killed "explicit_apply" option in Sledgehammer -- the "smart" default is about as lightweight as "false" and just as complete as "true"
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 -> bool -> term list -> term -> ((string * locality) * term) list
135 -> string problem * string Symtab.table * int * int
136 * (string * locality) list vector * int list * int Symtab.table
137 val atp_problem_weights : string problem -> (string * real) list
140 structure ATP_Translate : ATP_TRANSLATE =
146 type name = string * string
149 fun union_all xss = fold (union (op =)) xss []
152 val generate_useful_info = false
154 fun useful_isabelle_info s =
155 if generate_useful_info then
156 SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
160 val intro_info = useful_isabelle_info "intro"
161 val elim_info = useful_isabelle_info "elim"
162 val simp_info = useful_isabelle_info "simp"
164 val bound_var_prefix = "B_"
165 val schematic_var_prefix = "V_"
166 val fixed_var_prefix = "v_"
168 val tvar_prefix = "T_"
169 val tfree_prefix = "t_"
171 val const_prefix = "c_"
172 val type_const_prefix = "tc_"
173 val class_prefix = "cl_"
175 val skolem_const_prefix = "Sledgehammer" ^ Long_Name.separator ^ "Sko"
176 val old_skolem_const_prefix = skolem_const_prefix ^ "o"
177 val new_skolem_const_prefix = skolem_const_prefix ^ "n"
179 val type_decl_prefix = "ty_"
180 val sym_decl_prefix = "sy_"
181 val preds_sym_formula_prefix = "psy_"
182 val lightweight_tags_sym_formula_prefix = "tsy_"
183 val fact_prefix = "fact_"
184 val conjecture_prefix = "conj_"
185 val helper_prefix = "help_"
186 val class_rel_clause_prefix = "clar_"
187 val arity_clause_prefix = "arity_"
188 val tfree_clause_prefix = "tfree_"
190 val typed_helper_suffix = "_T"
191 val untyped_helper_suffix = "_U"
192 val type_tag_idempotence_helper_name = helper_prefix ^ "ti_idem"
194 val predicator_name = "hBOOL"
195 val app_op_name = "hAPP"
196 val type_tag_name = "ti"
197 val type_pred_name = "is"
198 val simple_type_prefix = "ty_"
200 val prefixed_predicator_name = const_prefix ^ predicator_name
201 val prefixed_app_op_name = const_prefix ^ app_op_name
202 val prefixed_type_tag_name = const_prefix ^ type_tag_name
204 (* Freshness almost guaranteed! *)
205 val sledgehammer_weak_prefix = "Sledgehammer:"
207 (*Escaping of special characters.
208 Alphanumeric characters are left unchanged.
209 The character _ goes to __
210 Characters in the range ASCII space to / go to _A to _P, respectively.
211 Other characters go to _nnn where nnn is the decimal ASCII code.*)
212 val upper_a_minus_space = Char.ord #"A" - Char.ord #" "
214 fun stringN_of_int 0 _ = ""
215 | stringN_of_int k n =
216 stringN_of_int (k - 1) (n div 10) ^ string_of_int (n mod 10)
218 fun ascii_of_char c =
219 if Char.isAlphaNum c then
221 else if c = #"_" then
223 else if #" " <= c andalso c <= #"/" then
224 "_" ^ String.str (Char.chr (Char.ord c + upper_a_minus_space))
226 (* fixed width, in case more digits follow *)
227 "_" ^ stringN_of_int 3 (Char.ord c)
229 val ascii_of = String.translate ascii_of_char
231 (** Remove ASCII armoring from names in proof files **)
233 (* We don't raise error exceptions because this code can run inside a worker
234 thread. Also, the errors are impossible. *)
237 fun un rcs [] = String.implode(rev rcs)
238 | un rcs [#"_"] = un (#"_" :: rcs) [] (* ERROR *)
239 (* Three types of _ escapes: __, _A to _P, _nnn *)
240 | un rcs (#"_" :: #"_" :: cs) = un (#"_"::rcs) cs
241 | un rcs (#"_" :: c :: cs) =
242 if #"A" <= c andalso c<= #"P" then
243 (* translation of #" " to #"/" *)
244 un (Char.chr (Char.ord c - upper_a_minus_space) :: rcs) cs
246 let val digits = List.take (c::cs, 3) handle Subscript => [] in
247 case Int.fromString (String.implode digits) of
248 SOME n => un (Char.chr n :: rcs) (List.drop (cs, 2))
249 | NONE => un (c:: #"_"::rcs) cs (* ERROR *)
251 | un rcs (c :: cs) = un (c :: rcs) cs
252 in un [] o String.explode end
254 (* If string s has the prefix s1, return the result of deleting it,
256 fun strip_prefix_and_unascii s1 s =
257 if String.isPrefix s1 s then
258 SOME (unascii_of (String.extract (s, size s1, NONE)))
263 [("c_False", (@{const_name False}, (@{thm fFalse_def},
264 ("fFalse", @{const_name ATP.fFalse})))),
265 ("c_True", (@{const_name True}, (@{thm fTrue_def},
266 ("fTrue", @{const_name ATP.fTrue})))),
267 ("c_Not", (@{const_name Not}, (@{thm fNot_def},
268 ("fNot", @{const_name ATP.fNot})))),
269 ("c_conj", (@{const_name conj}, (@{thm fconj_def},
270 ("fconj", @{const_name ATP.fconj})))),
271 ("c_disj", (@{const_name disj}, (@{thm fdisj_def},
272 ("fdisj", @{const_name ATP.fdisj})))),
273 ("c_implies", (@{const_name implies}, (@{thm fimplies_def},
274 ("fimplies", @{const_name ATP.fimplies})))),
275 ("equal", (@{const_name HOL.eq}, (@{thm fequal_def},
276 ("fequal", @{const_name ATP.fequal}))))]
278 val proxify_const = AList.lookup (op =) proxy_table #> Option.map (snd o snd)
280 (* Readable names for the more common symbolic functions. Do not mess with the
281 table unless you know what you are doing. *)
282 val const_trans_table =
283 [(@{type_name Product_Type.prod}, "prod"),
284 (@{type_name Sum_Type.sum}, "sum"),
285 (@{const_name False}, "False"),
286 (@{const_name True}, "True"),
287 (@{const_name Not}, "Not"),
288 (@{const_name conj}, "conj"),
289 (@{const_name disj}, "disj"),
290 (@{const_name implies}, "implies"),
291 (@{const_name HOL.eq}, "equal"),
292 (@{const_name If}, "If"),
293 (@{const_name Set.member}, "member"),
294 (@{const_name Meson.COMBI}, "COMBI"),
295 (@{const_name Meson.COMBK}, "COMBK"),
296 (@{const_name Meson.COMBB}, "COMBB"),
297 (@{const_name Meson.COMBC}, "COMBC"),
298 (@{const_name Meson.COMBS}, "COMBS")]
300 |> fold (Symtab.update o swap o snd o snd o snd) proxy_table
302 (* Invert the table of translations between Isabelle and ATPs. *)
303 val const_trans_table_inv =
304 const_trans_table |> Symtab.dest |> map swap |> Symtab.make
305 val const_trans_table_unprox =
307 |> fold (fn (_, (isa, (_, (_, atp)))) => Symtab.update (atp, isa)) proxy_table
309 val invert_const = perhaps (Symtab.lookup const_trans_table_inv)
310 val unproxify_const = perhaps (Symtab.lookup const_trans_table_unprox)
313 case Symtab.lookup const_trans_table c of
317 (*Remove the initial ' character from a type variable, if it is present*)
318 fun trim_type_var s =
319 if s <> "" andalso String.sub(s,0) = #"'" then String.extract(s,1,NONE)
320 else raise Fail ("trim_type: Malformed type variable encountered: " ^ s)
322 fun ascii_of_indexname (v,0) = ascii_of v
323 | ascii_of_indexname (v,i) = ascii_of v ^ "_" ^ string_of_int i
325 fun make_bound_var x = bound_var_prefix ^ ascii_of x
326 fun make_schematic_var v = schematic_var_prefix ^ ascii_of_indexname v
327 fun make_fixed_var x = fixed_var_prefix ^ ascii_of x
329 fun make_schematic_type_var (x,i) =
330 tvar_prefix ^ (ascii_of_indexname (trim_type_var x, i))
331 fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (trim_type_var x))
333 (* HOL.eq MUST BE "equal" because it's built into ATPs. *)
334 fun make_fixed_const @{const_name HOL.eq} = "equal"
335 | make_fixed_const c = const_prefix ^ lookup_const c
337 fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
339 fun make_type_class clas = class_prefix ^ ascii_of clas
