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Topic: Partial function

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	Partial function - Wikipedia, the free encyclopedia
		An example of a partial function that is not a total function.
		In mathematics, a partial function is a relation that associates each element of a set (sometimes called its domain) with at most one element of another (possibly the same) set, called the codomain.
		Therefore, the natural logarithm function is not a total function when viewed as a function from the reals to themselves, but it is a partial function.
	en.wikipedia.org /wiki/Partial_function (381 words)

	Encyclopedia :: encyclopedia : Function (mathematics) (Site not responding. Last check: 2007-10-21)
		In mathematics, a function is a relation, such that each element of a set (the domain) is associated with a unique element of another (possibly the same) set (the codomain, not to be confused with the range).
		A very common type of function occurs when the argument (input) and the value (output) are both numbers, the functional relationship is expressed by a formula, and the value (output) of the function is obtained by direct substitution of the argument into the formula.
		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.
	www.hallencyclopedia.com /Function_(mathematics) (3005 words)

	Function (mathematics) - Wikipedia, the free encyclopedia
		Thus, the "is a square root of" relation is a function, and it contains for example, the pairs (3, 9) and (-3, 9); while the converse, "is the square of" relation, is not a function because it contains both the pairs (9, 3) and (9, −3), and 3 is not equal to −3.
		In this definition, a function is a special case of a relation, in particular a function is a relation in which every first element has a unique second element.
		The squaring function is the inverse of the non-negative square root function.
	en.wikipedia.org /wiki/Function_(mathematics) (3457 words)

	PEP 309 -- Partial Function Application
		This proposal is for a function or callable class that allows a new callable to be constructed from a callable and a partial argument list (including positional and keyword arguments).
		Expressing a function in terms of partial application of arguments to another function can be both elegant and powerful, and in functional languages it is heavily used.
		Partially applying arguments from the right, or inserting arguments at arbitrary positions creates its own problems, but pending discovery of a good implementation and non-confusing semantics, I don't think it should be ruled out.
	www.python.org /dev/peps/pep-0309 (1161 words)

	PlanetMath: recursive function
		Intuitively, a recursive function is a positive integer valued function of one or more positive integer arguments which may be computed by a definite algorithm.
		Recursive functions may be defined more rigorously as the largest class of partial functions from
		This is version 12 of recursive function, born on 2004-09-04, modified 2006-01-13.
	planetmath.org /encyclopedia/RecursiveFunction.html (249 words)

	Partial recursive functions
		Primitive Recursive Functions are a subset of Total Recursive Functions with the restriction that only primitive recursion is used a finite number of times and recursion uses zero and the successor function.
		This can be extended to partial recursive functions over the integers and over the rational numbers, ratio of two integers, but can not be extended to the set of real numbers.
		y=f(x) is not a partial recursive function when x and y are from the set of real numbers and f(x) is defined as the square root of x, also written as the value of y that satisfies y2 = x or y2 - x = 0.
	www.cs.wwc.edu /~aabyan/Logic/Book/book/node151.html (294 words)

	Functions and Function Definitions (Site not responding. Last check: 2007-10-21)
		Partial functions necessarily arise when functions are defined by computations because for some values of the arguments the computation defining the value of the function may not terminate.
		A predicate is a function whose range consists of the truth values T and F. c.
		That is, we may change the names of the bound variables in a function expression without changing the value of the expression, provided that we make the same change for each occurrence of the variable and do not make two variables the same that previously were different.
	www-formal.stanford.edu /jmc/recursive/node2.html (993 words)

	Peter Suber, "Recursive Function Theory"
		Because recursive function theory was developed in part to capture the intuitive sense of effectiveness in a rigorous, formal theory, it is important to the theory that the class of recursive functions can be built up from intuitively effective simple functions by intuitively effective techniques.
		The factorial function is derived by primitive recursion from the functions for multiplication and subtraction.
		Functions using unbounded minimization that does not terminate are called partial recursive because they are partial functions.
	www.earlham.edu /~peters/courses/logsys/recursiv.htm (3359 words)

	Assessment of Airway Function Using Partial Expiratory Flow-Volume Curves . How Reliable are Measurements of Maximal ...
		By superimposing the partial flow-volume curves shown in (a) and (b) on that obtained from the same infant at raised lung volume (c), the magnitude of the shift in end-expiratory level during the recordings of the partial curves became apparent.
		Diminished lung function as a predisposing factor for wheezing respiratory illness in infants.
		Bronchial responsiveness and lung function in recurrently wheezy infants.
	ajrccm.atsjournals.org /cgi/content/full/159/2/480 (4228 words)

