1 (* Title: HOL/Tools/ATP/atp_translate.ML
2 Author: Fabian Immler, TU Muenchen
4 Author: Jasmin Blanchette, TU Muenchen
6 Translation of HOL to FOL for Sledgehammer.
9 signature ATP_TRANSLATE =
11 type 'a fo_term = 'a ATP_Problem.fo_term
12 type connective = ATP_Problem.connective
13 type ('a, 'b, 'c) formula = ('a, 'b, 'c) ATP_Problem.formula
14 type format = ATP_Problem.format
15 type formula_kind = ATP_Problem.formula_kind
16 type 'a problem = 'a ATP_Problem.problem
18 type name = string * string
20 datatype type_literal =
21 TyLitVar of name * name |
22 TyLitFree of name * name
24 datatype arity_literal =
25 TConsLit of name * name * name list |
26 TVarLit of name * name
30 prem_lits: arity_literal list,
31 concl_lits: arity_literal}
33 type class_rel_clause =
39 CombConst of name * typ * typ list |
40 CombVar of name * typ |
41 CombApp of combterm * combterm
44 General | Helper | Extensionality | Intro | Elim | Simp | Local | Assum |
47 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
49 All_Types | Noninf_Nonmono_Types | Fin_Nonmono_Types | Const_Arg_Types |
51 datatype type_heaviness = Heavyweight | Lightweight
54 Simple_Types of type_level |
55 Preds of polymorphism * type_level * type_heaviness |
56 Tags of polymorphism * type_level * type_heaviness
58 val bound_var_prefix : string
59 val schematic_var_prefix: string
60 val fixed_var_prefix: string
61 val tvar_prefix: string
62 val tfree_prefix: string
63 val const_prefix: string
64 val type_const_prefix: string
65 val class_prefix: string
66 val skolem_const_prefix : string
67 val old_skolem_const_prefix : string
68 val new_skolem_const_prefix : string
69 val type_decl_prefix : string
70 val sym_decl_prefix : string
71 val preds_sym_formula_prefix : string
72 val lightweight_tags_sym_formula_prefix : string
73 val fact_prefix : string
74 val conjecture_prefix : string
75 val helper_prefix : string
76 val class_rel_clause_prefix : string
77 val arity_clause_prefix : string
78 val tfree_clause_prefix : string
79 val typed_helper_suffix : string
80 val untyped_helper_suffix : string
81 val type_tag_idempotence_helper_name : string
82 val predicator_name : string
83 val app_op_name : string
84 val type_tag_name : string
85 val type_pred_name : string
86 val simple_type_prefix : string
87 val prefixed_predicator_name : string
88 val prefixed_app_op_name : string
89 val prefixed_type_tag_name : string
90 val ascii_of: string -> string
91 val unascii_of: string -> string
92 val strip_prefix_and_unascii : string -> string -> string option
93 val proxy_table : (string * (string * (thm * (string * string)))) list
94 val proxify_const : string -> (string * string) option
95 val invert_const: string -> string
96 val unproxify_const: string -> string
97 val make_bound_var : string -> string
98 val make_schematic_var : string * int -> string
99 val make_fixed_var : string -> string
100 val make_schematic_type_var : string * int -> string
101 val make_fixed_type_var : string -> string
102 val make_fixed_const : string -> string
103 val make_fixed_type_const : string -> string
104 val make_type_class : string -> string
105 val new_skolem_var_name_from_const : string -> string
106 val num_type_args : theory -> string -> int
107 val atp_irrelevant_consts : string list
108 val atp_schematic_consts_of : term -> typ list Symtab.table
109 val make_arity_clauses :
110 theory -> string list -> class list -> class list * arity_clause list
111 val make_class_rel_clauses :
112 theory -> class list -> class list -> class_rel_clause list
113 val combtyp_of : combterm -> typ
114 val strip_combterm_comb : combterm -> combterm * combterm list
115 val atyps_of : typ -> typ list
116 val combterm_from_term :
117 theory -> (string * typ) list -> term -> combterm * typ list
118 val is_locality_global : locality -> bool
119 val type_sys_from_string : string -> type_sys
120 val polymorphism_of_type_sys : type_sys -> polymorphism
121 val level_of_type_sys : type_sys -> type_level
122 val is_type_sys_virtually_sound : type_sys -> bool
123 val is_type_sys_fairly_sound : type_sys -> bool
124 val choose_format : format list -> type_sys -> format * type_sys
126 connective -> ('a, 'b, 'c) formula list -> ('a, 'b, 'c) formula
127 val unmangled_const_name : string -> string
128 val unmangled_const : string -> string * string fo_term list
129 val helper_table : ((string * bool) * thm list) list
130 val should_specialize_helper : type_sys -> term -> bool
131 val tfree_classes_of_terms : term list -> string list
132 val tvar_classes_of_terms : term list -> string list
133 val type_constrs_of_terms : theory -> term list -> string list
134 val prepare_atp_problem :
135 Proof.context -> format -> formula_kind -> formula_kind -> type_sys
136 -> bool -> bool -> bool -> term list -> term
137 -> ((string * locality) * term) list
138 -> string problem * string Symtab.table * int * int
139 * (string * locality) list vector * int list * int Symtab.table
140 val atp_problem_weights : string problem -> (string * real) list
143 structure ATP_Translate : ATP_TRANSLATE =
149 type name = string * string
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 General.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 val type_class = the_single @{sort type}
398 fun add_packed_sort tvar =
399 fold (fn s => s <> type_class ? cons (`make_type_class s, `I tvar))
403 prem_lits: arity_literal list,
404 concl_lits: arity_literal}
406 (* Arity of type constructor "tcon :: (arg1, ..., argN) res" *)
407 fun make_axiom_arity_clause (tcons, name, (cls, args)) =
409 val tvars = gen_TVars (length args)
410 val tvars_srts = ListPair.zip (tvars, args)
413 prem_lits = [] |> fold (uncurry add_packed_sort) tvars_srts |> map TVarLit,
414 concl_lits = TConsLit (`make_type_class cls,
415 `make_fixed_type_const tcons,
419 fun arity_clause _ _ (_, []) = []
420 | arity_clause seen n (tcons, ("HOL.type", _) :: ars) = (* ignore *)
421 arity_clause seen n (tcons, ars)
422 | arity_clause seen n (tcons, (ar as (class, _)) :: ars) =
423 if member (op =) seen class then
424 (* multiple arities for the same (tycon, class) pair *)
425 make_axiom_arity_clause (tcons,
426 lookup_const tcons ^ "___" ^ ascii_of class ^ "_" ^ string_of_int n,
428 arity_clause seen (n + 1) (tcons, ars)
430 make_axiom_arity_clause (tcons, lookup_const tcons ^ "___" ^
431 ascii_of class, ar) ::
432 arity_clause (class :: seen) n (tcons, ars)
434 fun multi_arity_clause [] = []
435 | multi_arity_clause ((tcons, ars) :: tc_arlists) =
436 arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
438 (*Generate all pairs (tycon,class,sorts) such that tycon belongs to class in theory thy
439 provided its arguments have the corresponding sorts.*)
440 fun type_class_pairs thy tycons classes =
442 val alg = Sign.classes_of thy
443 fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
444 fun add_class tycon class =
445 cons (class, domain_sorts tycon class)
446 handle Sorts.CLASS_ERROR _ => I
447 fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
448 in map try_classes tycons end
450 (*Proving one (tycon, class) membership may require proving others, so iterate.*)
451 fun iter_type_class_pairs _ _ [] = ([], [])
