distinguish between recursive and nonrecursive definitions + clean up typedef dependencies in MaSh
1 (* Title: HOL/Tools/Sledgehammer/sledgehammer_fact.ML
2 Author: Jia Meng, Cambridge University Computer Laboratory and NICTA
3 Author: Jasmin Blanchette, TU Muenchen
5 Sledgehammer fact handling.
8 signature SLEDGEHAMMER_FACT =
10 type status = ATP_Problem_Generate.status
11 type stature = ATP_Problem_Generate.stature
13 type fact = ((unit -> string) * stature) * thm
16 {add : (Facts.ref * Attrib.src list) list,
17 del : (Facts.ref * Attrib.src list) list,
20 val ignore_no_atp : bool Config.T
21 val instantiate_inducts : bool Config.T
22 val no_fact_override : fact_override
24 Proof.context -> unit Symtab.table -> thm list -> status Termtab.table
25 -> Facts.ref * Attrib.src list -> ((string * stature) * thm) list
26 val backquote_thm : thm -> string
27 val clasimpset_rule_table_of : Proof.context -> status Termtab.table
28 val maybe_instantiate_inducts :
29 Proof.context -> term list -> term -> (((unit -> string) * 'a) * thm) list
30 -> (((unit -> string) * 'a) * thm) list
31 val maybe_filter_no_atps : Proof.context -> ('a * thm) list -> ('a * thm) list
32 val all_facts_of : Proof.context -> status Termtab.table -> fact list
33 val nearly_all_facts :
34 Proof.context -> bool -> fact_override -> unit Symtab.table
35 -> status Termtab.table -> thm list -> term list -> term -> fact list
38 structure Sledgehammer_Fact : SLEDGEHAMMER_FACT =
41 open ATP_Problem_Generate
43 open Sledgehammer_Util
45 type fact = ((unit -> string) * stature) * thm
48 {add : (Facts.ref * Attrib.src list) list,
49 del : (Facts.ref * Attrib.src list) list,
52 val sledgehammer_prefixes =
53 ["ATP", "Meson", "Metis", "Sledgehammer"] |> map (suffix Long_Name.separator)
55 (* experimental features *)
57 Attrib.setup_config_bool @{binding sledgehammer_ignore_no_atp} (K false)
58 val instantiate_inducts =
59 Attrib.setup_config_bool @{binding sledgehammer_instantiate_inducts} (K false)
61 val no_fact_override = {add = [], del = [], only = false}
63 fun needs_quoting reserved s =
64 Symtab.defined reserved s orelse
65 exists (not o Lexicon.is_identifier) (Long_Name.explode s)
67 fun make_name reserved multi j name =
68 (name |> needs_quoting reserved name ? quote) ^
69 (if multi then "(" ^ string_of_int j ^ ")" else "")
71 fun explode_interval _ (Facts.FromTo (i, j)) = i upto j
72 | explode_interval max (Facts.From i) = i upto i + max - 1
73 | explode_interval _ (Facts.Single i) = [i]
76 raw_explode #> map (fn "`" => "\\`" | s => s) #> implode #> enclose "`" "`"
78 (* unfolding these can yield really huge terms *)
79 val risky_defs = @{thms Bit0_def Bit1_def}
81 fun is_rec_eq lhs = Term.exists_subterm (curry (op =) (head_of lhs))
82 fun is_rec_def (@{const Trueprop} $ t) = is_rec_def t
83 | is_rec_def (@{const ==>} $ _ $ t2) = is_rec_def t2
84 | is_rec_def (Const (@{const_name "=="}, _) $ t1 $ t2) = is_rec_eq t1 t2
85 | is_rec_def (Const (@{const_name HOL.eq}, _) $ t1 $ t2) = is_rec_eq t1 t2
86 | is_rec_def _ = false
88 fun is_assum assms th = exists (fn ct => prop_of th aconv term_of ct) assms
89 fun is_chained chained = member Thm.eq_thm_prop chained
91 fun scope_of_thm global assms chained th =
92 if is_chained chained th then Chained
93 else if global then Global
94 else if is_assum assms th then Assum
97 val may_be_induction =
98 exists_subterm (fn Var (_, Type (@{type_name fun}, [_, T])) =>
99 body_type T = @{typ bool}
102 fun status_of_thm css name th =
103 (* FIXME: use structured name *)
104 if (String.isSubstring ".induct" name orelse
105 String.isSubstring ".inducts" name) andalso
106 may_be_induction (prop_of th) then
108 else case Termtab.lookup css (prop_of th) of
109 SOME status => status
112 fun stature_of_thm global assms chained css name th =
