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In the [[lambda calculus]], a term is in '''beta normal form''' if no ''[[lambda calculus#β-reduction|beta reduction]]'' is possible.<ref>{{cite web| url=http://encyclopedia2.thefreedictionary.com/Beta+normal+form | title=Beta normal form | work=[http://encyclopedia2.thefreedictionary.com/ Encyclopedia] | publisher=[[The Free Dictionary]] |accessdate=18 November 2013 }}</ref> A term is in '''beta-eta normal form''' if neither a beta reduction nor an ''[[lambda calculus#η-conversion|eta reduction]]'' is possible. A term is in '''head normal form''' if there is no ''beta-redex in head position''.
== you and I shot four people at the same time ==


==Beta reduction==
Roared.<br><br>'Tang Zhen Gu Zhu, glaciers Guzhu, and the Xiao Yan little friend, you and I shot four people at the same time, [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-6.html 腕時計 メンズ casio] to help fight the holy bones stardom solve this old devil, how?' Old Devil roar heard [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-1.html カシオ 腕時計 チタン] stardom , the day the demon Phoenix family man also knows not look black robe drama, the moment the attention is turned to Tang Zhen, glaciers, such as strength reached a five-star and four stars statue strong, but so was a bit surprised people is that he this opening times, even the strength of the stars just a statue of Xiao Yan [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-7.html casio 腕時計 説明書] also called on to.<br><br>Xiao Yan fingers moved, glances at the old man a black robe, this old guy is obviously worried about too leisurely, the remaining spare capacity too much against them, so he [http://nrcil.net/sitemap.xml http://nrcil.net/sitemap.xml] wanted to pull into this that the most dangerous Battle circle.<br><br>'ah.' Xiao Yan [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-13.html casio 腕時計 edifice] Shen between 'Yin', Tang Zhen and ice Venerable'd nodded slightly, seeing this, Xiao Yan could only nod, eyes looked around, and said: 'As the six with
In the lambda calculus, a '''beta redex''' is a term of the form
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:<math> ((\mathbf{\lambda} x . A(x)) t) </math>
== the other one is bound to be hit. ==


where <math>A(x)</math> is a term (possibly) involving variable <math>x</math>.
Xiao Yan is taking into account the two difficult position, [http://nrcil.net/sitemap.xml http://nrcil.net/sitemap.xml] if only anti Xiao [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-0.html casio 腕時計] Yan a, the other one is bound to be hit.<br><br>in numerous road gaze, as sculptural Xiao Yan, the two Quanfeng getting to that Yi Sha, stature and shoved shocked, everyone is stunned immediately saw two illusory shadow flotation [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-15.html カシオ 腕時計 gps] feet on both sides , while two unreal foot shadow, while Cliff and Lin Xiu Qing and Liu fist collision, but like turning [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-3.html カシオ 腕時計 電波 ソーラー] to [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-14.html casio 腕時計 デジタル] the substance of like, an instant burst of extremely terror forces.<br><br>first trick!<br><br>'bang!'<br><br>sounded muffled muffled presence, fury Effort at that moment, such as a flood vent out, so that was also a direct cliff and Liu Qing Lin Xiu figure Baotui nearly ten steps, every foot of the fall, will be in left deep marks on the floor in the foot.<br><br>'This guy, good speed and strength of terror,' Liu Qing stabilize stature, heart an idea just flashed, muddy
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A ''beta reduction'' is an application of the following rewrite rule to a beta redex
== is sharp with a little overbearing ==


:<math> ((\mathbf{\lambda} x . A(x)) t) \rightarrow A(t)</math>
Warm sun shining on the peaks sit cross-legged black robe young body, and seems to feel the outside world weather changes, quivering young eyes closed for a moment, fingertips lingering hint of silver 'color' lightning, but also quietly into body, and finally disappear.<br><br>with silver 'color' lightning disappeared, the young black robe eyelashes 'gross' trembling increasingly violent, after a moment, as if finally broke loose in general, suddenly opened, suddenly, like real silver 'color' lightning, is sharp with a little overbearing, violent [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-3.html casio 腕時計 レディース] 'shoot' out of its eyes, and reached full distance [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-15.html カシオ 腕時計 gps] Cunxu long!<br><br>eyes 'shoot' the silver 'color' lightning lasted just one moment of time is dissipated abruptly, and with silver 'color' lightning disappeared, and that the black eye is once again caught in peace.<br><br>hand printed statement dispersed, Xiao [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-2.html 腕時計 casio] Yan slightly [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-12.html 時計 カシオ] raised his head, looked exudes [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-5.html カシオの時計] the warmth of the sun on the sky Yaori chest
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where <math>A(t)</math> is the result of substituting the term <math>t</math> for the variable <math>x</math> in the term <math>A(x)</math>.
== that he ==


