--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/Sledgehammer/sledgehammer_fact.ML Wed Jul 11 21:43:19 2012 +0200
@@ -0,0 +1,439 @@
+(* Title: HOL/Tools/Sledgehammer/sledgehammer_fact.ML
+ Author: Jia Meng, Cambridge University Computer Laboratory and NICTA
+ Author: Jasmin Blanchette, TU Muenchen
+
+Sledgehammer fact handling.
+*)
+
+signature SLEDGEHAMMER_FACT =
+sig
+ type status = ATP_Problem_Generate.status
+ type stature = ATP_Problem_Generate.stature
+
+ type relevance_override =
+ {add : (Facts.ref * Attrib.src list) list,
+ del : (Facts.ref * Attrib.src list) list,
+ only : bool}
+
+ val ignore_no_atp : bool Config.T
+ val instantiate_inducts : bool Config.T
+ val no_relevance_override : relevance_override
+ val fact_from_ref :
+ Proof.context -> unit Symtab.table -> thm list -> status Termtab.table
+ -> Facts.ref * Attrib.src list -> ((string * stature) * thm) list
+ val all_facts :
+ Proof.context -> bool -> 'a Symtab.table -> bool -> thm list
+ -> thm list -> status Termtab.table
+ -> (((unit -> string) * stature) * thm) list
+ val clasimpset_rule_table_of : Proof.context -> status Termtab.table
+ val maybe_instantiate_inducts :
+ Proof.context -> term list -> term -> (((unit -> string) * 'a) * thm) list
+ -> (((unit -> string) * 'a) * thm) list
+ val maybe_filter_no_atps : Proof.context -> ('a * thm) list -> ('a * thm) list
+ val nearly_all_facts :
+ Proof.context -> bool -> relevance_override -> thm list -> term list -> term
+ -> (((unit -> string) * stature) * thm) list
+end;
+
+structure Sledgehammer_Fact : SLEDGEHAMMER_FACT =
+struct
+
+open ATP_Problem_Generate
+open Metis_Tactic
+open Sledgehammer_Util
+
+type relevance_override =
+ {add : (Facts.ref * Attrib.src list) list,
+ del : (Facts.ref * Attrib.src list) list,
+ only : bool}
+
+val sledgehammer_prefix = "Sledgehammer" ^ Long_Name.separator
+
+(* experimental features *)
+val ignore_no_atp =
+ Attrib.setup_config_bool @{binding sledgehammer_ignore_no_atp} (K false)
+val instantiate_inducts =
+ Attrib.setup_config_bool @{binding sledgehammer_instantiate_inducts} (K false)
+
+val no_relevance_override = {add = [], del = [], only = false}
+
+fun needs_quoting reserved s =
+ Symtab.defined reserved s orelse
+ exists (not o Lexicon.is_identifier) (Long_Name.explode s)
+
+fun make_name reserved multi j name =
+ (name |> needs_quoting reserved name ? quote) ^
+ (if multi then "(" ^ string_of_int j ^ ")" else "")
+
+fun explode_interval _ (Facts.FromTo (i, j)) = i upto j
+ | explode_interval max (Facts.From i) = i upto i + max - 1
+ | explode_interval _ (Facts.Single i) = [i]
+
+val backquote =
+ raw_explode #> map (fn "`" => "\\`" | s => s) #> implode #> enclose "`" "`"
+
+(* unfolding these can yield really huge terms *)
+val risky_defs = @{thms Bit0_def Bit1_def}
+
