cleaner fact freshening, which also works in corner cases, e.g. if two backquoted facts have the same name (but have different variable indices)
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
43 datatype locality = General | Intro | Elim | Simp | Local | Assum | Chained
45 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
47 All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
48 datatype type_heaviness = Heavyweight | Lightweight
51 Simple_Types of type_level |
52 Preds of polymorphism * type_level * type_heaviness |
53 Tags of polymorphism * type_level * type_heaviness
55 val bound_var_prefix : string
56 val schematic_var_prefix: string
57 val fixed_var_prefix: string
58 val tvar_prefix: string
59 val tfree_prefix: string
60 val const_prefix: string
61 val type_const_prefix: string
62 val class_prefix: string
63 val skolem_const_prefix : string
64 val old_skolem_const_prefix : string
65 val new_skolem_const_prefix : string
66 val type_decl_prefix : string
67 val sym_decl_prefix : string
68 val preds_sym_formula_prefix : string
69 val lightweight_tags_sym_formula_prefix : string
70 val fact_prefix : string
71 val conjecture_prefix : string
72 val helper_prefix : string
73 val class_rel_clause_prefix : string
74 val arity_clause_prefix : string
75 val tfree_clause_prefix : string
76 val typed_helper_suffix : string
77 val untyped_helper_suffix : string
78 val type_tag_idempotence_helper_name : string
79 val predicator_name : string
80 val app_op_name : string
81 val type_tag_name : string
82 val type_pred_name : string
83 val simple_type_prefix : string
84 val prefixed_predicator_name : string
85 val prefixed_app_op_name : string
86 val prefixed_type_tag_name : string
87 val ascii_of: string -> string
88 val unascii_of: string -> string
89 val strip_prefix_and_unascii : string -> string -> string option
90 val proxy_table : (string * (string * (thm * (string * string)))) list
91 val proxify_const : string -> (string * string) option
92 val invert_const: string -> string
93 val unproxify_const: string -> string
94 val make_bound_var : string -> string
95 val make_schematic_var : string * int -> string
96 val make_fixed_var : string -> string
97 val make_schematic_type_var : string * int -> string
98 val make_fixed_type_var : string -> string
99 val make_fixed_const : string -> string
100 val make_fixed_type_const : string -> string
101 val make_type_class : string -> string
102 val new_skolem_var_name_from_const : string -> string
103 val num_type_args : theory -> string -> int
104 val atp_irrelevant_consts : string list
105 val atp_schematic_consts_of : term -> typ list Symtab.table
106 val make_arity_clauses :
107 theory -> string list -> class list -> class list * arity_clause list
108 val make_class_rel_clauses :
109 theory -> class list -> class list -> class_rel_clause list
110 val combtyp_of : combterm -> typ
111 val strip_combterm_comb : combterm -> combterm * combterm list
112 val atyps_of : typ -> typ list
113 val combterm_from_term :
114 theory -> (string * typ) list -> term -> combterm * typ list
115 val is_locality_global : locality -> bool
116 val type_sys_from_string : string -> type_sys
117 val polymorphism_of_type_sys : type_sys -> polymorphism
118 val level_of_type_sys : type_sys -> type_level
119 val is_type_sys_virtually_sound : type_sys -> bool
120 val is_type_sys_fairly_sound : type_sys -> bool
121 val choose_format : format list -> type_sys -> format * type_sys
123 connective -> ('a, 'b, 'c) formula list -> ('a, 'b, 'c) formula
124 val unmangled_const_name : string -> string
125 val unmangled_const : string -> string * string fo_term list
126 val helper_table : ((string * bool) * thm list) list
127 val should_specialize_helper : type_sys -> term -> bool
128 val tfree_classes_of_terms : term list -> string list
129 val tvar_classes_of_terms : term list -> string list
130 val type_constrs_of_terms : theory -> term list -> string list
131 val prepare_atp_problem :
132 Proof.context -> format -> formula_kind -> formula_kind -> type_sys
133 -> bool -> bool -> bool -> term list -> term
134 -> ((string * locality) * term) list
135 -> string problem * string Symtab.table * int * int
136 * (string * locality) list vector * int list * int Symtab.table
137 val atp_problem_weights : string problem -> (string * real) list
140 structure ATP_Translate : ATP_TRANSLATE =
146 type name = string * string
149 val generate_useful_info = false
151 fun useful_isabelle_info s =
152 if generate_useful_info then
153 SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
157 val intro_info = useful_isabelle_info "intro"
158 val elim_info = useful_isabelle_info "elim"
159 val simp_info = useful_isabelle_info "simp"
161 val bound_var_prefix = "B_"
162 val schematic_var_prefix = "V_"
163 val fixed_var_prefix = "v_"
165 val tvar_prefix = "T_"
166 val tfree_prefix = "t_"
168 val const_prefix = "c_"
169 val type_const_prefix = "tc_"
170 val class_prefix = "cl_"
172 val skolem_const_prefix = "Sledgehammer" ^ Long_Name.separator ^ "Sko"
173 val old_skolem_const_prefix = skolem_const_prefix ^ "o"
174 val new_skolem_const_prefix = skolem_const_prefix ^ "n"
176 val type_decl_prefix = "ty_"
177 val sym_decl_prefix = "sy_"
178 val preds_sym_formula_prefix = "psy_"
179 val lightweight_tags_sym_formula_prefix = "tsy_"
180 val fact_prefix = "fact_"
181 val conjecture_prefix = "conj_"
182 val helper_prefix = "help_"
183 val class_rel_clause_prefix = "clar_"
184 val arity_clause_prefix = "arity_"
185 val tfree_clause_prefix = "tfree_"
187 val typed_helper_suffix = "_T"
188 val untyped_helper_suffix = "_U"
189 val type_tag_idempotence_helper_name = helper_prefix ^ "ti_idem"
191 val predicator_name = "hBOOL"
192 val app_op_name = "hAPP"
193 val type_tag_name = "ti"
194 val type_pred_name = "is"
195 val simple_type_prefix = "ty_"
197 val prefixed_predicator_name = const_prefix ^ predicator_name
198 val prefixed_app_op_name = const_prefix ^ app_op_name
199 val prefixed_type_tag_name = const_prefix ^ type_tag_name
201 (* Freshness almost guaranteed! *)
202 val sledgehammer_weak_prefix = "Sledgehammer:"
204 (*Escaping of special characters.