A beta reduction is in head position if it is of the following form:
'Color' a little bit pale Yao Sheng Road.<br><br>'to the boss's strength, [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-6.html 電波腕時計 カシオ] he is naturally easy to beat, no matter how he jumped himself, can always just a big wave of insects it is difficult to reveal.' Yao Sheng cold eyes staring at the field Hsiao-yen, after the defeated hands on his batting is quite small. Therefore, not how broad-minded he naturally will fail suffered insults are rooted in Xiao Yan body, but, when saying this, [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-8.html カシオ レディース 電波ソーラー腕時計] he is forgotten, was one he thought was a [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-14.html カシオ 時計 電波 ソーラー] worm who beat , that [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-14.html casio 腕時計 phys] he, what is it?<br><br>Yao Sheng words, suddenly make too proud Liu Fei cheek some more rich, Meimou implied the opposite down the elegant and high-profile man sitting Tsing Yi girl, slight bit Yinya to a woman's perspective say, the other side looks even even she could not see any flaws are picky, [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-6.html casio 腕時計 説明書] but it is precisely because the other side of perfect, she just always unpopular with women jealous,
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* <math> \lambda x_0 \ldots \lambda x_{i-1} . (\lambda x_i . A(x_i)) M_1 M_2 \ldots M_n \rightarrow
== relying on a stone bench ==
        \lambda x_0 \ldots \lambda x_{i-1} . A(M_1) M_2 \ldots M_n </math>, where <math> i \geq 0, n \geq 1 </math>.


Any reduction not in this form is an internal beta reduction.
The dense seat, at the moment, in these seats are like a 'boom' like water poured countless dense mass of the head, this time with Han Hung family confrontation, attracting the attention of the entire day north of the city.<br><br>day in both directions east and north of the top of the stone, with some obvious exceptionally gorgeous seats, those seats, only a day just [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-14.html カシオ 時計 電波 ソーラー] north of the city are eligible to mind some forces seat, where the eyes of the whole can be [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-2.html カシオの時計] condescending Square income, and North seat at the moment, is already filled with a lot of shadows, where most people are a red robe, in their chest, wearing a pretty [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-0.html カシオ 時計 価格] badge that symbolizes the [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-11.html casio 腕時計 メンズ] Hung family<br><br>on the Hung family seat, the day Hung Chen Xiao Yan had ever seen, being arms Baoxiong, relying on a stone bench, his face looked red-hot Plaza export orientation, that [http://www.ispsc.edu.ph/nav/japandi/casio-rakuten-2.html カシオの時計] road was so haunted by him Hunmeng shadows, has been branded deep in their hearts, in his mind, has determined that this woman must
 
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==Reduction strategies==
<ul>
In general, there can be several different beta reductions possible for a given term. '''Normal-order reduction''' is the [[evaluation strategy]] in which one continually applies the rule for ''beta reduction in head position'' until no more such reductions are possible. At that point, the resulting term is in ''head normal form''.
 
 
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In contrast, in '''applicative order reduction''', one applies the internal reductions first, and then only applies the head reduction when no more internal reductions are possible.
 
 
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Normal-order reduction is complete, in the sense that if a term has a head normal form, then normal order reduction will eventually reach it. In contrast, applicative order reduction may not terminate, even when the term has a normal form. For example, using applicative order reduction, the following sequence of reductions is possible:
 
 
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:<math> (\mathbf{\lambda} x . z) ((\lambda w. w w w) (\lambda w. w w w)) </math>
 
:<math> \rightarrow (\lambda x . z) ((\lambda w. w w w) (\lambda w. w w w) (\lambda w. w w w))</math>
</ul>
:<math> \rightarrow (\lambda x . z) ((\lambda w. w w w) (\lambda w. w w w) (\lambda w. w w w) (\lambda w. w w w))</math>
:<math> \rightarrow (\lambda x . z) ((\lambda w. w w w) (\lambda w. w w w) (\lambda w. w w w) (\lambda w. w w w) (\lambda w. w w w))</math>
:<math>\ldots</math>
 
But using normal-order reduction, the same starting point reduces quickly to normal form:
 
:<math> (\mathbf{\lambda} x . z) ((\lambda w. w w w) (\lambda w. w w w)) </math>
:<math> \rightarrow z </math>
 
Sinot's [[director string]]s is one method by which the computational complexity of beta reduction can be optimized.
 
==See also==
* [[Lambda calculus]]
* [[Normal form (disambiguation)]]
 
==References==
{{reflist}}
 
{{DEFAULTSORT:Beta Normal Form}}
[[Category:Lambda calculus]]
[[Category:Normal forms (logic)]]

Latest revision as of 12:52, 18 November 2014

you and I shot four people at the same time

Roared.

