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In Haskell and PureScript, Monad is a typeclass just like any other. They are an abstraction, effectful computation is not inherent to them, they represent com

In Haskell and PureScript, Monad is a typeclass just like any other. They are an abstraction, effectful computation is not inherent to them, they represent computational contexts, e.g. the list monad is used to model non-determinism, the maybe monad represents computations that can fail, both of these are pure. This is an excellent set of posts for building an intuition about monads: http://mvanier.livejournal.com/3917.html http://mvanier.livejournal.com/3917.html

sdegutis 10y ago
> the list monad is used to model non-determinism See this is the kind of thing that made learning Haskell so hard for me. I'm not a math guy, I'm terrible at math. I have no idea what "non-determinism" means, and I'd venture to guess that list monad is used to model "ordered collections of things".
- Senji 10y ago
  "non-determinism" implies unordered.
  - bertiewhykovich 10y ago
    See, to me, the sequence of keypresses I make while banging on my keyboard seem like it could be represented as an ordered list. I may be missing something, though.
    - kodfodrasz 10y ago
      If something is unordered it does not mean it may not be ordered. It only says you cannot assume that it is ordered. (A Collection in Java/C# is an unordered contract, but a List is also a Collection.) But the idea of a list also suggests an ordering to me.
- dpratt71 10y ago
  I'm not a math guy either and I did indeed find it difficult to penetrate the inner sanctum of Haskell for this very reason. I won't say I've completely succeeded in that effort, but I've come quite a long way. I'm fairly certain that in this context, non-determinism means that there can be more than one answer/result.
- kazagistar 10y ago
  Scala calls the monad bind "flatMap". Java actually implements it for Streams. If you have a `Stream<Deck> decks;` of card decks, and want to get all the cards from all the decks, you might try to do something like `decks.map(deck -> deck.getCards().stream())`, but that will give you the type `Stream<Stream<Deck>>`. That sucks, we just want a single stream, not a stream of streams, so we call the function that flattens at the same time. `decks.flatMap(deck -> deck.getCards().stream())`. Nondeterminism is just a standard use for this construction: given one choice, generate more choices, given that choice, generate more choices, do some computation with the choices, and then return the list of possible final results.

sdegutis 10y ago

> the list monad is used to model non-determinism See this is the kind of thing that made learning Haskell so hard for me. I'm not a math guy, I'm terrible at math. I have no idea what "non-determinism" means, and I'd venture to guess that list monad is used to model "ordered collections of things".

Senji 10y ago
"non-determinism" implies unordered.
- bertiewhykovich 10y ago
  See, to me, the sequence of keypresses I make while banging on my keyboard seem like it could be represented as an ordered list. I may be missing something, though.
  - kodfodrasz 10y ago
    If something is unordered it does not mean it may not be ordered. It only says you cannot assume that it is ordered. (A Collection in Java/C# is an unordered contract, but a List is also a Collection.) But the idea of a list also suggests an ordering to me.
dpratt71 10y ago
I'm not a math guy either and I did indeed find it difficult to penetrate the inner sanctum of Haskell for this very reason. I won't say I've completely succeeded in that effort, but I've come quite a long way. I'm fairly certain that in this context, non-determinism means that there can be more than one answer/result.
kazagistar 10y ago
Scala calls the monad bind "flatMap". Java actually implements it for Streams. If you have a `Stream<Deck> decks;` of card decks, and want to get all the cards from all the decks, you might try to do something like `decks.map(deck -> deck.getCards().stream())`, but that will give you the type `Stream<Stream<Deck>>`. That sucks, we just want a single stream, not a stream of streams, so we call the function that flattens at the same time. `decks.flatMap(deck -> deck.getCards().stream())`. Nondeterminism is just a standard use for this construction: given one choice, generate more choices, given that choice, generate more choices, do some computation with the choices, and then return the list of possible final results.