Difference between pages "Inference Rules" and "User:Tommy/Collections/Deploy Deliverable D45"

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<font color=red>CAUTION! Any modification to this page shall be announced on the [[#Mailing_lists |User]] mailing list!</font>
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{{saved_book}}
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== Introduction ==
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The purpose of this page is to give a base for the final DEPLOY Deliverable D45 (Model Construction tools &  Analysis IV) which will be delivered to the European Commission (27 April 2012).
  
Rules that are marked with a <tt>*</tt> in the first column are implemented in the latest version of Rodin.
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== Template ==
Rules without a <tt>*</tt> are planned to be implemented in future versions.
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For each section covered in this document, a wiki page has been created and <b>shall be completed</b> (see [[#Contents | Contents]]). Each of them should give a brief description of the work that was carried on during the last year of the project (Feb 2011-April 2012 [Extension included]) within the WP9 package, without going deeply into technical details.<br>
Other conventions used in these tables are described in [[The_Proving_Perspective_%28Rodin_User_Manual%29#Inference_Rules]].
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:<b>Goal: give to the project reviewers some insight which should look like an executive summary on a given WP9 topic.<br>
<!--
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:All details (papers, detailed wiki pages, etc.) should be made available as pointers.</b>
Rules that are marked with a <tt>b</tt> in the first column are currently broken in Rodin 1.1 (see [http://sourceforge.net/tracker/?func=detail&aid=2895507&group_id=108850&atid=651669 bug 2895507]).
 
-->
 
  
{{RRHeader}}
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This template provides a common structure for all of these pages.<br>
 +
Each page shall be quite short (ca. 4-5 printed pages as the D45 contains 7 sections).<br>
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Each section is decomposed into 5 paragraphs. <b>For each topic, a subparagraph should be written.</b><br>
  
{{RRRow}}|*||{{Rulename|HYP}}|| <math>\frac{}{\textbf{H},\textbf{P} \;\;\vdash \;\; \textbf{P}} </math>||  || A
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=== Overview ===
 +
This first paragraph shall identify the involved partners and give an overview of the contribution. In particular, it shall provide answers to the following questions:
 +
* What are the common denominations?
 +
* Is it a new feature or an improvement?
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* What is the main purpose?
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* Who was in charge?
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* Who was involved?
  
{{RRRow}}|*||{{Rulename|HYP_OR}}|| <math>\frac{}{\textbf{H},\textbf{Q} \;\;\vdash \;\; \textbf{P} \lor \ldots \lor  \textbf{Q} \lor \ldots \lor \textbf{R}}</math> ||  || A
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=== Motivations ===
 +
This paragraph shall express the motivation for each tool extension and improvement. More precisely, it shall first indicate the state before the work, the encountered difficulties, and shall highlight the requirements (eg. those of industrial partners). Then, it shall summarize how these requirements are addressed and what are the main benefits.
  
{{RRRow}}|*||{{Rulename|CNTR}}|| <math>\frac{}{\textbf{H},\;\textbf{P},\;\neg\,\textbf{P} \;\;\vdash \;\; \textbf{Q}}</math> ||  || A
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=== Choices / Decisions ===
 +
This paragraph shall summarize the decisions (eg. design decisions) and justify them. Thus, it may present the studied solutions, through their main advantages and inconvenients, to legitimate the final choices.
  
{{RRRow}}|*||{{Rulename|FALSE_HYP}}|| <math>\frac{}{\textbf{H},\bfalse \;\;\vdash \;\; \textbf{P}}</math> ||  || A
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=== Available Documentation ===
 +
This paragraph shall give pointers to the available wiki pages or related publications. This documentation may contain:
 +
* Requirements.
 +
* Pre-studies (states of the art, proposals, discussions).
 +
* Technical details (specifications).
 +
* Teaching materials (tutorials).
 +
* User's guides.
 +
A distinction shall be made on the one hand between these different categories, and on the other hand between documentation written for developers and documentation written for end-users.
  
{{RRRow}}|*||{{Rulename|TRUE_GOAL}}|| <math>\frac{}{\textbf{H} \;\;\vdash \;\; \btrue}</math> ||  || A
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=== Status ===
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This paragraph shall give the current status of the work being done for a given topic (as of 27 Apr 2012).
  
{{RRRow}}|*||{{Rulename|FUN_GOAL}}|| <math>\frac{}{\textbf{H},\; f\in E\;\mathit{op}\;F \;\;\vdash\;\; f\in T_1\pfun T_2}</math> || where <math>T_1</math> and <math>T_2</math> denote types and <math>\mathit{op}</math> is one of <math>\pfun</math>, <math>\tfun</math>, <math>\pinj</math>, <math>\tinj</math>, <math>\psur</math>, <math>\tsur</math>, <math>\tbij</math>. || A
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== Formatting rules ==
 +
In order to homogeneize the contributions and to ensure consistent spelling the following formatting rules shall be enforced:
 +
* See §4 of [http://wiki.event-b.org/images/Llncsdoc.pdf How to Edit Your Input File] for LLNCS formatting rules.
 +
* DEPLOY and Rodin shall be typed this way.
 +
* Contractions shall not be used (eg. write "does not" instead of "doesn't", "let us" instead of "let's", etc).
 +
* British english spelling shall be retained.
 +
* "plug-in" shall be preferred to "plugin".
 +
* Remember that the document is dated 27 Apr 2012, use past, present and future accordingly.
 +
* The dedicated category, <nowiki>[[Category:D45 Deliverable]]</nowiki>, shall be specified for wiki pages.
 +
* If you intend to use the same reference multiple times, please use the Cite extension [http://www.mediawiki.org/wiki/Extension:Cite/Cite.php] that has been installed since the D32.
 +
: By doing so, you will have to add the additional paragraph (below) at the end of the page you complete:
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==References==
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<nowiki><references/></nowiki>
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: Note that you can add references using the normal wikimedia links as well as using references nevertheless only the latter ones will appear in the references section on the wiki (e.g. all references will appear in the final PDF document whatever their type).
  
