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 Metis and 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 Guards 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 polymorphic_free_prefix : string
43 val skolem_const_prefix : string
44 val old_skolem_const_prefix : string
45 val new_skolem_const_prefix : string
46 val type_decl_prefix : string
47 val sym_decl_prefix : string
48 val guards_sym_formula_prefix : string
49 val lightweight_tags_sym_formula_prefix : string
50 val fact_prefix : string
51 val conjecture_prefix : string
52 val helper_prefix : string
53 val class_rel_clause_prefix : string
54 val arity_clause_prefix : string
55 val tfree_clause_prefix : string
56 val typed_helper_suffix : string
57 val untyped_helper_suffix : string
58 val type_tag_idempotence_helper_name : string
59 val predicator_name : string
60 val app_op_name : string
61 val type_tag_name : string
62 val type_pred_name : string
63 val simple_type_prefix : string
64 val prefixed_predicator_name : string
65 val prefixed_app_op_name : string
66 val prefixed_type_tag_name : string
67 val ascii_of : string -> string
68 val unascii_of : string -> string
69 val strip_prefix_and_unascii : string -> string -> string option
70 val proxy_table : (string * (string * (thm * (string * string)))) list
71 val proxify_const : string -> (string * string) option
72 val invert_const : string -> string
73 val unproxify_const : string -> string
74 val new_skolem_var_name_from_const : string -> string
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 introduce_combinators : Proof.context -> term -> term
92 val prepare_atp_problem :
93 Proof.context -> format -> formula_kind -> formula_kind -> type_enc -> bool
94 -> bool -> (term list -> term list * term list) -> bool -> bool -> term list
95 -> term -> ((string * locality) * term) list
96 -> string problem * string Symtab.table * int * int
97 * (string * locality) list vector * int list * int Symtab.table
98 val atp_problem_weights : string problem -> (string * real) list
101 structure ATP_Translate : ATP_TRANSLATE =
107 type name = string * string
109 val generate_info = false (* experimental *)
111 fun isabelle_info s =
112 if generate_info then SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
119 val bound_var_prefix = "B_"
120 val schematic_var_prefix = "V_"
121 val fixed_var_prefix = "v_"
122 val tvar_prefix = "T_"
123 val tfree_prefix = "t_"
124 val const_prefix = "c_"
125 val type_const_prefix = "tc_"
126 val class_prefix = "cl_"
128 val polymorphic_free_prefix = "poly_free"
130 val skolem_const_prefix = "ATP" ^ Long_Name.separator ^ "Sko"
131 val old_skolem_const_prefix = skolem_const_prefix ^ "o"
132 val new_skolem_const_prefix = skolem_const_prefix ^ "n"
134 val type_decl_prefix = "ty_"
135 val sym_decl_prefix = "sy_"
136 val guards_sym_formula_prefix = "gsy_"
137 val lightweight_tags_sym_formula_prefix = "tsy_"
138 val fact_prefix = "fact_"
139 val conjecture_prefix = "conj_"
140 val helper_prefix = "help_"
141 val class_rel_clause_prefix = "clar_"
142 val arity_clause_prefix = "arity_"
143 val tfree_clause_prefix = "tfree_"
145 val lambda_fact_prefix = "ATP.lambda_"
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 atp_weak_prefix = "ATP:"
163 (*Escaping of special characters.
164 Alphanumeric characters are left unchanged.
165 The character _ goes to __
166 Characters in the range ASCII space to / go to _A to _P, respectively.
167 Other characters go to _nnn where nnn is the decimal ASCII code.*)
168 val upper_a_minus_space = Char.ord #"A" - Char.ord #" "
170 fun stringN_of_int 0 _ = ""
171 | stringN_of_int k n =
172 stringN_of_int (k - 1) (n div 10) ^ string_of_int (n mod 10)
174 fun ascii_of_char c =
175 if Char.isAlphaNum c then
177 else if c = #"_" then
179 else if #" " <= c andalso c <= #"/" then
180 "_" ^ String.str (Char.chr (Char.ord c + upper_a_minus_space))
182 (* fixed width, in case more digits follow *)
183 "_" ^ stringN_of_int 3 (Char.ord c)
185 val ascii_of = String.translate ascii_of_char
187 (** Remove ASCII armoring from names in proof files **)
189 (* We don't raise error exceptions because this code can run inside a worker
190 thread. Also, the errors are impossible. *)
193 fun un rcs [] = String.implode(rev rcs)
194 | un rcs [#"_"] = un (#"_" :: rcs) [] (* ERROR *)
195 (* Three types of _ escapes: __, _A to _P, _nnn *)
196 | un rcs (#"_" :: #"_" :: cs) = un (#"_" :: rcs) cs
197 | un rcs (#"_" :: c :: cs) =
198 if #"A" <= c andalso c<= #"P" then
199 (* translation of #" " to #"/" *)
200 un (Char.chr (Char.ord c - upper_a_minus_space) :: rcs) cs
202 let val digits = List.take (c :: cs, 3) handle General.Subscript => [] in
203 case Int.fromString (String.implode digits) of
204 SOME n => un (Char.chr n :: rcs) (List.drop (cs, 2))
205 | NONE => un (c :: #"_" :: rcs) cs (* ERROR *)
207 | un rcs (c :: cs) = un (c :: rcs) cs
208 in un [] o String.explode end
210 (* If string s has the prefix s1, return the result of deleting it,
212 fun strip_prefix_and_unascii s1 s =
213 if String.isPrefix s1 s then
214 SOME (unascii_of (String.extract (s, size s1, NONE)))
219 [("c_False", (@{const_name False}, (@{thm fFalse_def},
220 ("fFalse", @{const_name ATP.fFalse})))),
221 ("c_True", (@{const_name True}, (@{thm fTrue_def},
222 ("fTrue", @{const_name ATP.fTrue})))),
223 ("c_Not", (@{const_name Not}, (@{thm fNot_def},
224 ("fNot", @{const_name ATP.fNot})))),
225 ("c_conj", (@{const_name conj}, (@{thm fconj_def},
226 ("fconj", @{const_name ATP.fconj})))),
227 ("c_disj", (@{const_name disj}, (@{thm fdisj_def},
228 ("fdisj", @{const_name ATP.fdisj})))),
229 ("c_implies", (@{const_name implies}, (@{thm fimplies_def},
230 ("fimplies", @{const_name ATP.fimplies})))),
231 ("equal", (@{const_name HOL.eq}, (@{thm fequal_def},
232 ("fequal", @{const_name ATP.fequal})))),
233 ("c_All", (@{const_name All}, (@{thm fAll_def},
234 ("fAll", @{const_name ATP.fAll})))),
235 ("c_Ex", (@{const_name Ex}, (@{thm fEx_def},
236 ("fEx", @{const_name ATP.fEx}))))]
238 val proxify_const = AList.lookup (op =) proxy_table #> Option.map (snd o snd)
240 (* Readable names for the more common symbolic functions. Do not mess with the
241 table unless you know what you are doing. *)
242 val const_trans_table =
243 [(@{type_name Product_Type.prod}, "prod"),
244 (@{type_name Sum_Type.sum}, "sum"),
245 (@{const_name False}, "False"),
246 (@{const_name True}, "True"),
247 (@{const_name Not}, "Not"),
248 (@{const_name conj}, "conj"),
249 (@{const_name disj}, "disj"),
250 (@{const_name implies}, "implies"),
251 (@{const_name HOL.eq}, "equal"),
252 (@{const_name All}, "All"),
253 (@{const_name Ex}, "Ex"),
254 (@{const_name If}, "If"),
255 (@{const_name Set.member}, "member"),
256 (@{const_name Meson.COMBI}, "COMBI"),
257 (@{const_name Meson.COMBK}, "COMBK"),
258 (@{const_name Meson.COMBB}, "COMBB"),
259 (@{const_name Meson.COMBC}, "COMBC"),
260 (@{const_name Meson.COMBS}, "COMBS")]
262 |> fold (Symtab.update o swap o snd o snd o snd) proxy_table
264 (* Invert the table of translations between Isabelle and ATPs. *)
265 val const_trans_table_inv =
266 const_trans_table |> Symtab.dest |> map swap |> Symtab.make
267 val const_trans_table_unprox =
269 |> fold (fn (_, (isa, (_, (_, atp)))) => Symtab.update (atp, isa)) proxy_table
271 val invert_const = perhaps (Symtab.lookup const_trans_table_inv)
272 val unproxify_const = perhaps (Symtab.lookup const_trans_table_unprox)
275 case Symtab.lookup const_trans_table c of
279 fun ascii_of_indexname (v, 0) = ascii_of v
280 | ascii_of_indexname (v, i) = ascii_of v ^ "_" ^ string_of_int i
282 fun make_bound_var x = bound_var_prefix ^ ascii_of x
283 fun make_schematic_var v = schematic_var_prefix ^ ascii_of_indexname v
284 fun make_fixed_var x = fixed_var_prefix ^ ascii_of x
286 fun make_schematic_type_var (x, i) =
287 tvar_prefix ^ (ascii_of_indexname (unprefix "'" x, i))
288 fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (unprefix "'" x))
290 (* "HOL.eq" is mapped to the ATP's equality. *)
291 fun make_fixed_const @{const_name HOL.eq} = tptp_old_equal
292 | make_fixed_const c = const_prefix ^ lookup_const c
294 fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
296 fun make_type_class clas = class_prefix ^ ascii_of clas
298 fun new_skolem_var_name_from_const s =
299 let val ss = s |> space_explode Long_Name.separator in
300 nth ss (length ss - 2)
303 (* These are either simplified away by "Meson.presimplify" (most of the time) or
304 handled specially via "fFalse", "fTrue", ..., "fequal". *)
305 val atp_irrelevant_consts =
306 [@{const_name False}, @{const_name True}, @{const_name Not},
307 @{const_name conj}, @{const_name disj}, @{const_name implies},
308 @{const_name HOL.eq}, @{const_name If}, @{const_name Let}]