341 fun new_skolem_var_name_from_const s =
342 let val ss = s |> space_explode Long_Name.separator in
343 nth ss (length ss - 2)
346 (* The number of type arguments of a constant, zero if it's monomorphic. For
347 (instances of) Skolem pseudoconstants, this information is encoded in the
349 fun num_type_args thy s =
350 if String.isPrefix skolem_const_prefix s then
351 s |> space_explode Long_Name.separator |> List.last |> Int.fromString |> the
353 (s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
355 (* These are either simplified away by "Meson.presimplify" (most of the time) or
356 handled specially via "fFalse", "fTrue", ..., "fequal". *)
357 val atp_irrelevant_consts =
358 [@{const_name False}, @{const_name True}, @{const_name Not},
359 @{const_name conj}, @{const_name disj}, @{const_name implies},
360 @{const_name HOL.eq}, @{const_name If}, @{const_name Let}]
362 val atp_monomorph_bad_consts =
363 atp_irrelevant_consts @
364 (* These are ignored anyway by the relevance filter (unless they appear in
365 higher-order places) but not by the monomorphizer. *)
366 [@{const_name all}, @{const_name "==>"}, @{const_name "=="},
367 @{const_name Trueprop}, @{const_name All}, @{const_name Ex},
368 @{const_name Ex1}, @{const_name Ball}, @{const_name Bex}]
370 fun add_schematic_const (x as (_, T)) =
371 Monomorph.typ_has_tvars T ? Symtab.insert_list (op =) x
372 val add_schematic_consts_of =
373 Term.fold_aterms (fn Const (x as (s, _)) =>
374 not (member (op =) atp_monomorph_bad_consts s)
375 ? add_schematic_const x
377 fun atp_schematic_consts_of t = add_schematic_consts_of t Symtab.empty
379 (** Definitions and functions for FOL clauses and formulas for TPTP **)
381 (* The first component is the type class; the second is a "TVar" or "TFree". *)
382 datatype type_literal =
383 TyLitVar of name * name |
384 TyLitFree of name * name
387 (** Isabelle arities **)
389 datatype arity_literal =
390 TConsLit of name * name * name list |
391 TVarLit of name * name
394 | gen_TVars n = ("T_" ^ string_of_int n) :: gen_TVars (n-1)
396 fun pack_sort (_,[]) = []
397 | pack_sort (tvar, "HOL.type" :: srt) =
398 pack_sort (tvar, srt) (* IGNORE sort "type" *)
399 | pack_sort (tvar, cls :: srt) =
400 (`make_type_class cls, `I tvar) :: pack_sort (tvar, srt)
404 prem_lits: arity_literal list,
405 concl_lits: arity_literal}
407 (* Arity of type constructor "tcon :: (arg1, ..., argN) res" *)
408 fun make_axiom_arity_clause (tcons, name, (cls, args)) =
410 val tvars = gen_TVars (length args)
411 val tvars_srts = ListPair.zip (tvars, args)
414 prem_lits = map TVarLit (union_all (map pack_sort tvars_srts)),
415 concl_lits = TConsLit (`make_type_class cls,
416 `make_fixed_type_const tcons,
420 fun arity_clause _ _ (_, []) = []
421 | arity_clause seen n (tcons, ("HOL.type",_)::ars) = (*ignore*)
422 arity_clause seen n (tcons,ars)
423 | arity_clause seen n (tcons, (ar as (class,_)) :: ars) =
424 if member (op =) seen class then (*multiple arities for the same tycon, class pair*)
425 make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class ^ "_" ^ string_of_int n, ar) ::
426 arity_clause seen (n+1) (tcons,ars)
428 make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class, ar) ::
429 arity_clause (class::seen) n (tcons,ars)
431 fun multi_arity_clause [] = []
432 | multi_arity_clause ((tcons, ars) :: tc_arlists) =
433 arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
435 (*Generate all pairs (tycon,class,sorts) such that tycon belongs to class in theory thy
436 provided its arguments have the corresponding sorts.*)
437 fun type_class_pairs thy tycons classes =
439 val alg = Sign.classes_of thy
440 fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
441 fun add_class tycon class =
442 cons (class, domain_sorts tycon class)
443 handle Sorts.CLASS_ERROR _ => I
444 fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
445 in map try_classes tycons end
447 (*Proving one (tycon, class) membership may require proving others, so iterate.*)
448 fun iter_type_class_pairs _ _ [] = ([], [])
449 | iter_type_class_pairs thy tycons classes =
450 let val cpairs = type_class_pairs thy tycons classes
451 val newclasses = union_all (union_all (union_all (map (map #2 o #2) cpairs)))
452 |> subtract (op =) classes |> subtract (op =) HOLogic.typeS
453 val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
454 in (union (op =) classes' classes, union (op =) cpairs' cpairs) end
456 fun make_arity_clauses thy tycons =
457 iter_type_class_pairs thy tycons ##> multi_arity_clause
460 (** Isabelle class relations **)
462 type class_rel_clause =
467 (*Generate all pairs (sub,super) such that sub is a proper subclass of super in theory thy.*)
468 fun class_pairs _ [] _ = []
469 | class_pairs thy subs supers =
471 val class_less = Sorts.class_less (Sign.classes_of thy)
472 fun add_super sub super = class_less (sub, super) ? cons (sub, super)
473 fun add_supers sub = fold (add_super sub) supers
474 in fold add_supers subs [] end
476 fun make_class_rel_clause (sub,super) =
477 {name = sub ^ "_" ^ super,
478 subclass = `make_type_class sub,
479 superclass = `make_type_class super}
481 fun make_class_rel_clauses thy subs supers =
482 map make_class_rel_clause (class_pairs thy subs supers)
485 CombConst of name * typ * typ list |
486 CombVar of name * typ |
487 CombApp of combterm * combterm
489 fun combtyp_of (CombConst (_, T, _)) = T
490 | combtyp_of (CombVar (_, T)) = T
491 | combtyp_of (CombApp (t1, _)) = snd (dest_funT (combtyp_of t1))
493 (*gets the head of a combinator application, along with the list of arguments*)
494 fun strip_combterm_comb u =
495 let fun stripc (CombApp(t,u), ts) = stripc (t, u::ts)
499 fun atyps_of T = fold_atyps (insert (op =)) T []
501 fun new_skolem_const_name s num_T_args =
502 [new_skolem_const_prefix, s, string_of_int num_T_args]
503 |> space_implode Long_Name.separator
505 (* Converts a term (with combinators) into a combterm. Also accumulates sort
507 fun combterm_from_term thy bs (P $ Q) =
509 val (P', P_atomics_Ts) = combterm_from_term thy bs P
510 val (Q', Q_atomics_Ts) = combterm_from_term thy bs Q
511 in (CombApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
512 | combterm_from_term thy _ (Const (c, T)) =
515 (if String.isPrefix old_skolem_const_prefix c then
516 [] |> Term.add_tvarsT T |> map TVar
518 (c, T) |> Sign.const_typargs thy)
519 val c' = CombConst (`make_fixed_const c, T, tvar_list)
520 in (c', atyps_of T) end
521 | combterm_from_term _ _ (Free (v, T)) =
522 (CombConst (`make_fixed_var v, T, []), atyps_of T)
523 | combterm_from_term _ _ (Var (v as (s, _), T)) =
524 (if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
526 val Ts = T |> strip_type |> swap |> op ::
527 val s' = new_skolem_const_name s (length Ts)
528 in CombConst (`make_fixed_const s', T, Ts) end
530 CombVar ((make_schematic_var v, s), T), atyps_of T)
531 | combterm_from_term _ bs (Bound j) =
533 |> (fn (s, T) => (CombConst (`make_bound_var s, T, []), atyps_of T))
534 | combterm_from_term _ _ (Abs _) = raise Fail "HOL clause: Abs"
536 datatype locality = General | Intro | Elim | Simp | Local | Assum | Chained
538 (* (quasi-)underapproximation of the truth *)
539 fun is_locality_global Local = false
