In the contemporary world, the concept of addition is almost as ubiquitous as the fabric of reality itself. Across multiple domains of human endeavor, the mathematical operation finds countless applications, from basic arithmetic taught in elementary schools to complex computations intrinsic to advanced technological systems. Haskell, a purely functional programming language, significantly simplifies the process of addition with its elegant syntax and high-level abstractions.

The topic of performing addition in Haskell might seem exceedingly straightforward, even trivial, but under the surface lie multiple important considerations and nuances. Let’s delve into it.

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## Operations in Haskell and the Primitive Function (+)

Haskell, like any other programming language, offers standard math operations such as addition, subtraction, multiplication, and division. In our case, we are interested in the simplest of those: The addition operation. This is achieved using the primitive function (+) in Haskell.

Operation of addition is performed with the (+) operator. The expression (x + y) adds x and y. Consider this simple Haskell code:

x = 5 y = 10 sum = x + y

**Here, we have two integers, 5 and 10, assigned to variables x and y respectively. Then we add these two integers with x + y** and **store the result in the sum. The value of sum will be 15.**

## Step-by-Step Explanation of the Code

Broadly, the code operates in three discrete steps. Let’s break it down for better understanding:

- The first line, ‘x = 5’, declares a variable x and assigns it the value 5.
- The second line does a similar task. It assigns the value 10 to the variable y.
- The third line, ‘sum = x + y’, is where addition operation happens. The (+) operator adds the values stored in x and y, and the result is assigned to the variable sum.

The simplicity and conciseness of Haskell syntax shines brightly here, as the entire operation of addition is encapsulated in a single line of code – ‘sum = x + y’.

## Mathematical Libraries in Haskell

While the (+) function is a primitive operation provided by the base package in Haskell, there are numerous mathematical libraries available that provide more complex features. Libraries such as Num, Real, Integral, Fractional, and Floating that form Haskell’s numeric type classes and can support multiple operations including, **but not limited to addition.** From addition to advanced numerical computations, Haskell can handle it all seamlessly with the aid of these robust libraries.

Understand that addition, as simple as it seems, forms the cornerstone of complex calculations. Learning how this operation is handled in Haskell will pave the way for understanding more complex mathematical functions in Haskell. As one delves deeper into Haskell programming, these basics will always hold importance.

The takeaway is, no matter the language, the concept of addition maintains its fundamental significance and continues to serve as an essential building block in the world of programming, mathematics, and beyond.