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, 'b) ho_term = ('a, 'b) ATP_Problem.ho_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
19 General | Helper | Extensionality | Intro | Elim | Simp | Local | Assum |
22 datatype order = First_Order | Higher_Order
23 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
25 All_Types | Noninf_Nonmono_Types | Fin_Nonmono_Types | Const_Arg_Types |
27 datatype type_heaviness = Heavyweight | Lightweight
30 Simple_Types of order * type_level |
31 Preds of polymorphism * type_level * type_heaviness |
32 Tags of polymorphism * type_level * type_heaviness
34 val bound_var_prefix : string
35 val schematic_var_prefix : string
36 val fixed_var_prefix : string
37 val tvar_prefix : string
38 val tfree_prefix : string
39 val const_prefix : string
40 val type_const_prefix : string
41 val class_prefix : string
42 val skolem_const_prefix : string
43 val old_skolem_const_prefix : string
44 val new_skolem_const_prefix : string
45 val type_decl_prefix : string
46 val sym_decl_prefix : string
47 val preds_sym_formula_prefix : string
48 val lightweight_tags_sym_formula_prefix : string
49 val fact_prefix : string
50 val conjecture_prefix : string
51 val helper_prefix : string
52 val class_rel_clause_prefix : string
53 val arity_clause_prefix : string
54 val tfree_clause_prefix : string
55 val typed_helper_suffix : string
56 val untyped_helper_suffix : string
57 val type_tag_idempotence_helper_name : string
58 val predicator_name : string
59 val app_op_name : string
60 val type_tag_name : string
61 val type_pred_name : string
62 val simple_type_prefix : string
63 val prefixed_predicator_name : string
64 val prefixed_app_op_name : string
65 val prefixed_type_tag_name : string
66 val ascii_of : string -> string
67 val unascii_of : string -> string
68 val strip_prefix_and_unascii : string -> string -> string option
69 val proxy_table : (string * (string * (thm * (string * string)))) list
70 val proxify_const : string -> (string * string) option
71 val invert_const : string -> string
72 val unproxify_const : string -> string
73 val new_skolem_var_name_from_const : string -> string
74 val num_type_args : theory -> string -> int
75 val atp_irrelevant_consts : string list
76 val atp_schematic_consts_of : term -> typ list Symtab.table
77 val is_locality_global : locality -> bool
78 val type_enc_from_string : string -> type_enc
79 val is_type_enc_higher_order : type_enc -> bool
80 val polymorphism_of_type_enc : type_enc -> polymorphism
81 val level_of_type_enc : type_enc -> type_level
82 val is_type_enc_virtually_sound : type_enc -> bool
83 val is_type_enc_fairly_sound : type_enc -> bool
84 val choose_format : format list -> type_enc -> format * type_enc
86 connective -> ('a, 'b, 'c) formula list -> ('a, 'b, 'c) formula
87 val unmangled_const : string -> string * (string, 'b) ho_term list
88 val unmangled_const_name : string -> string
89 val helper_table : ((string * bool) * thm list) list
91 val conceal_lambdas : Proof.context -> term -> term
92 val introduce_combinators : Proof.context -> term -> term
93 val prepare_atp_problem :
94 Proof.context -> format -> formula_kind -> formula_kind -> type_enc -> bool
95 -> bool -> (term list -> term list) -> bool -> bool -> term list -> term
96 -> ((string * locality) * term) list
97 -> string problem * string Symtab.table * int * int
98 * (string * locality) list vector * int list * int Symtab.table
99 val atp_problem_weights : string problem -> (string * real) list
102 structure ATP_Translate : ATP_TRANSLATE =
108 type name = string * string
110 val generate_info = false (* experimental *)
112 fun isabelle_info s =
113 if generate_info then SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
120 val bound_var_prefix = "B_"
121 val schematic_var_prefix = "V_"
122 val fixed_var_prefix = "v_"
124 val tvar_prefix = "T_"
125 val tfree_prefix = "t_"
127 val const_prefix = "c_"
128 val type_const_prefix = "tc_"
129 val class_prefix = "cl_"
131 val skolem_const_prefix = "Sledgehammer" ^ Long_Name.separator ^ "Sko"
132 val old_skolem_const_prefix = skolem_const_prefix ^ "o"
133 val new_skolem_const_prefix = skolem_const_prefix ^ "n"
135 val type_decl_prefix = "ty_"
136 val sym_decl_prefix = "sy_"
137 val preds_sym_formula_prefix = "psy_"
138 val lightweight_tags_sym_formula_prefix = "tsy_"
139 val fact_prefix = "fact_"
140 val conjecture_prefix = "conj_"
141 val helper_prefix = "help_"
142 val class_rel_clause_prefix = "clar_"
143 val arity_clause_prefix = "arity_"
144 val tfree_clause_prefix = "tfree_"
146 val typed_helper_suffix = "_T"
147 val untyped_helper_suffix = "_U"
148 val type_tag_idempotence_helper_name = helper_prefix ^ "ti_idem"
150 val predicator_name = "hBOOL"
151 val app_op_name = "hAPP"
152 val type_tag_name = "ti"
153 val type_pred_name = "is"
154 val simple_type_prefix = "ty_"
156 val prefixed_predicator_name = const_prefix ^ predicator_name
157 val prefixed_app_op_name = const_prefix ^ app_op_name
158 val prefixed_type_tag_name = const_prefix ^ type_tag_name
160 (* Freshness almost guaranteed! *)
161 val sledgehammer_weak_prefix = "Sledgehammer:"
163 val concealed_lambda_prefix = sledgehammer_weak_prefix ^ "lambda_"
165 (*Escaping of special characters.
166 Alphanumeric characters are left unchanged.
167 The character _ goes to __
168 Characters in the range ASCII space to / go to _A to _P, respectively.
169 Other characters go to _nnn where nnn is the decimal ASCII code.*)
170 val upper_a_minus_space = Char.ord #"A" - Char.ord #" "
172 fun stringN_of_int 0 _ = ""
173 | stringN_of_int k n =
174 stringN_of_int (k - 1) (n div 10) ^ string_of_int (n mod 10)
176 fun ascii_of_char c =
177 if Char.isAlphaNum c then
179 else if c = #"_" then
181 else if #" " <= c andalso c <= #"/" then
182 "_" ^ String.str (Char.chr (Char.ord c + upper_a_minus_space))
184 (* fixed width, in case more digits follow *)
185 "_" ^ stringN_of_int 3 (Char.ord c)
187 val ascii_of = String.translate ascii_of_char
189 (** Remove ASCII armoring from names in proof files **)
191 (* We don't raise error exceptions because this code can run inside a worker
192 thread. Also, the errors are impossible. *)
195 fun un rcs [] = String.implode(rev rcs)
196 | un rcs [#"_"] = un (#"_" :: rcs) [] (* ERROR *)
197 (* Three types of _ escapes: __, _A to _P, _nnn *)
198 | un rcs (#"_" :: #"_" :: cs) = un (#"_" :: rcs) cs
199 | un rcs (#"_" :: c :: cs) =
200 if #"A" <= c andalso c<= #"P" then
201 (* translation of #" " to #"/" *)
202 un (Char.chr (Char.ord c - upper_a_minus_space) :: rcs) cs
204 let val digits = List.take (c :: cs, 3) handle General.Subscript => [] in
205 case Int.fromString (String.implode digits) of
206 SOME n => un (Char.chr n :: rcs) (List.drop (cs, 2))
207 | NONE => un (c :: #"_" :: rcs) cs (* ERROR *)
209 | un rcs (c :: cs) = un (c :: rcs) cs
210 in un [] o String.explode end
212 (* If string s has the prefix s1, return the result of deleting it,
214 fun strip_prefix_and_unascii s1 s =
215 if String.isPrefix s1 s then
216 SOME (unascii_of (String.extract (s, size s1, NONE)))
221 [("c_False", (@{const_name False}, (@{thm fFalse_def},
222 ("fFalse", @{const_name ATP.fFalse})))),
223 ("c_True", (@{const_name True}, (@{thm fTrue_def},
224 ("fTrue", @{const_name ATP.fTrue})))),
225 ("c_Not", (@{const_name Not}, (@{thm fNot_def},
226 ("fNot", @{const_name ATP.fNot})))),
227 ("c_conj", (@{const_name conj}, (@{thm fconj_def},
228 ("fconj", @{const_name ATP.fconj})))),
229 ("c_disj", (@{const_name disj}, (@{thm fdisj_def},
230 ("fdisj", @{const_name ATP.fdisj})))),
231 ("c_implies", (@{const_name implies}, (@{thm fimplies_def},
232 ("fimplies", @{const_name ATP.fimplies})))),
233 ("equal", (@{const_name HOL.eq}, (@{thm fequal_def},
234 ("fequal", @{const_name ATP.fequal})))),
235 ("c_All", (@{const_name All}, (@{thm fAll_def},
236 ("fAll", @{const_name ATP.fAll})))),
237 ("c_Ex", (@{const_name Ex}, (@{thm fEx_def},
238 ("fEx", @{const_name ATP.fEx}))))]
240 val proxify_const = AList.lookup (op =) proxy_table #> Option.map (snd o snd)
242 (* Readable names for the more common symbolic functions. Do not mess with the
