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Topic: Compatibility equivalence

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Compatibility decomposition

Character encoding

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	UAX #15: Unicode Normalization Forms
		However, some characters with compatibility decompositions are used in mathematical notation to represent distinction of a semantic nature; replacing the use of distinct character codes by formatting may cause problems.
		For example, a compatibility composition of “office” does not produce “o\uFB03ce”, even though “\uFB03” is a character that is the compatibility equivalent of the sequence of three characters “ffi”.
		Compatibility decomposition is the process of taking a string, replacing composite characters using both the Unicode canonical decomposition mappings and the Unicode compatibility decomposition mappings, and putting the result in canonical order.
	www.unicode.org /reports/tr15 (9142 words)

	Compatibility equivalence - Wikipedia, the free encyclopedia
		Compatibility equivalence refers to a state in which two technically dissimilar things may be considered functionally identical.
		In Unicode, for instance, the compatibility equivalence of two strings (sequences of letters, numbers, or other characters) means that they can be reduced to identical strings by recursive application of both canonical decomposition and compatibility decomposition routines.
		Two Unicode strings that have the relation of compatibility equivalence may sometimes be considered identical, but generally they are not—the "micro sign" (µ) and "greek small letter mu" (μ) are similar, for example, but they are not considered strictly identical.
	en.wikipedia.org /wiki/Compatibility_equivalence (141 words)

	Canonical equivalence - Wikipedia, the free encyclopedia
		Canonical equivalence refers to the state in which two things are in every significant respect identical.
		In Unicode, for instance, the canonical equivalence of two strings means that they can be reduced to identical strings by recursive application of canonical decomposition routines.
		(Compare compatibility equivalence.) Canonically equivalent strings always have the same meaning and behaviour; they should also look the same and be indistinguishable to the user.
	en.wikipedia.org /wiki/Canonical_equivalence (114 words)

	Equivalence
		Compatibility equivalence Compatibility equivalence refers to a state in which two technically dissimilar things may be...
		Equivalence of categories In mathematics, an equivalence of categories is a relation between two categories that establi...
		Equivalence of matter and energy An equivalance between the mass and enery of matter is quantified by the relationship p...
	www.brainyencyclopedia.com /topics/equivalence.html (287 words)

	Riemann surface - Wikipedia, the free encyclopedia
		If A is a collection of compatible charts and if any x in X is in the domain of some f in A, then we say that A is an atlas.
		The theory of compact Riemann surfaces can be shown to be equivalent to that of algebraic curves that are defined over the complex numbers and non-singular.
		The two Riemann surfaces M and N are called conformally equivalent if there exists a bijective holomorphic function from M to N whose inverse is also holomorphic (it turns out that the latter condition is automatic and can therefore be omitted).
	en.wikipedia.org /wiki/Riemann_surface (1187 words)

	Compatibility
		Compatibility decomposition In Unicode, the compatibility decomposition of a character is a string that holds the relati...
		Compatibility layer In libraries for the emulated system, this will often be sufficient to run binaries for the host sys...
		Forward compatibility Forward compatibility is the ability of a system to accept input from later versions of itself.
	www.brainyencyclopedia.com /topics/compatibility.html (167 words)

	Datatype - Wikipedia, the free encyclopedia
		The equivalent of the first example would fail (one operand not a number), and the second would yield "9", unambiguously.
		The question of compatibility and equivalence is a complicated and controversial topic and it is related to the problem of substitutability: that is, given type A and type B, are they equal types or compatible?
		If type A is compatible with type B, A is a subtype of B while not always vice versa.
	en.wikipedia.org /wiki/Data_type (2464 words)

	Text Normalization - 秋梦无痕 - 阅读网志
		One example of canonical equivalence is a precomposed character and its equivalent combining sequence.
		The single character and the character sequence are canonically equivalent because they are visually indistinguishable and mean exactly the same for the purposes of text comparison and rendering.
		Compatibility equivalence, on the other hand, deals mostly with legacy character sets which define alternate visual representations of the same character or character sequence.
	www.sinzy.net /blog/Read.asp?ID=44&BID=12044 (1058 words)

