Chapter 15. Programming with monads

Table of Contents

Golfing practice: association lists
Generalised lifting
Looking for alternatives
The name mplus does not imply addition
Rules for working with MonadPlus
Failing safely with MonadPlus
Adventures in hiding the plumbing
Supplying random numbers
Another round of golf
Separating interface from implementation
Multi-parameter typeclasses
Functional dependencies
Rounding out our module
Programming to a monad's interface
The reader monad
A return to automated deriving
Hiding the IO monad
Using a newtype
Designing for unexpected uses
Using typeclasses
Isolation and testing
The writer monad and lists
Arbitrary I/O revisited

Golfing practice: association lists

Web clients and servers often pass information around as a simple textual list of key-value pairs.


The encoding is named application/x-www-form-urlencoded, and it's easy to understand. Each key-value pair is separated by an “&” character. Within a pair, a key is a series of characters, followed by an “=”, followed by a value.

We can obviously represent a key as a String, but the HTTP specification is not clear about whether a key must be followed by a value. We can capture this ambiguity by representing a value as a Maybe String. If we use Nothing for a value, then there was no value present. If we wrap a string in Just, then there was a value. Using Maybe lets us distinguish between “no value” and “empty value”.

Haskell programmers use the name association list for the type [(a, b)], where we can think of each element as an association between a key and a value. The name originates in the Lisp community, where it's usually abbreviated as an alist. We could thus represent the above string as the following Haskell value.

-- file: ch15/MovieReview.hs
    [("name",       Just "Attila \"The Hun\""),
     ("occupation", Just "Khan")]

In the section called “Parsing an URL-encoded query string”, we'll parse an application/x-www-form-urlencoded string, and represent the result as an alist of [(String, Maybe String)]. Let's say we want to use one of these alists to fill out a data structure.

-- file: ch15/MovieReview.hs
data MovieReview = MovieReview {
      revTitle :: String
    , revUser :: String
    , revReview :: String

We'll begin by belabouring the obvious with a naive function.

-- file: ch15/MovieReview.hs
simpleReview :: [(String, Maybe String)] -> Maybe MovieReview
simpleReview alist =
  case lookup "title" alist of
    Just (Just title@(_:_)) ->
      case lookup "user" alist of
        Just (Just user@(_:_)) ->
          case lookup "review" alist of
            Just (Just review@(_:_)) ->
                Just (MovieReview title user review)
            _ -> Nothing -- no review
        _ -> Nothing -- no user
    _ -> Nothing -- no title

It only returns a MovieReview if the alist contains all of the necessary values, and they're all non-empty strings. However, the fact that it validates its inputs is its only merit: it suffers badly from the “staircasing” that we've learned to be wary of, and it knows the intimate details of the representation of an alist.

Since we're now well acquainted with the Maybe monad, we can tidy up the staircasing.

-- file: ch15/MovieReview.hs
maybeReview alist = do
    title <- lookup1 "title" alist
    user <- lookup1 "user" alist
    review <- lookup1 "review" alist
    return (MovieReview title user review)

lookup1 key alist = case lookup key alist of
                      Just (Just s@(_:_)) -> Just s
                      _ -> Nothing

Although this is much tidier, we're still repeating ourselves. We can take advantage of the fact that the MovieReview constructor acts as a normal, pure function by lifting it into the monad, as we discussed in the section called “Mixing pure and monadic code”.

-- file: ch15/MovieReview.hs
liftedReview alist =
    liftM3 MovieReview (lookup1 "title" alist)
                       (lookup1 "user" alist)
                       (lookup1 "review" alist)

We still have some repetition here, but it is dramatically reduced, and also more difficult to remove.

Generalised lifting

Although using liftM3 tidies up our code, we can't use a liftM-family function to solve this sort of problem in general, because they're only defined up to liftM5 by the standard libraries. We could write variants up to whatever number we pleased, but that would amount to drudgery.

If we had a constructor or pure function that took, say, ten parameters, and decided to stick with the standard libraries you might think we'd be out of luck.

Of course, our toolbox isn't yet empty. In Control.Monad, there's a function named ap with an interesting type signature.

ghci> :m +Control.Monad
ghci> :type ap
ap :: (Monad m) => m (a -> b) -> m a -> m b

You might wonder who would put a single-argument pure function inside a monad, and why. Recall, however, that all Haskell functions really take only one argument, and you'll begin to see how this might relate to the MovieReview constructor.

ghci> :type MovieReview
MovieReview :: String -> String -> String -> MovieReview

We can just as easily write that type as String -> (String -> (String -> MovieReview)). If we use plain old liftM to lift MovieReview into the Maybe monad, we'll have a value of type Maybe (String -> (String -> (String -> MovieReview))). We can now see that this type is suitable as an argument for ap, in which case the result type will be Maybe (String -> (String -> MovieReview)). We can pass this, in turn, to ap, and continue to chain until we end up with this definition.

-- file: ch15/MovieReview.hs
apReview alist =
    MovieReview `liftM` lookup1 "title" alist
                   `ap` lookup1 "user" alist
                   `ap` lookup1 "review" alist

We can chain applications of ap like this as many times as we need to, thereby bypassing the liftM family of functions.

