src/HOL/Tools/Sledgehammer/sledgehammer_fact.ML
author blanchet
Tue Sep 10 15:56:52 2013 +0200 (2013-09-10 ago)
changeset 53513 1082a6fb36c6
parent 53512 b9bc867e49f6
child 53529 1eb7c65b526c
permissions -rw-r--r--
faster detection of tautologies
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(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_fact.ML
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    Author:     Jia Meng, Cambridge University Computer Laboratory and NICTA
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    Author:     Jasmin Blanchette, TU Muenchen
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Sledgehammer fact handling.
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*)
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signature SLEDGEHAMMER_FACT =
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sig
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  type status = ATP_Problem_Generate.status
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  type stature = ATP_Problem_Generate.stature
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  type raw_fact = ((unit -> string) * stature) * thm
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  type fact = (string * stature) * thm
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  type fact_override =
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    {add : (Facts.ref * Attrib.src list) list,
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     del : (Facts.ref * Attrib.src list) list,
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     only : bool}
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  val instantiate_inducts : bool Config.T
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  val no_fact_override : fact_override
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  val fact_of_ref :
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    Proof.context -> unit Symtab.table -> thm list -> status Termtab.table
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    -> Facts.ref * Attrib.src list -> ((string * stature) * thm) list
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  val backquote_thm : Proof.context -> thm -> string
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  val is_blacklisted_or_something : Proof.context -> bool -> string -> bool
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  val clasimpset_rule_table_of : Proof.context -> status Termtab.table
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  val build_name_tables :
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    (thm -> string) -> ('a * thm) list
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    -> string Symtab.table * string Symtab.table
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  val maybe_instantiate_inducts :
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    Proof.context -> term list -> term -> (((unit -> string) * 'a) * thm) list
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    -> (((unit -> string) * 'a) * thm) list
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  val fact_of_raw_fact : raw_fact -> fact
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  val all_facts :
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    Proof.context -> bool -> bool -> unit Symtab.table -> thm list -> thm list
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    -> status Termtab.table -> raw_fact list
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  val nearly_all_facts :
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    Proof.context -> bool -> fact_override -> unit Symtab.table
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    -> status Termtab.table -> thm list -> term list -> term -> raw_fact list
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end;
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structure Sledgehammer_Fact : SLEDGEHAMMER_FACT =
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struct
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open ATP_Util
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open ATP_Problem_Generate
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open Metis_Tactic
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open Sledgehammer_Util
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type raw_fact = ((unit -> string) * stature) * thm
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type fact = (string * stature) * thm
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type fact_override =
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  {add : (Facts.ref * Attrib.src list) list,
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   del : (Facts.ref * Attrib.src list) list,
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   only : bool}
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(* experimental feature *)
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val instantiate_inducts =
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  Attrib.setup_config_bool @{binding sledgehammer_instantiate_inducts} (K false)
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val no_fact_override = {add = [], del = [], only = false}
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fun needs_quoting reserved s =
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  Symtab.defined reserved s orelse
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  exists (not o Symbol_Pos.is_identifier) (Long_Name.explode s)
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fun make_name reserved multi j name =
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  (name |> needs_quoting reserved name ? quote) ^
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  (if multi then "(" ^ string_of_int j ^ ")" else "")
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fun explode_interval _ (Facts.FromTo (i, j)) = i upto j
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  | explode_interval max (Facts.From i) = i upto i + max - 1
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  | explode_interval _ (Facts.Single i) = [i]
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val backquote =
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  raw_explode #> map (fn "`" => "\\`" | s => s) #> implode #> enclose "`" "`"
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(* unfolding these can yield really huge terms *)
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val risky_defs = @{thms Bit0_def Bit1_def}
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fun is_rec_eq lhs = Term.exists_subterm (curry (op =) (head_of lhs))
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fun is_rec_def (@{const Trueprop} $ t) = is_rec_def t
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  | is_rec_def (@{const ==>} $ _ $ t2) = is_rec_def t2
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  | is_rec_def (Const (@{const_name "=="}, _) $ t1 $ t2) = is_rec_eq t1 t2
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  | is_rec_def (Const (@{const_name HOL.eq}, _) $ t1 $ t2) = is_rec_eq t1 t2
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  | is_rec_def _ = false
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fun is_assum assms th = exists (fn ct => prop_of th aconv term_of ct) assms
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fun is_chained chained = member Thm.eq_thm_prop chained
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fun scope_of_thm global assms chained th =
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  if is_chained chained th then Chained
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  else if global then Global
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  else if is_assum assms th then Assum
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  else Local
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val may_be_induction =
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  exists_subterm (fn Var (_, Type (@{type_name fun}, [_, T])) =>
