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
18 type name = string * string
20 datatype type_literal =
21 TyLitVar of name * name |
22 TyLitFree of name * name
24 datatype arity_literal =
25 TConsLit of name * name * name list |
26 TVarLit of name * name
30 prem_lits: arity_literal list,
31 concl_lits: arity_literal}
33 type class_rel_clause =
39 CombConst of name * typ * typ list |
40 CombVar of name * typ |
41 CombApp of combterm * combterm
43 datatype locality = General | Intro | Elim | Simp | Local | Assum | Chained
45 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
47 All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
48 datatype type_heaviness = Heavyweight | Lightweight
51 Simple_Types of type_level |
52 Preds of polymorphism * type_level * type_heaviness |
53 Tags of polymorphism * type_level * type_heaviness
55 val bound_var_prefix : string
56 val schematic_var_prefix: string
57 val fixed_var_prefix: string
58 val tvar_prefix: string
59 val tfree_prefix: string
60 val const_prefix: string
61 val type_const_prefix: string
62 val class_prefix: string
63 val skolem_const_prefix : string
64 val old_skolem_const_prefix : string
65 val new_skolem_const_prefix : string
66 val type_decl_prefix : string
67 val sym_decl_prefix : string
68 val preds_sym_formula_prefix : string
69 val lightweight_tags_sym_formula_prefix : string
70 val fact_prefix : string
71 val conjecture_prefix : string
72 val helper_prefix : string
73 val class_rel_clause_prefix : string
74 val arity_clause_prefix : string
75 val tfree_clause_prefix : string
76 val typed_helper_suffix : string
77 val untyped_helper_suffix : string
78 val type_tag_idempotence_helper_name : string
79 val predicator_name : string
80 val app_op_name : string
81 val type_tag_name : string
82 val type_pred_name : string
83 val simple_type_prefix : string
84 val prefixed_predicator_name : string
85 val prefixed_app_op_name : string
86 val prefixed_type_tag_name : string
87 val ascii_of: string -> string
88 val unascii_of: string -> string
89 val strip_prefix_and_unascii : string -> string -> string option
90 val proxy_table : (string * (string * (thm * (string * string)))) list
91 val proxify_const : string -> (string * string) option
92 val invert_const: string -> string
93 val unproxify_const: string -> string
94 val make_bound_var : string -> string
95 val make_schematic_var : string * int -> string
96 val make_fixed_var : string -> string
97 val make_schematic_type_var : string * int -> string
98 val make_fixed_type_var : string -> string
99 val make_fixed_const : string -> string
100 val make_fixed_type_const : string -> string
101 val make_type_class : string -> string
102 val new_skolem_var_name_from_const : string -> string
103 val num_type_args : theory -> string -> int
104 val atp_irrelevant_consts : string list
105 val atp_schematic_consts_of : term -> typ list Symtab.table
106 val make_arity_clauses :
107 theory -> string list -> class list -> class list * arity_clause list
108 val make_class_rel_clauses :
109 theory -> class list -> class list -> class_rel_clause list
110 val combtyp_of : combterm -> typ
111 val strip_combterm_comb : combterm -> combterm * combterm list
112 val atyps_of : typ -> typ list
113 val combterm_from_term :
114 theory -> (string * typ) list -> term -> combterm * typ list
115 val is_locality_global : locality -> bool
116 val type_sys_from_string : string -> type_sys
117 val polymorphism_of_type_sys : type_sys -> polymorphism
118 val level_of_type_sys : type_sys -> type_level
119 val is_type_sys_virtually_sound : type_sys -> bool
120 val is_type_sys_fairly_sound : type_sys -> bool
121 val choose_format : format list -> type_sys -> format * type_sys
123 connective -> ('a, 'b, 'c) formula list -> ('a, 'b, 'c) formula
124 val unmangled_const_name : string -> string
125 val unmangled_const : string -> string * string fo_term list
126 val helper_table : ((string * bool) * thm list) list
127 val should_specialize_helper : type_sys -> term -> bool
128 val tfree_classes_of_terms : term list -> string list
129 val tvar_classes_of_terms : term list -> string list
130 val type_constrs_of_terms : theory -> term list -> string list
131 val prepare_atp_problem :
132 Proof.context -> format -> formula_kind -> formula_kind -> type_sys
133 -> bool -> bool -> term list -> term -> ((string * locality) * term) list
134 -> string problem * string Symtab.table * int * int
135 * (string * locality) list vector * int list * int Symtab.table
136 val atp_problem_weights : string problem -> (string * real) list
139 structure ATP_Translate : ATP_TRANSLATE =
145 type name = string * string
148 val generate_useful_info = false
150 fun useful_isabelle_info s =
151 if generate_useful_info then
152 SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
156 val intro_info = useful_isabelle_info "intro"
157 val elim_info = useful_isabelle_info "elim"
158 val simp_info = useful_isabelle_info "simp"
160 val bound_var_prefix = "B_"
161 val schematic_var_prefix = "V_"
162 val fixed_var_prefix = "v_"
164 val tvar_prefix = "T_"
165 val tfree_prefix = "t_"
167 val const_prefix = "c_"
168 val type_const_prefix = "tc_"
169 val class_prefix = "cl_"
171 val skolem_const_prefix = "Sledgehammer" ^ Long_Name.separator ^ "Sko"
172 val old_skolem_const_prefix = skolem_const_prefix ^ "o"
173 val new_skolem_const_prefix = skolem_const_prefix ^ "n"
175 val type_decl_prefix = "ty_"
176 val sym_decl_prefix = "sy_"
177 val preds_sym_formula_prefix = "psy_"
178 val lightweight_tags_sym_formula_prefix = "tsy_"
179 val fact_prefix = "fact_"
180 val conjecture_prefix = "conj_"
181 val helper_prefix = "help_"
182 val class_rel_clause_prefix = "clar_"
183 val arity_clause_prefix = "arity_"
184 val tfree_clause_prefix = "tfree_"
186 val typed_helper_suffix = "_T"
187 val untyped_helper_suffix = "_U"
188 val type_tag_idempotence_helper_name = helper_prefix ^ "ti_idem"
190 val predicator_name = "hBOOL"
191 val app_op_name = "hAPP"
192 val type_tag_name = "ti"
193 val type_pred_name = "is"
194 val simple_type_prefix = "ty_"
196 val prefixed_predicator_name = const_prefix ^ predicator_name
197 val prefixed_app_op_name = const_prefix ^ app_op_name
198 val prefixed_type_tag_name = const_prefix ^ type_tag_name
200 (* Freshness almost guaranteed! *)
201 val sledgehammer_weak_prefix = "Sledgehammer:"
203 (*Escaping of special characters.
