--- a/src/HOL/Auth/Message.thy Mon Dec 28 21:47:32 2015 +0100
+++ b/src/HOL/Auth/Message.thy Mon Dec 28 23:13:33 2015 +0100
@@ -48,21 +48,17 @@
| Crypt key msg \<comment>\<open>Encryption, public- or shared-key\<close>
-text\<open>Concrete syntax: messages appear as {|A,B,NA|}, etc...\<close>
+text\<open>Concrete syntax: messages appear as \<open>\<lbrace>A,B,NA\<rbrace>\<close>, etc...\<close>
syntax
- "_MTuple" :: "['a, args] => 'a * 'b" ("(2{|_,/ _|})")
-
-syntax (xsymbols)
- "_MTuple" :: "['a, args] => 'a * 'b" ("(2\<lbrace>_,/ _\<rbrace>)")
-
+ "_MTuple" :: "['a, args] \<Rightarrow> 'a * 'b" ("(2\<lbrace>_,/ _\<rbrace>)")
translations
- "{|x, y, z|}" == "{|x, {|y, z|}|}"
- "{|x, y|}" == "CONST MPair x y"
+ "\<lbrace>x, y, z\<rbrace>" \<rightleftharpoons> "\<lbrace>x, \<lbrace>y, z\<rbrace>\<rbrace>"
+ "\<lbrace>x, y\<rbrace>" \<rightleftharpoons> "CONST MPair x y"
definition HPair :: "[msg,msg] => msg" ("(4Hash[_] /_)" [0, 1000]) where
\<comment>\<open>Message Y paired with a MAC computed with the help of X\<close>
- "Hash[X] Y == {| Hash{|X,Y|}, Y|}"
+ "Hash[X] Y == \<lbrace>Hash\<lbrace>X,Y\<rbrace>, Y\<rbrace>"
definition keysFor :: "msg set => key set" where
\<comment>\<open>Keys useful to decrypt elements of a message set\<close>
@@ -75,9 +71,9 @@
parts :: "msg set => msg set"
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"
+ Inj [intro]: "X \<in> H ==> X \<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"
@@ -136,7 +132,7 @@
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]:
@@ -153,7 +149,7 @@
subsection\<open>Inductive relation "parts"\<close>
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)
@@ -294,8 +290,8 @@
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)
@@ -330,9 +326,9 @@
analz :: "msg set => msg set"
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"
+ Inj [intro,simp]: "X \<in> H ==> X \<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"
@@ -346,7 +342,7 @@
text\<open>Making it safe speeds up proofs\<close>
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)
@@ -427,8 +423,8 @@
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)
@@ -540,7 +536,7 @@
text\<open>If there are no pairs or encryptions then analz does nothing\<close>
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
@@ -571,7 +567,7 @@
| 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"
text\<open>Monotonicity\<close>
@@ -585,7 +581,7 @@
"Nonce n \<in> synth H"
"Key K \<in> synth H"
"Hash X \<in> synth H"
- "{|X,Y|} \<in> synth H"
+ "\<lbrace>X,Y\<rbrace> \<in> synth H"
"Crypt K X \<in> synth H"
lemma synth_increasing: "H \<subseteq> synth(H)"
@@ -694,7 +690,7 @@
text\<open>Without this equation, other rules for synth and analz would yield
redundant cases\<close>
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
@@ -706,7 +702,7 @@
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
@@ -742,11 +738,11 @@
by (simp add: HPair_def)
lemma MPair_eq_HPair [iff]:
- "({|X',Y'|} = Hash[X] Y) = (X' = Hash{|X,Y|} & Y'=Y)"
+ "(\<lbrace>X',Y'\<rbrace> = Hash[X] Y) = (X' = Hash\<lbrace>X,Y\<rbrace> & Y'=Y)"
by (simp add: HPair_def)
lemma HPair_eq_MPair [iff]:
- "(Hash[X] Y = {|X',Y'|}) = (X' = Hash{|X,Y|} & Y'=Y)"
+ "(Hash[X] Y = \<lbrace>X',Y'\<rbrace>) = (X' = Hash\<lbrace>X,Y\<rbrace> & Y'=Y)"
by (auto simp add: HPair_def)
@@ -757,18 +753,18 @@
lemma parts_insert_HPair [simp]:
"parts (insert (Hash[X] Y) H) =
- insert (Hash[X] Y) (insert (Hash{|X,Y|}) (parts (insert Y H)))"
+ insert (Hash[X] Y) (insert (Hash\<lbrace>X,Y\<rbrace>) (parts (insert Y H)))"
by (simp add: HPair_def)
lemma analz_insert_HPair [simp]:
"analz (insert (Hash[X] Y) H) =
- insert (Hash[X] Y) (insert (Hash{|X,Y|}) (analz (insert Y H)))"
+ insert (Hash[X] Y) (insert (Hash\<lbrace>X,Y\<rbrace>) (analz (insert Y H)))"
by (simp add: HPair_def)
lemma HPair_synth_analz [simp]:
"X \<notin> synth (analz H)
==> (Hash[X] Y \<in> synth (analz H)) =
- (Hash {|X, Y|} \<in> analz H & Y \<in> synth (analz H))"
+ (Hash \<lbrace>X, Y\<rbrace> \<in> analz H & Y \<in> synth (analz H))"
by (auto simp add: HPair_def)
@@ -814,14 +810,14 @@
| Number: "Number N \<in> keyfree"
| Nonce: "Nonce N \<in> keyfree"
| Hash: "Hash X \<in> keyfree"
- | MPair: "[|X \<in> keyfree; Y \<in> keyfree|] ==> {|X,Y|} \<in> keyfree"
+ | MPair: "[|X \<in> keyfree; Y \<in> keyfree|] ==> \<lbrace>X,Y\<rbrace> \<in> keyfree"
| Crypt: "[|X \<in> keyfree|] ==> Crypt K X \<in> keyfree"
declare keyfree.intros [intro]
inductive_cases keyfree_KeyE: "Key K \<in> keyfree"
-inductive_cases keyfree_MPairE: "{|X,Y|} \<in> keyfree"
+inductive_cases keyfree_MPairE: "\<lbrace>X,Y\<rbrace> \<in> keyfree"
inductive_cases keyfree_CryptE: "Crypt K X \<in> keyfree"
lemma parts_keyfree: "parts (keyfree) \<subseteq> keyfree"