452 | iter_type_class_pairs thy tycons classes =
454 fun maybe_insert_class s =
455 (s <> type_class andalso not (member (op =) classes s))
457 val cpairs = type_class_pairs thy tycons classes
459 [] |> fold (fold (fold (fold maybe_insert_class) o snd) o snd) cpairs
460 val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
461 in (classes' @ classes, union (op =) cpairs' cpairs) end
463 fun make_arity_clauses thy tycons =
464 iter_type_class_pairs thy tycons ##> multi_arity_clause
467 (** Isabelle class relations **)
469 type class_rel_clause =
474 (*Generate all pairs (sub,super) such that sub is a proper subclass of super in theory thy.*)
475 fun class_pairs _ [] _ = []
476 | class_pairs thy subs supers =
478 val class_less = Sorts.class_less (Sign.classes_of thy)
479 fun add_super sub super = class_less (sub, super) ? cons (sub, super)
480 fun add_supers sub = fold (add_super sub) supers
481 in fold add_supers subs [] end
483 fun make_class_rel_clause (sub,super) =
484 {name = sub ^ "_" ^ super,
485 subclass = `make_type_class sub,
486 superclass = `make_type_class super}
488 fun make_class_rel_clauses thy subs supers =
489 map make_class_rel_clause (class_pairs thy subs supers)
492 CombConst of name * typ * typ list |
493 CombVar of name * typ |
494 CombApp of combterm * combterm
496 fun combtyp_of (CombConst (_, T, _)) = T
497 | combtyp_of (CombVar (_, T)) = T
498 | combtyp_of (CombApp (t1, _)) = snd (dest_funT (combtyp_of t1))
500 (*gets the head of a combinator application, along with the list of arguments*)
501 fun strip_combterm_comb u =
502 let fun stripc (CombApp(t,u), ts) = stripc (t, u::ts)
506 fun atyps_of T = fold_atyps (insert (op =)) T []
508 fun new_skolem_const_name s num_T_args =
509 [new_skolem_const_prefix, s, string_of_int num_T_args]
510 |> space_implode Long_Name.separator
512 (* Converts a term (with combinators) into a combterm. Also accumulates sort
514 fun combterm_from_term thy bs (P $ Q) =
516 val (P', P_atomics_Ts) = combterm_from_term thy bs P
517 val (Q', Q_atomics_Ts) = combterm_from_term thy bs Q
518 in (CombApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
519 | combterm_from_term thy _ (Const (c, T)) =
522 (if String.isPrefix old_skolem_const_prefix c then
523 [] |> Term.add_tvarsT T |> map TVar
525 (c, T) |> Sign.const_typargs thy)
526 val c' = CombConst (`make_fixed_const c, T, tvar_list)
527 in (c', atyps_of T) end
528 | combterm_from_term _ _ (Free (v, T)) =
529 (CombConst (`make_fixed_var v, T, []), atyps_of T)
530 | combterm_from_term _ _ (Var (v as (s, _), T)) =
531 (if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
533 val Ts = T |> strip_type |> swap |> op ::
534 val s' = new_skolem_const_name s (length Ts)
535 in CombConst (`make_fixed_const s', T, Ts) end
537 CombVar ((make_schematic_var v, s), T), atyps_of T)
538 | combterm_from_term _ bs (Bound j) =
540 |> (fn (s, T) => (CombConst (`make_bound_var s, T, []), atyps_of T))
541 | combterm_from_term _ _ (Abs _) = raise Fail "HOL clause: Abs"
544 General | Helper | Extensionality | Intro | Elim | Simp | Local | Assum |
547 (* (quasi-)underapproximation of the truth *)
548 fun is_locality_global Local = false
549 | is_locality_global Assum = false
550 | is_locality_global Chained = false
551 | is_locality_global _ = true
553 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
554 datatype type_level =
555 All_Types | Noninf_Nonmono_Types | Fin_Nonmono_Types | Const_Arg_Types |
557 datatype type_heaviness = Heavyweight | Lightweight
560 Simple_Types of type_level |
561 Preds of polymorphism * type_level * type_heaviness |
562 Tags of polymorphism * type_level * type_heaviness
564 fun try_unsuffixes ss s =
565 fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
567 fun type_sys_from_string s =
568 (case try (unprefix "poly_") s of
569 SOME s => (SOME Polymorphic, s)
571 case try (unprefix "mono_") s of
572 SOME s => (SOME Monomorphic, s)
574 case try (unprefix "mangled_") s of
575 SOME s => (SOME Mangled_Monomorphic, s)
578 (* "_query" and "_bang" are for the ASCII-challenged Mirabelle. *)
579 case try_unsuffixes ["?", "_query"] s of
580 SOME s => (Noninf_Nonmono_Types, s)
582 case try_unsuffixes ["!", "_bang"] s of
583 SOME s => (Fin_Nonmono_Types, s)
584 | NONE => (All_Types, s))
586 case try (unsuffix "_heavy") s of
587 SOME s => (Heavyweight, s)
588 | NONE => (Lightweight, s))
589 |> (fn (poly, (level, (heaviness, core))) =>
590 case (core, (poly, level, heaviness)) of
591 ("simple", (NONE, _, Lightweight)) => Simple_Types level
592 | ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
593 | ("tags", (SOME Polymorphic, _, _)) =>
594 Tags (Polymorphic, level, heaviness)
595 | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
596 | ("args", (SOME poly, All_Types (* naja *), Lightweight)) =>
597 Preds (poly, Const_Arg_Types, Lightweight)
598 | ("erased", (NONE, All_Types (* naja *), Lightweight)) =>
599 Preds (Polymorphic, No_Types, Lightweight)
600 | _ => raise Same.SAME)
601 handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
603 fun polymorphism_of_type_sys (Simple_Types _) = Mangled_Monomorphic
604 | polymorphism_of_type_sys (Preds (poly, _, _)) = poly
605 | polymorphism_of_type_sys (Tags (poly, _, _)) = poly
607 fun level_of_type_sys (Simple_Types level) = level
608 | level_of_type_sys (Preds (_, level, _)) = level
609 | level_of_type_sys (Tags (_, level, _)) = level
611 fun heaviness_of_type_sys (Simple_Types _) = Heavyweight
612 | heaviness_of_type_sys (Preds (_, _, heaviness)) = heaviness
613 | heaviness_of_type_sys (Tags (_, _, heaviness)) = heaviness
615 fun is_type_level_virtually_sound level =
616 level = All_Types orelse level = Noninf_Nonmono_Types
617 val is_type_sys_virtually_sound =
618 is_type_level_virtually_sound o level_of_type_sys
620 fun is_type_level_fairly_sound level =
621 is_type_level_virtually_sound level orelse level = Fin_Nonmono_Types
622 val is_type_sys_fairly_sound = is_type_level_fairly_sound o level_of_type_sys
624 fun is_setting_higher_order THF (Simple_Types _) = true
625 | is_setting_higher_order _ _ = false
627 fun choose_format formats (Simple_Types level) =
628 if member (op =) formats THF then (THF, Simple_Types level)
629 else if member (op =) formats TFF then (TFF, Simple_Types level)
630 else choose_format formats (Preds (Mangled_Monomorphic, level, Heavyweight))
631 | choose_format formats type_sys =
634 (CNF_UEQ, case type_sys of
636 (if is_type_sys_fairly_sound type_sys then Tags else Preds)
639 | format => (format, type_sys))
641 type translated_formula =
645 combformula: (name, typ, combterm) formula,
646 atomic_types: typ list}
648 fun update_combformula f ({name, locality, kind, combformula, atomic_types}
649 : translated_formula) =
650 {name = name, locality = locality, kind = kind, combformula = f combformula,
651 atomic_types = atomic_types} : translated_formula
653 fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
655 val type_instance = Sign.typ_instance o Proof_Context.theory_of
657 fun insert_type ctxt get_T x xs =
658 let val T = get_T x in
659 if exists (curry (type_instance ctxt) T o get_T) xs then xs