204 Alphanumeric characters are left unchanged.
205 The character _ goes to __
206 Characters in the range ASCII space to / go to _A to _P, respectively.
207 Other characters go to _nnn where nnn is the decimal ASCII code.*)
208 val upper_a_minus_space = Char.ord #"A" - Char.ord #" "
210 fun stringN_of_int 0 _ = ""
211 | stringN_of_int k n =
212 stringN_of_int (k - 1) (n div 10) ^ string_of_int (n mod 10)
214 fun ascii_of_char c =
215 if Char.isAlphaNum c then
217 else if c = #"_" then
219 else if #" " <= c andalso c <= #"/" then
220 "_" ^ String.str (Char.chr (Char.ord c + upper_a_minus_space))
222 (* fixed width, in case more digits follow *)
223 "_" ^ stringN_of_int 3 (Char.ord c)
225 val ascii_of = String.translate ascii_of_char
227 (** Remove ASCII armoring from names in proof files **)
229 (* We don't raise error exceptions because this code can run inside a worker
230 thread. Also, the errors are impossible. *)
233 fun un rcs [] = String.implode(rev rcs)
234 | un rcs [#"_"] = un (#"_" :: rcs) [] (* ERROR *)
235 (* Three types of _ escapes: __, _A to _P, _nnn *)
236 | un rcs (#"_" :: #"_" :: cs) = un (#"_"::rcs) cs
237 | un rcs (#"_" :: c :: cs) =
238 if #"A" <= c andalso c<= #"P" then
239 (* translation of #" " to #"/" *)
240 un (Char.chr (Char.ord c - upper_a_minus_space) :: rcs) cs
242 let val digits = List.take (c::cs, 3) handle General.Subscript => [] in
243 case Int.fromString (String.implode digits) of
244 SOME n => un (Char.chr n :: rcs) (List.drop (cs, 2))
245 | NONE => un (c:: #"_"::rcs) cs (* ERROR *)
247 | un rcs (c :: cs) = un (c :: rcs) cs
248 in un [] o String.explode end
250 (* If string s has the prefix s1, return the result of deleting it,
252 fun strip_prefix_and_unascii s1 s =
253 if String.isPrefix s1 s then
254 SOME (unascii_of (String.extract (s, size s1, NONE)))
259 [("c_False", (@{const_name False}, (@{thm fFalse_def},
260 ("fFalse", @{const_name ATP.fFalse})))),
261 ("c_True", (@{const_name True}, (@{thm fTrue_def},
262 ("fTrue", @{const_name ATP.fTrue})))),
263 ("c_Not", (@{const_name Not}, (@{thm fNot_def},
264 ("fNot", @{const_name ATP.fNot})))),
265 ("c_conj", (@{const_name conj}, (@{thm fconj_def},
266 ("fconj", @{const_name ATP.fconj})))),
267 ("c_disj", (@{const_name disj}, (@{thm fdisj_def},
268 ("fdisj", @{const_name ATP.fdisj})))),
269 ("c_implies", (@{const_name implies}, (@{thm fimplies_def},
270 ("fimplies", @{const_name ATP.fimplies})))),
271 ("equal", (@{const_name HOL.eq}, (@{thm fequal_def},
272 ("fequal", @{const_name ATP.fequal}))))]
274 val proxify_const = AList.lookup (op =) proxy_table #> Option.map (snd o snd)
276 (* Readable names for the more common symbolic functions. Do not mess with the
277 table unless you know what you are doing. *)
278 val const_trans_table =
279 [(@{type_name Product_Type.prod}, "prod"),
280 (@{type_name Sum_Type.sum}, "sum"),
281 (@{const_name False}, "False"),
282 (@{const_name True}, "True"),
283 (@{const_name Not}, "Not"),
284 (@{const_name conj}, "conj"),
285 (@{const_name disj}, "disj"),
286 (@{const_name implies}, "implies"),
287 (@{const_name HOL.eq}, "equal"),
288 (@{const_name If}, "If"),
289 (@{const_name Set.member}, "member"),
290 (@{const_name Meson.COMBI}, "COMBI"),
291 (@{const_name Meson.COMBK}, "COMBK"),
292 (@{const_name Meson.COMBB}, "COMBB"),
293 (@{const_name Meson.COMBC}, "COMBC"),
294 (@{const_name Meson.COMBS}, "COMBS")]
296 |> fold (Symtab.update o swap o snd o snd o snd) proxy_table
298 (* Invert the table of translations between Isabelle and ATPs. *)
299 val const_trans_table_inv =
300 const_trans_table |> Symtab.dest |> map swap |> Symtab.make
301 val const_trans_table_unprox =
303 |> fold (fn (_, (isa, (_, (_, atp)))) => Symtab.update (atp, isa)) proxy_table
305 val invert_const = perhaps (Symtab.lookup const_trans_table_inv)
306 val unproxify_const = perhaps (Symtab.lookup const_trans_table_unprox)
309 case Symtab.lookup const_trans_table c of
313 (*Remove the initial ' character from a type variable, if it is present*)
314 fun trim_type_var s =
315 if s <> "" andalso String.sub(s,0) = #"'" then String.extract(s,1,NONE)
316 else raise Fail ("trim_type: Malformed type variable encountered: " ^ s)
318 fun ascii_of_indexname (v,0) = ascii_of v
319 | ascii_of_indexname (v,i) = ascii_of v ^ "_" ^ string_of_int i
321 fun make_bound_var x = bound_var_prefix ^ ascii_of x
322 fun make_schematic_var v = schematic_var_prefix ^ ascii_of_indexname v
323 fun make_fixed_var x = fixed_var_prefix ^ ascii_of x
325 fun make_schematic_type_var (x,i) =
326 tvar_prefix ^ (ascii_of_indexname (trim_type_var x, i))
327 fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (trim_type_var x))
329 (* HOL.eq MUST BE "equal" because it's built into ATPs. *)
330 fun make_fixed_const @{const_name HOL.eq} = "equal"
331 | make_fixed_const c = const_prefix ^ lookup_const c
333 fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
335 fun make_type_class clas = class_prefix ^ ascii_of clas
337 fun new_skolem_var_name_from_const s =
338 let val ss = s |> space_explode Long_Name.separator in
339 nth ss (length ss - 2)
342 (* The number of type arguments of a constant, zero if it's monomorphic. For
343 (instances of) Skolem pseudoconstants, this information is encoded in the
345 fun num_type_args thy s =
346 if String.isPrefix skolem_const_prefix s then
347 s |> space_explode Long_Name.separator |> List.last |> Int.fromString |> the
349 (s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
351 (* These are either simplified away by "Meson.presimplify" (most of the time) or
352 handled specially via "fFalse", "fTrue", ..., "fequal". *)
353 val atp_irrelevant_consts =
354 [@{const_name False}, @{const_name True}, @{const_name Not},
355 @{const_name conj}, @{const_name disj}, @{const_name implies},
356 @{const_name HOL.eq}, @{const_name If}, @{const_name Let}]
358 val atp_monomorph_bad_consts =
359 atp_irrelevant_consts @
360 (* These are ignored anyway by the relevance filter (unless they appear in
361 higher-order places) but not by the monomorphizer. *)
362 [@{const_name all}, @{const_name "==>"}, @{const_name "=="},
363 @{const_name Trueprop}, @{const_name All}, @{const_name Ex},
364 @{const_name Ex1}, @{const_name Ball}, @{const_name Bex}]
366 fun add_schematic_const (x as (_, T)) =
367 Monomorph.typ_has_tvars T ? Symtab.insert_list (op =) x
368 val add_schematic_consts_of =
369 Term.fold_aterms (fn Const (x as (s, _)) =>
370 not (member (op =) atp_monomorph_bad_consts s)
371 ? add_schematic_const x
373 fun atp_schematic_consts_of t = add_schematic_consts_of t Symtab.empty
375 (** Definitions and functions for FOL clauses and formulas for TPTP **)
377 (* The first component is the type class; the second is a "TVar" or "TFree". *)
378 datatype type_literal =
379 TyLitVar of name * name |
380 TyLitFree of name * name
383 (** Isabelle arities **)
385 datatype arity_literal =
386 TConsLit of name * name * name list |
387 TVarLit of name * name
390 | gen_TVars n = ("T_" ^ string_of_int n) :: gen_TVars (n-1)
392 val type_class = the_single @{sort type}
394 fun add_packed_sort tvar =
395 fold (fn s => s <> type_class ? cons (`make_type_class s, `I tvar))
399 prem_lits: arity_literal list,
400 concl_lits: arity_literal}
402 (* Arity of type constructor "tcon :: (arg1, ..., argN) res" *)
403 fun make_axiom_arity_clause (tcons, name, (cls, args)) =
405 val tvars = gen_TVars (length args)
406 val tvars_srts = ListPair.zip (tvars, args)
409 prem_lits = [] |> fold (uncurry add_packed_sort) tvars_srts |> map TVarLit,
410 concl_lits = TConsLit (`make_type_class cls,
411 `make_fixed_type_const tcons,
415 fun arity_clause _ _ (_, []) = []
416 | arity_clause seen n (tcons, ("HOL.type",_)::ars) = (*ignore*)
417 arity_clause seen n (tcons,ars)
418 | arity_clause seen n (tcons, (ar as (class,_)) :: ars) =
419 if member (op =) seen class then (*multiple arities for the same tycon, class pair*)
420 make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class ^ "_" ^ string_of_int n, ar) ::
421 arity_clause seen (n+1) (tcons,ars)
423 make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class, ar) ::
424 arity_clause (class::seen) n (tcons,ars)
426 fun multi_arity_clause [] = []
427 | multi_arity_clause ((tcons, ars) :: tc_arlists) =
428 arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
430 (*Generate all pairs (tycon,class,sorts) such that tycon belongs to class in theory thy
431 provided its arguments have the corresponding sorts.*)
432 fun type_class_pairs thy tycons classes =
434 val alg = Sign.classes_of thy
435 fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
436 fun add_class tycon class =
437 cons (class, domain_sorts tycon class)
438 handle Sorts.CLASS_ERROR _ => I
439 fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
440 in map try_classes tycons end
442 (*Proving one (tycon, class) membership may require proving others, so iterate.*)
443 fun iter_type_class_pairs _ _ [] = ([], [])
444 | iter_type_class_pairs thy tycons classes =
446 fun maybe_insert_class s =
447 (s <> type_class andalso not (member (op =) classes s))
449 val cpairs = type_class_pairs thy tycons classes
451 [] |> fold (fold (fold (fold maybe_insert_class) o snd) o snd) cpairs
452 val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
