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As presented in FunctionalConf 2014

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- 1. Property based Testing generative data & executable domain rules Debasish Ghosh (@debasishg) Friday, 10 October 14
- 2. Agenda Why xUnit based testing is not enough What is a property? Properties for free? What to verify in property based testing ScalaCheck Domain Model Testing Friday, 10 October 14
- 3. xUnit based testing • Convenient • Widely used • Rich tool support Friday, 10 October 14
- 4. xUnit based testing • Often grows out of bounds (verbosity), being at a lower level of abstraction • Difﬁcult to manage data/logic isolation • Always scared that I may have missed some edge cases & boundary conditions Friday, 10 October 14
- 5. // polymorphic list append def append[A](xs: List[A], ys: List[A]): List[A] = { //.. } How do you show the correctness of the above implementation ? Friday, 10 October 14
- 6. (1) Theorem Proving length [] = 0 (length.1) length (z : zs) = 1 + length zs (length.2) [] ++ zs = zs (++.1) (w : ws) ++ zs = w : (ws ++ zs) (++.2) length ([] ++ ys) = length [] + length ys (base) length (xs ++ ys) = length xs + length ys (hypothesis) Length & Append Induction length ((x : xs) ++ ys) = length (x : xs) + length ys To Prove Friday, 10 October 14
- 7. Base Case length ([] ++ ys) = length [] + length ys (base) length ([] ++ ys) = length ys (by ++.1) length [] + length ys = 0 + length ys = length ys (by length.1) length [] = 0 (length.1) length (z : zs) = 1 + length zs (length.2) [] ++ zs = zs (++.1) (w : ws) ++ zs = w : (ws ++ zs) (++.2) Friday, 10 October 14
- 8. Induction length ((x : xs) ++ ys) = length (x : xs) + length ys length ((x : xs) ++ ys) = length (x : (xs ++ ys)) (by ++.2) = 1 + length (xs ++ ys) (by length.2) = 1 + length xs + length ys length (x : xs) + length ys = 1 + length xs + length ys (by length.2) length [] = 0 (length.1) length (z : zs) = 1 + length zs (length.2) [] ++ zs = zs (++.1) (w : ws) ++ zs = w : (ws ++ zs) (++.2) Friday, 10 October 14
- 9. (2) Use your favorite unit testing library // ScalaTest based assertions List(1,2,3).length + List(4,5).length should equal (append(List(1,2,3), List(4,5)).length) List().length + List(4,5).length should equal (append(List(), List(4,5)).length) List(1,2,3).length + List().length should equal (append(List(1,2,3), List()).length) Friday, 10 October 14
- 10. • Hard coded data sets • May not be exhaustive • Coverage depends upon the knowledge of the test creator But .. Friday, 10 October 14
- 11. (3) Use dependent typing - an example of append in Idris, a dependently typed language -- Vectors lists that have size as part of type data Vect : Nat -> Type -> Type where Nil : Vect Z a (::) : a -> Vect k a -> Vect (S k) a -- the app function is correct by construction app : Vect n a -> Vect m a -> Vect (n + m) a app Nil ys = ys app (x :: xs) ys = x :: app xs ys Future ? Friday, 10 October 14
- 12. • Types depend on values • Powerful constraints encoded within the type signature • Correct by construction - correct before the program runs! Future ? Friday, 10 October 14
- 13. • Miles Sabin has been working on shapeless (https://github.com/milessabin/shapeless) • Flavors of dependent typing in Scala • Sized containers, polymorphic function values, heterogeneous lists & a host of other goodness built on top of Scala typesystem today .. Friday, 10 October 14
- 14. • Till such time the ecosystem matures, we all start programming in dependently typed languages .. • We have better options than using only xUnit based testing .. Mature? Friday, 10 October 14
- 15. What exactly are we trying to verify ? property("List append adds up the 2 sizes") = forAll((l1: List[Int], l2: List[Int]) => l1.length + l2.length == append(l1, l2).length ) Friday, 10 October 14
- 16. What exactly are we trying to verify ? property("List append adds up the 2 sizes") = forAll((l1: List[Int], l2: List[Int]) => l1.length + l2.length == append(l1, l2).length ) invariant of our function encoded as a generic property Friday, 10 October 14
- 17. What is a property? • Constraints and invariants that must be honored within the bounded context of the model • Sometimes called “laws” or the “algebra” • Ensures well-formed-ness of abstractions Friday, 10 October 14
- 18. A Monoid An algebraic structure having • an identity element • a binary associative operation trait Monoid[A] { def zero: A def op(l: A, r: => A): A } object MonoidLaws { def associative[A: Equal: Monoid] (a1: A, a2: A, a3: A): Boolean = //.. def rightIdentity[A: Equal: Monoid] (a: A) = //.. def leftIdentity[A: Equal: Monoid] (a: A) = //.. } Friday, 10 October 14
