Monadic Adventures
Chapter Goals
The goal of this chapter will be to learn about monad transformers, which provide a way to combine sideeffects provided by different monads. The motivating example will be a text adventure game which can be played on the console in NodeJS. The various sideeffects of the game (logging, state, and configuration) will all be provided by a monad transformer stack.
Project Setup
This module's project introduces the following new dependencies:
orderedcollections
, which provides data typs for immutable maps and setstransformers
, which provides implementations of standard monad transformersnodereadline
, which provides FFI bindings to thereadline
interface provided by NodeJSyargs
, which provides an applicative interface to theyargs
command line argument processing library
It is also necessary to install the yargs
module using NPM:
npm install
How To Play The Game
To run the project, use spago run
By default you will see a usage message:
node ./dist/Main.js p <player name>
Options:
p, player Player name [required]
d, debug Use debug mode
Missing required arguments: p
The player name is required
Provide the player name using the p
option:
spago run a "p Phil"
>
From the prompt, you can enter commands like look
, inventory
, take
, use
, north
, south
, east
, and west
. There is also a debug
command, which can be used to print the game state when the debug
command line option is provided.
The game is played on a twodimensional grid, and the player moves by issuing commands north
, south
, east
, and west
. The game contains a collection of items which can either be in the player's possession (in the user's inventory), or on the game grid at some location. Items can be picked up by the player, using the take
command.
For reference, here is a complete walkthrough of the game:
$ spago run a "p Phil"
> look
You are at (0, 0)
You are in a dark forest. You see a path to the north.
You can see the Matches.
> take Matches
You now have the Matches
> north
> look
You are at (0, 1)
You are in a clearing.
You can see the Candle.
> take Candle
You now have the Candle
> inventory
You have the Candle.
You have the Matches.
> use Matches
You light the candle.
Congratulations, Phil!
You win!
The game is very simple, but the aim of the chapter is to use the transformers
package to build a library which will enable rapid development of this type of game.
The State Monad
We will start by looking at some of the monads provided by the transformers
package.
The first example is the State
monad, which provides a way to model mutable state in pure code. We have already seen an approach to mutable state provided by the Effect
monad. State
provides an alternative.
The State
type constructor takes two type parameters: the type s
of the state, and the return type a
. Even though we speak of the "State
monad", the instance of the Monad
type class is actually provided for the State s
type constructor, for any type s
.
The Control.Monad.State
module provides the following API:
get :: forall s. State s s
gets :: forall s. (s > a) > State s a
put :: forall s. s > State s Unit
modify :: forall s. (s > s) > State s s
modify_ :: forall s. (s > s) > State s Unit
Note that these API signatures are presented in a simplified form using the State
type constructor for now. The actual API involves MonadState
which we'll cover in the later "Type Classes" section of this chapter, so don't worry if you see different signatures in your IDE tooltips or on Pursuit.
Let's see an example. One use of the State
monad might be to add the values in an array of numbers to the current state. We could do that by choosing Number
as the state type s
, and using traverse_
to traverse the array, with a call to modify
for each array element:
import Data.Foldable (traverse_)
import Control.Monad.State
import Control.Monad.State.Class
sumArray :: Array Int > State Int Unit
sumArray = traverse_ \n > modify \sum > sum + n
The Control.Monad.State
module provides three functions for running a computation in the State
monad:
evalState :: forall s a. State s a > s > a
execState :: forall s a. State s a > s > s
runState :: forall s a. State s a > s > Tuple a s
Each of these functions takes an initial state of type s
and a computation of type State s a
. evalState
only returns the return value, execState
only returns the final state, and runState
returns both, expressed as a value of type Tuple a s
.
Given the sumArray
function above, we could use execState
in PSCi to sum the numbers in several arrays as follows:
> :paste
… execState (do
… sumArray [1, 2, 3]
… sumArray [4, 5]
… sumArray [6]) 0
… ^D
21
Exercises

(Easy) What is the result of replacing
execState
withrunState
orevalState
in our example above? 
(Medium) A string of parentheses is balanced if it is obtained by either concatenating zeroormore shorter balanced strings, or by wrapping a shorter balanced string in a pair of parentheses.
Use the
State
monad and thetraverse_
function to write a functiontestParens :: String > Boolean
which tests whether or not a
String
of parentheses is balanced, by keeping track of the number of opening parentheses which have not been closed. Your function should work as follows:> testParens "" true > testParens "(()(())())" true > testParens ")" false > testParens "(()()" false
Hint: you may like to use the
toCharArray
function from theData.String.CodeUnits
module to turn the input string into an array of characters.
The Reader Monad
Another monad provided by the transformers
package is the Reader
monad. This monad provides the ability to read from a global configuration. Whereas the State
monad provides the ability to read and write a single piece of mutable state, the Reader
monad only provides the ability to read a single piece of data.