	Recursive function theory - HaskellWiki
		f is a partial function from A to B (it may be either a total function or a proper partial function).
		It may mean that proper partial functions simply fail to terminate, without reflecting this possibility in the type system in any way.
		Remark: these operations take partial functions as arguments, but they are total operations themselves in the sense that they always yield a result -- at worst an empty function (as an ultimate partial function).
	www.haskell.org /haskellwiki/Recursive_function_theory (938 words)

	Dr. Dobb's \| Functional Programming in Java \| September 29, 2005
		Partial function objects are function objects that have received at least one of their arguments and have at least one argument that has not been specified.
		Partial function objects with three or more arguments left are similar to a partial function object with two arguments left.
		Another advantage of partial function objects extending from function object base classes is that the function object base classes may be used for typing function objects.
	www.ddj.com /184406320 (3185 words)

	World Web Math: Vector Calculus: Partial Differentiation
		A partial function is a one-variable function obtained from a function of several variables by assigning constant values to all but one of the independent variables.
		A partial derivative is the rate of change of a multi-variable function when we allow only one of the variables to change.
		To get an intuitive grasp of partial derivatives, suppose you were an ant crawling over some rugged terrain (a two-variable function) where the x-axis is north-south with positive x to the north, the y-axis is east-west and the z-axis is up-down.
	web.mit.edu /wwmath/vectorc/scalar/partial.html (706 words)

	functional :: documentation (Site not responding. Last check: 2007-10-21)
		Those looking to learn more about functional programming are encouraged to do a Google search for "python functional programming".
		The function is applied to the starting value and the first element of the list, then the result of that and the second element of the list, then the result of that and the third element of the list, and so on.
		is used for partial function application which "freezes" some portion of a function's arguments and/or keywords resulting in a new object with a simplified signature.
	oakwinter.com /code/functional/documentation.html (555 words)

	Scattering: the Partial Wave Expansion
		Note that the Bessel function is the one well-behaved at the origin: it could be generated by integrating out from the origin with initial boundary conditions of value one, slope zero.
		It is perhaps worth mentioning that for scattering in just one partial wave, the outgoing current is equal to the ingoing current, whether there is a phase shift or not.
		This becomes evident when one considers that the depth at which the scattering length becomes infinite can be thought of as formally having a zero energy bound state, in that although the wave function outside is not normalizable, it is equivalent to an exponentially decaying function with infinite decay length.
	galileo.phys.virginia.edu /classes/752.mf1i.spring03/Scattering_II.htm (2124 words)

	Function following partial fibulectomy - Wheeless' Textbook of Orthopaedics
		1987 Jul(220): 206-10 The fibula is a valuable source of a bone graft, but because the fibula has a role in lower extremity function, it is important to determine whether partial removal results in dysfunction or other problems.
		Forty-one patients (48 +/- 10 years of age) had a portion of their fibula removed for a bone graft.
		This study demonstrates that most patients will have subjective complaints and mild muscular weakness after removal of a portion of the fibula.
	www.wheelessonline.com /ortho/function_following_partial_fibulectomy (170 words)

	NIH Press Release - ACTG 315 Preliminary Results: Drug Cocktail Restores Partial Immune Function - 01/26/1997
		In-depth studies of immune function in people with moderately advanced HIV disease who were treated for three months with an antiretroviral drug cocktail show that immunity can be partially restored, according to preliminary results from AIDS Clinical Trials Group (ACTG) 315, supported by the National Institute of Allergy and Infectious Diseases (NIAID).
		The data show that the dramatic rise in CD4 counts and fall in plasma levels of virus seen early after starting HAART are accompanied by partial restoration of the immune response.
		Functional immune response, as measured by delayed-type hypersensitivity (a skin test used to assess cellular immune function) and lymphocyte proliferation assays (to assess immune memory), was only partially restored.
	www.nih.gov /news/pr/jan97/niaid-26.htm (991 words)

	Serialization - Implementation Notes
		the function declaration is first matched against templates with an integer for the third argument.
		We have managed to use function overloading to achieve the same effect as PFTO were it correctly implemented.
		To function save/load/serialize member function templates must be defined within the class definition.
	www.boost.org /libs/serialization/doc/implementation.html (2144 words)

	Partial Recursive Functions (Site not responding. Last check: 2007-10-21)
		Partial recursive functions are particular functions from some subset of vectors of NaturalNumbers to NaturalNumbers.
		A partial recursive function may be undefined (divergent) at some points.
		Also if f(x,y1,...,yn) is a partial recursive function of n+1 variables then (uf)(y1,...,yn) is a partial recursive function of n variables.
	c2.com /cgi/wiki?PartialRecursiveFunctions (148 words)

