src/HOL/SET_Protocol/Message_SET.thy

--- a/src/HOL/SET_Protocol/Message_SET.thy	Wed Dec 30 18:07:10 2015 +0100
+++ b/src/HOL/SET_Protocol/Message_SET.thy	Wed Dec 30 18:17:28 2015 +0100
@@ -67,16 +67,12 @@
          | Crypt  key msg   --{*Encryption, public- or shared-key*}
 
 
-(*Concrete syntax: messages appear as {|A,B,NA|}, etc...*)
+(*Concrete syntax: messages appear as \<open>\<lbrace>A,B,NA\<rbrace>\<close>, etc...*)
 syntax
-  "_MTuple"      :: "['a, args] => 'a * 'b"       ("(2{|_,/ _|})")
-
-syntax (xsymbols)
   "_MTuple"      :: "['a, args] => 'a * 'b"       ("(2\<lbrace>_,/ _\<rbrace>)")
-
 translations
-  "{|x, y, z|}"   == "{|x, {|y, z|}|}"
-  "{|x, y|}"      == "CONST MPair x y"
+  "\<lbrace>x, y, z\<rbrace>"   == "\<lbrace>x, \<lbrace>y, z\<rbrace>\<rbrace>"
+  "\<lbrace>x, y\<rbrace>"      == "CONST MPair x y"
 
 
 definition nat_of_agent :: "agent => nat" where
@@ -104,8 +100,8 @@
   for H :: "msg set"
   where
     Inj [intro]:               "X \<in> H ==> X \<in> parts H"
-  | Fst:         "{|X,Y|}   \<in> parts H ==> X \<in> parts H"
-  | Snd:         "{|X,Y|}   \<in> parts H ==> Y \<in> parts H"
+  | Fst:         "\<lbrace>X,Y\<rbrace>   \<in> parts H ==> X \<in> parts H"
+  | Snd:         "\<lbrace>X,Y\<rbrace>   \<in> parts H ==> Y \<in> parts H"
   | Body:        "Crypt K X \<in> parts H ==> X \<in> parts H"
 
 
@@ -180,7 +176,7 @@
 lemma keysFor_insert_Hash [simp]: "keysFor (insert (Hash X) H) = keysFor H"
 by (unfold keysFor_def, auto)
 
-lemma keysFor_insert_MPair [simp]: "keysFor (insert {|X,Y|} H) = keysFor H"
+lemma keysFor_insert_MPair [simp]: "keysFor (insert \<lbrace>X,Y\<rbrace> H) = keysFor H"
 by (unfold keysFor_def, auto)
 
 lemma keysFor_insert_Crypt [simp]:
@@ -197,7 +193,7 @@
 subsection{*Inductive relation "parts"*}
 
 lemma MPair_parts:
-     "[| {|X,Y|} \<in> parts H;
+     "[| \<lbrace>X,Y\<rbrace> \<in> parts H;
          [| X \<in> parts H; Y \<in> parts H |] ==> P |] ==> P"
 by (blast dest: parts.Fst parts.Snd)
 
@@ -346,8 +342,8 @@
 done
 
 lemma parts_insert_MPair [simp]:
-     "parts (insert {|X,Y|} H) =
-          insert {|X,Y|} (parts (insert X (insert Y H)))"
+     "parts (insert \<lbrace>X,Y\<rbrace> H) =
+          insert \<lbrace>X,Y\<rbrace> (parts (insert X (insert Y H)))"
 apply (rule equalityI)
 apply (rule subsetI)
 apply (erule parts.induct, auto)
@@ -398,8 +394,8 @@
   for H :: "msg set"
   where
     Inj [intro,simp] :    "X \<in> H ==> X \<in> analz H"
-  | Fst:     "{|X,Y|} \<in> analz H ==> X \<in> analz H"
-  | Snd:     "{|X,Y|} \<in> analz H ==> Y \<in> analz H"
+  | Fst:     "\<lbrace>X,Y\<rbrace> \<in> analz H ==> X \<in> analz H"
+  | Snd:     "\<lbrace>X,Y\<rbrace> \<in> analz H ==> Y \<in> analz H"
   | Decrypt [dest]:
              "[|Crypt K X \<in> analz H; Key(invKey K): analz H|] ==> X \<in> analz H"
 
