src/Pure/simplifier.ML
author wenzelm
Sun Nov 11 20:31:46 2012 +0100 (2012-11-11)
changeset 50081 9b92ee8dec98
parent 48776 37cd53e69840
child 50107 289181e3e524
permissions -rw-r--r--
tuned;
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(*  Title:      Pure/simplifier.ML
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    Author:     Tobias Nipkow and Markus Wenzel, TU Muenchen
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Generic simplifier, suitable for most logics (see also
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raw_simplifier.ML for the actual meta-level rewriting engine).
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*)
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signature BASIC_SIMPLIFIER =
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sig
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  include BASIC_RAW_SIMPLIFIER
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  val map_simpset: (simpset -> simpset) -> Proof.context -> Proof.context
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  val simpset_of: Proof.context -> simpset
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  val global_simpset_of: theory -> simpset
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  val Addsimprocs: simproc list -> unit
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  val Delsimprocs: simproc list -> unit
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  val generic_simp_tac: bool -> bool * bool * bool -> simpset -> int -> tactic
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  val safe_asm_full_simp_tac: simpset -> int -> tactic
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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 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_lr_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 map_simpset_global: (simpset -> simpset) -> theory -> theory
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  val pretty_ss: Proof.context -> simpset -> Pretty.T
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  val clear_ss: simpset -> simpset
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  val default_mk_sym: simpset -> thm -> thm option
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  val debug_bounds: bool Unsynchronized.ref
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  val prems_of: simpset -> thm list
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  val add_simp: thm -> simpset -> simpset
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  val del_simp: thm -> simpset -> simpset
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  val add_eqcong: thm -> simpset -> simpset
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  val del_eqcong: thm -> simpset -> simpset
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  val add_cong: thm -> simpset -> simpset
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  val del_cong: thm -> simpset -> simpset
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  val add_prems: thm list -> simpset -> simpset
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  val mksimps: simpset -> thm -> thm list
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  val set_mksimps: (simpset -> thm -> thm list) -> simpset -> simpset
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  val set_mkcong: (simpset -> thm -> thm) -> simpset -> simpset
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  val set_mksym: (simpset -> thm -> thm option) -> simpset -> simpset
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  val set_mkeqTrue: (simpset -> thm -> thm option) -> simpset -> simpset
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  val set_termless: (term * term -> bool) -> simpset -> simpset
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  val set_subgoaler: (simpset -> int -> tactic) -> simpset -> simpset
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  val inherit_context: simpset -> simpset -> simpset
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  val the_context: simpset -> Proof.context
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  val context: Proof.context -> simpset -> simpset
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  val global_context: theory -> simpset -> simpset
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  val with_context: Proof.context -> (simpset -> simpset) -> simpset -> simpset
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  val simproc_global_i: theory -> string -> term list ->
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    (theory -> simpset -> term -> thm option) -> simproc
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  val simproc_global: theory -> string -> string list ->
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    (theory -> simpset -> term -> thm option) -> simproc
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  val rewrite: simpset -> conv
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  val asm_rewrite: simpset -> conv
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  val full_rewrite: simpset -> conv
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  val asm_lr_rewrite: simpset -> conv
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  val asm_full_rewrite: simpset -> conv
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  val get_ss: Context.generic -> simpset
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  val map_ss: (simpset -> simpset) -> Context.generic -> Context.generic
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  val attrib: (thm -> simpset -> simpset) -> attribute
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  val simp_add: attribute
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  val simp_del: attribute
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  val cong_add: attribute
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  val cong_del: attribute
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  val check_simproc: Proof.context -> xstring * Position.T -> string
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  val the_simproc: Proof.context -> string -> simproc
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  val def_simproc: {name: binding, lhss: term list,
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    proc: morphism -> simpset -> cterm -> thm option, identifier: thm list} ->
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    local_theory -> local_theory
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  val def_simproc_cmd: {name: binding, lhss: string list,
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    proc: morphism -> simpset -> cterm -> thm option, identifier: thm list} ->
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    local_theory -> local_theory
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  val cong_modifiers: Method.modifier parser list
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  val simp_modifiers': Method.modifier parser list
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  val simp_modifiers: Method.modifier parser list
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  val method_setup: Method.modifier parser list -> theory -> theory
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  val easy_setup: thm -> thm list -> theory -> theory
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end;
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structure Simplifier: SIMPLIFIER =
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struct
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open Raw_Simplifier;
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(** data **)
