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en>Cnilep: disambiguate

2014-04-03T04:28:41Z

disambiguate

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	~~{{Other uses\|LOOP (disambiguation){{!}}LOOP}}~~		Letrado desde hace 20 años<br><br>My page; [http://www.acanizaresabogados.com/abogados-divorcios/ abogado divorcio]

	'''LOOP''' is a pedagogical programming language designed by [[Uwe Schöning]], along with [[GOTO (programming language)\|GOTO]] and [[WHILE (programming language)\|WHILE]]. The only operations supported in the language are assignment, addition and looping.

	The key property of the LOOP language is that the functions it can compute are exactly the [[primitive recursive function]]s.<ref>{{cite book\|author=Herbert Enderton\|year=2012\|title=Computability Theory\|publisher=Academic Press}}</ref>

	~~== Features ==~~
	Each [[primitive recursive function]] is LOOP-computable and vice versa.<ref>{{Cite book \| first=Uwe \| last=Schöning \| title=Theoretische Informatik-kurz gefasst \| edition=5 \| publisher=Oxford University Press \| location=London \| year=2008 \| page=105 \| ISBN=978-3-8274-1824-1 \| dnb=986529222}}</ref>

	~~In contrast to [[GOTO (programming language)\|GOTO]] programs and [[WHILE (programming language)\|WHILE]] programs, LOOP programs always [[terminating computation\|terminate]].~~<~~ref~~>{{Cite book \| first=Uwe \| last=Schöning \| title=Theoretische Informatik-kurz gefasst \| edition=5 \| publisher=Oxford University Press \| location=London \| year=2008 \| page=93 \| ISBN=978-3-8274-1824-1 \| dnb=986529222}}<~~/ref~~> Therefore, the set of functions computable by LOOP-programs is a proper subset of [[computable function]]s (and thus a subset of the computable by WHILE and GOTO program functions).<ref>{{Cite book \| first=Uwe \| last=Schöning \| edition=4 \| title=Theoretische Informatik-kurz gefasst \| year=2001 \| publisher=Oxford University Press \| location=London \| page=122 \| ISBN=3-8274-1099-1}}</ref>

	An example of a total computable function that is not LOOP computable is the [[Ackermann function]].<ref>{{Cite book \| first=Uwe \| last=Schöning \| title=Theoretische Informatik-kurz gefasst \| edition=5 \| publisher=Oxford University Press \| location=London \| year=2008 \| page~~=112 \| ISBN=978-3-8274-1824-1 \| dnb=986529222}}</ref>~~

	~~== Formal definition ==~~

	~~=== Syntax ===~~
	~~LOOP-programs consist of the symbols <code>LOOP</code>, <code>DO</code>, <code>END</code>, <code>:=</code>, <code>+</code>, <code>-</code> and <code>~~;~~</code> as well as any number of variables and constants. LOOP-programs have the following~~ [~~[syntax]] in modified [[Backus-Naur Form]]:~~

	~~:<math>\begin{array}{lrl}~~
	~~P & := & x_i := x_j + c \\~~
	~~& \| & x_i := x_j - c \\~~
	~~& \| & P;P \\~~
	~~& \| & \mathrm{LOOP} \, x_i \, \mathrm{DO} \, P \, \mathrm{END}~~
	~~\end{array}~~
	~~</math>~~
	~~Here, <math>Var~~ :~~= \{ x_0, x_1, ... \}<~~/~~math> are variable names and <math>c \in \mathbb{N}<~~/~~math> are constants~~.

