Menu
May anyone give me an example how we can improve our code reusability using algebraic structures like groups, monoids and rings? (or how can i make use of these kind of structures in programming, knowing at least that i didn't learn all that theory in highschool for nothing).
I heard this is possible but i can't figure out a way applying them in programming and genereally applying hardcore mathematics in programming.
892
In mathematics, an algebraic structure consists of a nonempty set A (called the underlying set, carrier set or domain), a collection of operations on A (typically binary operations such as addition and multiplication), and a finite set of identities, known as axioms, that these operations must satisfy.
The Algebra of Programming group researches mathematically sound yet convenient techniques for manipulating and reasoning with programs, with a particular interest in the functional and relational paradigms and in generic programming.
Cryptography requires sets of integers and specific operations that are defined for those sets. The combination of the set and the operations that are applied to the elements of the set is called an algebraic structure.
One set with no binary operations Set: a degenerate algebraic structure S having no operations. Pointed set: S has one or more distinguished elements, often 0, 1, or both. Unary system: S and a single unary operation over S. Pointed unary system: a unary system with S a pointed set.
It is not really the mathematical stuff that helps as is the mathematical thinking. Abstraction is the key in programming. Transforming real live concepts into numbers and relations is what we do every day. Algebra is the mother of all, algebra is the set of rules that defines correctness, it is the highest level of abstraction, so, understanding algebra means you can think more clear, more faster, more efficient. Commencing from Sets theory to Category Theory, Domain Theory etc everything comes from practical challenges, abstraction and generalization requirements. In common practice you will not need to actually know these, although if you are thinking of developing stuff like AI Agents, programming languages, fundamental concepts and tools then they are a must.
172
If you love us? You can donate to us via Paypal or buy me a coffee so we can maintain and grow! Thank you!
Donate Us With
