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> The essence of monads is to use abstract types to enclose a mutable state, providing only a set of carefully-crafted combinators for using it in such a way th

> The essence of monads is to use abstract types to enclose a mutable state, providing only a set of carefully-crafted combinators for using it in such a way that you can't duplicate the state but have to use it in a linear, non-branching fashion When I was reading about these stuff, I was not lucky enough to find such a clear high level description of what is the purpose of a monad. I got it eventually, but I wish I encountered this concise description earlier.

tromp 4y ago
It's a rather incomplete description of monads, since besides "mutable state", monads also cover optional state (Maybe), multiple states (List), dependent state (Reader), exceptional state, etcetera.
platz 4y ago
> you can't duplicate the state but have to use it in a linear, non-branching fashion So so you're saying bitcoin should have been made out of monads?
Koshkin 4y ago
I suspect that it is only after you ‘got it’ that you can find this description nicer than anything else that you can find in the swath of monad tutorials.
- jerf 4y ago
  Unfortunately, if this is your understanding of monad, that is itself proof that you did not "get it". It is neither required for mutable state, nor required for mutable state in Haskell, nor are all monad implementations about mutability. That is, that understanding is neither a subset of understanding monads, nor is a proper understanding of monads a subset of thinking of them as being about mutability. It's just wrong, unfortunately. I wrote about this extensively in http://www.jerf.org/iri/post/2958 http://www.jerf.org/iri/post/2958, "Functors and Monads For People Who Have Read Too Many 'Tutorials'". If original post is from 2008, then it is the sort of "too many 'tutorials'" that you may have read about them.
  - sudosysgen 4y ago
    Sure, the idea that they have to be mutable in practice is incorrect, but Haskell has "do notation" which makes Monads act as if they always introduced mutability, and in the spirit of a simplification it is correct in the essence. The essence of the understanding that Monads act as a wrapper and define lifting and composition of wrapped types is correct in essence and that's the meat of the understanding. Define it a bit more rigorously and it's literally mathematically équivalent to saying "monoid over the category of endofunctors".
    - nightski 4y ago
      No. Do notation has nothing to do with mutability. Do notation is a convenient syntax for monads period. You can use it with the list monad for example and not IO at all.
      - sudosysgen 4y ago
        Do notation gives the syntax and almost the semantics of mutability. I never said it actually means they are mutable, just that it is practically as if they were. Which is what the author says about Monads, they mean that practically it's as if they were mutable. And yes, that goes with the list monad too when using do notation. It's syntactically and in practice almost as if you were mutating a new list and then returning it.
        nightski 4y ago
        I don't agree. Maybe let's use a different example to illustrate more clearly - the maybe monad. Let's pretend you have a series of functions a, b, and c which take a value of type X and return a value of type Maybe X. With do notation you can chain the functions like this - do r1 <- a 1 r2 <- b r1 r3 <- c r2 r3 This is about composing functions. It has nothing to do with mutability. It is just a convenient way to write the composition rather than using nested bind operators.
        4y ago
cuteboy19 4y ago
now that you have understood it, it is your duty to write yet another monad tutorial
mrkeen 4y ago
> The essence of monads is to use abstract types to enclose a mutable state, providing only a set of carefully-crafted combinators for using it in such a way that you can't duplicate the state but have to use it in a linear, non-branching fashion This is a good description of one particular monad, the ST monad: https://wiki.haskell.org/Monad/ST https://wiki.haskell.org/Monad/ST
- sudosysgen 4y ago
  The ST monad is a good example, but that's the basic pattern of the Monad. Lifting a base type into a monadic type and composing monadic functions.
  - mrkeen 4y ago
    I may not have been harsh enough. The ST monad (enclosing mutable state to use it in a linear, non-branching fashion) is indeed a good example of a monad. Calling that the essence of monads is as accurate and helpful as calling it a burrito [1]. Future downvoters may want to try to reconcile any of the other common monads (Maybe, Either, List, State, Parser, Reader, Writer) against this enclosed/mutable/linear/non-branching definition and see if the essence fits. [1] https://kjaer.io/a-monad-is-not-a-burrito/ https://kjaer.io/a-monad-is-not-a-burrito/
    - sudosysgen 4y ago
      I have considered all of those Monads and more when assessing that definition. The Maybe monad is in essence a Boolean wrapped around the base type (for which a value may be null but is part of the monoidal type nonetheless). The Either monad is another Boolean wrapped around the union of two types which itself a type. In all cases an operation on an object of the monoidal type will mutate the wrapper type but not the wrapped type which always stays the same. The List monad is even simpler, it's a linked list, so the wrapper contains another successor list which may be empty but of the same type and a value of the current type with mapping being an operation that maps function in the base type into functions on the monoidal type. The State monad is obvious. The Parser monad typically wraps around some form of string which is partially parsed and then contains an element or a list thereof of the parsed type such that operations on the string type yield a partial parse. The Reader and Writer Monads are obvious. This type of intuition always works on Monads. If you want to learn more about it I'd recommend to learn about the relationship between the Kleisli Triple and the monad. In reality this way of understanding this is just an intuition of how the Kleisli Triple works and how it is an equivalent to the traditional representation of the monad.
pyrale 4y ago
It's also wrong. Lists are monads, and whether the implementation you use is mutable or not is not relevant to how you use them. The essence of monads is not about what use can be made of them either, just like the essence of things that have a hook is not that you can use them to hang your coat. Simply put, monads are data types that share a set of properties. Think of them as you would think of the atoms that are halogens, or of the animals that are mammal. In the case of monads, the property is that functions can be chained on them in a specific way, and that the result of this chaining respects some rules. The reason it is so hard to explain or understand monads is that this property in many different ways for many different ends, and that the what and the why are often mixed in the explanation.
- deleted 4y ago
  [deleted]
- quelltext 4y ago
  > Lists are monads Isn't it just that you can define monadic interfaces for lists, as you can with (probably all) parametric data types? Saying "the list monad" wouldn't be correct, right? Although it's pretty common to see that phrase.
  - jerf 4y ago
    Monad is just an interface; all "monad"s are things that declare some function that conforms to the interface. You can say "the list monad" reasonably because there is only one sensible implementation of (List a -> (a -> List b) -> List b) in Haskell. You could unconditionally return an empty List b and fulfill that interface, but what would be the point of that? You can't just return a list of all the things the function call resulted in because that would be a List of a List of b, which is not the same as a List of b. You can't sort them in Haskell because you don't have any form of comparability available in that interface specification. etc. Technically in other languages this may be less true as due to having fewer restrictions (for example, you may in a language that defines ordering on all values, and thus you could sort the result regardless of the types involved) you can do more things, but there's still really only one sensible and unsurprising implementation.
imtringued 4y ago
I disagree with the description though, a monad is effectively the hot cell of functional programming. You aren't allowed to touch the contents of the hot cell, instead you must send a robot arm into the hot cell. What is surprising though, is that the robot constructs another hot cell inside the hot cell and then merges it with the outer hot cell The problem with monad is that it is a typeclass with not much meat on it, it would be more appropriate to talk about monad instances.