{{RRRow}}| ||{{Rulename|FUN_IMAGE_GOAL}}|| <math>\frac{\textbf{H},\; f\in S_1\;\mathit{op}\;S_2,\; f(E)\in S_2\;\;\vdash\;\; \mathbf{P}(f(E))}{\textbf{H},\; f\in S_1\;\mathit{op}\;S_2\;\;\vdash\;\; \mathbf{P}(f(E))}</math> || where <math>\mathit{op}</math> denotes a set of relations (any arrow) and <math>f(E)</math> occurs at the top level || M
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== Deploy Deliverable ==
 +
=== D45 ===
  
{{RRRow}}| ||{{Rulename|FUN_GOAL_REC}}|| <math>\frac{}{\textbf{H},\; f\in S_1\;\mathit{op_1}\;(S_2\;\mathit{op_2}\;(\ldots(S_n\;\mathit{op_n}(U\;\mathit{opf}\;V\;))\ldots)) \;\vdash\;\; f(E_1)(E_2)...(E_n)\in T_1\pfun T_2}</math> || where <math>T_1</math> and <math>T_2</math> denote types, <math>\mathit{op}</math> denotes a set of relations (any arrow) and <math>\mathit{opf}</math> is one of <math>\pfun</math>, <math>\tfun</math>, <math>\pinj</math>, <math>\tinj</math>, <math>\psur</math>, <math>\tsur</math>, <math>\tbij</math>. || A
 
  
{{RRRow}}|*||{{Rulename|DBL_HYP}}|| <math>\frac{\textbf{H},\;\textbf{P} \;\;\vdash \;\; \textbf{Q}}{\textbf{H},\;\textbf{P},\;\textbf{P}  \;\;\vdash \;\; \textbf{Q}}</math> ||  || A
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:[[D45 Introduction|Introduction]] (Laurent Voisin)
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:[[D45 General Platform Maintenance|General Platform Maintenance]]
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:*Platform maintenance (Thomas Muller)
  
{{RRRow}}|*||{{Rulename|AND_L}}|| <math>\frac{\textbf{H},\textbf{P},\textbf{Q} \; \; \vdash \; \;  \textbf{R}}{\textbf{H},\; \textbf{P} \land \textbf{Q} \; \; \vdash \; \; 
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:*Mathematical extensions / Theory Plug-in (Issam Maamria)
\textbf{R}}</math> ||  || A
 
  
{{RRRow}}|*||{{Rulename|AND_R}}|| <math>\frac{\textbf{H} \; \; \vdash \; \;  \textbf{P} \qquad \textbf{H} \; \; \vdash \; \; \textbf{Q}}{\textbf{H} \; \; \vdash \; \;  \textbf{P} \; \land \; \textbf{Q}}</math> ||  || A
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:*Plug-in Incompatibilities (All partners)
  
{{RRRow}}|||{{Rulename|IMP_L1}}|| <math>\frac{\textbf{H},\; \textbf{Q},\; \textbf{P} \land \ldots \land \textbf{R} \limp \textbf{S} \;\;\vdash \;\; \textbf{T}}{\textbf{H},\; \textbf{Q},\; \textbf{P} \land \ldots \land \textbf{Q} \land \ldots \land \textbf{R} \limp \textbf{S} \;\;\vdash \;\; \textbf{T} }</math> ||  || A
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:*Modularisation (Alexei Illiasov)
  
{{RRRow}}|*||{{Rulename|IMP_R}}|| <math>\frac{\textbf{H}, \textbf{P} \;\;\vdash \;\; \textbf{Q}}{\textbf{H} \;\;\vdash \;\; \textbf{P} \limp \textbf{Q}}</math> ||  || A
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:*Decomposition (Renato Silva)
  
{{RRRow}}|*||{{Rulename|IMP_AND_L}}|| <math>\frac{\textbf{H},\textbf{P} \limp \textbf{Q},  \textbf{P} \limp \textbf{R}\;\;\vdash \;\; \textbf{S}}{\textbf{H},\;\textbf{P} \limp  \textbf{Q} \land \textbf{R}  \;\;\vdash \;\; \textbf{S}}</math> ||  || A
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:*Team-based Development (Colin Snook, Vitaly Savicks)
  
{{RRRow}}|*||{{Rulename|IMP_OR_L}}|| <math>\frac{
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:*UML-B (Colin Snook, Vitaly Savicks)
\textbf{H},\textbf{P} \limp \textbf{R},  \textbf{Q} \limp \textbf{R}\;\;\vdash \;\; \textbf{S} }{\textbf{H},\;\textbf{P} \lor  \textbf{Q} \limp \textbf{R}  \;\;\vdash \;\; \textbf{S}}</math> ||  || A
 
  
{{RRRow}}|*||{{Rulename|AUTO_MH}}|| <math>\frac{
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:*ProR (Michael Jastram)
\textbf{H},\textbf{P},\;\textbf{Q}\limp \textbf{R}\;\;\vdash \;\; \textbf{S} }{\textbf{H},\;\textbf{P},\; \textbf{P} \land  \textbf{Q} \limp \textbf{R}  \;\;\vdash \;\; \textbf{S}}</math> ||  || A
 
  
{{RRRow}}|*||{{Rulename|NEG_IN_L}}|| <math>\frac{\textbf{H},\; E \in \{ a,\ldots , c\} \; \; \vdash \; \; \textbf{P} }{\textbf{H},\; E \in \{ a,\ldots , b, \ldots , c\} , \neg \, (E=b) \; \; \vdash \; \;  \textbf{P} }</math> ||  || A
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:[[D45 Scalability|Scalability]]
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:*Improved performance (Laurent Voisin, Nicolas Beauger, Thomas Muller)
  
{{RRRow}}|*||{{Rulename|NEG_IN_R}}|| <math>\frac{\textbf{H},\; E \in \{ a,\ldots , c\}  \; \; \vdash \; \; \textbf{P} }{\textbf{H},\; E \in \{ a,\ldots , b, \ldots , c\} , \neg \, (b=E) \; \; \vdash \; \;  \textbf{P} }</math> ||  || A
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:*Design Pattern Management / Generic Instantiation (Thai Son Hoang)
  
{{RRRow}}|*||{{Rulename|XST_L}}|| <math>\frac{\textbf{H},\;  \textbf{P(x)} \; \; \vdash \; \;  \textbf{Q}
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:*Edition (Thomas Muller, Ingo Weigelt)
}{
 
\textbf{H},\;  \exists \, \textbf{x}\, \qdot\, \textbf{P(x)} \; \; \vdash \; \;  \textbf{Q}
 
