+\documentclass[toc]{beamer}
+
+\usepackage[british]{babel}
+\usepackage{tikz}
+\usepackage{fontspec}
+\setsansfont[Mapping=tex-text]{Linux Biolinum O}
+
+\author{Christophe Rhodes, Jan Moringen, David Lichteblau}
+\title{Generalizers}
+\subtitle{New Metaobjects for Generalized Dispatch}
+\date{5th May 2014}
+
+\pgfdeclareimage[height=0.4cm]{Goldsmiths}{Goldsmiths}
+\logo{\pgfuseimage{Goldsmiths}}
+
+\begin{document}
+
+\begin{frame}
+ \maketitle
+\end{frame}
+
+\begin{frame}
+ \tableofcontents
+\end{frame}
+
+\section{Introduction}
+
+\subsection{Method Dispatch}
+
+\begin{frame}
+ \frametitle{Method dispatch}
+ \framesubtitle{CL algorithm}
+
+ \begin{enumerate}[widest=10]
+ \item[7.6.6.1] \href{http://l1sp.org/cl/7.6.6.1}{Determining the
+ Effective Method}
+ \begin{enumerate}
+ \item[1] \href{http://l1sp.org/cl/7.6.6.1.1}{Selecting the
+ Applicable Methods}
+ \item[2] \href{http://l1sp.org/cl/7.6.6.1.2}{Sorting the
+ Applicable Methods by Precedence Order}
+ \item[3] \href{http://l1sp.org/cl/7.6.6.1.3}{Applying method
+ combination to the sorted list of applicable methods}
+ \end{enumerate}
+ \end{enumerate}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Method dispatch}
+ \framesubtitle{MOP for standard-generic-function}
+
+ \begin{itemize}
+ \item \href{http://l1sp.org/mop/compute-discriminating-function}{\tt compute-discriminating-function}
+ \item<3-> \href{http://l1sp.org/mop/compute-applicable-methods-using-classes}{\tt compute-applicable-methods-using-classes}
+ \item \href{http://l1sp.org/cl/compute-applicable-methods}{\tt compute-applicable-methods}
+ \item \href{http://l1sp.org/mop/compute-effective-method}{\tt compute-effective-method}
+ \item<2-> invoke the effective method somehow
+ \end{itemize}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Method dispatch}
+ \framesubtitle{compute-applicable-methods-using-classes}
+
+ \href{http://l1sp.org/mop/compute-applicable-methods-using-classes}{\texttt{compute-applicable-methods-using-classes}}
+ (gf list)
+ \begin{itemize}
+ \item \textit{gf} argument is the generic function being called
+ \item \textit{list} argument is a list of the \alert{classes} of the
+ objects in the required-argument position
+ \end{itemize}
+
+ \uncover<2->{
+ Computes sorted list of applicable methods of the generic function
+ \begin{itemize}
+ \item ... or defers to \texttt{compute-applicable-methods}
+ \end{itemize}
+ }
+ \uncover<3->{
+ If \texttt{c-a-m-u-c} succeeds, its return value is usable for all
+ actual arguments to the generic function of the same classes.
+ \begin{itemize}
+ \item effective method can be cached and reused!
