figures

[paper-els-specializers.git] / els-specializers.org

#+TITLE: Generalizers: New Metaobjects for Generalized Dispatch
#+AUTHOR: Christophe Rhodes, Jan Moringen, David Lichteblau
#+OPTIONS: toc:nil

#+LaTeX_CLASS: acm_proc_article-sp
#+LaTeX_HEADER: \DeclareTextFontCommand{\texttt}{\ttfamily\hyphenchar\font=45\relax}

#+begin_src elisp :exports none
;;; use C-x C-e on this if org refuses to export
(add-to-list 'org-latex-classes
             '("acm_proc_article-sp" "\\documentclass{acm_proc_article-sp}"
               ("\\section{%s}" . "\\section*{%s}")
               ("\\subsection{%s}" . "\\subsection*{%s}")
               ("\\subsubsection{%s}" . "\\subsubsection*{%s}")
               ("\\paragraph{%s}" . "\\paragraph*{%s}")
               ("\\subparagraph{%s}" . "\\subparagraph*{%s}")))
(set (make-local-variable 'org-latex-title-command)
     "\\numberofauthors{3}
\\author{
\\alignauthor Christophe Rhodes\\\\
  \\affaddr{Department of Computing}\\\\
  \\affaddr{Goldsmiths, University of London}\\\\
  \\affaddr{London SE14 6NW}\\\\
  \\email{c.rhodes@gold.ac.uk}
\\alignauthor Jan Moringen\\\\
  \\affaddr{Universität Bielefeld}\\\\
  \\affaddr{Technische Fakultät}\\\\
  \\affaddr{33594 Bielefeld}\\\\
  \\email{jmoringe@techfak.uni-bielefeld.de}
\\alignauthor David Lichteblau\\\\
  \\affaddr{ZenRobotics Ltd}\\\\
  \\affaddr{Vilhonkatu 5 A}\\\\
  \\affaddr{FI-00100 Helsinki}\\\\
  \\email{david@lichteblau.com}
}
\\maketitle")
#+end_src

#+begin_abstract
This paper introduces a new metaobject, the generalizer, which
complements the existing specializer metaobject.  With the help of
examples, we show that this metaobject allows for the efficient
implementation of complex non-class-based dispatch within the
framework of existing metaobject protocols.  We present our
modifications to the generic function invocation protocol from the
/Art of the Metaobject Protocol/; in combination with previous work,
this produces a fully-functional extension of the existing mechanism
for method selection and combination, including support for method
combination completely independent from method selection.  We discuss
our implementation, within the SBCL implementation of Common Lisp, and
in that context compare the performance of the new protocol with the
standard one, demonstrating that the new protocol can be tolerably
efficient.
#+end_abstract

#+begin_LaTeX
\category{D.1}{Software}{Programming Techniques}[Object-oriented Programming]
\category{D.3.3}{Programming Languages}{Language Constructs and Features}
\terms{Languages, Design}
\keywords{generic functions, specialization-oriented programming, method selection, method combination}
#+end_LaTeX

* Introduction
  The revisions to the original Common Lisp language \cite{CLtL}
  included the detailed specification of an object system, known as
  the Common Lisp Object System (CLOS), which was eventually
  standardized as part of the ANSI Common Lisp standard \cite{CLtS}.
  The object system as presented to the standardization committee was
  formed of three chapters.  The first two chapters covered programmer
  interface concepts and the functions in the programmer interface
  \cite[Chapter 28]{CLtL2} and were largely incorporated into the
  final standard; the third chapter, covering a Metaobject Protocol
  (MOP) for CLOS, was not.

  Nevertheless, the CLOS MOP has proven to be a robust design, and
  while many implementations have derived their implementations of
  CLOS from either the Closette illustrative implementation in
  \cite{AMOP}, or the Portable Common Loops implementation of CLOS
  from Xerox Parc, there have been largely from-scratch
  reimplementations of CLOS (in CLISP[fn:1] and CCL[fn:2], at least)
  incorporating substantial fractions of the Metaobject Protocol as
  described.

  #+CAPTION:    MOP Design Space
  #+LABEL:      fig:mopdesign
  #+ATTR_LATEX: width=\linewidth float
  [[file:figures/mop-design-space.pdf]]

  Although it has stood the test of time, the CLOS MOP is neither
  without issues (e.g. semantic problems with =make-method-lambda=
  \cite{Costanza.Herzeel:2008}; useful functions such as
  =compute-effective-slot-definition-initargs= being missing from the
  standard) nor is it a complete framework for the metaprogrammer to
  implement all conceivable variations of object-oriented behaviour.
  While metaprogramming offers some possibilities for customization of
  the object system behaviour, those possibilities cannot extend
  arbitrarily in all directions (conceptually, if a given object
  system is a point in design space, then a MOP for that object system
  allows exploration of a region of design space around that point;
  see figure \ref{fig:mopdesign}).  In the case of the CLOS MOP, there is
  still an expectation that functionality is implemented with methods
  on generic functions, acting on objects with slots; it is not
  possible, for example, to transparently implement support for
  “message not understood” as in the message-passing paradigm, because
  the analogue of messages (generic functions) need to be defined
  before they are used.

