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List is a monad

alexyorke.github.io

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Re: List is a monad

#111

Post by 4ad »

kevinventullo wrote: post #108

So I come at this from a math background but I’ve always found these explanations to be overly complex. In the parlance of C++, I think of a monad as a template class T with the following properties: 1. For any class X, there is a canonical method F: X -> T 2. For any class X, there is a canonical method G: T > -> T . 3. For classes X and Y, and any method f: X -> Y, there is a corresponding method “T ”: T -> T . ———…

So you think that a monad which is an object with a simple definition in category theory is better explained in terms of C++?

I would agree that most of these articles about monads are bad. Just study the definition, then study what you can do with monads, it's not that hard.

Re: List is a monad

#112

Post by Kranar »

kevinventullo wrote: post #108

So I come at this from a math background but I’ve always found these explanations to be overly complex. In the parlance of C++, I think of a monad as a template class T with the following properties: 1. For any class X, there is a canonical method F: X -> T 2. For any class X, there is a canonical method G: T > -> T . 3. For classes X and Y, and any method f: X -> Y, there is a corresponding method “T ”: T -> T . ———…

This is like explaining chess by simply stating the rules. Like sure explaining the rules of chess is important but only knowing the rules provides for nothing more than a superficial understanding of a topic.

Re: List is a monad

#114

Post by danieltanfh95 »

polygot wrote: post #72
nemo1618 wrote: post #31

I think this adds more confusion than it removes. A list is not a monad. A list is a data structure; a monad is more like a "trait" or "interface." So you can define a List type that "implements" the monad interface, but this is not an inherent property of lists themselves. That's the sense in which a list "is a" monad: the OOP sense. Haskell's List monad provides a model for nondeterminism. But that certainly isn't…

Hi, I completely agree. "A" list isn't inherently a monad, and that is where my metaphor starts to fall apart a bit (my post title furthers this issue.) I can clarify this earlier in part 1 or 2 instead of in to-be-written part 3.

Its a harmful metaphor and clickbait title.

Re: List is a monad

#115

Post by danieltanfh95 »

The obsession with trying to explain a monad ultimately stems from conflicting explanations and the inability to differentiate between a mathematical monad and monads implemented in software.

Monads in software are just a standard API for any given type. That’s it. Theres no magic here. Just implement the standard and you have a monad.

It grinds my gears seeing monad tutorial after tutorial using the wrong metaphors or misleading explanations

Re: List is a monad

#116

Post by kevinventullo »

4ad wrote: post #111
kevinventullo wrote: post #108

So I come at this from a math background but I’ve always found these explanations to be overly complex. In the parlance of C++, I think of a monad as a template class T with the following properties: 1. For any class X, there is a canonical method F: X -> T 2. For any class X, there is a canonical method G: T > -> T . 3. For classes X and Y, and any method f: X -> Y, there is a corresponding method “T ”: T -> T . ———…

So you think that a monad which is an object with a simple definition in category theory is better explained in terms of C++? I would agree that most of these articles about monads are bad. Just study the definition, then study what you can do with monads, it's not that hard.

For people who are more familiar with C++ than category theory, yes.

Re: List is a monad

#117

Post by kevinventullo »

Kranar wrote: post #112
kevinventullo wrote: post #108

So I come at this from a math background but I’ve always found these explanations to be overly complex. In the parlance of C++, I think of a monad as a template class T with the following properties: 1. For any class X, there is a canonical method F: X -> T 2. For any class X, there is a canonical method G: T > -> T . 3. For classes X and Y, and any method f: X -> Y, there is a corresponding method “T ”: T -> T . ———…

This is like explaining chess by simply stating the rules. Like sure explaining the rules of chess is important but only knowing the rules provides for nothing more than a superficial understanding of a topic.

I mean if someone is learning chess for the first time, then yes you should start with the rules rather than jumping right into waxing philosophic about positional strategy to show off how smart you are.

Re: List is a monad

#119

Post by solomonb »

tel wrote: post #109
solomonb wrote: post #106

Earlier quoted context omitted.

Not if you need to perform two /Monadic/ operations as the commenter stated explicitly.

Every monad is also an applicative and liftA2 does/is the same thing as liftM2. The only reason they both exist was due to Monad being popularized in Haskell earlier than Applicative and thus not having it as a superclass until the Functor-Applicative-Monad Proposal in Haskell 2014. It was obviously correct, but a major breaking change that also got pork barreled a bit and so took a while to land.

Yes you're absolutely right. I had a bit of a brain fart moment here. If they were Applicative operations then you would not be able to use `liftM2`, not the other way around.
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