}</math> ||  || A
 
  
{{RRRow}}|*||{{Rulename|ALL_R}}|| <math>\frac{\textbf{H}\; \; \vdash \; \;  \textbf{P(x)} }{ \textbf{H} \; \; \vdash \; \;  \forall \textbf{x}\, \qdot\, \textbf{P(x)} }</math> ||  || A
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:[[D45 Prover Enhancement|Prover Enhancement]]
  
{{RRRow}}|*||{{Rulename|EQL_LR}}|| <math>\frac{\textbf{H(E)} \; \; \vdash \; \; \textbf{P(E)} }{\textbf{H(x)},\; x=E \; \; \vdash \; \;  \textbf{P(x)} }</math> || <math>x</math> is a variable which is not free in <math>E</math> || A
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:*New rewriting and inference rules (Laurent Voisin)
  
{{RRRow}}|*||{{Rulename|EQL_RL}}|| <math>\frac{\textbf{H(E)} \; \; \vdash \; \; \textbf{P(E)} }{\textbf{H(x)},\; E=x \; \; \vdash \; \;  \textbf{P(x)} }</math> || <math>x</math> is a variable which is not free in <math>E</math> || A
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:*Advanced Preferences for Auto-tactics (Nicolas Beauger)  
  
{{RRRow}}| ||{{Rulename|SUBSET_INTER}}|| <math>\frac{\textbf{H},\;\textbf{T} \subseteq \textbf{U} \;\;\vdash \;\;
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:*Isabelle Plug-in (Matthias Schmaltz)
\textbf{G}(\textbf{S} \binter \dots \binter \textbf{T} \binter \dots \binter \textbf{V})}
 
{\textbf{H},\;\textbf{T} \subseteq \textbf{U} \;\;\vdash \;\;
 
\textbf{G}(\textbf{S} \binter \dots \binter \textbf{T} \binter \dots \binter \textbf{U} \binter \dots \binter \textbf{V})}</math> || the <math>\binter</math> operator must appear at the "top level" || A
 
  
{{RRRow}}| ||{{Rulename|IN_INTER}}|| <math>\frac{\textbf{H},\;\textbf{E} \in \textbf{T} \;\;\vdash \;\;
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:*ProB Disprover (Daniel Plagge, Jens Bendiposto)
\textbf{G}(\textbf{S} \binter \dots \binter \{\textbf{E}\} \binter \dots \binter \textbf{U})}
 
{\textbf{H},\;\textbf{E} \in \textbf{T} \;\;\vdash \;\;
 
\textbf{G}(\textbf{S} \binter \dots \binter \{\textbf{E}\} \binter \dots \binter \textbf{T} \binter \dots \binter \textbf{U})}</math> || the <math>\binter</math> operator must appear at the "top level" || A
 
  
{{RRRow}}| ||{{Rulename|NOTIN_INTER}}|| <math>\frac{\textbf{H},\;\lnot\;\textbf{E} \in \textbf{T} \;\;\vdash \;\;
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:*SMT Solver Integration (Laurent Voisin)
\textbf{G}(\emptyset)}
 
{\textbf{H},\;\lnot\;\textbf{E} \in \textbf{T} \;\;\vdash \;\;
 
\textbf{G}(\textbf{S} \binter \dots \binter \{\textbf{E}\} \binter \dots \binter \textbf{T} \binter \dots \binter \textbf{U})}</math> || the <math>\binter</math> operator must appear at the "top level" || A
 
  
{{RRRow}}|*||{{Rulename|FIN_L_LOWER_BOUND_L}}|| <math>\frac{}{\textbf{H},\;\finite(S) \;\;\vdash \;\; \exists n\,\qdot\, (\forall x \,\qdot\, x \in S \;\limp\; n \leq x)}</math> || The goal is discharged || A
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:[[D45 Code Generation|Code Generation]] (Andy Edmunds)
  
{{RRRow}}|*||{{Rulename|FIN_L_LOWER_BOUND_R}}|| <math>\frac{}{\textbf{H},\;\finite(S) \;\;\vdash \;\; \exists n\,\qdot\, (\forall x \,\qdot\, x \in S \;\limp\; x \geq n)}</math> || The goal is discharged || A
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:[[D45 Model-based testing| Model-based testing]] (Michael Leuschel, Alin Stefanescu)  
  
{{RRRow}}|*||{{Rulename|FIN_L_UPPER_BOUND_L}}|| <math>\frac{}{\textbf{H},\;\finite(S) \;\;\vdash \;\; \exists n\,\qdot\, (\forall x \,\qdot\, x \in S \;\limp\; n \geq x)}</math> || The goal is discharged || A
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:[[D45 Model Checking|Model Checking]] (Michael Leuschel)
  
{{RRRow}}|*||{{Rulename|FIN_L_UPPER_BOUND_R}}|| <math>\frac{}{\textbf{H},\;\finite(S) \;\;\vdash \;\; \exists n\,\qdot\, (\forall x \,\qdot\, x \in S \;\limp\; x \leq n)}</math> || The goal is discharged || A
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[[Category:D45 Deliverable]]
 
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[[Category:Books]]
{{RRRow}}|*||{{Rulename|CONTRADICT_L}}|| <math>\frac{\textbf{H},\;\neg\,\textbf{Q} \;\;\vdash \;\; \neg\,\textbf{P}}{\textbf{H},\;\textbf{P} \;\;\vdash \;\; \textbf{Q}}</math> ||  || M
 
 
 
{{RRRow}}|*||{{Rulename|CONTRADICT_R}}|| <math>\frac{\textbf{H},\;\neg\,\textbf{Q} \;\;\vdash \;\; \bfalse}{\textbf{H} \;\;\vdash \;\; \textbf{Q}}</math> ||  || M
 
 
 
{{RRRow}}|*||{{Rulename|CASE}}|| <math>\frac{\textbf{H}, \; \textbf{P} \; \; \vdash \; \;  \textbf{R} \qquad\ldots\qquad \textbf{H}, \; \textbf{Q} \; \; \vdash \; \;  \textbf{R} }{\textbf{H},\; \textbf{P} \lor \ldots \lor \textbf{Q} \; \; \vdash \; \;  \textbf{R} }</math> ||  || M
 
 
 
