# Maybe

 import Data.Maybe

The Maybe type is defined as follows:

```data Maybe a = Just a | Nothing
deriving (Eq, Ord)
```

It allows the programmer to specify something may not be there.

## 1 Type Equation

Maybe satisfies the type equation FX = 1 + FX, where the functor F takes a set to a point plus that set.

## 2 Comparison to imperative languages

Most imperative languages will ignore this, or allow one to use NULL (defined in some manner) to specify a value might not be there.

## 3 Classes

As one can see from the type definition, Maybe will be an instance of Eq and Ord when the base type is. As well, instances of Functor and Monad are defined for Maybe.

For Functor, the `fmap` function moves inside the Just constructor and is identity on the Nothing constructor.

For Monad, the bind operation passes through Just, while Nothing will force the result to always be Nothing.

### 3.1 Usage example

Using the Monad class definition can lead to much more compact code. For example:

```f::Int -> Maybe Int
f 0 = Nothing
f x = Just x
```
```g :: Int -> Maybe Int
g 100 = Nothing
g x = Just x
```
```h ::Int -> Maybe Int
h x = case f x of
Just n -> g n
Nothing -> Nothing

h' :: Int -> Maybe Int
h' x = do n <- f x
g n
```

The functions `h` and `h'` will give the same results. ($h 0 = h' 0 = h 100 = h' 100 = Nothing;\ h x = h' x = Just\, x$). In this case the savings in code size is quite modest, stringing together multiple functions like `f` and `g` will be more noticeable.