# HG changeset patch
# User Christian Urban <urbanc@in.tum.de>
# Date 1308828505 -3600
# Node ID 0435c4dfd6f6014d9ba557aa5b3719188a78b025
# Parent  eda5aeb056a64f91ddf5aaad67b17bdfaa5cd9be
expanded the example

diff -r eda5aeb056a6 -r 0435c4dfd6f6 Nominal/Ex/Classical.thy
--- a/Nominal/Ex/Classical.thy	Thu Jun 23 11:30:39 2011 +0100
+++ b/Nominal/Ex/Classical.thy	Thu Jun 23 12:28:25 2011 +0100
@@ -8,13 +8,29 @@
 atom_decl coname
 
 nominal_datatype trm =
-   Ax "name" "coname"
-|  Cut n::"coname" t1::"trm" c::"coname" t2::"trm"             bind n in t1, bind c in t2
-|  AndR c1::"coname" t1::"trm" c2::"coname" t2::"trm" "coname" bind c1 in t1, bind c2 in t2
-|  AndL1 n::"name" t::"trm" "name"                             bind n in t
-|  AndL2 n::"name" t::"trm" "name"                             bind n in t
-|  ImpL c::"coname" t1::"trm" n::"name" t2::"trm" "name"       bind c in t1, bind n in t2
-|  ImpR c::"coname" n::"name" t::"trm" "coname"                bind n c in t
+  Ax "name" "coname"
+| Cut n::"coname" t1::"trm" c::"coname" t2::"trm"             bind n in t1, bind c in t2  
+     ("Cut <_>._ '(_')._" [100,100,100,100] 100)
+| NotR n::"name" t::"trm" "coname"                            bind n in t
+     ("NotR '(_')._ _" [100,100,100] 100)
+| NotL c::"coname" t::"trm" "name"                            bind c in t   
+     ("NotL <_>._ _" [100,100,100] 100)
+| AndR c1::"coname" t1::"trm" c2::"coname" t2::"trm" "coname" bind c1 in t1, bind c2 in t2
+     ("AndR <_>._ <_>._ _" [100,100,100,100,100] 100)
+| AndL1 n::"name" t::"trm" "name"                             bind n in t
+     ("AndL1 '(_')._ _" [100,100,100] 100)
+| AndL2 n::"name" t::"trm" "name"                             bind n in t
+     ("AndL2 '(_')._ _" [100,100,100] 100)
+| OrR1 c::"coname" t::"trm" "coname"                          bind c in t             
+     ("OrR1 <_>._ _" [100,100,100] 100)
+| OrR2 c::"coname" t::"trm" "coname"                          bind c in t     
+     ("OrR2 <_>._ _" [100,100,100] 100)
+| OrL n1::"name" t1::"trm" n2::"name" t2::"trm" "name"        bind n1 in t1, bind n2 in t2       
+     ("OrL '(_')._ '(_')._ _" [100,100,100,100,100] 100)
+| ImpL c::"coname" t1::"trm" n::"name" t2::"trm" "name"       bind c in t1, bind n in t2
+     ("ImpL <_>._ '(_')._ _" [100,100,100,100,100] 100)
+| ImpR c::"coname" n::"name" t::"trm" "coname"                bind n c in t
+     ("ImpR '(_').<_>._ _" [100,100,100,100] 100)
 
 thm trm.distinct
 thm trm.induct
@@ -30,8 +46,59 @@
 thm trm.supp
 thm trm.supp[simplified]
 
