author  wenzelm 
Fri, 16 Feb 2018 21:43:52 +0100  
changeset 67636  e4eb21f8331c 
parent 67635  28f926146986 
child 69597  ff784d5a5bfb 
permissions  rwrr 
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(* Title: HOL/Nonstandard_Analysis/transfer_principle.ML 
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Author: Brian Huffman 
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Transfer principle tactic for nonstandard analysis. 

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*) 

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signature TRANSFER_PRINCIPLE = 
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sig 
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val transfer_tac: Proof.context > thm list > int > tactic 

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val add_const: string > theory > theory 

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end; 

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structure Transfer_Principle: TRANSFER_PRINCIPLE = 
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struct 
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structure Data = Generic_Data 
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( 
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type T = { 

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intros: thm list, 

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unfolds: thm list, 

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refolds: thm list, 

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consts: string list 

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}; 

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val empty = {intros = [], unfolds = [], refolds = [], consts = []}; 

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val extend = I; 

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fun merge 
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({intros = intros1, unfolds = unfolds1, 
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refolds = refolds1, consts = consts1}, 

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{intros = intros2, unfolds = unfolds2, 

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refolds = refolds2, consts = consts2}) : T = 
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{intros = Thm.merge_thms (intros1, intros2), 
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unfolds = Thm.merge_thms (unfolds1, unfolds2), 

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refolds = Thm.merge_thms (refolds1, refolds2), 

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consts = Library.merge (op =) (consts1, consts2)}; 
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); 
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fun unstar_typ (Type (@{type_name star}, [t])) = unstar_typ t 
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 unstar_typ (Type (a, Ts)) = Type (a, map unstar_typ Ts) 
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 unstar_typ T = T 

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fun unstar_term consts term = 

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let 

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fun unstar (Const(a,T) $ t) = if member (op =) consts a then (unstar t) 

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else (Const(a,unstar_typ T) $ unstar t) 

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 unstar (f $ t) = unstar f $ unstar t 

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 unstar (Const(a,T)) = Const(a,unstar_typ T) 

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 unstar (Abs(a,T,t)) = Abs(a,unstar_typ T,unstar t) 

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 unstar t = t 

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in 

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unstar term 

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end 

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local exception MATCH 
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parents:
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in 
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fun transfer_star_tac ctxt = 
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let 
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fun thm_of (Const (@{const_name Ifun}, _) $ t $ u) = @{thm transfer_Ifun} OF [thm_of t, thm_of u] 
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 thm_of (Const (@{const_name star_of}, _) $ _) = @{thm star_of_def} 
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 thm_of (Const (@{const_name star_n}, _) $ _) = @{thm Pure.reflexive} 

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 thm_of _ = raise MATCH; 

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parents:
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parents:
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fun thm_of_goal (Const (@{const_name Pure.eq}, _) $ t $ (Const (@{const_name star_n}, _) $ _)) = 
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thm_of t 
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 thm_of_goal _ = raise MATCH; 

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parents:
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in 
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SUBGOAL (fn (t, i) => 
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resolve_tac ctxt [thm_of_goal (strip_all_body t > Logic.strip_imp_concl)] i 
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handle MATCH => no_tac) 
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end; 
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end; 
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parents:
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fun transfer_thm_of ctxt ths t = 
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let 

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val {intros,unfolds,refolds,consts} = Data.get (Context.Proof ctxt); 
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val meta = Local_Defs.meta_rewrite_rule ctxt; 
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val ths' = map meta ths; 
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val unfolds' = map meta unfolds and refolds' = map meta refolds; 

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val (_$_$t') = Thm.concl_of (Raw_Simplifier.rewrite ctxt true unfolds' (Thm.cterm_of ctxt t)) 
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val u = unstar_term consts t' 
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val tac = 
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rewrite_goals_tac ctxt (ths' @ refolds' @ unfolds') THEN 
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ALLGOALS (Object_Logic.full_atomize_tac ctxt) THEN 
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match_tac ctxt [transitive_thm] 1 THEN 
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resolve_tac ctxt [@{thm transfer_start}] 1 THEN 
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parents:
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REPEAT_ALL_NEW (resolve_tac ctxt intros ORELSE' transfer_star_tac ctxt) 1 THEN 
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match_tac ctxt [reflexive_thm] 1 
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in Goal.prove ctxt [] [] (Logic.mk_equals (t,u)) (K tac) end; 
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fun transfer_tac ctxt ths = SUBGOAL (fn (t, _) => (fn th => 
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let 

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val tr = transfer_thm_of ctxt ths t 

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val (_$ l $ r) = Thm.concl_of tr; 

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val trs = if l aconv r then [] else [tr]; 

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in rewrite_goals_tac ctxt trs th end)); 

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local 

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

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

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

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in 

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val intro_add = Thm.declaration_attribute (map_intros o Thm.add_thm o Thm.trim_context); 
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val intro_del = Thm.declaration_attribute (map_intros o Thm.del_thm); 
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val unfold_add = Thm.declaration_attribute (map_unfolds o Thm.add_thm o Thm.trim_context); 
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val unfold_del = Thm.declaration_attribute (map_unfolds o Thm.del_thm); 
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val refold_add = Thm.declaration_attribute (map_refolds o Thm.add_thm o Thm.trim_context); 
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val refold_del = Thm.declaration_attribute (map_refolds o Thm.del_thm); 
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end 
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fun add_const c = Context.theory_map (Data.map 
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(fn {intros,unfolds,refolds,consts} => 
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{intros=intros, unfolds=unfolds, refolds=refolds, consts=c::consts})) 

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val _ = 
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Theory.setup 

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(Attrib.setup @{binding transfer_intro} (Attrib.add_del intro_add intro_del) 

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"declaration of transfer introduction rule" #> 

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Attrib.setup @{binding transfer_unfold} (Attrib.add_del unfold_add unfold_del) 

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"declaration of transfer unfolding rule" #> 

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Attrib.setup @{binding transfer_refold} (Attrib.add_del refold_add refold_del) 

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"declaration of transfer refolding rule") 

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end; 