
diff -r e4afe3f46c29 -r 5d85dc9779b1 hws/hw05.tex
--- a/hws/hw05.tex	Wed Apr 06 12:18:54 2016 +0100
+++ b/hws/hw05.tex	Wed Apr 06 15:55:01 2016 +0100
@@ -18,21 +18,21 @@
 \item Consider the basic regular expressions
 
 \begin{center}
-$r ::= \varnothing \;|\; \epsilon \;|\; c  \;|\; r_1 + r_2  \;|\; r_1 \cdot r_2 \;|\; r^*$
+$r ::= \ZERO \;|\; \ONE \;|\; c  \;|\; r_1 + r_2  \;|\; r_1 \cdot r_2 \;|\; r^*$
 \end{center}
 
-and suppose you want to show a property $P(r)$ for all regular
-expressions $r$ by structural induction. Write down which cases do you 
-need to analyse. State clearly the induction hypotheses if applicable
-in a case.
+      and suppose you want to show a property $P(r)$ for all
+      regular expressions $r$ by structural induction. Write
+      down which cases do you need to analyse. State clearly
+      the induction hypotheses if applicable in a case.
 
-\item Define a regular expression, written $ALL$, that can match 
-every string. This definition should be in terms of the
-following extended regular expressions:
+\item Define a regular expression, written $ALL$, that can
+      match every string. This definition should be in terms
+      of the following extended regular expressions:
 
 \begin{center}
-$r ::= \varnothing \;|\; 
-       \epsilon \;|\;  
+$r ::= \ZERO \;|\; 
+       \ONE \;|\;  
        c  \;|\; 
        r_1 + r_2 \;|\; 
        r_1 \cdot r_2 \;|\; 
@@ -66,17 +66,17 @@
 in terms of the usual basic regular expressions
 
 \begin{center}
-$r ::= \varnothing \;|\; \epsilon \;|\; c  \;|\; r_1 + r_2  \;|\; r_1 \cdot r_2 \;|\; r^*$
+$r ::= \ZERO \;|\; \ONE \;|\; c  \;|\; r_1 + r_2  \;|\; r_1 \cdot r_2 \;|\; r^*$
 \end{center}
 
 \item Give the regular expressions for lexing a language
-consisting of identifiers, left-parenthesis \texttt{(},
-right-parenthesis \texttt{)}, numbers that can be either
-positive or negative, and the operations \texttt{+},
-\texttt{-} and \texttt{*}. 
+      consisting of identifiers, left-parenthesis \texttt{(},
+      right-parenthesis \texttt{)}, numbers that can be either
+      positive or negative, and the operations \texttt{+},
+      \texttt{-} and \texttt{*}. 
 
-Decide whether the following strings 
-can be lexed in this language?
+      Decide whether the following strings can be lexed in
+      this language?
 
 \begin{enumerate}
 \item \texttt{"(a3+3)*b"}
@@ -88,14 +88,15 @@
 Observe the maximal munch rule and the priorities of your regular
 expressions that make the process of lexing unambiguous.)
 
-\item (Optional) Recall the definitions for $Der$ and $der$ from the lectures. 
-Prove by induction on $r$ the property that 
+\item (Optional) Recall the definitions for $Der$ and $der$
+      from the lectures. Prove by induction on $r$ the
+      property that 
 
 \[
 L(der\,c\,r) = Der\,c\,(L(r))
 \]
 
-holds.
+      holds.
 
 \end{enumerate}
 