  Nevertheless, the MOP is flexible, and is used for a number of
  things, including: documentation generation (where introspection in
  the MOP is used to extract information from a running system);
  object-relational mapping and other approaches to object
  persistence; alternative backing stores for slots (hash-tables or
  symbols); and programmatic construction of metaobjects, for example
  for IDL compilers and model transformations.

  One area of functionality where there is scope for customization by
  the metaprogrammer is in the mechanics and semantics of method
  applicability and dispatch.  While in principle AMOP allows
  customization of dispatch in various different ways (the
  metaprogrammer can define methods on protocol functions such as
  =compute-applicable-methods=,
  =compute-applicable-methods-using-classes=), for example, in
  practice implementation support for this was weak until relatively
  recently[fn:3].

  Another potential mechanism for customizing dispatch is implicit in
  the class structure defined by AMOP: standard specializer objects
  (instances of =class= and =eql-specializer=) are generalized
  instances of the =specializer= protocol class, and in principle
  there are no restrictions on the metaprogrammer constructing
  additional subclasses.  Previous work \cite{Newton.Rhodes:2008} has
  explored the potential for customizing generic function dispatch
  using extended specializers, but there the metaprogrammer must
  override the entirety of the generic function invocation protocol
  (from =compute-discriminating-function= on down), leading to toy
  implementations and duplicated effort.

  This paper introduces a protocol for efficient and controlled
  handling of new subclasses of =specializer=.  In particular, it
  introduces the =generalizer= protocol class, which generalizes the
  return value of =class-of= in method applicability computation, and
  allows the metaprogrammer to hook into cacheing schemes to avoid
  needless recomputation of effective methods for sufficiently similar
  generic function arguments (See Figure\nbsp\ref{fig:dispatch}).

  #+CAPTION:    Dispatch Comparison
  #+LABEL:      fig:dispatch
  #+ATTR_LATEX: width=\linewidth float
  [[file:figures/dispatch-relationships.pdf]]

  The remaining sections in this paper can be read in any order.  We
  give some motivating examples in section [[#Examples]], including
  reimplementations of examples from previous work, as well as
  examples which are poorly supported by previous protocols.  We
  describe the protocol itself in section [[#Protocol]], describing each
  protocol function in detail and, where applicable, relating it to
  existing protocol functions within the CLOS MOP.  We survey related
  work in more detail in section [[#Related Work]], touching on work on
  customized dispatch schemes in other environments.  Finally, we draw
  our conclusions from this work, and indicate directions for further
  development, in section [[#Conclusions]]; reading that section before the
  others indicates substantial trust in the authors' work.
* Examples
  :PROPERTIES:
  :CUSTOM_ID: Examples
  :END:
  In this section, we present a number of examples of dispatch
  implemented using our protocol, which we describe in section
  [[#Protocol]].  For reasons of space, the metaprogram code examples in
  this section do not include some of the necessary support code to
  run; complete implementations of each of these cases, along with the
  integration of this protocol into the SBCL implementation
  \cite{Rhodes:2008} of Common Lisp, are included in an appendix / in
  the accompanying repository snapshot / at this location.

  A note on terminology: we will attempt to distinguish between the
  user of an individual case of generalized dispatch (the
  “programmer”), the implementor of a particular case of generalized
  dispatch (the “metaprogrammer”), and the authors as the designers
  and implementors of our generalized dispatch protocol (the
  “metametaprogammer”, or more likely “we”).
** CONS specializers
   :PROPERTIES:
   :CUSTOM_ID: Cons
   :END:
   One motivation for the use of generalized dispatch is in an
   extensible code walker: a new special form can be handled simply by
   writing an additional method on the walking generic function,
   seamlessly interoperating with all existing methods. In this
   use-case, dispatch is performed on the first element of lists.
   Semantically, we allow the programmer to specialize any argument of
   methods with a new kind of specializer, =cons-specializer=, which
   is applicable if and only if the corresponding object is a =cons=
   whose =car= is =eql= to the symbol associated with the
   =cons-specializer=; these specializers are more specific than the
   =cons= class, but less specific than an =eql-specializer= on any
   given =cons=.

   The programmer code using these specializers is unchanged from
   \cite{Newton.Rhodes:2008}; the benefits of the protocol described
   here are: that the separation of concerns is complete – method
   selection is independent of method combination – and that the
   protocol allows for efficient implementation where possible, even
   when method selection is customized.  In an application such as
   walking source code, we would expect to encounter special forms
   (distinguished by particular atoms in the =car= position) multiple
   times, and hence to dispatch to the same effective method
   repeatedly.  We discuss the efficiency aspects of the protocol in
   more detail in section [[#Memoization]]; we present the metaprogrammer
   code to implement the =cons-specializer= below.

