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Topic: Functor


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In the News (Sun 21 Jul 19)

  
  Functor   (Site not responding. Last check: 2007-10-22)
In category theory a functor is a mapping from one category to another which maps objects to objects and morphisms to morphisms in such a manner that the composition of morphisms and the identities are preserved.
Functors were first considered in algebraic topology, where algebraic objects are associated to topological spaces, and algebraic homomorphisms are associated to continuous maps.
In functional programming languages such as ML, a functor represents a mapping that maps modules to modules, representing a tool for the reuse of code, and is used in a manner analogous to the original mathematical meaning of the term.
www.theezine.net /f/functor.html   (366 words)

  
 Limit (category theory) - Wikipedia, the free encyclopedia
The importance of adjoint functors lies in the fact that every functor which has a left adjoint (and therefore is a right adjoint) is continuous.
A covariant functor that commutes with the construction of colimits is said to be cocontinuous or colimit preserving.
Every functor which has a right adjoint (and hence is a left adjoint) is cocontinuous.
en.wikipedia.org /wiki/Limit_(category_theory)   (1907 words)

  
 Adjoint functors   (Site not responding. Last check: 2007-10-22)
The existence of many pairs of adjoint functors is a major observation of the branch of mathematics known as category theory.
This functor is left adjoint to the functor that associates to a given ring its underlying multiplicative monoid.
Similarly, the group ring construction yields a functor from groupss to rings, left adjoint to the functor that assigns to a given ring its group of units.
www.sciencedaily.com /encyclopedia/adjoint_functors   (3182 words)

  
 Functor Package
Functor list classes are an extension to the functor class hierarchy, as shown in Figure 4.
The Functor Map subpackage is made up of classes designed for creating functors which are themselves a collection of functors, one of which is to be invoked according to a given key.
Functor map classes are an extension to the functor class hierarchy, as shown in Figure 5.
www.roguewave.com /support/docs/sourcepro/threadsref/2-4.html   (843 words)

  
 Category theory   (Site not responding. Last check: 2007-10-22)
Then it becomes possible to relate different categories by functors, generalizations of functions which associate to every object of one category an object of another category and to every morphism in the first category a morphism in the second.
Algebra of continuous functions: a contravariant functor from the category of topological spaces (with continuous maps as morphisms) to the category of real associative algebras is given by assigning to every topological space X the algebra C(X) of all real-valued continuous functions on that space.
Functors like these are called representable, and a major goal in many settings is to determine whether a given functor is representable.
www.sciencedaily.com /encyclopedia/category_theory   (3251 words)

  
 Functions
This special functor is expected to have a nested template class result (where N is the number of arguments of its member operator()).
Such nullary functors are only required to define a typedef result_type that reflects the return type of its operator().
for functors with state), an instance of the functor may be passed on to the constructor.
spirit.sourceforge.net /dl_more/phoenix_v1_0_docs/doc/functions.html   (474 words)

  
 SML/NJ Special Features
But there are occasions when one like to parameterize over functors as well as structures, which requires a truly higher-order module system (see, for instance, the powerset functor example.
Functor specifications were already part of the module syntax of the Definition of Standard ML (Figure 8, p.
A common use of functors returning functors in their result is to approximate a curried functor with multiple parameters.
www.smlnj.org /doc/features.html   (1135 words)

  
 Hierarchies and Parameterization
A functor is a parameterized module, or a generic structure, that is defined in terms of zero or more argument structures with a specified signature.
functor encapsulates the implementation of dictionaries as a generic structure that is independent of the specific choice of keys.
Notice that functor application uses keyword parameter passing --- the parameter is explicitly bound to a structure using a structure binding.
www.cs.cmu.edu /~rwh/introsml/modules/subfun.htm   (1711 words)

  
 The Functor List Subpackage
Because the invocation of the list invokes all the functors within the list, they all must have the same invocation signature and either share the same functor handle type or be derived from the same functor handle type.
Copying functor lists follows the general rules discussed in Section 7.3.1.4, "Handle-Body Mechanics." With this technique, the copy constructor and assignment operators reference the old object and, as a result, are very fast.
Functor list classes are an extension to the functor class hierarchy, as shown in Figure 52.
www.roguewave.com /support/docs/leif/sourcepro/html/threadsug/8-6.html   (1010 words)

