First-class function

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Topic: First-class function

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	Function (mathematics) - Wikipedia, the free encyclopedia
		The number of computable functions from integers to integers is countable, because the number of possible algorithms is. The number of all functions from integers to integers is higher: the same as the cardinality of the real numbers.
		As a mathematical term, "function" was coined by Gottfried Leibniz in 1694, to describe a quantity related to a curve, such as a curve's slope at a specific point of a curve.
		For this type of function, one can talk about limits and derivatives; both are measurements of the output or the change in the output as it depends on the input or the change in the input.
	en.wikipedia.org /wiki/Function_(mathematics) (3277 words)

	FUNCTION - LoveToKnow Article on FUNCTION
		Such functions were introduced into analysis somewhat unsystematically as the need for them arose, and the later developments of analysis led to the introduction of other classes of functions.
		This class of functions includes all those which have a finite number of maxima and minima in a finite-interval, and some which have an infinite number.
		The function may be given by specifying the domain of the argument and the rule of calculation, or else the function may have to be determined in accordance with certain conditions; for example, it may have to satisfy in a prescribed domain an assigned differential equation.
	www.1911encyclopedia.org /F/FU/FUNCTION.htm (14583 words)

	Inverse Function Encyclopedia Article @ LandCompany.com
		is also used for the (set valued) function associating to an element or a subset of the codomain, the inverse image of this subset (or element, seen as a singleton).
		If f is a real-valued function, then for f to have a valid inverse, it must pass the horizontal line test, that is a horizontal line y = k placed on the graph of f must pass through f exactly once for all real k.
		In mathematics, an inverse function is in simple terms a function which "does the reverse" of a given function.
	www.landcompany.com /encyclopedia/Inverse_function (627 words)

	Function - Wikipedia, the free encyclopedia
		In fact, it is possible to realize the same function using different physical processes, and one process can be a carrier of multiple functions.
		In language studies, the grammatical function of a word or phrase in a sentence.
		For example, the main function of a clock, the presentation of time, can be realized by different physical processes, including atomic, electronic, and mechanical processes.
	en.wikipedia.org /wiki/Function (407 words)

	Continuous Function Encyclopedia Article @ Encyclopedia.LocalColorArt.com
		In mathematics, a continuous function is a function in which changes in the output can be kept arbitrarily small (or even zero) by limiting changes in the input.
		Such a function can be represented by a graph in the Cartesian plane; the function is continuous if, roughly speaking, the graph is a single unbroken curve with no "holes" or "jumps".
		If a function has a domain which is not an interval, the notion of a continuous function as one whose graph you can draw without taking your pencil off the paper is not quite correct.
	encyclopedia.localcolorart.com /encyclopedia/Continuous_function (1546 words)

	Limit of A Function Encyclopedia Article @ LaunchBase.org
		In this case, the function happens to be continuous and the value is defined at the point, so the limit is equal to the direct evaluation of the function.
		In mathematics, the limit of a function is a fundamental concept in mathematical analysis.
		Rather informally, to say that a function f has limit L at a point p, is to say that we can make the value of f as close to L as we want, by taking points close enough to p.
	www.launchbase.org /encyclopedia/Limit_of_a_function (1451 words)

	Utility Function Encyclopedia Article @ aNewLow.com
		If the value of the utility function were to be, for example, doubled, squared, or subjected to any other strictly monotonically increasing function, it would still describe the same preferences.
		While preferences are the conventional foundation of microeconomics, it is convenient to represent preferences with a utility function and reason indirectly about preferences with utility functions.
		The expected utility theorem says that a von Neumann-Morgenstern utility function exists if and only if the agent's preference relation on the space of simple lotteries satisfies four axioms: completeness, transitivity, convexity/continuity (also called the Archimedean property), and independence.
	www.anewlow.com /encyclopedia/Utility_function (1330 words)