'Tang Zhen Gu Zhu, glaciers Guzhu, and the Xiao Yan little friend, you and I shot four people at the same time, 腕時計 メンズ casio to help fight the holy bones stardom solve this old devil, how?' Old Devil roar heard カシオ 腕時計 チタン stardom , the day the demon Phoenix family man also knows not look black robe drama, the moment the attention is turned to Tang Zhen, glaciers, such as strength reached a five-star and four stars statue strong, but so was a bit surprised people is that he this opening times, even the strength of the stars just a statue of Xiao Yan casio 腕時計 説明書 also called on to.

Xiao Yan fingers moved, glances at the old man a black robe, this old guy is obviously worried about too leisurely, the remaining spare capacity too much against them, so he http://nrcil.net/sitemap.xml wanted to pull into this that the most dangerous Battle circle.

'ah.' Xiao Yan casio 腕時計 edifice Shen between 'Yin', Tang Zhen and ice Venerable'd nodded slightly, seeing this, Xiao Yan could only nod, eyes looked around, and said: 'As the six with 相关的主题文章:

the other one is bound to be hit.

Xiao Yan is taking into account the two difficult position, http://nrcil.net/sitemap.xml if only anti Xiao casio 腕時計 Yan a, the other one is bound to be hit.

in numerous road gaze, as sculptural Xiao Yan, the two Quanfeng getting to that Yi Sha, stature and shoved shocked, everyone is stunned immediately saw two illusory shadow flotation カシオ 腕時計 gps feet on both sides , while two unreal foot shadow, while Cliff and Lin Xiu Qing and Liu fist collision, but like turning カシオ 腕時計 電波 ソーラー to casio 腕時計 デジタル the substance of like, an instant burst of extremely terror forces.

first trick!

'bang!'

sounded muffled muffled presence, fury Effort at that moment, such as a flood vent out, so that was also a direct cliff and Liu Qing Lin Xiu figure Baotui nearly ten steps, every foot of the fall, will be in left deep marks on the floor in the foot.

'This guy, good speed and strength of terror,' Liu Qing stabilize stature, heart an idea just flashed, muddy 相关的主题文章:

is sharp with a little overbearing

Warm sun shining on the peaks sit cross-legged black robe young body, and seems to feel the outside world weather changes, quivering young eyes closed for a moment, fingertips lingering hint of silver 'color' lightning, but also quietly into body, and finally disappear.

with silver 'color' lightning disappeared, the young black robe eyelashes 'gross' trembling increasingly violent, after a moment, as if finally broke loose in general, suddenly opened, suddenly, like real silver 'color' lightning, is sharp with a little overbearing, violent casio 腕時計 レディース 'shoot' out of its eyes, and reached full distance カシオ 腕時計 gps Cunxu long!

eyes 'shoot' the silver 'color' lightning lasted just one moment of time is dissipated abruptly, and with silver 'color' lightning disappeared, and that the black eye is once again caught in peace.

hand printed statement dispersed, Xiao 腕時計 casio Yan slightly 時計 カシオ raised his head, looked exudes カシオの時計 the warmth of the sun on the sky Yaori chest 相关的主题文章:

that he

'Color' a little bit pale Yao Sheng Road.

'to the boss's strength, 電波腕時計 カシオ he is naturally easy to beat, no matter how he jumped himself, can always just a big wave of insects it is difficult to reveal.' Yao Sheng cold eyes staring at the field Hsiao-yen, after the defeated hands on his batting is quite small. Therefore, not how broad-minded he naturally will fail suffered insults are rooted in Xiao Yan body, but, when saying this, カシオ レディース 電波ソーラー腕時計 he is forgotten, was one he thought was a カシオ 時計 電波 ソーラー worm who beat , that casio 腕時計 phys he, what is it?

Yao Sheng words, suddenly make too proud Liu Fei cheek some more rich, Meimou implied the opposite down the elegant and high-profile man sitting Tsing Yi girl, slight bit Yinya to a woman's perspective say, the other side looks even even she could not see any flaws are picky, casio 腕時計 説明書 but it is precisely because the other side of perfect, she just always unpopular with women jealous, 相关的主题文章:

relying on a stone bench

The dense seat, at the moment, in these seats are like a 'boom' like water poured countless dense mass of the head, this time with Han Hung family confrontation, attracting the attention of the entire day north of the city.

day in both directions east and north of the top of the stone, with some obvious exceptionally gorgeous seats, those seats, only a day just カシオ 時計 電波 ソーラー north of the city are eligible to mind some forces seat, where the eyes of the whole can be カシオの時計 condescending Square income, and North seat at the moment, is already filled with a lot of shadows, where most people are a red robe, in their chest, wearing a pretty カシオ 時計 価格 badge that symbolizes the casio 腕時計 メンズ Hung family

on the Hung family seat, the day Hung Chen Xiao Yan had ever seen, being arms Baoxiong, relying on a stone bench, his face looked red-hot Plaza export orientation, that カシオの時計 road was so haunted by him Hunmeng shadows, has been branded deep in their hearts, in his mind, has determined that this woman must 相关的主题文章: