type arguments now (unlike back when fa2cf11d6351 was done) normally carry enough information to reconstruct the type of an applied constant, so no need to constraint the argument types in those cases
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 | Noninf_Nonmono_Types | Fin_Nonmono_Types | Const_Arg_Types |
49 datatype type_heaviness = Heavyweight | Lightweight
52 Simple_Types of type_level |
53 Preds of polymorphism * type_level * type_heaviness |
54 Tags of polymorphism * type_level * type_heaviness
56 val bound_var_prefix : string
57 val schematic_var_prefix: string
58 val fixed_var_prefix: string
59 val tvar_prefix: string
60 val tfree_prefix: string
61 val const_prefix: string
62 val type_const_prefix: string
63 val class_prefix: string
64 val skolem_const_prefix : string
65 val old_skolem_const_prefix : string
66 val new_skolem_const_prefix : string
67 val type_decl_prefix : string
68 val sym_decl_prefix : string
69 val preds_sym_formula_prefix : string
70 val lightweight_tags_sym_formula_prefix : string
71 val fact_prefix : string
72 val conjecture_prefix : string
73 val helper_prefix : string
74 val class_rel_clause_prefix : string
75 val arity_clause_prefix : string
76 val tfree_clause_prefix : string
77 val typed_helper_suffix : string
78 val untyped_helper_suffix : string
79 val type_tag_idempotence_helper_name : string
80 val predicator_name : string
81 val app_op_name : string
82 val type_tag_name : string
83 val type_pred_name : string
84 val simple_type_prefix : string
85 val prefixed_predicator_name : string
86 val prefixed_app_op_name : string
87 val prefixed_type_tag_name : string
88 val ascii_of: string -> string
89 val unascii_of: string -> string
90 val strip_prefix_and_unascii : string -> string -> string option
91 val proxy_table : (string * (string * (thm * (string * string)))) list
92 val proxify_const : string -> (string * string) option
93 val invert_const: string -> string
94 val unproxify_const: string -> string
95 val make_bound_var : string -> string
96 val make_schematic_var : string * int -> string
97 val make_fixed_var : string -> string
98 val make_schematic_type_var : string * int -> string
99 val make_fixed_type_var : string -> string
100 val make_fixed_const : string -> string
101 val make_fixed_type_const : string -> string
102 val make_type_class : string -> string
103 val new_skolem_var_name_from_const : string -> string
104 val num_type_args : theory -> string -> int
105 val atp_irrelevant_consts : string list
106 val atp_schematic_consts_of : term -> typ list Symtab.table
107 val make_arity_clauses :
108 theory -> string list -> class list -> class list * arity_clause list
109 val make_class_rel_clauses :
110 theory -> class list -> class list -> class_rel_clause list
111 val combtyp_of : combterm -> typ
112 val strip_combterm_comb : combterm -> combterm * combterm list
113 val atyps_of : typ -> typ list
114 val combterm_from_term :
115 theory -> (string * typ) list -> term -> combterm * typ list
116 val is_locality_global : locality -> bool
117 val type_sys_from_string : string -> type_sys
118 val polymorphism_of_type_sys : type_sys -> polymorphism
119 val level_of_type_sys : type_sys -> type_level
120 val is_type_sys_virtually_sound : type_sys -> bool
121 val is_type_sys_fairly_sound : type_sys -> bool
122 val choose_format : format list -> type_sys -> format * type_sys
124 connective -> ('a, 'b, 'c) formula list -> ('a, 'b, 'c) formula
125 val unmangled_const_name : string -> string
126 val unmangled_const : string -> string * string fo_term list
127 val helper_table : ((string * bool) * thm list) list
128 val should_specialize_helper : type_sys -> term -> bool
129 val tfree_classes_of_terms : term list -> string list
130 val tvar_classes_of_terms : term list -> string list
131 val type_constrs_of_terms : theory -> term list -> string list
132 val prepare_atp_problem :
133 Proof.context -> format -> formula_kind -> formula_kind -> type_sys
134 -> bool -> bool -> bool -> term list -> term
135 -> ((string * locality) * term) list
136 -> string problem * string Symtab.table * int * int
137 * (string * locality) list vector * int list * int Symtab.table
138 val atp_problem_weights : string problem -> (string * real) list
141 structure ATP_Translate : ATP_TRANSLATE =
147 type name = string * string
150 val generate_useful_info = false
152 fun useful_isabelle_info s =
153 if generate_useful_info then
154 SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
158 val intro_info = useful_isabelle_info "intro"
159 val elim_info = useful_isabelle_info "elim"
160 val simp_info = useful_isabelle_info "simp"
162 val bound_var_prefix = "B_"
163 val schematic_var_prefix = "V_"
164 val fixed_var_prefix = "v_"
166 val tvar_prefix = "T_"
167 val tfree_prefix = "t_"
169 val const_prefix = "c_"
170 val type_const_prefix = "tc_"
171 val class_prefix = "cl_"
173 val skolem_const_prefix = "Sledgehammer" ^ Long_Name.separator ^ "Sko"
174 val old_skolem_const_prefix = skolem_const_prefix ^ "o"
175 val new_skolem_const_prefix = skolem_const_prefix ^ "n"
177 val type_decl_prefix = "ty_"
178 val sym_decl_prefix = "sy_"
179 val preds_sym_formula_prefix = "psy_"
180 val lightweight_tags_sym_formula_prefix = "tsy_"
181 val fact_prefix = "fact_"
182 val conjecture_prefix = "conj_"
183 val helper_prefix = "help_"
184 val class_rel_clause_prefix = "clar_"
185 val arity_clause_prefix = "arity_"
186 val tfree_clause_prefix = "tfree_"
188 val typed_helper_suffix = "_T"
189 val untyped_helper_suffix = "_U"
190 val type_tag_idempotence_helper_name = helper_prefix ^ "ti_idem"
192 val predicator_name = "hBOOL"
193 val app_op_name = "hAPP"
194 val type_tag_name = "ti"
195 val type_pred_name = "is"
196 val simple_type_prefix = "ty_"
198 val prefixed_predicator_name = const_prefix ^ predicator_name
199 val prefixed_app_op_name = const_prefix ^ app_op_name
200 val prefixed_type_tag_name = const_prefix ^ type_tag_name
202 (* Freshness almost guaranteed! *)
203 val sledgehammer_weak_prefix = "Sledgehammer:"
205 (*Escaping of special characters.