113 (scope_of_thm global assms chained th, status_of_thm css name th)
115 fun fact_from_ref ctxt reserved chained css (xthm as (xref, args)) =
117 val ths = Attrib.eval_thms ctxt [xthm]
119 map (enclose "[" "]" o Pretty.str_of o Args.pretty_src ctxt) args
123 Facts.Fact s => backquote s ^ bracket
124 | Facts.Named (("", _), _) => "[" ^ bracket ^ "]"
125 | Facts.Named ((name, _), NONE) =>
126 make_name reserved (length ths > 1) (j + 1) name ^ bracket
127 | Facts.Named ((name, _), SOME intervals) =>
128 make_name reserved true
129 (nth (maps (explode_interval (length ths)) intervals) j) name ^
131 fun add_nth th (j, rest) =
132 let val name = nth_name j in
133 (j + 1, ((name, stature_of_thm false [] chained css name th), th)
136 in (0, []) |> fold add_nth ths |> snd end
138 (* Reject theorems with names like "List.filter.filter_list_def" or
139 "Accessible_Part.acc.defs", as these are definitions arising from packages. *)
140 fun is_package_def a =
141 let val names = Long_Name.explode a in
142 (length names > 2 andalso not (hd names = "local") andalso
143 String.isSuffix "_def" a) orelse String.isSuffix "_defs" a
146 (* FIXME: put other record thms here, or declare as "no_atp" *)
147 fun multi_base_blacklist ctxt ho_atp =
148 ["defs", "select_defs", "update_defs", "split", "splits", "split_asm",
149 "cases", "ext_cases", "eq.simps", "eq.refl", "nchotomy", "case_cong",
151 |> not (ho_atp orelse (Config.get ctxt instantiate_inducts)) ?
152 append ["induct", "inducts"]
155 val max_lambda_nesting = 3 (*only applies if not ho_atp*)
157 fun term_has_too_many_lambdas max (t1 $ t2) =
158 exists (term_has_too_many_lambdas max) [t1, t2]
159 | term_has_too_many_lambdas max (Abs (_, _, t)) =
160 max = 0 orelse term_has_too_many_lambdas (max - 1) t
161 | term_has_too_many_lambdas _ _ = false
163 (* Don't count nested lambdas at the level of formulas, since they are
165 fun formula_has_too_many_lambdas Ts (Abs (_, T, t)) =
166 formula_has_too_many_lambdas (T :: Ts) t
167 | formula_has_too_many_lambdas Ts t =
168 if member (op =) [HOLogic.boolT, propT] (fastype_of1 (Ts, t)) then
169 exists (formula_has_too_many_lambdas Ts) (#2 (strip_comb t))
171 term_has_too_many_lambdas max_lambda_nesting t
173 (* The max apply depth of any "metis" call in "Metis_Examples" (on 2007-10-31)
175 val max_apply_depth = 15
177 fun apply_depth (f $ t) = Int.max (apply_depth f, apply_depth t + 1)
178 | apply_depth (Abs (_, _, t)) = apply_depth t
181 fun is_formula_too_complex ho_atp t =
182 apply_depth t > max_apply_depth orelse
183 (not ho_atp andalso formula_has_too_many_lambdas [] t)
185 val exists_sledgehammer_const =
186 exists_Const (fn (s, _) =>
187 exists (fn pref => String.isPrefix pref s) sledgehammer_prefixes)
189 (* FIXME: make more reliable *)
190 val exists_low_level_class_const =
191 exists_Const (fn (s, _) =>
192 s = @{const_name equal_class.equal} orelse
193 String.isSubstring (Long_Name.separator ^ "class" ^ Long_Name.separator) s)
195 fun is_that_fact th =
196 String.isSuffix (Long_Name.separator ^ Obtain.thatN) (Thm.get_name_hint th)
197 andalso exists_subterm (fn Free (s, _) => s = Name.skolem Auto_Bind.thesisN
198 | _ => false) (prop_of th)
200 fun is_likely_tautology_or_too_meta th =
202 val is_boring_const = member (op =) atp_widely_irrelevant_consts
203 fun is_boring_bool t =
204 not (exists_Const (not o is_boring_const o fst) t) orelse
205 exists_type (exists_subtype (curry (op =) @{typ prop})) t
206 fun is_boring_prop (@{const Trueprop} $ t) = is_boring_bool t
207 | is_boring_prop (@{const "==>"} $ t $ u) =
208 is_boring_prop t andalso is_boring_prop u
209 | is_boring_prop (Const (@{const_name all}, _) $ (Abs (_, _, t)) $ u) =
210 is_boring_prop t andalso is_boring_prop u
211 | is_boring_prop (Const (@{const_name "=="}, _) $ t $ u) =
212 is_boring_bool t andalso is_boring_bool u
213 | is_boring_prop _ = true