243 table unless you know what you are doing. *)
244 val const_trans_table =
245 [(@{type_name Product_Type.prod}, "prod"),
246 (@{type_name Sum_Type.sum}, "sum"),
247 (@{const_name False}, "False"),
248 (@{const_name True}, "True"),
249 (@{const_name Not}, "Not"),
250 (@{const_name conj}, "conj"),
251 (@{const_name disj}, "disj"),
252 (@{const_name implies}, "implies"),
253 (@{const_name HOL.eq}, "equal"),
254 (@{const_name All}, "All"),
255 (@{const_name Ex}, "Ex"),
256 (@{const_name If}, "If"),
257 (@{const_name Set.member}, "member"),
258 (@{const_name Meson.COMBI}, "COMBI"),
259 (@{const_name Meson.COMBK}, "COMBK"),
260 (@{const_name Meson.COMBB}, "COMBB"),
261 (@{const_name Meson.COMBC}, "COMBC"),
262 (@{const_name Meson.COMBS}, "COMBS")]
264 |> fold (Symtab.update o swap o snd o snd o snd) proxy_table
266 (* Invert the table of translations between Isabelle and ATPs. *)
267 val const_trans_table_inv =
268 const_trans_table |> Symtab.dest |> map swap |> Symtab.make
269 val const_trans_table_unprox =
271 |> fold (fn (_, (isa, (_, (_, atp)))) => Symtab.update (atp, isa)) proxy_table
273 val invert_const = perhaps (Symtab.lookup const_trans_table_inv)
274 val unproxify_const = perhaps (Symtab.lookup const_trans_table_unprox)
277 case Symtab.lookup const_trans_table c of
281 fun ascii_of_indexname (v, 0) = ascii_of v
282 | ascii_of_indexname (v, i) = ascii_of v ^ "_" ^ string_of_int i
284 fun make_bound_var x = bound_var_prefix ^ ascii_of x
285 fun make_schematic_var v = schematic_var_prefix ^ ascii_of_indexname v
286 fun make_fixed_var x = fixed_var_prefix ^ ascii_of x
288 fun make_schematic_type_var (x, i) =
289 tvar_prefix ^ (ascii_of_indexname (unprefix "'" x, i))
290 fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (unprefix "'" x))
292 (* "HOL.eq" is mapped to the ATP's equality. *)
293 fun make_fixed_const @{const_name HOL.eq} = tptp_old_equal
294 | make_fixed_const c = const_prefix ^ lookup_const c
296 fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
298 fun make_type_class clas = class_prefix ^ ascii_of clas
300 fun new_skolem_var_name_from_const s =
301 let val ss = s |> space_explode Long_Name.separator in
302 nth ss (length ss - 2)
305 (* The number of type arguments of a constant, zero if it's monomorphic. For
306 (instances of) Skolem pseudoconstants, this information is encoded in the
308 fun num_type_args thy s =
309 if String.isPrefix skolem_const_prefix s then
310 s |> space_explode Long_Name.separator |> List.last |> Int.fromString |> the
312 (s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
314 (* These are either simplified away by "Meson.presimplify" (most of the time) or
315 handled specially via "fFalse", "fTrue", ..., "fequal". *)
316 val atp_irrelevant_consts =
317 [@{const_name False}, @{const_name True}, @{const_name Not},
318 @{const_name conj}, @{const_name disj}, @{const_name implies},
319 @{const_name HOL.eq}, @{const_name If}, @{const_name Let}]
321 val atp_monomorph_bad_consts =
322 atp_irrelevant_consts @
323 (* These are ignored anyway by the relevance filter (unless they appear in
324 higher-order places) but not by the monomorphizer. *)
325 [@{const_name all}, @{const_name "==>"}, @{const_name "=="},
326 @{const_name Trueprop}, @{const_name All}, @{const_name Ex},
327 @{const_name Ex1}, @{const_name Ball}, @{const_name Bex}]
329 fun add_schematic_const (x as (_, T)) =
330 Monomorph.typ_has_tvars T ? Symtab.insert_list (op =) x
331 val add_schematic_consts_of =
332 Term.fold_aterms (fn Const (x as (s, _)) =>
333 not (member (op =) atp_monomorph_bad_consts s)
334 ? add_schematic_const x
336 fun atp_schematic_consts_of t = add_schematic_consts_of t Symtab.empty
338 (** Definitions and functions for FOL clauses and formulas for TPTP **)
340 (* The first component is the type class; the second is a "TVar" or "TFree". *)
341 datatype type_literal =
342 TyLitVar of name * name |
343 TyLitFree of name * name
346 (** Isabelle arities **)
348 datatype arity_literal =
349 TConsLit of name * name * name list |
350 TVarLit of name * name
353 | gen_TVars n = ("T_" ^ string_of_int n) :: gen_TVars (n-1)
355 val type_class = the_single @{sort type}
357 fun add_packed_sort tvar =
358 fold (fn s => s <> type_class ? cons (`make_type_class s, `I tvar))
362 prem_lits : arity_literal list,
363 concl_lits : arity_literal}
365 (* Arity of type constructor "tcon :: (arg1, ..., argN) res" *)
366 fun make_axiom_arity_clause (tcons, name, (cls, args)) =
368 val tvars = gen_TVars (length args)
369 val tvars_srts = ListPair.zip (tvars, args)
372 prem_lits = [] |> fold (uncurry add_packed_sort) tvars_srts |> map TVarLit,
373 concl_lits = TConsLit (`make_type_class cls,
374 `make_fixed_type_const tcons,
378 fun arity_clause _ _ (_, []) = []
379 | arity_clause seen n (tcons, ("HOL.type", _) :: ars) = (* ignore *)
380 arity_clause seen n (tcons, ars)
381 | arity_clause seen n (tcons, (ar as (class, _)) :: ars) =
382 if member (op =) seen class then
383 (* multiple arities for the same (tycon, class) pair *)
384 make_axiom_arity_clause (tcons,
385 lookup_const tcons ^ "___" ^ ascii_of class ^ "_" ^ string_of_int n,
387 arity_clause seen (n + 1) (tcons, ars)
389 make_axiom_arity_clause (tcons, lookup_const tcons ^ "___" ^
390 ascii_of class, ar) ::
391 arity_clause (class :: seen) n (tcons, ars)
393 fun multi_arity_clause [] = []
394 | multi_arity_clause ((tcons, ars) :: tc_arlists) =
395 arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
397 (* Generate all pairs (tycon, class, sorts) such that tycon belongs to class in
398 theory thy provided its arguments have the corresponding sorts. *)
399 fun type_class_pairs thy tycons classes =
401 val alg = Sign.classes_of thy
402 fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
403 fun add_class tycon class =
404 cons (class, domain_sorts tycon class)
405 handle Sorts.CLASS_ERROR _ => I
406 fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
407 in map try_classes tycons end
409 (*Proving one (tycon, class) membership may require proving others, so iterate.*)
410 fun iter_type_class_pairs _ _ [] = ([], [])
411 | iter_type_class_pairs thy tycons classes =
413 fun maybe_insert_class s =
414 (s <> type_class andalso not (member (op =) classes s))
416 val cpairs = type_class_pairs thy tycons classes
418 [] |> fold (fold (fold (fold maybe_insert_class) o snd) o snd) cpairs
419 val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
420 in (classes' @ classes, union (op =) cpairs' cpairs) end
422 fun make_arity_clauses thy tycons =
423 iter_type_class_pairs thy tycons ##> multi_arity_clause
426 (** Isabelle class relations **)
428 type class_rel_clause =
433 (* Generate all pairs (sub, super) such that sub is a proper subclass of super
435 fun class_pairs _ [] _ = []
436 | class_pairs thy subs supers =
438 val class_less = Sorts.class_less (Sign.classes_of thy)
439 fun add_super sub super = class_less (sub, super) ? cons (sub, super)
440 fun add_supers sub = fold (add_super sub) supers
441 in fold add_supers subs [] end
443 fun make_class_rel_clause (sub, super) =
444 {name = sub ^ "_" ^ super, subclass = `make_type_class sub,
445 superclass = `make_type_class super}
447 fun make_class_rel_clauses thy subs supers =
448 map make_class_rel_clause (class_pairs thy subs supers)
450 (* intermediate terms *)
452 IConst of name * typ * typ list |
454 IApp of iterm * iterm |
455 IAbs of (name * typ) * iterm
457 fun ityp_of (IConst (_, T, _)) = T
458 | ityp_of (IVar (_, T)) = T
459 | ityp_of (IApp (t1, _)) = snd (dest_funT (ityp_of t1))
460 | ityp_of (IAbs ((_, T), tm)) = T --> ityp_of tm
462 (*gets the head of a combinator application, along with the list of arguments*)
463 fun strip_iterm_comb u =
465 fun stripc (IApp (t, u), ts) = stripc (t, u :: ts)
467 in stripc (u, []) end
469 fun atyps_of T = fold_atyps (insert (op =)) T []
471 fun new_skolem_const_name s num_T_args =
472 [new_skolem_const_prefix, s, string_of_int num_T_args]
473 |> space_implode Long_Name.separator
475 (* Converts an Isabelle/HOL term (with combinators) into an intermediate term.
