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(* Title: HOL/Tools/Sledgehammer/sledgehammer_fact_filter.ML
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Author: Jia Meng, Cambridge University Computer Laboratory and NICTA
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blanchet@36393
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Author: Jasmin Blanchette, TU Muenchen
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wenzelm@33317
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*)
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paulson@15452
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signature SLEDGEHAMMER_FACT_FILTER =
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sig
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type relevance_override =
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{add: Facts.ref list,
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del: Facts.ref list,
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only: bool}
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val trace : bool Unsynchronized.ref
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val name_thm_pairs_from_ref :
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Proof.context -> unit Symtab.table -> thm list -> Facts.ref
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-> ((unit -> string * bool) * (bool * thm)) list
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val relevant_facts :
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bool -> real * real -> int -> bool -> relevance_override
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-> Proof.context * (thm list * 'a) -> term list -> term
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-> ((string * bool) * thm) list
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end;
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paulson@15347
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structure Sledgehammer_Fact_Filter : SLEDGEHAMMER_FACT_FILTER =
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struct
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open Sledgehammer_Util
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val trace = Unsynchronized.ref false
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fun trace_msg msg = if !trace then tracing (msg ()) else ()
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val respect_no_atp = true
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type relevance_override =
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{add: Facts.ref list,
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del: Facts.ref list,
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only: bool}
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paulson@21070
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val sledgehammer_prefix = "Sledgehammer" ^ Long_Name.separator
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fun repair_name reserved multi j name =
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(name |> Symtab.defined reserved name ? quote) ^
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(if multi then "(" ^ Int.toString j ^ ")" else "")
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blanchet@38983
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fun name_thm_pairs_from_ref ctxt reserved chained_ths xref =
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let
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val ths = ProofContext.get_fact ctxt xref
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val name = Facts.string_of_ref xref
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val multi = length ths > 1
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in
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fold (fn th => fn (j, rest) =>
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(j + 1, (fn () => (repair_name reserved multi j name,
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member Thm.eq_thm chained_ths th),
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(multi, th)) :: rest))
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ths (1, [])
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|> snd
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end
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(***************************************************************)
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wenzelm@28477
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(* Relevance Filtering *)
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wenzelm@28477
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(***************************************************************)
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mengj@19194
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paulson@24287
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(*** constants with types ***)
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(*An abstraction of Isabelle types*)
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datatype pseudotype = PVar | PType of string * pseudotype list
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fun string_for_pseudotype PVar = "?"
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| string_for_pseudotype (PType (s, Ts)) =
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(case Ts of
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[] => ""
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| [T] => string_for_pseudotype T
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| Ts => string_for_pseudotypes Ts ^ " ") ^ s
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and string_for_pseudotypes Ts =
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"(" ^ commas (map string_for_pseudotype Ts) ^ ")"
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paulson@24287
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(*Is the second type an instance of the first one?*)
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fun match_pseudotype (PType (a, T), PType (b, U)) =
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a = b andalso match_pseudotypes (T, U)
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| match_pseudotype (PVar, _) = true
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| match_pseudotype (_, PVar) = false
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and match_pseudotypes ([], []) = true
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| match_pseudotypes (T :: Ts, U :: Us) =
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match_pseudotype (T, U) andalso match_pseudotypes (Ts, Us)
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paulson@24287
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paulson@24287
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(*Is there a unifiable constant?*)
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blanchet@38983
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fun pseudoconst_mem f const_tab (c, c_typ) =
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exists (curry (match_pseudotypes o f) c_typ)
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(these (Symtab.lookup const_tab c))
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fun pseudotype_for (Type (c,typs)) = PType (c, map pseudotype_for typs)
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| pseudotype_for (TFree _) = PVar
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| pseudotype_for (TVar _) = PVar
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(* Pairs a constant with the list of its type instantiations. *)
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fun pseudoconst_for thy (c, T) =
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(c, map pseudotype_for (Sign.const_typargs thy (c, T)))
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handle TYPE _ => (c, []) (* Variable (locale constant): monomorphic *)
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paulson@24287
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blanchet@38983
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fun string_for_pseudoconst (s, []) = s
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| string_for_pseudoconst (s, Ts) = s ^ string_for_pseudotypes Ts
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fun string_for_super_pseudoconst (s, [[]]) = s
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blanchet@38983
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| string_for_super_pseudoconst (s, Tss) =
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s ^ "{" ^ commas (map string_for_pseudotypes Tss) ^ "}"
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paulson@24287
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val skolem_prefix = "Sledgehammer."
