made "query" type systes a bit more sound -- local facts, e.g. the negated conjecture, may make invalid the infinity check, e.g. if we are proving that there exists two values of an infinite type, we can use the negated conjecture that there is only one value to derive unsound proofs unless the type is properly encoded
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
123 connective -> ('a, 'b, 'c) formula list -> ('a, 'b, 'c) formula
124 val unmangled_const_name : string -> string
125 val unmangled_const : string -> string * string fo_term list
126 val helper_table : ((string * bool) * thm list) list
127 val should_specialize_helper : type_sys -> term -> bool
128 val tfree_classes_of_terms : term list -> string list
129 val tvar_classes_of_terms : term list -> string list
130 val type_constrs_of_terms : theory -> term list -> string list
131 val prepare_atp_problem :
132 Proof.context -> format -> formula_kind -> formula_kind -> type_sys
133 -> bool -> bool -> term list -> term -> ((string * locality) * term) list
134 -> string problem * string Symtab.table * int * int
135 * (string * locality) list vector * int list * int Symtab.table
136 val atp_problem_weights : string problem -> (string * real) list
139 structure ATP_Translate : ATP_TRANSLATE =
145 type name = string * string
148 val generate_useful_info = false
150 fun useful_isabelle_info s =
151 if generate_useful_info then
152 SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
156 val intro_info = useful_isabelle_info "intro"
157 val elim_info = useful_isabelle_info "elim"
158 val simp_info = useful_isabelle_info "simp"
160 val bound_var_prefix = "B_"
161 val schematic_var_prefix = "V_"
162 val fixed_var_prefix = "v_"
164 val tvar_prefix = "T_"
165 val tfree_prefix = "t_"
167 val const_prefix = "c_"
168 val type_const_prefix = "tc_"
169 val class_prefix = "cl_"
171 val skolem_const_prefix = "Sledgehammer" ^ Long_Name.separator ^ "Sko"
172 val old_skolem_const_prefix = skolem_const_prefix ^ "o"
173 val new_skolem_const_prefix = skolem_const_prefix ^ "n"
175 val type_decl_prefix = "ty_"
176 val sym_decl_prefix = "sy_"
177 val preds_sym_formula_prefix = "psy_"
178 val lightweight_tags_sym_formula_prefix = "tsy_"
179 val fact_prefix = "fact_"
180 val conjecture_prefix = "conj_"
181 val helper_prefix = "help_"
182 val class_rel_clause_prefix = "clar_"
183 val arity_clause_prefix = "arity_"
184 val tfree_clause_prefix = "tfree_"
186 val typed_helper_suffix = "_T"
187 val untyped_helper_suffix = "_U"
188 val type_tag_idempotence_helper_name = helper_prefix ^ "ti_idem"
190 val predicator_name = "hBOOL"
191 val app_op_name = "hAPP"
192 val type_tag_name = "ti"
193 val type_pred_name = "is"
194 val simple_type_prefix = "ty_"
196 val prefixed_predicator_name = const_prefix ^ predicator_name
197 val prefixed_app_op_name = const_prefix ^ app_op_name
198 val prefixed_type_tag_name = const_prefix ^ type_tag_name
200 (* Freshness almost guaranteed! *)
201 val sledgehammer_weak_prefix = "Sledgehammer:"
203 (*Escaping of special characters.
204 Alphanumeric characters are left unchanged.
205 The character _ goes to __
206 Characters in the range ASCII space to / go to _A to _P, respectively.
207 Other characters go to _nnn where nnn is the decimal ASCII code.*)
208 val upper_a_minus_space = Char.ord #"A" - Char.ord #" "
210 fun stringN_of_int 0 _ = ""
211 | stringN_of_int k n =
212 stringN_of_int (k - 1) (n div 10) ^ string_of_int (n mod 10)
214 fun ascii_of_char c =
215 if Char.isAlphaNum c then
217 else if c = #"_" then
219 else if #" " <= c andalso c <= #"/" then
220 "_" ^ String.str (Char.chr (Char.ord c + upper_a_minus_space))
222 (* fixed width, in case more digits follow *)
223 "_" ^ stringN_of_int 3 (Char.ord c)
225 val ascii_of = String.translate ascii_of_char
227 (** Remove ASCII armoring from names in proof files **)
229 (* We don't raise error exceptions because this code can run inside a worker
230 thread. Also, the errors are impossible. *)
233 fun un rcs [] = String.implode(rev rcs)
234 | un rcs [#"_"] = un (#"_" :: rcs) [] (* ERROR *)
235 (* Three types of _ escapes: __, _A to _P, _nnn *)
236 | un rcs (#"_" :: #"_" :: cs) = un (#"_"::rcs) cs
237 | un rcs (#"_" :: c :: cs) =
238 if #"A" <= c andalso c<= #"P" then
239 (* translation of #" " to #"/" *)
240 un (Char.chr (Char.ord c - upper_a_minus_space) :: rcs) cs
242 let val digits = List.take (c::cs, 3) handle Subscript => [] in
243 case Int.fromString (String.implode digits) of
244 SOME n => un (Char.chr n :: rcs) (List.drop (cs, 2))
245 | NONE => un (c:: #"_"::rcs) cs (* ERROR *)
247 | un rcs (c :: cs) = un (c :: rcs) cs
248 in un [] o String.explode end
250 (* If string s has the prefix s1, return the result of deleting it,
252 fun strip_prefix_and_unascii s1 s =
253 if String.isPrefix s1 s then
254 SOME (unascii_of (String.extract (s, size s1, NONE)))
259 [("c_False", (@{const_name False}, (@{thm fFalse_def},
260 ("fFalse", @{const_name ATP.fFalse})))),
261 ("c_True", (@{const_name True}, (@{thm fTrue_def},
262 ("fTrue", @{const_name ATP.fTrue})))),
263 ("c_Not", (@{const_name Not}, (@{thm fNot_def},
264 ("fNot", @{const_name ATP.fNot})))),
265 ("c_conj", (@{const_name conj}, (@{thm fconj_def},
266 ("fconj", @{const_name ATP.fconj})))),
267 ("c_disj", (@{const_name disj}, (@{thm fdisj_def},
268 ("fdisj", @{const_name ATP.fdisj})))),
269 ("c_implies", (@{const_name implies}, (@{thm fimplies_def},
270 ("fimplies", @{const_name ATP.fimplies})))),
271 ("equal", (@{const_name HOL.eq}, (@{thm fequal_def},
272 ("fequal", @{const_name ATP.fequal}))))]
274 val proxify_const = AList.lookup (op =) proxy_table #> Option.map (snd o snd)
276 (* Readable names for the more common symbolic functions. Do not mess with the
277 table unless you know what you are doing. *)
278 val const_trans_table =
279 [(@{type_name Product_Type.prod}, "prod"),
280 (@{type_name Sum_Type.sum}, "sum"),
281 (@{const_name False}, "False"),
282 (@{const_name True}, "True"),
283 (@{const_name Not}, "Not"),
284 (@{const_name conj}, "conj"),
285 (@{const_name disj}, "disj"),
286 (@{const_name implies}, "implies"),
287 (@{const_name HOL.eq}, "equal"),
288 (@{const_name If}, "If"),
289 (@{const_name Set.member}, "member"),
290 (@{const_name Meson.COMBI}, "COMBI"),
291 (@{const_name Meson.COMBK}, "COMBK"),
292 (@{const_name Meson.COMBB}, "COMBB"),
293 (@{const_name Meson.COMBC}, "COMBC"),
294 (@{const_name Meson.COMBS}, "COMBS")]
296 |> fold (Symtab.update o swap o snd o snd o snd) proxy_table
298 (* Invert the table of translations between Isabelle and ATPs. *)
299 val const_trans_table_inv =
300 const_trans_table |> Symtab.dest |> map swap |> Symtab.make
301 val const_trans_table_unprox =
303 |> fold (fn (_, (isa, (_, (_, atp)))) => Symtab.update (atp, isa)) proxy_table
305 val invert_const = perhaps (Symtab.lookup const_trans_table_inv)
306 val unproxify_const = perhaps (Symtab.lookup const_trans_table_unprox)
309 case Symtab.lookup const_trans_table c of
313 (*Remove the initial ' character from a type variable, if it is present*)
314 fun trim_type_var s =
315 if s <> "" andalso String.sub(s,0) = #"'" then String.extract(s,1,NONE)
316 else raise Fail ("trim_type: Malformed type variable encountered: " ^ s)
318 fun ascii_of_indexname (v,0) = ascii_of v
319 | ascii_of_indexname (v,i) = ascii_of v ^ "_" ^ string_of_int i
321 fun make_bound_var x = bound_var_prefix ^ ascii_of x
322 fun make_schematic_var v = schematic_var_prefix ^ ascii_of_indexname v
323 fun make_fixed_var x = fixed_var_prefix ^ ascii_of x
325 fun make_schematic_type_var (x,i) =
326 tvar_prefix ^ (ascii_of_indexname (trim_type_var x, i))
327 fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (trim_type_var x))
329 (* HOL.eq MUST BE "equal" because it's built into ATPs. *)
330 fun make_fixed_const @{const_name HOL.eq} = "equal"
331 | make_fixed_const c = const_prefix ^ lookup_const c
333 fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
335 fun make_type_class clas = class_prefix ^ ascii_of clas
337 fun new_skolem_var_name_from_const s =
