T1 --> homo (ary - 1) T2
1070 | homo _ _ = raise Fail "expected function type"
1073 (** "hBOOL" and "hAPP" **)
1076 {pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
1078 fun add_iterm_syms_to_table ctxt explicit_apply =
1080 fun consider_var_arity const_T var_T max_ary =
1083 if ary = max_ary orelse type_instance ctxt (var_T, T) orelse
1084 type_instance ctxt (T, var_T) then
1087 iter (ary + 1) (range_type T)
1088 in iter 0 const_T end
1089 fun add_var_or_bound_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1090 if explicit_apply = NONE andalso
1091 (can dest_funT T orelse T = @{typ bool}) then
1093 val bool_vars' = bool_vars orelse body_type T = @{typ bool}
1094 fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
1095 {pred_sym = pred_sym andalso not bool_vars',
1096 min_ary = fold (fn T' => consider_var_arity T' T) types min_ary,
1097 max_ary = max_ary, types = types}
1099 fun_var_Ts |> can dest_funT T ? insert_type ctxt I T
1101 if bool_vars' = bool_vars andalso
1102 pointer_eq (fun_var_Ts', fun_var_Ts) then
1105 ((bool_vars', fun_var_Ts'), Symtab.map (K repair_min_arity) sym_tab)
1109 fun add top_level tm (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1110 let val (head, args) = strip_iterm_comb tm in
1112 IConst ((s, _), T, _) =>
1113 if String.isPrefix bound_var_prefix s then
1114 add_var_or_bound_var T accum
1116 let val ary = length args in
1117 ((bool_vars, fun_var_Ts),
1118 case Symtab.lookup sym_tab s of
1119 SOME {pred_sym, min_ary, max_ary, types} =>
1122 pred_sym andalso top_level andalso not bool_vars
1123 val types' = types |> insert_type ctxt I T
1125 if is_some explicit_apply orelse
1126 pointer_eq (types', types) then
1129 fold (consider_var_arity T) fun_var_Ts min_ary
1131 Symtab.update (s, {pred_sym = pred_sym,
1132 min_ary = Int.min (ary, min_ary),
1133 max_ary = Int.max (ary, max_ary),
1139 val pred_sym = top_level andalso not bool_vars
1141 case explicit_apply of
1144 | NONE => fold (consider_var_arity T) fun_var_Ts ary
1146 Symtab.update_new (s, {pred_sym = pred_sym,
1147 min_ary = min_ary, max_ary = ary,
1152 | IVar (_, T) => add_var_or_bound_var T accum
1153 | IAbs ((_, T), tm) => accum |> add_var_or_bound_var T |> add false tm
1155 |> fold (add false) args
1158 fun add_fact_syms_to_table ctxt explicit_apply =
1159 fact_lift (formula_fold NONE
1160 (K (add_iterm_syms_to_table ctxt explicit_apply)))
1162 val default_sym_tab_entries : (string * sym_info) list =
1163 (prefixed_predicator_name,
1164 {pred_sym = true, min_ary = 1, max_ary = 1, types = []}) ::
1165 ([tptp_false, tptp_true]
1166 |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []})) @
1167 ([tptp_equal, tptp_old_equal]
1168 |> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = []}))
1170 fun sym_table_for_facts ctxt explicit_apply facts =
1171 ((false, []), Symtab.empty)
1172 |> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
1173 |> fold Symtab.update default_sym_tab_entries
1175 fun min_arity_of sym_tab s =
1176 case Symtab.lookup sym_tab s of
1177 SOME ({min_ary, ...} : sym_info) => min_ary
1179 case strip_prefix_and_unascii const_prefix s of
1181 let val s = s |> unmangled_const_name |> invert_const in
1182 if s = predicator_name then 1
1183 else if s = app_op_name then 2
1184 else if s = type_pred_name then 1
1189 (* True if the constant ever appears outside of the top-level position in
1190 literals, or if it appears with different arities (e.g., because of different
1191 type instantiations). If false, the constant always receives all of its
1192 arguments and is used as a predicate. *)
1193 fun is_pred_sym sym_tab s =
1194 case Symtab.lookup sym_tab s of
1195 SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
1196 pred_sym andalso min_ary = max_ary
1199 val predicator_combconst =
1200 IConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
1201 fun predicator tm = IApp (predicator_combconst, tm)
