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This module provides various utilities, mostly with a mathematical bent, for writing scala programs.

Data structures

Covariant set

The Set[A] data type in scala is invariant. A CovariantSet[A] is, as you might expect, covariant in A. It is more or less a small modification of Scalaz's ISet, modified to be covariant.

As a result, this means that member method essentially has type Any => Boolean. That's not quite true - the actual type is member[B >: A]: B => Boolean, but B must have an Order[B] instance.


Unfortunately, using Lenses can involve a lot of duplicated effort relative to using lazy val on an object. To eliminate some of this added work, we provide two replacements for the existing scalaz Lens, which avoid this effort.

def cachedLens[A,B <: AnyRef,K <: AnyRef](set: (A,B) => A, get: A => B, cacheKey: A => K, maxCacheSize: Int = 512, maxCacheDurationSeconds: Int = 10*60)

This method will cache the results of calling get using a google guava cache. The key to the cache will be computed via the cacheKey argument.

def singletonCachedLens[A,B <: AnyRef,K <: AnyRef](set: (A,B) => A, get: A => B, cacheKey: A => K)

This method will cache only the last result computed, and the cache will be stored with weak references. Cache equality is computed via memory location equality, i.e. using x eq y rather than x == y. The rationale for this is that many times, a single lens will be used in a lot of (mostly unrelated) locations in rapid succession. E.g.:

val myLens: Lens[Event,P] = LensUtils.singletonCachedLens(...)

def checkEventForP1(event: Event) = if (myLens.get(event) == ...)
def checkEventForP2(event: Event) = if (myLens.get(event) == ...)


def processEvent(event: Event) = {
  if (checkEventForP1(event)) { p1Handler ! event }
  if (checkEventForP2(event)) { p2Handler ! event }

Free objects

A free object is a functor together with a natural transformation that preserves it's structure. It can be thought of as the most expansive possible version of that structure, only obeying the minimum laws necessary.

Somewhat concretely:

trait FreeThing[F[_]] extends Functor[F] {
  implicit def structure[A]: Structure[F[A]]
  def point[A](a: =>A): F[A]

  def nat[A,B](f: A => B)(implicit s: Structure[B]): F[A] => B

Here, "structure" can be a Monoid, a Group, a Bool, etc - basically any useful algebraic structure. The key fact about the nat operation is that nat(f) must be a homomorphism, i.e. it must preserve the operations of that structure. For example, for a Monoid:

nat(f)(x |+| y) = nat(f)(x) |+| nat(f)(y)

It must also commute with point:

nat(f)(point[A](x)) = point[B](f(x))

Another way to think of it is that it's a data structure with no interpretation.



A couple of useful deduplication objects can be found here. To save memory, there is the Deduplicator[T]: T => T which lifts semantic equality to memory equality:

    val f = Deduplicator[List[String]]()
    f(x) === x
    f(x) eq x
    f(x) eq f(f(x))

(There are of course cache-based limitations on this.)

Here, eq means that the object on the left has the same memory location as the object on the right. Semantically a deduplicator is the identity function.


There is also the IdempotentEffect which is a way of reducing the number of times an effectful function is called.

    var cnt: Int = 0
    val f = IdempotentEffect((k:String) => {
      cnt = cnt + 1
    cnt === 1

IdempotentEffect is useful when we want to run a function only once per input - an example use case might be:

val markEventAsOccurredInDatabase: Event => Unit = IdempotentEffect((e:Event) => {...})

Repeated calls to this function for the same event will not cause repeated round trips to the database.


There is also the DelayedIdempotentEffect. The method DelayedIdempotentEffect.apply will return an Option[DelayedIdempotentEffect.IdempotentMarker] object. Future calls to the effectful method will only be called after the IdempotentMarker is called. A concrete example illustrating both how and why:

val insertIntoDatabase = DelayedIdempotentEffect[X,java.sql.Connection]((x,conn) => insertIntoDatabaseNoCommit(x, conn))

val conn = databse.getConnection()
val marker = insertIntoDatabase(key, conn)
... // Future calls to insertIntoDatabase(key) will attempt to insert
marker.foreach(x => x()) //Now, *after* the insert is committed, future attempts will be prevented

Deduplication is handled based on the first argument, the second argument is ignored. So repeated calls to insertIntoDatabase with the same value of x but different values of conn will be deduplicated.

There is also a DelayedIdempotentEffect.simple[X](x => f(x)) method which ignores the other argument.


Assorted scala utilities - deduplicators, free algebras,




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