205 Alphanumeric characters are left unchanged.
206 The character _ goes to __
207 Characters in the range ASCII space to / go to _A to _P, respectively.
208 Other characters go to _nnn where nnn is the decimal ASCII code.*)
209 val upper_a_minus_space = Char.ord #"A" - Char.ord #" "
211 fun stringN_of_int 0 _ = ""
212 | stringN_of_int k n =
213 stringN_of_int (k - 1) (n div 10) ^ string_of_int (n mod 10)
215 fun ascii_of_char c =
216 if Char.isAlphaNum c then
218 else if c = #"_" then
220 else if #" " <= c andalso c <= #"/" then
221 "_" ^ String.str (Char.chr (Char.ord c + upper_a_minus_space))
223 (* fixed width, in case more digits follow *)
224 "_" ^ stringN_of_int 3 (Char.ord c)
226 val ascii_of = String.translate ascii_of_char
228 (** Remove ASCII armoring from names in proof files **)
230 (* We don't raise error exceptions because this code can run inside a worker
231 thread. Also, the errors are impossible. *)
234 fun un rcs [] = String.implode(rev rcs)
235 | un rcs [#"_"] = un (#"_" :: rcs) [] (* ERROR *)
236 (* Three types of _ escapes: __, _A to _P, _nnn *)
237 | un rcs (#"_" :: #"_" :: cs) = un (#"_"::rcs) cs
238 | un rcs (#"_" :: c :: cs) =
239 if #"A" <= c andalso c<= #"P" then
240 (* translation of #" " to #"/" *)
241 un (Char.chr (Char.ord c - upper_a_minus_space) :: rcs) cs
243 let val digits = List.take (c::cs, 3) handle General.Subscript => [] in
244 case Int.fromString (String.implode digits) of
245 SOME n => un (Char.chr n :: rcs) (List.drop (cs, 2))
246 | NONE => un (c:: #"_"::rcs) cs (* ERROR *)
248 | un rcs (c :: cs) = un (c :: rcs) cs
249 in un [] o String.explode end
251 (* If string s has the prefix s1, return the result of deleting it,
253 fun strip_prefix_and_unascii s1 s =
254 if String.isPrefix s1 s then
255 SOME (unascii_of (String.extract (s, size s1, NONE)))
260 [("c_False", (@{const_name False}, (@{thm fFalse_def},
261 ("fFalse", @{const_name ATP.fFalse})))),
262 ("c_True", (@{const_name True}, (@{thm fTrue_def},
263 ("fTrue", @{const_name ATP.fTrue})))),
264 ("c_Not", (@{const_name Not}, (@{thm fNot_def},
265 ("fNot", @{const_name ATP.fNot})))),
266 ("c_conj", (@{const_name conj}, (@{thm fconj_def},
267 ("fconj", @{const_name ATP.fconj})))),
268 ("c_disj", (@{const_name disj}, (@{thm fdisj_def},
269 ("fdisj", @{const_name ATP.fdisj})))),
270 ("c_implies", (@{const_name implies}, (@{thm fimplies_def},
271 ("fimplies", @{const_name ATP.fimplies})))),
272 ("equal", (@{const_name HOL.eq}, (@{thm fequal_def},
273 ("fequal", @{const_name ATP.fequal}))))]
275 val proxify_const = AList.lookup (op =) proxy_table #> Option.map (snd o snd)
277 (* Readable names for the more common symbolic functions. Do not mess with the
278 table unless you know what you are doing. *)
279 val const_trans_table =
280 [(@{type_name Product_Type.prod}, "prod"),
281 (@{type_name Sum_Type.sum}, "sum"),
282 (@{const_name False}, "False"),
283 (@{const_name True}, "True"),
284 (@{const_name Not}, "Not"),
285 (@{const_name conj}, "conj"),
286 (@{const_name disj}, "disj"),
287 (@{const_name implies}, "implies"),
288 (@{const_name HOL.eq}, "equal"),
289 (@{const_name If}, "If"),
290 (@{const_name Set.member}, "member"),
291 (@{const_name Meson.COMBI}, "COMBI"),
292 (@{const_name Meson.COMBK}, "COMBK"),
293 (@{const_name Meson.COMBB}, "COMBB"),
294 (@{const_name Meson.COMBC}, "COMBC"),
295 (@{const_name Meson.COMBS}, "COMBS")]
297 |> fold (Symtab.update o swap o snd o snd o snd) proxy_table
299 (* Invert the table of translations between Isabelle and ATPs. *)
300 val const_trans_table_inv =
301 const_trans_table |> Symtab.dest |> map swap |> Symtab.make
302 val const_trans_table_unprox =
304 |> fold (fn (_, (isa, (_, (_, atp)))) => Symtab.update (atp, isa)) proxy_table
306 val invert_const = perhaps (Symtab.lookup const_trans_table_inv)
307 val unproxify_const = perhaps (Symtab.lookup const_trans_table_unprox)
310 case Symtab.lookup const_trans_table c of
314 (*Remove the initial ' character from a type variable, if it is present*)
315 fun trim_type_var s =
316 if s <> "" andalso String.sub(s,0) = #"'" then String.extract(s,1,NONE)
317 else raise Fail ("trim_type: Malformed type variable encountered: " ^ s)
319 fun ascii_of_indexname (v,0) = ascii_of v
320 | ascii_of_indexname (v,i) = ascii_of v ^ "_" ^ string_of_int i
322 fun make_bound_var x = bound_var_prefix ^ ascii_of x
323 fun make_schematic_var v = schematic_var_prefix ^ ascii_of_indexname v
324 fun make_fixed_var x = fixed_var_prefix ^ ascii_of x
326 fun make_schematic_type_var (x,i) =
327 tvar_prefix ^ (ascii_of_indexname (trim_type_var x, i))
328 fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (trim_type_var x))
330 (* HOL.eq MUST BE "equal" because it's built into ATPs. *)
331 fun make_fixed_const @{const_name HOL.eq} = "equal"
332 | make_fixed_const c = const_prefix ^ lookup_const c
334 fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
336 fun make_type_class clas = class_prefix ^ ascii_of clas
338 fun new_skolem_var_name_from_const s =
339 let val ss = s |> space_explode Long_Name.separator in
340 nth ss (length ss - 2)
343 (* The number of type arguments of a constant, zero if it's monomorphic. For
344 (instances of) Skolem pseudoconstants, this information is encoded in the
346 fun num_type_args thy s =
347 if String.isPrefix skolem_const_prefix s then
348 s |> space_explode Long_Name.separator |> List.last |> Int.fromString |> the
350 (s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
352 (* These are either simplified away by "Meson.presimplify" (most of the time) or
353 handled specially via "fFalse", "fTrue", ..., "fequal". *)
354 val atp_irrelevant_consts =
355 [@{const_name False}, @{const_name True}, @{const_name Not},
356 @{const_name conj}, @{const_name disj}, @{const_name implies},
357 @{const_name HOL.eq}, @{const_name If}, @{const_name Let}]
359 val atp_monomorph_bad_consts =
360 atp_irrelevant_consts @
361 (* These are ignored anyway by the relevance filter (unless they appear in
362 higher-order places) but not by the monomorphizer. *)
363 [@{const_name all}, @{const_name "==>"}, @{const_name "=="},
364 @{const_name Trueprop}, @{const_name All}, @{const_name Ex},
365 @{const_name Ex1}, @{const_name Ball}, @{const_name Bex}]
367 fun add_schematic_const (x as (_, T)) =
368 Monomorph.typ_has_tvars T ? Symtab.insert_list (op =) x
369 val add_schematic_consts_of =
370 Term.fold_aterms (fn Const (x as (s, _)) =>
371 not (member (op =) atp_monomorph_bad_consts s)
372 ? add_schematic_const x
374 fun atp_schematic_consts_of t = add_schematic_consts_of t Symtab.empty
376 (** Definitions and functions for FOL clauses and formulas for TPTP **)
378 (* The first component is the type class; the second is a "TVar" or "TFree". *)
379 datatype type_literal =
380 TyLitVar of name * name |
381 TyLitFree of name * name
384 (** Isabelle arities **)
386 datatype arity_literal =
387 TConsLit of name * name * name list |
388 TVarLit of name * name
391 | gen_TVars n = ("T_" ^ string_of_int n) :: gen_TVars (n-1)
393 val type_class = the_single @{sort type}
395 fun add_packed_sort tvar =
396 fold (fn s => s <> type_class ? cons (`make_type_class s, `I tvar))
400 prem_lits: arity_literal list,
401 concl_lits: arity_literal}
403 (* Arity of type constructor "tcon :: (arg1, ..., argN) res" *)
404 fun make_axiom_arity_clause (tcons, name, (cls, args)) =
406 val tvars = gen_TVars (length args)
407 val tvars_srts = ListPair.zip (tvars, args)
410 prem_lits = [] |> fold (uncurry add_packed_sort) tvars_srts |> map TVarLit,
411 concl_lits = TConsLit (`make_type_class cls,
412 `make_fixed_type_const tcons,
416 fun arity_clause _ _ (_, []) = []
417 | arity_clause seen n (tcons, ("HOL.type",_)::ars) = (*ignore*)
418 arity_clause seen n (tcons,ars)
419 | arity_clause seen n (tcons, (ar as (class,_)) :: ars) =
420 if member (op =) seen class then (*multiple arities for the same tycon, class pair*)
421 make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class ^ "_" ^ string_of_int n, ar) ::
422 arity_clause seen (n+1) (tcons,ars)
424 make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class, ar) ::
425 arity_clause (class::seen) n (tcons,ars)
427 fun multi_arity_clause [] = []
428 | multi_arity_clause ((tcons, ars) :: tc_arlists) =
429 arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
431 (*Generate all pairs (tycon,class,sorts) such that tycon belongs to class in theory thy
432 provided its arguments have the corresponding sorts.*)
433 fun type_class_pairs thy tycons classes =
435 val alg = Sign.classes_of thy
436 fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
437 fun add_class tycon class =
438 cons (class, domain_sorts tycon class)
439 handle Sorts.CLASS_ERROR _ => I
440 fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
441 in map try_classes tycons end
443 (*Proving one (tycon, class) membership may require proving others, so iterate.*)
444 fun iter_type_class_pairs _ _ [] = ([], [])
445 | iter_type_class_pairs thy tycons classes =
447 fun maybe_insert_class s =
448 (s <> type_class andalso not (member (op =) classes s))
450 val cpairs = type_class_pairs thy tycons classes
452 [] |> fold (fold (fold (fold maybe_insert_class) o snd) o snd) cpairs
453 val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
