Import of official AFP entry for Isabelle 2019.
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@ -3,7 +3,7 @@ pipeline {
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stages {
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stage('Build') {
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steps {
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sh 'docker run -v $PWD/UPF:/UPF logicalhacking:isabelle2018 isabelle build -D /UPF'
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sh 'docker run -v $PWD/UPF:/UPF logicalhacking:isabelle2019 isabelle build -D /UPF'
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}
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}
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}
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@ -42,7 +42,7 @@
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******************************************************************************)
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section{* Properties on Policies *}
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section\<open>Properties on Policies\<close>
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theory
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Analysis
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imports
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@ -50,19 +50,19 @@ theory
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SeqComposition
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begin
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text {*
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text \<open>
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In this theory, several standard policy properties are paraphrased in UPF terms.
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*}
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\<close>
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subsection{* Basic Properties *}
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subsection\<open>Basic Properties\<close>
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subsubsection{* A Policy Has no Gaps *}
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subsubsection\<open>A Policy Has no Gaps\<close>
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definition gap_free :: "('a \<mapsto> 'b) \<Rightarrow> bool"
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where "gap_free p = (dom p = UNIV)"
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subsubsection{* Comparing Policies *}
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text {* Policy p is more defined than q: *}
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subsubsection\<open>Comparing Policies\<close>
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text \<open>Policy p is more defined than q:\<close>
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definition more_defined :: "('a \<mapsto> 'b) \<Rightarrow>('a \<mapsto> 'b) \<Rightarrow>bool"
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where "more_defined p q = (dom q \<subseteq> dom p)"
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@ -74,7 +74,7 @@ lemma strictly_more_vs_more: "strictly_more_defined p q \<Longrightarrow> more_d
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unfolding more_defined_def strictly_more_defined_def
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by auto
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text{* Policy p is more permissive than q: *}
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text\<open>Policy p is more permissive than q:\<close>
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definition more_permissive :: "('a \<mapsto> 'b) \<Rightarrow> ('a \<mapsto> 'b) \<Rightarrow> bool" (infixl "\<sqsubseteq>\<^sub>A" 60)
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where " p \<sqsubseteq>\<^sub>A q = (\<forall> x. (case q x of \<lfloor>allow y\<rfloor> \<Rightarrow> (\<exists> z. (p x = \<lfloor>allow z\<rfloor>))
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| \<lfloor>deny y\<rfloor> \<Rightarrow> True
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@ -97,7 +97,7 @@ lemma more_permissive_trans : "p \<sqsubseteq>\<^sub>A p' \<Longrightarrow> p' \
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by(erule_tac x = x in allE, simp)
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done
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text{* Policy p is more rejective than q: *}
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text\<open>Policy p is more rejective than q:\<close>
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definition more_rejective :: "('a \<mapsto> 'b) \<Rightarrow> ('a \<mapsto> 'b) \<Rightarrow> bool" (infixl "\<sqsubseteq>\<^sub>D" 60)
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where " p \<sqsubseteq>\<^sub>D q = (\<forall> x. (case q x of \<lfloor>deny y\<rfloor> \<Rightarrow> (\<exists> z. (p x = \<lfloor>deny z\<rfloor>))
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| \<lfloor>allow y\<rfloor> \<Rightarrow> True
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@ -130,7 +130,7 @@ lemma "A\<^sub>I \<sqsubseteq>\<^sub>A p"
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unfolding more_permissive_def allow_all_fun_def allow_pfun_def allow_all_id_def
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by(auto split: option.split decision.split)
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subsection{* Combined Data-Policy Refinement *}
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subsection\<open>Combined Data-Policy Refinement\<close>
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definition policy_refinement ::
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"('a \<mapsto> 'b) \<Rightarrow> ('a' \<Rightarrow> 'a) \<Rightarrow>('b' \<Rightarrow> 'b) \<Rightarrow> ('a' \<mapsto> 'b') \<Rightarrow> bool"
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@ -168,13 +168,13 @@ theorem polref_trans:
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done
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done
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subsection {* Equivalence of Policies *}
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subsubsection{* Equivalence over domain D *}
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subsection \<open>Equivalence of Policies\<close>
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subsubsection\<open>Equivalence over domain D\<close>
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definition p_eq_dom :: "('a \<mapsto> 'b) \<Rightarrow> 'a set \<Rightarrow> ('a \<mapsto> 'b) \<Rightarrow>bool" ("_ \<approx>\<^bsub>_\<^esub> _" [60,60,60]60)
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where "p \<approx>\<^bsub>D\<^esub> q = (\<forall>x\<in>D. p x = q x)"
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text{* p and q have no conflicts *}
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text\<open>p and q have no conflicts\<close>
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definition no_conflicts :: "('a \<mapsto> 'b) \<Rightarrow>('a \<mapsto> 'b) \<Rightarrow>bool" where
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"no_conflicts p q = (dom p = dom q \<and> (\<forall>x\<in>(dom p).
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(case p x of \<lfloor>allow y\<rfloor> \<Rightarrow> (\<exists>z. q x = \<lfloor>allow z\<rfloor>)
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@ -195,7 +195,7 @@ lemma policy_eq:
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apply (metis)+
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done
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subsubsection{* Miscellaneous *}
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subsubsection\<open>Miscellaneous\<close>
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lemma dom_inter: "\<lbrakk>dom p \<inter> dom q = {}; p x = \<lfloor>y\<rfloor>\<rbrakk> \<Longrightarrow> q x = \<bottom>"
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by (auto)
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@ -41,20 +41,20 @@
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* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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******************************************************************************)
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section{* Elementary Policies *}
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section\<open>Elementary Policies\<close>
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theory
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ElementaryPolicies
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imports
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UPFCore
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begin
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text{*
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text\<open>
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In this theory, we introduce the elementary policies of UPF that build the basis
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for more complex policies. These complex policies, respectively, embedding of
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well-known access control or security models, are build by composing the elementary
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policies defined in this theory.
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*}
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\<close>
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subsection{* The Core Policy Combinators: Allow and Deny Everything *}
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subsection\<open>The Core Policy Combinators: Allow and Deny Everything\<close>
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definition
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deny_pfun :: "('\<alpha> \<rightharpoonup>'\<beta>) \<Rightarrow> ('\<alpha> \<mapsto> '\<beta>)" ("AllD")
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@ -113,7 +113,7 @@ lemma neq_Allow_Deny: "pf \<noteq> \<emptyset> \<Longrightarrow> (deny_pfun pf)
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done
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done
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subsection{* Common Instances *}
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subsection\<open>Common Instances\<close>
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definition allow_all_fun :: "('\<alpha> \<Rightarrow> '\<beta>) \<Rightarrow> ('\<alpha> \<mapsto> '\<beta>)" ("A\<^sub>f")
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where "allow_all_fun f = allow_pfun (Some o f)"
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@ -137,7 +137,7 @@ definition
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deny_all :: "('\<alpha> \<mapsto> unit)" ("D\<^sub>U") where
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"deny_all p = \<lfloor>deny ()\<rfloor>"
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text{* ... and resulting properties: *}
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text\<open>... and resulting properties:\<close>
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lemma "A\<^sub>I \<Oplus> Map.empty = A\<^sub>I"
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by simp
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@ -160,9 +160,9 @@ lemma deny_left_cancel :"dom pf = UNIV \<Longrightarrow> (deny_pfun pf) \<Oplus>
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apply (rule ext)+
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by (auto simp: deny_pfun_def option.splits)
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subsection{* Domain, Range, and Restrictions *}
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subsection\<open>Domain, Range, and Restrictions\<close>
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text{*
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text\<open>
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Since policies are essentially maps, we inherit the basic definitions for
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domain and range on Maps: \\
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\verb+Map.dom_def+ : @{thm Map.dom_def} \\
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@ -186,11 +186,11 @@ text{*
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\item\verb+Map.dom_if+ @{thm Map.dom_if}
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\item\verb+Map.dom_map_add+ @{thm Map.dom_map_add}
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\end{itemize}
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*}
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\<close>
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text{*
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text\<open>
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However, some properties are specific to policy concepts:
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*}
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\<close>
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lemma sub_ran : "ran p \<subseteq> Allow \<union> Deny"
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apply (auto simp: Allow_def Deny_def ran_def full_SetCompr_eq[symmetric])[1]
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subgoal for x a
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@ -261,7 +261,7 @@ lemma ran_deny_all: "ran(D\<^sub>f id) = Deny"
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done
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text{*
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text\<open>
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Reasoning over \verb+dom+ is most crucial since it paves the way for simplification and
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reordering of policies composed by override (i.e. by the normal left-to-right rule composition
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method.
