Related
I am building some product monads from Control.Monad.Product package. For reference, the product monad type is:
newtype Product g h a = Product { runProduct :: (g a, h a) }
Its monad instance is:
instance (Monad g, Monad h) => Monad (Product g h) where
return a = Product (return a, return a)
Product (g, h) >>= k = Product (g >>= fst . runProduct . k, h >>= snd . runProduct . k)
Product (ga, ha) >> Product (gb, hb) = Product (ga >> gb, ha >> hb)
source: http://hackage.haskell.org/packages/archive/monad-products/3.0.1/doc/html/src/Control-Monad-Product.html
Problem I
I build a simple monad that is a product of two State Int Monads, However, when I try to access the underlying state next:
ss :: Product (State Int) (State Int) Int
ss = do
let (a,b) = unp $ P.Product (get,get) :: (State Int Int,State Int Int)
return 404
You see get just creates another State Int Int, and I am not sure how to actually get the value of the underlying state, how might I do that? Note I could potentially runState a and b to get the underlying value, but this solution doesn't seem very useful since the two states' initial values must be fixed a priori.
Question II.
I would really like to be able to create a product monad over states of different types, ie:
ss2 :: Product (State Int) (State String) ()
ss2 = do
let (a,b) = unp $ P.Product (get,get) :: (State Int Int,State Int String)
return ()
But I get this type error:
Couldn't match expected type `String' with actual type `Int'
Expected type: (State Int Int, State String String)
Actual type: (StateT Int Identity Int,
StateT String Identity Int)
Because I presume the two get must return the same type, which is an unfortunate restriction. Any thoughts on how to get around this?
The solution is to use a state monad with a product of your states:
m :: State (Int, String) ()
Then you can run an operation that interacts with one of the two fields of the product using zoom and _1/_2 from the lens library, like this:
m = do
n <- zoom _1 get
zoom _2 $ put (show n)
To learn more about this technique, you can read my blog post on lenses which goes into much more detail.
It can't be done the way you want. Suppose there would be a way how to get the current state out of the left monad. Then you'd have a function of type
getLeft :: Product (State a) (State b) a
which is isomorphic to (State a a, State b a).
Now we can choose to throw away the left part and run only the right part:
evalState (snd (runProduct getLeft)) () :: a
So we get an inhabitant of an arbitrary type a.
In other words, the two monads inside Product are completely independent. They don't influence each other and can be run separately. Therefore we can't take a value out of one and use it in another (or both of them).
Let's say I have these two functions:
errorm :: ( MonadError String m ) => Bool -> m Int
errorm cond = if cond then return 1 else throwError "this is an error"
errorms :: ( MonadError String m ) => Bool -> m String
errorms cond = if cond then return "works" else throwError "does not work"
As you can see, one returns a string in the safe case, while the other returns an int
I now want to use them together within another monad. Trivially:
errErr :: MonadError String m => Bool -> Bool -> m (Int, String)
errErr b1 b2 = do
a <- errorm b1
b <- errorms b2
return (a,b)
The function signature here is derived by the GHC, and I am not sure how to use this function. I tried this:
runErrorT ( runErrorT ( errErr1 True True ) ) -- should give me (Right 1, Right "works")
But instead it gives me:
Ambiguous type variable `e0' in the constraint:
(Error e0) arising from a use of `errErr1'
Probable fix: add a type signature that fixes these type variable(s)
In the first argument of `runErrorT', namely `(errErr1 True True)'
In the first argument of `runErrorT', namely
`(runErrorT (errErr1 True True))'
In the expression: runErrorT (runErrorT (errErr1 True True))
In general, this is just one instance of my problem. I feel like I am not grasping how exactly to stack two monadT that are of the same class, but have different type parameters. Another example might be stacking the pair of a functions:
f :: ( MonadState Int m ) => m ()
g :: ( MonadState String m ) => m ()
---------------------------------------------------- Update ----------------------------------------------------
Per Daniel's comment below, I added a concrete instance of functions f and g from above. But thanks to Tikhon's answer, I think I figured it out.
type Counter = Int
type Msg = String
incr :: (MonadState Counter m) => Counter -> m ()
incr i = modify (+i)
addMsg :: ( MonadState Msg m ) => Msg -> m()
addMsg msg = modify ( ++ msg )
incrMsg:: (MonadTrans t, MonadState Msg m, MonadState Counter (t m)) => t m ()
incrMsg = do
lift . addMsg $ "one"
incr 1
return ()
incrMsgt = runIdentity $ runStateT ( runStateT incrMsg 1 ) "hello" :: (((), Int), String)
In this particular case, you do not need to stack two transformers--since both are MonadError String, they can be used as the same monad. You can use errorm and errorms together just like you would use two values in any other monad.