540 | is_locality_global Assum = false
541 | is_locality_global Chained = false
542 | is_locality_global _ = true
544 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
545 datatype type_level =
546 All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
547 datatype type_heaviness = Heavyweight | Lightweight
550 Simple_Types of type_level |
551 Preds of polymorphism * type_level * type_heaviness |
552 Tags of polymorphism * type_level * type_heaviness
554 fun try_unsuffixes ss s =
555 fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
557 fun type_sys_from_string s =
558 (case try (unprefix "poly_") s of
559 SOME s => (SOME Polymorphic, s)
561 case try (unprefix "mono_") s of
562 SOME s => (SOME Monomorphic, s)
564 case try (unprefix "mangled_") s of
565 SOME s => (SOME Mangled_Monomorphic, s)
568 (* "_query" and "_bang" are for the ASCII-challenged Mirabelle. *)
569 case try_unsuffixes ["?", "_query"] s of
570 SOME s => (Nonmonotonic_Types, s)
572 case try_unsuffixes ["!", "_bang"] s of
573 SOME s => (Finite_Types, s)
574 | NONE => (All_Types, s))
576 case try (unsuffix "_heavy") s of
577 SOME s => (Heavyweight, s)
578 | NONE => (Lightweight, s))
579 |> (fn (poly, (level, (heaviness, core))) =>
580 case (core, (poly, level, heaviness)) of
581 ("simple", (NONE, _, Lightweight)) => Simple_Types level
582 | ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
583 | ("tags", (SOME Polymorphic, All_Types, _)) =>
584 Tags (Polymorphic, All_Types, heaviness)
585 | ("tags", (SOME Polymorphic, _, _)) =>
586 (* The actual light encoding is very unsound. *)
587 Tags (Polymorphic, level, Heavyweight)
588 | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
589 | ("args", (SOME poly, All_Types (* naja *), Lightweight)) =>
590 Preds (poly, Const_Arg_Types, Lightweight)
591 | ("erased", (NONE, All_Types (* naja *), Lightweight)) =>
592 Preds (Polymorphic, No_Types, Lightweight)
593 | _ => raise Same.SAME)
594 handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
596 fun polymorphism_of_type_sys (Simple_Types _) = Mangled_Monomorphic
597 | polymorphism_of_type_sys (Preds (poly, _, _)) = poly
598 | polymorphism_of_type_sys (Tags (poly, _, _)) = poly
600 fun level_of_type_sys (Simple_Types level) = level
601 | level_of_type_sys (Preds (_, level, _)) = level
602 | level_of_type_sys (Tags (_, level, _)) = level
604 fun heaviness_of_type_sys (Simple_Types _) = Heavyweight
605 | heaviness_of_type_sys (Preds (_, _, heaviness)) = heaviness
606 | heaviness_of_type_sys (Tags (_, _, heaviness)) = heaviness
608 fun is_type_level_virtually_sound level =
609 level = All_Types orelse level = Nonmonotonic_Types
610 val is_type_sys_virtually_sound =
611 is_type_level_virtually_sound o level_of_type_sys
613 fun is_type_level_fairly_sound level =
614 is_type_level_virtually_sound level orelse level = Finite_Types
615 val is_type_sys_fairly_sound = is_type_level_fairly_sound o level_of_type_sys
617 fun is_setting_higher_order THF (Simple_Types _) = true
618 | is_setting_higher_order _ _ = false
620 fun choose_format formats (Simple_Types level) =
621 if member (op =) formats THF then (THF, Simple_Types level)
622 else if member (op =) formats TFF then (TFF, Simple_Types level)
623 else choose_format formats (Preds (Mangled_Monomorphic, level, Heavyweight))
624 | choose_format formats type_sys =
627 (CNF_UEQ, case type_sys of
629 (if is_type_sys_fairly_sound type_sys then Preds else Tags)
632 | format => (format, type_sys))
634 type translated_formula =
638 combformula: (name, typ, combterm) formula,
639 atomic_types: typ list}
641 fun update_combformula f ({name, locality, kind, combformula, atomic_types}
642 : translated_formula) =
643 {name = name, locality = locality, kind = kind, combformula = f combformula,
644 atomic_types = atomic_types} : translated_formula
646 fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
648 val type_instance = Sign.typ_instance o Proof_Context.theory_of
650 fun insert_type ctxt get_T x xs =
651 let val T = get_T x in
652 if exists (curry (type_instance ctxt) T o get_T) xs then xs
653 else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
656 (* The Booleans indicate whether all type arguments should be kept. *)
657 datatype type_arg_policy =
658 Explicit_Type_Args of bool |
659 Mangled_Type_Args of bool |
662 fun should_drop_arg_type_args (Simple_Types _) =
663 false (* since TFF doesn't support overloading *)
664 | should_drop_arg_type_args type_sys =
665 level_of_type_sys type_sys = All_Types andalso
666 heaviness_of_type_sys type_sys = Heavyweight
668 fun general_type_arg_policy (Tags (_, All_Types, Heavyweight)) = No_Type_Args
669 | general_type_arg_policy type_sys =
670 if level_of_type_sys type_sys = No_Types then
672 else if polymorphism_of_type_sys type_sys = Mangled_Monomorphic then
673 Mangled_Type_Args (should_drop_arg_type_args type_sys)
675 Explicit_Type_Args (should_drop_arg_type_args type_sys)
677 fun type_arg_policy type_sys s =
678 if s = @{const_name HOL.eq} orelse
679 (s = app_op_name andalso level_of_type_sys type_sys = Const_Arg_Types) then
681 else if s = type_tag_name then
682 Explicit_Type_Args false
684 general_type_arg_policy type_sys
686 (*Make literals for sorted type variables*)
687 fun generic_sorts_on_type (_, []) = []
688 | generic_sorts_on_type ((x, i), s :: ss) =
689 generic_sorts_on_type ((x, i), ss)
690 |> (if s = the_single @{sort HOL.type} then
693 cons (TyLitFree (`make_type_class s, `make_fixed_type_var x))
695 cons (TyLitVar (`make_type_class s,
696 (make_schematic_type_var (x, i), x))))
697 fun sorts_on_tfree (TFree (s, S)) = generic_sorts_on_type ((s, ~1), S)
698 | sorts_on_tfree _ = []
699 fun sorts_on_tvar (TVar z) = generic_sorts_on_type z
700 | sorts_on_tvar _ = []
702 (* Given a list of sorted type variables, return a list of type literals. *)
703 fun raw_type_literals_for_types Ts =
704 union_all (map sorts_on_tfree Ts @ map sorts_on_tvar Ts)
706 fun type_literals_for_types type_sys sorts_on_typ Ts =
707 if level_of_type_sys type_sys = No_Types then []
708 else union_all (map sorts_on_typ Ts)
710 fun mk_aconns c phis =
711 let val (phis', phi') = split_last phis in
712 fold_rev (mk_aconn c) phis' phi'
714 fun mk_ahorn [] phi = phi
715 | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
716 fun mk_aquant _ [] phi = phi
717 | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
718 if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
719 | mk_aquant q xs phi = AQuant (q, xs, phi)
721 fun close_universally atom_vars phi =
723 fun formula_vars bounds (AQuant (_, xs, phi)) =
724 formula_vars (map fst xs @ bounds) phi
725 | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
726 | formula_vars bounds (AAtom tm) =
727 union (op =) (atom_vars tm []
728 |> filter_out (member (op =) bounds o fst))
729 in mk_aquant AForall (formula_vars [] phi []) phi end
731 fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
732 | combterm_vars (CombConst _) = I
733 | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
734 fun close_combformula_universally phi = close_universally combterm_vars phi
736 fun term_vars (ATerm (name as (s, _), tms)) =
737 is_tptp_variable s ? insert (op =) (name, NONE) #> fold term_vars tms
738 fun close_formula_universally phi = close_universally term_vars phi