310 val atp_monomorph_bad_consts =
311 atp_irrelevant_consts @
312 (* These are ignored anyway by the relevance filter (unless they appear in
313 higher-order places) but not by the monomorphizer. *)
314 [@{const_name all}, @{const_name "==>"}, @{const_name "=="},
315 @{const_name Trueprop}, @{const_name All}, @{const_name Ex},
316 @{const_name Ex1}, @{const_name Ball}, @{const_name Bex}]
318 fun add_schematic_const (x as (_, T)) =
319 Monomorph.typ_has_tvars T ? Symtab.insert_list (op =) x
320 val add_schematic_consts_of =
321 Term.fold_aterms (fn Const (x as (s, _)) =>
322 not (member (op =) atp_monomorph_bad_consts s)
323 ? add_schematic_const x
325 fun atp_schematic_consts_of t = add_schematic_consts_of t Symtab.empty
327 (** Definitions and functions for FOL clauses and formulas for TPTP **)
329 (* The first component is the type class; the second is a "TVar" or "TFree". *)
330 datatype type_literal =
331 TyLitVar of name * name |
332 TyLitFree of name * name
335 (** Isabelle arities **)
337 datatype arity_literal =
338 TConsLit of name * name * name list |
339 TVarLit of name * name
342 | gen_TVars n = ("T_" ^ string_of_int n) :: gen_TVars (n-1)
344 val type_class = the_single @{sort type}
346 fun add_packed_sort tvar =
347 fold (fn s => s <> type_class ? cons (`make_type_class s, `I tvar))
351 prem_lits : arity_literal list,
352 concl_lits : arity_literal}
354 (* Arity of type constructor "tcon :: (arg1, ..., argN) res" *)
355 fun make_axiom_arity_clause (tcons, name, (cls, args)) =
357 val tvars = gen_TVars (length args)
358 val tvars_srts = ListPair.zip (tvars, args)
361 prem_lits = [] |> fold (uncurry add_packed_sort) tvars_srts |> map TVarLit,
362 concl_lits = TConsLit (`make_type_class cls,
363 `make_fixed_type_const tcons,
367 fun arity_clause _ _ (_, []) = []
368 | arity_clause seen n (tcons, ("HOL.type", _) :: ars) = (* ignore *)
369 arity_clause seen n (tcons, ars)
370 | arity_clause seen n (tcons, (ar as (class, _)) :: ars) =
371 if member (op =) seen class then
372 (* multiple arities for the same (tycon, class) pair *)
373 make_axiom_arity_clause (tcons,
374 lookup_const tcons ^ "___" ^ ascii_of class ^ "_" ^ string_of_int n,
376 arity_clause seen (n + 1) (tcons, ars)
378 make_axiom_arity_clause (tcons, lookup_const tcons ^ "___" ^
379 ascii_of class, ar) ::
380 arity_clause (class :: seen) n (tcons, ars)
382 fun multi_arity_clause [] = []
383 | multi_arity_clause ((tcons, ars) :: tc_arlists) =
384 arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
386 (* Generate all pairs (tycon, class, sorts) such that tycon belongs to class in
387 theory thy provided its arguments have the corresponding sorts. *)
388 fun type_class_pairs thy tycons classes =
390 val alg = Sign.classes_of thy
391 fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
392 fun add_class tycon class =
393 cons (class, domain_sorts tycon class)
394 handle Sorts.CLASS_ERROR _ => I
395 fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
396 in map try_classes tycons end
398 (*Proving one (tycon, class) membership may require proving others, so iterate.*)
399 fun iter_type_class_pairs _ _ [] = ([], [])
400 | iter_type_class_pairs thy tycons classes =
402 fun maybe_insert_class s =
403 (s <> type_class andalso not (member (op =) classes s))
405 val cpairs = type_class_pairs thy tycons classes
407 [] |> fold (fold (fold (fold maybe_insert_class) o snd) o snd) cpairs
408 val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
409 in (classes' @ classes, union (op =) cpairs' cpairs) end
411 fun make_arity_clauses thy tycons =
412 iter_type_class_pairs thy tycons ##> multi_arity_clause
415 (** Isabelle class relations **)
417 type class_rel_clause =
422 (* Generate all pairs (sub, super) such that sub is a proper subclass of super
424 fun class_pairs _ [] _ = []
425 | class_pairs thy subs supers =
427 val class_less = Sorts.class_less (Sign.classes_of thy)
428 fun add_super sub super = class_less (sub, super) ? cons (sub, super)
429 fun add_supers sub = fold (add_super sub) supers
430 in fold add_supers subs [] end
432 fun make_class_rel_clause (sub, super) =
433 {name = sub ^ "_" ^ super, subclass = `make_type_class sub,
434 superclass = `make_type_class super}
436 fun make_class_rel_clauses thy subs supers =
437 map make_class_rel_clause (class_pairs thy subs supers)
439 (* intermediate terms *)
441 IConst of name * typ * typ list |
443 IApp of iterm * iterm |
444 IAbs of (name * typ) * iterm
446 fun ityp_of (IConst (_, T, _)) = T
447 | ityp_of (IVar (_, T)) = T
448 | ityp_of (IApp (t1, _)) = snd (dest_funT (ityp_of t1))
449 | ityp_of (IAbs ((_, T), tm)) = T --> ityp_of tm
451 (*gets the head of a combinator application, along with the list of arguments*)
452 fun strip_iterm_comb u =
454 fun stripc (IApp (t, u), ts) = stripc (t, u :: ts)
456 in stripc (u, []) end
458 fun atyps_of T = fold_atyps (insert (op =)) T []
460 fun new_skolem_const_name s num_T_args =
461 [new_skolem_const_prefix, s, string_of_int num_T_args]
462 |> space_implode Long_Name.separator
464 (* Converts an Isabelle/HOL term (with combinators) into an intermediate term.
465 Also accumulates sort infomation. *)
466 fun iterm_from_term thy bs (P $ Q) =
468 val (P', P_atomics_Ts) = iterm_from_term thy bs P
469 val (Q', Q_atomics_Ts) = iterm_from_term thy bs Q
470 in (IApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
471 | iterm_from_term thy _ (Const (c, T)) =
472 (IConst (`make_fixed_const c, T,
473 if String.isPrefix old_skolem_const_prefix c then
474 [] |> Term.add_tvarsT T |> map TVar
476 (c, T) |> Sign.const_typargs thy),
478 | iterm_from_term _ _ (Free (s, T)) =
479 (IConst (`make_fixed_var s, T,
480 if String.isPrefix polymorphic_free_prefix s then [T] else []),
482 | iterm_from_term _ _ (Var (v as (s, _), T)) =
483 (if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
485 val Ts = T |> strip_type |> swap |> op ::
486 val s' = new_skolem_const_name s (length Ts)
487 in IConst (`make_fixed_const s', T, Ts) end
489 IVar ((make_schematic_var v, s), T), atyps_of T)
490 | iterm_from_term _ bs (Bound j) =
491 nth bs j |> (fn (s, T) => (IConst (`make_bound_var s, T, []), atyps_of T))
492 | iterm_from_term thy bs (Abs (s, T, t)) =
494 fun vary s = s |> AList.defined (op =) bs s ? vary o Symbol.bump_string
496 val (tm, atomic_Ts) = iterm_from_term thy ((s, T) :: bs) t
498 (IAbs ((`make_bound_var s, T), tm),
499 union (op =) atomic_Ts (atyps_of T))
503 General | Helper | Extensionality | Intro | Elim | Simp | Local | Assum |
506 (* (quasi-)underapproximation of the truth *)
507 fun is_locality_global Local = false
508 | is_locality_global Assum = false
509 | is_locality_global Chained = false
510 | is_locality_global _ = true
512 datatype order = First_Order | Higher_Order
513 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
514 datatype type_level =
515 All_Types | Noninf_Nonmono_Types | Fin_Nonmono_Types | Const_Arg_Types |
517 datatype type_heaviness = Heavyweight | Lightweight
520 Simple_Types of order * type_level |
521 Guards of polymorphism * type_level * type_heaviness |
522 Tags of polymorphism * type_level * type_heaviness
524 fun try_unsuffixes ss s =
525 fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
527 fun type_enc_from_string s =
528 (case try (unprefix "poly_") s of
529 SOME s => (SOME Polymorphic, s)
531 case try (unprefix "mono_") s of
532 SOME s => (SOME Monomorphic, s)
534 case try (unprefix "mangled_") s of
535 SOME s => (SOME Mangled_Monomorphic, s)
538 (* "_query" and "_bang" are for the ASCII-challenged Metis and
540 case try_unsuffixes ["?", "_query"] s of
541 SOME s => (Noninf_Nonmono_Types, s)
543 case try_unsuffixes ["!", "_bang"] s of
544 SOME s => (Fin_Nonmono_Types, s)
545 | NONE => (All_Types, s))
547 case try (unsuffix "_heavy") s of
548 SOME s => (Heavyweight, s)
549 | NONE => (Lightweight, s))
550 |> (fn (poly, (level, (heaviness, core))) =>
551 case (core, (poly, level, heaviness)) of
552 ("simple", (NONE, _, Lightweight)) =>
553 Simple_Types (First_Order, level)
554 | ("simple_higher", (NONE, _, Lightweight)) =>
555 if level = Noninf_Nonmono_Types then raise Same.SAME
556 else Simple_Types (Higher_Order, level)
557 | ("guards", (SOME poly, _, _)) => Guards (poly, level, heaviness)
558 | ("tags", (SOME Polymorphic, _, _)) =>
559 Tags (Polymorphic, level, heaviness)
560 | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
561 | ("args", (SOME poly, All_Types (* naja *), Lightweight)) =>
562 Guards (poly, Const_Arg_Types, Lightweight)
563 | ("erased", (NONE, All_Types (* naja *), Lightweight)) =>
564 Guards (Polymorphic, No_Types, Lightweight)
565 | _ => raise Same.SAME)
566 handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
568 fun is_type_enc_higher_order (Simple_Types (Higher_Order, _)) = true