660 else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
663 (* The Booleans indicate whether all type arguments should be kept. *)
664 datatype type_arg_policy =
665 Explicit_Type_Args of bool |
666 Mangled_Type_Args of bool |
669 fun should_drop_arg_type_args (Simple_Types _) =
670 false (* since TFF doesn't support overloading *)
671 | should_drop_arg_type_args type_sys =
672 level_of_type_sys type_sys = All_Types andalso
673 heaviness_of_type_sys type_sys = Heavyweight
675 fun general_type_arg_policy (Tags (_, All_Types, Heavyweight)) = No_Type_Args
676 | general_type_arg_policy type_sys =
677 if level_of_type_sys type_sys = No_Types then
679 else if polymorphism_of_type_sys type_sys = Mangled_Monomorphic then
680 Mangled_Type_Args (should_drop_arg_type_args type_sys)
682 Explicit_Type_Args (should_drop_arg_type_args type_sys)
684 fun type_arg_policy type_sys s =
685 if s = @{const_name HOL.eq} orelse
686 (s = app_op_name andalso level_of_type_sys type_sys = Const_Arg_Types) then
688 else if s = type_tag_name then
689 Explicit_Type_Args false
691 general_type_arg_policy type_sys
693 (*Make literals for sorted type variables*)
694 fun generic_add_sorts_on_type (_, []) = I
695 | generic_add_sorts_on_type ((x, i), s :: ss) =
696 generic_add_sorts_on_type ((x, i), ss)
697 #> (if s = the_single @{sort HOL.type} then
700 insert (op =) (TyLitFree (`make_type_class s, `make_fixed_type_var x))
702 insert (op =) (TyLitVar (`make_type_class s,
703 (make_schematic_type_var (x, i), x))))
704 fun add_sorts_on_tfree (TFree (s, S)) = generic_add_sorts_on_type ((s, ~1), S)
705 | add_sorts_on_tfree _ = I
706 fun add_sorts_on_tvar (TVar z) = generic_add_sorts_on_type z
707 | add_sorts_on_tvar _ = I
709 fun type_literals_for_types type_sys add_sorts_on_typ Ts =
710 [] |> level_of_type_sys type_sys <> No_Types ? fold add_sorts_on_typ Ts
712 fun mk_aconns c phis =
713 let val (phis', phi') = split_last phis in
714 fold_rev (mk_aconn c) phis' phi'
716 fun mk_ahorn [] phi = phi
717 | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
718 fun mk_aquant _ [] phi = phi
719 | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
720 if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
721 | mk_aquant q xs phi = AQuant (q, xs, phi)
723 fun close_universally atom_vars phi =
725 fun formula_vars bounds (AQuant (_, xs, phi)) =
726 formula_vars (map fst xs @ bounds) phi
727 | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
728 | formula_vars bounds (AAtom tm) =
729 union (op =) (atom_vars tm []
730 |> filter_out (member (op =) bounds o fst))
731 in mk_aquant AForall (formula_vars [] phi []) phi end
733 fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
734 | combterm_vars (CombConst _) = I
735 | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
736 fun close_combformula_universally phi = close_universally combterm_vars phi
738 fun term_vars (ATerm (name as (s, _), tms)) =
739 is_tptp_variable s ? insert (op =) (name, NONE) #> fold term_vars tms
740 fun close_formula_universally phi = close_universally term_vars phi
742 val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
743 val homo_infinite_type = Type (homo_infinite_type_name, [])
745 fun fo_term_from_typ format type_sys =
747 fun term (Type (s, Ts)) =
748 ATerm (case (is_setting_higher_order format type_sys, s) of
749 (true, @{type_name bool}) => `I tptp_bool_type
750 | (true, @{type_name fun}) => `I tptp_fun_type
751 | _ => if s = homo_infinite_type_name andalso
752 (format = TFF orelse format = THF) then
753 `I tptp_individual_type
755 `make_fixed_type_const s,
757 | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
758 | term (TVar ((x as (s, _)), _)) =
759 ATerm ((make_schematic_type_var x, s), [])
762 fun fo_term_for_type_arg format type_sys T =
763 if T = dummyT then NONE else SOME (fo_term_from_typ format type_sys T)
765 (* This shouldn't clash with anything else. *)
766 val mangled_type_sep = "\000"
768 fun generic_mangled_type_name f (ATerm (name, [])) = f name
769 | generic_mangled_type_name f (ATerm (name, tys)) =
770 f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
773 val bool_atype = AType (`I tptp_bool_type)
775 fun make_simple_type s =
776 if s = tptp_bool_type orelse s = tptp_fun_type orelse
777 s = tptp_individual_type then
780 simple_type_prefix ^ ascii_of s
782 fun ho_type_from_fo_term format type_sys pred_sym ary =
785 AType ((make_simple_type (generic_mangled_type_name fst ty),
786 generic_mangled_type_name snd ty))
787 fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
788 fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
789 | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
790 fun to_ho (ty as ATerm ((s, _), tys)) =
791 if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
792 in if is_setting_higher_order format type_sys then to_ho else to_fo ary end
794 fun mangled_type format type_sys pred_sym ary =
795 ho_type_from_fo_term format type_sys pred_sym ary
796 o fo_term_from_typ format type_sys
798 fun mangled_const_name format type_sys T_args (s, s') =
800 val ty_args = T_args |> map_filter (fo_term_for_type_arg format type_sys)
801 fun type_suffix f g =
802 fold_rev (curry (op ^) o g o prefix mangled_type_sep
803 o generic_mangled_type_name f) ty_args ""
804 in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
806 val parse_mangled_ident =
807 Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
809 fun parse_mangled_type x =
811 -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
813 and parse_mangled_types x =
814 (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
816 fun unmangled_type s =
817 s |> suffix ")" |> raw_explode
818 |> Scan.finite Symbol.stopper
819 (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
820 quote s)) parse_mangled_type))
823 val unmangled_const_name = space_explode mangled_type_sep #> hd
824 fun unmangled_const s =
825 let val ss = space_explode mangled_type_sep s in
826 (hd ss, map unmangled_type (tl ss))
829 fun introduce_proxies format type_sys =
831 fun intro top_level (CombApp (tm1, tm2)) =
832 CombApp (intro top_level tm1, intro false tm2)
833 | intro top_level (CombConst (name as (s, _), T, T_args)) =
834 (case proxify_const s of
836 if top_level orelse is_setting_higher_order format type_sys then
837 case (top_level, s) of
838 (_, "c_False") => (`I tptp_false, [])
839 | (_, "c_True") => (`I tptp_true, [])
840 | (false, "c_Not") => (`I tptp_not, [])
841 | (false, "c_conj") => (`I tptp_and, [])
842 | (false, "c_disj") => (`I tptp_or, [])
843 | (false, "c_implies") => (`I tptp_implies, [])
845 if is_tptp_equal s then (`I tptp_equal, [])
846 else (proxy_base |>> prefix const_prefix, T_args)
849 (proxy_base |>> prefix const_prefix, T_args)
850 | NONE => (name, T_args))
851 |> (fn (name, T_args) => CombConst (name, T, T_args))
855 fun combformula_from_prop thy format type_sys eq_as_iff =
857 fun do_term bs t atomic_types =
858 combterm_from_term thy bs (Envir.eta_contract t)
859 |>> (introduce_proxies format type_sys #> AAtom)
860 ||> union (op =) atomic_types
861 fun do_quant bs q s T t' =
862 let val s = singleton (Name.variant_list (map fst bs)) s in
863 do_formula ((s, T) :: bs) t'