215 is_boring_prop (prop_of th) andalso not (Thm.eq_thm_prop (@{thm ext}, th))
218 fun is_theorem_bad_for_atps ho_atp th =
219 is_likely_tautology_or_too_meta th orelse
220 let val t = prop_of th in
221 is_formula_too_complex ho_atp t orelse
222 exists_type type_has_top_sort t orelse
223 exists_sledgehammer_const t orelse exists_low_level_class_const t orelse
227 fun hackish_string_for_term thy t =
228 Print_Mode.setmp (filter (curry (op =) Symbol.xsymbolsN)
229 (print_mode_value ())) (Syntax.string_of_term_global thy) t
230 |> String.translate (fn c => if Char.isPrint c then str c else "")
233 (* This is a terrible hack. Free variables are sometimes coded as "M__" when
234 they are displayed as "M" and we want to avoid clashes with these. But
235 sometimes it's even worse: "Ma__" encodes "M". So we simply reserve all
236 prefixes of all free variables. In the worse case scenario, where the fact
237 won't be resolved correctly, the user can fix it manually, e.g., by naming
238 the fact in question. Ideally we would need nothing of it, but backticks
239 simply don't work with schematic variables. *)
240 fun all_prefixes_of s =
241 map (fn i => String.extract (s, 0, SOME i)) (1 upto size s - 1)
244 (t, [] |> Term.add_free_names t |> maps all_prefixes_of)
245 |> fold (fn ((s, i), T) => fn (t', taken) =>
246 let val s' = singleton (Name.variant_list taken) s in
247 ((if fastype_of t' = HOLogic.boolT then HOLogic.all_const
248 else Logic.all_const) T
249 $ Abs (s', T, abstract_over (Var ((s, i), T), t')),
252 (Term.add_vars t [] |> sort_wrt (fst o fst))
255 fun backquote_term thy t =
257 |> hackish_string_for_term thy
260 fun backquote_thm th = backquote_term (theory_of_thm th) (prop_of th)
262 fun clasimpset_rule_table_of ctxt =
264 val thy = Proof_Context.theory_of ctxt
265 val atomize = HOLogic.mk_Trueprop o Object_Logic.atomize_term thy
266 fun add stature normalizers get_th =
269 val th = rule |> get_th
271 th |> Thm.maxidx_of th > 0 ? zero_var_indexes |> prop_of
273 fold (fn normalize => Termtab.update (normalize t, stature))
276 val {safeIs, (* safeEs, *) hazIs, (* hazEs, *) ...} =
277 ctxt |> claset_of |> Classical.rep_cs
278 val intros = Item_Net.content safeIs @ Item_Net.content hazIs
279 (* Add once it is used:
281 Item_Net.content safeEs @ Item_Net.content hazEs
282 |> map Classical.classical_rule
284 val simps = ctxt |> simpset_of |> dest_ss |> #simps
285 val specs = ctxt |> Spec_Rules.get
286 val (rec_defs, nonrec_defs) =
287 specs |> filter (curry (op =) Spec_Rules.Equational o fst)
289 |> filter_out (member Thm.eq_thm_prop risky_defs)
290 |> List.partition (is_rec_def o prop_of)
292 specs |> filter (member (op =) [Spec_Rules.Inductive,
293 Spec_Rules.Co_Inductive] o fst)
296 Termtab.empty |> add Simp [atomize] snd simps
297 |> add Rec_Def [] I rec_defs
298 |> add Non_Rec_Def [] I nonrec_defs
299 (* Add once it is used:
300 |> add Elim [] I elims
302 |> add Intro [] I intros
303 |> add Inductive [] I spec_intros
307 Termtab.fold (cons o snd)
308 (fold (Termtab.update o `(prop_of o snd)) xs Termtab.empty) []
310 fun struct_induct_rule_on th =
311 case Logic.strip_horn (prop_of th) of
312 (prems, @{const Trueprop}
313 $ ((p as Var ((p_name, 0), _)) $ (a as Var (_, ind_T)))) =>
314 if not (is_TVar ind_T) andalso length prems > 1 andalso
315 exists (exists_subterm (curry (op aconv) p)) prems andalso
316 not (exists (exists_subterm (curry (op aconv) a)) prems) then
322 fun instantiate_induct_rule ctxt concl_prop p_name ((name, stature), th) ind_x =
324 val thy = Proof_Context.theory_of ctxt
325 fun varify_noninducts (t as Free (s, T)) =
326 if (s, T) = ind_x orelse can dest_funT T then t else Var ((s, 0), T)
327 | varify_noninducts t = t
329 concl_prop |> map_aterms varify_noninducts |> close_form
330 |> lambda (Free ind_x)
331 |> hackish_string_for_term thy