740 val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
741 val homo_infinite_type = Type (homo_infinite_type_name, [])
743 fun fo_term_from_typ format type_sys =
745 fun term (Type (s, Ts)) =
746 ATerm (case (is_setting_higher_order format type_sys, s) of
747 (true, @{type_name bool}) => `I tptp_bool_type
748 | (true, @{type_name fun}) => `I tptp_fun_type
749 | _ => if s = homo_infinite_type_name andalso
750 (format = TFF orelse format = THF) then
751 `I tptp_individual_type
753 `make_fixed_type_const s,
755 | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
756 | term (TVar ((x as (s, _)), _)) =
757 ATerm ((make_schematic_type_var x, s), [])
760 (* This shouldn't clash with anything else. *)
761 val mangled_type_sep = "\000"
763 fun generic_mangled_type_name f (ATerm (name, [])) = f name
764 | generic_mangled_type_name f (ATerm (name, tys)) =
765 f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
768 val bool_atype = AType (`I tptp_bool_type)
770 fun make_simple_type s =
771 if s = tptp_bool_type orelse s = tptp_fun_type orelse
772 s = tptp_individual_type then
775 simple_type_prefix ^ ascii_of s
777 fun ho_type_from_fo_term format type_sys pred_sym ary =
780 AType ((make_simple_type (generic_mangled_type_name fst ty),
781 generic_mangled_type_name snd ty))
782 fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
783 fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
784 | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
785 fun to_ho (ty as ATerm ((s, _), tys)) =
786 if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
787 in if is_setting_higher_order format type_sys then to_ho else to_fo ary end
789 fun mangled_type format type_sys pred_sym ary =
790 ho_type_from_fo_term format type_sys pred_sym ary
791 o fo_term_from_typ format type_sys
793 fun mangled_const_name format type_sys T_args (s, s') =
795 val ty_args = map (fo_term_from_typ format type_sys) T_args
796 fun type_suffix f g =
797 fold_rev (curry (op ^) o g o prefix mangled_type_sep
798 o generic_mangled_type_name f) ty_args ""
799 in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
801 val parse_mangled_ident =
802 Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
804 fun parse_mangled_type x =
806 -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
808 and parse_mangled_types x =
809 (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
811 fun unmangled_type s =
812 s |> suffix ")" |> raw_explode
813 |> Scan.finite Symbol.stopper
814 (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
815 quote s)) parse_mangled_type))
818 val unmangled_const_name = space_explode mangled_type_sep #> hd
819 fun unmangled_const s =
820 let val ss = space_explode mangled_type_sep s in
821 (hd ss, map unmangled_type (tl ss))
824 fun introduce_proxies format type_sys =
826 fun intro top_level (CombApp (tm1, tm2)) =
827 CombApp (intro top_level tm1, intro false tm2)
828 | intro top_level (CombConst (name as (s, _), T, T_args)) =
829 (case proxify_const s of
831 if top_level orelse is_setting_higher_order format type_sys then
832 case (top_level, s) of
833 (_, "c_False") => (`I tptp_false, [])
834 | (_, "c_True") => (`I tptp_true, [])
835 | (false, "c_Not") => (`I tptp_not, [])
836 | (false, "c_conj") => (`I tptp_and, [])
837 | (false, "c_disj") => (`I tptp_or, [])
838 | (false, "c_implies") => (`I tptp_implies, [])
840 if is_tptp_equal s then (`I tptp_equal, [])
841 else (proxy_base |>> prefix const_prefix, T_args)
844 (proxy_base |>> prefix const_prefix, T_args)
845 | NONE => (name, T_args))
846 |> (fn (name, T_args) => CombConst (name, T, T_args))
850 fun combformula_from_prop thy format type_sys eq_as_iff =
852 fun do_term bs t atomic_types =
853 combterm_from_term thy bs (Envir.eta_contract t)
854 |>> (introduce_proxies format type_sys #> AAtom)
855 ||> union (op =) atomic_types
856 fun do_quant bs q s T t' =
857 let val s = Name.variant (map fst bs) s in
858 do_formula ((s, T) :: bs) t'
859 #>> mk_aquant q [(`make_bound_var s, SOME T)]
861 and do_conn bs c t1 t2 =
862 do_formula bs t1 ##>> do_formula bs t2 #>> uncurry (mk_aconn c)
863 and do_formula bs t =
865 @{const Trueprop} $ t1 => do_formula bs t1
866 | @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
867 | Const (@{const_name All}, _) $ Abs (s, T, t') =>
868 do_quant bs AForall s T t'
869 | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
870 do_quant bs AExists s T t'
871 | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
872 | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
873 | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
874 | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
875 if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
879 fun presimplify_term ctxt =
880 Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
881 #> Meson.presimplify ctxt
884 fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
885 fun conceal_bounds Ts t =
886 subst_bounds (map (Free o apfst concealed_bound_name)
887 (0 upto length Ts - 1 ~~ Ts), t)
888 fun reveal_bounds Ts =
889 subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
890 (0 upto length Ts - 1 ~~ Ts))
892 fun extensionalize_term ctxt t =
893 let val thy = Proof_Context.theory_of ctxt in
894 t |> cterm_of thy |> Meson.extensionalize_conv ctxt
895 |> prop_of |> Logic.dest_equals |> snd
898 fun introduce_combinators_in_term ctxt kind t =
899 let val thy = Proof_Context.theory_of ctxt in
900 if Meson.is_fol_term thy t then
906 @{const Not} $ t1 => @{const Not} $ aux Ts t1
907 | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
908 t0 $ Abs (s, T, aux (T :: Ts) t')
909 | (t0 as Const (@{const_name All}, _)) $ t1 =>
910 aux Ts (t0 $ eta_expand Ts t1 1)
911 | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
912 t0 $ Abs (s, T, aux (T :: Ts) t')
913 | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
914 aux Ts (t0 $ eta_expand Ts t1 1)
915 | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
916 | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
917 | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
918 | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
920 t0 $ aux Ts t1 $ aux Ts t2
921 | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
924 t |> conceal_bounds Ts
925 |> Envir.eta_contract
927 |> Meson_Clausify.introduce_combinators_in_cterm
928 |> prop_of |> Logic.dest_equals |> snd
930 val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
931 in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
933 (* A type variable of sort "{}" will make abstraction fail. *)
934 if kind = Conjecture then HOLogic.false_const
935 else HOLogic.true_const
938 (* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
939 same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
942 fun aux (t $ u) = aux t $ aux u
943 | aux (Abs (s, T, t)) = Abs (s, T, aux t)
944 | aux (Var ((s, i), T)) =
945 Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
947 in t |> exists_subterm is_Var t ? aux end
949 fun preprocess_prop ctxt presimp kind t =
951 val thy = Proof_Context.theory_of ctxt
952 val t = t |> Envir.beta_eta_contract
953 |> transform_elim_prop
954 |> Object_Logic.atomize_term thy
955 val need_trueprop = (fastype_of t = @{typ bool})
957 t |> need_trueprop ? HOLogic.mk_Trueprop
