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When is it OK to use an IORef?

One thing that has always confused me is whether or not it's an okay time to use an IORef. Are there any guidelines that should be followed when deciding whether or not to use an IORef for a task? When is a good time to use the State monad over an IORef?

Monads as adjunctions

I've been reading about monads in category theory. One definition of monads uses a pair of adjoint functors. A monad is defined by a round-trip using those functors. Apparently adjunctions are very important in category theory, but I haven't seen any explanation of Haskell monads in terms of adjoint functors. Has anyone given it a thought?

Why do we need monads?

In my humble opinion the answers to the famous question "What is a monad?", especially the most voted ones, try to explain what is a monad without clearly explaining why monads are really necessary. Can they be explained as the solution to a problem?

What are free monads?

I've seen the term Free Monad pop up every now and then for some time, but everyone just seems to use/discuss them without giving an explanation of what they are. So: what are free monads? (I'd say I'm familiar with monads and the Haskell basics, but have only a very rough knowledge of category theory.)

What is a monad?

Having briefly looked at Haskell recently, what would be a brief, succinct, practical explanation as to what a monad essentially is?

I have found most explanations I've come across to be fairly inaccessible and lacking in practical detail.

Help a C# developer understand: What is a monad?

There is a lot of talk about monads these days. I have read a few articles / blog posts, but I can't go far enough with their examples to fully grasp the concept. The reason is that monads are a functional language concept, and thus the examples are in languages I haven't worked with (since I haven't used a functional language in depth). I can't grasp the syntax deeply enough to follow the articles fully ... but I can tell there's something worth understanding there.

However, I know C# pretty well, including lambda expressions and other functional features. I know C# only has a subset of functional features, and so maybe monads can't be expressed in C#.

However, surely it is possible to convey the concept? At least I hope so. Maybe you can present a C# example as a foundation, and then describe what a C# developer would wish he could do from there but can't because the language lacks functional programming features. This would be fantastic, because it would convey the intent and benefits of monads. So here's my question: What is the best explanation you can give of monads to a C# 3 developer?

Thanks!

(EDIT: By the way, I know there are at least 3 "what is a monad" questions already on SO. However, I face the same problem with them ... so this question is needed imo, because of the C#-developer focus. Thanks.)

Large-scale design in Haskell?

What is a good way to design/structure large functional programs, especially in Haskell?

I've been through a bunch of the tutorials (Write Yourself a Scheme being my favorite, with Real World Haskell a close second) - but most of the programs are relatively small, and single-purpose. Additionally, I don't consider some of them to be particularly elegant (for example, the vast lookup tables in WYAS).

I'm now wanting to write larger programs, with more moving parts - acquiring data from a variety of different sources, cleaning it, processing it in various ways, displaying it in user interfaces, persisting it, communicating over networks, etc. How could one best structure such code to be legible, maintainable, and adaptable to changing requirements?

There is quite a large literature addressing these questions for large object-oriented imperative programs. Ideas like MVC, design patterns, etc. are decent prescriptions for realizing broad goals like separation of concerns and reusability in an OO style. Additionally, newer imperative languages lend themselves to a 'design as you grow' style of refactoring to which, in my novice opinion, Haskell appears less well-suited.

Is there an equivalent literature for Haskell? How is the zoo of exotic control structures available in functional programming (monads, arrows, applicative, etc.) best employed for this purpose? What best practices could you recommend?

Thanks!

EDIT (this is a follow-up to Don Stewart's answer):

@dons mentioned: "Monads capture key architectural designs in types."

I guess my question is: how should one think about key architectural designs in a pure functional language?

Consider the example of several data streams, and several processing steps. I can write modular parsers for the data streams to a set of data structures, and I can implement each processing step as a pure function. The processing steps required for one piece of data will depend on its value and others'. Some of the steps should be followed by side-effects like GUI updates or database queries.

What's the 'Right' way to tie the data and the parsing steps in a nice way? One could write a big function which does the right thing for the various data types. Or one could use a monad to keep track of what's been processed so far and have each processing step get whatever it needs next from the monad state. Or one could write largely separate programs and send messages around (I don't much like this option).

