In other words though, for those just starting their monad journey:
An endofunctor is a box. If you have a box of soup, and a function to turn soup into nuts, you can probably turn the box of soup into a box of nuts. You don’t have to write a new function for this, if the box can take your existing function and “apply” it to its contents.
Arrays are endofunctors, because they hold things, and you can use Array.map to turn an array of X into an array of Y.
Monoids are things you can add together. Integer plus integer equals integer, so ints are monoids. String plus string (concatenation) equals a longer string, so strings are monoids. Grocery lists are monoids.
Arrays are monoids!
Arrays are both endofunctors and monoids, so for everyone except category theory purists, they are monads.
Javascript promises hold things, and you can transform their contents with .then - so they are endofunctors. You can “add them together” with Promise.all (returning a new promise), so they are monoids. They are both monoids and endofunctors, so they are monads.
I’ve just upset all the category theorists, but in the context of programming, that’s all it is. It’s surprisingly simple once you get it, it’s just complicated names for simple features.
Of course!
In other words though, for those just starting their monad journey:
An endofunctor is a box. If you have a box of soup, and a function to turn soup into nuts, you can probably turn the box of soup into a box of nuts. You don’t have to write a new function for this, if the box can take your existing function and “apply” it to its contents.
Arrays are endofunctors, because they hold things, and you can use Array.map to turn an array of X into an array of Y.
Monoids are things you can add together. Integer plus integer equals integer, so ints are monoids. String plus string (concatenation) equals a longer string, so strings are monoids. Grocery lists are monoids.
Arrays are monoids!
Arrays are both endofunctors and monoids, so for everyone except category theory purists, they are monads.
Javascript promises hold things, and you can transform their contents with .then - so they are endofunctors. You can “add them together” with Promise.all (returning a new promise), so they are monoids. They are both monoids and endofunctors, so they are monads.
I’ve just upset all the category theorists, but in the context of programming, that’s all it is. It’s surprisingly simple once you get it, it’s just complicated names for simple features.
“Complicated names for simple features” seems to describe Haskell crowd pretty well.
Thank you for a straightforward explanation!