453 in (classes' @ classes, union (op =) cpairs' cpairs) end
455 fun make_arity_clauses thy tycons =
456 iter_type_class_pairs thy tycons ##> multi_arity_clause
459 (** Isabelle class relations **)
461 type class_rel_clause =
466 (*Generate all pairs (sub,super) such that sub is a proper subclass of super in theory thy.*)
467 fun class_pairs _ [] _ = []
468 | class_pairs thy subs supers =
470 val class_less = Sorts.class_less (Sign.classes_of thy)
471 fun add_super sub super = class_less (sub, super) ? cons (sub, super)
472 fun add_supers sub = fold (add_super sub) supers
473 in fold add_supers subs [] end
475 fun make_class_rel_clause (sub,super) =
476 {name = sub ^ "_" ^ super,
477 subclass = `make_type_class sub,
478 superclass = `make_type_class super}
480 fun make_class_rel_clauses thy subs supers =
481 map make_class_rel_clause (class_pairs thy subs supers)
484 CombConst of name * typ * typ list |
485 CombVar of name * typ |
486 CombApp of combterm * combterm
488 fun combtyp_of (CombConst (_, T, _)) = T
489 | combtyp_of (CombVar (_, T)) = T
490 | combtyp_of (CombApp (t1, _)) = snd (dest_funT (combtyp_of t1))
492 (*gets the head of a combinator application, along with the list of arguments*)
493 fun strip_combterm_comb u =
494 let fun stripc (CombApp(t,u), ts) = stripc (t, u::ts)
498 fun atyps_of T = fold_atyps (insert (op =)) T []
500 fun new_skolem_const_name s num_T_args =
501 [new_skolem_const_prefix, s, string_of_int num_T_args]
502 |> space_implode Long_Name.separator
504 (* Converts a term (with combinators) into a combterm. Also accumulates sort
506 fun combterm_from_term thy bs (P $ Q) =
508 val (P', P_atomics_Ts) = combterm_from_term thy bs P
509 val (Q', Q_atomics_Ts) = combterm_from_term thy bs Q
510 in (CombApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
511 | combterm_from_term thy _ (Const (c, T)) =
514 (if String.isPrefix old_skolem_const_prefix c then
515 [] |> Term.add_tvarsT T |> map TVar
517 (c, T) |> Sign.const_typargs thy)
518 val c' = CombConst (`make_fixed_const c, T, tvar_list)
519 in (c', atyps_of T) end
520 | combterm_from_term _ _ (Free (v, T)) =
521 (CombConst (`make_fixed_var v, T, []), atyps_of T)
522 | combterm_from_term _ _ (Var (v as (s, _), T)) =
523 (if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
525 val Ts = T |> strip_type |> swap |> op ::
526 val s' = new_skolem_const_name s (length Ts)
527 in CombConst (`make_fixed_const s', T, Ts) end
529 CombVar ((make_schematic_var v, s), T), atyps_of T)
530 | combterm_from_term _ bs (Bound j) =
532 |> (fn (s, T) => (CombConst (`make_bound_var s, T, []), atyps_of T))
533 | combterm_from_term _ _ (Abs _) = raise Fail "HOL clause: Abs"
535 datatype locality = General | Intro | Elim | Simp | Local | Assum | Chained
537 (* (quasi-)underapproximation of the truth *)
538 fun is_locality_global Local = false
539 | is_locality_global Assum = false
540 | is_locality_global Chained = false
541 | is_locality_global _ = true
543 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
544 datatype type_level =
545 All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
546 datatype type_heaviness = Heavyweight | Lightweight
549 Simple_Types of type_level |
550 Preds of polymorphism * type_level * type_heaviness |
551 Tags of polymorphism * type_level * type_heaviness
553 fun try_unsuffixes ss s =
554 fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
556 fun type_sys_from_string s =
557 (case try (unprefix "poly_") s of
558 SOME s => (SOME Polymorphic, s)
560 case try (unprefix "mono_") s of
561 SOME s => (SOME Monomorphic, s)
563 case try (unprefix "mangled_") s of
564 SOME s => (SOME Mangled_Monomorphic, s)
567 (* "_query" and "_bang" are for the ASCII-challenged Mirabelle. *)
568 case try_unsuffixes ["?", "_query"] s of
569 SOME s => (Nonmonotonic_Types, s)
571 case try_unsuffixes ["!", "_bang"] s of
572 SOME s => (Finite_Types, s)
573 | NONE => (All_Types, s))
575 case try (unsuffix "_heavy") s of
576 SOME s => (Heavyweight, s)
577 | NONE => (Lightweight, s))
578 |> (fn (poly, (level, (heaviness, core))) =>
579 case (core, (poly, level, heaviness)) of
580 ("simple", (NONE, _, Lightweight)) => Simple_Types level
581 | ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
582 | ("tags", (SOME Polymorphic, All_Types, _)) =>
583 Tags (Polymorphic, All_Types, heaviness)
584 | ("tags", (SOME Polymorphic, _, _)) =>
585 (* The actual light encoding is very unsound. *)
586 Tags (Polymorphic, level, Heavyweight)
587 | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
588 | ("args", (SOME poly, All_Types (* naja *), Lightweight)) =>
589 Preds (poly, Const_Arg_Types, Lightweight)
590 | ("erased", (NONE, All_Types (* naja *), Lightweight)) =>
591 Preds (Polymorphic, No_Types, Lightweight)
592 | _ => raise Same.SAME)
593 handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
595 fun polymorphism_of_type_sys (Simple_Types _) = Mangled_Monomorphic
596 | polymorphism_of_type_sys (Preds (poly, _, _)) = poly
597 | polymorphism_of_type_sys (Tags (poly, _, _)) = poly
599 fun level_of_type_sys (Simple_Types level) = level
600 | level_of_type_sys (Preds (_, level, _)) = level
601 | level_of_type_sys (Tags (_, level, _)) = level
603 fun heaviness_of_type_sys (Simple_Types _) = Heavyweight
604 | heaviness_of_type_sys (Preds (_, _, heaviness)) = heaviness
605 | heaviness_of_type_sys (Tags (_, _, heaviness)) = heaviness
607 fun is_type_level_virtually_sound level =
608 level = All_Types orelse level = Nonmonotonic_Types
609 val is_type_sys_virtually_sound =
610 is_type_level_virtually_sound o level_of_type_sys
612 fun is_type_level_fairly_sound level =
613 is_type_level_virtually_sound level orelse level = Finite_Types
614 val is_type_sys_fairly_sound = is_type_level_fairly_sound o level_of_type_sys
616 fun is_setting_higher_order THF (Simple_Types _) = true
617 | is_setting_higher_order _ _ = false
619 fun choose_format formats (Simple_Types level) =
620 if member (op =) formats THF then (THF, Simple_Types level)
621 else if member (op =) formats TFF then (TFF, Simple_Types level)
622 else choose_format formats (Preds (Mangled_Monomorphic, level, Heavyweight))
623 | choose_format formats type_sys =
626 (CNF_UEQ, case type_sys of
628 (if is_type_sys_fairly_sound type_sys then Tags else Preds)
631 | format => (format, type_sys))
633 type translated_formula =
637 combformula: (name, typ, combterm) formula,
638 atomic_types: typ list}
640 fun update_combformula f ({name, locality, kind, combformula, atomic_types}
641 : translated_formula) =
642 {name = name, locality = locality, kind = kind, combformula = f combformula,
643 atomic_types = atomic_types} : translated_formula
645 fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
647 val type_instance = Sign.typ_instance o Proof_Context.theory_of
649 fun insert_type ctxt get_T x xs =
650 let val T = get_T x in
651 if exists (curry (type_instance ctxt) T o get_T) xs then xs
652 else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
655 (* The Booleans indicate whether all type arguments should be kept. *)
656 datatype type_arg_policy =
657 Explicit_Type_Args of bool |
658 Mangled_Type_Args of bool |
661 fun should_drop_arg_type_args (Simple_Types _) =
662 false (* since TFF doesn't support overloading *)
663 | should_drop_arg_type_args type_sys =
664 level_of_type_sys type_sys = All_Types andalso
665 heaviness_of_type_sys type_sys = Heavyweight
667 fun general_type_arg_policy (Tags (_, All_Types, Heavyweight)) = No_Type_Args
668 | general_type_arg_policy type_sys =
669 if level_of_type_sys type_sys = No_Types then
671 else if polymorphism_of_type_sys type_sys = Mangled_Monomorphic then
672 Mangled_Type_Args (should_drop_arg_type_args type_sys)
674 Explicit_Type_Args (should_drop_arg_type_args type_sys)
676 fun type_arg_policy type_sys s =
677 if s = @{const_name HOL.eq} orelse
678 (s = app_op_name andalso level_of_type_sys type_sys = Const_Arg_Types) then
680 else if s = type_tag_name then
681 Explicit_Type_Args false
683 general_type_arg_policy type_sys
685 (*Make literals for sorted type variables*)
686 fun generic_add_sorts_on_type (_, []) = I
687 | generic_add_sorts_on_type ((x, i), s :: ss) =
688 generic_add_sorts_on_type ((x, i), ss)
689 #> (if s = the_single @{sort HOL.type} then
692 insert (op =) (TyLitFree (`make_type_class s, `make_fixed_type_var x))
694 insert (op =) (TyLitVar (`make_type_class s,
695 (make_schematic_type_var (x, i), x))))
696 fun add_sorts_on_tfree (TFree (s, S)) = generic_add_sorts_on_type ((s, ~1), S)
697 | add_sorts_on_tfree _ = I
698 fun add_sorts_on_tvar (TVar z) = generic_add_sorts_on_type z
699 | add_sorts_on_tvar _ = I
701 fun type_literals_for_types type_sys add_sorts_on_typ Ts =
702 [] |> level_of_type_sys type_sys <> No_Types ? fold add_sorts_on_typ Ts
704 fun mk_aconns c phis =
705 let val (phis', phi') = split_last phis in
706 fold_rev (mk_aconn c) phis' phi'
708 fun mk_ahorn [] phi = phi
709 | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
710 fun mk_aquant _ [] phi = phi
711 | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
712 if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
713 | mk_aquant q xs phi = AQuant (q, xs, phi)
715 fun close_universally atom_vars phi =
717 fun formula_vars bounds (AQuant (_, xs, phi)) =
718 formula_vars (map fst xs @ bounds) phi
