
diff -r 40b7efa5fbed -r 02bc5af1c5f2 coursework/cw05.tex
--- a/coursework/cw05.tex	Tue Sep 01 12:44:07 2020 +0100
+++ b/coursework/cw05.tex	Tue Sep 01 15:57:55 2020 +0100
@@ -5,237 +5,33 @@
 
 \begin{document}
 
-\section*{Coursework (Strand 2)}
-
-\noindent This coursework is worth 20\% and is due on \cwISABELLE{} at
-18:00. You are asked to prove the correctness of the regular expression
-matcher from the lectures using the Isabelle theorem prover. You need to
-submit a theory file containing this proof and also a document
-describing your proof. The Isabelle theorem prover is available from
-
-\begin{center}
-\url{http://isabelle.in.tum.de}
-\end{center}
-
-\noindent This is an interactive theorem prover, meaning that
-you can make definitions and state properties, and then help
-the system with proving these properties. Sometimes the proofs
-are also completely automatic. There is a shortish user guide for
-Isabelle, called ``Programming and Proving in Isabelle/HOL''
-at
-
-\begin{center}
-\url{http://isabelle.in.tum.de/documentation.html}
-\end{center}
-
-\noindent
-and also a longer (free) book at
-
-\begin{center}
-\url{http://www.concrete-semantics.org}
-\end{center}
-
-\noindent The Isabelle theorem prover is operated through the
-jEdit IDE, which might not be an editor that is widely known.
-JEdit is documented in
+\section*{Coursework 5}
 
-\begin{center}
-\url{http://isabelle.in.tum.de/dist/Isabelle2014/doc/jedit.pdf}
-\end{center}
-
-
-\noindent If you need more help or you are stuck somewhere,
-please feel free to contact me (christian.urban at kcl.ac.uk). I
-am one of the main developers of Isabelle and have used it for
-approximately 16 years. One of the success stories of
-Isabelle is the recent verification of a microkernel operating
-system by an Australian group, see \url{http://sel4.systems}.
-Their operating system is the only one that has been proved
-correct according to its specification and is used for
-application where high assurance, security and reliability is
-needed (like in helicopters which fly over enemy territory).
-
-
-\subsection*{The Task}
-
-In this coursework you are asked to prove the correctness of the
-regular expression matcher from the lectures in Isabelle.  The matcher
-should be able to deal with the usual (basic) regular expressions
-
-\[
-\ZERO,\; \ONE,\; c,\; r_1 + r_2,\; r_1 \cdot r_2,\; r^*
-\]
-
-\noindent
-but also with the following extended regular expressions:
-
-\begin{center}
-\begin{tabular}{ll}
-  $r^{\{n\}}$ & exactly $n$-times\\
-  $r^{\{..m\}}$ & zero or more times $r$ but no more than $m$-times\\
-  $r^{\{n..\}}$ & at least $n$-times $r$\\
-  $r^{\{n..m\}}$ & at least $n$-times $r$ but no more than $m$-times\\
-  $\sim{}r$ & not-regular-expression of $r$\\
-\end{tabular}
-\end{center}
 
 
-\noindent
-You need to first specify what the matcher is
-supposed to do and then to implement the algorithm. Finally you need
-to prove that the algorithm meets the specification.  The first two
-parts are relatively easy, because the definitions in Isabelle will
-look very similar to the mathematical definitions from the lectures or
-the Scala code that is supplied at KEATS. For example very similar to
-Scala, regular expressions are defined in Isabelle as an inductive
-datatype:
-
-\begin{lstlisting}[language={},numbers=none]
-datatype rexp =
-  ZERO
-| ONE
-| CHAR char
-| SEQ rexp rexp
-| ALT rexp rexp
-| STAR rexp
-\end{lstlisting}
-
-\noindent The meaning of regular expressions is given as 
-usual:
-
-\begin{center}
-\begin{tabular}{rcl@{\hspace{10mm}}l}
-$L(\ZERO)$  & $\dn$ & $\varnothing$   & \pcode{ZERO}\\
-$L(\ONE)$     & $\dn$ & $\{[]\}$        & \pcode{ONE}\\ 
-$L(c)$            & $\dn$ & $\{[c]\}$       & \pcode{CHAR}\\
-$L(r_1 + r_2)$     & $\dn$ & $L(r_1) \cup L(r_2)$ & \pcode{ALT}\\
-$L(r_1 \cdot r_2)$ & $\dn$ & $L(r_1) \,@\, L(r_2)$ & \pcode{SEQ}\\
-$L(r^*)$           & $\dn$ & $(L(r))^*$ & \pcode{STAR}\\
-\end{tabular}
-\end{center}
+\noindent This coursework is worth 12\% and is due on \cwFIVE{} at
+18:00. You are asked to implement a compiler targetting the LLVM-IR.
+You can do the implementation in any programming
+language you like, but you need to submit the source code with which
+you answered the questions, otherwise a mark of 0\% will be
+awarded. You should use the lexer from the previous coursework for the
+parser.  Please package everything(!) in a zip-file that creates a
+directory with the name \texttt{YournameYourFamilyname} on my end.
 