The Reader
type constructor takes two type arguments: a type r
which represents the configuration type, and the return type a
.
The Control.Monad.Reader
module provides the following API:
ask :: forall r. Reader r r
local :: forall r a. (r > r) > Reader r a > Reader r a
The ask
action can be used to read the current configuration, and the local
action can be used to run a computation with a modified configuration.
For example, suppose we were developing an application controlled by permissions, and we wanted to use the Reader
monad to hold the current user's permissions object. We might choose the type r
to be some type Permissions
with the following API:
hasPermission :: String > Permissions > Boolean
addPermission :: String > Permissions > Permissions
Whenever we wanted to check if the user had a particular permission, we could use ask
to retrieve the current permissions object. For example, only administrators might be allowed to create new users:
createUser :: Reader Permissions (Maybe User)
createUser = do
permissions < ask
if hasPermission "admin" permissions
then map Just newUser
else pure Nothing
To elevate the user's permissions, we might use the local
action to modify the Permissions
object during the execution of some computation:
runAsAdmin :: forall a. Reader Permissions a > Reader Permissions a
runAsAdmin = local (addPermission "admin")
Then we could write a function to create a new user, even if the user did not have the admin
permission:
createUserAsAdmin :: Reader Permissions (Maybe User)
createUserAsAdmin = runAsAdmin createUser
To run a computation in the Reader
monad, the runReader
function can be used to provide the global configuration:
runReader :: forall r a. Reader r a > r > a
Exercises
In these exercises, we will use the Reader
monad to build a small library for rendering documents with indentation. The "global configuration" will be a number indicating the current indentation level:
type Level = Int
type Doc = Reader Level String

(Easy) Write a function
line
which renders a function at the current indentation level. Your function should have the following type:line :: String > Doc
Hint: use the
ask
function to read the current indentation level. Thepower
function fromData.Monoid
may be helpful too. 
(Easy) Use the
local
function to write a functionindent :: Doc > Doc
which increases the indentation level for a block of code.

(Medium) Use the
sequence
function defined inData.Traversable
to write a functioncat :: Array Doc > Doc
which concatenates a collection of documents, separating them with new lines.

(Medium) Use the
runReader
function to write a functionrender :: Doc > String
which renders a document as a String.
You should now be able to use your library to write simple documents, as follows:
render $ cat
[ line "Here is some indented text:"
, indent $ cat
[ line "I am indented"
, line "So am I"
, indent $ line "I am even more indented"
]
]
The Writer Monad
The Writer
monad provides the ability to accumulate a secondary value in addition to the return value of a computation.
A common use case is to accumulate a log of type String
or Array String
, but the Writer
monad is more general than this. It can actually be used to accumulate a value in any monoid, so it might be used to keep track of an integer total using the Additive Int
monoid, or to track whether any of several intermediate Boolean
values were true, using the Disj Boolean
monoid.
The Writer
type constructor takes two type arguments: a type w
which should be an instance of the Monoid
type class, and the return type a
.
The key element of the Writer
API is the tell
function:
tell :: forall w a. Monoid w => w > Writer w Unit
The tell
action appends the provided value to the current accumulated result.
As an example, let's add a log to an existing function by using the Array String
monoid. Consider our previous implementation of the greatest common divisor function:
gcd :: Int > Int > Int
gcd n 0 = n
gcd 0 m = m
gcd n m = if n > m
then gcd (n  m) m
else gcd n (m  n)
We could add a log to this function by changing the return type to Writer (Array String) Int
:
import Control.Monad.Writer
import Control.Monad.Writer.Class
gcdLog :: Int > Int > Writer (Array String) Int
We only have to change our function slightly to log the two inputs at each step:
gcdLog n 0 = pure n
gcdLog 0 m = pure m
gcdLog n m = do
tell ["gcdLog " <> show n <> " " <> show m]
if n > m
then gcdLog (n  m) m
else gcdLog n (m  n)
We can run a computation in the Writer
monad by using either of the execWriter
or runWriter
functions:
execWriter :: forall w a. Writer w a > w
runWriter :: forall w a. Writer w a > Tuple a w
Just like in the case of the State
monad, execWriter
only returns the accumulated log, whereas runWriter
returns both the log and the result.
We can test our modified function in PSCi:
> import Control.Monad.Writer
> import Control.Monad.Writer.Class
> runWriter (gcdLog 21 15)
Tuple 3 ["gcdLog 21 15","gcdLog 6 15","gcdLog 6 9","gcdLog 6 3","gcdLog 3 3"]
Exercises

(Medium) Rewrite the
sumArray
function above using theWriter
monad and theAdditive Int
monoid from themonoid
package. 