454 in (classes' @ classes, union (op =) cpairs' cpairs) end
456 fun make_arity_clauses thy tycons =
457 iter_type_class_pairs thy tycons ##> multi_arity_clause
460 (** Isabelle class relations **)
462 type class_rel_clause =
467 (*Generate all pairs (sub,super) such that sub is a proper subclass of super in theory thy.*)
468 fun class_pairs _ [] _ = []
469 | class_pairs thy subs supers =
471 val class_less = Sorts.class_less (Sign.classes_of thy)
472 fun add_super sub super = class_less (sub, super) ? cons (sub, super)
473 fun add_supers sub = fold (add_super sub) supers
474 in fold add_supers subs [] end
476 fun make_class_rel_clause (sub,super) =
477 {name = sub ^ "_" ^ super,
478 subclass = `make_type_class sub,
479 superclass = `make_type_class super}
481 fun make_class_rel_clauses thy subs supers =
482 map make_class_rel_clause (class_pairs thy subs supers)
485 CombConst of name * typ * typ list |
486 CombVar of name * typ |
487 CombApp of combterm * combterm
489 fun combtyp_of (CombConst (_, T, _)) = T
490 | combtyp_of (CombVar (_, T)) = T
491 | combtyp_of (CombApp (t1, _)) = snd (dest_funT (combtyp_of t1))
493 (*gets the head of a combinator application, along with the list of arguments*)
494 fun strip_combterm_comb u =
495 let fun stripc (CombApp(t,u), ts) = stripc (t, u::ts)
499 fun atyps_of T = fold_atyps (insert (op =)) T []
501 fun new_skolem_const_name s num_T_args =
502 [new_skolem_const_prefix, s, string_of_int num_T_args]
503 |> space_implode Long_Name.separator
505 (* Converts a term (with combinators) into a combterm. Also accumulates sort
507 fun combterm_from_term thy bs (P $ Q) =
509 val (P', P_atomics_Ts) = combterm_from_term thy bs P
510 val (Q', Q_atomics_Ts) = combterm_from_term thy bs Q
511 in (CombApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
512 | combterm_from_term thy _ (Const (c, T)) =
515 (if String.isPrefix old_skolem_const_prefix c then
516 [] |> Term.add_tvarsT T |> map TVar
518 (c, T) |> Sign.const_typargs thy)
519 val c' = CombConst (`make_fixed_const c, T, tvar_list)
520 in (c', atyps_of T) end
521 | combterm_from_term _ _ (Free (v, T)) =
522 (CombConst (`make_fixed_var v, T, []), atyps_of T)
523 | combterm_from_term _ _ (Var (v as (s, _), T)) =
524 (if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
526 val Ts = T |> strip_type |> swap |> op ::
527 val s' = new_skolem_const_name s (length Ts)
528 in CombConst (`make_fixed_const s', T, Ts) end
530 CombVar ((make_schematic_var v, s), T), atyps_of T)
531 | combterm_from_term _ bs (Bound j) =
533 |> (fn (s, T) => (CombConst (`make_bound_var s, T, []), atyps_of T))
534 | combterm_from_term _ _ (Abs _) = raise Fail "HOL clause: Abs"
536 datatype locality = General | Intro | Elim | Simp | Local | Assum | Chained
538 (* (quasi-)underapproximation of the truth *)
539 fun is_locality_global Local = false
540 | is_locality_global Assum = false
541 | is_locality_global Chained = false
542 | is_locality_global _ = true
544 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
545 datatype type_level =
546 All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
547 datatype type_heaviness = Heavyweight | Lightweight
550 Simple_Types of type_level |
551 Preds of polymorphism * type_level * type_heaviness |
552 Tags of polymorphism * type_level * type_heaviness
554 fun try_unsuffixes ss s =
555 fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
557 fun type_sys_from_string s =
558 (case try (unprefix "poly_") s of
559 SOME s => (SOME Polymorphic, s)
561 case try (unprefix "mono_") s of
562 SOME s => (SOME Monomorphic, s)
564 case try (unprefix "mangled_") s of
565 SOME s => (SOME Mangled_Monomorphic, s)
568 (* "_query" and "_bang" are for the ASCII-challenged Mirabelle. *)
569 case try_unsuffixes ["?", "_query"] s of
570 SOME s => (Nonmonotonic_Types, s)
572 case try_unsuffixes ["!", "_bang"] s of
573 SOME s => (Finite_Types, s)
574 | NONE => (All_Types, s))
576 case try (unsuffix "_heavy") s of
577 SOME s => (Heavyweight, s)
578 | NONE => (Lightweight, s))
579 |> (fn (poly, (level, (heaviness, core))) =>
580 case (core, (poly, level, heaviness)) of
581 ("simple", (NONE, _, Lightweight)) => Simple_Types level
582 | ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
583 | ("tags", (SOME Polymorphic, All_Types, _)) =>
584 Tags (Polymorphic, All_Types, heaviness)
585 | ("tags", (SOME Polymorphic, _, _)) =>
586 (* The actual light encoding is very unsound. *)
587 Tags (Polymorphic, level, Heavyweight)
588 | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
589 | ("args", (SOME poly, All_Types (* naja *), Lightweight)) =>
590 Preds (poly, Const_Arg_Types, Lightweight)
591 | ("erased", (NONE, All_Types (* naja *), Lightweight)) =>
592 Preds (Polymorphic, No_Types, Lightweight)
593 | _ => raise Same.SAME)
594 handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
596 fun polymorphism_of_type_sys (Simple_Types _) = Mangled_Monomorphic
597 | polymorphism_of_type_sys (Preds (poly, _, _)) = poly
598 | polymorphism_of_type_sys (Tags (poly, _, _)) = poly
600 fun level_of_type_sys (Simple_Types level) = level
601 | level_of_type_sys (Preds (_, level, _)) = level
602 | level_of_type_sys (Tags (_, level, _)) = level
604 fun heaviness_of_type_sys (Simple_Types _) = Heavyweight
605 | heaviness_of_type_sys (Preds (_, _, heaviness)) = heaviness
606 | heaviness_of_type_sys (Tags (_, _, heaviness)) = heaviness
608 fun is_type_level_virtually_sound level =
609 level = All_Types orelse level = Nonmonotonic_Types
610 val is_type_sys_virtually_sound =
611 is_type_level_virtually_sound o level_of_type_sys
613 fun is_type_level_fairly_sound level =
614 is_type_level_virtually_sound level orelse level = Finite_Types
615 val is_type_sys_fairly_sound = is_type_level_fairly_sound o level_of_type_sys
617 fun is_setting_higher_order THF (Simple_Types _) = true
618 | is_setting_higher_order _ _ = false
620 fun choose_format formats (Simple_Types level) =
621 if member (op =) formats THF then (THF, Simple_Types level)
622 else if member (op =) formats TFF then (TFF, Simple_Types level)
623 else choose_format formats (Preds (Mangled_Monomorphic, level, Heavyweight))
624 | choose_format formats type_sys =
627 (CNF_UEQ, case type_sys of
629 (if is_type_sys_fairly_sound type_sys then Tags else Preds)
632 | format => (format, type_sys))
634 type translated_formula =
638 combformula: (name, typ, combterm) formula,
639 atomic_types: typ list}
641 fun update_combformula f ({name, locality, kind, combformula, atomic_types}
642 : translated_formula) =
643 {name = name, locality = locality, kind = kind, combformula = f combformula,
644 atomic_types = atomic_types} : translated_formula
646 fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
648 val type_instance = Sign.typ_instance o Proof_Context.theory_of
650 fun insert_type ctxt get_T x xs =
651 let val T = get_T x in
652 if exists (curry (type_instance ctxt) T o get_T) xs then xs
653 else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
656 (* The Booleans indicate whether all type arguments should be kept. *)
657 datatype type_arg_policy =
658 Explicit_Type_Args of bool |
659 Mangled_Type_Args of bool |
662 fun should_drop_arg_type_args (Simple_Types _) =
663 false (* since TFF doesn't support overloading *)
664 | should_drop_arg_type_args type_sys =
665 level_of_type_sys type_sys = All_Types andalso
666 heaviness_of_type_sys type_sys = Heavyweight
668 fun general_type_arg_policy (Tags (_, All_Types, Heavyweight)) = No_Type_Args
669 | general_type_arg_policy type_sys =
670 if level_of_type_sys type_sys = No_Types then
672 else if polymorphism_of_type_sys type_sys = Mangled_Monomorphic then
673 Mangled_Type_Args (should_drop_arg_type_args type_sys)
675 Explicit_Type_Args (should_drop_arg_type_args type_sys)
677 fun type_arg_policy type_sys s =
678 if s = @{const_name HOL.eq} orelse
679 (s = app_op_name andalso level_of_type_sys type_sys = Const_Arg_Types) then
681 else if s = type_tag_name then
682 Explicit_Type_Args false
684 general_type_arg_policy type_sys
686 (*Make literals for sorted type variables*)
687 fun generic_add_sorts_on_type (_, []) = I
688 | generic_add_sorts_on_type ((x, i), s :: ss) =
689 generic_add_sorts_on_type ((x, i), ss)
690 #> (if s = the_single @{sort HOL.type} then
693 insert (op =) (TyLitFree (`make_type_class s, `make_fixed_type_var x))
695 insert (op =) (TyLitVar (`make_type_class s,
696 (make_schematic_type_var (x, i), x))))
697 fun add_sorts_on_tfree (TFree (s, S)) = generic_add_sorts_on_type ((s, ~1), S)
698 | add_sorts_on_tfree _ = I
699 fun add_sorts_on_tvar (TVar z) = generic_add_sorts_on_type z
700 | add_sorts_on_tvar _ = I
702 fun type_literals_for_types type_sys add_sorts_on_typ Ts =
703 [] |> level_of_type_sys type_sys <> No_Types ? fold add_sorts_on_typ Ts
705 fun mk_aconns c phis =
706 let val (phis', phi') = split_last phis in
707 fold_rev (mk_aconn c) phis' phi'
709 fun mk_ahorn [] phi = phi
710 | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
711 fun mk_aquant _ [] phi = phi
712 | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
713 if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
714 | mk_aquant q xs phi = AQuant (q, xs, phi)
716 fun close_universally atom_vars phi =
