Ajout des autres règles de typage + domaines de leurs variables

dm.tex

@@ -199,7 +199,66 @@ We also introduce a new subsumption typing rule:
   \inference{\Gamma \vdash e : S & S <: T}{\Gamma \vdash e : T}
 \]
 
-% TODO : booléens… (autre photo)
+Assignment
+\[
+  \inference{\Gamma \vdash x : T & \Gamma \vdash a : T}{\Gamma \vdash x := a}
+\]
+
+Sequence
+\[
+  \inference{\Gamma \vdash S_1 & \Gamma \vdash S_2}{\Gamma \vdash (S_1 ; S_2)}
+\]
+
+While loop
+\[
+  \inference{\Gamma \vdash b & \Gamma \vdash S}{\Gamma \vdash \<while>\ b\ \<do>\ S}
+\]
+
+Condition
+\[
+  \inference{\Gamma \vdash b & \Gamma \vdash S_1 & \Gamma \vdash S_2}{\Gamma \vdash \<if>\ b\ \<then>\ S_1\ \<else>\ S_2}
+\]
+
+Booleans
+\[
+  \inference{}{\Gamma \vdash \<true>}
+\]
+\[
+  \inference{}{\Gamma \vdash \<false>}
+\]
+\[
+  \inference{\Gamma \vdash b}{\Gamma \vdash \<not>\ b}
+\]
+\[
+  \inference{\Gamma \vdash b_1 & \Gamma \vdash b_2}{\Gamma \vdash b_1\ o\ b_2}{o \in \{\<and>, \<or>\}}
+\]
+\[
+  \inference{\Gamma \vdash a_1 : int & \Gamma \vdash a_2 : int}{\Gamma \vdash a_1 \le a_2}
+\]
+\[
+  \inference{\Gamma \vdash a_1 : T & \Gamma \vdash a_2 : T}{\Gamma \vdash a_1 = a_2}
+\]
+Note: for the equality test, the rule works for \<int> as well as for records.
+
+% Domains
+\[
+  n \in Num
+\]
+\[
+  x \in Var
+\]
+\[
+  e,e_1,e_2,a,a_1,a_2 \in AExpr
+\]
+\[
+  b,b_1,b_2 \in BExpr
+\]
+\[
+  f,f_1,\dots,f_n,f_i,g_1,\dots,g_k, \in Field % Field n'est pas défini…
+\]
+\[
+  S,S_1,S_2 \in Statement
+\]
 
 \subsection{Correctness}