(Medium) The Collatz function is defined on natural numbers
n
asn / 2
whenn
is even, and3 * n + 1
whenn
is odd. For example, the iterated Collatz sequence starting at10
is as follows:10, 5, 16, 8, 4, 2, 1, ...
It is conjectured that the iterated Collatz sequence always reaches
1
after some finite number of applications of the Collatz function.Write a function which uses recursion to calculate how many iterations of the Collatz function are required before the sequence reaches
1
.Modify your function to use the
Writer
monad to log each application of the Collatz function.
Monad Transformers
Each of the three monads above: State
, Reader
and Writer
, are also examples of socalled monad transformers. The equivalent monad transformers are called StateT
, ReaderT
, and WriterT
respectively.
What is a monad transformer? Well, as we have seen, a monad augments PureScript code with some type of side effect, which can be interpreted in PureScript by using the appropriate handler (runState
, runReader
, runWriter
, etc.) This is fine if we only need to use one sideeffect. However, it is often useful to use more than one sideeffect at once. For example, we might want to use Reader
together with Maybe
to express optional results in the context of some global configuration. Or we might want the mutable state provided by the State
monad together with the pure error tracking capability of the Either
monad. This is the problem solved by monad transformers.
Note that we have already seen that the Effect
monad provides a partial solution to this problem. Monad transformers provide another solution, and each approach has its own benefits and limitations.
A monad transformer is a type constructor which is parameterized not only by a type, but by another type constructor. It takes one monad and turns it into another monad, adding its own variety of sideeffects.
Let's see an example. The monad transformer version of the State
monad is StateT
, defined in the Control.Monad.State.Trans
module. We can find the kind of StateT
using PSCi:
> import Control.Monad.State.Trans
> :kind StateT
Type > (Type > Type) > Type > Type
This looks quite confusing, but we can apply StateT
one argument at a time to understand how to use it.
The first type argument is the type of the state we wish to use, as was the case for State
. Let's use a state of type String
:
> :kind StateT String
(Type > Type) > Type > Type
The next argument is a type constructor of kind Type > Type
. It represents the underlying monad, which we want to add the effects of StateT
to. For the sake of an example, let's choose the Either String
monad:
> :kind StateT String (Either String)
Type > Type
We are left with a type constructor. The final argument represents the return type, and we might instantiate it to Number
for example:
> :kind StateT String (Either String) Number
Type
Finally we are left with something of kind Type
, which means we can try to find values of this type.
The monad we have constructed  StateT String (Either String)
 represents computations which can fail with an error, and which can use mutable state.
We can use the actions of the outer StateT String
monad (get
, put
, and modify
) directly, but in order to use the effects of the wrapped monad (Either String
), we need to "lift" them over the monad transformer. The Control.Monad.Trans
module defines the MonadTrans
type class, which captures those type constructors which are monad transformers, as follows:
class MonadTrans t where
lift :: forall m a. Monad m => m a > t m a
This class contains a single member, lift
, which takes computations in any underlying monad m
and lifts them into the wrapped monad t m
. In our case, the type constructor t
is StateT String
, and m
is the Either String
monad, so lift
provides a way to lift computations of type Either String a
to computations of type StateT String (Either String) a
. This means that we can use the effects of StateT String
and Either String
sidebyside, as long as we use lift
every time we use a computation of type Either String a
.
For example, the following computation reads the underlying state, and then throws an error if the state is the empty string:
import Data.String (drop, take)
split :: StateT String (Either String) String
split = do
s < get
case s of
"" > lift $ Left "Empty string"
_ > do
put (drop 1 s)
pure (take 1 s)
If the state is not empty, the computation uses put
to update the state to drop 1 s
(that is, s
with the first character removed), and returns take 1 s
(that is, the first character of s
).
Let's try this in PSCi:
> runStateT split "test"
Right (Tuple "t" "est")
> runStateT split ""
Left "Empty string"
This is not very remarkable, since we could have implemented this without StateT
. However, since we are working in a monad, we can use do notation or applicative combinators to build larger computations from smaller ones. For example, we can apply split
twice to read the first two characters from a string:
> runStateT ((<>) <$> split <*> split) "test"
(Right (Tuple "te" "st"))
We can use the split
function with a handful of other actions to build a basic parsing library. In fact, this is the approach taken by the parsing
library. This is the power of monad transformers  we can create custombuilt monads for a variety of problems, choosing the sideeffects that we need, and keeping the expressiveness of do notation and applicative combinators.
