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KFRmzo{{H|#!E#Fg literal 0 HcmV?d00001 diff --git a/RapportPresentation/ex-presentation.tex b/RapportPresentation/ex-presentation.tex index 83ef093..8634a3c 100644 --- a/RapportPresentation/ex-presentation.tex +++ b/RapportPresentation/ex-presentation.tex @@ -92,6 +92,8 @@ \lstinline{Qed} + \lstinline{Check} + Tactiques: \lstinline{exact} @@ -166,7 +168,7 @@ \begin{frame}{Fiabilité} \begin{itemize} - \item Comment être sûrs de nos preuves + \item Comment être sûrs de nos preuves ? \pause \item Envoyer nos termes de preuves à \textbf{\color{blue}{Coq}}. \end{itemize} diff --git a/RapportPresentation/ex-rapport.pdf b/RapportPresentation/ex-rapport.pdf index dede05d2394999dfb81505e99818acbb562d7878..551edeae2b6c5206d450f63cb74fdf12026cd6fe 100644 GIT binary patch delta 98969 zcmV(yKuGy$umuzpuv6>gHRIh(2$zvYl3U$hfBmqd;68|gAKygJjNje7dHaJ*0vwcmPVQ+aX8MSDE!#oO3gdl>?9BStS=8M#-Oj!rw-pZw+Q|=fZAZWRg@0pN+4h=_RaujR1#ZjwBST+SWk;(?*c|$H^!tXEBZn=x 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Mimram~\cite{SMIM} et \textit{très} brièvement dans le livre de Landin~\cite{PJL700}. - +L'implémentation du~\textit{OU} et du~\textit{ET} est incomplète. +Nous n'avons pas eu le temps d'implémenter les déconstructeurs associés +(les projecteurs et le \verb|match|). \section{Preuves} \label{s:proof} @@ -173,9 +174,11 @@ Compléter la preuve correspond Lorsqu'on déclare un but, on lui assigne donc : \begin{itemize} - \item un lambda terme creux (\verb|Ref (ref Hole)|) que l'on construit petit à petit à l'aide des tactiques. + \item un lambda terme creux (\verb|Ref (ref Hole)|) que + l'on construit petit à petit à l'aide des tactiques. \item le type associé à ce que l'on souhaite prouver - \item son contexte, c'est à dire un liste d'hypothèses (nom de l'hypothèse, type, $\lambda$-terme possiblement encore creux qui sera mis à jour facilement grâce aux \verb|ref|s) + \item son contexte, c'est à dire un liste d'hypothèses + (nom de l'hypothèse, type, $\lambda$-terme possiblement encore creux qui sera mis à jour facilement grâce aux \verb|ref|s) \end{itemize} Au moment du \verb|Qed|, ce $\lambda$-terme de preuve qui a été gardé de côté est $\beta$-réduit puis typé contre le type @@ -190,8 +193,14 @@ Voici les commandes et tactiques implémentées: \begin{itemize} \item \verb|Goal| pour émettre un nouveau but - \item \verb|Undo| pour annuler la dernière tactique + \item \verb|Undo| pour annuler la dernière tactique. + Son implémentation est très brutale, on se contente de maintenir une pile des états + du terme de preuve. Appliquer cette tactique revient à dépiler l'état courant et à + revenir au précédent. L'implémentation pourrait être plus judicieuse. \item \verb|Qed| pour clore la preuve d'un but + \item \verb|Check| construit le fichier \lstinline{checker.v} qui contient + le but courant ainsi qu'un \lstinline{exact} du terme de preuve. + Ce fichier est envoyé au top-level de Coq afin d'être vérifié. \item \verb|exact| si une hypothèse correspond parfaitement à notre but courant \item \verb|assumption| recherche automatique d'une hypothèse correspondant au but courant \item \verb|intro| pour défaire une implication @@ -209,6 +218,11 @@ Voici les commandes et tactiques implémentées: rien ne se passe. \end{itemize} + +Là encore, il manque la tactique~\lstinline|destruct|. + +On peut prouver~\lstinline{A -> A /\ A} mais pas l'implication inverse. + \section{Conlusion} Nous avons présenté notre assistant de preuve \textbf{Pieuvre}. Il permet de prouver des prédicats logiques simples. @@ -225,8 +239,13 @@ Enfin, il faut se poser la question de la fiabilité de notre assistant de preuve. Il serait difficile de prouver formellement toutes les composantes du programme (la~$\beta$-réduction, l'~$\alpha$-conversion, le \verb|typecheck|, etc.). -Ainsi, on propose de sauvegarder les termes de preuves puis de -les envoyer à Coq pour valider la preuve. +Ainsi, on propose de sauvegarder les termes de preuves +puis de les envoyer à Coq pour valider la preuve. +Cette approche est assez satisfaisante dans la mesure où +la construction du terme de preuve repose uniquement sur les tactiques +et pas sur notre implémentation du~$\lambda$-calcul. +Ainsi, on peut supposer qu'on n'a jamais de faux-positif: +si Check valide notre preuve, c'est quelle est valide. \section{Répartition du travail} diff --git a/typing.ml b/typing.ml index 5430637..e9132d0 100644 --- a/typing.ml +++ b/typing.ml @@ -5,7 +5,10 @@ exception Could_not_infer let rec typecheck (g : gam) (e : lam) (expected_t : ty) : bool = match e with - Var x -> (List.assoc x g) = expected_t + Var x -> + begin try (List.assoc x g) = expected_t + with Not_found -> false + end | Fun ((x, actual_t1), e) -> begin match expected_t with Arr (expected_t1, expected_t2) -> @@ -52,13 +55,13 @@ and typeinfer (g : gam) (e : lam) : ty = Arr (t1, t2) -> if typecheck g e2 t1 then t2 - else raise Could_not_infer - | _ -> raise Could_not_infer + else raise Could_not_infer + | _ -> raise Could_not_infer end | Exf (e, t) -> if typecheck g e t then Bot - else raise Could_not_infer + else raise Could_not_infer | Pair (e1, e2) -> And ( typeinfer g e1, @@ -69,14 +72,14 @@ and typeinfer (g : gam) (e : lam) : ty = Or (t_l, _) -> if typecheck g e t_l then t - else raise Could_not_infer - | _ -> raise Could_not_infer + else raise Could_not_infer + | _ -> raise Could_not_infer end | Right (e, t) -> begin match t with Or (_, t_r) -> if typecheck g e t_r then t - else raise Could_not_infer - | _ -> raise Could_not_infer + else raise Could_not_infer + | _ -> raise Could_not_infer end