	SENG 609.03 Object Theory: Course Work (Site not responding. Last check: 2007-10-14)
		In this paper first the classification by evolutionary hierarchy in biology and then by equivalence relations in mathematics are analyzed and their relations are explored (Wegner, 1988, p:479).
		Equivalence relations are the canonical classification mechanisms of mathematics.
		The partial equivalence and compatibility relations are used in the discussion of typed versus untyped formalisms.
	sern.ucalgary.ca /~moussavm/609.03/presentation6.html (2319 words)

	[No title] (Site not responding. Last check: 2007-10-14)
		Name equivalence is used for these types with the exception that a subclass type object may be assigned to a superclass variable.
		Structural equivalence for scalars Arrays must be structurally equivalent (ignoring size) with name equivalent component types¡Z:Z:ª« ó¨Type Compatibility¨èGeneral term type compatibility* applies both to assignment and comparison with relational operators.
		C and Java: all numeric types are compatible Ada subranges of the same type are compatible¡L""ª,» !ó¨Assignment Compatibility¨¼Assignment compatibility is used to determine when a value of one type may be assigned or passed as a parameter to a variable of another type.
	www.cise.ufl.edu /~jnw/COP5555-200308/Lectures/Types2.ppt (292 words)

	Internationalized Resource Identifiers (IRIs)
		The compatibility is provided by specifying a well defined and deterministic mapping from the IRI character sequence to the functionally equivalent URI character sequence.
		Equivalence of IRIs MUST rely on the assumption that IRIs are appropriately pre-character-normalized, rather than applying character normalization when comparing two IRIs.
		This kind of technique is only appropriate when equivalence is clearly indicated by both the result of accessing the resources and the common conventions of their scheme's dereference algorithm (in this case, use of redirection by HTTP origin servers to avoid problems with relative references).
	www.w3.org /International/iri-edit/draft-duerst-iri.html (13647 words)

	UAX #15: Unicode Normalization Forms
		Canonical equivalence is a fundamental equivalency between characters or sequences of characters that represent the same abstract character, and when correctly displayed should always have the same visual appearance and behavior.
		Compatibility equivalence is a weaker equivalence between characters or sequences of characters that represent the same abstract character, but may have different visual appearance or behavior.
		Generate the compatibility decomposition for the source string S according to the decomposition mappings in the latest supported version of the Unicode Character Database.
	www.unicode.org /reports/tr15/tr15-28.html (9774 words)

	[No title]
		The equivalence of Ho GKB and hGWB 112 9.2.
		Compatibility relations The term "compatibility relation" has been used in algebraic geometry in the context of Grothendieck's six functor formalism that relates base change functo* *rs to tensor product and internal hom functors in sheaf theory.
		For example, the Whitehead theorem that a weak equivalence between cell complexes is a homotopy equivalence, or its analogue that a quasi-isomorph* ism between projective complexes is a homotopy equivalence*, is a formal consequence of this adjunction between homotopy categories.
	hopf.math.purdue.edu /May-Sigurdsson/MSMaster.txt (21075 words)

	Unicode Character Encoding of Archived Linguistic Data
		The relationship between a compatibility character and its near synonym is captured in Unicode in the same manner as canonical equivalence: a normative decomposition mapping is provided for compatibility characters.
		Compatibility characters are those that would not have been encoded (except for compatibility) because they are in some sense variants of characters that have already been coded...
		In general, we can recommend that compatibility characters not be used, except in the case of the specific superscript characters (many of which have yet to be added to the standard) that are used for phonetic and phonemic transcription or for other linguistic purposes, such as transliteration.
	www.ldc.upenn.edu /exploration/expl2000/papers/constable2/constable2.html (10148 words)

	4.9 unicodedata -- Unicode Database
		The Unicode standard defines various normalization forms of a Unicode string, based on the definition of canonical equivalence and compatibility equivalence.
		In addition to these two forms, there are two additional normal forms based on compatibility equivalence.
		The normal form KC (NFKC) first applies the compatibility decomposition, followed by the canonical composition.
	www.python.org /doc/current/lib/module-unicodedata.html (487 words)