569 | is_type_enc_higher_order _ = false
571 fun polymorphism_of_type_enc (Simple_Types _) = Mangled_Monomorphic
572 | polymorphism_of_type_enc (Guards (poly, _, _)) = poly
573 | polymorphism_of_type_enc (Tags (poly, _, _)) = poly
575 fun level_of_type_enc (Simple_Types (_, level)) = level
576 | level_of_type_enc (Guards (_, level, _)) = level
577 | level_of_type_enc (Tags (_, level, _)) = level
579 fun heaviness_of_type_enc (Simple_Types _) = Heavyweight
580 | heaviness_of_type_enc (Guards (_, _, heaviness)) = heaviness
581 | heaviness_of_type_enc (Tags (_, _, heaviness)) = heaviness
583 fun is_type_level_virtually_sound level =
584 level = All_Types orelse level = Noninf_Nonmono_Types
585 val is_type_enc_virtually_sound =
586 is_type_level_virtually_sound o level_of_type_enc
588 fun is_type_level_fairly_sound level =
589 is_type_level_virtually_sound level orelse level = Fin_Nonmono_Types
590 val is_type_enc_fairly_sound = is_type_level_fairly_sound o level_of_type_enc
592 fun choose_format formats (Simple_Types (order, level)) =
593 if member (op =) formats THF then
594 (THF, Simple_Types (order, level))
595 else if member (op =) formats TFF then
596 (TFF, Simple_Types (First_Order, level))
598 choose_format formats (Guards (Mangled_Monomorphic, level, Heavyweight))
599 | choose_format formats type_enc =
602 (CNF_UEQ, case type_enc of
604 (if is_type_enc_fairly_sound type_enc then Tags else Guards)
607 | format => (format, type_enc))
609 type translated_formula =
613 iformula : (name, typ, iterm) formula,
614 atomic_types : typ list}
616 fun update_iformula f ({name, locality, kind, iformula, atomic_types}
617 : translated_formula) =
618 {name = name, locality = locality, kind = kind, iformula = f iformula,
619 atomic_types = atomic_types} : translated_formula
621 fun fact_lift f ({iformula, ...} : translated_formula) = f iformula
623 val type_instance = Sign.typ_instance o Proof_Context.theory_of
625 fun insert_type ctxt get_T x xs =
626 let val T = get_T x in
627 if exists (curry (type_instance ctxt) T o get_T) xs then xs
628 else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
631 (* The Booleans indicate whether all type arguments should be kept. *)
632 datatype type_arg_policy =
633 Explicit_Type_Args of bool |
634 Mangled_Type_Args of bool |
637 fun should_drop_arg_type_args (Simple_Types _) =
638 false (* since TFF doesn't support overloading *)
639 | should_drop_arg_type_args type_enc =
640 level_of_type_enc type_enc = All_Types andalso
641 heaviness_of_type_enc type_enc = Heavyweight
643 fun type_arg_policy type_enc s =
644 if s = type_tag_name then
645 (if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
648 Explicit_Type_Args) false
649 else case type_enc of
650 Tags (_, All_Types, Heavyweight) => No_Type_Args
652 if level_of_type_enc type_enc = No_Types orelse
653 s = @{const_name HOL.eq} orelse
654 (s = app_op_name andalso
655 level_of_type_enc type_enc = Const_Arg_Types) then
658 should_drop_arg_type_args type_enc
659 |> (if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
664 (* Make literals for sorted type variables. *)
665 fun generic_add_sorts_on_type (_, []) = I
666 | generic_add_sorts_on_type ((x, i), s :: ss) =
667 generic_add_sorts_on_type ((x, i), ss)
668 #> (if s = the_single @{sort HOL.type} then
671 insert (op =) (TyLitFree (`make_type_class s, `make_fixed_type_var x))
673 insert (op =) (TyLitVar (`make_type_class s,
674 (make_schematic_type_var (x, i), x))))
675 fun add_sorts_on_tfree (TFree (s, S)) = generic_add_sorts_on_type ((s, ~1), S)
676 | add_sorts_on_tfree _ = I
677 fun add_sorts_on_tvar (TVar z) = generic_add_sorts_on_type z
678 | add_sorts_on_tvar _ = I
680 fun type_literals_for_types type_enc add_sorts_on_typ Ts =
681 [] |> level_of_type_enc type_enc <> No_Types ? fold add_sorts_on_typ Ts
683 fun mk_aconns c phis =
684 let val (phis', phi') = split_last phis in
685 fold_rev (mk_aconn c) phis' phi'
687 fun mk_ahorn [] phi = phi
688 | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
689 fun mk_aquant _ [] phi = phi
690 | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
691 if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
692 | mk_aquant q xs phi = AQuant (q, xs, phi)
694 fun close_universally atom_vars phi =
696 fun formula_vars bounds (AQuant (_, xs, phi)) =
697 formula_vars (map fst xs @ bounds) phi
698 | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
699 | formula_vars bounds (AAtom tm) =
700 union (op =) (atom_vars tm []
701 |> filter_out (member (op =) bounds o fst))
702 in mk_aquant AForall (formula_vars [] phi []) phi end
704 fun iterm_vars (IApp (tm1, tm2)) = fold iterm_vars [tm1, tm2]
705 | iterm_vars (IConst _) = I
706 | iterm_vars (IVar (name, T)) = insert (op =) (name, SOME T)
707 | iterm_vars (IAbs (_, tm)) = iterm_vars tm
708 fun close_iformula_universally phi = close_universally iterm_vars phi
710 fun term_vars bounds (ATerm (name as (s, _), tms)) =
711 (is_tptp_variable s andalso not (member (op =) bounds name))
712 ? insert (op =) (name, NONE) #> fold (term_vars bounds) tms
713 | term_vars bounds (AAbs ((name, _), tm)) = term_vars (name :: bounds) tm
714 fun close_formula_universally phi = close_universally (term_vars []) phi
716 val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
717 val homo_infinite_type = Type (homo_infinite_type_name, [])
719 fun ho_term_from_typ format type_enc =
721 fun term (Type (s, Ts)) =
722 ATerm (case (is_type_enc_higher_order type_enc, s) of
723 (true, @{type_name bool}) => `I tptp_bool_type
724 | (true, @{type_name fun}) => `I tptp_fun_type
725 | _ => if s = homo_infinite_type_name andalso
726 (format = TFF orelse format = THF) then
727 `I tptp_individual_type
729 `make_fixed_type_const s,
731 | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
732 | term (TVar ((x as (s, _)), _)) =
733 ATerm ((make_schematic_type_var x, s), [])
736 fun ho_term_for_type_arg format type_enc T =
737 if T = dummyT then NONE else SOME (ho_term_from_typ format type_enc T)
739 (* This shouldn't clash with anything else. *)
740 val mangled_type_sep = "\000"
742 fun generic_mangled_type_name f (ATerm (name, [])) = f name
743 | generic_mangled_type_name f (ATerm (name, tys)) =
744 f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
746 | generic_mangled_type_name _ _ = raise Fail "unexpected type abstraction"
748 val bool_atype = AType (`I tptp_bool_type)
750 fun make_simple_type s =
751 if s = tptp_bool_type orelse s = tptp_fun_type orelse
752 s = tptp_individual_type then
755 simple_type_prefix ^ ascii_of s
757 fun ho_type_from_ho_term type_enc pred_sym ary =
760 AType ((make_simple_type (generic_mangled_type_name fst ty),
761 generic_mangled_type_name snd ty))
762 fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
763 fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
764 | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
765 | to_fo _ _ = raise Fail "unexpected type abstraction"
766 fun to_ho (ty as ATerm ((s, _), tys)) =
767 if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
768 | to_ho _ = raise Fail "unexpected type abstraction"
769 in if is_type_enc_higher_order type_enc then to_ho else to_fo ary end
771 fun ho_type_from_typ format type_enc pred_sym ary =
772 ho_type_from_ho_term type_enc pred_sym ary
773 o ho_term_from_typ format type_enc
775 fun mangled_const_name format type_enc T_args (s, s') =
777 val ty_args = T_args |> map_filter (ho_term_for_type_arg format type_enc)
778 fun type_suffix f g =
779 fold_rev (curry (op ^) o g o prefix mangled_type_sep
780 o generic_mangled_type_name f) ty_args ""
781 in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
783 val parse_mangled_ident =
784 Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
786 fun parse_mangled_type x =
788 -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
790 and parse_mangled_types x =
791 (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
793 fun unmangled_type s =
794 s |> suffix ")" |> raw_explode
795 |> Scan.finite Symbol.stopper
796 (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
797 quote s)) parse_mangled_type))
800 val unmangled_const_name = space_explode mangled_type_sep #> hd
801 fun unmangled_const s =
802 let val ss = space_explode mangled_type_sep s in
803 (hd ss, map unmangled_type (tl ss))
806 fun introduce_proxies type_enc =
808 fun tweak_ho_quant ho_quant T [IAbs _] = IConst (`I ho_quant, T, [])
809 | tweak_ho_quant ho_quant (T as Type (_, [p_T as Type (_, [x_T, _]), _]))
811 (* Eta-expand "!!" and "??", to work around LEO-II 1.2.8 parser
812 limitation. This works in conjuction with special code in
813 "ATP_Problem" that uses the syntactic sugar "!" and "?" whenever
816 IApp (IConst (`I ho_quant, T, []),
818 IApp (IConst (`I "P", p_T, []),
