From 461ca6aeaa1e93ef5bb7314940e4d64206ec4a0b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Th=C3=A9ophile=20Bastian?= <contact@tobast.fr>
Date: Sun, 21 Aug 2016 00:41:37 +0200
Subject: [PATCH] Fix few sentences starting with math.

---
 report.tex | 17 +++++++++--------
 1 file changed, 9 insertions(+), 8 deletions(-)

diff --git a/report.tex b/report.tex
index eae8e9d..a322d4c 100644
--- a/report.tex
+++ b/report.tex
@@ -473,11 +473,12 @@ The ESP of the previous example would then be
 	\vspace{-0.5em}
 	\[ {\forall x \in X}, {\forall e \in A}, {e \leq_A x} \implies {e \in X}.\]
 
-	$\config(A)$ is the set of configurations of $A$.
+	We write $\config(A)$ the set of configurations of $A$.
 \end{definition}
 
-A configuration can thus be seen as a valid state of the game. $\config(A)$
-plays a major role in definitions and proofs on games and strategies.
+A configuration can thus be seen as a valid state of the game. The set
+$\config(A)$ plays a major role in definitions and proofs on games and
+strategies.
 
 \begin{notation}
 	For $x,y \in \config(A)$, $x \forkover{e} y$ states that $y =
@@ -713,10 +714,10 @@ adding ``neutral'' states for $A$ and $C$, which gives us two strategies
 playing on the same game (if we ignore polarities), $A \parallel B \parallel
 C$.
 
-$\tau \strInteract \sigma$ is an \emph{event structure} (\ie, without
-polarities): indeed, the two strategies disagree on the polarities of the
-middle part. Alternatively, it can be seen as an ESP with a polarity function
-over $\set{+,-,?}$.
+Here, we define $\tau \strInteract \sigma$ as an \emph{event structure} (\ie,
+without polarities): indeed, the two strategies disagree on the polarities of
+the middle part. Alternatively, it can be seen as an ESP with a polarity
+function over $\set{+,-,?}$.
 
 From this point, the notion of composition we sought is only a matter of
 ``hiding'' the middle part:
@@ -1027,7 +1028,7 @@ can compute its associated strategy and check whether it is $\seman{1}$.
 
 \vspace{1em}
 
-One of the objectives of my internship was also to implement the operations on
+One of the goals of my internship was also to implement the operations on
 games and strategies described in §\ref{sssec:es_operations}, and to use them
 to provide a convenient Dot representation of the operational semantics of
 \llccs{} described in §\ref{ssec:llccs_interp}.