1203 fun introduce_predicators_in_iterm sym_tab tm =
1204 case strip_iterm_comb tm of
1205 (IConst ((s, _), _, _), _) =>
1206 if is_pred_sym sym_tab s then tm else predicator tm
1207 | _ => predicator tm
1209 fun list_app head args = fold (curry (IApp o swap)) args head
1211 val app_op = `make_fixed_const app_op_name
1213 fun explicit_app arg head =
1215 val head_T = ityp_of head
1216 val (arg_T, res_T) = dest_funT head_T
1217 val explicit_app = IConst (app_op, head_T --> head_T, [arg_T, res_T])
1218 in list_app explicit_app [head, arg] end
1219 fun list_explicit_app head args = fold explicit_app args head
1221 fun introduce_explicit_apps_in_iterm sym_tab =
1224 case strip_iterm_comb tm of
1225 (head as IConst ((s, _), _, _), args) =>
1227 |> chop (min_arity_of sym_tab s)
1229 |-> list_explicit_app
1230 | (head, args) => list_explicit_app head (map aux args)
1233 fun chop_fun 0 T = ([], T)
1234 | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
1235 chop_fun (n - 1) ran_T |>> cons dom_T
1236 | chop_fun _ _ = raise Fail "unexpected non-function"
1238 fun filter_type_args _ _ _ [] = []
1239 | filter_type_args thy s arity T_args =
1241 (* will throw "TYPE" for pseudo-constants *)
1242 val U = if s = app_op_name then
1243 @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
1245 s |> Sign.the_const_type thy
1247 case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
1250 let val U_args = (s, U) |> Sign.const_typargs thy in
1252 |> map (fn (U, T) =>
1253 if member (op =) res_U_vars (dest_TVar U) then T
1257 handle TYPE _ => T_args
1259 fun enforce_type_arg_policy_in_iterm ctxt format type_enc =
1261 val thy = Proof_Context.theory_of ctxt
1262 fun aux arity (IApp (tm1, tm2)) = IApp (aux (arity + 1) tm1, aux 0 tm2)
1263 | aux arity (IConst (name as (s, _), T, T_args)) =
1264 (case strip_prefix_and_unascii const_prefix s of
1265 NONE => (name, T_args)
1268 val s'' = invert_const s''
1269 fun filtered_T_args false = T_args
1270 | filtered_T_args true = filter_type_args thy s'' arity T_args
1272 case type_arg_policy type_enc s'' of
1273 Explicit_Type_Args drop_args =>
1274 (name, filtered_T_args drop_args)
1275 | Mangled_Type_Args drop_args =>
1276 (mangled_const_name format type_enc (filtered_T_args drop_args)
1278 | No_Type_Args => (name, [])
1280 |> (fn (name, T_args) => IConst (name, T, T_args))
1281 | aux _ (IAbs (bound, tm)) = IAbs (bound, aux 0 tm)
1285 fun repair_iterm ctxt format type_enc sym_tab =
1286 not (is_type_enc_higher_order type_enc)
1287 ? (introduce_explicit_apps_in_iterm sym_tab
1288 #> introduce_predicators_in_iterm sym_tab)
1289 #> enforce_type_arg_policy_in_iterm ctxt format type_enc
1290 fun repair_fact ctxt format type_enc sym_tab =
1291 update_iformula (formula_map (repair_iterm ctxt format type_enc sym_tab))
1293 (** Helper facts **)
1295 (* The Boolean indicates that a fairly sound type encoding is needed. *)
1297 [(("COMBI", false), @{thms Meson.COMBI_def}),
1298 (("COMBK", false), @{thms Meson.COMBK_def}),
1299 (("COMBB", false), @{thms Meson.COMBB_def}),
1300 (("COMBC", false), @{thms Meson.COMBC_def}),
1301 (("COMBS", false), @{thms Meson.COMBS_def}),
1302 (("fFalse", false), [@{lemma "~ fFalse" by (unfold fFalse_def) fast}]),
1303 (("fFalse", true), @{thms True_or_False}),
1304 (("fTrue", false), [@{lemma "fTrue" by (unfold fTrue_def) fast}]),
1305 (("fTrue", true), @{thms True_or_False}),
1307 @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1308 fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1310 @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
1311 by (unfold fconj_def) fast+}),
1313 @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
1314 by (unfold fdisj_def) fast+}),
1315 (("fimplies", false),
1316 @{lemma "P | fimplies P Q" "~ Q | fimplies P Q" "~ fimplies P Q | ~ P | Q"
1317 by (unfold fimplies_def) fast+}),
1319 (* This is a lie: Higher-order equality doesn't need a sound type encoding.