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                     body_type T = @{typ bool}
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                   | _ => false)
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fun normalize_vars t =
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  let
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    fun normT (Type (s, Ts)) = fold_map normT Ts #>> curry Type s
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      | normT (TVar (z as (_, S))) =
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        (fn ((knownT, nT), accum) =>
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            case find_index (equal z) knownT of
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              ~1 => (TVar ((Name.uu, nT), S), ((z :: knownT, nT + 1), accum))
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            | j => (TVar ((Name.uu, nT - j - 1), S), ((knownT, nT), accum)))
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      | normT (T as TFree _) = pair T
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    fun norm (t $ u) = norm t ##>> norm u #>> op $
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      | norm (Const (s, T)) = normT T #>> curry Const s
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      | norm (Var (z as (_, T))) =
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        normT T
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        #> (fn (T, (accumT, (known, n))) =>
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               case find_index (equal z) known of
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                 ~1 => (Var ((Name.uu, n), T), (accumT, (z :: known, n + 1)))
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               | j => (Var ((Name.uu, n - j - 1), T), (accumT, (known, n))))
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      | norm (Abs (_, T, t)) =
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        norm t ##>> normT T #>> (fn (t, T) => Abs (Name.uu, T, t))
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      | norm (Bound j) = pair (Bound j)
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      | norm (Free (s, T)) = normT T #>> curry Free s
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  in fst (norm t (([], 0), ([], 0))) end
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fun status_of_thm css name th =
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  let val t = normalize_vars (prop_of th) in
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    (* FIXME: use structured name *)
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    if String.isSubstring ".induct" name andalso may_be_induction t then
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      Induction
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    else case Termtab.lookup css t of
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      SOME status => status
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    | NONE =>
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      let val concl = Logic.strip_imp_concl t in
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        case try (HOLogic.dest_eq o HOLogic.dest_Trueprop) concl of
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          SOME lrhss =>
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          let
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            val prems = Logic.strip_imp_prems t
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            val t' = Logic.list_implies (prems, Logic.mk_equals lrhss)
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          in
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            Termtab.lookup css t' |> the_default General
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          end
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        | NONE => General
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      end
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  end
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fun stature_of_thm global assms chained css name th =
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  (scope_of_thm global assms chained th, status_of_thm css name th)
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fun fact_of_ref ctxt reserved chained css (xthm as (xref, args)) =
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  let
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    val ths = Attrib.eval_thms ctxt [xthm]
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    val bracket =
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      map (enclose "[" "]" o Pretty.str_of o Args.pretty_src ctxt) args
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      |> implode
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    fun nth_name j =
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      case xref of
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        Facts.Fact s => backquote s ^ bracket
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      | Facts.Named (("", _), _) => "[" ^ bracket ^ "]"
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      | Facts.Named ((name, _), NONE) =>
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        make_name reserved (length ths > 1) (j + 1) name ^ bracket
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      | Facts.Named ((name, _), SOME intervals) =>
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        make_name reserved true
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                 (nth (maps (explode_interval (length ths)) intervals) j) name ^
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        bracket
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    fun add_nth th (j, rest) =
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      let val name = nth_name j in
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        (j + 1, ((name, stature_of_thm false [] chained css name th), th)
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                :: rest)
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      end
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  in (0, []) |> fold add_nth ths |> snd end
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(* Reject theorems with names like "List.filter.filter_list_def" or
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  "Accessible_Part.acc.defs", as these are definitions arising from packages. *)
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fun is_package_def s =
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  let val ss = Long_Name.explode s in
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    length ss > 2 andalso not (hd ss = "local") andalso
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    exists (fn suf => String.isSuffix suf s)
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           ["_case_def", "_rec_def", "_size_def", "_size_overloaded_def"]
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  end
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(* FIXME: put other record thms here, or declare as "no_atp" *)
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fun multi_base_blacklist ctxt ho_atp =
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  ["defs", "select_defs", "update_defs", "split", "splits", "split_asm",
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   "ext_cases", "eq.simps", "eq.refl", "nchotomy", "case_cong",
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   "weak_case_cong", "nat_of_char_simps", "nibble.simps",
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   "nibble.distinct"]
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  |> not (ho_atp orelse (Config.get ctxt instantiate_inducts)) ?