The ExceptT Monad Transformer
The transformers
package also defines the ExceptT e
monad transformer, which is the transformer corresponding to the Either e
monad. It provides the following API:
class MonadError e m where
throwError :: forall a. e > m a
catchError :: forall a. m a > (e > m a) > m a
instance monadErrorExceptT :: Monad m => MonadError e (ExceptT e m)
runExceptT :: forall e m a. ExceptT e m a > m (Either e a)
The MonadError
class captures those monads which support throwing and catching of errors of some type e
, and an instance is provided for the ExceptT e
monad transformer. The throwError
action can be used to indicate failure, just like Left
in the Either e
monad. The catchError
action allows us to continue after an error is thrown using throwError
.
The runExceptT
handler is used to run a computation of type ExceptT e m a
.
This API is similar to that provided by the exceptions
package and the Exception
effect. However, there are some important differences:
Exception
uses actual JavaScript exceptions, whereasExceptT
models errors as a pure data structure. The
Exception
effect only supports exceptions of one type, namely JavaScript'sError
type, whereasExceptT
supports errors of any type. In particular, we are free to define new error types.
Let's try out ExceptT
by using it to wrap the Writer
monad. Again, we are free to use actions from the monad transformer ExceptT e
directly, but computations in the Writer
monad should be lifted using lift
:
import Control.Monad.Trans
import Control.Monad.Writer
import Control.Monad.Writer.Class
import Control.Monad.Error.Class
import Control.Monad.Except.Trans
writerAndExceptT :: ExceptT String (Writer (Array String)) String
writerAndExceptT = do
lift $ tell ["Before the error"]
throwError "Error!"
lift $ tell ["After the error"]
pure "Return value"
If we test this function in PSCi, we can see how the two effects of accumulating a log and throwing an error interact. First, we can run the outer ExceptT
computation of type by using runExceptT
, leaving a result of type Writer String (Either String String)
. We can then use runWriter
to run the inner Writer
computation:
> runWriter $ runExceptT writerAndExceptT
Tuple (Left "Error!") ["Before the error"]
Note that only those log messages which were written before the error was thrown actually get appended to the log.
Monad Transformer Stacks
As we have seen, monad transformers can be used to build new monads on top of existing monads. For some monad transformer t1
and some monad m
, the application t1 m
is also a monad. That means that we can apply a second monad transformer t2
to the result t1 m
to construct a third monad t2 (t1 m)
. In this way, we can construct a stack of monad transformers, which combine the sideeffects provided by their constituent monads.
In practice, the underlying monad m
is either the Effect
monad, if native sideeffects are required, or the Identity
monad, defined in the Data.Identity
module. The Identity
monad adds no new sideeffects, so transforming the Identity
monad only provides the effects of the monad transformer. In fact, the State
, Reader
and Writer
monads are implemented by transforming the Identity
monad with StateT
, ReaderT
and WriterT
respectively.
Let's see an example in which three side effects are combined. We will use the StateT
, WriterT
and ExceptT
effects, with the Identity
monad on the bottom of the stack. This monad transformer stack will provide the side effects of mutable state, accumulating a log, and pure errors.
We can use this monad transformer stack to reproduce our split
action with the added feature of logging.
type Errors = Array String
type Log = Array String
type Parser = StateT String (WriterT Log (ExceptT Errors Identity))
split :: Parser String
split = do
s < get
lift $ tell ["The state is " <> s]
case s of
"" > lift $ lift $ throwError ["Empty string"]
_ > do
put (drop 1 s)
pure (take 1 s)
If we test this computation in PSCi, we see that the state is appended to the log for every invocation of split
.
Note that we have to remove the sideeffects in the order in which they appear in the monad transformer stack: first we use runStateT
to remove the StateT
type constructor, then runWriterT
, then runExceptT
. Finally, we run the computation in the Identity
monad by using unwrap
.
> runParser p s = unwrap $ runExceptT $ runWriterT $ runStateT p s
> runParser split "test"
(Right (Tuple (Tuple "t" "est") ["The state is test"]))
> runParser ((<>) <$> split <*> split) "test"
(Right (Tuple (Tuple "te" "st") ["The state is test", "The state is est"]))
However, if the parse is unsuccessful because the state is empty, then no log is printed at all:
> runParser split ""
(Left ["Empty string"])
This is because of the way in which the sideeffects provided by the ExceptT
monad transformer interact with the sideeffects provided by the WriterT
monad transformer. We can address this by changing the order in which the monad transformer stack is composed. If we move the ExceptT
transformer to the top of the stack, then the log will contain all messages written up until the first error, as we saw earlier when we transformed Writer
with ExceptT
.
One problem with this code is that we have to use the lift
function multiple times to lift computations over multiple monad transformers: for example, the call to throwError
has to be lifted twice, once over WriterT
and a second time over StateT
. This is fine for small monad transformer stacks, but quickly becomes inconvenient.
Fortunately, as we will see, we can use the automatic code generation provided by type class inference to do most of this "heavy lifting" for us.
