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| -rw-r--r-- | exercices2.tex | 100 | ||||
| -rw-r--r-- | figs/ex2p1a.dot | 36 | ||||
| -rw-r--r-- | figs/ex2p1b.dot | 36 |
3 files changed, 171 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} diff --git a/figs/ex2p1a.dot b/figs/ex2p1a.dot new file mode 100644 index 0000000..fbf84b0 --- /dev/null +++ b/figs/ex2p1a.dot @@ -0,0 +1,36 @@ +graph ex2p1a { + node [texmode="math",shape="none"]; + I0 [label="I"]; + C0 [label="C"]; + if0 [label="if",texlbl="$\mathtt{if}$"]; + E0 [label="E"]; + then0 [label="then",texlbl="$\mathtt{then}$"]; + I1 [label="I"]; + happy [label="happy",texlbl="$\mathtt{happy}$"]; + C1 [label="C"]; + if1 [label="if",texlbl="$\mathtt{if}$"]; + E1 [label="E"]; + then1 [label="then",texlbl="$\mathtt{then}$"]; + I2 [label="I"]; + else1 [label="else",texlbl="$\mathtt{else}$"]; + I3 [label="I"]; + trippy [label="trippy",texlbl="$\mathtt{trippy}$"]; + foo [label="foo",texlbl="$\mathtt{foo}$"]; + bar [label="bar",texlbl="$\mathtt{bar}$"]; + I0 -- C0; + C0 -- if0; + C0 -- E0; + C0 -- then0; + C0 -- I1; + E0 -- happy; + I1 -- C1; + C1 -- if1; + C1 -- E1; + C1 -- then1; + C1 -- I2; + C1 -- else1; + C1 -- I3; + E1 -- trippy; + I2 -- foo; + I3 -- bar; +} diff --git a/figs/ex2p1b.dot b/figs/ex2p1b.dot new file mode 100644 index 0000000..79ad50c --- /dev/null +++ b/figs/ex2p1b.dot @@ -0,0 +1,36 @@ +graph ex2p1b { + node [texmode="math",shape="none"]; + I0 [label="I"]; + C0 [label="C"]; + if0 [label="if",texlbl="$\mathtt{if}$"]; + E0 [label="E"]; + then0 [label="then",texlbl="$\mathtt{then}$"]; + I1 [label="I"]; + else0 [label="else",texlbl="$\mathtt{else}$"]; + I4 [label="I"]; + happy [label="happy",texlbl="$\mathtt{happy}$"]; + C1 [label="C"]; + if1 [label="if",texlbl="$\mathtt{if}$"]; + E1 [label="E"]; + then1 [label="then",texlbl="$\mathtt{then}$"]; + I2 [label="I"]; + bar [label="bar",texlbl="$\mathtt{bar}$"]; + trippy [label="trippy",texlbl="$\mathtt{trippy}$"]; + foo [label="foo",texlbl="$\mathtt{foo}$"]; + I0 -- C0; + C0 -- if0; + C0 -- E0; + C0 -- then0; + C0 -- I1; + C0 -- else0; + C0 -- I4; + E0 -- happy; + I1 -- C1; + I4 -- bar; + C1 -- if1; + C1 -- E1; + C1 -- then1; + C1 -- I2; + E1 -- trippy; + I2 -- foo; +} |