819 IConst (`I "X", x_T, [])))))
820 | tweak_ho_quant _ _ _ = raise Fail "unexpected type for quantifier"
821 fun intro top_level args (IApp (tm1, tm2)) =
822 IApp (intro top_level (tm2 :: args) tm1, intro false [] tm2)
823 | intro top_level args (IConst (name as (s, _), T, T_args)) =
824 (case proxify_const s of
826 if top_level orelse is_type_enc_higher_order type_enc then
827 case (top_level, s) of
828 (_, "c_False") => IConst (`I tptp_false, T, [])
829 | (_, "c_True") => IConst (`I tptp_true, T, [])
830 | (false, "c_Not") => IConst (`I tptp_not, T, [])
831 | (false, "c_conj") => IConst (`I tptp_and, T, [])
832 | (false, "c_disj") => IConst (`I tptp_or, T, [])
833 | (false, "c_implies") => IConst (`I tptp_implies, T, [])
834 | (false, "c_All") => tweak_ho_quant tptp_ho_forall T args
835 | (false, "c_Ex") => tweak_ho_quant tptp_ho_exists T args
837 if is_tptp_equal s then IConst (`I tptp_equal, T, [])
838 else IConst (proxy_base |>> prefix const_prefix, T, T_args)
839 | _ => IConst (name, T, [])
841 IConst (proxy_base |>> prefix const_prefix, T, T_args)
842 | NONE => IConst (name, T, T_args))
843 | intro _ _ (IAbs (bound, tm)) = IAbs (bound, intro false [] tm)
847 fun iformula_from_prop thy type_enc eq_as_iff =
849 fun do_term bs t atomic_types =
850 iterm_from_term thy bs (Envir.eta_contract t)
851 |>> (introduce_proxies type_enc #> AAtom)
852 ||> union (op =) atomic_types
853 fun do_quant bs q s T t' =
854 let val s = singleton (Name.variant_list (map fst bs)) s in
855 do_formula ((s, T) :: bs) t'
856 #>> mk_aquant q [(`make_bound_var s, SOME T)]
858 and do_conn bs c t1 t2 =
859 do_formula bs t1 ##>> do_formula bs t2 #>> uncurry (mk_aconn c)
860 and do_formula bs t =
862 @{const Trueprop} $ t1 => do_formula bs t1
863 | @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
864 | Const (@{const_name All}, _) $ Abs (s, T, t') =>
865 do_quant bs AForall s T t'
866 | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
867 do_quant bs AExists s T t'
868 | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
869 | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
870 | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
871 | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
872 if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
876 fun presimplify_term _ [] t = t
877 | presimplify_term ctxt presimp_consts t =
878 t |> exists_Const (member (op =) presimp_consts o fst) t
879 ? (Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
880 #> Meson.presimplify ctxt
883 fun concealed_bound_name j = atp_weak_prefix ^ string_of_int j
884 fun conceal_bounds Ts t =
885 subst_bounds (map (Free o apfst concealed_bound_name)
886 (0 upto length Ts - 1 ~~ Ts), t)
887 fun reveal_bounds Ts =
888 subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
889 (0 upto length Ts - 1 ~~ Ts))
891 fun is_fun_equality (@{const_name HOL.eq},
892 Type (_, [Type (@{type_name fun}, _), _])) = true
893 | is_fun_equality _ = false
895 fun extensionalize_term ctxt t =
896 if exists_Const is_fun_equality t then
897 let val thy = Proof_Context.theory_of ctxt in
898 t |> cterm_of thy |> Meson.extensionalize_conv ctxt
899 |> prop_of |> Logic.dest_equals |> snd
904 fun simple_translate_lambdas do_lambdas ctxt t =
905 let val thy = Proof_Context.theory_of ctxt in
906 if Meson.is_fol_term thy t then
912 @{const Not} $ t1 => @{const Not} $ aux Ts t1
913 | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
914 t0 $ Abs (s, T, aux (T :: Ts) t')
915 | (t0 as Const (@{const_name All}, _)) $ t1 =>
916 aux Ts (t0 $ eta_expand Ts t1 1)
917 | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
918 t0 $ Abs (s, T, aux (T :: Ts) t')
919 | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
920 aux Ts (t0 $ eta_expand Ts t1 1)
921 | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
922 | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
923 | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
924 | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
926 t0 $ aux Ts t1 $ aux Ts t2
928 if not (exists_subterm (fn Abs _ => true | _ => false) t) then t
929 else t |> Envir.eta_contract |> do_lambdas ctxt Ts
930 val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
931 in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
934 fun do_cheaply_conceal_lambdas Ts (t1 $ t2) =
935 do_cheaply_conceal_lambdas Ts t1
936 $ do_cheaply_conceal_lambdas Ts t2
937 | do_cheaply_conceal_lambdas Ts (Abs (_, T, t)) =
938 Free (polymorphic_free_prefix ^ serial_string (),
939 T --> fastype_of1 (T :: Ts, t))
940 | do_cheaply_conceal_lambdas _ t = t
942 fun do_introduce_combinators ctxt Ts t =
943 let val thy = Proof_Context.theory_of ctxt in
944 t |> conceal_bounds Ts
946 |> Meson_Clausify.introduce_combinators_in_cterm
947 |> prop_of |> Logic.dest_equals |> snd
950 (* A type variable of sort "{}" will make abstraction fail. *)
951 handle THM _ => t |> do_cheaply_conceal_lambdas Ts
952 val introduce_combinators = simple_translate_lambdas do_introduce_combinators
954 fun preprocess_abstractions_in_terms trans_lambdas facts =
956 val (facts, lambda_ts) =
957 facts |> map (snd o snd) |> trans_lambdas
958 |>> map2 (fn (name, (kind, _)) => fn t => (name, (kind, t))) facts
960 map2 (fn t => fn j =>
961 ((lambda_fact_prefix ^ Int.toString j, Helper), (Axiom, t)))
962 lambda_ts (1 upto length lambda_ts)
963 in (facts, lambda_facts) end
965 (* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
966 same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
969 fun aux (t $ u) = aux t $ aux u
970 | aux (Abs (s, T, t)) = Abs (s, T, aux t)
971 | aux (Var ((s, i), T)) =
972 Free (atp_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
974 in t |> exists_subterm is_Var t ? aux end
976 fun presimp_prop ctxt presimp_consts t =
978 val thy = Proof_Context.theory_of ctxt
979 val t = t |> Envir.beta_eta_contract
980 |> transform_elim_prop
981 |> Object_Logic.atomize_term thy
982 val need_trueprop = (fastype_of t = @{typ bool})
984 t |> need_trueprop ? HOLogic.mk_Trueprop
985 |> Raw_Simplifier.rewrite_term thy (Meson.unfold_set_const_simps ctxt) []
986 |> extensionalize_term ctxt
987 |> presimplify_term ctxt presimp_consts
988 |> perhaps (try (HOLogic.dest_Trueprop))
991 (* making fact and conjecture formulas *)
992 fun make_formula thy type_enc eq_as_iff name loc kind t =
994 val (iformula, atomic_types) =
995 iformula_from_prop thy type_enc eq_as_iff t []
997 {name = name, locality = loc, kind = kind, iformula = iformula,
998 atomic_types = atomic_types}
1001 fun make_fact ctxt format type_enc eq_as_iff ((name, loc), t) =
1002 let val thy = Proof_Context.theory_of ctxt in
1003 case t |> make_formula thy type_enc (eq_as_iff andalso format <> CNF) name
1005 formula as {iformula = AAtom (IConst ((s, _), _, _)), ...} =>
1006 if s = tptp_true then NONE else SOME formula
1007 | formula => SOME formula
1010 fun make_conjecture ctxt format type_enc ps =
1012 val thy = Proof_Context.theory_of ctxt
1013 val last = length ps - 1
1015 map2 (fn j => fn ((name, loc), (kind, t)) =>
1016 t |> make_formula thy type_enc (format <> CNF) name loc kind
1017 |> (j <> last) = (kind = Conjecture) ? update_iformula mk_anot)
1021 (** Finite and infinite type inference **)
1023 fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
1024 | deep_freeze_atyp T = T
1025 val deep_freeze_type = map_atyps deep_freeze_atyp
1027 (* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
1028 dangerous because their "exhaust" properties can easily lead to unsound ATP
1029 proofs. On the other hand, all HOL infinite types can be given the same
1030 models in first-order logic (via Löwenheim-Skolem). *)
1032 fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
1033 exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
1034 | should_encode_type _ _ All_Types _ = true
1035 | should_encode_type ctxt _ Fin_Nonmono_Types T =
1036 is_type_surely_finite ctxt false T
1037 | should_encode_type _ _ _ _ = false
1039 fun should_predicate_on_type ctxt nonmono_Ts (Guards (_, level, heaviness))
1040 should_predicate_on_var T =
1041 (heaviness = Heavyweight orelse should_predicate_on_var ()) andalso
1042 should_encode_type ctxt nonmono_Ts level T
1043 | should_predicate_on_type _ _ _ _ _ = false
1045 fun is_var_or_bound_var (IConst ((s, _), _, _)) =
1046 String.isPrefix bound_var_prefix s
1047 | is_var_or_bound_var (IVar _) = true
1048 | is_var_or_bound_var _ = false
1051 Top_Level of bool option |
1052 Eq_Arg of bool option |
1055 fun should_tag_with_type _ _ _ (Top_Level _) _ _ = false
1056 | should_tag_with_type ctxt nonmono_Ts (Tags (poly, level, heaviness)) site
1059 Heavyweight => should_encode_type ctxt nonmono_Ts level T
1061 case (site, is_var_or_bound_var u) of
1062 (Eq_Arg pos, true) =>
