summaryrefslogtreecommitdiffstats
path: root/transp-inf110-02-typage.tex
diff options
context:
space:
mode:
authorDavid A. Madore <david+git@madore.org>2023-12-09 11:37:43 +0100
committerDavid A. Madore <david+git@madore.org>2023-12-09 11:37:43 +0100
commit663e73acd329df0ed327d94845730e77f3c59e09 (patch)
treef4fbf34a2f0d5e60a0e2d953d99eed1646604dd3 /transp-inf110-02-typage.tex
parent2cf14e0c73464472b0ea04630bcf1e01f3caaa61 (diff)
downloadinf110-lfi-663e73acd329df0ed327d94845730e77f3c59e09.tar.gz
inf110-lfi-663e73acd329df0ed327d94845730e77f3c59e09.tar.bz2
inf110-lfi-663e73acd329df0ed327d94845730e77f3c59e09.zip
Fix a mistake: contraction rule cannot be dispensed with.
(See discussion in example 3.1.3 in Troelstra & Schwichtenberg: the system I presented is essentially their G2i, and the contraction rule is necessary.)
Diffstat (limited to 'transp-inf110-02-typage.tex')
-rw-r--r--transp-inf110-02-typage.tex17
1 files changed, 7 insertions, 10 deletions
diff --git a/transp-inf110-02-typage.tex b/transp-inf110-02-typage.tex
index f3e8b1d..35425f0 100644
--- a/transp-inf110-02-typage.tex
+++ b/transp-inf110-02-typage.tex
@@ -2675,22 +2675,19 @@ droite \alert{ou à gauche} du symbole « $\vdash$ ».
\medskip
\itempoint On garde la règle $\inferrule*[left=Ax]{ }{\Gamma,Q \vdash
- Q}$, qu'on peut choisir de séparer en :
+ Q}$, ou on peut en séparer une règle d'qffaibilissement ; et on va
+reparler des règles de « contraction » et « coupure » :
+
\begin{center}
-\begin{tabular}{c|c|c}
+\begin{tabular}{c|c}
$\inferrule*[left=Ax]{ }{Q \vdash Q}$
&$\inferrule*[left=Weak]{\Gamma \vdash Q}{\Gamma,P\vdash Q}$
-&$\inferrule*[left=Contr]{\Gamma,P,P \vdash Q}{\Gamma,P\vdash Q}$
+\\\hline
+$\inferrule*[left=Contr]{\Gamma,P,P \vdash Q}{\Gamma,P\vdash Q}$
+&$\inferrule*[left=Cut]{\Gamma \vdash P\\\Gamma,P\vdash Q}{\Gamma\vdash Q}$
\end{tabular}
\end{center}
-\medskip
-
-\itempoint On va reparler de la règle de « coupure » :
-\[
-\inferrule*[left=Cut]{\Gamma \vdash P\\\Gamma,P\vdash Q}{\Gamma\vdash Q}
-\]
-
\end{frame}
%
\begin{frame}