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small fixes

master
zapashcanon 3 years ago
parent
commit
9c7b559021
Signed by: zapashcanon GPG Key ID: 8981C3C62D1D28F1
  1. 69
      img/universite-paris-saclay.svg
  2. 270
      img/upsud.svg
  3. 4
      src/mf.tex
  4. 10
      src/parcoursup.tex
  5. 2
      src/perspectives.tex
  6. 4
      src/preuves.tex
  7. 6
      src/title.tex

69
img/universite-paris-saclay.svg

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270
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4
src/mf.tex

@ -30,8 +30,8 @@ Il existe plusieurs méthodes permettant de vérifier une propriété d'un progr
L'énoncé permet alors de générer des \bsc{vc}\footnote{Verification Conditions, ou conditions de vérification en français.}, qu'il faut prouver. Pour cela, deux méthodes sont possibles :
\begin{itemize}
\item une preuve interactive, au moyen d'assistants de preuve tels que Coq, HOL ou Isabelle\ldots
\item une preuve automatique, où l'on délègue à des prouveur automatiques de théorèmes tels qu'Alt-Ergo, Z3 ou CVC4\ldots
\item une preuve interactive, au moyen d'assistants de preuve tels que Coq, HOL ou Isabelle ;
\item une preuve automatique, où l'on délègue à des prouveur automatiques de théorèmes tels qu'Alt-Ergo, Z3 ou CVC4.
\end{itemize}
La vérification déductive peut mener à la génération d'un important nombre de \bsc{vc}. On préfère éviter d'avoir à toutes les traiter interactivement et donc, on essaie autant que faire se peut de passer par une preuve automatique. Cela présente plusieurs avantages: l'effort à fournir est réduit et l'on peut plus facilement modifier le programme ou bien l'énoncé que l'on cherche à vérifier.

10
src/parcoursup.tex

@ -2,12 +2,14 @@
\subsection{Généralités}
Parcoursup est une plateforme gouvernementale française utilisée par les étudiants pour candidater à des formations de l'enseignement supérieur. Le principe général est le suivant:
\begin{itemize}
\item les étudiants candidatent à plusieurs formations
\item chaque formation classe l'ensemble des étudiants selon les critères de son choix\footnote{On parlera de \emph{classement pédagogique}.}
\item la plateforme Parcoursup apporte des modifications aux classements pédagogiques\footnote{Le nouveau classement est appelé l'\emph{ordre d'appel}.}, selon des critères et des algorithmes publics et notifie les candidats acceptés, qui doivent alors faire un choix parmi les formations où ils sont acceptés\footnote{Tout en gardant la possibilité de choisir une autre formation où ils sont sur liste d'attente pour le moment.}
\item lorsqu'un candidat choisi une formation parmi celles où il a été accepté, cela libère des places dans les autres, et les candidats suivants sur l'ordre d'appel sont alors acceptés
\item les étudiants candidatent à plusieurs formations ;
\item chaque formation classe l'ensemble des étudiants selon les critères de son choix\footnote{On parlera de \emph{classement pédagogique}.} ;
\item la plateforme Parcoursup apporte des modifications aux classements pédagogiques\footnote{Le nouveau classement est appelé l'\emph{ordre d'appel}.}, selon des critères et des algorithmes publics et notifie les candidats acceptés, qui doivent alors faire un choix parmi les formations où ils sont acceptés\footnote{Tout en gardant la possibilité de choisir une autre formation où ils sont sur liste d'attente pour le moment.} ;
\item lorsqu'un candidat choisi une formation parmi celles où il a été accepté, cela libère des places dans les autres, et les candidats suivants sur l'ordre d'appel sont alors acceptés.
\end{itemize}
Plus de détails sont donnés dans \cite{AlgoPS}.
\subsection{Algorithme avec taux de boursiers}
Pour passer du classement pédagogique à l'ordre d'appel, il existe plusieurs cas, selon les formations. Chaque cas correspond à un algorithme particulier. Le cas le plus simple est celui avec un taux de boursiers.