1320 However, this is done so for backward compatibility: Including the
1321 equality helpers by default in Metis breaks a few existing proofs. *)
1322 @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1323 fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1324 (("fAll", false), []), (*TODO: add helpers*)
1325 (("fEx", false), []), (*TODO: add helpers*)
1326 (("If", true), @{thms if_True if_False True_or_False})]
1327 |> map (apsnd (map zero_var_indexes))
1329 val type_tag = `make_fixed_const type_tag_name
1331 fun type_tag_idempotence_fact () =
1333 fun var s = ATerm (`I s, [])
1334 fun tag tm = ATerm (type_tag, [var "T", tm])
1335 val tagged_a = tag (var "A")
1337 Formula (type_tag_idempotence_helper_name, Axiom,
1338 AAtom (ATerm (`I tptp_equal, [tag tagged_a, tagged_a]))
1339 |> close_formula_universally, isabelle_info simpN, NONE)
1342 fun should_specialize_helper type_enc t =
1343 polymorphism_of_type_enc type_enc = Mangled_Monomorphic andalso
1344 level_of_type_enc type_enc <> No_Types andalso
1345 not (null (Term.hidden_polymorphism t))
1347 fun helper_facts_for_sym ctxt format type_enc (s, {types, ...} : sym_info) =
1348 case strip_prefix_and_unascii const_prefix s of
1351 val thy = Proof_Context.theory_of ctxt
1352 val unmangled_s = mangled_s |> unmangled_const_name
1353 fun dub needs_fairly_sound j k =
1354 (unmangled_s ^ "_" ^ string_of_int j ^ "_" ^ string_of_int k ^
1355 (if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^
1356 (if needs_fairly_sound then typed_helper_suffix
1357 else untyped_helper_suffix),
1359 fun dub_and_inst needs_fairly_sound (th, j) =
1360 let val t = prop_of th in
1361 if should_specialize_helper type_enc t then
1362 map (fn T => specialize_type thy (invert_const unmangled_s, T) t)
1367 |> map (fn (k, t) => (dub needs_fairly_sound j k, t)) o tag_list 1
1368 val make_facts = map_filter (make_fact ctxt format type_enc false)
1369 val fairly_sound = is_type_enc_fairly_sound type_enc
1372 |> maps (fn ((helper_s, needs_fairly_sound), ths) =>
1373 if helper_s <> unmangled_s orelse
1374 (needs_fairly_sound andalso not fairly_sound) then
1377 ths ~~ (1 upto length ths)
1378 |> maps (dub_and_inst needs_fairly_sound)
1382 fun helper_facts_for_sym_table ctxt format type_enc sym_tab =
1383 Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_enc) sym_tab
1386 (***************************************************************)
1387 (* Type Classes Present in the Axiom or Conjecture Clauses *)
1388 (***************************************************************)
1390 fun set_insert (x, s) = Symtab.update (x, ()) s
1392 fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
1394 (* Remove this trivial type class (FIXME: similar code elsewhere) *)
1395 fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
1397 fun classes_of_terms get_Ts =
1398 map (map snd o get_Ts)
1399 #> List.foldl add_classes Symtab.empty
1400 #> delete_type #> Symtab.keys
1402 val tfree_classes_of_terms = classes_of_terms OldTerm.term_tfrees
1403 val tvar_classes_of_terms = classes_of_terms OldTerm.term_tvars
1405 fun fold_type_constrs f (Type (s, Ts)) x =
1406 fold (fold_type_constrs f) Ts (f (s, x))
1407 | fold_type_constrs _ _ x = x
1409 (*Type constructors used to instantiate overloaded constants are the only ones needed.*)
1410 fun add_type_constrs_in_term thy =
1412 fun add (Const (@{const_name Meson.skolem}, _) $ _) = I
1413 | add (t $ u) = add t #> add u
1414 | add (Const (x as (s, _))) =
1415 if String.isPrefix skolem_const_prefix s then I
1416 else x |> Sign.const_typargs thy |> fold (fold_type_constrs set_insert)
1417 | add (Abs (_, _, u)) = add u