476 Also accumulates sort infomation. *)
477 fun iterm_from_term thy bs (P $ Q) =
479 val (P', P_atomics_Ts) = iterm_from_term thy bs P
480 val (Q', Q_atomics_Ts) = iterm_from_term thy bs Q
481 in (IApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
482 | iterm_from_term thy _ (Const (c, T)) =
485 (if String.isPrefix old_skolem_const_prefix c then
486 [] |> Term.add_tvarsT T |> map TVar
488 (c, T) |> Sign.const_typargs thy)
489 val c' = IConst (`make_fixed_const c, T, tvar_list)
490 in (c', atyps_of T) end
491 | iterm_from_term _ _ (Free (v, T)) =
492 (IConst (`make_fixed_var v, T, []), atyps_of T)
493 | iterm_from_term _ _ (Var (v as (s, _), T)) =
494 (if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
496 val Ts = T |> strip_type |> swap |> op ::
497 val s' = new_skolem_const_name s (length Ts)
498 in IConst (`make_fixed_const s', T, Ts) end
500 IVar ((make_schematic_var v, s), T), atyps_of T)
501 | iterm_from_term _ bs (Bound j) =
502 nth bs j |> (fn (s, T) => (IConst (`make_bound_var s, T, []), atyps_of T))
503 | iterm_from_term thy bs (Abs (s, T, t)) =
505 fun vary s = s |> AList.defined (op =) bs s ? vary o Symbol.bump_string
507 val (tm, atomic_Ts) = iterm_from_term thy ((s, T) :: bs) t
509 (IAbs ((`make_bound_var s, T), tm),
510 union (op =) atomic_Ts (atyps_of T))
514 General | Helper | Extensionality | Intro | Elim | Simp | Local | Assum |
517 (* (quasi-)underapproximation of the truth *)
518 fun is_locality_global Local = false
519 | is_locality_global Assum = false
520 | is_locality_global Chained = false
521 | is_locality_global _ = true
523 datatype order = First_Order | Higher_Order
524 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
525 datatype type_level =
526 All_Types | Noninf_Nonmono_Types | Fin_Nonmono_Types | Const_Arg_Types |
528 datatype type_heaviness = Heavyweight | Lightweight
531 Simple_Types of order * type_level |
532 Preds of polymorphism * type_level * type_heaviness |
533 Tags of polymorphism * type_level * type_heaviness
535 fun try_unsuffixes ss s =
536 fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
538 fun type_enc_from_string s =
539 (case try (unprefix "poly_") s of
540 SOME s => (SOME Polymorphic, s)
542 case try (unprefix "mono_") s of
543 SOME s => (SOME Monomorphic, s)
545 case try (unprefix "mangled_") s of
546 SOME s => (SOME Mangled_Monomorphic, s)
549 (* "_query" and "_bang" are for the ASCII-challenged Metis and
551 case try_unsuffixes ["?", "_query"] s of
552 SOME s => (Noninf_Nonmono_Types, s)
554 case try_unsuffixes ["!", "_bang"] s of
555 SOME s => (Fin_Nonmono_Types, s)
556 | NONE => (All_Types, s))
558 case try (unsuffix "_heavy") s of
559 SOME s => (Heavyweight, s)
560 | NONE => (Lightweight, s))
561 |> (fn (poly, (level, (heaviness, core))) =>
562 case (core, (poly, level, heaviness)) of
563 ("simple", (NONE, _, Lightweight)) =>
564 Simple_Types (First_Order, level)
565 | ("simple_higher", (NONE, _, Lightweight)) =>
566 if level = Noninf_Nonmono_Types then raise Same.SAME
567 else Simple_Types (Higher_Order, level)
568 | ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
569 | ("tags", (SOME Polymorphic, _, _)) =>
570 Tags (Polymorphic, level, heaviness)
571 | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
572 | ("args", (SOME poly, All_Types (* naja *), Lightweight)) =>
573 Preds (poly, Const_Arg_Types, Lightweight)
574 | ("erased", (NONE, All_Types (* naja *), Lightweight)) =>
575 Preds (Polymorphic, No_Types, Lightweight)
576 | _ => raise Same.SAME)
577 handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
579 fun is_type_enc_higher_order (Simple_Types (Higher_Order, _)) = true
580 | is_type_enc_higher_order _ = false
582 fun polymorphism_of_type_enc (Simple_Types _) = Mangled_Monomorphic
583 | polymorphism_of_type_enc (Preds (poly, _, _)) = poly
584 | polymorphism_of_type_enc (Tags (poly, _, _)) = poly
586 fun level_of_type_enc (Simple_Types (_, level)) = level
587 | level_of_type_enc (Preds (_, level, _)) = level
588 | level_of_type_enc (Tags (_, level, _)) = level
590 fun heaviness_of_type_enc (Simple_Types _) = Heavyweight
591 | heaviness_of_type_enc (Preds (_, _, heaviness)) = heaviness
592 | heaviness_of_type_enc (Tags (_, _, heaviness)) = heaviness
594 fun is_type_level_virtually_sound level =
595 level = All_Types orelse level = Noninf_Nonmono_Types
596 val is_type_enc_virtually_sound =
597 is_type_level_virtually_sound o level_of_type_enc
599 fun is_type_level_fairly_sound level =
600 is_type_level_virtually_sound level orelse level = Fin_Nonmono_Types
601 val is_type_enc_fairly_sound = is_type_level_fairly_sound o level_of_type_enc
603 fun choose_format formats (Simple_Types (order, level)) =
604 if member (op =) formats THF then
605 (THF, Simple_Types (order, level))
606 else if member (op =) formats TFF then
607 (TFF, Simple_Types (First_Order, level))
609 choose_format formats (Preds (Mangled_Monomorphic, level, Heavyweight))
610 | choose_format formats type_enc =
613 (CNF_UEQ, case type_enc of
615 (if is_type_enc_fairly_sound type_enc then Tags else Preds)
618 | format => (format, type_enc))
620 type translated_formula =
624 iformula : (name, typ, iterm) formula,
625 atomic_types : typ list}
627 fun update_iformula f ({name, locality, kind, iformula, atomic_types}
628 : translated_formula) =
629 {name = name, locality = locality, kind = kind, iformula = f iformula,
630 atomic_types = atomic_types} : translated_formula
632 fun fact_lift f ({iformula, ...} : translated_formula) = f iformula
634 val type_instance = Sign.typ_instance o Proof_Context.theory_of
636 fun insert_type ctxt get_T x xs =
637 let val T = get_T x in
638 if exists (curry (type_instance ctxt) T o get_T) xs then xs
639 else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
642 (* The Booleans indicate whether all type arguments should be kept. *)
643 datatype type_arg_policy =
644 Explicit_Type_Args of bool |
645 Mangled_Type_Args of bool |
648 fun should_drop_arg_type_args (Simple_Types _) =
649 false (* since TFF doesn't support overloading *)
650 | should_drop_arg_type_args type_enc =
651 level_of_type_enc type_enc = All_Types andalso
652 heaviness_of_type_enc type_enc = Heavyweight
654 fun type_arg_policy type_enc s =
655 if s = type_tag_name then
656 (if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
659 Explicit_Type_Args) false
660 else case type_enc of
661 Tags (_, All_Types, Heavyweight) => No_Type_Args
663 if level_of_type_enc type_enc = No_Types orelse
664 s = @{const_name HOL.eq} orelse
665 (s = app_op_name andalso
666 level_of_type_enc type_enc = Const_Arg_Types) then
669 should_drop_arg_type_args type_enc
670 |> (if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
675 (* Make literals for sorted type variables. *)
676 fun generic_add_sorts_on_type (_, []) = I
677 | generic_add_sorts_on_type ((x, i), s :: ss) =
678 generic_add_sorts_on_type ((x, i), ss)
679 #> (if s = the_single @{sort HOL.type} then
682 insert (op =) (TyLitFree (`make_type_class s, `make_fixed_type_var x))
684 insert (op =) (TyLitVar (`make_type_class s,
685 (make_schematic_type_var (x, i), x))))
686 fun add_sorts_on_tfree (TFree (s, S)) = generic_add_sorts_on_type ((s, ~1), S)
687 | add_sorts_on_tfree _ = I
688 fun add_sorts_on_tvar (TVar z) = generic_add_sorts_on_type z
689 | add_sorts_on_tvar _ = I
691 fun type_literals_for_types type_enc add_sorts_on_typ Ts =
692 [] |> level_of_type_enc type_enc <> No_Types ? fold add_sorts_on_typ Ts
694 fun mk_aconns c phis =
695 let val (phis', phi') = split_last phis in
696 fold_rev (mk_aconn c) phis' phi'
698 fun mk_ahorn [] phi = phi
699 | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
700 fun mk_aquant _ [] phi = phi
701 | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
702 if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
703 | mk_aquant q xs phi = AQuant (q, xs, phi)
705 fun close_universally atom_vars phi =
707 fun formula_vars bounds (AQuant (_, xs, phi)) =
708 formula_vars (map fst xs @ bounds) phi
709 | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
710 | formula_vars bounds (AAtom tm) =
711 union (op =) (atom_vars tm []
712 |> filter_out (member (op =) bounds o fst))
713 in mk_aquant AForall (formula_vars [] phi []) phi end
715 fun iterm_vars (IApp (tm1, tm2)) = fold iterm_vars [tm1, tm2]
716 | iterm_vars (IConst _) = I
717 | iterm_vars (IVar (name, T)) = insert (op =) (name, SOME T)
718 | iterm_vars (IAbs (_, tm)) = iterm_vars tm
719 fun close_iformula_universally phi = close_universally iterm_vars phi
721 fun term_vars bounds (ATerm (name as (s, _), tms)) =
722 (is_tptp_variable s andalso not (member (op =) bounds name))
723 ? insert (op =) (name, NONE) #> fold (term_vars bounds) tms
724 | term_vars bounds (AAbs ((name, _), tm)) = term_vars (name :: bounds) tm
725 fun close_formula_universally phi = close_universally (term_vars []) phi
727 val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
728 val homo_infinite_type = Type (homo_infinite_type_name, [])
730 fun ho_term_from_typ format type_enc =
732 fun term (Type (s, Ts)) =
733 ATerm (case (is_type_enc_higher_order type_enc, s) of
734 (true, @{type_name bool}) => `I tptp_bool_type
735 | (true, @{type_name fun}) => `I tptp_fun_type
736 | _ => if s = homo_infinite_type_name andalso
737 (format = TFF orelse format = THF) then
738 `I tptp_individual_type
740 `make_fixed_type_const s,
742 | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
743 | term (TVar ((x as (s, _)), _)) =
744 ATerm ((make_schematic_type_var x, s), [])
747 fun ho_term_for_type_arg format type_enc T =
748 if T = dummyT then NONE else SOME (ho_term_from_typ format type_enc T)