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blanchet@38986
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(* Add a pseudoconstant to the table, but a [] entry means a standard
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connective, which we ignore.*)
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fun add_pseudoconst_to_table also_skolem (c, ctyps) =
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if also_skolem orelse not (String.isPrefix skolem_prefix c) then
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Symtab.map_default (c, [ctyps])
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(fn [] => [] | ctypss => insert (op =) ctyps ctypss)
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else
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I
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paulson@24287
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fun is_formula_type T = (T = HOLogic.boolT orelse T = propT)
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blanchet@38931
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val flip = Option.map not
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blanchet@38337
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(* These are typically simplified away by "Meson.presimplify". *)
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blanchet@38921
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val boring_consts =
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[@{const_name False}, @{const_name True}, @{const_name If}, @{const_name Let}]
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blanchet@37533
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blanchet@38986
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fun get_pseudoconsts thy also_skolems pos ts =
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let
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(* We include free variables, as well as constants, to handle locales. For
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each quantifiers that must necessarily be skolemized by the ATP, we
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blanchet@38810
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introduce a fresh constant to simulate the effect of Skolemization. *)
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blanchet@37533
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fun do_term t =
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case t of
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Const x => add_pseudoconst_to_table also_skolems (pseudoconst_for thy x)
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| Free (s, _) => add_pseudoconst_to_table also_skolems (s, [])
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| t1 $ t2 => fold do_term [t1, t2]
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| Abs (_, _, t') => do_term t' (* FIXME: add penalty? *)
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| _ => I
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fun do_quantifier will_surely_be_skolemized body_t =
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do_formula pos body_t
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#> (if also_skolems andalso will_surely_be_skolemized then
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add_pseudoconst_to_table true (gensym skolem_prefix, [])
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else
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I)
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blanchet@38810
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and do_term_or_formula T =
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if is_formula_type T then do_formula NONE else do_term
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and do_formula pos t =
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case t of
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blanchet@37533
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Const (@{const_name all}, _) $ Abs (_, _, body_t) =>
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do_quantifier (pos = SOME false) body_t
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blanchet@37533
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| @{const "==>"} $ t1 $ t2 =>
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blanchet@37533
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do_formula (flip pos) t1 #> do_formula pos t2
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blanchet@37533
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| Const (@{const_name "=="}, Type (_, [T, _])) $ t1 $ t2 =>
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fold (do_term_or_formula T) [t1, t2]
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| @{const Trueprop} $ t1 => do_formula pos t1
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blanchet@37533
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| @{const Not} $ t1 => do_formula (flip pos) t1
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blanchet@37533
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| Const (@{const_name All}, _) $ Abs (_, _, body_t) =>
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do_quantifier (pos = SOME false) body_t
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blanchet@37533
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| Const (@{const_name Ex}, _) $ Abs (_, _, body_t) =>
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do_quantifier (pos = SOME true) body_t
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blanchet@37533
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| @{const "op &"} $ t1 $ t2 => fold (do_formula pos) [t1, t2]
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blanchet@37533
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| @{const "op |"} $ t1 $ t2 => fold (do_formula pos) [t1, t2]
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blanchet@37533
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| @{const "op -->"} $ t1 $ t2 =>
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blanchet@37533
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do_formula (flip pos) t1 #> do_formula pos t2
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blanchet@37533
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| Const (@{const_name "op ="}, Type (_, [T, _])) $ t1 $ t2 =>
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blanchet@38810
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fold (do_term_or_formula T) [t1, t2]
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blanchet@38810
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| Const (@{const_name If}, Type (_, [_, Type (_, [T, _])]))
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blanchet@38810
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$ t1 $ t2 $ t3 =>
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blanchet@38810
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do_formula NONE t1 #> fold (do_term_or_formula T) [t2, t3]
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blanchet@38810
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| Const (@{const_name Ex1}, _) $ Abs (_, _, body_t) =>
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blanchet@38810
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do_quantifier (is_some pos) body_t
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blanchet@38810
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| Const (@{const_name Ball}, _) $ t1 $ Abs (_, _, body_t) =>
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blanchet@38810
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do_quantifier (pos = SOME false)
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blanchet@38810
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(HOLogic.mk_imp (incr_boundvars 1 t1 $ Bound 0, body_t))
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blanchet@38810
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| Const (@{const_name Bex}, _) $ t1 $ Abs (_, _, body_t) =>
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blanchet@38810
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do_quantifier (pos = SOME true)
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blanchet@38810
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(HOLogic.mk_conj (incr_boundvars 1 t1 $ Bound 0, body_t))
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blanchet@37533
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| (t0 as Const (_, @{typ bool})) $ t1 =>
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blanchet@37533
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do_term t0 #> do_formula pos t1 (* theory constant *)
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blanchet@37533
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| _ => do_term t
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in
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blanchet@38337
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Symtab.empty |> fold (Symtab.update o rpair []) boring_consts
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|> fold (do_formula pos) ts
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end
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paulson@24287
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paulson@24287
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(*Inserts a dummy "constant" referring to the theory name, so that relevance
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paulson@24287
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takes the given theory into account.*)
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blanchet@37616
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fun theory_const_prop_of theory_relevant th =
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blanchet@37505
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if theory_relevant then
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let
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blanchet@37505
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val name = Context.theory_name (theory_of_thm th)
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blanchet@37505
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val t = Const (name ^ ". 1", @{typ bool})
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blanchet@37505
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in t $ prop_of th end
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else
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blanchet@37505
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prop_of th
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blanchet@37505
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paulson@24287
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(**** Constant / Type Frequencies ****)
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paulson@24287
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blanchet@38982
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(* A two-dimensional symbol table counts frequencies of constants. It's keyed
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blanchet@38982
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first by constant name and second by its list of type instantiations. For the
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blanchet@38983
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latter, we need a linear ordering on "pseudotype list". *)
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blanchet@37505
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blanchet@38983
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fun pseudotype_ord p =
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blanchet@38982
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case p of
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blanchet@38983
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(PVar, PVar) => EQUAL
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blanchet@38983
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| (PVar, PType _) => LESS
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blanchet@38983
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| (PType _, PVar) => GREATER
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blanchet@38983
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| (PType q1, PType q2) =>
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blanchet@38983
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prod_ord fast_string_ord (dict_ord pseudotype_ord) (q1, q2)
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paulson@24287
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blanchet@38982
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structure CTtab =
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blanchet@38983
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Table(type key = pseudotype list val ord = dict_ord pseudotype_ord)
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paulson@24287
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blanchet@37616
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fun count_axiom_consts theory_relevant thy (_, th) =
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blanchet@37503
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let
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blanchet@37503
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fun do_const (a, T) =
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blanchet@38983
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let val (c, cts) = pseudoconst_for thy (a, T) in
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blanchet@37503
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(* Two-dimensional table update. Constant maps to types maps to
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blanchet@37503
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count. *)
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blanchet@37503
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CTtab.map_default (cts, 0) (Integer.add 1)
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blanchet@37503
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|> Symtab.map_default (c, CTtab.empty)
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blanchet@37503
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end
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blanchet@37503
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fun do_term (Const x) = do_const x
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blanchet@37503
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| do_term (Free x) = do_const x
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blanchet@37503
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| do_term (t $ u) = do_term t #> do_term u
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blanchet@37503
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| do_term (Abs (_, _, t)) = do_term t
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blanchet@37503
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| do_term _ = I
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blanchet@37616
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in th |> theory_const_prop_of theory_relevant |> do_term end
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paulson@24287
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paulson@24287
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paulson@24287
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(**** Actual Filtering Code ****)
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paulson@24287
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paulson@24287
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(*The frequency of a constant is the sum of those of all instances of its type.*)
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blanchet@38983
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fun pseudoconst_freq match const_tab (c, cts) =
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blanchet@38983
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CTtab.fold (fn (cts', m) => match (cts, cts') ? Integer.add m)
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blanchet@38925
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(the (Symtab.lookup const_tab c)) 0
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blanchet@38925
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handle Option.Option => 0
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blanchet@38925
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paulson@24287
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blanchet@38331
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(* A surprising number of theorems contain only a few significant constants.
