State monads are a kind of monad that carry a state that might change during each computation run in the monad. Implementations are usually of the form

`State s a`

which represents a computation that carries and potentially modifies a state of type `s`

and produces a result of type `a`

, but the term "state monad" may generally refer to any monad which carries a state. The `mtl`

and `transformers`

package provide general implementations of state monads.
Newcomers to Haskell often shy away from the `State`

monad and treat it like a taboo—like the claimed benefit of functional programming is the avoidance of state, so don't you lose that when you use `State`

? A more nuanced view is that:

- State can be useful in
*small, controlled doses*; - The
`State`

type provides the ability to control the dose very precisely.

The reasons being that if you have `action :: State s a`

, this tells you that:

`action`

is special because it depends on a state;- The state has type
`s`

, so`action`

cannot be influenced by any old value in your program—only an`s`

or some value reachable from some`s`

; - The
`runState :: State s a -> s -> (a, s)`

puts a "barrier" around the stateful action, so that its effectfulness*cannot*be observed from outside that barrier.

So this is a good set of criteria for whether to use `State`

in particular scenario. You want to see that your code is *minimizing the scope of the state*, both by choosing a narrow type for `s`

and by putting `runState`

as close to "the bottom" as possible, (so that your actions can be influenced by as few thing as possible.

We have a tree data type like this:

```
data Tree a = Tree a [Tree a] deriving Show
```

And we wish to write a function that assigns a number to each node of the tree, from an incrementing counter:

```
tag :: Tree a -> Tree (a, Int)
```

First we'll do it the long way around, since it illustrates the `State`

monad's low-level mechanics quite nicely.

```
import Control.Monad.State
-- Function that numbers the nodes of a `Tree`.
tag :: Tree a -> Tree (a, Int)
tag tree =
-- tagStep is where the action happens. This just gets the ball
-- rolling, with `0` as the initial counter value.
evalState (tagStep tree) 0
-- This is one monadic "step" of the calculation. It assumes that
-- it has access to the current counter value implicitly.
tagStep :: Tree a -> State Int (Tree (a, Int))
tagStep (Tree a subtrees) = do
-- The `get :: State s s` action accesses the implicit state
-- parameter of the State monad. Here we bind that value to
-- the variable `counter`.
counter <- get
-- The `put :: s -> State s ()` sets the implicit state parameter
-- of the `State` monad. The next `get` that we execute will see
-- the value of `counter + 1` (assuming no other puts in between).
put (counter + 1)
-- Recurse into the subtrees. `mapM` is a utility function
-- for executing a monadic actions (like `tagStep`) on a list of
-- elements, and producing the list of results. Each execution of
-- `tagStep` will be executed with the counter value that resulted
-- from the previous list element's execution.
subtrees' <- mapM tagStep subtrees
return $ Tree (a, counter) subtrees'
```

The bit where we are `get`

ting the current counter and then `put`

ting counter + 1 can be split off into a `postIncrement`

action, similar to what many C-style languages provide:

```
postIncrement :: Enum s => State s s
postIncrement = do
result <- get
modify succ
return result
```

The tree walk logic can be split out into its own function, like this:

```
mapTreeM :: Monad m => (a -> m b) -> Tree a -> m (Tree b)
mapTreeM action (Tree a subtrees) = do
a' <- action a
subtrees' <- mapM (mapTreeM action) subtrees
return $ Tree a' subtrees'
```

With this and the `postIncrement`

function we can rewrite `tagStep`

:

```
tagStep :: Tree a -> State Int (Tree (a, Int))
tagStep = mapTreeM step
where step :: a -> State Int (a, Int)
step a = do
counter <- postIncrement
return (a, counter)
```

`Traversable`

classThe `mapTreeM`

solution above can be easily rewritten into an instance of the `Traversable`

class:

```
instance Traversable Tree where
traverse action (Tree a subtrees) =
Tree <$> action a <*> traverse action subtrees
```

Note that this required us to use `Applicative`

(the `<*>`

operator) instead of `Monad`

.

With that, now we can write `tag`

like a pro:

```
tag :: Traversable t => t a -> t (a, Int)
tag init t = evalState (traverse step t) 0
where step a = do tag <- postIncrement
return (a, tag)
```

Note that this works for any `Traversable`

type, not just our `Tree`

type!

`Traversable`

boilerplateGHC has a `DeriveTraversable`

extension that eliminates the need for writing the instance above:

```
{-# LANGUAGE DeriveFunctor, DeriveFoldable, DeriveTraversable #-}
data Tree a = Tree a [Tree a]
deriving (Show, Functor, Foldable, Traversable)
```

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