An introduction to property based testing

The lazy programmer's guide to
writing 1000's of tests
An introduction to property based testing
@ScottWlaschin
fsharpforfunandprofit.com

Part 1:
In which I have a conversation with a
remote developer
This was a project from a long time ago,
in a galaxy far far away

For some reason
we needed a
custom "add"
function

So I decide to start writing the
unit tests myself

[<Test>]
let ``When I add 1 + 3, I expect 4``()=
let result = add 1 3
Assert.AreEqual(4,result)
[<Test>]


First, I had a look at the existing tests...

[<Test>]
let ``When I add -1 + 3, I expect 2``()=
let result = add -1 3
Assert.AreEqual(2,result) 
Ok, now for my first new test...

let add x y =
4
wtf!
Hmm.. let's look at the implementation...

[<Test>]
[<Test>]


Time for some more tests...

let add x y =
match (x,y) with
| (2,3) -> 5
| (1,41) -> 42
| (_,_) -> 4 // all other cases
Let's just check the implementation again...

Write the minimal code that will make the
test pass
At this point you need to write code that will
successfully pass the test.
The code written at this stage will not be 100%
final, you will improve it later stages.
Do not try to write the perfect code at this stage,
just write code that will pass the test.
From http://www.typemock.com/test-driven-development-tdd/
TDD best practices

[<Test>]
let ``When I add two numbers,
I expect to get their sum``()=
for (x,y,expected) in [
(1,2,3);
(2,2,4);
(3,5,8);
(27,15,42); ]
let actual = add x y
Assert.AreEqual(expected,actual)
Another attempt at a test


let add x y =
match (x,y) with
| (1,2) -> 3
| (2,3) -> 5
| (3,5) -> 8
| (1,41) -> 42
| (25,15) -> 42
| (_,_) -> 4 // all other cases
Let's check the implementation one more time....

It dawned on me who I was
dealing with...
...the legendary burned-out, always lazy and
often malicious programmer called...

The Enterprise
Developer From Hell

Rethinking the approach
The EDFH will always make
specific examples pass, no
matter what I do...
So let's not use
specific examples!

[<Test>]
let ``When I add two random numbers,
I expect their sum to be correct``()=
let x = randInt()
let y = randInt()
let expected = x + y
Let's use random numbers instead...

[<Test>]
let ``When I add two random numbers (100 times),
for _ in [1..100] do
let x = randInt()
let y = randInt()
Yea! Problem solved!
And why not do it 100 times just to be sure...
The EDFH can't beat this!

[<Test>]
let ``When I add two random numbers (100 times),
for _ in [1..100] do
let x = randInt()
let y = randInt()
Uh-oh!
But if you can't test by using +, how CAN you test?
We can't test "add" using +!

Part II:
Property based testing

What are the "requirements" for
the "add" function?
It's hard to know where to get started, but one
approach is to compare it with something different...
How does "add" differ from "subtract", for example?

[<Test>]
let ``When I add two numbers, the result
should not depend on parameter order``()=
for _ in [1..100] do
let x = randInt()
let y = randInt()
let result1 = add x y
let result2 = add y x
Assert.AreEqual(result1,result2)
reversed params
So how does "add" differ from "subtract"?
For "subtract", the order of the parameters makes a
difference, while for "add" it doesn't.

let add x y =
x * y
The EDFH responds with:
TEST: ``When I add two numbers, the result
should not depend on parameter order``

Ok, what's the difference
between add and multiply?
Example: two "add 1"s is the same as one "add 2".

[<Test>]
let ``Adding 1 twice is the same as adding 2``()=
for _ in [1..100] do
let x = randInt()
let y = randInt()
let result1 = x |> add 1 |> add 1
let result2 = x |> add 2
Test: two "add 1"s is the same as one "add 2".

let add x y =
x - y
The EDFH responds with:

TEST: ``When I add two numbers, the result
TEST: ``Adding 1 twice is the same as adding 2``
Ha! Gotcha, EDFH!
But luckily we have the previous test as well!

let add x y =
0
The EDFH responds with another implementation:

TEST: ``When I add two numbers, the result

Aarrghh! Where did our approach go wrong?

[<Test>]
let ``Adding zero is the same as doing nothing``()=
for _ in [1..100] do
let x = randInt()
let result2 = x
Yes! Adding zero is the same as doing nothing
We have to check that the result is somehow connected to the input.
Is there a trivial property of add that we know the answer to
without reimplementing our own version?

Finally, the EDFH is defeated...