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blanchet@38331
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These include all induction rules, and other general theorems. *)
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blanchet@37503
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blanchet@37503
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(* "log" seems best in practice. A constant function of one ignores the constant
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blanchet@37503
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frequencies. *)
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blanchet@38986
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fun rel_log n = 1.0 + 2.0 / Math.ln (Real.fromInt n + 1.0)
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blanchet@38986
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(* TODO: experiment
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blanchet@38986
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fun irrel_log n = 0.5 + 1.0 / Math.ln (Real.fromInt n + 1.0)
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blanchet@38986
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*)
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blanchet@38986
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244 |
fun irrel_log n = Math.ln (Real.fromInt n + 19.0) / 6.4
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blanchet@37503
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blanchet@37503
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(* Computes a constant's weight, as determined by its frequency. *)
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blanchet@38986
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val rel_weight = rel_log oo pseudoconst_freq match_pseudotypes
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blanchet@38986
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248 |
fun irrel_weight const_tab (c as (s, _)) =
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blanchet@38986
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if String.isPrefix skolem_prefix s then 1.0
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blanchet@38986
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else irrel_log (pseudoconst_freq (match_pseudotypes o swap) const_tab c)
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blanchet@38986
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251 |
(* TODO: experiment
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blanchet@38986
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252 |
fun irrel_weight _ _ = 1.0
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blanchet@38986
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253 |
*)
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paulson@24287
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254 |
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blanchet@38926
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255 |
fun axiom_weight const_tab relevant_consts axiom_consts =
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blanchet@38983
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256 |
case axiom_consts |> List.partition (pseudoconst_mem I relevant_consts)
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blanchet@38983
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257 |
||> filter_out (pseudoconst_mem swap relevant_consts) of
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blanchet@38983
|
258 |
([], []) => 0.0
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blanchet@38983
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259 |
| (_, []) => 1.0
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blanchet@38983
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260 |
| (rel, irrel) =>
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blanchet@38983
|
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let
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blanchet@38983
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262 |
val rel_weight = fold (curry Real.+ o rel_weight const_tab) rel 0.0
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blanchet@38983
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263 |
val irrel_weight = fold (curry Real.+ o irrel_weight const_tab) irrel 0.0
|
blanchet@38983
|
264 |
val res = rel_weight / (rel_weight + irrel_weight)
|
blanchet@38983
|
265 |
in if Real.isFinite res then res else 0.0 end
|
blanchet@37505
|
266 |
|
blanchet@38986
|
267 |
(* TODO: experiment
|
blanchet@38986
|
268 |
fun debug_axiom_weight const_tab relevant_consts axiom_consts =
|
blanchet@38986
|
269 |
case axiom_consts |> List.partition (pseudoconst_mem I relevant_consts)
|
blanchet@38986
|
270 |
||> filter_out (pseudoconst_mem swap relevant_consts) of
|
blanchet@38986
|
271 |
([], []) => 0.0
|
blanchet@38986
|
272 |
| (_, []) => 1.0
|
blanchet@38986
|
273 |
| (rel, irrel) =>
|
blanchet@38986
|
274 |
let
|
blanchet@38986
|
275 |
val _ = tracing (PolyML.makestring ("REL: ", rel))
|
blanchet@38986
|
276 |
val _ = tracing (PolyML.makestring ("IRREL: ", irrel))