As a more concrete explanation, ignore the transformers for a second: you can imagine that the values are just Either String Int and Either String String. Clearly, you can just use them together. This is why you only need one runErrorT at the end rather than two: both values are in the same monad.
Now, what about your actual question: how do you stack two monad transformers? It works just like combining any two monad transformers. Two state transformers stacked upon each other look just like two different transformers stacked upon each other.
Now, it is a little tricky to use them. Depending on which one you're using, you will need to use lift differently. If you have a value in the base monad, you need to lift twice. If you have a value in the inner state monad, you will need to use it once. And if you have one in the outer level, you won't need it at all. This is just like normal transformers.
Going back to your error example, let's imagine you actually did want to stack two different error monad transformers instead of using them as one. This would mean that if you want to throw an error in the inner one, you would have to write lift (throwError "message"). If you had actually done this and had two stacked error transformers, than using runErrorT twice would have worked.
I am writing a program that runs as a daemon.
To create the daemon, the user supplies a set of
implementations for each of the required classes (one of them is a database)
All of these classes have functions have
type signatures of the form StateT s IO a,
but s is different for each class.
Suppose each of the classes follows this pattern:
import Control.Monad (liftM)
import Control.Monad.State (StateT(..), get)
class Hammer h where
driveNail :: StateT h IO ()
data ClawHammer = MkClawHammer Int -- the real implementation is more complex
instance Hammer ClawHammer where
driveNail = return () -- the real implementation is more complex
-- Plus additional classes for wrenches, screwdrivers, etc.
Now I can define a record that represents the implementation chosen by
the user for each "slot".
data MultiTool h = MultiTool {
hammer :: h
-- Plus additional fields for wrenches, screwdrivers, etc.
}
And the daemon does most of its work in the StateT (MultiTool h ...) IO ()
monad.
Now, since the multitool contains a hammer, I can use it in any situation
where a hammer is needed. In other words, the MultiTool type
can implement any of the classes it contains, if I write code like this:
stateMap :: Monad m => (s -> t) -> (t -> s) -> StateT s m a -> StateT t m a
stateMap f g (StateT h) = StateT $ liftM (fmap f) . h . g
withHammer :: StateT h IO () -> StateT (MultiTool h) IO ()
withHammer runProgram = do
t <- get
stateMap (\h -> t {hammer=h}) hammer runProgram
instance Hammer h => Hammer (MultiTool h) where
driveNail = withHammer driveNail
But the implementations of withHammer, withWrench, withScrewdriver, etc.
are basically identical. It would be nice to be able to write something
like this...
--withMember accessor runProgram = do
-- u <- get
-- stateMap (\h -> u {accessor=h}) accessor runProgram
-- instance Hammer h => Hammer (MultiTool h) where
-- driveNail = withMember hammer driveNail
But of course that won't compile.
I suspect my solution is too object-oriented.
Is there a better way?
Monad transformers, maybe?
Thank you in advance for any suggestions.
If you want to go with a large global state like in your case, then what you want to use is lenses, as suggested by Ben. I too recommend Edward Kmett's lens library. However, there is another, perhaps nicer way.
Servers have the property that the program runs continuously and performs the same operation over a state space. The trouble starts when you want to modularize your server, in which case you want more than just some global state. You want modules to have their own state.
Let's think of a module as something that transforms a Request to a Response:
Module :: (Request -> m Response) -> Module m
Now if it has some state, then this state becomes noticable in that the module might give a different answer the next time. There are a number of ways to do this, for example the following:
Module :: s -> ((Request, s) -> m (Response s)) -> Module m
But a much nicer and equivalent way to express this is the following constructor (we will build a type around it soon):
Module :: (Request -> m (Response, Module m)) -> Module m
This module maps a request to a response, but along the way also returns a new version of itself. Let's go further and make requests and responses polymorphic:
Module :: (a -> m (b, Module m a b)) -> Module m a b
Now if the output type of a module matches another module's input type, then you can compose them like regular functions. This composition is associative and has a polymorphic identity. This sounds a lot like a category, and in fact it is! It is a category, an applicative functor and an arrow.