718 fun formula_vars bounds (AQuant (_, xs, phi)) =
719 formula_vars (map fst xs @ bounds) phi
720 | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
721 | formula_vars bounds (AAtom tm) =
722 union (op =) (atom_vars tm []
723 |> filter_out (member (op =) bounds o fst))
724 in mk_aquant AForall (formula_vars [] phi []) phi end
726 fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
727 | combterm_vars (CombConst _) = I
728 | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
729 fun close_combformula_universally phi = close_universally combterm_vars phi
731 fun term_vars (ATerm (name as (s, _), tms)) =
732 is_tptp_variable s ? insert (op =) (name, NONE) #> fold term_vars tms
733 fun close_formula_universally phi = close_universally term_vars phi
735 val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
736 val homo_infinite_type = Type (homo_infinite_type_name, [])
738 fun fo_term_from_typ format type_sys =
740 fun term (Type (s, Ts)) =
741 ATerm (case (is_setting_higher_order format type_sys, s) of
742 (true, @{type_name bool}) => `I tptp_bool_type
743 | (true, @{type_name fun}) => `I tptp_fun_type
744 | _ => if s = homo_infinite_type_name andalso
745 (format = TFF orelse format = THF) then
746 `I tptp_individual_type
748 `make_fixed_type_const s,
750 | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
751 | term (TVar ((x as (s, _)), _)) =
752 ATerm ((make_schematic_type_var x, s), [])
755 (* This shouldn't clash with anything else. *)
756 val mangled_type_sep = "\000"
758 fun generic_mangled_type_name f (ATerm (name, [])) = f name
759 | generic_mangled_type_name f (ATerm (name, tys)) =
760 f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
763 val bool_atype = AType (`I tptp_bool_type)
765 fun make_simple_type s =
766 if s = tptp_bool_type orelse s = tptp_fun_type orelse
767 s = tptp_individual_type then
770 simple_type_prefix ^ ascii_of s
772 fun ho_type_from_fo_term format type_sys pred_sym ary =
775 AType ((make_simple_type (generic_mangled_type_name fst ty),
776 generic_mangled_type_name snd ty))
777 fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
778 fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
779 | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
780 fun to_ho (ty as ATerm ((s, _), tys)) =
781 if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
782 in if is_setting_higher_order format type_sys then to_ho else to_fo ary end
784 fun mangled_type format type_sys pred_sym ary =
785 ho_type_from_fo_term format type_sys pred_sym ary
786 o fo_term_from_typ format type_sys
788 fun mangled_const_name format type_sys T_args (s, s') =
790 val ty_args = map (fo_term_from_typ format type_sys) T_args
791 fun type_suffix f g =
792 fold_rev (curry (op ^) o g o prefix mangled_type_sep
793 o generic_mangled_type_name f) ty_args ""
794 in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
796 val parse_mangled_ident =
797 Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
799 fun parse_mangled_type x =
801 -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
803 and parse_mangled_types x =
804 (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
806 fun unmangled_type s =
807 s |> suffix ")" |> raw_explode
808 |> Scan.finite Symbol.stopper
809 (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
810 quote s)) parse_mangled_type))
813 val unmangled_const_name = space_explode mangled_type_sep #> hd
814 fun unmangled_const s =
815 let val ss = space_explode mangled_type_sep s in
816 (hd ss, map unmangled_type (tl ss))
819 fun introduce_proxies format type_sys =
821 fun intro top_level (CombApp (tm1, tm2)) =
822 CombApp (intro top_level tm1, intro false tm2)
823 | intro top_level (CombConst (name as (s, _), T, T_args)) =
824 (case proxify_const s of
826 if top_level orelse is_setting_higher_order format type_sys then
827 case (top_level, s) of
828 (_, "c_False") => (`I tptp_false, [])
829 | (_, "c_True") => (`I tptp_true, [])
830 | (false, "c_Not") => (`I tptp_not, [])
831 | (false, "c_conj") => (`I tptp_and, [])
832 | (false, "c_disj") => (`I tptp_or, [])
833 | (false, "c_implies") => (`I tptp_implies, [])
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) => CombConst (name, T, T_args))
845 fun combformula_from_prop thy format type_sys eq_as_iff =
847 fun do_term bs t atomic_types =
848 combterm_from_term thy bs (Envir.eta_contract t)
849 |>> (introduce_proxies format type_sys #> AAtom)
850 ||> union (op =) atomic_types
851 fun do_quant bs q s T t' =
852 let val s = Name.variant (map fst bs) s in
853 do_formula ((s, T) :: bs) t'
854 #>> mk_aquant q [(`make_bound_var s, SOME T)]
856 and do_conn bs c t1 t2 =
857 do_formula bs t1 ##>> do_formula bs t2 #>> uncurry (mk_aconn c)
858 and do_formula bs t =
860 @{const Trueprop} $ t1 => do_formula bs t1
861 | @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
862 | Const (@{const_name All}, _) $ Abs (s, T, t') =>
863 do_quant bs AForall s T t'
864 | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
865 do_quant bs AExists s T t'
866 | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
867 | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
868 | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
869 | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
870 if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
874 fun presimplify_term _ [] t = t
875 | presimplify_term ctxt presimp_consts t =
876 t |> exists_Const (member (op =) presimp_consts o fst) t
877 ? (Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
878 #> Meson.presimplify ctxt
881 fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
882 fun conceal_bounds Ts t =
883 subst_bounds (map (Free o apfst concealed_bound_name)
884 (0 upto length Ts - 1 ~~ Ts), t)
885 fun reveal_bounds Ts =
886 subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
887 (0 upto length Ts - 1 ~~ Ts))
889 fun is_fun_equality (@{const_name HOL.eq},
890 Type (_, [Type (@{type_name fun}, _), _])) = true
891 | is_fun_equality _ = false
893 fun extensionalize_term ctxt t =
894 if exists_Const is_fun_equality t then
895 let val thy = Proof_Context.theory_of ctxt in
896 t |> cterm_of thy |> Meson.extensionalize_conv ctxt
897 |> prop_of |> Logic.dest_equals |> snd
902 fun introduce_combinators_in_term ctxt kind t =
903 let val thy = Proof_Context.theory_of ctxt in
904 if Meson.is_fol_term thy t then
910 @{const Not} $ t1 => @{const Not} $ aux Ts t1
911 | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
912 t0 $ Abs (s, T, aux (T :: Ts) t')
913 | (t0 as Const (@{const_name All}, _)) $ t1 =>
914 aux Ts (t0 $ eta_expand Ts t1 1)
915 | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
916 t0 $ Abs (s, T, aux (T :: Ts) t')
917 | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
918 aux Ts (t0 $ eta_expand Ts t1 1)
919 | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
920 | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
921 | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
922 | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
924 t0 $ aux Ts t1 $ aux Ts t2
925 | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
928 t |> conceal_bounds Ts
929 |> Envir.eta_contract
931 |> Meson_Clausify.introduce_combinators_in_cterm
932 |> prop_of |> Logic.dest_equals |> snd
934 val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
935 in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
937 (* A type variable of sort "{}" will make abstraction fail. *)
938 if kind = Conjecture then HOLogic.false_const
939 else HOLogic.true_const
942 (* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
943 same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
946 fun aux (t $ u) = aux t $ aux u
947 | aux (Abs (s, T, t)) = Abs (s, T, aux t)
948 | aux (Var ((s, i), T)) =
949 Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
951 in t |> exists_subterm is_Var t ? aux end
953 fun preprocess_prop ctxt presimp_consts kind t =
955 val thy = Proof_Context.theory_of ctxt
956 val t = t |> Envir.beta_eta_contract
957 |> transform_elim_prop
958 |> Object_Logic.atomize_term thy
959 val need_trueprop = (fastype_of t = @{typ bool})
961 t |> need_trueprop ? HOLogic.mk_Trueprop
962 |> Raw_Simplifier.rewrite_term thy (Meson.unfold_set_const_simps ctxt) []
963 |> extensionalize_term ctxt
964 |> presimplify_term ctxt presimp_consts
965 |> perhaps (try (HOLogic.dest_Trueprop))
966 |> introduce_combinators_in_term ctxt kind
969 (* making fact and conjecture formulas *)
970 fun make_formula thy format type_sys eq_as_iff name loc kind t =
972 val (combformula, atomic_types) =
973 combformula_from_prop thy format type_sys eq_as_iff t []
975 {name = name, locality = loc, kind = kind, combformula = combformula,
976 atomic_types = atomic_types}
979 fun make_fact ctxt format type_sys eq_as_iff preproc presimp_consts
981 let val thy = Proof_Context.theory_of ctxt in
982 case t |> preproc ? preprocess_prop ctxt presimp_consts Axiom
983 |> make_formula thy format type_sys (eq_as_iff andalso format <> CNF)
985 formula as {combformula = AAtom (CombConst ((s, _), _, _)), ...} =>
986 if s = tptp_true then NONE else SOME formula
987 | formula => SOME formula
990 fun make_conjecture ctxt format prem_kind type_sys preproc presimp_consts ts =
992 val thy = Proof_Context.theory_of ctxt