-
-
+nominal_primrec 
+  crename :: "trm \<Rightarrow> coname \<Rightarrow> coname \<Rightarrow> trm"  ("_[_\<turnstile>c>_]" [100,100,100] 100) 
+where
+  "(Ax x a)[d\<turnstile>c>e] = (if a=d then Ax x e else Ax x a)" 
+| "atom a \<sharp> (d, e) \<Longrightarrow> (Cut <a>.M (x).N)[d\<turnstile>c>e] = Cut <a>.(M[d\<turnstile>c>e]) (x).(N[d\<turnstile>c>e])" 
+| "(NotR (x).M a)[d\<turnstile>c>e] = (if a=d then NotR (x).(M[d\<turnstile>c>e]) e else NotR (x).(M[d\<turnstile>c>e]) a)" 
+| "atom a \<sharp> (d, e) \<Longrightarrow> (NotL <a>.M x)[d\<turnstile>c>e] = (NotL <a>.(M[d\<turnstile>c>e]) x)" 
+| "\<lbrakk>atom a \<sharp> (d, e); atom b \<sharp> (d, e)\<rbrakk> \<Longrightarrow> (AndR <a>.M <b>.N c)[d\<turnstile>c>e] = 
+          (if c=d then AndR <a>.(M[d\<turnstile>c>e]) <b>.(N[d \<turnstile>c>e]) e else AndR <a>.(M[d\<turnstile>c>e]) <b>.(N[d\<turnstile>c>e]) c)" 
+| "(AndL1 (x).M y)[d\<turnstile>c>e] = AndL1 (x).(M[d\<turnstile>c>e]) y"
+| "(AndL2 (x).M y)[d\<turnstile>c>e] = AndL2 (x).(M[d\<turnstile>c>e]) y"
+| "atom a \<sharp> (d, e) \<Longrightarrow> (OrR1 <a>.M b)[d\<turnstile>c>e] = 
+          (if b=d then OrR1 <a>.(M[d\<turnstile>c>e]) e else OrR1 <a>.(M[d\<turnstile>c>e]) b)"
+| "atom a \<sharp> (d, e) \<Longrightarrow> (OrR2 <a>.M b)[d\<turnstile>c>e] = 
+          (if b=d then OrR2 <a>.(M[d\<turnstile>c>e]) e else OrR2 <a>.(M[d\<turnstile>c>e]) b)"
+| "(OrL (x).M (y).N z)[d\<turnstile>c>e] = OrL (x).(M[d\<turnstile>c>e]) (y).(N[d\<turnstile>c>e]) z"
+| "atom a \<sharp> (d, e) \<Longrightarrow> (ImpR (x).<a>.M b)[d\<turnstile>c>e] = 
+          (if b=d then ImpR (x).<a>.(M[d\<turnstile>c>e]) e else ImpR (x).<a>.(M[d\<turnstile>c>e]) b)"
+| "atom a \<sharp> (d, e) \<Longrightarrow> (ImpL <a>.M (x).N y)[d\<turnstile>c>e] = ImpL <a>.(M[d\<turnstile>c>e]) (x).(N[d\<turnstile>c>e]) y"
+  apply(simp only: eqvt_def)
+  apply(simp only: crename_graph_def)
+  apply (rule, perm_simp, rule)
+  apply(rule TrueI)
+  -- "covered all cases"
+  apply(case_tac x)
+  apply(rule_tac y="a" and c="(b, c)" in trm.strong_exhaust)
+  apply(simp)
+  apply(blast)
+  apply(simp add: fresh_star_def)
+  apply(blast)
+  apply(simp add: fresh_star_def)
+  apply(blast)
+  apply(simp add: fresh_star_def)
+  apply(blast)  
+  apply(simp add: fresh_star_def)
+  apply(blast)
+  apply(simp add: fresh_star_def)
+  apply(blast)
+  apply(simp add: fresh_star_def)
+  apply(blast)
+  apply(simp add: fresh_star_def)
+  apply(blast)  
+  apply(simp add: fresh_star_def)
+  apply(blast)
+  apply(simp add: fresh_star_def)
+  apply(metis)
+  apply(simp add: fresh_star_def)
+  apply(metis)  
+  apply(simp add: fresh_star_def)
+  apply(metis)
+  -- "clashes"
+  apply(simp_all)
+  oops
 
 end