--- a/src/HOL/Metis_Examples/Message.thy Thu May 26 16:57:14 2016 +0200
+++ b/src/HOL/Metis_Examples/Message.thy Thu May 26 17:51:22 2016 +0200
@@ -5,7 +5,7 @@
Metis example featuring message authentication.
*)
-section {* Metis Example Featuring Message Authentication *}
+section \<open>Metis Example Featuring Message Authentication\<close>
theory Message
imports Main
@@ -19,8 +19,8 @@
type_synonym key = nat
consts
- all_symmetric :: bool --{*true if all keys are symmetric*}
- invKey :: "key=>key" --{*inverse of a symmetric key*}
+ all_symmetric :: bool \<comment>\<open>true if all keys are symmetric\<close>
+ invKey :: "key=>key" \<comment>\<open>inverse of a symmetric key\<close>
specification (invKey)
invKey [simp]: "invKey (invKey K) = K"
@@ -28,26 +28,26 @@
by (metis id_apply)
-text{*The inverse of a symmetric key is itself; that of a public key
- is the private key and vice versa*}
+text\<open>The inverse of a symmetric key is itself; that of a public key
+ is the private key and vice versa\<close>
definition symKeys :: "key set" where
"symKeys == {K. invKey K = K}"
-datatype --{*We allow any number of friendly agents*}
+datatype \<comment>\<open>We allow any number of friendly agents\<close>
agent = Server | Friend nat | Spy
datatype
- msg = Agent agent --{*Agent names*}
- | Number nat --{*Ordinary integers, timestamps, ...*}
- | Nonce nat --{*Unguessable nonces*}
- | Key key --{*Crypto keys*}
- | Hash msg --{*Hashing*}
- | MPair msg msg --{*Compound messages*}
- | Crypt key msg --{*Encryption, public- or shared-key*}
+ msg = Agent agent \<comment>\<open>Agent names\<close>
+ | Number nat \<comment>\<open>Ordinary integers, timestamps, ...\<close>
+ | Nonce nat \<comment>\<open>Unguessable nonces\<close>
+ | Key key \<comment>\<open>Crypto keys\<close>
+ | Hash msg \<comment>\<open>Hashing\<close>
+ | MPair msg msg \<comment>\<open>Compound messages\<close>
+ | Crypt key msg \<comment>\<open>Encryption, public- or shared-key\<close>
-text{*Concrete syntax: messages appear as \<open>\<lbrace>A,B,NA\<rbrace>\<close>, etc...*}
+text\<open>Concrete syntax: messages appear as \<open>\<lbrace>A,B,NA\<rbrace>\<close>, etc...\<close>
syntax
"_MTuple" :: "['a, args] => 'a * 'b" ("(2\<lbrace>_,/ _\<rbrace>)")
translations
@@ -56,15 +56,15 @@
definition HPair :: "[msg,msg] => msg" ("(4Hash[_] /_)" [0, 1000]) where
- --{*Message Y paired with a MAC computed with the help of X*}
+ \<comment>\<open>Message Y paired with a MAC computed with the help of X\<close>
"Hash[X] Y == \<lbrace> Hash\<lbrace>X,Y\<rbrace>, Y\<rbrace>"
definition keysFor :: "msg set => key set" where
- --{*Keys useful to decrypt elements of a message set*}
+ \<comment>\<open>Keys useful to decrypt elements of a message set\<close>
"keysFor H == invKey ` {K. \<exists>X. Crypt K X \<in> H}"
-subsubsection{*Inductive Definition of All Parts" of a Message*}
+subsubsection\<open>Inductive Definition of All Parts" of a Message\<close>
inductive_set
parts :: "msg set => msg set"
@@ -83,7 +83,7 @@
apply (metis parts.Snd)
by (metis parts.Body)
-text{*Equations hold because constructors are injective.*}
+text\<open>Equations hold because constructors are injective.\<close>
lemma Friend_image_eq [simp]: "(Friend x \<in> Friend`A) = (x:A)"
by (metis agent.inject image_iff)
@@ -94,13 +94,13 @@
by (metis image_iff msg.distinct(23))
-subsubsection{*Inverse of keys *}
+subsubsection\<open>Inverse of keys\<close>
lemma invKey_eq [simp]: "(invKey K = invKey K') = (K = K')"
by (metis invKey)
-subsection{*keysFor operator*}
+subsection\<open>keysFor operator\<close>
lemma keysFor_empty [simp]: "keysFor {} = {}"
by (unfold keysFor_def, blast)
@@ -111,7 +111,7 @@
lemma keysFor_UN [simp]: "keysFor (\<Union>i\<in>A. H i) = (\<Union>i\<in>A. keysFor (H i))"
by (unfold keysFor_def, blast)
-text{*Monotonicity*}
+text\<open>Monotonicity\<close>
lemma keysFor_mono: "G \<subseteq> H ==> keysFor(G) \<subseteq> keysFor(H)"
by (unfold keysFor_def, blast)
@@ -144,7 +144,7 @@
by (unfold keysFor_def, blast)
-subsection{*Inductive relation "parts"*}
+subsection\<open>Inductive relation "parts"\<close>
lemma MPair_parts:
"[| \<lbrace>X,Y\<rbrace> \<in> parts H;
@@ -152,10 +152,10 @@
by (blast dest: parts.Fst parts.Snd)
declare MPair_parts [elim!] parts.Body [dest!]
