1 (* Title: HOL/Tools/Sledgehammer/sledgehammer_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
122 val raw_type_literals_for_types : typ list -> type_literal list
124 connective -> ('a, 'b, 'c) formula list -> ('a, 'b, 'c) formula
125 val unmangled_const_name : string -> string
126 val unmangled_const : string -> string * string fo_term list
127 val helper_table : ((string * bool) * thm list) list
128 val should_specialize_helper : type_sys -> term -> bool
129 val tfree_classes_of_terms : term list -> string list
130 val tvar_classes_of_terms : term list -> string list
131 val type_constrs_of_terms : theory -> term list -> string list
132 val prepare_atp_problem :
133 Proof.context -> format -> formula_kind -> formula_kind -> type_sys
134 -> bool option -> bool -> bool -> term list -> term
135 -> ((string * locality) * term) list
136 -> string problem * string Symtab.table * int * int
137 * (string * locality) list vector * int list * int Symtab.table
138 val atp_problem_weights : string problem -> (string * real) list
141 structure ATP_Translate : ATP_TRANSLATE =
147 type name = string * string
150 fun union_all xss = fold (union (op =)) xss []
153 val generate_useful_info = false
155 fun useful_isabelle_info s =
156 if generate_useful_info then
157 SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
161 val intro_info = useful_isabelle_info "intro"
162 val elim_info = useful_isabelle_info "elim"
163 val simp_info = useful_isabelle_info "simp"
165 val bound_var_prefix = "B_"
166 val schematic_var_prefix = "V_"
167 val fixed_var_prefix = "v_"
169 val tvar_prefix = "T_"
170 val tfree_prefix = "t_"
172 val const_prefix = "c_"
173 val type_const_prefix = "tc_"
174 val class_prefix = "cl_"
176 val skolem_const_prefix = "Sledgehammer" ^ Long_Name.separator ^ "Sko"
177 val old_skolem_const_prefix = skolem_const_prefix ^ "o"
178 val new_skolem_const_prefix = skolem_const_prefix ^ "n"
180 val type_decl_prefix = "ty_"
181 val sym_decl_prefix = "sy_"
182 val preds_sym_formula_prefix = "psy_"
183 val lightweight_tags_sym_formula_prefix = "tsy_"
184 val fact_prefix = "fact_"
185 val conjecture_prefix = "conj_"
186 val helper_prefix = "help_"
187 val class_rel_clause_prefix = "clar_"
188 val arity_clause_prefix = "arity_"
189 val tfree_clause_prefix = "tfree_"
191 val typed_helper_suffix = "_T"
192 val untyped_helper_suffix = "_U"
193 val type_tag_idempotence_helper_name = helper_prefix ^ "ti_idem"
195 val predicator_name = "hBOOL"
196 val app_op_name = "hAPP"
197 val type_tag_name = "ti"
198 val type_pred_name = "is"
199 val simple_type_prefix = "ty_"
201 val prefixed_predicator_name = const_prefix ^ predicator_name
202 val prefixed_app_op_name = const_prefix ^ app_op_name
203 val prefixed_type_tag_name = const_prefix ^ type_tag_name
205 (* Freshness almost guaranteed! *)
206 val sledgehammer_weak_prefix = "Sledgehammer:"
208 (*Escaping of special characters.
209 Alphanumeric characters are left unchanged.
210 The character _ goes to __
211 Characters in the range ASCII space to / go to _A to _P, respectively.
212 Other characters go to _nnn where nnn is the decimal ASCII code.*)
213 val upper_a_minus_space = Char.ord #"A" - Char.ord #" "
215 fun stringN_of_int 0 _ = ""
216 | stringN_of_int k n =
217 stringN_of_int (k - 1) (n div 10) ^ string_of_int (n mod 10)
219 fun ascii_of_char c =
220 if Char.isAlphaNum c then
222 else if c = #"_" then
224 else if #" " <= c andalso c <= #"/" then
225 "_" ^ String.str (Char.chr (Char.ord c + upper_a_minus_space))
227 (* fixed width, in case more digits follow *)
228 "_" ^ stringN_of_int 3 (Char.ord c)
230 val ascii_of = String.translate ascii_of_char
232 (** Remove ASCII armoring from names in proof files **)
234 (* We don't raise error exceptions because this code can run inside a worker
235 thread. Also, the errors are impossible. *)
238 fun un rcs [] = String.implode(rev rcs)
239 | un rcs [#"_"] = un (#"_" :: rcs) [] (* ERROR *)
240 (* Three types of _ escapes: __, _A to _P, _nnn *)
241 | un rcs (#"_" :: #"_" :: cs) = un (#"_"::rcs) cs
242 | un rcs (#"_" :: c :: cs) =
243 if #"A" <= c andalso c<= #"P" then
244 (* translation of #" " to #"/" *)
245 un (Char.chr (Char.ord c - upper_a_minus_space) :: rcs) cs
247 let val digits = List.take (c::cs, 3) handle Subscript => [] in
248 case Int.fromString (String.implode digits) of
249 SOME n => un (Char.chr n :: rcs) (List.drop (cs, 2))
250 | NONE => un (c:: #"_"::rcs) cs (* ERROR *)
252 | un rcs (c :: cs) = un (c :: rcs) cs
253 in un [] o String.explode end
255 (* If string s has the prefix s1, return the result of deleting it,
257 fun strip_prefix_and_unascii s1 s =
258 if String.isPrefix s1 s then
259 SOME (unascii_of (String.extract (s, size s1, NONE)))
264 [("c_False", (@{const_name False}, (@{thm fFalse_def},
265 ("fFalse", @{const_name ATP.fFalse})))),
266 ("c_True", (@{const_name True}, (@{thm fTrue_def},
267 ("fTrue", @{const_name ATP.fTrue})))),
268 ("c_Not", (@{const_name Not}, (@{thm fNot_def},
269 ("fNot", @{const_name ATP.fNot})))),
270 ("c_conj", (@{const_name conj}, (@{thm fconj_def},
271 ("fconj", @{const_name ATP.fconj})))),
272 ("c_disj", (@{const_name disj}, (@{thm fdisj_def},
273 ("fdisj", @{const_name ATP.fdisj})))),
274 ("c_implies", (@{const_name implies}, (@{thm fimplies_def},
275 ("fimplies", @{const_name ATP.fimplies})))),
276 ("equal", (@{const_name HOL.eq}, (@{thm fequal_def},
277 ("fequal", @{const_name ATP.fequal}))))]
279 val proxify_const = AList.lookup (op =) proxy_table #> Option.map (snd o snd)
281 (* Readable names for the more common symbolic functions. Do not mess with the
282 table unless you know what you are doing. *)
283 val const_trans_table =
284 [(@{type_name Product_Type.prod}, "prod"),
285 (@{type_name Sum_Type.sum}, "sum"),
286 (@{const_name False}, "False"),
287 (@{const_name True}, "True"),
288 (@{const_name Not}, "Not"),
289 (@{const_name conj}, "conj"),
290 (@{const_name disj}, "disj"),
291 (@{const_name implies}, "implies"),
292 (@{const_name HOL.eq}, "equal"),
293 (@{const_name If}, "If"),
294 (@{const_name Set.member}, "member"),
295 (@{const_name Meson.COMBI}, "COMBI"),
296 (@{const_name Meson.COMBK}, "COMBK"),
297 (@{const_name Meson.COMBB}, "COMBB"),
298 (@{const_name Meson.COMBC}, "COMBC"),
299 (@{const_name Meson.COMBS}, "COMBS")]
301 |> fold (Symtab.update o swap o snd o snd o snd) proxy_table
303 (* Invert the table of translations between Isabelle and ATPs. *)
304 val const_trans_table_inv =
305 const_trans_table |> Symtab.dest |> map swap |> Symtab.make
306 val const_trans_table_unprox =
308 |> fold (fn (_, (isa, (_, (_, atp)))) => Symtab.update (atp, isa)) proxy_table
310 val invert_const = perhaps (Symtab.lookup const_trans_table_inv)
311 val unproxify_const = perhaps (Symtab.lookup const_trans_table_unprox)
314 case Symtab.lookup const_trans_table c of
318 (*Remove the initial ' character from a type variable, if it is present*)
319 fun trim_type_var s =
320 if s <> "" andalso String.sub(s,0) = #"'" then String.extract(s,1,NONE)
321 else raise Fail ("trim_type: Malformed type variable encountered: " ^ s)
323 fun ascii_of_indexname (v,0) = ascii_of v
324 | ascii_of_indexname (v,i) = ascii_of v ^ "_" ^ string_of_int i
326 fun make_bound_var x = bound_var_prefix ^ ascii_of x
327 fun make_schematic_var v = schematic_var_prefix ^ ascii_of_indexname v
328 fun make_fixed_var x = fixed_var_prefix ^ ascii_of x
330 fun make_schematic_type_var (x,i) =
331 tvar_prefix ^ (ascii_of_indexname (trim_type_var x, i))
332 fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (trim_type_var x))
334 (* HOL.eq MUST BE "equal" because it's built into ATPs. *)
335 fun make_fixed_const @{const_name HOL.eq} = "equal"
336 | make_fixed_const c = const_prefix ^ lookup_const c
338 fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
340 fun make_type_class clas = class_prefix ^ ascii_of clas
342 fun new_skolem_var_name_from_const s =
343 let val ss = s |> space_explode Long_Name.separator in