+ \end{itemize}
+}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Method dispatch}
+ \framesubtitle{MOP class hierarchy}
+
+ \begin{tikzpicture}
+ \draw[white] (-1,-1) rectangle (10,3);
+ \node (specializer) at (4,2) {specializer};
+ \node (class) at (3,1) {class};
+ \node (eql-specializer) at (6,1) {eql-specializer};
+
+ \draw (specializer) -- (class);
+ \draw (specializer) -- (eql-specializer);
+
+ \only<2>{
+ \node (xxx) at (4.5,0) {?};
+ \draw (specializer) -- (xxx);
+ }
+ \end{tikzpicture}
+
+ \begin{flushright}
+ \scriptsize Jim Newton and Christophe Rhodes,
+ \href{http://dx/doi.org/10.3217/jucs-014-20-3370}{\textit{Custom
+ Specializers in Object-Oriented Lisp}}, 2008
+ \end{flushright}
+\end{frame}
+
+\subsection{Simple Example}
+
+\begin{frame}[fragile]
+ \frametitle{Custom specializers}
+ \framesubtitle{Example: dispatch on signum}
+
+\begin{verbatim}
+(defgeneric fact (n)
+ (:generic-function-class signum-generic-function))
+
+(defmethod fact ((n (signum 1)))
+ (* n (fact (1- n))))
+(defmethod fact ((n (signum 0)))
+ 1)
+
+(fact 0) ; => 1
+(fact 10) ; => 3628800
+(fact -1) ; error "no applicable method"
+\end{verbatim}
+\end{frame}
+
+\section{Generalizers}
+
+\begin{frame}
+ \frametitle{Generalizers}
+
+ How to replace \texttt{compute-applicable-methods-using-classes}
+ for custom specializers?
+
+ \vspace{1ex}
+
+ 1st try: \texttt{compute-applicable-methods-using-specializers}
+ \begin{itemize}
+ \item does not work!
+ \item (does not even make sense)
+ \end{itemize}
+
+ \vspace{1ex}
+
+ \uncover<2->{
+ 2nd try: distinguish between class as specializer (restrictive) and
+ class as equivalence class (expansive)
+ \begin{itemize}
+ \item works!
+ \item motivates the \texttt{generalizer} metaobject
+ \end{itemize}
+ }
+\end{frame}
+
+\subsection{Protocol}
+
+\begin{frame}
+ \frametitle{Generalizers}
+ \framesubtitle{The Generalizer protocol}
+
+ \begin{itemize}
+ \item \texttt{generalizer} [class]
+ \item \texttt{generalizer-of-using-class (gf ob)} [gf]
+
+ \item<2-> \texttt{specializer-accepts-generalizer-p (gf sp ge)} [gf]
+ \item<2-> \texttt{specializer-accepts-p (sp ob)} [gf]
+
+ \item<3-> \texttt{specializer< (gf sp1 sp2 ge)} [gf]
+
+ \item<4-> \texttt{generalizer-equal-hash-key (gf ge)} [gf]
+ \end{itemize}
+\end{frame}
+
+\subsection{Examples}
+
+\begin{frame}[fragile]
+ \frametitle{Generalizer protocol}
+ \framesubtitle{Example: dispatch on signum revisited}
+
+{\footnotesize
+\begin{verbatim}
+(defclass signum-generalizer (generalizer)
+ ((%signum :reader %signum :initarg :signum)))
+
+(defmethod generalizer-of-using-class
+ ((gf signum-generic-function) (arg real))
+ (make-instance 'signum-generalizer :signum (signum arg)))
+(defmethod generalizer-equal-hash-key
+ ((gf signum-generic-function) (g signum-generalizer))
+ (%signum g))
+
+(defmethod specializer-accepts-generalizer-p
+ ((gf signum-generic-function)
+ (s signum-specializer) (g signum-generalizer))
+ (if (= (%signum s) (%signum g))
+ (values t t)
+ (values nil t)))
+(defmethod specializer-accepts-p ((s signum-specializer) o)
+ (and (realp o) (= (%signum s) (signum o))))
+\end{verbatim}
+}
+\end{frame}
+
+\begin{frame}[fragile]
+ \frametitle{Generalizer protocol}
+ \framesubtitle{Example: HTTP content negotiation}
+
+{\footnotesize
+\begin{verbatim}
+(defgeneric foo (request)
+ (:generic-function-class accept-generic-function))
+(defmethod foo ((request t)) (http:406 request))
+
+(defmethod foo ((request (accept "text/html")))
+ "<!DOCTYPE html>
+<html><head><title>Foo</title></head>
+<body><p>Foo</p></body></html>")
+
+(defmethod foo ((request (accept "text/turtle")))
+ "@prefix foo: <http://example.org/ns#> .
