Isabelle_DOF
/
Isabelle_DOF
1
0
Fork 2
Code Issues 1 Pull Requests Releases Wiki Activity

added Lemma*, Theorem* and Definition* support. Bug: referencing does not work.

This commit is contained in:
Burkhart Wolff 2020-11-04 15:55:43 +01:00
parent 4ad06ce39a
commit 2ecb62a80e
5 changed files with 26 additions and 22 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

39
examples/scholarly_paper/2020-iFM-CSP/paper.thy
View File

@ -353,7 +353,7 @@ Roscoe and Brooks @{cite "Roscoe1992AnAO"} finally proposed another ordering, ca
that completeness could at least be assured for read-operations. This more complex ordering
is based on the concept \<^emph>\<open>refusals after\<close> a trace \<open>s\<close> and defined by \<open>\<R> P s \<equiv> {X | (s, X) \<in> \<F> P}\<close>.\<close>
text*[process_ordering::"definition", short_name="''process ordering''"]\<open>
Definition*[process_ordering, short_name="''process ordering''"]\<open>
We define \<open>P \<sqsubseteq> Q \<equiv> \<psi>\<^sub>\<D> \<and> \<psi>\<^sub>\<R> \<and> \<psi>\<^sub>\<M> \<close>, where \<^vs>\<open>-0.2cm\<close>
\<^enum> \<^vs>\<open>-0.2cm\<close> \<open>\<psi>\<^sub>\<D> = \<D> P \<supseteq> \<D> Q \<close>
\<^enum> \<open>\<psi>\<^sub>\<R> = s \<notin> \<D> P \<Rightarrow> \<R> P s = \<R> Q s\<close>
@ -528,21 +528,21 @@ To handle termination better, we added two new processes \<open>CHAOS\<^sub>S\<^
%thus must be without it.
\<close>
(*
text*[X2::"definition"]\<open>\<open>RUN A \<equiv> \<mu> X. \<box> x \<in> A \<rightarrow> X\<close> \<^vs>\<open>-0.7cm\<close>\<close>
text*[X3::"definition"]\<open>\<open>CHAOS A \<equiv> \<mu> X. (STOP \<sqinter> (\<box> x \<in> A \<rightarrow> X))\<close> \<^vs>\<open>-0.7cm\<close>\<close>
text*[X4::"definition"]\<open>\<open>CHAOS\<^sub>S\<^sub>K\<^sub>I\<^sub>P A \<equiv> \<mu> X. (SKIP \<sqinter> STOP \<sqinter> (\<box> x \<in> A \<rightarrow> X))\<close>\<^vs>\<open>-0.7cm\<close>\<close>
Definition*[X22]\<open>\<open>RUN A \<equiv> \<mu> X. \<box> x \<in> A \<rightarrow> X\<close> \<^vs>\<open>-0.7cm\<close>\<close>
Definition*[X32]\<open>\<open>CHAOS A \<equiv> \<mu> X. (STOP \<sqinter> (\<box> x \<in> A \<rightarrow> X))\<close> \<^vs>\<open>-0.7cm\<close>\<close>
Definition*[X42]\<open>\<open>CHAOS\<^sub>S\<^sub>K\<^sub>I\<^sub>P A \<equiv> \<mu> X. (SKIP \<sqinter> STOP \<sqinter> (\<box> x \<in> A \<rightarrow> X))\<close>\<^vs>\<open>-0.7cm\<close>\<close>
text\<open> The \<open>RUN\<close>-process defined @{definition X2} represents the process that accepts all
text\<open> The \<open>RUN\<close>-process defined @{definition X22} represents the process that accepts all
events, but never stops nor deadlocks. The \<open>CHAOS\<close>-process comes in two variants shown in
@{definition X3} and @{definition X4}: the process that non-deterministically stops or
@{definition X32} and @{definition X42}: the process that non-deterministically stops or
accepts any offered event, whereas \<open>CHAOS\<^sub>S\<^sub>K\<^sub>I\<^sub>P\<close> can additionally terminate.\<close>
*)
text*[X2::"definition"]\<open>\<open>RUN A \<equiv> \<mu> X. \<box> x \<in> A \<rightarrow> X\<close> \<^vs>\<open>-0.7cm\<close>\<close>
text*[X3::"definition"]\<open>\<open>CHAOS A \<equiv> \<mu> X. (STOP \<sqinter> (\<box> x \<in> A \<rightarrow> X))\<close> \<^vs>\<open>-0.7cm\<close>\<close>