-\noindent You would need to implement this function in order
-to state the theorem about the correctness of the algorithm.
-The function $L$ should in Isabelle take a \pcode{rexp} as
-input and return a set of strings. Its type is
-therefore 
-
-\begin{center}
-\pcode{L} \pcode{::} \pcode{rexp} $\Rightarrow$ \pcode{string set}
-\end{center}
-
-\noindent Isabelle treats strings as an abbreviation for lists
-of characters. This means you can pattern-match strings like
-lists. The union operation on sets (for the \pcode{ALT}-case)
-is a standard definition in Isabelle, but not the
-concatenation operation on sets and also not the
-star-operation. You would have to supply these definitions.
-The concatenation operation can be defined in terms of the
-append function, written \code{_ @ _} in Isabelle, for lists.
-The star-operation can be defined as a ``big-union'' of 
-powers, like in the lectures, or directly as an inductive set.
-
-The functions for the matcher are shown in
-Figure~\ref{matcher}. The theorem that needs to be proved is
-
-\begin{lstlisting}[numbers=none,language={},keywordstyle=\color{black}\ttfamily,mathescape]
-theorem 
-  "matches r s $\longleftrightarrow$ s $\in$ L r"
-\end{lstlisting}
-
-\noindent which states that the function \emph{matches} is
-true if and only if the string is in the language of the
-regular expression. A proof for this lemma will need
-side-lemmas about \pcode{nullable} and \pcode{der}. An example
-proof in Isabelle that will not be relevant for the theorem
-above is given in Figure~\ref{proof}.
+\subsection*{Disclaimer\alert}
 
-\begin{figure}[p]
-\begin{lstlisting}[language={},keywordstyle=\color{black}\ttfamily,mathescape]
-fun 
-  nullable :: "rexp $\Rightarrow$ bool"
-where
-  "nullable ZERO = False"
-| "nullable ONE = True"
-| "nullable (CHAR _) = False"
-| "nullable (ALT r1 r2) = (nullable(r1) $\vee$ nullable(r2))"
-| "nullable (SEQ r1 r2) = (nullable(r1) $\wedge$ nullable(r2))"
-| "nullable (STAR _) = True"
-
-fun 
-  der :: "char $\Rightarrow$ rexp $\Rightarrow$ rexp"
-where
-  "der c ZERO = ZERO"
-| "der c ONE = ZERO"
-| "der c (CHAR d) = (if c = d then ONE else ZERO)"
-| "der c (ALT r1 r2) = ALT (der c r1) (der c r2)"
-| "der c (SEQ r1 r2) = 
-     (if (nullable r1) then ALT (SEQ (der c r1) r2) (der c r2)
-                       else SEQ (der c r1) r2)"
-| "der c (STAR r) = SEQ (der c r) (STAR r)"
-
-fun 
-  ders :: "rexp $\Rightarrow$ string $\Rightarrow$ rexp"
-where
-  "ders r [] = r"
-| "ders r (c # s) = ders (der c r) s"
-
-fun 
-  matches :: "rexp $\Rightarrow$ string $\Rightarrow$ bool"
-where
-  "matches r s = nullable (ders r s)" 
-\end{lstlisting}
-\caption{The definition of the matcher algorithm in 
-Isabelle.\label{matcher}}
-\end{figure}
+It should be understood that the work you submit represents your own
+effort. You have not copied from anyone else. An exception is the
+Scala code I showed during the lectures or uploaded to KEATS, which
+you can both use. You can also use your own code from the CW~1 --
+CW~4.
 
-\begin{figure}[p]
-\begin{lstlisting}[language={},keywordstyle=\color{black}\ttfamily,mathescape]
-fun 
-  zeroable :: "rexp $\Rightarrow$ bool"
-where
-  "zeroable ZERO = True"
-| "zeroable ONE = False"
-| "zeroable (CHAR _) = False"
-| "zeroable (ALT r1 r2) = (zeroable(r1) $\wedge$ zeroable(r2))"
-| "zeroable (SEQ r1 r2) = (zeroable(r1) $\vee$ zeroable(r2))"
-| "zeroable (STAR _) = False"
+
+\subsection*{Question 1}
 
-lemma
-  "zeroable r $\longleftrightarrow$ L r = {}"
-proof (induct)
-  case (ZERO)
-  have "zeroable ZERO" "L ZERO = {}" by simp_all
-  then show "zeroable ZERO $\longleftrightarrow$ (L ZERO = {})" by simp
-next
-  case (ONE)
-  have "$\neg$ zeroable ONE" "L ONE = {[]}" by simp_all
-  then show "zeroable ONE $\longleftrightarrow$ (L ONE = {})" by simp
-next
-  case (CHAR c)
-  have "$\neg$ zeroable (CHAR c)" "L (CHAR c) = {[c]}" by simp_all
-  then show "zeroable (CHAR c) $\longleftrightarrow$ (L (CHAR c) = {})" by simp
-next 
-  case (ALT r1 r2)
-  have ih1: "zeroable r1 $\longleftrightarrow$ L r1 = {}" by fact
-  have ih2: "zeroable r2 $\longleftrightarrow$ L r2 = {}" by fact
-  show "zeroable (ALT r1 r2) $\longleftrightarrow$ (L (ALT r1 r2) = {})" 
-    using ih1 ih2 by simp
-next
-  case (SEQ r1 r2)
-  have ih1: "zeroable r1 $\longleftrightarrow$ L r1 = {}" by fact
-  have ih2: "zeroable r2 $\longleftrightarrow$ L r2 = {}" by fact
-  show "zeroable (SEQ r1 r2) $\longleftrightarrow$ (L (SEQ r1 r2) = {})" 
-    using ih1 ih2 by (auto simp add: Conc_def)
-next
-  case (STAR r)
-  have "$\neg$ zeroable (STAR r)" "[] $\in$ L (r) ^ 0" by simp_all
-  then show "zeroable (STAR r) $\longleftrightarrow$ (L (STAR r) = {})" 
-    by (simp (no_asm) add: Star_def) blast
-qed
-\end{lstlisting}
-\caption{An Isabelle proof about the function \texttt{zeroable}.\label{proof}}
-\end{figure}
+\subsection*{Question 2}
+
+\subsection*{Question 3}
 
 \end{document}
 