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@ -275,7 +275,7 @@ text{*
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\item \verb+Map.map_add_upd_left+ @{thm Map.map_add_upd_left}
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\end{itemize}
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The latter rule also applies to allow- and deny-override.
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*}
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\<close>
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definition dom_restrict :: "['\<alpha> set, '\<alpha>\<mapsto>'\<beta>] \<Rightarrow> '\<alpha>\<mapsto>'\<beta>" (infixr "\<triangleleft>" 55)
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where "S \<triangleleft> p \<equiv> (\<lambda>x. if x \<in> S then p x else \<bottom>)"
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@ -41,15 +41,15 @@
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* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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******************************************************************************)
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section {* Basic Monad Theory for Sequential Computations *}
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section \<open>Basic Monad Theory for Sequential Computations\<close>
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theory
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Monads
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imports
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Main
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begin
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subsection{* General Framework for Monad-based Sequence-Test *}
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text{*
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subsection\<open>General Framework for Monad-based Sequence-Test\<close>
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text\<open>
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As such, Higher-order Logic as a purely functional specification formalism has no built-in
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mechanism for state and state-transitions. Forms of testing involving state require therefore
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explicit mechanisms for their treatment inside the logic; a well-known technique to model
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@ -67,9 +67,9 @@ text{*
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\item non-deterministic i/o automata, and
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\item labelled transition systems (LTS)
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\end{enumerate}
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*}
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\<close>
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subsubsection{* State Exception Monads *}
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subsubsection\<open>State Exception Monads\<close>
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type_synonym ('o, '\<sigma>) MON\<^sub>S\<^sub>E = "'\<sigma> \<rightharpoonup> ('o \<times> '\<sigma>)"
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definition bind_SE :: "('o,'\<sigma>)MON\<^sub>S\<^sub>E \<Rightarrow> ('o \<Rightarrow> ('o','\<sigma>)MON\<^sub>S\<^sub>E) \<Rightarrow> ('o','\<sigma>)MON\<^sub>S\<^sub>E"
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@ -103,9 +103,9 @@ definition if_SE :: "['\<sigma> \<Rightarrow> bool, ('\<alpha>, '\<sigma>)MON\<^
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where "if_SE c E F = (\<lambda>\<sigma>. if c \<sigma> then E \<sigma> else F \<sigma>)"
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notation if_SE ("if\<^sub>S\<^sub>E")
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text{*
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text\<open>
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The standard monad theorems about unit and associativity:
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*}
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\<close>
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lemma bind_left_unit : "(x \<leftarrow> return a; k) = k"
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apply (simp add: unit_SE_def bind_SE_def)
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@ -131,7 +131,7 @@ lemma bind_assoc: "(y \<leftarrow> (x \<leftarrow> m; k); h) = (x \<leftarrow> m
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done
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done
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text{*
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text\<open>
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In order to express test-sequences also on the object-level and to make our theory amenable to
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formal reasoning over test-sequences, we represent them as lists of input and generalize the
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bind-operator of the state-exception monad accordingly. The approach is straightforward, but
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@ -147,9 +147,9 @@ text{*
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of side-conditions have to be expressed inside \HOL. From the user perspective, this will not
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make much difference, since junk-data resulting from too weak typing can be ruled out by adopted
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front-ends.
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*}
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\<close>
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text{*
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text\<open>
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In order to express test-sequences also on the object-level and to make our theory amenable to
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formal reasoning over test-sequences, we represent them as lists of input and generalize the
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bind-operator of the state-exception monad accordingly. Thus, the notion of test-sequence
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@ -168,15 +168,15 @@ text{*
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same operation will occur; this form of side-conditions have to be expressed
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inside \HOL. From the user perspective, this will not make much difference,
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since junk-data resulting from too weak typing can be ruled out by adopted
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front-ends. *}
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front-ends.\<close>
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text{* Note that the subsequent notion of a test-sequence allows the io stepping
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text\<open>Note that the subsequent notion of a test-sequence allows the io stepping
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function (and the special case of a program under test) to stop execution
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\emph{within} the sequence; such premature terminations are characterized by an
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output list which is shorter than the input list. Note that our primary
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notion of multiple execution ignores failure and reports failure
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steps only by missing results ... *}
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steps only by missing results ...\<close>
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fun mbind :: "'\<iota> list \<Rightarrow> ('\<iota> \<Rightarrow> ('o,'\<sigma>) MON\<^sub>S\<^sub>E) \<Rightarrow> ('o list,'\<sigma>) MON\<^sub>S\<^sub>E"
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@ -188,9 +188,9 @@ fun mbind :: "'\<iota> list \<Rightarrow> ('\<iota> \<Rightarrow> ('o,'\<si
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None \<Rightarrow> Some([out],\<sigma>')
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| Some(outs,\<sigma>'') \<Rightarrow> Some(out#outs,\<sigma>'')))"
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text{* As mentioned, this definition is fail-safe; in case of an exception,
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text\<open>As mentioned, this definition is fail-safe; in case of an exception,
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the current state is maintained, no result is reported.
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An alternative is the fail-strict variant @{text "mbind'"} defined below. *}
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An alternative is the fail-strict variant \<open>mbind'\<close> defined below.\<close>
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lemma mbind_unit [simp]: "mbind [] f = (return [])"
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by(rule ext, simp add: unit_SE_def)
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@ -214,7 +214,7 @@ lemma mbind_nofailure [simp]: "mbind S f \<sigma> \<noteq> None"
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done
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done
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text{* The fail-strict version of @{text mbind'} looks as follows: *}
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text\<open>The fail-strict version of \<open>mbind'\<close> looks as follows:\<close>
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fun mbind' :: "'\<iota> list \<Rightarrow> ('\<iota> \<Rightarrow> ('o,'\<sigma>) MON\<^sub>S\<^sub>E) \<Rightarrow> ('o list,'\<sigma>) MON\<^sub>S\<^sub>E"
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where "mbind' [] iostep \<sigma> = Some([], \<sigma>)" |
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"mbind' (a#H) iostep \<sigma> =
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@ -224,21 +224,21 @@ where "mbind' [] iostep \<sigma> = Some([], \<sigma>)" |
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None \<Rightarrow> None \<comment> \<open>fail-strict\<close>
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| Some(outs,\<sigma>'') \<Rightarrow> Some(out#outs,\<sigma>'')))"
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text{*
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text\<open>
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mbind' as failure strict operator can be seen as a foldr on bind---if the types would
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match \ldots
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*}
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\<close>
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definition try_SE :: "('o,'\<sigma>) MON\<^sub>S\<^sub>E \<Rightarrow> ('o option,'\<sigma>) MON\<^sub>S\<^sub>E"
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where "try_SE ioprog = (\<lambda>\<sigma>. case ioprog \<sigma> of
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None \<Rightarrow> Some(None, \<sigma>)
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| Some(outs, \<sigma>') \<Rightarrow> Some(Some outs, \<sigma>'))"
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text{* In contrast @{term mbind} as a failure safe operator can roughly be seen
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text\<open>In contrast @{term mbind} as a failure safe operator can roughly be seen
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as a @{term foldr} on bind - try:
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@{text "m1 ; try m2 ; try m3; ..."}. Note, that the rough equivalence only holds for
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\<open>m1 ; try m2 ; try m3; ...\<close>. Note, that the rough equivalence only holds for
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certain predicates in the sequence - length equivalence modulo None,
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for example. However, if a conditional is added, the equivalence
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can be made precise: *}
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can be made precise:\<close>
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lemma mbind_try:
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@ -261,8 +261,8 @@ lemma mbind_try:
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done
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done
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text{* On this basis, a symbolic evaluation scheme can be established
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that reduces @{term mbind}-code to @{term try_SE}-code and If-cascades. *}
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text\<open>On this basis, a symbolic evaluation scheme can be established
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that reduces @{term mbind}-code to @{term try_SE}-code and If-cascades.\<close>
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definition alt_SE :: "[('o, '\<sigma>)MON\<^sub>S\<^sub>E, ('o, '\<sigma>)MON\<^sub>S\<^sub>E] \<Rightarrow> ('o, '\<sigma>)MON\<^sub>S\<^sub>E" (infixl "\<sqinter>\<^sub>S\<^sub>E" 10)
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@ -279,13 +279,13 @@ lemma malt_SE_mt [simp]: "\<Sqinter>\<^sub>S\<^sub>E [] = fail\<^sub>S\<^sub>E"
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lemma malt_SE_cons [simp]: "\<Sqinter>\<^sub>S\<^sub>E (a # S) = (a \<sqinter>\<^sub>S\<^sub>E (\<Sqinter>\<^sub>S\<^sub>E S))"
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by(simp add: malt_SE_def)
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subsubsection{* State-Backtrack Monads *}
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text{*This subsection is still rudimentary and as such an interesting
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subsubsection\<open>State-Backtrack Monads\<close>
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text\<open>This subsection is still rudimentary and as such an interesting
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formal analogue to the previous monad definitions. It is doubtful that it is
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interesting for testing and as a computational structure at all.
