doc: typos

doc/syntax.tex

@@ -67,7 +67,7 @@ length. The \texttt{use import List} command indicates that this new
 theory may refer to symbols from theory \texttt{List}. These symbols
 are accessible in a qualified form, such as \texttt{List.list} or
 \texttt{List.Cons}. The \texttt{import} qualifier additionally allows
-use to use them without qualification.
+us to use them without qualification.
 
 Similarly, the next command \texttt{use import int.Int} adds to our
 context the theory \texttt{int.Int} from the standard library. The
@@ -76,7 +76,7 @@ containing theory \texttt{Int}. Theories referred to without prefix
 either appear earlier in the current file, \eg\ \texttt{List}, or are
 predefined.
 
-The next declaration defines a recursive function, \emph{length},
+The next declaration defines a recursive function, \texttt{length},
 which computes the length of a list. The \texttt{logic} keyword is
 used to introduce or define both function and predicate symbols.
 \why\ checks every recursive, or mutually recursive, definition for
@@ -115,7 +115,7 @@ declarations of another theory, coming either from the same input
 text or from the library. Another way to referring to a theory is
 by ``cloning''. A \texttt{clone} declaration constructs a local
 copy of the cloned theory, possibly instantiating some of its
-abstract (i.e.~declared but not defined) symbols.
+abstract (\emph{i.e.}~declared but not defined) symbols.
 
 \begin{figure}
 \centering
@@ -177,7 +177,7 @@ use of it (see Section~\ref{sec:drivers}).
 
 Notice an important difference between \texttt{use}
 and \texttt{clone}. If we \texttt{use} a theory, say
-\texttt{List}, twice (directly or indirectly: e.g.~by
+\texttt{List}, twice (directly or indirectly: \emph{e.g.}~by
 making \texttt{use} of both \texttt{Length} and
 \texttt{Sorted}), there is no duplication: there is
 still only one type of lists and a unique pair
@@ -194,7 +194,7 @@ this time we use the abstract order on the values of type
 Now, we can instantiate theory \texttt{SortedGen} to any
 ordered type, without having to retype the definition of
 \texttt{sorted}. For example, theory \texttt{SortedIntList}
-makes \texttt{clone} of \texttt{SortedGen} (i.e.~copies its
+makes \texttt{clone} of \texttt{SortedGen} (\emph{i.e.}~copies its
 declarations) substituting type \texttt{int} for type
 \texttt{O.t} of \texttt{SortedGen} and the default order
 on integers for predicate \texttt{O.(<=)}. \why\ will
@@ -268,7 +268,7 @@ optional, if it is omitted, the name of the symbol is \texttt{List.$s$}.
 \item \texttt{use import List as L} --- every symbol $s$ from
 \texttt{List} is accessible under the name \texttt{L.$s$}. It is also
 accessible simply as \texttt{$s$}, but only up to the end of the current
-namespace, e.g.~the current theory. If the current theory, that is the
+namespace, \emph{e.g.}~the current theory. If the current theory, that is the
 one making \texttt{use}, is later used under the name \texttt{T},
 the name of the symbol would be \texttt{T.L.$s$}. (This is why we
 could refer directly to the symbols of \texttt{Order} in theory
@@ -298,7 +298,7 @@ this feature is rarely used.
 
 We now consider another, slightly more complex example: to use \why\
 to solve a little puzzle known as ``Einstein's logic
-problem''\footnote{This was contributed by St\'ephane Lescuyer.}.
+problem''\footnote{This \why\ example was contributed by St\'ephane Lescuyer.}.
 The problem is stated as follows. Five persons, of five
 different nationalities, live in five houses in a row, all
 painted with different colors.