Describe the process of input/output and mutable state management in Haskell.

In Haskell, a purely functional programming language, the concept of mutable state is handled differently compared to imperative programming languages. Rather than directly mutating state, Haskell embraces immutability and uses a combination of functional programming techniques to manage state. Additionally, input/output (I/O) operations are handled in a pure and referentially transparent manner through the use of monads. Let's explore the process of I/O and mutable state management in Haskell.

Input/Output (I/O) Operations:
Haskell's approach to I/O is based on the idea of separating pure computations from side-effecting actions. This is achieved through the use of monads, specifically the `IO` monad. The `IO` monad allows you to describe and sequence I/O actions in a pure and composable manner, ensuring referential transparency.

To perform I/O in Haskell, you define a main function of type `IO ()`, which serves as the entry point of your program. Within the main function, you can use various functions provided by the standard library to interact with the outside world, such as reading from and writing to files, accessing command-line arguments, or interacting with the console.

For example, to read a line of input from the user, you can use the `getLine` function, which has a type of `IO String`. The result of the `getLine` action can be bound to a variable using the `<-` operator. This allows you to work with the user input in subsequent pure computations within the `do` block.

```
haskell`main :: IO ()
main = do
putStrLn "Enter your name: "
name <- getLine
putStrLn ("Hello, " ++ name ++ "!")`
```
In this example, the `putStrLn` function is used to output a string to the console, while `getLine` is used to read a line of input from the user. The value of `name` is then used within the `putStrLn` function to generate a personalized greeting.

The key point to note is that I/O operations are encapsulated within the `IO` monad, ensuring that side effects are controlled and confined to specific parts of the code.

Mutable State Management:
In Haskell, mutable state is managed through the use of data structures called references, represented by the `IORef` type. `IORef` allows you to create mutable variables within the `IO` monad, which can be updated and accessed within the context of I/O actions.

To work with mutable state in Haskell, you create an `IORef` using the `newIORef` function, which returns an `IO` action that yields a reference to the mutable variable. You can then use functions like `readIORef` and `writeIORef` to read and modify the value contained within the reference.

Here's an example that demonstrates the usage of `IORef`:

```
haskell`import Data.IORef

main :: IO ()
main = do
counter <- newIORef 0
incrementCounter counter
currentValue <- readIORef counter
putStrLn ("Current value: " ++ show currentValue)

incrementCounter :: IORef Int -> IO ()
incrementCounter counter = do
value <- readIORef counter
writeIORef counter (value + 1)`
```
In this example, the `incrementCounter` function takes an `IORef Int` as an argument, reads the current value using `readIORef`, increments it by one, and updates the value using `writeIORef`. The final value is then read using `readIORef` within the `main` function and printed to the console.

By using `IORef`, you can achieve mutable state within the context of the `IO` monad, allowing for limited mutation