1 (* Title: HOL/Tools/ATP/atp_proof_reconstruct.ML
2 Author: Lawrence C. Paulson, Cambridge University Computer Laboratory
3 Author: Claire Quigley, Cambridge University Computer Laboratory
4 Author: Jasmin Blanchette, TU Muenchen
6 Proof reconstruction from ATP proofs.
9 signature ATP_PROOF_RECONSTRUCT =
11 type ('a, 'b) ho_term = ('a, 'b) ATP_Problem.ho_term
12 type ('a, 'b, 'c) formula = ('a, 'b, 'c) ATP_Problem.formula
13 type 'a proof = 'a ATP_Proof.proof
14 type stature = ATP_Problem_Generate.stature
16 datatype reconstructor =
17 Metis of string * string |
21 Played of reconstructor * Time.time |
22 Trust_Playable of reconstructor * Time.time option |
23 Failed_to_Play of reconstructor
25 type minimize_command = string list -> string
26 type one_line_params =
27 play * string * (string * stature) list * minimize_command * int * int
29 bool * int * string Symtab.table * (string * stature) list vector
30 * int Symtab.table * string proof * thm
34 val full_typesN : string
35 val partial_typesN : string
36 val no_typesN : string
37 val really_full_type_enc : string
38 val full_type_enc : string
39 val partial_type_enc : string
40 val no_type_enc : string
41 val full_type_encs : string list
42 val partial_type_encs : string list
43 val metis_default_lam_trans : string
44 val metis_call : string -> string -> string
45 val string_for_reconstructor : reconstructor -> string
46 val used_facts_in_atp_proof :
47 Proof.context -> (string * stature) list vector -> string proof
48 -> (string * stature) list
49 val lam_trans_from_atp_proof : string proof -> string -> string
50 val is_typed_helper_used_in_atp_proof : string proof -> bool
51 val used_facts_in_unsound_atp_proof :
52 Proof.context -> (string * stature) list vector -> 'a proof
54 val unalias_type_enc : string -> string list
55 val one_line_proof_text : one_line_params -> string
56 val make_tvar : string -> typ
57 val make_tfree : Proof.context -> string -> typ
59 Proof.context -> bool -> int Symtab.table -> typ option
60 -> (string, string) ho_term -> term
62 Proof.context -> bool -> int Symtab.table
63 -> (string, string, (string, string) ho_term) formula -> term
65 Proof.context -> bool -> isar_params -> one_line_params -> string
67 Proof.context -> bool -> isar_params -> one_line_params -> string
70 structure ATP_Proof_Reconstruct : ATP_PROOF_RECONSTRUCT =
76 open ATP_Problem_Generate
78 structure String_Redirect = ATP_Proof_Redirect(
80 val ord = fn ((s, _ : string list), (s', _)) => fast_string_ord (s, s')
85 datatype reconstructor =
86 Metis of string * string |
90 Played of reconstructor * Time.time |
91 Trust_Playable of reconstructor * Time.time option |
92 Failed_to_Play of reconstructor
94 type minimize_command = string list -> string
95 type one_line_params =
96 play * string * (string * stature) list * minimize_command * int * int
98 bool * int * string Symtab.table * (string * stature) list vector
99 * int Symtab.table * string proof * thm
104 val full_typesN = "full_types"
105 val partial_typesN = "partial_types"
106 val no_typesN = "no_types"
108 val really_full_type_enc = "mono_tags"
109 val full_type_enc = "poly_guards_query"
110 val partial_type_enc = "poly_args"
111 val no_type_enc = "erased"
113 val full_type_encs = [full_type_enc, really_full_type_enc]
114 val partial_type_encs = partial_type_enc :: full_type_encs
116 val type_enc_aliases =
117 [(full_typesN, full_type_encs),
118 (partial_typesN, partial_type_encs),
119 (no_typesN, [no_type_enc])]
121 fun unalias_type_enc s =
122 AList.lookup (op =) type_enc_aliases s |> the_default [s]
124 val metis_default_lam_trans = combsN
126 fun metis_call type_enc lam_trans =
129 case AList.find (fn (enc, encs) => enc = hd encs) type_enc_aliases
133 val opts = [] |> type_enc <> partial_typesN ? cons type_enc
134 |> lam_trans <> metis_default_lam_trans ? cons lam_trans
135 in metisN ^ (if null opts then "" else " (" ^ commas opts ^ ")") end
137 fun string_for_reconstructor (Metis (type_enc, lam_trans)) =
138 metis_call type_enc lam_trans
139 | string_for_reconstructor SMT = smtN
141 fun find_first_in_list_vector vec key =
142 Vector.foldl (fn (ps, NONE) => AList.lookup (op =) ps key
143 | (_, value) => value) NONE vec
145 val unprefix_fact_number = space_implode "_" o tl o space_explode "_"
147 fun resolve_one_named_fact fact_names s =