338 let val ss = s |> space_explode Long_Name.separator in
339 nth ss (length ss - 2)
342 (* The number of type arguments of a constant, zero if it's monomorphic. For
343 (instances of) Skolem pseudoconstants, this information is encoded in the
345 fun num_type_args thy s =
346 if String.isPrefix skolem_const_prefix s then
347 s |> space_explode Long_Name.separator |> List.last |> Int.fromString |> the
349 (s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
351 (* These are either simplified away by "Meson.presimplify" (most of the time) or
352 handled specially via "fFalse", "fTrue", ..., "fequal". *)
353 val atp_irrelevant_consts =
354 [@{const_name False}, @{const_name True}, @{const_name Not},
355 @{const_name conj}, @{const_name disj}, @{const_name implies},
356 @{const_name HOL.eq}, @{const_name If}, @{const_name Let}]
358 val atp_monomorph_bad_consts =
359 atp_irrelevant_consts @
360 (* These are ignored anyway by the relevance filter (unless they appear in
361 higher-order places) but not by the monomorphizer. *)
362 [@{const_name all}, @{const_name "==>"}, @{const_name "=="},
363 @{const_name Trueprop}, @{const_name All}, @{const_name Ex},
364 @{const_name Ex1}, @{const_name Ball}, @{const_name Bex}]
366 fun add_schematic_const (x as (_, T)) =
367 Monomorph.typ_has_tvars T ? Symtab.insert_list (op =) x
368 val add_schematic_consts_of =
369 Term.fold_aterms (fn Const (x as (s, _)) =>
370 not (member (op =) atp_monomorph_bad_consts s)
371 ? add_schematic_const x
373 fun atp_schematic_consts_of t = add_schematic_consts_of t Symtab.empty
375 (** Definitions and functions for FOL clauses and formulas for TPTP **)
377 (* The first component is the type class; the second is a "TVar" or "TFree". *)
378 datatype type_literal =
379 TyLitVar of name * name |
380 TyLitFree of name * name
383 (** Isabelle arities **)
385 datatype arity_literal =
386 TConsLit of name * name * name list |
387 TVarLit of name * name
390 | gen_TVars n = ("T_" ^ string_of_int n) :: gen_TVars (n-1)
392 val type_class = the_single @{sort type}
394 fun add_packed_sort tvar =
395 fold (fn s => s <> type_class ? cons (`make_type_class s, `I tvar))
399 prem_lits: arity_literal list,
400 concl_lits: arity_literal}
402 (* Arity of type constructor "tcon :: (arg1, ..., argN) res" *)
403 fun make_axiom_arity_clause (tcons, name, (cls, args)) =
405 val tvars = gen_TVars (length args)
406 val tvars_srts = ListPair.zip (tvars, args)
409 prem_lits = [] |> fold (uncurry add_packed_sort) tvars_srts |> map TVarLit,
410 concl_lits = TConsLit (`make_type_class cls,
411 `make_fixed_type_const tcons,
415 fun arity_clause _ _ (_, []) = []
416 | arity_clause seen n (tcons, ("HOL.type",_)::ars) = (*ignore*)
417 arity_clause seen n (tcons,ars)
418 | arity_clause seen n (tcons, (ar as (class,_)) :: ars) =
419 if member (op =) seen class then (*multiple arities for the same tycon, class pair*)
420 make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class ^ "_" ^ string_of_int n, ar) ::
421 arity_clause seen (n+1) (tcons,ars)
423 make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class, ar) ::
424 arity_clause (class::seen) n (tcons,ars)
426 fun multi_arity_clause [] = []
427 | multi_arity_clause ((tcons, ars) :: tc_arlists) =
428 arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
430 (*Generate all pairs (tycon,class,sorts) such that tycon belongs to class in theory thy
431 provided its arguments have the corresponding sorts.*)
432 fun type_class_pairs thy tycons classes =
434 val alg = Sign.classes_of thy
435 fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
436 fun add_class tycon class =
437 cons (class, domain_sorts tycon class)
438 handle Sorts.CLASS_ERROR _ => I
439 fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
440 in map try_classes tycons end
442 (*Proving one (tycon, class) membership may require proving others, so iterate.*)
443 fun iter_type_class_pairs _ _ [] = ([], [])
444 | iter_type_class_pairs thy tycons classes =
446 fun maybe_insert_class s =
447 (s <> type_class andalso not (member (op =) classes s))
449 val cpairs = type_class_pairs thy tycons classes
451 [] |> fold (fold (fold (fold maybe_insert_class) o snd) o snd) cpairs
452 val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
453 in (classes' @ classes, union (op =) cpairs' cpairs) end
455 fun make_arity_clauses thy tycons =
456 iter_type_class_pairs thy tycons ##> multi_arity_clause
459 (** Isabelle class relations **)
461 type class_rel_clause =
466 (*Generate all pairs (sub,super) such that sub is a proper subclass of super in theory thy.*)
467 fun class_pairs _ [] _ = []
468 | class_pairs thy subs supers =
470 val class_less = Sorts.class_less (Sign.classes_of thy)
471 fun add_super sub super = class_less (sub, super) ? cons (sub, super)
472 fun add_supers sub = fold (add_super sub) supers
473 in fold add_supers subs [] end
475 fun make_class_rel_clause (sub,super) =
476 {name = sub ^ "_" ^ super,
477 subclass = `make_type_class sub,
478 superclass = `make_type_class super}
480 fun make_class_rel_clauses thy subs supers =
481 map make_class_rel_clause (class_pairs thy subs supers)
484 CombConst of name * typ * typ list |
485 CombVar of name * typ |
486 CombApp of combterm * combterm
488 fun combtyp_of (CombConst (_, T, _)) = T
489 | combtyp_of (CombVar (_, T)) = T
490 | combtyp_of (CombApp (t1, _)) = snd (dest_funT (combtyp_of t1))
492 (*gets the head of a combinator application, along with the list of arguments*)
493 fun strip_combterm_comb u =
494 let fun stripc (CombApp(t,u), ts) = stripc (t, u::ts)
498 fun atyps_of T = fold_atyps (insert (op =)) T []
500 fun new_skolem_const_name s num_T_args =
501 [new_skolem_const_prefix, s, string_of_int num_T_args]
502 |> space_implode Long_Name.separator
504 (* Converts a term (with combinators) into a combterm. Also accumulates sort
506 fun combterm_from_term thy bs (P $ Q) =
508 val (P', P_atomics_Ts) = combterm_from_term thy bs P
509 val (Q', Q_atomics_Ts) = combterm_from_term thy bs Q
510 in (CombApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
511 | combterm_from_term thy _ (Const (c, T)) =
514 (if String.isPrefix old_skolem_const_prefix c then
515 [] |> Term.add_tvarsT T |> map TVar
517 (c, T) |> Sign.const_typargs thy)
518 val c' = CombConst (`make_fixed_const c, T, tvar_list)
519 in (c', atyps_of T) end
520 | combterm_from_term _ _ (Free (v, T)) =
521 (CombConst (`make_fixed_var v, T, []), atyps_of T)
522 | combterm_from_term _ _ (Var (v as (s, _), T)) =
523 (if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
525 val Ts = T |> strip_type |> swap |> op ::
526 val s' = new_skolem_const_name s (length Ts)
527 in CombConst (`make_fixed_const s', T, Ts) end
529 CombVar ((make_schematic_var v, s), T), atyps_of T)
530 | combterm_from_term _ bs (Bound j) =
532 |> (fn (s, T) => (CombConst (`make_bound_var s, T, []), atyps_of T))
533 | combterm_from_term _ _ (Abs _) = raise Fail "HOL clause: Abs"
535 datatype locality = General | Intro | Elim | Simp | Local | Assum | Chained
537 (* (quasi-)underapproximation of the truth *)
538 fun is_locality_global Local = false
539 | is_locality_global Assum = false
540 | is_locality_global Chained = false
541 | is_locality_global _ = true
543 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
544 datatype type_level =
545 All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
546 datatype type_heaviness = Heavyweight | Lightweight
549 Simple_Types of type_level |
550 Preds of polymorphism * type_level * type_heaviness |
551 Tags of polymorphism * type_level * type_heaviness
553 fun try_unsuffixes ss s =
554 fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
556 fun type_sys_from_string s =
557 (case try (unprefix "poly_") s of
558 SOME s => (SOME Polymorphic, s)
560 case try (unprefix "mono_") s of
561 SOME s => (SOME Monomorphic, s)
563 case try (unprefix "mangled_") s of
564 SOME s => (SOME Mangled_Monomorphic, s)
567 (* "_query" and "_bang" are for the ASCII-challenged Mirabelle. *)
568 case try_unsuffixes ["?", "_query"] s of