#+begin_src lisp
(defclass cons-specializer (specializer)
  ((%car :reader %car :initarg :car)))
(defclass cons-generalizer (generalizer)
  ((%car :reader %car :initarg :car)))
(defmethod generalizer-of-using-class
    ((gf cons-generic-function) arg)
  (typecase arg
    ((cons symbol)
     (make-instance 'cons-generalizer
                    :car (car arg)))
    (t (call-next-method))))
(defmethod generalizer-equal-hash-key
    ((gf cons-generic-function)
     (g cons-generalizer))
  (%car g))
(defmethod specializer-accepts-generalizer-p
    ((gf cons-generic-function)
     (s cons-specializer)
     (g cons-generalizer))
  (if (eql (%car s) (%car g))
      (values t t)
      (values nil t)))
(defmethod specializer-accepts-p
    ((s cons-specializer) o)
  (and (consp o) (eql (car o) (%car s))))
#+end_src

The code above shows a minimal use of our protocol.  We have elided
some support code for parsing and unparsing specializers, and for
handling introspective functions such as finding generic functions for
a given specializer.  We have also elided methods on the protocol
functions =specializer<= and =same-specializer-p=; for
=cons-specializer= objects, specializer ordering is trivial, as only
one =cons-specializer= (up to equality) can ever be applicable to any
given argument.  See section [[#Accept]] for a case where specializer
ordering is non-trivial.

As in \cite{Newton.Rhodes:2008}, the programmer can use these
specializers to implement a modular code walker, where they define one
method per special operator.  We show two of those methods below, in
the context of a walker which checks for unused bindings and uses of
unbound variables.

#+begin_src
(defgeneric walk (form env stack)
  (:generic-function-class cons-generic-function))
(defmethod walk
    ((expr (cons lambda)) env call-stack)
  (let ((lambda-list (cadr expr))
        (body (cddr expr)))
    (with-checked-bindings
        ((bindings-from-ll lambda-list)
         env call-stack)
      (dolist (form body)
        (walk form env (cons form call-stack))))))
(defmethod walk
    ((expr (cons let)) env call-stack)
  (flet ((let-binding (x)
           (walk (cadr x) env
                 (cons (cadr x) call-stack))
           (cons (car x)
                 (make-instance 'binding))))
    (with-checked-bindings
        ((mapcar #'let-binding (cadr expr))
          env call-stack)
      (dolist (form (cddr expr))
        (walk form env (cons form call-stack))))))
#+end_src

   Note that in this example there is no strict need for
   =cons-specializer= and =cons-generalizer= to be distinct classes.
   In standard generic function dispatch, the =class= functions both
   as the specializer for methods and as the generalizer for generic
   function arguments; we can think of the dispatch implemented by
   =cons-specializer= objects as providing for subclasses of the
   =cons= class distinguished by the =car= of the =cons=.  This
   analogy also characterizes those use cases where the metaprogrammer
   could straightforwardly use filtered dispatch
   \cite{Costanza.etal:2008} to implement their dispatch semantics.
   We will see in section [[#Accept]] an example of a case where filtered
   dispatch is incapable of straightforwardly expressing the dispatch,
   but first we present our implementation of the motivating case from
   \cite{Costanza.etal:2008}.
** SIGNUM specializers
   :PROPERTIES:
   :CUSTOM_ID: Signum
   :END:
   Our second example of the implementation and use of generalized
   specializers is a reimplementation of one of the examples in
   \cite{Costanza.etal:2008}: specifically, the factorial function.
   Here, dispatch will be performed based on the =signum= of the
   argument, and again, at most one method with a =signum= specializer
   will be applicable to any given argument, which makes the structure
   of the specializer implementation very similar to the =cons=
   specializers in the previous section.

   The metaprogrammer has chosen in the example below to compare
   signum values using \texttt{=}, which means that a method with
   specializer =(signum 1)= will be applicable to positive
   floating-point arguments (see the first method on
   =specializer-accepts-generalizer-p= and the method on
   =specializer-accepts-p= below).  This leads to one subtle
   difference in behaviour compared to that of the =cons=
   specializers: in the case of =signum= specializers, the /next/
   method after any =signum= specializer can be different, depending
   on the class of the argument.  This aspect of the dispatch is
   handled by the second method on =specializer-accepts-generalizer-p=
   below.