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        append ["induct", "inducts"]
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  |> map (prefix Long_Name.separator)
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(* FIXME: Ad hoc list *)
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val technical_prefixes =
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  ["ATP", "Code_Evaluation", "Datatype", "Enum", "Lazy_Sequence",
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   "Limited_Sequence", "Meson", "Metis", "Nitpick",
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   "Quickcheck_Random", "Quickcheck_Exhaustive", "Quickcheck_Narrowing",
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   "Random_Sequence", "Sledgehammer", "SMT"]
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  |> map (suffix Long_Name.separator)
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fun is_technical_const (s, _) =
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  exists (fn pref => String.isPrefix pref s) technical_prefixes
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(* FIXME: make more reliable *)
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val sep_class_sep = Long_Name.separator ^ "class" ^ Long_Name.separator
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fun is_low_level_class_const (s, _) =
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  s = @{const_name equal_class.equal} orelse String.isSubstring sep_class_sep s
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val sep_that = Long_Name.separator ^ Obtain.thatN
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fun is_that_fact th =
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  String.isSuffix sep_that (Thm.get_name_hint th)
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  andalso exists_subterm (fn Free (s, _) => s = Name.skolem Auto_Bind.thesisN
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                           | _ => false) (prop_of th)
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datatype interest = Deal_Breaker | Interesting | Boring
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fun combine_interests Deal_Breaker _ = Deal_Breaker
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  | combine_interests _ Deal_Breaker = Deal_Breaker
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  | combine_interests Interesting _ = Interesting
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  | combine_interests _ Interesting = Interesting
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  | combine_interests Boring Boring = Boring
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fun is_likely_tautology_too_meta_or_too_technical th =
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  let
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    fun is_interesting_subterm (Const (s, _)) =
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        not (member (op =) atp_widely_irrelevant_consts s)
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      | is_interesting_subterm (Free _) = true
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      | is_interesting_subterm _ = false
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    fun interest_of_bool t =
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      if exists_Const (is_technical_const orf is_low_level_class_const) t then
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        Deal_Breaker
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      else if exists_type (exists_subtype (curry (op =) @{typ prop})) t orelse
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              not (exists_subterm is_interesting_subterm t) then
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        Boring
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      else
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        Interesting
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    fun interest_of_prop _ (@{const Trueprop} $ t) = interest_of_bool t
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      | interest_of_prop Ts (@{const "==>"} $ t $ u) =
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        combine_interests (interest_of_prop Ts t) (interest_of_prop Ts u)
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      | interest_of_prop Ts (Const (@{const_name all}, _) $ Abs (_, T, t)) =
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        interest_of_prop (T :: Ts) t
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      | interest_of_prop Ts ((t as Const (@{const_name all}, _)) $ u) =
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        interest_of_prop Ts (t $ eta_expand Ts u 1)
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      | interest_of_prop _ (Const (@{const_name "=="}, _) $ t $ u) =
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        combine_interests (interest_of_bool t) (interest_of_bool u)
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      | interest_of_prop _ _ = Deal_Breaker
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    val t = prop_of th
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  in
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    (interest_of_prop [] t <> Interesting andalso
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     not (Thm.eq_thm_prop (@{thm ext}, th))) orelse
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    is_that_fact th
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  end
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fun is_blacklisted_or_something ctxt ho_atp =
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  let
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    val blist = multi_base_blacklist ctxt ho_atp
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    fun is_blisted name =
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      is_package_def name orelse exists (fn s => String.isSuffix s name) blist
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  in is_blisted end
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fun hackish_string_of_term ctxt =
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  with_vanilla_print_mode (Syntax.string_of_term ctxt) #> simplify_spaces
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(* This is a terrible hack. Free variables are sometimes coded as "M__" when
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   they are displayed as "M" and we want to avoid clashes with these. But
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   sometimes it's even worse: "Ma__" encodes "M". So we simply reserve all
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   prefixes of all free variables. In the worse case scenario, where the fact
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   won't be resolved correctly, the user can fix it manually, e.g., by giving a
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   name to the offending fact. *)
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fun all_prefixes_of s =
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  map (fn i => String.extract (s, 0, SOME i)) (1 upto size s - 1)
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fun close_form t =
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  (t, [] |> Term.add_free_names t |> maps all_prefixes_of)
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  |> fold (fn ((s, i), T) => fn (t', taken) =>