148 case try (unprefix fact_prefix) s of
150 let val s' = s' |> unprefix_fact_number |> unascii_of in
151 s' |> find_first_in_list_vector fact_names |> Option.map (pair s')
154 fun resolve_fact fact_names = map_filter (resolve_one_named_fact fact_names)
155 fun is_fact fact_names = not o null o resolve_fact fact_names
157 fun resolve_one_named_conjecture s =
158 case try (unprefix conjecture_prefix) s of
159 SOME s' => Int.fromString s'
162 val resolve_conjecture = map_filter resolve_one_named_conjecture
163 val is_conjecture = not o null o resolve_conjecture
165 fun is_axiom_used_in_proof pred =
166 exists (fn Inference_Step ((_, ss), _, _, []) => exists pred ss | _ => false)
168 val is_combinator_def = String.isPrefix (helper_prefix ^ combinator_prefix)
170 val ascii_of_lam_fact_prefix = ascii_of lam_fact_prefix
172 (* overapproximation (good enough) *)
173 fun is_lam_lifted s =
174 String.isPrefix fact_prefix s andalso
175 String.isSubstring ascii_of_lam_fact_prefix s
177 fun lam_trans_from_atp_proof atp_proof default =
178 case (is_axiom_used_in_proof is_combinator_def atp_proof,
179 is_axiom_used_in_proof is_lam_lifted atp_proof) of
180 (false, false) => default
181 | (false, true) => liftingN
182 (* | (true, true) => combs_and_liftingN -- not supported by "metis" *)
183 | (true, _) => combsN
185 val is_typed_helper_name =
186 String.isPrefix helper_prefix andf String.isSuffix typed_helper_suffix
187 fun is_typed_helper_used_in_atp_proof atp_proof =
188 is_axiom_used_in_proof is_typed_helper_name atp_proof
190 val leo2_ext = "extcnf_equal_neg"
191 val leo2_unfold_def = "unfold_def"
193 val isa_ext = Thm.get_name_hint @{thm ext}
194 val isa_short_ext = Long_Name.base_name isa_ext
197 if Thm.eq_thm_prop (@{thm ext},
198 singleton (Attrib.eval_thms ctxt) (Facts.named isa_short_ext, [])) then
203 fun add_all_defs fact_names accum =
205 (fn (facts, facts') =>
206 union (op =) (filter (fn (_, (_, status)) => status = Def) facts)
210 fun add_fact ctxt fact_names (Inference_Step ((_, ss), _, rule, deps)) =
211 (if rule = leo2_ext then
212 insert (op =) (ext_name ctxt, (Global, General))
213 else if rule = leo2_unfold_def then
214 (* LEO 1.3.3 does not record definitions properly, leading to missing
215 dependencies in the TSTP proof. Remove the next line once this is
217 add_all_defs fact_names
218 else if rule = satallax_unsat_coreN then
220 (* Satallax doesn't include definitions in its unsatisfiable cores,
221 so we assume the worst and include them all here. *)
222 [(ext_name ctxt, (Global, General))] |> add_all_defs fact_names
226 #> (if null deps then union (op =) (resolve_fact fact_names ss)
230 fun used_facts_in_atp_proof ctxt fact_names atp_proof =
231 if null atp_proof then Vector.foldl (uncurry (union (op =))) [] fact_names
232 else fold (add_fact ctxt fact_names) atp_proof []
234 fun used_facts_in_unsound_atp_proof _ _ [] = NONE
235 | used_facts_in_unsound_atp_proof ctxt fact_names atp_proof =
236 let val used_facts = used_facts_in_atp_proof ctxt fact_names atp_proof in
237 if forall (fn (_, (sc, _)) => sc = Global) used_facts andalso
238 not (is_axiom_used_in_proof (is_conjecture o single) atp_proof) then
239 SOME (map fst used_facts)
245 (** Soft-core proof reconstruction: one-liners **)
247 fun string_for_label (s, num) = s ^ string_of_int num
249 fun show_time NONE = ""
250 | show_time (SOME ext_time) = " (" ^ string_from_ext_time ext_time ^ ")"
252 fun apply_on_subgoal _ 1 = "by "
253 | apply_on_subgoal 1 _ = "apply "
254 | apply_on_subgoal i n =
255 "prefer " ^ string_of_int i ^ " " ^ apply_on_subgoal 1 n
256 fun command_call name [] =
257 name |> not (Lexicon.is_identifier name) ? enclose "(" ")"
258 | command_call name args = "(" ^ name ^ " " ^ space_implode " " args ^ ")"
259 fun try_command_line banner time command =
260 banner ^ ": " ^ Markup.markup Isabelle_Markup.sendback command ^ show_time time ^ "."
261 fun using_labels [] = ""
263 "using " ^ space_implode " " (map string_for_label ls) ^ " "
264 fun reconstructor_command reconstr i n (ls, ss) =
265 using_labels ls ^ apply_on_subgoal i n ^
266 command_call (string_for_reconstructor reconstr) ss
267 fun minimize_line _ [] = ""
268 | minimize_line minimize_command ss =
269 case minimize_command ss of
272 "\nTo minimize: " ^ Markup.markup Isabelle_Markup.sendback command ^ "."