344 nth ss (length ss - 2)
347 (* The number of type arguments of a constant, zero if it's monomorphic. For
348 (instances of) Skolem pseudoconstants, this information is encoded in the
350 fun num_type_args thy s =
351 if String.isPrefix skolem_const_prefix s then
352 s |> space_explode Long_Name.separator |> List.last |> Int.fromString |> the
354 (s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
356 (* These are either simplified away by "Meson.presimplify" (most of the time) or
357 handled specially via "fFalse", "fTrue", ..., "fequal". *)
358 val atp_irrelevant_consts =
359 [@{const_name False}, @{const_name True}, @{const_name Not},
360 @{const_name conj}, @{const_name disj}, @{const_name implies},
361 @{const_name HOL.eq}, @{const_name If}, @{const_name Let}]
363 val atp_monomorph_bad_consts =
364 atp_irrelevant_consts @
365 (* These are ignored anyway by the relevance filter (unless they appear in
366 higher-order places) but not by the monomorphizer. *)
367 [@{const_name all}, @{const_name "==>"}, @{const_name "=="},
368 @{const_name Trueprop}, @{const_name All}, @{const_name Ex},
369 @{const_name Ex1}, @{const_name Ball}, @{const_name Bex}]
371 fun add_schematic_const (x as (_, T)) =
372 Monomorph.typ_has_tvars T ? Symtab.insert_list (op =) x
373 val add_schematic_consts_of =
374 Term.fold_aterms (fn Const (x as (s, _)) =>
375 not (member (op =) atp_monomorph_bad_consts s)
376 ? add_schematic_const x
378 fun atp_schematic_consts_of t = add_schematic_consts_of t Symtab.empty
380 (** Definitions and functions for FOL clauses and formulas for TPTP **)
382 (* The first component is the type class; the second is a "TVar" or "TFree". *)
383 datatype type_literal =
384 TyLitVar of name * name |
385 TyLitFree of name * name
388 (** Isabelle arities **)
390 datatype arity_literal =
391 TConsLit of name * name * name list |
392 TVarLit of name * name
395 | gen_TVars n = ("T_" ^ string_of_int n) :: gen_TVars (n-1)
397 fun pack_sort (_,[]) = []
398 | pack_sort (tvar, "HOL.type" :: srt) =
399 pack_sort (tvar, srt) (* IGNORE sort "type" *)
400 | pack_sort (tvar, cls :: srt) =
401 (`make_type_class cls, `I tvar) :: pack_sort (tvar, srt)
405 prem_lits: arity_literal list,
406 concl_lits: arity_literal}
408 (* Arity of type constructor "tcon :: (arg1, ..., argN) res" *)
409 fun make_axiom_arity_clause (tcons, name, (cls, args)) =
411 val tvars = gen_TVars (length args)
412 val tvars_srts = ListPair.zip (tvars, args)
415 prem_lits = map TVarLit (union_all (map pack_sort tvars_srts)),
416 concl_lits = TConsLit (`make_type_class cls,
417 `make_fixed_type_const tcons,
421 fun arity_clause _ _ (_, []) = []
422 | arity_clause seen n (tcons, ("HOL.type",_)::ars) = (*ignore*)
423 arity_clause seen n (tcons,ars)
424 | arity_clause seen n (tcons, (ar as (class,_)) :: ars) =
425 if member (op =) seen class then (*multiple arities for the same tycon, class pair*)
426 make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class ^ "_" ^ string_of_int n, ar) ::
427 arity_clause seen (n+1) (tcons,ars)
429 make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class, ar) ::
430 arity_clause (class::seen) n (tcons,ars)
432 fun multi_arity_clause [] = []
433 | multi_arity_clause ((tcons, ars) :: tc_arlists) =
434 arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
436 (*Generate all pairs (tycon,class,sorts) such that tycon belongs to class in theory thy
437 provided its arguments have the corresponding sorts.*)
438 fun type_class_pairs thy tycons classes =
440 val alg = Sign.classes_of thy
441 fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
442 fun add_class tycon class =
443 cons (class, domain_sorts tycon class)
444 handle Sorts.CLASS_ERROR _ => I
445 fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
446 in map try_classes tycons end
448 (*Proving one (tycon, class) membership may require proving others, so iterate.*)
449 fun iter_type_class_pairs _ _ [] = ([], [])
450 | iter_type_class_pairs thy tycons classes =
451 let val cpairs = type_class_pairs thy tycons classes
452 val newclasses = union_all (union_all (union_all (map (map #2 o #2) cpairs)))
453 |> subtract (op =) classes |> subtract (op =) HOLogic.typeS
454 val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
455 in (union (op =) classes' classes, union (op =) cpairs' cpairs) end
457 fun make_arity_clauses thy tycons =
458 iter_type_class_pairs thy tycons ##> multi_arity_clause
461 (** Isabelle class relations **)
463 type class_rel_clause =
468 (*Generate all pairs (sub,super) such that sub is a proper subclass of super in theory thy.*)
469 fun class_pairs _ [] _ = []
470 | class_pairs thy subs supers =
472 val class_less = Sorts.class_less (Sign.classes_of thy)
473 fun add_super sub super = class_less (sub, super) ? cons (sub, super)
474 fun add_supers sub = fold (add_super sub) supers
475 in fold add_supers subs [] end
477 fun make_class_rel_clause (sub,super) =
478 {name = sub ^ "_" ^ super,
479 subclass = `make_type_class sub,
480 superclass = `make_type_class super}
482 fun make_class_rel_clauses thy subs supers =
483 map make_class_rel_clause (class_pairs thy subs supers)
486 CombConst of name * typ * typ list |
487 CombVar of name * typ |
488 CombApp of combterm * combterm
490 fun combtyp_of (CombConst (_, T, _)) = T
491 | combtyp_of (CombVar (_, T)) = T
492 | combtyp_of (CombApp (t1, _)) = snd (dest_funT (combtyp_of t1))
494 (*gets the head of a combinator application, along with the list of arguments*)
495 fun strip_combterm_comb u =
496 let fun stripc (CombApp(t,u), ts) = stripc (t, u::ts)
500 fun atyps_of T = fold_atyps (insert (op =)) T []
502 fun new_skolem_const_name s num_T_args =
503 [new_skolem_const_prefix, s, string_of_int num_T_args]
504 |> space_implode Long_Name.separator
506 (* Converts a term (with combinators) into a combterm. Also accumulates sort
508 fun combterm_from_term thy bs (P $ Q) =
510 val (P', P_atomics_Ts) = combterm_from_term thy bs P
511 val (Q', Q_atomics_Ts) = combterm_from_term thy bs Q
512 in (CombApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
513 | combterm_from_term thy _ (Const (c, T)) =
516 (if String.isPrefix old_skolem_const_prefix c then
517 [] |> Term.add_tvarsT T |> map TVar
519 (c, T) |> Sign.const_typargs thy)
520 val c' = CombConst (`make_fixed_const c, T, tvar_list)
521 in (c', atyps_of T) end
522 | combterm_from_term _ _ (Free (v, T)) =
523 (CombConst (`make_fixed_var v, T, []), atyps_of T)
524 | combterm_from_term _ _ (Var (v as (s, _), T)) =
525 (if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
527 val Ts = T |> strip_type |> swap |> op ::
528 val s' = new_skolem_const_name s (length Ts)
529 in CombConst (`make_fixed_const s', T, Ts) end
531 CombVar ((make_schematic_var v, s), T), atyps_of T)
532 | combterm_from_term _ bs (Bound j) =
534 |> (fn (s, T) => (CombConst (`make_bound_var s, T, []), atyps_of T))
535 | combterm_from_term _ _ (Abs _) = raise Fail "HOL clause: Abs"
537 datatype locality = General | Intro | Elim | Simp | Local | Assum | Chained
539 (* (quasi-)underapproximation of the truth *)
540 fun is_locality_global Local = false
541 | is_locality_global Assum = false
542 | is_locality_global Chained = false
543 | is_locality_global _ = true
545 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
546 datatype type_level =
547 All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
548 datatype type_heaviness = Heavyweight | Lightweight
551 Simple_Types of type_level |
552 Preds of polymorphism * type_level * type_heaviness |
553 Tags of polymorphism * type_level * type_heaviness
555 fun try_unsuffixes ss s =
556 fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
558 fun type_sys_from_string s =
559 (case try (unprefix "poly_") s of
560 SOME s => (SOME Polymorphic, s)
562 case try (unprefix "mono_") s of
563 SOME s => (SOME Monomorphic, s)
565 case try (unprefix "mangled_") s of
566 SOME s => (SOME Mangled_Monomorphic, s)
569 (* "_query" and "_bang" are for the ASCII-challenged Mirabelle. *)