993 val last = length ts - 1
995 map2 (fn j => fn t =>
997 val (kind, maybe_negate) =
1002 if prem_kind = Conjecture then update_combformula mk_anot
1006 (preprocess_prop ctxt presimp_consts kind #> freeze_term)
1007 |> make_formula thy format type_sys (format <> CNF)
1008 (string_of_int j) Local kind
1014 (** Finite and infinite type inference **)
1016 fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
1017 | deep_freeze_atyp T = T
1018 val deep_freeze_type = map_atyps deep_freeze_atyp
1020 (* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
1021 dangerous because their "exhaust" properties can easily lead to unsound ATP
1022 proofs. On the other hand, all HOL infinite types can be given the same
1023 models in first-order logic (via Löwenheim-Skolem). *)
1025 fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
1026 exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
1027 | should_encode_type _ _ All_Types _ = true
1028 | should_encode_type ctxt _ Finite_Types T = is_type_surely_finite ctxt T
1029 | should_encode_type _ _ _ _ = false
1031 fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
1032 should_predicate_on_var T =
1033 (heaviness = Heavyweight orelse should_predicate_on_var ()) andalso
1034 should_encode_type ctxt nonmono_Ts level T
1035 | should_predicate_on_type _ _ _ _ _ = false
1037 fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
1038 String.isPrefix bound_var_prefix s
1039 | is_var_or_bound_var (CombVar _) = true
1040 | is_var_or_bound_var _ = false
1042 datatype tag_site = Top_Level | Eq_Arg | Elsewhere
1044 fun should_tag_with_type _ _ _ Top_Level _ _ = false
1045 | should_tag_with_type ctxt nonmono_Ts (Tags (_, level, heaviness)) site u T =
1047 Heavyweight => should_encode_type ctxt nonmono_Ts level T
1049 case (site, is_var_or_bound_var u) of
1050 (Eq_Arg, true) => should_encode_type ctxt nonmono_Ts level T
1052 | should_tag_with_type _ _ _ _ _ _ = false
1054 fun homogenized_type ctxt nonmono_Ts level =
1056 val should_encode = should_encode_type ctxt nonmono_Ts level
1057 fun homo 0 T = if should_encode T then T else homo_infinite_type
1058 | homo ary (Type (@{type_name fun}, [T1, T2])) =
1059 homo 0 T1 --> homo (ary - 1) T2
1060 | homo _ _ = raise Fail "expected function type"
1063 (** "hBOOL" and "hAPP" **)
1066 {pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
1068 fun add_combterm_syms_to_table ctxt explicit_apply =
1070 fun consider_var_arity const_T var_T max_ary =
1073 if ary = max_ary orelse type_instance ctxt (var_T, T) orelse
1074 type_instance ctxt (T, var_T) then
1077 iter (ary + 1) (range_type T)
1078 in iter 0 const_T end
1079 fun add_var_or_bound_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1080 if explicit_apply = NONE andalso
1081 (can dest_funT T orelse T = @{typ bool}) then
1083 val bool_vars' = bool_vars orelse body_type T = @{typ bool}
1084 fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
1085 {pred_sym = pred_sym andalso not bool_vars',
1086 min_ary = fold (fn T' => consider_var_arity T' T) types min_ary,
1087 max_ary = max_ary, types = types}
1089 fun_var_Ts |> can dest_funT T ? insert_type ctxt I T
1091 if bool_vars' = bool_vars andalso
1092 pointer_eq (fun_var_Ts', fun_var_Ts) then
1095 ((bool_vars', fun_var_Ts'), Symtab.map (K repair_min_arity) sym_tab)
1099 fun add top_level tm (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1100 let val (head, args) = strip_combterm_comb tm in
1102 CombConst ((s, _), T, _) =>
1103 if String.isPrefix bound_var_prefix s then
1104 add_var_or_bound_var T accum
1106 let val ary = length args in
1107 ((bool_vars, fun_var_Ts),
1108 case Symtab.lookup sym_tab s of
1109 SOME {pred_sym, min_ary, max_ary, types} =>
1112 pred_sym andalso top_level andalso not bool_vars
1113 val types' = types |> insert_type ctxt I T
1115 if is_some explicit_apply orelse
1116 pointer_eq (types', types) then
1119 fold (consider_var_arity T) fun_var_Ts min_ary
1121 Symtab.update (s, {pred_sym = pred_sym,
1122 min_ary = Int.min (ary, min_ary),
1123 max_ary = Int.max (ary, max_ary),
1129 val pred_sym = top_level andalso not bool_vars
1131 case explicit_apply of
1134 | NONE => fold (consider_var_arity T) fun_var_Ts ary
1136 Symtab.update_new (s, {pred_sym = pred_sym,
1137 min_ary = min_ary, max_ary = ary,
1142 | CombVar (_, T) => add_var_or_bound_var T accum
1144 |> fold (add false) args
1147 fun add_fact_syms_to_table ctxt explicit_apply =
1148 fact_lift (formula_fold NONE
1149 (K (add_combterm_syms_to_table ctxt explicit_apply)))
1151 val default_sym_tab_entries : (string * sym_info) list =
1152 (prefixed_predicator_name,
1153 {pred_sym = true, min_ary = 1, max_ary = 1, types = []}) ::
1154 ([tptp_false, tptp_true]
1155 |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []})) @
1156 ([tptp_equal, tptp_old_equal]
1157 |> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = []}))
1159 fun sym_table_for_facts ctxt explicit_apply facts =
1160 ((false, []), Symtab.empty)
1161 |> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
1162 |> fold Symtab.update default_sym_tab_entries
1164 fun min_arity_of sym_tab s =
1165 case Symtab.lookup sym_tab s of
1166 SOME ({min_ary, ...} : sym_info) => min_ary
1168 case strip_prefix_and_unascii const_prefix s of
1170 let val s = s |> unmangled_const_name |> invert_const in
1171 if s = predicator_name then 1
1172 else if s = app_op_name then 2
1173 else if s = type_pred_name then 1
1178 (* True if the constant ever appears outside of the top-level position in
1179 literals, or if it appears with different arities (e.g., because of different
1180 type instantiations). If false, the constant always receives all of its
1181 arguments and is used as a predicate. *)
1182 fun is_pred_sym sym_tab s =
1183 case Symtab.lookup sym_tab s of
1184 SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
1185 pred_sym andalso min_ary = max_ary
1188 val predicator_combconst =
1189 CombConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
1190 fun predicator tm = CombApp (predicator_combconst, tm)
1192 fun introduce_predicators_in_combterm sym_tab tm =
1193 case strip_combterm_comb tm of
1194 (CombConst ((s, _), _, _), _) =>
1195 if is_pred_sym sym_tab s then tm else predicator tm
1196 | _ => predicator tm
1198 fun list_app head args = fold (curry (CombApp o swap)) args head
1200 val app_op = `make_fixed_const app_op_name
1202 fun explicit_app arg head =
1204 val head_T = combtyp_of head
1205 val (arg_T, res_T) = dest_funT head_T
1207 CombConst (app_op, head_T --> head_T, [arg_T, res_T])
1208 in list_app explicit_app [head, arg] end
1209 fun list_explicit_app head args = fold explicit_app args head
1211 fun introduce_explicit_apps_in_combterm sym_tab =
1214 case strip_combterm_comb tm of
1215 (head as CombConst ((s, _), _, _), args) =>
1217 |> chop (min_arity_of sym_tab s)
1219 |-> list_explicit_app
1220 | (head, args) => list_explicit_app head (map aux args)
1223 fun chop_fun 0 T = ([], T)
1224 | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
1225 chop_fun (n - 1) ran_T |>> cons dom_T
1226 | chop_fun _ _ = raise Fail "unexpected non-function"
1228 fun filter_type_args _ _ _ [] = []
1229 | filter_type_args thy s arity T_args =
1231 (* will throw "TYPE" for pseudo-constants *)
1232 val U = if s = app_op_name then
1233 @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
1235 s |> Sign.the_const_type thy
1237 case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
1240 let val U_args = (s, U) |> Sign.const_typargs thy in
1242 |> map_filter (fn (U, T) =>
1243 if member (op =) res_U_vars (dest_TVar U) then
1249 handle TYPE _ => T_args
1251 fun enforce_type_arg_policy_in_combterm ctxt format type_sys =
1253 val thy = Proof_Context.theory_of ctxt
1254 fun aux arity (CombApp (tm1, tm2)) =
1255 CombApp (aux (arity + 1) tm1, aux 0 tm2)
1256 | aux arity (CombConst (name as (s, _), T, T_args)) =
1257 (case strip_prefix_and_unascii const_prefix s of
1258 NONE => (name, T_args)
1261 val s'' = invert_const s''
1262 fun filtered_T_args false = T_args
1263 | filtered_T_args true = filter_type_args thy s'' arity T_args
1265 case type_arg_policy type_sys s'' of
1266 Explicit_Type_Args drop_args =>
1267 (name, filtered_T_args drop_args)
1268 | Mangled_Type_Args drop_args =>
1269 (mangled_const_name format type_sys (filtered_T_args drop_args)
1271 | No_Type_Args => (name, [])
1273 |> (fn (name, T_args) => CombConst (name, T, T_args))
1277 fun repair_combterm ctxt format type_sys sym_tab =
1278 not (is_setting_higher_order format type_sys)
1279 ? (introduce_explicit_apps_in_combterm sym_tab
1280 #> introduce_predicators_in_combterm sym_tab)
1281 #> enforce_type_arg_policy_in_combterm ctxt format type_sys
1282 fun repair_fact ctxt format type_sys sym_tab =
1283 update_combformula (formula_map
1284 (repair_combterm ctxt format type_sys sym_tab))
1286 (** Helper facts **)
1288 (* The Boolean indicates that a fairly sound type encoding is needed. *)
1290 [(("COMBI", false), @{thms Meson.COMBI_def}),
1291 (("COMBK", false), @{thms Meson.COMBK_def}),
1292 (("COMBB", false), @{thms Meson.COMBB_def}),
1293 (("COMBC", false), @{thms Meson.COMBC_def}),
1294 (("COMBS", false), @{thms Meson.COMBS_def}),
1296 (* This is a lie: Higher-order equality doesn't need a sound type encoding.
