Continue writing about the dangling else ambiguity.

1 files changed, 99 insertions, 1 deletions

diff --git a/exercices2.tex b/exercices2.tex
index 70d030b..aac8a19 100644
--- a/exercices2.tex
+++ b/exercices2.tex
@@ -127,7 +127,7 @@ Que peut-on dire de la grammaire présentée ?
   $\mathit{Instruction}$, $\mathit{Condition}$ et
   $\mathit{Expression}$ respectivement) :
 \begin{center}
-\tikzstyle{automaton}=[scale=0.5]
+\tikzstyle{automaton}=[scale=0.4]
 %%% begin ex2p1 %%%
 
 \begin{tikzpicture}[>=latex,line join=bevel,automaton]
@@ -183,6 +183,104 @@ descendant de façon unique (l'instruction est forcément une condition,
 qui s'analyse en $\mathtt{if}\ E\ \mathtt{then}\ I\ \mathtt{else}\ I$
 de façon unique, et chacun des morceaux s'analyse de nouveau de façon
 unique).
+
+\vskip .5explus.1fil
+
+(2) Un arbre d'analyse possible consiste à associer le
+$\mathtt{else}\penalty0\ \mathtt{bar}$ avec
+$\mathtt{if}\penalty0\ \mathtt{trippy}\penalty0\ \mathtt{then}\penalty0\ \mathtt{foo}$ :
+\begin{center}
+\tikzstyle{automaton}=[scale=0.4]
+%%% begin ex2p1a %%%
+
+\begin{tikzpicture}[>=latex,line join=bevel,automaton]
+%%
+\node (bar) at (423bp,18bp) [draw,draw=none] {$\mathtt{bar}$};
+  \node (then1) at (207bp,90bp) [draw,draw=none] {$\mathtt{then}$};
+  \node (if0) at (27bp,234bp) [draw,draw=none] {$\mathtt{if}$};
+  \node (if1) at (63bp,90bp) [draw,draw=none] {$\mathtt{if}$};
+  \node (I1) at (243bp,234bp) [draw,draw=none] {$I$};
+  \node (I0) at (135bp,378bp) [draw,draw=none] {$I$};
+  \node (I3) at (423bp,90bp) [draw,draw=none] {$I$};
+  \node (I2) at (279bp,90bp) [draw,draw=none] {$I$};
+  \node (trippy) at (135bp,18bp) [draw,draw=none] {$\mathtt{trippy}$};
+  \node (else1) at (351bp,90bp) [draw,draw=none] {$\mathtt{else}$};
+  \node (foo) at (279bp,18bp) [draw,draw=none] {$\mathtt{foo}$};
+  \node (C1) at (243bp,162bp) [draw,draw=none] {$C$};
+  \node (then0) at (171bp,234bp) [draw,draw=none] {$\mathtt{then}$};
+  \node (C0) at (135bp,306bp) [draw,draw=none] {$C$};
+  \node (E1) at (135bp,90bp) [draw,draw=none] {$E$};
+  \node (E0) at (99bp,234bp) [draw,draw=none] {$E$};
+  \node (happy) at (99bp,162bp) [draw,draw=none] {$\mathtt{happy}$};
+  \draw [] (I2) ..controls (279bp,60.846bp) and (279bp,46.917bp)  .. (foo);
+  \draw [] (C0) ..controls (149.48bp,276.85bp) and (156.64bp,262.92bp)  .. (then0);
+  \draw [] (I0) ..controls (135bp,348.85bp) and (135bp,334.92bp)  .. (C0);
+  \draw [] (C1) ..controls (228.52bp,132.85bp) and (221.36bp,118.92bp)  .. (then1);
+  \draw [] (C1) ..controls (286.16bp,133.03bp) and (307.72bp,119.05bp)  .. (else1);
+  \draw [] (I3) ..controls (423bp,60.846bp) and (423bp,46.917bp)  .. (bar);
+  \draw [] (E0) ..controls (99bp,204.85bp) and (99bp,190.92bp)  .. (happy);
+  \draw [] (C1) ..controls (199.84bp,133.03bp) and (178.28bp,119.05bp)  .. (E1);
+  \draw [] (C1) ..controls (186.77bp,141.79bp) and (139.17bp,124.84bp)  .. (99bp,108bp) .. controls (96.068bp,106.77bp) and (93.027bp,105.43bp)  .. (if1);
+  \draw [] (C0) ..controls (91.844bp,277.03bp) and (70.277bp,263.05bp)  .. (if0);
+  \draw [] (E1) ..controls (135bp,60.846bp) and (135bp,46.917bp)  .. (trippy);
+  \draw [] (C1) ..controls (299.23bp,141.79bp) and (346.83bp,124.84bp)  .. (387bp,108bp) .. controls (389.93bp,106.77bp) and (392.97bp,105.43bp)  .. (I3);