274 fun split_used_facts facts =
275 facts |> List.partition (fn (_, (sc, _)) => sc = Chained)
276 |> pairself (sort_distinct (string_ord o pairself fst))
278 fun one_line_proof_text (preplay, banner, used_facts, minimize_command,
279 subgoal, subgoal_count) =
281 val (chained, extra) = split_used_facts used_facts
282 val (failed, reconstr, ext_time) =
284 Played (reconstr, time) => (false, reconstr, (SOME (false, time)))
285 | Trust_Playable (reconstr, time) =>
290 if time = Time.zeroTime then NONE else SOME (true, time))
291 | Failed_to_Play reconstr => (true, reconstr, NONE)
294 |> reconstructor_command reconstr subgoal subgoal_count
296 enclose "One-line proof reconstruction failed: "
297 ".\n(Invoking \"sledgehammer\" with \"[strict]\" might \
300 try_command_line banner ext_time)
301 in try_line ^ minimize_line minimize_command (map fst (extra @ chained)) end
303 (** Hard-core proof reconstruction: structured Isar proofs **)
305 fun forall_of v t = HOLogic.all_const (fastype_of v) $ lambda v t
306 fun exists_of v t = HOLogic.exists_const (fastype_of v) $ lambda v t
308 fun make_tvar s = TVar (("'" ^ s, 0), HOLogic.typeS)
309 fun make_tfree ctxt w =
310 let val ww = "'" ^ w in
311 TFree (ww, the_default HOLogic.typeS (Variable.def_sort ctxt (ww, ~1)))
315 val no_label = ("", ~1)
318 val assum_prefix = "a"
319 val have_prefix = "f"
321 fun raw_label_for_name (num, ss) =
322 case resolve_conjecture ss of
323 [j] => (conjecture_prefix, j)
324 | _ => (raw_prefix ^ ascii_of num, 0)
326 (**** INTERPRETATION OF TSTP SYNTAX TREES ****)
328 exception HO_TERM of (string, string) ho_term list
329 exception FORMULA of (string, string, (string, string) ho_term) formula list
330 exception SAME of unit
332 (* Type variables are given the basic sort "HOL.type". Some will later be
333 constrained by information from type literals, or by type inference. *)
334 fun typ_from_atp ctxt (u as ATerm ((a, _), us)) =
335 let val Ts = map (typ_from_atp ctxt) us in
336 case unprefix_and_unascii type_const_prefix a of
337 SOME b => Type (invert_const b, Ts)
339 if not (null us) then
340 raise HO_TERM [u] (* only "tconst"s have type arguments *)
341 else case unprefix_and_unascii tfree_prefix a of
342 SOME b => make_tfree ctxt b
344 (* Could be an Isabelle variable or a variable from the ATP, say "X1"
345 or "_5018". Sometimes variables from the ATP are indistinguishable
346 from Isabelle variables, which forces us to use a type parameter in
348 (a |> perhaps (unprefix_and_unascii tvar_prefix), HOLogic.typeS)
349 |> Type_Infer.param 0
352 (* Type class literal applied to a type. Returns triple of polarity, class,
354 fun type_constraint_from_term ctxt (u as ATerm ((a, _), us)) =
355 case (unprefix_and_unascii class_prefix a, map (typ_from_atp ctxt) us) of
356 (SOME b, [T]) => (b, T)
357 | _ => raise HO_TERM [u]
359 (* Accumulate type constraints in a formula: negative type literals. *)
360 fun add_var (key, z) = Vartab.map_default (key, []) (cons z)
361 fun add_type_constraint false (cl, TFree (a ,_)) = add_var ((a, ~1), cl)
362 | add_type_constraint false (cl, TVar (ix, _)) = add_var (ix, cl)
363 | add_type_constraint _ _ = I
365 fun repair_variable_name f s =
367 fun subscript_name s n = s ^ nat_subscript n
368 val s = String.map f s
370 case space_explode "_" s of
371 [_] => (case take_suffix Char.isDigit (String.explode s) of
372 (cs1 as _ :: _, cs2 as _ :: _) =>
373 subscript_name (String.implode cs1)
374 (the (Int.fromString (String.implode cs2)))
376 | [s1, s2] => (case Int.fromString s2 of
377 SOME n => subscript_name s1 n
382 (* The number of type arguments of a constant, zero if it's monomorphic. For
383 (instances of) Skolem pseudoconstants, this information is encoded in the
385 fun num_type_args thy s =
386 if String.isPrefix skolem_const_prefix s then
387 s |> Long_Name.explode |> List.last |> Int.fromString |> the
388 else if String.isPrefix lam_lifted_prefix s then
389 if String.isPrefix lam_lifted_poly_prefix s then 2 else 0
391 (s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
393 fun slack_fastype_of t = fastype_of t handle TERM _ => HOLogic.typeT