text*[X4::"definition"]\<open>\<open>CHAOS\<^sub>S\<^sub>K\<^sub>I\<^sub>P A \<equiv> \<mu> X. (SKIP \<sqinter> STOP \<sqinter> (\<box> x \<in> A \<rightarrow> X))\<close>\<^vs>\<open>-0.7cm\<close>\<close>
text*[X5::"definition"]\<open>\<open>DF A \<equiv> \<mu> X. (\<sqinter> x \<in> A \<rightarrow> X)\<close> \<^vs>\<open>-0.7cm\<close>\<close>
text*[X6::"definition"]\<open>\<open>DF\<^sub>S\<^sub>K\<^sub>I\<^sub>P A \<equiv> \<mu> X. ((\<sqinter> x \<in> A \<rightarrow> X) \<sqinter> SKIP)\<close> \<^vs>\<open>-0.7cm\<close> \<close>
Definition*[X2]\<open>\<open>RUN A \<equiv> \<mu> X. \<box> x \<in> A \<rightarrow> X\<close> \<^vs>\<open>-0.7cm\<close>\<close>
Definition*[X3]\<open>\<open>CHAOS A \<equiv> \<mu> X. (STOP \<sqinter> (\<box> x \<in> A \<rightarrow> X))\<close> \<^vs>\<open>-0.7cm\<close>\<close>
Definition*[X4]\<open>\<open>CHAOS\<^sub>S\<^sub>K\<^sub>I\<^sub>P A \<equiv> \<mu> X. (SKIP \<sqinter> STOP \<sqinter> (\<box> x \<in> A \<rightarrow> X))\<close>\<^vs>\<open>-0.7cm\<close>\<close>
Definition*[X5]\<open>\<open>DF A \<equiv> \<mu> X. (\<sqinter> x \<in> A \<rightarrow> X)\<close> \<^vs>\<open>-0.7cm\<close>\<close>
Definition*[X6]\<open>\<open>DF\<^sub>S\<^sub>K\<^sub>I\<^sub>P A \<equiv> \<mu> X. ((\<sqinter> x \<in> A \<rightarrow> X) \<sqinter> SKIP)\<close> \<^vs>\<open>-0.7cm\<close> \<close>
text\<open> \<^vs>\<open>-0.3cm\<close> \<^noindent>
In the following, we denote \<open> \<R>\<P> = {DF\<^sub>S\<^sub>K\<^sub>I\<^sub>P, DF, RUN, CHAOS, CHAOS\<^sub>S\<^sub>K\<^sub>I\<^sub>P}\<close>.
@ -605,18 +605,19 @@ In the literature, deadlock and lifelock are phenomena that are often
handled separately. One contribution of our work is establish their precise relationship inside
the Failure/Divergence Semantics of \<^csp>.\<close>
text*[X10::"definition"] \<open> \<open>deadlock\<^sub>-free P \<equiv> DF\<^sub>S\<^sub>K\<^sub>I\<^sub>P UNIV \<sqsubseteq>\<^sub>\<F> P\<close> \<^vs>\<open>-0.3cm\<close> \<close>
(* bizarre: Definition* does not work for this single case *)
text*[X10::"definition"]\<open> \<open>deadlock\<^sub>-free P \<equiv> DF\<^sub>S\<^sub>K\<^sub>I\<^sub>P UNIV \<sqsubseteq>\<^sub>\<F> P\<close> \<^vs>\<open>-0.3cm\<close> \<close>
text\<open>\<^noindent> A process \<open>P\<close> is deadlock-free if and only if after any trace \<open>s\<close> without \<open>\<surd>\<close>, the union of \<open>\<surd>\<close>
and all events of \<open>P\<close> can never be a refusal set associated to \<open>s\<close>, which means that \<open>P\<close> cannot
be deadlocked after any non-terminating trace.
\<^vs>\<open>-0.2cm\<close>\<close>
text*[T1::"theorem", short_name="\<open>DF definition captures deadlock-freeness\<close>"]
Theorem*[T1, short_name="\<open>DF definition captures deadlock-freeness\<close>"]
\<open> \hfill \break \<open>deadlock_free P \<longleftrightarrow> (\<forall>s\<in>\<T> P. tickFree s \<longrightarrow> (s, {\<surd>}\<union>events_of P) \<notin> \<F> P)\<close> \<^vs>\<open>-0.4cm\<close>\<close>
text*[X11::"definition"]\<open> \<open>livelock\<^sub>-free P \<equiv> \<D> P = {} \<close> \<^vs>\<open>-0.2cm\<close>\<close>
Definition*[X11]\<open> \<open>livelock\<^sub>-free P \<equiv> \<D> P = {} \<close> \<^vs>\<open>-0.2cm\<close>\<close>
text\<open> Recall that all five reference processes are livelock-free.