569 SOME s => (Nonmonotonic_Types, s)
571 case try_unsuffixes ["!", "_bang"] s of
572 SOME s => (Finite_Types, s)
573 | NONE => (All_Types, s))
575 case try (unsuffix "_heavy") s of
576 SOME s => (Heavyweight, s)
577 | NONE => (Lightweight, s))
578 |> (fn (poly, (level, (heaviness, core))) =>
579 case (core, (poly, level, heaviness)) of
580 ("simple", (NONE, _, Lightweight)) => Simple_Types level
581 | ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
582 | ("tags", (SOME Polymorphic, All_Types, _)) =>
583 Tags (Polymorphic, All_Types, heaviness)
584 | ("tags", (SOME Polymorphic, _, _)) =>
585 (* The actual light encoding is very unsound. *)
586 Tags (Polymorphic, level, Heavyweight)
587 | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
588 | ("args", (SOME poly, All_Types (* naja *), Lightweight)) =>
589 Preds (poly, Const_Arg_Types, Lightweight)
590 | ("erased", (NONE, All_Types (* naja *), Lightweight)) =>
591 Preds (Polymorphic, No_Types, Lightweight)
592 | _ => raise Same.SAME)
593 handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
595 fun polymorphism_of_type_sys (Simple_Types _) = Mangled_Monomorphic
596 | polymorphism_of_type_sys (Preds (poly, _, _)) = poly
597 | polymorphism_of_type_sys (Tags (poly, _, _)) = poly
599 fun level_of_type_sys (Simple_Types level) = level
600 | level_of_type_sys (Preds (_, level, _)) = level
601 | level_of_type_sys (Tags (_, level, _)) = level
603 fun heaviness_of_type_sys (Simple_Types _) = Heavyweight
604 | heaviness_of_type_sys (Preds (_, _, heaviness)) = heaviness
605 | heaviness_of_type_sys (Tags (_, _, heaviness)) = heaviness
607 fun is_type_level_virtually_sound level =
608 level = All_Types orelse level = Nonmonotonic_Types
609 val is_type_sys_virtually_sound =
610 is_type_level_virtually_sound o level_of_type_sys
612 fun is_type_level_fairly_sound level =
613 is_type_level_virtually_sound level orelse level = Finite_Types
614 val is_type_sys_fairly_sound = is_type_level_fairly_sound o level_of_type_sys
616 fun is_setting_higher_order THF (Simple_Types _) = true
617 | is_setting_higher_order _ _ = false
619 fun choose_format formats (Simple_Types level) =
620 if member (op =) formats THF then (THF, Simple_Types level)
621 else if member (op =) formats TFF then (TFF, Simple_Types level)
622 else choose_format formats (Preds (Mangled_Monomorphic, level, Heavyweight))
623 | choose_format formats type_sys =
626 (CNF_UEQ, case type_sys of
628 (if is_type_sys_fairly_sound type_sys then Tags else Preds)
631 | format => (format, type_sys))
633 type translated_formula =
637 combformula: (name, typ, combterm) formula,
638 atomic_types: typ list}
640 fun update_combformula f ({name, locality, kind, combformula, atomic_types}
641 : translated_formula) =
642 {name = name, locality = locality, kind = kind, combformula = f combformula,
643 atomic_types = atomic_types} : translated_formula
645 fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
647 val type_instance = Sign.typ_instance o Proof_Context.theory_of
649 fun insert_type ctxt get_T x xs =
650 let val T = get_T x in
651 if exists (curry (type_instance ctxt) T o get_T) xs then xs
652 else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
655 (* The Booleans indicate whether all type arguments should be kept. *)
656 datatype type_arg_policy =
657 Explicit_Type_Args of bool |
658 Mangled_Type_Args of bool |
661 fun should_drop_arg_type_args (Simple_Types _) =
662 false (* since TFF doesn't support overloading *)
663 | should_drop_arg_type_args type_sys =
664 level_of_type_sys type_sys = All_Types andalso
665 heaviness_of_type_sys type_sys = Heavyweight
667 fun general_type_arg_policy (Tags (_, All_Types, Heavyweight)) = No_Type_Args
668 | general_type_arg_policy type_sys =
669 if level_of_type_sys type_sys = No_Types then
671 else if polymorphism_of_type_sys type_sys = Mangled_Monomorphic then
672 Mangled_Type_Args (should_drop_arg_type_args type_sys)
674 Explicit_Type_Args (should_drop_arg_type_args type_sys)
676 fun type_arg_policy type_sys s =
677 if s = @{const_name HOL.eq} orelse
678 (s = app_op_name andalso level_of_type_sys type_sys = Const_Arg_Types) then
680 else if s = type_tag_name then
681 Explicit_Type_Args false
683 general_type_arg_policy type_sys
685 (*Make literals for sorted type variables*)
686 fun generic_add_sorts_on_type (_, []) = I
687 | generic_add_sorts_on_type ((x, i), s :: ss) =
688 generic_add_sorts_on_type ((x, i), ss)
689 #> (if s = the_single @{sort HOL.type} then
692 insert (op =) (TyLitFree (`make_type_class s, `make_fixed_type_var x))
694 insert (op =) (TyLitVar (`make_type_class s,
695 (make_schematic_type_var (x, i), x))))
696 fun add_sorts_on_tfree (TFree (s, S)) = generic_add_sorts_on_type ((s, ~1), S)
697 | add_sorts_on_tfree _ = I
698 fun add_sorts_on_tvar (TVar z) = generic_add_sorts_on_type z
699 | add_sorts_on_tvar _ = I
701 fun type_literals_for_types type_sys add_sorts_on_typ Ts =
702 [] |> level_of_type_sys type_sys <> No_Types ? fold add_sorts_on_typ Ts
704 fun mk_aconns c phis =
705 let val (phis', phi') = split_last phis in
706 fold_rev (mk_aconn c) phis' phi'
708 fun mk_ahorn [] phi = phi
709 | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
710 fun mk_aquant _ [] phi = phi
711 | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
712 if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
713 | mk_aquant q xs phi = AQuant (q, xs, phi)
715 fun close_universally atom_vars phi =
717 fun formula_vars bounds (AQuant (_, xs, phi)) =
718 formula_vars (map fst xs @ bounds) phi
719 | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
720 | formula_vars bounds (AAtom tm) =
721 union (op =) (atom_vars tm []
722 |> filter_out (member (op =) bounds o fst))
723 in mk_aquant AForall (formula_vars [] phi []) phi end
725 fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
726 | combterm_vars (CombConst _) = I
727 | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
728 fun close_combformula_universally phi = close_universally combterm_vars phi
730 fun term_vars (ATerm (name as (s, _), tms)) =
731 is_tptp_variable s ? insert (op =) (name, NONE) #> fold term_vars tms
732 fun close_formula_universally phi = close_universally term_vars phi
734 val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
735 val homo_infinite_type = Type (homo_infinite_type_name, [])
737 fun fo_term_from_typ format type_sys =
739 fun term (Type (s, Ts)) =
740 ATerm (case (is_setting_higher_order format type_sys, s) of
741 (true, @{type_name bool}) => `I tptp_bool_type
742 | (true, @{type_name fun}) => `I tptp_fun_type
743 | _ => if s = homo_infinite_type_name andalso
744 (format = TFF orelse format = THF) then
745 `I tptp_individual_type
747 `make_fixed_type_const s,
749 | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
750 | term (TVar ((x as (s, _)), _)) =
751 ATerm ((make_schematic_type_var x, s), [])
754 (* This shouldn't clash with anything else. *)
755 val mangled_type_sep = "\000"
757 fun generic_mangled_type_name f (ATerm (name, [])) = f name
758 | generic_mangled_type_name f (ATerm (name, tys)) =
759 f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
762 val bool_atype = AType (`I tptp_bool_type)
764 fun make_simple_type s =
765 if s = tptp_bool_type orelse s = tptp_fun_type orelse
766 s = tptp_individual_type then
769 simple_type_prefix ^ ascii_of s
771 fun ho_type_from_fo_term format type_sys pred_sym ary =
774 AType ((make_simple_type (generic_mangled_type_name fst ty),
775 generic_mangled_type_name snd ty))
776 fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
777 fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
778 | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
779 fun to_ho (ty as ATerm ((s, _), tys)) =
780 if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
781 in if is_setting_higher_order format type_sys then to_ho else to_fo ary end
783 fun mangled_type format type_sys pred_sym ary =
784 ho_type_from_fo_term format type_sys pred_sym ary
785 o fo_term_from_typ format type_sys
787 fun mangled_const_name format type_sys T_args (s, s') =