@@ -413,7 +409,7 @@
 
 text{*Making it safe speeds up proofs*}
 lemma MPair_analz [elim!]:
-     "[| {|X,Y|} \<in> analz H;
+     "[| \<lbrace>X,Y\<rbrace> \<in> analz H;
              [| X \<in> analz H; Y \<in> analz H |] ==> P
           |] ==> P"
 by (blast dest: analz.Fst analz.Snd)
@@ -497,8 +493,8 @@
 done
 
 lemma analz_insert_MPair [simp]:
-     "analz (insert {|X,Y|} H) =
-          insert {|X,Y|} (analz (insert X (insert Y H)))"
+     "analz (insert \<lbrace>X,Y\<rbrace> H) =
+          insert \<lbrace>X,Y\<rbrace> (analz (insert X (insert Y H)))"
 apply (rule equalityI)
 apply (rule subsetI)
 apply (erule analz.induct, auto)
@@ -619,7 +615,7 @@
 
 (*If there are no pairs or encryptions then analz does nothing*)
 lemma analz_trivial:
-     "[| \<forall>X Y. {|X,Y|} \<notin> H;  \<forall>X K. Crypt K X \<notin> H |] ==> analz H = H"
+     "[| \<forall>X Y. \<lbrace>X,Y\<rbrace> \<notin> H;  \<forall>X K. Crypt K X \<notin> H |] ==> analz H = H"
 apply safe
 apply (erule analz.induct, blast+)
 done
@@ -650,7 +646,7 @@
   | Agent  [intro]:   "Agent agt \<in> synth H"
   | Number [intro]:   "Number n  \<in> synth H"
   | Hash   [intro]:   "X \<in> synth H ==> Hash X \<in> synth H"
-  | MPair  [intro]:   "[|X \<in> synth H;  Y \<in> synth H|] ==> {|X,Y|} \<in> synth H"
+  | MPair  [intro]:   "[|X \<in> synth H;  Y \<in> synth H|] ==> \<lbrace>X,Y\<rbrace> \<in> synth H"
   | Crypt  [intro]:   "[|X \<in> synth H;  Key(K) \<in> H|] ==> Crypt K X \<in> synth H"
 
 (*Monotonicity*)
@@ -664,7 +660,7 @@
 inductive_cases Nonce_synth [elim!]: "Nonce n \<in> synth H"
 inductive_cases Key_synth   [elim!]: "Key K \<in> synth H"
 inductive_cases Hash_synth  [elim!]: "Hash X \<in> synth H"
-inductive_cases MPair_synth [elim!]: "{|X,Y|} \<in> synth H"
+inductive_cases MPair_synth [elim!]: "\<lbrace>X,Y\<rbrace> \<in> synth H"
 inductive_cases Crypt_synth [elim!]: "Crypt K X \<in> synth H"
 inductive_cases Pan_synth   [elim!]: "Pan A \<in> synth H"
 
@@ -790,7 +786,7 @@
 (*Without this equation, other rules for synth and analz would yield
   redundant cases*)
 lemma MPair_synth_analz [iff]:
-     "({|X,Y|} \<in> synth (analz H)) =
+     "(\<lbrace>X,Y\<rbrace> \<in> synth (analz H)) =
       (X \<in> synth (analz H) & Y \<in> synth (analz H))"
 by blast
 
@@ -802,7 +798,7 @@
 
 lemma Hash_synth_analz [simp]:
      "X \<notin> synth (analz H)
-      ==> (Hash{|X,Y|} \<in> synth (analz H)) = (Hash{|X,Y|} \<in> analz H)"
+      ==> (Hash\<lbrace>X,Y\<rbrace> \<in> synth (analz H)) = (Hash\<lbrace>X,Y\<rbrace> \<in> analz H)"
 by blast