719 | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
720 | formula_vars bounds (AAtom tm) =
721 union (op =) (atom_vars tm []
722 |> filter_out (member (op =) bounds o fst))
723 in mk_aquant AForall (formula_vars [] phi []) phi end
725 fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
726 | combterm_vars (CombConst _) = I
727 | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
728 fun close_combformula_universally phi = close_universally combterm_vars phi
730 fun term_vars (ATerm (name as (s, _), tms)) =
731 is_tptp_variable s ? insert (op =) (name, NONE) #> fold term_vars tms
732 fun close_formula_universally phi = close_universally term_vars phi
734 val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
735 val homo_infinite_type = Type (homo_infinite_type_name, [])
737 fun fo_term_from_typ format type_sys =
739 fun term (Type (s, Ts)) =
740 ATerm (case (is_setting_higher_order format type_sys, s) of
741 (true, @{type_name bool}) => `I tptp_bool_type
742 | (true, @{type_name fun}) => `I tptp_fun_type
743 | _ => if s = homo_infinite_type_name andalso
744 (format = TFF orelse format = THF) then
745 `I tptp_individual_type
747 `make_fixed_type_const s,
749 | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
750 | term (TVar ((x as (s, _)), _)) =
751 ATerm ((make_schematic_type_var x, s), [])
754 (* This shouldn't clash with anything else. *)
755 val mangled_type_sep = "\000"
757 fun generic_mangled_type_name f (ATerm (name, [])) = f name
758 | generic_mangled_type_name f (ATerm (name, tys)) =
759 f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
762 val bool_atype = AType (`I tptp_bool_type)
764 fun make_simple_type s =
765 if s = tptp_bool_type orelse s = tptp_fun_type orelse
766 s = tptp_individual_type then
769 simple_type_prefix ^ ascii_of s
771 fun ho_type_from_fo_term format type_sys pred_sym ary =
774 AType ((make_simple_type (generic_mangled_type_name fst ty),
775 generic_mangled_type_name snd ty))
776 fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
777 fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
778 | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
779 fun to_ho (ty as ATerm ((s, _), tys)) =
780 if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
781 in if is_setting_higher_order format type_sys then to_ho else to_fo ary end
783 fun mangled_type format type_sys pred_sym ary =
784 ho_type_from_fo_term format type_sys pred_sym ary
785 o fo_term_from_typ format type_sys
787 fun mangled_const_name format type_sys T_args (s, s') =
789 val ty_args = map (fo_term_from_typ format type_sys) T_args
790 fun type_suffix f g =
791 fold_rev (curry (op ^) o g o prefix mangled_type_sep
792 o generic_mangled_type_name f) ty_args ""
793 in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
795 val parse_mangled_ident =
796 Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
798 fun parse_mangled_type x =
800 -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
802 and parse_mangled_types x =
803 (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
805 fun unmangled_type s =
806 s |> suffix ")" |> raw_explode
807 |> Scan.finite Symbol.stopper
808 (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
809 quote s)) parse_mangled_type))
812 val unmangled_const_name = space_explode mangled_type_sep #> hd
813 fun unmangled_const s =
814 let val ss = space_explode mangled_type_sep s in
815 (hd ss, map unmangled_type (tl ss))
818 fun introduce_proxies format type_sys =
820 fun intro top_level (CombApp (tm1, tm2)) =
821 CombApp (intro top_level tm1, intro false tm2)
822 | intro top_level (CombConst (name as (s, _), T, T_args)) =
823 (case proxify_const s of
825 if top_level orelse is_setting_higher_order format type_sys then
826 case (top_level, s) of
827 (_, "c_False") => (`I tptp_false, [])
828 | (_, "c_True") => (`I tptp_true, [])
829 | (false, "c_Not") => (`I tptp_not, [])
830 | (false, "c_conj") => (`I tptp_and, [])
831 | (false, "c_disj") => (`I tptp_or, [])
832 | (false, "c_implies") => (`I tptp_implies, [])
834 if is_tptp_equal s then (`I tptp_equal, [])
835 else (proxy_base |>> prefix const_prefix, T_args)
838 (proxy_base |>> prefix const_prefix, T_args)
839 | NONE => (name, T_args))
840 |> (fn (name, T_args) => CombConst (name, T, T_args))
844 fun combformula_from_prop thy format type_sys eq_as_iff =
846 fun do_term bs t atomic_types =
847 combterm_from_term thy bs (Envir.eta_contract t)
848 |>> (introduce_proxies format type_sys #> AAtom)
849 ||> union (op =) atomic_types
850 fun do_quant bs q s T t' =
851 let val s = Name.variant (map fst bs) s in
852 do_formula ((s, T) :: bs) t'
853 #>> mk_aquant q [(`make_bound_var s, SOME T)]
855 and do_conn bs c t1 t2 =
856 do_formula bs t1 ##>> do_formula bs t2 #>> uncurry (mk_aconn c)
857 and do_formula bs t =
859 @{const Trueprop} $ t1 => do_formula bs t1
860 | @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
861 | Const (@{const_name All}, _) $ Abs (s, T, t') =>
862 do_quant bs AForall s T t'
863 | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
864 do_quant bs AExists s T t'
865 | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
866 | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
867 | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
868 | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
869 if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
873 fun presimplify_term _ [] t = t
874 | presimplify_term ctxt presimp_consts t =
875 t |> exists_Const (member (op =) presimp_consts o fst) t
876 ? (Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
877 #> Meson.presimplify ctxt
880 fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
881 fun conceal_bounds Ts t =
882 subst_bounds (map (Free o apfst concealed_bound_name)
883 (0 upto length Ts - 1 ~~ Ts), t)
884 fun reveal_bounds Ts =
885 subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
886 (0 upto length Ts - 1 ~~ Ts))
888 fun is_fun_equality (@{const_name HOL.eq},
889 Type (_, [Type (@{type_name fun}, _), _])) = true
890 | is_fun_equality _ = false
892 fun extensionalize_term ctxt t =
893 if exists_Const is_fun_equality t then
894 let val thy = Proof_Context.theory_of ctxt in
895 t |> cterm_of thy |> Meson.extensionalize_conv ctxt
896 |> prop_of |> Logic.dest_equals |> snd
901 fun introduce_combinators_in_term ctxt kind t =
902 let val thy = Proof_Context.theory_of ctxt in
903 if Meson.is_fol_term thy t then
909 @{const Not} $ t1 => @{const Not} $ aux Ts t1
910 | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
911 t0 $ Abs (s, T, aux (T :: Ts) t')
912 | (t0 as Const (@{const_name All}, _)) $ t1 =>
913 aux Ts (t0 $ eta_expand Ts t1 1)
914 | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
915 t0 $ Abs (s, T, aux (T :: Ts) t')
916 | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
917 aux Ts (t0 $ eta_expand Ts t1 1)
918 | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
919 | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
920 | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
921 | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
923 t0 $ aux Ts t1 $ aux Ts t2
924 | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
927 t |> conceal_bounds Ts
928 |> Envir.eta_contract
930 |> Meson_Clausify.introduce_combinators_in_cterm
931 |> prop_of |> Logic.dest_equals |> snd
933 val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
934 in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
936 (* A type variable of sort "{}" will make abstraction fail. *)
937 if kind = Conjecture then HOLogic.false_const
938 else HOLogic.true_const
941 (* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
942 same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
945 fun aux (t $ u) = aux t $ aux u
946 | aux (Abs (s, T, t)) = Abs (s, T, aux t)
947 | aux (Var ((s, i), T)) =
948 Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
950 in t |> exists_subterm is_Var t ? aux end
952 fun preprocess_prop ctxt presimp_consts kind t =
954 val thy = Proof_Context.theory_of ctxt
955 val t = t |> Envir.beta_eta_contract
956 |> transform_elim_prop
957 |> Object_Logic.atomize_term thy
958 val need_trueprop = (fastype_of t = @{typ bool})
960 t |> need_trueprop ? HOLogic.mk_Trueprop
961 |> Raw_Simplifier.rewrite_term thy (Meson.unfold_set_const_simps ctxt) []
962 |> extensionalize_term ctxt
963 |> presimplify_term ctxt presimp_consts
964 |> perhaps (try (HOLogic.dest_Trueprop))
965 |> introduce_combinators_in_term ctxt kind
968 (* making fact and conjecture formulas *)
969 fun make_formula thy format type_sys eq_as_iff name loc kind t =
971 val (combformula, atomic_types) =
972 combformula_from_prop thy format type_sys eq_as_iff t []
974 {name = name, locality = loc, kind = kind, combformula = combformula,
975 atomic_types = atomic_types}
978 fun make_fact ctxt format type_sys eq_as_iff preproc presimp_consts
980 let val thy = Proof_Context.theory_of ctxt in
981 case t |> preproc ? preprocess_prop ctxt presimp_consts Axiom
982 |> make_formula thy format type_sys (eq_as_iff andalso format <> CNF)
984 formula as {combformula = AAtom (CombConst ((s, _), _, _)), ...} =>
985 if s = tptp_true then NONE else SOME formula
986 | formula => SOME formula
989 fun make_conjecture ctxt format prem_kind type_sys preproc presimp_consts ts =