789 val ty_args = map (fo_term_from_typ format type_sys) T_args
790 fun type_suffix f g =
791 fold_rev (curry (op ^) o g o prefix mangled_type_sep
792 o generic_mangled_type_name f) ty_args ""
793 in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
795 val parse_mangled_ident =
796 Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
798 fun parse_mangled_type x =
800 -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
802 and parse_mangled_types x =
803 (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
805 fun unmangled_type s =
806 s |> suffix ")" |> raw_explode
807 |> Scan.finite Symbol.stopper
808 (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
809 quote s)) parse_mangled_type))
812 val unmangled_const_name = space_explode mangled_type_sep #> hd
813 fun unmangled_const s =
814 let val ss = space_explode mangled_type_sep s in
815 (hd ss, map unmangled_type (tl ss))
818 fun introduce_proxies format type_sys =
820 fun intro top_level (CombApp (tm1, tm2)) =
821 CombApp (intro top_level tm1, intro false tm2)
822 | intro top_level (CombConst (name as (s, _), T, T_args)) =
823 (case proxify_const s of
825 if top_level orelse is_setting_higher_order format type_sys then
826 case (top_level, s) of
827 (_, "c_False") => (`I tptp_false, [])
828 | (_, "c_True") => (`I tptp_true, [])
829 | (false, "c_Not") => (`I tptp_not, [])
830 | (false, "c_conj") => (`I tptp_and, [])
831 | (false, "c_disj") => (`I tptp_or, [])
832 | (false, "c_implies") => (`I tptp_implies, [])
834 if is_tptp_equal s then (`I tptp_equal, [])
835 else (proxy_base |>> prefix const_prefix, T_args)
838 (proxy_base |>> prefix const_prefix, T_args)
839 | NONE => (name, T_args))
840 |> (fn (name, T_args) => CombConst (name, T, T_args))
844 fun combformula_from_prop thy format type_sys eq_as_iff =
846 fun do_term bs t atomic_types =
847 combterm_from_term thy bs (Envir.eta_contract t)
848 |>> (introduce_proxies format type_sys #> AAtom)
849 ||> union (op =) atomic_types
850 fun do_quant bs q s T t' =
851 let val s = Name.variant (map fst bs) s in
852 do_formula ((s, T) :: bs) t'
853 #>> mk_aquant q [(`make_bound_var s, SOME T)]
855 and do_conn bs c t1 t2 =
856 do_formula bs t1 ##>> do_formula bs t2 #>> uncurry (mk_aconn c)
857 and do_formula bs t =
859 @{const Trueprop} $ t1 => do_formula bs t1
860 | @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
861 | Const (@{const_name All}, _) $ Abs (s, T, t') =>
862 do_quant bs AForall s T t'
863 | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
864 do_quant bs AExists s T t'
865 | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
866 | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
867 | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
868 | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
869 if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
873 fun presimplify_term _ [] t = t
874 | presimplify_term ctxt presimp_consts t =
875 t |> exists_Const (member (op =) presimp_consts o fst) t
876 ? (Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
877 #> Meson.presimplify ctxt
880 fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
881 fun conceal_bounds Ts t =
882 subst_bounds (map (Free o apfst concealed_bound_name)
883 (0 upto length Ts - 1 ~~ Ts), t)
884 fun reveal_bounds Ts =
885 subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
886 (0 upto length Ts - 1 ~~ Ts))
888 fun is_fun_equality (@{const_name HOL.eq},
889 Type (_, [Type (@{type_name fun}, _), _])) = true
890 | is_fun_equality _ = false
892 fun extensionalize_term ctxt t =
893 if exists_Const is_fun_equality t then
894 let val thy = Proof_Context.theory_of ctxt in
895 t |> cterm_of thy |> Meson.extensionalize_conv ctxt
896 |> prop_of |> Logic.dest_equals |> snd
901 fun introduce_combinators_in_term ctxt kind t =
902 let val thy = Proof_Context.theory_of ctxt in
903 if Meson.is_fol_term thy t then
909 @{const Not} $ t1 => @{const Not} $ aux Ts t1
910 | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
911 t0 $ Abs (s, T, aux (T :: Ts) t')
912 | (t0 as Const (@{const_name All}, _)) $ t1 =>
913 aux Ts (t0 $ eta_expand Ts t1 1)
914 | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
915 t0 $ Abs (s, T, aux (T :: Ts) t')
916 | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
917 aux Ts (t0 $ eta_expand Ts t1 1)
918 | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
919 | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
920 | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
921 | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
923 t0 $ aux Ts t1 $ aux Ts t2
924 | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
927 t |> conceal_bounds Ts
928 |> Envir.eta_contract
930 |> Meson_Clausify.introduce_combinators_in_cterm
931 |> prop_of |> Logic.dest_equals |> snd
933 val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
934 in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
936 (* A type variable of sort "{}" will make abstraction fail. *)
937 if kind = Conjecture then HOLogic.false_const
938 else HOLogic.true_const
941 (* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
942 same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
945 fun aux (t $ u) = aux t $ aux u
946 | aux (Abs (s, T, t)) = Abs (s, T, aux t)
947 | aux (Var ((s, i), T)) =
948 Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
950 in t |> exists_subterm is_Var t ? aux end
952 fun preprocess_prop ctxt presimp_consts kind t =
954 val thy = Proof_Context.theory_of ctxt
955 val t = t |> Envir.beta_eta_contract
956 |> transform_elim_prop
957 |> Object_Logic.atomize_term thy
958 val need_trueprop = (fastype_of t = @{typ bool})
960 t |> need_trueprop ? HOLogic.mk_Trueprop
961 |> Raw_Simplifier.rewrite_term thy (Meson.unfold_set_const_simps ctxt) []
962 |> extensionalize_term ctxt
963 |> presimplify_term ctxt presimp_consts
964 |> perhaps (try (HOLogic.dest_Trueprop))
965 |> introduce_combinators_in_term ctxt kind
968 (* making fact and conjecture formulas *)
969 fun make_formula thy format type_sys eq_as_iff name loc kind t =
971 val (combformula, atomic_types) =
972 combformula_from_prop thy format type_sys eq_as_iff t []
974 {name = name, locality = loc, kind = kind, combformula = combformula,
975 atomic_types = atomic_types}
978 fun make_fact ctxt format type_sys keep_trivial eq_as_iff preproc presimp_consts
980 let val thy = Proof_Context.theory_of ctxt in
982 t |> preproc ? preprocess_prop ctxt presimp_consts Axiom
983 |> make_formula thy format type_sys eq_as_iff name loc Axiom) of
985 formula as {combformula = AAtom (CombConst ((s, _), _, _)), ...}) =>
986 if s = tptp_true then NONE else SOME formula
987 | (_, formula) => SOME formula
990 fun make_conjecture ctxt format prem_kind type_sys preproc presimp_consts ts =
992 val thy = Proof_Context.theory_of ctxt
993 val last = length ts - 1
995 map2 (fn j => fn t =>
997 val (kind, maybe_negate) =
1002 if prem_kind = Conjecture then update_combformula mk_anot
1006 (preprocess_prop ctxt presimp_consts kind #> freeze_term)
1007 |> make_formula thy format type_sys (format <> CNF)
1008 (string_of_int j) Local kind
1014 (** Finite and infinite type inference **)
1016 fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
1017 | deep_freeze_atyp T = T
1018 val deep_freeze_type = map_atyps deep_freeze_atyp
1020 (* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
1021 dangerous because their "exhaust" properties can easily lead to unsound ATP
1022 proofs. On the other hand, all HOL infinite types can be given the same
1023 models in first-order logic (via Löwenheim-Skolem). *)
1025 fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
1026 exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
1027 | should_encode_type _ _ All_Types _ = true
1028 | should_encode_type ctxt _ Finite_Types T = is_type_surely_finite ctxt T
1029 | should_encode_type _ _ _ _ = false
1031 fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
1032 should_predicate_on_var T =
1033 (heaviness = Heavyweight orelse should_predicate_on_var ()) andalso
