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1 (* Title : HOL/Hyperreal/transfer.ML |
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2 ID : $Id$ |
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3 Author : Brian Huffman |
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4 |
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5 Transfer principle tactic for nonstandard analysis. |
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6 *) |
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7 |
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8 signature TRANSFER = |
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9 sig |
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10 val transfer_tac: Proof.context -> thm list -> int -> tactic |
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11 val add_const: string -> theory -> theory |
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12 val setup: theory -> theory |
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13 end; |
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14 |
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15 structure Transfer: TRANSFER = |
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16 struct |
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17 |
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18 structure TransferData = GenericDataFun |
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19 ( |
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20 type T = { |
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21 intros: thm list, |
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22 unfolds: thm list, |
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23 refolds: thm list, |
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24 consts: string list |
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25 }; |
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26 val empty = {intros = [], unfolds = [], refolds = [], consts = []}; |
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27 val extend = I; |
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28 fun merge _ |
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29 ({intros = intros1, unfolds = unfolds1, |
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30 refolds = refolds1, consts = consts1}, |
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31 {intros = intros2, unfolds = unfolds2, |
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32 refolds = refolds2, consts = consts2}) = |
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33 {intros = Thm.merge_thms (intros1, intros2), |
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34 unfolds = Thm.merge_thms (unfolds1, unfolds2), |
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35 refolds = Thm.merge_thms (refolds1, refolds2), |
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36 consts = Library.merge (op =) (consts1, consts2)} : T; |
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37 ); |
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38 |
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39 fun unstar_typ (Type ("StarDef.star",[t])) = unstar_typ t |
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40 | unstar_typ (Type (a, Ts)) = Type (a, map unstar_typ Ts) |
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41 | unstar_typ T = T |
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42 |
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43 fun unstar_term consts term = |
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44 let |
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45 fun unstar (Const(a,T) $ t) = if member (op =) consts a then (unstar t) |
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46 else (Const(a,unstar_typ T) $ unstar t) |
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47 | unstar (f $ t) = unstar f $ unstar t |
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48 | unstar (Const(a,T)) = Const(a,unstar_typ T) |
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49 | unstar (Abs(a,T,t)) = Abs(a,unstar_typ T,unstar t) |
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50 | unstar t = t |
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51 in |
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52 unstar term |
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53 end |
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54 |
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55 fun transfer_thm_of ctxt ths t = |
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56 let |
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57 val thy = ProofContext.theory_of ctxt; |
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58 val {intros,unfolds,refolds,consts} = TransferData.get (Context.Proof ctxt); |
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59 val meta = LocalDefs.meta_rewrite_rule ctxt; |
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60 val ths' = map meta ths; |
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61 val unfolds' = map meta unfolds and refolds' = map meta refolds; |
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62 val (_$_$t') = concl_of (MetaSimplifier.rewrite true unfolds' (cterm_of thy t)) |
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63 val u = unstar_term consts t' |
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64 val tac = |
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65 rewrite_goals_tac (ths' @ refolds' @ unfolds') THEN |
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66 ALLGOALS ObjectLogic.full_atomize_tac THEN |
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67 match_tac [transitive_thm] 1 THEN |
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68 resolve_tac [@{thm transfer_start}] 1 THEN |
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69 REPEAT_ALL_NEW (resolve_tac intros) 1 THEN |
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70 match_tac [reflexive_thm] 1 |
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71 in Goal.prove ctxt [] [] (Logic.mk_equals (t,u)) (K tac) end |
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72 |
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73 fun transfer_tac ctxt ths = |
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74 SUBGOAL (fn (t,i) => |
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75 (fn th => |
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76 let |
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77 val tr = transfer_thm_of ctxt ths t |
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78 val (_$l$r) = concl_of tr; |
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79 val trs = if l aconv r then [] else [tr]; |
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80 in rewrite_goals_tac trs th end)) |
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81 |
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82 local |
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83 |
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84 fun map_intros f = TransferData.map |
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85 (fn {intros,unfolds,refolds,consts} => |
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86 {intros=f intros, unfolds=unfolds, refolds=refolds, consts=consts}) |
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87 |
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88 fun map_unfolds f = TransferData.map |
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89 (fn {intros,unfolds,refolds,consts} => |
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90 {intros=intros, unfolds=f unfolds, refolds=refolds, consts=consts}) |
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91 |
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92 fun map_refolds f = TransferData.map |
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93 (fn {intros,unfolds,refolds,consts} => |
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94 {intros=intros, unfolds=unfolds, refolds=f refolds, consts=consts}) |
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95 in |
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96 val intro_add = Thm.declaration_attribute (map_intros o Thm.add_thm); |
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97 val intro_del = Thm.declaration_attribute (map_intros o Thm.del_thm); |
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98 |
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99 val unfold_add = Thm.declaration_attribute (map_unfolds o Thm.add_thm); |
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100 val unfold_del = Thm.declaration_attribute (map_unfolds o Thm.del_thm); |
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101 |
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102 val refold_add = Thm.declaration_attribute (map_refolds o Thm.add_thm); |
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103 val refold_del = Thm.declaration_attribute (map_refolds o Thm.del_thm); |
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104 end |
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105 |
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106 fun add_const c = Context.theory_map (TransferData.map |
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107 (fn {intros,unfolds,refolds,consts} => |
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108 {intros=intros, unfolds=unfolds, refolds=refolds, consts=c::consts})) |
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109 |
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110 val setup = |
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111 Attrib.add_attributes |
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112 [("transfer_intro", Attrib.add_del_args intro_add intro_del, |
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113 "declaration of transfer introduction rule"), |
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114 ("transfer_unfold", Attrib.add_del_args unfold_add unfold_del, |
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115 "declaration of transfer unfolding rule"), |
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116 ("transfer_refold", Attrib.add_del_args refold_add refold_del, |
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117 "declaration of transfer refolding rule")] #> |
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118 Method.add_method ("transfer", Method.thms_ctxt_args (fn ths => fn ctxt => |
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119 Method.SIMPLE_METHOD' (transfer_tac ctxt ths)), "transfer principle"); |
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120 |
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121 end; |