-text{*NB These two rules are UNSAFE in the formal sense, as they discard the
+text\<open>NB These two rules are UNSAFE in the formal sense, as they discard the
compound message. They work well on THIS FILE.
- @{text MPair_parts} is left as SAFE because it speeds up proofs.
- The Crypt rule is normally kept UNSAFE to avoid breaking up certificates.*}
+ \<open>MPair_parts\<close> is left as SAFE because it speeds up proofs.
+ The Crypt rule is normally kept UNSAFE to avoid breaking up certificates.\<close>
lemma parts_increasing: "H \<subseteq> parts(H)"
by blast
@@ -171,14 +171,14 @@
lemma parts_emptyE [elim!]: "X\<in> parts{} ==> P"
by simp
-text{*WARNING: loops if H = {Y}, therefore must not be repeated!*}
+text\<open>WARNING: loops if H = {Y}, therefore must not be repeated!\<close>
lemma parts_singleton: "X\<in> parts H ==> \<exists>Y\<in>H. X\<in> parts {Y}"
apply (erule parts.induct)
apply fast+
done
-subsubsection{*Unions *}
+subsubsection\<open>Unions\<close>
lemma parts_Un_subset1: "parts(G) \<union> parts(H) \<subseteq> parts(G \<union> H)"
by (intro Un_least parts_mono Un_upper1 Un_upper2)
@@ -212,19 +212,19 @@
lemma parts_UN [simp]: "parts(\<Union>x\<in>A. H x) = (\<Union>x\<in>A. parts(H x))"
by (intro equalityI parts_UN_subset1 parts_UN_subset2)
-text{*Added to simplify arguments to parts, analz and synth.
- NOTE: the UN versions are no longer used!*}
+text\<open>Added to simplify arguments to parts, analz and synth.
+ NOTE: the UN versions are no longer used!\<close>
-text{*This allows @{text blast} to simplify occurrences of
- @{term "parts(G\<union>H)"} in the assumption.*}
+text\<open>This allows \<open>blast\<close> to simplify occurrences of
+ @{term "parts(G\<union>H)"} in the assumption.\<close>
lemmas in_parts_UnE = parts_Un [THEN equalityD1, THEN subsetD, THEN UnE]
declare in_parts_UnE [elim!]
