Domain models, Algebraic laws and Unit tests

In a domain model, when you have a domain element that forms an algebraic abstraction honoring certain laws, you can get rid of many of your explicitly written unit tests just by checking the laws. Of course you have to squint hard and discover the lawful abstraction that hides behind your concrete domain element.

Consider this simple abstraction for Money that keeps track of amounts in various currencies.

scala> import Money._
import Money._

// 1000 USD
scala> val m = Money(1000, USD)
m: laws.Money = (USD,1000)

// add 248 AUD
scala> val n = add(m, Money(248, AUD))
n: laws.Money = (AUD,248),(USD,1000)

// add 230 USD more
scala> val p = add(n, Money(230, USD))
p: laws.Money = (AUD,248),(USD,1230)

// value of the money in base currency (USD)
scala> p.toBaseCurrency
res1: BigDecimal = 1418.48

// debit amount
scala> val q = Money(-250, USD)
q: laws.Money = (USD,-250)

scala> val r = add(p, q)
r: laws.Money = (AUD,248),(USD,980)

The valuation of Money is done in terms of its base currency which is usually USD. One of the possible implementations of Money is the following (some parts elided for future explanations) ..

sealed trait Currency
case object USD extends Currency
case object AUD extends Currency
case object JPY extends Currency
case object INR extends Currency

class Money private[laws] (val items: Map[Currency, BigDecimal]) {
  def toBaseCurrency: BigDecimal = 
    items.foldLeft(BigDecimal(0)) { case (a, (ccy, amount)) =>
      a + Money.exchangeRateWithUSD.get(ccy).getOrElse(BigDecimal(1)) * amount

  override def toString = items.toList.mkString(",")

object Money {
  final val zeroMoney = new Money(Map.empty[Currency, BigDecimal])

  def apply(amount: BigDecimal, ccy: Currency) = new Money(Map(ccy -> amount))
  def add(m: Money, amount: BigDecimal, ccy: Currency) = ???

  final val exchangeRateWithUSD: Map[Currency, BigDecimal] = 
    Map(AUD -> 0.76, JPY -> 0.009, INR -> 0.016, USD -> 1.0)

Needless to say we will have quite a number of unit tests that check for addition of Money, including the boundary cases of adding to zeroMoney.

It’s not very hard to see that the type Money forms a Monoid under the add operation. Or to speak a bit loosely we can say that Money is a Monoid under the add operation.

A Monoid has laws that every instance needs to honor – associativity, left identity and right identity. And when your model element needs to honor the laws of algebra, it’s always recommended to include the verification of the laws as part of your test suite. Besides validating the sanity of your abstractions, one side-effect of verifying laws is that you can get rid of many of your explicitly written unit tests for the operation that forms the Monoid. They will be automatically verified when verifying the laws of Monoid[Money].

Here’s how we define Monoid[Money] using Cats ..

val MoneyAddMonoid: Monoid[Money] = new Monoid[Money] {
  def combine(m: Money, n: Money): Money = add(m, n)
  def empty: Money = zeroMoney

and the implementation of the previously elided add operation on Money using Monoid on Map ..

object Money {

  def add(m: Money, amount: BigDecimal, ccy: Currency) = 
    new Money(m.items |+| Map(ccy -> amount))



Now we can verify the laws of Monoid[Money] using specs2 and ScalaCheck and the helper classes that Cats offers ..

import cats._
import kernel.laws.GroupLaws
import org.scalacheck.{ Arbitrary, Gen }
import Arbitrary.arbitrary

class MoneySpec extends CatsSpec { def is = s2"""

  This is a specification for validating laws of Money

  (Money) should
     form a monoid under addition    $e1 

  implicit lazy val arbCurrency: Arbitrary[Currency] = Arbitrary { 
    Gen.oneOf(AUD, USD, INR, JPY) 

  implicit def moneyArbitrary: Arbitrary[Money] = 
    Arbitrary {
      for {
        i <- Arbitrary.arbitrary[Map[Currency, BigDecimal]]
      } yield new Money(i)

  def e1 = checkAll("Money", GroupLaws[Money].monoid(Money.MoneyAddMonoid))

and running the test suite will verify the Monoid laws for Monoid[Money] ..

[info] This is a specification for validating laws of Money
[info] (Money) should
[info] form a monoid under addition monoid laws must hold for Money
[info] + monoid.associativity
[info] + monoid.combineAll
[info] + monoid.combineAll(Nil) == id
[info] + monoid.combineAllOption
[info] + monoid.combineN(a, 0) == id
[info] + monoid.combineN(a, 1) == a
[info] + monoid.combineN(a, 2) == a |+| a
[info] + monoid.isEmpty
[info] + monoid.leftIdentity
[info] + monoid.rightIdentity
[info] + monoid.serializable

In summary ..

  • strive to find abstractions in your domain model that are constrained by algebraic laws
  • check all laws as part of your test suite
  • you will find that you can get rid of quite a few explicitly written unit tests just by checking the laws of your abstraction
  • and of course use property based testing for unit tests

In case you want to take a look at the full code base, it’s there on my Github repo. In the next post we will take the next step towards modeling with generic algebraic code using the Monoid pattern from this example. Code written in parametric form without depending on specialized concrete types can be more robust, easier to test and easier to reason about. I have also discussed this at length in my book Functional and Reactive Domain Modeling. I plan to supplement the materials covered there with more examples and code patterns ..

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