958 |> Raw_Simplifier.rewrite_term thy (Meson.unfold_set_const_simps ctxt) []
959 |> extensionalize_term ctxt
960 |> presimp ? presimplify_term ctxt
961 |> perhaps (try (HOLogic.dest_Trueprop))
962 |> introduce_combinators_in_term ctxt kind
965 (* making fact and conjecture formulas *)
966 fun make_formula thy format type_sys eq_as_iff name loc kind t =
968 val (combformula, atomic_types) =
969 combformula_from_prop thy format type_sys eq_as_iff t []
971 {name = name, locality = loc, kind = kind, combformula = combformula,
972 atomic_types = atomic_types}
975 fun make_fact ctxt format type_sys keep_trivial eq_as_iff preproc presimp
977 let val thy = Proof_Context.theory_of ctxt in
979 t |> preproc ? preprocess_prop ctxt presimp Axiom
980 |> make_formula thy format type_sys eq_as_iff name loc Axiom) of
982 formula as {combformula = AAtom (CombConst ((s, _), _, _)), ...}) =>
983 if s = tptp_true then NONE else SOME formula
984 | (_, formula) => SOME formula
987 fun make_conjecture ctxt format prem_kind type_sys preproc ts =
989 val thy = Proof_Context.theory_of ctxt
990 val last = length ts - 1
992 map2 (fn j => fn t =>
994 val (kind, maybe_negate) =
999 if prem_kind = Conjecture then update_combformula mk_anot
1002 t |> preproc ? (preprocess_prop ctxt true kind #> freeze_term)
1003 |> make_formula thy format type_sys (format <> CNF)
1004 (string_of_int j) General kind
1010 (** Finite and infinite type inference **)
1012 fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
1013 | deep_freeze_atyp T = T
1014 val deep_freeze_type = map_atyps deep_freeze_atyp
1016 (* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
1017 dangerous because their "exhaust" properties can easily lead to unsound ATP
1018 proofs. On the other hand, all HOL infinite types can be given the same
1019 models in first-order logic (via Löwenheim-Skolem). *)
1021 fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
1022 exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
1023 | should_encode_type _ _ All_Types _ = true
1024 | should_encode_type ctxt _ Finite_Types T = is_type_surely_finite ctxt T
1025 | should_encode_type _ _ _ _ = false
1027 fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
1028 should_predicate_on_var T =
1029 (heaviness = Heavyweight orelse should_predicate_on_var ()) andalso
1030 should_encode_type ctxt nonmono_Ts level T
1031 | should_predicate_on_type _ _ _ _ _ = false
1033 fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
1034 String.isPrefix bound_var_prefix s
1035 | is_var_or_bound_var (CombVar _) = true
1036 | is_var_or_bound_var _ = false
1038 datatype tag_site = Top_Level | Eq_Arg | Elsewhere
1040 fun should_tag_with_type _ _ _ Top_Level _ _ = false
1041 | should_tag_with_type ctxt nonmono_Ts (Tags (_, level, heaviness)) site u T =
1043 Heavyweight => should_encode_type ctxt nonmono_Ts level T
1045 case (site, is_var_or_bound_var u) of
1046 (Eq_Arg, true) => should_encode_type ctxt nonmono_Ts level T
1048 | should_tag_with_type _ _ _ _ _ _ = false
1050 fun homogenized_type ctxt nonmono_Ts level =
1052 val should_encode = should_encode_type ctxt nonmono_Ts level
1053 fun homo 0 T = if should_encode T then T else homo_infinite_type
1054 | homo ary (Type (@{type_name fun}, [T1, T2])) =
1055 homo 0 T1 --> homo (ary - 1) T2
1056 | homo _ _ = raise Fail "expected function type"
1059 (** "hBOOL" and "hAPP" **)
1062 {pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
1064 fun add_combterm_syms_to_table ctxt explicit_apply =
1066 fun consider_var_arity const_T var_T max_ary =
1069 if ary = max_ary orelse type_instance ctxt (var_T, T) orelse
1070 type_instance ctxt (T, var_T) then
1073 iter (ary + 1) (range_type T)
1074 in iter 0 const_T end
1075 fun add_var_or_bound_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1076 if explicit_apply = NONE andalso
1077 (can dest_funT T orelse T = @{typ bool}) then
1079 val bool_vars' = bool_vars orelse body_type T = @{typ bool}
1080 fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
1081 {pred_sym = pred_sym andalso not bool_vars',
1082 min_ary = fold (fn T' => consider_var_arity T' T) types min_ary,
1083 max_ary = max_ary, types = types}
1085 fun_var_Ts |> can dest_funT T ? insert_type ctxt I T
1087 if bool_vars' = bool_vars andalso
1088 pointer_eq (fun_var_Ts', fun_var_Ts) then
1091 ((bool_vars', fun_var_Ts'), Symtab.map (K repair_min_arity) sym_tab)
1095 fun add top_level tm (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1096 let val (head, args) = strip_combterm_comb tm in
1098 CombConst ((s, _), T, _) =>
1099 if String.isPrefix bound_var_prefix s then
1100 add_var_or_bound_var T accum
1102 let val ary = length args in
1103 ((bool_vars, fun_var_Ts),
1104 case Symtab.lookup sym_tab s of
1105 SOME {pred_sym, min_ary, max_ary, types} =>
1108 pred_sym andalso top_level andalso not bool_vars
1109 val types' = types |> insert_type ctxt I T
1111 if is_some explicit_apply orelse
1112 pointer_eq (types', types) then
1115 fold (consider_var_arity T) fun_var_Ts min_ary
1117 Symtab.update (s, {pred_sym = pred_sym,
1118 min_ary = Int.min (ary, min_ary),
1119 max_ary = Int.max (ary, max_ary),
1125 val pred_sym = top_level andalso not bool_vars
1127 case explicit_apply of
1130 | NONE => fold (consider_var_arity T) fun_var_Ts ary
1132 Symtab.update_new (s, {pred_sym = pred_sym,
1133 min_ary = min_ary, max_ary = ary,
1138 | CombVar (_, T) => add_var_or_bound_var T accum
1140 |> fold (add false) args
1143 fun add_fact_syms_to_table ctxt explicit_apply =
1144 fact_lift (formula_fold NONE
1145 (K (add_combterm_syms_to_table ctxt explicit_apply)))
1147 val default_sym_tab_entries : (string * sym_info) list =
1148 (prefixed_predicator_name,
1149 {pred_sym = true, min_ary = 1, max_ary = 1, types = []}) ::
1150 ([tptp_false, tptp_true]
1151 |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []})) @
1152 ([tptp_equal, tptp_old_equal]
1153 |> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = []}))
1155 fun sym_table_for_facts ctxt explicit_apply facts =
1156 ((false, []), Symtab.empty)
1157 |> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
1158 |> fold Symtab.update default_sym_tab_entries
1160 fun min_arity_of sym_tab s =
1161 case Symtab.lookup sym_tab s of
1162 SOME ({min_ary, ...} : sym_info) => min_ary
1164 case strip_prefix_and_unascii const_prefix s of
1166 let val s = s |> unmangled_const_name |> invert_const in
1167 if s = predicator_name then 1
1168 else if s = app_op_name then 2
1169 else if s = type_pred_name then 1
1174 (* True if the constant ever appears outside of the top-level position in
1175 literals, or if it appears with different arities (e.g., because of different
1176 type instantiations). If false, the constant always receives all of its
1177 arguments and is used as a predicate. *)
1178 fun is_pred_sym sym_tab s =
1179 case Symtab.lookup sym_tab s of
1180 SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
1181 pred_sym andalso min_ary = max_ary
1184 val predicator_combconst =
1185 CombConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
1186 fun predicator tm = CombApp (predicator_combconst, tm)
1188 fun introduce_predicators_in_combterm sym_tab tm =
1189 case strip_combterm_comb tm of
1190 (CombConst ((s, _), _, _), _) =>