1421 fun type_constrs_of_terms thy ts =
1422 Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty)
1424 fun translate_formulas ctxt format prem_kind type_enc trans_lambdas preproc
1425 hyp_ts concl_t facts =
1427 val thy = Proof_Context.theory_of ctxt
1428 val presimp_consts = Meson.presimplified_consts ctxt
1429 fun preprocess kind =
1430 preprocess_prop ctxt presimp_consts
1431 #> pair kind #> single
1432 #> process_abstractions_in_terms ctxt trans_lambdas
1434 val fact_ts = facts |> map snd
1435 (* Remove existing facts from the conjecture, as this can dramatically
1436 boost an ATP's performance (for some reason). *)
1439 |> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t)
1440 val fact_ts = facts |> map snd |> preproc ? map (preprocess Axiom)
1442 map (pair prem_kind) hyp_ts @ [(Conjecture, concl_t)]
1444 ? map (fn (kind, t) => (kind, t |> preprocess kind |> freeze_term))
1445 val (facts, fact_names) =
1446 map2 (fn (name, _) => fn t =>
1447 (make_fact ctxt format type_enc true (name, t), name))
1449 |> map_filter (try (apfst the))
1451 val conjs = make_conjecture ctxt format type_enc conj_ps
1452 val all_ts = concl_t :: hyp_ts @ fact_ts
1453 val subs = tfree_classes_of_terms all_ts
1454 val supers = tvar_classes_of_terms all_ts
1455 val tycons = type_constrs_of_terms thy all_ts
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_iterm ctxt format type_enc T tm =
1474 IApp (IConst (type_pred, T --> @{typ bool}, [T])
1475 |> enforce_type_arg_policy_in_iterm 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 IConst (type_tag, T --> T, [T])
1490 |> enforce_type_arg_policy_in_iterm ctxt format type_enc
1491 |> ho_term_from_iterm 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_iterm ctxt format nonmono_Ts type_enc =
1498 val (head, args) = strip_iterm_comb u
1501 Top_Level pos => pos
1506 IConst (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)
1513 mk_aterm format type_enc name [] (map (aux Elsewhere) args)
1514 | IAbs ((name, T), tm) =>
1515 AAbs ((name, ho_type_from_typ format type_enc true 0 T),
1517 | IApp _ => raise Fail "impossible \"IApp\""
1520 t |> (if should_tag_with_type ctxt nonmono_Ts type_enc site u T then
1521 tag_with_type ctxt format nonmono_Ts type_enc pos T
1526 and formula_from_iformula ctxt format nonmono_Ts type_enc
1527 should_predicate_on_var =
1529 val do_term = ho_term_from_iterm ctxt format nonmono_Ts type_enc o Top_Level
1532 Simple_Types (_, level) =>
1533 homogenized_type ctxt nonmono_Ts level 0
1534 #> ho_type_from_typ format type_enc false 0 #> SOME
1536 fun do_out_of_bound_type pos phi universal (name, T) =
1537 if should_predicate_on_type ctxt nonmono_Ts type_enc
1538 (fn () => should_predicate_on_var pos phi universal name) T then
1540 |> type_pred_iterm ctxt format type_enc T
1541 |> do_term pos |> AAtom |> SOME
1544 fun do_formula pos (AQuant (q, xs, phi)) =
1546 val phi = phi |> do_formula pos
1547 val universal = Option.map (q = AExists ? not) pos
1549 AQuant (q, xs |> map (apsnd (fn NONE => NONE
1550 | SOME T => do_bound_type T)),
1551 (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
1553 (fn (_, NONE) => NONE
1555 do_out_of_bound_type pos phi universal (s, T))
1559 | do_formula pos (AConn conn) = aconn_map pos do_formula conn
1560 | do_formula pos (AAtom tm) = AAtom (do_term pos tm)
1563 fun bound_tvars type_enc Ts =
1564 mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
1565 (type_literals_for_types type_enc add_sorts_on_tvar Ts))
1567 (* Each fact is given a unique fact number to avoid name clashes (e.g., because
1568 of monomorphization). The TPTP explicitly forbids name clashes, and some of
