chapter8

The Effect and Aff Monads

Chapter Goals

In the last chapter, we introduced applicative functors, an abstraction which we used to deal with side-effects: optional values, error messages and validation. This chapter will introduce another abstraction for dealing with side-effects in a more expressive way: monads.

The goal of this chapter is to explain why monads are a useful abstraction, and their connection with do notation. We will also learn how to do computations with asynchronous side-effects.

Project Setup

The project adds the following dependencies:

  • effect, which defines the Effect monad, the subject of the second half of the chapter.

  • aff, an asynchronous effect monad.

  • random, a monadic random number generator.

Monads and Do Notation

Do notation was first introduced when we covered array comprehensions. Array comprehensions provide syntactic sugar for the concatMap function from the Data.Array module.

Consider the following example. Suppose we throw two dice and want to count the number of ways in which we can score a total of n. We could do this using the following non-deterministic algorithm:

  • Choose the value x of the first throw.

  • Choose the value y of the second throw.

  • If the sum of x and y is n then return the pair [x, y], else fail.

Array comprehensions allow us to write this non-deterministic algorithm in a natural way:

import Prelude

import Control.Plus (empty)
import Data.Array ((..))

countThrows :: Int -> Array (Array Int)
countThrows n = do
  x <- 1 .. 6
  y <- 1 .. 6
  if x + y == n
    then pure [x, y]
    else empty

We can see that this function works in PSCi:

> countThrows 10
[[4,6],[5,5],[6,4]]

> countThrows 12  
[[6,6]]

In the last chapter, we formed an intuition for the Maybe applicative functor, embedding PureScript functions into a larger programming language supporting optional values. In the same way, we can form an intuition for the array monad, embedding PureScript functions into a larger programming language supporting non-deterministic choice.

In general, a monad for some type constructor m provides a way to use do notation with values of type m a. Note that in the array comprehension above, every line contains a computation of type Array a for some type a. In general, every line of a do notation block will contain a computation of type m a for some type a and our monad m. The monad m must be the same on every line (i.e. we fix the side-effect), but the types a can differ (i.e. individual computations can have different result types).

Here is another example of do notation, this type applied to the type constructor Maybe. Suppose we have some type XML representing XML nodes, and a function

child :: XML -> String -> Maybe XML

which looks for a child element of a node, and returns Nothing if no such element exists.

In this case, we can look for a deeply-nested element by using do notation. Suppose we wanted to read a user's city from a user profile which had been encoded as an XML document:

userCity :: XML -> Maybe XML
userCity root = do
  prof <- child root "profile"
  addr <- child prof "address"
  city <- child addr "city"
  pure city

The userCity function looks for a child element profile, an element address inside the profile element, and finally an element city inside the address element. If any of these elements are missing, the return value will be Nothing. Otherwise, the return value is constructed using Just from the city node.

Remember, the pure function in the last line is defined for every Applicative functor. Since pure is defined as Just for the Maybe applicative functor, it would be equally valid to change the last line to Just city.

The Monad Type Class

The Monad type class is defined as follows:

class Apply m <= Bind m where
  bind :: forall a b. m a -> (a -> m b) -> m b

class (Applicative m, Bind m) <= Monad m

The key function here is bind, defined in the Bind type class. Just like for the <$> and <*> operators in the Functor and Apply type classes, the Prelude defines an infix alias >>= for the bind function.

The Monad type class extends Bind with the operations of the Applicative type class that we have already seen.

It will be useful to see some examples of the Bind type class. A sensible definition for Bind on arrays can be given as follows:

instance bindArray :: Bind Array where
  bind xs f = concatMap f xs

This explains the connection between array comprehensions and the concatMap function that has been alluded to before.

Here is an implementation of Bind for the Maybe type constructor:

instance bindMaybe :: Bind Maybe where
  bind Nothing  _ = Nothing
  bind (Just a) f = f a

This definition confirms the intuition that missing values are propagated through a do notation block.

Let's see how the Bind type class is related to do notation. Consider a simple do notation block which starts by binding a value from the result of some computation:

do value <- someComputation
   whatToDoNext

Every time the PureScript compiler sees this pattern, it replaces the code with this:

bind someComputation \value -> whatToDoNext

or, written infix:

someComputation >>= \value -> whatToDoNext

The computation whatToDoNext is allowed to depend on value.