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Clearly more relevant is ``sequence'' instead of ``set,'' which would
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rephrase Isabelle's internal tactic concept.
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*}
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\<close>
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type_synonym ('o, '\<sigma>) MON\<^sub>S\<^sub>B = "'\<sigma> \<Rightarrow> ('o \<times> '\<sigma>) set"
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@ -318,13 +318,13 @@ lemma bind_assoc_SB: "(y := (x := m; k); h) = (x := m; (y := k; h))"
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apply (simp add: unit_SB_def bind_SB_def split_def)
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done
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subsubsection{* State Backtrack Exception Monad *}
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text{*
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subsubsection\<open>State Backtrack Exception Monad\<close>
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text\<open>
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The following combination of the previous two Monad-Constructions allows for the semantic
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foundation of a simple generic assertion language in the style of Schirmer's Simpl-Language or
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Rustan Leino's Boogie-PL language. The key is to use the exceptional element None for violations
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of the assert-statement.
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*}
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\<close>
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type_synonym ('o, '\<sigma>) MON\<^sub>S\<^sub>B\<^sub>E = "'\<sigma> \<Rightarrow> (('o \<times> '\<sigma>) set) option"
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definition bind_SBE :: "('o,'\<sigma>)MON\<^sub>S\<^sub>B\<^sub>E \<Rightarrow> ('o \<Rightarrow> ('o','\<sigma>)MON\<^sub>S\<^sub>B\<^sub>E) \<Rightarrow> ('o','\<sigma>)MON\<^sub>S\<^sub>B\<^sub>E"
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@ -412,20 +412,20 @@ qed
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subsection{* Valid Test Sequences in the State Exception Monad *}
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text{*
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subsection\<open>Valid Test Sequences in the State Exception Monad\<close>
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text\<open>
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This is still an unstructured merge of executable monad concepts and specification oriented
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high-level properties initiating test procedures.
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*}
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\<close>
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|
||||
definition valid_SE :: "'\<sigma> \<Rightarrow> (bool,'\<sigma>) MON\<^sub>S\<^sub>E \<Rightarrow> bool" (infix "\<Turnstile>" 15)
|
||||
where "(\<sigma> \<Turnstile> m) = (m \<sigma> \<noteq> None \<and> fst(the (m \<sigma>)))"
|
||||
text{*
|
||||
text\<open>
|
||||
This notation consideres failures as valid---a definition inspired by I/O conformance.
|
||||
Note that it is not possible to define this concept once and for all in a Hindley-Milner
|
||||
type-system. For the moment, we present it only for the state-exception monad, although for
|
||||
the same definition, this notion is applicable to other monads as well.
|
||||
*}
|
||||
\<close>
|
||||
|
||||
lemma syntax_test :
|
||||
"\<sigma> \<Turnstile> (os \<leftarrow> (mbind \<iota>s ioprog); return(length \<iota>s = length os))"
|
||||
|
@ -435,7 +435,7 @@ oops
|
|||
lemma valid_true[simp]: "(\<sigma> \<Turnstile> (s \<leftarrow> return x ; return (P s))) = P x"
|
||||
by(simp add: valid_SE_def unit_SE_def bind_SE_def)
|
||||
|
||||
text{* Recall mbind\_unit for the base case. *}
|
||||
text\<open>Recall mbind\_unit for the base case.\<close>
|
||||
|
||||
lemma valid_failure: "ioprog a \<sigma> = None \<Longrightarrow>
|
||||
(\<sigma> \<Turnstile> (s \<leftarrow> mbind (a#S) ioprog ; M s)) =
|
||||
|
@ -549,12 +549,12 @@ lemma assume_D : "(\<sigma> \<Turnstile> (x \<leftarrow> assume\<^sub>S\<^sub>E
|
|||
apply (simp)
|
||||
done
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
These two rule prove that the SE Monad in connection with the notion of valid sequence is
|
||||
actually sufficient for a representation of a Boogie-like language. The SBE monad with explicit
|
||||
sets of states---to be shown below---is strictly speaking not necessary (and will therefore
|
||||
be discontinued in the development).
|
||||
*}
|
||||
\<close>
|
||||
|
||||
lemma if_SE_D1 : "P \<sigma> \<Longrightarrow> (\<sigma> \<Turnstile> if\<^sub>S\<^sub>E P B\<^sub>1 B\<^sub>2) = (\<sigma> \<Turnstile> B\<^sub>1)"
|
||||
by(auto simp: if_SE_def valid_SE_def)
|
||||
|
@ -576,17 +576,17 @@ lemma [code]: "(\<sigma> \<Turnstile> m) = (case (m \<sigma>) of None \<Rightar
|
|||
apply (auto)
|
||||
done
|
||||
|
||||
subsection{* Valid Test Sequences in the State Exception Backtrack Monad *}
|
||||
text{*
|
||||
subsection\<open>Valid Test Sequences in the State Exception Backtrack Monad\<close>
|
||||
text\<open>
|
||||
This is still an unstructured merge of executable monad concepts and specification oriented
|
||||
high-level properties initiating test procedures.
|
||||
*}
|
||||
\<close>
|
||||
|
||||
definition valid_SBE :: "'\<sigma> \<Rightarrow> ('a,'\<sigma>) MON\<^sub>S\<^sub>B\<^sub>E \<Rightarrow> bool" (infix "\<Turnstile>\<^sub>S\<^sub>B\<^sub>E" 15)
|
||||
where "\<sigma> \<Turnstile>\<^sub>S\<^sub>B\<^sub>E m \<equiv> (m \<sigma> \<noteq> None)"
|
||||
text{*
|
||||
text\<open>
|
||||
This notation considers all non-failures as valid.
|
||||
*}
|
||||
\<close>
|
||||
|
||||
lemma assume_assert: "(\<sigma> \<Turnstile>\<^sub>S\<^sub>B\<^sub>E ( _ :\<equiv> assume\<^sub>S\<^sub>B\<^sub>E P ; assert\<^sub>S\<^sub>B\<^sub>E Q)) = (P \<sigma> \<longrightarrow> Q \<sigma>)"
|
||||
by(simp add: valid_SBE_def assume_SBE_def assert_SBE_def bind_SBE_def)
|
||||
|
|
|
@ -40,7 +40,7 @@
|
|||
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
******************************************************************************)
|
||||
|
||||
section{* Policy Transformations *}
|
||||
section\<open>Policy Transformations\<close>
|
||||
theory
|
||||
Normalisation
|
||||
imports
|
||||
|
@ -48,75 +48,75 @@ theory
|
|||
ParallelComposition
|
||||
begin
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
This theory provides the formalisations required for the transformation of UPF policies.
|
||||
A typical usage scenario can be observed in the firewall case
|
||||
study~\cite{brucker.ea:formal-fw-testing:2014}.
|
||||
*}
|
||||
\<close>
|
||||
|
||||
subsection{* Elementary Operators *}
|
||||
text{*
|
||||
subsection\<open>Elementary Operators\<close>
|
||||
text\<open>
|
||||
We start by providing several operators and theorems useful when reasoning about a list of
|
||||
rules which should eventually be interpreted as combined using the standard override operator.
|
||||
*}
|
||||
\<close>
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
The following definition takes as argument a list of rules and returns a policy where the
|
||||
rules are combined using the standard override operator.
|
||||
*}
|
||||
\<close>
|
||||
definition list2policy::"('a \<mapsto> 'b) list \<Rightarrow> ('a \<mapsto> 'b)" where
|
||||
"list2policy l = foldr (\<lambda> x y. (x \<Oplus> y)) l \<emptyset>"
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
Determine the position of element of a list.
|
||||
*}
|
||||
\<close>
|
||||
fun position :: "'\<alpha> \<Rightarrow> '\<alpha> list \<Rightarrow> nat" where
|
||||
"position a [] = 0"
|
||||
|"(position a (x#xs)) = (if a = x then 1 else (Suc (position a xs)))"
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
Provides the first applied rule of a policy given as a list of rules.
|
||||
*}
|
||||
\<close>
|
||||
fun applied_rule where
|
||||
"applied_rule C a (x#xs) = (if a \<in> dom (C x) then (Some x)
|
||||
else (applied_rule C a xs))"
|
||||
|"applied_rule C a [] = None"
|
||||
|
||||
text {*
|
||||
text \<open>
|
||||
The following is used if the list is constructed backwards.