395 (* First-order translation. No types are known for variables. "HOLogic.typeT"
396 should allow them to be inferred. *)
397 fun term_from_atp ctxt textual sym_tab =
399 val thy = Proof_Context.theory_of ctxt
400 (* For Metis, we use 1 rather than 0 because variable references in clauses
401 may otherwise conflict with variable constraints in the goal. At least,
402 type inference often fails otherwise. See also "axiom_inference" in
403 "Metis_Reconstruct". *)
404 val var_index = if textual then 0 else 1
405 fun do_term extra_ts opt_T u =
407 ATerm ((s, _), us) =>
408 if String.isPrefix native_type_prefix s then
409 @{const True} (* ignore TPTP type information *)
410 else if s = tptp_equal then
411 let val ts = map (do_term [] NONE) us in
412 if textual andalso length ts = 2 andalso
413 hd ts aconv List.last ts then
414 (* Vampire is keen on producing these. *)
417 list_comb (Const (@{const_name HOL.eq}, HOLogic.typeT), ts)
419 else case unprefix_and_unascii const_prefix s of
422 val ((s', s''), mangled_us) =
423 s' |> unmangled_const |>> `invert_const
425 if s' = type_tag_name then
426 case mangled_us @ us of
428 do_term extra_ts (SOME (typ_from_atp ctxt typ_u)) term_u
429 | _ => raise HO_TERM us
430 else if s' = predicator_name then
431 do_term [] (SOME @{typ bool}) (hd us)
432 else if s' = app_op_name then
433 let val extra_t = do_term [] NONE (List.last us) in
434 do_term (extra_t :: extra_ts)
436 SOME T => SOME (slack_fastype_of extra_t --> T)
438 (nth us (length us - 2))
440 else if s' = type_guard_name then
441 @{const True} (* ignore type predicates *)
444 val new_skolem = String.isPrefix new_skolem_const_prefix s''
446 length us - the_default 0 (Symtab.lookup sym_tab s)
447 val (type_us, term_us) =
448 chop num_ty_args us |>> append mangled_us
449 val term_ts = map (do_term [] NONE) term_us
451 (if not (null type_us) andalso
452 num_type_args thy s' = length type_us then
453 let val Ts = type_us |> map (typ_from_atp ctxt) in
455 SOME (Type_Infer.paramify_vars (tl Ts ---> hd Ts))
457 try (Sign.const_instance thy) (s', Ts)
464 | NONE => map slack_fastype_of term_ts --->
467 | NONE => HOLogic.typeT))
470 Var ((new_skolem_var_name_from_const s'', var_index), T)
472 Const (unproxify_const s', T)
473 in list_comb (t, term_ts @ extra_ts) end
475 | NONE => (* a free or schematic variable *)
477 val term_ts = map (do_term [] NONE) us
478 val ts = term_ts @ extra_ts
481 SOME T => map slack_fastype_of term_ts ---> T
482 | NONE => map slack_fastype_of ts ---> HOLogic.typeT
484 case unprefix_and_unascii fixed_var_prefix s of
485 SOME s => Free (s, T)
487 case unprefix_and_unascii schematic_var_prefix s of
488 SOME s => Var ((s, var_index), T)
490 Var ((s |> textual ? repair_variable_name Char.toLower,
492 in list_comb (t, ts) end
495 fun term_from_atom ctxt textual sym_tab pos (u as ATerm ((s, _), _)) =
496 if String.isPrefix class_prefix s then
497 add_type_constraint pos (type_constraint_from_term ctxt u)
498 #> pair @{const True}
500 pair (term_from_atp ctxt textual sym_tab (SOME @{typ bool}) u)
502 val combinator_table =
503 [(@{const_name Meson.COMBI}, @{thm Meson.COMBI_def [abs_def]}),
504 (@{const_name Meson.COMBK}, @{thm Meson.COMBK_def [abs_def]}),
505 (@{const_name Meson.COMBB}, @{thm Meson.COMBB_def [abs_def]}),
506 (@{const_name Meson.COMBC}, @{thm Meson.COMBC_def [abs_def]}),
507 (@{const_name Meson.COMBS}, @{thm Meson.COMBS_def [abs_def]})]
509 fun uncombine_term thy =
511 fun aux (t1 $ t2) = betapply (pairself aux (t1, t2))
512 | aux (Abs (s, T, t')) = Abs (s, T, aux t')
513 | aux (t as Const (x as (s, _))) =
514 (case AList.lookup (op =) combinator_table s of
515 SOME thm => thm |> prop_of |> specialize_type thy x
516 |> Logic.dest_equals |> snd
521 (* Update schematic type variables with detected sort constraints. It's not
522 totally clear whether this code is necessary. *)
523 fun repair_tvar_sorts (t, tvar_tab) =
525 fun do_type (Type (a, Ts)) = Type (a, map do_type Ts)
526 | do_type (TVar (xi, s)) =
527 TVar (xi, the_default s (Vartab.lookup tvar_tab xi))
528 | do_type (TFree z) = TFree z