{{RRRow}}|*||{{Rulename|MH}}|| <math>\frac{\textbf{H} \;\;\vdash\;\;\textbf{P} \qquad \textbf{H},\; \textbf{Q} \;\;\vdash \;\; \textbf{R} }{\textbf{H},\;\textbf{P} \limp \textbf{Q} \;\;\vdash \;\; \textbf{R}}</math> ||  || M
 
 
 
{{RRRow}}|*||{{Rulename|HM}}|| <math>\frac{\textbf{H} \;\;\vdash\;\;\neg\,\textbf{Q} \qquad \textbf{H},\; \neg\,\textbf{P} \;\;\vdash \;\; \textbf{R} }{\textbf{H},\;\textbf{P} \limp \textbf{Q} \;\;\vdash \;\; \textbf{R}}</math> ||  || M
 
 
 
{{RRRow}}|||{{Rulename|EQV}}|| <math>\frac{\textbf{H(Q)},\; \textbf{P} \leqv \textbf{Q}
 
\;\;\vdash\;\; \textbf{G(Q)}}{\textbf{H(P)},\;\textbf{P} \leqv \textbf{Q}
 
\;\;\vdash \;\; \textbf{G(P)}}</math> ||  || M
 
 
 
{{RRRow}}|*||{{Rulename|OV_SETENUM_L}}|| <math>\frac{\textbf{H},\; G=E 
 
,\;\textbf{P}(F)\;\;\vdash\;\;\textbf{Q} \qquad \textbf{H},\; \neg\,(G=E) 
 
,\;\textbf{P}((\{E\}) \domsub f)(G))\;\;\vdash\;\;\textbf{Q}}{\textbf{H},\;\textbf{P}((f\ovl\{E
 
\mapsto F\})(G)) \;\;\vdash \;\; \textbf{Q}}</math> || the <math>\ovl</math> operator must appear at the "top level" || A
 
 
 
{{RRRow}}|*||{{Rulename|OV_SETENUM_R}}|| <math>\frac{\textbf{H},\; G=E \;\;\vdash\;\;\textbf{Q}(F)
 
\qquad \textbf{H},\; \neg\,(G=E)  \;\;\vdash\;\;\textbf{Q}((\{E\}) \domsub f)(G))}{\textbf{H}
 
\;\;\vdash \;\; \textbf{Q}((f\ovl\{E \mapsto F\})(G))}</math> || the <math>\ovl</math> operator must appear at the "top level" || A
 
 
 
{{RRRow}}|*||{{Rulename|OV_L}}|| <math>\frac{\textbf{H},\; G \in \dom(g)  ,\;\textbf{P}(g(G))\;\;\vdash\;\;\textbf{Q} \qquad \textbf{H},\; \neg\,G \in \dom(g)  ,\;\textbf{P}((\dom(g) \domsub f)(G))\;\;\vdash\;\;\textbf{Q}}{\textbf{H},\;\textbf{P}((f\ovl g)(G)) \;\;\vdash \;\; \textbf{Q}}</math> || the <math>\ovl</math> operator must appear at the "top level" || A
 
 
 
{{RRRow}}|*||{{Rulename|OV_R}}|| <math>\frac{\textbf{H},\; G \in \dom(g) \;\;\vdash\;\;\textbf{Q}(g(G)) \qquad \textbf{H},\; \neg\, G \in \dom(g) \;\;\vdash\;\;\textbf{Q}((\dom(g) \domsub f)(G))}{\textbf{H} \;\;\vdash \;\; \textbf{Q}((f\ovl g)(G))}</math> || the <math>\ovl</math> operator must appear at the "top level" || A
 
 
 
{{RRRow}}|*||{{Rulename|DIS_BINTER_R}}|| <math>\frac{\textbf{H} \;\;\vdash\;\; f^{-1} \in A \pfun B    \qquad\textbf{H} \;\;\vdash\;\;\textbf{Q}(f[S] \binter f[T]) }{\textbf{H} \;\;\vdash \;\; \textbf{Q}(f[S \binter T])}</math> || the occurrence of <math>f</math> must appear at the "top level". Moreover <math>A</math> and <math>B</math> denote some type. || M
 
 
 
{{RRRow}}|*||{{Rulename|DIS_BINTER_L}}|| <math>\frac{\textbf{H} \;\;\vdash\;\; f^{-1} \in A \pfun B    \qquad\textbf{H},\;\textbf{Q}(f[S] \binter f[T]) \;\;\vdash\;\;\textbf{G}}{\textbf{H},\; \textbf{Q}(f[S \binter T]) \;\;\vdash \;\; \textbf{G}}</math> || the occurrence of <math>f</math> must appear at the "top level". Moreover <math>A</math> and <math>B</math> denote some type. || M
 
 
 
{{RRRow}}|*||{{Rulename|DIS_SETMINUS_R}}|| <math>\frac{\textbf{H} \;\;\vdash\;\; f^{-1} \in A \pfun B    \qquad\textbf{H} \;\;\vdash\;\;\textbf{Q}(f[S] \setminus f[T]) }{\textbf{H} \;\;\vdash \;\; \textbf{Q}(f[S \setminus T])}</math> || the occurrence of <math>f</math> must appear at the "top level". Moreover <math>A</math> and <math>B</math> denote some type. || M
 
 
 
{{RRRow}}|*||{{Rulename|DIS_SETMINUS_L}}|| <math>\frac{\textbf{H} \;\;\vdash\;\; f^{-1} \in A \pfun B    \qquad\textbf{H},\;\textbf{Q}(f[S] \setminus f[T]) \;\;\vdash\;\; \textbf{G}}{\textbf{H},\; \textbf{Q}(f[S \setminus T]) \;\;\vdash \;\; \textbf{G}}</math> || the occurrence of <math>f</math> must appear at the "top level". Moreover <math>A</math> and <math>B</math> denote some type. || M
 
 
 
{{RRRow}}|*||{{Rulename|SIM_REL_IMAGE_R}}|| <math>\frac{\textbf{H} \; \; \vdash \; \; {WD}(\textbf{Q}(\{ f(E)\} )) \qquad\textbf{H} \; \; \vdash \; \; \textbf{Q}(\{ f(E)\} ) }{\textbf{H} \; \; \vdash \; \;  \textbf{Q}(f[\{ E\} ])} </math> || the occurrence of <math>f</math> must appear at the "top level". || M
 
 
 