Exercises

(Easy) Use the
ExceptT
monad transformer over theIdentity
functor to write a functionsafeDivide
which divides two numbers, throwing an error if the denominator is zero. 
(Medium) Write a parser
string :: String > Parser String
which matches a string as a prefix of the current state, or fails with an error message.
Your parser should work as follows:
> runParser (string "abc") "abcdef" (Right (Tuple (Tuple "abc" "def") ["The state is abcdef"]))
Hint: you can use the implementation of
split
as a starting point. You might find thestripPrefix
function useful. 
(Difficult) Use the
ReaderT
andWriterT
monad transformers to reimplement the document printing library which we wrote earlier using theReader
monad.Instead of using
line
to emit strings andcat
to concatenate strings, use theArray String
monoid with theWriterT
monad transformer, andtell
to append a line to the result.
Type Classes to the Rescue!
When we looked at the State
monad at the start of this chapter, I gave the following types for the actions of the State
monad:
get :: forall s. State s s
put :: forall s. s > State s Unit
modify :: forall s. (s > s) > State s Unit
In reality, the types given in the Control.Monad.State.Class
module are more general than this:
get :: forall m s. MonadState s m => m s
put :: forall m s. MonadState s m => s > m Unit
modify :: forall m s. MonadState s m => (s > s) > m Unit
The Control.Monad.State.Class
module defines the MonadState
(multiparameter) type class, which allows us to abstract over "monads which support pure mutable state". As one would expect, the State s
type constructor is an instance of the MonadState s
type class, but there are many more interesting instances of this class.
In particular, there are instances of MonadState
for the WriterT
, ReaderT
and ExceptT
monad transformers, provided in the transformers
package. Each of these monad transformers has an instance for MonadState
whenever the underlying Monad
does. In practice, this means that as long as StateT
appears somewhere in the monad transformer stack, and everything above StateT
is an instance of MonadState
, then we are free to use get
, put
and modify
directly, without the need to use lift
.
Indeed, the same is true of the actions we covered for the ReaderT
, WriterT
, and ExceptT
transformers. transformers
defines a type class for each of the major transformers, allowing us to abstract over monads which support their operations.
In the case of the split
function above, the monad stack we constructed is an instance of each of the MonadState
, MonadWriter
and MonadError
type classes. This means that we don't need to call lift
at all! We can just use the actions get
, put
, tell
and throwError
as if they were defined on the monad stack itself:
split :: Parser String
split = do
s < get
tell ["The state is " <> show s]
case s of
"" > throwError "Empty string"
_ > do
put (drop 1 s)
pure (take 1 s)
This computation really looks like we have extended our programming language to support the three new sideeffects of mutable state, logging and error handling. However, everything is still implemented using pure functions and immutable data under the hood.
Alternatives
The control
package defines a number of abstractions for working with computations which can fail. One of these is the Alternative
type class:
class Functor f <= Alt f where
alt :: forall a. f a > f a > f a
class Alt f <= Plus f where
empty :: forall a. f a
class (Applicative f, Plus f) <= Alternative f
Alternative
provides two new combinators: the empty
value, which provides a prototype for a failing computation, and the alt
function (and its alias, <>
) which provides the ability to fall back to an alternative computation in the case of an error.
The Data.Array
module provides two useful functions for working with type constructors in the Alternative
type class:
many :: forall f a. Alternative f => Lazy (f (Array a)) => f a > f (Array a)
some :: forall f a. Alternative f => Lazy (f (Array a)) => f a > f (Array a)
There is also an equivalent many
and some
for Data.List
The many
combinator uses the Alternative
type class to repeatedly run a computation zeroormore times. The some
combinator is similar, but requires at least the first computation to succeed.
In the case of our Parser
monad transformer stack, there is an instance of Alternative
induced by the ExceptT
component, which supports failure by composing errors in different branches using a Monoid
instance (this is why we chose Array String
for our Errors
type). This means that we can use the many
and some
functions to run a parser multiple times:
> import Data.Array (many)
> runParser (many split) "test"
(Right (Tuple (Tuple ["t", "e", "s", "t"] "")
[ "The state is \"test\""
, "The state is \"est\""
, "The state is \"st\""
, "The state is \"t\""
]))
Here, the input string "test"
has been repeatedly split to return an array of four singlecharacter strings, the leftover state is empty, and the log shows that we applied the split
combinator four times.
Monad Comprehensions
The Control.MonadPlus
module defines a subclass of the Alternative
type class, called MonadPlus
. MonadPlus
captures those type constructors which are both monads and instances of Alternative
:
class (Monad m, Alternative m) <= MonadZero m
class MonadZero m <= MonadPlus m
In particular, our Parser
monad is an instance of MonadPlus
.