206 Alphanumeric characters are left unchanged.
207 The character _ goes to __
208 Characters in the range ASCII space to / go to _A to _P, respectively.
209 Other characters go to _nnn where nnn is the decimal ASCII code.*)
210 val upper_a_minus_space = Char.ord #"A" - Char.ord #" "
212 fun stringN_of_int 0 _ = ""
213 | stringN_of_int k n =
214 stringN_of_int (k - 1) (n div 10) ^ string_of_int (n mod 10)
216 fun ascii_of_char c =
217 if Char.isAlphaNum c then
219 else if c = #"_" then
221 else if #" " <= c andalso c <= #"/" then
222 "_" ^ String.str (Char.chr (Char.ord c + upper_a_minus_space))
224 (* fixed width, in case more digits follow *)
225 "_" ^ stringN_of_int 3 (Char.ord c)
227 val ascii_of = String.translate ascii_of_char
229 (** Remove ASCII armoring from names in proof files **)
231 (* We don't raise error exceptions because this code can run inside a worker
232 thread. Also, the errors are impossible. *)
235 fun un rcs [] = String.implode(rev rcs)
236 | un rcs [#"_"] = un (#"_" :: rcs) [] (* ERROR *)
237 (* Three types of _ escapes: __, _A to _P, _nnn *)
238 | un rcs (#"_" :: #"_" :: cs) = un (#"_"::rcs) cs
239 | un rcs (#"_" :: c :: cs) =
240 if #"A" <= c andalso c<= #"P" then
241 (* translation of #" " to #"/" *)
242 un (Char.chr (Char.ord c - upper_a_minus_space) :: rcs) cs
244 let val digits = List.take (c::cs, 3) handle General.Subscript => [] in
245 case Int.fromString (String.implode digits) of
246 SOME n => un (Char.chr n :: rcs) (List.drop (cs, 2))
247 | NONE => un (c:: #"_"::rcs) cs (* ERROR *)
249 | un rcs (c :: cs) = un (c :: rcs) cs
250 in un [] o String.explode end
252 (* If string s has the prefix s1, return the result of deleting it,
254 fun strip_prefix_and_unascii s1 s =
255 if String.isPrefix s1 s then
256 SOME (unascii_of (String.extract (s, size s1, NONE)))
261 [("c_False", (@{const_name False}, (@{thm fFalse_def},
262 ("fFalse", @{const_name ATP.fFalse})))),
263 ("c_True", (@{const_name True}, (@{thm fTrue_def},
264 ("fTrue", @{const_name ATP.fTrue})))),
265 ("c_Not", (@{const_name Not}, (@{thm fNot_def},
266 ("fNot", @{const_name ATP.fNot})))),
267 ("c_conj", (@{const_name conj}, (@{thm fconj_def},
268 ("fconj", @{const_name ATP.fconj})))),
269 ("c_disj", (@{const_name disj}, (@{thm fdisj_def},
270 ("fdisj", @{const_name ATP.fdisj})))),
271 ("c_implies", (@{const_name implies}, (@{thm fimplies_def},
272 ("fimplies", @{const_name ATP.fimplies})))),
273 ("equal", (@{const_name HOL.eq}, (@{thm fequal_def},
274 ("fequal", @{const_name ATP.fequal}))))]
276 val proxify_const = AList.lookup (op =) proxy_table #> Option.map (snd o snd)
278 (* Readable names for the more common symbolic functions. Do not mess with the
279 table unless you know what you are doing. *)
280 val const_trans_table =
281 [(@{type_name Product_Type.prod}, "prod"),
282 (@{type_name Sum_Type.sum}, "sum"),
283 (@{const_name False}, "False"),
284 (@{const_name True}, "True"),
285 (@{const_name Not}, "Not"),
286 (@{const_name conj}, "conj"),
287 (@{const_name disj}, "disj"),
288 (@{const_name implies}, "implies"),
289 (@{const_name HOL.eq}, "equal"),
290 (@{const_name If}, "If"),
291 (@{const_name Set.member}, "member"),
292 (@{const_name Meson.COMBI}, "COMBI"),
293 (@{const_name Meson.COMBK}, "COMBK"),
294 (@{const_name Meson.COMBB}, "COMBB"),
295 (@{const_name Meson.COMBC}, "COMBC"),
296 (@{const_name Meson.COMBS}, "COMBS")]
298 |> fold (Symtab.update o swap o snd o snd o snd) proxy_table
300 (* Invert the table of translations between Isabelle and ATPs. *)
301 val const_trans_table_inv =
302 const_trans_table |> Symtab.dest |> map swap |> Symtab.make
303 val const_trans_table_unprox =
305 |> fold (fn (_, (isa, (_, (_, atp)))) => Symtab.update (atp, isa)) proxy_table
307 val invert_const = perhaps (Symtab.lookup const_trans_table_inv)
308 val unproxify_const = perhaps (Symtab.lookup const_trans_table_unprox)
311 case Symtab.lookup const_trans_table c of
315 (*Remove the initial ' character from a type variable, if it is present*)
316 fun trim_type_var s =
317 if s <> "" andalso String.sub(s,0) = #"'" then String.extract(s,1,NONE)
318 else raise Fail ("trim_type: Malformed type variable encountered: " ^ s)
320 fun ascii_of_indexname (v,0) = ascii_of v
321 | ascii_of_indexname (v,i) = ascii_of v ^ "_" ^ string_of_int i
323 fun make_bound_var x = bound_var_prefix ^ ascii_of x
324 fun make_schematic_var v = schematic_var_prefix ^ ascii_of_indexname v
325 fun make_fixed_var x = fixed_var_prefix ^ ascii_of x
327 fun make_schematic_type_var (x,i) =
328 tvar_prefix ^ (ascii_of_indexname (trim_type_var x, i))
329 fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (trim_type_var x))
331 (* HOL.eq MUST BE "equal" because it's built into ATPs. *)
332 fun make_fixed_const @{const_name HOL.eq} = "equal"
333 | make_fixed_const c = const_prefix ^ lookup_const c
335 fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
337 fun make_type_class clas = class_prefix ^ ascii_of clas
339 fun new_skolem_var_name_from_const s =
340 let val ss = s |> space_explode Long_Name.separator in
341 nth ss (length ss - 2)
344 (* The number of type arguments of a constant, zero if it's monomorphic. For
345 (instances of) Skolem pseudoconstants, this information is encoded in the
347 fun num_type_args thy s =
348 if String.isPrefix skolem_const_prefix s then
349 s |> space_explode Long_Name.separator |> List.last |> Int.fromString |> the
351 (s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
353 (* These are either simplified away by "Meson.presimplify" (most of the time) or
354 handled specially via "fFalse", "fTrue", ..., "fequal". *)
355 val atp_irrelevant_consts =
356 [@{const_name False}, @{const_name True}, @{const_name Not},
357 @{const_name conj}, @{const_name disj}, @{const_name implies},
358 @{const_name HOL.eq}, @{const_name If}, @{const_name Let}]
360 val atp_monomorph_bad_consts =
361 atp_irrelevant_consts @
362 (* These are ignored anyway by the relevance filter (unless they appear in
363 higher-order places) but not by the monomorphizer. *)
364 [@{const_name all}, @{const_name "==>"}, @{const_name "=="},
365 @{const_name Trueprop}, @{const_name All}, @{const_name Ex},
366 @{const_name Ex1}, @{const_name Ball}, @{const_name Bex}]
368 fun add_schematic_const (x as (_, T)) =
369 Monomorph.typ_has_tvars T ? Symtab.insert_list (op =) x
370 val add_schematic_consts_of =
371 Term.fold_aterms (fn Const (x as (s, _)) =>
372 not (member (op =) atp_monomorph_bad_consts s)
373 ? add_schematic_const x
375 fun atp_schematic_consts_of t = add_schematic_consts_of t Symtab.empty
377 (** Definitions and functions for FOL clauses and formulas for TPTP **)
379 (* The first component is the type class; the second is a "TVar" or "TFree". *)
380 datatype type_literal =
381 TyLitVar of name * name |
382 TyLitFree of name * name
385 (** Isabelle arities **)
387 datatype arity_literal =
388 TConsLit of name * name * name list |
389 TVarLit of name * name
392 | gen_TVars n = ("T_" ^ string_of_int n) :: gen_TVars (n-1)
394 val type_class = the_single @{sort type}
396 fun add_packed_sort tvar =
397 fold (fn s => s <> type_class ? cons (`make_type_class s, `I tvar))
401 prem_lits: arity_literal list,
402 concl_lits: arity_literal}
404 (* Arity of type constructor "tcon :: (arg1, ..., argN) res" *)
405 fun make_axiom_arity_clause (tcons, name, (cls, args)) =
407 val tvars = gen_TVars (length args)
408 val tvars_srts = ListPair.zip (tvars, args)
411 prem_lits = [] |> fold (uncurry add_packed_sort) tvars_srts |> map TVarLit,
412 concl_lits = TConsLit (`make_type_class cls,
413 `make_fixed_type_const tcons,
417 fun arity_clause _ _ (_, []) = []
418 | arity_clause seen n (tcons, ("HOL.type",_)::ars) = (*ignore*)
419 arity_clause seen n (tcons,ars)
420 | arity_clause seen n (tcons, (ar as (class,_)) :: ars) =
421 if member (op =) seen class then (*multiple arities for the same tycon, class pair*)
422 make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class ^ "_" ^ string_of_int n, ar) ::
423 arity_clause seen (n+1) (tcons,ars)
425 make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class, ar) ::
426 arity_clause (class::seen) n (tcons,ars)
428 fun multi_arity_clause [] = []
429 | multi_arity_clause ((tcons, ars) :: tc_arlists) =
430 arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
432 (*Generate all pairs (tycon,class,sorts) such that tycon belongs to class in theory thy
433 provided its arguments have the corresponding sorts.*)
434 fun type_class_pairs thy tycons classes =
436 val alg = Sign.classes_of thy
437 fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
438 fun add_class tycon class =
439 cons (class, domain_sorts tycon class)
440 handle Sorts.CLASS_ERROR _ => I
441 fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
442 in map try_classes tycons end
444 (*Proving one (tycon, class) membership may require proving others, so iterate.*)
445 fun iter_type_class_pairs _ _ [] = ([], [])
446 | iter_type_class_pairs thy tycons classes =
448 fun maybe_insert_class s =
449 (s <> type_class andalso not (member (op =) classes s))
451 val cpairs = type_class_pairs thy tycons classes
453 [] |> fold (fold (fold (fold maybe_insert_class) o snd) o snd) cpairs
454 val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
455 in (classes' @ classes, union (op =) cpairs' cpairs) end
457 fun make_arity_clauses thy tycons =