1297 However, this is done so for backward compatibility: Including the
1298 equality helpers by default in Metis breaks a few existing proofs. *)
1299 @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1300 fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1301 (("fFalse", false), [@{lemma "~ fFalse" by (unfold fFalse_def) fast}]),
1302 (("fFalse", true), @{thms True_or_False}),
1303 (("fTrue", false), [@{lemma "fTrue" by (unfold fTrue_def) fast}]),
1304 (("fTrue", true), @{thms True_or_False}),
1306 @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1307 fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1309 @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
1310 by (unfold fconj_def) fast+}),
1312 @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
1313 by (unfold fdisj_def) fast+}),
1314 (("fimplies", false),
1315 @{lemma "P | fimplies P Q" "~ Q | fimplies P Q" "~ fimplies P Q | ~ P | Q"
1316 by (unfold fimplies_def) fast+}),
1317 (("If", true), @{thms if_True if_False True_or_False})]
1318 |> map (apsnd (map zero_var_indexes))
1320 val type_tag = `make_fixed_const type_tag_name
1322 fun type_tag_idempotence_fact () =
1324 fun var s = ATerm (`I s, [])
1325 fun tag tm = ATerm (type_tag, [var "T", tm])
1326 val tagged_a = tag (var "A")
1328 Formula (type_tag_idempotence_helper_name, Axiom,
1329 AAtom (ATerm (`I tptp_equal, [tag tagged_a, tagged_a]))
1330 |> close_formula_universally, simp_info, NONE)
1333 fun should_specialize_helper type_sys t =
1334 case general_type_arg_policy type_sys of
1335 Mangled_Type_Args _ => not (null (Term.hidden_polymorphism t))
1338 fun helper_facts_for_sym ctxt format type_sys (s, {types, ...} : sym_info) =
1339 case strip_prefix_and_unascii const_prefix s of
1342 val thy = Proof_Context.theory_of ctxt
1343 val unmangled_s = mangled_s |> unmangled_const_name
1344 fun dub_and_inst needs_fairly_sound (th, j) =
1345 ((unmangled_s ^ "_" ^ string_of_int j ^
1346 (if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^
1347 (if needs_fairly_sound then typed_helper_suffix
1348 else untyped_helper_suffix),
1350 let val t = th |> prop_of in
1351 t |> should_specialize_helper type_sys t
1353 [T] => specialize_type thy (invert_const unmangled_s, T)
1357 map_filter (make_fact ctxt format type_sys false false [])
1358 val fairly_sound = is_type_sys_fairly_sound type_sys
1361 |> maps (fn ((helper_s, needs_fairly_sound), ths) =>
1362 if helper_s <> unmangled_s orelse
1363 (needs_fairly_sound andalso not fairly_sound) then
1366 ths ~~ (1 upto length ths)
1367 |> map (dub_and_inst needs_fairly_sound)
1371 fun helper_facts_for_sym_table ctxt format type_sys sym_tab =
1372 Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_sys) sym_tab
1375 (***************************************************************)
1376 (* Type Classes Present in the Axiom or Conjecture Clauses *)
1377 (***************************************************************)
1379 fun set_insert (x, s) = Symtab.update (x, ()) s
1381 fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
1383 (* Remove this trivial type class (FIXME: similar code elsewhere) *)
1384 fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
1386 fun classes_of_terms get_Ts =
1387 map (map snd o get_Ts)
1388 #> List.foldl add_classes Symtab.empty
1389 #> delete_type #> Symtab.keys
1391 val tfree_classes_of_terms = classes_of_terms OldTerm.term_tfrees
1392 val tvar_classes_of_terms = classes_of_terms OldTerm.term_tvars
1394 (*fold type constructors*)
1395 fun fold_type_constrs f (Type (a, Ts)) x =
1396 fold (fold_type_constrs f) Ts (f (a,x))
1397 | fold_type_constrs _ _ x = x
1399 (*Type constructors used to instantiate overloaded constants are the only ones needed.*)
1400 fun add_type_constrs_in_term thy =
1402 fun add (Const (@{const_name Meson.skolem}, _) $ _) = I
1403 | add (t $ u) = add t #> add u
1404 | add (Const (x as (s, _))) =
1405 if String.isPrefix skolem_const_prefix s then I
1406 else x |> Sign.const_typargs thy |> fold (fold_type_constrs set_insert)
1407 | add (Abs (_, _, u)) = add u
1411 fun type_constrs_of_terms thy ts =
1412 Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty)
1414 fun translate_formulas ctxt format prem_kind type_sys preproc hyp_ts concl_t
1417 val thy = Proof_Context.theory_of ctxt
1418 val fact_ts = facts |> map snd
1419 val presimp_consts = Meson.presimplified_consts ctxt
1420 val make_fact = make_fact ctxt format type_sys true preproc presimp_consts
1421 val (facts, fact_names) =
1422 facts |> map (fn (name, t) => (name, t) |> make_fact |> rpair name)
1423 |> map_filter (try (apfst the))
1425 (* Remove existing facts from the conjecture, as this can dramatically
1426 boost an ATP's performance (for some reason). *)
1429 |> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t)
1430 val goal_t = Logic.list_implies (hyp_ts, concl_t)
1431 val all_ts = goal_t :: fact_ts
1432 val subs = tfree_classes_of_terms all_ts
1433 val supers = tvar_classes_of_terms all_ts
1434 val tycons = type_constrs_of_terms thy all_ts
1437 |> make_conjecture ctxt format prem_kind type_sys preproc presimp_consts
1438 val (supers', arity_clauses) =
1439 if level_of_type_sys type_sys = No_Types then ([], [])
1440 else make_arity_clauses thy tycons supers
1441 val class_rel_clauses = make_class_rel_clauses thy subs supers'
1443 (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
1446 fun fo_literal_from_type_literal (TyLitVar (class, name)) =
1447 (true, ATerm (class, [ATerm (name, [])]))
1448 | fo_literal_from_type_literal (TyLitFree (class, name)) =
1449 (true, ATerm (class, [ATerm (name, [])]))
1451 fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
1453 val type_pred = `make_fixed_const type_pred_name
1455 fun type_pred_combterm ctxt format type_sys T tm =
1456 CombApp (CombConst (type_pred, T --> @{typ bool}, [T])
1457 |> enforce_type_arg_policy_in_combterm ctxt format type_sys, tm)
1459 fun var_occurs_positively_naked_in_term _ (SOME false) _ accum = accum
1460 | var_occurs_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
1461 accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
1462 fun is_var_nonmonotonic_in_formula _ _ (SOME false) _ = false
1463 | is_var_nonmonotonic_in_formula pos phi _ name =
1464 formula_fold pos (var_occurs_positively_naked_in_term name) phi false
1466 fun mk_const_aterm format type_sys x T_args args =
1467 ATerm (x, map (fo_term_from_typ format type_sys) T_args @ args)
1469 fun tag_with_type ctxt format nonmono_Ts type_sys T tm =
1470 CombConst (type_tag, T --> T, [T])
1471 |> enforce_type_arg_policy_in_combterm ctxt format type_sys
1472 |> term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
1473 |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
1474 and term_from_combterm ctxt format nonmono_Ts type_sys =
1478 val (head, args) = strip_combterm_comb u
1479 val (x as (s, _), T_args) =
1481 CombConst (name, _, T_args) => (name, T_args)
1482 | CombVar (name, _) => (name, [])
1483 | CombApp _ => raise Fail "impossible \"CombApp\""
1484 val arg_site = if site = Top_Level andalso is_tptp_equal s then Eq_Arg
1486 val t = mk_const_aterm format type_sys x T_args
1487 (map (aux arg_site) args)
1488 val T = combtyp_of u
1490 t |> (if should_tag_with_type ctxt nonmono_Ts type_sys site u T then
1491 tag_with_type ctxt format nonmono_Ts type_sys T
1496 and formula_from_combformula ctxt format nonmono_Ts type_sys
1497 should_predicate_on_var =
1499 val do_term = term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
1502 Simple_Types level =>
1503 homogenized_type ctxt nonmono_Ts level 0
1504 #> mangled_type format type_sys false 0 #> SOME