TEST: ``When I add two numbers, the result

TEST: ``Adding zero is the same as doing nothing``

If these are all true we
MUST have a correct
implementation*
* not quite true

let propertyCheck property =
// property has type: int -> int -> bool
for _ in [1..100] do
let x = randInt()
let y = randInt()
let result = property x y
Assert.IsTrue(result)
Let's extract the shared code... Pass in a "property"
Check the property is
true for random inputs

let commutativeProperty x y =
result1 = result2
And the tests now look like:
[<Test>]
let ``When I add two numbers, the result
should not depend on parameter order``()=
propertyCheck commutativeProperty

let adding1TwiceIsAdding2OnceProperty x _ =
let result1 = x |> add 1 |> add 1
result1 = result2
And the second property
[<Test>]
let ``Adding 1 twice is the same as adding 2``()=
propertyCheck adding1TwiceIsAdding2OnceProperty

let identityProperty x _ =
result1 = x
And the third property
[<Test>]
let ``Adding zero is the same as doing nothing``()=
propertyCheck identityProperty

Testing with properties
• The parameter order doesn't matter
• Doing "add 1" twice is the same as
doing "add 2" once
• Adding zero does nothing
These properties
apply to ALL inputs
So we have a very
high confidence that
the implementation is
correct

Testing with properties
• "Commutativity" property
• "Associativity" property
• "Identity" property
These properties
define addition!
The EDFH can't create an
incorrect implementation!
Bonus: By using specifications, we have
understood the requirements in a deeper way.
Specification

Why bother with the EDFH?
Surely such a malicious programmer is
unrealistic and over-the-top?

Evil
Stupid
Lazy
In practice,
no difference!

In my career, I've always had to deal with one
stupid person in particular 
Me!
When I look at my old code, I almost always see something wrong!
I've often created flawed implementations, not out of evil
intent, but out of unawareness and blindness
The real EDFH!

Part III:
QuickCheck and its ilk
Wouldn't it be nice to have a toolkit for doing this?
The "QuickCheck" library was originally developed for Haskell by
Koen Claessen and John Hughes, and has been ported to many
other languages.

QuickCheck
Generator Shrinker
Your Property Function that returns bool
Checker API
Pass to checker
Generates
random inputs
Creates minimal
failing input

// correct implementation of add!
let add x y = x + y
let commutativeProperty x y =
result1 = result2
// check the property interactively
Check.Quick commutativeProperty
Using QuickCheck (FsCheck) looks like this:
Ok, passed 100 tests.
And get the output:

Generators:
making random inputs
QuickCheck
Generator Shrinker
Checker API

Generates ints
"int" generator 0, 1, 3, -2, ... etc
Generates strings
"string" generator "", "eiX$a^", "U%0Ika&r", ... etc
"bool" generator true, false, false, true, ... etc
Generating primitive types
Generates bools

Generates pairs of ints
"int*int" generator (0,0), (1,0), (2,0), (-1,1), (-1,2) ... etc
Generates options
"int option" generator Some 0, Some -1, None, Some -4; None ...
"Color" generator Green 47, Red, Blue true, Green -12, ...
Generating compound types
type Color = Red | Green of int | Blue of bool
Generates values of custom type
Define custom type

let commutativeProperty (x,y) =
let result2 = add y x // reversed params
result1 = result2
(b) Appropriate generator will
be automatically created
int*int generator
(0,0) (1,0) (2,0) (-1,1) (100,-99) ...
(a) Checker detects that the
input is a pair of ints
Checker API
(c) Valid values will be generated...
(d) ...and passed to
the property for
evaluation
How it works in practice

Shrinking:
dealing with failure
QuickCheck
Generator Shrinker
Checker API

let smallerThan81Property x =
x < 81
Property to test – we know it's gonna fail!
"int" generator 0, 1, 3, -2, 34, -65, 100
Fails at 100!
So 100 fails, but knowing that is not very helpful
How shrinking works
Time to start shrinking!

x < 81
Shrink again starting at 88
How shrinking works
Shrink list for 100 0, 50, 75, 88, 94, 97, 99
Fails at 88!
Generate a new
sequence up to 100

x < 81
How shrinking works
Shrink list for 88 0, 44, 66, 77, 83, 86, 87
Fails at 83!
Generate a new
sequence up to 88

x < 81
How shrinking works
Shrink list for 83 0, 42, 63, 73, 78, 81, 82
Fails at 81!
Generate a new
sequence up to 83

x < 81
Shrink has determined that 81 is
the smallest failing input!
How shrinking works
Shrink list for 81 0, 41, 61, 71, 76, 79, 80
All pass!
Generate a new
sequence up to 81

