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 fo_term = 'a ATP_Problem.fo_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 polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
24 All_Types | Noninf_Nonmono_Types | Fin_Nonmono_Types | Const_Arg_Types |
26 datatype type_heaviness = Heavyweight | Lightweight
29 Simple_Types of type_level |
30 Preds of polymorphism * type_level * type_heaviness |
31 Tags of polymorphism * type_level * type_heaviness
33 val bound_var_prefix : string
34 val schematic_var_prefix : string
35 val fixed_var_prefix : string
36 val tvar_prefix : string
37 val tfree_prefix : string
38 val const_prefix : string
39 val type_const_prefix : string
40 val class_prefix : string
41 val skolem_const_prefix : string
42 val old_skolem_const_prefix : string
43 val new_skolem_const_prefix : string
44 val type_decl_prefix : string
45 val sym_decl_prefix : string
46 val preds_sym_formula_prefix : string
47 val lightweight_tags_sym_formula_prefix : string
48 val fact_prefix : string
49 val conjecture_prefix : string
50 val helper_prefix : string
51 val class_rel_clause_prefix : string
52 val arity_clause_prefix : string
53 val tfree_clause_prefix : string
54 val typed_helper_suffix : string
55 val untyped_helper_suffix : string
56 val type_tag_idempotence_helper_name : string
57 val predicator_name : string
58 val app_op_name : string
59 val type_tag_name : string
60 val type_pred_name : string
61 val simple_type_prefix : string
62 val prefixed_predicator_name : string
63 val prefixed_app_op_name : string
64 val prefixed_type_tag_name : string
65 val ascii_of : string -> string
66 val unascii_of : string -> string
67 val strip_prefix_and_unascii : string -> string -> string option
68 val proxy_table : (string * (string * (thm * (string * string)))) list
69 val proxify_const : string -> (string * string) option
70 val invert_const : string -> string
71 val unproxify_const : string -> string
72 val new_skolem_var_name_from_const : string -> string
73 val num_type_args : theory -> string -> int
74 val atp_irrelevant_consts : string list
75 val atp_schematic_consts_of : term -> typ list Symtab.table
76 val is_locality_global : locality -> bool
77 val type_sys_from_string : string -> type_sys
78 val polymorphism_of_type_sys : type_sys -> polymorphism
79 val level_of_type_sys : type_sys -> type_level
80 val is_type_sys_virtually_sound : type_sys -> bool
81 val is_type_sys_fairly_sound : type_sys -> bool
82 val choose_format : format list -> type_sys -> format * type_sys
84 connective -> ('a, 'b, 'c) formula list -> ('a, 'b, 'c) formula
85 val unmangled_const : string -> string * string fo_term list
86 val unmangled_const_name : string -> string
87 val helper_table : ((string * bool) * thm list) list
89 val prepare_atp_problem :
90 Proof.context -> format -> formula_kind -> formula_kind -> type_sys -> bool
91 -> bool -> bool -> bool -> term list -> term
92 -> ((string * locality) * term) list
93 -> string problem * string Symtab.table * int * int
94 * (string * locality) list vector * int list * int Symtab.table
95 val atp_problem_weights : string problem -> (string * real) list
98 structure ATP_Translate : ATP_TRANSLATE =
104 type name = string * string
107 val generate_useful_info = false
109 fun useful_isabelle_info s =
110 if generate_useful_info then
111 SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
115 val intro_info = useful_isabelle_info "intro"
116 val elim_info = useful_isabelle_info "elim"
117 val simp_info = useful_isabelle_info "simp"
119 val bound_var_prefix = "B_"
120 val schematic_var_prefix = "V_"
121 val fixed_var_prefix = "v_"
123 val tvar_prefix = "T_"
124 val tfree_prefix = "t_"
126 val const_prefix = "c_"
127 val type_const_prefix = "tc_"
128 val class_prefix = "cl_"
130 val skolem_const_prefix = "Sledgehammer" ^ 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 preds_sym_formula_prefix = "psy_"
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 typed_helper_suffix = "_T"
146 val untyped_helper_suffix = "_U"
147 val type_tag_idempotence_helper_name = helper_prefix ^ "ti_idem"
149 val predicator_name = "hBOOL"
150 val app_op_name = "hAPP"
151 val type_tag_name = "ti"
152 val type_pred_name = "is"
153 val simple_type_prefix = "ty_"
155 val prefixed_predicator_name = const_prefix ^ predicator_name
156 val prefixed_app_op_name = const_prefix ^ app_op_name
157 val prefixed_type_tag_name = const_prefix ^ type_tag_name
159 (* Freshness almost guaranteed! *)
160 val sledgehammer_weak_prefix = "Sledgehammer:"
162 (*Escaping of special characters.
163 Alphanumeric characters are left unchanged.
164 The character _ goes to __
165 Characters in the range ASCII space to / go to _A to _P, respectively.
166 Other characters go to _nnn where nnn is the decimal ASCII code.*)
167 val upper_a_minus_space = Char.ord #"A" - Char.ord #" "
169 fun stringN_of_int 0 _ = ""
170 | stringN_of_int k n =
171 stringN_of_int (k - 1) (n div 10) ^ string_of_int (n mod 10)
173 fun ascii_of_char c =
174 if Char.isAlphaNum c then
176 else if c = #"_" then
178 else if #" " <= c andalso c <= #"/" then
179 "_" ^ String.str (Char.chr (Char.ord c + upper_a_minus_space))
181 (* fixed width, in case more digits follow *)
182 "_" ^ stringN_of_int 3 (Char.ord c)
184 val ascii_of = String.translate ascii_of_char
186 (** Remove ASCII armoring from names in proof files **)
188 (* We don't raise error exceptions because this code can run inside a worker
189 thread. Also, the errors are impossible. *)
192 fun un rcs [] = String.implode(rev rcs)
193 | un rcs [#"_"] = un (#"_" :: rcs) [] (* ERROR *)
194 (* Three types of _ escapes: __, _A to _P, _nnn *)
195 | un rcs (#"_" :: #"_" :: cs) = un (#"_" :: rcs) cs
196 | un rcs (#"_" :: c :: cs) =
197 if #"A" <= c andalso c<= #"P" then
198 (* translation of #" " to #"/" *)
199 un (Char.chr (Char.ord c - upper_a_minus_space) :: rcs) cs
201 let val digits = List.take (c :: cs, 3) handle General.Subscript => [] in
202 case Int.fromString (String.implode digits) of
203 SOME n => un (Char.chr n :: rcs) (List.drop (cs, 2))
204 | NONE => un (c :: #"_" :: rcs) cs (* ERROR *)
206 | un rcs (c :: cs) = un (c :: rcs) cs
207 in un [] o String.explode end
209 (* If string s has the prefix s1, return the result of deleting it,
211 fun strip_prefix_and_unascii s1 s =
212 if String.isPrefix s1 s then
213 SOME (unascii_of (String.extract (s, size s1, NONE)))
218 [("c_False", (@{const_name False}, (@{thm fFalse_def},
219 ("fFalse", @{const_name ATP.fFalse})))),
220 ("c_True", (@{const_name True}, (@{thm fTrue_def},
221 ("fTrue", @{const_name ATP.fTrue})))),
222 ("c_Not", (@{const_name Not}, (@{thm fNot_def},
223 ("fNot", @{const_name ATP.fNot})))),
224 ("c_conj", (@{const_name conj}, (@{thm fconj_def},
225 ("fconj", @{const_name ATP.fconj})))),
226 ("c_disj", (@{const_name disj}, (@{thm fdisj_def},
227 ("fdisj", @{const_name ATP.fdisj})))),
228 ("c_implies", (@{const_name implies}, (@{thm fimplies_def},
229 ("fimplies", @{const_name ATP.fimplies})))),
230 ("equal", (@{const_name HOL.eq}, (@{thm fequal_def},
231 ("fequal", @{const_name ATP.fequal}))))]
233 val proxify_const = AList.lookup (op =) proxy_table #> Option.map (snd o snd)
235 (* Readable names for the more common symbolic functions. Do not mess with the
236 table unless you know what you are doing. *)
237 val const_trans_table =
238 [(@{type_name Product_Type.prod}, "prod"),
239 (@{type_name Sum_Type.sum}, "sum"),
240 (@{const_name False}, "False"),
241 (@{const_name True}, "True"),
242 (@{const_name Not}, "Not"),
243 (@{const_name conj}, "conj"),
244 (@{const_name disj}, "disj"),
245 (@{const_name implies}, "implies"),
246 (@{const_name HOL.eq}, "equal"),
247 (@{const_name If}, "If"),
248 (@{const_name Set.member}, "member"),
249 (@{const_name Meson.COMBI}, "COMBI"),
250 (@{const_name Meson.COMBK}, "COMBK"),
251 (@{const_name Meson.COMBB}, "COMBB"),
252 (@{const_name Meson.COMBC}, "COMBC"),
253 (@{const_name Meson.COMBS}, "COMBS")]
255 |> fold (Symtab.update o swap o snd o snd o snd) proxy_table
257 (* Invert the table of translations between Isabelle and ATPs. *)
258 val const_trans_table_inv =
259 const_trans_table |> Symtab.dest |> map swap |> Symtab.make
260 val const_trans_table_unprox =
262 |> fold (fn (_, (isa, (_, (_, atp)))) => Symtab.update (atp, isa)) proxy_table
264 val invert_const = perhaps (Symtab.lookup const_trans_table_inv)
265 val unproxify_const = perhaps (Symtab.lookup const_trans_table_unprox)