	Computable Function Encyclopedia Article @ ArtisticNudity.com
		According to the Church–Turing thesis, the class of computable functions is equivalent to the class of functions defined by recursive functions, lambda calculus, or Markov algorithms.
		The notion of computability of a function can be relativized to an arbitrary set of natural numbers A, or equivalently to an arbitrary function f from the naturals to the naturals, by using Turing machines extended by an oracle for A or f.
		In computational complexity theory, the problem of determining the complexity of a computable function is known as a function problem.
	www.artisticnudity.com /encyclopedia/Computable_function (478 words)

	Function Attributes - Using the GNU Compiler Collection (GCC)
		This happens when the class has a dllimport'ed constructor or a non-inline, non-pure virtual function and, for either of those two conditions, the class also has a inline constructor or destructor and has a key function that is defined in the current translation unit.
		Use this attribute on the Blackfin to indicate that the specified function is an NMI handler.
		Use this attribute on the Blackfin, m68k, H8/300, H8/300H, H8S, and SH to indicate that the specified function is an interrupt handler.
	gcc.gnu.org /onlinedocs/gcc/Function-Attributes.html (4138 words)

	PlanetMath: function
		Some authors define the range of a function to be equal to the codomain, and others define the range of a function to be equal to the image.
		This is version 11 of function, born on 2001-10-19, modified 2005-06-01.
		There is no universal agreement as to the definition of the range of a function.
	planetmath.org /encyclopedia/Codomain.html (139 words)

	Function Definitions
		A function is something that associates each element of a set with an element of another set (which may or may not be the same as the first set).
		Definition (composite function): Let g be a function from a set A to a set B, and let f be a function from B to a set C.
		For example, the rightmost function in the above figure is a bijection and its inverse is obtained by reversing the direction of each arrow.
	www.cs.odu.edu /~toida/nerzic/content/function/definitions.html (841 words)

	Functions
		Function is a correspondence f between elements of a space X and those of a space Y such that any element x of X has a unique corresponding element y of Y which is denoted
		Furthermore, there are numerous terms (vector, sequence, measure, length, volume, etc.) that are functions in disguise and their functional ancestry is seldom mentioned.
		Two functions with the same domain and region but defined by different rules, will be distinguished by different function names.
	www.cut-the-knot.org /do_you_know/function.shtml (448 words)

	Define function - a Whatis.com definition
		Functions are often graphed, and they usually appear as lines or curves on a coordinate plane.
		A function is usually symbolized by a lowercase, italicized letter of the alphabet, followed by the independent variable in parentheses.
		Other functions need to make requests of the operating system in order to perform their work.
	whatis.techtarget.com /definition/0,,sid9_gci212167,00.html (325 words)

	CLHS: Special Operator FUNCTION
		It is an error to use function on a function name that does not denote a function in the lexical environment in which the function form appears.
		The value of function is the functional value of name in the current lexical environment.
		If name is a function name, the functional definition of that name is that established by the innermost lexically enclosing flet, labels, or macrolet form, if there is one.
	www.lisp.org /HyperSpec/Body/speope_function.html (245 words)

	A Proposal to add a Polymorphic Function Object Wrapper to the Standard Library
		class template is a function object type whose call signature is defined by its first template argument (a function type).
		Several function object wrappers (often referred to as "callbacks") have appeared with similar interfaces [1, 2, 10, 11], suggesting that this class template is appropriate for standardization.
		Function pointers in C and C++ are used in both user and library code to customize the behavior of components by substituting a user-supplied function for part of a computation.
	std.dkuug.dk /jtc1/sc22/wg21/docs/papers/2002/n1402.html (2122 words)

	the function ensemble den of suprises
		function are signing to locust music, chicago - the exceptional home of recordings by espers, sir richard bishop, born heller, cyann & ben, tetuzi akiyama, sun city girls re-issues, josephine foster, henry flynt, tod dockstader, alan watts, alan ginsberg, matmos & many more fine psychadelic, archival and varying treats of unusual kinship.
		Function perform Thursday 16th March at Locust showcase and Saturday 18th instore at "End Of An Ear" Records.
		function will be performing in expanded form at sxsw, austin, march 16th, and at tonic, NYC, around then, among other appearances under consideration presently.
	functionensemble.com (1166 words)