When we covered array comprehensions earlier in the book, we introduced the guard
function, which could be used to filter out unwanted results. In fact, the guard
function is more general, and can be used for any monad which is an instance of MonadPlus
:
guard :: forall m. MonadZero m => Boolean > m Unit
The <>
operator allows us to backtrack in case of failure. To see how this is useful, let's define a variant of the split
combinator which only matches upper case characters:
upper :: Parser String
upper = do
s < split
guard $ toUpper s == s
pure s
Here, we use a guard
to fail if the string is not upper case. Note that this code looks very similar to the array comprehensions we saw earlier  using MonadPlus
in this way, we sometimes refer to constructing monad comprehensions.
Backtracking
We can use the <>
operator to backtrack to another alternative in case of failure. To demonstrate this, let's define one more parser, which matches lower case characters:
lower :: Parser String
lower = do
s < split
guard $ toLower s == s
pure s
With this, we can define a parser which eagerly matches many upper case characters if the first character is upper case, or many lower case character if the first character is lower case:
> upperOrLower = some upper <> some lower
This parser will match characters until the case changes:
> runParser upperOrLower "abcDEF"
(Right (Tuple (Tuple ["a","b","c"] ("DEF"))
[ "The state is \"abcDEF\""
, "The state is \"bcDEF\""
, "The state is \"cDEF\""
]))
We can even use many
to fully split a string into its lower and upper case components:
> components = many upperOrLower
> runParser components "abCDeFgh"
(Right (Tuple (Tuple [["a","b"],["C","D"],["e"],["F"],["g","h"]] "")
[ "The state is \"abCDeFgh\""
, "The state is \"bCDeFgh\""
, "The state is \"CDeFgh\""
, "The state is \"DeFgh\""
, "The state is \"eFgh\""
, "The state is \"Fgh\""
, "The state is \"gh\""
, "The state is \"h\""
]))
Again, this illustrates the power of reusability that monad transformers bring  we were able to write a backtracking parser in a declarative style with only a few lines of code, by reusing standard abstractions!
Exercises

(Easy) Remove the calls to the
lift
function from your implementation of thestring
parser. Verify that the new implementation type checks, and convince yourself that it should. 
(Medium) Use your
string
parser with themany
combinator to write a parser which recognizes strings consisting of several copies of the string"a"
followed by several copies of the string"b"
. 
(Medium) Use the
<>
operator to write a parser which recognizes strings of the lettersa
orb
in any order. 
(Difficult) The
Parser
monad might also be defined as follows:type Parser = ExceptT Errors (StateT String (WriterT Log Identity))
What effect does this change have on our parsing functions?
The RWS Monad
One particular combination of monad transformers is so common that it is provided as a single monad transformer in the transformers
package. The Reader
, Writer
and State
monads are combined into the readerwriterstate monad, or more simply the RWS
monad. This monad has a corresponding monad transformer called the RWST
monad transformer.
We will use the RWS
monad to model the game logic for our text adventure game.
The RWS
monad is defined in terms of three type parameters (in addition to its return type):
type RWS r w s = RWST r w s Identity
Notice that the RWS
monad is defined in terms of its own monad transformer, by setting the base monad to Identity
which provides no sideeffects.
The first type parameter, r
, represents the global configuration type. The second, w
, represents the monoid which we will use to accumulate a log, and the third, s
is the type of our mutable state.
In the case of our game, our global configuration is defined in a type called GameEnvironment
in the Data.GameEnvironment
module:
type PlayerName = String
newtype GameEnvironment = GameEnvironment
{ playerName :: PlayerName
, debugMode :: Boolean
}
It defines the player name, and a flag which indicates whether or not the game is running in debug mode. These options will be set from the command line when we come to run our monad transformer.
The mutable state is defined in a type called GameState
in the Data.GameState
module:
import qualified Data.Map as M
import qualified Data.Set as S
newtype GameState = GameState
{ items :: M.Map Coords (S.Set GameItem)
, player :: Coords
, inventory :: S.Set GameItem
}
The Coords
data type represents points on a twodimensional grid, and the GameItem
data type is an enumeration of the items in the game:
data GameItem = Candle  Matches
The GameState
type uses two new data structures: Map
and Set
, which represent sorted maps and sorted sets respectively. The items
property is a mapping from coordinates of the game grid to sets of game items at that location. The player
property stores the current coordinates of the player, and the inventory
property stores a set of game items currently held by the player.
The Map
and Set
data structures are sorted by their keys, can be used with any key type in the Ord
type class. This means that the keys in our data structures should be totally ordered.
We will see how the Map
and Set
structures are used as we write the actions for our game.