We also have the following lemmas about the
@ -630,12 +631,12 @@ text\<open>\<^vs>\<open>-0.3cm\<close>
Finally, we proved the following theorem that confirms the relationship between the two vital
properties:\<^vs>\<open>-0.3cm\<close>
\<close>
text*[T2::"theorem", short_name="''DF implies LF''"]
Theorem*[T2, short_name="''DF implies LF''"]
\<open> \hspace{0.5cm} \<open>deadlock_free P \<longrightarrow> livelock_free P\<close> \<^vs>\<open>-0.3cm\<close>\<close>
text\<open>
This is totally natural, at a first glance, but surprising as the proof of deadlock-freeness only requires
failure refinement \<open>\<sqsubseteq>\<^sub>\<F>\<close> (see @{definition X10}) where divergence traces are mixed within the failures set.
failure refinement \<open>\<sqsubseteq>\<^sub>\<F>\<close> (see @{definition \<open>X10\<close>}) where divergence traces are mixed within the failures set.
Note that the existing tools in the literature normally detect these two phenomena
separately, such as FDR for which checking livelock-freeness is very costly.
In our framework, deadlock-freeness of a given system
@ -684,7 +685,7 @@ processes and we call the resulting process \<open>SYSTEM\<close>: \<^vs>\<open>
@{theory_text [display,indent=5] \<open>
definition SEND \<equiv> (\<mu> X. left?x \<rightarrow> (mid!x \<rightarrow> (ack \<rightarrow> X)))
definition REC \<equiv> (\<mu> X. mid?x \<rightarrow> (right!x \<rightarrow> (ack \<rightarrow> X)))
definition REC \<equiv> (\<mu> X. mid?x \<rightarrow> (right!x \<rightarrow> (ack \<rightarrow> X)))
definition SYN \<equiv> (range mid) \<union> {ack}
definition "SYSTEM \<equiv> (SEND \<lbrakk>SYN\<rbrakk> REC) \\ SYN"\<close>}
@ -788,7 +789,7 @@ Roughly similar to labelled transition systems, we provide for deterministic \<^
form that is based on an explicit state. The general schema of normalized processes is defined as
follows:
\<^vs>\<open>0.1cm\<close>
@{cartouche [display,indent=20] \<open>P\<^sub>n\<^sub>o\<^sub>r\<^sub>m\<lbrakk>\<tau>\<^sub>,\<upsilon>\<rbrakk> \<equiv> \<mu> X. (\<lambda>\<sigma>. \<box>e\<in>(\<tau> \<sigma>) \<rightarrow> X (\<upsilon> \<sigma> e))\<close>}
@{cartouche [display,indent=20] \<open>P\<^sub>n\<^sub>o\<^sub>r\<^sub>m\<lbrakk>\<tau>\<^sub>,\<upsilon>\<rbrakk> \<equiv> \<mu> X. (\<lambda>\<sigma>. \<box>e\<in>(\<tau> \<sigma>) \<rightarrow> X(\<upsilon> \<sigma> e))\<close>}
\<^vs>\<open>-0.1cm\<close> where \<open>\<tau>\<close> is a transition function which returns the set of events that can be triggered from
the current state \<open>\<sigma>\<close> given as parameter.
The update function \<open>\<upsilon>\<close> takes two parameters \<open>\<sigma>\<close> and an event \<open>e\<close> and returns the new state.
@ -893,7 +894,7 @@ denotational semantics.
%\<open>FORK i = picks \<rightarrow> putsdown \<rightarrow> FORK i\<close>. After that we apply the same method
%to get the philosopher process under a normal form.
Thanks to @{math_content \<open>T3\<close>}, we obtain normalized processes
Thanks to @{theorem \<open>T3\<close>}, we obtain normalized processes
for \<open>FORKs\<close>, \<open>PHILs\<close> and \<open>DINING\<close>:
@{theory_text [display,indent=5]
\<open>definition "trans\<^sub>F \<equiv> \<lambda>fs. (\<Inter>\<^sub>i\<^sub><\<^sub>N. trans\<^sub>f i (fs!i))"