- 19. Monoid Laws An algebraic structure havingsa • an identity element • a binary associative operation trait Monoid[A] { def zero: A def op(l: A, r: => A): A } object MonoidLaws { def associative[A: Equal: Monoid] (a1: A, a2: A, a3: A): Boolean = //.. def rightIdentity[A: Equal: Monoid] (a: A) = //.. def leftIdentity[A: Equal: Monoid] (a: A) = //.. } satisﬁes op(x, zero) == x and op(zero, x) == x satisﬁes op(op(x, y), z) == op(x, op(y, z)) Friday, 10 October 14
- 20. • Every monoid that you deﬁne must honor all the laws of the abstraction • The question is how do we verify that all laws are satisﬁed it’s the LAW Friday, 10 October 14
- 21. But before that another important important question is what properties do we need to verify .. Friday, 10 October 14
- 22. def f[A](a: A): A •The function f takes as input a value and returns a value of the same type • But we don’t know the exact type of A • Hence we cannot do any type speciﬁc operation within f •All we know is that f is a polymorphic function parameterized on type A, that returns the same type as the input •A little thought makes us realize that the only possible implementation of f is that of an identity function Friday, 10 October 14
- 23. def f[A](a: A): A = a •This is the only possible implementation of f (unless we decide to launch a missile and do all evil stuff like throwing exceptions or do typecasing) • If the type-checker checks it ok, we are done.The compiler has proved the theorem and we don’t need to verify the property ourselves • So we have proved a theorem out of the types - this technique is called parametricity and PhilWadler calls these free theorems Fast and Loose Reasoning is Morally Correct (2006) by by Nils Anders Danielsson, John Hughes, Jeremy Gibbons, Patrik Jansson (http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.59.8232) Friday, 10 October 14
- 24. Free theorems are ensured by the type- checker in a statically typed language that supports parametric polymorphism and we don’t need to write tests for verifying any of those properties Theorems for Free! by Phil Wadler (http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.38.9875) Friday, 10 October 14
- 25. Parametricity tests a lot of properties in your model. “Parametricity constantly tests more conditions than your unit test suite ever will” - Edward Kmett on #scala Friday, 10 October 14
- 26. What properties do we need to verify ? Friday, 10 October 14
- 27. Summarizing .. • if your programming language has a decent static type system and • support for parametric polymorphism and • you play to the rules of parametricity • .... Friday, 10 October 14
- 28. Summarizing .. • if your programming language has a decent static type system and • support for parametric polymorphism and • you play to the rules of parametricity • .... You get a lot of properties veriﬁed for FREE Friday, 10 October 14
- 29. • Property based testing library for Scala (and also for Java) • Inspired by QuickCheck (Erlang & Haskell) • Works on property speciﬁcations • Does automatic data generation ScalaCheck .. Friday, 10 October 14
- 30. ScalaCheck • You specify the property to be tested • ScalaCheck veriﬁes that the property holds by generating random data • No burden on programmer to maintain data, no fear of missed edge cases Friday, 10 October 14
- 31. “Property-based testing encourages a high level approach to testing in the form of abstract invariants functions should satisfy universally, with the actual test data generated for the programmer by the testing library. In this way code can be hammered with thousands of tests that would be infeasible to write by hand, often uncovering subtle corner cases that wouldn't be found otherwise.” Real World Haskell by Bryan O’Sullivan, Don Stewart & John Goerzen Friday, 10 October 14
- 32. scala> import org.scalacheck._ import org.scalacheck._ scala> import Prop.forAll import Prop.forAll scala> forAll((l1: List[Int], l2: List[Int]) => | l1.length + l2.length == append(l1, l2).length | ) res5: org.scalacheck.Prop = Prop scala> res5.check + OK, passed 100 tests. generates 100 test cases randomly and veriﬁes the property speciﬁcation of the property to be veriﬁed Verifying properties universal quantiﬁer Friday, 10 October 14
- 33. scala> val propSqrt = forAll { (n: Int) => scala.math.sqrt(n*n) == n } propSqrt: org.scalacheck.Prop = Prop scala> propSqrt.check ! Falsified after 0 passed tests. > ARG_0: -2147483648 scala> propSqrt.check ! Falsified after 0 passed tests. > ARG_0: -1 not only says that the property fails, but also points to failure data set Verifying properties A word about minimization of test cases. Whenever a property fails, scalacheck starts shrinking the test cases until it ﬁnds the minimal failing test case.This is a huge feature that helps debugging failures Friday, 10 October 14
