Fernando Cejas
May 05, 2022
190

Just a tiny presentation trying to explain monadic types in 10 minutes by giving a bit of an overview of Mathematics Category Theory.

May 05, 2022

## Transcript

2. ### — Someone not Famous “The goal of Category theory is

to show that trivial things are trivially trivial…”

4. ### Category Theory is a mathematical discipline with a wide range

of applications in theoretical computer science. Concepts like Category, Functor, Monad, and others, which were originally deﬁned in Category Theory, have become pivotal for the understanding of modern Functional Programming (FP) languages and paradigms. The meaning and applications of these terms in FP can be understood without in-depth knowledge of the corresponding mathematical deﬁnitions and axiomatic. However, a common knowledge of the underlying theory can help FP programmers understand the design and structure of commonly used libraries and tools and be more productive. Category Theory
5. ### Whoa! • Categories • Monoids • Isomorphisms • Duality Principle

• Functors Shamelessly taken from wikibooks of haskell Hask category treats Haskell types as objects and Haskell functions as morphisms and uses for composition ((\circ)) the function ((.)), a function (f :: A -> B) for types A and B is a morphism in Hask.
6. ### Categories Map of the Middle Earth of the Lord of

the Rings. Elves have made it.

of Thrones.

10. ### Monads Now another map of the Middle Earth, but this

time, drawn by a Dwarf.
11. ### Monads If an endofunctor also fulﬁlls that it has two

natural transformations such as the identity function and another function that is associative, we can say that we have a monad (this we call monadic laws)

13. ### MONAD: a bubble that encapsulates a computation that supports 2

main functions: map() ﬂatMap()