"Abstraction is the elimination of the irrelevantand the amplification of the essential." |

Mark Seeman's blog of October 2017 quotes Robert C Martin and goes on to explore:

... What's a good abstraction? As already quoted, it's a model that amplifies the essentials, etcetera. I think a good abstraction should also be

intuitive.What's the most intuitive abstractions ever?

Mathematics. ...

Seeman explains through the example of arithmetic:

... Notice that there's more than one way to combine numbers. You can add them together, but you can also multiply them. Could there be a common abstraction for that? What about objects that can somehow be combined, even if they aren't 'number-like'? The generalisation of such operations is a branch of mathematics called category theory, and it has turned out to be productive when applied to functional programming. Haskell is the most prominent example.

By an interesting coincidence, the 'things' in category theory are called

objects, and while they aren't objects in the sense that we think of in object-oriented design, there is some equivalence. Category theory concerns itself with how objects map to other objects. A functional programmer would interpret suchmorphismsas functions, but in a sense, you can also think of them as well-defined behaviour that's associated with data.The objects of category theory are universal abstractions. Some of them, it turns out, coincide with known design patterns. The difference is, however, that category theory concepts are governed by specific laws. In order to be a functor, for example, an object must obey certain simple and intuitive laws. This makes the category theory concepts more specific, and less ambiguous, than design patterns. ...

He summarizes and motivates:

... I believe that learning about these universal abstractions is the next step in software design. If you know design patterns, you have a vocabulary, but the details are still open to interpretation. If you know category theory, you have a better vocabulary. Just like design patterns, you have to learn these things, but once you've learned them, you've learned something that transcends a particular software library, a particular framework, a particular programming language. Learning about functors, monoids, and so on, is a good investment, because these concepts are rooted in mathematics, not any particular technology. ...

Worth learning for the long game of *thinking better!*

*(cf Design Patterns and Category Theory (2019-06-12), ...)* - * ^z* - 2019-11-10