{{RRRow}}|*||{{Rulename|SIM_REL_IMAGE_L}}|| <math>\frac{\textbf{H} \; \; \vdash \; \; {WD}(\textbf{Q}(\{ f(E)\} )) \qquad\textbf{H},\; \textbf{Q}(\{ f(E)\}) \;\;\vdash\;\; \textbf{G}}{\textbf{H},\; \textbf{Q}(f[\{ E\} ]) \;\;\vdash\;\; \textbf{G} } </math> || the occurrence of <math>f</math> must appear at the "top level". || M
 
 
 
{{RRRow}}|*||{{Rulename|SIM_FCOMP_R}}|| <math>\frac{\textbf{H} \;\;\vdash\;\;{WD}(\textbf{Q}(g(f(x))))    \qquad\textbf{H} \;\;\vdash\;\;\textbf{Q}(g(f(x))) }{\textbf{H} \;\;\vdash \;\; \textbf{Q}((f \fcomp g)(x))}</math> || the occurrence of <math>f \fcomp g</math> must appear at the "top level". || M
 
 
 
{{RRRow}}|*||{{Rulename|SIM_FCOMP_L}}|| <math>\frac{\textbf{H} \;\;\vdash\;\;{WD}(\textbf{Q}(g(f(x))))    \qquad\textbf{H},\; \textbf{Q}(g(f(x))) \;\;\vdash\;\; \textbf{G}}{\textbf{H},\; \textbf{Q}((f \fcomp g)(x)) \;\;\vdash \;\; \textbf{G}}</math> || the occurrence of <math>f \fcomp g</math> must appear at the "top level". || M
 
 
 
{{RRRow}}|*||{{Rulename|FIN_SUBSETEQ_R}}|| <math>\frac{\textbf{H} \;\;\vdash\;\;{WD}(T) \qquad\textbf{H} \;\;\vdash \;\; S \subseteq T \qquad \textbf{H} \;\;\vdash \;\; \finite\,(T)}{\textbf{H} \;\;\vdash \;\; \finite\,(S)}</math> || the user has to write the set corresponding to <math>T</math> in the editing area of the Proof Control Window || M
 
 
 
{{RRRow}}|*||{{Rulename|FIN_BINTER_R}}|| <math>\frac{\textbf{H} \;\;\vdash
 
\;\;\finite\,(S) \;\lor\;\ldots \;\lor\; \finite\,(T)}{\textbf{H} \;\;\vdash
 
\;\; \finite\,(S \;\binter\;\ldots \;\binter\; T)}</math> ||  || M
 
 
 
{{RRRow}}|*||{{Rulename|FIN_SETMINUS_R}}|| <math>\frac{\textbf{H} \;\;\vdash
 
\;\;\finite\,(S)}{\textbf{H} \;\;\vdash \;\; \finite\,(S \;\setminus\; T)}</math> ||  || M
 
 
 
{{RRRow}}|*||{{Rulename|FIN_REL_R}}|| <math>\frac{\textbf{H} \;\;\vdash\;\;{WD}(S\rel T) \qquad\textbf{H} \;\;\vdash \;\; r \;\in\; S \rel T \qquad \textbf{H} \;\;\vdash \;\; \finite\,(S) \qquad \textbf{H} \;\;\vdash \;\; \finite\,(T)}{\textbf{H} \;\;\vdash \;\; \finite\,(r)}</math> || the user has to write the set corresponding to <math>S \rel T</math> in the editing area of the Proof Control Window || M
 
 
 
{{RRRow}}|*||{{Rulename|FIN_REL_IMG_R}}|| <math>\frac{\textbf{H} \;\;\vdash \;\; \finite\,(r) }{\textbf{H} \;\;\vdash \;\; \finite\,(r[s])}</math> ||  || M
 
 
 
{{RRRow}}|*||{{Rulename|FIN_REL_RAN_R}}|| <math>\frac{\textbf{H} \;\;\vdash \;\; \finite\,(r) }{\textbf{H} \;\;\vdash \;\; \finite\,(\ran(r))}</math> ||  || M
 
 
 
{{RRRow}}|*||{{Rulename|FIN_REL_DOM_R}}|| <math>\frac{\textbf{H} \;\;\vdash \;\; \finite\,(r) }{\textbf{H} \;\;\vdash \;\; \finite\,(\dom(r))}</math> ||  || M
 
 
 
{{RRRow}}|*||{{Rulename|FIN_FUN1_R}}|| <math>\frac{\textbf{H} \;\;\vdash\;\;{WD}(S\pfun T) \qquad\textbf{H} \;\;\vdash \;\; f \;\in\; S \pfun T \qquad \textbf{H} \;\;\vdash \;\; \finite\,(S) }{\textbf{H} \;\;\vdash \;\; \finite\,(f)}</math> || the user has to write the set corresponding to <math>S  \pfun T</math> in the editing area of the Proof Control Window || M
 
 
 
{{RRRow}}|*||{{Rulename|FIN_FUN2_R}}|| <math>\frac{\textbf{H} \;\;\vdash\;\;{WD}(S\pfun T) \qquad\textbf{H} \;\;\vdash \;\; f^{-1} \;\in\; S \pfun T \qquad \textbf{H} \;\;\vdash \;\; \finite\,(S) }{\textbf{H} \;\;\vdash \;\; \finite\,(f)}</math> || the user has to write the set corresponding to <math>S  \pfun T</math> in the editing area of the Proof Control Window || M
 
 
 
{{RRRow}}|*||{{Rulename|FIN_FUN_IMG_R}}|| <math>\frac{\textbf{H} \;\;\vdash\;\;{WD}(S\pfun T) \qquad\textbf{H} \;\;\vdash \;\; f \;\in\; S \pfun T \qquad \textbf{H} \;\;\vdash \;\; \finite\,(s) }{\textbf{H} \;\;\vdash \;\; \finite\,(f[s])}</math> || the user has to write the set corresponding to <math>S  \pfun T</math> in the editing area of the Proof Control Window || M
 
 
 
{{RRRow}}|*||{{Rulename|FIN_FUN_RAN_R}}|| <math>\frac{\textbf{H} \;\;\vdash\;\;{WD}(S\pfun T) \qquad\textbf{H} \;\;\vdash \;\; f \;\in\; S \pfun T \qquad \textbf{H} \;\;\vdash \;\; \finite\,(S) }{\textbf{H} \;\;\vdash \;\; \finite\,(\ran(f))}</math> || the user has to write the set corresponding to <math>S  \pfun T</math> in the editing area of the Proof Control Window || M
 