864 #>> mk_aquant q [(`make_bound_var s, SOME T)]
866 and do_conn bs c t1 t2 =
867 do_formula bs t1 ##>> do_formula bs t2 #>> uncurry (mk_aconn c)
868 and do_formula bs t =
870 @{const Trueprop} $ t1 => do_formula bs t1
871 | @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
872 | Const (@{const_name All}, _) $ Abs (s, T, t') =>
873 do_quant bs AForall s T t'
874 | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
875 do_quant bs AExists s T t'
876 | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
877 | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
878 | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
879 | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
880 if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
884 fun presimplify_term _ [] t = t
885 | presimplify_term ctxt presimp_consts t =
886 t |> exists_Const (member (op =) presimp_consts o fst) t
887 ? (Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
888 #> Meson.presimplify ctxt
891 fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
892 fun conceal_bounds Ts t =
893 subst_bounds (map (Free o apfst concealed_bound_name)
894 (0 upto length Ts - 1 ~~ Ts), t)
895 fun reveal_bounds Ts =
896 subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
897 (0 upto length Ts - 1 ~~ Ts))
899 fun is_fun_equality (@{const_name HOL.eq},
900 Type (_, [Type (@{type_name fun}, _), _])) = true
901 | is_fun_equality _ = false
903 fun extensionalize_term ctxt t =
904 if exists_Const is_fun_equality t then
905 let val thy = Proof_Context.theory_of ctxt in
906 t |> cterm_of thy |> Meson.extensionalize_conv ctxt
907 |> prop_of |> Logic.dest_equals |> snd
912 fun introduce_combinators_in_term ctxt kind t =
913 let val thy = Proof_Context.theory_of ctxt in
914 if Meson.is_fol_term thy t then
920 @{const Not} $ t1 => @{const Not} $ aux Ts t1
921 | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
922 t0 $ Abs (s, T, aux (T :: Ts) t')
923 | (t0 as Const (@{const_name All}, _)) $ t1 =>
924 aux Ts (t0 $ eta_expand Ts t1 1)
925 | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
926 t0 $ Abs (s, T, aux (T :: Ts) t')
927 | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
928 aux Ts (t0 $ eta_expand Ts t1 1)
929 | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
930 | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
931 | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
932 | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
934 t0 $ aux Ts t1 $ aux Ts t2
935 | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
938 t |> conceal_bounds Ts
939 |> Envir.eta_contract
941 |> Meson_Clausify.introduce_combinators_in_cterm
942 |> prop_of |> Logic.dest_equals |> snd
944 val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
945 in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
947 (* A type variable of sort "{}" will make abstraction fail. *)
948 if kind = Conjecture then HOLogic.false_const
949 else HOLogic.true_const
952 (* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
953 same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
956 fun aux (t $ u) = aux t $ aux u
957 | aux (Abs (s, T, t)) = Abs (s, T, aux t)
958 | aux (Var ((s, i), T)) =
959 Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
961 in t |> exists_subterm is_Var t ? aux end
963 fun preprocess_prop ctxt presimp_consts kind t =
965 val thy = Proof_Context.theory_of ctxt
966 val t = t |> Envir.beta_eta_contract
967 |> transform_elim_prop
968 |> Object_Logic.atomize_term thy
969 val need_trueprop = (fastype_of t = @{typ bool})
971 t |> need_trueprop ? HOLogic.mk_Trueprop
972 |> Raw_Simplifier.rewrite_term thy (Meson.unfold_set_const_simps ctxt) []
973 |> extensionalize_term ctxt
974 |> presimplify_term ctxt presimp_consts
975 |> perhaps (try (HOLogic.dest_Trueprop))
976 |> introduce_combinators_in_term ctxt kind
979 (* making fact and conjecture formulas *)
980 fun make_formula thy format type_sys eq_as_iff name loc kind t =
982 val (combformula, atomic_types) =
983 combformula_from_prop thy format type_sys eq_as_iff t []
985 {name = name, locality = loc, kind = kind, combformula = combformula,
986 atomic_types = atomic_types}
989 fun make_fact ctxt format type_sys eq_as_iff preproc presimp_consts
991 let val thy = Proof_Context.theory_of ctxt in
992 case t |> preproc ? preprocess_prop ctxt presimp_consts Axiom
993 |> make_formula thy format type_sys (eq_as_iff andalso format <> CNF)
995 formula as {combformula = AAtom (CombConst ((s, _), _, _)), ...} =>
996 if s = tptp_true then NONE else SOME formula
997 | formula => SOME formula
1000 fun make_conjecture ctxt format prem_kind type_sys preproc presimp_consts ts =
1002 val thy = Proof_Context.theory_of ctxt
1003 val last = length ts - 1
1005 map2 (fn j => fn t =>
1007 val (kind, maybe_negate) =
1012 if prem_kind = Conjecture then update_combformula mk_anot
1016 (preprocess_prop ctxt presimp_consts kind #> freeze_term)
1017 |> make_formula thy format type_sys (format <> CNF)
1018 (string_of_int j) Local kind
1024 (** Finite and infinite type inference **)
1026 fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
1027 | deep_freeze_atyp T = T
1028 val deep_freeze_type = map_atyps deep_freeze_atyp
1030 (* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
1031 dangerous because their "exhaust" properties can easily lead to unsound ATP
1032 proofs. On the other hand, all HOL infinite types can be given the same
1033 models in first-order logic (via Löwenheim-Skolem). *)
1035 fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
1036 exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
1037 | should_encode_type _ _ All_Types _ = true
1038 | should_encode_type ctxt _ Fin_Nonmono_Types T = is_type_surely_finite ctxt T
1039 | should_encode_type _ _ _ _ = false
1041 fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
1042 should_predicate_on_var T =
1043 (heaviness = Heavyweight orelse should_predicate_on_var ()) andalso
1044 should_encode_type ctxt nonmono_Ts level T
1045 | should_predicate_on_type _ _ _ _ _ = false
1047 fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
1048 String.isPrefix bound_var_prefix s
1049 | is_var_or_bound_var (CombVar _) = true
1050 | is_var_or_bound_var _ = false
1053 Top_Level of bool option |
1054 Eq_Arg of bool option |
1057 fun should_tag_with_type _ _ _ (Top_Level _) _ _ = false
1058 | should_tag_with_type ctxt nonmono_Ts (Tags (poly, level, heaviness)) site
1061 Heavyweight => should_encode_type ctxt nonmono_Ts level T
1063 case (site, is_var_or_bound_var u) of
1064 (Eq_Arg pos, true) =>
1065 (* The first disjunct prevents a subtle soundness issue explained in
1066 Blanchette's Ph.D. thesis. See also
1067 "formula_lines_for_lightweight_tags_sym_decl". *)
1068 (pos <> SOME false andalso poly = Polymorphic andalso
1069 level <> All_Types andalso heaviness = Lightweight andalso
1070 exists (fn T' => type_instance ctxt (T', T)) nonmono_Ts) orelse
1071 should_encode_type ctxt nonmono_Ts level T
1073 | should_tag_with_type _ _ _ _ _ _ = false
1075 fun homogenized_type ctxt nonmono_Ts level =
1077 val should_encode = should_encode_type ctxt nonmono_Ts level
1078 fun homo 0 T = if should_encode T then T else homo_infinite_type