|
blanchet@38986
|
277 |
val rel_weight = fold (curry Real.+ o rel_weight const_tab) rel 0.0
|
blanchet@38986
|
278 |
val irrel_weight = fold (curry Real.+ o irrel_weight const_tab) irrel 0.0
|
blanchet@38986
|
279 |
val res = rel_weight / (rel_weight + irrel_weight)
|
blanchet@38986
|
280 |
in if Real.isFinite res then res else 0.0 end
|
blanchet@38986
|
281 |
*)
|
blanchet@38986
|
282 |
|
blanchet@38986
|
283 |
fun pseudoconsts_of_term thy t =
|
blanchet@38981
|
284 |
Symtab.fold (fn (x, ys) => fold (fn y => cons (x, y)) ys)
|
blanchet@38986
|
285 |
(get_pseudoconsts thy true (SOME true) [t]) []
|
blanchet@38926
|
286 |
fun pair_consts_axiom theory_relevant thy axiom =
|
blanchet@37616
|
287 |
(axiom, axiom |> snd |> theory_const_prop_of theory_relevant
|
blanchet@38986
|
288 |
|> pseudoconsts_of_term thy)
|
paulson@24287
|
289 |
|
blanchet@38938
|
290 |
type annotated_thm =
|
blanchet@38983
|
291 |
((unit -> string * bool) * thm) * (string * pseudotype list) list
|
blanchet@37505
|
292 |
|
blanchet@38986
|
293 |
fun take_most_relevant max_max_imperfect max_relevant remaining_max
|
blanchet@38986
|
294 |
(candidates : (annotated_thm * real) list) =
|
blanchet@38983
|
295 |
let
|
blanchet@38986
|
296 |
val max_imperfect =
|
blanchet@38986
|
297 |
Real.ceil (Math.pow (max_max_imperfect,
|
blanchet@38986
|
298 |
Real.fromInt remaining_max
|
blanchet@38986
|
299 |
/ Real.fromInt max_relevant))
|
blanchet@38986
|
300 |
val (perfect, imperfect) =
|
blanchet@38986
|
301 |
candidates |> List.partition (fn (_, w) => w > 0.99999)
|
blanchet@38984
|
302 |
||> sort (Real.compare o swap o pairself snd)
|
blanchet@38986
|
303 |
val ((accepts, more_rejects), rejects) =
|
blanchet@38986
|
304 |
chop max_imperfect imperfect |>> append perfect |>> chop remaining_max
|
blanchet@38983
|
305 |
in
|
blanchet@38983
|
306 |
trace_msg (fn () => "Number of candidates: " ^
|
blanchet@38984
|
307 |
string_of_int (length candidates));
|
blanchet@38983
|
308 |
trace_msg (fn () => "Effective threshold: " ^
|
blanchet@38984
|
309 |
Real.toString (#2 (hd accepts)));
|
blanchet@38986
|
310 |
trace_msg (fn () => "Actually passed (" ^ Int.toString (length accepts) ^
|
blanchet@38986
|
311 |
"): " ^ (accepts
|
blanchet@38986
|
312 |
|> map (fn (((name, _), _), weight) =>
|
blanchet@38984
|
313 |
fst (name ()) ^ " [" ^ Real.toString weight ^ "]")
|
blanchet@38984
|
314 |
|> commas));
|
blanchet@38986
|
315 |
(accepts, more_rejects @ rejects)
|
blanchet@38983
|
316 |
end
|
paulson@24287
|
317 |
|
blanchet@38922
|
318 |
val threshold_divisor = 2.0
|
blanchet@38922
|
319 |
val ridiculous_threshold = 0.1
|
blanchet@38986
|
320 |
val max_max_imperfect_fudge_factor = 0.66
|
blanchet@38922
|
321 |
|
blanchet@38984
|
322 |
fun relevance_filter ctxt threshold0 decay max_relevant theory_relevant
|
blanchet@38984
|
323 |
({add, del, ...} : relevance_override) axioms goal_ts =
|
blanchet@38978
|
324 |
let
|
blanchet@38978
|
325 |
val thy = ProofContext.theory_of ctxt
|
blanchet@38978
|
326 |
val const_tab = fold (count_axiom_consts theory_relevant thy) axioms
|
blanchet@38978
|
327 |
Symtab.empty
|
blanchet@38978
|
328 |
val add_thms = maps (ProofContext.get_fact ctxt) add
|
blanchet@38978
|
329 |
val del_thms = maps (ProofContext.get_fact ctxt) del
|
blanchet@38986
|
330 |
val max_max_imperfect =
|
blanchet@38986
|
331 |
Math.sqrt (Real.fromInt max_relevant * max_max_imperfect_fudge_factor)
|
blanchet@38986
|
332 |
fun iter j remaining_max threshold rel_const_tab hopeless hopeful =
|
blanchet@38978
|
333 |
let
|
blanchet@38983
|
334 |
fun game_over rejects =
|
blanchet@38986
|
335 |
(* Add "add:" facts. *)
|
blanchet@38986
|
336 |
if null add_thms then
|
blanchet@38986
|
337 |
[]
|
blanchet@38983
|
338 |
else
|
blanchet@38986
|
339 |
map_filter (fn ((p as (_, th), _), _) =>
|
blanchet@38986
|
340 |
if member Thm.eq_thm add_thms th then SOME p
|
blanchet@38986
|
341 |
else NONE) rejects
|
blanchet@38986
|
342 |
fun relevant [] rejects hopeless [] =
|
blanchet@38986
|
343 |
(* Nothing has been added this iteration. *)
|
blanchet@38986
|
344 |
if j = 0 andalso threshold >= ridiculous_threshold then
|
blanchet@38986
|
345 |
(* First iteration? Try again. *)
|
blanchet@38986
|
346 |
iter 0 max_relevant (threshold / threshold_divisor) rel_const_tab
|
blanchet@38986
|
347 |
hopeless hopeful
|
blanchet@38983
|
348 |
else
|
blanchet@38986
|
349 |
game_over (rejects @ hopeless)
|
blanchet@38986
|
350 |
| relevant candidates rejects hopeless [] =
|
blanchet@38978
|
351 |
let
|
blanchet@38986
|
352 |
val (accepts, more_rejects) =
|
blanchet@38986
|
353 |
take_most_relevant max_max_imperfect max_relevant remaining_max
|
blanchet@38986
|
354 |
candidates
|
blanchet@38978
|
355 |
val rel_const_tab' =
|
blanchet@38984
|
356 |
rel_const_tab
|
blanchet@38986
|
357 |
|> fold (add_pseudoconst_to_table false)
|
blanchet@38986
|
358 |
(maps (snd o fst) accepts)
|
blanchet@38983
|
359 |
fun is_dirty (c, _) =
|
blanchet@38983
|
360 |
Symtab.lookup rel_const_tab' c <> Symtab.lookup rel_const_tab c
|
blanchet@38984
|
361 |
val (hopeful_rejects, hopeless_rejects) =
|
blanchet@38984
|
362 |
(rejects @ hopeless, ([], []))
|