  
 Functor   (Site not responding. Last check: 2007-10-22)
Constant functor: A very boring functor C → D is one which maps every object of C to a fixed object X in D and every morphism in C to the identity morphism on X.
In general, a functor G → C can be considered as an "action" of G on an object in the category C.
This is a functor which is contravariant in the first and covariant in the second argument, i.e.
www.yotor.com /wiki/en/fu/Functor.htm   (1530 words)

  
 CenterSpace API Documentation - CenterSpace.NMath.Core
Functor that takes a double-precision complex number and an integer and returns a double-precision complex number.
Functor that takes a double-precision floating point number and an integer and returns a double-precision floating point number.
Functor that takes a single-precision complex number and an integer and returns a single-precision complex number.
www.centerspace.net /doc/NMath/Core/ref/CenterSpace.NMath.Core.html   (1532 words)

  
 DKGS Prolog
Functor is the functor of term and arity is the arity.
Term is a term with functor, Functor and an arity of Arity.
Y is a list such that the first element is the functor of X and the remaining elements are the arguments of X. If X is an atom then the remaining list is empty.
www.geocities.com /SiliconValley/Campus/7816/help.html   (461 words)

  
 PlanetMath: representable functor
A vast number of important objects in mathematics are defined as representing functors.
Much of the motivation for this way of thinking about objects comes from a philosophy of A. Grothendieck which says that we define certain objects by having the characterizing property that they represent certain functors.
This is version 7 of representable functor, born on 2001-12-12, modified 2005-09-16.
planetmath.org /encyclopedia/RepresentableFunctor.html   (217 words)

  
 Commons Functor - Examples
By encapsulating tiny bits of logic, functors provide a useful solution to this problem, as illustrated in the SupermarketPricingExample.
The Functor package, and more generally, a functional approach to program design, supports a powerful technique for balancing behavior specialization and code reuse.
Functors encourage another, complementary approach to code reuse and behavior specialiazation: composition.
jakarta.apache.org /commons/sandbox/functor/examples.html   (588 words)

  
 LTI-Lib: lti::functor Class Reference
Exception thrown when a method of a functor is not implemented for a specific parameter set.
If you call an apply() method of a functor in which you changed the attributes of the parameters instance without updating them, you have to expect an unpredictible behaviour: segmentation fault, system crash, blue screens, etc. can occur as the sizes of internal structures may not be consistent with the given parameters.
Note that the given reference can be rewritten by the functor, specially if some shortcuts are used or the read method is called, then their content will be changed (another reason to prefer setParameters()).
ltilib.sourceforge.net /doc/html/classlti_1_1functor.html   (879 words)

  
 functor
In category theory, a functor F is an operator on types.
F is also considered to be a polymorphic operator on functions with the type
Functors are a generalisation of the function "map".
www.linuxguruz.com /foldoc/foldoc.php?functor   (107 words)

  
 CategoryTheory/Functor - The Haskell Wiki   (Site not responding. Last check: 2007-10-22)
The starting point of Category Theory is the premise that every kind of mathematically structured object comes equipped with a notion of "acceptable" transformation or construction, that is, a morphism that preserves the structure of the object.
The functors described above are covariant functors, meaning they preserve the direction of arrows.
Two (covariant) functors F: A → B and G: B → C can be composed to create a new functor GF: A → C.
www.haskell.org /hawiki/CategoryTheory/Functor   (1117 words)

  
 PlanetMath: forgetful functor
Forgetful functors are often instrumental in studying adjoint functors.
Cross-references: adjoint functors, arrows, identity, abelian groups, continuous maps, topological spaces, maps, group homomorphisms, groups, functor, structures, categories
This is version 1 of forgetful functor, born on 2002-05-17.
planetmath.org /encyclopedia/Forgetful.html   (106 words)

  
 Commons Functor - Building
To build Commons Functor from scratch, you must first obtain the source, either from the CVS server or from a source snapshot.
Commons Functor can be built using Maven or Ant.
Note that JUnit is a needed to compile and run the unit tests, but is not needed at runtime by clients of Commons Functor.
jakarta.apache.org /commons/sandbox/functor/building.html   (126 words)