1569 the remote provers might care. *)
1570 fun formula_line_for_fact ctxt format prefix encode freshen pos nonmono_Ts
1571 type_enc (j, {name, locality, kind, iformula, atomic_types}) =
1572 (prefix ^ (if freshen then string_of_int j ^ "_" else "") ^ encode name,
1575 |> close_iformula_universally
1576 |> formula_from_iformula ctxt format nonmono_Ts type_enc
1577 should_predicate_on_var_in_formula
1578 (if pos then SOME true else NONE)
1579 |> bound_tvars type_enc atomic_types
1580 |> close_formula_universally,
1583 Intro => isabelle_info introN
1584 | Elim => isabelle_info elimN
1585 | Simp => isabelle_info simpN
1589 fun formula_line_for_class_rel_clause ({name, subclass, superclass, ...}
1590 : class_rel_clause) =
1591 let val ty_arg = ATerm (`I "T", []) in
1592 Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
1593 AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
1594 AAtom (ATerm (superclass, [ty_arg]))])
1595 |> close_formula_universally, isabelle_info introN, NONE)
1598 fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
1599 (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
1600 | fo_literal_from_arity_literal (TVarLit (c, sort)) =
1601 (false, ATerm (c, [ATerm (sort, [])]))
1603 fun formula_line_for_arity_clause ({name, prem_lits, concl_lits, ...}
1605 Formula (arity_clause_prefix ^ name, Axiom,
1606 mk_ahorn (map (formula_from_fo_literal o apfst not
1607 o fo_literal_from_arity_literal) prem_lits)
1608 (formula_from_fo_literal
1609 (fo_literal_from_arity_literal concl_lits))
1610 |> close_formula_universally, isabelle_info introN, NONE)
1612 fun formula_line_for_conjecture ctxt format nonmono_Ts type_enc
1613 ({name, kind, iformula, atomic_types, ...} : translated_formula) =
1614 Formula (conjecture_prefix ^ name, kind,
1615 formula_from_iformula ctxt format nonmono_Ts type_enc
1616 should_predicate_on_var_in_formula (SOME false)
1617 (close_iformula_universally iformula)
1618 |> bound_tvars type_enc atomic_types
1619 |> close_formula_universally, NONE, NONE)
1621 fun free_type_literals type_enc ({atomic_types, ...} : translated_formula) =
1622 atomic_types |> type_literals_for_types type_enc add_sorts_on_tfree
1623 |> map fo_literal_from_type_literal
1625 fun formula_line_for_free_type j lit =
1626 Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis,
1627 formula_from_fo_literal lit, NONE, NONE)
1628 fun formula_lines_for_free_types type_enc facts =
1630 val litss = map (free_type_literals type_enc) facts
1631 val lits = fold (union (op =)) litss []
1632 in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
1634 (** Symbol declarations **)
1636 fun should_declare_sym type_enc pred_sym s =
1637 is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
1639 Simple_Types _ => true
1640 | Tags (_, _, Lightweight) => true
1641 | _ => not pred_sym)
1643 fun sym_decl_table_for_facts ctxt type_enc repaired_sym_tab (conjs, facts) =
1645 fun add_iterm in_conj tm =
1646 let val (head, args) = strip_iterm_comb tm in
1648 IConst ((s, s'), T, T_args) =>
1649 let val pred_sym = is_pred_sym repaired_sym_tab s in
1650 if should_declare_sym type_enc pred_sym s then
1651 Symtab.map_default (s, [])
1652 (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
1657 | IAbs (_, tm) => add_iterm in_conj tm
1659 #> fold (add_iterm in_conj) args
1661 fun add_fact in_conj = fact_lift (formula_fold NONE (K (add_iterm 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_iterm_nonmonotonic_types _ _ _ _ (SOME false) _ = I
1671 | add_iterm_nonmonotonic_types ctxt level sound locality _
1672 (IApp (IApp (IConst ((s, _), Type (_, [T, _]), _), tm1), tm2)) =