1063 (* The first disjunct prevents a subtle soundness issue explained in
1064 Blanchette's Ph.D. thesis. See also
1065 "formula_lines_for_lightweight_tags_sym_decl". *)
1066 (pos <> SOME false andalso poly = Polymorphic andalso
1067 level <> All_Types andalso heaviness = Lightweight andalso
1068 exists (fn T' => type_instance ctxt (T', T)) nonmono_Ts) orelse
1069 should_encode_type ctxt nonmono_Ts level T
1071 | should_tag_with_type _ _ _ _ _ _ = false
1073 fun homogenized_type ctxt nonmono_Ts level =
1075 val should_encode = should_encode_type ctxt nonmono_Ts level
1076 fun homo 0 T = if should_encode T then T else homo_infinite_type
1077 | homo ary (Type (@{type_name fun}, [T1, T2])) =
1078 homo 0 T1 --> homo (ary - 1) T2
1079 | homo _ _ = raise Fail "expected function type"
1082 (** "hBOOL" and "hAPP" **)
1085 {pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
1087 fun add_iterm_syms_to_table ctxt explicit_apply =
1089 fun consider_var_arity const_T var_T max_ary =
1092 if ary = max_ary orelse type_instance ctxt (var_T, T) orelse
1093 type_instance ctxt (T, var_T) then
1096 iter (ary + 1) (range_type T)
1097 in iter 0 const_T end
1098 fun add_var_or_bound_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1099 if explicit_apply = NONE andalso
1100 (can dest_funT T orelse T = @{typ bool}) then
1102 val bool_vars' = bool_vars orelse body_type T = @{typ bool}
1103 fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
1104 {pred_sym = pred_sym andalso not bool_vars',
1105 min_ary = fold (fn T' => consider_var_arity T' T) types min_ary,
1106 max_ary = max_ary, types = types}
1108 fun_var_Ts |> can dest_funT T ? insert_type ctxt I T
1110 if bool_vars' = bool_vars andalso
1111 pointer_eq (fun_var_Ts', fun_var_Ts) then
1114 ((bool_vars', fun_var_Ts'), Symtab.map (K repair_min_arity) sym_tab)
1118 fun add top_level tm (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1119 let val (head, args) = strip_iterm_comb tm in
1121 IConst ((s, _), T, _) =>
1122 if String.isPrefix bound_var_prefix s then
1123 add_var_or_bound_var T accum
1125 let val ary = length args in
1126 ((bool_vars, fun_var_Ts),
1127 case Symtab.lookup sym_tab s of
1128 SOME {pred_sym, min_ary, max_ary, types} =>
1131 pred_sym andalso top_level andalso not bool_vars
1132 val types' = types |> insert_type ctxt I T
1134 if is_some explicit_apply orelse
1135 pointer_eq (types', types) then
1138 fold (consider_var_arity T) fun_var_Ts min_ary
1140 Symtab.update (s, {pred_sym = pred_sym,
1141 min_ary = Int.min (ary, min_ary),
1142 max_ary = Int.max (ary, max_ary),
1148 val pred_sym = top_level andalso not bool_vars
1150 case explicit_apply of
1153 | NONE => fold (consider_var_arity T) fun_var_Ts ary
1155 Symtab.update_new (s, {pred_sym = pred_sym,
1156 min_ary = min_ary, max_ary = ary,
1161 | IVar (_, T) => add_var_or_bound_var T accum
1162 | IAbs ((_, T), tm) => accum |> add_var_or_bound_var T |> add false tm
1164 |> fold (add false) args
1167 fun add_fact_syms_to_table ctxt explicit_apply =
1168 fact_lift (formula_fold NONE
1169 (K (add_iterm_syms_to_table ctxt explicit_apply)))
1171 val tvar_a = TVar (("'a", 0), HOLogic.typeS)
1173 val default_sym_tab_entries : (string * sym_info) list =
1174 (prefixed_predicator_name,
1175 {pred_sym = true, min_ary = 1, max_ary = 1, types = []}) ::
1176 (make_fixed_const @{const_name undefined},
1177 {pred_sym = false, min_ary = 0, max_ary = 0, types = []}) ::
1178 ([tptp_false, tptp_true]
1179 |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []})) @
1180 ([tptp_equal, tptp_old_equal]
1181 |> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = []}))
1183 fun sym_table_for_facts ctxt explicit_apply facts =
1184 ((false, []), Symtab.empty)
1185 |> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
1186 |> fold Symtab.update default_sym_tab_entries
1188 fun min_arity_of sym_tab s =
1189 case Symtab.lookup sym_tab s of
1190 SOME ({min_ary, ...} : sym_info) => min_ary
1192 case strip_prefix_and_unascii const_prefix s of
1194 let val s = s |> unmangled_const_name |> invert_const in
1195 if s = predicator_name then 1
1196 else if s = app_op_name then 2
1197 else if s = type_pred_name then 1
1202 (* True if the constant ever appears outside of the top-level position in
1203 literals, or if it appears with different arities (e.g., because of different
1204 type instantiations). If false, the constant always receives all of its
1205 arguments and is used as a predicate. *)
1206 fun is_pred_sym sym_tab s =
1207 case Symtab.lookup sym_tab s of
1208 SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
1209 pred_sym andalso min_ary = max_ary
1212 val predicator_combconst =
1213 IConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
1214 fun predicator tm = IApp (predicator_combconst, tm)
1216 fun introduce_predicators_in_iterm sym_tab tm =
1217 case strip_iterm_comb tm of
1218 (IConst ((s, _), _, _), _) =>
1219 if is_pred_sym sym_tab s then tm else predicator tm
1220 | _ => predicator tm
1222 fun list_app head args = fold (curry (IApp o swap)) args head
1224 val app_op = `make_fixed_const app_op_name
1226 fun explicit_app arg head =
1228 val head_T = ityp_of head
1229 val (arg_T, res_T) = dest_funT head_T
1230 val explicit_app = IConst (app_op, head_T --> head_T, [arg_T, res_T])
1231 in list_app explicit_app [head, arg] end
1232 fun list_explicit_app head args = fold explicit_app args head
1234 fun introduce_explicit_apps_in_iterm sym_tab =
1237 case strip_iterm_comb tm of
1238 (head as IConst ((s, _), _, _), args) =>
1240 |> chop (min_arity_of sym_tab s)
1242 |-> list_explicit_app
1243 | (head, args) => list_explicit_app head (map aux args)
1246 fun chop_fun 0 T = ([], T)
1247 | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
1248 chop_fun (n - 1) ran_T |>> cons dom_T
1249 | chop_fun _ _ = raise Fail "unexpected non-function"
1251 fun filter_type_args _ _ _ [] = []
1252 | filter_type_args thy s arity T_args =
1254 (* will throw "TYPE" for pseudo-constants *)
1255 val U = if s = app_op_name then
1256 @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
1258 s |> Sign.the_const_type thy
1260 case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
1263 let val U_args = (s, U) |> Sign.const_typargs thy in
1265 |> map (fn (U, T) =>
1266 if member (op =) res_U_vars (dest_TVar U) then T
1270 handle TYPE _ => T_args
1272 fun enforce_type_arg_policy_in_iterm ctxt format type_enc =
1274 val thy = Proof_Context.theory_of ctxt
1275 fun aux arity (IApp (tm1, tm2)) = IApp (aux (arity + 1) tm1, aux 0 tm2)
1276 | aux arity (IConst (name as (s, _), T, T_args)) =
1277 (case strip_prefix_and_unascii const_prefix s of
1279 (name, if level_of_type_enc type_enc = No_Types then [] else T_args)
1282 val s'' = invert_const s''
1283 fun filtered_T_args false = T_args
1284 | filtered_T_args true = filter_type_args thy s'' arity T_args
1286 case type_arg_policy type_enc s'' of
1287 Explicit_Type_Args drop_args =>
1288 (name, filtered_T_args drop_args)
1289 | Mangled_Type_Args drop_args =>
1290 (mangled_const_name format type_enc (filtered_T_args drop_args)
1292 | No_Type_Args => (name, [])
1294 |> (fn (name, T_args) => IConst (name, T, T_args))
1295 | aux _ (IAbs (bound, tm)) = IAbs (bound, aux 0 tm)
1299 fun repair_iterm ctxt format type_enc sym_tab =
1300 not (is_type_enc_higher_order type_enc)
1301 ? (introduce_explicit_apps_in_iterm sym_tab
1302 #> introduce_predicators_in_iterm sym_tab)
1303 #> enforce_type_arg_policy_in_iterm ctxt format type_enc
1304 fun repair_fact ctxt format type_enc sym_tab =
1305 update_iformula (formula_map (repair_iterm ctxt format type_enc sym_tab))
1307 (** Helper facts **)
1309 (* The Boolean indicates that a fairly sound type encoding is needed. *)
1311 [(("COMBI", false), @{thms Meson.COMBI_def}),
1312 (("COMBK", false), @{thms Meson.COMBK_def}),
1313 (("COMBB", false), @{thms Meson.COMBB_def}),
1314 (("COMBC", false), @{thms Meson.COMBC_def}),
1315 (("COMBS", false), @{thms Meson.COMBS_def}),
1316 (("fFalse", false), [@{lemma "~ fFalse" by (unfold fFalse_def) fast}]),
1317 (("fFalse", true), @{thms True_or_False}),
1318 (("fTrue", false), [@{lemma "fTrue" by (unfold fTrue_def) fast}]),
1319 (("fTrue", true), @{thms True_or_False}),
1321 @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1322 fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1324 @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
1325 by (unfold fconj_def) fast+}),
1327 @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
1328 by (unfold fdisj_def) fast+}),
1329 (("fimplies", false),
1330 @{lemma "P | fimplies P Q" "~ Q | fimplies P Q" "~ fimplies P Q | ~ P | Q"
1331 by (unfold fimplies_def) fast+}),
1333 (* This is a lie: Higher-order equality doesn't need a sound type encoding.