#+begin_src lisp
(defclass signum-specializer (specializer)
  ((%signum :reader %signum :initarg :signum)))
(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-generalizer-p
    ((gf signum-generic-function)
     (s specializer)
     (g signum-generalizer))
  (specializer-accepts-generalizer-p
   gf s (class-of (%signum g))))

(defmethod specializer-accepts-p
    ((s signum-specializer) o)
  (and (realp o) (= (%signum s) (signum o))))
#+end_src

   Given these definitions, and once again some more straightforward
   ones elided for reasons of space, the programmer can implement the
   factorial function as follows:

#+begin_src lisp
(defgeneric fact (n)
  (:generic-function-class signum-generic-function))
(defmethod fact ((n (signum 0))) 1)
(defmethod fact ((n (signum 1))) (* n (fact (1- n))))
#+end_src

   The programmer does not need to include a method on =(signum -1)=,
   as the standard =no-applicable-method= protocol will automatically
   apply to negative real or non-real arguments.
** Accept HTTP header specializers
   :PROPERTIES:
   :CUSTOM_ID: Accept
   :END:
   In this section, we implement a non-trivial form of dispatch.  The
   application in question is a web server, and specifically to allow
   the programmer to support RFC 2616 \cite{rfc2616} content
   negotiation, of particular interest to publishers and consumers of
   REST-style Web APIs.

   The basic mechanism in content negotiation is as follows: the web
   client sends an HTTP request with an =Accept= header, which is a
   string describing the media types it is willing to receive as a
   response to the request, along with numerical preferences.  The web
   server compares these stated client preferences with the resources
   it has available to satisfy this request, and sends the best
   matching resource in its response.

   For example, a graphical web browser might send an =Accept= header
   of =text/html,application/xml;q=0.9,*/*;q=0.8= for a request of a
   resource typed in to the URL bar.  This should be interpreted as
   meaning that: if the server can provide content of type =text/html=
   (i.e. HTML) for that resource, then it should do so.  Otherwise, if
   it can provide =application/xml= content (i.e. XML of any schema),
   then that should be provided; failing that, any other content type
   is acceptable.

   In the case where there are static files on the filesystem, and the
   web server must merely select between them, there is not much more
   to say.  However, it is not unusual for a web service to be backed
   by some other form of data, and responses computed and sent on the
   fly, and in these circumstances the web server must compute which
   of its known output formats it can use to satisfy the request
   before actually generating the best matching response.  This can be
   modelled as one generic function responsible for generating the
   response, with methods corresponding to content-types -- and the
   generic function must then perform method selection against the
   request's =Accept= header to compute the appropriate response.

   The =accept-specializer= below implements this dispatch.  It depends
   on a lazily-computed =tree= slot to represent the information in
   the accept header (generated by =parse-accept-string=), and a
   function =q= to compute the (defaulted) preference level for a
   given content-type and =tree=; then, method selection and ordering
   involves finding the =q= for each =accept-specializer='s content
   type given the =tree=, and sorting them according to the preference
   level.

#+begin_src lisp
(defclass accept-specializer (specializer)
  ((media-type :initarg :media-type :reader media-type)))
(defclass accept-generalizer (generalizer)
  ((header :initarg :header :reader header)
   (tree)
   (next :initarg :next :reader next)))
(defmethod generalizer-equal-hash-key
    ((gf accept-generic-function)
     (g accept-generalizer))
  `(accept-generalizer ,(header g)))
(defmethod specializer-accepts-generalizer-p
    ((gf accept-generic-function)
     (s accept-specializer)
     (g accept-generalizer))
  (values (q (media-type s) (tree g)) t))
(defmethod specializer-accepts-generalizer-p
    ((gf accept-generic-function)
     (s specializer)
     (g accept-generalizer))
  (specializer-accepts-generalizer-p
   gf s (next g)))

(defmethod specializer<
    ((gf accept-generic-function)
     (s1 accept-specializer)
     (s2 accept-specializer)
     (g accept-generalizer))
  (let ((m1 (media-type s1))
        (m2 (media-type s2))
        (tree (tree g)))
    (cond
      ((string= m1 m2) '=)
      (t (let ((q1 (q m1 tree)))
               (q2 (q m2 tree))))
           (cond
             ((= q1 q2) '=)
             ((< q1 q2) '>)
             (t '<))))))
#+end_src

   The metaprogrammer can then add support for objects representing
   client requests, such as instances of the =request= class in the
   Hunchentoot web server, by translating these into
   =accept-generalizer= instances.  The code below implements this, by
   defining the computation of a =generalizer= object for a given
   request, and specifying how to compute whether the specializer
   accepts the given request object (=q= returns a number between 0
   and 1 if any pattern in the =tree= matches the media type, and
   =nil= if the media type cannot be matched at all).

#+begin_src
(defmethod generalizer-of-using-class
    ((gf accept-generic-function)
     (arg tbnl:request))
  (make-instance 'accept-generalizer
                 :header (tbnl:header-in :accept arg)
                 :next (call-next-method)))
(defmethod specializer-accepts-p
    ((s accept-specializer)
     (o tbnl:request))
  (let* ((accept (tbnl:header-in :accept o))
         (tree (parse-accept-string accept))
         (q (q (media-type s) tree)))
    (and q (> q 0))))
#+end_src

   This dispatch cannot be implemented using filtered dispatch, except
   by generating anonymous classes with all the right mime-types as
   direct superclasses in dispatch order; the filter would generate
#+begin_src lisp
(ensure-class nil :direct-superclasses
 '(text/html image/webp ...))
#+end_src
   and dispatch would operate using those anonymous classes.  While
   this is possible to do, it is awkward to express content-type
   negotiation in this way, as it means that the dispatcher must know
   about the universe of mime-types that clients might declare that
   they accept, rather than merely the set of mime-types that a
   particular generic function is capable of serving; handling
   wildcards in accept strings is particularly awkward in the
   filtering paradigm.