newtype Module m a b =
Module (a -> m (b, Module m a b))
instance (Monad m) => Applicative (Module m a)
instance (Monad m) => Arrow (Module m)
instance (Monad m) => Category (Module m)
instance (Monad m) => Functor (Module m a)
We can now compose two modules that have their own individual local state without even knowing about it! But that's not sufficient. We want more. How about modules that can be switched among? Let's extend our little module system such that modules can actually choose not to give an answer:
newtype Module m a b =
Module (a -> m (Maybe b, Module m a b))
This allows another form of composition that is orthogonal to (.): Now our type is also a family of Alternative functors:
instance (Monad m) => Alternative (Module m a)
Now a module can choose whether to respond to a request, and if not, the next module will be tried. Simple. You have just reinvented the wire category. =)
Of course you don't need to reinvent this. The Netwire library implements this design pattern and comes with a large library of predefined "modules" (called wires). See the Control.Wire module for a tutorial.
Here's a concrete example of how to use lens like everybody else is talking about. In the following code example, Type1 is the local state (i.e. your hammer), and Type2 is the global state (i.e. your multitool). lens provides the zoom function which lets you run a localized state computation that zooms in on any field defined by a lens:
import Control.Lens
import Control.Monad.Trans.Class (lift)
import Control.Monad.Trans.State
data Type1 = Type1 {
_field1 :: Int ,
_field2 :: Double}
field1 :: SimpleLens Type1 Int
field1 = lens _field1 (\x a -> x { _field1 = a})
field2 :: SimpleLens Type1 Double
field2 = lens _field2 (\x a -> x { _field2 = a})
data Type2 = Type2 {
_type1 :: Type1 ,
_field3 :: String}
type1 :: SimpleLens Type2 Type1
type1 = lens _type1 (\x a -> x { _type1 = a})
field3 :: SimpleLens Type2 String
field3 = lens _field3 (\x a -> x { _field3 = a})
localCode :: StateT Type1 IO ()
localCode = do
field1 += 3
field2 .= 5.0
lift $ putStrLn "Done!"
globalCode :: StateT Type2 IO ()
globalCode = do
f1 <- zoom type1 $ do
localCode
use field1
field3 %= (++ show f1)
f3 <- use field3
lift $ putStrLn f3
main = runStateT globalCode (Type2 (Type1 9 4.0) "Hello: ")
zoom is not limited to immediate sub-fields of a type. Since lenses are composable, you can zoom as deep as you want in a single operation just by doing something like:
zoom (field1a . field2c . field3b . field4j) $ do ...
This sounds very much like an application of lenses.
Lenses are a specification of a sub-field of some data. The idea is you have some value toolLens and functions view and set so that view toolLens :: MultiTool h -> h fetches the tool and set toolLens :: MultiTool h -> h -> MultiTool h replaces it with a new value. Then you can easily define your withMember as a function just accepting a lens.
Lens technology has advanced a great deal recently, and they are now incredibly capable. The most powerful library around at the time of writing is Edward Kmett's lens library, which is a bit much to swallow, but pretty simple once you find the features you want. You can also search for more questions about lenses here on SO, e.g. Functional lenses which links to lenses, fclabels, data-accessor - which library for structure access and mutation is better, or the lenses tag.
I created a lensed extensible record library called data-diverse-lens which allows combining multiple ReaderT (or StateT) like this gist:
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE TypeApplications #-}
module Main where
import Control.Lens
import Control.Monad.Reader
import Control.Monad.State
import Data.Diverse.Lens
import Data.Semigroup
foo :: (MonadReader r m, HasItem' Int r, HasItem' String r) => m (Int, String)
foo = do
i <- view (item' #Int) -- explicitly specify type
s <- view item' -- type can also be inferred
pure (i + 10, s <> "bar")
bar :: (MonadState s m, HasItem' Int s, HasItem' String s) => m ()
bar = do
(item' #Int) %= (+10) -- explicitly specify type
item' %= (<> "bar") -- type can also be inferred
pure ()
main :: IO ()
main = do
-- example of running ReaderT with multiple items
(i, s) <- runReaderT foo ((2 :: Int) ./ "foo" ./ nil)
putStrLn $ show i <> s -- prints out "12foobar"
-- example of running StateT with multiple items
is <- execStateT bar ((2 :: Int) ./ "foo" ./ nil)
putStrLn $ show (view (item #Int) is) <> (view (item #String) is) -- prints out "12foobar"
Data.Has is a simpler library that does the same with tuples. Example from the library front page:
{-# LANGUAGE FlexibleContexts #-}
-- in some library code
...
logInAnyReaderHasLogger :: (Has Logger r, MonadReader r m) => LogString -> m ()
logInAnyReaderHasLogger s = asks getter >>= logWithLogger s
queryInAnyReaderHasSQL :: (Has SqlBackEnd r, MonadReader r m) => Query -> m a
queryInAnyReaderHasSQL q = asks getter >>= queryWithSQL q
...