Another helpful way to look at ap is that it's the monadic equivalent of the familiar ($) operator: think of pronouncing ap as apply. We can see this clearly when we compare the type signatures of the two functions.

ghci> :type ($)
($) :: (a -> b) -> a -> b
ghci> :type ap
ap :: (Monad m) => m (a -> b) -> m a -> m b

In fact, ap is usually defined as either liftM2 id or liftM2 ($).

Looking for alternatives

Here's a simple representation of a person's phone numbers.

-- file: ch15/VCard.hs
data Context = Home | Mobile | Business
               deriving (Eq, Show)

type Phone = String

albulena = [(Home, "+355-652-55512")]

nils = [(Mobile, "+47-922-55-512"), (Business, "+47-922-12-121"),
        (Home, "+47-925-55-121"), (Business, "+47-922-25-551")]

twalumba = [(Business, "+260-02-55-5121")]

Suppose we want to get in touch with someone to make a personal call. We don't want their business number, and we'd prefer to use their home number (if they have one) instead of their mobile number.

-- file: ch15/VCard.hs
onePersonalPhone :: [(Context, Phone)] -> Maybe Phone
onePersonalPhone ps = case lookup Home ps of
                        Nothing -> lookup Mobile ps
                        Just n -> Just n

Of course, if we use Maybe as the result type, we can't accommodate the possibility that someone might have more than one number that meet our criteria. For that, we switch to a list.

-- file: ch15/VCard.hs
allBusinessPhones :: [(Context, Phone)] -> [Phone]
allBusinessPhones ps = map snd numbers
    where numbers = case filter (contextIs Business) ps of
                      [] -> filter (contextIs Mobile) ps
                      ns -> ns

contextIs a (b, _) = a == b

Notice that these two functions structure their case expressions similarly: one alternative handles the case where the first lookup returns an empty result, while the other handles the non-empty case.

ghci> onePersonalPhone twalumba
ghci> onePersonalPhone albulena
Just "+355-652-55512"
ghci> allBusinessPhones nils

Haskell's Control.Monad module defines a typeclass, MonadPlus, that lets us abstract the common pattern out of our case expressions.

-- file: ch15/VCard.hs
class Monad m => MonadPlus m where
   mzero :: m a	
   mplus :: m a -> m a -> m a

The value mzero represents an empty result, while mplus combines two results into one. Here are the standard definitions of mzero and mplus for Maybe and lists.

-- file: ch15/VCard.hs
instance MonadPlus [] where
   mzero = []
   mplus = (++)

instance MonadPlus Maybe where
   mzero = Nothing

   Nothing `mplus` ys  = ys
   xs      `mplus` _ = xs

We can now use mplus to get rid of our case expressions entirely. For variety, let's fetch one business and all personal phone numbers.

-- file: ch15/VCard.hs
oneBusinessPhone :: [(Context, Phone)] -> Maybe Phone
oneBusinessPhone ps = lookup Business ps `mplus` lookup Mobile ps

allPersonalPhones :: [(Context, Phone)] -> [Phone]
allPersonalPhones ps = map snd $ filter (contextIs Home) ps `mplus`
                                 filter (contextIs Mobile) ps

In these functions, because we know that lookup returns a value of type Maybe, and filter returns a list, it's obvious which version of mplus is going to be used in each case.

What's more interesting is that we can use mzero and mplus to write functions that will be useful for any MonadPlus instance. As an example, here's the standard lookup function, which returns a value of type Maybe.

-- file: ch15/VCard.hs
lookup :: (Eq a) => a -> [(a, b)] -> Maybe b
lookup _ []                      = Nothing
lookup k ((x,y):xys) | x == k    = Just y
                     | otherwise = lookup k xys

We can easily generalise the result type to any instance of MonadPlus as follows.

-- file: ch15/VCard.hs
lookupM :: (MonadPlus m, Eq a) => a -> [(a, b)] -> m b
lookupM _ []    = mzero
lookupM k ((x,y):xys)
    | x == k    = return y `mplus` lookupM k xys
    | otherwise = lookupM k xys

This lets us get either no result or one, if our result type is Maybe; all results, if our result type is a list; or something more appropriate for some other exotic instance of MonadPlus.

For small functions, such as those we present above, there's little benefit to using mplus. The advantage lies in more complex code and in code that is independent of the monad in which it executes. Even if you don't find yourself needing MonadPlus for your own code, you are likely to encounter it in other people's projects.

The name mplus does not imply addition

Even though the mplus function contains the text “plus”, you should not think of it as necessarily implying that we're trying to add two values.

Depending on the monad we're working in, mplus may implement an operation that looks like addition. For example, mplus in the list monad is implemented as the (++) operator.

ghci> [1,2,3] `mplus` [4,5,6]

However, if we switch to another monad, the obvious similarity to addition falls away.

ghci> Just 1 `mplus` Just 2
Just 1

Rules for working with MonadPlus

Instances of the MonadPlus typeclass must follow a few simple rules, in addition to the usual monad rules.

An instance must short circuit if mzero appears on the left of a bind expression. In other words, an expression mzero >>= f must evaluate to the same result as mzero alone.

-- file: ch15/MonadPlus.hs
    mzero >>= f == mzero

An instance must short circuit if mzero appears on the right of a sequence expression.

-- file: ch15/MonadPlus.hs
    v >> mzero == mzero

Failing safely with MonadPlus

When we introduced the fail function in the section called “The Monad typeclass”, we took pains to warn against its use: in many monads, it's implemented as a call to error, which has unpleasant consequences.

