# Functors Compose, Monads Do Not

###
Riccardo Odone
*
Originally published at
odone.io
on
*
・2 min read

## Functor Composition

Let’s start with a refresher of `map`

:

```
map :: forall a b. (a -> b) -> f a -> f b
```

In other words, map takes a function `a -> b`

and gives us a function `f a -> f b`

. For that reason, we can take any two nested functors (e.g. `Array`

and `Maybe`

) and run a function on the nested values by putting two `map`

s together:

```
v :: Array (Maybe Int)
v = [Just 1, Nothing, Just 3]
f1 :: Int -> String
f1 = show
main :: Effect Unit
main = do
logShow $ map (map f1) v
-- [(Just "1"),Nothing,(Just "3")]
```

## Monad Composition

This time we want to take a look at `bind`

:

```
bind :: forall a b. m a -> (a -> m b) -> m b
```

If we tried to compose the same way we did with functors, we would notice the code does not compile:

```
v :: Array (Maybe Int)
v = [Just 1, Nothing, Just 3]
f2 :: Int -> Array (Maybe String)
f2 i = [Just $ show i]
main :: Effect Unit
main = do
logShow $ bind v (\x -> bind x f2) -- DOES NOT COMPILE!!
```

The problem here is in the nested `bind`

:

```
bind v (\x -> bind x f2)
^ Maybe Int
^ Int -> Array (Maybe String)
```

In fact, `Maybe Int -> (Int -> Array (Maybe String)) -> ??`

is not what `bind`

expects: the first argument seems to indicate that `m`

is `Maybe`

but the second seems to indicate that `m`

is `Array`

. This does not compile since the monad `m`

is supposed to be the same.

To make the program compile we have to make use of a function (i.e. `maybe`

) specific to the monad we are dealing with (i.e. `Maybe`

):

```
main :: Effect Unit
main = do
-- logShow $ bind v (\x -> bind x f2) -- DOES NOT COMPILE!!
logShow $ bind v (maybe (pure Nothing) f2)
```

Or we could use the `MaybeT`

monad transformer:

```
v2 :: MaybeT Array Int
v2 = MaybeT [Just 1, Nothing, Just 3]
f3 :: Int -> MaybeT Array String
f3 i = MaybeT [Just $ show i]
main :: Effect Unit
main = do
--logShow $ bind v (\x -> bind x f2)
logShow $ bind v (maybe [Nothing] f2)
logShow $ runMaybeT $ bind v2 f3
```

## Outro

I’ve blatantly copied the content of this blog post out of a talk by Tony Morris. So be sure to check the original stuff out!

If you liked the post and want to help spread the word, please make some noise 🤘 But only if you really liked it. Otherwise, please feel free to comment or tweet me with any suggestions or feedback. And please do cause I need help with my FP!