1506 fun do_out_of_bound_type pos phi universal (name, T) =
1507 if should_predicate_on_type ctxt nonmono_Ts type_sys
1508 (fn () => should_predicate_on_var pos phi universal name) T then
1510 |> type_pred_combterm ctxt format type_sys T
1511 |> do_term |> AAtom |> SOME
1514 fun do_formula pos (AQuant (q, xs, phi)) =
1516 val phi = phi |> do_formula pos
1517 val universal = Option.map (q = AExists ? not) pos
1519 AQuant (q, xs |> map (apsnd (fn NONE => NONE
1520 | SOME T => do_bound_type T)),
1521 (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
1523 (fn (_, NONE) => NONE
1525 do_out_of_bound_type pos phi universal (s, T))
1529 | do_formula pos (AConn conn) = aconn_map pos do_formula conn
1530 | do_formula _ (AAtom tm) = AAtom (do_term tm)
1531 in do_formula o SOME end
1533 fun bound_tvars type_sys Ts =
1534 mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
1535 (type_literals_for_types type_sys add_sorts_on_tvar Ts))
1537 fun formula_for_fact ctxt format nonmono_Ts type_sys
1538 ({combformula, atomic_types, ...} : translated_formula) =
1540 |> close_combformula_universally
1541 |> formula_from_combformula ctxt format nonmono_Ts type_sys
1542 is_var_nonmonotonic_in_formula true
1543 |> bound_tvars type_sys atomic_types
1544 |> close_formula_universally
1546 (* Each fact is given a unique fact number to avoid name clashes (e.g., because
1547 of monomorphization). The TPTP explicitly forbids name clashes, and some of
1548 the remote provers might care. *)
1549 fun formula_line_for_fact ctxt format prefix encode freshen nonmono_Ts type_sys
1550 (j, formula as {name, locality, kind, ...}) =
1551 Formula (prefix ^ (if freshen then string_of_int j ^ "_" else "") ^
1553 kind, formula_for_fact ctxt format nonmono_Ts type_sys formula, NONE,
1560 fun formula_line_for_class_rel_clause ({name, subclass, superclass, ...}
1561 : class_rel_clause) =
1562 let val ty_arg = ATerm (`I "T", []) in
1563 Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
1564 AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
1565 AAtom (ATerm (superclass, [ty_arg]))])
1566 |> close_formula_universally, intro_info, NONE)
1569 fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
1570 (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
1571 | fo_literal_from_arity_literal (TVarLit (c, sort)) =
1572 (false, ATerm (c, [ATerm (sort, [])]))
1574 fun formula_line_for_arity_clause ({name, prem_lits, concl_lits, ...}
1576 Formula (arity_clause_prefix ^ ascii_of name, Axiom,
1577 mk_ahorn (map (formula_from_fo_literal o apfst not
1578 o fo_literal_from_arity_literal) prem_lits)
1579 (formula_from_fo_literal
1580 (fo_literal_from_arity_literal concl_lits))
1581 |> close_formula_universally, intro_info, NONE)
1583 fun formula_line_for_conjecture ctxt format nonmono_Ts type_sys
1584 ({name, kind, combformula, atomic_types, ...} : translated_formula) =
1585 Formula (conjecture_prefix ^ name, kind,
1586 formula_from_combformula ctxt format nonmono_Ts type_sys
1587 is_var_nonmonotonic_in_formula false
1588 (close_combformula_universally combformula)
1589 |> bound_tvars type_sys atomic_types
1590 |> close_formula_universally, NONE, NONE)
1592 fun free_type_literals type_sys ({atomic_types, ...} : translated_formula) =
1593 atomic_types |> type_literals_for_types type_sys add_sorts_on_tfree
1594 |> map fo_literal_from_type_literal
1596 fun formula_line_for_free_type j lit =
1597 Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis,
1598 formula_from_fo_literal lit, NONE, NONE)
1599 fun formula_lines_for_free_types type_sys facts =
1601 val litss = map (free_type_literals type_sys) facts
1602 val lits = fold (union (op =)) litss []
1603 in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
1605 (** Symbol declarations **)
1607 fun should_declare_sym type_sys pred_sym s =
1608 is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
1610 Simple_Types _ => true
1611 | Tags (_, _, Lightweight) => true
1612 | _ => not pred_sym)
1614 fun sym_decl_table_for_facts ctxt type_sys repaired_sym_tab (conjs, facts) =
1616 fun add_combterm in_conj tm =
1617 let val (head, args) = strip_combterm_comb tm in
1619 CombConst ((s, s'), T, T_args) =>
1620 let val pred_sym = is_pred_sym repaired_sym_tab s in
1621 if should_declare_sym type_sys pred_sym s then
1622 Symtab.map_default (s, [])
1623 (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
1629 #> fold (add_combterm in_conj) args
1631 fun add_fact in_conj =
1632 fact_lift (formula_fold NONE (K (add_combterm in_conj)))
1635 |> is_type_sys_fairly_sound type_sys
1636 ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
1639 (* These types witness that the type classes they belong to allow infinite
1640 models and hence that any types with these type classes is monotonic. *)
1641 val known_infinite_types =
1642 [@{typ nat}, Type ("Int.int", []), @{typ "nat => bool"}]
1644 (* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
1645 out with monotonicity" paper presented at CADE 2011. *)
1646 fun add_combterm_nonmonotonic_types _ _ _ (SOME false) _ = I
1647 | add_combterm_nonmonotonic_types ctxt level locality _
1648 (CombApp (CombApp (CombConst ((s, _), Type (_, [T, _]), _), tm1),
1650 (is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
1652 Nonmonotonic_Types =>
1653 not (is_locality_global locality) orelse
1654 not (is_type_surely_infinite ctxt known_infinite_types T)
1655 | Finite_Types => is_type_surely_finite ctxt T
1656 | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
1657 | add_combterm_nonmonotonic_types _ _ _ _ _ = I
1658 fun add_fact_nonmonotonic_types ctxt level ({kind, locality, combformula, ...}
1659 : translated_formula) =
1660 formula_fold (SOME (kind <> Conjecture))
1661 (add_combterm_nonmonotonic_types ctxt level locality) combformula
1662 fun nonmonotonic_types_for_facts ctxt type_sys facts =
1663 let val level = level_of_type_sys type_sys in
1664 if level = Nonmonotonic_Types orelse level = Finite_Types then
1665 [] |> fold (add_fact_nonmonotonic_types ctxt level) facts
1666 (* We must add "bool" in case the helper "True_or_False" is added
1667 later. In addition, several places in the code rely on the list of
1668 nonmonotonic types not being empty. *)
1669 |> insert_type ctxt I @{typ bool}
1674 fun decl_line_for_sym ctxt format nonmono_Ts type_sys s
1675 (s', T_args, T, pred_sym, ary, _) =
1677 val (T_arg_Ts, level) =
1679 Simple_Types level => ([], level)
1680 | _ => (replicate (length T_args) homo_infinite_type, No_Types)
1682 Decl (sym_decl_prefix ^ s, (s, s'),
1683 (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
1684 |> mangled_type format type_sys pred_sym (length T_arg_Ts + ary))
1687 fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
1689 fun formula_line_for_preds_sym_decl ctxt format conj_sym_kind nonmono_Ts
1690 type_sys n s j (s', T_args, T, _, ary, in_conj) =
1692 val (kind, maybe_negate) =
1693 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1695 val (arg_Ts, res_T) = chop_fun ary T
1697 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
1699 bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
1701 arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
1704 Formula (preds_sym_formula_prefix ^ s ^
1705 (if n > 1 then "_" ^ string_of_int j else ""), kind,
1706 CombConst ((s, s'), T, T_args)
1707 |> fold (curry (CombApp o swap)) bounds
1708 |> type_pred_combterm ctxt format type_sys res_T
1709 |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
1710 |> formula_from_combformula ctxt format nonmono_Ts type_sys
1711 (K (K (K (K true)))) true
1712 |> n > 1 ? bound_tvars type_sys (atyps_of T)
1713 |> close_formula_universally