570 case try_unsuffixes ["?", "_query"] s of
571 SOME s => (Nonmonotonic_Types, s)
573 case try_unsuffixes ["!", "_bang"] s of
574 SOME s => (Finite_Types, s)
575 | NONE => (All_Types, s))
577 case try (unsuffix "_heavy") s of
578 SOME s => (Heavyweight, s)
579 | NONE => (Lightweight, s))
580 |> (fn (poly, (level, (heaviness, core))) =>
581 case (core, (poly, level, heaviness)) of
582 ("simple", (NONE, _, Lightweight)) => Simple_Types level
583 | ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
584 | ("tags", (SOME Polymorphic, All_Types, _)) =>
585 Tags (Polymorphic, All_Types, heaviness)
586 | ("tags", (SOME Polymorphic, _, _)) =>
587 (* The actual light encoding is very unsound. *)
588 Tags (Polymorphic, level, Heavyweight)
589 | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
590 | ("args", (SOME poly, All_Types (* naja *), Lightweight)) =>
591 Preds (poly, Const_Arg_Types, Lightweight)
592 | ("erased", (NONE, All_Types (* naja *), Lightweight)) =>
593 Preds (Polymorphic, No_Types, Lightweight)
594 | _ => raise Same.SAME)
595 handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
597 fun polymorphism_of_type_sys (Simple_Types _) = Mangled_Monomorphic
598 | polymorphism_of_type_sys (Preds (poly, _, _)) = poly
599 | polymorphism_of_type_sys (Tags (poly, _, _)) = poly
601 fun level_of_type_sys (Simple_Types level) = level
602 | level_of_type_sys (Preds (_, level, _)) = level
603 | level_of_type_sys (Tags (_, level, _)) = level
605 fun heaviness_of_type_sys (Simple_Types _) = Heavyweight
606 | heaviness_of_type_sys (Preds (_, _, heaviness)) = heaviness
607 | heaviness_of_type_sys (Tags (_, _, heaviness)) = heaviness
609 fun is_type_level_virtually_sound level =
610 level = All_Types orelse level = Nonmonotonic_Types
611 val is_type_sys_virtually_sound =
612 is_type_level_virtually_sound o level_of_type_sys
614 fun is_type_level_fairly_sound level =
615 is_type_level_virtually_sound level orelse level = Finite_Types
616 val is_type_sys_fairly_sound = is_type_level_fairly_sound o level_of_type_sys
618 fun is_setting_higher_order THF (Simple_Types _) = true
619 | is_setting_higher_order _ _ = false
621 fun choose_format formats (Simple_Types level) =
622 if member (op =) formats THF then (THF, Simple_Types level)
623 else if member (op =) formats TFF then (TFF, Simple_Types level)
624 else choose_format formats (Preds (Mangled_Monomorphic, level, Heavyweight))
625 | choose_format formats type_sys =
628 (CNF_UEQ, case type_sys of
630 (if is_type_sys_fairly_sound type_sys then Preds else Tags)
633 | format => (format, type_sys))
635 type translated_formula =
639 combformula: (name, typ, combterm) formula,
640 atomic_types: typ list}
642 fun update_combformula f ({name, locality, kind, combformula, atomic_types}
643 : translated_formula) =
644 {name = name, locality = locality, kind = kind, combformula = f combformula,
645 atomic_types = atomic_types} : translated_formula
647 fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
649 val type_instance = Sign.typ_instance o Proof_Context.theory_of
651 fun insert_type ctxt get_T x xs =
652 let val T = get_T x in
653 if exists (curry (type_instance ctxt) T o get_T) xs then xs
654 else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
657 (* The Booleans indicate whether all type arguments should be kept. *)
658 datatype type_arg_policy =
659 Explicit_Type_Args of bool |
660 Mangled_Type_Args of bool |
663 fun should_drop_arg_type_args (Simple_Types _) =
664 false (* since TFF doesn't support overloading *)
665 | should_drop_arg_type_args type_sys =
666 level_of_type_sys type_sys = All_Types andalso
667 heaviness_of_type_sys type_sys = Heavyweight
669 fun general_type_arg_policy (Tags (_, All_Types, Heavyweight)) = No_Type_Args
670 | general_type_arg_policy type_sys =
671 if level_of_type_sys type_sys = No_Types then
673 else if polymorphism_of_type_sys type_sys = Mangled_Monomorphic then
674 Mangled_Type_Args (should_drop_arg_type_args type_sys)
676 Explicit_Type_Args (should_drop_arg_type_args type_sys)
678 fun type_arg_policy type_sys s =
679 if s = @{const_name HOL.eq} orelse
680 (s = app_op_name andalso level_of_type_sys type_sys = Const_Arg_Types) then
682 else if s = type_tag_name then
683 Explicit_Type_Args false
685 general_type_arg_policy type_sys
687 (*Make literals for sorted type variables*)
688 fun generic_sorts_on_type (_, []) = []
689 | generic_sorts_on_type ((x, i), s :: ss) =
690 generic_sorts_on_type ((x, i), ss)
691 |> (if s = the_single @{sort HOL.type} then
694 cons (TyLitFree (`make_type_class s, `make_fixed_type_var x))
696 cons (TyLitVar (`make_type_class s,
697 (make_schematic_type_var (x, i), x))))
698 fun sorts_on_tfree (TFree (s, S)) = generic_sorts_on_type ((s, ~1), S)
699 | sorts_on_tfree _ = []
700 fun sorts_on_tvar (TVar z) = generic_sorts_on_type z
701 | sorts_on_tvar _ = []
703 (* Given a list of sorted type variables, return a list of type literals. *)
704 fun raw_type_literals_for_types Ts =
705 union_all (map sorts_on_tfree Ts @ map sorts_on_tvar Ts)
707 fun type_literals_for_types type_sys sorts_on_typ Ts =
708 if level_of_type_sys type_sys = No_Types then []
709 else union_all (map sorts_on_typ Ts)
711 fun mk_aconns c phis =
712 let val (phis', phi') = split_last phis in
713 fold_rev (mk_aconn c) phis' phi'
715 fun mk_ahorn [] phi = phi
716 | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
717 fun mk_aquant _ [] phi = phi
718 | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
719 if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
720 | mk_aquant q xs phi = AQuant (q, xs, phi)
722 fun close_universally atom_vars phi =
724 fun formula_vars bounds (AQuant (_, xs, phi)) =
725 formula_vars (map fst xs @ bounds) phi
726 | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
727 | formula_vars bounds (AAtom tm) =
728 union (op =) (atom_vars tm []
729 |> filter_out (member (op =) bounds o fst))
730 in mk_aquant AForall (formula_vars [] phi []) phi end
732 fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
733 | combterm_vars (CombConst _) = I
734 | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
735 fun close_combformula_universally phi = close_universally combterm_vars phi
737 fun term_vars (ATerm (name as (s, _), tms)) =
738 is_tptp_variable s ? insert (op =) (name, NONE) #> fold term_vars tms
739 fun close_formula_universally phi = close_universally term_vars phi
741 val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
742 val homo_infinite_type = Type (homo_infinite_type_name, [])
744 fun fo_term_from_typ format type_sys =
746 fun term (Type (s, Ts)) =
747 ATerm (case (is_setting_higher_order format type_sys, s) of
748 (true, @{type_name bool}) => `I tptp_bool_type
749 | (true, @{type_name fun}) => `I tptp_fun_type
750 | _ => if s = homo_infinite_type_name andalso
751 (format = TFF orelse format = THF) then
752 `I tptp_individual_type
754 `make_fixed_type_const s,
756 | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
757 | term (TVar ((x as (s, _)), _)) =
758 ATerm ((make_schematic_type_var x, s), [])
761 (* This shouldn't clash with anything else. *)
762 val mangled_type_sep = "\000"
764 fun generic_mangled_type_name f (ATerm (name, [])) = f name
765 | generic_mangled_type_name f (ATerm (name, tys)) =
766 f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
769 val bool_atype = AType (`I tptp_bool_type)
771 fun make_simple_type s =
772 if s = tptp_bool_type orelse s = tptp_fun_type orelse
773 s = tptp_individual_type then
776 simple_type_prefix ^ ascii_of s
778 fun ho_type_from_fo_term format type_sys pred_sym ary =
781 AType ((make_simple_type (generic_mangled_type_name fst ty),
782 generic_mangled_type_name snd ty))
783 fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
784 fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
785 | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
786 fun to_ho (ty as ATerm ((s, _), tys)) =
787 if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