lemma parts_insert_subset: "insert X (parts H) \<subseteq> parts(insert X H)"
by (blast intro: parts_mono [THEN [2] rev_subsetD])
-subsubsection{*Idempotence and transitivity *}
+subsubsection\<open>Idempotence and transitivity\<close>
lemma parts_partsD [dest!]: "X\<in> parts (parts H) ==> X\<in> parts H"
by (erule parts.induct, blast+)
@@ -245,7 +245,7 @@
by (metis (no_types) Un_insert_left Un_insert_right insert_absorb le_supE
parts_Un parts_idem parts_increasing parts_trans)
-subsubsection{*Rewrite rules for pulling out atomic messages *}
+subsubsection\<open>Rewrite rules for pulling out atomic messages\<close>
lemmas parts_insert_eq_I = equalityI [OF subsetI parts_insert_subset]
@@ -310,11 +310,11 @@
apply (metis le_trans linorder_linear)
done
-subsection{*Inductive relation "analz"*}
+subsection\<open>Inductive relation "analz"\<close>
-text{*Inductive definition of "analz" -- what can be broken down from a set of
+text\<open>Inductive definition of "analz" -- what can be broken down from a set of
messages, including keys. A form of downward closure. Pairs can
- be taken apart; messages decrypted with known keys. *}
+ be taken apart; messages decrypted with known keys.\<close>
inductive_set
analz :: "msg set => msg set"
@@ -327,14 +327,14 @@
"[|Crypt K X \<in> analz H; Key(invKey K): analz H|] ==> X \<in> analz H"
-text{*Monotonicity; Lemma 1 of Lowe's paper*}
+text\<open>Monotonicity; Lemma 1 of Lowe's paper\<close>
lemma analz_mono: "G\<subseteq>H ==> analz(G) \<subseteq> analz(H)"
apply auto
apply (erule analz.induct)
apply (auto dest: analz.Fst analz.Snd)
done
-text{*Making it safe speeds up proofs*}
+text\<open>Making it safe speeds up proofs\<close>
lemma MPair_analz [elim!]:
"[| \<lbrace>X,Y\<rbrace> \<in> analz H;
[| X \<in> analz H; Y \<in> analz H |] ==> P
@@ -367,22 +367,22 @@
lemmas analz_insertI = subset_insertI [THEN analz_mono, THEN [2] rev_subsetD]
-subsubsection{*General equational properties *}
+subsubsection\<open>General equational properties\<close>
lemma analz_empty [simp]: "analz{} = {}"
apply safe
apply (erule analz.induct, blast+)
done
-text{*Converse fails: we can analz more from the union than from the
- separate parts, as a key in one might decrypt a message in the other*}
+text\<open>Converse fails: we can analz more from the union than from the
+ separate parts, as a key in one might decrypt a message in the other\<close>
lemma analz_Un: "analz(G) \<union> analz(H) \<subseteq> analz(G \<union> H)"
by (intro Un_least analz_mono Un_upper1 Un_upper2)
lemma analz_insert: "insert X (analz H) \<subseteq> analz(insert X H)"
by (blast intro: analz_mono [THEN [2] rev_subsetD])
-subsubsection{*Rewrite rules for pulling out atomic messages *}
+subsubsection\<open>Rewrite rules for pulling out atomic messages\<close>
lemmas analz_insert_eq_I = equalityI [OF subsetI analz_insert]
@@ -410,7 +410,7 @@
apply (erule analz.induct, auto)
done
-text{*Can only pull out Keys if they are not needed to decrypt the rest*}
+text\<open>Can only pull out Keys if they are not needed to decrypt the rest\<close>
lemma analz_insert_Key [simp]:
"K \<notin> keysFor (analz H) ==>
analz (insert (Key K) H) = insert (Key K) (analz H)"
@@ -429,7 +429,7 @@
apply (blast intro: analz.Fst analz.Snd)+
done
-text{*Can pull out enCrypted message if the Key is not known*}
+text\<open>Can pull out enCrypted message if the Key is not known\<close>
lemma analz_insert_Crypt:
"Key (invKey K) \<notin> analz H
==> analz (insert (Crypt K X) H) = insert (Crypt K X) (analz H)"
@@ -459,10 +459,10 @@
insert (Crypt K X) (analz (insert X H))"
by (intro equalityI lemma1 lemma2)
-text{*Case analysis: either the message is secure, or it is not! Effective,
-but can cause subgoals to blow up! Use with @{text "if_split"}; apparently
-@{text "split_tac"} does not cope with patterns such as @{term"analz (insert
-(Crypt K X) H)"} *}
+text\<open>Case analysis: either the message is secure, or it is not! Effective,
+but can cause subgoals to blow up! Use with \<open>if_split\<close>; apparently
+\<open>split_tac\<close> does not cope with patterns such as @{term"analz (insert
+(Crypt K X) H)"}\<close>
lemma analz_Crypt_if [simp]:
"analz (insert (Crypt K X) H) =
(if (Key (invKey K) \<in> analz H)
@@ -471,7 +471,7 @@
by (simp add: analz_insert_Crypt analz_insert_Decrypt)
-text{*This rule supposes "for the sake of argument" that we have the key.*}
+text\<open>This rule supposes "for the sake of argument" that we have the key.\<close>