991 val thy = Proof_Context.theory_of ctxt
992 val last = length ts - 1
994 map2 (fn j => fn t =>
996 val (kind, maybe_negate) =
1001 if prem_kind = Conjecture then update_combformula mk_anot
1005 (preprocess_prop ctxt presimp_consts kind #> freeze_term)
1006 |> make_formula thy format type_sys (format <> CNF)
1007 (string_of_int j) Local kind
1013 (** Finite and infinite type inference **)
1015 fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
1016 | deep_freeze_atyp T = T
1017 val deep_freeze_type = map_atyps deep_freeze_atyp
1019 (* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
1020 dangerous because their "exhaust" properties can easily lead to unsound ATP
1021 proofs. On the other hand, all HOL infinite types can be given the same
1022 models in first-order logic (via Löwenheim-Skolem). *)
1024 fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
1025 exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
1026 | should_encode_type _ _ All_Types _ = true
1027 | should_encode_type ctxt _ Finite_Types T = is_type_surely_finite ctxt T
1028 | should_encode_type _ _ _ _ = false
1030 fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
1031 should_predicate_on_var T =
1032 (heaviness = Heavyweight orelse should_predicate_on_var ()) andalso
1033 should_encode_type ctxt nonmono_Ts level T
1034 | should_predicate_on_type _ _ _ _ _ = false
1036 fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
1037 String.isPrefix bound_var_prefix s
1038 | is_var_or_bound_var (CombVar _) = true
1039 | is_var_or_bound_var _ = false
1041 datatype tag_site = Top_Level | Eq_Arg | Elsewhere
1043 fun should_tag_with_type _ _ _ Top_Level _ _ = false
1044 | should_tag_with_type ctxt nonmono_Ts (Tags (_, level, heaviness)) site u T =
1046 Heavyweight => should_encode_type ctxt nonmono_Ts level T
1048 case (site, is_var_or_bound_var u) of
1049 (Eq_Arg, true) => should_encode_type ctxt nonmono_Ts level T
1051 | should_tag_with_type _ _ _ _ _ _ = false
1053 fun homogenized_type ctxt nonmono_Ts level =
1055 val should_encode = should_encode_type ctxt nonmono_Ts level
1056 fun homo 0 T = if should_encode T then T else homo_infinite_type
1057 | homo ary (Type (@{type_name fun}, [T1, T2])) =
1058 homo 0 T1 --> homo (ary - 1) T2
1059 | homo _ _ = raise Fail "expected function type"
1062 (** "hBOOL" and "hAPP" **)
1065 {pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
1067 fun add_combterm_syms_to_table ctxt explicit_apply =
1069 fun consider_var_arity const_T var_T max_ary =
1072 if ary = max_ary orelse type_instance ctxt (var_T, T) orelse
1073 type_instance ctxt (T, var_T) then
1076 iter (ary + 1) (range_type T)
1077 in iter 0 const_T end
1078 fun add_var_or_bound_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1079 if explicit_apply = NONE andalso
1080 (can dest_funT T orelse T = @{typ bool}) then
1082 val bool_vars' = bool_vars orelse body_type T = @{typ bool}
1083 fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
1084 {pred_sym = pred_sym andalso not bool_vars',
1085 min_ary = fold (fn T' => consider_var_arity T' T) types min_ary,
1086 max_ary = max_ary, types = types}
1088 fun_var_Ts |> can dest_funT T ? insert_type ctxt I T
1090 if bool_vars' = bool_vars andalso
1091 pointer_eq (fun_var_Ts', fun_var_Ts) then
1094 ((bool_vars', fun_var_Ts'), Symtab.map (K repair_min_arity) sym_tab)
1098 fun add top_level tm (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1099 let val (head, args) = strip_combterm_comb tm in
1101 CombConst ((s, _), T, _) =>
1102 if String.isPrefix bound_var_prefix s then
1103 add_var_or_bound_var T accum
1105 let val ary = length args in
1106 ((bool_vars, fun_var_Ts),
1107 case Symtab.lookup sym_tab s of
1108 SOME {pred_sym, min_ary, max_ary, types} =>
1111 pred_sym andalso top_level andalso not bool_vars
1112 val types' = types |> insert_type ctxt I T
1114 if is_some explicit_apply orelse
1115 pointer_eq (types', types) then
1118 fold (consider_var_arity T) fun_var_Ts min_ary
1120 Symtab.update (s, {pred_sym = pred_sym,
1121 min_ary = Int.min (ary, min_ary),
1122 max_ary = Int.max (ary, max_ary),
1128 val pred_sym = top_level andalso not bool_vars
1130 case explicit_apply of
1133 | NONE => fold (consider_var_arity T) fun_var_Ts ary
1135 Symtab.update_new (s, {pred_sym = pred_sym,
1136 min_ary = min_ary, max_ary = ary,
1141 | CombVar (_, T) => add_var_or_bound_var T accum
1143 |> fold (add false) args
1146 fun add_fact_syms_to_table ctxt explicit_apply =
1147 fact_lift (formula_fold NONE
1148 (K (add_combterm_syms_to_table ctxt explicit_apply)))
1150 val default_sym_tab_entries : (string * sym_info) list =
1151 (prefixed_predicator_name,
1152 {pred_sym = true, min_ary = 1, max_ary = 1, types = []}) ::
1153 ([tptp_false, tptp_true]
1154 |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []})) @
1155 ([tptp_equal, tptp_old_equal]
1156 |> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = []}))
1158 fun sym_table_for_facts ctxt explicit_apply facts =
1159 ((false, []), Symtab.empty)
1160 |> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
1161 |> fold Symtab.update default_sym_tab_entries
1163 fun min_arity_of sym_tab s =
1164 case Symtab.lookup sym_tab s of
1165 SOME ({min_ary, ...} : sym_info) => min_ary
1167 case strip_prefix_and_unascii const_prefix s of
1169 let val s = s |> unmangled_const_name |> invert_const in
1170 if s = predicator_name then 1
1171 else if s = app_op_name then 2
1172 else if s = type_pred_name then 1
1177 (* True if the constant ever appears outside of the top-level position in
1178 literals, or if it appears with different arities (e.g., because of different
1179 type instantiations). If false, the constant always receives all of its
1180 arguments and is used as a predicate. *)
1181 fun is_pred_sym sym_tab s =
1182 case Symtab.lookup sym_tab s of
1183 SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
1184 pred_sym andalso min_ary = max_ary
1187 val predicator_combconst =
1188 CombConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
1189 fun predicator tm = CombApp (predicator_combconst, tm)
1191 fun introduce_predicators_in_combterm sym_tab tm =
1192 case strip_combterm_comb tm of
1193 (CombConst ((s, _), _, _), _) =>
1194 if is_pred_sym sym_tab s then tm else predicator tm
1195 | _ => predicator tm
1197 fun list_app head args = fold (curry (CombApp o swap)) args head
1199 val app_op = `make_fixed_const app_op_name
1201 fun explicit_app arg head =
1203 val head_T = combtyp_of head
1204 val (arg_T, res_T) = dest_funT head_T
1206 CombConst (app_op, head_T --> head_T, [arg_T, res_T])
1207 in list_app explicit_app [head, arg] end
1208 fun list_explicit_app head args = fold explicit_app args head
1210 fun introduce_explicit_apps_in_combterm sym_tab =
1213 case strip_combterm_comb tm of
1214 (head as CombConst ((s, _), _, _), args) =>
1216 |> chop (min_arity_of sym_tab s)
1218 |-> list_explicit_app
1219 | (head, args) => list_explicit_app head (map aux args)
1222 fun chop_fun 0 T = ([], T)
1223 | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
1224 chop_fun (n - 1) ran_T |>> cons dom_T
1225 | chop_fun _ _ = raise Fail "unexpected non-function"
1227 fun filter_type_args _ _ _ [] = []
1228 | filter_type_args thy s arity T_args =
1230 (* will throw "TYPE" for pseudo-constants *)
1231 val U = if s = app_op_name then
1232 @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
1234 s |> Sign.the_const_type thy
1236 case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
1239 let val U_args = (s, U) |> Sign.const_typargs thy in
1241 |> map_filter (fn (U, T) =>
1242 if member (op =) res_U_vars (dest_TVar U) then
1248 handle TYPE _ => T_args
1250 fun enforce_type_arg_policy_in_combterm ctxt format type_sys =
1252 val thy = Proof_Context.theory_of ctxt
1253 fun aux arity (CombApp (tm1, tm2)) =
1254 CombApp (aux (arity + 1) tm1, aux 0 tm2)
1255 | aux arity (CombConst (name as (s, _), T, T_args)) =
1256 (case strip_prefix_and_unascii const_prefix s of
1257 NONE => (name, T_args)
1260 val s'' = invert_const s''
1261 fun filtered_T_args false = T_args
1262 | filtered_T_args true = filter_type_args thy s'' arity T_args
1264 case type_arg_policy type_sys s'' of
1265 Explicit_Type_Args drop_args =>
1266 (name, filtered_T_args drop_args)
1267 | Mangled_Type_Args drop_args =>
1268 (mangled_const_name format type_sys (filtered_T_args drop_args)
1270 | No_Type_Args => (name, [])
1272 |> (fn (name, T_args) => CombConst (name, T, T_args))
1276 fun repair_combterm ctxt format type_sys sym_tab =
1277 not (is_setting_higher_order format type_sys)
1278 ? (introduce_explicit_apps_in_combterm sym_tab
1279 #> introduce_predicators_in_combterm sym_tab)
1280 #> enforce_type_arg_policy_in_combterm ctxt format type_sys
1281 fun repair_fact ctxt format type_sys sym_tab =
1282 update_combformula (formula_map
1283 (repair_combterm ctxt format type_sys sym_tab))
1285 (** Helper facts **)
1287 (* The Boolean indicates that a fairly sound type encoding is needed. *)
1289 [(("COMBI", false), @{thms Meson.COMBI_def}),
1290 (("COMBK", false), @{thms Meson.COMBK_def}),
1291 (("COMBB", false), @{thms Meson.COMBB_def}),
1292 (("COMBC", false), @{thms Meson.COMBC_def}),
1293 (("COMBS", false), @{thms Meson.COMBS_def}),
1295 (* This is a lie: Higher-order equality doesn't need a sound type encoding.