+fun is_rec_eq lhs = Term.exists_subterm (curry (op =) (head_of lhs))
+fun is_rec_def (@{const Trueprop} $ t) = is_rec_def t
+ | is_rec_def (@{const ==>} $ _ $ t2) = is_rec_def t2
+ | is_rec_def (Const (@{const_name "=="}, _) $ t1 $ t2) = is_rec_eq t1 t2
+ | is_rec_def (Const (@{const_name HOL.eq}, _) $ t1 $ t2) = is_rec_eq t1 t2
+ | is_rec_def _ = false
+
+fun is_assum assms th = exists (fn ct => prop_of th aconv term_of ct) assms
+fun is_chained chained_ths = member Thm.eq_thm_prop chained_ths
+
+fun scope_of_thm global assms chained_ths th =
+ if is_chained chained_ths th then Chained
+ else if global then Global
+ else if is_assum assms th then Assum
+ else Local
+
+val may_be_induction =
+ exists_subterm (fn Var (_, Type (@{type_name fun}, [_, T])) =>
+ body_type T = @{typ bool}
+ | _ => false)
+
+fun status_of_thm css_table name th =
+ (* FIXME: use structured name *)
+ if (String.isSubstring ".induct" name orelse
+ String.isSubstring ".inducts" name) andalso
+ may_be_induction (prop_of th) then
+ Induction
+ else case Termtab.lookup css_table (prop_of th) of
+ SOME status => status
+ | NONE => General
+
+fun stature_of_thm global assms chained_ths css_table name th =
+ (scope_of_thm global assms chained_ths th, status_of_thm css_table name th)
+
+fun fact_from_ref ctxt reserved chained_ths css_table (xthm as (xref, args)) =
+ let
+ val ths = Attrib.eval_thms ctxt [xthm]
+ val bracket =
+ map (enclose "[" "]" o Pretty.str_of o Args.pretty_src ctxt) args
+ |> implode
+ fun nth_name j =
+ case xref of
+ Facts.Fact s => backquote s ^ bracket
+ | Facts.Named (("", _), _) => "[" ^ bracket ^ "]"
+ | Facts.Named ((name, _), NONE) =>
+ make_name reserved (length ths > 1) (j + 1) name ^ bracket
+ | Facts.Named ((name, _), SOME intervals) =>
+ make_name reserved true
+ (nth (maps (explode_interval (length ths)) intervals) j) name ^
+ bracket
+ in
+ (ths, (0, []))
+ |-> fold (fn th => fn (j, rest) =>
+ let val name = nth_name j in
+ (j + 1, ((name, stature_of_thm false [] chained_ths
+ css_table name th), th) :: rest)
+ end)
+ |> snd
+ end
+
+(* Reject theorems with names like "List.filter.filter_list_def" or
+ "Accessible_Part.acc.defs", as these are definitions arising from packages. *)
+fun is_package_def a =
+ let val names = Long_Name.explode a in
+ (length names > 2 andalso not (hd names = "local") andalso
+ String.isSuffix "_def" a) orelse String.isSuffix "_defs" a
+ end
+
+(* FIXME: put other record thms here, or declare as "no_atp" *)
+fun multi_base_blacklist ctxt ho_atp =
+ ["defs", "select_defs", "update_defs", "split", "splits", "split_asm",
+ "cases", "ext_cases", "eq.simps", "eq.refl", "nchotomy", "case_cong",
+ "weak_case_cong"]
+ |> not (ho_atp orelse (Config.get ctxt instantiate_inducts)) ?
+ append ["induct", "inducts"]
+ |> map (prefix ".")
