## Concept:

# Module

## Headline

A unit of composition and separation of concerns

## Illustration

Consider the following "naive" (inefficiently recursive) definition of the Fibonacci numbers in Language:Haskell:

```
-- Naive definition of Fibonacci numbers
fib :: Int -> Int
fib 0 = 0
fib 1 = 1
fib x = fib (x-2) + fib (x-1)
```

For what it matters, we may place the function in a module as follows:

```
module Fibonacci.Inefficient where
-- The Fibonacci numbers
fib :: Int -> Int
fib 0 = 0
fib 1 = 1
fib x = fib (x-2) + fib (x-1)
```

Suppose you want to compute the Fibonacci numbers more efficiently. To this end, you need an auxiliary function which keeps track of the two previous Fibonacci numbers so that binary (exponential) recursion can be avoided:

```
-- The Fibonacci numbers
fib :: Int -> Int
fib x = fib2 x 0 1
-- Helper function for efficient Fibonacci numbers
fib2 :: Int -> Int -> Int -> Int
fib2 0 y _ = y
fib2 1 _ y = y
fib2 x y1 y2 = fib2 (x-1) y2 (y1+y2)
```

These two functions are reasonably embedded into a module as follows:

```
module Fibonacci.Efficient (
fib
) where
-- The Fibonacci numbers
fib :: Int -> Int
fib x = fib2 x 0 1
-- Helper function for efficient Fibonacci numbers
fib2 :: Int -> Int -> Int -> Int
fib2 0 y _ = y
fib2 1 _ y = y
fib2 x y1 y2 = fib2 (x-1) y2 (y1+y2)
```

Notably, the primary function for the Fibonacci numbers is exported while the helper function isn't. In this manner, we express that one function is of general interest whereas the other one is an implementational artifact.

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