1191 if is_pred_sym sym_tab s then tm else predicator tm
1192 | _ => predicator tm
1194 fun list_app head args = fold (curry (CombApp o swap)) args head
1196 val app_op = `make_fixed_const app_op_name
1198 fun explicit_app arg head =
1200 val head_T = combtyp_of head
1201 val (arg_T, res_T) = dest_funT head_T
1203 CombConst (app_op, head_T --> head_T, [arg_T, res_T])
1204 in list_app explicit_app [head, arg] end
1205 fun list_explicit_app head args = fold explicit_app args head
1207 fun introduce_explicit_apps_in_combterm sym_tab =
1210 case strip_combterm_comb tm of
1211 (head as CombConst ((s, _), _, _), args) =>
1213 |> chop (min_arity_of sym_tab s)
1215 |-> list_explicit_app
1216 | (head, args) => list_explicit_app head (map aux args)
1219 fun chop_fun 0 T = ([], T)
1220 | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
1221 chop_fun (n - 1) ran_T |>> cons dom_T
1222 | chop_fun _ _ = raise Fail "unexpected non-function"
1224 fun filter_type_args _ _ _ [] = []
1225 | filter_type_args thy s arity T_args =
1227 (* will throw "TYPE" for pseudo-constants *)
1228 val U = if s = app_op_name then
1229 @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
1231 s |> Sign.the_const_type thy
1233 case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
1236 let val U_args = (s, U) |> Sign.const_typargs thy in
1238 |> map_filter (fn (U, T) =>
1239 if member (op =) res_U_vars (dest_TVar U) then
1245 handle TYPE _ => T_args
1247 fun enforce_type_arg_policy_in_combterm ctxt format type_sys =
1249 val thy = Proof_Context.theory_of ctxt
1250 fun aux arity (CombApp (tm1, tm2)) =
1251 CombApp (aux (arity + 1) tm1, aux 0 tm2)
1252 | aux arity (CombConst (name as (s, _), T, T_args)) =
1253 (case strip_prefix_and_unascii const_prefix s of
1254 NONE => (name, T_args)
1257 val s'' = invert_const s''
1258 fun filtered_T_args false = T_args
1259 | filtered_T_args true = filter_type_args thy s'' arity T_args
1261 case type_arg_policy type_sys s'' of
1262 Explicit_Type_Args drop_args =>
1263 (name, filtered_T_args drop_args)
1264 | Mangled_Type_Args drop_args =>
1265 (mangled_const_name format type_sys (filtered_T_args drop_args)
1267 | No_Type_Args => (name, [])
1269 |> (fn (name, T_args) => CombConst (name, T, T_args))
1273 fun repair_combterm ctxt format type_sys sym_tab =
1274 not (is_setting_higher_order format type_sys)
1275 ? (introduce_explicit_apps_in_combterm sym_tab
1276 #> introduce_predicators_in_combterm sym_tab)
1277 #> enforce_type_arg_policy_in_combterm ctxt format type_sys
1278 fun repair_fact ctxt format type_sys sym_tab =
1279 update_combformula (formula_map
1280 (repair_combterm ctxt format type_sys sym_tab))
1282 (** Helper facts **)
1284 (* The Boolean indicates that a fairly sound type encoding is needed. *)
1286 [(("COMBI", false), @{thms Meson.COMBI_def}),
1287 (("COMBK", false), @{thms Meson.COMBK_def}),
1288 (("COMBB", false), @{thms Meson.COMBB_def}),
1289 (("COMBC", false), @{thms Meson.COMBC_def}),
1290 (("COMBS", false), @{thms Meson.COMBS_def}),
1292 (* This is a lie: Higher-order equality doesn't need a sound type encoding.
1293 However, this is done so for backward compatibility: Including the
1294 equality helpers by default in Metis breaks a few existing proofs. *)
1295 @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1296 fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1297 (("fFalse", false), [@{lemma "~ fFalse" by (unfold fFalse_def) fast}]),
1298 (("fFalse", true), @{thms True_or_False}),
1299 (("fTrue", false), [@{lemma "fTrue" by (unfold fTrue_def) fast}]),
1300 (("fTrue", true), @{thms True_or_False}),
1302 @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1303 fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1305 @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
1306 by (unfold fconj_def) fast+}),
1308 @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
1309 by (unfold fdisj_def) fast+}),
1310 (("fimplies", false),
1311 @{lemma "P | fimplies P Q" "~ Q | fimplies P Q" "~ fimplies P Q | ~ P | Q"
1312 by (unfold fimplies_def) fast+}),
1313 (("If", true), @{thms if_True if_False True_or_False})]
1314 |> map (apsnd (map zero_var_indexes))
1316 val type_tag = `make_fixed_const type_tag_name
1318 fun type_tag_idempotence_fact () =
1320 fun var s = ATerm (`I s, [])
1321 fun tag tm = ATerm (type_tag, [var "T", tm])
1322 val tagged_a = tag (var "A")
1324 Formula (type_tag_idempotence_helper_name, Axiom,
1325 AAtom (ATerm (`I tptp_equal, [tag tagged_a, tagged_a]))
1326 |> close_formula_universally, simp_info, NONE)
1329 fun should_specialize_helper type_sys t =
1330 case general_type_arg_policy type_sys of
1331 Mangled_Type_Args _ => not (null (Term.hidden_polymorphism t))
1334 fun helper_facts_for_sym ctxt format type_sys (s, {types, ...} : sym_info) =
1335 case strip_prefix_and_unascii const_prefix s of
1338 val thy = Proof_Context.theory_of ctxt
1339 val unmangled_s = mangled_s |> unmangled_const_name
1340 fun dub_and_inst needs_fairly_sound (th, j) =
1341 ((unmangled_s ^ "_" ^ string_of_int j ^
1342 (if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^
1343 (if needs_fairly_sound then typed_helper_suffix
1344 else untyped_helper_suffix),
1346 let val t = th |> prop_of in
1347 t |> should_specialize_helper type_sys t
1349 [T] => specialize_type thy (invert_const unmangled_s, T)
1353 map_filter (make_fact ctxt format type_sys false false false false)
1354 val fairly_sound = is_type_sys_fairly_sound type_sys
1357 |> maps (fn ((helper_s, needs_fairly_sound), ths) =>
1358 if helper_s <> unmangled_s orelse
1359 (needs_fairly_sound andalso not fairly_sound) then
1362 ths ~~ (1 upto length ths)
1363 |> map (dub_and_inst needs_fairly_sound)
1367 fun helper_facts_for_sym_table ctxt format type_sys sym_tab =
1368 Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_sys) sym_tab
1371 (***************************************************************)
1372 (* Type Classes Present in the Axiom or Conjecture Clauses *)
1373 (***************************************************************)
1375 fun set_insert (x, s) = Symtab.update (x, ()) s
1377 fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
1379 (* Remove this trivial type class (FIXME: similar code elsewhere) *)
1380 fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
1382 fun classes_of_terms get_Ts =
1383 map (map snd o get_Ts)
1384 #> List.foldl add_classes Symtab.empty
1385 #> delete_type #> Symtab.keys
1387 val tfree_classes_of_terms = classes_of_terms OldTerm.term_tfrees
1388 val tvar_classes_of_terms = classes_of_terms OldTerm.term_tvars
1390 (*fold type constructors*)
1391 fun fold_type_constrs f (Type (a, Ts)) x =
1392 fold (fold_type_constrs f) Ts (f (a,x))
1393 | fold_type_constrs _ _ x = x
1395 (*Type constructors used to instantiate overloaded constants are the only ones needed.*)
1396 fun add_type_constrs_in_term thy =
1398 fun add (Const (@{const_name Meson.skolem}, _) $ _) = I
1399 | add (t $ u) = add t #> add u
1400 | add (Const (x as (s, _))) =
1401 if String.isPrefix skolem_const_prefix s then I
1402 else x |> Sign.const_typargs thy |> fold (fold_type_constrs set_insert)
1403 | add (Abs (_, _, u)) = add u
1407 fun type_constrs_of_terms thy ts =
1408 Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty)