+
+val max_lambda_nesting = 3 (*only applies if not ho_atp*)
+
+fun term_has_too_many_lambdas max (t1 $ t2) =
+ exists (term_has_too_many_lambdas max) [t1, t2]
+ | term_has_too_many_lambdas max (Abs (_, _, t)) =
+ max = 0 orelse term_has_too_many_lambdas (max - 1) t
+ | term_has_too_many_lambdas _ _ = false
+
+(* Don't count nested lambdas at the level of formulas, since they are
+ quantifiers. *)
+fun formula_has_too_many_lambdas true _ _ = false (*i.e. ho_atp*)
+ | formula_has_too_many_lambdas _ Ts (Abs (_, T, t)) =
+ formula_has_too_many_lambdas false (T :: Ts) t
+ | formula_has_too_many_lambdas _ Ts t =
+ if member (op =) [HOLogic.boolT, propT] (fastype_of1 (Ts, t)) then
+ exists (formula_has_too_many_lambdas false Ts) (#2 (strip_comb t))
+ else
+ term_has_too_many_lambdas max_lambda_nesting t
+
+(* The max apply depth of any "metis" call in "Metis_Examples" (on 2007-10-31)
+ was 11. *)
+val max_apply_depth = 15
+
+fun apply_depth (f $ t) = Int.max (apply_depth f, apply_depth t + 1)
+ | apply_depth (Abs (_, _, t)) = apply_depth t
+ | apply_depth _ = 0
+
+fun is_formula_too_complex ho_atp t =
+ apply_depth t > max_apply_depth orelse formula_has_too_many_lambdas ho_atp [] t
+
+(* FIXME: Extend to "Meson" and "Metis" *)
+val exists_sledgehammer_const =
+ exists_Const (fn (s, _) => String.isPrefix sledgehammer_prefix s)
+
+(* FIXME: make more reliable *)
+val exists_low_level_class_const =
+ exists_Const (fn (s, _) =>
+ s = @{const_name equal_class.equal} orelse
+ String.isSubstring (Long_Name.separator ^ "class" ^ Long_Name.separator) s)
+
+fun is_metastrange_theorem th =
+ case head_of (concl_of th) of
+ Const (s, _) => (s <> @{const_name Trueprop} andalso
+ s <> @{const_name "=="})
+ | _ => false
+
+fun is_that_fact th =
+ String.isSuffix (Long_Name.separator ^ Obtain.thatN) (Thm.get_name_hint th)
+ andalso exists_subterm (fn Free (s, _) => s = Name.skolem Auto_Bind.thesisN
+ | _ => false) (prop_of th)
+
+fun is_theorem_bad_for_atps ho_atp exporter thm =
+ is_metastrange_theorem thm orelse
+ (not exporter andalso
+ let val t = prop_of thm in
+ is_formula_too_complex ho_atp t orelse exists_type type_has_top_sort t orelse
+ exists_sledgehammer_const t orelse exists_low_level_class_const t orelse
+ is_that_fact thm
+ end)
+
+fun hackish_string_for_term ctxt t =
+ Print_Mode.setmp (filter (curry (op =) Symbol.xsymbolsN)
+ (print_mode_value ())) (Syntax.string_of_term ctxt) t
+ |> String.translate (fn c => if Char.isPrint c then str c else "")
+ |> simplify_spaces
+
+(* This is a terrible hack. Free variables are sometimes coded as "M__" when
+ they are displayed as "M" and we want to avoid clashes with these. But
+ sometimes it's even worse: "Ma__" encodes "M". So we simply reserve all
+ prefixes of all free variables. In the worse case scenario, where the fact
+ won't be resolved correctly, the user can fix it manually, e.g., by naming
+ the fact in question. Ideally we would need nothing of it, but backticks
+ simply don't work with schematic variables. *)
+fun all_prefixes_of s =
+ map (fn i => String.extract (s, 0, SOME i)) (1 upto size s - 1)
+
+fun close_form t =
+ (t, [] |> Term.add_free_names t |> maps all_prefixes_of)
+ |> fold (fn ((s, i), T) => fn (t', taken) =>
+ let val s' = singleton (Name.variant_list taken) s in