1079 | homo ary (Type (@{type_name fun}, [T1, T2])) =
1080 homo 0 T1 --> homo (ary - 1) T2
1081 | homo _ _ = raise Fail "expected function type"
1084 (** "hBOOL" and "hAPP" **)
1087 {pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
1089 fun add_combterm_syms_to_table ctxt explicit_apply =
1091 fun consider_var_arity const_T var_T max_ary =
1094 if ary = max_ary orelse type_instance ctxt (var_T, T) orelse
1095 type_instance ctxt (T, var_T) then
1098 iter (ary + 1) (range_type T)
1099 in iter 0 const_T end
1100 fun add_var_or_bound_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1101 if explicit_apply = NONE andalso
1102 (can dest_funT T orelse T = @{typ bool}) then
1104 val bool_vars' = bool_vars orelse body_type T = @{typ bool}
1105 fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
1106 {pred_sym = pred_sym andalso not bool_vars',
1107 min_ary = fold (fn T' => consider_var_arity T' T) types min_ary,
1108 max_ary = max_ary, types = types}
1110 fun_var_Ts |> can dest_funT T ? insert_type ctxt I T
1112 if bool_vars' = bool_vars andalso
1113 pointer_eq (fun_var_Ts', fun_var_Ts) then
1116 ((bool_vars', fun_var_Ts'), Symtab.map (K repair_min_arity) sym_tab)
1120 fun add top_level tm (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1121 let val (head, args) = strip_combterm_comb tm in
1123 CombConst ((s, _), T, _) =>
1124 if String.isPrefix bound_var_prefix s then
1125 add_var_or_bound_var T accum
1127 let val ary = length args in
1128 ((bool_vars, fun_var_Ts),
1129 case Symtab.lookup sym_tab s of
1130 SOME {pred_sym, min_ary, max_ary, types} =>
1133 pred_sym andalso top_level andalso not bool_vars
1134 val types' = types |> insert_type ctxt I T
1136 if is_some explicit_apply orelse
1137 pointer_eq (types', types) then
1140 fold (consider_var_arity T) fun_var_Ts min_ary
1142 Symtab.update (s, {pred_sym = pred_sym,
1143 min_ary = Int.min (ary, min_ary),
1144 max_ary = Int.max (ary, max_ary),
1150 val pred_sym = top_level andalso not bool_vars
1152 case explicit_apply of
1155 | NONE => fold (consider_var_arity T) fun_var_Ts ary
1157 Symtab.update_new (s, {pred_sym = pred_sym,
1158 min_ary = min_ary, max_ary = ary,
1163 | CombVar (_, T) => add_var_or_bound_var T accum
1165 |> fold (add false) args
1168 fun add_fact_syms_to_table ctxt explicit_apply =
1169 fact_lift (formula_fold NONE
1170 (K (add_combterm_syms_to_table ctxt explicit_apply)))
1172 val default_sym_tab_entries : (string * sym_info) list =
1173 (prefixed_predicator_name,
1174 {pred_sym = true, min_ary = 1, max_ary = 1, types = []}) ::
1175 ([tptp_false, tptp_true]
1176 |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []})) @
1177 ([tptp_equal, tptp_old_equal]
1178 |> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = []}))
1180 fun sym_table_for_facts ctxt explicit_apply facts =
1181 ((false, []), Symtab.empty)
1182 |> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
1183 |> fold Symtab.update default_sym_tab_entries
1185 fun min_arity_of sym_tab s =
1186 case Symtab.lookup sym_tab s of
1187 SOME ({min_ary, ...} : sym_info) => min_ary
1189 case strip_prefix_and_unascii const_prefix s of
1191 let val s = s |> unmangled_const_name |> invert_const in
1192 if s = predicator_name then 1
1193 else if s = app_op_name then 2
1194 else if s = type_pred_name then 1
1199 (* True if the constant ever appears outside of the top-level position in
1200 literals, or if it appears with different arities (e.g., because of different
1201 type instantiations). If false, the constant always receives all of its
1202 arguments and is used as a predicate. *)
1203 fun is_pred_sym sym_tab s =
1204 case Symtab.lookup sym_tab s of
1205 SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
1206 pred_sym andalso min_ary = max_ary
1209 val predicator_combconst =
1210 CombConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
1211 fun predicator tm = CombApp (predicator_combconst, tm)
1213 fun introduce_predicators_in_combterm sym_tab tm =
1214 case strip_combterm_comb tm of
1215 (CombConst ((s, _), _, _), _) =>
1216 if is_pred_sym sym_tab s then tm else predicator tm
1217 | _ => predicator tm
1219 fun list_app head args = fold (curry (CombApp o swap)) args head
1221 val app_op = `make_fixed_const app_op_name
1223 fun explicit_app arg head =
1225 val head_T = combtyp_of head
1226 val (arg_T, res_T) = dest_funT head_T
1228 CombConst (app_op, head_T --> head_T, [arg_T, res_T])
1229 in list_app explicit_app [head, arg] end
1230 fun list_explicit_app head args = fold explicit_app args head
1232 fun introduce_explicit_apps_in_combterm sym_tab =
1235 case strip_combterm_comb tm of
1236 (head as CombConst ((s, _), _, _), args) =>
1238 |> chop (min_arity_of sym_tab s)
1240 |-> list_explicit_app
1241 | (head, args) => list_explicit_app head (map aux args)
1244 fun chop_fun 0 T = ([], T)
1245 | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
1246 chop_fun (n - 1) ran_T |>> cons dom_T
1247 | chop_fun _ _ = raise Fail "unexpected non-function"
1249 fun filter_type_args _ _ _ [] = []
1250 | filter_type_args thy s arity T_args =
1252 (* will throw "TYPE" for pseudo-constants *)
1253 val U = if s = app_op_name then
1254 @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
1256 s |> Sign.the_const_type thy
1258 case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
1261 let val U_args = (s, U) |> Sign.const_typargs thy in
1263 |> map (fn (U, T) =>
1264 if member (op =) res_U_vars (dest_TVar U) then T
1268 handle TYPE _ => T_args
1270 fun enforce_type_arg_policy_in_combterm ctxt format type_sys =
1272 val thy = Proof_Context.theory_of ctxt
1273 fun aux arity (CombApp (tm1, tm2)) =
1274 CombApp (aux (arity + 1) tm1, aux 0 tm2)
1275 | aux arity (CombConst (name as (s, _), T, T_args)) =
1276 (case strip_prefix_and_unascii const_prefix s of
1277 NONE => (name, T_args)
1280 val s'' = invert_const s''
1281 fun filtered_T_args false = T_args
1282 | filtered_T_args true = filter_type_args thy s'' arity T_args
1284 case type_arg_policy type_sys s'' of
1285 Explicit_Type_Args drop_args =>
1286 (name, filtered_T_args drop_args)
1287 | Mangled_Type_Args drop_args =>
1288 (mangled_const_name format type_sys (filtered_T_args drop_args)
1290 | No_Type_Args => (name, [])
1292 |> (fn (name, T_args) => CombConst (name, T, T_args))
1296 fun repair_combterm ctxt format type_sys sym_tab =
1297 not (is_setting_higher_order format type_sys)
1298 ? (introduce_explicit_apps_in_combterm sym_tab
1299 #> introduce_predicators_in_combterm sym_tab)
1300 #> enforce_type_arg_policy_in_combterm ctxt format type_sys
1301 fun repair_fact ctxt format type_sys sym_tab =
1302 update_combformula (formula_map
1303 (repair_combterm ctxt format type_sys sym_tab))
1305 (** Helper facts **)
1307 (* The Boolean indicates that a fairly sound type encoding is needed. *)
1309 [(("COMBI", false), @{thms Meson.COMBI_def}),
1310 (("COMBK", false), @{thms Meson.COMBK_def}),
1311 (("COMBB", false), @{thms Meson.COMBB_def}),
1312 (("COMBC", false), @{thms Meson.COMBC_def}),
1313 (("COMBS", false), @{thms Meson.COMBS_def}),
1315 (* This is a lie: Higher-order equality doesn't need a sound type encoding.