268 case Symtab.lookup const_trans_table c of
272 (*Remove the initial ' character from a type variable, if it is present*)
273 fun trim_type_var s =
274 if s <> "" andalso String.sub(s,0) = #"'" then String.extract(s,1,NONE)
275 else raise Fail ("trim_type: Malformed type variable encountered: " ^ s)
277 fun ascii_of_indexname (v,0) = ascii_of v
278 | ascii_of_indexname (v,i) = ascii_of v ^ "_" ^ string_of_int i
280 fun make_bound_var x = bound_var_prefix ^ ascii_of x
281 fun make_schematic_var v = schematic_var_prefix ^ ascii_of_indexname v
282 fun make_fixed_var x = fixed_var_prefix ^ ascii_of x
284 fun make_schematic_type_var (x,i) =
285 tvar_prefix ^ (ascii_of_indexname (trim_type_var x, i))
286 fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (trim_type_var x))
288 (* HOL.eq MUST BE "equal" because it's built into ATPs. *)
289 fun make_fixed_const @{const_name HOL.eq} = "equal"
290 | make_fixed_const c = const_prefix ^ lookup_const c
292 fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
294 fun make_type_class clas = class_prefix ^ ascii_of clas
296 fun new_skolem_var_name_from_const s =
297 let val ss = s |> space_explode Long_Name.separator in
298 nth ss (length ss - 2)
301 (* The number of type arguments of a constant, zero if it's monomorphic. For
302 (instances of) Skolem pseudoconstants, this information is encoded in the
304 fun num_type_args thy s =
305 if String.isPrefix skolem_const_prefix s then
306 s |> space_explode Long_Name.separator |> List.last |> Int.fromString |> the
308 (s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
310 (* These are either simplified away by "Meson.presimplify" (most of the time) or
311 handled specially via "fFalse", "fTrue", ..., "fequal". *)
312 val atp_irrelevant_consts =
313 [@{const_name False}, @{const_name True}, @{const_name Not},
314 @{const_name conj}, @{const_name disj}, @{const_name implies},
315 @{const_name HOL.eq}, @{const_name If}, @{const_name Let}]
317 val atp_monomorph_bad_consts =
318 atp_irrelevant_consts @
319 (* These are ignored anyway by the relevance filter (unless they appear in
320 higher-order places) but not by the monomorphizer. *)
321 [@{const_name all}, @{const_name "==>"}, @{const_name "=="},
322 @{const_name Trueprop}, @{const_name All}, @{const_name Ex},
323 @{const_name Ex1}, @{const_name Ball}, @{const_name Bex}]
325 fun add_schematic_const (x as (_, T)) =
326 Monomorph.typ_has_tvars T ? Symtab.insert_list (op =) x
327 val add_schematic_consts_of =
328 Term.fold_aterms (fn Const (x as (s, _)) =>
329 not (member (op =) atp_monomorph_bad_consts s)
330 ? add_schematic_const x
332 fun atp_schematic_consts_of t = add_schematic_consts_of t Symtab.empty
334 (** Definitions and functions for FOL clauses and formulas for TPTP **)
336 (* The first component is the type class; the second is a "TVar" or "TFree". *)
337 datatype type_literal =
338 TyLitVar of name * name |
339 TyLitFree of name * name
342 (** Isabelle arities **)
344 datatype arity_literal =
345 TConsLit of name * name * name list |
346 TVarLit of name * name
349 | gen_TVars n = ("T_" ^ string_of_int n) :: gen_TVars (n-1)
351 val type_class = the_single @{sort type}
353 fun add_packed_sort tvar =
354 fold (fn s => s <> type_class ? cons (`make_type_class s, `I tvar))
358 prem_lits : arity_literal list,
359 concl_lits : arity_literal}
361 (* Arity of type constructor "tcon :: (arg1, ..., argN) res" *)
362 fun make_axiom_arity_clause (tcons, name, (cls, args)) =
364 val tvars = gen_TVars (length args)
365 val tvars_srts = ListPair.zip (tvars, args)
368 prem_lits = [] |> fold (uncurry add_packed_sort) tvars_srts |> map TVarLit,
369 concl_lits = TConsLit (`make_type_class cls,
370 `make_fixed_type_const tcons,
374 fun arity_clause _ _ (_, []) = []
375 | arity_clause seen n (tcons, ("HOL.type", _) :: ars) = (* ignore *)
376 arity_clause seen n (tcons, ars)
377 | arity_clause seen n (tcons, (ar as (class, _)) :: ars) =
378 if member (op =) seen class then
379 (* multiple arities for the same (tycon, class) pair *)
380 make_axiom_arity_clause (tcons,
381 lookup_const tcons ^ "___" ^ ascii_of class ^ "_" ^ string_of_int n,
383 arity_clause seen (n + 1) (tcons, ars)
385 make_axiom_arity_clause (tcons, lookup_const tcons ^ "___" ^
386 ascii_of class, ar) ::
387 arity_clause (class :: seen) n (tcons, ars)
389 fun multi_arity_clause [] = []
390 | multi_arity_clause ((tcons, ars) :: tc_arlists) =
391 arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
393 (*Generate all pairs (tycon,class,sorts) such that tycon belongs to class in theory thy
394 provided its arguments have the corresponding sorts.*)
395 fun type_class_pairs thy tycons classes =
397 val alg = Sign.classes_of thy
398 fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
399 fun add_class tycon class =
400 cons (class, domain_sorts tycon class)
401 handle Sorts.CLASS_ERROR _ => I
402 fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
403 in map try_classes tycons end
405 (*Proving one (tycon, class) membership may require proving others, so iterate.*)
406 fun iter_type_class_pairs _ _ [] = ([], [])
407 | iter_type_class_pairs thy tycons classes =
409 fun maybe_insert_class s =
410 (s <> type_class andalso not (member (op =) classes s))
412 val cpairs = type_class_pairs thy tycons classes
414 [] |> fold (fold (fold (fold maybe_insert_class) o snd) o snd) cpairs
415 val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
416 in (classes' @ classes, union (op =) cpairs' cpairs) end
418 fun make_arity_clauses thy tycons =
419 iter_type_class_pairs thy tycons ##> multi_arity_clause
422 (** Isabelle class relations **)
424 type class_rel_clause =
429 (*Generate all pairs (sub,super) such that sub is a proper subclass of super in theory thy.*)
430 fun class_pairs _ [] _ = []
431 | class_pairs thy subs supers =
433 val class_less = Sorts.class_less (Sign.classes_of thy)
434 fun add_super sub super = class_less (sub, super) ? cons (sub, super)
435 fun add_supers sub = fold (add_super sub) supers
436 in fold add_supers subs [] end
438 fun make_class_rel_clause (sub,super) =
439 {name = sub ^ "_" ^ super,
440 subclass = `make_type_class sub,
441 superclass = `make_type_class super}
443 fun make_class_rel_clauses thy subs supers =
444 map make_class_rel_clause (class_pairs thy subs supers)
447 CombConst of name * typ * typ list |
448 CombVar of name * typ |
449 CombApp of combterm * combterm
451 fun combtyp_of (CombConst (_, T, _)) = T
452 | combtyp_of (CombVar (_, T)) = T
453 | combtyp_of (CombApp (t1, _)) = snd (dest_funT (combtyp_of t1))
455 (*gets the head of a combinator application, along with the list of arguments*)
456 fun strip_combterm_comb u =
458 fun stripc (CombApp (t, u), ts) = stripc (t, u :: ts)
460 in stripc (u, []) end
462 fun atyps_of T = fold_atyps (insert (op =)) T []
464 fun new_skolem_const_name s num_T_args =
465 [new_skolem_const_prefix, s, string_of_int num_T_args]
466 |> space_implode Long_Name.separator
468 (* Converts a term (with combinators) into a combterm. Also accumulates sort
470 fun combterm_from_term thy bs (P $ Q) =
472 val (P', P_atomics_Ts) = combterm_from_term thy bs P
473 val (Q', Q_atomics_Ts) = combterm_from_term thy bs Q
474 in (CombApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
475 | combterm_from_term thy _ (Const (c, T)) =
478 (if String.isPrefix old_skolem_const_prefix c then
479 [] |> Term.add_tvarsT T |> map TVar
481 (c, T) |> Sign.const_typargs thy)
482 val c' = CombConst (`make_fixed_const c, T, tvar_list)
483 in (c', atyps_of T) end
484 | combterm_from_term _ _ (Free (v, T)) =
485 (CombConst (`make_fixed_var v, T, []), atyps_of T)
486 | combterm_from_term _ _ (Var (v as (s, _), T)) =
487 (if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
489 val Ts = T |> strip_type |> swap |> op ::
490 val s' = new_skolem_const_name s (length Ts)
491 in CombConst (`make_fixed_const s', T, Ts) end
493 CombVar ((make_schematic_var v, s), T), atyps_of T)
494 | combterm_from_term _ bs (Bound j) =
496 |> (fn (s, T) => (CombConst (`make_bound_var s, T, []), atyps_of T))
497 | combterm_from_term _ _ (Abs _) = raise Fail "HOL clause: Abs"
500 General | Helper | Extensionality | Intro | Elim | Simp | Local | Assum |
503 (* (quasi-)underapproximation of the truth *)
504 fun is_locality_global Local = false
505 | is_locality_global Assum = false
506 | is_locality_global Chained = false
507 | is_locality_global _ = true