1410 fun translate_formulas ctxt format prem_kind type_sys preproc hyp_ts concl_t
1413 val thy = Proof_Context.theory_of ctxt
1414 val fact_ts = facts |> map snd
1415 val (facts, fact_names) =
1416 facts |> map (fn (name, t) =>
1418 |> make_fact ctxt format type_sys false true true true
1420 |> map_filter (try (apfst the))
1422 (* Remove existing facts from the conjecture, as this can dramatically
1423 boost an ATP's performance (for some reason). *)
1426 |> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t)
1427 val goal_t = Logic.list_implies (hyp_ts, concl_t)
1428 val all_ts = goal_t :: fact_ts
1429 val subs = tfree_classes_of_terms all_ts
1430 val supers = tvar_classes_of_terms all_ts
1431 val tycons = type_constrs_of_terms thy all_ts
1434 |> make_conjecture ctxt format prem_kind type_sys preproc
1435 val (supers', arity_clauses) =
1436 if level_of_type_sys type_sys = No_Types then ([], [])
1437 else make_arity_clauses thy tycons supers
1438 val class_rel_clauses = make_class_rel_clauses thy subs supers'
1440 (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
1443 fun fo_literal_from_type_literal (TyLitVar (class, name)) =
1444 (true, ATerm (class, [ATerm (name, [])]))
1445 | fo_literal_from_type_literal (TyLitFree (class, name)) =
1446 (true, ATerm (class, [ATerm (name, [])]))
1448 fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
1450 val type_pred = `make_fixed_const type_pred_name
1452 fun type_pred_combterm ctxt format type_sys T tm =
1453 CombApp (CombConst (type_pred, T --> @{typ bool}, [T])
1454 |> enforce_type_arg_policy_in_combterm ctxt format type_sys, tm)
1456 fun var_occurs_positively_naked_in_term _ (SOME false) _ accum = accum
1457 | var_occurs_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
1458 accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
1459 fun is_var_nonmonotonic_in_formula _ _ (SOME false) _ = false
1460 | is_var_nonmonotonic_in_formula pos phi _ name =
1461 formula_fold pos (var_occurs_positively_naked_in_term name) phi false
1463 fun mk_const_aterm format type_sys x T_args args =
1464 ATerm (x, map (fo_term_from_typ format type_sys) T_args @ args)
1466 fun tag_with_type ctxt format nonmono_Ts type_sys T tm =
1467 CombConst (type_tag, T --> T, [T])
1468 |> enforce_type_arg_policy_in_combterm ctxt format type_sys
1469 |> term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
1470 |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
1471 and term_from_combterm ctxt format nonmono_Ts type_sys =
1475 val (head, args) = strip_combterm_comb u
1476 val (x as (s, _), T_args) =
1478 CombConst (name, _, T_args) => (name, T_args)
1479 | CombVar (name, _) => (name, [])
1480 | CombApp _ => raise Fail "impossible \"CombApp\""
1481 val arg_site = if site = Top_Level andalso is_tptp_equal s then Eq_Arg
1483 val t = mk_const_aterm format type_sys x T_args
1484 (map (aux arg_site) args)
1485 val T = combtyp_of u
1487 t |> (if should_tag_with_type ctxt nonmono_Ts type_sys site u T then
1488 tag_with_type ctxt format nonmono_Ts type_sys T
1493 and formula_from_combformula ctxt format nonmono_Ts type_sys
1494 should_predicate_on_var =
1496 val do_term = term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
1499 Simple_Types level =>
1500 homogenized_type ctxt nonmono_Ts level 0
1501 #> mangled_type format type_sys false 0 #> SOME
1503 fun do_out_of_bound_type pos phi universal (name, T) =
1504 if should_predicate_on_type ctxt nonmono_Ts type_sys
1505 (fn () => should_predicate_on_var pos phi universal name) T then
1507 |> type_pred_combterm ctxt format type_sys T
1508 |> do_term |> AAtom |> SOME
1511 fun do_formula pos (AQuant (q, xs, phi)) =
1513 val phi = phi |> do_formula pos
1514 val universal = Option.map (q = AExists ? not) pos
1516 AQuant (q, xs |> map (apsnd (fn NONE => NONE
1517 | SOME T => do_bound_type T)),
1518 (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
1520 (fn (_, NONE) => NONE
1522 do_out_of_bound_type pos phi universal (s, T))
1526 | do_formula pos (AConn conn) = aconn_map pos do_formula conn
1527 | do_formula _ (AAtom tm) = AAtom (do_term tm)
1528 in do_formula o SOME end
1530 fun bound_tvars type_sys Ts =
1531 mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
1532 (type_literals_for_types type_sys sorts_on_tvar Ts))
1534 fun formula_for_fact ctxt format nonmono_Ts type_sys
1535 ({combformula, atomic_types, ...} : translated_formula) =
1537 |> close_combformula_universally
1538 |> formula_from_combformula ctxt format nonmono_Ts type_sys
1539 is_var_nonmonotonic_in_formula true
1540 |> bound_tvars type_sys atomic_types
1541 |> close_formula_universally
1543 (* Each fact is given a unique fact number to avoid name clashes (e.g., because
1544 of monomorphization). The TPTP explicitly forbids name clashes, and some of
1545 the remote provers might care. *)
1546 fun formula_line_for_fact ctxt format prefix encode freshen nonmono_Ts type_sys
1547 (j, formula as {name, locality, kind, ...}) =
1550 polymorphism_of_type_sys type_sys <> Polymorphic then
1551 string_of_int j ^ "_"
1554 kind, formula_for_fact ctxt format nonmono_Ts type_sys formula, NONE,
1561 fun formula_line_for_class_rel_clause ({name, subclass, superclass, ...}
1562 : class_rel_clause) =
1563 let val ty_arg = ATerm (`I "T", []) in
1564 Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
1565 AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
1566 AAtom (ATerm (superclass, [ty_arg]))])
1567 |> close_formula_universally, intro_info, NONE)
1570 fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
1571 (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
1572 | fo_literal_from_arity_literal (TVarLit (c, sort)) =
1573 (false, ATerm (c, [ATerm (sort, [])]))
1575 fun formula_line_for_arity_clause ({name, prem_lits, concl_lits, ...}
1577 Formula (arity_clause_prefix ^ ascii_of name, Axiom,
1578 mk_ahorn (map (formula_from_fo_literal o apfst not
1579 o fo_literal_from_arity_literal) prem_lits)
1580 (formula_from_fo_literal
1581 (fo_literal_from_arity_literal concl_lits))
1582 |> close_formula_universally, intro_info, NONE)
1584 fun formula_line_for_conjecture ctxt format nonmono_Ts type_sys
1585 ({name, kind, combformula, atomic_types, ...} : translated_formula) =
1586 Formula (conjecture_prefix ^ name, kind,
1587 formula_from_combformula ctxt format nonmono_Ts type_sys
1588 is_var_nonmonotonic_in_formula false
1589 (close_combformula_universally combformula)
1590 |> bound_tvars type_sys atomic_types
1591 |> close_formula_universally, NONE, NONE)
1593 fun free_type_literals type_sys ({atomic_types, ...} : translated_formula) =
1594 atomic_types |> type_literals_for_types type_sys sorts_on_tfree
1595 |> map fo_literal_from_type_literal
1597 fun formula_line_for_free_type j lit =
1598 Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis,
1599 formula_from_fo_literal lit, NONE, NONE)
1600 fun formula_lines_for_free_types type_sys facts =
1602 val litss = map (free_type_literals type_sys) facts
1603 val lits = fold (union (op =)) litss []
1604 in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
1606 (** Symbol declarations **)
1608 fun should_declare_sym type_sys pred_sym s =
1609 is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