 
 
{{RRRow}}|*||{{Rulename|FIN_FUN_DOM_R}}|| <math>\frac{\textbf{H} \;\;\vdash\;\;{WD}(S\pfun T) \qquad\textbf{H} \;\;\vdash \;\; f^{-1} \;\in\; S \pfun T \qquad \textbf{H} \;\;\vdash \;\; \finite\,(S) }{\textbf{H} \;\;\vdash \;\; \finite\,(\dom(f))}</math> || the user has to write the set corresponding to <math>S  \pfun T</math> in the editing area of the Proof Control Window || M
 
 
 
{{RRRow}}|*||{{Rulename|LOWER_BOUND_L}}|| <math>\frac{\textbf{H} \;\;\vdash \;\; \finite(S)  }{\textbf{H} \;\;\vdash \;\; \exists n\,\qdot\, (\forall x \,\qdot\, x \in S \;\limp\; n \leq x)}</math> || <math>S</math> must not contain any bound variable || M
 
 
 
{{RRRow}}|*||{{Rulename|LOWER_BOUND_R}}|| <math>\frac{\textbf{H} \;\;\vdash \;\; \finite(S)  }{\textbf{H} \;\;\vdash \;\; \exists n\,\qdot\, (\forall x \,\qdot\, x \in S \;\limp\; x \geq n)}</math> || <math>S</math> must not contain any bound variable || M
 
 
 
{{RRRow}}|*||{{Rulename|UPPER_BOUND_L}}|| <math>\frac{\textbf{H} \;\;\vdash \;\; \finite(S)  }{\textbf{H} \;\;\vdash \;\; \exists n\,\qdot\, (\forall x \,\qdot\, x \in S \;\limp\; n \geq x)}</math> || <math>S</math> must not contain any bound variable || M
 
 
 
{{RRRow}}|*||{{Rulename|UPPER_BOUND_R}}|| <math>\frac{\textbf{H} \;\;\vdash \;\; \finite(S)  }{\textbf{H} \;\;\vdash \;\; \exists n\,\qdot\, (\forall x \,\qdot\, x \in S \;\limp\; x \leq n)}</math> || <math>S</math> must not contain any bound variable || M
 
 
 
{{RRRow}}|*||{{Rulename|FIN_LT_0}}|| <math>\frac{\textbf{H} \;\;\vdash \;\; \exists n\,\qdot\, (\forall x \,\qdot\, x \in S \;\limp\; n \leq x)  \qquad \textbf{H} \;\;\vdash \;\; S \subseteq \intg \setminus \natn }{\textbf{H} \;\;\vdash \;\; \finite(S)}</math> ||  || M
 
 
 
{{RRRow}}|*||{{Rulename|FIN_GE_0}}|| <math>\frac{\textbf{H} \;\;\vdash \;\; \exists n\,\qdot\, (\forall x \,\qdot\, x \in S \;\limp\; x \leq n)  \qquad \textbf{H} \;\;\vdash \;\; S \subseteq \nat }{\textbf{H} \;\;\vdash \;\; \finite(S)}</math> ||  || M
 
 
 
{{RRRow}}|||{{Rulename|CARD_INTERV}}|| <math>\frac{\textbf{H},\, a \leq b \;\;\vdash \;\; \textbf{Q}(b-a+1) \qquad \textbf{H},\, b < a \;\;\vdash \;\; \textbf{Q}(0) }{\textbf{H} \;\;\vdash\;\; \textbf{Q}(\card\,(a\upto b))}</math> || <math>\card (a \upto b)</math> must appear at "top-level" || M
 
 
 
{{RRRow}}| ||{{Rulename|CARD_EMPTY_INTERV}}|| <math>\frac{\textbf{H},\, a \leq b,\,\textbf{P}(b-a+1)  \;\;\vdash \;\; \textbf{Q} \qquad \textbf{H},\, b < a ,\, \textbf{P}(0)\;\;\vdash \;\; \textbf{Q} }{\textbf{H},\,\textbf{P}(\card\,(a\upto b))  \;\;\vdash\;\; \textbf{Q}}</math> || <math>\card (a \upto b)</math> must appear at "top-level" || M
 
 
 
{{RRRow}}|*||{{Rulename|DERIV_LE_CARD}}|| <math>\frac{\textbf{H}  \;\;\vdash\;\; S \subseteq T}{\textbf{H} \;\;\vdash\;\; \card(S) \leq \card(T)}</math> || <math>S</math> and <math>T</math> bear the same type || M
 
 
 
{{RRRow}}|*||{{Rulename|DERIV_GE_CARD}}|| <math>\frac{\textbf{H}  \;\;\vdash\;\; T \subseteq S}{\textbf{H} \;\;\vdash\;\; \card(S) \geq \card(T)}</math> || <math>S</math> and <math>T</math> bear the same type || M
 
 
 
{{RRRow}}|*||{{Rulename|DERIV_LT_CARD}}|| <math>\frac{\textbf{H}  \;\;\vdash\;\; S \subset T}{\textbf{H} \;\;\vdash\;\; \card(S) < \card(T)}</math> || <math>S</math> and <math>T</math> bear the same type || M
 
 
 
{{RRRow}}|*||{{Rulename|DERIV_GT_CARD}}|| <math>\frac{\textbf{H}  \;\;\vdash\;\; T \subset S}{\textbf{H} \;\;\vdash\;\; \card(S) > \card(T)}</math> || <math>S</math> and <math>T</math> bear the same type || M
 
 
 
{{RRRow}}|*||{{Rulename|DERIV_EQUAL_CARD}}|| <math>\frac{\textbf{H}  \;\;\vdash\;\; S = T}{\textbf{H} \;\;\vdash\;\; \card(S) = \card(T)}</math> || <math>S</math> and <math>T</math> bear the same type || M
 
 
 