509 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
510 datatype type_level =
511 All_Types | Noninf_Nonmono_Types | Fin_Nonmono_Types | Const_Arg_Types |
513 datatype type_heaviness = Heavyweight | Lightweight
516 Simple_Types of type_level |
517 Preds of polymorphism * type_level * type_heaviness |
518 Tags of polymorphism * type_level * type_heaviness
520 fun try_unsuffixes ss s =
521 fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
523 fun type_sys_from_string s =
524 (case try (unprefix "poly_") s of
525 SOME s => (SOME Polymorphic, s)
527 case try (unprefix "mono_") s of
528 SOME s => (SOME Monomorphic, s)
530 case try (unprefix "mangled_") s of
531 SOME s => (SOME Mangled_Monomorphic, s)
534 (* "_query" and "_bang" are for the ASCII-challenged Mirabelle. *)
535 case try_unsuffixes ["?", "_query"] s of
536 SOME s => (Noninf_Nonmono_Types, s)
538 case try_unsuffixes ["!", "_bang"] s of
539 SOME s => (Fin_Nonmono_Types, s)
540 | NONE => (All_Types, s))
542 case try (unsuffix "_heavy") s of
543 SOME s => (Heavyweight, s)
544 | NONE => (Lightweight, s))
545 |> (fn (poly, (level, (heaviness, core))) =>
546 case (core, (poly, level, heaviness)) of
547 ("simple", (NONE, _, Lightweight)) => Simple_Types level
548 | ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
549 | ("tags", (SOME Polymorphic, _, _)) =>
550 Tags (Polymorphic, level, heaviness)
551 | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
552 | ("args", (SOME poly, All_Types (* naja *), Lightweight)) =>
553 Preds (poly, Const_Arg_Types, Lightweight)
554 | ("erased", (NONE, All_Types (* naja *), Lightweight)) =>
555 Preds (Polymorphic, No_Types, Lightweight)
556 | _ => raise Same.SAME)
557 handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
559 fun polymorphism_of_type_sys (Simple_Types _) = Mangled_Monomorphic
560 | polymorphism_of_type_sys (Preds (poly, _, _)) = poly
561 | polymorphism_of_type_sys (Tags (poly, _, _)) = poly
563 fun level_of_type_sys (Simple_Types level) = level
564 | level_of_type_sys (Preds (_, level, _)) = level
565 | level_of_type_sys (Tags (_, level, _)) = level
567 fun heaviness_of_type_sys (Simple_Types _) = Heavyweight
568 | heaviness_of_type_sys (Preds (_, _, heaviness)) = heaviness
569 | heaviness_of_type_sys (Tags (_, _, heaviness)) = heaviness
571 fun is_type_level_virtually_sound level =
572 level = All_Types orelse level = Noninf_Nonmono_Types
573 val is_type_sys_virtually_sound =
574 is_type_level_virtually_sound o level_of_type_sys
576 fun is_type_level_fairly_sound level =
577 is_type_level_virtually_sound level orelse level = Fin_Nonmono_Types
578 val is_type_sys_fairly_sound = is_type_level_fairly_sound o level_of_type_sys
580 fun is_setting_higher_order THF (Simple_Types _) = true
581 | is_setting_higher_order _ _ = false
583 fun choose_format formats (Simple_Types level) =
584 if member (op =) formats THF then (THF, Simple_Types level)
585 else if member (op =) formats TFF then (TFF, Simple_Types level)
586 else choose_format formats (Preds (Mangled_Monomorphic, level, Heavyweight))
587 | choose_format formats type_sys =
590 (CNF_UEQ, case type_sys of
592 (if is_type_sys_fairly_sound type_sys then Tags else Preds)
595 | format => (format, type_sys))
597 type translated_formula =
601 combformula : (name, typ, combterm) formula,
602 atomic_types : typ list}
604 fun update_combformula f ({name, locality, kind, combformula, atomic_types}
605 : translated_formula) =
606 {name = name, locality = locality, kind = kind, combformula = f combformula,
607 atomic_types = atomic_types} : translated_formula
609 fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
611 val type_instance = Sign.typ_instance o Proof_Context.theory_of
613 fun insert_type ctxt get_T x xs =
614 let val T = get_T x in
615 if exists (curry (type_instance ctxt) T o get_T) xs then xs
616 else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
619 (* The Booleans indicate whether all type arguments should be kept. *)
620 datatype type_arg_policy =
621 Explicit_Type_Args of bool |
622 Mangled_Type_Args of bool |
625 fun should_drop_arg_type_args (Simple_Types _) =
626 false (* since TFF doesn't support overloading *)
627 | should_drop_arg_type_args type_sys =
628 level_of_type_sys type_sys = All_Types andalso
629 heaviness_of_type_sys type_sys = Heavyweight
631 fun general_type_arg_policy (Tags (_, All_Types, Heavyweight)) = No_Type_Args
632 | general_type_arg_policy type_sys =
633 if level_of_type_sys type_sys = No_Types then
635 else if polymorphism_of_type_sys type_sys = Mangled_Monomorphic then
636 Mangled_Type_Args (should_drop_arg_type_args type_sys)
638 Explicit_Type_Args (should_drop_arg_type_args type_sys)
640 fun type_arg_policy type_sys s =
641 if s = @{const_name HOL.eq} orelse
642 (s = app_op_name andalso level_of_type_sys type_sys = Const_Arg_Types) then
644 else if s = type_tag_name then
645 Explicit_Type_Args false
647 general_type_arg_policy type_sys
649 (*Make literals for sorted type variables*)
650 fun generic_add_sorts_on_type (_, []) = I
651 | generic_add_sorts_on_type ((x, i), s :: ss) =
652 generic_add_sorts_on_type ((x, i), ss)
653 #> (if s = the_single @{sort HOL.type} then
656 insert (op =) (TyLitFree (`make_type_class s, `make_fixed_type_var x))
658 insert (op =) (TyLitVar (`make_type_class s,
659 (make_schematic_type_var (x, i), x))))
660 fun add_sorts_on_tfree (TFree (s, S)) = generic_add_sorts_on_type ((s, ~1), S)
661 | add_sorts_on_tfree _ = I
662 fun add_sorts_on_tvar (TVar z) = generic_add_sorts_on_type z
663 | add_sorts_on_tvar _ = I
665 fun type_literals_for_types type_sys add_sorts_on_typ Ts =
666 [] |> level_of_type_sys type_sys <> No_Types ? fold add_sorts_on_typ Ts
668 fun mk_aconns c phis =
669 let val (phis', phi') = split_last phis in
670 fold_rev (mk_aconn c) phis' phi'
672 fun mk_ahorn [] phi = phi
673 | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
674 fun mk_aquant _ [] phi = phi
675 | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
676 if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
677 | mk_aquant q xs phi = AQuant (q, xs, phi)
679 fun close_universally atom_vars phi =
681 fun formula_vars bounds (AQuant (_, xs, phi)) =
682 formula_vars (map fst xs @ bounds) phi
683 | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
684 | formula_vars bounds (AAtom tm) =
685 union (op =) (atom_vars tm []
686 |> filter_out (member (op =) bounds o fst))
687 in mk_aquant AForall (formula_vars [] phi []) phi end
689 fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
690 | combterm_vars (CombConst _) = I
691 | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
692 fun close_combformula_universally phi = close_universally combterm_vars phi
694 fun term_vars (ATerm (name as (s, _), tms)) =
695 is_tptp_variable s ? insert (op =) (name, NONE) #> fold term_vars tms
696 fun close_formula_universally phi = close_universally term_vars phi
698 val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
699 val homo_infinite_type = Type (homo_infinite_type_name, [])
701 fun fo_term_from_typ format type_sys =
703 fun term (Type (s, Ts)) =
704 ATerm (case (is_setting_higher_order format type_sys, s) of
705 (true, @{type_name bool}) => `I tptp_bool_type
706 | (true, @{type_name fun}) => `I tptp_fun_type
707 | _ => if s = homo_infinite_type_name andalso
708 (format = TFF orelse format = THF) then
709 `I tptp_individual_type
711 `make_fixed_type_const s,
713 | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
714 | term (TVar ((x as (s, _)), _)) =
715 ATerm ((make_schematic_type_var x, s), [])
718 fun fo_term_for_type_arg format type_sys T =
719 if T = dummyT then NONE else SOME (fo_term_from_typ format type_sys T)
721 (* This shouldn't clash with anything else. *)
722 val mangled_type_sep = "\000"
724 fun generic_mangled_type_name f (ATerm (name, [])) = f name
725 | generic_mangled_type_name f (ATerm (name, tys)) =
726 f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
729 val bool_atype = AType (`I tptp_bool_type)
731 fun make_simple_type s =
732 if s = tptp_bool_type orelse s = tptp_fun_type orelse
733 s = tptp_individual_type then
736 simple_type_prefix ^ ascii_of s
738 fun ho_type_from_fo_term format type_sys pred_sym ary =
741 AType ((make_simple_type (generic_mangled_type_name fst ty),
742 generic_mangled_type_name snd ty))
743 fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
744 fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