	PlanetMath: partial function
		is sometimes called a total function, to signify that
		, but a partial function need not be defined for every element of its domain.
		This is version 7 of partial function, born on 2002-08-23, modified 2005-05-08.
	planetmath.org /encyclopedia/TotalFunction.html (56 words)

	Is the Halting problem effectively solvable non-algorithmically?
		Classically ([Me64], p120-121, p214), a partial function F of n arguments is called partial recursive if, and only if, F can be obtained from the initial functions (zero function), projection functions, and successor function (of classical recursive function theory) by means of substitution, recursion and the classical, unrestricted, μ-operator.
		We define a number-theoretic function, or relation, as total if, and only if, it is effectively computable, or effectively decidable, respectively, for any, given, set of natural number values assigned to its free variables.
		We define a partial number theoretic function, or relation, as effectively computable, or decidable, respectively, if, and only if, it is effectively computable, or decidable, respectively, for any, given, set of values, assigned to its free variables, for which it is defined.
	alixcomsi.com /Is_the_Halting_problem.htm (2836 words)

	New for Python 2.5 \| Lambda the Ultimate
		If the Python crew is adding partial application to the language, I'm curious why they wouldn't have gone the whole hog and added in partial evaulation.
		Partial function application is being added to the library, not the language.
		My experience with Dylan/Scheme, which also have a "curry" function (yeah, they get the name wrong), is that brevity is very important for partial application.
	lambda-the-ultimate.org /node/view/1227 (1206 words)

	partial ordering from FOLDOC (Site not responding. Last check: 2007-10-21)
		A relation R is a partial ordering if it is a pre-order (i.e.
		The ordering is partial, rather than total, because there may exist elements x and y for which neither x R y nor y R x.
		A lattice is a partial ordering where all finite subsets have a least upper bound and a greatest lower bound.
	www.instantweb.com /foldoc/foldoc.cgi?partial+ordering (229 words)

	Partial Continuations
		Given a native implementation of partial continuations in the programming languge this would be a faster operation and less memory intensive.
		The function that resumes an URL first captures the 'exit-continuation', and calls the continuation associated with the requested URL.
		The 'show' function is used to display a page to the user and return.
	double.co.nz /scheme/partial-continuations/partial-continuations.html (1777 words)

	3 PEP 309: Partial Function Application
		function, but new functions will probably be added in future versions of Python.
		For programs written in a functional style, it can be useful to construct variants of existing functions that have some of the parameters filled in.
		This is called ``partial function application'', and is provided by the
	docs.python.org /dev/whatsnew/node4.html (166 words)

	6. Partial Recursive Functions (Site not responding. Last check: 2007-10-21)
		Definition 6.3 A function is partial recursive if it can be obtained from the base functions (null, successor, projections) by finitely many applications of the operations of substitution, primitive recursion, and minimization.
		A partial recursive function which is total is called total recursive.
		is identical to the class of partial recursive functions.
	www.cs.pitt.edu /~daley/cs2110/notes/cs2110w_node26.html (406 words)

	[grape] 9 Partial Linear Spaces
		It calls functions making use of the nauty package within GRAPE, and so can only be used on UNIX systems on which GRAPE has been fully installed.
		It follows from basic theory of partial geometries that the Haemers partial geometry is uniquely determined up to isomorphism (as a partial geometry) by its point graph.
		We also show that the dual of the Haemers partial geometry is also uniquely determined by its point graph.
	www-groups.dcs.st-and.ac.uk /~gap/Manuals/pkg/grape/htm/CHAP009.htm (663 words)

	Partial Hyperdoctrines: Categorical Models for Partial Function Logic and Hoare Logic - Knijnenburg, Nordemann ...
		To this end, we extend the well-known notion of a (first-order) hyperdoctrine to include partial maps.
		The most important new aspect of the resulting partial (first order) hyperdoctrine is a different notion of morphism between the fibres.
		Partial hyperdoctrines: categorical models for partial function logic and Hoare logic.
	citeseer.ist.psu.edu /307548.html (530 words)

	Partial Function Types
		This approach to partial functions has not been retained in standard Nuprl developments.
		We handle partial functions by viewing them as total functions over their domains of convergence.
		Thus, for a partial function application to be sensible one must prove that the domain of convergence predicate is true for the argument, i.e., that the argument is in the domain of convergence of the function.
	www.cs.cornell.edu /Info/Projects/NuPrl/book/node220.html (168 words)

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