The MonadPlus typeclass gives us a gentler way to fail a computation, without fail or error blowing up in our faces. The rules that we introduced above allow us to introduce an mzero into our code wherever we need to, and computation will short circuit at that point.

In the Control.Monad module, the standard function guard packages up this idea in a convenient form.

-- file: ch15/MonadPlus.hs
guard        :: (MonadPlus m) => Bool -> m ()
guard True   =  return ()
guard False  =  mzero

As a simple example, here's a function that takes a number x and computes its value modulo some other number n. If the result is zero, it returns x, otherwise the current monad's mzero.

-- file: ch15/MonadPlus.hs
x `zeroMod` n = guard ((x `mod` n) == 0) >> return x

Adventures in hiding the plumbing

In the section called “Using the state monad: generating random values”, we showed how to use the State monad to give ourselves access to random numbers in a way that is easy to use.

A drawback of the code we developed is that it's leaky: someone who uses it knows that they're executing inside the State monad. This means that they can inspect and modify the state of the random number generator just as easily as we, the authors, can.

Human nature dictates that if we leave our internal workings exposed, someone will surely come along and monkey with them. For a sufficiently small program, this may be fine, but in a larger software project, when one consumer of a library modifies its internals in a way that other consumers are not prepared for, the resulting bugs can be among the hardest of all to track down. These bugs occur at a level where we're unlikely to question our basic assumptions about a library until long after we've exhausted all other avenues of inquiry.

Even worse, once we leave our implementation exposed for a while, and some well-intentioned person inevitably bypasses our APIs and uses the implementation directly, we create a nasty quandary for ourselves if we need to fix a bug or make an enhancement. Either we can modify our internals, and break code that depends on them; or we're stuck with our existing internals, and must try to find some other way to make the change we need.

How can we revise our random number monad so that the fact that we're using the State monad is hidden? We need to somehow prevent our users from being able to call get or put. This is not difficult to do, and it introduces some tricks that we'll reuse often in day-to-day Haskell programming.

To widen our scope, we'll move beyond random numbers, and implement a monad that supplies unique values of any kind. The name we'll give to our monad is Supply. We'll provide the execution function, runSupply, with a list of values; it will be up to us to ensure that each one is unique.

-- file: ch15/Supply.hs
runSupply :: Supply s a -> [s] -> (a, [s])

The monad won't care what the values are: they might be random numbers, or names for temporary files, or identifiers for HTTP cookies.

Within the monad, every time a consumer asks for a value, the next action will take the next one from the list and give it to the consumer. Each value is wrapped in a Maybe constructor in case the list isn't long enough to satisfy the demand.

-- file: ch15/Supply.hs
next :: Supply s (Maybe s)

To hide our plumbing, in our module declaration we only export the type constructor, the execution function, and the next action.

-- file: ch15/Supply.hs
module Supply
    , next
    , runSupply
    ) where

Since a module that imports the library can't see the internals of the monad, it can't manipulate them.

Our plumbing is exceedingly simple: we use a newtype declaration to wrap the existing State monad.

-- file: ch15/Supply.hs
import Control.Monad.State

newtype Supply s a = S (State [s] a)

The s parameter is the type of the unique values we are going to supply, and a is the usual type parameter that we must provide in order to make our type a monad.

Our use of newtype for the Supply type and our module header join forces to prevent our clients from using the State monad's get and set actions. Because our module does not export the S data constructor, clients have no programmatic way to see that we're wrapping the State monad, or to access it.

At this point, we've got a type, Supply, that we need to make an instance of the Monad type class. We could follow the usual pattern of defining (>>=) and return, but this would be pure boilerplate code. All we'd be doing is wrapping and unwrapping the State monad's versions of (>>=) and return using our S value constructor. Here is how such code would look.

-- file: ch15/AltSupply.hs
unwrapS :: Supply s a -> State [s] a
unwrapS (S s) = s

instance Monad (Supply s) where
    s >>= m = S (unwrapS s >>= unwrapS . m)
    return = S . return

Haskell programmers are not fond of boilerplate, and sure enough, GHC has a lovely language extension that eliminates the work. To use it, we add the following directive to the top of our source file, before the module header.

-- file: ch15/Supply.hs
{-# LANGUAGE GeneralizedNewtypeDeriving #-}

Usually, we can only automatically derive instances of a handful of standard typeclasses, such as Show and Eq. As its name suggests, the GeneralizedNewtypeDeriving extension broadens our ability to derive typeclass instances, and it is specific to newtype declarations. If the type we're wrapping is an instance of any typeclass, the extensions can automatically make our new type an instance of that typeclass as follows.

-- file: ch15/Supply.hs
    deriving (Monad)

This takes the underlying type's implementations of (>>=) and return, adds the necessary wrapping and unwrapping with our S data constructor, and uses the new versions of those functions to derive a Monad instance for us.

What we gain here is very useful beyond just this example. We can use newtype to wrap any underlying type; we selectively expose only those typeclass instances that we want; and we expend almost no effort to create these narrower, more specialised types.

Now that we've seen the GeneralizedNewtypeDeriving technique, all that remains is to provide definitions of next and runSupply.