745 | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
746 fun to_ho (ty as ATerm ((s, _), tys)) =
747 if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
748 in if is_setting_higher_order format type_sys then to_ho else to_fo ary end
750 fun mangled_type format type_sys pred_sym ary =
751 ho_type_from_fo_term format type_sys pred_sym ary
752 o fo_term_from_typ format type_sys
754 fun mangled_const_name format type_sys T_args (s, s') =
756 val ty_args = T_args |> map_filter (fo_term_for_type_arg format type_sys)
757 fun type_suffix f g =
758 fold_rev (curry (op ^) o g o prefix mangled_type_sep
759 o generic_mangled_type_name f) ty_args ""
760 in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
762 val parse_mangled_ident =
763 Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
765 fun parse_mangled_type x =
767 -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
769 and parse_mangled_types x =
770 (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
772 fun unmangled_type s =
773 s |> suffix ")" |> raw_explode
774 |> Scan.finite Symbol.stopper
775 (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
776 quote s)) parse_mangled_type))
779 val unmangled_const_name = space_explode mangled_type_sep #> hd
780 fun unmangled_const s =
781 let val ss = space_explode mangled_type_sep s in
782 (hd ss, map unmangled_type (tl ss))
785 fun introduce_proxies format type_sys =
787 fun intro top_level (CombApp (tm1, tm2)) =
788 CombApp (intro top_level tm1, intro false tm2)
789 | intro top_level (CombConst (name as (s, _), T, T_args)) =
790 (case proxify_const s of
792 if top_level orelse is_setting_higher_order format type_sys then
793 case (top_level, s) of
794 (_, "c_False") => (`I tptp_false, [])
795 | (_, "c_True") => (`I tptp_true, [])
796 | (false, "c_Not") => (`I tptp_not, [])
797 | (false, "c_conj") => (`I tptp_and, [])
798 | (false, "c_disj") => (`I tptp_or, [])
799 | (false, "c_implies") => (`I tptp_implies, [])
801 if is_tptp_equal s then (`I tptp_equal, [])
802 else (proxy_base |>> prefix const_prefix, T_args)
805 (proxy_base |>> prefix const_prefix, T_args)
806 | NONE => (name, T_args))
807 |> (fn (name, T_args) => CombConst (name, T, T_args))
811 fun combformula_from_prop thy format type_sys eq_as_iff =
813 fun do_term bs t atomic_types =
814 combterm_from_term thy bs (Envir.eta_contract t)
815 |>> (introduce_proxies format type_sys #> AAtom)
816 ||> union (op =) atomic_types
817 fun do_quant bs q s T t' =
818 let val s = singleton (Name.variant_list (map fst bs)) s in
819 do_formula ((s, T) :: bs) t'
820 #>> mk_aquant q [(`make_bound_var s, SOME T)]
822 and do_conn bs c t1 t2 =
823 do_formula bs t1 ##>> do_formula bs t2 #>> uncurry (mk_aconn c)
824 and do_formula bs t =
826 @{const Trueprop} $ t1 => do_formula bs t1
827 | @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
828 | Const (@{const_name All}, _) $ Abs (s, T, t') =>
829 do_quant bs AForall s T t'
830 | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
831 do_quant bs AExists s T t'
832 | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
833 | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
834 | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
835 | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
836 if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
840 fun presimplify_term _ [] t = t
841 | presimplify_term ctxt presimp_consts t =
842 t |> exists_Const (member (op =) presimp_consts o fst) t
843 ? (Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
844 #> Meson.presimplify ctxt
847 fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
848 fun conceal_bounds Ts t =
849 subst_bounds (map (Free o apfst concealed_bound_name)
850 (0 upto length Ts - 1 ~~ Ts), t)
851 fun reveal_bounds Ts =
852 subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
853 (0 upto length Ts - 1 ~~ Ts))
855 fun is_fun_equality (@{const_name HOL.eq},
856 Type (_, [Type (@{type_name fun}, _), _])) = true
857 | is_fun_equality _ = false
859 fun extensionalize_term ctxt t =
860 if exists_Const is_fun_equality t then
861 let val thy = Proof_Context.theory_of ctxt in
862 t |> cterm_of thy |> Meson.extensionalize_conv ctxt
863 |> prop_of |> Logic.dest_equals |> snd
868 fun introduce_combinators_in_term ctxt kind t =
869 let val thy = Proof_Context.theory_of ctxt in
870 if Meson.is_fol_term thy t then
876 @{const Not} $ t1 => @{const Not} $ aux Ts t1
877 | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
878 t0 $ Abs (s, T, aux (T :: Ts) t')
879 | (t0 as Const (@{const_name All}, _)) $ t1 =>
880 aux Ts (t0 $ eta_expand Ts t1 1)
881 | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
882 t0 $ Abs (s, T, aux (T :: Ts) t')
883 | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
884 aux Ts (t0 $ eta_expand Ts t1 1)
885 | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
886 | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
887 | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
888 | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
890 t0 $ aux Ts t1 $ aux Ts t2
891 | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
894 t |> conceal_bounds Ts
895 |> Envir.eta_contract
897 |> Meson_Clausify.introduce_combinators_in_cterm
898 |> prop_of |> Logic.dest_equals |> snd
900 val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
901 in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
903 (* A type variable of sort "{}" will make abstraction fail. *)
904 if kind = Conjecture then HOLogic.false_const
905 else HOLogic.true_const
908 (* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
909 same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
912 fun aux (t $ u) = aux t $ aux u
913 | aux (Abs (s, T, t)) = Abs (s, T, aux t)
914 | aux (Var ((s, i), T)) =
915 Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
917 in t |> exists_subterm is_Var t ? aux end
919 fun preprocess_prop ctxt presimp_consts kind t =
921 val thy = Proof_Context.theory_of ctxt
922 val t = t |> Envir.beta_eta_contract
923 |> transform_elim_prop
924 |> Object_Logic.atomize_term thy
925 val need_trueprop = (fastype_of t = @{typ bool})
927 t |> need_trueprop ? HOLogic.mk_Trueprop
928 |> Raw_Simplifier.rewrite_term thy (Meson.unfold_set_const_simps ctxt) []
929 |> extensionalize_term ctxt
930 |> presimplify_term ctxt presimp_consts
931 |> perhaps (try (HOLogic.dest_Trueprop))
932 |> introduce_combinators_in_term ctxt kind
935 (* making fact and conjecture formulas *)
936 fun make_formula thy format type_sys eq_as_iff name loc kind t =
938 val (combformula, atomic_types) =
939 combformula_from_prop thy format type_sys eq_as_iff t []
941 {name = name, locality = loc, kind = kind, combformula = combformula,
942 atomic_types = atomic_types}
945 fun make_fact ctxt format type_sys eq_as_iff preproc presimp_consts
947 let val thy = Proof_Context.theory_of ctxt in
948 case t |> preproc ? preprocess_prop ctxt presimp_consts Axiom
949 |> make_formula thy format type_sys (eq_as_iff andalso format <> CNF)
951 formula as {combformula = AAtom (CombConst ((s, _), _, _)), ...} =>
952 if s = tptp_true then NONE else SOME formula
953 | formula => SOME formula
956 fun make_conjecture ctxt format prem_kind type_sys preproc presimp_consts ts =
958 val thy = Proof_Context.theory_of ctxt
959 val last = length ts - 1
961 map2 (fn j => fn t =>
963 val (kind, maybe_negate) =
968 if prem_kind = Conjecture then update_combformula mk_anot
972 (preprocess_prop ctxt presimp_consts kind #> freeze_term)
973 |> make_formula thy format type_sys (format <> CNF)
974 (string_of_int j) Local kind
980 (** Finite and infinite type inference **)
982 fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
983 | deep_freeze_atyp T = T
984 val deep_freeze_type = map_atyps deep_freeze_atyp
986 (* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
987 dangerous because their "exhaust" properties can easily lead to unsound ATP
988 proofs. On the other hand, all HOL infinite types can be given the same
989 models in first-order logic (via Löwenheim-Skolem). *)
991 fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
992 exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
993 | should_encode_type _ _ All_Types _ = true
994 | should_encode_type ctxt _ Fin_Nonmono_Types T =
995 is_type_surely_finite ctxt false T
996 | should_encode_type _ _ _ _ = false
998 fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
999 should_predicate_on_var T =
