Just for fun, monads as modalities is missing:
https://hackage.haskell.org/package/Agda-2.6.4.2/docs/Agda-S...
List is a monad
11–20 of 187 posts
Re: List is a monad
#12As far as monad tutorials go, this one seems quite good. I like the categorization of monads between "containers" and "recipes". However, I personally think that monad tutorials tend to give people the wrong impression and leave them more confused than they were before, because they focus on the wrong thing. A monad is not a complex concept, at all. IMO a more useful way to present the topic would be with one separat…
If all monad instances work differently what is the value of the Monad interface? What kind of usefull generic code can one write against the Monad interface.
Related: https://buttondown.com/j2kun/archive/weak-and-strong-algebra...
Re: List is a monad
#13Nit, in Haskell it's a MonadPlus. Which IIRC is a monad that supports filtering.
In Haskell List is a Monad as well as MonadPlus. Since List's Monad instance is used probably 100x more than its MonadPlus instance, I think it makes sense to focus on that,
Re: List is a monad
#14As far as monad tutorials go, this one seems quite good. I like the categorization of monads between "containers" and "recipes". However, I personally think that monad tutorials tend to give people the wrong impression and leave them more confused than they were before, because they focus on the wrong thing. A monad is not a complex concept, at all. IMO a more useful way to present the topic would be with one separat…
[deleted]
Re: List is a monad
#15Hi
Re: List is a monad
#16As far as monad tutorials go, this one seems quite good. I like the categorization of monads between "containers" and "recipes". However, I personally think that monad tutorials tend to give people the wrong impression and leave them more confused than they were before, because they focus on the wrong thing. A monad is not a complex concept, at all. IMO a more useful way to present the topic would be with one separat…
If all monad instances work differently what is the value of the Monad interface? What kind of usefull generic code can one write against the Monad interface. Related: https://buttondown.com/j2kun/archive/weak-and-strong-algebra...
Lots of useful generic code. MapM is a version of `map` that works with any Monad, `sequence` works with any monad, and so on. These are used very frequently.
But the bigger benefit is when syntax sugar like `do` notation comes in. Because it works for any Monad, people can write their own Monads and take advantage of the syntax sugar. That leads to an explosion of creativity unavailable to languages who "lock down" their syntax sugar to just what the language designers intended. In other words, what requires a change to other languages can often be a library in Haskell.
Re: List is a monad
#17As far as monad tutorials go, this one seems quite good. I like the categorization of monads between "containers" and "recipes". However, I personally think that monad tutorials tend to give people the wrong impression and leave them more confused than they were before, because they focus on the wrong thing. A monad is not a complex concept, at all. IMO a more useful way to present the topic would be with one separat…
If all monad instances work differently what is the value of the Monad interface? What kind of usefull generic code can one write against the Monad interface. Related: https://buttondown.com/j2kun/archive/weak-and-strong-algebra...
Your basic problem is that your programming language can’t express the concept cleanly. You need what’s called “Higher-Kinded Types”.
To give you a concrete example, in C#
Func, List -> List
Func, Task -> Task
Func, Func -> Func
Can’t be expressed using a generalisation. But in Haskell, you can write
(Functor F) => Func, F -> F
One of the biggest things that makes monads hard to understand is that the type systems of most languages can’t represent them. Annoying, that includes the “typeless” ones.
Re: List is a monad
#18I expect the author has done this knowingly, but the title is rather painful for a mathematician to read. A list is not a monad. List is a monad. A list is an algebra for the List monad.
What you said is not correct!
In detail:
* "A list is not a monad" - True!
* "List is a monad" - True. But I think "`List` is a monad" might be clearer.
* "A list is an algebra for the `List` monad." - False!
What's correct is the following:
* "An algebra for the `List` Monad is precisely a monoid."
Sketch of the construction:
(an algebra for the list monad is a monoid): Recall that an algebra is a set/type `A` together with a function `mult: List A -> A` together with some axioms. Think of such a function `mult: List A -> A` as the function that assigns to each list with elements in `A` the product over all those elements. The aforementioned axioms boil down to: (1) `mult([])` is a neutral element and (2) `mult` is an associative binary operation when restricted to two-element lists.
(a monoid is an algebra for the list monad): Same Idea - Given a monoid, we define a function `mult: List A -> A` by assigning to a list of elements of `A` the product of these elements. And the empty list we assign to the neutral element. Then we can use the associativity and properties of the neutral element to show that this function constitutes an algebra for the list monad.
Re: List is a monad
#19The article sort of danced around what I think is the most natural way List is a "recipe": it's the bounded nondeterminism monad (a `List` is a nondeterministic result; one could implement `List -> T` by selecting an answer uniformly at random from the finite multiset).
Re: List is a monad
#20As far as monad tutorials go, this one seems quite good. I like the categorization of monads between "containers" and "recipes". However, I personally think that monad tutorials tend to give people the wrong impression and leave them more confused than they were before, because they focus on the wrong thing. A monad is not a complex concept, at all. IMO a more useful way to present the topic would be with one separat…
If all monad instances work differently what is the value of the Monad interface? What kind of usefull generic code can one write against the Monad interface. Related: https://buttondown.com/j2kun/archive/weak-and-strong-algebra...
Traverse (or foldM) is probably a good start, likely the most useful monad-generic (or applicative-generic) function, that is simple but incredibly powerful and useful.
More generally, Monads essentially support function composition between monadic functions, so you can use it to write code that is agnostic to the monad it runs in. This can let you write e.g. prod. Code that is in IO or Async or Maybe, but for unit testing run it in Identity.
Also, it allows syntax sugar such as do notation that makes it clear to work with even when you know which monad you're working in.