blanchet@38984
|
363 |
|-> fold (fn (ax as (_, consts), old_weight) =>
|
blanchet@38984
|
364 |
if exists is_dirty consts then
|
blanchet@38984
|
365 |
apfst (cons (ax, NONE))
|
blanchet@38984
|
366 |
else
|
blanchet@38984
|
367 |
apsnd (cons (ax, old_weight)))
|
blanchet@38984
|
368 |
|>> append (more_rejects
|
blanchet@38984
|
369 |
|> map (fn (ax as (_, consts), old_weight) =>
|
blanchet@38984
|
370 |
(ax, if exists is_dirty consts then NONE
|
blanchet@38984
|
371 |
else SOME old_weight)))
|
blanchet@38986
|
372 |
val threshold =
|
blanchet@38986
|
373 |
threshold + (1.0 - threshold)
|
blanchet@38986
|
374 |
* Math.pow (decay, Real.fromInt (length accepts))
|
blanchet@38986
|
375 |
val remaining_max = remaining_max - length accepts
|
blanchet@38978
|
376 |
in
|
blanchet@38983
|
377 |
trace_msg (fn () => "New or updated constants: " ^
|
blanchet@38983
|
378 |
commas (rel_const_tab' |> Symtab.dest
|
blanchet@38983
|
379 |
|> subtract (op =) (Symtab.dest rel_const_tab)
|
blanchet@38983
|
380 |
|> map string_for_super_pseudoconst));
|
blanchet@38984
|
381 |
map (fst o fst) accepts @
|
blanchet@38986
|
382 |
(if remaining_max = 0 then
|
blanchet@38984
|
383 |
game_over (hopeful_rejects @ map (apsnd SOME) hopeless_rejects)
|
blanchet@38984
|
384 |
else
|
blanchet@38986
|
385 |
iter (j + 1) remaining_max threshold rel_const_tab'
|
blanchet@38986
|
386 |
hopeless_rejects hopeful_rejects)
|
blanchet@38978
|
387 |
end
|
blanchet@38986
|
388 |
| relevant candidates rejects hopeless
|
blanchet@38978
|
389 |
(((ax as ((name, th), axiom_consts)), cached_weight)
|
blanchet@38986
|
390 |
:: hopeful) =
|
blanchet@38978
|
391 |
let
|
blanchet@38978
|
392 |
val weight =
|
blanchet@38978
|
393 |
case cached_weight of
|
blanchet@38978
|
394 |
SOME w => w
|
blanchet@38978
|
395 |
| NONE => axiom_weight const_tab rel_const_tab axiom_consts
|
blanchet@38986
|
396 |
(* TODO: experiment
|
blanchet@38986
|
397 |
val _ = if String.isPrefix "lift.simps(3" (fst (name ())) then
|
blanchet@38986
|
398 |
tracing ("*** " ^ (fst (name ())) ^ PolyML.makestring (debug_axiom_weight const_tab rel_const_tab axiom_consts))
|
blanchet@38986
|
399 |
else
|
blanchet@38986
|
400 |
()
|
blanchet@38986
|
401 |
*)
|
blanchet@38978
|
402 |
in
|
blanchet@38980
|
403 |
if weight >= threshold then
|
blanchet@38986
|
404 |
relevant ((ax, weight) :: candidates) rejects hopeless hopeful
|
blanchet@38978
|
405 |
else
|
blanchet@38986
|
406 |
relevant candidates ((ax, weight) :: rejects) hopeless hopeful
|
blanchet@38978
|
407 |
end
|
blanchet@38978
|
408 |
in
|
blanchet@38983
|
409 |
trace_msg (fn () =>
|
blanchet@38983
|
410 |
"ITERATION " ^ string_of_int j ^ ": current threshold: " ^
|
blanchet@38983
|
411 |
Real.toString threshold ^ ", constants: " ^
|
blanchet@38983
|
412 |
commas (rel_const_tab |> Symtab.dest
|
blanchet@38983
|
413 |
|> filter (curry (op <>) [] o snd)
|
blanchet@38983
|
414 |
|> map string_for_super_pseudoconst));
|
blanchet@38986
|
415 |
relevant [] [] hopeless hopeful
|
blanchet@38978
|
416 |
end
|
blanchet@38978
|
417 |
in
|
blanchet@38978
|
418 |
axioms |> filter_out (member Thm.eq_thm del_thms o snd)
|
blanchet@38978
|
419 |
|> map (rpair NONE o pair_consts_axiom theory_relevant thy)
|
blanchet@38984
|
420 |
|> iter 0 max_relevant threshold0
|
blanchet@38986
|
421 |
(get_pseudoconsts thy false (SOME false) goal_ts) []
|
blanchet@38978
|
422 |
|> tap (fn res => trace_msg (fn () =>
|
blanchet@38925
|
423 |
"Total relevant: " ^ Int.toString (length res)))
|
blanchet@38978
|
424 |
end
|
paulson@24287
|
425 |
|
blanchet@38983
|
426 |
|
paulson@24287
|
427 |
(***************************************************************)
|
mengj@19768
|
428 |
(* Retrieving and filtering lemmas *)
|
mengj@19768
|
429 |
(***************************************************************)
|
mengj@19768
|
430 |
|
paulson@33022
|
431 |
(*** retrieve lemmas and filter them ***)
|
mengj@19768
|
432 |
|
paulson@20757
|
433 |
(*Reject theorems with names like "List.filter.filter_list_def" or
|
paulson@21690
|
434 |
"Accessible_Part.acc.defs", as these are definitions arising from packages.*)
|
paulson@20757
|
435 |
fun is_package_def a =
|
wenzelm@30364
|
436 |
let val names = Long_Name.explode a
|
paulson@21690
|
437 |
in
|
paulson@21690
|
438 |
length names > 2 andalso
|
paulson@21690
|
439 |
not (hd names = "local") andalso
|
paulson@21690
|
440 |
String.isSuffix "_def" a orelse String.isSuffix "_defs" a
|
paulson@21690
|
441 |
end;
|
paulson@20757
|
442 |
|
blanchet@38331
|
443 |
fun make_fact_table xs =
|
blanchet@37616
|
444 |
fold (Termtab.update o `(prop_of o snd)) xs Termtab.empty
|
blanchet@38331
|
445 |
fun make_unique xs = Termtab.fold (cons o snd) (make_fact_table xs) []
|
mengj@19768
|
446 |
|
blanchet@37626
|
447 |
(* FIXME: put other record thms here, or declare as "no_atp" *)
|
blanchet@37626
|
448 |
val multi_base_blacklist =
|
blanchet@37626
|
449 |
["defs", "select_defs", "update_defs", "induct", "inducts", "split", "splits",
|
blanchet@38921
|
450 |
"split_asm", "cases", "ext_cases", "eq.simps", "eq.refl", "nchotomy",
|
blanchet@38921
|
451 |
"case_cong", "weak_case_cong"]
|
blanchet@38921
|
452 |
|> map (prefix ".")
