conceptoriented

Assume f: X -> Y. We can now map x_1 to y_1 f(x_1)=y_1. And then change this same function by mapping x_1 to y_2: f(x_1)=y_2. Thus we can easily modify functions. Moreover, we do it constantly when we modify object fields in OOP. It is probably easier to comprehend if a function is represented as a table which we modify.

In contrast, we cannot modify data values (mathematical tuples). Say, x=42+1 means that a new value 43 is created rather than the existing value 42 is modified.

> I would expect the domain and codomain to be immutable;

No. Domains, codomains and any set can well be modified by adding or removing tuples. What is immutable are values (in the sets).

Well, it depends on what you mean by data. To avoid ambiguity it is better to talk about data values and data objects which have different properties. This can be formalized as follows [1]:

o data values are modelled via mathematical tuples – tuples are immutable

o data objects are modelled via mathematical functions (one field is a function from this reference to the field value) - functions are supposed to be mutable

(In reality of course we meet quite different situations, for example, struct is mutable and objects can be immutable.)

[1] Concept-oriented model: Modeling and processing data using functions https://www.researchgate.net/publication/337336089_Concept-o...

(0) https://www.researchgate.net/publication/337336089_Concept-o...

Many platforms do not have GPUs or special instructions, for example, at the edge.

"Fashion-MNIST is a dataset of Zalando's article images—consisting of a training set of 60,000 examples and a test set of 10,000 examples. Each example is a 28x28 grayscale image, associated with a label from 10 classes. We intend Fashion-MNIST to serve as a direct drop-in replacement for the original MNIST dataset for benchmarking machine learning algorithms. It shares the same image size and structure of training and testing splits."

There are many projects aimed at making Excel "a thing of the past" but they focus on different needs:

o https://airtable.com - use tables for data organization (organize anything)

o https://fieldbook.com - spreadsheet as a database

o https://www.rowshare.com share data (share rows, not data)

o http://conceptoriented.com - data transformations and data wrangling (I am the author)

o Coda - integration with documents

It is interesting if one of these approaches will eventually dominate or we will have a zoo of spreadsheet-like applications.

  Scalars -> Vectors -> Matrices -> Tensors (really tensors?)