-- now you want to use these effects together
...
logger <- initLogger ...
sql <- initSqlBackEnd ...
(`runReader` (logger, sql)) $ do
...
logInAnyReaderHasLogger ...
...
x <- queryInAnyReaderHasSQL ...
...
I'm working on a Haskell project that involves tying a big knot: I'm parsing a serialized representation of a graph, where each node is at some offset into the file, and may reference another node by its offset. So I need to build up a map from offsets to nodes while parsing, which I can feed back to myself in a do rec block.
I have this working, and kinda-sorta-reasonably abstracted into a StateT-esque monad transformer:
{-# LANGUAGE DoRec, GeneralizedNewtypeDeriving #-}
import qualified Control.Monad.State as S
data Knot s = Knot { past :: s, future :: s }
newtype RecStateT s m a = RecStateT (S.StateT (Knot s) m a) deriving
( Alternative
, Applicative
, Functor
, Monad
, MonadCont
, MonadError e
, MonadFix
, MonadIO
, MonadPlus
, MonadReader r
, MonadTrans
, MonadWriter w )
runRecStateT :: RecStateT s m a -> Knot s -> m (a, Knot s)
runRecStateT (RecStateT st) = S.runStateT st
tie :: MonadFix m => RecStateT s m a -> s -> m (a, s)
tie m s = do
rec (a, Knot s' _) <- runRecStateT m (Knot s s')
return (a, s')
get :: Monad m => RecStateT s m (Knot s)
get = RecStateT S.get
put :: Monad m => s -> RecStateT s m ()
put s = RecStateT $ S.modify $ \ ~(Knot _ s') -> Knot s s'
The tie function is where the magic happens: the call to runRecStateT produces a value and a state, which I feed it as its own future. Note that get allows you to read from both the past and future states, but put only allows you to modify the "present."
Question 1: Does this seem like a decent way to implement this knot-tying pattern in general? Or better still, has somebody implemented a general solution to this, that I overlooked when snooping through Hackage? I beat my head against the Cont monad for a while, since it seemed possibly more elegant (see similar post from Dan Burton), but I just couldn't work it out.
Totally subjective Question 2: I'm not totally thrilled with the way my calling code ends up looking:
do
Knot past future <- get
let {- ... -} = past
{- ... -} = future
node = {- ... -}
put $ {- ... -}
return node
Implementation details here omitted, obviously, the important point being that I have to get the past and future state, pattern-match them inside a let binding (or explicitly make the previous pattern lazy) to extract whatever I care about, then build my node, update my state and finally return the node. Seems unnecessarily verbose, and I particularly dislike how easy it is to accidentally make the pattern that extracts the past and future states strict. So, can anybody think of a nicer interface?
I've been playing around with stuff, and I think I've come up with something... interesting. I call it the "Seer" monad, and it provides (aside from Monad operations) two primitive operations:
see :: Monoid s => Seer s s
send :: Monoid s => s -> Seer s ()
and a run operation:
runSeer :: Monoid s => Seer s a -> a
The way this monad works is that see allows a seer to see everything, and send allows a seer to "send" information to all other seers for them to see. Whenever any seer performs the see operation, they are able to see all of the information that has been sent, and all of the information that will be sent. In other words, within a given run, see will always produce the same result no matter where or when you call it. Another way of saying it is that see is how you get a working reference to the "tied" knot.
This is actually very similar to just using fix, except that all of the sub-parts are added incrementally and implicitly, rather than explicitly. Obviously, seers will not work correctly in the presence of a paradox, and sufficient laziness is required. For example, see >>= send may cause an explosion of information, trapping you in a time loop.
A dumb example:
import Control.Seer
import qualified Data.Map as M
import Data.Map (Map, (!))
bar :: Seer (Map Int Char) String
bar = do
m <- see
send (M.singleton 1 $ succ (m ! 2))
send (M.singleton 2 'c')
return [m ! 1, m ! 2]
As I said, I've just been toying around, so I have no idea if this is any better than what you've got, or if it's any good at all! But it's nifty, and relevant, and if your "knot" state is a Monoid, then it just might be useful to you. Fair warning: I built Seer by using a Tardis.
https://github.com/DanBurton/tardis/blob/master/Control/Seer.hs
I wrote up an article on this topic at entitled Assembly: Circular Programming with Recursive do where I describe two methods for building an assembler using knot tying. Like your problem, an assembler has to be able to resolve address of labels that may occur later in the file.