Shrinking – final result
Check.Quick smallerThan81Property
// result: Falsifiable, after 23 tests (3 shrinks)
// 81
Shrinking is really helpful to show
the boundaries where errors happen
Shrinking is built into the check:

Part IV:
How to choose properties

ABC
123
do X do X
do Y
do Y
"Different paths, same destination"
Examples:
- Commutivity
- Associativity
- Map
- Monad & Functor laws

Applied to a sort function
[1;2;3]
?
do ? do ?
List.sort
List.sort

Applied to a sort function
[2;3;1]
[-2;-3;-1] [-3;-2;-1]
[1;2;3]
Negate
List.sort
List.sort
Negate
then reverse

Applied to a map function
Some(2)
.Map(x => x * 3)
Some(2 * 3)
x
Option (x) Option (f x)
f x
Create
Map f
f
Create
f x = x * 3

"There and back again"
ABC 100101001
Do X
Inverse
Examples:
- Serialization/Deserialization
- Addition/Subtraction
-Write/Read
- SetProperty/GetProperty

"There and back again"
Applied to a list reverse function
[1;2;3] [3;2;1]
reverse
reverse

"Some things never change"
 
transform
Examples:
- Size of a collection
- Contents of a collection
- Balanced trees

[2;3;1]
[-2;-3;-1] [-3;-2;-1]
[1;2;3]
Negate
List.sort
List.sort
Negate
then reverse
The EDFH and List.Sort
The EDFH can beat this!

The EDFH and List.Sort
[2;3;1]
[-2;-3;-1] [ ]
[ ]
Negate
List.evilSort
List.evilSort
Negate
then reverse
EvilSort just returns an empty list!
This passes the "commutivity" test!

"Some things never change"
[2;3;1]
[1; 2; 3]; [2; 1; 3]; [2; 3; 1];
[1; 3; 2]; [3; 1; 2]; [3; 2; 1]
[1;2;3]
List.sort
Must be one of these
permutations
Used to ensure the sort function is good

"The more things change,
the more they stay the same"
 
distinct

distinct
Idempotence:
- Sort
- Filter
- Event processing
- Required for distributed designs

"Solve a smaller problem first"
     
- Divide and conquer algorithms (e.g. quicksort)
- Structural induction (recursive data structures)

"Hard to prove, easy to verify"
- Prime number factorization
-Too many others to mention!

Applied to a tokenizer
“a,b,c”
split
“a” “b” “c”
“a,b,c”
Combine and
verify
To verify the tokenizer, just check that the
concatenated tokens give us back the original string

Applied to a sort
To verify the sort,
check that each pair is ordered
[2;3;1]
(1<=2) (2<=3)
[1;2;3]
List.sort

ABC
ABC 123
123
Compare
System
under test
Test Oracle
"The test oracle"
- Compare optimized with slow brute-force version
- Compare parallel with single thread version.

PartV:
Model based testing
Using the test oracle approach
for complex implementations

Testing a simple database
Open Incr Close Incr Open Close
Open Decr Open
Four operations: Open, Close, Increment, Decrement
How do we know that our db works?
Let QuickCheck generate a random list of these actions for each client
Open Incr
Client
A
Client
B
Two clients: Client A and Client B

Testing a simple database
Compare model result with real system!
Open Decr Open Open Incr
Test on real
system
Open Decr Open Open Incr
Test on very
simple model1 00 0 1
(just an in-memory
accumulator)Connection closed,
so no change

Real world example
• Subtle bugs in an Erlang module
• The steps to reproduce were bizarre
– open-close-open file then exactly 3 parallel ops
– no human would ever think to write this test case
• Shrinker critical in finding minimal sequence
• War stories from John Hughes at
https://vimeo.com/68383317

Example-based tests vs.
Property-based tests

Example-based tests vs. Property-based tests
• PBTs are more general
– One property-based test can replace many example-
based tests.
• PBTs can reveal overlooked edge cases
– Nulls, negative numbers, weird strings, etc.
• PBTs ensure deep understanding of requirements
– Property-based tests force you to think! 
• Example-based tests are still helpful though!
– Easier to understand for newcomers

Summary
Be lazy! Don't write tests, generate them!
Use property-based thinking to gain
deeper insight into the requirements

The lazy programmer's guide to
writing 1000's of tests
An introduction to property based testing
Let us know if you
need help with F#
Thanks!
@ScottWlaschin
fsharpforfunandprofit.com/pbt
fsharpworks.com Slides and video here
Contact me

An introduction to property based testing

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