Using \tuple{} for expressing tuples

[iotcloud.git] / doc / iotcloud.tex

diff --git a/doc/iotcloud.tex b/doc/iotcloud.tex
index 79525458af929316271ceaa4b1fc6de003ced8b1..f7c7ea10fbb614504eb57ff1f8ba1cf7e0198a44 100644 (file)
--- a/doc/iotcloud.tex
+++ b/doc/iotcloud.tex
@@ -134,12 +134,12 @@ $slot_s = \tuple{s, sv} \in SL \subseteq SN \times SV$ \\
 \textit{max = maximum number of slots (input only for resize message)} \\\r
 \textit{n = number of slots} \\ \\\r
 \textbf{Helper Function} \\\r
-$MaxSlot(SL')= \langle s, sv \rangle \mid \langle s, sv \rangle \r
-\in SL' \wedge \forall \langle s', sv' \rangle \in SL', s \geq s'$ \\\r
-$MinSlot(SL')= \langle s, sv \rangle \mid \langle s, sv \rangle \r
-\in SL' \wedge \forall \langle s', sv' \rangle \in SL', s \leq s'$ \\\r
-$SeqN(\langle s, sv \rangle)=s$ \\\r
-$SlotVal(\langle s, sv \rangle)=sv$ \\\r
+$MaxSlot(SL')= \tuple{s, sv} \mid \tuple{s, sv}\r
+\in SL' \wedge \forall \tuple{s', sv'} \in SL', s \geq s'$ \\\r
+$MinSlot(SL')= \tuple{s, sv} \mid \tuple{s, sv} \r
+\in SL' \wedge \forall \tuple{s', sv'} \in SL', s \leq s'$ \\\r
+$SeqN(\tuple{s, sv})=s$ \\\r
+$SlotVal(\tuple{s, sv})=sv$ \\\r
 \r
 \begin{algorithmic}[1]\r
 \Function{GetSlot}{$s_g$}\r
@@ -152,19 +152,19 @@ $SlotVal(\langle s, sv \rangle)=sv$ \\
 \If{$(max' \neq \emptyset)$}\Comment{Resize}\r
 \State $max \gets max'$\r
 \EndIf\r
-\State $\langle s_n,sv_n \rangle \gets MaxSlot(SL)$\Comment{Last sv}\r
-\State $s_n \gets SeqN(\langle s_n,sv_n \rangle)$\r
+\State $\tuple{s_n,sv_n} \gets MaxSlot(SL)$\Comment{Last sv}\r
+\State $s_n \gets SeqN(\tuple{s_n,sv_n})$\r
 \If{$(s_p = s_n + 1)$}\r
        \If{$n = max$}\r
-       \State $\langle s_m,sv_m \rangle \gets MinSlot(SL)$\Comment{First sv}\r
-               \State $SL \gets SL - \{\langle s_m,sv_m \rangle\}$\r
+       \State $\tuple{s_m,sv_m} \gets MinSlot(SL)$\Comment{First sv}\r
+               \State $SL \gets SL - \{\tuple{s_m,sv_m}\}$\r
        \Else \Comment{$n < max$}\r
                \State $n \gets n + 1$\r
        \EndIf\r
-    \State $SL \gets SL \cup \{\langle s_p,sv_p \rangle\}$\r
+    \State $SL \gets SL \cup \{\tuple{s_p,sv_p}\}$\r
        \State \Return{$true$}\r
 \Else\r
-       \State \Return{$(false,\{\langle s,sv \rangle \in SL \mid \r
+       \State \Return{$(false,\{\tuple{s,sv}\in SL \mid \r
     s \geq s_p\})$}\r
 \EndIf\r
 \EndFunction\r