en>Dexbot: Removing Link GA template (handled by wikidata)

2014-09-03T13:46:56Z

Removing Link GA template (handled by wikidata)

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en>JohnThorne at 19:12, 12 February 2014

2014-02-12T19:12:11Z

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	~~{{Data transformation}}~~		Hi, everybody! My name is Clifford. <br>It is a little about myself: I live in Netherlands, my city of Veghel. <br>It's called often Eastern or cultural capital of NB. I've married 3 years ago.<br>I have two children - a son (Catherine) and the daughter (Monroe). We all like Agriculture Show.<br><br>My page :: [http://www.21ccnn.com/timeplaza/Shownews.asp?id=833 Fifa 15 coin generator]

	~~{{refimprove\|date=September 2010}}~~

	~~'''Refinement'''~~ is a generic term of computer science that encompasses various approaches for producing [[correctness (computer science)\|correct]] computer programs and simplifying existing programs to enable their formal verification.

	~~== Program refinement ==~~
	~~In [[formal methods]], '''program refinement'''~~ is ~~the [[formal verification\|verifiable]] transformation of an ''abstract'' (high-level) [[formal specification]] into~~ a ~~''concrete'' (low-level) [[executable program]].{{fact\|date=September 2010}} ''[[Stepwise refinement]]'' allows this process to be done~~ in ~~stages. Logically~~, ~~refinement normally involves [[logical consequence\|implication]], but there can be additional complications~~.

	~~== Data refinement ==~~
	~~'''Data refinement'''~~<~~!-- REDIRECTs HERE--~~> ~~is used to convert an abstract data model (in terms of [[set (mathematics)\|set]]~~s for example) into implementable [[data structures]] (such as [[Array data structure\|arrays]]).{{fact\|date=September 2010}} ''[[Operation refinement]]'' converts a [[specification]] of an operation on a system into an implementable [[computer program\|program]] (e.g., a [[Procedure (computer science)\|procedure]]). The [[postcondition]] can be strengthened and/or ~~the [[precondition]] weakened in this process. This reduces any [[Nondeterministic algorithm\|nondeterminism]] in the specification, typically to a completely [[deterministic]] implementation.~~

	~~For example, ''x'' ∈ {1,2,3} (where ''x'' is the value~~ of ~~the [[Variable (programming)\|variable]] ''x'' after an operation) could be refined to ''x'' ∈ {1,2}, then ''x'' ∈ {1}, and implemented as ''x'' := 1~~. ~~Implementations of ''x'' := 2 and~~ '~~'x'' :=~~ 3 ~~would be equally acceptable in this case, using a different route for the refinement~~. ~~However, we must be careful not to refine to ''x'' ∈ {} (equivalent to ''false'') since this is unimplementable; it is impossible to select~~ a ~~[[Element~~ (~~mathematics~~)~~\|member]] from~~ the ~~[[empty set]].~~

	~~The term [[Reification (computer science)\|reification]] is also sometimes used (coined by [[Cliff Jones~~ (~~computer scientist)\|Cliff Jones]]~~). ~~[[Retrenchment (computing)\|Retrenchment]] is an alternative technique when formal refinement is not possible~~. ~~The opposite of refinement is [[Abstraction (computer science)\|abstraction]].~~

	~~== Refinement calculus ==~~
	[[Refinement calculus]] is a [[formal system]] (inspired from [[Hoare logic]]) that promotes program refinement. The [[FermaT Transformation System]] is an industrial-strength implementation of refinement. The [[B-Method]] is also a [[formal method]] that extends refinement calculus with a component language: it has been used in industrial developments.

	~~== Refinement types ==~~
	In [[type theory]], a '''refinement type'''<ref>{{cite conference\|first1=T.\|last1=Freeman\|first2=F.\|last2=Pfenning\|url=ftp://ftp.cs.cmu.edu/usr/rwh/www/home/courses/refinements/papers/Freeman94/phd.pdf\|doi=10.1145/113445.113468 \|title=Reﬁnement types for ML\|booktitle=Proceedings of the ACM Conference on Programming Language Design and Implementation\|pages=268–277\|year=1991}}<~~/ref~~><~~ref~~>~~{{cite conference\|first=S.\|last=Hayashi\|title=Logic of reﬁnement types\|url=~~http://~~citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.38.6346&rep=rep1&type=pdf#page=167\|doi=10~~.~~1007/3-540-58085-9_74\|booktitle=Proceedings of the Workshop on Types for Proofs and Programs\|pages=157–172\|year=1993}}</ref><ref>{{cite conference\|first=E~~.~~\|last=Denney\|url=http:~~//~~citeseerx.ist.psu~~.~~edu/viewdoc/download~~?doi=10.1.1.22.4988&rep=rep1&type=pdf\|title=Reﬁnement types for speciﬁcation\|booktitle=Proceedings of the IFIP International Conference on Programming Concepts and Methods\|volume=125\|pages=148–166\|publisher=Chapman & Hall\|year=1998}}</ref> is a type endowed with a predicate which is assumed to hold for any element of the refined type. Refinement types can express [[precondition]]s when used as [[function argument]]s or [[postcondition]]s when used as [[return type]]s: for instance, the type of a function which accepts natural numbers and returns natural numbers greater than 5 may be written as <math>f: \mathbb{N} \rarr \{n: \mathbb{N} \| n > 5\}</math>. Refinement types are thus related to [[behavioral subtyping]].

	=~~= References ==~~
	~~{{reflist}}~~

	~~{{soft-eng-stub}}~~

	~~[[Category:Formal methods]]~~
	~~[[Category:Computer programming]~~]

en>Djongkind: /* External links */

2014-01-16T14:27:15Z

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en>ChuispastonBot: r2.7.1) (Robot: Adding eo:Kodekso klaromontana

2012-03-10T16:04:41Z

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en>Dexbot: Removing Link GA template (handled by wikidata)

en>JohnThorne at 19:12, 12 February 2014

en>Djongkind: /* External links */

en>ChuispastonBot: r2.7.1) (Robot: Adding eo:Kodekso klaromontana