{{RRRow}}| ||{{Rulename|SIMP_CARD_SETMINUS_L}}||<math>\frac{\textbf{H},\, \textbf{P}(\card (S \setminus  T)) \;\;\vdash\;\; \finite(S) \qquad \textbf{H},\, \textbf{P}(\card(S) - \card(S\binter T)) \;\;\vdash\;\; \textbf{G}}{\textbf{H},\, \textbf{P}(\card (S \setminus  T)) \;\;\vdash\;\; \textbf{G}} </math>|| <math>\card (S \setminus  T)</math> must appear at "top-level" ||  M
 
{{RRRow}}| ||{{Rulename|SIMP_CARD_SETMINUS_R}}||<math>\frac{\textbf{H} \;\;\vdash\;\; \finite(S) \qquad \textbf{H} \;\;\vdash\;\; \textbf{P}(\card(S) - \card(S\binter T))}{\textbf{H} \;\;\vdash\;\; \textbf{P}(\card (S \setminus  T))} </math>|| <math>\card (S \setminus  T)</math> must appear at "top-level" ||  M
 
 
 
{{RRRow}}| ||{{Rulename|SIMP_CARD_CPROD_L}}||<math>\frac{\textbf{H},\, \textbf{P}(\card (S \cprod  T)) \;\;\vdash\;\; \finite(S) \qquad \textbf{H},\, \textbf{P}(\card (S \cprod  T)) \;\;\vdash\;\; \finite(T) \qquad \textbf{H},\, \textbf{P}(\card(S) * \card(T)) \;\;\vdash\;\; \textbf{G}}{\textbf{H},\, \textbf{P}(\card (S \cprod  T)) \;\;\vdash\;\; \textbf{G}} </math>|| <math>\card (S \cprod  T)</math> must appear at "top-level" ||  M
 
{{RRRow}}| ||{{Rulename|SIMP_CARD_CPROD_R}}||<math>\frac{\textbf{H} \;\;\vdash\;\; \finite(S) \qquad \textbf{H} \;\;\vdash\;\; \finite(T) \qquad \textbf{H} \;\;\vdash\;\; \textbf{P}(\card(S) * \card(T))}{\textbf{H} \;\;\vdash\;\; \textbf{P}(\card (S \cprod  T))} </math>|| <math>\card (S \cprod  T)</math> must appear at "top-level" ||  M
 
 
 
{{RRRow}}|*||{{Rulename|FORALL_INST}}|| <math>\frac{\textbf{H} \;\;\vdash \;\; {WD}(E) \qquad \textbf{H} , [x \bcmeq E]\textbf{P} \;\;\vdash \;\; \textbf{G}}{\textbf{H}, \forall x \qdot \textbf{P}  \;\;\vdash\;\; \textbf{G}}</math> || <math>x</math> is instantiated with <math>E</math> || M
 
 
 
{{RRRow}}|*||{{Rulename|FORALL_INST_MP}}|| <math>\frac{\textbf{H} \;\;\vdash \;\; {WD}(E) \qquad  \textbf{H}, {WD}(E) \;\;\vdash \;\; [x \bcmeq E]\textbf{P} \qquad  \textbf{H}, {WD}(E), [x \bcmeq E]\textbf{Q} \;\;\vdash \;\; \textbf{G}}{\textbf{H}, \forall x \qdot \textbf{P} \limp \textbf{Q}  \;\;\vdash\;\; \textbf{G}}</math> || <math>x</math> is instantiated with <math>E</math> and a Modus Ponens is applied|| M
 
 
 
{{RRRow}}|*||{{Rulename|CUT}}|| <math>\frac{\textbf{H} \;\;\vdash \;\; {WD}(\textbf{P}) \qquad  \textbf{H}, {WD}(\textbf{P}) \;\;\vdash \;\; \textbf{\textbf{P}} \qquad  \textbf{H}, {WD}(\textbf{P}), \textbf{P} \;\;\vdash \;\; \textbf{G}}{\textbf{H} \;\;\vdash\;\; \textbf{G}}</math> || hypothesis <math>\textbf{P}</math> is added || M
 
 
 
{{RRRow}}|*||{{Rulename|EXISTS_INST}}|| <math>\frac{\textbf{H} \;\;\vdash \;\; {WD}(E) \qquad \textbf{H} \;\;\vdash \;\; \textbf{P}(E)}{\textbf{H} \;\;\vdash\;\; \exists x \qdot \textbf{P}(x)}</math> || <math>x</math> is instantiated with <math>E</math> || M
 
 
 
{{RRRow}}|*||{{Rulename|DISTINCT_CASE}}|| <math>\frac{\textbf{H} \;\;\vdash \;\; {WD}(\textbf{P}) \qquad  \textbf{H}, {WD}(\textbf{P}), \textbf{P} \;\;\vdash \;\; \textbf{\textbf{G}} \qquad  \textbf{H}, {WD}(\textbf{P}), \lnot \textbf{P} \;\;\vdash \;\; \textbf{G}}{\textbf{H} \;\;\vdash\;\; \textbf{G}}</math> || case distinction on predicate <math>\textbf{P}</math> || M
 
 
 
{{RRRow}}| ||{{Rulename|ONE_POINT_L}}||<math>\frac{\textbf{H} \;\;\vdash \;\; {WD}(E) \qquad  \textbf{H}, \forall x, \ldots, \ldots,z \qdot [y \bcmeq E]\textbf{P} \land \ldots \land \ldots \land [y \bcmeq E]\textbf{Q} \limp [y \bcmeq E]\textbf{R} \;\;\vdash \;\; \textbf{G}}{ \textbf{H}, \forall x, \ldots, y, \ldots, z \qdot \textbf{P} \land \ldots \land y = E \land \ldots \land \textbf{Q} \limp \textbf{R}  \;\;\vdash\;\; \textbf{G}}</math>|| The rule can be applied with <math>\forall</math> as well as with <math>\exists</math> ||  A
 
 
 
{{RRRow}}| ||{{Rulename|ONE_POINT_R}}||<math>\frac{\textbf{H} \;\;\vdash \;\; {WD}(E) \qquad  \textbf{H} \;\;\vdash \;\; \forall x, \ldots, \ldots,z \qdot [y \bcmeq E]\textbf{P} \land \ldots \land \ldots \land [y \bcmeq E]\textbf{Q} \limp [y \bcmeq E]\textbf{R} }{ \textbf{H}  \;\;\vdash\;\; \forall x, \ldots, y, \ldots, z \qdot \textbf{P} \land \ldots \land y = E \land \ldots \land \textbf{Q} \limp \textbf{R} }</math>|| The rule can be applied with <math>\forall</math> as well as with <math>\exists</math> ||  A
 
