handouts/ho04.tex
changeset 874 ffe02fd574a5
parent 792 34132a854d03
child 936 0b5f06539a84
equal deleted inserted replaced
873:a25da86f7c8c 874:ffe02fd574a5
   420 \begin{center}
   420 \begin{center}
   421 $\ldots \dn Stars(\inj\,r\,c\,v\,::\,vs)$
   421 $\ldots \dn Stars(\inj\,r\,c\,v\,::\,vs)$
   422 \end{center}  
   422 \end{center}  
   423 
   423 
   424 \noindent It is a value of the right shape, namely $Stars$. It injected 
   424 \noindent It is a value of the right shape, namely $Stars$. It injected 
   425 $c$ into the first-value, which is in fact the value where we need to 
   425 $c$ into the first-value, which is in fact the value where we need in order to 
   426 undo the derivative. Remember again the shape of the derivative of $r^*$.
   426 undo the derivative. Remember again the shape of the derivative of $r^*$.
   427 In place where we chopped off the $c$, we now need to do the $\inj$ of $c$.
   427 In place where we chopped off the $c$, we now need to do the $\inj$ of $c$.
   428 Therefore $\inj\,r\,c\,v$ in the definition above. That is the same with
   428 Therefore $\inj\,r\,c\,v$ in the definition above. That is the same with
   429 the other clauses in $\inj$. 
   429 the other clauses in $\inj$. 
   430 
   430 
   745 is for strings where the first character is $c$, say, and the
   745 is for strings where the first character is $c$, say, and the
   746 rest of the string is $s$. We first build the derivative of
   746 rest of the string is $s$. We first build the derivative of
   747 $r$ with respect to $c$; simplify the resulting regular
   747 $r$ with respect to $c$; simplify the resulting regular
   748 expression. We continue lexing with the simplified regular
   748 expression. We continue lexing with the simplified regular
   749 expression and the string $s$. Whatever will be returned as
   749 expression and the string $s$. Whatever will be returned as
   750 value, we sill need to rectify using the $f_{rect}$ from the
   750 value, we still need to rectify using the $f_{rect}$ from the
   751 simplification and finally inject $c$ back into the
   751 simplification and finally inject $c$ back into the
   752 (rectified) value.
   752 (rectified) value.
   753 
   753 
   754 
   754 
   755 \subsubsection*{Records}
   755 \subsubsection*{Records}