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Monads are monoids in the category of endofunctors

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Re: Monads are monoids in the category of endofunctors

#41

Post by zabzonk »

jkhdigital wrote: post #20
brundolf wrote: post #5

Wait, a functor is just a pure unary function? And an endofunctor is just one of those where the argument type and return type are the same? This could have been explained to me years ago, in five minutes? Sometimes it makes me mad that so much confusion (and as another commenter put it, gatekeeping) has been sown in FP circles through the invention of pointlessly-obfuscated terminology for everything (and through -…

Functors are type constructors, not functions (which map values). But you could be forgiven the misunderstanding, because it is easy to trip over this distinction given the identical syntax. So, to make this absolutely clear, a monad is a type constructor in functional programming. This is why I personally prefer the more “creative” explanations of monads, because they attempt to explain what the monad is doing to th…

> a monad is a type constructor

Now explain what a "type constructor" is, otherwise these words are worthless.

Re: Monads are monoids in the category of endofunctors

#42

Post by tantalor »

dwohnitmok wrote: post #15
brundolf wrote: post #5

Wait, a functor is just a pure unary function? And an endofunctor is just one of those where the argument type and return type are the same? This could have been explained to me years ago, in five minutes? Sometimes it makes me mad that so much confusion (and as another commenter put it, gatekeeping) has been sown in FP circles through the invention of pointlessly-obfuscated terminology for everything (and through -…

> a functor is just a pure unary function? No, although a pure unary function could be viewed as a functor, the other direction doesn't hold. The common FP definition of a functor is anything that supports a notion of `map` (subject to the restriction that `map`ping the identity function does nothing, this is why a Functor is slightly more than just a Mappable). This is not a unary function although map takes a unary…

> why a Functor is slightly more than just a Mappable

Explain that again?

Re: Monads are monoids in the category of endofunctors

#43

Post by epolanski »

lmm wrote: post #28
Tade0 wrote: post #3

Functional programming is subject to an enormous amount of gatekeeping. Kudos to the author for pushing that gate wide open.

Author is completely wrong, and as such is a perfect demonstration of why that "gatekeeping" (actually just being precise and correct) is necessary.

I would say that the biggest gatekeeping to functional programming is the abundance of messy "dumbed down" content like this.

Re: Monads are monoids in the category of endofunctors

#44

Post by brundolf »

epolanski wrote: post #34
jkhdigital wrote: post #20

Earlier quoted context omitted.

Functors are type constructors, not functions (which map values). But you could be forgiven the misunderstanding, because it is easy to trip over this distinction given the identical syntax. So, to make this absolutely clear, a monad is a type constructor in functional programming. This is why I personally prefer the more “creative” explanations of monads, because they attempt to explain what the monad is doing to th…

I don't like creative explanations. Definitions are easier. A functor is a PAIR, please notice the emphasis, of a type constructor F and a map function with the following signature: a -> b -> f a -> f b. Its not a type constructor, it's a pair of two things, the type constructor AND its map function. Now that we said what it is we provide the usual simple example of Array, Record or Option, show the type constructors…

> I wish people understood that fp is much easier to understand by reading definitions.

The real landscape of its adoption begs to differ. For the great majority of people, examples and analogies are fantastically more efficient for communicating ideas than building up from first principles. You get to re-use existing mental machinery, intuition, etc, until enough experience has been gained to refine it.

Re: Monads are monoids in the category of endofunctors

#46

Post by lvs »

slumpt_ wrote: post #19
CognitiveLens wrote: post #16

Earlier quoted context omitted.

Language evolves, as the wiki article you linked describes. Your prescriptivist nit-picking doesn't contribute to the discussion. From the HN guidelines: - Please respond to the strongest plausible interpretation of what someone says, not a weaker one that's easier to criticize. Assume good faith. - Please don't post shallow dismissals, especially of other people's work. A good critical comment teaches us something.…

I’m helping the dude improve his writing with a short and minimally critical comment. Hall monitor elsewhere.

How can you tell that he's well dressed or lives in a city?

https://en.m.wikipedia.org/wiki/Dude

Re: Monads are monoids in the category of endofunctors

#47

Post by epolanski »

brundolf wrote: post #44
epolanski wrote: post #34

Earlier quoted context omitted.