   Note that in this example, the method on =specializer<= involves a
   non-trivial ordering of methods based on the =q= values specified
   in the accept header (whereas in sections [[#Cons]] and [[#Signum]] only a
   single extended specializer could be applicable to any given
   argument).

   Also note that the accept specializer protocol is straightforwardly
   extensible to other suitable objects; for example, one simple
   debugging aid is to define that an =accept-specializer= should be
   applicable to =string= objects.  This can be done in a modular
   fashion (see the code below, which can be completely disconnected
   from the code for Hunchentoot request objects), and generalizes to
   dealing with multiple web server libraries, so that
   content-negotiation methods are applicable to each web server's
   request objects.

#+begin_src lisp
(defmethod generalizer-of-using-class
    ((gf accept-generic-function)
     (s string))
  (make-instance 'accept-generalizer
                 :header s
                 :next (call-next-method)))
(defmethod specializer-accepts-p
    ((s accept-specializer) (o string))
  (let* ((tree (parse-accept-string o))
         (q (q (media-type s) tree)))
    (and q (> q 0))))
#+end_src

   The =next= slot in the =accept-generalizer= is used to deal with
   the case of methods specialized on the classes of objects as well
   as on the acceptable media types; there is a method on
   =specializer-accepts-generalizer-p= for specializers that are not
   of type =accept-specializer= which calls the generic function again
   with the next generalizer, so that methods specialized on the
   classes =tbnl:request= and =string= are treated as applicable to
   corresponding objects, though less specific than methods with
   =accept-specializer= specializations.

** COMMENT Pattern / xpattern / regex / optima
   Here's the /really/ interesting bit, but on the other hand we're
   probably going to run out of space, and the full description of
   these is going to take us into =make-method-lambda= territory.
   A second paper?  Future work?
* Protocol
  :PROPERTIES:
  :CUSTOM_ID: Protocol
  :END:

  In section [[#Examples]], we have seen a number of code fragments as
  partial implementations of particular non-standard method dispatch
  strategies, using =generalizer= metaobjects to mediate between the
  methods of the generic function and the actual arguments passed to
  it.  In section [[#Generalizer metaobjects]], we go into more detail
  regarding these =generalizer= metaobjects, describing the generic
  function invocation protocol in full, and showing how this protocol
  allows a similar form of effective method cacheing as the standard
  one does.  In section [[#Generalizer performance]], we show the results
  of some simple performance measurements on our implementation of
  this protocol in the SBCL implementation \cite{Rhodes:2008} of
  Common Lisp to highlight the improvement that this protocol can
  bring over a naïve implementation of generalized dispatch, as well
  as to make the potential for further improvement clear.

** Generalizer metaobjects
   :PROPERTIES:
   :CUSTOM_ID: Generalizer metaobjects
   :END:

*** Generic function invocation
    As in the standard generic function invocation protocol, the
    generic function's actual functionality is provided by a
    discriminating function.  The functionality described in this
    protocol is implemented by having a distinct subclass of
    =standard-generic-function=, and a method on
    =compute-discriminating-function= which produces a custom
    discriminating function.  The basic outline of the discriminating
    function is the same as the standard one: it must first compute the
    set of applicable methods given particular arguments; from that, it
    must compute the effective method by combining the methods
    appropriately according to the generic function's method
    combination; finally, it must call the effective method with the
    arguments.

    Computing the set of applicable methods is done using a pair of
    functions: =compute-applicable-methods=, the standard metaobject
    function, and a new function
    =compute-applicable-methods-using-generalizers=.  We define a
    custom method on =compute-applicable-methods= which tests the
    applicability of a particular specializer against a given argument
    using =specializer-accepts-p=, a new protocol function with
    default implementations on =class= and =eql-specializer= to
    implement the expected behaviour.  To order the methods, as
    required by the protocol, we define a pairwise comparison operator
    =specializer<= which defines an ordering between specializers for
    a given generalizer argument (remembering that even in standard
    CLOS the ordering between =class= specializers can change
    depending on the actual class of the argument).

    The new =compute-applicable-methods-using-generalizers= is the
    analogue of the MOP's =compute-applicable-methods-using-classes=.
    Instead of calling it with the =class-of= each argument, we compute
    the generalizers of each argument using the new function
    =generalizer-of-using-class= (where the =-using-class= refers to
    the class of the generic function rather than the class of the
    object), and call it with the list of generalizers.  As with the
    standard function, a secondary return value indicates whether the
    result of the function is definitive for that list of generalizers.