458 iter_type_class_pairs thy tycons ##> multi_arity_clause
461 (** Isabelle class relations **)
463 type class_rel_clause =
468 (*Generate all pairs (sub,super) such that sub is a proper subclass of super in theory thy.*)
469 fun class_pairs _ [] _ = []
470 | class_pairs thy subs supers =
472 val class_less = Sorts.class_less (Sign.classes_of thy)
473 fun add_super sub super = class_less (sub, super) ? cons (sub, super)
474 fun add_supers sub = fold (add_super sub) supers
475 in fold add_supers subs [] end
477 fun make_class_rel_clause (sub,super) =
478 {name = sub ^ "_" ^ super,
479 subclass = `make_type_class sub,
480 superclass = `make_type_class super}
482 fun make_class_rel_clauses thy subs supers =
483 map make_class_rel_clause (class_pairs thy subs supers)
486 CombConst of name * typ * typ list |
487 CombVar of name * typ |
488 CombApp of combterm * combterm
490 fun combtyp_of (CombConst (_, T, _)) = T
491 | combtyp_of (CombVar (_, T)) = T
492 | combtyp_of (CombApp (t1, _)) = snd (dest_funT (combtyp_of t1))
494 (*gets the head of a combinator application, along with the list of arguments*)
495 fun strip_combterm_comb u =
496 let fun stripc (CombApp(t,u), ts) = stripc (t, u::ts)
500 fun atyps_of T = fold_atyps (insert (op =)) T []
502 fun new_skolem_const_name s num_T_args =
503 [new_skolem_const_prefix, s, string_of_int num_T_args]
504 |> space_implode Long_Name.separator
506 (* Converts a term (with combinators) into a combterm. Also accumulates sort
508 fun combterm_from_term thy bs (P $ Q) =
510 val (P', P_atomics_Ts) = combterm_from_term thy bs P
511 val (Q', Q_atomics_Ts) = combterm_from_term thy bs Q
512 in (CombApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
513 | combterm_from_term thy _ (Const (c, T)) =
516 (if String.isPrefix old_skolem_const_prefix c then
517 [] |> Term.add_tvarsT T |> map TVar
519 (c, T) |> Sign.const_typargs thy)
520 val c' = CombConst (`make_fixed_const c, T, tvar_list)
521 in (c', atyps_of T) end
522 | combterm_from_term _ _ (Free (v, T)) =
523 (CombConst (`make_fixed_var v, T, []), atyps_of T)
524 | combterm_from_term _ _ (Var (v as (s, _), T)) =
525 (if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
527 val Ts = T |> strip_type |> swap |> op ::
528 val s' = new_skolem_const_name s (length Ts)
529 in CombConst (`make_fixed_const s', T, Ts) end
531 CombVar ((make_schematic_var v, s), T), atyps_of T)
532 | combterm_from_term _ bs (Bound j) =
534 |> (fn (s, T) => (CombConst (`make_bound_var s, T, []), atyps_of T))
535 | combterm_from_term _ _ (Abs _) = raise Fail "HOL clause: Abs"
537 datatype locality = General | Intro | Elim | Simp | Local | Assum | Chained
539 (* (quasi-)underapproximation of the truth *)
540 fun is_locality_global Local = false
541 | is_locality_global Assum = false
542 | is_locality_global Chained = false
543 | is_locality_global _ = true
545 datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
546 datatype type_level =
547 All_Types | Noninf_Nonmono_Types | Fin_Nonmono_Types | Const_Arg_Types |
549 datatype type_heaviness = Heavyweight | Lightweight
552 Simple_Types of type_level |
553 Preds of polymorphism * type_level * type_heaviness |
554 Tags of polymorphism * type_level * type_heaviness
556 fun try_unsuffixes ss s =
557 fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
559 fun type_sys_from_string s =
560 (case try (unprefix "poly_") s of
561 SOME s => (SOME Polymorphic, s)
563 case try (unprefix "mono_") s of
564 SOME s => (SOME Monomorphic, s)
566 case try (unprefix "mangled_") s of
567 SOME s => (SOME Mangled_Monomorphic, s)
570 (* "_query" and "_bang" are for the ASCII-challenged Mirabelle. *)
571 case try_unsuffixes ["?", "_query"] s of
572 SOME s => (Noninf_Nonmono_Types, s)
574 case try_unsuffixes ["!", "_bang"] s of
575 SOME s => (Fin_Nonmono_Types, s)
576 | NONE => (All_Types, s))
578 case try (unsuffix "_heavy") s of
579 SOME s => (Heavyweight, s)
580 | NONE => (Lightweight, s))
581 |> (fn (poly, (level, (heaviness, core))) =>
582 case (core, (poly, level, heaviness)) of
583 ("simple", (NONE, _, Lightweight)) => Simple_Types level
584 | ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
585 | ("tags", (SOME Polymorphic, _, _)) =>
586 Tags (Polymorphic, level, heaviness)
587 | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
588 | ("args", (SOME poly, All_Types (* naja *), Lightweight)) =>
589 Preds (poly, Const_Arg_Types, Lightweight)
590 | ("erased", (NONE, All_Types (* naja *), Lightweight)) =>
591 Preds (Polymorphic, No_Types, Lightweight)
592 | _ => raise Same.SAME)
593 handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
595 fun polymorphism_of_type_sys (Simple_Types _) = Mangled_Monomorphic
596 | polymorphism_of_type_sys (Preds (poly, _, _)) = poly
597 | polymorphism_of_type_sys (Tags (poly, _, _)) = poly
599 fun level_of_type_sys (Simple_Types level) = level
600 | level_of_type_sys (Preds (_, level, _)) = level
601 | level_of_type_sys (Tags (_, level, _)) = level
603 fun heaviness_of_type_sys (Simple_Types _) = Heavyweight
604 | heaviness_of_type_sys (Preds (_, _, heaviness)) = heaviness
605 | heaviness_of_type_sys (Tags (_, _, heaviness)) = heaviness
607 fun is_type_level_virtually_sound level =
608 level = All_Types orelse level = Noninf_Nonmono_Types
609 val is_type_sys_virtually_sound =
610 is_type_level_virtually_sound o level_of_type_sys
612 fun is_type_level_fairly_sound level =
613 is_type_level_virtually_sound level orelse level = Fin_Nonmono_Types
614 val is_type_sys_fairly_sound = is_type_level_fairly_sound o level_of_type_sys
616 fun is_setting_higher_order THF (Simple_Types _) = true
617 | is_setting_higher_order _ _ = false
619 fun choose_format formats (Simple_Types level) =
620 if member (op =) formats THF then (THF, Simple_Types level)
621 else if member (op =) formats TFF then (TFF, Simple_Types level)
622 else choose_format formats (Preds (Mangled_Monomorphic, level, Heavyweight))
623 | choose_format formats type_sys =
626 (CNF_UEQ, case type_sys of
628 (if is_type_sys_fairly_sound type_sys then Tags else Preds)
631 | format => (format, type_sys))
633 type translated_formula =
637 combformula: (name, typ, combterm) formula,
638 atomic_types: typ list}
640 fun update_combformula f ({name, locality, kind, combformula, atomic_types}
641 : translated_formula) =
642 {name = name, locality = locality, kind = kind, combformula = f combformula,
643 atomic_types = atomic_types} : translated_formula
645 fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
647 val type_instance = Sign.typ_instance o Proof_Context.theory_of
649 fun insert_type ctxt get_T x xs =
650 let val T = get_T x in
651 if exists (curry (type_instance ctxt) T o get_T) xs then xs
652 else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
655 (* The Booleans indicate whether all type arguments should be kept. *)
656 datatype type_arg_policy =
657 Explicit_Type_Args of bool |
658 Mangled_Type_Args of bool |
661 fun should_drop_arg_type_args (Simple_Types _) =
662 false (* since TFF doesn't support overloading *)
663 | should_drop_arg_type_args type_sys =
664 level_of_type_sys type_sys = All_Types andalso
665 heaviness_of_type_sys type_sys = Heavyweight
667 fun general_type_arg_policy (Tags (_, All_Types, Heavyweight)) = No_Type_Args
668 | general_type_arg_policy type_sys =
669 if level_of_type_sys type_sys = No_Types then
671 else if polymorphism_of_type_sys type_sys = Mangled_Monomorphic then
672 Mangled_Type_Args (should_drop_arg_type_args type_sys)
674 Explicit_Type_Args (should_drop_arg_type_args type_sys)
676 fun type_arg_policy type_sys s =
677 if s = @{const_name HOL.eq} orelse
678 (s = app_op_name andalso level_of_type_sys type_sys = Const_Arg_Types) then
680 else if s = type_tag_name then
681 Explicit_Type_Args false
683 general_type_arg_policy type_sys
685 (*Make literals for sorted type variables*)
686 fun generic_add_sorts_on_type (_, []) = I
687 | generic_add_sorts_on_type ((x, i), s :: ss) =
688 generic_add_sorts_on_type ((x, i), ss)
689 #> (if s = the_single @{sort HOL.type} then
692 insert (op =) (TyLitFree (`make_type_class s, `make_fixed_type_var x))
694 insert (op =) (TyLitVar (`make_type_class s,
695 (make_schematic_type_var (x, i), x))))
696 fun add_sorts_on_tfree (TFree (s, S)) = generic_add_sorts_on_type ((s, ~1), S)
697 | add_sorts_on_tfree _ = I
698 fun add_sorts_on_tvar (TVar z) = generic_add_sorts_on_type z
699 | add_sorts_on_tvar _ = I
701 fun type_literals_for_types type_sys add_sorts_on_typ Ts =
702 [] |> level_of_type_sys type_sys <> No_Types ? fold add_sorts_on_typ Ts
704 fun mk_aconns c phis =
705 let val (phis', phi') = split_last phis in
706 fold_rev (mk_aconn c) phis' phi'
708 fun mk_ahorn [] phi = phi
709 | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
710 fun mk_aquant _ [] phi = phi
711 | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
712 if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
713 | mk_aquant q xs phi = AQuant (q, xs, phi)
715 fun close_universally atom_vars phi =
717 fun formula_vars bounds (AQuant (_, xs, phi)) =
718 formula_vars (map fst xs @ bounds) phi
719 | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
720 | formula_vars bounds (AAtom tm) =
721 union (op =) (atom_vars tm []
722 |> filter_out (member (op =) bounds o fst))
723 in mk_aquant AForall (formula_vars [] phi []) phi end