750 (* This shouldn't clash with anything else. *)
751 val mangled_type_sep = "\000"
753 fun generic_mangled_type_name f (ATerm (name, [])) = f name
754 | generic_mangled_type_name f (ATerm (name, tys)) =
755 f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
757 | generic_mangled_type_name _ _ = raise Fail "unexpected type abstraction"
759 val bool_atype = AType (`I tptp_bool_type)
761 fun make_simple_type s =
762 if s = tptp_bool_type orelse s = tptp_fun_type orelse
763 s = tptp_individual_type then
766 simple_type_prefix ^ ascii_of s
768 fun ho_type_from_ho_term type_enc pred_sym ary =
771 AType ((make_simple_type (generic_mangled_type_name fst ty),
772 generic_mangled_type_name snd ty))
773 fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
774 fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
775 | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
776 | to_fo _ _ = raise Fail "unexpected type abstraction"
777 fun to_ho (ty as ATerm ((s, _), tys)) =
778 if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
779 | to_ho _ = raise Fail "unexpected type abstraction"
780 in if is_type_enc_higher_order type_enc then to_ho else to_fo ary end
782 fun ho_type_from_typ format type_enc pred_sym ary =
783 ho_type_from_ho_term type_enc pred_sym ary
784 o ho_term_from_typ format type_enc
786 fun mangled_const_name format type_enc T_args (s, s') =
788 val ty_args = T_args |> map_filter (ho_term_for_type_arg format type_enc)
789 fun type_suffix f g =
790 fold_rev (curry (op ^) o g o prefix mangled_type_sep
791 o generic_mangled_type_name f) ty_args ""
792 in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
794 val parse_mangled_ident =
795 Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
797 fun parse_mangled_type x =
799 -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
801 and parse_mangled_types x =
802 (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
804 fun unmangled_type s =
805 s |> suffix ")" |> raw_explode
806 |> Scan.finite Symbol.stopper
807 (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
808 quote s)) parse_mangled_type))
811 val unmangled_const_name = space_explode mangled_type_sep #> hd
812 fun unmangled_const s =
813 let val ss = space_explode mangled_type_sep s in
814 (hd ss, map unmangled_type (tl ss))
817 fun introduce_proxies type_enc =
819 fun intro top_level (IApp (tm1, tm2)) =
820 IApp (intro top_level tm1, intro false tm2)
821 | intro top_level (IConst (name as (s, _), T, T_args)) =
822 (case proxify_const s of
824 if top_level orelse is_type_enc_higher_order type_enc then
825 case (top_level, s) of
826 (_, "c_False") => (`I tptp_false, [])
827 | (_, "c_True") => (`I tptp_true, [])
828 | (false, "c_Not") => (`I tptp_not, [])
829 | (false, "c_conj") => (`I tptp_and, [])
830 | (false, "c_disj") => (`I tptp_or, [])
831 | (false, "c_implies") => (`I tptp_implies, [])
832 | (false, "c_All") => (`I tptp_ho_forall, [])
833 | (false, "c_Ex") => (`I tptp_ho_exists, [])
835 if is_tptp_equal s then (`I tptp_equal, [])
836 else (proxy_base |>> prefix const_prefix, T_args)
839 (proxy_base |>> prefix const_prefix, T_args)
840 | NONE => (name, T_args))
841 |> (fn (name, T_args) => IConst (name, T, T_args))
842 | intro _ (IAbs (bound, tm)) = IAbs (bound, intro false tm)
846 fun iformula_from_prop thy type_enc eq_as_iff =
848 fun do_term bs t atomic_types =
849 iterm_from_term thy bs (Envir.eta_contract t)
850 |>> (introduce_proxies type_enc #> AAtom)
851 ||> union (op =) atomic_types
852 fun do_quant bs q s T t' =
853 let val s = singleton (Name.variant_list (map fst bs)) s in
854 do_formula ((s, T) :: bs) t'
855 #>> mk_aquant q [(`make_bound_var s, SOME T)]
857 and do_conn bs c t1 t2 =
858 do_formula bs t1 ##>> do_formula bs t2 #>> uncurry (mk_aconn c)
859 and do_formula bs t =
861 @{const Trueprop} $ t1 => do_formula bs t1
862 | @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
863 | Const (@{const_name All}, _) $ Abs (s, T, t') =>
864 do_quant bs AForall s T t'
865 | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
866 do_quant bs AExists s T t'
867 | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
868 | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
869 | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
870 | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
871 if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
875 fun presimplify_term _ [] t = t
876 | presimplify_term ctxt presimp_consts t =
877 t |> exists_Const (member (op =) presimp_consts o fst) t
878 ? (Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
879 #> Meson.presimplify ctxt
882 fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
883 fun conceal_bounds Ts t =
884 subst_bounds (map (Free o apfst concealed_bound_name)
885 (0 upto length Ts - 1 ~~ Ts), t)
886 fun reveal_bounds Ts =
887 subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
888 (0 upto length Ts - 1 ~~ Ts))
890 fun is_fun_equality (@{const_name HOL.eq},
891 Type (_, [Type (@{type_name fun}, _), _])) = true
892 | is_fun_equality _ = false
894 fun extensionalize_term ctxt t =
895 if exists_Const is_fun_equality t then
896 let val thy = Proof_Context.theory_of ctxt in
897 t |> cterm_of thy |> Meson.extensionalize_conv ctxt
898 |> prop_of |> Logic.dest_equals |> snd
903 fun generic_translate_lambdas do_lambdas ctxt t =
907 @{const Not} $ t1 => @{const Not} $ aux Ts t1
908 | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
909 t0 $ Abs (s, T, aux (T :: Ts) t')
910 | (t0 as Const (@{const_name All}, _)) $ t1 =>
911 aux Ts (t0 $ eta_expand Ts t1 1)
912 | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
913 t0 $ Abs (s, T, aux (T :: Ts) t')
914 | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
915 aux Ts (t0 $ eta_expand Ts t1 1)
916 | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
917 | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
918 | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
919 | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
921 t0 $ aux Ts t1 $ aux Ts t2
923 if not (exists_subterm (fn Abs _ => true | _ => false) t) then t
924 else t |> Envir.eta_contract |> do_lambdas ctxt Ts
925 val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
926 in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
928 fun do_conceal_lambdas Ts (t1 $ t2) =
929 do_conceal_lambdas Ts t1 $ do_conceal_lambdas Ts t2
930 | do_conceal_lambdas Ts (Abs (_, T, t)) =
931 (* slightly unsound because of hash collisions *)
932 Free (concealed_lambda_prefix ^ string_of_int (hash_term t),
933 T --> fastype_of1 (Ts, t))
934 | do_conceal_lambdas _ t = t
935 val conceal_lambdas = generic_translate_lambdas (K do_conceal_lambdas)
937 fun do_introduce_combinators ctxt Ts =
938 let val thy = Proof_Context.theory_of ctxt in
941 #> Meson_Clausify.introduce_combinators_in_cterm
942 #> prop_of #> Logic.dest_equals #> snd
945 val introduce_combinators = generic_translate_lambdas do_introduce_combinators
947 fun process_abstractions_in_term ctxt trans_lambdas kind t =
948 let val thy = Proof_Context.theory_of ctxt in
949 if Meson.is_fol_term thy t then
952 t |> singleton trans_lambdas
954 (* A type variable of sort "{}" will make abstraction fail. *)
955 if kind = Conjecture then HOLogic.false_const
956 else HOLogic.true_const
959 (* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
960 same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
963 fun aux (t $ u) = aux t $ aux u
964 | aux (Abs (s, T, t)) = Abs (s, T, aux t)
965 | aux (Var ((s, i), T)) =
966 Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
968 in t |> exists_subterm is_Var t ? aux end
970 fun preprocess_prop ctxt trans_lambdas presimp_consts kind t =
972 val thy = Proof_Context.theory_of ctxt
973 val t = t |> Envir.beta_eta_contract
974 |> transform_elim_prop
975 |> Object_Logic.atomize_term thy
976 val need_trueprop = (fastype_of t = @{typ bool})
978 t |> need_trueprop ? HOLogic.mk_Trueprop
979 |> Raw_Simplifier.rewrite_term thy (Meson.unfold_set_const_simps ctxt) []
980 |> extensionalize_term ctxt
981 |> presimplify_term ctxt presimp_consts
982 |> perhaps (try (HOLogic.dest_Trueprop))
983 |> process_abstractions_in_term ctxt trans_lambdas kind
986 (* making fact and conjecture formulas *)
987 fun make_formula thy type_enc eq_as_iff name loc kind t =
989 val (iformula, atomic_types) =
990 iformula_from_prop thy type_enc eq_as_iff t []
992 {name = name, locality = loc, kind = kind, iformula = iformula,
993 atomic_types = atomic_types}
996 fun make_fact ctxt format type_enc eq_as_iff ((name, loc), t) =
997 let val thy = Proof_Context.theory_of ctxt in
998 case t |> make_formula thy type_enc (eq_as_iff andalso format <> CNF) name
1000 formula as {iformula = AAtom (IConst ((s, _), _, _)), ...} =>
1001 if s = tptp_true then NONE else SOME formula
1002 | formula => SOME formula
1005 fun make_conjecture ctxt format type_enc ps =
1007 val thy = Proof_Context.theory_of ctxt
1008 val last = length ps - 1
1010 map2 (fn j => fn (kind, t) =>
1011 t |> make_formula thy type_enc (format <> CNF) (string_of_int j)
1013 |> (j <> last) = (kind = Conjecture) ? update_iformula mk_anot)
1017 (** Finite and infinite type inference **)
1019 fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
1020 | deep_freeze_atyp T = T
1021 val deep_freeze_type = map_atyps deep_freeze_atyp
1023 (* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
1024 dangerous because their "exhaust" properties can easily lead to unsound ATP
1025 proofs. On the other hand, all HOL infinite types can be given the same
1026 models in first-order logic (via Löwenheim-Skolem). *)
