*This post is being resurrected from the dustbin of history - it was originally posted on the precog.com engineering blog, which has since been lost to acquisition and bitrot. My opinion on the applicability of the following techniques has changed somewhat since I originally wrote this post; I will address this in a followup post in the near future. Briefly, though, I believe that parameterizing each method with an implicit monad constraint is preferable where possible; it provides the user with greater flexibility.*

In our last blog post on Precog development, Daniel wrote about how we use the Cake Pattern to structure our codebase and to leave the implementation types abstract as long as possible. As he showed in that post, this is an extremely powerful concept; by keeping a type existential, values of that type remain opaque to any modules that aren’t “aware” of the eventual type chosen, and so are prevented by the compiler from breaking encapsulation boundaries.

In today’s post, we’re going to extend this notion beyond types to handle type constructors, and in so doing will show a mechanism that allows us to switch out entire models of computation.

If you’ve been working with Scala for any length of time, you’ve undoubtedly heard the word “monad” floating around in one context or another, perhaps in a discussion about the syntactic sugar provided by Scala’s ‘for’ keyword or a blog post discussing how the Option type can be used to avoid the pitfalls of null references. While a significant amount of discussion of monads in Scala focuses on the “container” types, a few types common in the Scala ecosystem display a more interesting facet of monadic composition – delimited computation. While all monadic types exhibit this in composition, perhaps the most commonly used monadic type in Scala that exemplifies this sort of use directly is akka.dispatch.Future, (which is scheduled to replace Scala’s current Future interface in the standard library in Scala 2.10) which encodes asynchronous computation. It embodies the aspect of monadic composition that we’re most concerned with here by providing a flexible way to order the steps of a computation.

I’d like to step back a moment here and state that this post isn’t intended to function as a monad tutorial; there are numerous (perhaps too many!) articles about monads, and their relevance to programming in Scala exist elsewhere. If you’re new to the concept it will be useful for you to take advantage of one or more of these resources before continuing here. It is, however, important to point out at first that the use of monads in Scala, while pervasive (as evidenced by the presence of ‘for’ as syntactic sugar for monadic composition) is somewhat idiosyncratic in that the Scala standard libraries actually provide no Monad type. For this, we have to look outside of the standard library to the excellent scalaz project. Scalaz’s encoding of the monadic abstraction relies upon the implicit typeclass pattern. The base Monad type is shown here, simplified, for reference:

trait Monad[M[_]] { def point[A](a: => A): M[A] def bind[A, B](m: M[A])(f: A => M[B]): M[B] def map[A, B](m: M[A])(f: A => B): M[B] = bind(m)(a => point(f(a))) }

You’ll note that the Monad trait is not parameterized by a specific type, but instead a type constructor of one argument. The methods defined inside of Monad are then parametrically polymorphic, which means that they must provide a specific type to be inserted into the “hole” at the invocation point. This will be important later, when we talk about how to actually take advantage of this abstraction.

Scalaz provides implementations of this type for most of the monadic types in the Scala standard library, as well as several more sophisticated monadic types, which we’ll return to in a moment. For now, however let’s talk a bit about Akka’s Futures.

An Akka Future represents a computation whose value is produced asynchronously, and which may fail. Also, as I noted before, akka.dispatch.Future is monadic; that is, it is a type for which the Monad trait above can be trivially implemented and which satisfies the monad laws, and so it provides an extremely useful primitive for composing asynchronous computations without all sorts of tedious mucking about with manual management of threads and shared mutable state. At Precog, we use Futures extensively, both in a direct fashion and to allow us a composable way to interact with subsystems that are implemented atop Akka’s actor framework. Futures are arguably one of the best tools we have for reining in the complexity of asynchronous programming, and so our many of our early versions of APIs in our codebase exposed Futures directly. For example, here’s a snippet of one of our internal APIs, which follows the Cake pattern as described previously.

trait DatasetModule { type Dataset trait DatasetLike { /** The members of this dataset will be used to determine what sets to load, and the resulting sets will be unioned together */ def load: Future[Dataset] /** Sorts the dataset by the specified value function. */ def sort(sortBy: /*...*/): Future[Dataset] /** Retains a prefix of this dataset. */ def take(size: Int): Dataset /** Map members of the dataset into the A type using the specified value function, then combine using the resulting monoid */ def reduce[A: Monoid](mapTo: /*...*/): Future[A] } }