+  \draw [] (C0) ..controls (178.16bp,277.03bp) and (199.72bp,263.05bp)  .. (I1);
+  \draw [] (C1) ..controls (257.48bp,132.85bp) and (264.64bp,118.92bp)  .. (I2);
+  \draw [] (I1) ..controls (243bp,204.85bp) and (243bp,190.92bp)  .. (C1);
+  \draw [] (C0) ..controls (120.52bp,276.85bp) and (113.36bp,262.92bp)  .. (E0);
+%
+\end{tikzpicture}
+
+%%% end ex2p1a %%%
+\end{center}
+un autre consiste à associer le $\mathtt{else}\penalty0\ \mathtt{bar}$
+avec
+$\mathtt{if}\penalty0\ \mathtt{happy}\penalty0\ \mathtt{then}\penalty0\ ...$ :
+\begin{center}
+\tikzstyle{automaton}=[scale=0.4]
+%%% begin ex2p1b %%%
+
+\begin{tikzpicture}[>=latex,line join=bevel,automaton]
+%%
+\node (bar) at (387bp,162bp) [draw,draw=none] {$\mathtt{bar}$};
+  \node (then1) at (279bp,90bp) [draw,draw=none] {$\mathtt{then}$};
+  \node (if0) at (27bp,234bp) [draw,draw=none] {$\mathtt{if}$};
+  \node (if1) at (135bp,90bp) [draw,draw=none] {$\mathtt{if}$};
+  \node (I1) at (243bp,234bp) [draw,draw=none] {$I$};
+  \node (I0) at (207bp,378bp) [draw,draw=none] {$I$};
+  \node (I2) at (351bp,90bp) [draw,draw=none] {$I$};
+  \node (I4) at (387bp,234bp) [draw,draw=none] {$I$};
+  \node (trippy) at (207bp,18bp) [draw,draw=none] {$\mathtt{trippy}$};
+  \node (else0) at (315bp,234bp) [draw,draw=none] {$\mathtt{else}$};
+  \node (foo) at (351bp,18bp) [draw,draw=none] {$\mathtt{foo}$};
+  \node (C1) at (243bp,162bp) [draw,draw=none] {$C$};
+  \node (then0) at (171bp,234bp) [draw,draw=none] {$\mathtt{then}$};
+  \node (C0) at (207bp,306bp) [draw,draw=none] {$C$};
+  \node (E1) at (207bp,90bp) [draw,draw=none] {$E$};
+  \node (E0) at (99bp,234bp) [draw,draw=none] {$E$};
+  \node (happy) at (99bp,162bp) [draw,draw=none] {$\mathtt{happy}$};
+  \draw [] (I2) ..controls (351bp,60.846bp) and (351bp,46.917bp)  .. (foo);
+  \draw [] (C0) ..controls (192.52bp,276.85bp) and (185.36bp,262.92bp)  .. (then0);
+  \draw [] (I0) ..controls (207bp,348.85bp) and (207bp,334.92bp)  .. (C0);
+  \draw [] (C0) ..controls (250.16bp,277.03bp) and (271.72bp,263.05bp)  .. (else0);
+  \draw [] (C1) ..controls (286.16bp,133.03bp) and (307.72bp,119.05bp)  .. (I2);
+  \draw [] (I4) ..controls (387bp,204.85bp) and (387bp,190.92bp)  .. (bar);
+  \draw [] (E0) ..controls (99bp,204.85bp) and (99bp,190.92bp)  .. (happy);
+  \draw [] (C1) ..controls (228.52bp,132.85bp) and (221.36bp,118.92bp)  .. (E1);
+  \draw [] (C0) ..controls (263.23bp,285.79bp) and (310.83bp,268.84bp)  .. (351bp,252bp) .. controls (353.93bp,250.77bp) and (356.97bp,249.43bp)  .. (I4);
+  \draw [] (C1) ..controls (199.84bp,133.03bp) and (178.28bp,119.05bp)  .. (if1);
+  \draw [] (C0) ..controls (150.77bp,285.79bp) and (103.17bp,268.84bp)  .. (63bp,252bp) .. controls (60.068bp,250.77bp) and (57.027bp,249.43bp)  .. (if0);
+  \draw [] (E1) ..controls (207bp,60.846bp) and (207bp,46.917bp)  .. (trippy);
+  \draw [] (C0) ..controls (221.48bp,276.85bp) and (228.64bp,262.92bp)  .. (I1);
+  \draw [] (C1) ..controls (257.48bp,132.85bp) and (264.64bp,118.92bp)  .. (then1);
+  \draw [] (I1) ..controls (243bp,204.85bp) and (243bp,190.92bp)  .. (C1);
+  \draw [] (C0) ..controls (163.84bp,277.03bp) and (142.28bp,263.05bp)  .. (E0);
+%
+\end{tikzpicture}
+
+%%% end ex2p1b %%%
+\end{center}
+La grammaire présentée est donc ambiguë.
 \end{corrige}