|
||||
*}
|
||||
\<close>
|
||||
definition applied_rule_rev where
|
||||
"applied_rule_rev C a x = applied_rule C a (rev x)"
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
The following is a typical policy transformation. It can be applied to any type of policy and
|
||||
removes all the rules from a policy with an empty domain. It takes two arguments: a semantic
|
||||
interpretation function and a list of rules.
|
||||
*}
|
||||
\<close>
|
||||
fun rm_MT_rules where
|
||||
"rm_MT_rules C (x#xs) = (if dom (C x)= {}
|
||||
then rm_MT_rules C xs
|
||||
else x#(rm_MT_rules C xs))"
|
||||
|"rm_MT_rules C [] = []"
|
||||
|
||||
text {*
|
||||
text \<open>
|
||||
The following invariant establishes that there are no rules with an empty domain in a list
|
||||
of rules.
|
||||
*}
|
||||
\<close>
|
||||
fun none_MT_rules where
|
||||
"none_MT_rules C (x#xs) = (dom (C x) \<noteq> {} \<and> (none_MT_rules C xs))"
|
||||
|"none_MT_rules C [] = True"
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
The following related invariant establishes that the policy has not a completely empty domain.
|
||||
*}
|
||||
\<close>
|
||||
fun not_MT where
|
||||
"not_MT C (x#xs) = (if (dom (C x) = {}) then (not_MT C xs) else True)"
|
||||
|"not_MT C [] = False"
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
Next, a few theorems about the two invariants and the transformation:
|
||||
*}
|
||||
\<close>
|
||||
lemma none_MT_rules_vs_notMT: "none_MT_rules C p \<Longrightarrow> p \<noteq> [] \<Longrightarrow> not_MT C p"
|
||||
apply (induct p)
|
||||
apply (simp_all)
|
||||
|
@ -174,7 +174,7 @@ lemma NMPrm: "not_MT C p \<Longrightarrow> not_MT C (rm_MT_rules C p)"
|
|||
apply (simp_all)
|
||||
done
|
||||
|
||||
text{* Next, a few theorems about applied\_rule: *}
|
||||
text\<open>Next, a few theorems about applied\_rule:\<close>
|
||||
lemma mrconc: "applied_rule_rev C x p = Some a \<Longrightarrow> applied_rule_rev C x (b#p) = Some a"
|
||||
proof (induct p rule: rev_induct)
|
||||
case Nil show ?case using Nil
|
||||
|
@ -236,8 +236,8 @@ next
|
|||
qed
|
||||
|
||||
|
||||
subsection{* Distributivity of the Transformation. *}
|
||||
text{*
|
||||
subsection\<open>Distributivity of the Transformation.\<close>
|
||||
text\<open>
|
||||
The scenario is the following (can be applied iteratively):
|
||||
\begin{itemize}
|
||||
\item Two policies are combined using one of the parallel combinators
|
||||
|
@ -246,12 +246,12 @@ text{*
|
|||
\item policies that are semantically equivalent to the original policy if
|
||||
\item combined from left to right using the override operator.
|
||||
\end{itemize}
|
||||
*}
|
||||
\<close>
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
The following function is crucial for the distribution. Its arguments are a policy, a list
|
||||
of policies, a parallel combinator, and a range and a domain coercion function.
|
||||
*}
|
||||
\<close>
|
||||
fun prod_list :: "('\<alpha> \<mapsto>'\<beta>) \<Rightarrow> (('\<gamma> \<mapsto>'\<delta>) list) \<Rightarrow>
|
||||
(('\<alpha> \<mapsto>'\<beta>) \<Rightarrow> ('\<gamma> \<mapsto>'\<delta>) \<Rightarrow> (('\<alpha> \<times> '\<gamma>) \<mapsto> ('\<beta> \<times> '\<delta>))) \<Rightarrow>
|
||||
(('\<beta> \<times> '\<delta>) \<Rightarrow> 'y) \<Rightarrow> ('x \<Rightarrow> ('\<alpha> \<times> '\<gamma>)) \<Rightarrow>
|
||||
|
@ -260,9 +260,9 @@ fun prod_list :: "('\<alpha> \<mapsto>'\<beta>) \<Rightarrow> (('\<gamma> \<maps
|
|||
((ran_adapt o_f ((par_comb x y) o dom_adapt))#(prod_list x ys par_comb ran_adapt dom_adapt))"
|
||||
| "prod_list x [] par_comb ran_adapt dom_adapt = []"
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
An instance, as usual there are four of them.
|
||||
*}
|
||||
\<close>
|
||||
|
||||
definition prod_2_list :: "[('\<alpha> \<mapsto>'\<beta>), (('\<gamma> \<mapsto>'\<delta>) list)] \<Rightarrow>
|
||||
(('\<beta> \<times> '\<delta>) \<Rightarrow> 'y) \<Rightarrow> ('x \<Rightarrow> ('\<alpha> \<times> '\<gamma>)) \<Rightarrow>
|
||||
|
@ -277,10 +277,10 @@ lemma list2listNMT: "x \<noteq> [] \<Longrightarrow> map sem x \<noteq> []"
|
|||
lemma two_conc: "(prod_list x (y#ys) p r d) = ((r o_f ((p x y) o d))#(prod_list x ys p r d))"
|
||||
by simp
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
The following two invariants establish if the law of distributivity holds for a combinator
|
||||
and if an operator is strict regarding undefinedness.
|
||||
*}
|
||||
\<close>
|
||||
definition is_distr where
|
||||
"is_distr p = (\<lambda> g f. (\<forall> N P1 P2. ((g o_f ((p N (P1 \<Oplus> P2)) o f)) =
|
||||
((g o_f ((p N P1) o f)) \<Oplus> (g o_f ((p N P2) o f))))))"
|
||||
|
@ -320,9 +320,9 @@ lemma notDom: "x \<in> dom A \<Longrightarrow> \<not> A x = None"
|
|||
apply auto
|
||||
done
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
The following theorems are crucial: they establish the correctness of the distribution.
|
||||
*}
|
||||
\<close>
|
||||
lemma Norm_Distr_1: "((r o_f (((\<Otimes>\<^sub>1) P1 (list2policy P2)) o d)) x =
|
||||
((list2policy ((P1 \<Otimes>\<^sub>L P2) (\<Otimes>\<^sub>1) r d)) x))"
|
||||
proof (induct P2)
|
||||
|
@ -395,7 +395,7 @@ next
|
|||
qed
|
||||
qed
|
||||
|
||||
text {* Some domain reasoning *}
|
||||
text \<open>Some domain reasoning\<close>
|
||||
lemma domSubsetDistr1: "dom A = UNIV \<Longrightarrow> dom ((\<lambda>(x, y). x) o_f (A \<Otimes>\<^sub>1 B) o (\<lambda> x. (x,x))) = dom B"
|
||||
apply (rule set_eqI)
|
||||
apply (rule iffI)
|
||||
|
|
|
@ -40,14 +40,14 @@
|
|||
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
******************************************************************************)
|
||||
|
||||
section {* Policy Transformation for Testing *}
|
||||
section \<open>Policy Transformation for Testing\<close>
|
||||
theory
|
||||
NormalisationTestSpecification
|
||||
imports
|
||||
Normalisation
|
||||
begin
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
This theory provides functions and theorems which are useful if one wants to test policy
|
||||
which are transformed. Most exist in two versions: one where the domains of the rules
|
||||
of the list (which is the result of a transformation) are pairwise disjoint, and one where
|
||||
|
@ -55,11 +55,11 @@ text{*
|
|||
|
||||
The examples in the firewall case study provide a good documentation how these theories can
|
||||
be applied.
|
||||
*}
|
||||
\<close>
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
This invariant establishes that the domains of a list of rules are pairwise disjoint.
|
||||
*}
|
||||
\<close>
|
||||
fun disjDom where
|
||||
"disjDom (x#xs) = ((\<forall>y\<in>(set xs). dom x \<inter> dom y = {}) \<and> disjDom xs)"
|
||||
|"disjDom [] = True"
|
||||
|
@ -110,11 +110,11 @@ lemma distrPUTL:
|
|||
apply (auto)
|
||||
done
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
It makes sense to cater for the common special case where the normalisation returns a list
|
||||
where the last element is a default-catch-all rule. It seems easier to cater for this globally,
|
||||
rather than to require the normalisation procedures to do this.
|
||||
*}
|
||||
\<close>
|
||||
|
||||
fun gatherDomain_aux where
|
||||
"gatherDomain_aux (x#xs) = (dom x \<union> (gatherDomain_aux xs))"
|
||||
|
|
|
@ -40,14 +40,14 @@
|
|||
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
******************************************************************************)
|
||||
|
||||
section{* Parallel Composition*}
|
||||
section\<open>Parallel Composition\<close>
|
||||
theory
|
||||
ParallelComposition
|
||||
imports
|
||||
ElementaryPolicies
|
||||
begin
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
The following combinators are based on the idea that two policies are executed in parallel.