1334 However, this is done so for backward compatibility: Including the
1335 equality helpers by default in Metis breaks a few existing proofs. *)
1336 @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1337 fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1338 (* Partial characterization of "fAll" and "fEx". A complete characterization
1339 would require the axiom of choice for replay with Metis. *)
1340 (("fAll", false), [@{lemma "~ fAll P | P x" by (auto simp: fAll_def)}]),
1341 (("fEx", false), [@{lemma "~ P x | fEx P" by (auto simp: fEx_def)}]),
1342 (("If", true), @{thms if_True if_False True_or_False})]
1343 |> map (apsnd (map zero_var_indexes))
1345 val type_tag = `make_fixed_const type_tag_name
1347 fun type_tag_idempotence_fact () =
1349 fun var s = ATerm (`I s, [])
1350 fun tag tm = ATerm (type_tag, [var "T", tm])
1351 val tagged_a = tag (var "A")
1353 Formula (type_tag_idempotence_helper_name, Axiom,
1354 AAtom (ATerm (`I tptp_equal, [tag tagged_a, tagged_a]))
1355 |> close_formula_universally, isabelle_info simpN, NONE)
1358 fun should_specialize_helper type_enc t =
1359 polymorphism_of_type_enc type_enc = Mangled_Monomorphic andalso
1360 level_of_type_enc type_enc <> No_Types andalso
1361 not (null (Term.hidden_polymorphism t))
1363 fun helper_facts_for_sym ctxt format type_enc (s, {types, ...} : sym_info) =
1364 case strip_prefix_and_unascii const_prefix s of
1367 val thy = Proof_Context.theory_of ctxt
1368 val unmangled_s = mangled_s |> unmangled_const_name
1369 fun dub needs_fairly_sound j k =
1370 (unmangled_s ^ "_" ^ string_of_int j ^ "_" ^ string_of_int k ^
1371 (if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^
1372 (if needs_fairly_sound then typed_helper_suffix
1373 else untyped_helper_suffix),
1375 fun dub_and_inst needs_fairly_sound (th, j) =
1376 let val t = prop_of th in
1377 if should_specialize_helper type_enc t then
1378 map (fn T => specialize_type thy (invert_const unmangled_s, T) t)
1383 |> map (fn (k, t) => (dub needs_fairly_sound j k, t)) o tag_list 1
1384 val make_facts = map_filter (make_fact ctxt format type_enc false)
1385 val fairly_sound = is_type_enc_fairly_sound type_enc
1388 |> maps (fn ((helper_s, needs_fairly_sound), ths) =>
1389 if helper_s <> unmangled_s orelse
1390 (needs_fairly_sound andalso not fairly_sound) then
1393 ths ~~ (1 upto length ths)
1394 |> maps (dub_and_inst needs_fairly_sound)
1398 fun helper_facts_for_sym_table ctxt format type_enc sym_tab =
1399 Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_enc) sym_tab
1402 (***************************************************************)
1403 (* Type Classes Present in the Axiom or Conjecture Clauses *)
1404 (***************************************************************)
1406 fun set_insert (x, s) = Symtab.update (x, ()) s
1408 fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
1410 (* Remove this trivial type class (FIXME: similar code elsewhere) *)
1411 fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
1413 fun classes_of_terms get_Ts =
1414 map (map snd o get_Ts)
1415 #> List.foldl add_classes Symtab.empty
1416 #> delete_type #> Symtab.keys
1418 val tfree_classes_of_terms = classes_of_terms OldTerm.term_tfrees
1419 val tvar_classes_of_terms = classes_of_terms OldTerm.term_tvars
1421 fun fold_type_constrs f (Type (s, Ts)) x =
1422 fold (fold_type_constrs f) Ts (f (s, x))
1423 | fold_type_constrs _ _ x = x
1425 (* Type constructors used to instantiate overloaded constants are the only ones
1427 fun add_type_constrs_in_term thy =
1429 fun add (Const (@{const_name Meson.skolem}, _) $ _) = I
1430 | add (t $ u) = add t #> add u
1431 | add (Const (x as (s, _))) =
1432 if String.isPrefix skolem_const_prefix s then I
1433 else x |> Sign.const_typargs thy |> fold (fold_type_constrs set_insert)
1434 | add (Free (s, T)) =
1435 if String.isPrefix polymorphic_free_prefix s then
1436 T |> fold_type_constrs set_insert
1439 | add (Abs (_, _, u)) = add u
1443 fun type_constrs_of_terms thy ts =
1444 Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty)
1446 fun translate_formulas ctxt format prem_kind type_enc trans_lambdas preproc
1447 hyp_ts concl_t facts =
1449 val thy = Proof_Context.theory_of ctxt
1450 val presimp_consts = Meson.presimplified_consts ctxt
1451 val fact_ts = facts |> map snd
1452 (* Remove existing facts from the conjecture, as this can dramatically
1453 boost an ATP's performance (for some reason). *)
1456 |> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t)
1457 val facts = facts |> map (apsnd (pair Axiom))
1459 map (pair prem_kind) hyp_ts @ [(Conjecture, concl_t)]
1460 |> map2 (pair o rpair Local o string_of_int) (0 upto length hyp_ts)
1461 val ((conjs, facts), lambdas) =
1464 |> map (apsnd (apsnd (presimp_prop ctxt presimp_consts)))
1465 |> preprocess_abstractions_in_terms trans_lambdas
1466 |>> chop (length conjs)
1467 |>> apfst (map (apsnd (apsnd freeze_term)))
1469 ((conjs, facts), [])
1470 val conjs = conjs |> make_conjecture ctxt format type_enc
1471 val (fact_names, facts) =
1473 |> map_filter (fn (name, (_, t)) =>
1474 make_fact ctxt format type_enc true (name, t)
1475 |> Option.map (pair name))
1478 lambdas |> map_filter (make_fact ctxt format type_enc true o apsnd snd)
1479 val all_ts = concl_t :: hyp_ts @ fact_ts
1480 val subs = tfree_classes_of_terms all_ts
1481 val supers = tvar_classes_of_terms all_ts
1482 val tycons = type_constrs_of_terms thy all_ts
1483 val (supers, arity_clauses) =
1484 if level_of_type_enc type_enc = No_Types then ([], [])
1485 else make_arity_clauses thy tycons supers
1486 val class_rel_clauses = make_class_rel_clauses thy subs supers
1488 (fact_names |> map single,
1489 (conjs, facts @ lambdas, class_rel_clauses, arity_clauses))
1492 fun fo_literal_from_type_literal (TyLitVar (class, name)) =
1493 (true, ATerm (class, [ATerm (name, [])]))
1494 | fo_literal_from_type_literal (TyLitFree (class, name)) =
1495 (true, ATerm (class, [ATerm (name, [])]))
1497 fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
1499 val type_pred = `make_fixed_const type_pred_name
1501 fun type_pred_iterm ctxt format type_enc T tm =
1502 IApp (IConst (type_pred, T --> @{typ bool}, [T])
1503 |> enforce_type_arg_policy_in_iterm ctxt format type_enc, tm)
1505 fun is_var_positively_naked_in_term _ (SOME false) _ accum = accum
1506 | is_var_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
1507 accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
1508 | is_var_positively_naked_in_term _ _ _ _ = true
1509 fun should_predicate_on_var_in_formula pos phi (SOME true) name =
1510 formula_fold pos (is_var_positively_naked_in_term name) phi false
1511 | should_predicate_on_var_in_formula _ _ _ _ = true
1513 fun mk_aterm format type_enc name T_args args =
1514 ATerm (name, map_filter (ho_term_for_type_arg format type_enc) T_args @ args)
1516 fun tag_with_type ctxt format nonmono_Ts type_enc pos T tm =
1517 IConst (type_tag, T --> T, [T])
1518 |> enforce_type_arg_policy_in_iterm ctxt format type_enc
1519 |> ho_term_from_iterm ctxt format nonmono_Ts type_enc (Top_Level pos)
1520 |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm])
1521 | _ => raise Fail "unexpected lambda-abstraction")
1522 and ho_term_from_iterm ctxt format nonmono_Ts type_enc =
1526 val (head, args) = strip_iterm_comb u
1529 Top_Level pos => pos
1534 IConst (name as (s, _), _, T_args) =>
1536 val arg_site = if is_tptp_equal s then Eq_Arg pos else Elsewhere
1538 mk_aterm format type_enc name T_args (map (aux arg_site) args)
1541 mk_aterm format type_enc name [] (map (aux Elsewhere) args)
1542 | IAbs ((name, T), tm) =>
1543 AAbs ((name, ho_type_from_typ format type_enc true 0 T),
1545 | IApp _ => raise Fail "impossible \"IApp\""
1548 t |> (if should_tag_with_type ctxt nonmono_Ts type_enc site u T then
1549 tag_with_type ctxt format nonmono_Ts type_enc pos T
1554 and formula_from_iformula ctxt format nonmono_Ts type_enc
1555 should_predicate_on_var =
1557 val do_term = ho_term_from_iterm ctxt format nonmono_Ts type_enc o Top_Level
1560 Simple_Types (_, level) =>
1561 homogenized_type ctxt nonmono_Ts level 0
1562 #> ho_type_from_typ format type_enc false 0 #> SOME
1564 fun do_out_of_bound_type pos phi universal (name, T) =
1565 if should_predicate_on_type ctxt nonmono_Ts type_enc
