Sure, I will explain the use of the dollar sign ($) in Haskell by including an introduction, a problem solution, a step-by-step code explanation, two sections with headers related to Haskell libraries or relevant functions and I’ll make sure to adhere to your other requests regarding SEO optimization.

Haskell is a standardized, purely functional programming language with non-strict semantics, named after Haskell Curry. In Haskell, the ($) operator is used in function application. The operator itself is just a function that takes a function and another argument and applies the function to the argument. The interesting thing about this operator is its low, right-associative binding precedence. This can be utilized to reduce the number of needed parentheses in an expression.

In Haskell programming, an important concept is function application which is the process of applying a function to its arguments. Haskell developers use the dollar sign ($) to reduce the amount of parentheses in their code.

f $ g $ h x

**The expression above is equivalent to:**

f (g (h x))

## A closer look into the function application operator

In Haskell, everything is a function. The dollar sign ($) is a function application operator. It is defined as an infix function in the Prelude, meaning it is a function that goes between its two arguments. Its precedence is lower than all other operators.

($) :: (a -> b) -> a -> b f $ x = f x

**The operator takes a function and an argument, and applies the function to that argument.**

## Working with the Control.Monad library

In Haskell, Monads are used to abstract away boilerplate code and to handle side effects, async computations, among other use-cases. The Control.Monad library provides the join function which can be used alongside the dollar function application operator.

import Control.Monad (join) main :: IO () main = join $ putStrLn "Hello, World!"

Here, the dollar sign is used to apply the putStrLn function to the string argument before applying join. This is equivalent to:

main :: IO () main = join (putStrLn "Hello, World!")

In conclusion, the dollar sign operator in Haskell is a convenient tool for reducing parentheses and making code cleaner and easier to read. It occupies a unique place in function application and works wonderfully with Haskell’s robust and complex type system.