	~~=== Semantics ===~~
	~~If '''P''' is a LOOP program, '''P''' is equivalent to a function <math>f: \mathbb{N}^k \rightarrow \mathbb{N}</math>~~. The variables <math>x_1</math> through <math>x_k</math> in a LOOP program correspond to the arguments of the function <math>f</math>, and are initialized before program execution with the appropriate values. All other variables are given the initial value zero. The variable <math>x_0</~~math> corresponds to the value that <math>f</math> takes when given the argument values from <math>x_1</math> through <math>x_k</math>.~~

	~~A statement of the form~~
	~~x<sub>0</sub> := x<sub>1</sub> + c~~
	means the value of the constant <math>c</math> is added to the value of the variable <math>x_1</math>, and the result is set as the value of the variable <math>x_0</math>. <math>c</math> can have the value zero, which allows the value of one variable to be assigned to another variable:
	~~x<sub>0</sub> := x<sub>1</sub> + 0~~

	~~A statement of the form~~
	~~x<sub>0</sub> := x<sub>1</sub>~~ - c
	means the value of the constant <math>c</math>is subtracted from the value of the variable <math>x_1</math>, and the result is set as the value of the variable <math>x_0</math>. Negative numbers aren't allowed, and are replaced by zeros.

	~~Variables are allowed to be simultaneously on the left and right side of an assignment. A statement of the form:~~
	~~x<sub>1<~~/~~sub>: = x<sub>1</sub> + c~~
	~~for example, adds the value of the constant <math>c</math> to the variable <math>x_1</math>.~~

	~~A statement of the form~~
	~~''P''<sub>1</sub>; ''P''<sub>2</sub>~~
	~~represents the sequential execution of sub-programs <math>P_1</math> and <math>P_2</math>, in that order.~~

	~~A statement of the form~~
	~~LOOP x DO ''P'' END~~
	means the repeated execution of the partial program <math>P</math> a total of <math>x</math> times, where the value that <math>x</math> has at the beginning of the execution of the statement is used. Even if <math>P</math> changes the value of <math>x</math>, it won't affect how many times <math>P</math> is executed in the loop. If <math>x</math> has the value zero, then <math>P</math> is not executed inside the <code>LOOP</code> statement. This allows for [[Conditional (programming)\|branches]] in LOOP programs, where the conditional execution of a partial program depends on whether a variable has value zero or one.

	~~== Example Programs ==~~

	~~=== Addition ===~~
	~~In the following program, the variable <math>x_0</math> is set to the sum of the variables <math>x_1</math> and <math>x_2</math>.~~
	~~x<sub>0</sub> := x<sub>1</sub> + 0;~~
	~~LOOP x<sub>2</sub> DO~~
	~~x<sub>0</sub> := x<sub>0</sub> + 1~~
	~~END~~
	#
	<math>x_0</math> is first assigned the value of <math>x_1</math>. Then, <math>x_0</math> is incremented a total of <math>x_2</math> times by the <code>LOOP</code> statement. This program can be used as a subroutine in other LOOP programs. The LOOP syntax can be extended with the following statement, equivalent to calling the above as a subroutine:
	~~x<sub>0</sub> := x<sub>1</sub> + x<sub>2</sub>~~

	~~=== Multiplication ===~~
	~~The following LOOP program sets the value of the variable <math>x_0</math> to the product of the variables <math>x_1</math> and <math>x_2</math>.~~
	~~LOOP x<sub>1</sub> DO~~
	~~x<sub>0</sub> := x<sub>0</sub> + x<sub>2</sub>~~
	~~END~~
	#
	This multiplication program uses the syntax introduced by the addition subroutine from the previous example. The multiplication is performed here by adding the value of <math>x_2</math> a total of <math>x_1</math> times, storing results in <math>x_0</math>.

	~~== See also ==~~
	* [[μ-recursive function]]

	~~== Notes and references ==~~
	~~<references />~~

	~~== External links ==~~
	* [http://web.archive.org/web/20120311032544/http://loopgotowhile.eugenkiss.com/ Loop, Goto & While]

	~~[[Category:Computability theory]~~]

en>Anne Bauval: Undid revision 552482251 by Anne Bauval (talk)

2013-04-28T14:41:45Z

Undid revision 552482251 by Anne Bauval (talk)