788 in if is_setting_higher_order format type_sys then to_ho else to_fo ary end
790 fun mangled_type format type_sys pred_sym ary =
791 ho_type_from_fo_term format type_sys pred_sym ary
792 o fo_term_from_typ format type_sys
794 fun mangled_const_name format type_sys T_args (s, s') =
796 val ty_args = map (fo_term_from_typ format type_sys) T_args
797 fun type_suffix f g =
798 fold_rev (curry (op ^) o g o prefix mangled_type_sep
799 o generic_mangled_type_name f) ty_args ""
800 in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
802 val parse_mangled_ident =
803 Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
805 fun parse_mangled_type x =
807 -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
809 and parse_mangled_types x =
810 (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
812 fun unmangled_type s =
813 s |> suffix ")" |> raw_explode
814 |> Scan.finite Symbol.stopper
815 (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
816 quote s)) parse_mangled_type))
819 val unmangled_const_name = space_explode mangled_type_sep #> hd
820 fun unmangled_const s =
821 let val ss = space_explode mangled_type_sep s in
822 (hd ss, map unmangled_type (tl ss))
825 fun introduce_proxies format type_sys =
827 fun intro top_level (CombApp (tm1, tm2)) =
828 CombApp (intro top_level tm1, intro false tm2)
829 | intro top_level (CombConst (name as (s, _), T, T_args)) =
830 (case proxify_const s of
832 if top_level orelse is_setting_higher_order format type_sys then
833 case (top_level, s) of
834 (_, "c_False") => (`I tptp_false, [])
835 | (_, "c_True") => (`I tptp_true, [])
836 | (false, "c_Not") => (`I tptp_not, [])
837 | (false, "c_conj") => (`I tptp_and, [])
838 | (false, "c_disj") => (`I tptp_or, [])
839 | (false, "c_implies") => (`I tptp_implies, [])
841 if is_tptp_equal s then (`I tptp_equal, [])
842 else (proxy_base |>> prefix const_prefix, T_args)
845 (proxy_base |>> prefix const_prefix, T_args)
846 | NONE => (name, T_args))
847 |> (fn (name, T_args) => CombConst (name, T, T_args))
851 fun combformula_from_prop thy format type_sys eq_as_iff =
853 fun do_term bs t atomic_types =
854 combterm_from_term thy bs (Envir.eta_contract t)
855 |>> (introduce_proxies format type_sys #> AAtom)
856 ||> union (op =) atomic_types
857 fun do_quant bs q s T t' =
858 let val s = Name.variant (map fst bs) s in
859 do_formula ((s, T) :: bs) t'
860 #>> mk_aquant q [(`make_bound_var s, SOME T)]
862 and do_conn bs c t1 t2 =
863 do_formula bs t1 ##>> do_formula bs t2 #>> uncurry (mk_aconn c)
864 and do_formula bs t =
866 @{const Trueprop} $ t1 => do_formula bs t1
867 | @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
868 | Const (@{const_name All}, _) $ Abs (s, T, t') =>
869 do_quant bs AForall s T t'
870 | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
871 do_quant bs AExists s T t'
872 | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
873 | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
874 | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
875 | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
876 if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
880 fun presimplify_term ctxt =
881 Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
882 #> Meson.presimplify ctxt
885 fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
886 fun conceal_bounds Ts t =
887 subst_bounds (map (Free o apfst concealed_bound_name)
888 (0 upto length Ts - 1 ~~ Ts), t)
889 fun reveal_bounds Ts =
890 subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
891 (0 upto length Ts - 1 ~~ Ts))
893 fun extensionalize_term ctxt t =
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
899 fun introduce_combinators_in_term ctxt kind t =
900 let val thy = Proof_Context.theory_of ctxt in
901 if Meson.is_fol_term thy t then
907 @{const Not} $ t1 => @{const Not} $ aux Ts t1
908 | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
909 t0 $ Abs (s, T, aux (T :: Ts) t')
910 | (t0 as Const (@{const_name All}, _)) $ t1 =>
911 aux Ts (t0 $ eta_expand Ts t1 1)
912 | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
913 t0 $ Abs (s, T, aux (T :: Ts) t')
914 | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
915 aux Ts (t0 $ eta_expand Ts t1 1)
916 | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
917 | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
918 | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
919 | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
921 t0 $ aux Ts t1 $ aux Ts t2
922 | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
925 t |> conceal_bounds Ts
926 |> Envir.eta_contract
928 |> Meson_Clausify.introduce_combinators_in_cterm
929 |> prop_of |> Logic.dest_equals |> snd
931 val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
932 in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
934 (* A type variable of sort "{}" will make abstraction fail. *)
935 if kind = Conjecture then HOLogic.false_const
936 else HOLogic.true_const
939 (* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
940 same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
943 fun aux (t $ u) = aux t $ aux u
944 | aux (Abs (s, T, t)) = Abs (s, T, aux t)
945 | aux (Var ((s, i), T)) =
946 Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
948 in t |> exists_subterm is_Var t ? aux end
950 fun preprocess_prop ctxt presimp kind t =
952 val thy = Proof_Context.theory_of ctxt
953 val t = t |> Envir.beta_eta_contract
954 |> transform_elim_prop
955 |> Object_Logic.atomize_term thy
956 val need_trueprop = (fastype_of t = @{typ bool})
958 t |> need_trueprop ? HOLogic.mk_Trueprop
959 |> Raw_Simplifier.rewrite_term thy (Meson.unfold_set_const_simps ctxt) []
960 |> extensionalize_term ctxt
961 |> presimp ? presimplify_term ctxt
962 |> perhaps (try (HOLogic.dest_Trueprop))
963 |> introduce_combinators_in_term ctxt kind
966 (* making fact and conjecture formulas *)
967 fun make_formula thy format type_sys eq_as_iff name loc kind t =
969 val (combformula, atomic_types) =
970 combformula_from_prop thy format type_sys eq_as_iff t []
972 {name = name, locality = loc, kind = kind, combformula = combformula,
973 atomic_types = atomic_types}
976 fun make_fact ctxt format type_sys keep_trivial eq_as_iff preproc presimp
978 let val thy = Proof_Context.theory_of ctxt in
980 t |> preproc ? preprocess_prop ctxt presimp Axiom
981 |> make_formula thy format type_sys eq_as_iff name loc Axiom) of
983 formula as {combformula = AAtom (CombConst ((s, _), _, _)), ...}) =>
984 if s = tptp_true then NONE else SOME formula
985 | (_, formula) => SOME formula
988 fun make_conjecture ctxt format prem_kind type_sys preproc ts =
990 val thy = Proof_Context.theory_of ctxt
991 val last = length ts - 1
993 map2 (fn j => fn t =>
995 val (kind, maybe_negate) =
1000 if prem_kind = Conjecture then update_combformula mk_anot
1003 t |> preproc ? (preprocess_prop ctxt true kind #> freeze_term)
1004 |> make_formula thy format type_sys (format <> CNF)
1005 (string_of_int j) General kind
1011 (** Finite and infinite type inference **)
1013 fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
1014 | deep_freeze_atyp T = T
1015 val deep_freeze_type = map_atyps deep_freeze_atyp
1017 (* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
1018 dangerous because their "exhaust" properties can easily lead to unsound ATP
1019 proofs. On the other hand, all HOL infinite types can be given the same
1020 models in first-order logic (via Löwenheim-Skolem). *)
1022 fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
1023 exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
1024 | should_encode_type _ _ All_Types _ = true
1025 | should_encode_type ctxt _ Finite_Types T = is_type_surely_finite ctxt T
1026 | should_encode_type _ _ _ _ = false
1028 fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
1029 should_predicate_on_var T =
1030 (heaviness = Heavyweight orelse should_predicate_on_var ()) andalso
1031 should_encode_type ctxt nonmono_Ts level T