1034 should_encode_type ctxt nonmono_Ts level T
1035 | should_predicate_on_type _ _ _ _ _ = false
1037 fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
1038 String.isPrefix bound_var_prefix s
1039 | is_var_or_bound_var (CombVar _) = true
1040 | is_var_or_bound_var _ = false
1042 datatype tag_site = Top_Level | Eq_Arg | Elsewhere
1044 fun should_tag_with_type _ _ _ Top_Level _ _ = false
1045 | should_tag_with_type ctxt nonmono_Ts (Tags (_, level, heaviness)) site u T =
1047 Heavyweight => should_encode_type ctxt nonmono_Ts level T
1049 case (site, is_var_or_bound_var u) of
1050 (Eq_Arg, true) => should_encode_type ctxt nonmono_Ts level T
1052 | should_tag_with_type _ _ _ _ _ _ = false
1054 fun homogenized_type ctxt nonmono_Ts level =
1056 val should_encode = should_encode_type ctxt nonmono_Ts level
1057 fun homo 0 T = if should_encode T then T else homo_infinite_type
1058 | homo ary (Type (@{type_name fun}, [T1, T2])) =
1059 homo 0 T1 --> homo (ary - 1) T2
1060 | homo _ _ = raise Fail "expected function type"
1063 (** "hBOOL" and "hAPP" **)
1066 {pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
1068 fun add_combterm_syms_to_table ctxt explicit_apply =
1070 fun consider_var_arity const_T var_T max_ary =
1073 if ary = max_ary orelse type_instance ctxt (var_T, T) orelse
1074 type_instance ctxt (T, var_T) then
1077 iter (ary + 1) (range_type T)
1078 in iter 0 const_T end
1079 fun add_var_or_bound_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1080 if explicit_apply = NONE andalso
1081 (can dest_funT T orelse T = @{typ bool}) then
1083 val bool_vars' = bool_vars orelse body_type T = @{typ bool}
1084 fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
1085 {pred_sym = pred_sym andalso not bool_vars',
1086 min_ary = fold (fn T' => consider_var_arity T' T) types min_ary,
1087 max_ary = max_ary, types = types}
1089 fun_var_Ts |> can dest_funT T ? insert_type ctxt I T
1091 if bool_vars' = bool_vars andalso
1092 pointer_eq (fun_var_Ts', fun_var_Ts) then
1095 ((bool_vars', fun_var_Ts'), Symtab.map (K repair_min_arity) sym_tab)
1099 fun add top_level tm (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1100 let val (head, args) = strip_combterm_comb tm in
1102 CombConst ((s, _), T, _) =>
1103 if String.isPrefix bound_var_prefix s then
1104 add_var_or_bound_var T accum
1106 let val ary = length args in
1107 ((bool_vars, fun_var_Ts),
1108 case Symtab.lookup sym_tab s of
1109 SOME {pred_sym, min_ary, max_ary, types} =>
1112 pred_sym andalso top_level andalso not bool_vars
1113 val types' = types |> insert_type ctxt I T
1115 if is_some explicit_apply orelse
1116 pointer_eq (types', types) then
1119 fold (consider_var_arity T) fun_var_Ts min_ary
1121 Symtab.update (s, {pred_sym = pred_sym,
1122 min_ary = Int.min (ary, min_ary),
1123 max_ary = Int.max (ary, max_ary),
1129 val pred_sym = top_level andalso not bool_vars
1131 case explicit_apply of
1134 | NONE => fold (consider_var_arity T) fun_var_Ts ary
1136 Symtab.update_new (s, {pred_sym = pred_sym,
1137 min_ary = min_ary, max_ary = ary,
1142 | CombVar (_, T) => add_var_or_bound_var T accum
1144 |> fold (add false) args
1147 fun add_fact_syms_to_table ctxt explicit_apply =
1148 fact_lift (formula_fold NONE
1149 (K (add_combterm_syms_to_table ctxt explicit_apply)))
1151 val default_sym_tab_entries : (string * sym_info) list =
1152 (prefixed_predicator_name,
1153 {pred_sym = true, min_ary = 1, max_ary = 1, types = []}) ::
1154 ([tptp_false, tptp_true]
1155 |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []})) @
1156 ([tptp_equal, tptp_old_equal]
1157 |> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = []}))
1159 fun sym_table_for_facts ctxt explicit_apply facts =
1160 ((false, []), Symtab.empty)
1161 |> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
1162 |> fold Symtab.update default_sym_tab_entries
1164 fun min_arity_of sym_tab s =
1165 case Symtab.lookup sym_tab s of
1166 SOME ({min_ary, ...} : sym_info) => min_ary
1168 case strip_prefix_and_unascii const_prefix s of
1170 let val s = s |> unmangled_const_name |> invert_const in
1171 if s = predicator_name then 1
1172 else if s = app_op_name then 2
1173 else if s = type_pred_name then 1
1178 (* True if the constant ever appears outside of the top-level position in
1179 literals, or if it appears with different arities (e.g., because of different
1180 type instantiations). If false, the constant always receives all of its
1181 arguments and is used as a predicate. *)
1182 fun is_pred_sym sym_tab s =
1183 case Symtab.lookup sym_tab s of
1184 SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
1185 pred_sym andalso min_ary = max_ary
1188 val predicator_combconst =
1189 CombConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
1190 fun predicator tm = CombApp (predicator_combconst, tm)
1192 fun introduce_predicators_in_combterm sym_tab tm =
1193 case strip_combterm_comb tm of
1194 (CombConst ((s, _), _, _), _) =>
1195 if is_pred_sym sym_tab s then tm else predicator tm
1196 | _ => predicator tm
1198 fun list_app head args = fold (curry (CombApp o swap)) args head
1200 val app_op = `make_fixed_const app_op_name
1202 fun explicit_app arg head =
1204 val head_T = combtyp_of head
1205 val (arg_T, res_T) = dest_funT head_T
1207 CombConst (app_op, head_T --> head_T, [arg_T, res_T])
1208 in list_app explicit_app [head, arg] end
1209 fun list_explicit_app head args = fold explicit_app args head
1211 fun introduce_explicit_apps_in_combterm sym_tab =
1214 case strip_combterm_comb tm of
1215 (head as CombConst ((s, _), _, _), args) =>
1217 |> chop (min_arity_of sym_tab s)
1219 |-> list_explicit_app
1220 | (head, args) => list_explicit_app head (map aux args)
1223 fun chop_fun 0 T = ([], T)
1224 | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
1225 chop_fun (n - 1) ran_T |>> cons dom_T
1226 | chop_fun _ _ = raise Fail "unexpected non-function"
1228 fun filter_type_args _ _ _ [] = []
1229 | filter_type_args thy s arity T_args =
1231 (* will throw "TYPE" for pseudo-constants *)
1232 val U = if s = app_op_name then
1233 @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
1235 s |> Sign.the_const_type thy
1237 case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
1240 let val U_args = (s, U) |> Sign.const_typargs thy in
1242 |> map_filter (fn (U, T) =>
1243 if member (op =) res_U_vars (dest_TVar U) then
1249 handle TYPE _ => T_args
1251 fun enforce_type_arg_policy_in_combterm ctxt format type_sys =
1253 val thy = Proof_Context.theory_of ctxt
1254 fun aux arity (CombApp (tm1, tm2)) =
1255 CombApp (aux (arity + 1) tm1, aux 0 tm2)
1256 | aux arity (CombConst (name as (s, _), T, T_args)) =
1257 (case strip_prefix_and_unascii const_prefix s of
1258 NONE => (name, T_args)
1261 val s'' = invert_const s''
1262 fun filtered_T_args false = T_args
1263 | filtered_T_args true = filter_type_args thy s'' arity T_args
1265 case type_arg_policy type_sys s'' of
1266 Explicit_Type_Args drop_args =>
1267 (name, filtered_T_args drop_args)
1268 | Mangled_Type_Args drop_args =>
1269 (mangled_const_name format type_sys (filtered_T_args drop_args)
1271 | No_Type_Args => (name, [])
1273 |> (fn (name, T_args) => CombConst (name, T, T_args))
1277 fun repair_combterm ctxt format type_sys sym_tab =
1278 not (is_setting_higher_order format type_sys)
1279 ? (introduce_explicit_apps_in_combterm sym_tab
1280 #> introduce_predicators_in_combterm sym_tab)
1281 #> enforce_type_arg_policy_in_combterm ctxt format type_sys
1282 fun repair_fact ctxt format type_sys sym_tab =
1283 update_combformula (formula_map
1284 (repair_combterm ctxt format type_sys sym_tab))
1286 (** Helper facts **)
1288 (* The Boolean indicates that a fairly sound type encoding is needed. *)
1290 [(("COMBI", false), @{thms Meson.COMBI_def}),
1291 (("COMBK", false), @{thms Meson.COMBK_def}),
1292 (("COMBB", false), @{thms Meson.COMBB_def}),
1293 (("COMBC", false), @{thms Meson.COMBC_def}),
1294 (("COMBS", false), @{thms Meson.COMBS_def}),
1296 (* This is a lie: Higher-order equality doesn't need a sound type encoding.