529 fun do_term (Const (a, T)) = Const (a, do_type T)
530 | do_term (Free (a, T)) = Free (a, do_type T)
531 | do_term (Var (xi, T)) = Var (xi, do_type T)
532 | do_term (t as Bound _) = t
533 | do_term (Abs (a, T, t)) = Abs (a, do_type T, do_term t)
534 | do_term (t1 $ t2) = do_term t1 $ do_term t2
535 in t |> not (Vartab.is_empty tvar_tab) ? do_term end
537 fun quantify_over_var quant_of var_s t =
539 val vars = [] |> Term.add_vars t |> filter (fn ((s, _), _) => s = var_s)
541 in fold_rev quant_of vars t end
543 (* Interpret an ATP formula as a HOL term, extracting sort constraints as they
544 appear in the formula. *)
545 fun prop_from_atp ctxt textual sym_tab phi =
547 fun do_formula pos phi =
549 AQuant (_, [], phi) => do_formula pos phi
550 | AQuant (q, (s, _) :: xs, phi') =>
551 do_formula pos (AQuant (q, xs, phi'))
553 #>> quantify_over_var (case q of
555 | AExists => exists_of)
556 (s |> textual ? repair_variable_name Char.toLower)
557 | AConn (ANot, [phi']) => do_formula (not pos) phi' #>> s_not
558 | AConn (c, [phi1, phi2]) =>
559 do_formula (pos |> c = AImplies ? not) phi1
560 ##>> do_formula pos phi2
566 | ANot => raise Fail "impossible connective")
567 | AAtom tm => term_from_atom ctxt textual sym_tab pos tm
568 | _ => raise FORMULA [phi]
569 in repair_tvar_sorts (do_formula true phi Vartab.empty) end
571 fun infer_formula_types ctxt =
572 Type.constraint HOLogic.boolT
574 (Proof_Context.set_mode Proof_Context.mode_schematic ctxt)
576 fun uncombined_etc_prop_from_atp ctxt textual sym_tab =
577 let val thy = Proof_Context.theory_of ctxt in
578 prop_from_atp ctxt textual sym_tab
579 #> textual ? uncombine_term thy #> infer_formula_types ctxt
582 (**** Translation of TSTP files to Isar proofs ****)
584 fun unvarify_term (Var ((s, 0), T)) = Free (s, T)
585 | unvarify_term t = raise TERM ("unvarify_term: non-Var", [t])
587 fun decode_line sym_tab (Definition_Step (name, phi1, phi2)) ctxt =
589 val thy = Proof_Context.theory_of ctxt
590 val t1 = prop_from_atp ctxt true sym_tab phi1
591 val vars = snd (strip_comb t1)
592 val frees = map unvarify_term vars
593 val unvarify_args = subst_atomic (vars ~~ frees)
594 val t2 = prop_from_atp ctxt true sym_tab phi2
596 HOLogic.eq_const HOLogic.typeT $ t1 $ t2
597 |> unvarify_args |> uncombine_term thy |> infer_formula_types ctxt
600 (Definition_Step (name, t1, t2),
601 fold Variable.declare_term (maps Misc_Legacy.term_frees [t1, t2]) ctxt)
603 | decode_line sym_tab (Inference_Step (name, u, rule, deps)) ctxt =
604 let val t = u |> uncombined_etc_prop_from_atp ctxt true sym_tab in
605 (Inference_Step (name, t, rule, deps),
606 fold Variable.declare_term (Misc_Legacy.term_frees t) ctxt)
608 fun decode_lines ctxt sym_tab lines =
609 fst (fold_map (decode_line sym_tab) lines ctxt)
611 fun is_same_inference _ (Definition_Step _) = false
612 | is_same_inference t (Inference_Step (_, t', _, _)) = t aconv t'
614 (* No "real" literals means only type information (tfree_tcs, clsrel, or
616 fun is_only_type_information t = t aconv @{term True}
618 fun replace_one_dependency (old, new) dep =
619 if is_same_atp_step dep old then new else [dep]
620 fun replace_dependencies_in_line _ (line as Definition_Step _) = line
621 | replace_dependencies_in_line p (Inference_Step (name, t, rule, deps)) =
622 Inference_Step (name, t, rule,
623 fold (union (op =) o replace_one_dependency p) deps [])
625 (* Discard facts; consolidate adjacent lines that prove the same formula, since
626 they differ only in type information.*)
627 fun add_line _ (line as Definition_Step _) lines = line :: lines
628 | add_line fact_names (Inference_Step (name as (_, ss), t, rule, [])) lines =
629 (* No dependencies: fact, conjecture, or (for Vampire) internal facts or
631 if is_fact fact_names ss then
632 (* Facts are not proof lines. *)
633 if is_only_type_information t then
634 map (replace_dependencies_in_line (name, [])) lines
635 (* Is there a repetition? If so, replace later line by earlier one. *)
636 else case take_prefix (not o is_same_inference t) lines of
637 (_, []) => lines (* no repetition of proof line *)
