\documentclass[dvipsnames,14pt,t]{beamer}

\usepackage{../slides}

\usepackage{../langs}

\usepackage{../data}

\usepackage{../graphics}

\usepackage{../grammar}

\usepackage{soul}

\tikzset{onslide/.code args={<#1>#2}{%

  \only<#1>{\pgfkeysalso{#2}} % \pgfkeysalso doesn't change the path

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\makeatletter

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\makeatother

\lstset{morekeywords={def,if,then,else,write,read},keywordstyle=\color{codepurple}\bfseries}

% beamer stuff

\renewcommand{\slidecaption}{AFL 09, King's College London}

\newcommand{\bl}[1]{\textcolor{blue}{#1}}       

\begin{document}

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\begin{frame}[t]

\frametitle{%

  \begin{tabular}{@ {}c@ {}}

  \\[-3mm]

  \LARGE Automata and \\[-2mm] 

  \LARGE Formal Languages (9)\\[3mm] 

  \end{tabular}}

  \normalsize

  \begin{center}

  \begin{tabular}{ll}

  Email:  & christian.urban at kcl.ac.uk\\

  Office: & S1.27 (1st floor Strand Building)\\

  Slides: & KEATS (also home work is there)\\

  \end{tabular}

  \end{center}

\end{frame}

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\begin{frame}[c,fragile]

\frametitle{Functional Programming}

\footnotesize

\begin{textblock}{13}(0.9,3)

\begin{lstlisting}[basicstyle=\ttfamily, numbers=none]

def fib(n) = if n == 0 then 0 

             else if n == 1 then 1 

             else fib(n - 1) + fib(n - 2);

def fact(n) = if n == 0 then 1 else n * fact(n - 1);

def ack(m, n) = if m == 0 then n + 1

                else if n == 0 then ack(m - 1, 1)

                else ack(m - 1, ack(m, n - 1));

def gcd(a, b) = if b == 0 then a else gcd(b, a % b);                

\end{lstlisting}

\end{textblock}

\end{frame}

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\begin{frame}[c]

\frametitle{Fun Grammar}

\bl{

\begin{plstx}[rhs style=]

: \meta{Exp} ::= \meta{Var} | \meta{Num}{\hspace{3cm}}

             |   \code{if} \meta{BExp} \code{then} \meta{Exp} \code{else} \meta{Exp}

             |   \code{write} \meta{Exp} {\hspace{3cm}}

             |   \meta{Exp} ; \meta{Exp}

: \meta{BExp} ::= ...\\

: \meta{Decl} ::= \meta{Def} ; \meta{Decl}

             | \meta{Exp}\\

\end{plstx}}

\end{frame}

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\begin{frame}[c, fragile]

\footnotesize

abstract class Exp

abstract class BExp 

abstract class Decl

case class 

  Def(name: String, args: List[String], body: Exp) 

                                          extends Decl

case class Main(e: Exp) extends Decl

case class Call(name: String, args: List[Exp]) extends Exp

case class If(a: BExp, e1: Exp, e2: Exp) extends Exp

case class Write(e: Exp) extends Exp

case class Var(s: String) extends Exp

case class Num(i: Int) extends Exp

case class Aop(o: String, a1: Exp, a2: Exp) extends Exp

case class Sequ(e1: Exp, e2: Exp) extends Exp

case class Bop(o: String, a1: Exp, a2: Exp) extends BExp

\end{lstlisting}

\end{frame}

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\begin{center}

\begin{tabular}{lcl}

\texttt{Aop("+", a1, a2)} & $\Rightarrow$ & \texttt{...iadd}\\

\texttt{Aop("-", a1, a2)} & $\Rightarrow$ & \texttt{...isub}\\

\texttt{Aop("*", a1, a2)} & $\Rightarrow$ & \texttt{...imul}\\

\texttt{Aop("/", a1, a2)} & $\Rightarrow$ & \texttt{...idiv}\\

\texttt{Aop("\%", a1, a2)} & $\Rightarrow$ & \texttt{...irem}\\

\end{tabular}

\end{center}

\end{frame}

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\frametitle{Boolean Expressions}

\begin{center}

\begin{tikzpicture}[node distance=2mm and 4mm,

 block/.style={rectangle, minimum size=1cm, draw=black, line width=1mm},

 point/.style={rectangle, inner sep=0mm, minimum size=0mm, fill=red},

 skip loop/.style={red, line width=1mm, to path={-- ++(0,-10mm) -| (\tikztotarget)}}]

\node (A1) [point] {};

\node (b) [block, right=of A1] {code of \bl{$b$}};

\node (A2) [point, right=of b] {};

\node (cs1) [block, right=of A2] {code of \bl{$cs_1$}};

\node (A3) [point, right=of cs1] {};

\node (cs2) [block, right=of A3] {code of \bl{$cs_2$}};

\node (A4) [point, right=of cs2] {};

\only<1>{

\draw (A1) edge [->, red, line width=1mm] (b);

\draw (b) edge [->, red, line width=1mm] (A2);

\draw (A2) edge [skip loop] (A3);

\draw (A3) edge [->, red, line width=1mm] (cs2);

\draw (cs2) edge [->,red, line width=1mm] (A4);

\node [below=of cs1] {\raisebox{-5mm}{\small{}conditional jump}};}

\end{tikzpicture}

\end{center}

\begin{center}

\begin{tabular}{lcl}

\texttt{Bop("==", a1, a2)} & $\Rightarrow$ & \texttt{...if\_icmpne...}\\

\texttt{Bop("!=", a1, a2)} & $\Rightarrow$ & \texttt{...if\_icmpeq...}\\

\texttt{Bop("<", a1, a2)} & $\Rightarrow$ & \texttt{...if\_icmpge...}\\

\texttt{Bop("<=", a1, a2)} & $\Rightarrow$ & \texttt{...if\_icmpgt...}\\

\end{tabular}

\end{center}

\end{frame}

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\frametitle{Sequences}

...arg1...

pop

...arg1...