725 fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
726 | combterm_vars (CombConst _) = I
727 | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
728 fun close_combformula_universally phi = close_universally combterm_vars phi
730 fun term_vars (ATerm (name as (s, _), tms)) =
731 is_tptp_variable s ? insert (op =) (name, NONE) #> fold term_vars tms
732 fun close_formula_universally phi = close_universally term_vars phi
734 val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
735 val homo_infinite_type = Type (homo_infinite_type_name, [])
737 fun fo_term_from_typ format type_sys =
739 fun term (Type (s, Ts)) =
740 ATerm (case (is_setting_higher_order format type_sys, s) of
741 (true, @{type_name bool}) => `I tptp_bool_type
742 | (true, @{type_name fun}) => `I tptp_fun_type
743 | _ => if s = homo_infinite_type_name andalso
744 (format = TFF orelse format = THF) then
745 `I tptp_individual_type
747 `make_fixed_type_const s,
749 | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
750 | term (TVar ((x as (s, _)), _)) =
751 ATerm ((make_schematic_type_var x, s), [])
754 (* This shouldn't clash with anything else. *)
755 val mangled_type_sep = "\000"
757 fun generic_mangled_type_name f (ATerm (name, [])) = f name
758 | generic_mangled_type_name f (ATerm (name, tys)) =
759 f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
762 val bool_atype = AType (`I tptp_bool_type)
764 fun make_simple_type s =
765 if s = tptp_bool_type orelse s = tptp_fun_type orelse
766 s = tptp_individual_type then
769 simple_type_prefix ^ ascii_of s
771 fun ho_type_from_fo_term format type_sys pred_sym ary =
774 AType ((make_simple_type (generic_mangled_type_name fst ty),
775 generic_mangled_type_name snd ty))
776 fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
777 fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
778 | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
779 fun to_ho (ty as ATerm ((s, _), tys)) =
780 if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
781 in if is_setting_higher_order format type_sys then to_ho else to_fo ary end
783 fun mangled_type format type_sys pred_sym ary =
784 ho_type_from_fo_term format type_sys pred_sym ary
785 o fo_term_from_typ format type_sys
787 fun mangled_const_name format type_sys T_args (s, s') =
789 val ty_args = map (fo_term_from_typ format type_sys) T_args
790 fun type_suffix f g =
791 fold_rev (curry (op ^) o g o prefix mangled_type_sep
792 o generic_mangled_type_name f) ty_args ""
793 in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
795 val parse_mangled_ident =
796 Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
798 fun parse_mangled_type x =
800 -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
802 and parse_mangled_types x =
803 (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
805 fun unmangled_type s =
806 s |> suffix ")" |> raw_explode
807 |> Scan.finite Symbol.stopper
808 (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
809 quote s)) parse_mangled_type))
812 val unmangled_const_name = space_explode mangled_type_sep #> hd
813 fun unmangled_const s =
814 let val ss = space_explode mangled_type_sep s in
815 (hd ss, map unmangled_type (tl ss))
818 fun introduce_proxies format type_sys =
820 fun intro top_level (CombApp (tm1, tm2)) =
821 CombApp (intro top_level tm1, intro false tm2)
822 | intro top_level (CombConst (name as (s, _), T, T_args)) =
823 (case proxify_const s of
825 if top_level orelse is_setting_higher_order format type_sys then
826 case (top_level, s) of
827 (_, "c_False") => (`I tptp_false, [])
828 | (_, "c_True") => (`I tptp_true, [])
829 | (false, "c_Not") => (`I tptp_not, [])
830 | (false, "c_conj") => (`I tptp_and, [])
831 | (false, "c_disj") => (`I tptp_or, [])
832 | (false, "c_implies") => (`I tptp_implies, [])
834 if is_tptp_equal s then (`I tptp_equal, [])
835 else (proxy_base |>> prefix const_prefix, T_args)
838 (proxy_base |>> prefix const_prefix, T_args)
839 | NONE => (name, T_args))
840 |> (fn (name, T_args) => CombConst (name, T, T_args))
844 fun combformula_from_prop thy format type_sys eq_as_iff =
846 fun do_term bs t atomic_types =
847 combterm_from_term thy bs (Envir.eta_contract t)
848 |>> (introduce_proxies format type_sys #> AAtom)
849 ||> union (op =) atomic_types
850 fun do_quant bs q s T t' =
851 let val s = singleton (Name.variant_list (map fst bs)) s in
852 do_formula ((s, T) :: bs) t'
853 #>> mk_aquant q [(`make_bound_var s, SOME T)]
855 and do_conn bs c t1 t2 =
856 do_formula bs t1 ##>> do_formula bs t2 #>> uncurry (mk_aconn c)
857 and do_formula bs t =
859 @{const Trueprop} $ t1 => do_formula bs t1
860 | @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
861 | Const (@{const_name All}, _) $ Abs (s, T, t') =>
862 do_quant bs AForall s T t'
863 | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
864 do_quant bs AExists s T t'
865 | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
866 | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
867 | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
868 | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
869 if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
873 fun presimplify_term _ [] t = t
874 | presimplify_term ctxt presimp_consts t =
875 t |> exists_Const (member (op =) presimp_consts o fst) t
876 ? (Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
877 #> Meson.presimplify ctxt
880 fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
881 fun conceal_bounds Ts t =
882 subst_bounds (map (Free o apfst concealed_bound_name)
883 (0 upto length Ts - 1 ~~ Ts), t)
884 fun reveal_bounds Ts =
885 subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
886 (0 upto length Ts - 1 ~~ Ts))
888 fun is_fun_equality (@{const_name HOL.eq},
889 Type (_, [Type (@{type_name fun}, _), _])) = true
890 | is_fun_equality _ = false
892 fun extensionalize_term ctxt t =
893 if exists_Const is_fun_equality t then
894 let val thy = Proof_Context.theory_of ctxt in
895 t |> cterm_of thy |> Meson.extensionalize_conv ctxt
896 |> prop_of |> Logic.dest_equals |> snd
901 fun introduce_combinators_in_term ctxt kind t =
902 let val thy = Proof_Context.theory_of ctxt in
903 if Meson.is_fol_term thy t then
909 @{const Not} $ t1 => @{const Not} $ aux Ts t1
910 | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
911 t0 $ Abs (s, T, aux (T :: Ts) t')
912 | (t0 as Const (@{const_name All}, _)) $ t1 =>
913 aux Ts (t0 $ eta_expand Ts t1 1)
914 | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
915 t0 $ Abs (s, T, aux (T :: Ts) t')
916 | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
917 aux Ts (t0 $ eta_expand Ts t1 1)
918 | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
919 | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
920 | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
921 | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
923 t0 $ aux Ts t1 $ aux Ts t2
924 | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
927 t |> conceal_bounds Ts
928 |> Envir.eta_contract
930 |> Meson_Clausify.introduce_combinators_in_cterm
931 |> prop_of |> Logic.dest_equals |> snd
933 val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
934 in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
936 (* A type variable of sort "{}" will make abstraction fail. *)
937 if kind = Conjecture then HOLogic.false_const
938 else HOLogic.true_const
941 (* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
942 same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
945 fun aux (t $ u) = aux t $ aux u
946 | aux (Abs (s, T, t)) = Abs (s, T, aux t)
947 | aux (Var ((s, i), T)) =
948 Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
950 in t |> exists_subterm is_Var t ? aux end
952 fun preprocess_prop ctxt presimp_consts kind t =
954 val thy = Proof_Context.theory_of ctxt
955 val t = t |> Envir.beta_eta_contract
956 |> transform_elim_prop
957 |> Object_Logic.atomize_term thy
958 val need_trueprop = (fastype_of t = @{typ bool})
960 t |> need_trueprop ? HOLogic.mk_Trueprop
961 |> Raw_Simplifier.rewrite_term thy (Meson.unfold_set_const_simps ctxt) []
962 |> extensionalize_term ctxt
963 |> presimplify_term ctxt presimp_consts
964 |> perhaps (try (HOLogic.dest_Trueprop))
965 |> introduce_combinators_in_term ctxt kind
968 (* making fact and conjecture formulas *)
969 fun make_formula thy format type_sys eq_as_iff name loc kind t =
971 val (combformula, atomic_types) =
972 combformula_from_prop thy format type_sys eq_as_iff t []
974 {name = name, locality = loc, kind = kind, combformula = combformula,
975 atomic_types = atomic_types}
978 fun make_fact ctxt format type_sys eq_as_iff preproc presimp_consts
980 let val thy = Proof_Context.theory_of ctxt in
981 case t |> preproc ? preprocess_prop ctxt presimp_consts Axiom
982 |> make_formula thy format type_sys (eq_as_iff andalso format <> CNF)
984 formula as {combformula = AAtom (CombConst ((s, _), _, _)), ...} =>
985 if s = tptp_true then NONE else SOME formula
986 | formula => SOME formula
989 fun make_conjecture ctxt format prem_kind type_sys preproc presimp_consts ts =
991 val thy = Proof_Context.theory_of ctxt
992 val last = length ts - 1
994 map2 (fn j => fn t =>
996 val (kind, maybe_negate) =
1001 if prem_kind = Conjecture then update_combformula mk_anot
1005 (preprocess_prop ctxt presimp_consts kind #> freeze_term)
1006 |> make_formula thy format type_sys (format <> CNF)
