ChengsongTanPhdThesis/Chapters/Inj.tex
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  1381 \]
  1381 \]
  1382 do not to contribute a POSIX lexical value,
  1382 do not to contribute a POSIX lexical value,
  1383 and therefore can be thrown away.
  1383 and therefore can be thrown away.
  1384 
  1384 
  1385 Ausaf et al. \cite{AusafDyckhoffUrban2016} 
  1385 Ausaf et al. \cite{AusafDyckhoffUrban2016} 
  1386 have come up with some simplification steps, however those steps
  1386 have come up with some simplification steps, 
       
  1387 and incorporated the simplification into $\lexer$.
       
  1388 They call this lexer $\textit{lexer}_{simp}$ and proved that
       
  1389 \[
       
  1390 	\lexer \; r\; s = \textit{lexer}_{simp} \; r \; s
       
  1391 \]
       
  1392 The function $\textit{lexer}_{simp}$
       
  1393 involves some fiddly manipulation of value rectification,
       
  1394 which we omit here.
       
  1395 however those steps
  1387 are not yet sufficiently strong, to achieve the above effects.
  1396 are not yet sufficiently strong, to achieve the above effects.
  1388 And even with these relatively mild simplifications, the proof
  1397 And even with these relatively mild simplifications, the proof
  1389 is already quite a bit more complicated than the theorem \ref{lexerCorrectness}.
  1398 is already quite a bit more complicated than the theorem \ref{lexerCorrectness}.
  1390 One would need to prove something like this: 
  1399 One would need to prove something like this: 
  1391 \[
  1400 \[