← Older revision		Revision as of 16:41, 28 April 2013
Line 1:		Line 1:
	~~45-degree angle from~~ the ~~back~~, the ~~body smooth~~, ~~graceful lines~~.<br>~~It was worn over~~ a ~~slip like sage dress~~ and ~~paired with~~ a ~~squared green clutch~~.~~Evening dresses were strapless sheaths with lime stones or stripes~~ of ~~green and black ribbon~~ that ~~gave them a modernist edge~~.~~Handbags included lime~~ and ~~black clutches~~, ~~top handle doctor~~'~~s bags and soft~~, ~~roomy daytime bags~~ in ~~black~~ with ~~lime highlights~~. In the ~~event you loved this post~~ and ~~you would like~~ to ~~receive much more information relating~~ to ~~[http~~://~~www~~.~~bendtrapclub~~.~~com~~/~~cheap~~/~~ugg~~.~~asp Cheap Uggs Boots] i implore you to visit our own web~~-~~page~~. ~~Shoes were feminine pumps with~~ a ~~skinny heel~~ or ~~lace up booties~~.<br>~~http:~~//~~eastwest-tours~~.~~com~~/~~style/?p~~=57 <br /> ~~http~~://~~eastwest-tours~~.~~com~~/~~style~~/~~?p=154~~ <br /> ~~http~~://~~eastwest-tours.com~~/~~style~~/~~?p=206~~ <br /> ~~http~~://~~eastwest-tours~~.~~com~~/~~style~~/?p=33 <br /> http://~~eastwest-tours~~.~~com~~/~~style~~/~~?p=212 <br~~ />		{{Other uses\|LOOP (disambiguation){{!}}LOOP}}

			'''LOOP''' is a pedagogical programming language designed by [[Uwe Schöning]], along with [[GOTO (programming language)\|GOTO]] and [[WHILE (programming language)\|WHILE]]. The only operations supported in the language are assignment, addition and looping.

			The key property of the LOOP language is that the functions it can compute are exactly the [[primitive recursive function]]s.<ref>{{cite book\|author=Herbert Enderton\|year=2012\|title=Computability Theory\|publisher=Academic Press}}</ref>

			== Features ==
			Each [[primitive recursive function]] is LOOP-computable and vice versa.<ref>{{Cite book \| first=Uwe \| last=Schöning \| title=Theoretische Informatik-kurz gefasst \| edition=5 \| publisher=Oxford University Press \| location=London \| year=2008 \| page=105 \| ISBN=978-3-8274-1824-1 \| dnb=986529222}}</ref>

			In contrast to [[GOTO (programming language)\|GOTO]] programs and [[WHILE (programming language)\|WHILE]] programs, LOOP programs always [[terminating computation\|terminate]].<ref>{{Cite book \| first=Uwe \| last=Schöning \| title=Theoretische Informatik-kurz gefasst \| edition=5 \| publisher=Oxford University Press \| location=London \| year=2008 \| page=93 \| ISBN=978-3-8274-1824-1 \| dnb=986529222}}</ref> Therefore, the set of functions computable by LOOP-programs is a proper subset of [[computable function]]s (and thus a subset of the computable by WHILE and GOTO program functions).<ref>{{Cite book \| first=Uwe \| last=Schöning \| edition=4 \| title=Theoretische Informatik-kurz gefasst \| year=2001 \| publisher=Oxford University Press \| location=London \| page=122 \| ISBN=3-8274-1099-1}}</ref>

			An example of a total computable function that is not LOOP computable is the [[Ackermann function]].<ref>{{Cite book \| first=Uwe \| last=Schöning \| title=Theoretische Informatik-kurz gefasst \| edition=5 \| publisher=Oxford University Press \| location=London \| year=2008 \| page=112 \| ISBN=978-3-8274-1824-1 \| dnb=986529222}}</ref>

			== Formal definition ==

			=== Syntax ===
			LOOP-programs consist of the symbols <code>LOOP</code>, <code>DO</code>, <code>END</code>, <code>:=</code>, <code>+</code>, <code>-</code> and <code>;</code> as well as any number of variables and constants. LOOP-programs have the following [[syntax]] in modified [[Backus-Naur Form]]:

			:<math>\begin{array}{lrl}
			P & := & x_i := x_j + c \\
			& \| & x_i := x_j - c \\
			& \| & P;P \\
			& \| & \mathrm{LOOP} \, x_i \, \mathrm{DO} \, P \, \mathrm{END}
			\end{array}
			</math>
			Here, <math>Var := \{ x_0, x_1, ... \}</math> are variable names and <math>c \in \mathbb{N}</math> are constants.