The slides he linked have a Things we Need bullet: "Idioms for mapping design onto types/functions/classes/monads". What are the idioms? :)

A monad is just a monoid in the category of endofunctors, what's the problem?

Who first said

A monad is just a monoid in the category of endofunctors, what's the problem?

and on a less important note is this true and if so could you give an explanation (hopefully one that can be understood by someone who doesn't have much haskell experience).

Pattern to avoid nested try catch blocks?

Consider a situation where I have three (or more) ways of performing a calculation, each of which can fail with an exception. In order to attempt each calculation until we find one that succeeds, I have been doing the following:

double val;

try { val = calc1(); }
catch (Calc1Exception e1)
{ 
    try { val = calc2(); }
    catch (Calc2Exception e2)
    {
        try { val = calc3(); }
        catch (Calc3Exception e3)
        {
            throw new NoCalcsWorkedException();
        }
    }
}

Is there any accepted pattern which achieves this in a nicer way? Of course I could wrap each calculation in a helper method which returns null on failure, and then just use the ?? operator, but is there a way of doing this more generally (i.e. without having to write a helper method for each method I want to use)? I've thought about writing a static method using generics which wraps any given method in a try/catch and returns null on failure, but I'm not sure how I would go about this. Any ideas?

Good examples of Not a Functor/Functor/Applicative/Monad?

While explaining to someone what a type class X is I struggle to find good examples of data structures which are exactly X.

So, I request examples for:

• A type constructor which is not a Functor.
• A type constructor which is a Functor, but not Applicative.
• A type constructor which is an Applicative, but is not a Monad.
• A type constructor which is a Monad.

I think there are plenty examples of Monad everywhere, but a good example of Monad with some relation to previous examples could complete the picture.

I look for examples which would be similar to each other, differing only in aspects important for belonging to the particular type class.

If one could manage to sneak up an example of Arrow somewhere in this hierarchy (is it between Applicative and Monad?), that would be great too!

What is the point of the class Option[T]?

I am not able to understand the point of Option[T] class in Scala. I mean, I am not able to see any advanages of None over null.

For example, consider the code:

object Main{
  class Person(name: String, var age: int){
    def display = println(name+" "+age)
  }

  def getPerson1: Person = {
    // returns a Person instance or null
  }

  def getPerson2: Option[Person] = {
    // returns either Some[Person] or None
  }

  def main(argv: Array[String]): Unit = {
    val p = getPerson1
    if (p!=null) p.display

    getPerson2 match{
      case Some(person) => person.display
      case None => /* Do nothing */
    }
  }
}

Now suppose, the method getPerson1 returns null, then the call made to display on first line of main is bound to fail with NPE. Similarly if getPerson2 returns None, the display call will again fail with some similar error.

If so, then why does Scala complicate things by introducing a new value wrapper (Option[T]) instead of following a simple approach used in Java?

UPDATE:

I have edited my code as per @Mitch's suggestion. I am still not able to see any particular advantage of Option[T]. I have to test for the exceptional null or None in both cases. :(

If I have understood correctly from @Michael's reply, is the only advantage of Option[T] is that it explicitly tells the programmer that this method could return None? Is this the only reason behind this design choice?

What is indexed monad?

What is indexed monad and the motivation for this monad?

I have read that it helps to keep track of the side effects. But the type signature and documentation doesn't lead me to anywhere.

What would be an example of how it can help to keep track of side effects (or any other valid example)?

Applicatives compose, monads don't

Applicatives compose, monads don't.

What does the above statement mean? And when is one preferable to other?

Why do we have map, fmap and liftM?

map :: (a -> b) -> [a] -> [b]

fmap :: Functor f => (a -> b) -> f a -> f b

liftM :: Monad m => (a -> b) -> m a -> m b

Why do we have three different functions that do essentially the same thing?

Reader Monad Purpose

I am newbie to Haskell. I read the Reader Monad several times, but still don't understand about what is the purpose of the Reader Monad. The Reader Monad is so complex and seems to be useless. In imperative language like Java or C++, there is no equivalent term for reader monad (if I am right). Can you give me a simple example and make me clear a little bit. Sorry for my ignorance.