1611 Simple_Types _ => true
1612 | Tags (_, _, Lightweight) => true
1613 | _ => not pred_sym)
1615 fun sym_decl_table_for_facts ctxt type_sys repaired_sym_tab (conjs, facts) =
1617 fun add_combterm in_conj tm =
1618 let val (head, args) = strip_combterm_comb tm in
1620 CombConst ((s, s'), T, T_args) =>
1621 let val pred_sym = is_pred_sym repaired_sym_tab s in
1622 if should_declare_sym type_sys pred_sym s then
1623 Symtab.map_default (s, [])
1624 (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
1630 #> fold (add_combterm in_conj) args
1632 fun add_fact in_conj =
1633 fact_lift (formula_fold NONE (K (add_combterm in_conj)))
1636 |> is_type_sys_fairly_sound type_sys
1637 ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
1640 (* These types witness that the type classes they belong to allow infinite
1641 models and hence that any types with these type classes is monotonic. *)
1642 val known_infinite_types =
1643 [@{typ nat}, Type ("Int.int", []), @{typ "nat => bool"}]
1645 (* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
1646 out with monotonicity" paper presented at CADE 2011. *)
1647 fun add_combterm_nonmonotonic_types _ _ (SOME false) _ = I
1648 | add_combterm_nonmonotonic_types ctxt level _
1649 (CombApp (CombApp (CombConst ((s, _), Type (_, [T, _]), _), tm1),
1651 (is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
1653 Nonmonotonic_Types =>
1654 not (is_type_surely_infinite ctxt known_infinite_types T)
1655 | Finite_Types => is_type_surely_finite ctxt T
1656 | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
1657 | add_combterm_nonmonotonic_types _ _ _ _ = I
1658 fun add_fact_nonmonotonic_types ctxt level ({kind, combformula, ...}
1659 : translated_formula) =
1660 formula_fold (SOME (kind <> Conjecture))
1661 (add_combterm_nonmonotonic_types ctxt level) combformula
1662 fun nonmonotonic_types_for_facts ctxt type_sys facts =
1663 let val level = level_of_type_sys type_sys in
1664 if level = Nonmonotonic_Types orelse level = Finite_Types then
1665 [] |> fold (add_fact_nonmonotonic_types ctxt level) facts
1666 (* We must add "bool" in case the helper "True_or_False" is added
1667 later. In addition, several places in the code rely on the list of
1668 nonmonotonic types not being empty. *)
1669 |> insert_type ctxt I @{typ bool}
1674 fun decl_line_for_sym ctxt format nonmono_Ts type_sys s
1675 (s', T_args, T, pred_sym, ary, _) =
1677 val (T_arg_Ts, level) =
1679 Simple_Types level => ([], level)
1680 | _ => (replicate (length T_args) homo_infinite_type, No_Types)
1682 Decl (sym_decl_prefix ^ s, (s, s'),
1683 (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
1684 |> mangled_type format type_sys pred_sym (length T_arg_Ts + ary))
1687 fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
1689 fun formula_line_for_preds_sym_decl ctxt format conj_sym_kind nonmono_Ts
1690 type_sys n s j (s', T_args, T, _, ary, in_conj) =
1692 val (kind, maybe_negate) =
1693 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1695 val (arg_Ts, res_T) = chop_fun ary T
1697 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
1699 bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
1701 arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
1704 Formula (preds_sym_formula_prefix ^ s ^
1705 (if n > 1 then "_" ^ string_of_int j else ""), kind,
1706 CombConst ((s, s'), T, T_args)
1707 |> fold (curry (CombApp o swap)) bounds
1708 |> type_pred_combterm ctxt format type_sys res_T
1709 |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
1710 |> formula_from_combformula ctxt format nonmono_Ts type_sys
1711 (K (K (K (K true)))) true
1712 |> n > 1 ? bound_tvars type_sys (atyps_of T)
1713 |> close_formula_universally
1718 fun formula_lines_for_lightweight_tags_sym_decl ctxt format conj_sym_kind
1719 nonmono_Ts type_sys n s (j, (s', T_args, T, pred_sym, ary, in_conj)) =
1722 lightweight_tags_sym_formula_prefix ^ s ^
1723 (if n > 1 then "_" ^ string_of_int j else "")
1724 val (kind, maybe_negate) =
1725 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1727 val (arg_Ts, res_T) = chop_fun ary T
1729 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
1730 val bounds = bound_names |> map (fn name => ATerm (name, []))
1731 val cst = mk_const_aterm format type_sys (s, s') T_args
1732 val atomic_Ts = atyps_of T
1734 (if pred_sym then AConn (AIff, map AAtom tms)
1735 else AAtom (ATerm (`I tptp_equal, tms)))
1736 |> bound_tvars type_sys atomic_Ts
1737 |> close_formula_universally
1739 val should_encode = should_encode_type ctxt nonmono_Ts All_Types
1740 val tag_with = tag_with_type ctxt format nonmono_Ts type_sys
1741 val add_formula_for_res =
1742 if should_encode res_T then
1743 cons (Formula (ident_base ^ "_res", kind,
1744 eq [tag_with res_T (cst bounds), cst bounds],
1748 fun add_formula_for_arg k =
1749 let val arg_T = nth arg_Ts k in
1750 if should_encode arg_T then
1751 case chop k bounds of
1752 (bounds1, bound :: bounds2) =>
1753 cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
1754 eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
1757 | _ => raise Fail "expected nonempty tail"
1762 [] |> not pred_sym ? add_formula_for_res
1763 |> fold add_formula_for_arg (ary - 1 downto 0)
1766 fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
1768 fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts type_sys
1772 decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_sys s)
1777 decl :: (decls' as _ :: _) =>
1778 let val T = result_type_of_decl decl in
1779 if forall (curry (type_instance ctxt o swap) T
1780 o result_type_of_decl) decls' then
1786 val n = length decls
1789 |> filter (should_predicate_on_type ctxt nonmono_Ts type_sys (K true)
1790 o result_type_of_decl)
1792 (0 upto length decls - 1, decls)
1793 |-> map2 (formula_line_for_preds_sym_decl ctxt format conj_sym_kind
1794 nonmono_Ts type_sys n s)
1796 | Tags (_, _, heaviness) =>
1800 let val n = length decls in
1801 (0 upto n - 1 ~~ decls)
1802 |> maps (formula_lines_for_lightweight_tags_sym_decl ctxt format
1803 conj_sym_kind nonmono_Ts type_sys n s)
1806 fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1807 type_sys sym_decl_tab =
1812 |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
1813 nonmono_Ts type_sys)
1815 fun needs_type_tag_idempotence (Tags (poly, level, heaviness)) =
1816 poly <> Mangled_Monomorphic andalso
1817 ((level = All_Types andalso heaviness = Lightweight) orelse
1818 level = Nonmonotonic_Types orelse level = Finite_Types)
1819 | needs_type_tag_idempotence _ = false
1821 fun offset_of_heading_in_problem _ [] j = j
1822 | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
1823 if heading = needle then j
1824 else offset_of_heading_in_problem needle problem (j + length lines)
1826 val implicit_declsN = "Should-be-implicit typings"
1827 val explicit_declsN = "Explicit typings"
1828 val factsN = "Relevant facts"
1829 val class_relsN = "Class relationships"
1830 val aritiesN = "Arities"
1831 val helpersN = "Helper facts"
1832 val conjsN = "Conjectures"
1833 val free_typesN = "Type variables"
1835 val explicit_apply = NONE (* for experimental purposes *)
1837 fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_sys
1838 readable_names preproc hyp_ts concl_t facts =
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)