# Solved: function composition

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In the world of functional programming, function composition occupies a royal spot. It is a principle that lifelines some of the most celebrated benefits of functional programming like code readability and mathematical tractability. In Haskell, function composition is at the pinnacle of its utility.

Haskell is a purely functional programming language where every function is a function in the mathematical sense (i.e., “pure”). Due to its purity, Haskell provides unique opportunities to explore and utilize various aspects of function composition in both simplistic and complex contexts.

In simple terms, function composition is a technique of combining two or more functions to create a new function. It is denoted with the dot operator (.) in Haskell.

```composeFunc = (f . g)
```

Here the function g will first process the input and then the resultini output will in-turn be processed by the function f.

## Deeper Dive into Function Composition

The way above function composition works is pretty interesting. The composeFunc takes an input x, it first applies the function g to it and then the resultant is processed by f.

```composeFunc x = f (g x)
```

This dual-layered processing imparts the power of reusability to Haskell code. By using function composition, the functions can keep their original logic intact and yet participate in creating a new logic.

This power of reusability and sequence of function application has turned out to be an incredibly helpful tool in managing complex programming situations.

## Haskell Libraries Supporting Function Composition

Haskell offers a wealth of libraries that leverage function composition to provide shared functionality, effective code reusability, and complex task breakdown.

One of such libraries is the ‘base’ library, which provides the basic operators and functions for function composition like the dot (.) operator.

```import Data.List

composeFunc = ((+) . length)
result = composeFunc [1,2,3,4]
```

In this example, composeFunc is a function which first calculates the length of the list and then adds it to some number. The ‘Data.List’ library provides us with list-specific functions that can be composed to create complex functionality.

To further leverage the power of function composition and Haskell’s type system, various other libraries like ‘lens’, ‘conduit’, ‘pipes’, etc., can be used – a testament to the role of function composition in expediting Haskell programming.

## The Power of Function Composition in Haskell

Not only does function composition make Haskell programming straightforward and mathematically satisfying, it also opens up new dimensions of programming patterns and practices that are yet to be fully explored.

It encourages the reusability of code, enhances readability, and reduces the chances of errors—all key traits of robust, maintainable code. And more importantly, it promotes the construction of rich and powerful abstractions that can help solve complex problems in a simpler and more efficient manner.

```g x = x + 1
f x = x * 2
composeFunc x = (f . g) x
result = composeFunc 4
```

In this example, composeFunc is a function that takes a number, adds 1 to it, and then multiplies the result by 2. Through such function compositions, complex operations can be presented in a simpler and more intuitive manner.

In a nutshell, Haskell’s function composition is an incredibly useful and powerful tool that forms the bedrock of functional programming.

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