-- file: ch15/Supply.hs
next = S $ do st <- get
              case st of
                [] -> return Nothing
                (x:xs) -> do put xs
                             return (Just x)

runSupply (S m) xs = runState m xs

If we load our module into ghci, we can try it out in a few simple ways.

ghci> :load Supply
[1 of 1] Compiling Supply           ( Supply.hs, interpreted )
Ok, modules loaded: Supply.
ghci> runSupply next [1,2,3]
Loading package mtl- ... linking ... done.
(Just 1,[2,3])
ghci> runSupply (liftM2 (,) next next) [1,2,3]
((Just 1,Just 2),[3])
ghci> runSupply (liftM2 (,) next next) [1]
((Just 1,Nothing),[])

We can also verify that the State monad has not somehow leaked out.

ghci> :browse Supply
data Supply s a
next :: Supply s (Maybe s)
runSupply :: Supply s a -> [s] -> (a, [s])
ghci> :info Supply
data Supply s a 	-- Defined at Supply.hs:17:8-13
instance Monad (Supply s) -- Defined at Supply.hs:17:8-13

Supplying random numbers

If we want to use our Supply monad as a source of random numbers, we have a small difficulty to face. Ideally, we'd like to be able to provide it with an infinite stream of random numbers. We can get a StdGen in the IO monad, but we must “put back” a different StdGen when we're done. If we don't, the next piece of code to get a StdGen will get the same state as we did. This means it will generate the same random numbers as we did, which is potentially catastrophic.

From the parts of the System.Random module we've seen so far, it's difficult to reconcile these demands. We can use getStdRandom, whose type ensures that when we get a StdGen, we put one back.

ghci> :type getStdRandom
getStdRandom :: (StdGen -> (a, StdGen)) -> IO a

We can use random to get back a new StdGen when they give us a random number. And we can use randoms to get an infinite list of random numbers. But how do we get both an infinite list of random numbers and a new StdGen?

The answer lies with the RandomGen type class's split function, which takes one random number generator, and turns it into two generators. Splitting a random generator like this is a most unusual thing to be able to do: it's obviously tremendously useful in a pure functional setting, but essentially never either necessary or provided by an impure language.

Using the split function, we can use one StdGen to generate an infinite list of random numbers to feed to runSupply, while we give the other back to the IO monad.

-- file: ch15/RandomSupply.hs
import Supply
import System.Random hiding (next)

randomsIO :: Random a => IO [a]
randomsIO =
    getStdRandom $ \g ->
        let (a, b) = split g
        in (randoms a, b)

If we've written this function properly, our example ought to print a different random number on each invocation.

ghci> :load RandomSupply
[1 of 2] Compiling Supply           ( Supply.hs, interpreted )
[2 of 2] Compiling RandomSupply     ( RandomSupply.hs, interpreted )
Ok, modules loaded: RandomSupply, Supply.
ghci> (fst . runSupply next) `fmap` randomsIO

    Ambiguous occurrence `next'
    It could refer to either `', imported from Supply at RandomSupply.hs:4:0-12
                                              (defined at Supply.hs:32:0)
                          or `', imported from System.Random
ghci> (fst . runSupply next) `fmap` randomsIO

    Ambiguous occurrence `next'
    It could refer to either `', imported from Supply at RandomSupply.hs:4:0-12
                                              (defined at Supply.hs:32:0)
                          or `', imported from System.Random

Recall that our runSupply function returns both the result of executing the monadic action and the unconsumed remainder of the list. Since we passed it an infinite list of random numbers, we compose with fst to ensure that we don't get drowned in random numbers when ghci tries to print the result.

Another round of golf

The pattern of applying a function to one element of a pair, and constructing a new pair with the other original element untouched, is common enough in Haskell code that it has been turned into standard code.

In the Control.Arrow module are two functions, first and second, that perform this operation.

ghci> :m +Control.Arrow
ghci> first (+3) (1,2)
ghci> second odd ('a',1)

(Indeed, we already encountered second, in the section called “JSON typeclasses without overlapping instances”.) We can use first to golf our definition of randomsIO, turning it into a one-liner.

-- file: ch15/RandomGolf.hs
import Control.Arrow (first)

randomsIO_golfed :: Random a => IO [a]
randomsIO_golfed = getStdRandom (first randoms . split)

Separating interface from implementation

In the previous section, we saw how to hide the fact that we're using a State monad to hold the state for our Supply monad.

Another important way to make code more modular involves separating its interface—what the code can do—from its implementation—how it does it.

The standard random number generator in System.Random is known to be quite slow. If we use our randomsIO function to provide it with random numbers, then our next action will not perform well.

One simple and effective way that we could deal with this is to provide Supply with a better source of random numbers. Let's set this idea aside, though, and consider an alternative approach, one that is useful in many settings. We will separate the actions we can perform with the monad from how it works using a typeclass.

-- file: ch15/SupplyClass.hs
class (Monad m) => MonadSupply s m | m -> s where
    next :: m (Maybe s)

This typeclass defines the interface that any supply monad must implement. It bears careful inspection, since it uses several unfamiliar Haskell language extensions. We will cover each one in the sections that follow.

Multi-parameter typeclasses

How should we read the snippet MonadSupply s m in the typeclass? If we add parentheses, an equivalent expression is (MonadSupply s) m, which is a little clearer. In other words, given some type variable m that is a Monad, we can make it an instance of the typeclass MonadSupply s. unlike a regular typeclass, this one has a parameter.

As this language extension allows a typeclass to have more than one parameter, its name is MultiParamTypeClasses. The parameter s serves the same purpose as the Supply type's parameter of the same name: it represents the type of the values handed out by the next function.