+ ((if fastype_of t' = HOLogic.boolT then HOLogic.all_const
+ else Logic.all_const) T
+ $ Abs (s', T, abstract_over (Var ((s, i), T), t')),
+ s' :: taken)
+ end)
+ (Term.add_vars t [] |> sort_wrt (fst o fst))
+ |> fst
+
+fun all_facts ctxt ho_atp reserved exporter add_ths chained_ths css_table =
+ let
+ val thy = Proof_Context.theory_of ctxt
+ val global_facts = Global_Theory.facts_of thy
+ val local_facts = Proof_Context.facts_of ctxt
+ val named_locals = local_facts |> Facts.dest_static []
+ val assms = Assumption.all_assms_of ctxt
+ fun is_good_unnamed_local th =
+ not (Thm.has_name_hint th) andalso
+ forall (fn (_, ths) => not (member Thm.eq_thm_prop ths th)) named_locals
+ val unnamed_locals =
+ union Thm.eq_thm_prop (Facts.props local_facts) chained_ths
+ |> filter is_good_unnamed_local |> map (pair "" o single)
+ val full_space =
+ Name_Space.merge (Facts.space_of global_facts, Facts.space_of local_facts)
+ fun add_facts global foldx facts =
+ foldx (fn (name0, ths) =>
+ if not exporter andalso name0 <> "" andalso
+ forall (not o member Thm.eq_thm_prop add_ths) ths andalso
+ (Facts.is_concealed facts name0 orelse
+ (not (Config.get ctxt ignore_no_atp) andalso
+ is_package_def name0) orelse
+ exists (fn s => String.isSuffix s name0)
+ (multi_base_blacklist ctxt ho_atp)) then
+ I
+ else
+ let
+ val multi = length ths > 1
+ val backquote_thm =
+ backquote o hackish_string_for_term ctxt o close_form o prop_of
+ fun check_thms a =
+ case try (Proof_Context.get_thms ctxt) a of
+ NONE => false
+ | SOME ths' => eq_list Thm.eq_thm_prop (ths, ths')
+ in
+ pair 1
+ #> fold (fn th => fn (j, (multis, unis)) =>
+ (j + 1,
+ if not (member Thm.eq_thm_prop add_ths th) andalso
+ is_theorem_bad_for_atps ho_atp exporter th then
+ (multis, unis)
+ else
+ let
+ val new =
+ (((fn () =>
+ if name0 = "" then
+ th |> backquote_thm
+ else
+ [Facts.extern ctxt facts name0,
+ Name_Space.extern ctxt full_space name0,
+ name0]
+ |> find_first check_thms
+ |> (fn SOME name =>
+ make_name reserved multi j name
+ | NONE => "")),
+ stature_of_thm global assms chained_ths
+ css_table name0 th), th)
+ in
+ if multi then (new :: multis, unis)
+ else (multis, new :: unis)
+ end)) ths
+ #> snd
+ end)
+ in
+ (* The single-name theorems go after the multiple-name ones, so that single
+ names are preferred when both are available. *)
+ ([], []) |> add_facts false fold local_facts (unnamed_locals @ named_locals)
+ |> add_facts true Facts.fold_static global_facts global_facts
+ |> op @
+ end
+
+fun clasimpset_rule_table_of ctxt =
+ let
+ val thy = Proof_Context.theory_of ctxt
+ val atomize = HOLogic.mk_Trueprop o Object_Logic.atomize_term thy
+ fun add stature normalizers get_th =
+ fold (fn rule =>
+ let
+ val th = rule |> get_th
+ val t =
+ th |> Thm.maxidx_of th > 0 ? zero_var_indexes |> prop_of
+ in
+ fold (fn normalize => Termtab.update (normalize t, stature))
+ (I :: normalizers)
+ end)
+ val {safeIs, (* safeEs, *) hazIs, (* hazEs, *) ...} =
+ ctxt |> claset_of |> Classical.rep_cs
+ val intros = Item_Net.content safeIs @ Item_Net.content hazIs
+(* Add once it is used:
+ val elims =
+ Item_Net.content safeEs @ Item_Net.content hazEs
+ |> map Classical.classical_rule
+*)
+ val simps = ctxt |> simpset_of |> dest_ss |> #simps
+ val specs = ctxt |> Spec_Rules.get