1316 However, this is done so for backward compatibility: Including the
1317 equality helpers by default in Metis breaks a few existing proofs. *)
1318 @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1319 fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1320 (("fFalse", false), [@{lemma "~ fFalse" by (unfold fFalse_def) fast}]),
1321 (("fFalse", true), @{thms True_or_False}),
1322 (("fTrue", false), [@{lemma "fTrue" by (unfold fTrue_def) fast}]),
1323 (("fTrue", true), @{thms True_or_False}),
1325 @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1326 fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1328 @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
1329 by (unfold fconj_def) fast+}),
1331 @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
1332 by (unfold fdisj_def) fast+}),
1333 (("fimplies", false),
1334 @{lemma "P | fimplies P Q" "~ Q | fimplies P Q" "~ fimplies P Q | ~ P | Q"
1335 by (unfold fimplies_def) fast+}),
1336 (("If", true), @{thms if_True if_False True_or_False})]
1337 |> map (apsnd (map zero_var_indexes))
1339 val type_tag = `make_fixed_const type_tag_name
1341 fun type_tag_idempotence_fact () =
1343 fun var s = ATerm (`I s, [])
1344 fun tag tm = ATerm (type_tag, [var "T", tm])
1345 val tagged_a = tag (var "A")
1347 Formula (type_tag_idempotence_helper_name, Axiom,
1348 AAtom (ATerm (`I tptp_equal, [tag tagged_a, tagged_a]))
1349 |> close_formula_universally, simp_info, NONE)
1352 fun should_specialize_helper type_sys t =
1353 case general_type_arg_policy type_sys of
1354 Mangled_Type_Args _ => not (null (Term.hidden_polymorphism t))
1357 fun helper_facts_for_sym ctxt format type_sys (s, {types, ...} : sym_info) =
1358 case strip_prefix_and_unascii const_prefix s of
1361 val thy = Proof_Context.theory_of ctxt
1362 val unmangled_s = mangled_s |> unmangled_const_name
1363 fun dub_and_inst needs_fairly_sound (th, j) =
1364 ((unmangled_s ^ "_" ^ string_of_int j ^
1365 (if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^
1366 (if needs_fairly_sound then typed_helper_suffix
1367 else untyped_helper_suffix),
1369 let val t = th |> prop_of in
1370 t |> should_specialize_helper type_sys t
1372 [T] => specialize_type thy (invert_const unmangled_s, T)
1376 map_filter (make_fact ctxt format type_sys false false [])
1377 val fairly_sound = is_type_sys_fairly_sound type_sys
1380 |> maps (fn ((helper_s, needs_fairly_sound), ths) =>
1381 if helper_s <> unmangled_s orelse
1382 (needs_fairly_sound andalso not fairly_sound) then
1385 ths ~~ (1 upto length ths)
1386 |> map (dub_and_inst needs_fairly_sound)
1390 fun helper_facts_for_sym_table ctxt format type_sys sym_tab =
1391 Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_sys) sym_tab
1394 (***************************************************************)
1395 (* Type Classes Present in the Axiom or Conjecture Clauses *)
1396 (***************************************************************)
1398 fun set_insert (x, s) = Symtab.update (x, ()) s
1400 fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
1402 (* Remove this trivial type class (FIXME: similar code elsewhere) *)
1403 fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
1405 fun classes_of_terms get_Ts =
1406 map (map snd o get_Ts)
1407 #> List.foldl add_classes Symtab.empty
1408 #> delete_type #> Symtab.keys
1410 val tfree_classes_of_terms = classes_of_terms OldTerm.term_tfrees
1411 val tvar_classes_of_terms = classes_of_terms OldTerm.term_tvars
1413 (*fold type constructors*)
1414 fun fold_type_constrs f (Type (a, Ts)) x =
1415 fold (fold_type_constrs f) Ts (f (a,x))
1416 | fold_type_constrs _ _ x = x
1418 (*Type constructors used to instantiate overloaded constants are the only ones needed.*)
1419 fun add_type_constrs_in_term thy =
1421 fun add (Const (@{const_name Meson.skolem}, _) $ _) = I
1422 | add (t $ u) = add t #> add u
1423 | add (Const (x as (s, _))) =
1424 if String.isPrefix skolem_const_prefix s then I
1425 else x |> Sign.const_typargs thy |> fold (fold_type_constrs set_insert)
1426 | add (Abs (_, _, u)) = add u
1430 fun type_constrs_of_terms thy ts =
1431 Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty)
1433 fun translate_formulas ctxt format prem_kind type_sys preproc hyp_ts concl_t
1436 val thy = Proof_Context.theory_of ctxt
1437 val fact_ts = facts |> map snd
1438 val presimp_consts = Meson.presimplified_consts ctxt
1439 val make_fact = make_fact ctxt format type_sys true preproc presimp_consts
1440 val (facts, fact_names) =
1441 facts |> map (fn (name, t) => (name, t) |> make_fact |> rpair name)
1442 |> map_filter (try (apfst the))
1444 (* Remove existing facts from the conjecture, as this can dramatically
1445 boost an ATP's performance (for some reason). *)
1448 |> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t)
1449 val goal_t = Logic.list_implies (hyp_ts, concl_t)
1450 val all_ts = goal_t :: fact_ts
1451 val subs = tfree_classes_of_terms all_ts
1452 val supers = tvar_classes_of_terms all_ts
1453 val tycons = type_constrs_of_terms thy all_ts
1456 |> make_conjecture ctxt format prem_kind type_sys preproc presimp_consts
1457 val (supers', arity_clauses) =
1458 if level_of_type_sys type_sys = No_Types then ([], [])
1459 else make_arity_clauses thy tycons supers
1460 val class_rel_clauses = make_class_rel_clauses thy subs supers'
1462 (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
1465 fun fo_literal_from_type_literal (TyLitVar (class, name)) =
1466 (true, ATerm (class, [ATerm (name, [])]))
1467 | fo_literal_from_type_literal (TyLitFree (class, name)) =
1468 (true, ATerm (class, [ATerm (name, [])]))
1470 fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
1472 val type_pred = `make_fixed_const type_pred_name
1474 fun type_pred_combterm ctxt format type_sys T tm =
1475 CombApp (CombConst (type_pred, T --> @{typ bool}, [T])
1476 |> enforce_type_arg_policy_in_combterm ctxt format type_sys, tm)
1478 fun is_var_positively_naked_in_term _ (SOME false) _ accum = accum
1479 | is_var_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
1480 accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
1481 fun should_predicate_on_var_in_formula pos phi (SOME true) name =
1482 formula_fold pos (is_var_positively_naked_in_term name) phi false
1483 | should_predicate_on_var_in_formula _ _ _ _ = true
1485 fun mk_const_aterm format type_sys x T_args args =
1486 ATerm (x, map_filter (fo_term_for_type_arg format type_sys) T_args @ args)
1488 fun tag_with_type ctxt format nonmono_Ts type_sys pos T tm =
1489 CombConst (type_tag, T --> T, [T])
1490 |> enforce_type_arg_policy_in_combterm ctxt format type_sys
1491 |> term_from_combterm ctxt format nonmono_Ts type_sys (Top_Level pos)
1492 |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
1493 and term_from_combterm ctxt format nonmono_Ts type_sys =
1497 val (head, args) = strip_combterm_comb u
1498 val (x as (s, _), T_args) =
1500 CombConst (name, _, T_args) => (name, T_args)
1501 | CombVar (name, _) => (name, [])
1502 | CombApp _ => raise Fail "impossible \"CombApp\""
1503 val (pos, arg_site) =
1506 (pos, if is_tptp_equal s then Eq_Arg pos else Elsewhere)
1507 | Eq_Arg pos => (pos, Elsewhere)
1508 | Elsewhere => (NONE, Elsewhere)
1509 val t = mk_const_aterm format type_sys x T_args
1510 (map (aux arg_site) args)
1511 val T = combtyp_of u
1513 t |> (if should_tag_with_type ctxt nonmono_Ts type_sys site u T then
1514 tag_with_type ctxt format nonmono_Ts type_sys pos T
1519 and formula_from_combformula ctxt format nonmono_Ts type_sys
1520 should_predicate_on_var =
1523 term_from_combterm ctxt format nonmono_Ts type_sys (Top_Level pos)
1526 Simple_Types level =>
1527 homogenized_type ctxt nonmono_Ts level 0
1528 #> mangled_type format type_sys false 0 #> SOME