1296 However, this is done so for backward compatibility: Including the
1297 equality helpers by default in Metis breaks a few existing proofs. *)
1298 @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1299 fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1300 (("fFalse", false), [@{lemma "~ fFalse" by (unfold fFalse_def) fast}]),
1301 (("fFalse", true), @{thms True_or_False}),
1302 (("fTrue", false), [@{lemma "fTrue" by (unfold fTrue_def) fast}]),
1303 (("fTrue", true), @{thms True_or_False}),
1305 @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1306 fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1308 @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
1309 by (unfold fconj_def) fast+}),
1311 @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
1312 by (unfold fdisj_def) fast+}),
1313 (("fimplies", false),
1314 @{lemma "P | fimplies P Q" "~ Q | fimplies P Q" "~ fimplies P Q | ~ P | Q"
1315 by (unfold fimplies_def) fast+}),
1316 (("If", true), @{thms if_True if_False True_or_False})]
1317 |> map (apsnd (map zero_var_indexes))
1319 val type_tag = `make_fixed_const type_tag_name
1321 fun type_tag_idempotence_fact () =
1323 fun var s = ATerm (`I s, [])
1324 fun tag tm = ATerm (type_tag, [var "T", tm])
1325 val tagged_a = tag (var "A")
1327 Formula (type_tag_idempotence_helper_name, Axiom,
1328 AAtom (ATerm (`I tptp_equal, [tag tagged_a, tagged_a]))
1329 |> close_formula_universally, simp_info, NONE)
1332 fun should_specialize_helper type_sys t =
1333 case general_type_arg_policy type_sys of
1334 Mangled_Type_Args _ => not (null (Term.hidden_polymorphism t))
1337 fun helper_facts_for_sym ctxt format type_sys (s, {types, ...} : sym_info) =
1338 case strip_prefix_and_unascii const_prefix s of
1341 val thy = Proof_Context.theory_of ctxt
1342 val unmangled_s = mangled_s |> unmangled_const_name
1343 fun dub_and_inst needs_fairly_sound (th, j) =
1344 ((unmangled_s ^ "_" ^ string_of_int j ^
1345 (if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^
1346 (if needs_fairly_sound then typed_helper_suffix
1347 else untyped_helper_suffix),
1349 let val t = th |> prop_of in
1350 t |> should_specialize_helper type_sys t
1352 [T] => specialize_type thy (invert_const unmangled_s, T)
1356 map_filter (make_fact ctxt format type_sys false false [])
1357 val fairly_sound = is_type_sys_fairly_sound type_sys
1360 |> maps (fn ((helper_s, needs_fairly_sound), ths) =>
1361 if helper_s <> unmangled_s orelse
1362 (needs_fairly_sound andalso not fairly_sound) then
1365 ths ~~ (1 upto length ths)
1366 |> map (dub_and_inst needs_fairly_sound)
1370 fun helper_facts_for_sym_table ctxt format type_sys sym_tab =
1371 Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_sys) sym_tab
1374 (***************************************************************)
1375 (* Type Classes Present in the Axiom or Conjecture Clauses *)
1376 (***************************************************************)
1378 fun set_insert (x, s) = Symtab.update (x, ()) s
1380 fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
1382 (* Remove this trivial type class (FIXME: similar code elsewhere) *)
1383 fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
1385 fun classes_of_terms get_Ts =
1386 map (map snd o get_Ts)
1387 #> List.foldl add_classes Symtab.empty
1388 #> delete_type #> Symtab.keys
1390 val tfree_classes_of_terms = classes_of_terms OldTerm.term_tfrees
1391 val tvar_classes_of_terms = classes_of_terms OldTerm.term_tvars
1393 (*fold type constructors*)
1394 fun fold_type_constrs f (Type (a, Ts)) x =
1395 fold (fold_type_constrs f) Ts (f (a,x))
1396 | fold_type_constrs _ _ x = x
1398 (*Type constructors used to instantiate overloaded constants are the only ones needed.*)
1399 fun add_type_constrs_in_term thy =
1401 fun add (Const (@{const_name Meson.skolem}, _) $ _) = I
1402 | add (t $ u) = add t #> add u
1403 | add (Const (x as (s, _))) =
1404 if String.isPrefix skolem_const_prefix s then I
1405 else x |> Sign.const_typargs thy |> fold (fold_type_constrs set_insert)
1406 | add (Abs (_, _, u)) = add u
1410 fun type_constrs_of_terms thy ts =
1411 Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty)
1413 fun translate_formulas ctxt format prem_kind type_sys preproc hyp_ts concl_t
1416 val thy = Proof_Context.theory_of ctxt
1417 val fact_ts = facts |> map snd
1418 val presimp_consts = Meson.presimplified_consts ctxt
1419 val make_fact = make_fact ctxt format type_sys true preproc presimp_consts
1420 val (facts, fact_names) =
1421 facts |> map (fn (name, t) => (name, t) |> make_fact |> rpair name)
1422 |> map_filter (try (apfst the))
1424 (* Remove existing facts from the conjecture, as this can dramatically
1425 boost an ATP's performance (for some reason). *)
1428 |> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t)
1429 val goal_t = Logic.list_implies (hyp_ts, concl_t)
1430 val all_ts = goal_t :: fact_ts
1431 val subs = tfree_classes_of_terms all_ts
1432 val supers = tvar_classes_of_terms all_ts
1433 val tycons = type_constrs_of_terms thy all_ts
1436 |> make_conjecture ctxt format prem_kind type_sys preproc presimp_consts
1437 val (supers', arity_clauses) =
1438 if level_of_type_sys type_sys = No_Types then ([], [])
1439 else make_arity_clauses thy tycons supers
1440 val class_rel_clauses = make_class_rel_clauses thy subs supers'
1442 (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
1445 fun fo_literal_from_type_literal (TyLitVar (class, name)) =
1446 (true, ATerm (class, [ATerm (name, [])]))
1447 | fo_literal_from_type_literal (TyLitFree (class, name)) =
1448 (true, ATerm (class, [ATerm (name, [])]))
1450 fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
1452 val type_pred = `make_fixed_const type_pred_name
1454 fun type_pred_combterm ctxt format type_sys T tm =
1455 CombApp (CombConst (type_pred, T --> @{typ bool}, [T])
1456 |> enforce_type_arg_policy_in_combterm ctxt format type_sys, tm)
1458 fun var_occurs_positively_naked_in_term _ (SOME false) _ accum = accum
1459 | var_occurs_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
1460 accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
1461 fun is_var_nonmonotonic_in_formula _ _ (SOME false) _ = false
1462 | is_var_nonmonotonic_in_formula pos phi _ name =
1463 formula_fold pos (var_occurs_positively_naked_in_term name) phi false
1465 fun mk_const_aterm format type_sys x T_args args =
1466 ATerm (x, map (fo_term_from_typ format type_sys) T_args @ args)
1468 fun tag_with_type ctxt format nonmono_Ts type_sys T tm =
1469 CombConst (type_tag, T --> T, [T])
1470 |> enforce_type_arg_policy_in_combterm ctxt format type_sys
1471 |> term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
1472 |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
1473 and term_from_combterm ctxt format nonmono_Ts type_sys =
1477 val (head, args) = strip_combterm_comb u
1478 val (x as (s, _), T_args) =
1480 CombConst (name, _, T_args) => (name, T_args)
1481 | CombVar (name, _) => (name, [])
1482 | CombApp _ => raise Fail "impossible \"CombApp\""
1483 val arg_site = if site = Top_Level andalso is_tptp_equal s then Eq_Arg
1485 val t = mk_const_aterm format type_sys x T_args
1486 (map (aux arg_site) args)
1487 val T = combtyp_of u
1489 t |> (if should_tag_with_type ctxt nonmono_Ts type_sys site u T then
1490 tag_with_type ctxt format nonmono_Ts type_sys T
1495 and formula_from_combformula ctxt format nonmono_Ts type_sys
1496 should_predicate_on_var =
1498 val do_term = term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
1501 Simple_Types level =>
1502 homogenized_type ctxt nonmono_Ts level 0
1503 #> mangled_type format type_sys false 0 #> SOME
