Monoid

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. This idea has been extended to Bayesian inferencing, and other ideas, such as The Master Algorithm.

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. Most importantly, the software pattern, or the mechanism of manipulating text-based expressions in an iterative loop, called (Read-eval-print loop)REPL, would be a kind 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 data space. Therefore, it is also possible to create a system, that universally treats all data objects as files, and therefore, the whole system becomes a monoidal structure. That would be very close to the approach that Unix took in its design intent.