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              let val s' = singleton (Name.variant_list taken) s in
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                ((if fastype_of t' = HOLogic.boolT then HOLogic.all_const
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                  else Logic.all_const) T
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                 $ Abs (s', T, abstract_over (Var ((s, i), T), t')),
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                 s' :: taken)
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              end)
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          (Term.add_vars t [] |> sort_wrt (fst o fst))
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  |> fst
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fun backquote_term ctxt = close_form #> hackish_string_of_term ctxt #> backquote
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fun backquote_thm ctxt = backquote_term ctxt o prop_of
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(* gracefully handle huge background theories *)
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val max_simps_for_clasimpset = 10000
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fun clasimpset_rule_table_of ctxt =
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  let val simps = ctxt |> simpset_of |> dest_ss |> #simps in
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    if length simps >= max_simps_for_clasimpset then
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      Termtab.empty
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    else
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      let
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        fun add stature th =
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          Termtab.update (normalize_vars (prop_of th), stature)
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        val {safeIs, (* safeEs, *) hazIs, (* hazEs, *) ...} =
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          ctxt |> claset_of |> Classical.rep_cs
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        val intros = Item_Net.content safeIs @ Item_Net.content hazIs
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(* Add once it is used:
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        val elims =
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          Item_Net.content safeEs @ Item_Net.content hazEs
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          |> map Classical.classical_rule
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*)
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        val specs = ctxt |> Spec_Rules.get
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        val (rec_defs, nonrec_defs) =
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          specs |> filter (curry (op =) Spec_Rules.Equational o fst)
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                |> maps (snd o snd)
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                |> filter_out (member Thm.eq_thm_prop risky_defs)
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                |> List.partition (is_rec_def o prop_of)
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        val spec_intros =
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          specs |> filter (member (op =) [Spec_Rules.Inductive,
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                                          Spec_Rules.Co_Inductive] o fst)
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                |> maps (snd o snd)
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      in
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        Termtab.empty |> fold (add Simp o snd) simps
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                      |> fold (add Rec_Def) rec_defs
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                      |> fold (add Non_Rec_Def) nonrec_defs
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(* Add once it is used:
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                      |> fold (add Elim) elims
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*)
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                      |> fold (add Intro) intros
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                      |> fold (add Inductive) spec_intros
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      end
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  end
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fun normalize_eq (t as @{const Trueprop}
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        $ ((t0 as Const (@{const_name HOL.eq}, _)) $ t1 $ t2)) =
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    if Term_Ord.fast_term_ord (t1, t2) <> GREATER then t
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    else HOLogic.mk_Trueprop (t0 $ t2 $ t1)
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  | normalize_eq (t as @{const Trueprop} $ (@{const Not}
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        $ ((t0 as Const (@{const_name HOL.eq}, _)) $ t1 $ t2))) =
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    if Term_Ord.fast_term_ord (t1, t2) <> GREATER then t
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    else HOLogic.mk_Trueprop (HOLogic.mk_not (t0 $ t2 $ t1))
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  | normalize_eq t = t
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val normalize_eq_vars = normalize_eq #> normalize_vars
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fun if_thm_before th th' =
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  if Theory.subthy (pairself Thm.theory_of_thm (th, th')) then th else th'
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(* Hack: Conflate the facts about a class as seen from the outside with the
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   corresponding low-level facts, so that MaSh can learn from the low-level
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   proofs. *)
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fun un_class_ify s =
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  case first_field "_class" s of
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    SOME (pref, suf) => [s, pref ^ suf]
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  | NONE => [s]
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fun build_name_tables name_of facts =
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  let
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    fun cons_thm (_, th) =
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      Termtab.cons_list (normalize_eq_vars (prop_of th), th)
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    fun add_plain canon alias =
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      Symtab.update (Thm.get_name_hint alias,
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                     name_of (if_thm_before canon alias))
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    fun add_plains (_, aliases as canon :: _) = fold (add_plain canon) aliases
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    fun add_inclass (name, target) =
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      fold (fn s => Symtab.update (s, target)) (un_class_ify name)