1007 (string_of_int j) Local kind
1013 (** Finite and infinite type inference **)
1015 fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
1016 | deep_freeze_atyp T = T
1017 val deep_freeze_type = map_atyps deep_freeze_atyp
1019 (* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
1020 dangerous because their "exhaust" properties can easily lead to unsound ATP
1021 proofs. On the other hand, all HOL infinite types can be given the same
1022 models in first-order logic (via Löwenheim-Skolem). *)
1024 fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
1025 exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
1026 | should_encode_type _ _ All_Types _ = true
1027 | should_encode_type ctxt _ Fin_Nonmono_Types T = is_type_surely_finite ctxt T
1028 | should_encode_type _ _ _ _ = false
1030 fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
1031 should_predicate_on_var T =
1032 (heaviness = Heavyweight orelse should_predicate_on_var ()) andalso
1033 should_encode_type ctxt nonmono_Ts level T
1034 | should_predicate_on_type _ _ _ _ _ = false
1036 fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
1037 String.isPrefix bound_var_prefix s
1038 | is_var_or_bound_var (CombVar _) = true
1039 | is_var_or_bound_var _ = false
1042 Top_Level of bool option |
1043 Eq_Arg of bool option |
1046 fun should_tag_with_type _ _ _ (Top_Level _) _ _ = false
1047 | should_tag_with_type ctxt nonmono_Ts (Tags (poly, level, heaviness)) site
1050 Heavyweight => should_encode_type ctxt nonmono_Ts level T
1052 case (site, is_var_or_bound_var u) of
1053 (Eq_Arg pos, true) =>
1054 (* The first disjunct prevents a subtle soundness issue explained in
1055 Blanchette's Ph.D. thesis. See also
1056 "formula_lines_for_lightweight_tags_sym_decl". *)
1057 (pos <> SOME false andalso poly = Polymorphic andalso
1058 level <> All_Types andalso heaviness = Lightweight andalso
1059 exists (fn T' => type_instance ctxt (T', T)) nonmono_Ts) orelse
1060 should_encode_type ctxt nonmono_Ts level T
1062 | should_tag_with_type _ _ _ _ _ _ = false
1064 fun homogenized_type ctxt nonmono_Ts level =
1066 val should_encode = should_encode_type ctxt nonmono_Ts level
1067 fun homo 0 T = if should_encode T then T else homo_infinite_type
1068 | homo ary (Type (@{type_name fun}, [T1, T2])) =
1069 homo 0 T1 --> homo (ary - 1) T2
1070 | homo _ _ = raise Fail "expected function type"
1073 (** "hBOOL" and "hAPP" **)
1076 {pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
1078 fun add_combterm_syms_to_table ctxt explicit_apply =
1080 fun consider_var_arity const_T var_T max_ary =
1083 if ary = max_ary orelse type_instance ctxt (var_T, T) orelse
1084 type_instance ctxt (T, var_T) then
1087 iter (ary + 1) (range_type T)
1088 in iter 0 const_T end
1089 fun add_var_or_bound_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1090 if explicit_apply = NONE andalso
1091 (can dest_funT T orelse T = @{typ bool}) then
1093 val bool_vars' = bool_vars orelse body_type T = @{typ bool}
1094 fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
1095 {pred_sym = pred_sym andalso not bool_vars',
1096 min_ary = fold (fn T' => consider_var_arity T' T) types min_ary,
1097 max_ary = max_ary, types = types}
1099 fun_var_Ts |> can dest_funT T ? insert_type ctxt I T
1101 if bool_vars' = bool_vars andalso
1102 pointer_eq (fun_var_Ts', fun_var_Ts) then
1105 ((bool_vars', fun_var_Ts'), Symtab.map (K repair_min_arity) sym_tab)
1109 fun add top_level tm (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
1110 let val (head, args) = strip_combterm_comb tm in
1112 CombConst ((s, _), T, _) =>
1113 if String.isPrefix bound_var_prefix s then
1114 add_var_or_bound_var T accum
1116 let val ary = length args in
1117 ((bool_vars, fun_var_Ts),
1118 case Symtab.lookup sym_tab s of
1119 SOME {pred_sym, min_ary, max_ary, types} =>
1122 pred_sym andalso top_level andalso not bool_vars
1123 val types' = types |> insert_type ctxt I T
1125 if is_some explicit_apply orelse
1126 pointer_eq (types', types) then
1129 fold (consider_var_arity T) fun_var_Ts min_ary
1131 Symtab.update (s, {pred_sym = pred_sym,
1132 min_ary = Int.min (ary, min_ary),
1133 max_ary = Int.max (ary, max_ary),
1139 val pred_sym = top_level andalso not bool_vars
1141 case explicit_apply of
1144 | NONE => fold (consider_var_arity T) fun_var_Ts ary
1146 Symtab.update_new (s, {pred_sym = pred_sym,
1147 min_ary = min_ary, max_ary = ary,
1152 | CombVar (_, T) => add_var_or_bound_var T accum
1154 |> fold (add false) args
1157 fun add_fact_syms_to_table ctxt explicit_apply =
1158 fact_lift (formula_fold NONE
1159 (K (add_combterm_syms_to_table ctxt explicit_apply)))
1161 val default_sym_tab_entries : (string * sym_info) list =
1162 (prefixed_predicator_name,
1163 {pred_sym = true, min_ary = 1, max_ary = 1, types = []}) ::
1164 ([tptp_false, tptp_true]
1165 |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []})) @
1166 ([tptp_equal, tptp_old_equal]
1167 |> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = []}))
1169 fun sym_table_for_facts ctxt explicit_apply facts =
1170 ((false, []), Symtab.empty)
1171 |> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
1172 |> fold Symtab.update default_sym_tab_entries
1174 fun min_arity_of sym_tab s =
1175 case Symtab.lookup sym_tab s of
1176 SOME ({min_ary, ...} : sym_info) => min_ary
1178 case strip_prefix_and_unascii const_prefix s of
1180 let val s = s |> unmangled_const_name |> invert_const in
1181 if s = predicator_name then 1
1182 else if s = app_op_name then 2
1183 else if s = type_pred_name then 1
1188 (* True if the constant ever appears outside of the top-level position in
1189 literals, or if it appears with different arities (e.g., because of different
1190 type instantiations). If false, the constant always receives all of its
1191 arguments and is used as a predicate. *)
1192 fun is_pred_sym sym_tab s =
1193 case Symtab.lookup sym_tab s of
1194 SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
1195 pred_sym andalso min_ary = max_ary
1198 val predicator_combconst =
1199 CombConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
1200 fun predicator tm = CombApp (predicator_combconst, tm)
1202 fun introduce_predicators_in_combterm sym_tab tm =
1203 case strip_combterm_comb tm of
1204 (CombConst ((s, _), _, _), _) =>
1205 if is_pred_sym sym_tab s then tm else predicator tm
1206 | _ => predicator tm
1208 fun list_app head args = fold (curry (CombApp o swap)) args head
1210 val app_op = `make_fixed_const app_op_name
1212 fun explicit_app arg head =
1214 val head_T = combtyp_of head
1215 val (arg_T, res_T) = dest_funT head_T
1217 CombConst (app_op, head_T --> head_T, [arg_T, res_T])
1218 in list_app explicit_app [head, arg] end
1219 fun list_explicit_app head args = fold explicit_app args head
1221 fun introduce_explicit_apps_in_combterm sym_tab =
1224 case strip_combterm_comb tm of
1225 (head as CombConst ((s, _), _, _), args) =>
1227 |> chop (min_arity_of sym_tab s)
1229 |-> list_explicit_app
1230 | (head, args) => list_explicit_app head (map aux args)
1233 fun chop_fun 0 T = ([], T)
1234 | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
1235 chop_fun (n - 1) ran_T |>> cons dom_T
1236 | chop_fun _ _ = raise Fail "unexpected non-function"
1238 fun filter_type_args _ _ _ [] = []
1239 | filter_type_args thy s arity T_args =
1241 (* will throw "TYPE" for pseudo-constants *)
1242 val U = if s = app_op_name then
1243 @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
1245 s |> Sign.the_const_type thy
1247 case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
1250 let val U_args = (s, U) |> Sign.const_typargs thy in
1252 |> map_filter (fn (U, T) =>
1253 if member (op =) res_U_vars (dest_TVar U) then
1259 handle TYPE _ => T_args
1261 fun enforce_type_arg_policy_in_combterm ctxt format type_sys =
1263 val thy = Proof_Context.theory_of ctxt
1264 fun aux arity (CombApp (tm1, tm2)) =
1265 CombApp (aux (arity + 1) tm1, aux 0 tm2)
1266 | aux arity (CombConst (name as (s, _), T, T_args)) =
1267 (case strip_prefix_and_unascii const_prefix s of
1268 NONE => (name, T_args)
1271 val s'' = invert_const s''
1272 fun filtered_T_args false = T_args
1273 | filtered_T_args true = filter_type_args thy s'' arity T_args
1275 case type_arg_policy type_sys s'' of
1276 Explicit_Type_Args drop_args =>
1277 (name, filtered_T_args drop_args)
1278 | Mangled_Type_Args drop_args =>
1279 (mangled_const_name format type_sys (filtered_T_args drop_args)
1281 | No_Type_Args => (name, [])
1283 |> (fn (name, T_args) => CombConst (name, T, T_args))
1287 fun repair_combterm ctxt format type_sys sym_tab =
1288 not (is_setting_higher_order format type_sys)
1289 ? (introduce_explicit_apps_in_combterm sym_tab
1290 #> introduce_predicators_in_combterm sym_tab)
1291 #> enforce_type_arg_policy_in_combterm ctxt format type_sys
1292 fun repair_fact ctxt format type_sys sym_tab =
1293 update_combformula (formula_map
1294 (repair_combterm ctxt format type_sys sym_tab))
1296 (** Helper facts **)
1298 (* The Boolean indicates that a fairly sound type encoding is needed. *)
1300 [(("COMBI", false), @{thms Meson.COMBI_def}),
1301 (("COMBK", false), @{thms Meson.COMBK_def}),
1302 (("COMBB", false), @{thms Meson.COMBB_def}),
1303 (("COMBC", false), @{thms Meson.COMBC_def}),
1304 (("COMBS", false), @{thms Meson.COMBS_def}),
1306 (* This is a lie: Higher-order equality doesn't need a sound type encoding.