- 34. scala> val propSqrt = forAll { (n: Int) => | scala.math.sqrt(n*n) == n | } propSqrt: org.scalacheck.Prop = Prop scala> val smallInteger = Gen.choose(1, 100) smallInteger: org.scalacheck.Gen[Int] = .. scala> val propSmallInteger = forAll(smallInteger)(n => | n >= 0 && n <= 100 | ) propSmallInteger: org.scalacheck.Prop = Prop uses default data generator custom generator forAll uses the custom generator Custom generators Friday, 10 October 14
- 35. // generate values in a range Gen.choose(10, 20) // conditional generator Gen.choose(0,200) suchThat (_ % 2 == 0) // generate specific values Gen.oneOf('A' | 'E' | 'I' | 'O' | 'U' | 'Y') // default distribution is random, but you can change val vowel = Gen.frequency( (3, 'A'), (4, 'E'), (2, 'I'), (3, 'O'), (1, 'U'), (1, 'Y') ) // generate containers Gen.containerOf[List,Int](Gen.oneOf(1, 3, 5)) Custom generators Friday, 10 October 14
- 36. Deﬁne your own generator case class Account(no: String, holder: String, openingDate: Date, closeDate: Option[Date]) val genAccount = for { no <- Gen.oneOf("1", "2", "3") nm <- Gen.oneOf("john", "david", "mary") od <- arbitrary[Date] cd <- arbitrary[Option[Date]] } yield Account(no, nm, od, cd) (model) (random data generator) Friday, 10 October 14
- 37. Deﬁne your own generator sealed abstract class Tree case object Leaf extends Tree case class Node(left: Tree, right: Tree, v: Int) extends Tree val genLeaf = value(Leaf) val genNode = for { v <- arbitrary[Int] left <- genTree right <- genTree } yield Node(left, right, v) def genTree: Gen[Tree] = oneOf(genLeaf, genNode) (model) (random data generator) Friday, 10 October 14
- 38. implicit val arbAccount: Arbitrary[Account] = Arbitrary { for { no <- Gen.oneOf("1", "2", "3") nm <- Gen.oneOf("john", "david", "mary") od <- arbitrary[Date] } yield checkingAccount(no, nm, od) } implicit val arbCcy: Arbitrary[Currency] = Arbitrary { Gen.oneOf(USD, SGD, AUD, INR) } implicit val arbMoney = Arbitrary { for { a <- Gen.oneOf(1 to 10) c <- arbitrary[Currency] } yield Money(a, c) } implicit val arbPosition: Arbitrary[Position] = Arbitrary { for { a <- arbitrary[Account] m <- arbitrary[Money] d <- arbitrary[Date] } yield Position(a, m, d) } Arbitrary is a special generator that scalacheck uses to generate random data. Need to specify an implicit Arbitrary instance of your speciﬁc data type which can be used to generate data Domain Model Testing Friday, 10 October 14
- 39. property("Equal debit & credit retains the same position") = forAll((a: Account, c: Currency, d: Date, i: BigDecimal) => { val Success((before, after)) = for { p <- position(a, c, d) r <- credit(p, Money(i, c), d) q <- debit(r, Money(i, c), d) } yield (q, p) before == after }) property("Can close account with close date > opening date") = forAll((a: Account) => close(a, new Date(a.openingDate.getTime + 10000)).isSuccess == true ) property("Cannot close account with close date < opening date") = forAll((a: Account) => close(a, new Date(a.openingDate.getTime - 10000)).isSuccess == false ) Domain Model Testing Verify your business rules and document them too Friday, 10 October 14
- 40. Some other features • Sized generators - restrict the set of generated data • Conditional generators - use combinators to specify ﬁlters • Classify generated test data to see statistical distribution Friday, 10 October 14
- 41. Some other features • Test case minimization for failed tests • Stateful testing - not only queries, but commands as well in the CQRS sense of the term Friday, 10 October 14
- 42. Essence of property based testing • Identify constraints & invariants of your abstraction that must hold within your domain model • Encode them as “properties” in your code (not as dumb documents) • Execute properties to verify the correctness of your abstraction Friday, 10 October 14
- 43. Essence of property based testing • In testing domain models, properties help you think at a higher level of abstraction • Basically you encode domain rules as properties and verify them using data generators that use the domain model itself • Executable domain rules Friday, 10 October 14
- 44. Property based testing & Functional programs • Functional programs are easier to test & debug (no global state) • Makes a good case for property based testing (immutable data, pure functions) • Usually concise & modular - easier to identify properties Friday, 10 October 14
- 45. ThankYou! Friday, 10 October 14

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