1505 fun do_out_of_bound_type pos phi universal (name, T) =
1506 if should_predicate_on_type ctxt nonmono_Ts type_sys
1507 (fn () => should_predicate_on_var pos phi universal name) T then
1509 |> type_pred_combterm ctxt format type_sys T
1510 |> do_term |> AAtom |> SOME
1513 fun do_formula pos (AQuant (q, xs, phi)) =
1515 val phi = phi |> do_formula pos
1516 val universal = Option.map (q = AExists ? not) pos
1518 AQuant (q, xs |> map (apsnd (fn NONE => NONE
1519 | SOME T => do_bound_type T)),
1520 (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
1522 (fn (_, NONE) => NONE
1524 do_out_of_bound_type pos phi universal (s, T))
1528 | do_formula pos (AConn conn) = aconn_map pos do_formula conn
1529 | do_formula _ (AAtom tm) = AAtom (do_term tm)
1530 in do_formula o SOME end
1532 fun bound_tvars type_sys Ts =
1533 mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
1534 (type_literals_for_types type_sys add_sorts_on_tvar Ts))
1536 fun formula_for_fact ctxt format nonmono_Ts type_sys
1537 ({combformula, atomic_types, ...} : translated_formula) =
1539 |> close_combformula_universally
1540 |> formula_from_combformula ctxt format nonmono_Ts type_sys
1541 is_var_nonmonotonic_in_formula true
1542 |> bound_tvars type_sys atomic_types
1543 |> close_formula_universally
1545 (* Each fact is given a unique fact number to avoid name clashes (e.g., because
1546 of monomorphization). The TPTP explicitly forbids name clashes, and some of
1547 the remote provers might care. *)
1548 fun formula_line_for_fact ctxt format prefix encode freshen nonmono_Ts type_sys
1549 (j, formula as {name, locality, kind, ...}) =
1552 polymorphism_of_type_sys type_sys <> Polymorphic then
1553 string_of_int j ^ "_"
1556 kind, formula_for_fact ctxt format nonmono_Ts type_sys formula, NONE,
1563 fun formula_line_for_class_rel_clause ({name, subclass, superclass, ...}
1564 : class_rel_clause) =
1565 let val ty_arg = ATerm (`I "T", []) in
1566 Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
1567 AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
1568 AAtom (ATerm (superclass, [ty_arg]))])
1569 |> close_formula_universally, intro_info, NONE)
1572 fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
1573 (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
1574 | fo_literal_from_arity_literal (TVarLit (c, sort)) =
1575 (false, ATerm (c, [ATerm (sort, [])]))
1577 fun formula_line_for_arity_clause ({name, prem_lits, concl_lits, ...}
1579 Formula (arity_clause_prefix ^ ascii_of name, Axiom,
1580 mk_ahorn (map (formula_from_fo_literal o apfst not
1581 o fo_literal_from_arity_literal) prem_lits)
1582 (formula_from_fo_literal
1583 (fo_literal_from_arity_literal concl_lits))
1584 |> close_formula_universally, intro_info, NONE)
1586 fun formula_line_for_conjecture ctxt format nonmono_Ts type_sys
1587 ({name, kind, combformula, atomic_types, ...} : translated_formula) =
1588 Formula (conjecture_prefix ^ name, kind,
1589 formula_from_combformula ctxt format nonmono_Ts type_sys
1590 is_var_nonmonotonic_in_formula false
1591 (close_combformula_universally combformula)
1592 |> bound_tvars type_sys atomic_types
1593 |> close_formula_universally, NONE, NONE)
1595 fun free_type_literals type_sys ({atomic_types, ...} : translated_formula) =
1596 atomic_types |> type_literals_for_types type_sys add_sorts_on_tfree
1597 |> map fo_literal_from_type_literal
1599 fun formula_line_for_free_type j lit =
1600 Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis,
1601 formula_from_fo_literal lit, NONE, NONE)
1602 fun formula_lines_for_free_types type_sys facts =
1604 val litss = map (free_type_literals type_sys) facts
1605 val lits = fold (union (op =)) litss []
1606 in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
1608 (** Symbol declarations **)
1610 fun should_declare_sym type_sys pred_sym s =
1611 is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
1613 Simple_Types _ => true
1614 | Tags (_, _, Lightweight) => true
1615 | _ => not pred_sym)
1617 fun sym_decl_table_for_facts ctxt type_sys repaired_sym_tab (conjs, facts) =
1619 fun add_combterm in_conj tm =
1620 let val (head, args) = strip_combterm_comb tm in
1622 CombConst ((s, s'), T, T_args) =>
1623 let val pred_sym = is_pred_sym repaired_sym_tab s in
1624 if should_declare_sym type_sys pred_sym s then
1625 Symtab.map_default (s, [])
1626 (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
1632 #> fold (add_combterm in_conj) args
1634 fun add_fact in_conj =
1635 fact_lift (formula_fold NONE (K (add_combterm in_conj)))
1638 |> is_type_sys_fairly_sound type_sys
1639 ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
1642 (* These types witness that the type classes they belong to allow infinite
1643 models and hence that any types with these type classes is monotonic. *)
1644 val known_infinite_types =
1645 [@{typ nat}, Type ("Int.int", []), @{typ "nat => bool"}]
1647 (* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
1648 out with monotonicity" paper presented at CADE 2011. *)
1649 fun add_combterm_nonmonotonic_types _ _ _ (SOME false) _ = I
1650 | add_combterm_nonmonotonic_types ctxt level locality _
1651 (CombApp (CombApp (CombConst ((s, _), Type (_, [T, _]), _), tm1),
1653 (is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
1655 Nonmonotonic_Types =>
1656 not (is_locality_global locality) orelse
1657 not (is_type_surely_infinite ctxt known_infinite_types T)
1658 | Finite_Types => is_type_surely_finite ctxt T
1659 | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
1660 | add_combterm_nonmonotonic_types _ _ _ _ _ = I
1661 fun add_fact_nonmonotonic_types ctxt level ({kind, locality, combformula, ...}
1662 : translated_formula) =
1663 formula_fold (SOME (kind <> Conjecture))
1664 (add_combterm_nonmonotonic_types ctxt level locality) combformula
1665 fun nonmonotonic_types_for_facts ctxt type_sys facts =
1666 let val level = level_of_type_sys type_sys in
1667 if level = Nonmonotonic_Types orelse level = Finite_Types then
1668 [] |> fold (add_fact_nonmonotonic_types ctxt level) facts
1669 (* We must add "bool" in case the helper "True_or_False" is added
1670 later. In addition, several places in the code rely on the list of
1671 nonmonotonic types not being empty. *)
1672 |> insert_type ctxt I @{typ bool}
1677 fun decl_line_for_sym ctxt format nonmono_Ts type_sys s
1678 (s', T_args, T, pred_sym, ary, _) =
1680 val (T_arg_Ts, level) =
1682 Simple_Types level => ([], level)
1683 | _ => (replicate (length T_args) homo_infinite_type, No_Types)
1685 Decl (sym_decl_prefix ^ s, (s, s'),
1686 (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
1687 |> mangled_type format type_sys pred_sym (length T_arg_Ts + ary))
1690 fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
1692 fun formula_line_for_preds_sym_decl ctxt format conj_sym_kind nonmono_Ts
1693 type_sys n s j (s', T_args, T, _, ary, in_conj) =
1695 val (kind, maybe_negate) =
1696 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1698 val (arg_Ts, res_T) = chop_fun ary T
1700 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
1702 bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
1704 arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
1707 Formula (preds_sym_formula_prefix ^ s ^
1708 (if n > 1 then "_" ^ string_of_int j else ""), kind,
1709 CombConst ((s, s'), T, T_args)
1710 |> fold (curry (CombApp o swap)) bounds
1711 |> type_pred_combterm ctxt format type_sys res_T
1712 |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
1713 |> formula_from_combformula ctxt format nonmono_Ts type_sys
1714 (K (K (K (K true)))) true
1715 |> n > 1 ? bound_tvars type_sys (atyps_of T)
1716 |> close_formula_universally