1307 However, this is done so for backward compatibility: Including the
1308 equality helpers by default in Metis breaks a few existing proofs. *)
1309 @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1310 fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1311 (("fFalse", false), [@{lemma "~ fFalse" by (unfold fFalse_def) fast}]),
1312 (("fFalse", true), @{thms True_or_False}),
1313 (("fTrue", false), [@{lemma "fTrue" by (unfold fTrue_def) fast}]),
1314 (("fTrue", true), @{thms True_or_False}),
1316 @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
1317 fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
1319 @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
1320 by (unfold fconj_def) fast+}),
1322 @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
1323 by (unfold fdisj_def) fast+}),
1324 (("fimplies", false),
1325 @{lemma "P | fimplies P Q" "~ Q | fimplies P Q" "~ fimplies P Q | ~ P | Q"
1326 by (unfold fimplies_def) fast+}),
1327 (("If", true), @{thms if_True if_False True_or_False})]
1328 |> map (apsnd (map zero_var_indexes))
1330 val type_tag = `make_fixed_const type_tag_name
1332 fun type_tag_idempotence_fact () =
1334 fun var s = ATerm (`I s, [])
1335 fun tag tm = ATerm (type_tag, [var "T", tm])
1336 val tagged_a = tag (var "A")
1338 Formula (type_tag_idempotence_helper_name, Axiom,
1339 AAtom (ATerm (`I tptp_equal, [tag tagged_a, tagged_a]))
1340 |> close_formula_universally, simp_info, NONE)
1343 fun should_specialize_helper type_sys t =
1344 case general_type_arg_policy type_sys of
1345 Mangled_Type_Args _ => not (null (Term.hidden_polymorphism t))
1348 fun helper_facts_for_sym ctxt format type_sys (s, {types, ...} : sym_info) =
1349 case strip_prefix_and_unascii const_prefix s of
1352 val thy = Proof_Context.theory_of ctxt
1353 val unmangled_s = mangled_s |> unmangled_const_name
1354 fun dub_and_inst needs_fairly_sound (th, j) =
1355 ((unmangled_s ^ "_" ^ string_of_int j ^
1356 (if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^
1357 (if needs_fairly_sound then typed_helper_suffix
1358 else untyped_helper_suffix),
1360 let val t = th |> prop_of in
1361 t |> should_specialize_helper type_sys t
1363 [T] => specialize_type thy (invert_const unmangled_s, T)
1367 map_filter (make_fact ctxt format type_sys false false [])
1368 val fairly_sound = is_type_sys_fairly_sound type_sys
1371 |> maps (fn ((helper_s, needs_fairly_sound), ths) =>
1372 if helper_s <> unmangled_s orelse
1373 (needs_fairly_sound andalso not fairly_sound) then
1376 ths ~~ (1 upto length ths)
1377 |> map (dub_and_inst needs_fairly_sound)
1381 fun helper_facts_for_sym_table ctxt format type_sys sym_tab =
1382 Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_sys) sym_tab
1385 (***************************************************************)
1386 (* Type Classes Present in the Axiom or Conjecture Clauses *)
1387 (***************************************************************)
1389 fun set_insert (x, s) = Symtab.update (x, ()) s
1391 fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
1393 (* Remove this trivial type class (FIXME: similar code elsewhere) *)
1394 fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
1396 fun classes_of_terms get_Ts =
1397 map (map snd o get_Ts)
1398 #> List.foldl add_classes Symtab.empty
1399 #> delete_type #> Symtab.keys
1401 val tfree_classes_of_terms = classes_of_terms OldTerm.term_tfrees
1402 val tvar_classes_of_terms = classes_of_terms OldTerm.term_tvars
1404 (*fold type constructors*)
1405 fun fold_type_constrs f (Type (a, Ts)) x =
1406 fold (fold_type_constrs f) Ts (f (a,x))
1407 | fold_type_constrs _ _ x = x
1409 (*Type constructors used to instantiate overloaded constants are the only ones needed.*)
1410 fun add_type_constrs_in_term thy =
1412 fun add (Const (@{const_name Meson.skolem}, _) $ _) = I
1413 | add (t $ u) = add t #> add u
1414 | add (Const (x as (s, _))) =
1415 if String.isPrefix skolem_const_prefix s then I
1416 else x |> Sign.const_typargs thy |> fold (fold_type_constrs set_insert)
1417 | add (Abs (_, _, u)) = add u
1421 fun type_constrs_of_terms thy ts =
1422 Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty)
1424 fun translate_formulas ctxt format prem_kind type_sys preproc hyp_ts concl_t
1427 val thy = Proof_Context.theory_of ctxt
1428 val fact_ts = facts |> map snd
1429 val presimp_consts = Meson.presimplified_consts ctxt
1430 val make_fact = make_fact ctxt format type_sys true preproc presimp_consts
1431 val (facts, fact_names) =
1432 facts |> map (fn (name, t) => (name, t) |> make_fact |> rpair name)
1433 |> map_filter (try (apfst the))
1435 (* Remove existing facts from the conjecture, as this can dramatically
1436 boost an ATP's performance (for some reason). *)
1439 |> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t)
1440 val goal_t = Logic.list_implies (hyp_ts, concl_t)
1441 val all_ts = goal_t :: fact_ts
1442 val subs = tfree_classes_of_terms all_ts
1443 val supers = tvar_classes_of_terms all_ts
1444 val tycons = type_constrs_of_terms thy all_ts
1447 |> make_conjecture ctxt format prem_kind type_sys preproc presimp_consts
1448 val (supers', arity_clauses) =
1449 if level_of_type_sys type_sys = No_Types then ([], [])
1450 else make_arity_clauses thy tycons supers
1451 val class_rel_clauses = make_class_rel_clauses thy subs supers'
1453 (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
1456 fun fo_literal_from_type_literal (TyLitVar (class, name)) =
1457 (true, ATerm (class, [ATerm (name, [])]))
1458 | fo_literal_from_type_literal (TyLitFree (class, name)) =
1459 (true, ATerm (class, [ATerm (name, [])]))
1461 fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
1463 val type_pred = `make_fixed_const type_pred_name
1465 fun type_pred_combterm ctxt format type_sys T tm =
1466 CombApp (CombConst (type_pred, T --> @{typ bool}, [T])
1467 |> enforce_type_arg_policy_in_combterm ctxt format type_sys, tm)
1469 fun var_occurs_positively_naked_in_term _ (SOME false) _ accum = accum
1470 | var_occurs_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
1471 accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
1472 fun is_var_nonmonotonic_in_formula _ _ (SOME false) _ = false
1473 | is_var_nonmonotonic_in_formula pos phi _ name =
1474 formula_fold pos (var_occurs_positively_naked_in_term name) phi false
1476 fun mk_const_aterm format type_sys x T_args args =
1477 ATerm (x, map (fo_term_from_typ format type_sys) T_args @ args)
1479 fun tag_with_type ctxt format nonmono_Ts type_sys pos T tm =
1480 CombConst (type_tag, T --> T, [T])
1481 |> enforce_type_arg_policy_in_combterm ctxt format type_sys
1482 |> term_from_combterm ctxt format nonmono_Ts type_sys (Top_Level pos)
1483 |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
1484 and term_from_combterm ctxt format nonmono_Ts type_sys =
1488 val (head, args) = strip_combterm_comb u
1489 val (x as (s, _), T_args) =
1491 CombConst (name, _, T_args) => (name, T_args)
1492 | CombVar (name, _) => (name, [])
1493 | CombApp _ => raise Fail "impossible \"CombApp\""
1494 val (pos, arg_site) =
1497 (pos, if is_tptp_equal s then Eq_Arg pos else Elsewhere)
1498 | Eq_Arg pos => (pos, Elsewhere)
1499 | Elsewhere => (NONE, Elsewhere)
1500 val t = mk_const_aterm format type_sys x T_args
1501 (map (aux arg_site) args)
1502 val T = combtyp_of u
1504 t |> (if should_tag_with_type ctxt nonmono_Ts type_sys site u T then
1505 tag_with_type ctxt format nonmono_Ts type_sys pos T
1510 and formula_from_combformula ctxt format nonmono_Ts type_sys
1511 should_predicate_on_var =
1514 term_from_combterm ctxt format nonmono_Ts type_sys (Top_Level pos)
1517 Simple_Types level =>
1518 homogenized_type ctxt nonmono_Ts level 0
1519 #> mangled_type format type_sys false 0 #> SOME
1521 fun do_out_of_bound_type pos phi universal (name, T) =
