src/HOL/Nonstandard_Analysis/transfer.ML
author haftmann
Mon Jun 05 15:59:41 2017 +0200 (2017-06-05)
changeset 66010 2f7d39285a1a
parent 64435 c93b0e6131c3
permissions -rw-r--r--
executable domain membership checks
     1 (*  Title:      HOL/Nonstandard_Analysis/transfer.ML
     2     Author:     Brian Huffman
     3 
     4 Transfer principle tactic for nonstandard analysis.
     5 *)
     6 
     7 signature TRANSFER_PRINCIPLE =
     8 sig
     9   val transfer_tac: Proof.context -> thm list -> int -> tactic
    10   val add_const: string -> theory -> theory
    11 end;
    12 
    13 structure Transfer_Principle: TRANSFER_PRINCIPLE =
    14 struct
    15 
    16 structure Data = Generic_Data
    17 (
    18   type T = {
    19     intros: thm list,
    20     unfolds: thm list,
    21     refolds: thm list,
    22     consts: string list
    23   };
    24   val empty = {intros = [], unfolds = [], refolds = [], consts = []};
    25   val extend = I;
    26   fun merge
    27     ({intros = intros1, unfolds = unfolds1,
    28       refolds = refolds1, consts = consts1},
    29      {intros = intros2, unfolds = unfolds2,
    30       refolds = refolds2, consts = consts2}) : T =
    31    {intros = Thm.merge_thms (intros1, intros2),
    32     unfolds = Thm.merge_thms (unfolds1, unfolds2),
    33     refolds = Thm.merge_thms (refolds1, refolds2),
    34     consts = Library.merge (op =) (consts1, consts2)};
    35 );
    36 
    37 fun unstar_typ (Type (@{type_name star}, [t])) = unstar_typ t
    38   | unstar_typ (Type (a, Ts)) = Type (a, map unstar_typ Ts)
    39   | unstar_typ T = T
    40 
    41 fun unstar_term consts term =
    42   let
    43     fun unstar (Const(a,T) $ t) = if member (op =) consts a then (unstar t)
    44           else (Const(a,unstar_typ T) $ unstar t)
    45       | unstar (f $ t) = unstar f $ unstar t
    46       | unstar (Const(a,T)) = Const(a,unstar_typ T)
    47       | unstar (Abs(a,T,t)) = Abs(a,unstar_typ T,unstar t)
    48       | unstar t = t
    49   in
    50     unstar term
    51   end
    52 
    53 local exception MATCH
    54 in
    55 fun transfer_star_tac ctxt =
    56   let
    57     fun thm_of (Const (@{const_name Ifun}, _) $ t $ u) = @{thm transfer_Ifun} OF [thm_of t, thm_of u]
    58       | thm_of (Const (@{const_name star_of}, _) $ _) = @{thm star_of_def}
    59       | thm_of (Const (@{const_name star_n}, _) $ _) = @{thm Pure.reflexive}
    60       | thm_of _ = raise MATCH;
    61 
    62     fun thm_of_goal (Const (@{const_name Pure.eq}, _) $ t $ (Const (@{const_name star_n}, _) $ _)) =
    63           thm_of t
    64       | thm_of_goal _ = raise MATCH;
    65   in
    66     SUBGOAL (fn (t, i) =>
    67       resolve_tac ctxt [thm_of_goal (strip_all_body t |> Logic.strip_imp_concl)] i
    68       handle MATCH => no_tac)
    69   end;
    70 end;
    71 
    72 fun transfer_thm_of ctxt ths t =
    73   let
    74     val {intros,unfolds,refolds,consts} = Data.get (Context.Proof ctxt);
    75     val meta = Local_Defs.meta_rewrite_rule ctxt;
    76     val ths' = map meta ths;
    77     val unfolds' = map meta unfolds and refolds' = map meta refolds;
    78     val (_$_$t') = Thm.concl_of (Raw_Simplifier.rewrite ctxt true unfolds' (Thm.cterm_of ctxt t))
    79     val u = unstar_term consts t'
    80     val tac =
    81       rewrite_goals_tac ctxt (ths' @ refolds' @ unfolds') THEN
    82       ALLGOALS (Object_Logic.full_atomize_tac ctxt) THEN
    83       match_tac ctxt [transitive_thm] 1 THEN
    84       resolve_tac ctxt [@{thm transfer_start}] 1 THEN
    85       REPEAT_ALL_NEW (resolve_tac ctxt intros ORELSE' transfer_star_tac ctxt) 1 THEN
    86       match_tac ctxt [reflexive_thm] 1
    87   in Goal.prove ctxt [] [] (Logic.mk_equals (t,u)) (K tac) end;
    88 
    89 fun transfer_tac ctxt ths = SUBGOAL (fn (t, _) => (fn th =>
    90   let
    91     val tr = transfer_thm_of ctxt ths t
    92     val (_$ l $ r) = Thm.concl_of tr;
    93     val trs = if l aconv r then [] else [tr];
    94   in rewrite_goals_tac ctxt trs th end));
    95 
    96 local
    97 
    98 fun map_intros f = Data.map
    99   (fn {intros,unfolds,refolds,consts} =>
   100     {intros=f intros, unfolds=unfolds, refolds=refolds, consts=consts})
   101 
   102 fun map_unfolds f = Data.map
   103   (fn {intros,unfolds,refolds,consts} =>
   104     {intros=intros, unfolds=f unfolds, refolds=refolds, consts=consts})
   105 
   106 fun map_refolds f = Data.map
   107   (fn {intros,unfolds,refolds,consts} =>
   108     {intros=intros, unfolds=unfolds, refolds=f refolds, consts=consts})
   109 in
   110 
   111 val intro_add = Thm.declaration_attribute (map_intros o Thm.add_thm);
   112 val intro_del = Thm.declaration_attribute (map_intros o Thm.del_thm);
   113 
   114 val unfold_add = Thm.declaration_attribute (map_unfolds o Thm.add_thm);
   115 val unfold_del = Thm.declaration_attribute (map_unfolds o Thm.del_thm);
   116 
   117 val refold_add = Thm.declaration_attribute (map_refolds o Thm.add_thm);
   118 val refold_del = Thm.declaration_attribute (map_refolds o Thm.del_thm);
   119 
   120 end
   121 
   122 fun add_const c = Context.theory_map (Data.map
   123   (fn {intros,unfolds,refolds,consts} =>
   124     {intros=intros, unfolds=unfolds, refolds=refolds, consts=c::consts}))
   125 
   126 val _ =
   127   Theory.setup
   128    (Attrib.setup @{binding transfer_intro} (Attrib.add_del intro_add intro_del)
   129       "declaration of transfer introduction rule" #>
   130     Attrib.setup @{binding transfer_unfold} (Attrib.add_del unfold_add unfold_del)
   131       "declaration of transfer unfolding rule" #>
   132     Attrib.setup @{binding transfer_refold} (Attrib.add_del refold_add refold_del)
   133       "declaration of transfer refolding rule")
   134 
   135 end;