I don't like creative explanations. Definitions are easier. A functor is a PAIR, please notice the emphasis, of a type constructor F and a map function with the following signature: a -> b -> f a -> f b. Its not a type constructor, it's a pair of two things, the type constructor AND its map function. Now that we said what it is we provide the usual simple example of Array, Record or Option, show the type constructors…

> I wish people understood that fp is much easier to understand by reading definitions. The real landscape of its adoption begs to differ. For the great majority of people, examples and analogies are fantastically more efficient for communicating ideas than building up from first principles. You get to re-use existing mental machinery, intuition, etc, until enough experience has been gained to refine it.

What do you mean?

Re: Monads are monoids in the category of endofunctors

#48

Post by 6nf »

jkhdigital wrote: post #20
brundolf wrote: post #5

Wait, a functor is just a pure unary function? And an endofunctor is just one of those where the argument type and return type are the same? This could have been explained to me years ago, in five minutes? Sometimes it makes me mad that so much confusion (and as another commenter put it, gatekeeping) has been sown in FP circles through the invention of pointlessly-obfuscated terminology for everything (and through -…

Functors are type constructors, not functions (which map values). But you could be forgiven the misunderstanding, because it is easy to trip over this distinction given the identical syntax. So, to make this absolutely clear, a monad is a type constructor in functional programming. This is why I personally prefer the more “creative” explanations of monads, because they attempt to explain what the monad is doing to th…

>Functors are type constructors

So why can't we just call the damn things 'Type constructors'?

Re: Monads are monoids in the category of endofunctors

#49

Post by lmm »

void_mint wrote: post #33
lmm wrote: post #26

Earlier quoted context omitted.

> Wait, a functor is just a pure unary function? No. > And an endofunctor is just one of those where the argument type and return type are the same? Yes - "endo" means that in general. E.g. endomorphism. > Sometimes it makes me mad that so much confusion (and as another commenter put it, gatekeeping) has been sown in FP circles through the invention of pointlessly-obfuscated terminology for everything (and through -…

> The precise terminology is vital; it's how we avoid these errors when talking about this very abstract stuff. Given that the OP is very wrong, precisely because of the kind of attitude you've taken here, I hope you'll take this opportunity to reconsider your views. Your behavior is precisely the behavior that someone new to FP would see and say "Hard pass on that", which goes into the greater problem of FP being un…

Communication is a two-way street. When someone is making an effort to learn, most FP advocates will happily make an effort to teach. But someone who comes in with guns blazing doesn't get to complain about being met with hostility, and if telling someone they're wrong when they're wrong is gatekeeping then it's a kind of gatekeeping that we need.

Re: Monads are monoids in the category of endofunctors

#50

Post by JadeNB »

void_mint wrote: post #33
lmm wrote: post #26

Earlier quoted context omitted.

> Wait, a functor is just a pure unary function? No. > And an endofunctor is just one of those where the argument type and return type are the same? Yes - "endo" means that in general. E.g. endomorphism. > Sometimes it makes me mad that so much confusion (and as another commenter put it, gatekeeping) has been sown in FP circles through the invention of pointlessly-obfuscated terminology for everything (and through -…

> The precise terminology is vital; it's how we avoid these errors when talking about this very abstract stuff. Given that the OP is very wrong, precisely because of the kind of attitude you've taken here, I hope you'll take this opportunity to reconsider your views. Your behavior is precisely the behavior that someone new to FP would see and say "Hard pass on that", which goes into the greater problem of FP being un…

> If you cannot communicate with a beginner in language they understand, A.) you don't really understand it either

This is true, but the problem is that people will always prefer the explanation that is, as the saying goes, "simple, neat, and wrong" over the explanation that is more complicated, especially if they (and possibly the person explaining) aren't aware that the simplified version is wrong. Even if one starts from an accessible viewpoint, any concept that is worth isolating as a concept will involve some difficult step in its exposition, and it is at that step that the person seeking to understand—not the explainer—has to decide whether to stick with the explanation despite the difficulty, or to be satisfied with an easy and wrong explanation.

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