Queries in Loops Without a Care in the World

If you’ve interacted with databases when programming, chances are you’ve heard about the “N+1 Selects Problem”, discussed in detail at Use the Index, Luke!. Roughly speaking, this problem is characterised by performing SELECT statements repeatedly inside a loop. For example,

do userIds <- getAllUsers
   users <- for userIds $ \userId -> do
     getUserById userId
   doSomething users

With the above approach, we do one query to find all user ids, and then we do another query for each user id to get user information. The problem is one of efficiency, as it reduces performance in two areas. Firstly, this increases network traffic and incurs more blocking, and it also reduces your ability to actually take advantage of your database to its full potential. The correct solution is to perform a constant amount of queries. Ideally a single query, though even two queries will perform and scale better.

However, I would argue that it’s easier to write code in the above form. I don’t want to have to think about collapsing data into single queries, nor do I want to worry about how to re-associate all that data. To take a more realistic example, lets imagine we are building a system where we have entities that have an owner and a type. If we want to get a list of all entities with their owner and type properties fully expanded, then we have two possibilities. The first is to throw good practice out of the window, and write the obvious solution:

do entities <- getAllEntities
   expandedEntities <- for entities $ \entity -> do
     entityType <- getEntityTypeById (entityTypeId entity)
     entityOwner <- getEntityOwnerById (entityOwnerId entity)
     return $ ExpandedEntity entity entityType entityOwner

   doSomething expandedEntities

This suffers from the “N+1 Selects Problem”, so we should instead collect all our data to perform a single query:

do entities <- getAllEntities
   let entityTypeIds = map entityTypeId entities
       entityOwnerIds = map entityOwnerId entities
   entityTypes <- getEntityTypesById entityTypeIds
   entityOwners <- getEntityOwnersById entityOwnerIds
   doSomething $ flip map entities $ \entity ->
    ExpandedEntity entity
                   (entityTypeId entity `lookup` entityTypes)
                   (entityOwnerId entity `lookup` entityOwners)

Oof. That got a lot more complicated!

Is it possible to write our code in the first way, but have it optimise away to only issue a constant amount of queries? With a little trickery it turns out - yes, we can.

Tell Me What You Want

Before we dive into the code, lets consider how we might reach the solution I’m going to demonstrate. There are two “phases” in our code, and we want to keep the two as separate as possible. In the first phase, we determine a set of keys that should be looked up in the database. I’ll call this the key collection phase. After we’ve got an idea of all these keys, we move onto the next phase, which is the querying phase. In this phase, we perform a query with all the keys we collected earlier, and then we route the results back to the places where the query was originally performed.

The type of keys and the data underlying these keys is determined by the query we are performing. A query for entity types by their id is a query from EntityTypeId to EntityType, whereas a query for entity owners would be from EntityOwnerId to EntityOwner. This suggests a data type parameterized on these two types:

data Query k v

Now, the code performing a query needs to somehow “communicate” with this query, registering both the key that is being queried for, and allowing information to flow back in order to use the query results. We can model this by using some imperative programming constructs (you don’t hear that often!). We’ll use an IORef to keep track of a mapping keys to query with, to MVars which store the result of the query (noting that the query might fail). Thus Query now becomes:

data Query k v = Query (IORef (Map k [MVar (Maybe v)]))

Now we can perform queries by adding a key to the Map inside the Query and providing an MVar for the result to be placed in:

(Query keys) @? k = do
  result <- newEmptyMVar
  modifyIORef' keys (Map.insertWith (++) k [result])

This doesn’t let us use the query result though, so we’ll also return an IO computation to read from the MVar:

(Query keys) @? k = do
  result <- newEmptyMVar
  modifyIORef' keys (Map.insertWith (++) k [result])
  return (takeMVar result)

This is preferred over returning the MVar itself, as we’ll see later that we can guarantee that the MVar is never read from before it is written to (which would hang the whole program indefinitely).

Now that we have some basic building blocks, we need a way to structure this in a safe way. Currently, if you issue a query and immediately ask for a result the whole computation will block. We need to guarantee that query results can only be asked for after performing the query that will populate the MVars. Lets see if we can find a way to both compose these queries in a non-blocking fashion.

Composing

When thinking of a way to compose things, we should first see if there is a well established form of composition that we could use. Monads are used extensively for modelling effects, but they don’t give us the ability to statically analyse the computation before executing it, as the computation can choose what to do next based on what has already happened. For example, consider the following:

do entity <- getEntityById 1
   if entityOwnerId entity `mod` 2 == 0
     then do owner <- getEntityOwnerById (entityOwnerId entity)
             return (entity, Just owner)
     else return (entity, Nothing)

If we only have this to consider, then there’s no way of determining which entity owners to select without running some of the computation. The choice of selecting entity owners depends on the result of the initial call to getEntityById.

However, if we choose a less powerful, though still effectful, structure - namely the applicative functor - then we do get the ability to statically analyse the computation, as we have given up the ability to make branches as above.