1032 | should_predicate_on_type _ _ _ _ _ = false
1034 fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
1035 String.isPrefix bound_var_prefix s
1036 | is_var_or_bound_var (CombVar _) = true
1037 | is_var_or_bound_var _ = false
1039 datatype tag_site = Top_Level | Eq_Arg | Elsewhere
1041 fun should_tag_with_type _ _ _ Top_Level _ _ = false
1042 | should_tag_with_type ctxt nonmono_Ts (Tags (_, level, heaviness)) site u T =
1044 Heavyweight => should_encode_type ctxt nonmono_Ts level T
1046 case (site, is_var_or_bound_var u) of
1047 (Eq_Arg, true) => should_encode_type ctxt nonmono_Ts level T
1049 | should_tag_with_type _ _ _ _ _ _ = false
1051 fun homogenized_type ctxt nonmono_Ts level =
1053 val should_encode = should_encode_type ctxt nonmono_Ts level
1054 fun homo 0 T = if should_encode T then T else homo_infinite_type
1055 | homo ary (Type (@{type_name fun}, [T1, T2])) =
1056 homo 0 T1 --> homo (ary - 1) T2
1057 | homo _ _ = raise Fail "expected function type"
1060 (** "hBOOL" and "hAPP" **)
1063 {pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
1065 fun add_combterm_syms_to_table ctxt explicit_apply =
1067 fun consider_var_arity const_T var_T max_ary =
1070 if ary = max_ary orelse type_instance ctxt (var_T, T) orelse
1071 type_instance ctxt (T, var_T) then
1074 iter (ary + 1) (range_type T)
1075 in iter 0 const_T end
1076 fun add_var_or_bound_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1077 if explicit_apply = NONE andalso
1078 (can dest_funT T orelse T = @{typ bool}) then
1080 val bool_vars' = bool_vars orelse body_type T = @{typ bool}
1081 fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
1082 {pred_sym = pred_sym andalso not bool_vars',
1083 min_ary = fold (fn T' => consider_var_arity T' T) types min_ary,
1084 max_ary = max_ary, types = types}
1086 fun_var_Ts |> can dest_funT T ? insert_type ctxt I T
1088 if bool_vars' = bool_vars andalso
1089 pointer_eq (fun_var_Ts', fun_var_Ts) then
1092 ((bool_vars', fun_var_Ts'), Symtab.map (K repair_min_arity) sym_tab)
1096 fun add top_level tm (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1097 let val (head, args) = strip_combterm_comb tm in
1099 CombConst ((s, _), T, _) =>
1100 if String.isPrefix bound_var_prefix s then
1101 add_var_or_bound_var T accum
1103 let val ary = length args in
1104 ((bool_vars, fun_var_Ts),
1105 case Symtab.lookup sym_tab s of
1106 SOME {pred_sym, min_ary, max_ary, types} =>
1109 pred_sym andalso top_level andalso not bool_vars
1110 val types' = types |> insert_type ctxt I T
1112 if is_some explicit_apply orelse
1113 pointer_eq (types', types) then
1116 fold (consider_var_arity T) fun_var_Ts min_ary
1118 Symtab.update (s, {pred_sym = pred_sym,
1119 min_ary = Int.min (ary, min_ary),
1120 max_ary = Int.max (ary, max_ary),
1126 val pred_sym = top_level andalso not bool_vars
1128 case explicit_apply of
1131 | NONE => fold (consider_var_arity T) fun_var_Ts ary
1133 Symtab.update_new (s, {pred_sym = pred_sym,
1134 min_ary = min_ary, max_ary = ary,
1139 | CombVar (_, T) => add_var_or_bound_var T accum
1141 |> fold (add false) args
1144 fun add_fact_syms_to_table ctxt explicit_apply =
1145 fact_lift (formula_fold NONE
1146 (K (add_combterm_syms_to_table ctxt explicit_apply)))
1148 val default_sym_tab_entries : (string * sym_info) list =
1149 (prefixed_predicator_name,
1150 {pred_sym = true, min_ary = 1, max_ary = 1, types = []}) ::
1151 ([tptp_false, tptp_true]
1152 |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []})) @
1153 ([tptp_equal, tptp_old_equal]
1154 |> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = []}))
1156 fun sym_table_for_facts ctxt explicit_apply facts =
1157 ((false, []), Symtab.empty)
1158 |> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
1159 |> fold Symtab.update default_sym_tab_entries
1161 fun min_arity_of sym_tab s =
1162 case Symtab.lookup sym_tab s of
1163 SOME ({min_ary, ...} : sym_info) => min_ary
1165 case strip_prefix_and_unascii const_prefix s of
1167 let val s = s |> unmangled_const_name |> invert_const in
1168 if s = predicator_name then 1
1169 else if s = app_op_name then 2
1170 else if s = type_pred_name then 1
1175 (* True if the constant ever appears outside of the top-level position in
1176 literals, or if it appears with different arities (e.g., because of different
1177 type instantiations). If false, the constant always receives all of its
1178 arguments and is used as a predicate. *)
1179 fun is_pred_sym sym_tab s =
1180 case Symtab.lookup sym_tab s of
1181 SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
1182 pred_sym andalso min_ary = max_ary
1185 val predicator_combconst =
1186 CombConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
1187 fun predicator tm = CombApp (predicator_combconst, tm)
1189 fun introduce_predicators_in_combterm sym_tab tm =
1190 case strip_combterm_comb tm of
1191 (CombConst ((s, _), _, _), _) =>
1192 if is_pred_sym sym_tab s then tm else predicator tm
1193 | _ => predicator tm
1195 fun list_app head args = fold (curry (CombApp o swap)) args head
1197 val app_op = `make_fixed_const app_op_name
1199 fun explicit_app arg head =
1201 val head_T = combtyp_of head
1202 val (arg_T, res_T) = dest_funT head_T
1204 CombConst (app_op, head_T --> head_T, [arg_T, res_T])
1205 in list_app explicit_app [head, arg] end
1206 fun list_explicit_app head args = fold explicit_app args head
1208 fun introduce_explicit_apps_in_combterm sym_tab =
1211 case strip_combterm_comb tm of
1212 (head as CombConst ((s, _), _, _), args) =>
1214 |> chop (min_arity_of sym_tab s)
1216 |-> list_explicit_app
1217 | (head, args) => list_explicit_app head (map aux args)
1220 fun chop_fun 0 T = ([], T)
1221 | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
1222 chop_fun (n - 1) ran_T |>> cons dom_T
1223 | chop_fun _ _ = raise Fail "unexpected non-function"
1225 fun filter_type_args _ _ _ [] = []
1226 | filter_type_args thy s arity T_args =
1228 (* will throw "TYPE" for pseudo-constants *)
1229 val U = if s = app_op_name then
1230 @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
1232 s |> Sign.the_const_type thy
1234 case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
1237 let val U_args = (s, U) |> Sign.const_typargs thy in
1239 |> map_filter (fn (U, T) =>
1240 if member (op =) res_U_vars (dest_TVar U) then
1246 handle TYPE _ => T_args
1248 fun enforce_type_arg_policy_in_combterm ctxt format type_sys =
1250 val thy = Proof_Context.theory_of ctxt
1251 fun aux arity (CombApp (tm1, tm2)) =
1252 CombApp (aux (arity + 1) tm1, aux 0 tm2)
1253 | aux arity (CombConst (name as (s, _), T, T_args)) =
1254 (case strip_prefix_and_unascii const_prefix s of
1255 NONE => (name, T_args)
1258 val s'' = invert_const s''
1259 fun filtered_T_args false = T_args
1260 | filtered_T_args true = filter_type_args thy s'' arity T_args
1262 case type_arg_policy type_sys s'' of
1263 Explicit_Type_Args drop_args =>
1264 (name, filtered_T_args drop_args)
1265 | Mangled_Type_Args drop_args =>
1266 (mangled_const_name format type_sys (filtered_T_args drop_args)
1268 | No_Type_Args => (name, [])
1270 |> (fn (name, T_args) => CombConst (name, T, T_args))
1274 fun repair_combterm ctxt format type_sys sym_tab =
1275 not (is_setting_higher_order format type_sys)
1276 ? (introduce_explicit_apps_in_combterm sym_tab
1277 #> introduce_predicators_in_combterm sym_tab)
1278 #> enforce_type_arg_policy_in_combterm ctxt format type_sys
1279 fun repair_fact ctxt format type_sys sym_tab =
1280 update_combformula (formula_map
1281 (repair_combterm ctxt format type_sys sym_tab))
1283 (** Helper facts **)
1285 (* The Boolean indicates that a fairly sound type encoding is needed. *)
1287 [(("COMBI", false), @{thms Meson.COMBI_def}),
1288 (("COMBK", false), @{thms Meson.COMBK_def}),
1289 (("COMBB", false), @{thms Meson.COMBB_def}),
1290 (("COMBC", false), @{thms Meson.COMBC_def}),
1291 (("COMBS", false), @{thms Meson.COMBS_def}),
1293 (* This is a lie: Higher-order equality doesn't need a sound type encoding.