Notice that we don't need to mention (>>=) or return in the definition of MonadSupply s, since the type class's context (superclass) requires that a MonadSupply s must already be a Monad.

Functional dependencies

To revisit a snippet that we ignored earlier, | m -> s is a functional dependency, often called a fundep. We can read the vertical bar | as “such that”, and the arrow -> as “uniquely determines”. Our functional dependency establishes a relationship between m and s.

The availability of functional dependencies is governed by the FunctionalDependencies language pragma.

The purpose behind us declaring a relationship is to help the type checker. Recall that a Haskell type checker is essentially a theorem prover, and that it is conservative in how it operates: it insists that its proofs must terminate. A non-terminating proof results in the compiler either giving up or getting stuck in an infinite loop.

With our functional dependency, we are telling the type checker that every time it sees some monad m being used in the context of a MonadSupply s, the type s is the only acceptable type to use with it. If we were to omit the functional dependency, the type checker would simply give up with an error message.

It's hard to picture what the relationship between m and s really means, so let's look at an instance of this typeclass.

-- file: ch15/SupplyClass.hs
import qualified Supply as S

instance MonadSupply s (S.Supply s) where
    next =

Here, the type variable m is replaced by the type S.Supply s. Thanks to our functional dependency, the type checker now knows that when it sees a type S.Supply s, the type can be used as an instance of the typeclass MonadSupply s.

If we didn't have a functional dependency, the type checker would not be able to figure out the relationship between the type parameter of the class MonadSupply s and that of the type Supply s, and it would abort compilation with an error. The definition itself would compile; the type error would not arise until the first time we tried to use it.

To strip away one final layer of abstraction, consider the type S.Supply Int. Without a functional dependency, we could declare this an instance of MonadSupply s. However, if we tried to write code using this instance, the compiler would not be able to figure out that the type's Int parameter needs to be the same as the typeclass's s parameter, and it would report an error.

Functional dependencies can be tricky to understand, and once we move beyond simple uses, they often prove difficult to work with in practice. Fortunately, the most frequent use of functional dependencies is in situations as simple as ours, where they cause little trouble.

Rounding out our module

If we save our typeclass and instance in a source file named SupplyClass.hs, we'll need to add a module header such as the following.

-- file: ch15/SupplyClass.hs
{-# LANGUAGE FlexibleInstances, FunctionalDependencies,
             MultiParamTypeClasses #-}

module SupplyClass
    , S.Supply
    , S.runSupply
    ) where

The FlexibleInstances extension is necessary so that the compiler will accept our instance declaration. This extension relaxes the normal rules for writing instances in some circumstances, in a way that still lets the compiler's type checker guarantee that it will terminate. Our need for FlexibleInstances here is caused by our use of functional dependencies, but the details are unfortunately beyond the scope of this book.

[Tip]How to know when a language extension is needed

If GHC cannot compile a piece of code because it would require some language extension to be enabled, it will tell us which extension we should use. For example, if it decides that our code needs flexible instance support, it will suggest that we try compiling with the -XFlexibleInstances option. A -X option has the same effect as a LANGUAGE directive: it enables a particular extension.

Finally, notice that we're re-exporting the runSupply and Supply names from this module. It's perfectly legal to export a name from one module even though it's defined in another. In our case, it means that client code only needs to import the SupplyClass module, without also importing the Supply module. This reduces the number of “moving parts” that a user of our code needs to keep in mind.

Programming to a monad's interface

Here is a simple function that fetches two values from our Supply monad, formats them as a string, and returns them.

-- file: ch15/Supply.hs
showTwo :: (Show s) => Supply s String
showTwo = do
  a <- next
  b <- next
  return (show "a: " ++ show a ++ ", b: " ++ show b)

This code is tied by its result type to our Supply monad. We can easily generalize to any monad that implements our MonadSupply interface by modifying our function's type. Notice that the body of the function remains unchanged.

-- file: ch15/SupplyClass.hs
showTwo_class :: (Show s, Monad m, MonadSupply s m) => m String
showTwo_class = do
  a <- next
  b <- next
  return (show "a: " ++ show a ++ ", b: " ++ show b)

The reader monad

The State monad lets us plumb a piece of mutable state through our code. Sometimes, we would like to be able to pass some immutable state around, such as a program's configuration data. We could use the State monad for this purpose, but we could then find ourselves accidentally modifying data that should remain unchanged.

Let's forget about monads for a moment and think about what a function with our desired characteristics ought to do. It should accept a value of some type e (for environment) that represents the data that we're passing in, and return a value of some other type a as its result. The overall type we want is e -> a.

To turn this type into a convenient Monad instance, we'll wrap it in a newtype.

-- file: ch15/SupplyInstance.hs
newtype Reader e a = R { runReader :: e -> a }

Making this into a Monad instance doesn't take much work.

-- file: ch15/SupplyInstance.hs
instance Monad (Reader e) where
    return a = R $ \_ -> a
    m >>= k = R $ \r -> runReader (k (runReader m r)) r

We can think of our value of type e as an environment in which we're evaluating some expression. The return action should have the same effect no matter what the environment is, so our version ignores its environment.

Our definition of (>>=) is a little more complicated, but only because we have to make the environment—here the variable r—available both in the current computation and in the computation we're chaining into.