|
||||
Since both input and the output can differ, we chose to pair them.
|
||||
|
||||
|
@ -60,13 +60,13 @@ text{*
|
|||
In any case, although we have strictly speaking a pairing of decisions and not a nesting of
|
||||
them, we will apply the same notational conventions as for the latter, i.e. as for
|
||||
flattening.
|
||||
*}
|
||||
\<close>
|
||||
|
||||
subsection{* Parallel Combinators: Foundations *}
|
||||
text {*
|
||||
subsection\<open>Parallel Combinators: Foundations\<close>
|
||||
text \<open>
|
||||
There are four possible semantics how the decision can be combined, thus there are four
|
||||
parallel composition operators. For each of them, we prove several properties.
|
||||
*}
|
||||
\<close>
|
||||
|
||||
definition prod_orA ::"['\<alpha>\<mapsto>'\<beta>, '\<gamma> \<mapsto>'\<delta>] \<Rightarrow> ('\<alpha>\<times>'\<gamma> \<mapsto> '\<beta>\<times>'\<delta>)" (infixr "\<Otimes>\<^sub>\<or>\<^sub>A" 55)
|
||||
where "p1 \<Otimes>\<^sub>\<or>\<^sub>A p2 =
|
||||
|
@ -132,9 +132,9 @@ lemma prod_orD_quasi_commute: "p2 \<Otimes>\<^sub>\<or>\<^sub>D p1 = (((\<lambda
|
|||
apply (simp split: option.splits decision.splits)
|
||||
done
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
The following two combinators are by definition non-commutative, but still strict.
|
||||
*}
|
||||
\<close>
|
||||
|
||||
definition prod_1 :: "['\<alpha>\<mapsto>'\<beta>, '\<gamma> \<mapsto>'\<delta>] \<Rightarrow> ('\<alpha>\<times>'\<gamma> \<mapsto> '\<beta>\<times>'\<delta>)" (infixr "\<Otimes>\<^sub>1" 55)
|
||||
where "p1 \<Otimes>\<^sub>1 p2 \<equiv>
|
||||
|
@ -212,11 +212,11 @@ lemma mt_prod_2_id[simp]:"\<emptyset> \<Otimes>\<^sub>2\<^sub>I p = \<emptyset>"
|
|||
apply (simp add: prod_2_id_def prod_2_def)
|
||||
done
|
||||
|
||||
subsection{* Combinators for Transition Policies *}
|
||||
text {*
|
||||
subsection\<open>Combinators for Transition Policies\<close>
|
||||
text \<open>
|
||||
For constructing transition policies, two additional combinators are required: one combines
|
||||
state transitions by pairing the states, the other works equivalently on general maps.
|
||||
*}
|
||||
\<close>
|
||||
|
||||
definition parallel_map :: "('\<alpha> \<rightharpoonup> '\<beta>) \<Rightarrow> ('\<delta> \<rightharpoonup> '\<gamma>) \<Rightarrow>
|
||||
('\<alpha> \<times> '\<delta> \<rightharpoonup> '\<beta> \<times> '\<gamma>)" (infixr "\<Otimes>\<^sub>M" 60)
|
||||
|
@ -231,11 +231,11 @@ where
|
|||
"p1 \<Otimes>\<^sub>S p2 = (p1 \<Otimes>\<^sub>M p2) o (\<lambda> (a,b,c). ((a,b),a,c))"
|
||||
|
||||
|
||||
subsection{* Range Splitting *}
|
||||
text{*
|
||||
subsection\<open>Range Splitting\<close>
|
||||
text\<open>
|
||||
The following combinator is a special case of both a parallel composition operator and a
|
||||
range splitting operator. Its primary use case is when combining a policy with state transitions.
|
||||
*}
|
||||
\<close>
|
||||
|
||||
definition comp_ran_split :: "[('\<alpha> \<rightharpoonup> '\<gamma>) \<times> ('\<alpha> \<rightharpoonup>'\<gamma>), 'd \<mapsto> '\<beta>] \<Rightarrow> ('d \<times> '\<alpha>) \<mapsto> ('\<beta> \<times> '\<gamma>)"
|
||||
(infixr "\<Otimes>\<^sub>\<nabla>" 100)
|
||||
|
@ -244,7 +244,7 @@ where "P \<Otimes>\<^sub>\<nabla> p \<equiv> \<lambda>x. case p (fst x) of
|
|||
| \<lfloor>deny y\<rfloor> \<Rightarrow> (case ((snd P) (snd x)) of \<bottom> \<Rightarrow> \<bottom> | \<lfloor>z\<rfloor> \<Rightarrow> \<lfloor>deny (y,z)\<rfloor>)
|
||||
| \<bottom> \<Rightarrow> \<bottom>"
|
||||
|
||||
text{* An alternative characterisation of the operator is as follows: *}
|
||||
text\<open>An alternative characterisation of the operator is as follows:\<close>
|
||||
lemma comp_ran_split_charn:
|
||||
"(f, g) \<Otimes>\<^sub>\<nabla> p = (
|
||||
(((p \<triangleright> Allow)\<Otimes>\<^sub>\<or>\<^sub>A (A\<^sub>p f)) \<Oplus>
|
||||
|
@ -257,7 +257,7 @@ lemma comp_ran_split_charn:
|
|||
apply (auto)
|
||||
done
|
||||
|
||||
subsection {* Distributivity of the parallel combinators *}
|
||||
subsection \<open>Distributivity of the parallel combinators\<close>
|
||||
|
||||
lemma distr_or1_a: "(F = F1 \<Oplus> F2) \<Longrightarrow> (((N \<Otimes>\<^sub>1 F) o f) =
|
||||
(((N \<Otimes>\<^sub>1 F1) o f) \<Oplus> ((N \<Otimes>\<^sub>1 F2) o f))) "
|
||||
|
|
2
UPF/ROOT
2
UPF/ROOT
|
@ -1,7 +1,7 @@
|
|||
chapter AFP
|
||||
|
||||
session "UPF-devel" (AFP) = HOL +
|
||||
description {* The Unified Policy Framework (UPF) *}
|
||||
description "The Unified Policy Framework (UPF) "
|
||||
options [timeout = 300]
|
||||
theories
|
||||
Monads
|
||||
|
|
|
@ -40,23 +40,23 @@
|
|||
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
******************************************************************************)
|
||||
|
||||
section{* Sequential Composition *}
|
||||
section\<open>Sequential Composition\<close>
|
||||
theory
|
||||
SeqComposition
|
||||
imports
|
||||
ElementaryPolicies
|
||||
begin
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
Sequential composition is based on the idea that two policies are to be combined by applying
|
||||
the second policy to the output of the first one. Again, there are four possibilities how the
|
||||
decisions can be combined. *}
|
||||
decisions can be combined.\<close>
|
||||
|
||||
subsection {* Flattening *}
|
||||
text{*
|
||||
subsection \<open>Flattening\<close>
|
||||
text\<open>
|
||||
A key concept of sequential policy composition is the flattening of nested decisions. There are
|
||||
four possibilities, and these possibilities will give the various flavours of policy composition.
|
||||
*}
|
||||
\<close>
|
||||
fun flat_orA :: "('\<alpha> decision) decision \<Rightarrow> ('\<alpha> decision)"
|
||||
where "flat_orA(allow(allow y)) = allow y"
|
||||
|"flat_orA(allow(deny y)) = allow y"
|
||||
|
@ -149,10 +149,10 @@ lemma flat_2_deny[dest]: "flat_2 x = deny y \<Longrightarrow> x = deny(deny y)
|
|||
apply (case_tac "\<alpha>", simp_all)[1]
|
||||
done
|
||||
|
||||
subsection{* Policy Composition *}
|
||||
text{*
|
||||
subsection\<open>Policy Composition\<close>
|
||||
text\<open>
|
||||
The following definition allows to compose two policies. Denies and allows are transferred.