1530 fun do_out_of_bound_type pos phi universal (name, T) =
1531 if should_predicate_on_type ctxt nonmono_Ts type_sys
1532 (fn () => should_predicate_on_var pos phi universal name) T then
1534 |> type_pred_combterm ctxt format type_sys T
1535 |> do_term pos |> AAtom |> SOME
1538 fun do_formula pos (AQuant (q, xs, phi)) =
1540 val phi = phi |> do_formula pos
1541 val universal = Option.map (q = AExists ? not) pos
1543 AQuant (q, xs |> map (apsnd (fn NONE => NONE
1544 | SOME T => do_bound_type T)),
1545 (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
1547 (fn (_, NONE) => NONE
1549 do_out_of_bound_type pos phi universal (s, T))
1553 | do_formula pos (AConn conn) = aconn_map pos do_formula conn
1554 | do_formula pos (AAtom tm) = AAtom (do_term pos tm)
1557 fun bound_tvars type_sys Ts =
1558 mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
1559 (type_literals_for_types type_sys add_sorts_on_tvar Ts))
1561 (* Each fact is given a unique fact number to avoid name clashes (e.g., because
1562 of monomorphization). The TPTP explicitly forbids name clashes, and some of
1563 the remote provers might care. *)
1564 fun formula_line_for_fact ctxt format prefix encode exporter nonmono_Ts type_sys
1565 (j, {name, locality, kind, combformula, atomic_types}) =
1566 (prefix ^ (if exporter then "" else string_of_int j ^ "_") ^ encode name,
1569 |> close_combformula_universally
1570 |> formula_from_combformula ctxt format nonmono_Ts type_sys
1571 should_predicate_on_var_in_formula
1572 (if exporter then NONE else SOME true)
1573 |> bound_tvars type_sys atomic_types
1574 |> close_formula_universally,
1583 fun formula_line_for_class_rel_clause ({name, subclass, superclass, ...}
1584 : class_rel_clause) =
1585 let val ty_arg = ATerm (`I "T", []) in
1586 Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
1587 AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
1588 AAtom (ATerm (superclass, [ty_arg]))])
1589 |> close_formula_universally, intro_info, NONE)
1592 fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
1593 (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
1594 | fo_literal_from_arity_literal (TVarLit (c, sort)) =
1595 (false, ATerm (c, [ATerm (sort, [])]))
1597 fun formula_line_for_arity_clause ({name, prem_lits, concl_lits, ...}
1599 Formula (arity_clause_prefix ^ name, Axiom,
1600 mk_ahorn (map (formula_from_fo_literal o apfst not
1601 o fo_literal_from_arity_literal) prem_lits)
1602 (formula_from_fo_literal
1603 (fo_literal_from_arity_literal concl_lits))
1604 |> close_formula_universally, intro_info, NONE)
1606 fun formula_line_for_conjecture ctxt format nonmono_Ts type_sys
1607 ({name, kind, combformula, atomic_types, ...} : translated_formula) =
1608 Formula (conjecture_prefix ^ name, kind,
1609 formula_from_combformula ctxt format nonmono_Ts type_sys
1610 should_predicate_on_var_in_formula (SOME false)
1611 (close_combformula_universally combformula)
1612 |> bound_tvars type_sys atomic_types
1613 |> close_formula_universally, NONE, NONE)
1615 fun free_type_literals type_sys ({atomic_types, ...} : translated_formula) =
1616 atomic_types |> type_literals_for_types type_sys add_sorts_on_tfree
1617 |> map fo_literal_from_type_literal
1619 fun formula_line_for_free_type j lit =
1620 Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis,
1621 formula_from_fo_literal lit, NONE, NONE)
1622 fun formula_lines_for_free_types type_sys facts =
1624 val litss = map (free_type_literals type_sys) facts
1625 val lits = fold (union (op =)) litss []
1626 in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
1628 (** Symbol declarations **)
1630 fun should_declare_sym type_sys pred_sym s =
1631 is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
1633 Simple_Types _ => true
1634 | Tags (_, _, Lightweight) => true
1635 | _ => not pred_sym)
1637 fun sym_decl_table_for_facts ctxt type_sys repaired_sym_tab (conjs, facts) =
1639 fun add_combterm in_conj tm =
1640 let val (head, args) = strip_combterm_comb tm in
1642 CombConst ((s, s'), T, T_args) =>
1643 let val pred_sym = is_pred_sym repaired_sym_tab s in
1644 if should_declare_sym type_sys pred_sym s then
1645 Symtab.map_default (s, [])
1646 (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
1652 #> fold (add_combterm in_conj) args
1654 fun add_fact in_conj =
1655 fact_lift (formula_fold NONE (K (add_combterm in_conj)))
1658 |> is_type_sys_fairly_sound type_sys
1659 ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
1662 (* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
1663 out with monotonicity" paper presented at CADE 2011. *)
1664 fun add_combterm_nonmonotonic_types _ _ _ (SOME false) _ = I
1665 | add_combterm_nonmonotonic_types ctxt level locality _
1666 (CombApp (CombApp (CombConst ((s, _), Type (_, [T, _]), _), tm1),
1668 (is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
1670 Noninf_Nonmono_Types =>
1671 not (is_locality_global locality) orelse
1672 not (is_type_surely_infinite ctxt T)
1673 | Fin_Nonmono_Types => is_type_surely_finite ctxt T
1674 | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
1675 | add_combterm_nonmonotonic_types _ _ _ _ _ = I
1676 fun add_fact_nonmonotonic_types ctxt level ({kind, locality, combformula, ...}
1677 : translated_formula) =
1678 formula_fold (SOME (kind <> Conjecture))
1679 (add_combterm_nonmonotonic_types ctxt level locality) combformula
1680 fun nonmonotonic_types_for_facts ctxt type_sys facts =
1681 let val level = level_of_type_sys type_sys in
1682 if level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types then
1683 [] |> fold (add_fact_nonmonotonic_types ctxt level) facts
1684 (* We must add "bool" in case the helper "True_or_False" is added
1685 later. In addition, several places in the code rely on the list of
1686 nonmonotonic types not being empty. *)
1687 |> insert_type ctxt I @{typ bool}
1692 fun decl_line_for_sym ctxt format nonmono_Ts type_sys s
1693 (s', T_args, T, pred_sym, ary, _) =
1695 val (T_arg_Ts, level) =
1697 Simple_Types level => ([], level)
1698 | _ => (replicate (length T_args) homo_infinite_type, No_Types)
1700 Decl (sym_decl_prefix ^ s, (s, s'),
1701 (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
1702 |> mangled_type format type_sys pred_sym (length T_arg_Ts + ary))
1705 fun formula_line_for_preds_sym_decl ctxt format conj_sym_kind nonmono_Ts
1706 poly_nonmono_Ts type_sys n s j (s', T_args, T, _, ary, in_conj) =
1708 val (kind, maybe_negate) =
1709 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1711 val (arg_Ts, res_T) = chop_fun ary T
1712 val num_args = length arg_Ts
1714 1 upto num_args |> map (`I o make_bound_var o string_of_int)
1716 bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
1717 val sym_needs_arg_types = n > 1 orelse exists (curry (op =) dummyT) T_args
1718 fun should_keep_arg_type T =
1719 sym_needs_arg_types orelse
1720 not (should_predicate_on_type ctxt nonmono_Ts type_sys (K false) T)
1722 arg_Ts |> map (fn T => if should_keep_arg_type T then SOME T else NONE)
1724 Formula (preds_sym_formula_prefix ^ s ^
1725 (if n > 1 then "_" ^ string_of_int j else ""), kind,
1726 CombConst ((s, s'), T, T_args)
1727 |> fold (curry (CombApp o swap)) bounds
1728 |> type_pred_combterm ctxt format type_sys res_T
1729 |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
1730 |> formula_from_combformula ctxt format poly_nonmono_Ts type_sys
1731 (K (K (K (K true)))) (SOME true)
1732 |> n > 1 ? bound_tvars type_sys (atyps_of T)
1733 |> close_formula_universally
1738 fun formula_lines_for_lightweight_tags_sym_decl ctxt format conj_sym_kind
1739 poly_nonmono_Ts type_sys n s
1740 (j, (s', T_args, T, pred_sym, ary, in_conj)) =
1743 lightweight_tags_sym_formula_prefix ^ s ^
1744 (if n > 1 then "_" ^ string_of_int j else "")
