Difference between revisions of "Partially-ordered set"
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Partially-ordered | {{WikiEntry|key=Partially-ordered set|qCode=474715}}([[Poset]]) are composed of directed relations, similar to a tuple whose data entries' ordered relations is a crucial aspect of information encoding. According to Data Scott<ref>{{:Paper/Outline of a Mathematical Theory of Computation}}</ref>, a [[Partially-ordered set]], also known as: [[POSet]], is the most universal building block for the theory of computation. In other words, it is the data representation of [[Universal abstraction]]. | ||
=[[Lattice]]:A Special kind of [[POSet]]= | |||
One should also notice that there is a special kind of [[POSet]], called [[Lattice]]. A [[lattice]] is a POSet with a unique [[Top]] and a unique [[Bottom]]. This kind of [[POSet]] basically bounds all information content within its reach, therefore, approximate all possibilities using a single [[universal]] data type. | |||
==Closure and Boundaries== | |||
The two types of boundaries, [[Top]] and [[Bottom]] are two kinds of boundaries in [[Lattice]], and they are related to the notion of closure of POSet. Please watch Dana Scott's talk<ref name="Scott Part 3">{{:Video/Dana Scott - Theory and Models of Lambda Calculus Untyped and Typed - Part 3 of 5 - λC 2017}}</ref><ref extends="Scott Part 3">[https://youtu.be/8zk0yS8Jp5w?t=190 A drawing of Lattice by Scott]</ref> on this matter. | |||
=Critical Revelation in Programming= | =Critical Revelation in Programming= | ||
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Latest revision as of 04:46, 4 August 2022
Partially-ordered set(Q474715)(Poset) are composed of directed relations, similar to a tuple whose data entries' ordered relations is a crucial aspect of information encoding. According to Data Scott[1], a Partially-ordered set, also known as: POSet, is the most universal building block for the theory of computation. In other words, it is the data representation of Universal abstraction.
Lattice:A Special kind of POSet
One should also notice that there is a special kind of POSet, called Lattice. A lattice is a POSet with a unique Top and a unique Bottom. This kind of POSet basically bounds all information content within its reach, therefore, approximate all possibilities using a single universal data type.
Closure and Boundaries
The two types of boundaries, Top and Bottom are two kinds of boundaries in Lattice, and they are related to the notion of closure of POSet. Please watch Dana Scott's talk[2]Cite error: Invalid <ref> tag; invalid names, e.g. too many on this matter.
Critical Revelation in Programming
Knowing that POSet is a universal data structure, that means all programs are some variants of POSet. The most important reason for knowing this must be true, is due to the single direction of time flow.
All events must be somehow ordered in time. Therefore, they must all be placed in a Partially ordered set.
This single-minded idea allows one to think of all algorithms in terms of traversing some POSet, or in an other word:Tree. This revelation helps us to see that all databases should be managed in terms of some kind of POSet, and therefore, should be taught and programmed accordingly.
References
- ↑ Scott, Dana (January 1, 1970). "Outline of a Mathematical Theory of Computation". local page: Oxford University Computing Laboratory Programming Research Group.
- ↑ Scott, Dana (Oct 12, 2017). Dana Scott - Theory and Models of Lambda Calculus Untyped and Typed - Part 3 of 5 - λC 2017. local page: LambdaConf.
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