src/Provers/simplifier.ML
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(*  Title:      Provers/simplifier.ML
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    ID:         $Id$
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    Author:     Tobias Nipkow and Markus Wenzel, TU Muenchen
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Generic simplifier, suitable for most logics.  See Pure/thm.ML for the
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actual meta-level rewriting engine.
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*)
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infix 4
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  setsubgoaler setloop addloop delloop setSSolver addSSolver setSolver
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  addSolver addsimps delsimps addeqcongs deleqcongs
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  setmksimps setmkeqTrue setmksym settermless addsimprocs delsimprocs;
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signature BASIC_SIMPLIFIER =
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sig
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  type simproc
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  val mk_simproc: string -> cterm list
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    -> (Sign.sg -> thm list -> term -> thm option) -> simproc
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  type simpset
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  val empty_ss: simpset
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  val rep_ss: simpset ->
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   {mss: meta_simpset,
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    subgoal_tac:        simpset -> int -> tactic,
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    loop_tacs:          (string * (int -> tactic))list,
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           finish_tac: thm list -> int -> tactic,
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    unsafe_finish_tac: thm list -> int -> tactic};
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  val print_ss: simpset -> unit
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  val print_simpset: theory -> unit
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  val setsubgoaler: simpset *  (simpset -> int -> tactic) -> simpset
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  val setloop:      simpset *             (int -> tactic) -> simpset
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  val addloop:      simpset *  (string * (int -> tactic)) -> simpset
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  val delloop:      simpset *   string                    -> simpset
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  val setSSolver:   simpset * (thm list -> int -> tactic) -> simpset
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  val addSSolver:   simpset * (thm list -> int -> tactic) -> simpset
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  val setSolver:    simpset * (thm list -> int -> tactic) -> simpset
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  val addSolver:    simpset * (thm list -> int -> tactic) -> simpset
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  val setmksimps:   simpset * (thm -> thm list) -> simpset
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  val setmkeqTrue:  simpset * (thm -> thm option) -> simpset
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  val setmksym:     simpset * (thm -> thm option) -> simpset
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  val settermless:  simpset * (term * term -> bool) -> simpset
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  val addsimps:     simpset * thm list -> simpset
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  val delsimps:     simpset * thm list -> simpset
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  val addeqcongs:   simpset * thm list -> simpset
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  val deleqcongs:   simpset * thm list -> simpset
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  val addsimprocs:  simpset * simproc list -> simpset
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  val delsimprocs:  simpset * simproc list -> simpset
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  val merge_ss:     simpset * simpset -> simpset
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  val prems_of_ss:  simpset -> thm list
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  val simpset_ref_of_sg: Sign.sg -> simpset ref
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  val simpset_ref_of: theory -> simpset ref
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  val simpset_of_sg: Sign.sg -> simpset
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  val simpset_of: theory -> simpset
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  val SIMPSET: (simpset -> tactic) -> tactic
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  val SIMPSET': (simpset -> 'a -> tactic) -> 'a -> tactic
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  val simpset: unit -> simpset
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  val simpset_ref: unit -> simpset ref
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  val Addsimps: thm list -> unit
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  val Delsimps: thm list -> unit
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  val Addsimprocs: simproc list -> unit
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  val Delsimprocs: simproc list -> unit
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  val               simp_tac: simpset -> int -> tactic
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  val           asm_simp_tac: simpset -> int -> tactic
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  val          full_simp_tac: simpset -> int -> tactic
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  val        asm_lr_simp_tac: simpset -> int -> tactic
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  val      asm_full_simp_tac: simpset -> int -> tactic
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  val safe_asm_full_simp_tac: simpset -> int -> tactic
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  val               Simp_tac:            int -> tactic
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  val           Asm_simp_tac:            int -> tactic
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  val          Full_simp_tac:            int -> tactic
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  val        Asm_lr_simp_tac:            int -> tactic
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  val      Asm_full_simp_tac:            int -> tactic
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  val          simplify: simpset -> thm -> thm
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  val      asm_simplify: simpset -> thm -> thm
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  val     full_simplify: simpset -> thm -> thm
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  val asm_full_simplify: simpset -> thm -> thm
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end;
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signature SIMPLIFIER =
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sig
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  include BASIC_SIMPLIFIER
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  val          rewrite: simpset -> cterm -> thm
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  val      asm_rewrite: simpset -> cterm -> thm
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  val     full_rewrite: simpset -> cterm -> thm
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  val asm_full_rewrite: simpset -> cterm -> thm
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  val setup: (theory -> theory) list