	UAX #15: Unicode Normalization
		However, some characters with compatibility decompostions are used in mathematical notation to represent distinction of a semantic nature; replacing the use of distinct character codes by formatting may cause problems.
		The difference between these depends on whether the resulting text is to be a canonical equivalent to the original unnormalized text, or is to be a compatibility equivalent to the original unnormalized text.
		An offset into a Unicode string is a number from 0 to n, where n is the length of the string, and indicates a position that is logically between Unicode code units (or at the very front or end in the case of 0 or n respectively).
	www.unicode.org /reports/tr15/tr15-24.html (7206 words)

	Character Equivalence (Site not responding. Last check: 2007-10-14)
		Canonical equivalence is a fundamental equivalence between individual Unicode characters and sequences of Unicode characters.
		The composite character and the two-character sequence are canonical equivalents.
		Another example of compatibility equivalence is between circled and un-circled versions of characters.
	www.roguewave.com /support/docs/sourcepro/i18nug/5-2.html (223 words)

	UTR #15: Unicode Normalization
		Because the characters are visually distinguished, replacing a character by a compatibility equivalent may lose formatting information unless supplemented by markup or styling.
		With forms D and C, compatibility characters (those with compatibility mappings) are retained; with KD and KC they are replaced.
		All of the definitions in this document depend on the rules for equivalence and decomposition found in Chapter 3 of The Unicode Standard and the decomposition and combining class mappings in the Unicode Character Database.
	www.unicode.org /reports/tr15/tr15-18.html (5528 words)

	8.2. The string Copy Constructor
		This is a holdover from C and is necessary for compatibility with C programs.
		People who like C will tell you how "flexible" the equivalence of pointers and arrays is in C. That's true, but it's also extremely dangerous because it means that arrays have no error checking whatsoever.
		In case this equivalence of arrays and pointers isn't immediately obvious to you, you're not alone; it wasn't obvious to Susan, either.
	www.steveheller.com /cppad/Output/downpath3a.html (4130 words)

	Understanding Unicode™ - II
		Formally, the compatibility equivalence relationship between two characters is shown in a compatibility decomposition mapping that is part of the Unicode character properties.
		Note that the tag is used for a variety of characters that stand in one of several types of relationship to their corresponding decomposed counterparts.
		As a consequence of this, it should be noted that an instance of compatibility equivalence always involved exactly two representations: the compatibility character and the corresponding decomposed representation given in the mapping.
	scripts.sil.org /cms/scripts/page.php?site_id=nrsi&item_id=IWS-Chapter04b&_sc=1 (12487 words)

	Syntactic Analysis - The Relationship Between Phrases and Tree Nodes
		Symbolic equivalence classes are used to group together symbols appearing in the concrete syntax because the semantics of the symbols are equivalent.
		Symbolic equivalence classes can only be created for symbols which are either all nonterminals or all terminals (see How to describe a context-free grammar).
		Aside from symbolic mappings (see Specifying symbolic equivalence classes) and the use of LISTOF constructs, the generated concrete and abstract syntaxes need to be identical in order to allow computations to take place during tree construction.
	eli-project.sourceforge.net /elionline4.4/syntax_2.html (3293 words)

	EQUIVALENCE (Site not responding. Last check: 2007-10-14)
		EQUIVALENCE statements require only the first subscript of a multidimensional array (unless the STRICT compiler directive is in effect).
		If an EQUIVALENCE object is default integer, default real, double-precision real, default complex, default logical, or a sequenced derived type of all numeric or logical components, all objects in the EQUIVALENCE statement must be one of these types, though it is not necessary that they be the same type.
		If an EQUIVALENCE object is a sequenced derived type that is not purely numeric or purely character, all objects in the EQUIVALENCE statement must be the same derived type.
	www.compaq.com /fortran/docs/vf-html/azsumm/rfequiv.htm (753 words)

