Papyrus 49 - Revision history

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

2014-09-03T19:00:59Z

Removing Link GA template (handled by wikidata)

← Older revision		Revision as of 21:00, 3 September 2014
Line 1:		Line 1:
	~~In [[type theory]]~~, ~~'''containers'''~~ are ~~abstractions which permit various "collection types"~~, ~~such as [[list (computing)\|lists]]~~ and ~~[[tree (data structure)\|trees]]~~, ~~to be represented in~~ a ~~uniform way~~. ~~A ([[unary operation\|unary]]) container~~ is ~~defined~~ by ~~a type~~ of ~~''shapes'' S and~~ a ~~type family of ''positions'' P, indexed by S~~. ~~The ''extension''~~ of a ~~container is a family of dependent pairs consisting of a shape (of type S) and a function from positions of that shape~~ to the ~~element type~~. ~~Containers~~ can be ~~seen~~ as ~~[[canonical form]]s~~ for ~~collection types~~.<~~ref name=~~'~~containers'>{{cite journal \|author=Michael Abbott, Thorsten Altenkirch~~ and ~~Neil Ghani\|year=2005 \|title=Containers~~: ~~Constructing strictly positive types \|journal=Theoretical Computer Science \|volume=342 \|issue=1 \|pages=3–27 \|doi=10.1016~~/j.~~tcs~~.~~2005.06.002}}<~~/~~ref>~~		CMS provides the best platform to create websites that fulfill all the specifications of SEO. The next step is to visit your Word - Press blog dashboard. I thought about what would happen by placing a text widget in the sidebar beneath my banner ad, and so it went. If you are using videos on your site then this is the plugin to use. All this is very simple, and the best thing is that it is totally free, and you don't need a domain name or web hosting. <br><br>Word - Press is known as the most popular blogging platform all over the web and is used by millions of blog enthusiasts worldwide. If you are a positive thinker businessman then today you have to put your business online. Our Daily Deal Software plugin brings the simplicity of setting up a Word - Press blog to the daily deal space. Being able to help with your customers can make a change in how a great deal work, repeat online business, and referrals you'll be given. As soon as you start developing your Word - Press MLM website you'll see how straightforward and simple it is to create an online presence for you and the products and services you offer. <br><br>Here are a few reasons as to why people prefer Word - Press over other software's. In the event you loved this post and you would love to receive much more information concerning [http://s.do-dance.com/wordpressbackup860432 backup plugin] kindly visit the webpage. The nominee in each category with the most votes was crowned the 2010 Parents Picks Awards WINNER and has been established as the best product, tip or place in that category. Are you considering getting your website redesigned. Our skilled expertise, skillfulness and excellence have been well known all across the world. Websites using this content based strategy are always given top scores by Google. <br><br>Google Maps Excellent navigation feature with Google Maps and latitude, for letting people who have access to your account Latitude know exactly where you are. The SEOPressor Word - Press SEO Plugin works by analysing each page and post against your chosen keyword (or keyword phrase) and giving a score, with instructions on how to improve it. Exacting subjects in reality must be accumulated in head ahead of planning on your high quality theme. Can you imagine where you would be now if someone in your family bought an original painting from van Gogh during his lifetime. Wordpress template is loaded with lots of prototype that unite graphic features and content area. <br><br>There is no denying that Magento is an ideal platform for building ecommerce websites, as it comes with an astounding number of options that can help your online business do extremely well. An ease of use which pertains to both internet site back-end and front-end users alike. By the time you get the Gallery Word - Press Themes, the first thing that you should know is on how to install it. Page speed is an important factor in ranking, especially with Google. I have never seen a plugin with such a massive array of features, this does everything that platinum SEO and All In One SEO, also throws in the functionality found within SEO Smart Links and a number of other plugins it is essentially the swiss army knife of Word - Press plugins.

	~~For lists, the shape type is~~ the ~~[[natural number]]s (including zero)~~. The ~~corresponding position types are~~ the ~~types of natural numbers less than~~ the ~~shape~~, ~~for each shape~~.

	~~For trees~~, the ~~shape type is the type of trees of units (that is, trees with no information in them, just structure)~~. ~~The corresponding position types~~ are ~~isomorphic to the types of valid paths from the root to particular nodes on the shape~~, for ~~each shape.~~

	~~Note that the natural numbers~~ are ~~isomorphic to lists of units~~. ~~In general the shape type will always be isomorphic to the original non~~-~~generic container type family~~ (~~list~~, ~~tree etc.) applied~~ to ~~unit~~.

	~~One~~ of ~~the main motivations for introducing the notion of containers is to support [[generic programming]]~~ in ~~a [[dependent type\|dependently-typed]] setting~~.~~<ref name='containers'/>~~

	~~== Categorical aspects ==~~
	~~{{Expand section\|date=October 2008}}~~
	~~The extension~~ of ~~a container is an [[endofunctor]]~~. ~~It takes a function~~ <~~code~~>g<~~/code~~> to

	~~<math>\lambda\left(s,f\right).\left(s,g\circ f\right)</math>~~

	~~This~~ is ~~equivalent to the familiar <code>map g</code> in the case of lists~~, ~~and does something similar for other containers.~~

	~~== Indexed containers ==~~
	~~{{Expand section\|date=October 2008}}~~
	~~'''Indexed containers''' (also known~~ as ~~'''dependent polynomial functors''') are a generalisation~~ of ~~containers, which~~ can ~~represent a wider class~~ of ~~types, such as vectors (sized lists).<ref name='indexed~~-~~containers'>{{cite journal~~
	~~\| author = Thorsten Altenkirch, Neil Ghani, Peter Hancock, [[Conor McBride]],~~ and ~~Peter Morris~~
	~~\| title = Indexed Containers~~
	~~\| version = Unpublished manuscript~~
	~~\| url = http://strictlypositive.org/indexed~~-~~containers~~.~~pdf~~
	~~\| format = PDF~~
	~~\| accessdate = 2008~~-~~10-30~~
	}}
	~~</ref>~~

	~~The element type (called~~ the ~~''input type'')~~ is ~~indexed by shape and position~~, ~~so it can vary by shape~~ and ~~position~~, and the ~~extension (called the ''output type'') is also indexed by shape~~.