1294 However, this is done so for backward compatibility: Including the
1295 equality helpers by default in Metis breaks a few existing proofs. *)
1296 @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1297 fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1298 (("fFalse", false), [@{lemma "~ fFalse" by (unfold fFalse_def) fast}]),
1299 (("fFalse", true), @{thms True_or_False}),
1300 (("fTrue", false), [@{lemma "fTrue" by (unfold fTrue_def) fast}]),
1301 (("fTrue", true), @{thms True_or_False}),
1303 @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1304 fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1306 @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
1307 by (unfold fconj_def) fast+}),
1309 @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
1310 by (unfold fdisj_def) fast+}),
1311 (("fimplies", false),
1312 @{lemma "P | fimplies P Q" "~ Q | fimplies P Q" "~ fimplies P Q | ~ P | Q"
1313 by (unfold fimplies_def) fast+}),
1314 (("If", true), @{thms if_True if_False True_or_False})]
1315 |> map (apsnd (map zero_var_indexes))
1317 val type_tag = `make_fixed_const type_tag_name
1319 fun type_tag_idempotence_fact () =
1321 fun var s = ATerm (`I s, [])
1322 fun tag tm = ATerm (type_tag, [var "T", tm])
1323 val tagged_a = tag (var "A")
1325 Formula (type_tag_idempotence_helper_name, Axiom,
1326 AAtom (ATerm (`I tptp_equal, [tag tagged_a, tagged_a]))
1327 |> close_formula_universally, simp_info, NONE)
1330 fun should_specialize_helper type_sys t =
1331 case general_type_arg_policy type_sys of
1332 Mangled_Type_Args _ => not (null (Term.hidden_polymorphism t))
1335 fun helper_facts_for_sym ctxt format type_sys (s, {types, ...} : sym_info) =
1336 case strip_prefix_and_unascii const_prefix s of
1339 val thy = Proof_Context.theory_of ctxt
1340 val unmangled_s = mangled_s |> unmangled_const_name
1341 fun dub_and_inst needs_fairly_sound (th, j) =
1342 ((unmangled_s ^ "_" ^ string_of_int j ^
1343 (if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^
1344 (if needs_fairly_sound then typed_helper_suffix
1345 else untyped_helper_suffix),
1347 let val t = th |> prop_of in
1348 t |> should_specialize_helper type_sys t
1350 [T] => specialize_type thy (invert_const unmangled_s, T)
1354 map_filter (make_fact ctxt format type_sys false false false false)
1355 val fairly_sound = is_type_sys_fairly_sound type_sys
1358 |> maps (fn ((helper_s, needs_fairly_sound), ths) =>
1359 if helper_s <> unmangled_s orelse
1360 (needs_fairly_sound andalso not fairly_sound) then
1363 ths ~~ (1 upto length ths)
1364 |> map (dub_and_inst needs_fairly_sound)
1368 fun helper_facts_for_sym_table ctxt format type_sys sym_tab =
1369 Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_sys) sym_tab
1372 (***************************************************************)
1373 (* Type Classes Present in the Axiom or Conjecture Clauses *)
1374 (***************************************************************)
1376 fun set_insert (x, s) = Symtab.update (x, ()) s
1378 fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
1380 (* Remove this trivial type class (FIXME: similar code elsewhere) *)
1381 fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
1383 fun classes_of_terms get_Ts =
1384 map (map snd o get_Ts)
1385 #> List.foldl add_classes Symtab.empty
1386 #> delete_type #> Symtab.keys
1388 val tfree_classes_of_terms = classes_of_terms OldTerm.term_tfrees
1389 val tvar_classes_of_terms = classes_of_terms OldTerm.term_tvars
1391 (*fold type constructors*)
1392 fun fold_type_constrs f (Type (a, Ts)) x =
1393 fold (fold_type_constrs f) Ts (f (a,x))
1394 | fold_type_constrs _ _ x = x
1396 (*Type constructors used to instantiate overloaded constants are the only ones needed.*)
1397 fun add_type_constrs_in_term thy =
1399 fun add (Const (@{const_name Meson.skolem}, _) $ _) = I
1400 | add (t $ u) = add t #> add u
1401 | add (Const (x as (s, _))) =
1402 if String.isPrefix skolem_const_prefix s then I
1403 else x |> Sign.const_typargs thy |> fold (fold_type_constrs set_insert)
1404 | add (Abs (_, _, u)) = add u
1408 fun type_constrs_of_terms thy ts =
1409 Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty)
1411 fun translate_formulas ctxt format prem_kind type_sys preproc hyp_ts concl_t
1414 val thy = Proof_Context.theory_of ctxt
1415 val fact_ts = facts |> map snd
1416 val (facts, fact_names) =
1417 facts |> map (fn (name, t) =>
1419 |> make_fact ctxt format type_sys false true true true
1421 |> map_filter (try (apfst the))
1423 (* Remove existing facts from the conjecture, as this can dramatically
1424 boost an ATP's performance (for some reason). *)
1427 |> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t)
1428 val goal_t = Logic.list_implies (hyp_ts, concl_t)
1429 val all_ts = goal_t :: fact_ts
1430 val subs = tfree_classes_of_terms all_ts
1431 val supers = tvar_classes_of_terms all_ts
1432 val tycons = type_constrs_of_terms thy all_ts
1435 |> make_conjecture ctxt format prem_kind type_sys preproc
1436 val (supers', arity_clauses) =
1437 if level_of_type_sys type_sys = No_Types then ([], [])
1438 else make_arity_clauses thy tycons supers
1439 val class_rel_clauses = make_class_rel_clauses thy subs supers'
1441 (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
1444 fun fo_literal_from_type_literal (TyLitVar (class, name)) =
1445 (true, ATerm (class, [ATerm (name, [])]))
1446 | fo_literal_from_type_literal (TyLitFree (class, name)) =
1447 (true, ATerm (class, [ATerm (name, [])]))
1449 fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
1451 val type_pred = `make_fixed_const type_pred_name
1453 fun type_pred_combterm ctxt format type_sys T tm =
1454 CombApp (CombConst (type_pred, T --> @{typ bool}, [T])
1455 |> enforce_type_arg_policy_in_combterm ctxt format type_sys, tm)
1457 fun var_occurs_positively_naked_in_term _ (SOME false) _ accum = accum
1458 | var_occurs_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
1459 accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
1460 fun is_var_nonmonotonic_in_formula _ _ (SOME false) _ = false
1461 | is_var_nonmonotonic_in_formula pos phi _ name =
1462 formula_fold pos (var_occurs_positively_naked_in_term name) phi false
1464 fun mk_const_aterm format type_sys x T_args args =
1465 ATerm (x, map (fo_term_from_typ format type_sys) T_args @ args)
1467 fun tag_with_type ctxt format nonmono_Ts type_sys T tm =
1468 CombConst (type_tag, T --> T, [T])
1469 |> enforce_type_arg_policy_in_combterm ctxt format type_sys
1470 |> term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
1471 |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
1472 and term_from_combterm ctxt format nonmono_Ts type_sys =
1476 val (head, args) = strip_combterm_comb u
1477 val (x as (s, _), T_args) =
1479 CombConst (name, _, T_args) => (name, T_args)
1480 | CombVar (name, _) => (name, [])
1481 | CombApp _ => raise Fail "impossible \"CombApp\""
1482 val arg_site = if site = Top_Level andalso is_tptp_equal s then Eq_Arg
1484 val t = mk_const_aterm format type_sys x T_args
1485 (map (aux arg_site) args)
1486 val T = combtyp_of u
1488 t |> (if should_tag_with_type ctxt nonmono_Ts type_sys site u T then
1489 tag_with_type ctxt format nonmono_Ts type_sys T
1494 and formula_from_combformula ctxt format nonmono_Ts type_sys
1495 should_predicate_on_var =
1497 val do_term = term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
1500 Simple_Types level =>
1501 homogenized_type ctxt nonmono_Ts level 0
1502 #> mangled_type format type_sys false 0 #> SOME
1504 fun do_out_of_bound_type pos phi universal (name, T) =