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  val get_local_simpset: local_theory -> simpset
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  val put_local_simpset: simpset -> local_theory -> local_theory
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  val simp_add: tag
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  val simp_del: tag
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  val simp_add_global: theory attribute
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  val simp_del_global: theory attribute
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  val simp_add_local: local_theory attribute
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  val simp_del_local: local_theory attribute
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end;
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structure Simplifier: SIMPLIFIER =
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struct
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(** simplification procedures **)
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(* datatype simproc *)
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datatype simproc =
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  Simproc of string * cterm list * (Sign.sg -> thm list -> term -> thm option) * stamp;
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fun mk_simproc name lhss proc =
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  Simproc (name, map (Thm.cterm_fun Logic.varify) lhss, proc, stamp ());
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fun rep_simproc (Simproc args) = args;
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(** simplification sets **)
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(* type simpset *)
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datatype simpset =
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  Simpset of {
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    mss: meta_simpset,
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    subgoal_tac:        simpset -> int -> tactic,
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    loop_tacs:          (string * (int -> tactic))list,
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           finish_tac: thm list -> int -> tactic,
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    unsafe_finish_tac: thm list -> int -> tactic};
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fun make_ss (mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac) =
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  Simpset {mss = mss, subgoal_tac = subgoal_tac, loop_tacs = loop_tacs,
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    finish_tac = finish_tac, unsafe_finish_tac = unsafe_finish_tac};
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val empty_ss =
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  let val mss = Thm.set_mk_sym(Thm.empty_mss, Some o symmetric_fun)
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  in make_ss (mss, K (K no_tac), [], K (K no_tac), K (K no_tac)) end;
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fun rep_ss (Simpset args) = args;
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fun prems_of_ss (Simpset {mss, ...}) = Thm.prems_of_mss mss;
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(* print simpsets *)
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fun print_ss ss =
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  let
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    val Simpset {mss, ...} = ss;
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    val {simps, procs, congs} = Thm.dest_mss mss;
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    val pretty_thms = map Display.pretty_thm;
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    fun pretty_proc (name, lhss) =
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      Pretty.big_list (name ^ ":") (map Display.pretty_cterm lhss);
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  in
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    Pretty.writeln (Pretty.big_list "simplification rules:" (pretty_thms simps));
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    Pretty.writeln (Pretty.big_list "simplification procedures:" (map pretty_proc procs));
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    Pretty.writeln (Pretty.big_list "congruences:" (pretty_thms congs))
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  end;
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(* extend simpsets *)
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fun (Simpset {mss, subgoal_tac = _, loop_tacs, finish_tac, unsafe_finish_tac})
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    setsubgoaler subgoal_tac =
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  make_ss (mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs = _, finish_tac, unsafe_finish_tac})
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    setloop tac =
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  make_ss (mss, subgoal_tac, [("",tac)], finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac})
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    addloop tac = make_ss (mss, subgoal_tac, 
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	(case assoc_string (loop_tacs,(fst tac)) of None => () | Some x => 
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	 warning ("overwriting looper "^fst tac); overwrite(loop_tacs,tac)),
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           finish_tac, unsafe_finish_tac);
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fun (ss as Simpset {mss,subgoal_tac,loop_tacs,finish_tac,unsafe_finish_tac})
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    delloop name =
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  let val (del,rest) = partition (fn (n,_) => n=name) loop_tacs
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  in if null del then (warning ("No such looper in simpset: " ^ name); ss)
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     else make_ss (mss, subgoal_tac, rest, finish_tac, unsafe_finish_tac)
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  end;
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac = _, unsafe_finish_tac})
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    setSSolver finish_tac =
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  make_ss (mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac})
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    addSSolver tac =
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  make_ss (mss, subgoal_tac, loop_tacs, fn hyps => finish_tac hyps ORELSE' tac hyps,
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    unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac = _})
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    setSolver unsafe_finish_tac =
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  make_ss (mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac})
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    addSolver tac =
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  make_ss (mss, subgoal_tac, loop_tacs, finish_tac,
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    fn hyps => unsafe_finish_tac hyps ORELSE' tac hyps);
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac})
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    setmksimps mk_simps =
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  make_ss (Thm.set_mk_rews (mss, map (Thm.strip_shyps o Drule.zero_var_indexes) o mk_simps),
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    subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac})
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    setmkeqTrue mk_eq_True =
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  make_ss (Thm.set_mk_eq_True (mss, mk_eq_True),
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    subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac})