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    val prop_tab = fold cons_thm facts Termtab.empty
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    val plain_name_tab = Termtab.fold add_plains prop_tab Symtab.empty
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    val inclass_name_tab = Symtab.fold add_inclass plain_name_tab Symtab.empty
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  in (plain_name_tab, inclass_name_tab) end
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fun keyed_distinct key_of xs =
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  let val tab = fold (Termtab.default o `key_of) xs Termtab.empty in
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    Termtab.fold (cons o snd) tab []
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  end
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fun hashed_keyed_distinct hash_of key_of xs =
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  let
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    val ys = map (`hash_of) xs
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    val sorted_ys = sort (int_ord o pairself fst) ys
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    val grouped_ys = AList.coalesce (op =) sorted_ys
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  in maps (keyed_distinct key_of o snd) grouped_ys end
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fun struct_induct_rule_on th =
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  case Logic.strip_horn (prop_of th) of
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    (prems, @{const Trueprop}
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            $ ((p as Var ((p_name, 0), _)) $ (a as Var (_, ind_T)))) =>
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    if not (is_TVar ind_T) andalso length prems > 1 andalso
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       exists (exists_subterm (curry (op aconv) p)) prems andalso
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       not (exists (exists_subterm (curry (op aconv) a)) prems) then
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      SOME (p_name, ind_T)
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    else
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      NONE
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  | _ => NONE
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val instantiate_induct_timeout = seconds 0.01
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fun instantiate_induct_rule ctxt concl_prop p_name ((name, stature), th) ind_x =
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  let
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    fun varify_noninducts (t as Free (s, T)) =
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        if (s, T) = ind_x orelse can dest_funT T then t else Var ((s, 0), T)
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      | varify_noninducts t = t
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   400
    val p_inst =
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   401
      concl_prop |> map_aterms varify_noninducts |> close_form
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   402
                 |> lambda (Free ind_x)
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   403
                 |> hackish_string_of_term ctxt
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   404
  in
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   405
    ((fn () => name () ^ "[where " ^ p_name ^ " = " ^ quote p_inst ^ "]",
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   406
      stature), th |> read_instantiate ctxt [((p_name, 0), p_inst)])
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   407
  end
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   408
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   409
fun type_match thy (T1, T2) =
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   410
  (Sign.typ_match thy (T2, T1) Vartab.empty; true)
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   411
  handle Type.TYPE_MATCH => false
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   412
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   413
fun instantiate_if_induct_rule ctxt stmt stmt_xs (ax as (_, th)) =
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   414
  case struct_induct_rule_on th of
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   415
    SOME (p_name, ind_T) =>
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   416
    let val thy = Proof_Context.theory_of ctxt in
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   417
      stmt_xs |> filter (fn (_, T) => type_match thy (T, ind_T))
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   418
              |> map_filter (try (TimeLimit.timeLimit instantiate_induct_timeout
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   419
                     (instantiate_induct_rule ctxt stmt p_name ax)))
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   420
    end
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   421
  | NONE => [ax]
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   422
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   423
fun external_frees t =
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   424
  [] |> Term.add_frees t |> filter_out (can Name.dest_internal o fst)
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   425
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   426
fun maybe_instantiate_inducts ctxt hyp_ts concl_t =
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   427
  if Config.get ctxt instantiate_inducts then
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   428
    let
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   429
      val thy = Proof_Context.theory_of ctxt
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   430
      val ind_stmt =
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   431
        (hyp_ts |> filter_out (null o external_frees), concl_t)
blanchet@48250
   432
        |> Logic.list_implies |> Object_Logic.atomize_term thy
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   433
      val ind_stmt_xs = external_frees ind_stmt
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   434
    in maps (instantiate_if_induct_rule ctxt ind_stmt ind_stmt_xs) end
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   435
  else
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   436
    I
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   437
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   438
fun fact_of_raw_fact ((name, stature), th) = ((name (), stature), th)
blanchet@51004
   439
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   440
fun all_facts ctxt generous ho_atp reserved add_ths chained css =
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   441
  let
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   442
    val thy = Proof_Context.theory_of ctxt
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   443
    val global_facts = Global_Theory.facts_of thy
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   444
    val local_facts = Proof_Context.facts_of ctxt
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   445
    val named_locals = local_facts |> Facts.dest_static []
blanchet@48251
   446
    val assms = Assumption.all_assms_of ctxt
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   447