1028 fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
1029 exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
1030 | should_encode_type _ _ All_Types _ = true
1031 | should_encode_type ctxt _ Fin_Nonmono_Types T =
1032 is_type_surely_finite ctxt false T
1033 | should_encode_type _ _ _ _ = false
1035 fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
1036 should_predicate_on_var T =
1037 (heaviness = Heavyweight orelse should_predicate_on_var ()) andalso
1038 should_encode_type ctxt nonmono_Ts level T
1039 | should_predicate_on_type _ _ _ _ _ = false
1041 fun is_var_or_bound_var (IConst ((s, _), _, _)) =
1042 String.isPrefix bound_var_prefix s
1043 | is_var_or_bound_var (IVar _) = true
1044 | is_var_or_bound_var _ = false
1047 Top_Level of bool option |
1048 Eq_Arg of bool option |
1051 fun should_tag_with_type _ _ _ (Top_Level _) _ _ = false
1052 | should_tag_with_type ctxt nonmono_Ts (Tags (poly, level, heaviness)) site
1055 Heavyweight => should_encode_type ctxt nonmono_Ts level T
1057 case (site, is_var_or_bound_var u) of
1058 (Eq_Arg pos, true) =>
1059 (* The first disjunct prevents a subtle soundness issue explained in
1060 Blanchette's Ph.D. thesis. See also
1061 "formula_lines_for_lightweight_tags_sym_decl". *)
1062 (pos <> SOME false andalso poly = Polymorphic andalso
1063 level <> All_Types andalso heaviness = Lightweight andalso
1064 exists (fn T' => type_instance ctxt (T', T)) nonmono_Ts) orelse
1065 should_encode_type ctxt nonmono_Ts level T
1067 | should_tag_with_type _ _ _ _ _ _ = false
1069 fun homogenized_type ctxt nonmono_Ts level =
1071 val should_encode = should_encode_type ctxt nonmono_Ts level
1072 fun homo 0 T = if should_encode T then T else homo_infinite_type
1073 | homo ary (Type (@{type_name fun}, [T1, T2])) =
1074 homo 0 T1 --> homo (ary - 1) T2
1075 | homo _ _ = raise Fail "expected function type"
1078 (** "hBOOL" and "hAPP" **)
1081 {pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
1083 fun add_iterm_syms_to_table ctxt explicit_apply =
1085 fun consider_var_arity const_T var_T max_ary =
1088 if ary = max_ary orelse type_instance ctxt (var_T, T) orelse
1089 type_instance ctxt (T, var_T) then
1092 iter (ary + 1) (range_type T)
1093 in iter 0 const_T end
1094 fun add_var_or_bound_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1095 if explicit_apply = NONE andalso
1096 (can dest_funT T orelse T = @{typ bool}) then
1098 val bool_vars' = bool_vars orelse body_type T = @{typ bool}
1099 fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
1100 {pred_sym = pred_sym andalso not bool_vars',
1101 min_ary = fold (fn T' => consider_var_arity T' T) types min_ary,
1102 max_ary = max_ary, types = types}
1104 fun_var_Ts |> can dest_funT T ? insert_type ctxt I T
1106 if bool_vars' = bool_vars andalso
1107 pointer_eq (fun_var_Ts', fun_var_Ts) then
1110 ((bool_vars', fun_var_Ts'), Symtab.map (K repair_min_arity) sym_tab)
1114 fun add top_level tm (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1115 let val (head, args) = strip_iterm_comb tm in
1117 IConst ((s, _), T, _) =>
1118 if String.isPrefix bound_var_prefix s then
1119 add_var_or_bound_var T accum
1121 let val ary = length args in
1122 ((bool_vars, fun_var_Ts),
1123 case Symtab.lookup sym_tab s of
1124 SOME {pred_sym, min_ary, max_ary, types} =>
1127 pred_sym andalso top_level andalso not bool_vars
1128 val types' = types |> insert_type ctxt I T
1130 if is_some explicit_apply orelse
1131 pointer_eq (types', types) then
1134 fold (consider_var_arity T) fun_var_Ts min_ary
1136 Symtab.update (s, {pred_sym = pred_sym,
1137 min_ary = Int.min (ary, min_ary),
1138 max_ary = Int.max (ary, max_ary),
1144 val pred_sym = top_level andalso not bool_vars
1146 case explicit_apply of
1149 | NONE => fold (consider_var_arity T) fun_var_Ts ary
1151 Symtab.update_new (s, {pred_sym = pred_sym,
1152 min_ary = min_ary, max_ary = ary,
1157 | IVar (_, T) => add_var_or_bound_var T accum
1158 | IAbs ((_, T), tm) => accum |> add_var_or_bound_var T |> add false tm
1160 |> fold (add false) args
1163 fun add_fact_syms_to_table ctxt explicit_apply =
1164 fact_lift (formula_fold NONE
1165 (K (add_iterm_syms_to_table ctxt explicit_apply)))
1167 val default_sym_tab_entries : (string * sym_info) list =
1168 (prefixed_predicator_name,
1169 {pred_sym = true, min_ary = 1, max_ary = 1, types = []}) ::
1170 ([tptp_false, tptp_true]
1171 |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []})) @
1172 ([tptp_equal, tptp_old_equal]
1173 |> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = []}))
1175 fun sym_table_for_facts ctxt explicit_apply facts =
1176 ((false, []), Symtab.empty)
1177 |> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
1178 |> fold Symtab.update default_sym_tab_entries
1180 fun min_arity_of sym_tab s =
1181 case Symtab.lookup sym_tab s of
1182 SOME ({min_ary, ...} : sym_info) => min_ary
1184 case strip_prefix_and_unascii const_prefix s of
1186 let val s = s |> unmangled_const_name |> invert_const in
1187 if s = predicator_name then 1
1188 else if s = app_op_name then 2
1189 else if s = type_pred_name then 1
1194 (* True if the constant ever appears outside of the top-level position in
1195 literals, or if it appears with different arities (e.g., because of different
1196 type instantiations). If false, the constant always receives all of its
1197 arguments and is used as a predicate. *)
1198 fun is_pred_sym sym_tab s =
1199 case Symtab.lookup sym_tab s of
1200 SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
1201 pred_sym andalso min_ary = max_ary
1204 val predicator_combconst =
1205 IConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
1206 fun predicator tm = IApp (predicator_combconst, tm)
1208 fun introduce_predicators_in_iterm sym_tab tm =
1209 case strip_iterm_comb tm of
1210 (IConst ((s, _), _, _), _) =>
1211 if is_pred_sym sym_tab s then tm else predicator tm
1212 | _ => predicator tm
1214 fun list_app head args = fold (curry (IApp o swap)) args head
1216 val app_op = `make_fixed_const app_op_name
1218 fun explicit_app arg head =
1220 val head_T = ityp_of head
1221 val (arg_T, res_T) = dest_funT head_T
1222 val explicit_app = IConst (app_op, head_T --> head_T, [arg_T, res_T])
1223 in list_app explicit_app [head, arg] end
1224 fun list_explicit_app head args = fold explicit_app args head
1226 fun introduce_explicit_apps_in_iterm sym_tab =
1229 case strip_iterm_comb tm of
1230 (head as IConst ((s, _), _, _), args) =>
1232 |> chop (min_arity_of sym_tab s)
1234 |-> list_explicit_app
1235 | (head, args) => list_explicit_app head (map aux args)
1238 fun chop_fun 0 T = ([], T)
1239 | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
1240 chop_fun (n - 1) ran_T |>> cons dom_T
1241 | chop_fun _ _ = raise Fail "unexpected non-function"
1243 fun filter_type_args _ _ _ [] = []
1244 | filter_type_args thy s arity T_args =
1246 (* will throw "TYPE" for pseudo-constants *)
1247 val U = if s = app_op_name then
1248 @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
1250 s |> Sign.the_const_type thy
1252 case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
1255 let val U_args = (s, U) |> Sign.const_typargs thy in
1257 |> map (fn (U, T) =>
1258 if member (op =) res_U_vars (dest_TVar U) then T
1262 handle TYPE _ => T_args
1264 fun enforce_type_arg_policy_in_iterm ctxt format type_enc =
1266 val thy = Proof_Context.theory_of ctxt
1267 fun aux arity (IApp (tm1, tm2)) = IApp (aux (arity + 1) tm1, aux 0 tm2)
1268 | aux arity (IConst (name as (s, _), T, T_args)) =
1269 (case strip_prefix_and_unascii const_prefix s of
1270 NONE => (name, T_args)
1273 val s'' = invert_const s''
1274 fun filtered_T_args false = T_args
1275 | filtered_T_args true = filter_type_args thy s'' arity T_args
1277 case type_arg_policy type_enc s'' of
1278 Explicit_Type_Args drop_args =>
1279 (name, filtered_T_args drop_args)
1280 | Mangled_Type_Args drop_args =>
1281 (mangled_const_name format type_enc (filtered_T_args drop_args)
1283 | No_Type_Args => (name, [])
1285 |> (fn (name, T_args) => IConst (name, T, T_args))
1286 | aux _ (IAbs (bound, tm)) = IAbs (bound, aux 0 tm)
1290 fun repair_iterm ctxt format type_enc sym_tab =
1291 not (is_type_enc_higher_order type_enc)
1292 ? (introduce_explicit_apps_in_iterm sym_tab
1293 #> introduce_predicators_in_iterm sym_tab)
1294 #> enforce_type_arg_policy_in_iterm ctxt format type_enc
1295 fun repair_fact ctxt format type_enc sym_tab =
1296 update_iformula (formula_map (repair_iterm ctxt format type_enc sym_tab))
1298 (** Helper facts **)
1300 (* The Boolean indicates that a fairly sound type encoding is needed. *)
1302 [(("COMBI", false), @{thms Meson.COMBI_def}),
1303 (("COMBK", false), @{thms Meson.COMBK_def}),
1304 (("COMBB", false), @{thms Meson.COMBB_def}),
1305 (("COMBC", false), @{thms Meson.COMBC_def}),
1306 (("COMBS", false), @{thms Meson.COMBS_def}),
1307 (("fFalse", false), [@{lemma "~ fFalse" by (unfold fFalse_def) fast}]),
1308 (("fFalse", true), @{thms True_or_False}),
1309 (("fTrue", false), [@{lemma "fTrue" by (unfold fTrue_def) fast}]),
1310 (("fTrue", true), @{thms True_or_False}),
1312 @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1313 fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1315 @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
1316 by (unfold fconj_def) fast+}),
1318 @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
1319 by (unfold fdisj_def) fast+}),
1320 (("fimplies", false),
1321 @{lemma "P | fimplies P Q" "~ Q | fimplies P Q" "~ fimplies P Q | ~ P | Q"
1322 by (unfold fimplies_def) fast+}),
1324 (* This is a lie: Higher-order equality doesn't need a sound type encoding.