Regarding the implementation, I would make it a composition of a Reader monad (for the future) and a State monad (for past/present). The reason is that you set your future only once (in tie) and then don't change it.
{-# LANGUAGE DoRec, GeneralizedNewtypeDeriving #-}
import Control.Monad.State
import Control.Monad.Reader
import Control.Applicative
newtype RecStateT s m a = RecStateT (StateT s (ReaderT s m) a) deriving
( Alternative
, Applicative
, Functor
, Monad
, MonadPlus
)
tie :: MonadFix m => RecStateT s m a -> s -> m (a, s)
tie (RecStateT m) s = do
rec (a, s') <- flip runReaderT s' $ flip runStateT s m
return (a, s')
getPast :: Monad m => RecStateT s m s
getPast = RecStateT get
getFuture :: Monad m => RecStateT s m s
getFuture = RecStateT ask
putPresent :: Monad m => s -> RecStateT s m ()
putPresent = RecStateT . put
Regarding your second question, it'd help to know your dataflow (i.e. to have a minimal example of your code). It's not true that strict patterns always lead to loops. It's true that you need to be careful so as not to create a non-producing loop, but the exact restrictions depend on what and how you're building.
I had a similar problem recently, but I chose a different approach. A recursive data structure can be represented as a type fixed point on a data type functor. Loading data can be then split into two parts:
Load the data into a structure that references other nodes only by some kind of identifier. In the example it's Loader Int (NodeF Int), which constructs a map of values of type NodeF Int Int.
Tie the knot by creating a recursive data structure by replacing the identifiers with actual data. In the example the resulting data structures have type Fix (NodeF Int), and they are later converted to Node Int for convenience.
It's lacking a proper error handling etc., but the idea should be clear from that.
-- Public Domain
import Control.Monad
import Data.Map (Map)
import qualified Data.Map as Map
import Data.Maybe (fromJust)
-- Fixed point operator on types and catamohism/anamorphism methods
-- for constructing/deconstructing them:
newtype Fix f = Fix { unfix :: f (Fix f) }
catam :: Functor f => (f a -> a) -> (Fix f -> a)
catam f = f . fmap (catam f) . unfix
anam :: Functor f => (a -> f a) -> (a -> Fix f)
anam f = Fix . fmap (anam f) . f
anam' :: Functor f => (a -> f a) -> (f a -> Fix f)
anam' f = Fix . fmap (anam f)
-- The loader itself
-- A representation of a loader. Type parameter 'k' represents the keys by
-- which the nodes are represented. Type parameter 'v' represents a functor
-- data type representing the values.
data Loader k v = Loader (Map k (v k))
-- | Creates an empty loader.
empty :: Loader k v
empty = Loader $ Map.empty
-- | Adds a new node into a loader.
update :: (Ord k) => k -> v k -> Loader k v -> Loader k v
update k v = update' k (const v)
-- | Modifies a node in a loader.
update' :: (Ord k) => k -> (Maybe (v k) -> (v k)) -> Loader k v -> Loader k v
update' k f (Loader m) = Loader $ Map.insertWith (const (f . Just)) k (f Nothing) $ m
-- | Does the actual knot-tying. Creates a new data structure
-- where the references to nodes are replaced by the actual data.
tie :: (Ord k, Functor v) => Loader k v -> Map k (Fix v)
tie (Loader m) = Map.map (anam' $ \k -> fromJust (Map.lookup k m)) m
-- -----------------------------------------------------------------
-- Usage example:
data NodeF n t = NodeF n [t]
instance Functor (NodeF n) where
fmap f (NodeF n xs) = NodeF n (map f xs)
-- A data structure isomorphic to Fix (NodeF n), but easier to work with.
data Node n = Node n [Node n]
deriving Show
-- The isomorphism that does the conversion.
nodeunfix :: Fix (NodeF n) -> Node n
nodeunfix = catam (\(NodeF n ts) -> Node n ts)
main :: IO ()
main = do
-- Each node description consist of an integer ID and a list of other nodes
-- it references.
let lss =
[ (1, [4])
, (2, [1])
, (3, [2, 1])
, (4, [3, 2, 1])
, (5, [5])
]
print lss
-- Fill a new loader with the data:
let
loader = foldr f empty lss
f (label, dependsOn) = update label (NodeF label dependsOn)
-- Tie the knot:
let tied' = tie loader
-- And convert Fix (NodeF n) into Node n:
let tied = Map.map nodeunfix tied'
-- For each node print the label of the first node it references
-- and the count of all referenced nodes.
print $ Map.map (\(Node n ls#((Node n1 _) : _)) -> (n1, length ls)) tied
I'm kind of overwhelmed by the amount of Monad usage.