1297 However, this is done so for backward compatibility: Including the
1298 equality helpers by default in Metis breaks a few existing proofs. *)
1299 @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1300 fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1301 (("fFalse", false), [@{lemma "~ fFalse" by (unfold fFalse_def) fast}]),
1302 (("fFalse", true), @{thms True_or_False}),
1303 (("fTrue", false), [@{lemma "fTrue" by (unfold fTrue_def) fast}]),
1304 (("fTrue", true), @{thms True_or_False}),
1306 @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1307 fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1309 @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
1310 by (unfold fconj_def) fast+}),
1312 @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
1313 by (unfold fdisj_def) fast+}),
1314 (("fimplies", false),
1315 @{lemma "P | fimplies P Q" "~ Q | fimplies P Q" "~ fimplies P Q | ~ P | Q"
1316 by (unfold fimplies_def) fast+}),
1317 (("If", true), @{thms if_True if_False True_or_False})]
1318 |> map (apsnd (map zero_var_indexes))
1320 val type_tag = `make_fixed_const type_tag_name
1322 fun type_tag_idempotence_fact () =
1324 fun var s = ATerm (`I s, [])
1325 fun tag tm = ATerm (type_tag, [var "T", tm])
1326 val tagged_a = tag (var "A")
1328 Formula (type_tag_idempotence_helper_name, Axiom,
1329 AAtom (ATerm (`I tptp_equal, [tag tagged_a, tagged_a]))
1330 |> close_formula_universally, simp_info, NONE)
1333 fun should_specialize_helper type_sys t =
1334 case general_type_arg_policy type_sys of
1335 Mangled_Type_Args _ => not (null (Term.hidden_polymorphism t))
1338 fun helper_facts_for_sym ctxt format type_sys (s, {types, ...} : sym_info) =
1339 case strip_prefix_and_unascii const_prefix s of
1342 val thy = Proof_Context.theory_of ctxt
1343 val unmangled_s = mangled_s |> unmangled_const_name
1344 fun dub_and_inst needs_fairly_sound (th, j) =
1345 ((unmangled_s ^ "_" ^ string_of_int j ^
1346 (if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^
1347 (if needs_fairly_sound then typed_helper_suffix
1348 else untyped_helper_suffix),
1350 let val t = th |> prop_of in
1351 t |> should_specialize_helper type_sys t
1353 [T] => specialize_type thy (invert_const unmangled_s, T)
1357 map_filter (make_fact ctxt format type_sys false false false [])
1358 val fairly_sound = is_type_sys_fairly_sound type_sys
1361 |> maps (fn ((helper_s, needs_fairly_sound), ths) =>
1362 if helper_s <> unmangled_s orelse
1363 (needs_fairly_sound andalso not fairly_sound) then
1366 ths ~~ (1 upto length ths)
1367 |> map (dub_and_inst needs_fairly_sound)
1371 fun helper_facts_for_sym_table ctxt format type_sys sym_tab =
1372 Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_sys) sym_tab
1375 (***************************************************************)
1376 (* Type Classes Present in the Axiom or Conjecture Clauses *)
1377 (***************************************************************)
1379 fun set_insert (x, s) = Symtab.update (x, ()) s
1381 fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
1383 (* Remove this trivial type class (FIXME: similar code elsewhere) *)
1384 fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
1386 fun classes_of_terms get_Ts =
1387 map (map snd o get_Ts)
1388 #> List.foldl add_classes Symtab.empty
1389 #> delete_type #> Symtab.keys
1391 val tfree_classes_of_terms = classes_of_terms OldTerm.term_tfrees
1392 val tvar_classes_of_terms = classes_of_terms OldTerm.term_tvars
1394 (*fold type constructors*)
1395 fun fold_type_constrs f (Type (a, Ts)) x =
1396 fold (fold_type_constrs f) Ts (f (a,x))
1397 | fold_type_constrs _ _ x = x
1399 (*Type constructors used to instantiate overloaded constants are the only ones needed.*)
1400 fun add_type_constrs_in_term thy =
1402 fun add (Const (@{const_name Meson.skolem}, _) $ _) = I
1403 | add (t $ u) = add t #> add u
1404 | add (Const (x as (s, _))) =
1405 if String.isPrefix skolem_const_prefix s then I
1406 else x |> Sign.const_typargs thy |> fold (fold_type_constrs set_insert)
1407 | add (Abs (_, _, u)) = add u
1411 fun type_constrs_of_terms thy ts =
1412 Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty)
1414 fun translate_formulas ctxt format prem_kind type_sys preproc hyp_ts concl_t
1417 val thy = Proof_Context.theory_of ctxt
1418 val fact_ts = facts |> map snd
1419 val presimp_consts = Meson.presimplified_consts ctxt
1421 make_fact ctxt format type_sys false true true presimp_consts
1422 val (facts, fact_names) =
1423 facts |> map (fn (name, t) => (name, t) |> make_fact |> rpair name)
1424 |> map_filter (try (apfst the))
1426 (* Remove existing facts from the conjecture, as this can dramatically
1427 boost an ATP's performance (for some reason). *)
1430 |> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t)
1431 val goal_t = Logic.list_implies (hyp_ts, concl_t)
1432 val all_ts = goal_t :: fact_ts
1433 val subs = tfree_classes_of_terms all_ts
1434 val supers = tvar_classes_of_terms all_ts
1435 val tycons = type_constrs_of_terms thy all_ts
1438 |> make_conjecture ctxt format prem_kind type_sys preproc presimp_consts
1439 val (supers', arity_clauses) =
1440 if level_of_type_sys type_sys = No_Types then ([], [])
1441 else make_arity_clauses thy tycons supers
1442 val class_rel_clauses = make_class_rel_clauses thy subs supers'
1444 (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
1447 fun fo_literal_from_type_literal (TyLitVar (class, name)) =
1448 (true, ATerm (class, [ATerm (name, [])]))
1449 | fo_literal_from_type_literal (TyLitFree (class, name)) =
1450 (true, ATerm (class, [ATerm (name, [])]))
1452 fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
1454 val type_pred = `make_fixed_const type_pred_name
1456 fun type_pred_combterm ctxt format type_sys T tm =
1457 CombApp (CombConst (type_pred, T --> @{typ bool}, [T])
1458 |> enforce_type_arg_policy_in_combterm ctxt format type_sys, tm)
1460 fun var_occurs_positively_naked_in_term _ (SOME false) _ accum = accum
1461 | var_occurs_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
1462 accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
1463 fun is_var_nonmonotonic_in_formula _ _ (SOME false) _ = false
1464 | is_var_nonmonotonic_in_formula pos phi _ name =
1465 formula_fold pos (var_occurs_positively_naked_in_term name) phi false
1467 fun mk_const_aterm format type_sys x T_args args =
1468 ATerm (x, map (fo_term_from_typ format type_sys) T_args @ args)
1470 fun tag_with_type ctxt format nonmono_Ts type_sys T tm =
1471 CombConst (type_tag, T --> T, [T])
1472 |> enforce_type_arg_policy_in_combterm ctxt format type_sys
1473 |> term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
1474 |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
1475 and term_from_combterm ctxt format nonmono_Ts type_sys =
1479 val (head, args) = strip_combterm_comb u
1480 val (x as (s, _), T_args) =
1482 CombConst (name, _, T_args) => (name, T_args)
1483 | CombVar (name, _) => (name, [])
1484 | CombApp _ => raise Fail "impossible \"CombApp\""
1485 val arg_site = if site = Top_Level andalso is_tptp_equal s then Eq_Arg
1487 val t = mk_const_aterm format type_sys x T_args
1488 (map (aux arg_site) args)
1489 val T = combtyp_of u
1491 t |> (if should_tag_with_type ctxt nonmono_Ts type_sys site u T then
1492 tag_with_type ctxt format nonmono_Ts type_sys T
1497 and formula_from_combformula ctxt format nonmono_Ts type_sys
1498 should_predicate_on_var =
1500 val do_term = term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
1503 Simple_Types level =>
1504 homogenized_type ctxt nonmono_Ts level 0
1505 #> mangled_type format type_sys false 0 #> SOME