1325 However, this is done so for backward compatibility: Including the
1326 equality helpers by default in Metis breaks a few existing proofs. *)
1327 @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1328 fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1329 (("fAll", false), []), (*TODO: add helpers*)
1330 (("fEx", false), []), (*TODO: add helpers*)
1331 (("If", true), @{thms if_True if_False True_or_False})]
1332 |> map (apsnd (map zero_var_indexes))
1334 val type_tag = `make_fixed_const type_tag_name
1336 fun type_tag_idempotence_fact () =
1338 fun var s = ATerm (`I s, [])
1339 fun tag tm = ATerm (type_tag, [var "T", tm])
1340 val tagged_a = tag (var "A")
1342 Formula (type_tag_idempotence_helper_name, Axiom,
1343 AAtom (ATerm (`I tptp_equal, [tag tagged_a, tagged_a]))
1344 |> close_formula_universally, isabelle_info simpN, NONE)
1347 fun should_specialize_helper type_enc t =
1348 polymorphism_of_type_enc type_enc = Mangled_Monomorphic andalso
1349 level_of_type_enc type_enc <> No_Types andalso
1350 not (null (Term.hidden_polymorphism t))
1352 fun helper_facts_for_sym ctxt format type_enc (s, {types, ...} : sym_info) =
1353 case strip_prefix_and_unascii const_prefix s of
1356 val thy = Proof_Context.theory_of ctxt
1357 val unmangled_s = mangled_s |> unmangled_const_name
1358 fun dub needs_fairly_sound j k =
1359 (unmangled_s ^ "_" ^ string_of_int j ^ "_" ^ string_of_int k ^
1360 (if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^
1361 (if needs_fairly_sound then typed_helper_suffix
1362 else untyped_helper_suffix),
1364 fun dub_and_inst needs_fairly_sound (th, j) =
1365 let val t = prop_of th in
1366 if should_specialize_helper type_enc t then
1367 map (fn T => specialize_type thy (invert_const unmangled_s, T) t)
1372 |> map (fn (k, t) => (dub needs_fairly_sound j k, t)) o tag_list 1
1373 val make_facts = map_filter (make_fact ctxt format type_enc false)
1374 val fairly_sound = is_type_enc_fairly_sound type_enc
1377 |> maps (fn ((helper_s, needs_fairly_sound), ths) =>
1378 if helper_s <> unmangled_s orelse
1379 (needs_fairly_sound andalso not fairly_sound) then
1382 ths ~~ (1 upto length ths)
1383 |> maps (dub_and_inst needs_fairly_sound)
1387 fun helper_facts_for_sym_table ctxt format type_enc sym_tab =
1388 Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_enc) sym_tab
1391 (***************************************************************)
1392 (* Type Classes Present in the Axiom or Conjecture Clauses *)
1393 (***************************************************************)
1395 fun set_insert (x, s) = Symtab.update (x, ()) s
1397 fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
1399 (* Remove this trivial type class (FIXME: similar code elsewhere) *)
1400 fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
1402 fun classes_of_terms get_Ts =
1403 map (map snd o get_Ts)
1404 #> List.foldl add_classes Symtab.empty
1405 #> delete_type #> Symtab.keys
1407 val tfree_classes_of_terms = classes_of_terms OldTerm.term_tfrees
1408 val tvar_classes_of_terms = classes_of_terms OldTerm.term_tvars
1410 fun fold_type_constrs f (Type (s, Ts)) x =
1411 fold (fold_type_constrs f) Ts (f (s, x))
1412 | fold_type_constrs _ _ x = x
1414 (*Type constructors used to instantiate overloaded constants are the only ones needed.*)
1415 fun add_type_constrs_in_term thy =
1417 fun add (Const (@{const_name Meson.skolem}, _) $ _) = I
1418 | add (t $ u) = add t #> add u
1419 | add (Const (x as (s, _))) =
1420 if String.isPrefix skolem_const_prefix s then I
1421 else x |> Sign.const_typargs thy |> fold (fold_type_constrs set_insert)
1422 | add (Abs (_, _, u)) = add u
1426 fun type_constrs_of_terms thy ts =
1427 Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty)
1429 fun translate_formulas ctxt format prem_kind type_enc trans_lambdas preproc
1430 hyp_ts concl_t facts =
1432 val thy = Proof_Context.theory_of ctxt
1433 val fact_ts = facts |> map snd
1434 val presimp_consts = Meson.presimplified_consts ctxt
1435 val preprocess = preprocess_prop ctxt trans_lambdas presimp_consts
1436 val (facts, fact_names) =
1437 facts |> map (fn (name, t) =>
1438 (name, t |> preproc ? preprocess Axiom)
1439 |> make_fact ctxt format type_enc true
1441 |> map_filter (try (apfst the))
1443 (* Remove existing facts from the conjecture, as this can dramatically
1444 boost an ATP's performance (for some reason). *)
1447 |> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t)
1448 val goal_t = Logic.list_implies (hyp_ts, concl_t)
1449 val all_ts = goal_t :: fact_ts
1450 val subs = tfree_classes_of_terms all_ts
1451 val supers = tvar_classes_of_terms all_ts
1452 val tycons = type_constrs_of_terms thy all_ts
1454 map (pair prem_kind) hyp_ts @ [(Conjecture, concl_t)]
1456 ? map (fn (kind, t) => (kind, t |> preprocess kind |> freeze_term))
1457 |> make_conjecture ctxt format type_enc
1458 val (supers', arity_clauses) =
1459 if level_of_type_enc type_enc = No_Types then ([], [])
1460 else make_arity_clauses thy tycons supers
1461 val class_rel_clauses = make_class_rel_clauses thy subs supers'
1463 (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
1466 fun fo_literal_from_type_literal (TyLitVar (class, name)) =
1467 (true, ATerm (class, [ATerm (name, [])]))
1468 | fo_literal_from_type_literal (TyLitFree (class, name)) =
1469 (true, ATerm (class, [ATerm (name, [])]))
1471 fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
1473 val type_pred = `make_fixed_const type_pred_name
1475 fun type_pred_iterm ctxt format type_enc T tm =
1476 IApp (IConst (type_pred, T --> @{typ bool}, [T])
1477 |> enforce_type_arg_policy_in_iterm ctxt format type_enc, tm)
1479 fun is_var_positively_naked_in_term _ (SOME false) _ accum = accum
1480 | is_var_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
1481 accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
1482 | is_var_positively_naked_in_term _ _ _ _ = true
1483 fun should_predicate_on_var_in_formula pos phi (SOME true) name =
1484 formula_fold pos (is_var_positively_naked_in_term name) phi false
1485 | should_predicate_on_var_in_formula _ _ _ _ = true
1487 fun mk_aterm format type_enc name T_args args =
1488 ATerm (name, map_filter (ho_term_for_type_arg format type_enc) T_args @ args)
1490 fun tag_with_type ctxt format nonmono_Ts type_enc pos T tm =
1491 IConst (type_tag, T --> T, [T])
1492 |> enforce_type_arg_policy_in_iterm ctxt format type_enc
1493 |> ho_term_from_iterm ctxt format nonmono_Ts type_enc (Top_Level pos)
1494 |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm])
1495 | _ => raise Fail "unexpected lambda-abstraction")
1496 and ho_term_from_iterm ctxt format nonmono_Ts type_enc =
1500 val (head, args) = strip_iterm_comb u
1503 Top_Level pos => pos
1508 IConst (name as (s, _), _, T_args) =>
1510 val arg_site = if is_tptp_equal s then Eq_Arg pos else Elsewhere
1512 mk_aterm format type_enc name T_args (map (aux arg_site) args)
1515 mk_aterm format type_enc name [] (map (aux Elsewhere) args)
1516 | IAbs ((name, T), tm) =>
1517 AAbs ((name, ho_type_from_typ format type_enc true 0 T),
1519 | IApp _ => raise Fail "impossible \"IApp\""
1522 t |> (if should_tag_with_type ctxt nonmono_Ts type_enc site u T then
1523 tag_with_type ctxt format nonmono_Ts type_enc pos T
1528 and formula_from_iformula ctxt format nonmono_Ts type_enc
1529 should_predicate_on_var =
1531 val do_term = ho_term_from_iterm ctxt format nonmono_Ts type_enc o Top_Level
1534 Simple_Types (_, level) =>
1535 homogenized_type ctxt nonmono_Ts level 0
1536 #> ho_type_from_typ format type_enc false 0 #> SOME
1538 fun do_out_of_bound_type pos phi universal (name, T) =
1539 if should_predicate_on_type ctxt nonmono_Ts type_enc
1540 (fn () => should_predicate_on_var pos phi universal name) T then
1542 |> type_pred_iterm ctxt format type_enc T