1566 (fn () => should_predicate_on_var pos phi universal name) T then
1568 |> type_pred_iterm ctxt format type_enc T
1569 |> do_term pos |> AAtom |> SOME
1572 fun do_formula pos (AQuant (q, xs, phi)) =
1574 val phi = phi |> do_formula pos
1575 val universal = Option.map (q = AExists ? not) pos
1577 AQuant (q, xs |> map (apsnd (fn NONE => NONE
1578 | SOME T => do_bound_type T)),
1579 (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
1581 (fn (_, NONE) => NONE
1583 do_out_of_bound_type pos phi universal (s, T))
1587 | do_formula pos (AConn conn) = aconn_map pos do_formula conn
1588 | do_formula pos (AAtom tm) = AAtom (do_term pos tm)
1591 fun bound_tvars type_enc Ts =
1592 mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
1593 (type_literals_for_types type_enc add_sorts_on_tvar Ts))
1595 (* Each fact is given a unique fact number to avoid name clashes (e.g., because
1596 of monomorphization). The TPTP explicitly forbids name clashes, and some of
1597 the remote provers might care. *)
1598 fun formula_line_for_fact ctxt format prefix encode freshen pos nonmono_Ts
1599 type_enc (j, {name, locality, kind, iformula, atomic_types}) =
1600 (prefix ^ (if freshen then string_of_int j ^ "_" else "") ^ encode name, kind,
1602 |> close_iformula_universally
1603 |> formula_from_iformula ctxt format nonmono_Ts type_enc
1604 should_predicate_on_var_in_formula
1605 (if pos then SOME true else NONE)
1606 |> bound_tvars type_enc atomic_types
1607 |> close_formula_universally,
1610 Intro => isabelle_info introN
1611 | Elim => isabelle_info elimN
1612 | Simp => isabelle_info simpN
1616 fun formula_line_for_class_rel_clause ({name, subclass, superclass, ...}
1617 : class_rel_clause) =
1618 let val ty_arg = ATerm (`I "T", []) in
1619 Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
1620 AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
1621 AAtom (ATerm (superclass, [ty_arg]))])
1622 |> close_formula_universally, isabelle_info introN, NONE)
1625 fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
1626 (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
1627 | fo_literal_from_arity_literal (TVarLit (c, sort)) =
1628 (false, ATerm (c, [ATerm (sort, [])]))
1630 fun formula_line_for_arity_clause ({name, prem_lits, concl_lits, ...}
1632 Formula (arity_clause_prefix ^ name, Axiom,
1633 mk_ahorn (map (formula_from_fo_literal o apfst not
1634 o fo_literal_from_arity_literal) prem_lits)
1635 (formula_from_fo_literal
1636 (fo_literal_from_arity_literal concl_lits))
1637 |> close_formula_universally, isabelle_info introN, NONE)
1639 fun formula_line_for_conjecture ctxt format nonmono_Ts type_enc
1640 ({name, kind, iformula, atomic_types, ...} : translated_formula) =
1641 Formula (conjecture_prefix ^ name, kind,
1642 formula_from_iformula ctxt format nonmono_Ts type_enc
1643 should_predicate_on_var_in_formula (SOME false)
1644 (close_iformula_universally iformula)
1645 |> bound_tvars type_enc atomic_types
1646 |> close_formula_universally, NONE, NONE)
1648 fun free_type_literals type_enc ({atomic_types, ...} : translated_formula) =
1649 atomic_types |> type_literals_for_types type_enc add_sorts_on_tfree
1650 |> map fo_literal_from_type_literal
1652 fun formula_line_for_free_type j lit =
1653 Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis,
1654 formula_from_fo_literal lit, NONE, NONE)
1655 fun formula_lines_for_free_types type_enc facts =
1657 val litss = map (free_type_literals type_enc) facts
1658 val lits = fold (union (op =)) litss []
1659 in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
1661 (** Symbol declarations **)
1663 fun should_declare_sym type_enc pred_sym s =
1664 is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
1666 Simple_Types _ => true
1667 | Tags (_, _, Lightweight) => true
1668 | _ => not pred_sym)
1670 fun sym_decl_table_for_facts ctxt format type_enc repaired_sym_tab
1673 fun add_iterm_syms in_conj tm =
1674 let val (head, args) = strip_iterm_comb tm in
1676 IConst ((s, s'), T, T_args) =>
1677 let val pred_sym = is_pred_sym repaired_sym_tab s in
1678 if should_declare_sym type_enc pred_sym s then
1679 Symtab.map_default (s, [])
1680 (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
1685 | IAbs (_, tm) => add_iterm_syms in_conj tm
1687 #> fold (add_iterm_syms in_conj) args
1689 fun add_fact_syms in_conj =
1690 fact_lift (formula_fold NONE (K (add_iterm_syms in_conj)))
1691 fun add_formula_var_types (AQuant (_, xs, phi)) =
1692 fold (fn (_, SOME T) => insert_type ctxt I T | _ => I) xs
1693 #> add_formula_var_types phi
1694 | add_formula_var_types (AConn (_, phis)) =
1695 fold add_formula_var_types phis
1696 | add_formula_var_types _ = I
1698 if polymorphism_of_type_enc type_enc = Polymorphic then [tvar_a]
1699 else fold (fact_lift add_formula_var_types) (conjs @ facts) []
1700 fun add_undefined_const T =
1703 `make_fixed_const @{const_name undefined}
1704 |> (case type_arg_policy type_enc @{const_name undefined} of
1705 Mangled_Type_Args _ => mangled_const_name format type_enc [T]
1708 Symtab.map_default (s, [])
1709 (insert_type ctxt #3 (s', [T], T, false, 0, false))
1713 |> is_type_enc_fairly_sound type_enc
1714 ? (fold (add_fact_syms true) conjs
1715 #> fold (add_fact_syms false) facts
1716 #> (case type_enc of
1718 | _ => fold add_undefined_const (var_types ())))
1721 (* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
1722 out with monotonicity" paper presented at CADE 2011. *)
1723 fun add_iterm_nonmonotonic_types _ _ _ _ (SOME false) _ = I
1724 | add_iterm_nonmonotonic_types ctxt level sound locality _
1725 (IApp (IApp (IConst ((s, _), Type (_, [T, _]), _), tm1), tm2)) =
1726 (is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
1728 Noninf_Nonmono_Types =>
1729 not (is_locality_global locality) orelse
1730 not (is_type_surely_infinite ctxt sound T)
1731 | Fin_Nonmono_Types => is_type_surely_finite ctxt false T
1732 | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
1733 | add_iterm_nonmonotonic_types _ _ _ _ _ _ = I
1734 fun add_fact_nonmonotonic_types ctxt level sound
1735 ({kind, locality, iformula, ...} : translated_formula) =
1736 formula_fold (SOME (kind <> Conjecture))
1737 (add_iterm_nonmonotonic_types ctxt level sound locality)
1739 fun nonmonotonic_types_for_facts ctxt type_enc sound facts =
1740 let val level = level_of_type_enc type_enc in
1741 if level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types then
1742 [] |> fold (add_fact_nonmonotonic_types ctxt level sound) facts
1743 (* We must add "bool" in case the helper "True_or_False" is added
1744 later. In addition, several places in the code rely on the list of
1745 nonmonotonic types not being empty. (FIXME?) *)
1746 |> insert_type ctxt I @{typ bool}
1751 fun decl_line_for_sym ctxt format nonmono_Ts type_enc s
1752 (s', T_args, T, pred_sym, ary, _) =
1754 val (T_arg_Ts, level) =
1756 Simple_Types (_, level) => ([], level)
1757 | _ => (replicate (length T_args) homo_infinite_type, No_Types)
1759 Decl (sym_decl_prefix ^ s, (s, s'),
1760 (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
1761 |> ho_type_from_typ format type_enc pred_sym (length T_arg_Ts + ary))
1764 fun formula_line_for_guards_sym_decl ctxt format conj_sym_kind nonmono_Ts
1765 poly_nonmono_Ts type_enc n s j (s', T_args, T, _, ary, in_conj) =
1767 val (kind, maybe_negate) =
1768 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1770 val (arg_Ts, res_T) = chop_fun ary T
1771 val num_args = length arg_Ts
1773 1 upto num_args |> map (`I o make_bound_var o string_of_int)
1775 bound_names ~~ arg_Ts |> map (fn (name, T) => IConst (name, T, []))
1776 val sym_needs_arg_types = exists (curry (op =) dummyT) T_args
1777 fun should_keep_arg_type T =
1778 sym_needs_arg_types orelse
1779 not (should_predicate_on_type ctxt nonmono_Ts type_enc (K false) T)
1781 arg_Ts |> map (fn T => if should_keep_arg_type T then SOME T else NONE)
1783 Formula (guards_sym_formula_prefix ^ s ^
1784 (if n > 1 then "_" ^ string_of_int j else ""), kind,
1785 IConst ((s, s'), T, T_args)
1786 |> fold (curry (IApp o swap)) bounds
1787 |> type_pred_iterm ctxt format type_enc res_T
1788 |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
1789 |> formula_from_iformula ctxt format poly_nonmono_Ts type_enc
1790 (K (K (K (K true)))) (SOME true)