  
 Functor instance for arbitrary polymorphic types
A difficulty seems to be that parts of the container type are based on a type constructor where the underlying type 'a' over which "fmap :: (a->b) -> t a -> t b" would operate is not the only or last parameter to the type constructor expression.
If I could easily go change the underlying data types used, I could declare a Functor by rearranging the constructor parameters, but in my application that would be a lot of code reworking that I'd rather avoid, and I'm not sure that the change wouldn't raise a conflict somewhere else.
In each case, the type that I wish to be an instance of Functor is 'EntryT'.
www.haskell.org /pipermail/haskell/2003-June/012040.html   (473 words)

  
 libsigc++ 2.0: struct Functors
ptr_fun() is used to convert a pointer to a function to a functor.
Adaptors are functors that alter the signature of a functor's operator()().
The basic functor types libsigc++ provides are created with ptr_fun() and mem_fun() and can be converted into slots implicitly.
libsigc.sourceforge.net /libsigc2/docs/reference/html/group__functors.html   (426 words)

  
 Functor Object
In CategoryTheory, the field of mathematics where the term Functor originates, a Functor is a mapping from one Category to another that respects Morphisms [functions].
In this case, we are talking about functors as they exist in programming languages where for decades, a functor has analogous to a function.
Functors may also inform a factory about what they can do - either by proxy, or directly, allowing the factory to select the "optimum" functor from a collection of functors, using hints provided by the invoker of the factory...
c2.com /cgi/wiki?FunctorObject   (1785 words)

  
 libsigc++ 2.0: hide(), hide_return()
sigc::hide() alters an arbitrary functor in that it adds a parameter whose value is ignored on invocation of the returned functor.
The functor sigc::hide() returns can be passed into sigc::signal::connect() directly.
sigc::hide_return() alters an arbitrary functor by dropping its return value, thus converting it to a void functor.
libsigc.sourceforge.net /libsigc2/docs/reference/html/group__hide.html   (429 words)

  
 Functor Functor is a math/scientific software, for graphical analyze of 3D algebraic...
Functor Functor is a math/scientific software, for graphical analyze of 3D algebraic...
Functor is a math/scientific software, for graphical analyze of 3D algebraic...
Functor is a math/scientific software, for graphical analyze of 3D algebraic functions Z = f(X, Y).
www.softempire.com /functor-downloads.html   (168 words)

  
 Commons Functor - Overview
A functor is a function that can be manipulated as an object, or an object representing a single, generic function.
The remaining packages provide common functor implementations, adapters and utilities.
Unofficial nightly builds are available, however these should be treated with care.
jakarta.apache.org /commons/sandbox/functor   (138 words)

  
 THE SEMANTIC FUNCTOR   (Site not responding. Last check: 2007-10-22)
My hypothesis is that the semantic functor is a feature different from other semantic components and features in that it is not in itself referential or expressive (attitudinal), but rather strengthens or amplifies another feature in the meaning of a word.
As an heritage from Charles Osgood's theories, attitudinal features and the semantic functor may be assumed to be of great relevance for the effect of the words in a text and hence for the style of that text.
POTENCY is seen as a semantic functor that gives a word its strength and which makes it possible to reduce Osgood's three variables to two: Osgood's variable ACTIVITY is explained as a function of the semantic functor POTENCY and a component of movement.
home.swipnet.se /cassirer/functor.htm   (6188 words)

  
 [e-cvs] cvs commit: e/src/jsrc/org/quasiliteral/term Functor.java Term.java Term.updoc TermBuilder.java TermLexer.java ...
+ * @serial If the functor represents a literal-data token, then this is + * the data, and myTag must represent the cononical corresponding + * token-type for this kind of data in this schema.
+ * If the functor represents a literal-data token, then this is + * the data, and myTag must represent the cononical corresponding + * token-type for this kind of data in this schema.
+ * */ public Term(Functor functor, ConstList args) { myFunctor = functor; myArgs = args; - E.require(null != functor); - E.require(null != args); - } - - /** - * Converts an Antlr AST to a Term tree, while preserving all the vanilla - * AST semantics.
www.eros-os.org /pipermail/e-cvs/2001-December/000287.html   (2528 words)

  
 Re: Functor application inside functor
Namely, move the creation of the shared > structure (in your case, Set) outside the functor definition (in your > case, PrioQueue) and pass it as an argument to the functor.
My first thought was to convert each structure to a functor parametrized by some kind of number datatype.
Also, all of the functor applications need to be written for each datatype that is chosen.
www.talkaboutprogramming.com /group/comp.lang.ml/messages/7330.html   (236 words)

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