2
src/perspectives.tex

@ -6,4 +6,4 @@
\subsection{Implémentation originale}
On souhaite pouvoir vérifier l'implémentation originale en Java. Pour cela, un outils appelé \texttt{jml2why3} est développé par Benedikt \bsc{Becker}. Il devrait permettre de produire du code WhyML à partir du code Java original. On espère alors pouvoir transposer les preuves de notre implémentation WhyML au code WhyML produit.
On souhaite pouvoir vérifier l'implémentation originale en Java. Pour cela, un outils appelé \texttt{jml2why3} est développé par Benedikt \bsc{Becker}. Il devrait permettre de produire du code WhyML à partir du code Java original. On espère alors pouvoir transposer les preuves de notre implémentation WhyML au code WhyML généré.

4
src/preuves.tex

@ -16,13 +16,13 @@ pour prouver la terminaison de la boucle.
On a montré la sûreté de l'ensemble du programme.
\subsection{Preuves des propriétés}
Les propriétés $P_0$, $P_1$, $P_2$ et $P_5$ on été prouvées. Pour $P_3$, seule la partie indiquant qu'un candidat de rang $r$ dans le classement pédagogique aura au mieux le rang $r$ dans l'ordre d'appel a été prouvé. La seconde partie de $P_3$ et $P_4$ ont été énoncées mais ne sont pas prouvées.
Les propriétés $P_0$, $P_1$, $P_2$ et $P_5$ on été prouvées. Pour $P_3$, seule la partie indiquant qu'un candidat de rang $r$ dans le classement pédagogique aura au mieux le rang $r$ dans l'ordre d'appel a été prouvé. $P_4$ et la seconde partie de $P_3$ ont été énoncées mais ne sont pas prouvées.
Les diverses preuves menées ont impliqué des techniques variées et intéressantes: preuves par l'absurde, par des \emph{lemma functions} pour simuler des preuves par induction etc. On ne les détaillera pas ici par manque de place, mais quelques points sont intéressants à souligner.
Tout d'abord, on avait au départ décider de maintenir divers invariants à l'intérieur même des fonctions de l'algorithme, cependant, en procédant ainsi, on créait de la redondance: un même invariant pouvait demander d'être ajouté en précondition et en postcondition de nombreuses fonctions, ce qui était fastidieux au vu du nombre d'invariants. On a alors décidé de créer un type contenant la majorité des variables utilisées par l'algorithme et de donner des invariants à ce type directement. Ainsi, on doit toujours prouver leur préservation, mais sans avoir à les spécifier plusieurs fois.
D'autre part, pour faciliter les preuves, plusieurs modifications ont été apportées à la bibliothèque standard de Why3. On peut notamment mentionner la réécriture du module de file et de permutation, ainsi que l'ajout de divers lemmes, sur les séquences notamment.
D'autre part, pour faciliter les preuves, plusieurs modifications ont été apportées à la bibliothèque standard de Why3. On peut notamment mentionner la réécriture des modules de file et de permutation, ainsi que l'ajout de divers lemmes, sur les séquences notamment.
\subsection{Production de code exécutable}
Il est possible de générer du code dans un autre langage à partir de l'implémentation WhyML, on appelle cela l'\emph{extraction}. On a extrait notre code vers OCaml. En compilant le code OCaml extrait, on obtient ainsi une imlémentation de référence, que l'on peut exécuter avec des données anonymisées et comparer les résultats obtenus.

6
src/title.tex

@ -16,9 +16,9 @@
\vspa{0.1}
\notimportant Master 1 Informatique\\
\vspa{0.02}
\includesvg{universite-paris-saclay.svg}\\
\notimportant Magistère 2 Informatique\\
\vspa{0.05}
\includesvg[width=100pt]{upsud.svg}\\
\vspa{0.1}

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