    Thus, in generic function invocation, we first compute the
    generalizers of the arguments; we compute the ordered set of
    applicable methods, either from the generalizers or (if that is
    not definitive) from the arguments themselves; then the normal
    effective method computation and call can occur.  Unfortunately,
    the nature of an effective method object is not specified, so we
    have to reach into implementation internals a little in order to
    call it, but otherwise the remainder of the generic function
    invocation protocol is unchanged from the standard one.  In
    particular, method combination is completely unchanged;
    programmers can choose arbitrary method combinations, including
    user-defined long form combinations, for their generic functions
    involving generalized dispatch.

*** Effective method memoization
    :PROPERTIES:
    :CUSTOM_ID: Memoization
    :END:
    The potential efficiency benefit to having =generalizer=
    metaobjects lies in the use of
    =compute-applicable-methods-using-generalizers=.  If a particular
    generalized specializer accepts a variety of objects (such as the
    =signum= specializer accepting all reals with a given sign, or the
    =accept= specializer accepting all HTTP requests with a particular
    =Accept= header), then there is the possibility of cacheing and
    reusing the results of the applicable and effective method
    computation.  If the computation of the applicable method from
    =compute-applicable-methods-using-generalizers= is definitive,
    then the ordered set of applicable methods and the effective
    method can be cached.

    One issue is what to use as the key for that cache.  We cannot use
    the generalizers themselves, as two generalizers that should be
    considered equal for cache lookup will not compare as =equal= –
    and indeed even the standard generalizer, the =class=, cannot be
    used as we must be able to invalidate cache entries upon class
    redefinition.  The issue of =class= generalizers we can solve as
    in \cite{Kiczales.Rodriguez:1990} by using the =wrapper= of a
    class, which is distinct for each distinct (re)definition of a
    class; for arbitrary generalizers, however, there is /a priori/ no
    good way of computing a suitable hash key automatically, so we
    allow the metaprogrammer to specify one by defining a method on
    =generalizer-equal-hash-key=, and combining the hash keys for all
    required arguments in a list to use as a key in an =equal=
    hash-table.

#+begin_comment
    [could we actually compute a suitable hash key using the
    generalizer's class name and initargs?]
#+end_comment

*** COMMENT
    - [X] =generalizer-of-using-class= (NB class of gf not class of object)
    - [X] =compute-applicable-methods-using-generalizers=
    - [X] =generalizer-equal-hash-key=
    - [X] =specializer-accepts-generalizer-p=
    - [X] =specializer-accepts-p=
    - [X] =specializer<=
** Performance
   :PROPERTIES:
   :CUSTOM_ID: Generalizer performance
   :END:
   We have argued that the protocol presented here allows for
   expressive control of method dispatch while preserving the
   possibility of efficiency.  In this section, we quantify the
   efficiency that the memoization protocol described in section
   [[#Memoization]] achieves, by comparing it both to the same protocol
   with no memoization, as well as with equivalent dispatch
   implementations in the context of methods with regular specializers
   (in an implementation similar to that in
   \cite{Kiczales.Rodriguez:1990}), and with implementation in
   straightforward functions.

   In the case of the =cons-specializer=, we benchmark the walker
   acting on a small but non-trivial form.  The implementation
   strategies in the table below refer to: an implementation in a
   single function with a large =typecase= to dispatch between all the
   cases; the natural implementation in terms of a standard generic
   function with multiple methods (the method on =cons= having a
   slightly reduced =typecase= to dispatch on the first element, and
   other methods handling =symbol= and other atoms); and three
   separate cases using =cons-specializer= objects.  As well as
   measuring the effect of memoization against the full invocation
   protocol, we can also introduce a special case: when only one
   argument participates in method selection (all the other required
   arguments only being specialized on =t=), we can avoid the
   construction of a list of hash keys and simply use the key
   from the single active generalizer directly.

   | implementation        | time (µs/call) | overhead |
   |-----------------------+----------------+----------|
   | function              |           3.17 |          |
   | standard-gf/methods   |            3.6 |     +14% |
   | cons-gf/one-arg-cache |            7.4 |    +130% |
   | cons-gf               |             15 |    +370% |
   | cons-gf/no-cache      |             90 |   +2700% |

   The benchmarking results from this exercise are promising: in
   particular, the introduction of the effective method cache speeds
   up the use of generic specializers in this case by a factor of 6,
   and the one-argument special case by another factor of 2.  For this
   workload, even the one-argument special case only gets to within a
   factor of 2-3 of the function and standard generic function
   implementations, but the overall picture is that the memoizability
   in the protocol does indeed drastically reduce the overhead
   compared with the full invocation.

   For the =signum-specializer= case, we choose to benchmark the
   computation of 20!, because that is the largest factorial whose
   answer fits in SBCL's 63-bit fixnums – in an attempt to measure the
   worst case for generic dispatch, where the work done within the
   methods is as small as possible without being meaningless, and in
   particular does not cause heap allocation or garbage collection to
   obscure the picture.