1522 if should_predicate_on_type ctxt nonmono_Ts type_sys
1523 (fn () => should_predicate_on_var pos phi universal name) T then
1525 |> type_pred_combterm ctxt format type_sys T
1526 |> do_term pos |> AAtom |> SOME
1529 fun do_formula pos (AQuant (q, xs, phi)) =
1531 val phi = phi |> do_formula pos
1532 val universal = Option.map (q = AExists ? not) pos
1534 AQuant (q, xs |> map (apsnd (fn NONE => NONE
1535 | SOME T => do_bound_type T)),
1536 (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
1538 (fn (_, NONE) => NONE
1540 do_out_of_bound_type pos phi universal (s, T))
1544 | do_formula pos (AConn conn) = aconn_map pos do_formula conn
1545 | do_formula pos (AAtom tm) = AAtom (do_term pos tm)
1546 in do_formula o SOME end
1548 fun bound_tvars type_sys Ts =
1549 mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
1550 (type_literals_for_types type_sys add_sorts_on_tvar Ts))
1552 fun formula_for_fact ctxt format nonmono_Ts type_sys
1553 ({combformula, atomic_types, ...} : translated_formula) =
1555 |> close_combformula_universally
1556 |> formula_from_combformula ctxt format nonmono_Ts type_sys
1557 is_var_nonmonotonic_in_formula true
1558 |> bound_tvars type_sys atomic_types
1559 |> close_formula_universally
1561 (* Each fact is given a unique fact number to avoid name clashes (e.g., because
1562 of monomorphization). The TPTP explicitly forbids name clashes, and some of
1563 the remote provers might care. *)
1564 fun formula_line_for_fact ctxt format prefix encode freshen nonmono_Ts type_sys
1565 (j, formula as {name, locality, kind, ...}) =
1566 Formula (prefix ^ (if freshen then string_of_int j ^ "_" else "") ^
1568 kind, formula_for_fact ctxt format nonmono_Ts type_sys formula, NONE,
1575 fun formula_line_for_class_rel_clause ({name, subclass, superclass, ...}
1576 : class_rel_clause) =
1577 let val ty_arg = ATerm (`I "T", []) in
1578 Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
1579 AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
1580 AAtom (ATerm (superclass, [ty_arg]))])
1581 |> close_formula_universally, intro_info, NONE)
1584 fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
1585 (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
1586 | fo_literal_from_arity_literal (TVarLit (c, sort)) =
1587 (false, ATerm (c, [ATerm (sort, [])]))
1589 fun formula_line_for_arity_clause ({name, prem_lits, concl_lits, ...}
1591 Formula (arity_clause_prefix ^ ascii_of name, Axiom,
1592 mk_ahorn (map (formula_from_fo_literal o apfst not
1593 o fo_literal_from_arity_literal) prem_lits)
1594 (formula_from_fo_literal
1595 (fo_literal_from_arity_literal concl_lits))
1596 |> close_formula_universally, intro_info, NONE)
1598 fun formula_line_for_conjecture ctxt format nonmono_Ts type_sys
1599 ({name, kind, combformula, atomic_types, ...} : translated_formula) =
1600 Formula (conjecture_prefix ^ name, kind,
1601 formula_from_combformula ctxt format nonmono_Ts type_sys
1602 is_var_nonmonotonic_in_formula false
1603 (close_combformula_universally combformula)
1604 |> bound_tvars type_sys atomic_types
1605 |> close_formula_universally, NONE, NONE)
1607 fun free_type_literals type_sys ({atomic_types, ...} : translated_formula) =
1608 atomic_types |> type_literals_for_types type_sys add_sorts_on_tfree
1609 |> map fo_literal_from_type_literal
1611 fun formula_line_for_free_type j lit =
1612 Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis,
1613 formula_from_fo_literal lit, NONE, NONE)
1614 fun formula_lines_for_free_types type_sys facts =
1616 val litss = map (free_type_literals type_sys) facts
1617 val lits = fold (union (op =)) litss []
1618 in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
1620 (** Symbol declarations **)
1622 fun should_declare_sym type_sys pred_sym s =
1623 is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
1625 Simple_Types _ => true
1626 | Tags (_, _, Lightweight) => true
1627 | _ => not pred_sym)
1629 fun sym_decl_table_for_facts ctxt type_sys repaired_sym_tab (conjs, facts) =
1631 fun add_combterm in_conj tm =
1632 let val (head, args) = strip_combterm_comb tm in
1634 CombConst ((s, s'), T, T_args) =>
1635 let val pred_sym = is_pred_sym repaired_sym_tab s in
1636 if should_declare_sym type_sys pred_sym s then
1637 Symtab.map_default (s, [])
1638 (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
1644 #> fold (add_combterm in_conj) args
1646 fun add_fact in_conj =
1647 fact_lift (formula_fold NONE (K (add_combterm in_conj)))
1650 |> is_type_sys_fairly_sound type_sys
1651 ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
1654 (* These types witness that the type classes they belong to allow infinite
1655 models and hence that any types with these type classes is monotonic. *)
1656 val known_infinite_types =
1657 [@{typ nat}, Type ("Int.int", []), @{typ "nat => bool"}]
1659 (* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
1660 out with monotonicity" paper presented at CADE 2011. *)
1661 fun add_combterm_nonmonotonic_types _ _ _ (SOME false) _ = I
1662 | add_combterm_nonmonotonic_types ctxt level locality _
1663 (CombApp (CombApp (CombConst ((s, _), Type (_, [T, _]), _), tm1),
1665 (is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
1667 Noninf_Nonmono_Types =>
1668 not (is_locality_global locality) orelse
1669 not (is_type_surely_infinite ctxt known_infinite_types T)
1670 | Fin_Nonmono_Types => is_type_surely_finite ctxt T
1671 | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
1672 | add_combterm_nonmonotonic_types _ _ _ _ _ = I
1673 fun add_fact_nonmonotonic_types ctxt level ({kind, locality, combformula, ...}
1674 : translated_formula) =
1675 formula_fold (SOME (kind <> Conjecture))
1676 (add_combterm_nonmonotonic_types ctxt level locality) combformula
1677 fun nonmonotonic_types_for_facts ctxt type_sys facts =
1678 let val level = level_of_type_sys type_sys in
1679 if level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types then
1680 [] |> fold (add_fact_nonmonotonic_types ctxt level) facts
1681 (* We must add "bool" in case the helper "True_or_False" is added
1682 later. In addition, several places in the code rely on the list of
1683 nonmonotonic types not being empty. *)
1684 |> insert_type ctxt I @{typ bool}
1689 fun decl_line_for_sym ctxt format nonmono_Ts type_sys s
1690 (s', T_args, T, pred_sym, ary, _) =
1692 val (T_arg_Ts, level) =
1694 Simple_Types level => ([], level)
1695 | _ => (replicate (length T_args) homo_infinite_type, No_Types)
1697 Decl (sym_decl_prefix ^ s, (s, s'),
1698 (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
1699 |> mangled_type format type_sys pred_sym (length T_arg_Ts + ary))
1702 fun formula_line_for_preds_sym_decl ctxt format conj_sym_kind nonmono_Ts
1703 type_sys n s j (s', T_args, T, _, ary, in_conj) =
1705 val (kind, maybe_negate) =
1706 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1708 val (arg_Ts, res_T) = chop_fun ary T
1709 val num_args = length arg_Ts
1711 1 upto num_args |> map (`I o make_bound_var o string_of_int)
1713 bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
1715 if n > 1 andalso should_drop_arg_type_args type_sys then map SOME arg_Ts
1716 else replicate num_args NONE
1718 Formula (preds_sym_formula_prefix ^ s ^
1719 (if n > 1 then "_" ^ string_of_int j else ""), kind,
1720 CombConst ((s, s'), T, T_args)
1721 |> fold (curry (CombApp o swap)) bounds
1722 |> type_pred_combterm ctxt format type_sys res_T
1723 |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
1724 |> formula_from_combformula ctxt format nonmono_Ts type_sys
1725 (K (K (K (K true)))) true
1726 |> n > 1 ? bound_tvars type_sys (atyps_of T)
1727 |> close_formula_universally
1732 fun formula_lines_for_lightweight_tags_sym_decl ctxt format conj_sym_kind