How does a piece of code executing in this monad find out what's in its environment? It simply has to ask.

-- file: ch15/SupplyInstance.hs
ask :: Reader e e
ask = R id

Within a given chain of actions, every invocation of ask will return the same value, since the value stored in the environment doesn't change. Our code is easy to test in ghci.

ghci> runReader (ask >>= \x -> return (x * 3)) 2
Loading package old-locale- ... linking ... done.
Loading package old-time- ... linking ... done.
Loading package random- ... linking ... done.

The Reader monad is included in the standard mtl library, which is usually bundled with GHC. You can find it in the Control.Monad.Reader module. The motivation for this monad may initially seem a little thin, because it is most often useful in complicated code. We'll often need to access a piece of configuration information deep in the bowels of a program; passing that information in as a normal parameter would require a painful restructuring of our code. By hiding this information in our monad's plumbing, intermediate functions that don't care about the configuration information don't need to see it.

The clearest motivation for the Reader monad will come in Chapter 18, Monad transformers, when we discuss combining several monads to build a new monad. There, we'll see how to gain finer control over state, so that our code can modify some values via the State monad, while other values remain immutable, courtesy of the Reader monad.

A return to automated deriving

Now that we know about the Reader monad, let's use it to create an instance of our MonadSupply typeclass. To keep our example simple, we'll violate the spirit of MonadSupply here: our next action will always return the same value, instead of always returning a different value.

It would be a bad idea to directly make the Reader type an instance of the MonadSupply class, because then any Reader could act as a MonadSupply. This would usually not make any sense.

Instead, we create a newtype based on Reader. The newtype hides the fact that we're using Reader internally. We must now make our type an instance of both of the typeclasses we care about. With the GeneralizedNewtypeDeriving extension enabled, GHC will do most of the hard work for us.

-- file: ch15/SupplyInstance.hs
newtype MySupply e a = MySupply { runMySupply :: Reader e a }
    deriving (Monad)

instance MonadSupply e (MySupply e) where
    next = MySupply $ do
             v <- ask
             return (Just v)

    -- more concise:
    -- next = MySupply (Just `liftM` ask)

Notice that we must make our type an instance of MonadSupply e, not MonadSupply. If we omit the type variable, the compiler will complain.

To try out our MySupply type, we'll first create a simple function that should work with any MonadSupply instance.

-- file: ch15/SupplyInstance.hs
xy :: (Num s, MonadSupply s m) => m s
xy = do
  Just x <- next
  Just y <- next
  return (x * y)

If we use this with our Supply monad and randomsIO function, we get a different answer every time, as we expect.

ghci> (fst . runSupply xy) `fmap` randomsIO
ghci> (fst . runSupply xy) `fmap` randomsIO

Because our MySupply monad has two layers of newtype wrapping, we can make it easier to use by writing a custom execution function for it.

-- file: ch15/SupplyInstance.hs
runMS :: MySupply i a -> i -> a
runMS = runReader . runMySupply

When we apply our xy action using this execution function, we get the same answer every time. Our code remains the same, but because we are executing it in a different implementation of MonadSupply, its behavior has changed.

ghci> runMS xy 2
ghci> runMS xy 2

Like our MonadSupply typeclass and Supply monad, almost all of the common Haskell monads are built with a split between interface and implementation. For example, the get and put functions that we introduced as “belonging to” the State monad are actually methods of the MonadState typeclass; the State type is an instance of this class.

Similarly, the standard Reader monad is an instance of the MonadReader typeclass, which specifies the ask method.

While the separation of interface and implementation that we've discussed above is appealing for its architectural cleanliness, it has important practical applications that will become clearer later. When we start combining monads in Chapter 18, Monad transformers, we will save a lot of effort through the use of GeneralizedNewtypeDeriving and typeclasses.

Hiding the IO monad

The blessing and curse of the IO monad is that it is extremely powerful. If we believe that careful use of types helps us to avoid programming mistakes, then the IO monad should be a great source of unease. Because the IO monad imposes no restrictions on what we can do, it leaves us vulnerable to all kinds of accidents.

How can we tame its power? Let's say that we would like to guarantee to ourselves that a piece of code can read and write files on the local filesystem, but that it will not access the network. We can't use the plain IO monad, because it won't restrict us.

Using a newtype

Let's create a module that provides a small set of functionality for reading and writing files.

-- file: ch15/HandleIO.hs
{-# LANGUAGE GeneralizedNewtypeDeriving #-}

module HandleIO
    , Handle
    , IOMode(..)
    , runHandleIO
    , openFile
    , hClose
    , hPutStrLn
    ) where
import System.IO (Handle, IOMode(..))
import qualified System.IO

Our first approach to creating a restricted version of IO is to wrap it with a newtype.

-- file: ch15/HandleIO.hs
newtype HandleIO a = HandleIO { runHandleIO :: IO a }
    deriving (Monad)

We do the by-now familiar trick of exporting the type constructor and the runHandleIO execution function from our module, but not the data constructor. This will prevent code running within the HandleIO monad from getting hold of the IO monad that it wraps.

All that remains is for us to wrap each of the actions we want our monad to allow. This is a simple matter of wrapping each IO with a HandleIO data constructor.