For our log, we will use the List String
monoid. We can define a type synonym for our Game
monad, implemented using RWS
:
type Log = L.List String
type Game = RWS GameEnvironment Log GameState
Implementing Game Logic
Our game is going to be built from simple actions defined in the Game
monad, by reusing the actions from the Reader
, Writer
and State
monads. At the top level of our application, we will run the pure computations in the Game
monad, and use the Effect
monad to turn the results into observable sideeffects, such as printing text to the console.
One of the simplest actions in our game is the has
action. This action tests whether the player's inventory contains a particular game item. It is defined as follows:
has :: GameItem > Game Boolean
has item = do
GameState state < get
pure $ item `S.member` state.inventory
This function uses the get
action defined in the MonadState
type class to read the current game state, and then uses the member
function defined in Data.Set
to test whether the specified GameItem
appears in the Set
of inventory items.
Another action is the pickUp
action. It adds a game item to the player's inventory if it appears in the current room. It uses actions from the MonadWriter
and MonadState
type classes. First of all, it reads the current game state:
pickUp :: GameItem > Game Unit
pickUp item = do
GameState state < get
Next, pickUp
looks up the set of items in the current room. It does this by using the lookup
function defined in Data.Map
:
case state.player `M.lookup` state.items of
The lookup
function returns an optional result indicated by the Maybe
type constructor. If the key does not appear in the map, the lookup
function returns Nothing
, otherwise it returns the corresponding value in the Just
constructor.
We are interested in the case where the corresponding item set contains the specified game item. Again we can test this using the member
function:
Just items  item `S.member` items > do
In this case, we can use put
to update the game state, and tell
to add a message to the log:
let newItems = M.update (Just <<< S.delete item) state.player state.items
newInventory = S.insert item state.inventory
put $ GameState state { items = newItems
, inventory = newInventory
}
tell (L.singleton ("You now have the " <> show item))
Note that there is no need to lift
either of the two computations here, because there are appropriate instances for both MonadState
and MonadWriter
for our Game
monad transformer stack.
The argument to put
uses a record update to modify the game state's items
and inventory
fields. We use the update
function from Data.Map
which modifies a value at a particular key. In this case, we modify the set of items at the player's current location, using the delete
function to remove the specified item from the set. inventory
is also updated, using insert
to add the new item to the player's inventory set.
Finally, the pickUp
function handles the remaining cases, by notifying the user using tell
:
_ > tell (L.singleton "I don't see that item here.")
As an example of using the Reader
monad, we can look at the code for the debug
command. This command allows the user to inspect the game state at runtime if the game is running in debug mode:
GameEnvironment env < ask
if env.debugMode
then do
state < get
tell (L.singleton (show state))
else tell (L.singleton "Not running in debug mode.")
Here, we use the ask
action to read the game configuration. Again, note that we don't need to lift
any computation, and we can use actions defined in the MonadState
, MonadReader
and MonadWriter
type classes in the same do notation block.
If the debugMode
flag is set, then the tell
action is used to write the state to the log. Otherwise, an error message is added.
The remainder of the Game
module defines a set of similar actions, each using only the actions defined by the MonadState
, MonadReader
and MonadWriter
type classes.
Running the Computation
Since our game logic runs in the RWS
monad, it is necessary to run the computation in order to respond to the user's commands.
The frontend of our game is built using two packages: yargs
, which provides an applicative interface to the yargs
command line parsing library, and nodereadline
, which wraps NodeJS' readline
module, allowing us to write interactive consolebased applications.
The interface to our game logic is provided by the function game
in the Game
module:
game :: Array String > Game Unit
To run this computation, we pass a list of words entered by the user as an array of strings, and run the resulting RWS
computation using runRWS
:
data RWSResult state result writer = RWSResult state result writer
runRWS :: forall r w s a. RWS r w s a > r > s > RWSResult s a w
runRWS
looks like a combination of runReader
, runWriter
and runState
. It takes a global configuration and an initial state as an argument, and returns a data structure containing the log, the result and the final state.
The frontend of our application is defined by a function runGame
, with the following type signature:
runGame :: GameEnvironment > Effect Unit
This function interacts with the user via the console (using the nodereadline
and console
packages). runGame
takes the game configuration as a function argument.
The nodereadline
package provides the LineHandler
type, which represents actions in the Effect
monad which handle user input from the terminal. Here is the corresponding API:
type LineHandler a = String > Effect a
foreign import setLineHandler
:: forall a
. Interface
> LineHandler a
> Effect Unit
The Interface
type represents a handle for the console, and is passed as an argument to the functions which interact with it. An Interface
can be created using the createConsoleInterface
function:
import Node.ReadLine as RL
runGame env = do
interface < RL.createConsoleInterface RL.noCompletion
The first step is to set the prompt at the console. We pass the interface
handle, and provide the prompt string and indentation level:
RL.setPrompt "> " 2 interface
In our case, we are interested in implementing the line handler function. Our line handler is defined using a helper function in a let
declaration, as follows:
lineHandler :: GameState > String > Effect Unit
lineHandler currentState input = do
case runRWS (game (split (wrap " ") input)) env currentState of
RWSResult state _ written > do
for_ written log
RL.setLineHandler interface $ lineHandler state
RL.prompt interface
pure unit
The let
binding is closed over both the game configuration, named env
, and the console handle, named interface
.
