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How do you figure? They're an abstract concept commonly used to represent values over a sequence of operations. How does that not describe state? Do you mean so

How do you figure? They're an abstract concept commonly used to represent values over a sequence of operations. How does that not describe state? Do you mean something very specific with the term "state" that might make it more meaningful?

Izkata 2y ago
They are an abstraction of a sequence of operations, not the state used in those operations.
- darby_nine 2y ago
  They're both, right? It's not like it specifically ignores the inputs and outputs of those operations. These are specifically entailed in the definition of the monad. I strongly, strongly suspect there's something about how F# processes monads in the context of a do expression that explains what is the focus here. Unfortunately I don't have the time to go through the steps now, hence why I specifically recommended modifying the introduction to give some clue about the terms involved.
  - Izkata 2y ago
    An "if" statement or "map" function also has inputs and outputs and probably some internal state due to implementation details, but we don't say they represent state either. They represent operations, or a sequence of operations.
    - darby_nine 2y ago
      > An "if" statement or "map" function also has inputs and outputs and probably some internal state due to implementation details, but we don't say they represent state either. They absolutely are in the context of a program and not just abstract expression, which never matters. The distinction strikes me as meaningless. At the very least it's worth qualifying with "mutable state" if that's the attribute of state you care about. There's still "constant expressions" as other forms of values and "statically initialized values" as other forms of state.
wavemode 2y ago
I think "context" is a bit more all-encompassing. If I have an Int, then I just have an Int. If I have an Identity Int, then I really still just have an Int. If I have a [Int] then I have a list of Ints. If I have a Maybe Int, then I either have an Int or I have Nothing. If I have a Reader r Int, then I have a computation taking some input of type r and producing an Int. That computation can't modify the value of r. If I have a State s Int, I have a computation taking some initial state of type s and producing an Int. The value of s may change during the computation. All of these are monads, but calling all of them "state" is somewhat reductive. The Haskell wiki tutorial on monads refers to them vaguely as "strategies" - I mostly agree with that description.
seanhunter 2y ago
Monads can encode state but they don't have to. I tend to think of a monad in computer science as something which is constructed from a type and a computation and wraps the return values of that computation in that type. That allows you to bake in "context" into that type which could be state in the conventional sense but it could be something else. To make this practical, let's make a simple example of a simple somewhat useful monad with no state. Imagine you have all the regular trigonometric functions sine, cosine etc which accept radians[1] and you need versions which work in degrees. You could make a unit conversion monad which converts arguments on the way in and wraps the result in an inverse conversion monad such that if you passed it to arcsine arccosine etc on it it would know and return degrees on the way out. Neither of those monads would have any state in the usual computer science sense, the main conversion is just multiplying all the inputs by pi/180 before calling the wrapped function and constructing a result monad type so the inverse trig functions do the opposite of that. [1] ie the correct versions. Fight me physicists and engineers and you freaks who use gradians whoever you are[2]. [2] I think it's surveyors but I could be wrong.
cryptonector 2y ago
Monads can be used to attach all sorts of things besides state to data. For example, you can associate read-only data, such as configuration, authenticated identies, etc. You can associate I/O methods, which can be real or mocked. You can have a place in which to scribble logs/traces (this feels like state). And yes, you can associate mutable state, of course. The point of monads, from the point of view of programmer convenience, is that they let you have a bag of contextual stuff along with your values. Thus if you think of a server application that processes requests, you might want to carry all of: - configuration applicable to this request (or global configuration) - request metadata (time received, from where, from whom, authenticated how, etc.) - request processing state - logs/traces - I/O methods, so that - you can make all your code deterministic and thus easier to write tests for - so you can mock the world (see previous item) with each request. Thus each function that handles a request can get all of that context, and can be fully deterministic, yet it can function in a non-deterministic world. Besides this there's everything about the Maybe ("Optional") and Error/Either monads that just makes it easy to make sure all errors and "nulls" are handled. And what makes all of this possible (in Haskell) is the use of operators (functions) and syntax that lets one write "statements" that are actually combined into large expressions.
- 12_throw_away 2y ago
  you might want to carry all of: - configuration applicable to this request (or global configuration) [...] Ok, this is super-interesting to me, as I'm currently dealing with the "configuration and interfaces as global state" pattern in a legacy application. Among other things, this makes it hell to test and refactor. Refactoring it into a functional abstraction like this seems like exactly what we need. But ... I'm kind of struggling to figure out what "global configuration as a monad" would look like (very much not a Haskell programmer). How would something like this work in practice?
  - cryptonector 2y ago
    In Java or C++ or other OOPish languages, say, you might make all your classes be Configurable (unless they are Configuration), which means their constructors would take a Configuration in some way, possibly with an explicit Configuration argument or with a Configurable argument whose configuration to copy. This way all your objects will know how to find configuration information.