|
||||
*}
|
||||
\<close>
|
||||
|
||||
fun lift :: "('\<alpha> \<mapsto> '\<beta>) \<Rightarrow> ('\<alpha> decision \<mapsto>'\<beta> decision)"
|
||||
where "lift f (deny s) = (case f s of
|
||||
|
@ -170,10 +170,10 @@ lemma lift_mt [simp]: "lift \<emptyset> = \<emptyset>"
|
|||
done
|
||||
done
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
Since policies are maps, we inherit a composition on them. However, this results in nestings
|
||||
of decisions---which must be flattened. As we now that there are four different forms of
|
||||
flattening, we have four different forms of policy composition: *}
|
||||
flattening, we have four different forms of policy composition:\<close>
|
||||
definition
|
||||
comp_orA :: "['\<beta>\<mapsto>'\<gamma>, '\<alpha>\<mapsto>'\<beta>] \<Rightarrow> '\<alpha>\<mapsto>'\<gamma>" (infixl "o'_orA" 55) where
|
||||
"p2 o_orA p1 \<equiv> (map_option flat_orA) o (lift p2 \<circ>\<^sub>m p1)"
|
||||
|
|
|
@ -40,52 +40,52 @@
|
|||
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
******************************************************************************)
|
||||
|
||||
section {* Secure Service Specification *}
|
||||
section \<open>Secure Service Specification\<close>
|
||||
theory
|
||||
Service
|
||||
imports
|
||||
UPF
|
||||
begin
|
||||
text {*
|
||||
text \<open>
|
||||
In this section, we model a simple Web service and its access control model
|
||||
that allows the staff in a hospital to access health care records of patients.
|
||||
*}
|
||||
\<close>
|
||||
|
||||
subsection{* Datatypes for Modelling Users and Roles*}
|
||||
subsubsection {* Users *}
|
||||
text{*
|
||||
subsection\<open>Datatypes for Modelling Users and Roles\<close>
|
||||
subsubsection \<open>Users\<close>
|
||||
text\<open>
|
||||
First, we introduce a type for users that we use to model that each
|
||||
staff member has a unique id:
|
||||
*}
|
||||
\<close>
|
||||
type_synonym user = int (* Each NHS employee has a unique NHS_ID. *)
|
||||
|
||||
text {*
|
||||
text \<open>
|
||||
Similarly, each patient has a unique id:
|
||||
*}
|
||||
\<close>
|
||||
type_synonym patient = int (* Each patient gets a unique id *)
|
||||
|
||||
subsubsection {* Roles and Relationships*}
|
||||
text{* In our example, we assume three different roles for members of the clinical staff: *}
|
||||
subsubsection \<open>Roles and Relationships\<close>
|
||||
text\<open>In our example, we assume three different roles for members of the clinical staff:\<close>
|
||||
|
||||
datatype role = ClinicalPractitioner | Nurse | Clerical
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
We model treatment relationships (legitimate relationships) between staff and patients
|
||||
(respectively, their health records. This access control model is inspired by our detailed
|
||||
NHS model.
|
||||
*}
|
||||
\<close>
|
||||
type_synonym lr_id = int
|
||||
type_synonym LR = "lr_id \<rightharpoonup> (user set)"
|
||||
|
||||
text{* The security context stores all the existing LRs. *}
|
||||
text\<open>The security context stores all the existing LRs.\<close>
|
||||
type_synonym \<Sigma> = "patient \<rightharpoonup> LR"
|
||||
|
||||
text{* The user context stores the roles the users are in. *}
|
||||
text\<open>The user context stores the roles the users are in.\<close>
|
||||
type_synonym \<upsilon> = "user \<rightharpoonup> role"
|
||||
|
||||
subsection {* Modelling Health Records and the Web Service API*}
|
||||
subsubsection {* Health Records *}
|
||||
text {* The content and the status of the entries of a health record *}
|
||||
subsection \<open>Modelling Health Records and the Web Service API\<close>
|
||||
subsubsection \<open>Health Records\<close>
|
||||
text \<open>The content and the status of the entries of a health record\<close>
|
||||
datatype data = dummyContent
|
||||
datatype status = Open | Closed
|
||||
type_synonym entry_id = int
|
||||
|
@ -93,8 +93,8 @@ type_synonym entry = "status \<times> user \<times> data"
|
|||
type_synonym SCR = "(entry_id \<rightharpoonup> entry)"
|
||||
type_synonym DB = "patient \<rightharpoonup> SCR"
|
||||
|
||||
subsubsection {* The Web Service API *}
|
||||
text{* The operations provided by the service: *}
|
||||
subsubsection \<open>The Web Service API\<close>
|
||||
text\<open>The operations provided by the service:\<close>
|
||||
datatype Operation = createSCR user role patient
|
||||
| appendEntry user role patient entry_id entry
|
||||
| deleteEntry user role patient entry_id
|
||||
|
@ -207,17 +207,17 @@ fun allContentStatic where
|
|||
|"allContentStatic [] = True"
|
||||
|
||||
|
||||
subsection{* Modelling Access Control*}
|
||||
text {*
|
||||
subsection\<open>Modelling Access Control\<close>
|
||||
text \<open>
|
||||
In the following, we define a rather complex access control model for our
|
||||
scenario that extends traditional role-based access control
|
||||
(RBAC)~\cite{sandhu.ea:role-based:1996} with treatment relationships and sealed
|
||||
envelopes. Sealed envelopes (see~\cite{bruegger:generation:2012} for details)
|
||||
are a variant of break-the-glass access control (see~\cite{brucker.ea:extending:2009}
|
||||
for a general motivation and explanation of break-the-glass access control).
|
||||
*}
|
||||
\<close>
|
||||
|
||||
subsubsection {* Sealed Envelopes *}
|
||||
subsubsection \<open>Sealed Envelopes\<close>
|
||||
|
||||
type_synonym SEPolicy = "(Operation \<times> DB \<mapsto> unit) "
|
||||
|
||||
|
@ -259,7 +259,7 @@ definition SEPolicy :: SEPolicy where
|
|||
lemmas SEsimps = SEPolicy_def get_entry_def userHasAccess_def
|
||||
editEntrySE_def deleteEntrySE_def readEntrySE_def
|
||||
|
||||
subsubsection {* Legitimate Relationships *}
|
||||
subsubsection \<open>Legitimate Relationships\<close>
|
||||
|
||||
type_synonym LRPolicy = "(Operation \<times> \<Sigma>, unit) policy"
|
||||
|
||||
|
@ -365,7 +365,7 @@ definition FunPolicy where
|
|||
removeLRFunPolicy \<Oplus> readSCRFunPolicy \<Oplus>
|
||||
addLRFunPolicy \<Oplus> createFunPolicy \<Oplus> A\<^sub>U"
|
||||
|
||||
subsubsection{* Modelling Core RBAC *}
|
||||
subsubsection\<open>Modelling Core RBAC\<close>
|
||||
|
||||
type_synonym RBACPolicy = "Operation \<times> \<upsilon> \<mapsto> unit"
|
||||
|
||||
|
@ -389,9 +389,9 @@ definition RBACPolicy :: RBACPolicy where
|
|||
then \<lfloor>allow ()\<rfloor>
|
||||
else \<lfloor>deny ()\<rfloor>)"
|
||||
|
||||
subsection {* The State Transitions and Output Function*}
|
||||
subsection \<open>The State Transitions and Output Function\<close>
|
||||
|
||||
subsubsection{* State Transition *}
|
||||
subsubsection\<open>State Transition\<close>
|
||||
|
||||
fun OpSuccessDB :: "(Operation \<times> DB) \<rightharpoonup> DB" where
|
||||
"OpSuccessDB (createSCR u r p,S) = (case S p of \<bottom> \<Rightarrow> \<lfloor>S(p\<mapsto>\<emptyset>)\<rfloor>
|
||||
|
@ -434,7 +434,7 @@ fun OpSuccessSigma :: "(Operation \<times> \<Sigma>) \<rightharpoonup> \<Sigma>"
|
|||
fun OpSuccessUC :: "(Operation \<times> \<upsilon>) \<rightharpoonup> \<upsilon>" where
|
||||
"OpSuccessUC (f,u) = \<lfloor>u\<rfloor>"
|
||||
|
||||
subsubsection {* Output *}
|
||||
subsubsection \<open>Output\<close>
|
||||
|
||||
type_synonym Output = unit
|
||||
|
||||
|
@ -445,7 +445,7 @@ fun OpSuccessOutput :: "(Operation) \<rightharpoonup> Output" where
|
|||
fun OpFailOutput :: "Operation \<rightharpoonup> Output" where
|
||||
