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{{Refimprove|date=December 2009}}
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.
In [[mathematical logic]] and [[theoretical computer science]], a [[rewrite system]] has the '''strong normalization property''' (in short: the '''normalization property''') if every term is ''strongly normalizing''; that is, if every sequence of rewrites eventually terminates to a term in [[Normal form (term rewriting)|normal form]]. A rewrite system may also have the '''weak normalization property''', meaning that for every term, there exists at least one particular sequence of rewrites that eventually yields a normal form.


== Lambda calculus ==
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
=== Untyped lambda calculus ===
* Only registered users will be able to execute this rendering mode.
The ''pure'' untyped [[lambda calculus]] does not satisfy the strong normalization property, and not even the weak normalization property. Consider the term <math>\lambda x . x x x</math>. It has the following rewrite rule: For any term <math>t</math>,
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: <math>(\mathbf{\lambda} x . x x x) t \rightarrow t t t</math>
Registered users will be able to choose between the following three rendering modes:  


But consider what happens when we apply <math>\lambda x . x x x</math> to itself:
'''MathML'''
{|
:<math forcemathmode="mathml">E=mc^2</math>
| <math>(\mathbf{\lambda} x . x x x) (\lambda x . x x x)</math>
| <math> \rightarrow (\mathbf{\lambda} x . x x x) (\lambda x . x x x) (\lambda x . x x x)</math>
|-
|
| <math>  \rightarrow (\mathbf{\lambda} x . x x x) (\lambda x . x x x) (\lambda x . x x x) (\lambda x . x x x)</math>
|-
|
| <math>  \rightarrow (\mathbf{\lambda} x . x x x) (\lambda x . x x x) (\lambda x . x x x) (\lambda x . x x x) (\lambda x . x x x)</math>
|-
|
| <math>\ldots\,</math>
|}


Therefore the term <math>(\lambda x . x x x) (\lambda x . x x x)</math> is not strongly normalizing.
<!--'''PNG'''  (currently default in production)
:<math forcemathmode="png">E=mc^2</math>


=== Typed lambda calculus ===
'''source'''
:<math forcemathmode="source">E=mc^2</math> -->


Various systems of [[typed lambda calculus]] including the
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].
[[typed lambda calculus|simply typed lambda calculus]], [[Jean-Yves Girard]]'s [[System F]], and [[Thierry Coquand]]'s [[calculus of constructions]] are strongly normalizing.


A lambda calculus system with the '''normalization property''' can be viewed as a programming language with the property that every program [[termination analysis|terminates]]. Although this is a very useful property, it has a drawback: a programming language with the normalization property cannot be [[turing completeness|Turing complete]]. That means that there are computable functions that cannot be defined in the simply typed lambda calculus (and similarly there are computable functions that cannot be computed in the calculus of constructions or System F).  As an example, it is impossible to define a [[self-interpreter]] in any of the calculi cited above.<ref>Conor McBride (May 2003), [http://www.haskell.org/pipermail/haskell-cafe/2003-May/004343.html "on termination"] (posted to the Haskell-Cafe mailing list).</ref>
==Demos==


==See also==
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:
* [[Typed lambda calculus]]
* [[Rewriting]]
* [[Total functional programming]]
* [[Barendregt&ndash;Geuvers&ndash;Klop conjecture]]


==References==
{{Reflist}}


{{DEFAULTSORT:Normalization Property (Lambda-Calculus)}}
* accessibility:
[[Category:Lambda calculus]]
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
[[Category:Logic in computer science]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


[[eo:Normaliga propraĵo (lambda-kalkulo)]]
==Test pages ==
[[zh:规范化性质]]
 
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
*[[Displaystyle]]
*[[MathAxisAlignment]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]
 
*[[Inputtypes|Inputtypes (private Wikis only)]]
*[[Url2Image|Url2Image (private Wikis only)]]
==Bug reporting==
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .

Latest revision as of 23:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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