1745 val (kind, maybe_negate) =
1746 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1748 val (arg_Ts, res_T) = chop_fun ary T
1750 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
1751 val bounds = bound_names |> map (fn name => ATerm (name, []))
1752 val cst = mk_const_aterm format type_sys (s, s') T_args
1753 val atomic_Ts = atyps_of T
1755 (if pred_sym then AConn (AIff, map AAtom tms)
1756 else AAtom (ATerm (`I tptp_equal, tms)))
1757 |> bound_tvars type_sys atomic_Ts
1758 |> close_formula_universally
1760 (* See also "should_tag_with_type". *)
1761 fun should_encode T =
1762 should_encode_type ctxt poly_nonmono_Ts All_Types T orelse
1764 Tags (Polymorphic, level, Lightweight) =>
1765 level <> All_Types andalso Monomorph.typ_has_tvars T
1767 val tag_with = tag_with_type ctxt format poly_nonmono_Ts type_sys NONE
1768 val add_formula_for_res =
1769 if should_encode res_T then
1770 cons (Formula (ident_base ^ "_res", kind,
1771 eq [tag_with res_T (cst bounds), cst bounds],
1775 fun add_formula_for_arg k =
1776 let val arg_T = nth arg_Ts k in
1777 if should_encode arg_T then
1778 case chop k bounds of
1779 (bounds1, bound :: bounds2) =>
1780 cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
1781 eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
1784 | _ => raise Fail "expected nonempty tail"
1789 [] |> not pred_sym ? add_formula_for_res
1790 |> fold add_formula_for_arg (ary - 1 downto 0)
1793 fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
1795 fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts
1796 poly_nonmono_Ts type_sys (s, decls) =
1799 decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_sys s)
1804 decl :: (decls' as _ :: _) =>
1805 let val T = result_type_of_decl decl in
1806 if forall (curry (type_instance ctxt o swap) T
1807 o result_type_of_decl) decls' then
1813 val n = length decls
1815 decls |> filter (should_predicate_on_type ctxt poly_nonmono_Ts type_sys
1817 o result_type_of_decl)
1819 (0 upto length decls - 1, decls)
1820 |-> map2 (formula_line_for_preds_sym_decl ctxt format conj_sym_kind
1821 nonmono_Ts poly_nonmono_Ts type_sys n s)
1823 | Tags (_, _, heaviness) =>
1827 let val n = length decls in
1828 (0 upto n - 1 ~~ decls)
1829 |> maps (formula_lines_for_lightweight_tags_sym_decl ctxt format
1830 conj_sym_kind poly_nonmono_Ts type_sys n s)
1833 fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1834 poly_nonmono_Ts type_sys sym_decl_tab =
1839 |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
1840 nonmono_Ts poly_nonmono_Ts type_sys)
1842 fun needs_type_tag_idempotence (Tags (poly, level, heaviness)) =
1843 poly <> Mangled_Monomorphic andalso
1844 ((level = All_Types andalso heaviness = Lightweight) orelse
1845 level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types)
1846 | needs_type_tag_idempotence _ = false
1848 fun offset_of_heading_in_problem _ [] j = j
1849 | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
1850 if heading = needle then j
1851 else offset_of_heading_in_problem needle problem (j + length lines)
1853 val implicit_declsN = "Should-be-implicit typings"
1854 val explicit_declsN = "Explicit typings"
1855 val factsN = "Relevant facts"
1856 val class_relsN = "Class relationships"
1857 val aritiesN = "Arities"
1858 val helpersN = "Helper facts"
1859 val conjsN = "Conjectures"
1860 val free_typesN = "Type variables"
1862 val explicit_apply = NONE (* for experimental purposes *)
1864 fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_sys
1865 exporter readable_names preproc hyp_ts concl_t facts =
1867 val (format, type_sys) = choose_format [format] type_sys
1868 val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
1869 translate_formulas ctxt format prem_kind type_sys preproc hyp_ts concl_t
1871 val sym_tab = conjs @ facts |> sym_table_for_facts ctxt explicit_apply
1872 val nonmono_Ts = conjs @ facts |> nonmonotonic_types_for_facts ctxt type_sys
1873 val repair = repair_fact ctxt format type_sys sym_tab
1874 val (conjs, facts) = (conjs, facts) |> pairself (map repair)
1875 val repaired_sym_tab =
1876 conjs @ facts |> sym_table_for_facts ctxt (SOME false)
1878 repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_sys
1880 val poly_nonmono_Ts =
1881 if null nonmono_Ts orelse nonmono_Ts = [@{typ bool}] orelse
1882 polymorphism_of_type_sys type_sys <> Polymorphic then
1885 [TVar (("'a", 0), HOLogic.typeS)]
1886 val sym_decl_lines =
1887 (conjs, helpers @ facts)
1888 |> sym_decl_table_for_facts ctxt type_sys repaired_sym_tab
1889 |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1890 poly_nonmono_Ts type_sys
1892 0 upto length helpers - 1 ~~ helpers
1893 |> map (formula_line_for_fact ctxt format helper_prefix I exporter
1894 poly_nonmono_Ts type_sys)
1895 |> (if needs_type_tag_idempotence type_sys then
1896 cons (type_tag_idempotence_fact ())
1899 (* Reordering these might confuse the proof reconstruction code or the SPASS
1902 [(explicit_declsN, sym_decl_lines),
1904 map (formula_line_for_fact ctxt format fact_prefix ascii_of exporter
1905 nonmono_Ts type_sys)
1906 (0 upto length facts - 1 ~~ facts)),
1907 (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
1908 (aritiesN, map formula_line_for_arity_clause arity_clauses),
1909 (helpersN, helper_lines),
1911 map (formula_line_for_conjecture ctxt format nonmono_Ts type_sys)
1913 (free_typesN, formula_lines_for_free_types type_sys (facts @ conjs))]
1917 CNF => ensure_cnf_problem
1918 | CNF_UEQ => filter_cnf_ueq_problem
1920 |> (if is_format_typed format then
1921 declare_undeclared_syms_in_atp_problem type_decl_prefix
1925 val (problem, pool) = problem |> nice_atp_problem readable_names
1926 val helpers_offset = offset_of_heading_in_problem helpersN problem 0
1928 map_filter (fn (j, {name, ...}) =>
1929 if String.isSuffix typed_helper_suffix name then SOME j
1931 ((helpers_offset + 1 upto helpers_offset + length helpers)
1933 fun add_sym_arity (s, {min_ary, ...} : sym_info) =
1935 case strip_prefix_and_unascii const_prefix s of
1936 SOME s => Symtab.insert (op =) (s, min_ary)
1942 case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
1943 offset_of_heading_in_problem conjsN problem 0,
1944 offset_of_heading_in_problem factsN problem 0,
1945 fact_names |> Vector.fromList,
1947 Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
1951 val conj_weight = 0.0
1952 val hyp_weight = 0.1
1953 val fact_min_weight = 0.2
1954 val fact_max_weight = 1.0
1955 val type_info_default_weight = 0.8
1957 fun add_term_weights weight (ATerm (s, tms)) =
1958 is_tptp_user_symbol s ? Symtab.default (s, weight)
1959 #> fold (add_term_weights weight) tms
1960 fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
1961 formula_fold NONE (K (add_term_weights weight)) phi
1962 | add_problem_line_weights _ _ = I
1964 fun add_conjectures_weights [] = I
1965 | add_conjectures_weights conjs =
1966 let val (hyps, conj) = split_last conjs in
1967 add_problem_line_weights conj_weight conj
1968 #> fold (add_problem_line_weights hyp_weight) hyps
1971 fun add_facts_weights facts =
1973 val num_facts = length facts
1975 fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
1976 / Real.fromInt num_facts
1978 map weight_of (0 upto num_facts - 1) ~~ facts
1979 |> fold (uncurry add_problem_line_weights)
1982 (* Weights are from 0.0 (most important) to 1.0 (least important). *)
1983 fun atp_problem_weights problem =
1984 let val get = these o AList.lookup (op =) problem in
1986 |> add_conjectures_weights (get free_typesN @ get conjsN)
1987 |> add_facts_weights (get factsN)
1988 |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
1989 [explicit_declsN, class_relsN, aritiesN]
1991 |> sort (prod_ord Real.compare string_ord o pairself swap)