1000 (heaviness = Heavyweight orelse should_predicate_on_var ()) andalso
1001 should_encode_type ctxt nonmono_Ts level T
1002 | should_predicate_on_type _ _ _ _ _ = false
1004 fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
1005 String.isPrefix bound_var_prefix s
1006 | is_var_or_bound_var (CombVar _) = true
1007 | is_var_or_bound_var _ = false
1010 Top_Level of bool option |
1011 Eq_Arg of bool option |
1014 fun should_tag_with_type _ _ _ (Top_Level _) _ _ = false
1015 | should_tag_with_type ctxt nonmono_Ts (Tags (poly, level, heaviness)) site
1018 Heavyweight => should_encode_type ctxt nonmono_Ts level T
1020 case (site, is_var_or_bound_var u) of
1021 (Eq_Arg pos, true) =>
1022 (* The first disjunct prevents a subtle soundness issue explained in
1023 Blanchette's Ph.D. thesis. See also
1024 "formula_lines_for_lightweight_tags_sym_decl". *)
1025 (pos <> SOME false andalso poly = Polymorphic andalso
1026 level <> All_Types andalso heaviness = Lightweight andalso
1027 exists (fn T' => type_instance ctxt (T', T)) nonmono_Ts) orelse
1028 should_encode_type ctxt nonmono_Ts level T
1030 | should_tag_with_type _ _ _ _ _ _ = false
1032 fun homogenized_type ctxt nonmono_Ts level =
1034 val should_encode = should_encode_type ctxt nonmono_Ts level
1035 fun homo 0 T = if should_encode T then T else homo_infinite_type
1036 | homo ary (Type (@{type_name fun}, [T1, T2])) =
1037 homo 0 T1 --> homo (ary - 1) T2
1038 | homo _ _ = raise Fail "expected function type"
1041 (** "hBOOL" and "hAPP" **)
1044 {pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
1046 fun add_combterm_syms_to_table ctxt explicit_apply =
1048 fun consider_var_arity const_T var_T max_ary =
1051 if ary = max_ary orelse type_instance ctxt (var_T, T) orelse
1052 type_instance ctxt (T, var_T) then
1055 iter (ary + 1) (range_type T)
1056 in iter 0 const_T end
1057 fun add_var_or_bound_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1058 if explicit_apply = NONE andalso
1059 (can dest_funT T orelse T = @{typ bool}) then
1061 val bool_vars' = bool_vars orelse body_type T = @{typ bool}
1062 fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
1063 {pred_sym = pred_sym andalso not bool_vars',
1064 min_ary = fold (fn T' => consider_var_arity T' T) types min_ary,
1065 max_ary = max_ary, types = types}
1067 fun_var_Ts |> can dest_funT T ? insert_type ctxt I T
1069 if bool_vars' = bool_vars andalso
1070 pointer_eq (fun_var_Ts', fun_var_Ts) then
1073 ((bool_vars', fun_var_Ts'), Symtab.map (K repair_min_arity) sym_tab)
1077 fun add top_level tm (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1078 let val (head, args) = strip_combterm_comb tm in
1080 CombConst ((s, _), T, _) =>
1081 if String.isPrefix bound_var_prefix s then
1082 add_var_or_bound_var T accum
1084 let val ary = length args in
1085 ((bool_vars, fun_var_Ts),
1086 case Symtab.lookup sym_tab s of
1087 SOME {pred_sym, min_ary, max_ary, types} =>
1090 pred_sym andalso top_level andalso not bool_vars
1091 val types' = types |> insert_type ctxt I T
1093 if is_some explicit_apply orelse
1094 pointer_eq (types', types) then
1097 fold (consider_var_arity T) fun_var_Ts min_ary
1099 Symtab.update (s, {pred_sym = pred_sym,
1100 min_ary = Int.min (ary, min_ary),
1101 max_ary = Int.max (ary, max_ary),
1107 val pred_sym = top_level andalso not bool_vars
1109 case explicit_apply of
1112 | NONE => fold (consider_var_arity T) fun_var_Ts ary
1114 Symtab.update_new (s, {pred_sym = pred_sym,
1115 min_ary = min_ary, max_ary = ary,
1120 | CombVar (_, T) => add_var_or_bound_var T accum
1122 |> fold (add false) args
1125 fun add_fact_syms_to_table ctxt explicit_apply =
1126 fact_lift (formula_fold NONE
1127 (K (add_combterm_syms_to_table ctxt explicit_apply)))
1129 val default_sym_tab_entries : (string * sym_info) list =
1130 (prefixed_predicator_name,
1131 {pred_sym = true, min_ary = 1, max_ary = 1, types = []}) ::
1132 ([tptp_false, tptp_true]
1133 |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []})) @
1134 ([tptp_equal, tptp_old_equal]
1135 |> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = []}))
1137 fun sym_table_for_facts ctxt explicit_apply facts =
1138 ((false, []), Symtab.empty)
1139 |> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
1140 |> fold Symtab.update default_sym_tab_entries
1142 fun min_arity_of sym_tab s =
1143 case Symtab.lookup sym_tab s of
1144 SOME ({min_ary, ...} : sym_info) => min_ary
1146 case strip_prefix_and_unascii const_prefix s of
1148 let val s = s |> unmangled_const_name |> invert_const in
1149 if s = predicator_name then 1
1150 else if s = app_op_name then 2
1151 else if s = type_pred_name then 1
1156 (* True if the constant ever appears outside of the top-level position in
1157 literals, or if it appears with different arities (e.g., because of different
1158 type instantiations). If false, the constant always receives all of its
1159 arguments and is used as a predicate. *)
1160 fun is_pred_sym sym_tab s =
1161 case Symtab.lookup sym_tab s of
1162 SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
1163 pred_sym andalso min_ary = max_ary
1166 val predicator_combconst =
1167 CombConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
1168 fun predicator tm = CombApp (predicator_combconst, tm)
1170 fun introduce_predicators_in_combterm sym_tab tm =
1171 case strip_combterm_comb tm of
1172 (CombConst ((s, _), _, _), _) =>
1173 if is_pred_sym sym_tab s then tm else predicator tm
1174 | _ => predicator tm
1176 fun list_app head args = fold (curry (CombApp o swap)) args head
1178 val app_op = `make_fixed_const app_op_name
1180 fun explicit_app arg head =
1182 val head_T = combtyp_of head
1183 val (arg_T, res_T) = dest_funT head_T
1185 CombConst (app_op, head_T --> head_T, [arg_T, res_T])
1186 in list_app explicit_app [head, arg] end
1187 fun list_explicit_app head args = fold explicit_app args head
1189 fun introduce_explicit_apps_in_combterm sym_tab =
1192 case strip_combterm_comb tm of
1193 (head as CombConst ((s, _), _, _), args) =>
1195 |> chop (min_arity_of sym_tab s)
1197 |-> list_explicit_app
1198 | (head, args) => list_explicit_app head (map aux args)
1201 fun chop_fun 0 T = ([], T)
1202 | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
1203 chop_fun (n - 1) ran_T |>> cons dom_T
1204 | chop_fun _ _ = raise Fail "unexpected non-function"
1206 fun filter_type_args _ _ _ [] = []
1207 | filter_type_args thy s arity T_args =
1209 (* will throw "TYPE" for pseudo-constants *)
1210 val U = if s = app_op_name then
1211 @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
1213 s |> Sign.the_const_type thy
1215 case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
1218 let val U_args = (s, U) |> Sign.const_typargs thy in
1220 |> map (fn (U, T) =>
1221 if member (op =) res_U_vars (dest_TVar U) then T
1225 handle TYPE _ => T_args
1227 fun enforce_type_arg_policy_in_combterm ctxt format type_sys =
1229 val thy = Proof_Context.theory_of ctxt
1230 fun aux arity (CombApp (tm1, tm2)) =
1231 CombApp (aux (arity + 1) tm1, aux 0 tm2)
1232 | aux arity (CombConst (name as (s, _), T, T_args)) =
1233 (case strip_prefix_and_unascii const_prefix s of
1234 NONE => (name, T_args)
1237 val s'' = invert_const s''
1238 fun filtered_T_args false = T_args
1239 | filtered_T_args true = filter_type_args thy s'' arity T_args
1241 case type_arg_policy type_sys s'' of
1242 Explicit_Type_Args drop_args =>
1243 (name, filtered_T_args drop_args)
1244 | Mangled_Type_Args drop_args =>
1245 (mangled_const_name format type_sys (filtered_T_args drop_args)
1247 | No_Type_Args => (name, [])
1249 |> (fn (name, T_args) => CombConst (name, T, T_args))
1253 fun repair_combterm ctxt format type_sys sym_tab =
1254 not (is_setting_higher_order format type_sys)
1255 ? (introduce_explicit_apps_in_combterm sym_tab
1256 #> introduce_predicators_in_combterm sym_tab)
1257 #> enforce_type_arg_policy_in_combterm ctxt format type_sys
1258 fun repair_fact ctxt format type_sys sym_tab =
1259 update_combformula (formula_map
1260 (repair_combterm ctxt format type_sys sym_tab))
1262 (** Helper facts **)
1264 (* The Boolean indicates that a fairly sound type encoding is needed. *)
1266 [(("COMBI", false), @{thms Meson.COMBI_def}),
1267 (("COMBK", false), @{thms Meson.COMBK_def}),
1268 (("COMBB", false), @{thms Meson.COMBB_def}),
1269 (("COMBC", false), @{thms Meson.COMBC_def}),
1270 (("COMBS", false), @{thms Meson.COMBS_def}),
1272 (* This is a lie: Higher-order equality doesn't need a sound type encoding.