1673 (is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
1675 Noninf_Nonmono_Types =>
1676 not (is_locality_global locality) orelse
1677 not (is_type_surely_infinite ctxt sound T)
1678 | Fin_Nonmono_Types => is_type_surely_finite ctxt false T
1679 | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
1680 | add_iterm_nonmonotonic_types _ _ _ _ _ _ = I
1681 fun add_fact_nonmonotonic_types ctxt level sound
1682 ({kind, locality, iformula, ...} : translated_formula) =
1683 formula_fold (SOME (kind <> Conjecture))
1684 (add_iterm_nonmonotonic_types ctxt level sound locality)
1686 fun nonmonotonic_types_for_facts ctxt type_enc sound facts =
1687 let val level = level_of_type_enc type_enc in
1688 if level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types then
1689 [] |> fold (add_fact_nonmonotonic_types ctxt level sound) facts
1690 (* We must add "bool" in case the helper "True_or_False" is added
1691 later. In addition, several places in the code rely on the list of
1692 nonmonotonic types not being empty. *)
1693 |> insert_type ctxt I @{typ bool}
1698 fun decl_line_for_sym ctxt format nonmono_Ts type_enc s
1699 (s', T_args, T, pred_sym, ary, _) =
1701 val (T_arg_Ts, level) =
1703 Simple_Types (_, level) => ([], level)
1704 | _ => (replicate (length T_args) homo_infinite_type, No_Types)
1706 Decl (sym_decl_prefix ^ s, (s, s'),
1707 (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
1708 |> ho_type_from_typ format type_enc pred_sym (length T_arg_Ts + ary))
1711 fun formula_line_for_preds_sym_decl ctxt format conj_sym_kind nonmono_Ts
1712 poly_nonmono_Ts type_enc n s j (s', T_args, T, _, ary, in_conj) =
1714 val (kind, maybe_negate) =
1715 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1717 val (arg_Ts, res_T) = chop_fun ary T
1718 val num_args = length arg_Ts
1720 1 upto num_args |> map (`I o make_bound_var o string_of_int)
1722 bound_names ~~ arg_Ts |> map (fn (name, T) => IConst (name, T, []))
1723 val sym_needs_arg_types = n > 1 orelse exists (curry (op =) dummyT) T_args
1724 fun should_keep_arg_type T =
1725 sym_needs_arg_types orelse
1726 not (should_predicate_on_type ctxt nonmono_Ts type_enc (K false) T)
1728 arg_Ts |> map (fn T => if should_keep_arg_type T then SOME T else NONE)
1730 Formula (preds_sym_formula_prefix ^ s ^
1731 (if n > 1 then "_" ^ string_of_int j else ""), kind,
1732 IConst ((s, s'), T, T_args)
1733 |> fold (curry (IApp o swap)) bounds
1734 |> type_pred_iterm ctxt format type_enc res_T
1735 |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
1736 |> formula_from_iformula ctxt format poly_nonmono_Ts type_enc
1737 (K (K (K (K true)))) (SOME true)
1738 |> n > 1 ? bound_tvars type_enc (atyps_of T)
1739 |> close_formula_universally
1741 isabelle_info introN, NONE)
1744 fun formula_lines_for_lightweight_tags_sym_decl ctxt format conj_sym_kind
1745 poly_nonmono_Ts type_enc n s
1746 (j, (s', T_args, T, pred_sym, ary, in_conj)) =
1749 lightweight_tags_sym_formula_prefix ^ s ^
1750 (if n > 1 then "_" ^ string_of_int j else "")
1751 val (kind, maybe_negate) =
1752 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1754 val (arg_Ts, res_T) = chop_fun ary T
1756 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
1757 val bounds = bound_names |> map (fn name => ATerm (name, []))
1758 val cst = mk_aterm format type_enc (s, s') T_args
1759 val atomic_Ts = atyps_of T
1761 (if pred_sym then AConn (AIff, map AAtom tms)
1762 else AAtom (ATerm (`I tptp_equal, tms)))
1763 |> bound_tvars type_enc atomic_Ts
1764 |> close_formula_universally
1766 (* See also "should_tag_with_type". *)
1767 fun should_encode T =