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    setmksym mksym =
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  make_ss (Thm.set_mk_sym (mss, mksym),
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    subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs,  finish_tac, unsafe_finish_tac})
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    settermless termless =
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  make_ss (Thm.set_termless (mss, termless), subgoal_tac, loop_tacs,
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    finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac})
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    addsimps rews =
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  make_ss (Thm.add_simps (mss, rews), subgoal_tac, loop_tacs,
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           finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac})
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    delsimps rews =
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  make_ss (Thm.del_simps (mss, rews), subgoal_tac, loop_tacs,
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           finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac})
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    addeqcongs newcongs =
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  make_ss (Thm.add_congs (mss, newcongs), subgoal_tac, loop_tacs,
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    finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac})
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    deleqcongs oldcongs =
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  make_ss (Thm.del_congs (mss, oldcongs), subgoal_tac, loop_tacs,
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    finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac})
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    addsimprocs simprocs =
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  make_ss
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    (Thm.add_simprocs (mss, map rep_simproc simprocs),
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      subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac);
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fun (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac})
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    delsimprocs simprocs =
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  make_ss
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    (Thm.del_simprocs (mss, map rep_simproc simprocs),
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      subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac);
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(* merge simpsets *)	(*NOTE: ignores tactics of 2nd simpset (except loopers)*)
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fun merge_ss
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   (Simpset {mss = mss1, loop_tacs = loop_tacs1, subgoal_tac, finish_tac, unsafe_finish_tac},
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    Simpset {mss = mss2, loop_tacs = loop_tacs2, ...}) =
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  make_ss (Thm.merge_mss (mss1, mss2), subgoal_tac,
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    merge_alists loop_tacs1 loop_tacs2, finish_tac, unsafe_finish_tac);
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(** global and local simpset data **)
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val simpsetN = "Provers/simpset";
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(* data kind 'Provers/simpset' *)
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structure SimpsetDataArgs =
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struct
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  val name = simpsetN;
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  type T = simpset ref;
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  val empty = ref empty_ss;
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  fun prep_ext (ref ss) = (ref ss): T;		  (*create new reference!*)
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  fun merge (ref ss1, ref ss2) = ref (merge_ss (ss1, ss2));
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  fun print _ (ref ss) = print_ss ss;
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end;
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structure SimpsetData = TheoryDataFun(SimpsetDataArgs);
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val print_simpset = SimpsetData.print;
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val simpset_ref_of_sg = SimpsetData.get_sg;
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val simpset_ref_of = SimpsetData.get;
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(* access global simpset *)
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val simpset_of_sg = ! o simpset_ref_of_sg;
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val simpset_of = simpset_of_sg o sign_of;
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fun SIMPSET tacf state = tacf (simpset_of_sg (sign_of_thm state)) state;
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fun SIMPSET' tacf i state = tacf (simpset_of_sg (sign_of_thm state)) i state;
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val simpset = simpset_of o Context.the_context;
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val simpset_ref = simpset_ref_of_sg o sign_of o Context.the_context;
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(* change global simpset *)
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fun change_simpset f x = simpset_ref () := (f (simpset (), x));
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val Addsimps = change_simpset (op addsimps);
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val Delsimps = change_simpset (op delsimps);
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val Addsimprocs = change_simpset (op addsimprocs);
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val Delsimprocs = change_simpset (op delsimprocs);
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(* local simpset *)
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exception SimpsetLocal of simpset;
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val simpset_localK = Object.kind simpsetN;
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fun get_local_simpset (thy, data) =
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  (case Symtab.lookup (data, simpsetN) of
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    Some (SimpsetLocal ss) => ss
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  | None => simpset_of thy
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  | _ => Object.kind_error simpset_localK);
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fun put_local_simpset ss (thy, data) =
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  (thy, Symtab.update ((simpsetN, SimpsetLocal ss), data));
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(** simplifier attributes **)
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(* tags *)
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val simpN = "simp";
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val simp_addN = "add";
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val simp_delN = "del";
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val simp_tag = (simpN, []);
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val simp_add = (simpN, [simp_addN]);
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val simp_del = (simpN, [simp_delN]);
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(* attributes *)
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local
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  fun simp_attr change args (x, tth) =