1721 fun formula_lines_for_lightweight_tags_sym_decl ctxt format conj_sym_kind
1722 nonmono_Ts type_sys n s (j, (s', T_args, T, pred_sym, ary, in_conj)) =
1725 lightweight_tags_sym_formula_prefix ^ s ^
1726 (if n > 1 then "_" ^ string_of_int j else "")
1727 val (kind, maybe_negate) =
1728 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1730 val (arg_Ts, res_T) = chop_fun ary T
1732 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
1733 val bounds = bound_names |> map (fn name => ATerm (name, []))
1734 val cst = mk_const_aterm format type_sys (s, s') T_args
1735 val atomic_Ts = atyps_of T
1737 (if pred_sym then AConn (AIff, map AAtom tms)
1738 else AAtom (ATerm (`I tptp_equal, tms)))
1739 |> bound_tvars type_sys atomic_Ts
1740 |> close_formula_universally
1742 val should_encode = should_encode_type ctxt nonmono_Ts All_Types
1743 val tag_with = tag_with_type ctxt format nonmono_Ts type_sys
1744 val add_formula_for_res =
1745 if should_encode res_T then
1746 cons (Formula (ident_base ^ "_res", kind,
1747 eq [tag_with res_T (cst bounds), cst bounds],
1751 fun add_formula_for_arg k =
1752 let val arg_T = nth arg_Ts k in
1753 if should_encode arg_T then
1754 case chop k bounds of
1755 (bounds1, bound :: bounds2) =>
1756 cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
1757 eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
1760 | _ => raise Fail "expected nonempty tail"
1765 [] |> not pred_sym ? add_formula_for_res
1766 |> fold add_formula_for_arg (ary - 1 downto 0)
1769 fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
1771 fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts type_sys
1775 decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_sys s)
1780 decl :: (decls' as _ :: _) =>
1781 let val T = result_type_of_decl decl in
1782 if forall (curry (type_instance ctxt o swap) T
1783 o result_type_of_decl) decls' then
1789 val n = length decls
1792 |> filter (should_predicate_on_type ctxt nonmono_Ts type_sys (K true)
1793 o result_type_of_decl)
1795 (0 upto length decls - 1, decls)
1796 |-> map2 (formula_line_for_preds_sym_decl ctxt format conj_sym_kind
1797 nonmono_Ts type_sys n s)
1799 | Tags (_, _, heaviness) =>
1803 let val n = length decls in
1804 (0 upto n - 1 ~~ decls)
1805 |> maps (formula_lines_for_lightweight_tags_sym_decl ctxt format
1806 conj_sym_kind nonmono_Ts type_sys n s)
1809 fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1810 type_sys sym_decl_tab =
1815 |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
1816 nonmono_Ts type_sys)
1818 fun needs_type_tag_idempotence (Tags (poly, level, heaviness)) =
1819 poly <> Mangled_Monomorphic andalso
1820 ((level = All_Types andalso heaviness = Lightweight) orelse
1821 level = Nonmonotonic_Types orelse level = Finite_Types)
1822 | needs_type_tag_idempotence _ = false
1824 fun offset_of_heading_in_problem _ [] j = j
1825 | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
1826 if heading = needle then j
1827 else offset_of_heading_in_problem needle problem (j + length lines)
1829 val implicit_declsN = "Should-be-implicit typings"
1830 val explicit_declsN = "Explicit typings"
1831 val factsN = "Relevant facts"
1832 val class_relsN = "Class relationships"
1833 val aritiesN = "Arities"
1834 val helpersN = "Helper facts"
1835 val conjsN = "Conjectures"
1836 val free_typesN = "Type variables"
1838 val explicit_apply = NONE (* for experimental purposes *)
1840 fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_sys
1841 readable_names preproc hyp_ts concl_t facts =
1843 val (format, type_sys) = choose_format [format] type_sys
1844 val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
1845 translate_formulas ctxt format prem_kind type_sys preproc hyp_ts concl_t
1847 val sym_tab = conjs @ facts |> sym_table_for_facts ctxt explicit_apply
1848 val nonmono_Ts = conjs @ facts |> nonmonotonic_types_for_facts ctxt type_sys
1849 val repair = repair_fact ctxt format type_sys sym_tab
1850 val (conjs, facts) = (conjs, facts) |> pairself (map repair)
1851 val repaired_sym_tab =
1852 conjs @ facts |> sym_table_for_facts ctxt (SOME false)
1854 repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_sys
1856 val lavish_nonmono_Ts =
1857 if null nonmono_Ts orelse nonmono_Ts = [@{typ bool}] orelse
1858 polymorphism_of_type_sys type_sys <> Polymorphic then
1861 [TVar (("'a", 0), HOLogic.typeS)]
1862 val sym_decl_lines =
1863 (conjs, helpers @ facts)
1864 |> sym_decl_table_for_facts ctxt type_sys repaired_sym_tab
1865 |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind
1866 lavish_nonmono_Ts type_sys
1868 0 upto length helpers - 1 ~~ helpers
1869 |> map (formula_line_for_fact ctxt format helper_prefix I false
1870 lavish_nonmono_Ts type_sys)
1871 |> (if needs_type_tag_idempotence type_sys then
1872 cons (type_tag_idempotence_fact ())
1875 (* Reordering these might confuse the proof reconstruction code or the SPASS
1878 [(explicit_declsN, sym_decl_lines),
1880 map (formula_line_for_fact ctxt format fact_prefix ascii_of true
1881 nonmono_Ts type_sys)
1882 (0 upto length facts - 1 ~~ facts)),
1883 (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
1884 (aritiesN, map formula_line_for_arity_clause arity_clauses),
1885 (helpersN, helper_lines),
1887 map (formula_line_for_conjecture ctxt format nonmono_Ts type_sys)
1889 (free_typesN, formula_lines_for_free_types type_sys (facts @ conjs))]
1893 CNF => ensure_cnf_problem
1894 | CNF_UEQ => filter_cnf_ueq_problem
1896 |> (if is_format_typed format then
1897 declare_undeclared_syms_in_atp_problem type_decl_prefix
1901 val (problem, pool) = problem |> nice_atp_problem readable_names
1902 val helpers_offset = offset_of_heading_in_problem helpersN problem 0
1904 map_filter (fn (j, {name, ...}) =>
1905 if String.isSuffix typed_helper_suffix name then SOME j
1907 ((helpers_offset + 1 upto helpers_offset + length helpers)
1909 fun add_sym_arity (s, {min_ary, ...} : sym_info) =
1911 case strip_prefix_and_unascii const_prefix s of
1912 SOME s => Symtab.insert (op =) (s, min_ary)
1918 case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
1919 offset_of_heading_in_problem conjsN problem 0,
1920 offset_of_heading_in_problem factsN problem 0,
1921 fact_names |> Vector.fromList,
1923 Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
1927 val conj_weight = 0.0
1928 val hyp_weight = 0.1
1929 val fact_min_weight = 0.2
1930 val fact_max_weight = 1.0
1931 val type_info_default_weight = 0.8
1933 fun add_term_weights weight (ATerm (s, tms)) =
1934 is_tptp_user_symbol s ? Symtab.default (s, weight)
1935 #> fold (add_term_weights weight) tms
1936 fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
1937 formula_fold NONE (K (add_term_weights weight)) phi
1938 | add_problem_line_weights _ _ = I
1940 fun add_conjectures_weights [] = I
1941 | add_conjectures_weights conjs =
1942 let val (hyps, conj) = split_last conjs in
1943 add_problem_line_weights conj_weight conj
1944 #> fold (add_problem_line_weights hyp_weight) hyps
1947 fun add_facts_weights facts =
1949 val num_facts = length facts
1951 fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
1952 / Real.fromInt num_facts
1954 map weight_of (0 upto num_facts - 1) ~~ facts
1955 |> fold (uncurry add_problem_line_weights)
1958 (* Weights are from 0.0 (most important) to 1.0 (least important). *)
1959 fun atp_problem_weights problem =
1960 let val get = these o AList.lookup (op =) problem in
1962 |> add_conjectures_weights (get free_typesN @ get conjsN)
1963 |> add_facts_weights (get factsN)
1964 |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
1965 [explicit_declsN, class_relsN, aritiesN]
1967 |> sort (prod_ord Real.compare string_ord o pairself swap)