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structure Data = Generic_Data
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(
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  type T = simpset * simproc Name_Space.table;
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  val empty : T = (empty_ss, Name_Space.empty_table "simproc");
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  fun extend (ss, tab) = (Raw_Simplifier.inherit_context empty_ss ss, tab);
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  fun merge ((ss1, tab1), (ss2, tab2)) =
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    (merge_ss (ss1, ss2), Name_Space.merge_tables (tab1, tab2));
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);
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val get_ss = fst o Data.get;
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fun map_ss f context =
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  Data.map (apfst ((Raw_Simplifier.with_context (Context.proof_of context) f))) context;
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val get_simprocs = snd o Data.get o Context.Proof;
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(** pretty printing **)
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fun pretty_ss ctxt ss =
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  let
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    val pretty_cterm = Syntax.pretty_term ctxt o Thm.term_of;
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    val pretty_thm = Display.pretty_thm ctxt;
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    fun pretty_proc (name, lhss) = Pretty.big_list (name ^ ":") (map pretty_cterm lhss);
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    fun pretty_cong (name, thm) =
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      Pretty.block [Pretty.str (name ^ ":"), Pretty.brk 1, pretty_thm thm];
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    val {simps, procs, congs, loopers, unsafe_solvers, safe_solvers, ...} = dest_ss ss;
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  in
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    [Pretty.big_list "simplification rules:" (map (pretty_thm o #2) simps),
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      Pretty.big_list "simplification procedures:" (map pretty_proc (sort_wrt #1 procs)),
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      Pretty.big_list "congruences:" (map pretty_cong congs),
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      Pretty.strs ("loopers:" :: map quote loopers),
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      Pretty.strs ("unsafe solvers:" :: map quote unsafe_solvers),
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      Pretty.strs ("safe solvers:" :: map quote safe_solvers)]
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    |> Pretty.chunks
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  end;
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(** simpset data **)
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(* attributes *)
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fun attrib f = Thm.declaration_attribute (map_ss o f);
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val simp_add = attrib add_simp;
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val simp_del = attrib del_simp;
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val cong_add = attrib add_cong;
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val cong_del = attrib del_cong;
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(* local simpset *)
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fun map_simpset f = Context.proof_map (map_ss f);
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fun simpset_of ctxt = Raw_Simplifier.context ctxt (get_ss (Context.Proof ctxt));
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val _ = Context.>> (Context.map_theory
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  (ML_Antiquote.value (Binding.name "simpset")
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    (Scan.succeed "Simplifier.simpset_of ML_context")));
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(* global simpset *)
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fun map_simpset_global f = Context.theory_map (map_ss f);
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fun global_simpset_of thy =
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  Raw_Simplifier.context (Proof_Context.init_global thy) (get_ss (Context.Theory thy));
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fun Addsimprocs args = Context.>> (map_ss (fn ss => ss addsimprocs args));
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fun Delsimprocs args = Context.>> (map_ss (fn ss => ss delsimprocs args));
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(** named simprocs **)
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(* get simprocs *)
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fun check_simproc ctxt = Name_Space.check (Context.Proof ctxt) (get_simprocs ctxt) #> #1;
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val the_simproc = Name_Space.get o get_simprocs;
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val _ =
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  Context.>> (Context.map_theory
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   (ML_Antiquote.value (Binding.name "simproc")
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      (Args.context -- Scan.lift (Parse.position Args.name)
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        >> (fn (ctxt, name) =>
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          "Simplifier.the_simproc ML_context " ^
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            ML_Syntax.print_string (check_simproc ctxt name)))));
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(* define simprocs *)
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local
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fun gen_simproc prep {name = b, lhss, proc, identifier} lthy =
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  let
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    val simproc = make_simproc
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      {name = Local_Theory.full_name lthy b,
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       lhss =
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        let
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          val lhss' = prep lthy lhss;
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          val ctxt' = fold Variable.auto_fixes lhss' lthy;
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        in Variable.export_terms ctxt' lthy lhss' end
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        |> map (Thm.cterm_of (Proof_Context.theory_of lthy)),
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       proc = proc,
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       identifier = identifier};
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  in
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    lthy |> Local_Theory.declaration {syntax = false, pervasive = true} (fn phi => fn context =>
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      let
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        val b' = Morphism.binding phi b;
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        val simproc' = transform_simproc phi simproc;
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      in
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        context
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        |> Data.map (fn (ss, tab) =>