Our handler takes an additional first argument, the game state. This is required since we need to pass the game state to runRWS
to run the game's logic.
The first thing this action does is to break the user input into words using the split
function from the Data.String
module. It then uses runRWS
to run the game
action (in the RWS
monad), passing the game environment and current game state.
Having run the game logic, which is a pure computation, we need to print any log messages to the screen and show the user a prompt for the next command. The for_
action is used to traverse the log (of type List String
) and print its entries to the console. Finally, setLineHandler
is used to update the line handler function to use the updated game state, and the prompt is displayed again using the prompt
action.
The runGame
function finally attaches the initial line handler to the console interface, and displays the initial prompt:
RL.setLineHandler interface $ lineHandler initialGameState
RL.prompt interface
Exercises

(Medium) Implement a new command
cheat
, which moves all game items from the game grid into the user's inventory. 
(Difficult) The
Writer
component of theRWS
monad is currently used for two types of messages: error messages and informational messages. Because of this, several parts of the code use case statements to handle error cases.Refactor the code to use the
ExceptT
monad transformer to handle the error messages, andRWS
to handle informational messages.
Handling Command Line Options
The final piece of the application is responsible for parsing command line options and creating the GameEnvironment
configuration record. For this, we use the yargs
package.
yargs
is an example of applicative command line option parsing. Recall that an applicative functor allows us to lift functions of arbitrary arity over a type constructor representing some type of sideeffect. In the case of the yargs
package, the functor we are interested in is the Y
functor, which adds the sideeffect of reading from command line options. It provides the following handler:
runY :: forall a. YargsSetup > Y (Effect a) > Effect a
This is best illustrated by example. The application's main
function is defined using runY
as follows:
main = runY (usage "$0 p <player name>") $ map runGame env
The first argument is used to configure the yargs
library. In our case, we simply provide a usage message, but the Node.Yargs.Setup
module provides several other options.
The second argument uses the map
function to lift the runGame
function over the Y
type constructor. The argument env
is constructed in a where
declaration using the applicative operators <$>
and <*>
:
where
env :: Y GameEnvironment
env = gameEnvironment
<$> yarg "p" ["player"]
(Just "Player name")
(Right "The player name is required")
false
<*> flag "d" ["debug"]
(Just "Use debug mode")
Here, the gameEnvironment
function, which has the type PlayerName > Boolean > GameEnvironment
, is lifted over Y
. The two arguments specify how to read the player name and debug flag from the command line options. The first argument describes the player name option, which is specified by the p
or player
options, and the second describes the debug mode flag, which is turned on using the d
or debug
options.
This demonstrates two basic functions defined in the Node.Yargs.Applicative
module: yarg
, which defines a command line option which takes an optional argument (of type String
, Number
or Boolean
), and flag
which defines a command line flag of type Boolean
.
Notice how we were able to use the notation afforded by the applicative operators to give a compact, declarative specification of our command line interface. In addition, it is simple to add new command line arguments, simply by adding a new function argument to runGame
, and then using <*>
to lift runGame
over an additional argument in the definition of env
.
Exercises
 (Medium) Add a new Booleanvalued property
cheatMode
to theGameEnvironment
record. Add a new command line flagc
to theyargs
configuration which enables cheat mode. Thecheat
command from the previous exercise should be disallowed if cheat mode is not enabled.
Conclusion
This chapter was a practical demonstration of the techniques we've learned so far, using monad transformers to build a pure specification of our game, and the Effect
monad to build a frontend using the console.
Because we separated our implementation from the user interface, it would be possible to create other frontends for our game. For example, we could use the Effect
monad to render the game in the browser using the Canvas API or the DOM.
We have seen how monad transformers allow us to write safe code in an imperative style, where effects are tracked by the type system. In addition, type classes provide a powerful way to abstract over the actions provided by a monad, enabling code reuse. We were able to use standard abstractions like Alternative
and MonadPlus
to build useful monads by combining standard monad transformers.
Monad transformers are an excellent demonstration of the sort of expressive code that can be written by relying on advanced type system features such as higherkinded polymorphism and multiparameter type classes.
In the next chapter, we will see how monad transformers can be used to give an elegant solution to a common complaint when working with asynchronous JavaScript code  the problem of callback hell.