Eigenclass model: Difference between revisions

Revision as of 08:04, 3 December 2012

Revision as of 13:51, 12 December 2012

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In [[object-oriented programming|object-oriented]] [[Computer programming|programming]], the '''eigenclass model''' is an [[abstract structure]]{{

{{efn|

In the wider sense,

the eigenclass model is an [[Abstract state machines|abstract state machine]] (ASM)

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As a complementary constituent to the eigenclass map, the model encompasses the [[Inheritance (object-oriented programming)|inheritance]] relation.

The composition of the eigenclass map with inheritance gives rise to ''object membership'',

a relation between objects,
denoted ϵ ([[lunate epsilon]]).<ref inname="ome">

.<ref name="ome">{{cite web | url=http://www.atalon.cz/om/object-membership/ | title=Object Membership: The core structure of object-oriented programming }}</ref>

This relation is a generalization of the ''instance-of'' relation

and can be viewed as a

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Right-directed arrows (in gray) show the eigenclass map,

up-directed arrows (in green) show the child-parent relation of [[#Inheritance|inheritance]].

The <ispan style="color:green">''∫''</span>-shaped arrows are the [[#Twist_links|twist links]].

[[#Eigenclasses|Eigenclasses]] are shown as unnamed nodes in gray.

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i.e. aside from higher-order eigenclasses, explicit metaclasses are ''classes-of'' classes (''<u>C</u>.class'') whereas implicit metaclasses are ''eigenclasses-of'' classes (''<u>C</u>.ec'').

The classical definition of metaclasses as "''classes whose instances are classes''" <ref>

<ref>{{cite book|author=Ira R. Forman and Scott Danforth|title=Putting Metaclasses to Work|year=1999|isbn=0-201-43305-2}}</ref>

applies as follows:

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==== Canonical reduct ====

The canonical reduct ''(<u>O</u>,'' ϵ'')'' is given by the superclass and eigenclass links between objects.<ref name="ruby-s1">

.<ref name="ruby-s1">{{cite web | url=http://www.atalon.cz/rb-om/ruby-object-model/rb-om-s1.pdf | title=Ruby Object Model – The S1 structure }}</ref>

In particular, the structure only allows single inheritance so that

except for ''<u>r</u>'', every non-terminal object has exactly one parent, detectable by the <code>superclass</code> method.

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This extended inheritance is a ''multiple'' inheritance.

In addition, since Ruby supports dynamic module inclusion,

≤' can have anomalies (as to transitivity and/or antisymmetry), the problem known as the ''double/dynamic inclusion problem''.<ref>

.<ref>{{cite web | url=http://web.archive.org/web/20101113235808/http://eigenclass.org/hiki/The+double+inclusion+problem | title=The double inclusion problem }}</ref>

=== In Python ===

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==== {{anchor|smalltalk-traits}} Traits ====

Similarly to Ruby module inclusion, Smalltalk-80 supports extension of inheritance via inclusion of terminal objects, called ''traits''.<ref name="traits">{{cite web | author=Nathanael Sch&auml;rli | url=http://scg.unibe.ch/archive/phd/schaerli-phd.pdf | title=Traits: Composing Classes from Behavioral Building Blocks}}</ref>

.<ref name="traits">{{cite web | author=Nathanael Sch&auml;rli | url=http://scg.unibe.ch/archive/phd/schaerli-phd.pdf | title=Traits: Composing Classes from Behavioral Building Blocks}}</ref>

Traits are <code style="color:#700000">Trait</code>s &ndash; instances of the built-in <code style="color:#700000">Trait</code> class.

Unlike in Ruby, the semantics of extended object membership, ϵ', is not reflected by the <code>isKindOf:</code> introspection method (as of Pharo 1.3).

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Actual objects comprise all primary objects (terminals and classes) plus some eigenclasses.

Except for Ruby, eigenclasses of eigenclasses (elements of ''<u>O</u>.ec(2)'') are never actual.

Even in Ruby, manipulating these higher-order eigenclasses did not find any practical use.<ref>

.<ref>{{cite book | publisher=Pragmatic Bookshelf | author=Paolo Perrotta | url=http://pragprog.com/book/ppmetr/metaprogramming-ruby | title=Metaprogramming Ruby | isbn=978-1-934356-47-0}}</ref>

=== {{anchor|actuality-axioms}} Axioms ===

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In Python, Java, CLOS, and Perl, eigenclasses are purely fictitious &ndash; they are never actual, so that the actualclass map coincides with the class map.

Scala allows eigenclasses of terminal objects, e.g. via the <code>object</code> definition.<ref>

.<ref>{{cite book | publisher=Artima Press | author=Martin Odersky, Lex Spoon, Bill Venners | url=http://www.artima.com/shop/programming_in_scala_2ed | title=Programming in Scala | isbn=978-0-9815316-4-9}}</ref>

In Smalltalk-80 and Objective-C, the set of actual eigenclasses equals ''<u>C</u>.ec'', i.e. all implicit metaclasses (without higher-order eigenclasses) are actual.

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In Ruby, all objects that are not ''immediate values''

can have actual eigenclasses.<ref name="rb-om">

<ref name="rb-om">{{cite web | url=http://www.atalon.cz/rb-om/ruby-object-model/ | title=The Ruby Object Model: Data structure in detail}}</ref> can have actual eigenclasses.

As of [[Ruby MRI|MRI]] 1.9, ancestors of actual objects are actual.

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In Smalltalk, the imposed class map has the corresponding ''imposed actualclass map'' which corresponds to the introspection method named <code>class</code>.

Due to the metaclass redirection, the imposed actualclass map does not form a tree but just a (directed) [[pseudotree]] with a 2-element cycle containing the <code>Metaclass</code> class and its eigenclass.<ref>

.<ref>{{cite book | publisher=Springer Verlag | author=John Hunt | url=http://stephane.ducasse.free.fr/FreeBooks/STandOO/Smalltalk-and-OO.pdf | title=Smalltalk and Object Orientation: An Introduction | isbn=978-3540761150}}</ref>

== Name resolution ==

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This is the primary mode, used in particular for finding arrows that point to methods, (a part of) the process known as ''method resolution'' or ''method lookup''.

Since containers of an object are just ancestors of the object's eigenclass, method lookup can be thought of as a two-stage process: first step to the eigenclass, then look up in ancestors.

In Ruby, this is expressed as a "method call mantra":<ref>

<ref>{{cite web | url=http://pragprog.com/screencasts/v-dtrubyom/the-ruby-object-model-and-metaprogramming | title=The Ruby Object Model and Metaprogramming }}</ref>:

:<cite style="font-style:italic;">one to the right, then up</cite>.

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(where ''q'' is not a metaclass and necessarily ''n'' = 0)

is syntactically differentiated from creation of classes ''x''

(where ''q'' is a metaclass).{{efn|

{{efn|

However, Ruby also supports the uniform expression:

<code>Class.new(A)</code> creates a new subclass of <code>A</code>.

}}.

In Perl, the pattern is not applicable to class creation due to the [[Chicken or the egg|chicken-egg problem]] caused by the circularity of classes.

In Objective-C, if ''q'' is an inheritance root, then one cannot recognize, if ''x'' should be terminal or a class.