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          (ss addsimprocs [simproc'], #2 (Name_Space.define context true (b', simproc') tab)))
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      end)
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  end;
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in
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val def_simproc = gen_simproc Syntax.check_terms;
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val def_simproc_cmd = gen_simproc Syntax.read_terms;
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end;
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(** simplification tactics and rules **)
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fun solve_all_tac solvers ss =
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  let
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    val (_, {subgoal_tac, ...}) = Raw_Simplifier.internal_ss ss;
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    val solve_tac = subgoal_tac (Raw_Simplifier.set_solvers solvers ss) THEN_ALL_NEW (K no_tac);
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  in DEPTH_SOLVE (solve_tac 1) end;
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(*NOTE: may instantiate unknowns that appear also in other subgoals*)
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fun generic_simp_tac safe mode ss =
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  let
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    val (_, {loop_tacs, solvers = (unsafe_solvers, solvers), ...}) = Raw_Simplifier.internal_ss ss;
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    val loop_tac = FIRST' (map (fn (_, tac) => tac ss) (rev loop_tacs));
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    val solve_tac = FIRST' (map (Raw_Simplifier.solver ss)
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      (rev (if safe then solvers else unsafe_solvers)));
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    fun simp_loop_tac i =
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      Raw_Simplifier.generic_rewrite_goal_tac mode (solve_all_tac unsafe_solvers) ss i THEN
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      (solve_tac i ORELSE TRY ((loop_tac THEN_ALL_NEW simp_loop_tac) i));
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  in SELECT_GOAL (simp_loop_tac 1) end;
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local
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fun simp rew mode ss thm =
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  let
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    val (_, {solvers = (unsafe_solvers, _), ...}) = Raw_Simplifier.internal_ss ss;
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    val tacf = solve_all_tac (rev unsafe_solvers);
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    fun prover s th = Option.map #1 (Seq.pull (tacf s th));
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  in rew mode prover ss thm end;
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in
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val simp_thm = simp Raw_Simplifier.rewrite_thm;
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val simp_cterm = simp Raw_Simplifier.rewrite_cterm;
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end;
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(* tactics *)
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val simp_tac = generic_simp_tac false (false, false, false);
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val asm_simp_tac = generic_simp_tac false (false, true, false);
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val full_simp_tac = generic_simp_tac false (true, false, false);
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val asm_lr_simp_tac = generic_simp_tac false (true, true, false);
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val asm_full_simp_tac = generic_simp_tac false (true, true, true);
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val safe_asm_full_simp_tac = generic_simp_tac true (true, true, true);
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(* conversions *)
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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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val   asm_lr_simplify = simp_thm (true, true, false);
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val asm_full_simplify = simp_thm (true, true, true);
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val          rewrite = simp_cterm (false, false, false);
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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_lr_rewrite = simp_cterm (true, true, false);
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val asm_full_rewrite = simp_cterm (true, true, true);
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(** concrete syntax of attributes **)
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(* add / del *)
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val simpN = "simp";
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val congN = "cong";
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val onlyN = "only";
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val no_asmN = "no_asm";
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val no_asm_useN = "no_asm_use";
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val no_asm_simpN = "no_asm_simp";
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val asm_lrN = "asm_lr";
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(* simprocs *)
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local
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val add_del =
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  (Args.del -- Args.colon >> K (op delsimprocs) ||
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    Scan.option (Args.add -- Args.colon) >> K (op addsimprocs))
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  >> (fn f => fn simproc => fn phi => Thm.declaration_attribute
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      (K (map_ss (fn ss => f (ss, [transform_simproc phi simproc])))));
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in
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val simproc_att =
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  (Args.context -- Scan.lift add_del) :|-- (fn (ctxt, decl) =>
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    Scan.repeat1 (Scan.lift (Args.named_attribute (decl o the_simproc ctxt o check_simproc ctxt))))
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  >> (fn atts => Thm.declaration_attribute (fn th =>
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        fold (fn att => Thm.attribute_declaration (Morphism.form att) th) atts));
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end;
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(* conversions *)
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local
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fun conv_mode x =
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  ((Args.parens (Args.$$$ no_asmN) >> K simplify ||
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    Args.parens (Args.$$$ no_asm_simpN) >> K asm_simplify ||
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    Args.parens (Args.$$$ no_asm_useN) >> K full_simplify ||
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    Scan.succeed asm_full_simplify) |> Scan.lift) x;
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in
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val simplified = conv_mode -- Attrib.thms >>