1273 However, this is done so for backward compatibility: Including the
1274 equality helpers by default in Metis breaks a few existing proofs. *)
1275 @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1276 fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1277 (("fFalse", false), [@{lemma "~ fFalse" by (unfold fFalse_def) fast}]),
1278 (("fFalse", true), @{thms True_or_False}),
1279 (("fTrue", false), [@{lemma "fTrue" by (unfold fTrue_def) fast}]),
1280 (("fTrue", true), @{thms True_or_False}),
1282 @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1283 fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1285 @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
1286 by (unfold fconj_def) fast+}),
1288 @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
1289 by (unfold fdisj_def) fast+}),
1290 (("fimplies", false),
1291 @{lemma "P | fimplies P Q" "~ Q | fimplies P Q" "~ fimplies P Q | ~ P | Q"
1292 by (unfold fimplies_def) fast+}),
1293 (("If", true), @{thms if_True if_False True_or_False})]
1294 |> map (apsnd (map zero_var_indexes))
1296 val type_tag = `make_fixed_const type_tag_name
1298 fun type_tag_idempotence_fact () =
1300 fun var s = ATerm (`I s, [])
1301 fun tag tm = ATerm (type_tag, [var "T", tm])
1302 val tagged_a = tag (var "A")
1304 Formula (type_tag_idempotence_helper_name, Axiom,
1305 AAtom (ATerm (`I tptp_equal, [tag tagged_a, tagged_a]))
1306 |> close_formula_universally, simp_info, NONE)
1309 fun should_specialize_helper type_sys t =
1310 case general_type_arg_policy type_sys of
1311 Mangled_Type_Args _ => not (null (Term.hidden_polymorphism t))
1314 fun helper_facts_for_sym ctxt format type_sys (s, {types, ...} : sym_info) =
1315 case strip_prefix_and_unascii const_prefix s of
1318 val thy = Proof_Context.theory_of ctxt
1319 val unmangled_s = mangled_s |> unmangled_const_name
1320 fun dub_and_inst needs_fairly_sound (th, j) =
1321 ((unmangled_s ^ "_" ^ string_of_int j ^
1322 (if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^
1323 (if needs_fairly_sound then typed_helper_suffix
1324 else untyped_helper_suffix),
1326 let val t = th |> prop_of in
1327 t |> should_specialize_helper type_sys t
1329 [T] => specialize_type thy (invert_const unmangled_s, T)
1333 map_filter (make_fact ctxt format type_sys false false [])
1334 val fairly_sound = is_type_sys_fairly_sound type_sys
1337 |> maps (fn ((helper_s, needs_fairly_sound), ths) =>
1338 if helper_s <> unmangled_s orelse
1339 (needs_fairly_sound andalso not fairly_sound) then
1342 ths ~~ (1 upto length ths)
1343 |> map (dub_and_inst needs_fairly_sound)
1347 fun helper_facts_for_sym_table ctxt format type_sys sym_tab =
1348 Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_sys) sym_tab
1351 (***************************************************************)
1352 (* Type Classes Present in the Axiom or Conjecture Clauses *)
1353 (***************************************************************)
1355 fun set_insert (x, s) = Symtab.update (x, ()) s
1357 fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
1359 (* Remove this trivial type class (FIXME: similar code elsewhere) *)
1360 fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
1362 fun classes_of_terms get_Ts =
1363 map (map snd o get_Ts)
1364 #> List.foldl add_classes Symtab.empty
1365 #> delete_type #> Symtab.keys
1367 val tfree_classes_of_terms = classes_of_terms OldTerm.term_tfrees
1368 val tvar_classes_of_terms = classes_of_terms OldTerm.term_tvars
1370 (*fold type constructors*)
1371 fun fold_type_constrs f (Type (a, Ts)) x =
1372 fold (fold_type_constrs f) Ts (f (a,x))
1373 | fold_type_constrs _ _ x = x
1375 (*Type constructors used to instantiate overloaded constants are the only ones needed.*)
1376 fun add_type_constrs_in_term thy =
1378 fun add (Const (@{const_name Meson.skolem}, _) $ _) = I
1379 | add (t $ u) = add t #> add u
1380 | add (Const (x as (s, _))) =
1381 if String.isPrefix skolem_const_prefix s then I
1382 else x |> Sign.const_typargs thy |> fold (fold_type_constrs set_insert)
1383 | add (Abs (_, _, u)) = add u
1387 fun type_constrs_of_terms thy ts =
1388 Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty)
1390 fun translate_formulas ctxt format prem_kind type_sys preproc hyp_ts concl_t
1393 val thy = Proof_Context.theory_of ctxt
1394 val fact_ts = facts |> map snd
1395 val presimp_consts = Meson.presimplified_consts ctxt
1396 val make_fact = make_fact ctxt format type_sys true preproc presimp_consts
1397 val (facts, fact_names) =
1398 facts |> map (fn (name, t) => (name, t) |> make_fact |> rpair name)
1399 |> map_filter (try (apfst the))
1401 (* Remove existing facts from the conjecture, as this can dramatically
1402 boost an ATP's performance (for some reason). *)
1405 |> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t)
1406 val goal_t = Logic.list_implies (hyp_ts, concl_t)
1407 val all_ts = goal_t :: fact_ts
1408 val subs = tfree_classes_of_terms all_ts
1409 val supers = tvar_classes_of_terms all_ts
1410 val tycons = type_constrs_of_terms thy all_ts
1413 |> make_conjecture ctxt format prem_kind type_sys preproc presimp_consts
1414 val (supers', arity_clauses) =
1415 if level_of_type_sys type_sys = No_Types then ([], [])
1416 else make_arity_clauses thy tycons supers
1417 val class_rel_clauses = make_class_rel_clauses thy subs supers'
1419 (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
1422 fun fo_literal_from_type_literal (TyLitVar (class, name)) =
1423 (true, ATerm (class, [ATerm (name, [])]))
1424 | fo_literal_from_type_literal (TyLitFree (class, name)) =
1425 (true, ATerm (class, [ATerm (name, [])]))
1427 fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
1429 val type_pred = `make_fixed_const type_pred_name
1431 fun type_pred_combterm ctxt format type_sys T tm =
1432 CombApp (CombConst (type_pred, T --> @{typ bool}, [T])
1433 |> enforce_type_arg_policy_in_combterm ctxt format type_sys, tm)
1435 fun is_var_positively_naked_in_term _ (SOME false) _ accum = accum
1436 | is_var_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
1437 accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
1438 fun should_predicate_on_var_in_formula pos phi (SOME true) name =
1439 formula_fold pos (is_var_positively_naked_in_term name) phi false
1440 | should_predicate_on_var_in_formula _ _ _ _ = true
1442 fun mk_const_aterm format type_sys x T_args args =
1443 ATerm (x, map_filter (fo_term_for_type_arg format type_sys) T_args @ args)
1445 fun tag_with_type ctxt format nonmono_Ts type_sys pos T tm =
1446 CombConst (type_tag, T --> T, [T])
1447 |> enforce_type_arg_policy_in_combterm ctxt format type_sys
1448 |> term_from_combterm ctxt format nonmono_Ts type_sys (Top_Level pos)
1449 |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
1450 and term_from_combterm ctxt format nonmono_Ts type_sys =
1454 val (head, args) = strip_combterm_comb u
1455 val (x as (s, _), T_args) =
1457 CombConst (name, _, T_args) => (name, T_args)
1458 | CombVar (name, _) => (name, [])
1459 | CombApp _ => raise Fail "impossible \"CombApp\""
1460 val (pos, arg_site) =
1463 (pos, if is_tptp_equal s then Eq_Arg pos else Elsewhere)
1464 | Eq_Arg pos => (pos, Elsewhere)
1465 | Elsewhere => (NONE, Elsewhere)
1466 val t = mk_const_aterm format type_sys x T_args
1467 (map (aux arg_site) args)
1468 val T = combtyp_of u
1470 t |> (if should_tag_with_type ctxt nonmono_Ts type_sys site u T then
1471 tag_with_type ctxt format nonmono_Ts type_sys pos T
1476 and formula_from_combformula ctxt format nonmono_Ts type_sys
1477 should_predicate_on_var =
1480 term_from_combterm ctxt format nonmono_Ts type_sys (Top_Level pos)
1483 Simple_Types level =>
1484 homogenized_type ctxt nonmono_Ts level 0
1485 #> mangled_type format type_sys false 0 #> SOME