If there are multiple binds involved, this rule is applied multiple times, starting from the top. For example, the userCity example that we saw earlier gets desugared as follows:

userCity :: XML -> Maybe XML
userCity root =
  child root "profile" >>= \prof ->
    child prof "address" >>= \addr ->
      child addr "city" >>= \city ->
        pure city

It is worth noting that code expressed using do notation is often much clearer than the equivalent code using the >>= operator. However, writing binds explicitly using >>= can often lead to opportunities to write code in point-free form - but the usual warnings about readability apply.

Monad Laws

The Monad type class comes equipped with three laws, called the monad laws. These tell us what we can expect from sensible implementations of the Monad type class.

It is simplest to explain these laws using do notation.

Identity Laws

The right-identity law is the simplest of the three laws. It tells us that we can eliminate a call to pure if it is the last expression in a do notation block:

do
  x <- expr
  pure x

The right-identity law says that this is equivalent to just expr.

The left-identity law states that we can eliminate a call to pure if it is the first expression in a do notation block:

do
  x <- pure y
  next

This code is equivalent to next, after the name x has been replaced with the expression y.

The last law is the associativity law. It tells us how to deal with nested do notation blocks. It states that the following piece of code:

c1 = do
  y <- do
    x <- m1
    m2
  m3

is equivalent to this code:

c2 = do
  x <- m1
  y <- m2
  m3

Each of these computations involves three monadic expression m1, m2 and m3. In each case, the result of m1 is eventually bound to the name x, and the result of m2 is bound to the name y.

In c1, the two expressions m1 and m2 are grouped into their own do notation block.

In c2, all three expressions m1, m2 and m3 appear in the same do notation block.

The associativity law tells us that it is safe to simplify nested do notation blocks in this way.

Note that by the definition of how do notation gets desugared into calls to bind, both of c1 and c2 are also equivalent to this code:

c3 = do
  x <- m1
  do
    y <- m2
    m3

Folding With Monads

As an example of working with monads abstractly, this section will present a function which works with any type constructor in the Monad type class. This should serve to solidify the intuition that monadic code corresponds to programming "in a larger language" with side-effects, and also illustrate the generality which programming with monads brings.

The function we will write is called foldM. It generalizes the foldl function that we met earlier to a monadic context. Here is its type signature:

foldM :: forall m a b
       . Monad m
      => (a -> b -> m a)
      -> a
      -> List b
      -> m a

Notice that this is the same as the type of foldl, except for the appearance of the monad m:

foldl :: forall a b
       . (a -> b -> a)
      -> a
      -> List b
      -> a

Intuitively, foldM performs a fold over a list in some context supporting some set of side-effects.

For example, if we picked m to be Maybe, then our fold would be allowed to fail by returning Nothing at any stage - every step returns an optional result, and the result of the fold is therefore also optional.

If we picked m to be the Array type constructor, then every step of the fold would be allowed to return zero or more results, and the fold would proceed to the next step independently for each result. At the end, the set of results would consist of all folds over all possible paths. This corresponds to a traversal of a graph!

To write foldM, we can simply break the input list into cases.

If the list is empty, then to produce the result of type a, we only have one option: we have to return the second argument:

foldM _ a Nil = pure a

Note that we have to use pure to lift a into the monad m.

What if the list is non-empty? In that case, we have a value of type a, a value of type b, and a function of type a -> b -> m a. If we apply the function, we obtain a monadic result of type m a. We can bind the result of this computation with a backwards arrow <-.

It only remains to recurse on the tail of the list. The implementation is simple:

foldM f a (b : bs) = do
  a' <- f a b
  foldM f a' bs

Note that this implementation is almost identical to that of foldl on lists, with the exception of do notation.

We can define and test this function in PSCi. Here is an example - suppose we defined a "safe division" function on integers, which tested for division by zero and used the Maybe type constructor to indicate failure:

safeDivide :: Int -> Int -> Maybe Int
safeDivide _ 0 = Nothing
safeDivide a b = Just (a / b)

Then we can use foldM to express iterated safe division:

> import Data.List

> foldM safeDivide 100 (fromFoldable [5, 2, 2])
(Just 5)

> foldM safeDivide 100 (fromFoldable [2, 0, 4])
Nothing

The foldM safeDivide function returns Nothing if a division by zero was attempted at any point. Otherwise it returns the result of repeatedly dividing the accumulator, wrapped in the Just constructor.

Monads and Applicatives

Every instance of the Monad type class is also an instance of the Applicative type class, by virtue of the superclass relationship between the two classes.