tromp 4y ago

It's a rather incomplete description of monads, since besides "mutable state", monads also cover optional state (Maybe), multiple states (List), dependent state (Reader), exceptional state, etcetera.

platz 4y ago

> you can't duplicate the state but have to use it in a linear, non-branching fashion So so you're saying bitcoin should have been made out of monads?

Koshkin 4y ago

I suspect that it is only after you ‘got it’ that you can find this description nicer than anything else that you can find in the swath of monad tutorials.

jerf 4y ago
Unfortunately, if this is your understanding of monad, that is itself proof that you did not "get it". It is neither required for mutable state, nor required for mutable state in Haskell, nor are all monad implementations about mutability. That is, that understanding is neither a subset of understanding monads, nor is a proper understanding of monads a subset of thinking of them as being about mutability. It's just wrong, unfortunately. I wrote about this extensively in http://www.jerf.org/iri/post/2958 http://www.jerf.org/iri/post/2958, "Functors and Monads For People Who Have Read Too Many 'Tutorials'". If original post is from 2008, then it is the sort of "too many 'tutorials'" that you may have read about them.
- sudosysgen 4y ago
  Sure, the idea that they have to be mutable in practice is incorrect, but Haskell has "do notation" which makes Monads act as if they always introduced mutability, and in the spirit of a simplification it is correct in the essence. The essence of the understanding that Monads act as a wrapper and define lifting and composition of wrapped types is correct in essence and that's the meat of the understanding. Define it a bit more rigorously and it's literally mathematically équivalent to saying "monoid over the category of endofunctors".
  - nightski 4y ago
    No. Do notation has nothing to do with mutability. Do notation is a convenient syntax for monads period. You can use it with the list monad for example and not IO at all.
    - sudosysgen 4y ago
      Do notation gives the syntax and almost the semantics of mutability. I never said it actually means they are mutable, just that it is practically as if they were. Which is what the author says about Monads, they mean that practically it's as if they were mutable. And yes, that goes with the list monad too when using do notation. It's syntactically and in practice almost as if you were mutating a new list and then returning it.
      - nightski 4y ago
        I don't agree. Maybe let's use a different example to illustrate more clearly - the maybe monad. Let's pretend you have a series of functions a, b, and c which take a value of type X and return a value of type Maybe X. With do notation you can chain the functions like this - do r1 <- a 1 r2 <- b r1 r3 <- c r2 r3 This is about composing functions. It has nothing to do with mutability. It is just a convenient way to write the composition rather than using nested bind operators.
        4y ago