	~~== See also ==~~
	* [[Container (abstract data type)]]
	* [[Functor (type theory)]]

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

	~~[[Category:Type theory]]~~


	~~{{type-theory-stub}}~~

en>Addbot: Bot: Migrating 6 interwiki links, now provided by Wikidata on d:q968059 (Report Errors)

2013-02-20T05:08:46Z

Bot: Migrating 6 interwiki links, now provided by Wikidata on d:q968059 (Report Errors)

← Older revision		Revision as of 07:08, 20 February 2013
Line 1:		Line 1:
	~~I would like to introduce myself to you~~, ~~I am Hosea~~ and ~~I fully dig that title~~. ~~Interviewing~~ is ~~my profession but the advertising never comes~~. ~~One~~ of ~~the points I adore most~~ is to ~~fish but I struggle to come across time~~ for it. ~~My wife~~ and ~~[http~~:/~~/www~~.~~ichose~~.~~com~~/ ~~I chose~~] ~~to reside~~ in ~~New Jersey~~. ~~I've been doing work~~ on ~~my internet site~~ for ~~some time now~~. ~~Look at it out right here: http://www~~.~~cdan~~.~~es/zapatillas~~-~~asics~~.~~asp?id~~=47<br><br>~~Feel free~~ to ~~visit my homepage:~~ [http://~~www~~.~~cdan~~.es/~~zapatillas-asics~~.~~asp?id~~=~~47 precios zapatillas asics~~]		In [[type theory]], '''containers''' are abstractions which permit various "collection types", such as [[list (computing)\|lists]] and [[tree (data structure)\|trees]], to be represented in a uniform way. A ([[unary operation\|unary]]) container is defined by a type of ''shapes'' S and a type family of ''positions'' P, indexed by S. The ''extension'' of a container is a family of dependent pairs consisting of a shape (of type S) and a function from positions of that shape to the element type. Containers can be seen as [[canonical form]]s for collection types.<ref name='containers'>{{cite journal \|author=Michael Abbott, Thorsten Altenkirch and Neil Ghani\|year=2005 \|title=Containers: Constructing strictly positive types \|journal=Theoretical Computer Science \|volume=342 \|issue=1 \|pages=3–27 \|doi=10.1016/j.tcs.2005.06.002}}</ref>

			For lists, the shape type is the [[natural number]]s (including zero). The corresponding position types are the types of natural numbers less than the shape, for each shape.

			For trees, the shape type is the type of trees of units (that is, trees with no information in them, just structure). The corresponding position types are isomorphic to the types of valid paths from the root to particular nodes on the shape, for each shape.

			Note that the natural numbers are isomorphic to lists of units. In general the shape type will always be isomorphic to the original non-generic container type family (list, tree etc.) applied to unit.

			One of the main motivations for introducing the notion of containers is to support [[generic programming]] in a [[dependent type\|dependently-typed]] setting.<ref name='containers'/>

			== Categorical aspects ==
			{{Expand section\|date=October 2008}}
			The extension of a container is an [[endofunctor]]. It takes a function <code>g</code> to

			<math>\lambda\left(s,f\right).\left(s,g\circ f\right)</math>

			This is equivalent to the familiar <code>map g</code> in the case of lists, and does something similar for other containers.

			== Indexed containers ==
			{{Expand section\|date=October 2008}}
			'''Indexed containers''' (also known as '''dependent polynomial functors''') are a generalisation of containers, which can represent a wider class of types, such as vectors (sized lists).<ref name='indexed-containers'>{{cite journal
			\| author = Thorsten Altenkirch, Neil Ghani, Peter Hancock, [[Conor McBride]], and Peter Morris
			\| title = Indexed Containers
			\| version = Unpublished manuscript
			\| url = http://strictlypositive.org/indexed-containers.pdf
			\| format = PDF
			\| accessdate = 2008-10-30
			}}
			</ref>

			The element type (called the ''input type'') is indexed by shape and position, so it can vary by shape and position, and the extension (called the ''output type'') is also indexed by shape.

			== See also ==
			* [[Container (abstract data type)]]
			* [[Functor (type theory)]]

			== References ==
			{{reflist}}

			[[Category:Type theory]]


			{{type-theory-stub}}

en>Rich Farmbrough: Fix refs and/or minor fixes using AWB

2012-01-16T12:37:09Z

Fix refs and/or minor fixes using AWB

New page

I would like to introduce myself to you, I am Hosea and I fully dig that title. Interviewing is my profession but the advertising never comes. One of the points I adore most is to fish but I struggle to come across time for it. My wife and [http://www.ichose.com/ I chose] to reside in New Jersey. I've been doing work on my internet site for some time now. Look at it out right here: http://www.cdan.es/zapatillas-asics.asp?id=47<br><br>Feel free to visit my homepage: [http://www.cdan.es/zapatillas-asics.asp?id=47 precios zapatillas asics]