638 | (pre, Inference_Step (name', _, _, _) :: post) =>
639 pre @ map (replace_dependencies_in_line (name', [name])) post
640 | _ => raise Fail "unexpected inference"
641 else if is_conjecture ss then
642 Inference_Step (name, t, rule, []) :: lines
644 map (replace_dependencies_in_line (name, [])) lines
645 | add_line _ (Inference_Step (name, t, rule, deps)) lines =
646 (* Type information will be deleted later; skip repetition test. *)
647 if is_only_type_information t then
648 Inference_Step (name, t, rule, deps) :: lines
649 (* Is there a repetition? If so, replace later line by earlier one. *)
650 else case take_prefix (not o is_same_inference t) lines of
651 (* FIXME: Doesn't this code risk conflating proofs involving different
653 (_, []) => Inference_Step (name, t, rule, deps) :: lines
654 | (pre, Inference_Step (name', t', rule, _) :: post) =>
655 Inference_Step (name, t', rule, deps) ::
656 pre @ map (replace_dependencies_in_line (name', [name])) post
657 | _ => raise Fail "unexpected inference"
659 val waldmeister_conjecture_num = "1.0.0.0"
661 val repair_waldmeister_endgame =
663 fun do_tail (Inference_Step (name, t, rule, deps)) =
664 Inference_Step (name, s_not t, rule, deps)
665 | do_tail line = line
667 | do_body ((line as Inference_Step ((num, _), _, _, _)) :: lines) =
668 if num = waldmeister_conjecture_num then map do_tail (line :: lines)
669 else line :: do_body lines
670 | do_body (line :: lines) = line :: do_body lines
673 (* Recursively delete empty lines (type information) from the proof. *)
674 fun add_nontrivial_line (line as Inference_Step (name, t, _, [])) lines =
675 if is_only_type_information t then delete_dependency name lines
677 | add_nontrivial_line line lines = line :: lines
678 and delete_dependency name lines =
679 fold_rev add_nontrivial_line
680 (map (replace_dependencies_in_line (name, [])) lines) []
682 (* ATPs sometimes reuse free variable names in the strangest ways. Removing
683 offending lines often does the trick. *)
684 fun is_bad_free frees (Free x) = not (member (op =) frees x)
685 | is_bad_free _ _ = false
687 fun add_desired_line _ _ _ (line as Definition_Step (name, _, _)) (j, lines) =
688 (j, line :: map (replace_dependencies_in_line (name, [])) lines)
689 | add_desired_line isar_shrink_factor fact_names frees
690 (Inference_Step (name as (_, ss), t, rule, deps)) (j, lines) =
692 if is_fact fact_names ss orelse
693 is_conjecture ss orelse
694 (* the last line must be kept *)
696 (not (is_only_type_information t) andalso
697 null (Term.add_tvars t []) andalso
698 not (exists_subterm (is_bad_free frees) t) andalso
699 length deps >= 2 andalso j mod isar_shrink_factor = 0 andalso
700 (* kill next to last line, which usually results in a trivial step *)
702 Inference_Step (name, t, rule, deps) :: lines (* keep line *)
704 map (replace_dependencies_in_line (name, deps)) lines) (* drop line *)
706 (** Isar proof construction and manipulation **)
708 type label = string * int
709 type facts = label list * string list
711 datatype isar_qualifier = Show | Then | Moreover | Ultimately
714 Fix of (string * typ) list |
716 Assume of label * term |
717 Prove of isar_qualifier list * label * term * byline
720 Case_Split of isar_step list list * facts
722 fun add_fact_from_dependency fact_names (name as (_, ss)) =
723 if is_fact fact_names ss then
724 apsnd (union (op =) (map fst (resolve_fact fact_names ss)))
726 apfst (insert (op =) (raw_label_for_name name))
728 fun repair_name "$true" = "c_True"
729 | repair_name "$false" = "c_False"
730 | repair_name "$$e" = tptp_equal (* seen in Vampire proofs *)
732 if is_tptp_equal s orelse
733 (* seen in Vampire proofs *)
734 (String.isPrefix "sQ" s andalso String.isSuffix "_eqProxy" s) then
739 (* FIXME: Still needed? Try with SPASS proofs perhaps. *)
740 val kill_duplicate_assumptions_in_proof =
742 fun relabel_facts subst =
743 apfst (map (fn l => AList.lookup (op =) subst l |> the_default l))
744 fun do_step (step as Assume (l, t)) (proof, subst, assums) =
745 (case AList.lookup (op aconv) assums t of
746 SOME l' => (proof, (l, l') :: subst, assums)