+ val (rec_defs, nonrec_defs) =
+ specs |> filter (curry (op =) Spec_Rules.Equational o fst)
+ |> maps (snd o snd)
+ |> filter_out (member Thm.eq_thm_prop risky_defs)
+ |> List.partition (is_rec_def o prop_of)
+ val spec_intros =
+ specs |> filter (member (op =) [Spec_Rules.Inductive,
+ Spec_Rules.Co_Inductive] o fst)
+ |> maps (snd o snd)
+ in
+ Termtab.empty |> add Simp [atomize] snd simps
+ |> add Simp [] I rec_defs
+ |> add Def [] I nonrec_defs
+(* Add once it is used:
+ |> add Elim [] I elims
+*)
+ |> add Intro [] I intros
+ |> add Inductive [] I spec_intros
+ end
+
+fun uniquify xs =
+ Termtab.fold (cons o snd)
+ (fold (Termtab.update o `(prop_of o snd)) xs Termtab.empty) []
+
+fun struct_induct_rule_on th =
+ case Logic.strip_horn (prop_of th) of
+ (prems, @{const Trueprop}
+ $ ((p as Var ((p_name, 0), _)) $ (a as Var (_, ind_T)))) =>
+ if not (is_TVar ind_T) andalso length prems > 1 andalso
+ exists (exists_subterm (curry (op aconv) p)) prems andalso
+ not (exists (exists_subterm (curry (op aconv) a)) prems) then
+ SOME (p_name, ind_T)
+ else
+ NONE
+ | _ => NONE
+
+fun instantiate_induct_rule ctxt concl_prop p_name ((name, stature), th) ind_x =
+ let
+ fun varify_noninducts (t as Free (s, T)) =
+ if (s, T) = ind_x orelse can dest_funT T then t else Var ((s, 0), T)
+ | varify_noninducts t = t
+ val p_inst =
+ concl_prop |> map_aterms varify_noninducts |> close_form
+ |> lambda (Free ind_x)
+ |> hackish_string_for_term ctxt
+ in
+ ((fn () => name () ^ "[where " ^ p_name ^ " = " ^ quote p_inst ^ "]",
+ stature), th |> read_instantiate ctxt [((p_name, 0), p_inst)])
+ end
+
+fun type_match thy (T1, T2) =
+ (Sign.typ_match thy (T2, T1) Vartab.empty; true)
+ handle Type.TYPE_MATCH => false
+
+fun instantiate_if_induct_rule ctxt stmt stmt_xs (ax as (_, th)) =
+ case struct_induct_rule_on th of
+ SOME (p_name, ind_T) =>
+ let val thy = Proof_Context.theory_of ctxt in
+ stmt_xs |> filter (fn (_, T) => type_match thy (T, ind_T))
+ |> map_filter (try (instantiate_induct_rule ctxt stmt p_name ax))
+ end
+ | NONE => [ax]
+
+fun external_frees t =
+ [] |> Term.add_frees t |> filter_out (can Name.dest_internal o fst)
+
+fun maybe_instantiate_inducts ctxt hyp_ts concl_t =
+ if Config.get ctxt instantiate_inducts then
+ let
+ val thy = Proof_Context.theory_of ctxt
+ val ind_stmt =
+ (hyp_ts |> filter_out (null o external_frees), concl_t)
+ |> Logic.list_implies |> Object_Logic.atomize_term thy
+ val ind_stmt_xs = external_frees ind_stmt
+ in maps (instantiate_if_induct_rule ctxt ind_stmt ind_stmt_xs) end
+ else
+ I
+
+fun maybe_filter_no_atps ctxt =
+ not (Config.get ctxt ignore_no_atp) ? filter_out (No_ATPs.member ctxt o snd)
+
+fun nearly_all_facts ctxt ho_atp ({add, only, ...} : relevance_override)
+ chained_ths hyp_ts concl_t =
+ if only andalso null add then
+ []
+ else
+ let
+ val reserved = reserved_isar_keyword_table ()
+ val add_ths = Attrib.eval_thms ctxt add
+ val css_table = clasimpset_rule_table_of ctxt
+ in
+ (if only then
+ maps (map (fn ((name, stature), th) => ((K name, stature), th))
+ o fact_from_ref ctxt reserved chained_ths css_table) add
+ else
+ all_facts ctxt ho_atp reserved false add_ths chained_ths css_table)
+ |> maybe_instantiate_inducts ctxt hyp_ts concl_t
+ |> not only ? maybe_filter_no_atps ctxt
+ |> uniquify
+ end
+
+end;