|
blanchet@37626
|
453 |
|
blanchet@37626
|
454 |
val max_lambda_nesting = 3
|
blanchet@37626
|
455 |
|
blanchet@37626
|
456 |
fun term_has_too_many_lambdas max (t1 $ t2) =
|
blanchet@37626
|
457 |
exists (term_has_too_many_lambdas max) [t1, t2]
|
blanchet@37626
|
458 |
| term_has_too_many_lambdas max (Abs (_, _, t)) =
|
blanchet@37626
|
459 |
max = 0 orelse term_has_too_many_lambdas (max - 1) t
|
blanchet@37626
|
460 |
| term_has_too_many_lambdas _ _ = false
|
blanchet@37626
|
461 |
|
blanchet@37626
|
462 |
(* Don't count nested lambdas at the level of formulas, since they are
|
blanchet@37626
|
463 |
quantifiers. *)
|
blanchet@37626
|
464 |
fun formula_has_too_many_lambdas Ts (Abs (_, T, t)) =
|
blanchet@37626
|
465 |
formula_has_too_many_lambdas (T :: Ts) t
|
blanchet@37626
|
466 |
| formula_has_too_many_lambdas Ts t =
|
blanchet@37626
|
467 |
if is_formula_type (fastype_of1 (Ts, t)) then
|
blanchet@37626
|
468 |
exists (formula_has_too_many_lambdas Ts) (#2 (strip_comb t))
|
blanchet@37626
|
469 |
else
|
blanchet@37626
|
470 |
term_has_too_many_lambdas max_lambda_nesting t
|
blanchet@37626
|
471 |
|
blanchet@38931
|
472 |
(* The max apply depth of any "metis" call in "Metis_Examples" (on 2007-10-31)
|
blanchet@37626
|
473 |
was 11. *)
|
blanchet@37626
|
474 |
val max_apply_depth = 15
|
blanchet@37626
|
475 |
|
blanchet@37626
|
476 |
fun apply_depth (f $ t) = Int.max (apply_depth f, apply_depth t + 1)
|
blanchet@37626
|
477 |
| apply_depth (Abs (_, _, t)) = apply_depth t
|
blanchet@37626
|
478 |
| apply_depth _ = 0
|
blanchet@37626
|
479 |
|
blanchet@37626
|
480 |
fun is_formula_too_complex t =
|
blanchet@38331
|
481 |
apply_depth t > max_apply_depth orelse formula_has_too_many_lambdas [] t
|
blanchet@37626
|
482 |
|
blanchet@37539
|
483 |
val exists_sledgehammer_const =
|
blanchet@37626
|
484 |
exists_Const (fn (s, _) => String.isPrefix sledgehammer_prefix s)
|
blanchet@37626
|
485 |
|
blanchet@38890
|
486 |
fun is_strange_theorem th =
|
blanchet@37626
|
487 |
case head_of (concl_of th) of
|
blanchet@37626
|
488 |
Const (a, _) => (a <> @{const_name Trueprop} andalso
|
blanchet@37626
|
489 |
a <> @{const_name "=="})
|
blanchet@37626
|
490 |
| _ => false
|
blanchet@37626
|
491 |
|
blanchet@37626
|
492 |
val type_has_top_sort =
|
blanchet@37626
|
493 |
exists_subtype (fn TFree (_, []) => true | TVar (_, []) => true | _ => false)
|
blanchet@37626
|
494 |
|
blanchet@38331
|
495 |
(**** Predicates to detect unwanted facts (prolific or likely to cause
|
blanchet@37347
|
496 |
unsoundness) ****)
|
paulson@21470
|
497 |
|
blanchet@38513
|
498 |
(* Too general means, positive equality literal with a variable X as one
|
blanchet@38513
|
499 |
operand, when X does not occur properly in the other operand. This rules out
|
blanchet@38513
|
500 |
clearly inconsistent facts such as X = a | X = b, though it by no means
|
blanchet@38513
|
501 |
guarantees soundness. *)
|
paulson@21470
|
502 |
|
blanchet@38513
|
503 |
(* Unwanted equalities are those between a (bound or schematic) variable that
|
blanchet@38513
|
504 |
does not properly occur in the second operand. *)
|
blanchet@38830
|
505 |
val is_exhaustive_finite =
|
blanchet@38830
|
506 |
let
|
blanchet@38852
|
507 |
fun is_bad_equal (Var z) t =
|
blanchet@38852
|
508 |
not (exists_subterm (fn Var z' => z = z' | _ => false) t)
|
blanchet@38852
|
509 |
| is_bad_equal (Bound j) t = not (loose_bvar1 (t, j))
|
blanchet@38852
|
510 |
| is_bad_equal _ _ = false
|
blanchet@38852
|
511 |
fun do_equals t1 t2 = is_bad_equal t1 t2 orelse is_bad_equal t2 t1
|
blanchet@38830
|
512 |
fun do_formula pos t =
|
blanchet@38830
|
513 |
case (pos, t) of
|
blanchet@38838
|
514 |
(_, @{const Trueprop} $ t1) => do_formula pos t1
|
blanchet@38830
|
515 |
| (true, Const (@{const_name all}, _) $ Abs (_, _, t')) =>
|
blanchet@38830
|
516 |
do_formula pos t'
|
blanchet@38830
|
517 |
| (true, Const (@{const_name All}, _) $ Abs (_, _, t')) =>
|
blanchet@38830
|
518 |
do_formula pos t'
|
blanchet@38830
|
519 |
| (false, Const (@{const_name Ex}, _) $ Abs (_, _, t')) =>
|
blanchet@38830
|
520 |
do_formula pos t'
|
blanchet@38830
|
521 |
| (_, @{const "==>"} $ t1 $ t2) =>
|
blanchet@38852
|
522 |
do_formula (not pos) t1 andalso
|
blanchet@38852
|
523 |
(t2 = @{prop False} orelse do_formula pos t2)
|
blanchet@38830
|
524 |
| (_, @{const "op -->"} $ t1 $ t2) =>
|
blanchet@38852