The Dataset type here is something of a strawman, but is loosely representative of the type that we use internally to represent an intermediate result of a computation - a lazy data structure with a number of operations that can be used to manipulate it, some of which may involve actually evaluating a function over the entire dataset and which may involve I/O, distributed evaluation, and asynchronous computation. Based on this interface, it’s easy to see that evaluation of some query with respect to a dataset might involve a load, a sort, taking a prefix, and a reduction of that prefix. Moreover, such an evaluation will not rely upon anything except the monadic nature of Future to compose its steps. What this means is that from the perspective of the consumer of the DatasetModule interface, the only aspect of Future that we’re relying upon is the ability to order operations in a statically checked fashion; the sequencing, rather than any particular semantics related to Future’s asynchrony, is the relevant piece of information provided by the type. So, the following generalization becomes natural:

trait DatasetModule[M[+_]] { type Dataset implicit def M: Monad[M] trait DatasetLike { /** The members of this dataset will be used to determine what sets to load, and the resulting sets will be unioned together */ def load: M[Dataset] /** Sorts the dataset by the specified value function. */ def sort(sortBy: /*...*/): M[Dataset] /** Retains a prefix of this dataset. */ def take(size: Int): Dataset /** Map members of the dataset into the A type using the specified value function, then combine using the resulting monoid */ def reduce[A: Monoid](mapTo: /*...*/): M[A] } }

and, of course, down the road some concrete implementation of DatasetModule will refine the type constructor M to be Future:

/** The implicit ExecutionContext is necessary for the implementation of M.point */ class FutureMonad(implicit executor: ExecutionContext) extends Monad[Future] { override def point[A](a: => A): Future[A] = Future { a } override def bind[A, B](m: Future[A])(f: A => Future[B]): Future[B] = m flatMap f } abstract class ConcreteDatasetModule(implicit executor: ExecutionContext) extends DatasetModule[Future] { val M: Monad[Future] = new FutureMonad }

In practice, we may actually leave M abstract until “the end of the universe.” In the Precog codebase, the M type will frequently represent the bottom of a stack of monad transformers including StateT, StreamT, EitherT and others that the actual implementation of the Dataset type depends upon.

This generalization has numerous benefits. First, as with the previous examples of our use of the Cake pattern, consumers of the DatasetModule trait are completely and statically insulated from irrelevant details of the implementation type. An important such consumer is a test suite. In a test, we probably don’t want to worry about the fact that the computation is being performed asynchronously; all that we care about is that we obtain a correct result. If our M is in fact at the bottom of a transformer stack, we can trivially replace it with the identity monad and use the “copointed” nature of this monad (the ability to “extract” a value from the monadic context). This allows us to build a similarly generic test harness:

/** Copointed is available from scalaz as well; reproduced here for clarity */ trait Copointed[M[_]] { /** Extract and return the value from the enclosing context. */ def copoint[A](m: M[A]): A } trait TestDatasetModule[M[+_]] extends DatasetModule { implicit def M: Monad[M] with Copointed[M] //... utilities for test dataset generation, stubbing load/sort, etc. }

For most cases, we’ll use the identity monad for testing. Suppose that we’re testing the piece of functionality described earlier, which has computed a result from the combination of a load, a sort, take and reduce. The test framework need never consider the monad that it’s operating in.

import scalaz._ import scalaz.syntax.monad._ import scalaz.syntax.copointed._ class MyEvaluationSpec extends Specification { val module = new TestDatasetModule[Id] with ConcreteDatasetModule[Id] { val M = Monad[Id] // the monad for Id is copointed in Scalaz. } “evaluation” should { “determine the correct result for the load/sort/take/reduce case” in { val loadFrom: module.Dataset = //... val expected: Int = //... val result = for { ds sorted - ds.sortBy(mySortFun) prefix = sorted.take(10) value - prefix.reduce[Int]myCountFunc) } yield value result.copoint must_== expected } } }

In the case that we have a portion of the implementation that actually depends upon the specific monadic type (say, for example, that our sort implementation relies on Akka actors and the “ask” pattern under the hood, so that we’re using Futures) we can simply encode this in our test in a straightforward fashion:

abstract class TestFutureDatasetModule(implicit executor: ExecutionContext) extends TestDatasetModule[Future] { def testTimeout: akka.util.Duration object M extends FutureMonad(executor) with Copointed[Future] { def copoint[A](m: Future[A]): A = Await.result(m, testTimeout) } }

Future is, of course, not properly copointed (since Await can throw an exception) but for the purposes of testing (and testing exclusively) this construction is ideal. As before, we get exactly the type that we need, statically determined, at exactly the place that we need it.

In practice, we’ve found that abstracting away the particular monad that our code is concerned with has aided tremendously with keeping the concerns of different parts of our codebase well isolated, and ensuring that we’re simply not able to sidestep the sequencing requirements that are necessary to make a large, functional codebase work together as a coherent whole. As an added benefit, many parts of our application that were not initially designed thinking in terms of parallel execution are able to execute concurrently. For example, in many cases we’ll be computing a List[M[...]] and then using the “sequence” function provided by scalaz.Traverse to turn this into an M[List[...]] - and when M is future, each element may be computed in parallel, with the final sequenced result becoming available only when all the computations to produce the members of the list are complete. And, ultimately, even this merely touches the surface of a deep pool of composing our computation that is made possible by making this abstraction.