1505 if should_predicate_on_type ctxt nonmono_Ts type_sys
1506 (fn () => should_predicate_on_var pos phi universal name) T then
1508 |> type_pred_combterm ctxt format type_sys T
1509 |> do_term |> AAtom |> SOME
1512 fun do_formula pos (AQuant (q, xs, phi)) =
1514 val phi = phi |> do_formula pos
1515 val universal = Option.map (q = AExists ? not) pos
1517 AQuant (q, xs |> map (apsnd (fn NONE => NONE
1518 | SOME T => do_bound_type T)),
1519 (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
1521 (fn (_, NONE) => NONE
1523 do_out_of_bound_type pos phi universal (s, T))
1527 | do_formula pos (AConn conn) = aconn_map pos do_formula conn
1528 | do_formula _ (AAtom tm) = AAtom (do_term tm)
1529 in do_formula o SOME end
1531 fun bound_tvars type_sys Ts =
1532 mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
1533 (type_literals_for_types type_sys sorts_on_tvar Ts))
1535 fun formula_for_fact ctxt format nonmono_Ts type_sys
1536 ({combformula, atomic_types, ...} : translated_formula) =
1538 |> close_combformula_universally
1539 |> formula_from_combformula ctxt format nonmono_Ts type_sys
1540 is_var_nonmonotonic_in_formula true
1541 |> bound_tvars type_sys atomic_types
1542 |> close_formula_universally
1544 (* Each fact is given a unique fact number to avoid name clashes (e.g., because
1545 of monomorphization). The TPTP explicitly forbids name clashes, and some of
1546 the remote provers might care. *)
1547 fun formula_line_for_fact ctxt format prefix encode freshen nonmono_Ts type_sys
1548 (j, formula as {name, locality, kind, ...}) =
1551 polymorphism_of_type_sys type_sys <> Polymorphic then
1552 string_of_int j ^ "_"
1555 kind, formula_for_fact ctxt format nonmono_Ts type_sys formula, NONE,
1562 fun formula_line_for_class_rel_clause ({name, subclass, superclass, ...}
1563 : class_rel_clause) =
1564 let val ty_arg = ATerm (`I "T", []) in
1565 Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
1566 AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
1567 AAtom (ATerm (superclass, [ty_arg]))])
1568 |> close_formula_universally, intro_info, NONE)
1571 fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
1572 (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
1573 | fo_literal_from_arity_literal (TVarLit (c, sort)) =
1574 (false, ATerm (c, [ATerm (sort, [])]))
1576 fun formula_line_for_arity_clause ({name, prem_lits, concl_lits, ...}
1578 Formula (arity_clause_prefix ^ ascii_of name, Axiom,
1579 mk_ahorn (map (formula_from_fo_literal o apfst not
1580 o fo_literal_from_arity_literal) prem_lits)
1581 (formula_from_fo_literal
1582 (fo_literal_from_arity_literal concl_lits))
1583 |> close_formula_universally, intro_info, NONE)
1585 fun formula_line_for_conjecture ctxt format nonmono_Ts type_sys
1586 ({name, kind, combformula, atomic_types, ...} : translated_formula) =
1587 Formula (conjecture_prefix ^ name, kind,
1588 formula_from_combformula ctxt format nonmono_Ts type_sys
1589 is_var_nonmonotonic_in_formula false
1590 (close_combformula_universally combformula)
1591 |> bound_tvars type_sys atomic_types
1592 |> close_formula_universally, NONE, NONE)
1594 fun free_type_literals type_sys ({atomic_types, ...} : translated_formula) =
1595 atomic_types |> type_literals_for_types type_sys sorts_on_tfree
1596 |> map fo_literal_from_type_literal
1598 fun formula_line_for_free_type j lit =
1599 Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis,
1600 formula_from_fo_literal lit, NONE, NONE)
1601 fun formula_lines_for_free_types type_sys facts =
1603 val litss = map (free_type_literals type_sys) facts
1604 val lits = fold (union (op =)) litss []
1605 in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
1607 (** Symbol declarations **)
1609 fun should_declare_sym type_sys pred_sym s =
1610 is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
1612 Simple_Types _ => true
1613 | Tags (_, _, Lightweight) => true
1614 | _ => not pred_sym)
1616 fun sym_decl_table_for_facts ctxt type_sys repaired_sym_tab (conjs, facts) =
1618 fun add_combterm in_conj tm =
1619 let val (head, args) = strip_combterm_comb tm in
1621 CombConst ((s, s'), T, T_args) =>
1622 let val pred_sym = is_pred_sym repaired_sym_tab s in
1623 if should_declare_sym type_sys pred_sym s then
1624 Symtab.map_default (s, [])
1625 (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
1631 #> fold (add_combterm in_conj) args
1633 fun add_fact in_conj =
1634 fact_lift (formula_fold NONE (K (add_combterm in_conj)))
1637 |> is_type_sys_fairly_sound type_sys
1638 ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
1641 (* These types witness that the type classes they belong to allow infinite
1642 models and hence that any types with these type classes is monotonic. *)
1643 val known_infinite_types =
1644 [@{typ nat}, Type ("Int.int", []), @{typ "nat => bool"}]
1646 (* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
1647 out with monotonicity" paper presented at CADE 2011. *)
1648 fun add_combterm_nonmonotonic_types _ _ (SOME false) _ = I
1649 | add_combterm_nonmonotonic_types ctxt level _
1650 (CombApp (CombApp (CombConst ((s, _), Type (_, [T, _]), _), tm1),
1652 (is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
1654 Nonmonotonic_Types =>
1655 not (is_type_surely_infinite ctxt known_infinite_types T)
1656 | Finite_Types => is_type_surely_finite ctxt T
1657 | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
1658 | add_combterm_nonmonotonic_types _ _ _ _ = I
1659 fun add_fact_nonmonotonic_types ctxt level ({kind, combformula, ...}
1660 : translated_formula) =
1661 formula_fold (SOME (kind <> Conjecture))
1662 (add_combterm_nonmonotonic_types ctxt level) combformula
1663 fun nonmonotonic_types_for_facts ctxt type_sys facts =
1664 let val level = level_of_type_sys type_sys in
1665 if level = Nonmonotonic_Types orelse level = Finite_Types then
1666 [] |> fold (add_fact_nonmonotonic_types ctxt level) facts
1667 (* We must add "bool" in case the helper "True_or_False" is added
1668 later. In addition, several places in the code rely on the list of
1669 nonmonotonic types not being empty. *)
1670 |> insert_type ctxt I @{typ bool}
1675 fun decl_line_for_sym ctxt format nonmono_Ts type_sys s
1676 (s', T_args, T, pred_sym, ary, _) =
1678 val (T_arg_Ts, level) =
1680 Simple_Types level => ([], level)
1681 | _ => (replicate (length T_args) homo_infinite_type, No_Types)
1683 Decl (sym_decl_prefix ^ s, (s, s'),
1684 (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
1685 |> mangled_type format type_sys pred_sym (length T_arg_Ts + ary))
1688 fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
1690 fun formula_line_for_preds_sym_decl ctxt format conj_sym_kind nonmono_Ts
1691 type_sys n s j (s', T_args, T, _, ary, in_conj) =
1693 val (kind, maybe_negate) =
1694 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1696 val (arg_Ts, res_T) = chop_fun ary T
1698 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
1700 bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
1702 arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
1705 Formula (preds_sym_formula_prefix ^ s ^
1706 (if n > 1 then "_" ^ string_of_int j else ""), kind,
1707 CombConst ((s, s'), T, T_args)
1708 |> fold (curry (CombApp o swap)) bounds
1709 |> type_pred_combterm ctxt format type_sys res_T
1710 |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
1711 |> formula_from_combformula ctxt format nonmono_Ts type_sys
1712 (K (K (K (K true)))) true
1713 |> n > 1 ? bound_tvars type_sys (atyps_of T)
1714 |> close_formula_universally
1719 fun formula_lines_for_lightweight_tags_sym_decl ctxt format conj_sym_kind