			=== Semantics ===
			If '''P''' is a LOOP program, '''P''' is equivalent to a function <math>f: \mathbb{N}^k \rightarrow \mathbb{N}</math>. The variables <math>x_1</math> through <math>x_k</math> in a LOOP program correspond to the arguments of the function <math>f</math>, and are initialized before program execution with the appropriate values. All other variables are given the initial value zero. The variable <math>x_0</math> corresponds to the value that <math>f</math> takes when given the argument values from <math>x_1</math> through <math>x_k</math>.

			A statement of the form
			x<sub>0</sub> := x<sub>1</sub> + c
			means the value of the constant <math>c</math> is added to the value of the variable <math>x_1</math>, and the result is set as the value of the variable <math>x_0</math>. <math>c</math> can have the value zero, which allows the value of one variable to be assigned to another variable:
			x<sub>0</sub> := x<sub>1</sub> + 0

			A statement of the form
			x<sub>0</sub> := x<sub>1</sub> - c
			means the value of the constant <math>c</math>is subtracted from the value of the variable <math>x_1</math>, and the result is set as the value of the variable <math>x_0</math>. Negative numbers aren't allowed, and are replaced by zeros.

			Variables are allowed to be simultaneously on the left and right side of an assignment. A statement of the form:
			x<sub>1</sub>: = x<sub>1</sub> + c
			for example, adds the value of the constant <math>c</math> to the variable <math>x_1</math>.

			A statement of the form
			''P''<sub>1</sub>; ''P''<sub>2</sub>
			represents the sequential execution of sub-programs <math>P_1</math> and <math>P_2</math>, in that order.

			A statement of the form
			LOOP x DO ''P'' END
			means the repeated execution of the partial program <math>P</math> a total of <math>x</math> times, where the value that <math>x</math> has at the beginning of the execution of the statement is used. Even if <math>P</math> changes the value of <math>x</math>, it won't affect how many times <math>P</math> is executed in the loop. If <math>x</math> has the value zero, then <math>P</math> is not executed inside the <code>LOOP</code> statement. This allows for [[Conditional (programming)\|branches]] in LOOP programs, where the conditional execution of a partial program depends on whether a variable has value zero or one.

			== Example Programs ==

			=== Addition ===
			In the following program, the variable <math>x_0</math> is set to the sum of the variables <math>x_1</math> and <math>x_2</math>.
			x<sub>0</sub> := x<sub>1</sub> + 0;
			LOOP x<sub>2</sub> DO
			x<sub>0</sub> := x<sub>0</sub> + 1
			END
			#
			<math>x_0</math> is first assigned the value of <math>x_1</math>. Then, <math>x_0</math> is incremented a total of <math>x_2</math> times by the <code>LOOP</code> statement. This program can be used as a subroutine in other LOOP programs. The LOOP syntax can be extended with the following statement, equivalent to calling the above as a subroutine:
			x<sub>0</sub> := x<sub>1</sub> + x<sub>2</sub>

			=== Multiplication ===
			The following LOOP program sets the value of the variable <math>x_0</math> to the product of the variables <math>x_1</math> and <math>x_2</math>.
			LOOP x<sub>1</sub> DO
			x<sub>0</sub> := x<sub>0</sub> + x<sub>2</sub>
			END
			#
			This multiplication program uses the syntax introduced by the addition subroutine from the previous example. The multiplication is performed here by adding the value of <math>x_2</math> a total of <math>x_1</math> times, storing results in <math>x_0</math>.

			== See also ==
			* [[μ-recursive function]]

			== Notes and references ==
			<references />

			== External links ==
			* [http://web.archive.org/web/20120311032544/http://loopgotowhile.eugenkiss.com/ Loop, Goto & While]

			[[Category:Computability theory]]

en>TakuyaMurata: cat

2012-08-06T01:56:51Z

cat

New page

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