    fun is_good_unnamed_local th =
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   448
      not (Thm.has_name_hint th) andalso
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   449
      forall (fn (_, ths) => not (member Thm.eq_thm_prop ths th)) named_locals
blanchet@48251
   450
    val unnamed_locals =
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   451
      union Thm.eq_thm_prop (Facts.props local_facts) chained
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   452
      |> filter is_good_unnamed_local |> map (pair "" o single)
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   453
    val full_space =
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   454
      Name_Space.merge (Facts.space_of global_facts, Facts.space_of local_facts)
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   455
    val is_blacklisted_or_something = is_blacklisted_or_something ctxt ho_atp
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   456
    fun add_facts global foldx facts =
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   457
      foldx (fn (name0, ths) =>
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   458
        if name0 <> "" andalso
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   459
           forall (not o member Thm.eq_thm_prop add_ths) ths andalso
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   460
           (Facts.is_concealed facts name0 orelse
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   461
            (not generous andalso is_blacklisted_or_something name0)) then
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   462
          I
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   463
        else
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   464
          let
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   465
            val n = length ths
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   466
            val multi = n > 1
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   467
            fun check_thms a =
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   468
              case try (Proof_Context.get_thms ctxt) a of
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   469
                NONE => false
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   470
              | SOME ths' => eq_list Thm.eq_thm_prop (ths, ths')
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   471
          in
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   472
            pair n
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   473
            #> fold_rev (fn th => fn (j, accum) =>
blanchet@50485
   474
                   (j - 1,
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   475
                    if not (member Thm.eq_thm_prop add_ths th) andalso
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   476
                       is_likely_tautology_too_meta_or_too_technical th then
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   477
                      accum
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   478
                    else
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   479
                      let
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   480
                        val new =
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   481
                          (((fn () =>
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   482
                                if name0 = "" then
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   483
                                  backquote_thm ctxt th
blanchet@50485
   484
                                else
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   485
                                  [Facts.extern ctxt facts name0,
blanchet@50485
   486
                                   Name_Space.extern ctxt full_space name0]
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   487
                                  |> distinct (op =)
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   488
                                  |> find_first check_thms
blanchet@50485
   489
                                  |> the_default name0
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   490
                                  |> make_name reserved multi j),
blanchet@50485
   491
                             stature_of_thm global assms chained css name0 th),
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   492
                           th)
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   493
                      in
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   494
                        accum |> (if multi then apsnd else apfst) (cons new)
blanchet@50485
   495
                      end)) ths
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   496
            #> snd
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   497
          end)
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   498
  in
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   499
    (* The single-theorem names go before the multiple-theorem ones (e.g.,
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   500
       "xxx" vs. "xxx(3)"), so that single names are preferred when both are
blanchet@50756
   501
       available. *)
blanchet@50756
   502
    `I [] |> add_facts false fold local_facts (unnamed_locals @ named_locals)
blanchet@50756
   503
          |> add_facts true Facts.fold_static global_facts global_facts
blanchet@50756
   504
          |> op @
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   505
  end
blanchet@48251
   506
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   507
fun nearly_all_facts ctxt ho_atp {add, del, only} reserved css chained hyp_ts
blanchet@48396
   508
                     concl_t =
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   509
  if only andalso null add then
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   510
    []
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   511
  else
blanchet@48250
   512
    let
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   513
      val chained =
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   514
        chained
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   515
        |> maps (fn th => insert Thm.eq_thm_prop (zero_var_indexes th) [th])
blanchet@48250
   516
    in
blanchet@48250
   517
      (if only then
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   518
         maps (map (fn ((name, stature), th) => ((K name, stature), th))
blanchet@52031
   519
               o fact_of_ref ctxt reserved chained css) add
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   520
       else
blanchet@48292
   521
         let val (add, del) = pairself (Attrib.eval_thms ctxt) (add, del) in
blanchet@50442
   522
           all_facts ctxt false ho_atp reserved add chained css
blanchet@53511
   523
           |> filter_out
blanchet@53511
   524
                  ((member Thm.eq_thm_prop del orf No_ATPs.member ctxt) o snd)
blanchet@53504
   525
           |> hashed_keyed_distinct (size_of_term o prop_of o snd)
blanchet@53504
   526
                  (normalize_eq_vars o prop_of o snd)
blanchet@48292
   527
         end)
blanchet@48250
   528
      |> maybe_instantiate_inducts ctxt hyp_ts concl_t
blanchet@48250
   529
    end
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   530
blanchet@48250
   531
end;