747 | NONE => (step :: proof, subst, (t, l) :: assums))
748 | do_step (Prove (qs, l, t, by)) (proof, subst, assums) =
751 By_Metis facts => By_Metis (relabel_facts subst facts)
752 | Case_Split (proofs, facts) =>
753 Case_Split (map do_proof proofs,
754 relabel_facts subst facts)) ::
755 proof, subst, assums)
756 | do_step step (proof, subst, assums) = (step :: proof, subst, assums)
757 and do_proof proof = fold do_step proof ([], [], []) |> #1 |> rev
760 fun used_labels_of_step (Prove (_, _, _, by)) =
762 By_Metis (ls, _) => ls
763 | Case_Split (proofs, (ls, _)) =>
764 fold (union (op =) o used_labels_of) proofs ls)
765 | used_labels_of_step _ = []
766 and used_labels_of proof = fold (union (op =) o used_labels_of_step) proof []
768 fun kill_useless_labels_in_proof proof =
770 val used_ls = used_labels_of proof
771 fun do_label l = if member (op =) used_ls l then l else no_label
772 fun do_step (Assume (l, t)) = Assume (do_label l, t)
773 | do_step (Prove (qs, l, t, by)) =
774 Prove (qs, do_label l, t,
776 Case_Split (proofs, facts) =>
777 Case_Split (map (map do_step) proofs, facts)
779 | do_step step = step
780 in map do_step proof end
782 fun prefix_for_depth n = replicate_string (n + 1)
786 fun aux _ _ _ [] = []
787 | aux subst depth (next_assum, next_fact) (Assume (l, t) :: proof) =
789 Assume (l, t) :: aux subst depth (next_assum, next_fact) proof
791 let val l' = (prefix_for_depth depth assum_prefix, next_assum) in
793 aux ((l, l') :: subst) depth (next_assum + 1, next_fact) proof
795 | aux subst depth (next_assum, next_fact)
796 (Prove (qs, l, t, by) :: proof) =
798 val (l', subst, next_fact) =
800 (l, subst, next_fact)
803 val l' = (prefix_for_depth depth have_prefix, next_fact)
804 in (l', (l, l') :: subst, next_fact + 1) end
806 apfst (maps (the_list o AList.lookup (op =) subst))
809 By_Metis facts => By_Metis (relabel_facts facts)
810 | Case_Split (proofs, facts) =>
811 Case_Split (map (aux subst (depth + 1) (1, 1)) proofs,
814 Prove (qs, l', t, by) :: aux subst depth (next_assum, next_fact) proof
816 | aux subst depth nextp (step :: proof) =
817 step :: aux subst depth nextp proof
818 in aux [] 0 (1, 1) end
820 fun string_for_proof ctxt0 type_enc lam_trans i n =
823 (* FIXME: Implement proper handling of type constraints:
824 |> Config.put show_free_types false
825 |> Config.put show_types false
826 |> Config.put show_sorts false
828 fun fix_print_mode f x =
829 Print_Mode.setmp (filter (curry (op =) Symbol.xsymbolsN)
830 (print_mode_value ())) f x
831 fun do_indent ind = replicate_string (ind * indent_size) " "
833 maybe_quote s ^ " :: " ^
834 maybe_quote (fix_print_mode (Syntax.string_of_typ ctxt) T)
835 fun do_label l = if l = no_label then "" else string_for_label l ^ ": "
837 (if member (op =) qs Moreover then "moreover " else "") ^
838 (if member (op =) qs Ultimately then "ultimately " else "") ^
839 (if member (op =) qs Then then
840 if member (op =) qs Show then "thus" else "hence"
842 if member (op =) qs Show then "show" else "have")
843 val do_term = maybe_quote o fix_print_mode (Syntax.string_of_term ctxt)
844 val reconstr = Metis (type_enc, lam_trans)
845 fun do_facts (ls, ss) =
846 reconstructor_command reconstr 1 1
847 (ls |> sort_distinct (prod_ord string_ord int_ord),
848 ss |> sort_distinct string_ord)
849 and do_step ind (Fix xs) =
850 do_indent ind ^ "fix " ^ space_implode " and " (map do_free xs) ^ "\n"
851 | do_step ind (Let (t1, t2)) =
852 do_indent ind ^ "let " ^ do_term t1 ^ " = " ^ do_term t2 ^ "\n"
853 | do_step ind (Assume (l, t)) =
854 do_indent ind ^ "assume " ^ do_label l ^ do_term t ^ "\n"
855 | do_step ind (Prove (qs, l, t, By_Metis facts)) =
856 do_indent ind ^ do_have qs ^ " " ^
857 do_label l ^ do_term t ^ " " ^ do_facts facts ^ "\n"
858 | do_step ind (Prove (qs, l, t, Case_Split (proofs, facts))) =
859 implode (map (prefix (do_indent ind ^ "moreover\n") o do_block ind)
861 do_indent ind ^ do_have qs ^ " " ^ do_label l ^ do_term t ^ " " ^
862 do_facts facts ^ "\n"
863 and do_steps prefix suffix ind steps =
864 let val s = implode (map (do_step ind) steps) in