 
 
{{RRRow}}| ||{{Rulename|DATATYPE_DISTINCT_CASE}}||<math>\frac{\textbf{H}, x=c_1(p_{11}, \ldots, p_{1k}) \;\;\vdash \;\; \textbf{G} \qquad \ldots \qquad \textbf{H}, x=c_n(p_{n1}, \ldots, p_{nl}) \;\;\vdash \;\; \textbf{G} }{ \textbf{H}  \;\;\vdash\;\;  \textbf{G} }</math>|| where <math>x</math> has a datatype <math>DT</math> as type and appears free in <math>\textbf{G}</math>, <math>DT</math> has constructors <math>c_1, \ldots, c_n</math>, parameters <math>p_{ij}</math> are introduced as fresh identifiers  ||  M
 
 
 
{{RRRow}}| ||{{Rulename|DATATYPE_INDUCTION}}||<math>\frac{ \textbf{H}, x=c_1(p_1, \ldots, p_k),\textbf{P}(p_{I_1}), \ldots, \textbf{P}(p_{I_l})  \;\;\vdash \;\; \textbf{P}(x)  \qquad \ldots \qquad}{ \textbf{H}  \;\;\vdash\;\;  \textbf{P}(x) }</math>|| where <math>x</math> has inductive datatype <math>DT</math> as type and appears free in <math>\textbf{P}</math>; <math>\{p_{I_1}, \ldots, p_{I_l}\} \subseteq \{p_1, \ldots, p_k\}</math> are the inductive parameters (if any); an antecedent is created for every constructor <math>c_i</math> of <math>DT</math>; all parameters are introduced as fresh identifiers; examples [[Datatype Rules|here]]  ||  M
 
 
 
|}
 
 
 
 
 
[[Category:User documentation|The Proving Perspective]]
 
[[Category:Rodin Platform|The Proving Perspective]]
 
[[Category:User manual|The Proving Perspective]]
 

Revision as of 11:37, 7 November 2011

Template:Saved book

Introduction

The purpose of this page is to give a base for the final DEPLOY Deliverable D45 (Model Construction tools & Analysis IV) which will be delivered to the European Commission (27 April 2012).

Template

For each section covered in this document, a wiki page has been created and shall be completed (see Contents). Each of them should give a brief description of the work that was carried on during the last year of the project (Feb 2011-April 2012 [Extension included]) within the WP9 package, without going deeply into technical details.

Goal: give to the project reviewers some insight which should look like an executive summary on a given WP9 topic.
All details (papers, detailed wiki pages, etc.) should be made available as pointers.

This template provides a common structure for all of these pages.
Each page shall be quite short (ca. 4-5 printed pages as the D45 contains 7 sections).
Each section is decomposed into 5 paragraphs. For each topic, a subparagraph should be written.

Overview

This first paragraph shall identify the involved partners and give an overview of the contribution. In particular, it shall provide answers to the following questions:

  • What are the common denominations?
  • Is it a new feature or an improvement?
  • What is the main purpose?
  • Who was in charge?
  • Who was involved?

Motivations

This paragraph shall express the motivation for each tool extension and improvement. More precisely, it shall first indicate the state before the work, the encountered difficulties, and shall highlight the requirements (eg. those of industrial partners). Then, it shall summarize how these requirements are addressed and what are the main benefits.

Choices / Decisions

This paragraph shall summarize the decisions (eg. design decisions) and justify them. Thus, it may present the studied solutions, through their main advantages and inconvenients, to legitimate the final choices.

Available Documentation

This paragraph shall give pointers to the available wiki pages or related publications. This documentation may contain:

  • Requirements.
  • Pre-studies (states of the art, proposals, discussions).
  • Technical details (specifications).
  • Teaching materials (tutorials).
  • User's guides.

A distinction shall be made on the one hand between these different categories, and on the other hand between documentation written for developers and documentation written for end-users.

Status

This paragraph shall give the current status of the work being done for a given topic (as of 27 Apr 2012).

Formatting rules

In order to homogeneize the contributions and to ensure consistent spelling the following formatting rules shall be enforced:

  • See §4 of How to Edit Your Input File for LLNCS formatting rules.
  • DEPLOY and Rodin shall be typed this way.
  • Contractions shall not be used (eg. write "does not" instead of "doesn't", "let us" instead of "let's", etc).
  • British english spelling shall be retained.
  • "plug-in" shall be preferred to "plugin".
  • Remember that the document is dated 27 Apr 2012, use past, present and future accordingly.
  • The dedicated category, [[Category:D45 Deliverable]], shall be specified for wiki pages.
  • If you intend to use the same reference multiple times, please use the Cite extension [1] that has been installed since the D32.
By doing so, you will have to add the additional paragraph (below) at the end of the page you complete:
==References==
<references/>
Note that you can add references using the normal wikimedia links as well as using references nevertheless only the latter ones will appear in the references section on the wiki (e.g. all references will appear in the final PDF document whatever their type).

Deploy Deliverable

D45

Introduction (Laurent Voisin)
General Platform Maintenance
  • Platform maintenance (Thomas Muller)
  • Mathematical extensions / Theory Plug-in (Issam Maamria)
  • Plug-in Incompatibilities (All partners)
  • Modularisation (Alexei Illiasov)
  • Decomposition (Renato Silva)
  • Team-based Development (Colin Snook, Vitaly Savicks)
  • UML-B (Colin Snook, Vitaly Savicks)
  • ProR (Michael Jastram)
Scalability
  • Improved performance (Laurent Voisin, Nicolas Beauger, Thomas Muller)
  • Design Pattern Management / Generic Instantiation (Thai Son Hoang)
  • Edition (Thomas Muller, Ingo Weigelt)
Prover Enhancement
  • New rewriting and inference rules (Laurent Voisin)
  • Advanced Preferences for Auto-tactics (Nicolas Beauger)
  • Isabelle Plug-in (Matthias Schmaltz)
  • ProB Disprover (Daniel Plagge, Jens Bendiposto)
  • SMT Solver Integration (Laurent Voisin)
Code Generation (Andy Edmunds)
Model-based testing (Michael Leuschel, Alin Stefanescu)
Model Checking (Michael Leuschel)