So maybe we’ll have luck with the applicative functor, but how do we form it? I like to construct applicative functors somewhat mechanically, so we’ll start by remembering that there were two phases to this computation - the key collection phase and the query phase. Both of these phases need IO - the former to modify an IORef and the latter to take from the result MVar. Applicative functors have the nice property of being closed under composition, and as all monads are applicative functors, we can compose two IO actions into one applicative functor:

newtype Querying a = Querying { runQuerying :: Compose IO IO a }

If you’ve never seen Compose before, allow me to repeat it’s definition here:

newtype Compose f g a = Compose { getCompose :: f (g a) }

instance (Applicative f, Applicative g) => Applicative (Compose f g) where
    pure x = Compose (pure (pure x))
    Compose f <*> Compose x = Compose ((<*>) <$> f <*> x)

The Applicative instance for Compose shows that pure is lifted through both layers, and <*> applies effects at the outer- and the inner-functors (f and g, respectively).

It turns out the (@?) operator we introduced above already fits the form above, if we simply wrap it all up with Querying . Compose:

(@?) :: (Ord k, Eq k) => Query k v -> k -> Querying (Maybe v)
(Query keys) @? k = Querying $ Compose $ do
  result <- newEmptyMVar
  modifyIORef' keys (Map.insertWith (++) k [result])
  return (takeMVar result)

Performing Queries

There are two omissions from this article so far - how do we introduce Query values, and perhaps more importantly - how do we actually run this thing? First of all, lets look at how to introduce a Query. When we introduce a Query, we need to ensure that people use them in a safe manner in order to avoid them blocking. We can do this by using a bracket-like construction. The only way to introduce a Query will be by using withQuery, which will provide a Query to a Querying computation. It will then inspect its own IORef, perform the query, and populate any related MVars:

withQuery :: (Ord k, Eq k) => ([k] -> IO (Map.Map k v)) -> (Query k v -> Querying a) -> Querying a
withQuery runner k = Querying $ Compose $ do
  -- Create a IORef to keep track of requested keys and result MVars
  keysRef <- newIORef Map.empty

  -- Run the first phase of the Querying action
  getResponse <- getCompose $ unQuerying (k (Query keysRef))

  -- Check which keys were requested and perform a query
  keys <- readIORef keysRef
  qResults <- runner (Map.keys keys)

  -- Populate all MVars with results
  flip Map.traverseWithKey keys $ \k mvars ->
    for_ mvars $ \mvar ->
      putMVar mvar (Map.lookup k qResults)

  -- Return the IO action that reads from the MVar
  return getResponse

Finally, we just need a way to run escape from Querying, which is trivial. The first phase has already been performed, so we only need to perform the second phase. This is eloquently expressed by joining the two IO actions:

runQuerying :: Querying a -> IO a
runQuerying (Querying (Compose io)) = join io

Examples

To wrap up, here’s a little example of everything in action:

getUserAgesById :: [Int] -> IO (Map.Map Int Int)
getUserAgesById keys = do
  putStrLn $ "Looking up " ++ show keys
  return $ Map.fromList $ [(1, 1), (2, 2)]

example :: IO (Maybe Int)
example = runQuerying $
  withQuery getUserAgesById $ \usersAgeById ->
    liftA2 (+) <$> (usersAgeById @? 1) <*> (usersAgeById @? 2)

And if we run example, we see:

> example
Looking up [1,2]
Just 3

Voila.

Addendum (or, IORefs!? MVars?! ARE YOU MAD?)

My first attempts to solve this problem didn’t use MVars or IORefs, but I’ve come to see them as a very useful tool to create a sort of request-response pattern internally. They allow me to separate the request type and the response type into something I can easily pass around, and by combining them with a suitable applicative functor, I think a lot of the details can be kept sufficiently abstract.

However, I would love to know how this could be done without mutable cells. I’ve had a little bit of a play with continuations (getting as far as delimited continuations and then rocking in a corner), but the problem here seems to be that the k and v types would have to be part of the Querying applicative itself. Worse, every time you introduce a new query, you’d have to some how get more types in.

I think that there may be a solution here that uses existential types, as we immediately consume the value that we ask for - but again, I couldn’t pull that off.

As a final bit of food for thought, Henrik Nilsson pointed out that this all feels very circular. The normal tool for circular programming is fix and laziness, and that extends to effectful computations with mfix. Again, maybe there is a way to do it using mfix, but I had difficult working out how to keep everything separated.

If anyone wants to take this idea and see what an even more Haskell-y solution would look like, I would love to see it!

One remaining piece of future work is to see if it’s possible to do this without withQuery. Currently there is a bit of duplication - you have to introduce a binding for every query you’re going to perform, which can be tedious - especially when you’re trying to extract common queries. On the flip side, it seems to make sense, in as far as it matches a functional API: we perform a query, and then we bind the results to some variable and we pull individual rows out of this result set.


You can contact me via email at ollie@ocharles.org.uk or tweet to me @acid2. I share almost all of my work at GitHub. This post is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

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