865 replicate_string (ind * indent_size - size prefix) " " ^ prefix ^
866 String.extract (s, ind * indent_size,
867 SOME (size s - ind * indent_size - 1)) ^
870 and do_block ind proof = do_steps "{ " " }" (ind + 1) proof
871 (* One-step proofs are pointless; better use the Metis one-liner
873 and do_proof [Prove (_, _, _, By_Metis _)] = ""
875 (if i <> 1 then "prefer " ^ string_of_int i ^ "\n" else "") ^
876 do_indent 0 ^ "proof -\n" ^ do_steps "" "" 1 proof ^ do_indent 0 ^
877 (if n <> 1 then "next" else "qed")
880 fun isar_proof_text ctxt isar_proof_requested
881 (debug, isar_shrink_factor, pool, fact_names, sym_tab, atp_proof, goal)
882 (one_line_params as (_, _, _, _, subgoal, subgoal_count)) =
884 val isar_shrink_factor =
885 (if isar_proof_requested then 1 else 2) * isar_shrink_factor
886 val (params, hyp_ts, concl_t) = strip_subgoal ctxt goal subgoal
887 val frees = fold Term.add_frees (concl_t :: hyp_ts) []
888 val one_line_proof = one_line_proof_text one_line_params
890 if is_typed_helper_used_in_atp_proof atp_proof then full_typesN
892 val lam_trans = lam_trans_from_atp_proof atp_proof metis_default_lam_trans
894 fun isar_proof_of () =
898 |> clean_up_atp_proof_dependencies
899 |> nasty_atp_proof pool
900 |> map_term_names_in_atp_proof repair_name
901 |> decode_lines ctxt sym_tab
902 |> rpair [] |-> fold_rev (add_line fact_names)
903 |> repair_waldmeister_endgame
904 |> rpair [] |-> fold_rev add_nontrivial_line
906 |-> fold_rev (add_desired_line isar_shrink_factor fact_names frees)
908 val conj_name = conjecture_prefix ^ string_of_int (length hyp_ts)
911 |> map_filter (fn Inference_Step (name as (_, ss), _, _, []) =>
912 if member (op =) ss conj_name then SOME name else NONE
914 fun dep_of_step (Definition_Step _) = NONE
915 | dep_of_step (Inference_Step (name, _, _, from)) = SOME (from, name)
916 val ref_graph = atp_proof |> map_filter dep_of_step |> make_ref_graph
917 val axioms = axioms_of_ref_graph ref_graph conjs
918 val tainted = tainted_atoms_of_ref_graph ref_graph conjs
921 |> fold (fn Definition_Step _ => I (* FIXME *)
922 | Inference_Step ((s, _), t, _, _) =>
923 Symtab.update_new (s,
924 t |> fold forall_of (map Var (Term.add_vars t []))
925 |> member (op = o apsnd fst) tainted s ? s_not))
927 fun prop_of_clause c =
928 fold (curry s_disj) (map_filter (Symtab.lookup props o fst) c)
930 fun label_of_clause [name] = raw_label_for_name name
931 | label_of_clause c = (space_implode "___" (map fst c), 0)
932 fun maybe_show outer c =
933 (outer andalso length c = 1 andalso subset (op =) (c, conjs))
935 fun do_have outer qs (gamma, c) =
936 Prove (maybe_show outer c qs, label_of_clause c, prop_of_clause c,
937 By_Metis (fold (add_fact_from_dependency fact_names
938 o the_single) gamma ([], [])))
939 fun do_inf outer (Have z) = do_have outer [] z
940 | do_inf outer (Hence z) = do_have outer [Then] z
941 | do_inf outer (Cases cases) =
942 let val c = succedent_of_cases cases in
943 Prove (maybe_show outer c [Ultimately], label_of_clause c,
945 Case_Split (map (do_case false) cases, ([], [])))
947 and do_case outer (c, infs) =
948 Assume (label_of_clause c, prop_of_clause c) ::
949 map (do_inf outer) infs
951 (if null params then [] else [Fix params]) @
953 |> redirect_graph axioms tainted
954 |> chain_direct_proof
956 |> kill_duplicate_assumptions_in_proof
957 |> kill_useless_labels_in_proof
959 |> string_for_proof ctxt type_enc lam_trans subgoal subgoal_count
963 if isar_proof_requested then
964 "\nNo structured proof available (proof too short)."
968 "\n\n" ^ (if isar_proof_requested then "Structured proof"
969 else "Perhaps this will work") ^
970 ":\n" ^ Markup.markup Isabelle_Markup.sendback isar_proof
975 else case try isar_proof_of () of
977 | NONE => if isar_proof_requested then
978 "\nWarning: The Isar proof construction failed."
981 in one_line_proof ^ isar_proof end
983 fun proof_text ctxt isar_proof isar_params
984 (one_line_params as (preplay, _, _, _, _, _)) =
985 (if case preplay of Failed_to_Play _ => true | _ => isar_proof then
986 isar_proof_text ctxt isar_proof isar_params
988 one_line_proof_text) one_line_params