1487 fun do_out_of_bound_type pos phi universal (name, T) =
1488 if should_predicate_on_type ctxt nonmono_Ts type_sys
1489 (fn () => should_predicate_on_var pos phi universal name) T then
1491 |> type_pred_combterm ctxt format type_sys T
1492 |> do_term pos |> AAtom |> SOME
1495 fun do_formula pos (AQuant (q, xs, phi)) =
1497 val phi = phi |> do_formula pos
1498 val universal = Option.map (q = AExists ? not) pos
1500 AQuant (q, xs |> map (apsnd (fn NONE => NONE
1501 | SOME T => do_bound_type T)),
1502 (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
1504 (fn (_, NONE) => NONE
1506 do_out_of_bound_type pos phi universal (s, T))
1510 | do_formula pos (AConn conn) = aconn_map pos do_formula conn
1511 | do_formula pos (AAtom tm) = AAtom (do_term pos tm)
1514 fun bound_tvars type_sys Ts =
1515 mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
1516 (type_literals_for_types type_sys add_sorts_on_tvar Ts))
1518 (* Each fact is given a unique fact number to avoid name clashes (e.g., because
1519 of monomorphization). The TPTP explicitly forbids name clashes, and some of
1520 the remote provers might care. *)
1521 fun formula_line_for_fact ctxt format prefix encode freshen pos nonmono_Ts
1522 type_sys (j, {name, locality, kind, combformula, atomic_types}) =
1523 (prefix ^ (if freshen then string_of_int j ^ "_" else "") ^ encode name,
1526 |> close_combformula_universally
1527 |> formula_from_combformula ctxt format nonmono_Ts type_sys
1528 should_predicate_on_var_in_formula
1529 (if pos then SOME true else NONE)
1530 |> bound_tvars type_sys atomic_types
1531 |> close_formula_universally,
1540 fun formula_line_for_class_rel_clause ({name, subclass, superclass, ...}
1541 : class_rel_clause) =
1542 let val ty_arg = ATerm (`I "T", []) in
1543 Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
1544 AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
1545 AAtom (ATerm (superclass, [ty_arg]))])
1546 |> close_formula_universally, intro_info, NONE)
1549 fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
1550 (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
1551 | fo_literal_from_arity_literal (TVarLit (c, sort)) =
1552 (false, ATerm (c, [ATerm (sort, [])]))
1554 fun formula_line_for_arity_clause ({name, prem_lits, concl_lits, ...}
1556 Formula (arity_clause_prefix ^ name, Axiom,
1557 mk_ahorn (map (formula_from_fo_literal o apfst not
1558 o fo_literal_from_arity_literal) prem_lits)
1559 (formula_from_fo_literal
1560 (fo_literal_from_arity_literal concl_lits))
1561 |> close_formula_universally, intro_info, NONE)
1563 fun formula_line_for_conjecture ctxt format nonmono_Ts type_sys
1564 ({name, kind, combformula, atomic_types, ...} : translated_formula) =
1565 Formula (conjecture_prefix ^ name, kind,
1566 formula_from_combformula ctxt format nonmono_Ts type_sys
1567 should_predicate_on_var_in_formula (SOME false)
1568 (close_combformula_universally combformula)
1569 |> bound_tvars type_sys atomic_types
1570 |> close_formula_universally, NONE, NONE)
1572 fun free_type_literals type_sys ({atomic_types, ...} : translated_formula) =
1573 atomic_types |> type_literals_for_types type_sys add_sorts_on_tfree
1574 |> map fo_literal_from_type_literal
1576 fun formula_line_for_free_type j lit =
1577 Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis,
1578 formula_from_fo_literal lit, NONE, NONE)
1579 fun formula_lines_for_free_types type_sys facts =
1581 val litss = map (free_type_literals type_sys) facts
1582 val lits = fold (union (op =)) litss []
1583 in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
1585 (** Symbol declarations **)
1587 fun should_declare_sym type_sys pred_sym s =
1588 is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
1590 Simple_Types _ => true
1591 | Tags (_, _, Lightweight) => true
1592 | _ => not pred_sym)
1594 fun sym_decl_table_for_facts ctxt type_sys repaired_sym_tab (conjs, facts) =
1596 fun add_combterm in_conj tm =
1597 let val (head, args) = strip_combterm_comb tm in
1599 CombConst ((s, s'), T, T_args) =>
1600 let val pred_sym = is_pred_sym repaired_sym_tab s in
1601 if should_declare_sym type_sys pred_sym s then
1602 Symtab.map_default (s, [])
1603 (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
1609 #> fold (add_combterm in_conj) args
1611 fun add_fact in_conj =
1612 fact_lift (formula_fold NONE (K (add_combterm in_conj)))
1615 |> is_type_sys_fairly_sound type_sys
1616 ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
1619 (* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
1620 out with monotonicity" paper presented at CADE 2011. *)
1621 fun add_combterm_nonmonotonic_types _ _ _ _ (SOME false) _ = I
1622 | add_combterm_nonmonotonic_types ctxt level sound locality _
1623 (CombApp (CombApp (CombConst ((s, _), Type (_, [T, _]), _), tm1),
1625 (is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
1627 Noninf_Nonmono_Types =>
1628 not (is_locality_global locality) orelse
1629 not (is_type_surely_infinite ctxt sound T)
1630 | Fin_Nonmono_Types => is_type_surely_finite ctxt false T
1631 | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
1632 | add_combterm_nonmonotonic_types _ _ _ _ _ _ = I
1633 fun add_fact_nonmonotonic_types ctxt level sound
1634 ({kind, locality, combformula, ...} : translated_formula) =
1635 formula_fold (SOME (kind <> Conjecture))
1636 (add_combterm_nonmonotonic_types ctxt level sound locality)
1638 fun nonmonotonic_types_for_facts ctxt type_sys sound facts =
1639 let val level = level_of_type_sys type_sys in
1640 if level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types then
1641 [] |> fold (add_fact_nonmonotonic_types ctxt level sound) facts
1642 (* We must add "bool" in case the helper "True_or_False" is added
1643 later. In addition, several places in the code rely on the list of
1644 nonmonotonic types not being empty. *)
1645 |> insert_type ctxt I @{typ bool}
1650 fun decl_line_for_sym ctxt format nonmono_Ts type_sys s
1651 (s', T_args, T, pred_sym, ary, _) =
1653 val (T_arg_Ts, level) =
1655 Simple_Types level => ([], level)
1656 | _ => (replicate (length T_args) homo_infinite_type, No_Types)
1658 Decl (sym_decl_prefix ^ s, (s, s'),
1659 (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
1660 |> mangled_type format type_sys pred_sym (length T_arg_Ts + ary))
1663 fun formula_line_for_preds_sym_decl ctxt format conj_sym_kind nonmono_Ts
1664 poly_nonmono_Ts type_sys n s j (s', T_args, T, _, ary, in_conj) =
1666 val (kind, maybe_negate) =
1667 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1669 val (arg_Ts, res_T) = chop_fun ary T
1670 val num_args = length arg_Ts
1672 1 upto num_args |> map (`I o make_bound_var o string_of_int)
1674 bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
1675 val sym_needs_arg_types = n > 1 orelse exists (curry (op =) dummyT) T_args
1676 fun should_keep_arg_type T =
1677 sym_needs_arg_types orelse
1678 not (should_predicate_on_type ctxt nonmono_Ts type_sys (K false) T)
1680 arg_Ts |> map (fn T => if should_keep_arg_type T then SOME T else NONE)
1682 Formula (preds_sym_formula_prefix ^ s ^
1683 (if n > 1 then "_" ^ string_of_int j else ""), kind,
1684 CombConst ((s, s'), T, T_args)
1685 |> fold (curry (CombApp o swap)) bounds
1686 |> type_pred_combterm ctxt format type_sys res_T
1687 |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
1688 |> formula_from_combformula ctxt format poly_nonmono_Ts type_sys
1689 (K (K (K (K true)))) (SOME true)
1690 |> n > 1 ? bound_tvars type_sys (atyps_of T)
1691 |> close_formula_universally
1696 fun formula_lines_for_lightweight_tags_sym_decl ctxt format conj_sym_kind
1697 poly_nonmono_Ts type_sys n s
1698 (j, (s', T_args, T, pred_sym, ary, in_conj)) =
1701 lightweight_tags_sym_formula_prefix ^ s ^
