Property based Testing - generative data & executable domain rules

Property based Testing
generative data & executable domain rules
Debasish Ghosh
(@debasishg)
Friday, 10 October 14

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

xUnit based testing
• Convenient
• Widely used
• Rich tool support

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

// polymorphic list append
def append[A](xs: List[A], ys: List[A]): List[A] = {
//..
}
How do you show the correctness of the
above implementation ?

(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

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)
[] ++ zs = zs (++.1)
(w : ws) ++ zs = w : (ws ++ zs) (++.2)

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)
[] ++ zs = zs (++.1)
(w : ws) ++ zs = w : (ws ++ zs) (++.2)

(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)

• Hard coded data sets
• May not be exhaustive
• Coverage depends upon the knowledge of
the test creator
But ..

(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 ?

• Types depend on values
• Powerful constraints encoded within the
type signature
• Correct by construction - correct before
the program runs!
Future ?

• 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 ..

• 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?

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
)

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

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

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) = //..
}

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))

• 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

But before that another important important
question is what properties do we need to verify ..

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

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)

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)

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

What properties do we need to verify ?

Summarizing ..
• if your programming language has a decent
static type system and
• support for parametric polymorphism and
• you play to the rules of parametricity
• ....

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

• Property based testing library for Scala
(and also for Java)
• Inspired by QuickCheck (Erlang & Haskell)
• Works on property speciﬁcations
• Does automatic data generation
ScalaCheck ..

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

“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

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

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

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

// 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

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)

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)

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

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
)
Verify your business rules and document them too

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

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

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

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

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

ThankYou!

Property based Testing - generative data & executable domain rules

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