	Exporter's Guides: NAFTA Chapter 9 (Site not responding. Last check: 2007-10-14)
		It states that the three countries shall, to the greatest extent practicable, make their standards-related measures compatible, without reducing levels of safety or protection for human, animal or plant life or health.
		Chapter Nine’s provisions relating to compatibility and equivalence make it less likely that U.S. companies will be faced with the costly and time-consuming burden of adapting their products to different standards in the three NAFTA countries.
		With respect to standards and comformity accessment procedures, each NAFTA country shall, on request, seek to promote the compatibility of a specific standard or conformity assessment procedure with standards or conformity assessment procedures maintained by the requesting country.
	www.mac.doc.gov /tcc/e-guides/eg_naf09.html (1106 words)

	[Nickle]Re: structure compatibility (was: I'm confused about type promotion) (Site not responding. Last check: 2007-10-14)
		Previous message: [Nickle]Re: structure compatibility (was: I'm confused about type promotion)
		Structural equivalence finesses these issues by comparing the type structure instead of the type pointers.
		I would personally prefer name equivalence, but I don't want to wreck Nickle for interactive use.
	keithp.com /pipermail/nickle/2002-July/000115.html (168 words)

	Compaq Fortran (Site not responding. Last check: 2007-10-14)
		Table A-1 summarizes the compatibility of Compaq Fortran for Compaq Tru64 UNIX and Linux Alpha systems with Compaq Fortran on OpenVMS Alpha Systems, Compaq Fortran 77 on other platforms (architecture/operating system pairs), and Compaq Visual Fortran for Windows systems.
		The file and record formats of Compaq Fortran 77 on Compaq Tru64 UNIX systems are compatible with Compaq Fortran on Compaq Tru64 UNIX and Linux Alpha systems; they share the same language run-time I/O environment (see Chapter 7).
		Equivalent record types must be copied carefully to preserve control information and record characteristics.
	h18009.www1.hp.com /fortran/docs/unix-um/dfumcompat.htm (7134 words)

	[No title]
		compare the two expanded strings, if they are the same, then the types are equivalent e.g., type foo = record a : integer b : integer end; type bar = record b : integer a : integer end; If structural equivalence is adopted, foo and bar are not the same type.
		(This is stricker than structural equivalence) e.g., in Java, Pascal, and Ada e.g., struct RecA { char x; int y; }; typedef struct RecA RecA; struct RecA a; RecA b; struct RecA c; struct { char x; int y; } d; all of the variables a, b, c, and d are structurally equivalent.
		a and c are name equivalent, and they are not name equivalent to b and d.
	www.eecis.udel.edu /~lliao/cis670/103102.txt (578 words)

	92 Frequently Asked Questions on the New 510(K) Paradigm
		According to this section of the act, a declaration of conformity to a recognized standard must certify that the device is in conformance.
		For example, if a manufacturer states that a device will conform to IEC-60601-1-2 Electromagnetic Compatibility and substantial equivalence for the predicate device had been determined without conformance to the standard, then the submission could be reviewed as an Abbreviated 510(k).
		Section 514 of the act requires persons declaring conformity to a standard to maintain data and information demonstrating conformity of the device to the standard for two years after the date of the substantial equivalency determination or for a period equal to the expected design life of the device, whichever is longer.
	www.fda.gov /cdrh/ode/92_a.html (3065 words)

	[No title]
		The equivalence between 1) and 2) is a precomposed/decomposed equivalence, where 1) is the precomposed representation, and 2) is the decomposed representation.
		Cases not dealt with by Canonical Equivalence This section gives a list of cases that are not dealt with by Canonical Equivalence and Normalization Form C. This is done to help the reader understand Normalization Form C and its limits.
		However, while Canonical Equivalence, which forms the base of Normalization Form C, deals with a very small number of very well defined cases of complete equivalence (from an user point of view), Compatibility Equivalence comprises a very wide range of cases that usually have to be examined one at a time.
	www.ietf.org /proceedings/00dec/I-D/draft-duerst-i18n-norm-04.txt (5193 words)

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