1720 nonmono_Ts type_sys n s (j, (s', T_args, T, pred_sym, ary, in_conj)) =
1723 lightweight_tags_sym_formula_prefix ^ s ^
1724 (if n > 1 then "_" ^ string_of_int j else "")
1725 val (kind, maybe_negate) =
1726 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1728 val (arg_Ts, res_T) = chop_fun ary T
1730 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
1731 val bounds = bound_names |> map (fn name => ATerm (name, []))
1732 val cst = mk_const_aterm format type_sys (s, s') T_args
1733 val atomic_Ts = atyps_of T
1735 (if pred_sym then AConn (AIff, map AAtom tms)
1736 else AAtom (ATerm (`I tptp_equal, tms)))
1737 |> bound_tvars type_sys atomic_Ts
1738 |> close_formula_universally
1740 val should_encode = should_encode_type ctxt nonmono_Ts All_Types
1741 val tag_with = tag_with_type ctxt format nonmono_Ts type_sys
1742 val add_formula_for_res =
1743 if should_encode res_T then
1744 cons (Formula (ident_base ^ "_res", kind,
1745 eq [tag_with res_T (cst bounds), cst bounds],
1749 fun add_formula_for_arg k =
1750 let val arg_T = nth arg_Ts k in
1751 if should_encode arg_T then
1752 case chop k bounds of
1753 (bounds1, bound :: bounds2) =>
1754 cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
1755 eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
1758 | _ => raise Fail "expected nonempty tail"
1763 [] |> not pred_sym ? add_formula_for_res
1764 |> fold add_formula_for_arg (ary - 1 downto 0)
1767 fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
1769 fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts type_sys
1773 decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_sys s)
1778 decl :: (decls' as _ :: _) =>
1779 let val T = result_type_of_decl decl in
1780 if forall (curry (type_instance ctxt o swap) T
1781 o result_type_of_decl) decls' then
1787 val n = length decls
1790 |> filter (should_predicate_on_type ctxt nonmono_Ts type_sys (K true)
1791 o result_type_of_decl)
1793 (0 upto length decls - 1, decls)
1794 |-> map2 (formula_line_for_preds_sym_decl ctxt format conj_sym_kind
1795 nonmono_Ts type_sys n s)
1797 | Tags (_, _, heaviness) =>
1801 let val n = length decls in
1802 (0 upto n - 1 ~~ decls)
1803 |> maps (formula_lines_for_lightweight_tags_sym_decl ctxt format
1804 conj_sym_kind nonmono_Ts type_sys n s)
1807 fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1808 type_sys sym_decl_tab =
1813 |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
1814 nonmono_Ts type_sys)
1816 fun needs_type_tag_idempotence (Tags (poly, level, heaviness)) =
1817 poly <> Mangled_Monomorphic andalso
1818 ((level = All_Types andalso heaviness = Lightweight) orelse
1819 level = Nonmonotonic_Types orelse level = Finite_Types)
1820 | needs_type_tag_idempotence _ = false
1822 fun offset_of_heading_in_problem _ [] j = j
1823 | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
1824 if heading = needle then j
1825 else offset_of_heading_in_problem needle problem (j + length lines)
1827 val implicit_declsN = "Should-be-implicit typings"
1828 val explicit_declsN = "Explicit typings"
1829 val factsN = "Relevant facts"
1830 val class_relsN = "Class relationships"
1831 val aritiesN = "Arities"
1832 val helpersN = "Helper facts"
1833 val conjsN = "Conjectures"
1834 val free_typesN = "Type variables"
1836 fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_sys
1837 explicit_apply readable_names preproc hyp_ts concl_t
1840 val (format, type_sys) = choose_format [format] type_sys
1841 val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
1842 translate_formulas ctxt format prem_kind type_sys preproc hyp_ts concl_t
1844 val sym_tab = conjs @ facts |> sym_table_for_facts ctxt explicit_apply
1845 val nonmono_Ts = conjs @ facts |> nonmonotonic_types_for_facts ctxt type_sys
1846 val repair = repair_fact ctxt format type_sys sym_tab
1847 val (conjs, facts) = (conjs, facts) |> pairself (map repair)
1848 val repaired_sym_tab =
1849 conjs @ facts |> sym_table_for_facts ctxt (SOME false)
1851 repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_sys
1853 val lavish_nonmono_Ts =
1854 if null nonmono_Ts orelse nonmono_Ts = [@{typ bool}] orelse
1855 polymorphism_of_type_sys type_sys <> Polymorphic then
1858 [TVar (("'a", 0), HOLogic.typeS)]
1859 val sym_decl_lines =
1860 (conjs, helpers @ facts)
1861 |> sym_decl_table_for_facts ctxt type_sys repaired_sym_tab
1862 |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind
1863 lavish_nonmono_Ts type_sys
1865 0 upto length helpers - 1 ~~ helpers
1866 |> map (formula_line_for_fact ctxt format helper_prefix I false
1867 lavish_nonmono_Ts type_sys)
1868 |> (if needs_type_tag_idempotence type_sys then
1869 cons (type_tag_idempotence_fact ())
1872 (* Reordering these might confuse the proof reconstruction code or the SPASS
1875 [(explicit_declsN, sym_decl_lines),
1877 map (formula_line_for_fact ctxt format fact_prefix ascii_of true
1878 nonmono_Ts type_sys)
1879 (0 upto length facts - 1 ~~ facts)),
1880 (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
1881 (aritiesN, map formula_line_for_arity_clause arity_clauses),
1882 (helpersN, helper_lines),
1884 map (formula_line_for_conjecture ctxt format nonmono_Ts type_sys)
1886 (free_typesN, formula_lines_for_free_types type_sys (facts @ conjs))]
1890 CNF => ensure_cnf_problem
1891 | CNF_UEQ => filter_cnf_ueq_problem
1893 |> (if is_format_typed format then
1894 declare_undeclared_syms_in_atp_problem type_decl_prefix
1898 val (problem, pool) = problem |> nice_atp_problem readable_names
1899 val helpers_offset = offset_of_heading_in_problem helpersN problem 0
1901 map_filter (fn (j, {name, ...}) =>
1902 if String.isSuffix typed_helper_suffix name then SOME j
1904 ((helpers_offset + 1 upto helpers_offset + length helpers)
1906 fun add_sym_arity (s, {min_ary, ...} : sym_info) =
1908 case strip_prefix_and_unascii const_prefix s of
1909 SOME s => Symtab.insert (op =) (s, min_ary)
1915 case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
1916 offset_of_heading_in_problem conjsN problem 0,
1917 offset_of_heading_in_problem factsN problem 0,
1918 fact_names |> Vector.fromList,
1920 Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
1924 val conj_weight = 0.0
1925 val hyp_weight = 0.1
1926 val fact_min_weight = 0.2
1927 val fact_max_weight = 1.0
1928 val type_info_default_weight = 0.8
1930 fun add_term_weights weight (ATerm (s, tms)) =
1931 is_tptp_user_symbol s ? Symtab.default (s, weight)
1932 #> fold (add_term_weights weight) tms
1933 fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
1934 formula_fold NONE (K (add_term_weights weight)) phi
1935 | add_problem_line_weights _ _ = I
1937 fun add_conjectures_weights [] = I
1938 | add_conjectures_weights conjs =
1939 let val (hyps, conj) = split_last conjs in
1940 add_problem_line_weights conj_weight conj
1941 #> fold (add_problem_line_weights hyp_weight) hyps
1944 fun add_facts_weights facts =
1946 val num_facts = length facts
1948 fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
1949 / Real.fromInt num_facts
1951 map weight_of (0 upto num_facts - 1) ~~ facts
1952 |> fold (uncurry add_problem_line_weights)
1955 (* Weights are from 0.0 (most important) to 1.0 (least important). *)
1956 fun atp_problem_weights problem =
1957 let val get = these o AList.lookup (op =) problem in
1959 |> add_conjectures_weights (get free_typesN @ get conjsN)
1960 |> add_facts_weights (get factsN)
1961 |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
1962 [explicit_declsN, class_relsN, aritiesN]
1964 |> sort (prod_ord Real.compare string_ord o pairself swap)