lemma analz_insert_Crypt_subset:
"analz (insert (Crypt K X) H) \<subseteq>
insert (Crypt K X) (analz (insert X H))"
@@ -486,7 +486,7 @@
done
-subsubsection{*Idempotence and transitivity *}
+subsubsection\<open>Idempotence and transitivity\<close>
lemma analz_analzD [dest!]: "X\<in> analz (analz H) ==> X\<in> analz H"
by (erule analz.induct, blast+)
@@ -509,14 +509,14 @@
lemma analz_cut: "[| Y\<in> analz (insert X H); X\<in> analz H |] ==> Y\<in> analz H"
by (metis analz_idem analz_increasing analz_mono insert_absorb insert_mono insert_subset)
-text{*This rewrite rule helps in the simplification of messages that involve
+text\<open>This rewrite rule helps in the simplification of messages that involve
the forwarding of unknown components (X). Without it, removing occurrences
- of X can be very complicated. *}
+ of X can be very complicated.\<close>
lemma analz_insert_eq: "X\<in> analz H ==> analz (insert X H) = analz H"
by (blast intro: analz_cut analz_insertI)
-text{*A congruence rule for "analz" *}
+text\<open>A congruence rule for "analz"\<close>
lemma analz_subset_cong:
"[| analz G \<subseteq> analz G'; analz H \<subseteq> analz H' |]
@@ -535,14 +535,14 @@
"analz H = analz H' ==> analz(insert X H) = analz(insert X H')"
by (force simp only: insert_def intro!: analz_cong)
-text{*If there are no pairs or encryptions then analz does nothing*}
+text\<open>If there are no pairs or encryptions then analz does nothing\<close>
lemma analz_trivial:
"[| \<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
-text{*These two are obsolete (with a single Spy) but cost little to prove...*}
+text\<open>These two are obsolete (with a single Spy) but cost little to prove...\<close>
lemma analz_UN_analz_lemma:
"X\<in> analz (\<Union>i\<in>A. analz (H i)) ==> X\<in> analz (\<Union>i\<in>A. H i)"
apply (erule analz.induct)
@@ -553,12 +553,12 @@
by (blast intro: analz_UN_analz_lemma analz_mono [THEN [2] rev_subsetD])
-subsection{*Inductive relation "synth"*}
+subsection\<open>Inductive relation "synth"\<close>
-text{*Inductive definition of "synth" -- what can be built up from a set of
+text\<open>Inductive definition of "synth" -- what can be built up from a set of
messages. A form of upward closure. Pairs can be built, messages
encrypted with known keys. Agent names are public domain.
- Numbers can be guessed, but Nonces cannot be. *}
+ Numbers can be guessed, but Nonces cannot be.\<close>
inductive_set
synth :: "msg set => msg set"
@@ -571,12 +571,12 @@
| 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{*Monotonicity*}
+text\<open>Monotonicity\<close>
lemma synth_mono: "G\<subseteq>H ==> synth(G) \<subseteq> synth(H)"
by (auto, erule synth.induct, auto)
-text{*NO @{text Agent_synth}, as any Agent name can be synthesized.
- The same holds for @{term Number}*}
+text\<open>NO \<open>Agent_synth\<close>, as any Agent name can be synthesized.
+ The same holds for @{term Number}\<close>
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"
@@ -587,17 +587,17 @@
lemma synth_increasing: "H \<subseteq> synth(H)"
by blast
-subsubsection{*Unions *}
+subsubsection\<open>Unions\<close>
-text{*Converse fails: we can synth more from the union than from the
- separate parts, building a compound message using elements of each.*}
+text\<open>Converse fails: we can synth more from the union than from the
+ separate parts, building a compound message using elements of each.\<close>
lemma synth_Un: "synth(G) \<union> synth(H) \<subseteq> synth(G \<union> H)"
by (intro Un_least synth_mono Un_upper1 Un_upper2)
lemma synth_insert: "insert X (synth H) \<subseteq> synth(insert X H)"
by (metis insert_iff insert_subset subset_insertI synth.Inj synth_mono)
-subsubsection{*Idempotence and transitivity *}
+subsubsection\<open>Idempotence and transitivity\<close>
lemma synth_synthD [dest!]: "X\<in> synth (synth H) ==> X\<in> synth H"
by (erule synth.induct, blast+)
@@ -639,7 +639,7 @@
by (unfold keysFor_def, blast)
-subsubsection{*Combinations of parts, analz and synth *}
+subsubsection\<open>Combinations of parts, analz and synth\<close>
lemma parts_synth [simp]: "parts (synth H) = parts H \<union> synth H"
apply (rule equalityI)
@@ -681,7 +681,7 @@
qed
-subsubsection{*For reasoning about the Fake rule in traces *}
+subsubsection\<open>For reasoning about the Fake rule in traces\<close>
lemma parts_insert_subset_Un: "X \<in> G ==> parts(insert X H) \<subseteq> parts G \<union> parts H"
proof -