1543 |> do_term pos |> AAtom |> SOME
1546 fun do_formula pos (AQuant (q, xs, phi)) =
1548 val phi = phi |> do_formula pos
1549 val universal = Option.map (q = AExists ? not) pos
1551 AQuant (q, xs |> map (apsnd (fn NONE => NONE
1552 | SOME T => do_bound_type T)),
1553 (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
1555 (fn (_, NONE) => NONE
1557 do_out_of_bound_type pos phi universal (s, T))
1561 | do_formula pos (AConn conn) = aconn_map pos do_formula conn
1562 | do_formula pos (AAtom tm) = AAtom (do_term pos tm)
1565 fun bound_tvars type_enc Ts =
1566 mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
1567 (type_literals_for_types type_enc add_sorts_on_tvar Ts))
1569 (* Each fact is given a unique fact number to avoid name clashes (e.g., because
1570 of monomorphization). The TPTP explicitly forbids name clashes, and some of
1571 the remote provers might care. *)
1572 fun formula_line_for_fact ctxt format prefix encode freshen pos nonmono_Ts
1573 type_enc (j, {name, locality, kind, iformula, atomic_types}) =
1574 (prefix ^ (if freshen then string_of_int j ^ "_" else "") ^ encode name,
1577 |> close_iformula_universally
1578 |> formula_from_iformula ctxt format nonmono_Ts type_enc
1579 should_predicate_on_var_in_formula
1580 (if pos then SOME true else NONE)
1581 |> bound_tvars type_enc atomic_types
1582 |> close_formula_universally,
1585 Intro => isabelle_info introN
1586 | Elim => isabelle_info elimN
1587 | Simp => isabelle_info simpN
1591 fun formula_line_for_class_rel_clause ({name, subclass, superclass, ...}
1592 : class_rel_clause) =
1593 let val ty_arg = ATerm (`I "T", []) in
1594 Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
1595 AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
1596 AAtom (ATerm (superclass, [ty_arg]))])
1597 |> close_formula_universally, isabelle_info introN, NONE)
1600 fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
1601 (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
1602 | fo_literal_from_arity_literal (TVarLit (c, sort)) =
1603 (false, ATerm (c, [ATerm (sort, [])]))
1605 fun formula_line_for_arity_clause ({name, prem_lits, concl_lits, ...}
1607 Formula (arity_clause_prefix ^ name, Axiom,
1608 mk_ahorn (map (formula_from_fo_literal o apfst not
1609 o fo_literal_from_arity_literal) prem_lits)
1610 (formula_from_fo_literal
1611 (fo_literal_from_arity_literal concl_lits))
1612 |> close_formula_universally, isabelle_info introN, NONE)
1614 fun formula_line_for_conjecture ctxt format nonmono_Ts type_enc
1615 ({name, kind, iformula, atomic_types, ...} : translated_formula) =
1616 Formula (conjecture_prefix ^ name, kind,
1617 formula_from_iformula ctxt format nonmono_Ts type_enc
1618 should_predicate_on_var_in_formula (SOME false)
1619 (close_iformula_universally iformula)
1620 |> bound_tvars type_enc atomic_types
1621 |> close_formula_universally, NONE, NONE)
1623 fun free_type_literals type_enc ({atomic_types, ...} : translated_formula) =
1624 atomic_types |> type_literals_for_types type_enc add_sorts_on_tfree
1625 |> map fo_literal_from_type_literal
1627 fun formula_line_for_free_type j lit =
1628 Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis,
1629 formula_from_fo_literal lit, NONE, NONE)
1630 fun formula_lines_for_free_types type_enc facts =
1632 val litss = map (free_type_literals type_enc) facts
1633 val lits = fold (union (op =)) litss []
1634 in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
1636 (** Symbol declarations **)
1638 fun should_declare_sym type_enc pred_sym s =
1639 is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
1641 Simple_Types _ => true
1642 | Tags (_, _, Lightweight) => true
1643 | _ => not pred_sym)
1645 fun sym_decl_table_for_facts ctxt type_enc repaired_sym_tab (conjs, facts) =
1647 fun add_iterm in_conj tm =
1648 let val (head, args) = strip_iterm_comb tm in
1650 IConst ((s, s'), T, T_args) =>
1651 let val pred_sym = is_pred_sym repaired_sym_tab s in
1652 if should_declare_sym type_enc pred_sym s then
1653 Symtab.map_default (s, [])
1654 (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
1659 | IAbs (_, tm) => add_iterm in_conj tm
1661 #> fold (add_iterm in_conj) args
1663 fun add_fact in_conj = fact_lift (formula_fold NONE (K (add_iterm in_conj)))
1666 |> is_type_enc_fairly_sound type_enc
1667 ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
1670 (* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
1671 out with monotonicity" paper presented at CADE 2011. *)
1672 fun add_iterm_nonmonotonic_types _ _ _ _ (SOME false) _ = I
1673 | add_iterm_nonmonotonic_types ctxt level sound locality _
1674 (IApp (IApp (IConst ((s, _), Type (_, [T, _]), _), tm1), tm2)) =
1675 (is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
1677 Noninf_Nonmono_Types =>
1678 not (is_locality_global locality) orelse
1679 not (is_type_surely_infinite ctxt sound T)
1680 | Fin_Nonmono_Types => is_type_surely_finite ctxt false T
1681 | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
1682 | add_iterm_nonmonotonic_types _ _ _ _ _ _ = I
1683 fun add_fact_nonmonotonic_types ctxt level sound
1684 ({kind, locality, iformula, ...} : translated_formula) =
1685 formula_fold (SOME (kind <> Conjecture))
1686 (add_iterm_nonmonotonic_types ctxt level sound locality)
1688 fun nonmonotonic_types_for_facts ctxt type_enc sound facts =
1689 let val level = level_of_type_enc type_enc in
1690 if level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types then
1691 [] |> fold (add_fact_nonmonotonic_types ctxt level sound) facts
1692 (* We must add "bool" in case the helper "True_or_False" is added
1693 later. In addition, several places in the code rely on the list of
1694 nonmonotonic types not being empty. *)
1695 |> insert_type ctxt I @{typ bool}
1700 fun decl_line_for_sym ctxt format nonmono_Ts type_enc s
1701 (s', T_args, T, pred_sym, ary, _) =
1703 val (T_arg_Ts, level) =
1705 Simple_Types (_, level) => ([], level)
1706 | _ => (replicate (length T_args) homo_infinite_type, No_Types)
1708 Decl (sym_decl_prefix ^ s, (s, s'),
1709 (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
1710 |> ho_type_from_typ format type_enc pred_sym (length T_arg_Ts + ary))
1713 fun formula_line_for_preds_sym_decl ctxt format conj_sym_kind nonmono_Ts
1714 poly_nonmono_Ts type_enc n s j (s', T_args, T, _, ary, in_conj) =
1716 val (kind, maybe_negate) =
1717 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1719 val (arg_Ts, res_T) = chop_fun ary T
1720 val num_args = length arg_Ts
1722 1 upto num_args |> map (`I o make_bound_var o string_of_int)
1724 bound_names ~~ arg_Ts |> map (fn (name, T) => IConst (name, T, []))
1725 val sym_needs_arg_types = n > 1 orelse exists (curry (op =) dummyT) T_args
1726 fun should_keep_arg_type T =
1727 sym_needs_arg_types orelse
1728 not (should_predicate_on_type ctxt nonmono_Ts type_enc (K false) T)
1730 arg_Ts |> map (fn T => if should_keep_arg_type T then SOME T else NONE)
1732 Formula (preds_sym_formula_prefix ^ s ^
1733 (if n > 1 then "_" ^ string_of_int j else ""), kind,
1734 IConst ((s, s'), T, T_args)
1735 |> fold (curry (IApp o swap)) bounds
1736 |> type_pred_iterm ctxt format type_enc res_T
1737 |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
1738 |> formula_from_iformula ctxt format poly_nonmono_Ts type_enc
1739 (K (K (K (K true)))) (SOME true)
1740 |> n > 1 ? bound_tvars type_enc (atyps_of T)
1741 |> close_formula_universally
1743 isabelle_info introN, NONE)
1746 fun formula_lines_for_lightweight_tags_sym_decl ctxt format conj_sym_kind
1747 poly_nonmono_Ts type_enc n s
1748 (j, (s', T_args, T, pred_sym, ary, in_conj)) =
1751 lightweight_tags_sym_formula_prefix ^ s ^
1752 (if n > 1 then "_" ^ string_of_int j else "")
1753 val (kind, maybe_negate) =
1754 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1756 val (arg_Ts, res_T) = chop_fun ary T