1702 (if n > 1 then "_" ^ string_of_int j else "")
1703 val (kind, maybe_negate) =
1704 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1706 val (arg_Ts, res_T) = chop_fun ary T
1708 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
1709 val bounds = bound_names |> map (fn name => ATerm (name, []))
1710 val cst = mk_const_aterm format type_sys (s, s') T_args
1711 val atomic_Ts = atyps_of T
1713 (if pred_sym then AConn (AIff, map AAtom tms)
1714 else AAtom (ATerm (`I tptp_equal, tms)))
1715 |> bound_tvars type_sys atomic_Ts
1716 |> close_formula_universally
1718 (* See also "should_tag_with_type". *)
1719 fun should_encode T =
1720 should_encode_type ctxt poly_nonmono_Ts All_Types T orelse
1722 Tags (Polymorphic, level, Lightweight) =>
1723 level <> All_Types andalso Monomorph.typ_has_tvars T
1725 val tag_with = tag_with_type ctxt format poly_nonmono_Ts type_sys NONE
1726 val add_formula_for_res =
1727 if should_encode res_T then
1728 cons (Formula (ident_base ^ "_res", kind,
1729 eq [tag_with res_T (cst bounds), cst bounds],
1733 fun add_formula_for_arg k =
1734 let val arg_T = nth arg_Ts k in
1735 if should_encode arg_T then
1736 case chop k bounds of
1737 (bounds1, bound :: bounds2) =>
1738 cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
1739 eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
1742 | _ => raise Fail "expected nonempty tail"
1747 [] |> not pred_sym ? add_formula_for_res
1748 |> fold add_formula_for_arg (ary - 1 downto 0)
1751 fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
1753 fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts
1754 poly_nonmono_Ts type_sys (s, decls) =
1757 decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_sys s)
1762 decl :: (decls' as _ :: _) =>
1763 let val T = result_type_of_decl decl in
1764 if forall (curry (type_instance ctxt o swap) T
1765 o result_type_of_decl) decls' then
1771 val n = length decls
1773 decls |> filter (should_predicate_on_type ctxt poly_nonmono_Ts type_sys
1775 o result_type_of_decl)
1777 (0 upto length decls - 1, decls)
1778 |-> map2 (formula_line_for_preds_sym_decl ctxt format conj_sym_kind
1779 nonmono_Ts poly_nonmono_Ts type_sys n s)
1781 | Tags (_, _, heaviness) =>
1785 let val n = length decls in
1786 (0 upto n - 1 ~~ decls)
1787 |> maps (formula_lines_for_lightweight_tags_sym_decl ctxt format
1788 conj_sym_kind poly_nonmono_Ts type_sys n s)
1791 fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1792 poly_nonmono_Ts type_sys sym_decl_tab =
1797 |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
1798 nonmono_Ts poly_nonmono_Ts type_sys)
1800 fun needs_type_tag_idempotence (Tags (poly, level, heaviness)) =
1801 poly <> Mangled_Monomorphic andalso
1802 ((level = All_Types andalso heaviness = Lightweight) orelse
1803 level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types)
1804 | needs_type_tag_idempotence _ = false
1806 fun offset_of_heading_in_problem _ [] j = j
1807 | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
1808 if heading = needle then j
1809 else offset_of_heading_in_problem needle problem (j + length lines)
1811 val implicit_declsN = "Should-be-implicit typings"
1812 val explicit_declsN = "Explicit typings"
1813 val factsN = "Relevant facts"
1814 val class_relsN = "Class relationships"
1815 val aritiesN = "Arities"
1816 val helpersN = "Helper facts"
1817 val conjsN = "Conjectures"
1818 val free_typesN = "Type variables"
1820 val explicit_apply = NONE (* for experimental purposes *)
1822 fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_sys sound
1823 exporter readable_names preproc hyp_ts concl_t facts =
1825 val (format, type_sys) = choose_format [format] type_sys
1826 val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
1827 translate_formulas ctxt format prem_kind type_sys preproc hyp_ts concl_t
1829 val sym_tab = conjs @ facts |> sym_table_for_facts ctxt explicit_apply
1831 conjs @ facts |> nonmonotonic_types_for_facts ctxt type_sys sound
1832 val repair = repair_fact ctxt format type_sys sym_tab
1833 val (conjs, facts) = (conjs, facts) |> pairself (map repair)
1834 val repaired_sym_tab =
1835 conjs @ facts |> sym_table_for_facts ctxt (SOME false)
1837 repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_sys
1839 val poly_nonmono_Ts =
1840 if null nonmono_Ts orelse nonmono_Ts = [@{typ bool}] orelse
1841 polymorphism_of_type_sys type_sys <> Polymorphic then
1844 [TVar (("'a", 0), HOLogic.typeS)]
1845 val sym_decl_lines =
1846 (conjs, helpers @ facts)
1847 |> sym_decl_table_for_facts ctxt type_sys repaired_sym_tab
1848 |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1849 poly_nonmono_Ts type_sys
1851 0 upto length helpers - 1 ~~ helpers
1852 |> map (formula_line_for_fact ctxt format helper_prefix I false true
1853 poly_nonmono_Ts type_sys)
1854 |> (if needs_type_tag_idempotence type_sys then
1855 cons (type_tag_idempotence_fact ())
1858 (* Reordering these might confuse the proof reconstruction code or the SPASS
1861 [(explicit_declsN, sym_decl_lines),
1863 map (formula_line_for_fact ctxt format fact_prefix ascii_of
1864 (not exporter) (not exporter) nonmono_Ts
1866 (0 upto length facts - 1 ~~ facts)),
1867 (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
1868 (aritiesN, map formula_line_for_arity_clause arity_clauses),
1869 (helpersN, helper_lines),
1871 map (formula_line_for_conjecture ctxt format nonmono_Ts type_sys)
1873 (free_typesN, formula_lines_for_free_types type_sys (facts @ conjs))]
1877 CNF => ensure_cnf_problem
1878 | CNF_UEQ => filter_cnf_ueq_problem
1880 |> (if is_format_typed format then
1881 declare_undeclared_syms_in_atp_problem type_decl_prefix
1885 val (problem, pool) = problem |> nice_atp_problem readable_names
1886 val helpers_offset = offset_of_heading_in_problem helpersN problem 0
1888 map_filter (fn (j, {name, ...}) =>
1889 if String.isSuffix typed_helper_suffix name then SOME j
1891 ((helpers_offset + 1 upto helpers_offset + length helpers)
1893 fun add_sym_arity (s, {min_ary, ...} : sym_info) =
1895 case strip_prefix_and_unascii const_prefix s of
1896 SOME s => Symtab.insert (op =) (s, min_ary)
1902 case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
1903 offset_of_heading_in_problem conjsN problem 0,
1904 offset_of_heading_in_problem factsN problem 0,
1905 fact_names |> Vector.fromList,
1907 Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
1911 val conj_weight = 0.0
1912 val hyp_weight = 0.1
1913 val fact_min_weight = 0.2
1914 val fact_max_weight = 1.0
1915 val type_info_default_weight = 0.8
1917 fun add_term_weights weight (ATerm (s, tms)) =
1918 is_tptp_user_symbol s ? Symtab.default (s, weight)
1919 #> fold (add_term_weights weight) tms
1920 fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
1921 formula_fold NONE (K (add_term_weights weight)) phi
1922 | add_problem_line_weights _ _ = I
1924 fun add_conjectures_weights [] = I
1925 | add_conjectures_weights conjs =
1926 let val (hyps, conj) = split_last conjs in
1927 add_problem_line_weights conj_weight conj
1928 #> fold (add_problem_line_weights hyp_weight) hyps
1931 fun add_facts_weights facts =
1933 val num_facts = length facts
1935 fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
1936 / Real.fromInt num_facts
1938 map weight_of (0 upto num_facts - 1) ~~ facts
1939 |> fold (uncurry add_problem_line_weights)
1942 (* Weights are from 0.0 (most important) to 1.0 (least important). *)
1943 fun atp_problem_weights problem =
1944 let val get = these o AList.lookup (op =) problem in
1946 |> add_conjectures_weights (get free_typesN @ get conjsN)
1947 |> add_facts_weights (get factsN)
1948 |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
1949 [explicit_declsN, class_relsN, aritiesN]
1951 |> sort (prod_ord Real.compare string_ord o pairself swap)