"OpFailOutput x = \<lfloor>()\<rfloor>"
|
||||
|
||||
subsection {* Combine All Parts *}
|
||||
subsection \<open>Combine All Parts\<close>
|
||||
|
||||
definition SE_LR_Policy :: "(Operation \<times> DB \<times> \<Sigma>, unit) policy" where
|
||||
"SE_LR_Policy = (\<lambda>(x,x). x) o\<^sub>f (SEPolicy \<Otimes>\<^sub>\<or>\<^sub>D LR_Policy) o (\<lambda>(a,b,c). ((a,b),a,c))"
|
||||
|
|
|
@ -39,19 +39,19 @@
|
|||
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
******************************************************************************)
|
||||
|
||||
section {* Instantiating Our Secure Service Example *}
|
||||
section \<open>Instantiating Our Secure Service Example\<close>
|
||||
theory
|
||||
ServiceExample
|
||||
imports
|
||||
Service
|
||||
begin
|
||||
text {*
|
||||
text \<open>
|
||||
In the following, we briefly present an instantiations of our secure service example
|
||||
from the last section. We assume three different members of the health care staff and
|
||||
two patients:
|
||||
*}
|
||||
\<close>
|
||||
|
||||
subsection {* Access Control Configuration *}
|
||||
subsection \<open>Access Control Configuration\<close>
|
||||
definition alice :: user where "alice = 1"
|
||||
definition bob :: user where "bob = 2"
|
||||
definition charlie :: user where "charlie = 3"
|
||||
|
@ -85,11 +85,11 @@ definition LR1 :: LR where
|
|||
definition \<Sigma>0 :: \<Sigma> where
|
||||
"\<Sigma>0 = (Map.empty(patient1\<mapsto>LR1))"
|
||||
|
||||
subsection {* The Initial System State *}
|
||||
subsection \<open>The Initial System State\<close>
|
||||
definition \<sigma>0 :: "DB \<times> \<Sigma>\<times>\<upsilon>" where
|
||||
"\<sigma>0 = (Spine0,\<Sigma>0,UC0)"
|
||||
|
||||
subsection{* Basic Properties *}
|
||||
subsection\<open>Basic Properties\<close>
|
||||
|
||||
lemma [simp]: "(case a of allow d \<Rightarrow> \<lfloor>X\<rfloor> | deny d2 \<Rightarrow> \<lfloor>Y\<rfloor>) = \<bottom> \<Longrightarrow> False"
|
||||
by (case_tac a,simp_all)
|
||||
|
@ -122,13 +122,13 @@ lemma deny_allow[simp]: " \<lfloor>deny ()\<rfloor> \<notin> Some ` range allow"
|
|||
lemma allow_deny[simp]: " \<lfloor>allow ()\<rfloor> \<notin> Some ` range deny"
|
||||
by auto
|
||||
|
||||
text{* Policy as monad. Alice using her first urp can read the SCR of patient1. *}
|
||||
text\<open>Policy as monad. Alice using her first urp can read the SCR of patient1.\<close>
|
||||
lemma
|
||||
"(\<sigma>0 \<Turnstile> (os \<leftarrow> mbind [(createSCR alice Clerical patient1)] (PolMon);
|
||||
(return (os = [(deny (Out) )]))))"
|
||||
by (simp add: PolMon_def MonSimps PolSimps)
|
||||
|
||||
text{* Presenting her other urp, she is not allowed to read it. *}
|
||||
text\<open>Presenting her other urp, she is not allowed to read it.\<close>
|
||||
lemma "SE_LR_RBAC_Policy ((appendEntry alice Clerical patient1 ei d),\<sigma>0)= \<lfloor>deny ()\<rfloor>"
|
||||
by (simp add: PolSimps)
|
||||
|
||||
|
|
|
@ -41,7 +41,7 @@
|
|||
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
******************************************************************************)
|
||||
|
||||
section {* Putting Everything Together: UPF *}
|
||||
section \<open>Putting Everything Together: UPF\<close>
|
||||
theory
|
||||
UPF
|
||||
imports
|
||||
|
@ -50,10 +50,10 @@ theory
|
|||
Analysis
|
||||
begin
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
This is the top-level theory for the Unified Policy Framework (UPF) and, thus,
|
||||
builds the base theory for using UPF. For the moment, we only define a set of
|
||||
lemmas for all core UPF definitions that is useful for using UPF:
|
||||
*}
|
||||
\<close>
|
||||
lemmas UPFDefs = UPFCoreDefs ParallelDefs ElementaryPoliciesDefs
|
||||
end
|
||||
|
|
|
@ -41,7 +41,7 @@
|
|||
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
******************************************************************************)
|
||||
|
||||
section{* The Core of the Unified Policy Framework (UPF) *}
|
||||
section\<open>The Core of the Unified Policy Framework (UPF)\<close>
|
||||
theory
|
||||
UPFCore
|
||||
imports
|
||||
|
@ -49,8 +49,8 @@ theory
|
|||
begin
|
||||
|
||||
|
||||
subsection{* Foundation *}
|
||||
text{*
|
||||
subsection\<open>Foundation\<close>
|
||||
text\<open>
|
||||
The purpose of this theory is to formalize a somewhat non-standard view
|
||||
on the fundamental concept of a security policy which is worth outlining.
|
||||
This view has arisen from prior experience in the modelling of network
|
||||
|
@ -74,37 +74,37 @@ text{*
|
|||
In more detail, we model policies as partial functions based on input
|
||||
data $\alpha$ (arguments, system state, security context, ...) to output
|
||||
data $\beta$:
|
||||
*}
|
||||
\<close>
|
||||
|
||||
datatype '\<alpha> decision = allow '\<alpha> | deny '\<alpha>
|
||||
|
||||
type_synonym ('\<alpha>,'\<beta>) policy = "'\<alpha> \<rightharpoonup> '\<beta> decision" (infixr "|->" 0)
|
||||
|
||||
text{*In the following, we introduce a number of shortcuts and alternative notations.
|
||||
The type of policies is represented as: *}
|
||||
text\<open>In the following, we introduce a number of shortcuts and alternative notations.
|
||||
The type of policies is represented as:\<close>
|
||||
|
||||
translations (type) "'\<alpha> |-> '\<beta>" <= (type) "'\<alpha> \<rightharpoonup> '\<beta> decision"
|
||||
type_notation "policy" (infixr "\<mapsto>" 0)
|
||||
|
||||
text{* ... allowing the notation @{typ "'\<alpha> \<mapsto> '\<beta>"} for the policy type and the
|
||||
text\<open>... allowing the notation @{typ "'\<alpha> \<mapsto> '\<beta>"} for the policy type and the
|
||||
alternative notations for @{term None} and @{term Some} of the \HOL library
|
||||
@{typ "'\<alpha> option"} type:*}
|
||||
@{typ "'\<alpha> option"} type:\<close>
|
||||
|
||||
notation "None" ("\<bottom>")
|
||||
notation "Some" ("\<lfloor>_\<rfloor>" 80)
|
||||
|
||||
text{* Thus, the range of a policy may consist of @{term "\<lfloor>accept x\<rfloor>"} data,
|
||||
text\<open>Thus, the range of a policy may consist of @{term "\<lfloor>accept x\<rfloor>"} data,
|
||||
of @{term "\<lfloor>deny x\<rfloor>"} data, as well as @{term "\<bottom>"} modeling the undefinedness
|
||||
of a policy, i.e. a policy is considered as a partial function. Partial
|
||||
functions are used since we describe elementary policies by partial system
|
||||
behaviour, which are glued together by operators such as function override and
|
||||
functional composition.
|
||||
*}
|
||||
\<close>
|
||||
|
||||
text{* We define the two fundamental sets, the allow-set $Allow$ and the
|
||||
text\<open>We define the two fundamental sets, the allow-set $Allow$ and the
|
||||
deny-set $Deny$ (written $A$ and $D$ set for short), to characterize these
|
||||
two main sets of the range of a policy.
|
||||
*}
|
||||
\<close>
|
||||
definition Allow :: "('\<alpha> decision) set"
|
||||
where "Allow = range allow"
|
||||
|
||||
|
@ -112,13 +112,13 @@ definition Deny :: "('\<alpha> decision) set"
|
|||
where "Deny = range deny"
|
||||
|
||||
|
||||
subsection{* Policy Constructors *}
|
||||
text{*
|
||||
subsection\<open>Policy Constructors\<close>
|
||||
text\<open>
|
||||
Most elementary policy constructors are based on the
|
||||
update operation @{thm [source] "Fun.fun_upd_def"} @{thm Fun.fun_upd_def}
|
||||
and the maplet-notation @{term "a(x \<mapsto> y)"} used for @{term "a(x:=\<lfloor>y\<rfloor>)"}.