-- file: ch15/HandleIO.hs
openFile :: FilePath -> IOMode -> HandleIO Handle
openFile path mode = HandleIO (System.IO.openFile path mode)

hClose :: Handle -> HandleIO ()
hClose = HandleIO . System.IO.hClose

hPutStrLn :: Handle -> String -> HandleIO ()
hPutStrLn h s = HandleIO (System.IO.hPutStrLn h s)

We can now use our restricted HandleIO monad to perform I/O.

-- file: ch15/HandleIO.hs
safeHello :: FilePath -> HandleIO ()
safeHello path = do
  h <- openFile path WriteMode
  hPutStrLn h "hello world"
  hClose h

To run this action, we use runHandleIO.

ghci> :load HandleIO
[1 of 1] Compiling HandleIO         ( HandleIO.hs, interpreted )
Ok, modules loaded: HandleIO.
ghci> runHandleIO (safeHello "hello_world_101.txt")
Loading package old-locale- ... linking ... done.
Loading package old-time- ... linking ... done.
Loading package filepath- ... linking ... done.
Loading package directory- ... linking ... done.
Loading package mtl- ... linking ... done.
ghci> :m +System.Directory
ghci> removeFile "hello_world_101.txt"

If we try to sequence an action that runs in the HandleIO monad with one that is not permitted, the type system forbids it.

ghci> runHandleIO (safeHello "goodbye" >> removeFile "goodbye")

    Couldn't match expected type `HandleIO a'
           against inferred type `IO ()'
    In the second argument of `(>>)', namely `removeFile "goodbye"'
    In the first argument of `runHandleIO', namely
        `(safeHello "goodbye" >> removeFile "goodbye")'
    In the expression:
        runHandleIO (safeHello "goodbye" >> removeFile "goodbye")

Designing for unexpected uses

There's one small, but significant, problem with our HandleIO monad: it doesn't take into account the possibility that we might occasionally need an escape hatch. If we define a monad like this, it is likely that we will occasionally need to perform an I/O action that isn't allowed for by the design of our monad.

Our purpose in defining a monad like this is to make it easier for us to write solid code in the common case, not to make corner cases impossible. Let's thus give ourselves a way out.

The Control.Monad.Trans module defines a “standard escape hatch”, the MonadIO typeclass. This defines a single function, liftIO, which lets us embed an IO action in another monad.

ghci> :m +Control.Monad.Trans
ghci> :info MonadIO
class (Monad m) => MonadIO m where liftIO :: IO a -> m a
  	-- Defined in Control.Monad.Trans
instance MonadIO IO -- Defined in Control.Monad.Trans

Our implementation of this typeclass is trivial: we just wrap IO with our data constructor.

-- file: ch15/HandleIO.hs
import Control.Monad.Trans (MonadIO(..))

instance MonadIO HandleIO where
    liftIO = HandleIO

With judicious use of liftIO, we can escape our shackles and invoke IO actions where necessary.

-- file: ch15/HandleIO.hs
tidyHello :: FilePath -> HandleIO ()
tidyHello path = do
  safeHello path
  liftIO (removeFile path)
[Tip]Automatic derivation and MonadIO

We could have had the compiler automatically derive an instance of MonadIO for us by adding the type class to the deriving clause of HandleIO. In fact, in production code, this would be our usual strategy. We avoided that here simply to separate the presentation of the earlier material from that of MonadIO.

Using typeclasses

The disadvantage of hiding IO in another monad is that we're still tied to a concrete implementation. If we want to swap HandleIO for some other monad, we must change the type of every action that uses HandleIO.

As an alternative, we can create a typeclass that specifies the interface we want from a monad that manipulates files.

-- file: ch15/MonadHandle.hs
{-# LANGUAGE FunctionalDependencies, MultiParamTypeClasses #-}

module MonadHandle (MonadHandle(..)) where

import System.IO (IOMode(..))

class Monad m => MonadHandle h m | m -> h where
    openFile :: FilePath -> IOMode -> m h
    hPutStr :: h -> String -> m ()
    hClose :: h -> m ()
    hGetContents :: h -> m String

    hPutStrLn :: h -> String -> m ()
    hPutStrLn h s = hPutStr h s >> hPutStr h "\n"

Here, we've chosen to abstract away both the type of the monad and the type of a file handle. To satisfy the type checker, we've added a functional dependency: for any instance of MonadHandle, there is exactly one handle type that we can use. When we make the IO monad an instance of this class, we use a regular Handle.

-- file: ch15/MonadHandleIO.hs
{-# LANGUAGE FunctionalDependencies, MultiParamTypeClasses #-}

import MonadHandle
import qualified System.IO

import System.IO (IOMode(..))
import Control.Monad.Trans (MonadIO(..), MonadTrans(..))
import System.Directory (removeFile)

import SafeHello

instance MonadHandle System.IO.Handle IO where
    openFile = System.IO.openFile
    hPutStr = System.IO.hPutStr
    hClose = System.IO.hClose
    hGetContents = System.IO.hGetContents
    hPutStrLn = System.IO.hPutStrLn

Because any MonadHandle must also be a Monad, we can write code that manipulates files using normal do notation, without caring what monad it will finally execute in.