1733 nonmono_Ts type_sys n s (j, (s', T_args, T, pred_sym, ary, in_conj)) =
1736 lightweight_tags_sym_formula_prefix ^ s ^
1737 (if n > 1 then "_" ^ string_of_int j else "")
1738 val (kind, maybe_negate) =
1739 if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
1741 val (arg_Ts, res_T) = chop_fun ary T
1743 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
1744 val bounds = bound_names |> map (fn name => ATerm (name, []))
1745 val cst = mk_const_aterm format type_sys (s, s') T_args
1746 val atomic_Ts = atyps_of T
1748 (if pred_sym then AConn (AIff, map AAtom tms)
1749 else AAtom (ATerm (`I tptp_equal, tms)))
1750 |> bound_tvars type_sys atomic_Ts
1751 |> close_formula_universally
1753 (* See also "should_tag_with_type". *)
1754 fun should_encode T =
1755 should_encode_type ctxt nonmono_Ts All_Types T orelse
1757 Tags (Polymorphic, level, Lightweight) =>
1758 level <> All_Types andalso Monomorph.typ_has_tvars T
1760 val tag_with = tag_with_type ctxt format nonmono_Ts type_sys NONE
1761 val add_formula_for_res =
1762 if should_encode res_T then
1763 cons (Formula (ident_base ^ "_res", kind,
1764 eq [tag_with res_T (cst bounds), cst bounds],
1768 fun add_formula_for_arg k =
1769 let val arg_T = nth arg_Ts k in
1770 if should_encode arg_T then
1771 case chop k bounds of
1772 (bounds1, bound :: bounds2) =>
1773 cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
1774 eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
1777 | _ => raise Fail "expected nonempty tail"
1782 [] |> not pred_sym ? add_formula_for_res
1783 |> fold add_formula_for_arg (ary - 1 downto 0)
1786 fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
1788 fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts type_sys
1792 decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_sys s)
1797 decl :: (decls' as _ :: _) =>
1798 let val T = result_type_of_decl decl in
1799 if forall (curry (type_instance ctxt o swap) T
1800 o result_type_of_decl) decls' then
1806 val n = length decls
1809 |> filter (should_predicate_on_type ctxt nonmono_Ts type_sys (K true)
1810 o result_type_of_decl)
1812 (0 upto length decls - 1, decls)
1813 |-> map2 (formula_line_for_preds_sym_decl ctxt format conj_sym_kind
1814 nonmono_Ts type_sys n s)
1816 | Tags (_, _, heaviness) =>
1820 let val n = length decls in
1821 (0 upto n - 1 ~~ decls)
1822 |> maps (formula_lines_for_lightweight_tags_sym_decl ctxt format
1823 conj_sym_kind nonmono_Ts type_sys n s)
1826 fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
1827 type_sys sym_decl_tab =
1832 |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
1833 nonmono_Ts type_sys)
1835 fun needs_type_tag_idempotence (Tags (poly, level, heaviness)) =
1836 poly <> Mangled_Monomorphic andalso
1837 ((level = All_Types andalso heaviness = Lightweight) orelse
1838 level = Noninf_Nonmono_Types orelse level = Fin_Nonmono_Types)
1839 | needs_type_tag_idempotence _ = false
1841 fun offset_of_heading_in_problem _ [] j = j
1842 | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
1843 if heading = needle then j
1844 else offset_of_heading_in_problem needle problem (j + length lines)
1846 val implicit_declsN = "Should-be-implicit typings"
1847 val explicit_declsN = "Explicit typings"
1848 val factsN = "Relevant facts"
1849 val class_relsN = "Class relationships"
1850 val aritiesN = "Arities"
1851 val helpersN = "Helper facts"
1852 val conjsN = "Conjectures"
1853 val free_typesN = "Type variables"
1855 val explicit_apply = NONE (* for experimental purposes *)
1857 fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_sys
1858 freshen_facts readable_names preproc hyp_ts concl_t facts =
1860 val (format, type_sys) = choose_format [format] type_sys
1861 val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
1862 translate_formulas ctxt format prem_kind type_sys preproc hyp_ts concl_t
1864 val sym_tab = conjs @ facts |> sym_table_for_facts ctxt explicit_apply
1865 val nonmono_Ts = conjs @ facts |> nonmonotonic_types_for_facts ctxt type_sys
1866 val repair = repair_fact ctxt format type_sys sym_tab
1867 val (conjs, facts) = (conjs, facts) |> pairself (map repair)
1868 val repaired_sym_tab =
1869 conjs @ facts |> sym_table_for_facts ctxt (SOME false)
1871 repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_sys
1873 val lavish_nonmono_Ts =
1874 if null nonmono_Ts orelse nonmono_Ts = [@{typ bool}] orelse
1875 polymorphism_of_type_sys type_sys <> Polymorphic then
1878 [TVar (("'a", 0), HOLogic.typeS)]
1879 val sym_decl_lines =
1880 (conjs, helpers @ facts)
1881 |> sym_decl_table_for_facts ctxt type_sys repaired_sym_tab
1882 |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind
1883 lavish_nonmono_Ts type_sys
1885 0 upto length helpers - 1 ~~ helpers
1886 |> map (formula_line_for_fact ctxt format helper_prefix I false
1887 lavish_nonmono_Ts type_sys)
1888 |> (if needs_type_tag_idempotence type_sys then
1889 cons (type_tag_idempotence_fact ())
1892 (* Reordering these might confuse the proof reconstruction code or the SPASS
1895 [(explicit_declsN, sym_decl_lines),
1897 map (formula_line_for_fact ctxt format fact_prefix ascii_of
1898 freshen_facts nonmono_Ts type_sys)
1899 (0 upto length facts - 1 ~~ facts)),
1900 (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
1901 (aritiesN, map formula_line_for_arity_clause arity_clauses),
1902 (helpersN, helper_lines),
1904 map (formula_line_for_conjecture ctxt format nonmono_Ts type_sys)
1906 (free_typesN, formula_lines_for_free_types type_sys (facts @ conjs))]
1910 CNF => ensure_cnf_problem
1911 | CNF_UEQ => filter_cnf_ueq_problem
1913 |> (if is_format_typed format then
1914 declare_undeclared_syms_in_atp_problem type_decl_prefix
1918 val (problem, pool) = problem |> nice_atp_problem readable_names
1919 val helpers_offset = offset_of_heading_in_problem helpersN problem 0
1921 map_filter (fn (j, {name, ...}) =>
1922 if String.isSuffix typed_helper_suffix name then SOME j
1924 ((helpers_offset + 1 upto helpers_offset + length helpers)
1926 fun add_sym_arity (s, {min_ary, ...} : sym_info) =
1928 case strip_prefix_and_unascii const_prefix s of
1929 SOME s => Symtab.insert (op =) (s, min_ary)
1935 case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
1936 offset_of_heading_in_problem conjsN problem 0,
1937 offset_of_heading_in_problem factsN problem 0,
1938 fact_names |> Vector.fromList,
1940 Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
1944 val conj_weight = 0.0
1945 val hyp_weight = 0.1
1946 val fact_min_weight = 0.2
1947 val fact_max_weight = 1.0
1948 val type_info_default_weight = 0.8
1950 fun add_term_weights weight (ATerm (s, tms)) =
1951 is_tptp_user_symbol s ? Symtab.default (s, weight)
1952 #> fold (add_term_weights weight) tms
1953 fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
1954 formula_fold NONE (K (add_term_weights weight)) phi
1955 | add_problem_line_weights _ _ = I
1957 fun add_conjectures_weights [] = I
1958 | add_conjectures_weights conjs =
1959 let val (hyps, conj) = split_last conjs in
1960 add_problem_line_weights conj_weight conj
1961 #> fold (add_problem_line_weights hyp_weight) hyps
1964 fun add_facts_weights facts =
1966 val num_facts = length facts
1968 fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
1969 / Real.fromInt num_facts
1971 map weight_of (0 upto num_facts - 1) ~~ facts
1972 |> fold (uncurry add_problem_line_weights)
1975 (* Weights are from 0.0 (most important) to 1.0 (least important). *)
1976 fun atp_problem_weights problem =
1977 let val get = these o AList.lookup (op =) problem in
1979 |> add_conjectures_weights (get free_typesN @ get conjsN)
1980 |> add_facts_weights (get factsN)
1981 |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
1982 [explicit_declsN, class_relsN, aritiesN]
1984 |> sort (prod_ord Real.compare string_ord o pairself swap)