1507 fun do_out_of_bound_type pos phi universal (name, T) =
1508 if should_predicate_on_type ctxt nonmono_Ts type_sys
1509 (fn () => should_predicate_on_var pos phi universal name) T then
1511 |> type_pred_combterm ctxt format type_sys T
1512 |> do_term |> AAtom |> SOME
1515 fun do_formula pos (AQuant (q, xs, phi)) =
1517 val phi = phi |> do_formula pos
1518 val universal = Option.map (q = AExists ? not) pos
1520 AQuant (q, xs |> map (apsnd (fn NONE => NONE
1521 | SOME T => do_bound_type T)),
1522 (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
1524 (fn (_, NONE) => NONE
1526 do_out_of_bound_type pos phi universal (s, T))
1530 | do_formula pos (AConn conn) = aconn_map pos do_formula conn
1531 | do_formula _ (AAtom tm) = AAtom (do_term tm)
1532 in do_formula o SOME end
1534 fun bound_tvars type_sys Ts =
1535 mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
1536 (type_literals_for_types type_sys add_sorts_on_tvar Ts))
1538 fun formula_for_fact ctxt format nonmono_Ts type_sys
1539 ({combformula, atomic_types, ...} : translated_formula) =
1541 |> close_combformula_universally
1542 |> formula_from_combformula ctxt format nonmono_Ts type_sys
1543 is_var_nonmonotonic_in_formula true
1544 |> bound_tvars type_sys atomic_types
1545 |> close_formula_universally
1547 (* Each fact is given a unique fact number to avoid name clashes (e.g., because
1548 of monomorphization). The TPTP explicitly forbids name clashes, and some of
1549 the remote provers might care. *)
1550 fun formula_line_for_fact ctxt format prefix encode freshen nonmono_Ts type_sys
1551 (j, formula as {name, locality, kind, ...}) =
1554 polymorphism_of_type_sys type_sys <> Polymorphic then
1555 string_of_int j ^ "_"
1558 kind, formula_for_fact ctxt format nonmono_Ts type_sys formula, NONE,
1565 fun formula_line_for_class_rel_clause ({name, subclass, superclass, ...}
1566 : class_rel_clause) =
1567 let val ty_arg = ATerm (`I "T", []) in
1568 Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
1569 AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
1570 AAtom (ATerm (superclass, [ty_arg]))])
1571 |> close_formula_universally, intro_info, NONE)
1574 fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
1575 (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
1576 | fo_literal_from_arity_literal (TVarLit (c, sort)) =
1577 (false, ATerm (c, [ATerm (sort, [])]))
1579 fun formula_line_for_arity_clause ({name, prem_lits, concl_lits, ...}
1581 Formula (arity_clause_prefix ^ ascii_of name, Axiom,
1582 mk_ahorn (map (formula_from_fo_literal o apfst not
1583 o fo_literal_from_arity_literal) prem_lits)
1584 (formula_from_fo_literal
1585 (fo_literal_from_arity_literal concl_lits))
1586 |> close_formula_universally, intro_info, NONE)
1588 fun formula_line_for_conjecture ctxt format nonmono_Ts type_sys
1589 ({name, kind, combformula, atomic_types, ...} : translated_formula) =
1590 Formula (conjecture_prefix ^ name, kind,
1591 formula_from_combformula ctxt format nonmono_Ts type_sys
1592 is_var_nonmonotonic_in_formula false
1593 (close_combformula_universally combformula)
1594 |> bound_tvars type_sys atomic_types
1595 |> close_formula_universally, NONE, NONE)
1597 fun free_type_literals type_sys ({atomic_types, ...} : translated_formula) =
1598 atomic_types |> type_literals_for_types type_sys add_sorts_on_tfree
1599 |> map fo_literal_from_type_literal
1601 fun formula_line_for_free_type j lit =
1602 Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis,
1603 formula_from_fo_literal lit, NONE, NONE)
1604 fun formula_lines_for_free_types type_sys facts =
1606 val litss = map (free_type_literals type_sys) facts
1607 val lits = fold (union (op =)) litss []
1608 in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
1610 (** Symbol declarations **)
1612 fun should_declare_sym type_sys pred_sym s =
1613 is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
1615 Simple_Types _ => true
1616 | Tags (_, _, Lightweight) => true
1617 | _ => not pred_sym)
1619 fun sym_decl_table_for_facts ctxt type_sys repaired_sym_tab (conjs, facts) =
1621 fun add_combterm in_conj tm =
1622 let val (head, args) = strip_combterm_comb tm in
1624 CombConst ((s, s'), T, T_args) =>
1625 let val pred_sym = is_pred_sym repaired_sym_tab s in
1626 if should_declare_sym type_sys pred_sym s then
1627 Symtab.map_default (s, [])
1628 (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
1634 #> fold (add_combterm in_conj) args
1636 fun add_fact in_conj =
1637 fact_lift (formula_fold NONE (K (add_combterm in_conj)))
1640 |> is_type_sys_fairly_sound type_sys
1641 ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
1644 (* These types witness that the type classes they belong to allow infinite
1645 models and hence that any types with these type classes is monotonic. *)
1646 val known_infinite_types =
1647 [@{typ nat}, Type ("Int.int", []), @{typ "nat => bool"}]
1649 (* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
1650 out with monotonicity" paper presented at CADE 2011. *)
1651 fun add_combterm_nonmonotonic_types _ _ _ (SOME false) _ = I
1652 | add_combterm_nonmonotonic_types ctxt level locality _
1653 (CombApp (CombApp (CombConst ((s, _), Type (_, [T, _]), _), tm1),
1655 (is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
1657 Nonmonotonic_Types =>
1658 not (is_locality_global locality) orelse
1659 not (is_type_surely_infinite ctxt known_infinite_types T)
1660 | Finite_Types => is_type_surely_finite ctxt T
1661 | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
1662 | add_combterm_nonmonotonic_types _ _ _ _ _ = I
1663 fun add_fact_nonmonotonic_types ctxt level ({kind, locality, combformula, ...}
1664 : translated_formula) =
1665 formula_fold (SOME (kind <> Conjecture))
1666 (add_combterm_nonmonotonic_types ctxt level locality) combformula
1667 fun nonmonotonic_types_for_facts ctxt type_sys facts =
1668 let val level = level_of_type_sys type_sys in
1669 if level = Nonmonotonic_Types orelse level = Finite_Types then
1670 [] |> fold (add_fact_nonmonotonic_types ctxt level) facts
1671 (* We must add "bool" in case the helper "True_or_False" is added
1672 later. In addition, several places in the code rely on the list of
1673 nonmonotonic types not being empty. *)
1674 |> insert_type ctxt I @{typ bool}
1679 fun decl_line_for_sym ctxt format nonmono_Ts type_sys s
1680 (s', T_args, T, pred_sym, ary, _) =
1682 val (T_arg_Ts, level) =
1684 Simple_Types level => ([], level)
1685 | _ => (replicate (length T_args) homo_infinite_type, No_Types)
1687 Decl (sym_decl_prefix ^ s, (s, s'),
1688 (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
1689 |> mangled_type format type_sys pred_sym (length T_arg_Ts + ary))
1692 fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
1694 fun formula_line_for_preds_sym_decl ctxt format conj_sym_kind nonmono_Ts
1695 type_sys n s j (s', T_args, T, _, ary, in_conj) =
1697 val (kind, maybe_negate) =
1698 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1700 val (arg_Ts, res_T) = chop_fun ary T
1702 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
1704 bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
1706 arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
1709 Formula (preds_sym_formula_prefix ^ s ^
1710 (if n > 1 then "_" ^ string_of_int j else ""), kind,
1711 CombConst ((s, s'), T, T_args)
1712 |> fold (curry (CombApp o swap)) bounds
1713 |> type_pred_combterm ctxt format type_sys res_T
1714 |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
1715 |> formula_from_combformula ctxt format nonmono_Ts type_sys
1716 (K (K (K (K true)))) true
1717 |> n > 1 ? bound_tvars type_sys (atyps_of T)
1718 |> close_formula_universally