|
||||
|
||||
Furthermore, we add notation adopted to our problem domain: *}
|
||||
Furthermore, we add notation adopted to our problem domain:\<close>
|
||||
|
||||
nonterminal policylets and policylet
|
||||
|
||||
|
@ -137,14 +137,14 @@ translations
|
|||
"_MapUpd m (_policylet2 x y)" \<rightleftharpoons> "m(x := CONST Some (CONST deny y))"
|
||||
"\<emptyset>" \<rightleftharpoons> "CONST Map.empty"
|
||||
|
||||
text{* Here are some lemmas essentially showing syntactic equivalences: *}
|
||||
text\<open>Here are some lemmas essentially showing syntactic equivalences:\<close>
|
||||
lemma test: "\<emptyset>(x\<mapsto>\<^sub>+a, y\<mapsto>\<^sub>-b) = \<emptyset>(x \<mapsto>\<^sub>+ a, y \<mapsto>\<^sub>- b)" by simp
|
||||
|
||||
lemma test2: "p(x\<mapsto>\<^sub>+a,x\<mapsto>\<^sub>-b) = p(x\<mapsto>\<^sub>-b)" by simp
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
We inherit a fairly rich theory on policy updates from Map here. Some examples are:
|
||||
*}
|
||||
\<close>
|
||||
|
||||
lemma pol_upd_triv1: "t k = \<lfloor>allow x\<rfloor> \<Longrightarrow> t(k\<mapsto>\<^sub>+x) = t"
|
||||
by (rule ext) simp
|
||||
|
@ -168,14 +168,14 @@ lemma pol_upd_neq1 [simp]: "m(a\<mapsto>\<^sub>+x) \<noteq> n(a\<mapsto>\<^sub>-
|
|||
by(auto dest: map_upd_eqD1)
|
||||
|
||||
|
||||
subsection{* Override Operators *}
|
||||
text{*
|
||||
subsection\<open>Override Operators\<close>
|
||||
text\<open>
|
||||
Key operators for constructing policies are the override operators. There are four different
|
||||
versions of them, with one of them being the override operator from the Map theory. As it is
|
||||
common to compose policy rules in a ``left-to-right-first-fit''-manner, that one is taken as
|
||||
default, defined by a syntax translation from the provided override operator from the Map
|
||||
theory (which does it in reverse order).
|
||||
*}
|
||||
\<close>
|
||||
|
||||
syntax
|
||||
"_policyoverride" :: "['a \<mapsto> 'b, 'a \<mapsto> 'b] \<Rightarrow> 'a \<mapsto> 'b" (infixl "\<Oplus>" 100)
|
||||
|
@ -183,9 +183,9 @@ translations
|
|||
"p \<Oplus> q" \<rightleftharpoons> "q ++ p"
|
||||
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
Some elementary facts inherited from Map are:
|
||||
*}
|
||||
\<close>
|
||||
|
||||
lemma override_empty: "p \<Oplus> \<emptyset> = p"
|
||||
by simp
|
||||
|
@ -196,10 +196,10 @@ lemma empty_override: "\<emptyset> \<Oplus> p = p"
|
|||
lemma override_assoc: "p1 \<Oplus> (p2 \<Oplus> p3) = (p1 \<Oplus> p2) \<Oplus> p3"
|
||||
by simp
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
The following two operators are variants of the standard override. For override\_A,
|
||||
an allow of wins over a deny. For override\_D, the situation is dual.
|
||||
*}
|
||||
\<close>
|
||||
|
||||
definition override_A :: "['\<alpha>\<mapsto>'\<beta>, '\<alpha>\<mapsto>'\<beta>] \<Rightarrow> '\<alpha>\<mapsto>'\<beta>" (infixl "++'_A" 100)
|
||||
where "m2 ++_A m1 =
|
||||
|
@ -268,15 +268,15 @@ lemma override_D_assoc: "p1 \<Oplus>\<^sub>D (p2 \<Oplus>\<^sub>D p3) = (p1 \<Op
|
|||
apply (simp add: override_D_def split: decision.splits option.splits)
|
||||
done
|
||||
|
||||
subsection{* Coercion Operators *}
|
||||
text{*
|
||||
subsection\<open>Coercion Operators\<close>
|
||||
text\<open>
|
||||
Often, especially when combining policies of different type, it is necessary to
|
||||
adapt the input or output domain of a policy to a more refined context.
|
||||
*}
|
||||
\<close>
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
An analogous for the range of a policy is defined as follows:
|
||||
*}
|
||||
\<close>
|
||||
|
||||
definition policy_range_comp :: "['\<beta>\<Rightarrow>'\<gamma>, '\<alpha>\<mapsto>'\<beta>] \<Rightarrow> '\<alpha> \<mapsto>'\<gamma>" (infixl "o'_f" 55)
|
||||
where
|
||||
|
@ -296,10 +296,10 @@ lemma policy_range_comp_strict : "f o\<^sub>f \<emptyset> = \<emptyset>"
|
|||
done
|
||||
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
A generalized version is, where separate coercion functions are applied to the result
|
||||
depending on the decision of the policy is as follows:
|
||||
*}
|
||||
\<close>
|
||||
|
||||
definition range_split :: "[('\<beta>\<Rightarrow>'\<gamma>)\<times>('\<beta>\<Rightarrow>'\<gamma>),'\<alpha> \<mapsto> '\<beta>] \<Rightarrow> '\<alpha> \<mapsto> '\<gamma>"
|
||||
(infixr "\<nabla>" 100)
|
||||
|
@ -331,9 +331,9 @@ lemma range_split_charn:
|
|||
done
|
||||
done
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
The connection between these two becomes apparent if considering the following lemma:
|
||||
*}
|
||||
\<close>
|
||||
|
||||
lemma range_split_vs_range_compose: "(f,f) \<nabla> p = f o\<^sub>f p"
|
||||
by(simp add: range_split_charn policy_range_comp_def)
|
||||
|
@ -364,14 +364,14 @@ lemma range_split_bi_compose [simp]: "(f1,f2) \<nabla> (g1,g2) \<nabla> p = (f1
|
|||
done
|
||||
done
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
The next three operators are rather exotic and in most cases not used.
|
||||
*}
|
||||
\<close>
|
||||
|
||||
text {*
|
||||
text \<open>
|
||||
The following is a variant of range\_split, where the change in the decision depends
|
||||
on the input instead of the output.
|
||||
*}
|
||||
\<close>
|
||||
|
||||
definition dom_split2a :: "[('\<alpha> \<rightharpoonup> '\<gamma>) \<times> ('\<alpha> \<rightharpoonup>'\<gamma>),'\<alpha> \<mapsto> '\<beta>] \<Rightarrow> '\<alpha> \<mapsto> '\<gamma>" (infixr "\<Delta>a" 100)
|
||||
where "P \<Delta>a p = (\<lambda>x. case p x of
|
||||
|
@ -391,11 +391,11 @@ where "P \<nabla>2 p = (\<lambda>x. case p x of
|
|||
| \<lfloor>deny y\<rfloor> \<Rightarrow> \<lfloor>deny (y,(snd P) x)\<rfloor>
|
||||
| \<bottom> \<Rightarrow> \<bottom>)"
|
||||
|
||||
text{*
|
||||
text\<open>
|
||||
The following operator is used for transition policies only: a transition policy is transformed
|
||||
into a state-exception monad. Such a monad can for example be used for test case generation using
|
||||
HOL-Testgen~\cite{brucker.ea:theorem-prover:2012}.
|
||||
*}
|
||||
\<close>
|
||||
|
||||
definition policy2MON :: "('\<iota>\<times>'\<sigma> \<mapsto> 'o\<times>'\<sigma>) \<Rightarrow> ('\<iota> \<Rightarrow>('o decision,'\<sigma>) MON\<^sub>S\<^sub>E)"
|
||||
where "policy2MON p = (\<lambda> \<iota> \<sigma>. case p (\<iota>,\<sigma>) of
|
||||
|
|
|
@ -8,7 +8,7 @@
|
|||
# {\providecommand{\isbn}{\textsc{isbn}} }
|
||||
# {\providecommand{\Cpp}{C++} }
|
||||
# {\providecommand{\Specsharp}{Spec\#} }
|
||||
# {\providecommand{\doi}[1]{\href{http://dx.doi.org/#1}{doi:
|
||||
# {\providecommand{\doi}[1]{\href{https://doi.org/#1}{doi:
|
||||
{\urlstyle{rm}\nolinkurl{#1}}}}} }
|
||||
@STRING{conf-sacmat="ACM symposium on access control models and technologies
|
||||
(SACMAT)" }
|
||||
|
@ -319,7 +319,7 @@
|
|||
revocation are provided, and proofs are given for the
|
||||
important properties of our delegation framework.},
|
||||
issn = {0306-4379},
|
||||
doi = {http://dx.doi.org/10.1016/j.is.2005.11.008},
|
||||
doi = {https://doi.org/10.1016/j.is.2005.11.008},
|
||||
publisher = pub-elsevier,
|
||||
address = {Oxford, UK, UK},
|
||||
tags = {ReadingList, SoKNOS},
|
||||
|
|
Loading…
Reference in New Issue