|
525 |
do_formula (not pos) t1 andalso
|
blanchet@38852
|
526 |
(t2 = @{const False} orelse do_formula pos t2)
|
blanchet@38830
|
527 |
| (_, @{const Not} $ t1) => do_formula (not pos) t1
|
blanchet@38830
|
528 |
| (true, @{const "op |"} $ t1 $ t2) => forall (do_formula pos) [t1, t2]
|
blanchet@38830
|
529 |
| (false, @{const "op &"} $ t1 $ t2) => forall (do_formula pos) [t1, t2]
|
blanchet@38830
|
530 |
| (true, Const (@{const_name "op ="}, _) $ t1 $ t2) => do_equals t1 t2
|
blanchet@38830
|
531 |
| (true, Const (@{const_name "=="}, _) $ t1 $ t2) => do_equals t1 t2
|
blanchet@38830
|
532 |
| _ => false
|
blanchet@38830
|
533 |
in do_formula true end
|
blanchet@38830
|
534 |
|
blanchet@38815
|
535 |
fun has_bound_or_var_of_type tycons =
|
blanchet@38815
|
536 |
exists_subterm (fn Var (_, Type (s, _)) => member (op =) tycons s
|
blanchet@38815
|
537 |
| Abs (_, Type (s, _), _) => member (op =) tycons s
|
blanchet@38815
|
538 |
| _ => false)
|
paulson@21431
|
539 |
|
blanchet@38331
|
540 |
(* Facts are forbidden to contain variables of these types. The typical reason
|
blanchet@37347
|
541 |
is that they lead to unsoundness. Note that "unit" satisfies numerous
|
blanchet@38331
|
542 |
equations like "?x = ()". The resulting clauses will have no type constraint,
|
blanchet@37347
|
543 |
yielding false proofs. Even "bool" leads to many unsound proofs, though only
|
blanchet@37347
|
544 |
for higher-order problems. *)
|
blanchet@38815
|
545 |
val dangerous_types = [@{type_name unit}, @{type_name bool}, @{type_name prop}];
|
paulson@22217
|
546 |
|
blanchet@38331
|
547 |
(* Facts containing variables of type "unit" or "bool" or of the form
|
blanchet@38514
|
548 |
"ALL x. x = A | x = B | x = C" are likely to lead to unsound proofs if types
|
blanchet@38514
|
549 |
are omitted. *)
|
blanchet@38816
|
550 |
fun is_dangerous_term full_types t =
|
blanchet@38832
|
551 |
not full_types andalso
|
blanchet@38918
|
552 |
let val t = transform_elim_term t in
|
blanchet@38918
|
553 |
has_bound_or_var_of_type dangerous_types t orelse
|
blanchet@38918
|
554 |
is_exhaustive_finite t
|
blanchet@38918
|
555 |
end
|
paulson@21470
|
556 |
|
blanchet@38850
|
557 |
fun is_theorem_bad_for_atps full_types thm =
|
blanchet@38850
|
558 |
let val t = prop_of thm in
|
blanchet@38850
|
559 |
is_formula_too_complex t orelse exists_type type_has_top_sort t orelse
|
blanchet@38850
|
560 |
is_dangerous_term full_types t orelse exists_sledgehammer_const t orelse
|
blanchet@38890
|
561 |
is_strange_theorem thm
|
blanchet@38850
|
562 |
end
|
blanchet@38850
|
563 |
|
blanchet@38935
|
564 |
fun all_name_thms_pairs ctxt reserved full_types add_thms chained_ths =
|
blanchet@38850
|
565 |
let
|
blanchet@38936
|
566 |
val is_chained = member Thm.eq_thm chained_ths
|
blanchet@38936
|
567 |
val global_facts = PureThy.facts_of (ProofContext.theory_of ctxt)
|
blanchet@38882
|
568 |
val local_facts = ProofContext.facts_of ctxt
|
blanchet@38882
|
569 |
val named_locals = local_facts |> Facts.dest_static []
|
blanchet@38936
|
570 |
(* Unnamed, not chained formulas with schematic variables are omitted,
|
blanchet@38936
|
571 |
because they are rejected by the backticks (`...`) parser for some
|
blanchet@38936
|
572 |
reason. *)
|
blanchet@38977
|
573 |
fun is_good_unnamed_local th =
|
blanchet@38977
|
574 |
forall (fn (_, ths) => not (member Thm.eq_thm ths th)) named_locals
|
blanchet@38977
|
575 |
andalso (not (exists_subterm is_Var (prop_of th)) orelse (is_chained th))
|
blanchet@38882
|
576 |
val unnamed_locals =
|
blanchet@38977
|
577 |
local_facts |> Facts.props |> filter is_good_unnamed_local
|
blanchet@38936
|
578 |
|> map (pair "" o single)
|
blanchet@38850
|
579 |
val full_space =
|
blanchet@38977
|
580 |
Name_Space.merge (Facts.space_of global_facts, Facts.space_of local_facts)
|
blanchet@38936
|
581 |
fun add_valid_facts foldx facts =
|
blanchet@38938
|
582 |
foldx (fn (name0, ths) =>
|
blanchet@38938
|
583 |
if name0 <> "" andalso
|
blanchet@38938
|
584 |
forall (not o member Thm.eq_thm add_thms) ths andalso
|
blanchet@38938
|
585 |
(Facts.is_concealed facts name0 orelse
|
blanchet@38938
|
586 |
(respect_no_atp andalso is_package_def name0) orelse
|
blanchet@38938
|
587 |
exists (fn s => String.isSuffix s name0) multi_base_blacklist orelse
|
blanchet@38938
|
588 |
String.isSuffix "_def_raw" (* FIXME: crude hack *) name0) then