#+begin_src lisp :exports none
(progn (gc :full t) (time (dotimes (i 10000) (%fact 20))))
#+end_src

   | implementation          | time (µs/call) | overhead |
   |-------------------------+----------------+----------|
   | 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% |

   The relative picture is similar to the =cons-specializer= case;
   including a cache saves a factor of 10 in this case, and another
   factor of 3 for the one-argument cache special case.  The cost of
   the genericity of the protocol here is starker; even the
   one-argument cache is a factor of 6 slower than the standard
   generic-function implementation, and a further factor of 2 away
   from the implementation of factorial as a function.  We discuss
   ways in which we expect to be able to improve performance in
   section [[#Future Work]].

   We could allow the metaprogrammer to improve on the one-argument
   performance by constructing a specialized cache: for =signum=
   arguments of =rational= arguments, the logical cache structure is
   to index a three-element vector with =(1+ signum)=.  The current
   protocol does not provide a way of eliding the two generic function
   calls for the generic cache; we discuss possible approaches in
   section [[#Conclusions]].
** Full protocol
   The protocol described in this paper is only part of a complete
   protocol for =specializer= and =generalizer= metaobjects.  Our
   development of this protocol is as yet incomplete; the work
   described here augments that in \cite{Newton.Rhodes:2008}, but is
   yet relatively untested – and additionally our recent experience of
   working with that earlier protocol suggests that there might be
   useful additions to the handling of =specializer= metaobjects,
   independent of the =generalizer= idea presented here.

*** COMMENT ideas
    Description and specification left for reasons of space (we'll see?)
    - [ ] =same-specializer-p=
    - [ ] =parse/unparse-specializer-using-class=
    - [ ] =make-method-specializers-form=
    - [ ] jmoringe: In an email, I suggested
      =make-specializer-form-using-class=:

      #+begin_quote
      Could we change =make-method-specializers-form='s default
      behaviour to call a new generic function
      #+begin_src
        make-specializer-form-using-class gf method name env
      #+end_src
      with builtin methods on =sb-mop:specializer=, =symbol=, =cons= (for
      eql-specializers)? This would make it unnecessary to repeat
      boilerplate along the lines of
      #+begin_src lisp
      (flet ((make-parse-form (name)
               (if <name-is-interesting>
                 <handle-interesting-specializer>
                 <repeat-handling-of-standard-specializers>)))
        `(list ,@(mapcar #'make-parse-form specializer-names)))
      #+end_src
      for each generic function class.
      #+end_quote
    - [ ] =make-method-lambda= revision (use environment arg?)

      jmoringe: would only be relevant for pattern dispatch, right? I
      think, we didn't finish the discussion regarding special
      variables vs. environment vs. new protocol function

* Related Work
  :PROPERTIES:
  :CUSTOM_ID: Related Work
  :END:

  The work presented here builds on specializer-oriented programming
  described in \cite{Newton.Rhodes:2008}.  Approximately
  contemporaneously, filtered dispatch \cite{Costanza.etal:2008} was
  introduced to address some of the same use cases: filtered dispatch
  works by having a custom discriminating function which wraps the
  usual one, where the wrapping function augments the set of
  applicable methods with applicable methods from other (hidden)
  generic functions, one per filter group; this step is not memoized,
  and using =eql= methods to capture behaviours of equivalence classes
  means that it is hard to see how it could be.  The methods are then
  combined using a custom method combination to mimic the standard
  one; in principle implementors of other method combinations could
  cater for filtered dispatch, but they would have to explicitly
  modify their method combinations.  The Clojure programming language
  supports multimethods[fn:5] with a variant of filtered dispatch as
  well as hierarchical and identity-based method selectors.

  In context-oriented programming
  \cite{Hirschfeld.etal:2008,Vallejos.etal:2010}, context dispatch
  occurs by maintaining the context state as an anonymous class with
  the superclasses representing all the currently active layers; this
  is then passed as a hidden argument to context-aware functions.  The
  set of layers is known and under programmer control, as layers must
  be defined beforehand.

  In some sense, all dispatch schemes are specializations of predicate
  dispatch \cite{Ernst.etal:1998}.  The main problem with predicate
  dispatch is its expressiveness: with arbitrary predicates able to
  control dispatch, it is essentially impossible to perform any
  substantial precomputation, or even to automatically determine an
  ordering of methods given a set of arguments.  Even Clojure's
  restricted dispatch scheme provides an explicit operator for stating
  a preference order among methods, where here we provide an operator
  to order specializers; in filtered dispatch the programmer
  implicitly gives the system an order of precedence, through the
  lexical ordering of filter specification in a filtered function
  definition.