cuteboy19 4y ago

now that you have understood it, it is your duty to write yet another monad tutorial

mrkeen 4y ago

> The essence of monads is to use abstract types to enclose a mutable state, providing only a set of carefully-crafted combinators for using it in such a way that you can't duplicate the state but have to use it in a linear, non-branching fashion This is a good description of one particular monad, the ST monad: https://wiki.haskell.org/Monad/ST https://wiki.haskell.org/Monad/ST

sudosysgen 4y ago
The ST monad is a good example, but that's the basic pattern of the Monad. Lifting a base type into a monadic type and composing monadic functions.
- mrkeen 4y ago
  I may not have been harsh enough. The ST monad (enclosing mutable state to use it in a linear, non-branching fashion) is indeed a good example of a monad. Calling that the essence of monads is as accurate and helpful as calling it a burrito [1]. Future downvoters may want to try to reconcile any of the other common monads (Maybe, Either, List, State, Parser, Reader, Writer) against this enclosed/mutable/linear/non-branching definition and see if the essence fits. [1] https://kjaer.io/a-monad-is-not-a-burrito/ https://kjaer.io/a-monad-is-not-a-burrito/
  - sudosysgen 4y ago
    I have considered all of those Monads and more when assessing that definition. The Maybe monad is in essence a Boolean wrapped around the base type (for which a value may be null but is part of the monoidal type nonetheless). The Either monad is another Boolean wrapped around the union of two types which itself a type. In all cases an operation on an object of the monoidal type will mutate the wrapper type but not the wrapped type which always stays the same. The List monad is even simpler, it's a linked list, so the wrapper contains another successor list which may be empty but of the same type and a value of the current type with mapping being an operation that maps function in the base type into functions on the monoidal type. The State monad is obvious. The Parser monad typically wraps around some form of string which is partially parsed and then contains an element or a list thereof of the parsed type such that operations on the string type yield a partial parse. The Reader and Writer Monads are obvious. This type of intuition always works on Monads. If you want to learn more about it I'd recommend to learn about the relationship between the Kleisli Triple and the monad. In reality this way of understanding this is just an intuition of how the Kleisli Triple works and how it is an equivalent to the traditional representation of the monad.

pyrale 4y ago

It's also wrong. Lists are monads, and whether the implementation you use is mutable or not is not relevant to how you use them. The essence of monads is not about what use can be made of them either, just like the essence of things that have a hook is not that you can use them to hang your coat. Simply put, monads are data types that share a set of properties. Think of them as you would think of the atoms that are halogens, or of the animals that are mammal. In the case of monads, the property is that functions can be chained on them in a specific way, and that the result of this chaining respects some rules. The reason it is so hard to explain or understand monads is that this property in many different ways for many different ends, and that the what and the why are often mixed in the explanation.

deleted 4y ago
[deleted]
quelltext 4y ago
> Lists are monads Isn't it just that you can define monadic interfaces for lists, as you can with (probably all) parametric data types? Saying "the list monad" wouldn't be correct, right? Although it's pretty common to see that phrase.
- jerf 4y ago
  Monad is just an interface; all "monad"s are things that declare some function that conforms to the interface. You can say "the list monad" reasonably because there is only one sensible implementation of (List a -> (a -> List b) -> List b) in Haskell. You could unconditionally return an empty List b and fulfill that interface, but what would be the point of that? You can't just return a list of all the things the function call resulted in because that would be a List of a List of b, which is not the same as a List of b. You can't sort them in Haskell because you don't have any form of comparability available in that interface specification. etc. Technically in other languages this may be less true as due to having fewer restrictions (for example, you may in a language that defines ordering on all values, and thus you could sort the result regardless of the types involved) you can do more things, but there's still really only one sensible and unsurprising implementation.

imtringued 4y ago

I disagree with the description though, a monad is effectively the hot cell of functional programming. You aren't allowed to touch the contents of the hot cell, instead you must send a robot arm into the hot cell. What is surprising though, is that the robot constructs another hot cell inside the hot cell and then merges it with the outer hot cell The problem with monad is that it is a typeclass with not much meat on it, it would be more appropriate to talk about monad instances.