File transfer.ML (Isabelle2005: October 2005)

# File transfer.ML

    (*  Title       : HOL/Hyperreal/transfer.ML
        ID          : $Id: transfer.ML,v 1.5 2005/09/15 23:42:57 huffman Exp $
        Author      : Brian Huffman

    Transfer principle tactic for nonstandard analysis
    *)

    signature TRANSFER_TAC =
    sig
      val transfer_tac: thm list -> int -> tactic
      val add_const: string -> theory -> theory
      val setup: (theory -> theory) list
    end;

    structure Transfer: TRANSFER_TAC =
    struct

    structure TransferData = TheoryDataFun
    (struct
      val name = "HOL/transfer";
      type T = {
        intros: thm list,
        unfolds: thm list,
        refolds: thm list,
        consts: string list
      };
      val empty = {intros = [], unfolds = [], refolds = [], consts = []};
      val copy = I;
      val extend = I;
      fun merge _
        ({intros = intros1, unfolds = unfolds1,
          refolds = refolds1, consts = consts1},
         {intros = intros2, unfolds = unfolds2,
          refolds = refolds2, consts = consts2}) =
       {intros = Drule.merge_rules (intros1, intros2),
        unfolds = Drule.merge_rules (unfolds1, unfolds2),
        refolds = Drule.merge_rules (refolds1, refolds2),
        consts = merge_lists consts1 consts2};
      fun print _ _ = ();
    end);

    val transfer_start = thm "transfer_start"

    fun unstar_typ (Type ("StarDef.star",[t])) = unstar_typ t
      | unstar_typ (Type (a, Ts)) = Type (a, map unstar_typ Ts)
      | unstar_typ T = T

    fun unstar_term consts term =
      let
        fun unstar (Const(a,T) $ t) = if (a mem consts) then (unstar t)
              else (Const(a,unstar_typ T) $ unstar t)
          | unstar (f $ t) = unstar f $ unstar t
          | unstar (Const(a,T)) = Const(a,unstar_typ T)
          | unstar (Abs(a,T,t)) = Abs(a,unstar_typ T,unstar t)
          | unstar t = t
      in
        unstar term
      end

    val atomizers = map thm ["atomize_all", "atomize_imp", "atomize_eq"]

    fun transfer_thm_of thy ths t =
      let
        val {intros,unfolds,refolds,consts} = TransferData.get thy
        val (_$_$t') = concl_of (Tactic.rewrite true unfolds (cterm_of thy t))
        val u = unstar_term consts t'
        val ct = cterm_of thy (Logic.mk_equals (t,u))
        val tacs =
          [ rewrite_goals_tac atomizers
          , match_tac [transitive_thm] 1
          , resolve_tac [transfer_start] 1
          , REPEAT_ALL_NEW (resolve_tac intros) 1
          , match_tac [reflexive_thm] 1 ]
      in
        prove_goalw_cterm (ths @ refolds @ unfolds) ct (fn _ => tacs)
      end

    fun transfer_tac ths =
        SUBGOAL (fn (t,i) =>
            (fn th =>
                let val thy = theory_of_thm th
                    val tr = transfer_thm_of thy ths t
                in rewrite_goals_tac [tr] th
                end
            )
        )

    local
    fun map_intros f = TransferData.map
      (fn {intros,unfolds,refolds,consts} =>
        {intros=f intros, unfolds=unfolds, refolds=refolds, consts=consts})

    fun map_unfolds f = TransferData.map
      (fn {intros,unfolds,refolds,consts} =>
        {intros=intros, unfolds=f unfolds, refolds=refolds, consts=consts})

    fun map_refolds f = TransferData.map
      (fn {intros,unfolds,refolds,consts} =>
        {intros=intros, unfolds=unfolds, refolds=f refolds, consts=consts})
    in
    fun intro_add_global (thy, thm) = (map_intros (Drule.add_rule thm) thy, thm);
    fun intro_del_global (thy, thm) = (map_intros (Drule.del_rule thm) thy, thm);

    fun unfold_add_global (thy, thm) = (map_unfolds (Drule.add_rule thm) thy, thm);
    fun unfold_del_global (thy, thm) = (map_unfolds (Drule.del_rule thm) thy, thm);

    fun refold_add_global (thy, thm) = (map_refolds (Drule.add_rule thm) thy, thm);
    fun refold_del_global (thy, thm) = (map_refolds (Drule.del_rule thm) thy, thm);
    end

    fun add_const c = TransferData.map
      (fn {intros,unfolds,refolds,consts} =>
        {intros=intros, unfolds=unfolds, refolds=refolds, consts=c::consts})

    local
      val undef_local =
        Attrib.add_del_args
          Attrib.undef_local_attribute
          Attrib.undef_local_attribute;
    in
      val intro_attr =
       (Attrib.add_del_args intro_add_global intro_del_global, undef_local);
      val unfold_attr =
       (Attrib.add_del_args unfold_add_global unfold_del_global, undef_local);
      val refold_attr =
       (Attrib.add_del_args refold_add_global refold_del_global, undef_local);
    end

    val transfer_method = Method.SIMPLE_METHOD' HEADGOAL o transfer_tac;

    val setup =
      [ TransferData.init,
        Attrib.add_attributes
        [ ("transfer_intro", intro_attr,
           "declaration of transfer introduction rule"),
          ("transfer_unfold", unfold_attr,
           "declaration of transfer unfolding rule"),
          ("transfer_refold", refold_attr,
           "declaration of transfer refolding rule")
        ],
        Method.add_method
        ("transfer", Method.thms_args transfer_method, "transfer principle")
      ];

    end;