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    if null args orelse args = [simp_addN] then change (op addsimps) (x, tth)
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    else if args = [simp_delN] then change (op delsimps) (x, tth)
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    else Attribute.fail simpN ("bad argument(s) " ^ commas_quote args);
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  fun change_global_ss f (thy, tth) =
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    let val r = simpset_ref_of thy
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    in r := f (! r, [Attribute.thm_of tth]); (thy, tth) end;
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  fun change_local_ss f (lthy, tth) =
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    let val ss = f (get_local_simpset lthy, [Attribute.thm_of tth])
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    in (put_local_simpset ss lthy, tth) end;
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  val simp_attr_global = simp_attr change_global_ss;
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  val simp_attr_local = simp_attr change_local_ss;
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in
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(* FIXME
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  val setup_attrs = IsarThy.add_attributes
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    [(simpN, simp_attr_global, simp_attr_local, "simplifier")];
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*)
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  val setup_attrs = I;
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  val simp_add_global = simp_attr_global [simp_addN];
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  val simp_del_global = simp_attr_global [simp_delN];
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  val simp_add_local = simp_attr_local [simp_addN];
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  val simp_del_local = simp_attr_local [simp_delN];
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end;
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(** simplification tactics **)
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fun solve_all_tac (subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac) mss =
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  let
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    val ss =
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      make_ss (mss, subgoal_tac, loop_tacs, unsafe_finish_tac, unsafe_finish_tac);
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    val solve1_tac = (subgoal_tac ss THEN_ALL_NEW (K no_tac)) 1
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  in DEPTH_SOLVE solve1_tac end;
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fun loop_tac loop_tacs = FIRST'(map snd loop_tacs);
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(*not totally safe: may instantiate unknowns that appear also in other subgoals*)
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fun basic_gen_simp_tac mode =
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  fn (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac}) =>
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    let
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      fun simp_loop_tac i =
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        asm_rewrite_goal_tac mode
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          (solve_all_tac (subgoal_tac,loop_tacs,finish_tac,unsafe_finish_tac))
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          mss i
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        THEN (finish_tac (prems_of_mss mss) i ORELSE
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              TRY ((loop_tac loop_tacs THEN_ALL_NEW simp_loop_tac) i))
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    in simp_loop_tac end;
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fun gen_simp_tac mode (ss as Simpset {unsafe_finish_tac, ...}) =
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  basic_gen_simp_tac mode (ss setSSolver unsafe_finish_tac);
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val          simp_tac = gen_simp_tac (false, false, false);
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val      asm_simp_tac = gen_simp_tac (false, true, false);
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val     full_simp_tac = gen_simp_tac (true,  false, false);
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val   asm_lr_simp_tac = gen_simp_tac (true,  true, false);
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val asm_full_simp_tac = gen_simp_tac (true,  true, true);
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(*not totally safe: may instantiate unknowns that appear also in other subgoals*)
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val safe_asm_full_simp_tac = basic_gen_simp_tac (true, true, false);
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(*the abstraction over the proof state delays the dereferencing*)
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fun          Simp_tac i st =          simp_tac (simpset ()) i st;
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fun      Asm_simp_tac i st =      asm_simp_tac (simpset ()) i st;
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fun     Full_simp_tac i st =     full_simp_tac (simpset ()) i st;
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fun   Asm_lr_simp_tac i st =   asm_lr_simp_tac (simpset ()) i st;
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fun Asm_full_simp_tac i st = asm_full_simp_tac (simpset ()) i st;
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4d4e0442b106 simpset is hidden in a functor now.
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(** simplification rules and conversions **)
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fun simp rew mode (Simpset {mss, subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac}) thm =
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  let
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    val tacf = solve_all_tac (subgoal_tac, loop_tacs, finish_tac, unsafe_finish_tac);
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    fun prover m th = apsome fst (Seq.pull (tacf m th));
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  in rew mode prover mss thm end;
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val simp_thm = simp Drule.rewrite_thm;
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val simp_cterm = simp Drule.rewrite_cterm;
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val          simplify = simp_thm (false, false, false);
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val      asm_simplify = simp_thm (false, true, false);
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val     full_simplify = simp_thm (true, false, false);
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   425
val asm_full_simplify = simp_thm (true, true, false);
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   427
val          rewrite = simp_cterm (false, false, false);
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   428
val      asm_rewrite = simp_cterm (false, true, false);
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val     full_rewrite = simp_cterm (true, false, false);
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val asm_full_rewrite = simp_cterm (true, true, false);
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(** theory setup **)
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   436
val setup = [SimpsetData.init, setup_attrs];
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fa09705a5890 added global simpset
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end;
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structure BasicSimplifier: BASIC_SIMPLIFIER = Simplifier;
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   443
open BasicSimplifier;