1718 fun formula_lines_for_lightweight_tags_sym_decl ctxt format conj_sym_kind
1719 nonmono_Ts type_sys n s (j, (s', T_args, T, pred_sym, ary, in_conj)) =
1722 lightweight_tags_sym_formula_prefix ^ s ^
1723 (if n > 1 then "_" ^ string_of_int j else "")
1724 val (kind, maybe_negate) =
1725 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1727 val (arg_Ts, res_T) = chop_fun ary T
1729 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
1730 val bounds = bound_names |> map (fn name => ATerm (name, []))
1731 val cst = mk_const_aterm format type_sys (s, s') T_args
1732 val atomic_Ts = atyps_of T
1734 (if pred_sym then AConn (AIff, map AAtom tms)
1735 else AAtom (ATerm (`I tptp_equal, tms)))
1736 |> bound_tvars type_sys atomic_Ts
1737 |> close_formula_universally
1739 val should_encode = should_encode_type ctxt nonmono_Ts All_Types
1740 val tag_with = tag_with_type ctxt format nonmono_Ts type_sys
1741 val add_formula_for_res =
1742 if should_encode res_T then
1743 cons (Formula (ident_base ^ "_res", kind,
1744 eq [tag_with res_T (cst bounds), cst bounds],
1748 fun add_formula_for_arg k =
1749 let val arg_T = nth arg_Ts k in
1750 if should_encode arg_T then
1751 case chop k bounds of
1752 (bounds1, bound :: bounds2) =>
1753 cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
1754 eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
1757 | _ => raise Fail "expected nonempty tail"
1762 [] |> not pred_sym ? add_formula_for_res
1763 |> fold add_formula_for_arg (ary - 1 downto 0)
1766 fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
1768 fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts type_sys
1772 decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_sys s)
1777 decl :: (decls' as _ :: _) =>
1778 let val T = result_type_of_decl decl in
1779 if forall (curry (type_instance ctxt o swap) T
1780 o result_type_of_decl) decls' then
1786 val n = length decls
1789 |> filter (should_predicate_on_type ctxt nonmono_Ts type_sys (K true)
1790 o result_type_of_decl)
1792 (0 upto length decls - 1, decls)
1793 |-> map2 (formula_line_for_preds_sym_decl ctxt format conj_sym_kind
1794 nonmono_Ts type_sys n s)
1796 | Tags (_, _, heaviness) =>
1800 let val n = length decls in
1801 (0 upto n - 1 ~~ decls)
1802 |> maps (formula_lines_for_lightweight_tags_sym_decl ctxt format
1803 conj_sym_kind nonmono_Ts type_sys n s)
1806 fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1807 type_sys sym_decl_tab =
1812 |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
1813 nonmono_Ts type_sys)
1815 fun needs_type_tag_idempotence (Tags (poly, level, heaviness)) =
1816 poly <> Mangled_Monomorphic andalso
1817 ((level = All_Types andalso heaviness = Lightweight) orelse
1818 level = Nonmonotonic_Types orelse level = Finite_Types)
1819 | needs_type_tag_idempotence _ = false
1821 fun offset_of_heading_in_problem _ [] j = j
1822 | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
1823 if heading = needle then j
1824 else offset_of_heading_in_problem needle problem (j + length lines)
1826 val implicit_declsN = "Should-be-implicit typings"
1827 val explicit_declsN = "Explicit typings"
1828 val factsN = "Relevant facts"
1829 val class_relsN = "Class relationships"
1830 val aritiesN = "Arities"
1831 val helpersN = "Helper facts"
1832 val conjsN = "Conjectures"
1833 val free_typesN = "Type variables"
1835 val explicit_apply = NONE (* for experimental purposes *)
1837 fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_sys
1838 freshen_facts readable_names preproc hyp_ts concl_t facts =
1840 val (format, type_sys) = choose_format [format] type_sys
1841 val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
1842 translate_formulas ctxt format prem_kind type_sys preproc hyp_ts concl_t
1844 val sym_tab = conjs @ facts |> sym_table_for_facts ctxt explicit_apply
1845 val nonmono_Ts = conjs @ facts |> nonmonotonic_types_for_facts ctxt type_sys
1846 val repair = repair_fact ctxt format type_sys sym_tab
1847 val (conjs, facts) = (conjs, facts) |> pairself (map repair)
1848 val repaired_sym_tab =
1849 conjs @ facts |> sym_table_for_facts ctxt (SOME false)
1851 repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_sys
1853 val lavish_nonmono_Ts =
1854 if null nonmono_Ts orelse nonmono_Ts = [@{typ bool}] orelse
1855 polymorphism_of_type_sys type_sys <> Polymorphic then
1858 [TVar (("'a", 0), HOLogic.typeS)]
1859 val sym_decl_lines =
1860 (conjs, helpers @ facts)
1861 |> sym_decl_table_for_facts ctxt type_sys repaired_sym_tab
1862 |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind
1863 lavish_nonmono_Ts type_sys
1865 0 upto length helpers - 1 ~~ helpers
1866 |> map (formula_line_for_fact ctxt format helper_prefix I false
1867 lavish_nonmono_Ts type_sys)
1868 |> (if needs_type_tag_idempotence type_sys then
1869 cons (type_tag_idempotence_fact ())
1872 (* Reordering these might confuse the proof reconstruction code or the SPASS
1875 [(explicit_declsN, sym_decl_lines),
1877 map (formula_line_for_fact ctxt format fact_prefix ascii_of
1878 freshen_facts nonmono_Ts type_sys)
1879 (0 upto length facts - 1 ~~ facts)),
1880 (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
1881 (aritiesN, map formula_line_for_arity_clause arity_clauses),
1882 (helpersN, helper_lines),
1884 map (formula_line_for_conjecture ctxt format nonmono_Ts type_sys)
1886 (free_typesN, formula_lines_for_free_types type_sys (facts @ conjs))]
1890 CNF => ensure_cnf_problem
1891 | CNF_UEQ => filter_cnf_ueq_problem
1893 |> (if is_format_typed format then
1894 declare_undeclared_syms_in_atp_problem type_decl_prefix
1898 val (problem, pool) = problem |> nice_atp_problem readable_names
1899 val helpers_offset = offset_of_heading_in_problem helpersN problem 0
1901 map_filter (fn (j, {name, ...}) =>
1902 if String.isSuffix typed_helper_suffix name then SOME j
1904 ((helpers_offset + 1 upto helpers_offset + length helpers)
1906 fun add_sym_arity (s, {min_ary, ...} : sym_info) =
1908 case strip_prefix_and_unascii const_prefix s of
1909 SOME s => Symtab.insert (op =) (s, min_ary)
1915 case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
1916 offset_of_heading_in_problem conjsN problem 0,
1917 offset_of_heading_in_problem factsN problem 0,
1918 fact_names |> Vector.fromList,
1920 Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
1924 val conj_weight = 0.0
1925 val hyp_weight = 0.1
1926 val fact_min_weight = 0.2
1927 val fact_max_weight = 1.0
1928 val type_info_default_weight = 0.8
1930 fun add_term_weights weight (ATerm (s, tms)) =
1931 is_tptp_user_symbol s ? Symtab.default (s, weight)
1932 #> fold (add_term_weights weight) tms
1933 fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
1934 formula_fold NONE (K (add_term_weights weight)) phi
1935 | add_problem_line_weights _ _ = I
1937 fun add_conjectures_weights [] = I
1938 | add_conjectures_weights conjs =
1939 let val (hyps, conj) = split_last conjs in
1940 add_problem_line_weights conj_weight conj
1941 #> fold (add_problem_line_weights hyp_weight) hyps
1944 fun add_facts_weights facts =
1946 val num_facts = length facts
1948 fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
1949 / Real.fromInt num_facts
1951 map weight_of (0 upto num_facts - 1) ~~ facts
1952 |> fold (uncurry add_problem_line_weights)
1955 (* Weights are from 0.0 (most important) to 1.0 (least important). *)
1956 fun atp_problem_weights problem =
1957 let val get = these o AList.lookup (op =) problem in
1959 |> add_conjectures_weights (get free_typesN @ get conjsN)
1960 |> add_facts_weights (get factsN)
1961 |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
1962 [explicit_declsN, class_relsN, aritiesN]
1964 |> sort (prod_ord Real.compare string_ord o pairself swap)