	Client-Side JavaScript Reference
		All parameters are passed to functions by value; the value is passed to the function, but if the function changes the value of the parameter, this change is not reflected globally or in the calling function.
		Thus, a called function can call its caller without knowing the name of the particular caller, provided it knows that all of its callers have the same form and fit, and that they will not call the called function again unconditionally (which would result in infinite recursion).
		If a function is assigned to a variable, you can assign the variable to an event handler.
	docs.sun.com /source/816-6408-10/function.htm (2297 words)

	CLHS: System Class FUNCTION
		A function can be directly invoked by using it as the first argument to funcall, apply, or multiple-value-call.
		A function is produced by the function special form, the function coerce, or the function compile.
		Every element of this type is a function that accepts arguments of the types specified by the argj-types and returns values that are members of the types specified by value-type.
	www.lisp.org /HyperSpec/Body/syscla_function.html (446 words)

	function
		When a function is executed, the arguments to the function become the positional parameters during its execution.
		The exit status of a function is the exit status of the last command executed in the body.
		Shell functions are a way to group commands for later execution using a single name for the group.
	www.ss64.com /bash/function.html (317 words)

	JavaScript Functions
		A function is a reusable code-block that will be executed by an event, or when the function is called.
		Functions are defined at the beginning of a page, in the section.
		You may call a function from anywhere within the page (or even from other pages if the function is embedded in an external.js file).
	www.w3schools.com /js/js_functions.asp (553 words)

	Control Tutorials for Matlab
		Functions can be rather tricky to write, and practice will be necessary to successfully write one that will achieve the desired goal.
		The new function must be given a filename with a '.m' extension.
		A function can input or output as many variables as are needed.
	www.engin.umich.edu /group/ctm/extras/function.html (354 words)

	function
		The inverse of a function, a mapping from the function's outputs to its inputs, may be a relation rather than another function.
		Since a function must return the same value for each input and the input cannot change (since it has no arguments), it must always return the same value.
		A function which takes no arguments is a constant function, or simply, a constant.
	www.nist.gov /dads/HTML/function.html (294 words)

	Chapter 4. Boost.Function
		The Boost.Function library contains a family of class templates that are function object wrappers.
		It shares features with function pointers in that both define a call interface (e.g., a function taking two integer arguments and returning a floating-point value) through which some implementation can be called, and the implementation that is invoked may change throughout the course of the program.
		Generally, any place in which a function pointer would be used to defer a call or make a callback, Boost.Function can be used instead to allow the user greater flexibility in the implementation of the target.
	www.boost.org /doc/html/function.html (156 words)

	function from FOLDOC
		In programming (except in functional programming), a function may return different values each time it is called with the same argument values and may have side effects.
		A procedure is a function which returns no value but has only side-effects.
		ANSI C even defines a type, void, for the result of a function that has no result.
	foldoc.org /?function (205 words)

	What is function? - A Word Definition From the Webopedia Computer Dictionary
		In this sense, a function is a type of procedure or routine.
		Most programming languages come with a prewritten set of functions that are kept in a library.
		Some programming languages make a distinction between a function, which returns a value, and a procedure, which performs some operation but does not return a value.
	www.webopedia.com /TERM/f/function.html (328 words)

	Functions
		The function definition must precede the first call to it.
		As in C, the function's opening bracket may optionally appear on the second line.
		f1 () { echo "Calling function \"f2\" from within function \"f1\"." f2 } f2 () { echo "Function \"f2\"." } f1 # Function "f2" is not actually called until this point, #+ although it is referenced before its definition.
	www.tldp.org /LDP/abs/html/functions.html (436 words)

	Function Objects
		In this example, the function object is an object of a user-defined class.
		An ordinary function is a function object, and so is a function pointer; more generally, so is an object of a class that defines
		In this example, the function object is of a user-defined class that has local state.
	www.sgi.com /tech/stl/functors.html (553 words)

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Topic: First-class function

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