However, there is also an implementation of the Applicative type class which comes "for free" for any instance of Monad, given by the ap function:

ap :: forall m a b. Monad m => m (a -> b) -> m a -> m b
ap mf ma = do
  f <- mf
  a <- ma
  pure (f a)

If m is a law-abiding member of the Monad type class, then there is a valid Applicative instance for m given by ap.

The interested reader can check that ap agrees with apply for the monads we have already encountered: Array, Maybe and Either e.

If every monad is also an applicative functor, then we should be able to apply our intuition for applicative functors to every monad. In particular, we can reasonably expect a monad to correspond, in some sense, to programming "in a larger language" augmented with some set of additional side-effects. We should be able to lift functions of arbitrary arities, using map and apply, into this new language.

But monads allow us to do more than we could do with just applicative functors, and the key difference is highlighted by the syntax of do notation. Consider the userCity example again, in which we looked for a user's city in an XML document which encoded their user profile:

userCity :: XML -> Maybe XML
userCity root = do
  prof <- child root "profile"
  addr <- child prof "address"
  city <- child addr "city"
  pure city

Do notation allows the second computation to depend on the result prof of the first, and the third computation to depend on the result addr of the second, and so on. This dependence on previous values is not possible using only the interface of the Applicative type class.

Try writing userCity using only pure and apply: you will see that it is impossible. Applicative functors only allow us to lift function arguments which are independent of each other, but monads allow us to write computations which involve more interesting data dependencies.

In the last chapter, we saw that the Applicative type class can be used to express parallelism. This was precisely because the function arguments being lifted were independent of one another. Since the Monad type class allows computations to depend on the results of previous computations, the same does not apply - a monad has to combine its side-effects in sequence.

Exercises

  1. (Easy) Look up the types of the head and tail functions from the Data.Array module in the arrays package. Use do notation with the Maybe monad to combine these functions into a function third which returns the third element of an array with three or more elements. Your function should return an appropriate Maybe type.

  2. (Medium) Write a function sums which uses foldM to determine all possible totals that could be made using a set of coins. The coins will be specified as an array which contains the value of each coin. Your function should have the following result:

     > sums []
 [0]

 > sums [1, 2, 10]
 [0,1,2,3,10,11,12,13]

    Hint: This function can be written as a one-liner using foldM. You might want to use the nub and sort functions to remove duplicates and sort the result respectively.

  3. (Medium) Confirm that the ap function and the apply operator agree for the Maybe monad.

  4. (Medium) Verify that the monad laws hold for the Monad instance for the Maybe type, as defined in the maybe package.

  5. (Medium) Write a function filterM which generalizes the filter function on lists. Your function should have the following type signature:

     filterM :: forall m a. Monad m => (a -> m Boolean) -> List a -> m (List a)

    Test your function in PSCi using the Maybe and Array monads.

  6. (Difficult) Every monad has a default Functor instance given by:

     map f a = do
   x <- a
   pure (f x)

    Use the monad laws to prove that for any monad, the following holds:

     lift2 f (pure a) (pure b) = pure (f a b)

    where the Applicative instance uses the ap function defined above. Recall that lift2 was defined as follows:

     lift2 :: forall f a b c. Applicative f => (a -> b -> c) -> f a -> f b -> f c
 lift2 f a b = f <$> a <*> b

Native Effects

We will now look at one particular monad which is of central importance in PureScript - the Effect monad.

The Effect monad is defined in the Effect module. It is used to manage so-called native side-effects. If you are familiar with Haskell, it is the equivalent of the IO monad.

What are native side-effects? They are the side-effects which distinguish JavaScript expressions from idiomatic PureScript expressions, which typically are free from side-effects. Some examples of native effects are:

  • Console IO

  • Random number generation

  • Exceptions

  • Reading/writing mutable state

And in the browser:

  • DOM manipulation

  • XMLHttpRequest / AJAX calls

  • Interacting with a websocket

  • Writing/reading to/from local storage

We have already seen plenty of examples of "non-native" side-effects:

  • Optional values, as represented by the Maybe data type

  • Errors, as represented by the Either data type

  • Multi-functions, as represented by arrays or lists

Note that the distinction is subtle. It is true, for example, that an error message is a possible side-effect of a JavaScript expression, in the form of an exception. In that sense, exceptions do represent native side-effects, and it is possible to represent them using Effect. However, error messages implemented using Either are not a side-effect of the JavaScript runtime, and so it is not appropriate to implement error messages in that style using Effect. So it is not the effect itself which is native, but rather how it is implemented at runtime.

Side-Effects and Purity

In a pure language like PureScript, one question which presents itself is: without side-effects, how can one write useful real-world code?