Izkata 2y ago

They are an abstraction of a sequence of operations, not the state used in those operations.

darby_nine 2y ago
They're both, right? It's not like it specifically ignores the inputs and outputs of those operations. These are specifically entailed in the definition of the monad. I strongly, strongly suspect there's something about how F# processes monads in the context of a do expression that explains what is the focus here. Unfortunately I don't have the time to go through the steps now, hence why I specifically recommended modifying the introduction to give some clue about the terms involved.
- Izkata 2y ago
  An "if" statement or "map" function also has inputs and outputs and probably some internal state due to implementation details, but we don't say they represent state either. They represent operations, or a sequence of operations.
  - darby_nine 2y ago
    > An "if" statement or "map" function also has inputs and outputs and probably some internal state due to implementation details, but we don't say they represent state either. They absolutely are in the context of a program and not just abstract expression, which never matters. The distinction strikes me as meaningless. At the very least it's worth qualifying with "mutable state" if that's the attribute of state you care about. There's still "constant expressions" as other forms of values and "statically initialized values" as other forms of state.

wavemode 2y ago

I think "context" is a bit more all-encompassing. If I have an Int, then I just have an Int. If I have an Identity Int, then I really still just have an Int. If I have a [Int] then I have a list of Ints. If I have a Maybe Int, then I either have an Int or I have Nothing. If I have a Reader r Int, then I have a computation taking some input of type r and producing an Int. That computation can't modify the value of r. If I have a State s Int, I have a computation taking some initial state of type s and producing an Int. The value of s may change during the computation. All of these are monads, but calling all of them "state" is somewhat reductive. The Haskell wiki tutorial on monads refers to them vaguely as "strategies" - I mostly agree with that description.

seanhunter 2y ago

Monads can encode state but they don't have to. I tend to think of a monad in computer science as something which is constructed from a type and a computation and wraps the return values of that computation in that type. That allows you to bake in "context" into that type which could be state in the conventional sense but it could be something else. To make this practical, let's make a simple example of a simple somewhat useful monad with no state. Imagine you have all the regular trigonometric functions sine, cosine etc which accept radians[1] and you need versions which work in degrees. You could make a unit conversion monad which converts arguments on the way in and wraps the result in an inverse conversion monad such that if you passed it to arcsine arccosine etc on it it would know and return degrees on the way out. Neither of those monads would have any state in the usual computer science sense, the main conversion is just multiplying all the inputs by pi/180 before calling the wrapped function and constructing a result monad type so the inverse trig functions do the opposite of that. [1] ie the correct versions. Fight me physicists and engineers and you freaks who use gradians whoever you are[2]. [2] I think it's surveyors but I could be wrong.

cryptonector 2y ago

Monads can be used to attach all sorts of things besides state to data. For example, you can associate read-only data, such as configuration, authenticated identies, etc. You can associate I/O methods, which can be real or mocked. You can have a place in which to scribble logs/traces (this feels like state). And yes, you can associate mutable state, of course. The point of monads, from the point of view of programmer convenience, is that they let you have a bag of contextual stuff along with your values. Thus if you think of a server application that processes requests, you might want to carry all of: - configuration applicable to this request (or global configuration) - request metadata (time received, from where, from whom, authenticated how, etc.) - request processing state - logs/traces - I/O methods, so that - you can make all your code deterministic and thus easier to write tests for - so you can mock the world (see previous item) with each request. Thus each function that handles a request can get all of that context, and can be fully deterministic, yet it can function in a non-deterministic world. Besides this there's everything about the Maybe ("Optional") and Error/Either monads that just makes it easy to make sure all errors and "nulls" are handled. And what makes all of this possible (in Haskell) is the use of operators (functions) and syntax that lets one write "statements" that are actually combined into large expressions.

12_throw_away 2y ago
you might want to carry all of: - configuration applicable to this request (or global configuration) [...] Ok, this is super-interesting to me, as I'm currently dealing with the "configuration and interfaces as global state" pattern in a legacy application. Among other things, this makes it hell to test and refactor. Refactoring it into a functional abstraction like this seems like exactly what we need. But ... I'm kind of struggling to figure out what "global configuration as a monad" would look like (very much not a Haskell programmer). How would something like this work in practice?
- cryptonector 2y ago
  In Java or C++ or other OOPish languages, say, you might make all your classes be Configurable (unless they are Configuration), which means their constructors would take a Configuration in some way, possibly with an explicit Configuration argument or with a Configurable argument whose configuration to copy. This way all your objects will know how to find configuration information.