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  (fn (f, ths) => Thm.rule_attribute (fn context =>
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    f ((if null ths then I else Raw_Simplifier.clear_ss)
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        (simpset_of (Context.proof_of context)) addsimps ths)));
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end;
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(* setup attributes *)
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val _ = Context.>> (Context.map_theory
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 (Attrib.setup (Binding.name simpN) (Attrib.add_del simp_add simp_del)
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    "declaration of Simplifier rewrite rule" #>
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  Attrib.setup (Binding.name congN) (Attrib.add_del cong_add cong_del)
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    "declaration of Simplifier congruence rule" #>
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  Attrib.setup (Binding.name "simproc") simproc_att
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    "declaration of simplification procedures" #>
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  Attrib.setup (Binding.name "simplified") simplified "simplified rule"));
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(** method syntax **)
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val cong_modifiers =
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 [Args.$$$ congN -- Args.colon >> K ((I, cong_add): Method.modifier),
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  Args.$$$ congN -- Args.add -- Args.colon >> K (I, cong_add),
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  Args.$$$ congN -- Args.del -- Args.colon >> K (I, cong_del)];
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val simp_modifiers =
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 [Args.$$$ simpN -- Args.colon >> K (I, simp_add),
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  Args.$$$ simpN -- Args.add -- Args.colon >> K (I, simp_add),
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  Args.$$$ simpN -- Args.del -- Args.colon >> K (I, simp_del),
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  Args.$$$ simpN -- Args.$$$ onlyN -- Args.colon
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    >> K (Context.proof_map (map_ss Raw_Simplifier.clear_ss), simp_add)]
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   @ cong_modifiers;
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val simp_modifiers' =
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 [Args.add -- Args.colon >> K (I, simp_add),
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  Args.del -- Args.colon >> K (I, simp_del),
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  Args.$$$ onlyN -- Args.colon
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    >> K (Context.proof_map (map_ss Raw_Simplifier.clear_ss), simp_add)]
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   @ cong_modifiers;
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val simp_options =
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 (Args.parens (Args.$$$ no_asmN) >> K simp_tac ||
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  Args.parens (Args.$$$ no_asm_simpN) >> K asm_simp_tac ||
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  Args.parens (Args.$$$ no_asm_useN) >> K full_simp_tac ||
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  Args.parens (Args.$$$ asm_lrN) >> K asm_lr_simp_tac ||
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  Scan.succeed asm_full_simp_tac);
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fun simp_method more_mods meth =
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  Scan.lift simp_options --|
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    Method.sections (more_mods @ simp_modifiers') >>
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    (fn tac => fn ctxt => METHOD (fn facts => meth ctxt tac facts));
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(** setup **)
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fun method_setup more_mods =
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  Method.setup (Binding.name simpN)
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    (simp_method more_mods (fn ctxt => fn tac => fn facts =>
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      HEADGOAL (Method.insert_tac facts THEN'
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        (CHANGED_PROP oo tac) (simpset_of ctxt))))
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    "simplification" #>
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  Method.setup (Binding.name "simp_all")
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    (simp_method more_mods (fn ctxt => fn tac => fn facts =>
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      ALLGOALS (Method.insert_tac facts) THEN
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        (CHANGED_PROP o PARALLEL_GOALS o ALLGOALS o tac) (simpset_of ctxt)))
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    "simplification (all goals)";
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fun easy_setup reflect trivs = method_setup [] #> Context.theory_map (map_ss (fn _ =>
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  let
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    val trivialities = Drule.reflexive_thm :: trivs;
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    fun unsafe_solver_tac ss =
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      FIRST' [resolve_tac (trivialities @ Raw_Simplifier.prems_of ss), assume_tac];
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    val unsafe_solver = mk_solver "easy unsafe" unsafe_solver_tac;
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    (*no premature instantiation of variables during simplification*)
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    fun safe_solver_tac ss =
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      FIRST' [match_tac (trivialities @ Raw_Simplifier.prems_of ss), eq_assume_tac];
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    val safe_solver = mk_solver "easy safe" safe_solver_tac;
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    fun mk_eq thm =
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      if can Logic.dest_equals (Thm.concl_of thm) then [thm]
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      else [thm RS reflect] handle THM _ => [];
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   421
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    fun mksimps thm = mk_eq (Thm.forall_elim_vars (Thm.maxidx_of thm + 1) thm);
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  in
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   424
    empty_ss
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    setSSolver safe_solver
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   426
    setSolver unsafe_solver
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    |> set_subgoaler asm_simp_tac
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    |> set_mksimps (K mksimps)
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  end));
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   430
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   431
end;
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   432
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   433
structure Basic_Simplifier: BASIC_SIMPLIFIER = Simplifier;
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open Basic_Simplifier;