1768 should_encode_type ctxt poly_nonmono_Ts All_Types T orelse
1770 Tags (Polymorphic, level, Lightweight) =>
1771 level <> All_Types andalso Monomorph.typ_has_tvars T
1773 val tag_with = tag_with_type ctxt format poly_nonmono_Ts type_enc NONE
1774 val add_formula_for_res =
1775 if should_encode res_T then
1776 cons (Formula (ident_base ^ "_res", kind,
1777 eq [tag_with res_T (cst bounds), cst bounds],
1778 isabelle_info simpN, NONE))
1781 fun add_formula_for_arg k =
1782 let val arg_T = nth arg_Ts k in
1783 if should_encode arg_T then
1784 case chop k bounds of
1785 (bounds1, bound :: bounds2) =>
1786 cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
1787 eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
1789 isabelle_info simpN, NONE))
1790 | _ => raise Fail "expected nonempty tail"
1795 [] |> not pred_sym ? add_formula_for_res
1796 |> fold add_formula_for_arg (ary - 1 downto 0)
1799 fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
1801 fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts
1802 poly_nonmono_Ts type_enc (s, decls) =
1805 decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_enc s)
1810 decl :: (decls' as _ :: _) =>
1811 let val T = result_type_of_decl decl in
1812 if forall (curry (type_instance ctxt o swap) T
1813 o result_type_of_decl) decls' then
1819 val n = length decls
1821 decls |> filter (should_predicate_on_type ctxt poly_nonmono_Ts type_enc
1823 o result_type_of_decl)
1825 (0 upto length decls - 1, decls)
1826 |-> map2 (formula_line_for_preds_sym_decl ctxt format conj_sym_kind
1827 nonmono_Ts poly_nonmono_Ts type_enc n s)
1829 | Tags (_, _, heaviness) =>
1833 let val n = length decls in
1834 (0 upto n - 1 ~~ decls)
1835 |> maps (formula_lines_for_lightweight_tags_sym_decl ctxt format
1836 conj_sym_kind poly_nonmono_Ts type_enc n s)
1839 fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1840 poly_nonmono_Ts type_enc sym_decl_tab =
1845 |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
1846 nonmono_Ts poly_nonmono_Ts type_enc)
1848 fun needs_type_tag_idempotence (Tags (poly, level, heaviness)) =
1849 poly <> Mangled_Monomorphic andalso
1850 ((level = All_Types andalso heaviness = Lightweight) orelse
1851 level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types)
1852 | needs_type_tag_idempotence _ = false
1854 fun offset_of_heading_in_problem _ [] j = j
1855 | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
1856 if heading = needle then j
1857 else offset_of_heading_in_problem needle problem (j + length lines)
1859 val implicit_declsN = "Should-be-implicit typings"
1860 val explicit_declsN = "Explicit typings"
1861 val factsN = "Relevant facts"
1862 val class_relsN = "Class relationships"
1863 val aritiesN = "Arities"
1864 val helpersN = "Helper facts"
1865 val conjsN = "Conjectures"
1866 val free_typesN = "Type variables"
1868 val explicit_apply = NONE (* for experiments *)
1870 fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_enc sound
1871 exporter trans_lambdas readable_names preproc hyp_ts concl_t facts =
1873 val (format, type_enc) = choose_format [format] type_enc
1874 val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
1875 translate_formulas ctxt format prem_kind type_enc trans_lambdas preproc
1876 hyp_ts concl_t facts
1877 val sym_tab = conjs @ facts |> sym_table_for_facts ctxt explicit_apply
1879 conjs @ facts |> nonmonotonic_types_for_facts ctxt type_enc sound
1880 val repair = repair_fact ctxt format type_enc sym_tab
1881 val (conjs, facts) = (conjs, facts) |> pairself (map repair)
1882 val repaired_sym_tab =
1883 conjs @ facts |> sym_table_for_facts ctxt (SOME false)