333 ((fn () => name () ^ "[where " ^ p_name ^ " = " ^ quote p_inst ^ "]",
334 stature), th |> read_instantiate ctxt [((p_name, 0), p_inst)])
337 fun type_match thy (T1, T2) =
338 (Sign.typ_match thy (T2, T1) Vartab.empty; true)
339 handle Type.TYPE_MATCH => false
341 fun instantiate_if_induct_rule ctxt stmt stmt_xs (ax as (_, th)) =
342 case struct_induct_rule_on th of
343 SOME (p_name, ind_T) =>
344 let val thy = Proof_Context.theory_of ctxt in
345 stmt_xs |> filter (fn (_, T) => type_match thy (T, ind_T))
346 |> map_filter (try (instantiate_induct_rule ctxt stmt p_name ax))
350 fun external_frees t =
351 [] |> Term.add_frees t |> filter_out (can Name.dest_internal o fst)
353 fun maybe_instantiate_inducts ctxt hyp_ts concl_t =
354 if Config.get ctxt instantiate_inducts then
356 val thy = Proof_Context.theory_of ctxt
358 (hyp_ts |> filter_out (null o external_frees), concl_t)
359 |> Logic.list_implies |> Object_Logic.atomize_term thy
360 val ind_stmt_xs = external_frees ind_stmt
361 in maps (instantiate_if_induct_rule ctxt ind_stmt ind_stmt_xs) end
365 fun maybe_filter_no_atps ctxt =
366 not (Config.get ctxt ignore_no_atp) ? filter_out (No_ATPs.member ctxt o snd)
368 fun all_facts ctxt ho_atp reserved add_ths chained css =
370 val thy = Proof_Context.theory_of ctxt
371 val global_facts = Global_Theory.facts_of thy
372 val local_facts = Proof_Context.facts_of ctxt
373 val named_locals = local_facts |> Facts.dest_static []
374 val assms = Assumption.all_assms_of ctxt
375 fun is_good_unnamed_local th =
376 not (Thm.has_name_hint th) andalso
377 forall (fn (_, ths) => not (member Thm.eq_thm_prop ths th)) named_locals
379 union Thm.eq_thm_prop (Facts.props local_facts) chained
380 |> filter is_good_unnamed_local |> map (pair "" o single)
382 Name_Space.merge (Facts.space_of global_facts, Facts.space_of local_facts)
383 fun add_facts global foldx facts =
384 foldx (fn (name0, ths) =>
385 if name0 <> "" andalso
386 forall (not o member Thm.eq_thm_prop add_ths) ths andalso
387 (Facts.is_concealed facts name0 orelse
388 not (can (Proof_Context.get_thms ctxt) name0) orelse
389 (not (Config.get ctxt ignore_no_atp) andalso
390 is_package_def name0) orelse
391 exists (fn s => String.isSuffix s name0)
392 (multi_base_blacklist ctxt ho_atp)) then
396 val multi = length ths > 1
398 case try (Proof_Context.get_thms ctxt) a of
400 | SOME ths' => eq_list Thm.eq_thm_prop (ths, ths')
403 #> fold (fn th => fn (j, (multis, unis)) =>
405 if not (member Thm.eq_thm_prop add_ths th) andalso
406 is_theorem_bad_for_atps ho_atp th then
415 [Facts.extern ctxt facts name0,
416 Name_Space.extern ctxt full_space name0]
417 |> find_first check_thms
419 |> make_name reserved multi j),
420 stature_of_thm global assms chained css name0
423 if multi then (new :: multis, unis)
424 else (multis, new :: unis)
429 (* The single-name theorems go after the multiple-name ones, so that single
430 names are preferred when both are available. *)
431 ([], []) |> add_facts false fold local_facts (unnamed_locals @ named_locals)
432 |> add_facts true Facts.fold_static global_facts global_facts
436 fun all_facts_of ctxt css =
437 all_facts ctxt false Symtab.empty [] [] css
438 |> rev (* partly restore the original order of facts, for MaSh *)
440 fun nearly_all_facts ctxt ho_atp {add, del, only} reserved css chained hyp_ts
442 if only andalso null add then
448 |> maps (fn th => insert Thm.eq_thm_prop (zero_var_indexes th) [th])
451 maps (map (fn ((name, stature), th) => ((K name, stature), th))
452 o fact_from_ref ctxt reserved chained css) add
454 let val (add, del) = pairself (Attrib.eval_thms ctxt) (add, del) in
455 all_facts ctxt ho_atp reserved add chained css
456 |> filter_out (member Thm.eq_thm_prop del o snd)
457 |> maybe_filter_no_atps ctxt
460 |> maybe_instantiate_inducts ctxt hyp_ts concl_t