BIN
examples/technical_report/Isabelle_DOF-Manual/document/figures/definition-use-CSP.png Executable file → Normal file
View File

Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 226 KiB

After

Width:  |  Height:  |  Size: 196 KiB

4
src/DOF/Isa_DOF.thy
View File

@ -1397,13 +1397,13 @@ fun meta_args_2_string thy ((((lab, _), cid_opt), attr_list) : ODL_Command_Parse
(* for the moment naive, i.e. without textual normalization of
attribute names and adapted term printing *)
let val l = "label = "^ (enclose "{" "}" lab)
val _ = writeln("meta_args_2_string lab:"^ lab ^":"^ (@{make_string } cid_opt) )
(* val _ = writeln("meta_args_2_string lab:"^ lab ^":"^ (@{make_string } cid_opt) ) *)
val cid_long = case cid_opt of
NONE => (case DOF_core.get_object_global lab thy of
NONE => DOF_core.default_cid
| SOME X => #cid X)
| SOME(cid,_) => DOF_core.parse_cid_global thy cid
val _ = writeln("meta_args_2_string cid_long:"^ cid_long )
(* val _ = writeln("meta_args_2_string cid_long:"^ cid_long ) *)
val cid_txt = "type = " ^ (enclose "{" "}" cid_long);
fun ltx_of_term _ _ (Const ("List.list.Cons", @{typ "char \<Rightarrow> char list \<Rightarrow> char list"}) $ t1 $ t2)

2
src/ontologies/scholarly_paper/DOF-scholarly_paper-thm.sty
View File

@ -20,7 +20,7 @@
\newtheorem{example}{Example}
\newtheorem{definition}{Definition}
\newtheorem{theorem}{Theorem}
\newtheorem{theorem}{Theorem}

3
src/ontologies/scholarly_paper/DOF-scholarly_paper.sty
View File

@ -341,6 +341,7 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Besser: Einfach durchreichen wg Vererbung !
\NewEnviron{isamarkupDefinition*}[1][]{\isaDof[env={text.scholarly_paper.definition},#1]{\BODY}}
\newisadof{text.scholarly_paper.definition}%
[label=,type=%
, scholarly_paper.math_content.short_name =%
@ -399,6 +400,7 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Besser: Einfach durchreichen wg Vererbung !
\NewEnviron{isamarkupLemma*}[1][]{\isaDof[env={text.scholarly_paper.lemma},#1]{\BODY}}
\newisadof{text.scholarly_paper.lemma}%
[label=,type=%
, scholarly_paper.math_content.short_name =%
@ -426,6 +428,7 @@
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Besser: Einfach durchreichen wg Vererbung !
\NewEnviron{isamarkupTheorem*}[1][]{\isaDof[env={text.scholarly_paper.theorem},#1]{\BODY}}
\newisadof{text.scholarly_paper.theorem}%
[label=,type=%
, scholarly_paper.math_content.short_name =%