The answer is that PureScript does not aim to eliminate side-effects. It aims to represent side-effects in such a way that pure computations can be distinguished from computations with side-effects in the type system. In this sense, the language is still pure.

Values with side-effects have different types from pure values. As such, it is not possible to pass a side-effecting argument to a function, for example, and have side-effects performed unexpectedly.

The only way in which side-effects managed by the Effect monad will be presented is to run a computation of type Effect a from JavaScript.

The Spago build tool (and other tools) provide a shortcut, by generating additional JavaScript to invoke the main computation when the application starts. main is required to be a computation in the Effect monad.

The Effect Monad

The goal of the Effect monad is to provide a well-typed API for computations with side-effects, while at the same time generating efficient JavaScript.

Here is an example. It uses the random package, which defines functions for generating random numbers:

module Main where

import Prelude

import Effect (Effect)
import Effect.Random (random)
import Effect.Console (logShow)

main :: Effect Unit
main = do
  n <- random
  logShow n

If this file is saved as src/Main.purs, then it can be compiled and run using Spago:

$ spago run

Running this command, you will see a randomly chosen number between 0 and 1 printed to the console.

This program uses do notation to combine two native effects provided by the JavaScript runtime: random number generation and console IO.

As mentioned previously, the Effect monad is of central importance to PureScript. The reason why it's central is because it is the conventional way to interoperate with PureScript's Foreign Function Interface, which provides the mechanism to execute a program and perform side effects. While it's desireable to avoid using the Foreign Function Interface, it's fairly critical to understand how it works and how to use it, so I recommend reading that chapter before doing any serious PureScript work. That said, the Effect monad is fairly simple. It has a few helper functions, but aside from that it doesn't do much except encapsulate side effects.

The Aff Monad

The Aff monad is an asynchronous effect monad and threading model for PureScipt.

Asynchrony is typically achieved in JavaScript with callbacks, for example:

function asyncFunction(onSuccess, onError){ ... }

The same thing can be modeled with the Effect monad:

asyncFunction :: forall success error. (success -> Effect Unit) -> (error -> Effect Unit) -> Effect Unit 
asyncFunction onSuccess onError = ...

But as is true in JavaScript, this can quickly get out of hand and result in "callback hell".

The Aff monad solves this problem similar to how Promise solves it in JavaScript, and there is a great library called aff-promise that provides interop with JavaScript Promise.

Effect to Aff and Aff to Effect

Any synchronous Effect can by lifted into an asynchronous Aff with liftEffect. Similarly, any Aff can be converted to an Effect Unit with launchAff_. Below is the code that prints a random number in terms of Aff, written in a few different styles:

module Main where

import Prelude

import Effect (Effect)
import Effect.Aff (Aff, launchAff_)
import Effect.Class (liftEffect)
import Effect.Console (logShow)
import Effect.Random (random)

printRandomStyle1a :: Aff Unit
printRandomStyle1a = liftEffect doRandom
  where
    doRandom :: Effect Unit
    doRandom = do 
      n <- random
      logShow n

printRandomStyle1b :: Aff Unit
printRandomStyle1b = liftEffect $ do
  n <- random
  logShow n

printRandomStyle2 :: Aff Unit
printRandomStyle2 = do
  n <- liftEffect random
  liftEffect $ logShow n

printRandomStyle3 :: Aff Unit
printRandomStyle3 = do
  n <- random # liftEffect
  (logShow n) # liftEffect


main :: Effect Unit
main = launchAff_  do
  printRandomStyle1a
  printRandomStyle1b
  printRandomStyle2
  printRandomStyle3

printRandomStyle1a and printRandomStyle1b are nearly the same, but the types more explicit in printRandomStyle1a to add additional clarity. In both, the do block results in something with type Effect Unit and is lifted to Aff outside of the do block. In printRandomStyle2, both random and logShow are lifted to Aff inside the do block, which results in an Aff. Often while writing PureScript, you'll encounter cases where Aff and Effect need to be mixed, so style 2 is the more common case. Finally in printRandomStyle3, the liftEffect function has been moved to the right with #, which applies an argument to a function instead of the regular function call with arguments. The purpose of this style is to make the intent of the statement more clear by moving the boilerplate out of the way to the right.

launchAff_ vs launchAff

Aff has two similar functions for converting from an Aff to an Effect:

launchAff_ :: forall a. Aff a -> Effect Unit
launchAff :: forall a. Aff a -> Effect (Fiber a)

launchAff gives back a Fiber wrapped in an Effect. A Fiber is a forked computation that can be joined back into an Aff. You can read more about Fiber in Pursuit, PureScript's library and documentation hub. The important thing to note is that there is no direct way to get the contained value in an Aff once it's been converted to an Effect. For this reason it makes sense to write most of your program in terms of Aff instead of Effect if you intend to perform asynchronous effects. This may sound limiting, but in practice it is not. Your programs are typically started in the main function by wiring up event handlers and listeners, which typically results in a Unit and can be run with launchAff_.