\end{lstlisting}

\end{frame}

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\frametitle{Write}

...arg...

dup

invokestatic XXX/XXX/write(I)V

\end{frame}

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\begin{frame}[c, fragile]

.method public static write(I)V 

   iload 0 

   invokevirtual java/io/PrintStream/println(I)V 

   return 

.end method

.method public static f (I...I)I

  .limit locals ??

  .limit stack ?? 

  ??

.end method

\end{lstlisting}

\end{frame}

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\begin{frame}[c, fragile]

\frametitle{Stack Estimation}

\footnotesize

\begin{center}

\begin{lstlisting}[language=Scala,basicstyle=\ttfamily, numbers=none]

def max_stack_exp(e: Exp): Int = e match {

  case Call(_, args) => args.map(max_stack_exp).sum

  case If(a, e1, e2) => max_stack_bexp(a) + 

  case Write(e) => max_stack_exp(e) + 1

  case Var(_) => 1

  case Num(_) => 1

  case Aop(_, a1, a2) => 

  case Sequ(e1, e2) => 

}

def max_stack_bexp(e: BExp): Int = e match {

  case Bop(_, a1, a2) => 

}

\end{lstlisting}

\end{center}

\end{frame}

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\begin{frame}[fragile]

\begin{textblock}{7}(1,2.5)\footnotesize

\begin{minipage}{6cm}

\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]

.method public static suc(I)I 

.limit locals 1

.limit stack 3

  iload 0

  ldc 1

  iadd

  ireturn

.end method 

\end{lstlisting}

\end{minipage}

\end{textblock}

\begin{textblock}{7}(6,8)

\begin{bubble}[5cm]\small

\begin{lstlisting}[language=Lisp,

                   basicstyle=\ttfamily, 

                   numbers=none,

                   xleftmargin=1mm]

def suc(x) = x + 1;

\end{lstlisting}

\end{bubble}

\end{textblock}

\end{frame}

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\begin{frame}[fragile]

\begin{minipage}{6cm}

\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]

.method public static add(II)I 

.limit locals 2

.limit stack 6

  iload 0

  ldc 0

  iload 1

  iload 0

  ldc 1

  isub

  iload 1

  ireturn

.end method

\end{lstlisting}

\end{minipage}

\end{textblock}

\begin{bubble}[7cm]\small

\begin{lstlisting}[language=Lisp,

                   basicstyle=\ttfamily, 

                   numbers=none,

                   xleftmargin=1mm]

def add(x, y) = 

    if x == 0 then y 

    else suc(add(x - 1, y));

\end{lstlisting}

\end{bubble}

\end{textblock}

\end{frame}

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\begin{frame}[fragile]

\frametitle{Factorial}

\begin{textblock}{7}(1,1.5)\footnotesize

\begin{minipage}{6cm}

\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none]

.method public static facT(II)I 

.limit locals 2

.limit stack 6

  iload 0

  ldc 0	

  if_icmpne If_else_2

  iload 1

  goto If_end_3

If_else_2:

  iload 0

  ldc 1

  isub

  iload 0

  iload 1

  imul

  invokestatic fact/fact/facT(II)I

If_end_3:

  ireturn

.end method 

\end{lstlisting}

\end{minipage}

\end{textblock}

\begin{textblock}{7}(6,7)

\begin{bubble}[7cm]\small

\begin{lstlisting}[language=Lisp,

                   basicstyle=\ttfamily, 

                   numbers=none,

                   xleftmargin=1mm]

def facT(n, acc) = 

  if n == 0 then acc 

  else facT(n - 1, n * acc);

\end{lstlisting}

\end{bubble}

\end{textblock}

\end{frame}

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\begin{frame}[fragile]

\begin{textblock}{7}(1,-0.2)\footnotesize

\begin{minipage}{6cm}

\begin{lstlisting}[language=JVMIS,basicstyle=\ttfamily, numbers=none, escapeinside={(*@}{@*)}]

.method public static facT(II)I 

.limit locals 2

.limit stack 7

(*@\hl{facT\_Start:} @*)

  iload 0

  ldc 0

  if_icmpne If_else_2

  iload 1

  goto If_end_3

If_else_2:

  iload 0

  ldc 1

  isub

  iload 0

  iload 1

  imul

  (*@\hl{istore 1} @*)

  (*@\hl{istore 0} @*)

  (*@\hl{goto facT\_Start} @*)

If_end_3:

  ireturn

.end method 

\end{lstlisting}

\end{minipage}

\end{textblock}

\begin{textblock}{7}(6,7)

\begin{bubble}[7cm]\small

\begin{lstlisting}[language=Lisp,

                   basicstyle=\ttfamily, 

                   numbers=none,

                   xleftmargin=1mm]

def facT(n, acc) = 

  if n == 0 then acc 

  else facT(n - 1, n * acc);

\end{lstlisting}

\end{bubble}

\end{textblock}

\end{frame}

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\begin{frame}[c, fragile]

\frametitle{Tail Recursion}

A call to \texttt{f(args)} is usually compiled as\medskip

{\small\begin{lstlisting}[basicstyle=\ttfamily, numbers=none]

  args onto stack

  invokestatic  .../f 

\end{lstlisting}}\pause

A call is in tail position provided:\medskip

{\small\begin{itemize}

\item \texttt{if Bexp then \hl{Exp} else \hl{Exp}}

\item \texttt{Exp ; \hl{Exp}}

\item \texttt{Exp  op Exp}

\end{itemize}}\medskip

then a call \texttt{f(args)} can be compiled as\medskip\small