1758 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
1759 val bounds = bound_names |> map (fn name => ATerm (name, []))
1760 val cst = mk_aterm format type_enc (s, s') T_args
1761 val atomic_Ts = atyps_of T
1763 (if pred_sym then AConn (AIff, map AAtom tms)
1764 else AAtom (ATerm (`I tptp_equal, tms)))
1765 |> bound_tvars type_enc atomic_Ts
1766 |> close_formula_universally
1768 (* See also "should_tag_with_type". *)
1769 fun should_encode T =
1770 should_encode_type ctxt poly_nonmono_Ts All_Types T orelse
1772 Tags (Polymorphic, level, Lightweight) =>
1773 level <> All_Types andalso Monomorph.typ_has_tvars T
1775 val tag_with = tag_with_type ctxt format poly_nonmono_Ts type_enc NONE
1776 val add_formula_for_res =
1777 if should_encode res_T then
1778 cons (Formula (ident_base ^ "_res", kind,
1779 eq [tag_with res_T (cst bounds), cst bounds],
1780 isabelle_info simpN, NONE))
1783 fun add_formula_for_arg k =
1784 let val arg_T = nth arg_Ts k in
1785 if should_encode arg_T then
1786 case chop k bounds of
1787 (bounds1, bound :: bounds2) =>
1788 cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
1789 eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
1791 isabelle_info simpN, NONE))
1792 | _ => raise Fail "expected nonempty tail"
1797 [] |> not pred_sym ? add_formula_for_res
1798 |> fold add_formula_for_arg (ary - 1 downto 0)
1801 fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
1803 fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts
1804 poly_nonmono_Ts type_enc (s, decls) =
1807 decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_enc s)
1812 decl :: (decls' as _ :: _) =>
1813 let val T = result_type_of_decl decl in
1814 if forall (curry (type_instance ctxt o swap) T
1815 o result_type_of_decl) decls' then
1821 val n = length decls
1823 decls |> filter (should_predicate_on_type ctxt poly_nonmono_Ts type_enc
1825 o result_type_of_decl)
1827 (0 upto length decls - 1, decls)
1828 |-> map2 (formula_line_for_preds_sym_decl ctxt format conj_sym_kind
1829 nonmono_Ts poly_nonmono_Ts type_enc n s)
1831 | Tags (_, _, heaviness) =>
1835 let val n = length decls in
1836 (0 upto n - 1 ~~ decls)
1837 |> maps (formula_lines_for_lightweight_tags_sym_decl ctxt format
1838 conj_sym_kind poly_nonmono_Ts type_enc n s)
1841 fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1842 poly_nonmono_Ts type_enc sym_decl_tab =
1847 |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
1848 nonmono_Ts poly_nonmono_Ts type_enc)
1850 fun needs_type_tag_idempotence (Tags (poly, level, heaviness)) =
1851 poly <> Mangled_Monomorphic andalso
1852 ((level = All_Types andalso heaviness = Lightweight) orelse
1853 level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types)
1854 | needs_type_tag_idempotence _ = false
1856 fun offset_of_heading_in_problem _ [] j = j
1857 | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
1858 if heading = needle then j
1859 else offset_of_heading_in_problem needle problem (j + length lines)
1861 val implicit_declsN = "Should-be-implicit typings"
1862 val explicit_declsN = "Explicit typings"
1863 val factsN = "Relevant facts"
1864 val class_relsN = "Class relationships"
1865 val aritiesN = "Arities"
1866 val helpersN = "Helper facts"
1867 val conjsN = "Conjectures"
1868 val free_typesN = "Type variables"
1870 val explicit_apply = NONE (* for experiments *)
1872 fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_enc sound
1873 exporter trans_lambdas readable_names preproc hyp_ts concl_t facts =
1875 val (format, type_enc) = choose_format [format] type_enc
1876 val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
1877 translate_formulas ctxt format prem_kind type_enc trans_lambdas preproc
1878 hyp_ts concl_t facts
1879 val sym_tab = conjs @ facts |> sym_table_for_facts ctxt explicit_apply
1881 conjs @ facts |> nonmonotonic_types_for_facts ctxt type_enc sound
1882 val repair = repair_fact ctxt format type_enc sym_tab
1883 val (conjs, facts) = (conjs, facts) |> pairself (map repair)
1884 val repaired_sym_tab =
1885 conjs @ facts |> sym_table_for_facts ctxt (SOME false)
1887 repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_enc
1889 val poly_nonmono_Ts =
1890 if null nonmono_Ts orelse nonmono_Ts = [@{typ bool}] orelse
1891 polymorphism_of_type_enc type_enc <> Polymorphic then
1894 [TVar (("'a", 0), HOLogic.typeS)]
1895 val sym_decl_lines =
1896 (conjs, helpers @ facts)
1897 |> sym_decl_table_for_facts ctxt type_enc repaired_sym_tab
1898 |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1899 poly_nonmono_Ts type_enc
1901 0 upto length helpers - 1 ~~ helpers
1902 |> map (formula_line_for_fact ctxt format helper_prefix I false true
1903 poly_nonmono_Ts type_enc)
1904 |> (if needs_type_tag_idempotence type_enc then
1905 cons (type_tag_idempotence_fact ())
1908 (* Reordering these might confuse the proof reconstruction code or the SPASS
1911 [(explicit_declsN, sym_decl_lines),
1913 map (formula_line_for_fact ctxt format fact_prefix ascii_of
1914 (not exporter) (not exporter) nonmono_Ts
1916 (0 upto length facts - 1 ~~ facts)),
1917 (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
1918 (aritiesN, map formula_line_for_arity_clause arity_clauses),
1919 (helpersN, helper_lines),
1921 map (formula_line_for_conjecture ctxt format nonmono_Ts type_enc)
1923 (free_typesN, formula_lines_for_free_types type_enc (facts @ conjs))]
1927 CNF => ensure_cnf_problem
1928 | CNF_UEQ => filter_cnf_ueq_problem
1930 |> (if is_format_typed format then
1931 declare_undeclared_syms_in_atp_problem type_decl_prefix
1935 val (problem, pool) = problem |> nice_atp_problem readable_names
1936 val helpers_offset = offset_of_heading_in_problem helpersN problem 0
1938 map_filter (fn (j, {name, ...}) =>
1939 if String.isSuffix typed_helper_suffix name then SOME j
1941 ((helpers_offset + 1 upto helpers_offset + length helpers)
1943 fun add_sym_arity (s, {min_ary, ...} : sym_info) =
1945 case strip_prefix_and_unascii const_prefix s of
1946 SOME s => Symtab.insert (op =) (s, min_ary)
1952 case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
1953 offset_of_heading_in_problem conjsN problem 0,
1954 offset_of_heading_in_problem factsN problem 0,
1955 fact_names |> Vector.fromList,
1957 Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
1961 val conj_weight = 0.0
1962 val hyp_weight = 0.1
1963 val fact_min_weight = 0.2
1964 val fact_max_weight = 1.0
1965 val type_info_default_weight = 0.8
1967 fun add_term_weights weight (ATerm (s, tms)) =
1968 is_tptp_user_symbol s ? Symtab.default (s, weight)
1969 #> fold (add_term_weights weight) tms
1970 | add_term_weights weight (AAbs (_, tm)) = add_term_weights weight tm
1971 fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
1972 formula_fold NONE (K (add_term_weights weight)) phi
1973 | add_problem_line_weights _ _ = I
1975 fun add_conjectures_weights [] = I
1976 | add_conjectures_weights conjs =
1977 let val (hyps, conj) = split_last conjs in
1978 add_problem_line_weights conj_weight conj
1979 #> fold (add_problem_line_weights hyp_weight) hyps
1982 fun add_facts_weights facts =
1984 val num_facts = length facts
1986 fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
1987 / Real.fromInt num_facts
1989 map weight_of (0 upto num_facts - 1) ~~ facts
1990 |> fold (uncurry add_problem_line_weights)
1993 (* Weights are from 0.0 (most important) to 1.0 (least important). *)
1994 fun atp_problem_weights problem =
1995 let val get = these o AList.lookup (op =) problem in
1997 |> add_conjectures_weights (get free_typesN @ get conjsN)
1998 |> add_facts_weights (get factsN)
1999 |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
2000 [explicit_declsN, class_relsN, aritiesN]
2002 |> sort (prod_ord Real.compare string_ord o pairself swap)