+@prefix : <http://other.example.org/ns#> .
+foo:bar foo: : .")
+
+(foo "text/html,application/xml;q=0.9,*/*;q=0.8")
+ ; => text/html version
+(foo "text/turtle") ; => text/turtle version
+
+\end{verbatim}
+}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Generalizer protocol}
+ \framesubtitle{Example: HTTP content negotiation}
+
+\begin{itemize}
+\item non-trivial non-standard dispatch
+\item distinct specializer and generalizer objects
+\item dispatch decoupled from web server implementation:
+ \begin{itemize}
+ \item one new method on \texttt{specializer-accepts-p}
+ \item one new method on \texttt{generalizer-of-using-class}
+ \end{itemize}
+\end{itemize}
+\end{frame}
+
+\subsection{Efficiency}
+
+\begin{frame}
+ \frametitle{Generalizer protocol}
+ \framesubtitle{Efficiency}
+
+ \only<1>{
+ Signum Specializers:
+
+ \begin{center}
+ \begin{tabular}{lrl}
+ implementation & time (µs/call) & overhead\\
+ \hline
+ function & 0.6 & \\
+ standard-gf/fixnum & 1.2 & +100\%\\
+ signum-gf/one-arg-cache & 7.5 & +1100\%\\
+ signum-gf & 23 & +3800\%\\
+ signum-gf/no-cache & 240 & +41000\%\\
+ \end{tabular}
+ \end{center}
+ }
+\end{frame}
+\section{Conclusions}
+
+\begin{frame}
+ \frametitle{Related Work}
+
+ \begin{itemize}
+ \item \alert<+>{predicate dispatch}
+ \item \alert<+>{filtered functions}
+ \item \alert<+>{layered functions}
+ \item \alert<+>{prototype dispatch}
+ \end{itemize}
+
+ \only<1>{
+ \begin{flushright}
+ \scriptsize Michael Ernst, Craig Kaplan, and Craig Chambers.
+ \href{http://dx.doi.org/10.1007/BFb0054092}{\textit{Predicate
+ dispatching: A unified theory of dispatch}}, 1998.
+ \end{flushright}
+ }
+ \only<2>{
+ \begin{flushright}
+ \scriptsize Pascal Costanza, Charlotte Herzeel, Jorge Vallejos,
+ and Theo D'Hondt. \href{http://dx.doi.org/10.1145/1408681.1408685}{\textit{Filtered Dispatch}}, 2008.
+ \end{flushright}
+ }
+ \only<3>{
+ \begin{flushright}
+ \scriptsize Robert Hirschfeld, Pascal Costanza, and Oscar
+ Nierstrasz. \href{http://dx.doi.org/10.5381/jot.2008.7.3.a4}{\textit{Context-oriented
+ programming}}, 2008
+
+ \end{flushright}
+ } \only<4>{
+ \begin{flushright}
+ \scriptsize Lee Salzman and Jonathan
+ Aldrich. \href{http://dx.doi.org/10.1007/11531142_14}{\textit{Prototypes
+ with Multiple Dispatch: An Expressive and Dynamic Object
+ Model}}, 2005.
+ \end{flushright}
+ }
+\end{frame}
+
+\begin{frame}
+ \frametitle{Conclusions}
+
+ Customizing specializers is now:
+ \begin{itemize}
+ \item \alert{easier} (thanks to a simple protocol with local
+ computations);
+ \item \alert{better-performing} (10-30 times faster than naïve
+ implementation, though still 2--6 times slower than standard
+ dispatch);
+ \item \alert{straightforwardly available} (simply load into a
+ running SBCL).
+ \end{itemize}
+
+ \uncover<2->{
+ Currently working on:
+ \begin{itemize}
+ \item pattern specializers (optima) with automatic variable
+ bindings;
+ \item more flexibility on cacheing / dispatch computation.
+ \end{itemize}
+ }
+\end{frame}
+
+\end{document}