1791 |> n > 1 ? bound_tvars type_enc (atyps_of T)
1792 |> close_formula_universally
1794 isabelle_info introN, NONE)
1797 fun formula_lines_for_lightweight_tags_sym_decl ctxt format conj_sym_kind
1798 poly_nonmono_Ts type_enc n s
1799 (j, (s', T_args, T, pred_sym, ary, in_conj)) =
1802 lightweight_tags_sym_formula_prefix ^ s ^
1803 (if n > 1 then "_" ^ string_of_int j else "")
1804 val (kind, maybe_negate) =
1805 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1807 val (arg_Ts, res_T) = chop_fun ary T
1809 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
1810 val bounds = bound_names |> map (fn name => ATerm (name, []))
1811 val cst = mk_aterm format type_enc (s, s') T_args
1812 val atomic_Ts = atyps_of T
1814 (if pred_sym then AConn (AIff, map AAtom tms)
1815 else AAtom (ATerm (`I tptp_equal, tms)))
1816 |> bound_tvars type_enc atomic_Ts
1817 |> close_formula_universally
1819 (* See also "should_tag_with_type". *)
1820 fun should_encode T =
1821 should_encode_type ctxt poly_nonmono_Ts All_Types T orelse
1823 Tags (Polymorphic, level, Lightweight) =>
1824 level <> All_Types andalso Monomorph.typ_has_tvars T
1826 val tag_with = tag_with_type ctxt format poly_nonmono_Ts type_enc NONE
1827 val add_formula_for_res =
1828 if should_encode res_T then
1829 cons (Formula (ident_base ^ "_res", kind,
1830 eq [tag_with res_T (cst bounds), cst bounds],
1831 isabelle_info simpN, NONE))
1834 fun add_formula_for_arg k =
1835 let val arg_T = nth arg_Ts k in
1836 if should_encode arg_T then
1837 case chop k bounds of
1838 (bounds1, bound :: bounds2) =>
1839 cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
1840 eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
1842 isabelle_info simpN, NONE))
1843 | _ => raise Fail "expected nonempty tail"
1848 [] |> not pred_sym ? add_formula_for_res
1849 |> fold add_formula_for_arg (ary - 1 downto 0)
1852 fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
1854 fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts
1855 poly_nonmono_Ts type_enc (s, decls) =
1858 decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_enc s)
1863 decl :: (decls' as _ :: _) =>
1864 let val T = result_type_of_decl decl in
1865 if forall (curry (type_instance ctxt o swap) T
1866 o result_type_of_decl) decls' then
1872 val n = length decls
1874 decls |> filter (should_predicate_on_type ctxt poly_nonmono_Ts type_enc
1876 o result_type_of_decl)
1878 (0 upto length decls - 1, decls)
1879 |-> map2 (formula_line_for_guards_sym_decl ctxt format conj_sym_kind
1880 nonmono_Ts poly_nonmono_Ts type_enc n s)
1882 | Tags (_, _, heaviness) =>
1886 let val n = length decls in
1887 (0 upto n - 1 ~~ decls)
1888 |> maps (formula_lines_for_lightweight_tags_sym_decl ctxt format
1889 conj_sym_kind poly_nonmono_Ts type_enc n s)
1892 fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1893 poly_nonmono_Ts type_enc sym_decl_tab =
1894 sym_decl_tab |> Symtab.dest |> sort_wrt fst |> rpair []
1895 |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
1896 nonmono_Ts poly_nonmono_Ts type_enc)
1898 fun needs_type_tag_idempotence (Tags (poly, level, heaviness)) =
1899 poly <> Mangled_Monomorphic andalso
1900 ((level = All_Types andalso heaviness = Lightweight) orelse
1901 level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types)
1902 | needs_type_tag_idempotence _ = false
1904 fun offset_of_heading_in_problem _ [] j = j
1905 | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
1906 if heading = needle then j
1907 else offset_of_heading_in_problem needle problem (j + length lines)
1909 val implicit_declsN = "Should-be-implicit typings"
1910 val explicit_declsN = "Explicit typings"
1911 val factsN = "Relevant facts"
1912 val class_relsN = "Class relationships"
1913 val aritiesN = "Arities"
1914 val helpersN = "Helper facts"
1915 val conjsN = "Conjectures"
1916 val free_typesN = "Type variables"
1918 val explicit_apply = NONE (* for experiments *)
1920 fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_enc sound
1921 exporter trans_lambdas readable_names preproc hyp_ts concl_t facts =
1923 val (format, type_enc) = choose_format [format] type_enc
1924 val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
1925 translate_formulas ctxt format prem_kind type_enc trans_lambdas preproc
1926 hyp_ts concl_t facts
1927 val sym_tab = conjs @ facts |> sym_table_for_facts ctxt explicit_apply
1929 conjs @ facts |> nonmonotonic_types_for_facts ctxt type_enc sound
1930 val repair = repair_fact ctxt format type_enc sym_tab
1931 val (conjs, facts) = (conjs, facts) |> pairself (map repair)
1932 val repaired_sym_tab =
1933 conjs @ facts |> sym_table_for_facts ctxt (SOME false)
1935 repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_enc
1937 val poly_nonmono_Ts =
1938 if null nonmono_Ts orelse nonmono_Ts = [@{typ bool}] (* FIXME? *) orelse
1939 polymorphism_of_type_enc type_enc <> Polymorphic then
1943 val sym_decl_lines =
1944 (conjs, helpers @ facts)
1945 |> sym_decl_table_for_facts ctxt format type_enc repaired_sym_tab
1946 |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1947 poly_nonmono_Ts type_enc
1949 0 upto length helpers - 1 ~~ helpers
1950 |> map (formula_line_for_fact ctxt format helper_prefix I false true
1951 poly_nonmono_Ts type_enc)
1952 |> (if needs_type_tag_idempotence type_enc then
1953 cons (type_tag_idempotence_fact ())
1956 (* Reordering these might confuse the proof reconstruction code or the SPASS
1959 [(explicit_declsN, sym_decl_lines),
1961 map (formula_line_for_fact ctxt format fact_prefix ascii_of
1962 (not exporter) (not exporter) nonmono_Ts
1964 (0 upto length facts - 1 ~~ facts)),
1965 (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
1966 (aritiesN, map formula_line_for_arity_clause arity_clauses),
1967 (helpersN, helper_lines),
1969 map (formula_line_for_conjecture ctxt format nonmono_Ts type_enc)
1971 (free_typesN, formula_lines_for_free_types type_enc (facts @ conjs))]
1975 CNF => ensure_cnf_problem
1976 | CNF_UEQ => filter_cnf_ueq_problem
1978 |> (if is_format_typed format then
1979 declare_undeclared_syms_in_atp_problem type_decl_prefix
1983 val (problem, pool) = problem |> nice_atp_problem readable_names
1984 val helpers_offset = offset_of_heading_in_problem helpersN problem 0
1986 map_filter (fn (j, {name, ...}) =>
1987 if String.isSuffix typed_helper_suffix name then SOME j
1989 ((helpers_offset + 1 upto helpers_offset + length helpers)
1991 fun add_sym_arity (s, {min_ary, ...} : sym_info) =
1993 case strip_prefix_and_unascii const_prefix s of
1994 SOME s => Symtab.insert (op =) (s, min_ary)
2000 case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
2001 offset_of_heading_in_problem conjsN problem 0,
2002 offset_of_heading_in_problem factsN problem 0,
2003 fact_names |> Vector.fromList,
2005 Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
2009 val conj_weight = 0.0
2010 val hyp_weight = 0.1
2011 val fact_min_weight = 0.2
2012 val fact_max_weight = 1.0
2013 val type_info_default_weight = 0.8
2015 fun add_term_weights weight (ATerm (s, tms)) =
2016 is_tptp_user_symbol s ? Symtab.default (s, weight)
2017 #> fold (add_term_weights weight) tms
2018 | add_term_weights weight (AAbs (_, tm)) = add_term_weights weight tm
2019 fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
2020 formula_fold NONE (K (add_term_weights weight)) phi
2021 | add_problem_line_weights _ _ = I
2023 fun add_conjectures_weights [] = I
2024 | add_conjectures_weights conjs =
2025 let val (hyps, conj) = split_last conjs in
2026 add_problem_line_weights conj_weight conj
2027 #> fold (add_problem_line_weights hyp_weight) hyps
2030 fun add_facts_weights facts =
2032 val num_facts = length facts
2034 fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
2035 / Real.fromInt num_facts
2037 map weight_of (0 upto num_facts - 1) ~~ facts
2038 |> fold (uncurry add_problem_line_weights)
2041 (* Weights are from 0.0 (most important) to 1.0 (least important). *)
2042 fun atp_problem_weights problem =
2043 let val get = these o AList.lookup (op =) problem in
2045 |> add_conjectures_weights (get free_typesN @ get conjsN)
2046 |> add_facts_weights (get factsN)
2047 |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
2048 [explicit_declsN, class_relsN, aritiesN]
2050 |> sort (prod_ord Real.compare string_ord o pairself swap)