MonadError

Aff has an instance of MonadError, a type class for clean error handling. MonadError is covered in more detail in the Monadic Adventures chapter, so below is just a motivating example.

Imagine you wished to write a quickCheckout function by combining several preexisting functions. Without utilizing MonadError the code might look like the following:

module Main where

import Prelude

import Data.Either (Either(..))
import Effect.Aff (Aff, throwError)
import Effect.Exception (Error)

data UserInfo = UserInfo
data User = User
data Item = Item
data Receipt = Receipt
data Basket = Basket

registerUser :: UserInfo -> Aff (Either Error User)
registerUser user = pure $ Right User

createBasket :: User -> Aff (Either Error Basket)
createBasket user = pure $ Right Basket

addItemToBasket :: Item -> Basket -> Aff (Either Error Basket)
addItemToBasket item basket = pure $ Right basket

purchaseBasket :: User -> Basket -> Aff (Either Error Receipt)
purchaseBasket user basket = pure $ Right Receipt

quickCheckout :: Item -> UserInfo -> Aff (Either Error Receipt)
quickCheckout item userInfo = do
  eitherRegister <- registerUser userInfo
  case eitherRegister of
    Left error -> pure $ Left error
    Right user -> do
      eitherBasket <- createBasket user
      case eitherBasket of
        Left error -> pure $ Left error
        Right basket -> do
          eitherItemInBasket <- addItemToBasket item basket
          case eitherItemInBasket of
            Left error -> pure $ Left error
            Right itemInBasket -> purchaseBasket user itemInBasket

All of the data types and functions (aside from quickCheckout) are stubs, and meant to be ignored aside from their types. Note that quickCheckout is pretty ugly and the error checking is deeply nested. This is because there is a monad (Either) inside of a monad (Aff). Monads don't nicely compose so, we've got to step down into each Aff and check each Either. It's a bit annoying. This is where MonadError can help.

Take a look at the alternate implementation below.

module Main where

import Prelude

import Data.Either (Either(..))
import Effect (Effect)
import Effect.Aff (Aff, launchAff_, throwError, try)
import Effect.Class (liftEffect)
import Effect.Console (log)
import Effect.Exception (Error)

data UserInfo = UserInfo
data User = User
data Item = Item
data Receipt = Receipt
data Basket = Basket

registerUser :: UserInfo -> Aff (Either Error User)
registerUser user = pure $ Right User

createBasket :: User -> Aff (Either Error Basket)
createBasket user = pure $ Right Basket

addItemToBasket :: Item -> Basket -> Aff (Either Error Basket)
addItemToBasket item basket = pure $ Right basket

purchaseBasket :: User -> Basket -> Aff (Either Error Receipt)
purchaseBasket user basket = pure $ Right Receipt

rethrow :: forall a. Aff (Either Error a) -> Aff a
rethrow aff = do
  either <- aff
  case either of
    Left error -> throwError error
    Right a -> pure a

quickCheckout :: Item -> UserInfo -> Aff Receipt
quickCheckout item userInfo = do
  user <- registerUser userInfo # rethrow
  basket <- createBasket user # rethrow
  itemInBasket <- addItemToBasket item basket # rethrow
  purchaseBasket user itemInBasket # rethrow

main :: Effect Unit
main = launchAff_ do
  either <- try $ quickCheckout Item UserInfo
  case either of
    Left error -> log "There was an error checking out!" # liftEffect
    Right _ -> log "Checkout Successful" # liftEffect

Note here that quickCheckout is much cleaner and the intent of the code is much clearer. This is made possible by the rethrow function, which uses throwError from MonadError to eliminate the Either type. Your next question might be, "but what happens to the error?". Notice in the main function, try is called on the result of quickCheckout. try will catch the error thrown by throwError - if one is thrown - and wrap the result in an Either, so you can handle it from there. If one doesn't use try as is done in the main function, then a runtime exception will be thrown. Because you can't really know if upstream code has made use of MonadError it's a good idea to call try on an Aff before converting it into an Effect.

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