Difference between revisions of "Monoid"
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One may consider the idea of using a single data type as a programming language to be associated with the idea of Monoid. That is also the basis of functional programming languages are nothing but the manipulation of [[S-expression]]s. Therefore, one may consider Lambda-Calculus as an implementation of this Monoid-like language specification. Later, the idea of all languages can be treated as some textual stream of data content, and processed by [[Large Language Model]]s, or [[Generative Pre-trained Transformer]]s, would be another example of Monoid. | In abstract algebra, a [[lattice]] can be considered as a [[monoid]]. One may consider the idea of using a single data type as a programming language to be associated with the idea of Monoid. That is also the basis of functional programming languages are nothing but the manipulation of [[S-expression]]s. Therefore, one may consider Lambda-Calculus as an implementation of this Monoid-like language specification. Later, the idea of all languages can be treated as some textual stream of data content, and processed by [[Large Language Model]]s, or [[Generative Pre-trained Transformer]]s, would be another example of Monoid. | ||
Based on the idea of singular data type, the creation of [[IPFS]] as a unifying namespace for all data content can be thought of as a Monoidal space. | Based on the idea of singular data type, the creation of [[IPFS]] as a unifying namespace for all data content can be thought of as a Monoidal space. | ||
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Revision as of 04:49, 6 July 2023
Monoid (幺半群), according to Wikipedia, it is a set equipped with an associative binary operation and an identity element. It is a foundational algebraic structure that can be applied to many fields.
For instance, in a Turing Machine, all operations can be thought of as some sequences of stack operations[1][2]. This idea has been extended to Bayesian inferencing[3], and other ideas, such as The Master Algorithm[4].
Implementation and Applications
In abstract algebra, a lattice can be considered as a monoid. One may consider the idea of using a single data type as a programming language to be associated with the idea of Monoid. That is also the basis of functional programming languages are nothing but the manipulation of S-expressions. Therefore, one may consider Lambda-Calculus as an implementation of this Monoid-like language specification. Later, the idea of all languages can be treated as some textual stream of data content, and processed by Large Language Models, or Generative Pre-trained Transformers, would be another example of Monoid.
Based on the idea of singular data type, the creation of IPFS as a unifying namespace for all data content can be thought of as a Monoidal space.
References
- ↑ Dolan, Stephen (July 19, 2013). "mov is Turing-complete" (PDF). local page: Computer Laboratory, University of Cambridge.
- ↑ All Angles, ed. (Aug 14, 2021). What is a monoid?. local page: All Angles.
- ↑ Fong, Brendan (2013). Causal Theories: A Categorical Perspective on Bayesian Networks (Master). local page: University of Oxford. Retrieved Jan 26, 2013.
- ↑ Domingos, Pedro (February 13, 2018). The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World (Revised ed.). local page: Basic Books. ISBN 978-0465094271.
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