-- file: ch15/SafeHello.hs
safeHello :: MonadHandle h m => FilePath -> m ()
safeHello path = do
  h <- openFile path WriteMode
  hPutStrLn h "hello world"
  hClose h

Because we made IO an instance of this type class, we can execute this action from ghci.

ghci> safeHello "hello to my fans in domestic surveillance"
Loading package old-locale- ... linking ... done.
Loading package old-time- ... linking ... done.
Loading package filepath- ... linking ... done.
Loading package directory- ... linking ... done.
Loading package mtl- ... linking ... done.
ghci> removeFile "hello to my fans in domestic surveillance"

The beauty of the typeclass approach is that we can swap one underlying monad for another without touching much code, as most of our code doesn't know or care about the implementation. For instance, we could replace IO with a monad that compresses files as it writes them out.

Defining a monad's interface through a typeclass has a further benefit. It lets other people hide our implementation in a newtype wrapper, and automatically derive instances of just the typeclasses they want to expose.

Isolation and testing

In fact, because our safeHello function doesn't use the IO type, we can even use a monad that can't perform I/O. This allows us to test code that would normally have side effects in a completely pure, controlled environment.

To do this, we will create a monad that doesn't perform I/O, but instead logs every file-related event for later processing.

-- file: ch15/WriterIO.hs
data Event = Open FilePath IOMode
           | Put String String
           | Close String
           | GetContents String
             deriving (Show)

Although we already developed a Logger type in the section called “Using a new monad: show your work!”, here we'll use the standard, and more general, Writer monad. Like other mtl monads, the API provided by Writer is defined in a typeclass, in this case MonadWriter. Its most useful method is tell, which logs a value.

ghci> :m +Control.Monad.Writer
ghci> :type tell
tell :: (MonadWriter w m) => w -> m ()

The values we log can be of any Monoid type. Since the list type is a Monoid, we'll log to a list of Event.

We could make Writer [Event] an instance of MonadHandle, but it's cheap, easy, and safer to make a special-purpose monad.

-- file: ch15/WriterIO.hs
newtype WriterIO a = W { runW :: Writer [Event] a }
    deriving (Monad, MonadWriter [Event])

Our execution function simply removes the newtype wrapper we added, then calls the normal Writer monad's execution function.

-- file: ch15/WriterIO.hs
runWriterIO :: WriterIO a -> (a, [Event])
runWriterIO = runWriter . runW

When we try this code out in ghci, it gives us a log of the function's file activities.

ghci> :load WriterIO
[1 of 3] Compiling MonadHandle      ( MonadHandle.hs, interpreted )
[2 of 3] Compiling SafeHello        ( SafeHello.hs, interpreted )
[3 of 3] Compiling WriterIO         ( WriterIO.hs, interpreted )
Ok, modules loaded: SafeHello, MonadHandle, WriterIO.
ghci> runWriterIO (safeHello "foo")
((),[Open "foo" WriteMode,Put "foo" "hello world",Put "foo" "\n",Close "foo"])

The writer monad and lists

The writer monad uses the monoid's mappend function every time we use tell. Because mappend for lists is (++), lists are not a good practical choice for use with Writer: repeated appends are expensive. We use lists above purely for simplicity.

In production code, if you want to use the Writer monad and you need list-like behaviour, use a type with better append characteristics. One such type is the difference list, which we introduced in the section called “Taking advantage of functions as data”. You don't need to roll your own difference list implementation: a well tuned library is available for download from Hackage, the Haskell package database. Alternatively, you can use the Seq type from the Data.Sequence module, which we introduced in the section called “General purpose sequences”.

Arbitrary I/O revisited

If we use the typeclass approach to restricting IO, we may still want to retain the ability to perform arbitrary I/O actions. We might try adding MonadIO as a constraint on our typeclass.

-- file: ch15/MonadHandleIO.hs
class (MonadHandle h m, MonadIO m) => MonadHandleIO h m | m -> h

instance MonadHandleIO System.IO.Handle IO

tidierHello :: (MonadHandleIO h m) => FilePath -> m ()
tidierHello path = do
  safeHello path
  liftIO (removeFile path)

This approach has a problem, though: the added MonadIO constraint loses us the ability to test our code in a pure environment, because we can no longer tell whether a test might have damaging side effects. The alternative is to move this constraint from the typeclass, where it “infects” all functions, to only those functions that really need to perform I/O.

-- file: ch15/MonadHandleIO.hs
tidyHello :: (MonadIO m, MonadHandle h m) => FilePath -> m ()
tidyHello path = do
  safeHello path
  liftIO (removeFile path)

We can use pure property tests on the functions that lack MonadIO constraints, and traditional unit tests on the rest.

Unfortunately, we've substituted one problem for another: we can't invoke code with both MonadIO and MonadHandle constraints from code that has the MonadHandle constraint alone. If we find that somewhere deep in our MonadHandle-only code, we really need the MonadIO constraint, we must add it to all the code paths that lead to this point.

Allowing arbitrary I/O is risky, and has a profound effect on how we develop and test our code. When we have to choose between being permissive on the one hand, and easier reasoning and testing on the other, we usually opt for the latter.



Using QuickCheck, write a test for an action in the MonadHandle monad, to see if it tries to write to a file handle that is not open. Try it out on safeHello.


Write an action that tries to write to a file handle that it has closed. Does your test catch this bug?


In a form-encoded string, the same key may appear several times, with or without values, e.g. key&key=1&key=2. What type might you use to represent the values associated with a key in this sort of string? Write a parser that correctly captures all of the information.

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Copyright 2007, 2008 Bryan O'Sullivan, Don Stewart, and John Goerzen. This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 License. Icons by Paul Davey aka Mattahan.