  The Slate programming environment combines prototype-oriented
  programming with multiple dispatch \cite{Salzman.Aldrich:2005}; in
  that context, the analogue of an argument's class (in Common Lisp)
  as a representation of the equivalence class of objects with the
  same behaviour is the tuple of roles and delegations: objects with
  the same roles and delegations tuple behave the same, much as
  objects with the same generalizer have the same behaviour in the
  protocol described in this paper.

  The idea of generalization is of course not new, and arises in other
  contexts.  Perhaps of particular interest is generalization in the
  context of partial evaluation; for example, \cite{Ruf:1993}
  considers generalization in online partial evaluation, where sets of
  possible values are represented by a type system construct
  representing an upper bound.  Exploring the relationship between
  generalizer metaobjects and approximation in type systems might
  yield strategies for automatically computing suitable generalizers
  and cache functions for a variety of forms of generalized dispatch.
* Conclusions
  :PROPERTIES:
  :CUSTOM_ID: Conclusions
  :END:
  In this paper, we have presented a new generalizer metaobject
  protocol allowing the metaprogrammer to implement in a
  straightforward manner metaobjects to implement custom method
  selection, rather than the standard method selection as standardized
  in Common Lisp.  This protocol seamlessly interoperates with the
  rest of CLOS and Common Lisp in general; the programmer (the user of
  the custom specializer metaobjects) may without constraints use
  arbitrary method combination, intercede in effective method
  combination, or write custom method function implementations.  The
  protocol is expressive, in that it handles forms of dispatch not
  possible in more restricted dispatch systems, while not suffering
  from the indeterminism present in predicate dispatch through the use
  of explicit ordering predicates.

  The protocol is also reasonably efficient; the metaprogrammer can
  indicate that a particular effective method computation can be
  memoized, and under those circumstances much of the overhead is
  amortized (though there remains a substantial overhead compared with
  standard generic-function or regular function calls).  We discuss
  how the efficiency could be improved below.
** Future work
   :PROPERTIES:
   :CUSTOM_ID: Future Work
   :END:
   Although the protocol described in this paper allows for a more
   efficient implementation, as described in section [[#Memoization]],
   than computing the applicable and effective methods at each generic
   function call, the efficiency is still some way away from a
   baseline of the standard generic-function, let alone a standard
   function.  Most of the invocation protocol is memoized, but there
   are still two full standard generic-function calls –
   =generalizer-of-using-class= and =generalizer-equal-hash-key= – per
   argument per call to a generic function with extended specializers,
   not to mention a hash table lookup.

   For many applications, the additional flexibility afforded by
   generalized specializers might be worth the cost in efficiency, but
   it would still be worth investigating how much the overhead from
   generalized specializers can be reduced; one possible avenue for
   investigation is giving greater control over the cacheing strategy
   to the metaprogrammer.

   As an example, consider the =signum-specializer=.  The natural
   cache structure for a single argument generic function specializing
   on =signum= is probably a four-element vector, where the first
   three elements hold the effective methods for =signum= values of
   -1, 0, and 1, and the fourth holds the cached effective methods for
   everything else.  This would make the invocation of such functions
   very fast for the (presumed) common case where the argument is in
   fact a real number.  We hope to develop and show the effectiveness
   of an appropriate protocol to allow the metaprogrammer to construct
   and exploit such cacheing strategies, and (more speculatively) to
   implement the lookup of an effective method function in other ways.

   We also aim to demonstrate support within this protocol for some
   particular cases of generalized specializers which seem to have
   widespread demand (in as much as any language extension can be said
   to be in “demand”).  In particular, we have preliminary work
   towards supporting efficient dispatch over pattern specializers
   such as implemented in the \textsf{Optima} library[fn:4], and over
   a prototype object system similar to that in Slate
   \cite{Salzman.Aldrich:2005}.  Our current source code for the work
   described in this paper can be seen in the git source code
   repository at [[http://christophe.rhodes.io/git/specializable.git]],
   which will be updated with future developments.

   Finally, after further experimentation (and, ideally, non-trivial
   use in production) if this protocol stands up to use as we hope, we
   aim to produce a standards-quality document so that other
   implementors of Common Lisp can, if they choose, independently
   reimplement the protocol, and so that users can use the protocol
   with confidence that the semantics will not change in a
   backwards-incompatible fashion.
** Acknowledgments
   We thank Lee Salzman, Pascal Costanza and Mikel Evins for helpful
   and informative discussions, and all the respondents to one
   author's request for imaginative uses for generalized specializers.

\bibliographystyle{plain}
\bibliography{crhodes,specializers}

* Footnotes

[fn:1] GNU CLISP, at http://www.clisp.org/

[fn:2] Clozure Common Lisp, at http://ccl.clozure.com/

[fn:3] the \textsf{Closer to MOP} project, at
   http://common-lisp.net/project/closer/, attempts to harmonize the
   different implementations of the metaobject protocol in Common
   Lisp.

[fn:4] https://github.com/m2ym/optima

[fn:5] http://clojure.org/multimethods