I might not understand the past/future things, but I guess you are just trying to express the lazy+fixpoint binding. (Correct me if I'm wrong.)
The RWS Monad usage with R=W is kind of funny, but you do not need the State and the loop, when you can do the same with fmap. There is no point in using Monads if they do not make things easier. (Only very few Monads represent chronological order, anyway.)
My general solution to tying the knot:
I parse everything to a List of nodes,
convert that list to a Data.Vector for O(1) access to boxed (=lazy) values,
bind that result to a name using let or the fix or mfix function,
and access that named Vector inside the parser. (see 1.)
That example solution in your blog, where you write sth. like this:
data Node = Node {
value :: Int,
next :: Node
} deriving Show
…
tie = …
parse = …
data ParserState = …
…
example :: Node
example =
let (_, _, m) = tie parse $ ParserState 0 [(0, 1), (1, 2), (2, 0)]
in (m Map.! 0)
I would have written this way:
{-# LANGUAGE ViewPatterns, NamedFieldPuns #-}
import Data.Vector as Vector
example :: Node
example =
let node :: Int -> Node
node = (Vector.!) $ Vector.fromList $
[ Node{value,next}
| (value,node->next) <- [(0, 1), (1, 2), (2, 0)]
]
in (node 0)
or shorter:
{-# LANGUAGE ViewPatterns, NamedFieldPuns #-}
import Data.Vector as Vector
example :: Node
example = (\node->(Vector.fromList[ Node{value,next}
| (value,node->next) <- [(0, 1), (1, 2), (2, 0)]
] Vector.!)) `fix` 0
This is the State Monad code I am trying to figure out
data State a = State (Int -> (a, Int))
instance Monad State where
return x = State (\c -> (x, c))
State m >>= f = State (\c ->
case m c of { (a, acount) ->
case f a of State b -> b acount})
getState = State (\c -> (c, c))
putState count = State (\_ -> ((), count))
instance Show State where -- doesn't work
show (State a) = show a -- doesn't work
I am trying to make State as instance of Show so that I can see the action of getState and putState count on the ghci prompt.
Any tutorial or link to State Monad material would be nice too.
Here's is a Show instance that can help see what's going on:
instance Show a => Show (State a) where
show (State f) = show [show i ++ " => " ++ show (f i) | i <- [0..3]]
Then you can do:
*Main> getState
["0 => (0,0)","1 => (1,1)","2 => (2,2)","3 => (3,3)"]
*Main> putState 1
["0 => ((),1)","1 => ((),1)","2 => ((),1)","3 => ((),1)"]
In Haskell, typeclasses classify only types of the same kind. Monad classifies types of kind * -> *, while Show classifies types of kind *. Your State type has kind * -> * which is why there isn't a problem with your Monad instance, but there is a problem with your Show instance. State is called a "type constructor" because it consumes a type in order to produce another type. Think of it sort of like function application at the type level. You can therefore apply a specific type and make instances of that:
instance Show (State Char) where
show _ = "<< Some State >>"
Now, this isn't a very useful instance, try something like Sjoerd's suggestion to get a more meaningful Show instance. Notice that his version uses a generic type with a constraint.
instance (Show a) => Show (State a) where
-- blah blah
The generic type is a, and the constraint is (Show a) =>, in other words, a itself must be an instance of Show.
Here's a great (and personally, my favorite) explanation of the State Monad: Learn You A Haskell. (Also a great resource for learning Haskell in general).
You may have noticed that functions aren't part of the Show typeclass in Haskell. And since State is basically just a newtype wrapper for functions of certain types, you can't make a (meaningful) State instance of Show.
Here's code using the State Monad from LYAH:
import Control.Monad.State -- first, import the state monad
pop :: State Stack Int
pop = State $ \(x:xs) -> (x,xs)
push :: Int -> State Stack ()
push a = State $ \xs -> ((),a:xs)
stackManip :: State Stack Int
stackManip = do
push 3
a <- pop
pop
And here's that code in action from ghci:
*Main> runState stackManip [1,2,3]
(1,[2,3])
The fst of the tuple is the result, and the snd of the tuple is the (modified) state.