1885 repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_enc
1887 val poly_nonmono_Ts =
1888 if null nonmono_Ts orelse nonmono_Ts = [@{typ bool}] orelse
1889 polymorphism_of_type_enc type_enc <> Polymorphic then
1892 [TVar (("'a", 0), HOLogic.typeS)]
1893 val sym_decl_lines =
1894 (conjs, helpers @ facts)
1895 |> sym_decl_table_for_facts ctxt type_enc repaired_sym_tab
1896 |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1897 poly_nonmono_Ts type_enc
1899 0 upto length helpers - 1 ~~ helpers
1900 |> map (formula_line_for_fact ctxt format helper_prefix I false true
1901 poly_nonmono_Ts type_enc)
1902 |> (if needs_type_tag_idempotence type_enc then
1903 cons (type_tag_idempotence_fact ())
1906 (* Reordering these might confuse the proof reconstruction code or the SPASS
1909 [(explicit_declsN, sym_decl_lines),
1911 map (formula_line_for_fact ctxt format fact_prefix ascii_of
1912 (not exporter) (not exporter) nonmono_Ts
1914 (0 upto length facts - 1 ~~ facts)),
1915 (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
1916 (aritiesN, map formula_line_for_arity_clause arity_clauses),
1917 (helpersN, helper_lines),
1919 map (formula_line_for_conjecture ctxt format nonmono_Ts type_enc)
1921 (free_typesN, formula_lines_for_free_types type_enc (facts @ conjs))]
1925 CNF => ensure_cnf_problem
1926 | CNF_UEQ => filter_cnf_ueq_problem
1928 |> (if is_format_typed format then
1929 declare_undeclared_syms_in_atp_problem type_decl_prefix
1933 val (problem, pool) = problem |> nice_atp_problem readable_names
1934 val helpers_offset = offset_of_heading_in_problem helpersN problem 0
1936 map_filter (fn (j, {name, ...}) =>
1937 if String.isSuffix typed_helper_suffix name then SOME j
1939 ((helpers_offset + 1 upto helpers_offset + length helpers)
1941 fun add_sym_arity (s, {min_ary, ...} : sym_info) =
1943 case strip_prefix_and_unascii const_prefix s of
1944 SOME s => Symtab.insert (op =) (s, min_ary)
1950 case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
1951 offset_of_heading_in_problem conjsN problem 0,
1952 offset_of_heading_in_problem factsN problem 0,
1953 fact_names |> Vector.fromList,
1955 Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
1959 val conj_weight = 0.0
1960 val hyp_weight = 0.1
1961 val fact_min_weight = 0.2
1962 val fact_max_weight = 1.0
1963 val type_info_default_weight = 0.8
1965 fun add_term_weights weight (ATerm (s, tms)) =
1966 is_tptp_user_symbol s ? Symtab.default (s, weight)
1967 #> fold (add_term_weights weight) tms
1968 | add_term_weights weight (AAbs (_, tm)) = add_term_weights weight tm
1969 fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
1970 formula_fold NONE (K (add_term_weights weight)) phi
1971 | add_problem_line_weights _ _ = I
1973 fun add_conjectures_weights [] = I
1974 | add_conjectures_weights conjs =
1975 let val (hyps, conj) = split_last conjs in
1976 add_problem_line_weights conj_weight conj
1977 #> fold (add_problem_line_weights hyp_weight) hyps
1980 fun add_facts_weights facts =
1982 val num_facts = length facts
1984 fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
1985 / Real.fromInt num_facts
1987 map weight_of (0 upto num_facts - 1) ~~ facts
1988 |> fold (uncurry add_problem_line_weights)
1991 (* Weights are from 0.0 (most important) to 1.0 (least important). *)
1992 fun atp_problem_weights problem =
1993 let val get = these o AList.lookup (op =) problem in
1995 |> add_conjectures_weights (get free_typesN @ get conjsN)
1996 |> add_facts_weights (get factsN)
1997 |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
1998 [explicit_declsN, class_relsN, aritiesN]
2000 |> sort (prod_ord Real.compare string_ord o pairself swap)