|
blanchet@38850
|
589 |
I
|
blanchet@38850
|
590 |
else
|
blanchet@38850
|
591 |
let
|
blanchet@38938
|
592 |
val multi = length ths > 1
|
blanchet@38935
|
593 |
fun backquotify th =
|
blanchet@38935
|
594 |
"`" ^ Print_Mode.setmp [Print_Mode.input]
|
blanchet@38935
|
595 |
(Syntax.string_of_term ctxt) (prop_of th) ^ "`"
|
blanchet@38977
|
596 |
|> String.translate (fn c => if Char.isPrint c then str c else "")
|
blanchet@38977
|
597 |
|> simplify_spaces
|
blanchet@38938
|
598 |
fun check_thms a =
|
blanchet@38938
|
599 |
case try (ProofContext.get_thms ctxt) a of
|
blanchet@38938
|
600 |
NONE => false
|
blanchet@38938
|
601 |
| SOME ths' => Thm.eq_thms (ths, ths')
|
blanchet@38850
|
602 |
in
|
blanchet@38938
|
603 |
pair 1
|
blanchet@38938
|
604 |
#> fold (fn th => fn (j, rest) =>
|
blanchet@38938
|
605 |
(j + 1,
|
blanchet@38938
|
606 |
if is_theorem_bad_for_atps full_types th andalso
|
blanchet@38938
|
607 |
not (member Thm.eq_thm add_thms th) then
|
blanchet@38938
|
608 |
rest
|
blanchet@38938
|
609 |
else
|
blanchet@38938
|
610 |
(fn () =>
|
blanchet@38938
|
611 |
(if name0 = "" then
|
blanchet@38938
|
612 |
th |> backquotify
|
blanchet@38938
|
613 |
else
|
blanchet@38938
|
614 |
let
|
blanchet@38938
|
615 |
val name1 = Facts.extern facts name0
|
blanchet@38938
|
616 |
val name2 = Name_Space.extern full_space name0
|
blanchet@38938
|
617 |
in
|
blanchet@38938
|
618 |
case find_first check_thms [name1, name2, name0] of
|
blanchet@38983
|
619 |
SOME name => repair_name reserved multi j name
|
blanchet@38938
|
620 |
| NONE => ""
|
blanchet@38938
|
621 |
end, is_chained th), (multi, th)) :: rest)) ths
|
blanchet@38938
|
622 |
#> snd
|
blanchet@38850
|
623 |
end)
|
blanchet@38882
|
624 |
in
|
blanchet@38927
|
625 |
[] |> add_valid_facts fold local_facts (unnamed_locals @ named_locals)
|
blanchet@38927
|
626 |
|> add_valid_facts Facts.fold_static global_facts global_facts
|
blanchet@38882
|
627 |
end
|
blanchet@38850
|
628 |
|
blanchet@38850
|
629 |
(* The single-name theorems go after the multiple-name ones, so that single
|
blanchet@38850
|
630 |
names are preferred when both are available. *)
|
blanchet@38938
|
631 |
fun name_thm_pairs ctxt respect_no_atp =
|
blanchet@38983
|
632 |
List.partition (fst o snd) #> op @ #> map (apsnd snd)
|
blanchet@38938
|
633 |
#> respect_no_atp ? filter_out (No_ATPs.member ctxt o snd)
|
blanchet@38850
|
634 |
|
blanchet@38850
|
635 |
(***************************************************************)
|
blanchet@38850
|
636 |
(* ATP invocation methods setup *)
|
blanchet@38850
|
637 |
(***************************************************************)
|
blanchet@38850
|
638 |
|
blanchet@38984
|
639 |
fun relevant_facts full_types (threshold0, threshold1) max_relevant
|
blanchet@38983
|
640 |
theory_relevant (relevance_override as {add, del, only})
|
blanchet@38229
|
641 |
(ctxt, (chained_ths, _)) hyp_ts concl_t =
|
blanchet@37534
|
642 |
let
|
blanchet@38984
|
643 |
val decay = 1.0 - Math.pow ((1.0 - threshold1) / (1.0 - threshold0),
|
blanchet@38984
|
644 |
1.0 / Real.fromInt (max_relevant + 1))
|
blanchet@37534
|
645 |
val add_thms = maps (ProofContext.get_fact ctxt) add
|
blanchet@38935
|
646 |
val reserved = reserved_isar_keyword_table ()
|
blanchet@37534
|
647 |
val axioms =
|
blanchet@38938
|
648 |
(if only then
|
blanchet@38983
|
649 |
maps (name_thm_pairs_from_ref ctxt reserved chained_ths) add
|
blanchet@38938
|
650 |
else
|
blanchet@38938
|
651 |
all_name_thms_pairs ctxt reserved full_types add_thms chained_ths)
|
blanchet@38927
|
652 |
|> name_thm_pairs ctxt (respect_no_atp andalso not only)
|
blanchet@38818
|
653 |
|> make_unique
|
blanchet@37534
|
654 |
in
|
blanchet@38927
|
655 |
trace_msg (fn () => "Considering " ^ Int.toString (length axioms) ^
|
blanchet@38927
|
656 |
" theorems");
|
blanchet@38984
|
657 |
(if threshold0 > 1.0 orelse threshold0 > threshold1 then
|
blanchet@38978
|
658 |
[]
|
blanchet@38984
|
659 |
else if threshold0 < 0.0 then
|
blanchet@38978
|
660 |
axioms
|
blanchet@38978
|
661 |
else
|
blanchet@38984
|
662 |
relevance_filter ctxt threshold0 decay max_relevant theory_relevant
|
blanchet@38984
|
663 |
relevance_override axioms (concl_t :: hyp_ts))
|
blanchet@38983
|
664 |
|> map (apfst (fn f => f ())) |> sort_wrt (fst o fst)
|
blanchet@37534
|
665 |
end
|
immler@30536
|
666 |
|
paulson@15347
|
667 |
end;
|