1723 fun formula_lines_for_lightweight_tags_sym_decl ctxt format conj_sym_kind
1724 nonmono_Ts type_sys n s (j, (s', T_args, T, pred_sym, ary, in_conj)) =
1727 lightweight_tags_sym_formula_prefix ^ s ^
1728 (if n > 1 then "_" ^ string_of_int j else "")
1729 val (kind, maybe_negate) =
1730 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1732 val (arg_Ts, res_T) = chop_fun ary T
1734 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
1735 val bounds = bound_names |> map (fn name => ATerm (name, []))
1736 val cst = mk_const_aterm format type_sys (s, s') T_args
1737 val atomic_Ts = atyps_of T
1739 (if pred_sym then AConn (AIff, map AAtom tms)
1740 else AAtom (ATerm (`I tptp_equal, tms)))
1741 |> bound_tvars type_sys atomic_Ts
1742 |> close_formula_universally
1744 val should_encode = should_encode_type ctxt nonmono_Ts All_Types
1745 val tag_with = tag_with_type ctxt format nonmono_Ts type_sys
1746 val add_formula_for_res =
1747 if should_encode res_T then
1748 cons (Formula (ident_base ^ "_res", kind,
1749 eq [tag_with res_T (cst bounds), cst bounds],
1753 fun add_formula_for_arg k =
1754 let val arg_T = nth arg_Ts k in
1755 if should_encode arg_T then
1756 case chop k bounds of
1757 (bounds1, bound :: bounds2) =>
1758 cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
1759 eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
1762 | _ => raise Fail "expected nonempty tail"
1767 [] |> not pred_sym ? add_formula_for_res
1768 |> fold add_formula_for_arg (ary - 1 downto 0)
1771 fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
1773 fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts type_sys
1777 decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_sys s)
1782 decl :: (decls' as _ :: _) =>
1783 let val T = result_type_of_decl decl in
1784 if forall (curry (type_instance ctxt o swap) T
1785 o result_type_of_decl) decls' then
1791 val n = length decls
1794 |> filter (should_predicate_on_type ctxt nonmono_Ts type_sys (K true)
1795 o result_type_of_decl)
1797 (0 upto length decls - 1, decls)
1798 |-> map2 (formula_line_for_preds_sym_decl ctxt format conj_sym_kind
1799 nonmono_Ts type_sys n s)
1801 | Tags (_, _, heaviness) =>
1805 let val n = length decls in
1806 (0 upto n - 1 ~~ decls)
1807 |> maps (formula_lines_for_lightweight_tags_sym_decl ctxt format
1808 conj_sym_kind nonmono_Ts type_sys n s)
1811 fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1812 type_sys sym_decl_tab =
1817 |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
1818 nonmono_Ts type_sys)
1820 fun needs_type_tag_idempotence (Tags (poly, level, heaviness)) =
1821 poly <> Mangled_Monomorphic andalso
1822 ((level = All_Types andalso heaviness = Lightweight) orelse
1823 level = Nonmonotonic_Types orelse level = Finite_Types)
1824 | needs_type_tag_idempotence _ = false
1826 fun offset_of_heading_in_problem _ [] j = j
1827 | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
1828 if heading = needle then j
1829 else offset_of_heading_in_problem needle problem (j + length lines)
1831 val implicit_declsN = "Should-be-implicit typings"
1832 val explicit_declsN = "Explicit typings"
1833 val factsN = "Relevant facts"
1834 val class_relsN = "Class relationships"
1835 val aritiesN = "Arities"
1836 val helpersN = "Helper facts"
1837 val conjsN = "Conjectures"
1838 val free_typesN = "Type variables"
1840 val explicit_apply = NONE (* for experimental purposes *)
1842 fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_sys
1843 readable_names preproc hyp_ts concl_t facts =
1845 val (format, type_sys) = choose_format [format] type_sys
1846 val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
1847 translate_formulas ctxt format prem_kind type_sys preproc hyp_ts concl_t
1849 val sym_tab = conjs @ facts |> sym_table_for_facts ctxt explicit_apply
1850 val nonmono_Ts = conjs @ facts |> nonmonotonic_types_for_facts ctxt type_sys
1851 val repair = repair_fact ctxt format type_sys sym_tab
1852 val (conjs, facts) = (conjs, facts) |> pairself (map repair)
1853 val repaired_sym_tab =
1854 conjs @ facts |> sym_table_for_facts ctxt (SOME false)
1856 repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_sys
1858 val lavish_nonmono_Ts =
1859 if null nonmono_Ts orelse nonmono_Ts = [@{typ bool}] orelse
1860 polymorphism_of_type_sys type_sys <> Polymorphic then
1863 [TVar (("'a", 0), HOLogic.typeS)]
1864 val sym_decl_lines =
1865 (conjs, helpers @ facts)
1866 |> sym_decl_table_for_facts ctxt type_sys repaired_sym_tab
1867 |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind
1868 lavish_nonmono_Ts type_sys
1870 0 upto length helpers - 1 ~~ helpers
1871 |> map (formula_line_for_fact ctxt format helper_prefix I false
1872 lavish_nonmono_Ts type_sys)
1873 |> (if needs_type_tag_idempotence type_sys then
1874 cons (type_tag_idempotence_fact ())
1877 (* Reordering these might confuse the proof reconstruction code or the SPASS
1880 [(explicit_declsN, sym_decl_lines),
1882 map (formula_line_for_fact ctxt format fact_prefix ascii_of true
1883 nonmono_Ts type_sys)
1884 (0 upto length facts - 1 ~~ facts)),
1885 (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
1886 (aritiesN, map formula_line_for_arity_clause arity_clauses),
1887 (helpersN, helper_lines),
1889 map (formula_line_for_conjecture ctxt format nonmono_Ts type_sys)
1891 (free_typesN, formula_lines_for_free_types type_sys (facts @ conjs))]
1895 CNF => ensure_cnf_problem
1896 | CNF_UEQ => filter_cnf_ueq_problem
1898 |> (if is_format_typed format then
1899 declare_undeclared_syms_in_atp_problem type_decl_prefix
1903 val (problem, pool) = problem |> nice_atp_problem readable_names
1904 val helpers_offset = offset_of_heading_in_problem helpersN problem 0
1906 map_filter (fn (j, {name, ...}) =>
1907 if String.isSuffix typed_helper_suffix name then SOME j
1909 ((helpers_offset + 1 upto helpers_offset + length helpers)
1911 fun add_sym_arity (s, {min_ary, ...} : sym_info) =
1913 case strip_prefix_and_unascii const_prefix s of
1914 SOME s => Symtab.insert (op =) (s, min_ary)
1920 case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
1921 offset_of_heading_in_problem conjsN problem 0,
1922 offset_of_heading_in_problem factsN problem 0,
1923 fact_names |> Vector.fromList,
1925 Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
1929 val conj_weight = 0.0
1930 val hyp_weight = 0.1
1931 val fact_min_weight = 0.2
1932 val fact_max_weight = 1.0
1933 val type_info_default_weight = 0.8
1935 fun add_term_weights weight (ATerm (s, tms)) =
1936 is_tptp_user_symbol s ? Symtab.default (s, weight)
1937 #> fold (add_term_weights weight) tms
1938 fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
1939 formula_fold NONE (K (add_term_weights weight)) phi
1940 | add_problem_line_weights _ _ = I
1942 fun add_conjectures_weights [] = I
1943 | add_conjectures_weights conjs =
1944 let val (hyps, conj) = split_last conjs in
1945 add_problem_line_weights conj_weight conj
1946 #> fold (add_problem_line_weights hyp_weight) hyps
1949 fun add_facts_weights facts =
1951 val num_facts = length facts
1953 fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
1954 / Real.fromInt num_facts
1956 map weight_of (0 upto num_facts - 1) ~~ facts
1957 |> fold (uncurry add_problem_line_weights)
1960 (* Weights are from 0.0 (most important) to 1.0 (least important). *)
1961 fun atp_problem_weights problem =
1962 let val get = these o AList.lookup (op =) problem in
1964 |> add_conjectures_weights (get free_typesN @ get conjsN)
1965 |> add_facts_weights (get factsN)
1966 |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
1967 [explicit_declsN, class_relsN, aritiesN]
1969 |> sort (prod_ord Real.compare string_ord o pairself swap)